Inference and the Metaphysic of Reason: An Onto-Epistemological Critique (Marquette Studies in Philosophy)

Inference and the Metaphysic of Reason

Inference and the Metaphysic of Reason An Onto-Epistemological Critique

By

phillip stambovsky

© 2009 Marquette University Press Milwaukee, Wisconsin 53201-3141 All rights reserved. www.marquette.edu/mupress/

founded 1916 Library of Congress Cataloging-in-Publication Data Stambovsky, Phillip, 1952Inference and the metaphysic of reason : an onto-epistemological critique / by Phillip Stambovsky. p. cm. — (Marquette studies in philosophy ; no. 67) Includes bibliographical references and index. ISBN-13: 978-0-87462-765-7 (pbk. : alk. paper) ISBN-10: 0-87462-765-6 (pbk. : alk. paper) 1. Inference. 2. Metaphysics. I. Title. BC199.I47S73 2009 110—dc22 2009025159

Cover photo by Paul Duda

The paper used in this publication meets the minimum requirements of the American National Standard for Information Sciences— Permanence of Paper for Printed Library Materials, ANSI Z39.48-1992.

contents Preface ~ 11 1 Introduction ~ 17 i. Prologue ~ 18 ii. Chapter Summaries ~ 36 iii. Onto-Epistemological Positing and the Philosophy of Inference: The Kantian Legacy ~ 40 2 Critique of Analytic Epistemologies of Inference: Carnap, Harman, Brandom, Williams, and Lonergan ~ 55 2.1.1 Leading Philosophical Orientations to Inference ~ 55 2.1.2 Problems with Received Philosophical Definitions of Inference ~ 64 2.1.3 The Metaphysical Challenge to Analytic Epistemologies of Inference ~ 74 2.2 Rudolf Carnap ~ 78 2.3 Gilbert Harman ~ 91 2.4 Robert Brandom ~ 94 2.5 Michael Williams ~ 102 2.6.1 Bernard Lonergan: The Metaphysician as Analytic Epistemologist of Inference ~ 109 2.6.2 Lonergan on Inferential Thinking: Compared with Carnap, Harman, Brandom, and Williams ~ 117 2.7 Summation ~ 127 3 Inference and Ontology in Systematic Philosophical Logic~ 133 3.1 Orientational Shift in Turning Back to Lotze and Bosanquet on Inference ~ 133 3.2 Speculative Standpoint of Philosophical Logicians ~ 136 3.3 Critique of Philosophical Logicians on Inference ~ 144 3.4.1 Overview of Lotze’s Thought and Influence ~ 148 3.4.2 Onto-Epistemological Reading of Lotze on Inference ~ 152 3.4.3 Lotze on Position oder Setzung ~ 164

6 Inference and the metaphysic of reason 3.4.4 Summary of Lotze’s Thinking that Anticipates the Onto-Epistemological Orientation ~ 175 3.5.1 Bosanquet as a Philosophical Logician of Inference ~ 179 3.5.2 Bosanquet’s Differences with Lotze on Inference ~ 185 3.5.3 Bosanquet’s Systematic Philosophy of Inference ~ 197 3.5.4 Summary of Bosanquet’s Doctrine of Inference Relative to the Onto-Epistemological Orientation ~ 201 4 An Essay in the Onto-Epistemology of Inference ~ 207 4.1 The Need of an Onto-Epistemological Approach to the Reason of the Act of Inference ~ 207 4.2 Synopsis of the Onto-Epistemological Orientation to Inference ~ 210 a. General definition ~ 211 b. The idea of inference as act ~ 214 c. Onto-epistemological positing and the dialectic essence of inferential reflection ~ 216 d. The reflective show (Schein) of premises that, as premises in a coherent act of inference, are formally ordered to a conclusion ~ 220 e. Formal cause as the Sufficient Reason of the act of inferential reflection ~ 222 f. Validation and the inferential process ~ 225 4.3 The Act of Inference ~ 226 4.4 Three Defining Moments of the Onto-Epistemology of Inference ~ 241 4.5.1 Onto-Epistemological Positing ~ 248 4.5.2 The Conceptual Logic of Inferential Reflection ~254 4.5.3 The Formal Moment ~ 267 4.6 The Onto-Epistemology of Inference and Ernst Cassirer’s Approach to Inductive Inference ~ 272 4.7 Conclusion ~ 280 a. Debts to Kant, Hegel, and Bosanquet ~ 280 b. Enumeration of this inquiry’s defining elements ~ 285 * Critical and constructive rethinking of Position oder Setzung as an onto-epistemological thetic concept * Retrieval of Lotze’s and Bosanquet’s formative insights into inference * Consideration of Hegel’s thinking on positing (as setzende Reflexion and Gesetztsein) and on the logic of essence as

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they relate to the conceptual logic of inferential reflection * Reconceiving the principle of sufficient reason, in terms of formal cause, as the ground of the reason of the act of inference * Identification of the inquiry’s most significant historical and philosophical precedent: Ernst Cassirer on induction, in Substance and Function (“The System of Relational Concepts and the Problem of Reality”) Coda ~ 286 Appendices ~ 291 I. Onto-Epistemological Positing ~ 291 i. Kant’s Originary Conception of Position oder Setzung ~ 291 ii. Onto-Epistemological Positing in Frege’s and Russell’s Reading of Kant ~ 297 iii. Speculative Implications of Kantian Positing for the Philosophy of Inference ~ 300 iv. Kant and the Privileging of Relative Positing ~ 304 II. W. V. Quine and Onto-Epistemological Positing ~ 306 III. Lonergan, Kant, and Cognitional Theory ~ 309 IV. The Challenge of Epistemological Critique to Bosanquet’s Inferentialism ~ 312 V. Reflection on the Reason of the Act of Inference ~ 315 Bibliography~ 321 Index ~ 335

Knowing is of being. Oliva Blanchette

La coïncidence de Réalité spirituelle et d’Idée fait voir que l’obtention de la réalité suprême s’opère formellement par l’intelligence…. Pierre Rousselot

Um die Sache zu wissen, dazu gehört Nachdenken, angestrengtes Nachdenken. Diesen Sinn hat es, wenn wir sagen, das Wahre ist Einheit des Denkens und des Seins. G. W. F. Hegel

To Oliva Blanchette

Preface As in science and in history, so in philosophy the ideal of thought demands that no proposition be admitted into the body of knowledge except for sufficient reason, or, in logical terms, as the conclusion of an inference.

R. G. Collingwood, An Essay on Philosophical Method This book is an inquiry into the reason of the act of inference. It investigates the nature of discursive thought conceived metaphysically, as the being of knowing. The “onto-epistemological” purport of this study differentiates it from what contemporary philosophers typically associate with “analytical metaphysics.” The first and third epigraphs on page eight, above, signal as much. The second indicates the underlying speculative end of this work, namely to elucidate the coincidence of inferential intelligence and the formal realization of fact. Beyond its metaphysical orientation, what sets apart the discussion in the chapters ahead from other philosophies of inference is a series of critical and constructive initiatives, enumerated below, that together establish a more deeply rational approach to the topic than those sponsored by either analytic epistemology or the older systematic expositions of inference as a species of judgment. The introductory chapter sketches in a preliminary way the inquiry’s lines of investigation and principal emphases. After providing an overview of the three chapters that compose the core of the study, it delineates the onto-epistemological orientation to inference that distinguishes this investigation from other philosophical approaches. Lastly, the Introduction identifies and explicates the most distinctive heuristic component of this inquiry: Kant’s metaphysical notion of “positing” (Position oder Setzung)—the concept that Kant identified with the concept of being in general (Sein überhaupt). Part I of the core exposition is a two-chapter critique. The first, chapter 2, assesses several leading analytic philosophies of inference, while the second, chapter 3, probes two important metaphysically keyed doctrines from the decades immediately preceding the period that saw analytic epistemologies of inference come to dominate the

12 Inference and the metaphysic of reason field. This extended critique sets the stage for Part II, the fourth chapter, which undertakes to trace the conceptual logic of inference from an onto-epistemological standpoint.1 With an eye toward making it clear how very far this part of the essay is from being a mere speculative idiosyncrasy, I indicate at virtually each step of this constructive phase anticipations and precedents in some of the deepest-running currents of idealist (critical and objective), medieval, and classical reflection on the relation of being and thinking. The point of the entire exercise is to illustrate one way of substantiating the truth that Knowing is of Being, a truth that appears largely to have eluded the grasp of philosophers of inference over the past century and more. Five appendices follow the body of the text. They supplement and substantiate defining elements of both the critical and constructive parts of the book. 3 Let me briefly pass in review each of the principal components that together distinguish this inquiry from other philosophical treatments of inference: a) Perhaps the most notable heuristic feature unique to this work is the move to incorporate what Kant identified as Position oder Setzung (“positing”), a metaphysical concept that he introduced in a famous discussion of being and predication. Upon close scrutiny Position oder Setzung discloses itself to be an onto-epistemological notion that, with certain qualifications serves as an effective means of assessing how existential and predicative (discursive) affirmation relate to each other when we draw inferences. b) With this onto-epistemological concept of Position in the background, chapter 2 exposes a telling metaphysical fault line that at different points runs through five paradigmatic analytic treatments of inference—those of Rudolf Carnap, Gilbert Harman, Robert Brandom, Michael Williams, and Bernard Lonergan.2 Excepting Lonergan’s account, each of these doctrines has previously come under critical scru1  What a Kantian would interpret as “the conditions and universal (although subjective) laws under which alone [a priori] cognition is pos-

sible as experience (merely according to form)”; cf., Prolegomena to Any Future Metaphysics, trans. Peter G. Lucas and Günter Zöller (Oxford: Oxford University Press, 2005), §17.

2  I explain in §2.6.1 why Lonergan’s focus on “formal” inference justifies his inclusion in this line-up of analytic philosophers.

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tiny from various quarters. Yet no critique of the analytic epistemology of inference has till now brought to bear, in its assessment, Kant’s metaphysical distinction of absolute and relative modes of “positing”; nor has anyone called attention to the common fault line extending through the five examples that come under review here. c) The third chapter marks a further departure from current studies of inference by featuring an in-depth treatment of Rudolf Hermann Lotze’s long-neglected philosophical logic of judgment. Lotze’s thinking is a speculative resource rich in acute insights, some of which are highly germane to a probe into the onto-epistemology of the act of inference. Lotze held, for example, that the “problem of all inferential processes” does not hinge on the specifics of the logic of the deductive patterns or rules that thought methodically tracks through premises to a conclusion. Anticipating Gilbert Harman by nearly a century, he dismisses such “methods” as “quite immaterial” to the task of determining the character and limits of inference. Lotze’s more penetrating view, one fundamentally consistent that of the present study, is that the proper speculative “method” for elucidating the inferential process “will be determined by the form of the premises” of any given inference. Lotze finds that the forms that the premises take in alternative genres of inference indicate “a limit of knowledge” that sheds light on the nature of the inferential process. We cannot determine these forms a priori, observes Lotze, but rather must “take [them] as experience, internal or external, offers them.” d) Chapter 3 features yet another distinctive component of the inquiry: a review and critique of Bernard Bosanquet’s inferentialism. Bosanquet’s contributions to the philosophy of the logic of inference have largely been lost to contemporary philosophical debate on the topic, the main exception being recent efforts to discredit the notion of “linear inference” (although even here Bosanquet is rarely credited for his original work on the problem). A close reading of Bosanquet on inference and on the metaphysics of implication reveals a penetration and nuance that must contribute significantly to any probe into the onto-epistemology of the act of inference. e) Following the distinctive critique that constitutes Part I of the book, Part II takes an equally original constructive turn. This it does by exploring the act of inference along paths of inquiry hitherto generally neglected in the philosophical literature. Perhaps the most singular of these open into the conceptual logic of Hegel’s Doctrine of Essence—

14 Inference and the metaphysic of reason this from the standpoint of inferential reflection (i.e., on the plane of reflective thought3). Among the many pregnant insights that one encounters in Hegel’s conceptual logic, two stand out as particularly relevant to the philosophy of inference. One is the notion of “positing” as Hegel employs it, which he does in ways that track beyond Kant’s limited development of the concept. The other is Hegel’s seminal remark (recorded in a Zusatz of the Encyclopedia Logic) on the principle of sufficient reason. Besides playing formative roles in Hegel’s metaphysical Logic, these elements of his thinking are also operative in the conceptual logic of the act of inference—although Hegel himself, for reasons to be explained in due course, would have been quick to repudiate any such associations. The main divergences here from Hegel’s thought reflect the fact that, in light of the conceptual logic of inferential reflection, the concerns in the present work do not extend beyond the cognitional plane of “pure thinking.” This essay thus largely confines itself to a “higher” spiritual (geistig) level than mere Essence (Hegel’s primordial “first negation”). f) A final distinctive aspect of this inquiry deserves mention at the outset. If not tagged Kantian or neo-Kantian, this work is likely to impel certain readers to class it as Hegelian. As with the thinking of Kant that deeply influences the treatment of onto-epistemological positing and the conceptual logic of inference explored here, this inquiry breaks radically with Hegelian philosophy on a number of issues. However pivotal specific passages of Hegel’s thinking show themselves to be in elucidating the reason of inference, the references in the ensuing chapters to such matters as “remote facts” and dunamis and energeia do not relate in any consistent way to Hegel’s system. The shift away from Hegelian doctrine is most significant relative to remarks that Hegel offers in the Zusatz appended to the initial section (§121) on Grund (ground/reason) in the Encyclopedia Logic. Hegel there explicates the principle of sufficient reason along lines that disclose two decisive respects in which the onto-epistemology of the reason of inference is at odds with his metaphysical Logic. One difference follows Hegel’s claim that in its non-trivial sense the principle of sufficient reason is a moment of the ontology of the Begriff in the latter’s objectivity—an objectivity that he describes as the “real Begriff that has emerged from its inwardness and passed over into determinate being.”4 The archi3  Rather than on the plane of the metaphysics of ontology. 4  Cf.: “die Objektivität der aus seiner Innerlichkeit hervorgetretene und in das Dasein übergegangene reelle Begriff ” (Wissenschaft der Logik II (Frank-

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tectonic of Hegel’s metaphysic of the Begriff has no place in the ontoepistemology explored in this book. A second departure here from Hegel follows from his very understanding of the principle of sufficient reason. Hegel contends that we properly grasp the non-trivial (Leibnizian) sense of this “law” of thought in terms of teleology (final cause) rather than of “mechanism” (efficient cause). While Hegel thus rightly enough rejects the most common reductive reading of the classic Leibnizian principle, the appeal to causa finales as the ground of sufficient reason in the act of inference is here repudiated. Instead, we shall see that discursive reflection manifests a principle of reason that is, in the first instance, ontogenetically formal in character. Hegel himself sees a formelle Grund in play at the logical juncture between “distinction” and “existence,” but he dismisses it as ante-cognitionally contentless and trivially general (“all [such] grounds are sufficient so…no ground is sufficient as such”).5 By contrast, we shall discover that the sufficient reason articulating the reason of the act of inference is formal cause—a postulate the onto-epistemological details of which prove deeply consistent with the Thomist view that “the esse of a thing follows upon its form, not so as to be efficiently caused by that form, but so as to be formally caused by it.”6 We shall find, moreover, that from an onto-epistemological standpoint this cognitional principle, as it applies to scientific knowledge, warrants Leibniz’s conclusion that as a fundamental “law” of rational thought Sufficient Reason is fully on a par with Noncontradiction. Indeed Leibniz understood them as complementary: Sufficient Reason is “founded on the principle of contingency, or of the existence of things,”7 whereas Noncontradiction is a matter of necessary truth. 3 Four basic assumptions about the inferential process that inform this essay disclose how it at once furthers and challenges the classical, furt am Main: Suhrkamp, 1986), p. 271; [Hegel’s Science of Logic, trans. A. V. Miller (Atlantic Highlands, N.J.: Humanities Press, 1993), p. 596]). 5  Encyclopedia Logic, p. 190. 6  Cf., John Wippel’s “Thomas Aquinas on Creatures as Causes of Esse,” where one finds a lucid and meticulous discussion of this view; in Wippel, Metaphysical Themes in Thomas Aquinas II (Washington, D.C.: Catholic University of America Press, 2007), chap. VII. 7  Leibniz Selections, ed. Philip P. Wiener (New York: Scribners, 1951), pp. 94-95.

16 Inference and the metaphysic of reason medieval, and idealist philosophical legacy under whose influence it evolved. A first assumption is that the premises in inferential reflection are, in accord with the logic of essence,8 a function of onto-epistemological positing. A second supposition is that whatever the experiences or ideas or purposes that may “show” as premises in a route of inference do so as always already reflectively ordered (properly or mistakenly) to some intelligible conclusion. The moment of order is hence an intrinsic constituent of any “show” of fact for inference, so far as one puts to thought (posits) as a premise what shows. On this view, thirdly, the conclusion that the premises in a coherent act of inference literally compose has the character of a totality. A fourth basic assumption is that the conclusion, in its formally determinate sense, amounts to the truth of the inference—however at variance that truth may be with the thinker’s expectations or other notions. In this respect, the conclusion is the sufficient reason of the order that sponsors the reflective determination of each premise. Each premise in an act of reflective thought accrues its determinate character (i.e., becomes intelligible as a premise) vis-à-vis a mediating other, through the ordered progress of the act of inferential concept formation. Readers there will be, doubtless, who will charge that this ontoepistemological orientation to inference is unwarrantably eclectic and trades on a series of idiosyncratic claims. Such impressions will not, I believe, stand scrutiny. As the epigraphs that head this Preface and the succeeding chapters suggest, this essay builds upon the thought of a constellation of canonical classical, medieval, and modern philosophers whose insights into the being of predicative thinking (the thetic) in different yet often interrelated ways anticipate, substantiate, or deeply correlate with what comes to light in the investigation undertaken in these pages. 3 Aside from my debts to the work of the many thinkers identified in notes throughout the text, I wish to express special thanks to Oliva Blanchette, Stephen Houlgate, Andrew Tallon, and to Linda P. Stambovsky. I dedicate this volume to Oliva Blanchette, philosopher of Being and master teacher. New Haven 2008

8  As operative on the conceptual plane of cognitional life.

Chapter 1 Introduction Diejenigen, welche von der Philosophie nichts verstehen, schlagen zwar die Hände über den Kopf zusammen, wenn sie den Satz vernehmen: Das Denken ist das Sein. Dennoch liegt allem unserem Tun die Voraussetzung der Einheit des Denkens und des Seins zugrunde. Diese Voraussetzung machen wir als vernünftige, als denkende Wesen. [Those who understand nothing of philosophy throw up their hands when they take in the proposition, Thinking is Being. Nevertheless, underlying all our actions is the presupposition of the unity of Thinking and Being. This assumption we make as rational, as thinking essence.]

G. W. F. Hegel, Die Philosophie des Geistes §465z Dans l’ordre spéeculatif nous n’échappons pas à une vérité objective… tant par la pensée… nous posons donc perpétuellement et catégoriquement l’être. [In the speculative order we cannot avoid an objective truth…hence when we think…we thus perpetually and categorically posit being.]

Joseph Maréchal, Le Point de Départ de la Métaphysique (Cahier V) All reasoning, apart from some metaphysical reference, is vicious.

Alfred North Whitehead, Adventures of Ideas Formalization is an expression of a metaphysical thesis or position….The thesis comes to regard itself as metaphysically neutral when it forgets that formal relations have a being more fundamental even than the values of their variables. This forgetfulness is induced primarily by the redefinition of being as existence and the definition of existence on the basis of quantifiers, functional analyses of propositions, and variables as quantifiable and ranging over domains of objects.

Stanley Rosen, “Logic and Dialectic”

18 Inference and the metaphysic of reason i. Prologue. Analytic epistemologies of inference have dominated philosophical discourse on the topic from the first decades of the twentieth century.1 But a most telling difficulty challenges their explanatory ground. The problem concerns the ontological authority or warrant that legitimates predicative assertion (the thetic) in discursive thinking. This fundamental issue is as much a problem of knowledge as it is of ontology, and for that reason I approach it in this study from an “onto-epistemological” standpoint. Kant had important things to say about the onto-epistemology of predicative assertion, decades before The Critique of Pure Reason (1781/1787). The original and highly influential way that he initially conceived the relation of being (Sein) and predication offers, as it turns out, a philosophically and historically pregnant frame of reference for critically assessing analytic theories of inference. A general aim of the chapters ahead is to explore and follow up upon the implications of this connection, and correlative contexts of analysis, in an effort more effectively to orient thinking, from the standpoint of the reason of the act of inference, to the fact that “knowing is of being.” It was as early as December 1762,2 that Kant described a metaphysical distinction between “absolute” (existential) and “relative” (predicative) dimensions of “positing,” or “position” (Position oder Setzung). Moreover, he identified the concept of such positing with that of Being as such (Sein überhaupt)—at first sight a most unexpected association. This onto-epistemological conception of Position subsequently occasioned sometimes-lively debate in post-Kantian German philosophical discourse, at least through the early twentieth century. Over the past century, however, it has only rarely figured as a theme of speculative deliberation, particularly in the contest of philosophical approaches to inference. To be sure, in recent times some distinguished students of Kant— the later Heidegger (1961), for example, Eckart Förster (2000) and 1  Such approaches range in character from mathematicized logic and philosophy of mind to semantic theory sometimes combined with neo-pragmatics. 2  The Only Possible Basis for a Proof of the Existence of God. In Theoretical Philosophy 1755-1770, translated and edited by David Walford and Ralf Meerbote (Cambridge, Engl.: Cambridge University Press, 1992) [Immanuel Kants Werke, vol. II, ed. Ernst Cassirer (Berlin: Bruno Cassirer, 1922)].

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Manfred Frank (2004)3—have explored the metaphysical implications of Kantian Position oder Setzung. Heidegger, Förster, and Frank are of particular interest here because they probe the infrequently remarked discrimination that Kant made between absolute and relative Position.4 And they analyze Kant’s distinction in ways that have a direct bearing, which we shall consider in due course,5 on the relation of the concepts of being and inferential reflection. Beyond its ramifications for the effort to conceptualize the reason of the act of inference, Kant’s classification of absolute and relative Position proves of considerable heuristic value when one probes in this connection the rational limits of analytic epistemologies. This is something that philosophers of discursive reason have yet sufficiently to recognize, and one principal goal of this book is to advance such recognition. The idea of “positing” as an onto-epistemological notion is ancient, tracing back as it does to the Greek term, thésis (qevs i~). As a speculative concept, the thetic thus has a very long and controverted history. Indeed, philosophical controversies originating in classical antiquity invoke the idea in various contexts, notably in the arguments over the

3  See Martin Heidegger, “Kant’s Thesis about Being,” trans. Ted E. Klein, Jr. and William E. Pohl, in Pathmarks, ed. William McNeil (Cambridge, Eng.: Cambridge University Press, 1999) [“Kants These über das Sein,” Wegmarken. (Frankfurt am Main: Klostermann, 1978)]; Eckart Förster, Kant’s Final Synthesis: An Essay on the “Opus postumum” (Cambridge, Mass.: Harvard University Press, 2000); and Manfred Frank, The Philosophical Foundations of Early German Romanticism, trans. Elizabeth Millán-Zaibert (Albany: State University of New York Press, 2004), Lecture III. Also see Mark Fisher and Eric Watkins, “Kant on the Material Ground of Possibility: From The Only Possible Argument to the Critique of Pure Reason,” Review of Metaphysics 52 (1998): 369-95; and Zygmunt Adamczewski, “Kant’s Existential Thought,” in New Essays in Phenomenology: Studies in the Philosophy of Experience, ed. James M. Edie (Chicago: Quadrangle Books, 1969), pp. 314-62. 4  Adamczewski does as well, although he terms “primary” positing what Kant early on identified as die absolute Position, and he limits his discussion to the first Critique (in a fifty-page essay published without a bibliography or a single note). 5  See chap. 4, and Appendix I.iv, below.

20 Inference and the metaphysic of reason relationship between onta (beings) and onomata (names).6 In Kant’s philosophy, which is the present essay’s point of departure, one initially encounters Position as a speculative term in analyses of the Ontological Proof. It appears in conjunction with Kant’s famed postulate that being is not a predicate. The implications of this axiom, as Kant saw them at play relationally in the copula (Verhältniswörtchen), tacitly underwrite the objective meaning of inferential (i.e., mediated) judgments. Kant would ultimately explain his view this way: “…I find that a judgment is nothing other than the way to bring given cognitions to the objective unity of apperception. That is the aim of the copula is in them: to distinguish the objective unity of given representations from the subjective” (B141-42).7 One could argue that the critical revolution in Kant’s thinking which came to light with the first Critique showcased, from a transcendental idealistic perspective, a metaphysical distinction prefigured in the early binary classification of Position as absolute and relative. For this binarism hinges on the distinction between the ontic (noumenal) and the epistemic (phenomenal) aspects of onto-epistemological positing. Perhaps more fatefully, in light of the Kantian legacy that at a deep level informs the currently dominant schools of analytic epistemology, the critical Kant classified intelligible being—the only way that the object of absolute positing is accessible through the relative positing—as a modal category of transcendental logic that includes being possible, being actual, being necessary.8 One sees in the onto-epistemology of contemporary symbolic logic a cardinal example of the decisive impact, a problematic one, which this speculative move has had in Western intellectual history. Reflecting on the limits of contemporary formal logic, Stanley Rosen puts his finger on a troubling aporia 6  Cf., F. E. Peters, Greek Philosophical Terms (New York: New York University Press, 1967). 7  Critique of Pure Reason, trans. Paul Guyer and Allen W. Wood (Cambridge, Engl.: Cambridge University Press, 1998), p. 251. Cassirer singles out this same point in his analysis of judgments and the concepts of relation; see The Philosophy of Symbolic Forms, Volume 1: Language, trans. Ralph Manheim (New Haven: Yale University Press, 1955), pp. 313-15. 8  A chief aim of Heidegger in “Kant’s Thesis about Being” is to explicate the development of Kant’s doctrine of positing, from its pre-critical to its final form in the first Critique.

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that relates precisely to this element of the Kantian (and Cartesian) epistemological legacy: We may distinguish initially between logical and physical structure. However, if physical structure is contingent, the applicability of logic to nature requires a corresponding contingency in logical principles, rules, or categories…. An interesting example of this failure [to credit this requirement of ontological “contingency” in formal logic] is the contemporary school of modal logicians who distinguish between logical and physical necessity. According to this distinction, whatever does not violate the principle of noncontradiction is physically possible. Another way in which to make this point is to say that thinking is implicitly conceived as distinct from being but at the same time as defining the structure of possible being. Let us call this a kind of logical Kantianism adapted to Cartesian goals.9

The radical challenges that Kant’s transcendental idealism faced virtually from the outset are legendary. Kant’s idealist heirs in particular sought to establish a broader speculative context for grasping the relation of being and thinking.10 Nonetheless, as an original development of the Cartesian rational spirit in Western intellectual culture, the Master’s epistemological reduction of thetic determination persists in the reigning epistemological hegemony, under the aegis of which contemporary analytic thinkers jettison philosophies of being (with their ante-discursive “noumenal” pretensions). This is no news. As long ago as 1913, Bernard Bosanquet, whose metaphysic of inference we shall examine in chapter 3, referred to a reigning view of the Kantian legacy that associates “with Kant an attempt to establish a fundamental science, consisting in Epistemology, and prior to [philosophical] Logic and Metaphysics.” 11 A voice from more recent times, Dermot Moran, 9  “Logic and Dialectic,” The Ancients and the Moderns: Rethinking Modernity (New Haven: Yale University Press, 1989), p. 137. Just as the concept of “necessity” must have that of “contingency” as its logical complement, so, in the philosophy of inference, (non)contradiction must be complemented by sufficient reason taken, I shall argue, as formal cause. 10  See Manfred Frank’s treatment of this in The Philosophical Foundations of Early German Romanticism, chap. 4 (“On the Search for the Unconditioned”). 11  Bosanquet, The Distinction between Mind and Its Objects (1913. Bristol, Engl.: Thoemmes Press, 1990), p. 53. The observation appears in Bosanquet’s repudiation of attacks on speculative idealism by realists who

22 Inference and the metaphysic of reason has remarked that it was the neo-Kantians who “made epistemology the ‘first philosophy.’”12 Many would conclude that it was Kant himself who inspired the idealist reactions symptomatic of the widespread perception (against which Kant struggled in vain) that the three Critiques themselves come close to doing what Moran ascribes to the neo-Kantians. Influential analytic philosophers, at least since the time of Mortiz Schlick, have too often isolated existential (absolute) positing from predicative positing or simply assimilated the former to the latter, as in effect an inoculation against jejune ontologisms, i.e., against bad metaphysics. (Schlick, for instance, dismissed “absolute Position” as “a formulation on whose meaninglessness we need waste no words.” 13) Consistent with such abstracting of the existential are the ontologically neutered, minimalist metaphysical horizons that limit the speculative range of many analytic theorists, from logical empiricists and linguistic analysts to philosophers of mind, and others. One of the liabilities that comes with this insufficiently developed metaphysical context of analytic thinking, a point underscored in chapter 2, bears directly upon the underlying theme of this investigation, namely the nature of what it is for being and thought to stand in relation in the act of inference. There is a price, we shall find, for taking one’s eye improbably “lumped” all such philosophies (notably those indebted to Hegel) as falling under the Kantian epistemological hegemony. “This,” declares Bosanquet, “seems to me quite exactly wrong” (ibid.). If ostensibly anti-epistemological, in the sense of rejecting the Kantian epistemological legacy, the realism of the early twentieth century was almost from the beginning sharply challenged by scientific, phenomenological, social, and linguistic epistemologies—all developments of thinking that in large measure converges in Kant. 12  “Heidegger’s Transcendental Phenomenology in the Light of Husserl’s Project of First Philosophy,” Transcendental Heidegger, ed. Steven Crowell and Jeff Malpas (Stanford: Stanford University Press, 2007), p. 135. 13  Schlick, General Theory of Knowledge, trans. Albert E. Blumberg (La Salle, Ill.: Open Court, 1985), p. 183. On Lotze’s rejection of Position oder Setzung, see §3.4.3, below. While both have been identified as analytic philosophers, Schlick in his first period (prior to the influence of Carnap and Wittgenstein) and Lotze were very far from analytic in the speculatively narrowing sense that one associates with positivistic logicism, linguisticism, (game-theoretical or socio-normative) semanticism, and cognitive scientism.

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off the absolute moment of the thetic act (positing, Setzung), which is an ontological moment presupposed even by Kantian transcendental logic and hence not limited to an a priori schedule of modalities, such as possibility, actuality, and necessity.14 When philosophers of inference fail to take account of the unbracketable dimension of inference as a living act of intelligence, their accounts too often exhibit antinomies and contradictions, some paradigmatic instances of which chapter 2 detects in prominent contemporary theory. Typically, the problem becomes apparent when, under whatever analytic rubric, the epistemologist of inference confronts the ineludible fact that if to think is to be, then to know this must be an act that “takes in the presence of being.”15 In view of this, what sort of metaphysically more robust orientation to inference might recommend itself as an alternative to those of the analytic epistemologists? The answer, I shall argue, is one that sponsors a conceptual logic able to render intelligible the intermediating relation between absolute (existential) and relative positing in the act of inferential reflection. The business of chapter 4 is to probe and substantiate defining elements of this alternative orientation. But to prepare the way for that phase of discussion, it is essential first to consider a historically and philosophically formative genre of approaches to inference as judgment. The line of speculative logic in mind here achieved its most mature articulation in the decades immediately preceding the rise of analytic epistemologies of inference. Chapter 3 critically probes two distinguished examples of such philosophies of the logic of inference: those of Lotze and Bosanquet, whose thought in key respects bridges the speculative divide between the analytic orientation critiqued in chapter 2 and the conceptual logic of inference that we shall undertake to think through in chapter 4. While the five doctrines canvassed in chapter 2 represent a major range of analytic inference theory, one might well question the decision, in chapter 3, to single out Lotze and Bosanquet. Why take up these two now-infrequently studied thinkers as paradigmatic theorists 14  Cf., Reiner Shürmann’s discussion of Kant’s “double comprehension of being,” categorial and precategorial, in Broken Hegemonies, trans. Reginald Lilly (Bloomington: Indiana University Press, 2003), p. 483. 15  Oliva Blanchette, Philosophy of Being: A Reconstructive Essay in Metaphysics (Washington, D.C.: Catholic University of America Press, 2003), p. 26.

24 Inference and the metaphysic of reason of an earlier philosophical epoch? Indeed, why select them for detailed scrutiny when the roll of distinguished philosophers of inference from their milieu16 includes such figures as J. S. Mill, Christoph Sigwart, F. H Bradley, and H. W. B. Joseph? Aside from penetrating analyses of the logic of inference that speak with particular force to specific concerns of the present inquiry, the work of Lotze and Bosanquet recommends itself on historical grounds. For both philosophers critically engaged the first champions of the trend to assimilate logic to mathematical and empirically positivist formalisms. Lotze in his last writings challenged the likes of George Boole, William Stanley Jevons, and the young Ernst Schröder—each of whom significantly influenced the growth and evolution of analytic epistemology.17 A generation later, Bosanquet also addressed the innovations of the early figures and in addition confronted, in his last years, Bertrand Russell’s logicism from the critical stance of a systematic philosophy of implication.18 Another reason why Lotze and Bosanquet compel attention in a study that concentrates on the onto-epistemology of inference is that as a systematic, metaphysically attuned logician each takes with radical seriousness the abiding relevance of the philosophy of being. Although an incomparably rich repository of orientational insight and pregnant speculative suggestions, this domain of traditional metaphysical thought is one that analytic epistemologists too rarely grasp in sufficient depth and with the requisite appreciation of context and telling nuance. As a result, the metaphysics of ontology is commonly construed reductively,19 when not dismissed outright. Those contem16  Which extended roughly from the 1830s to its eclipse somewhat less than a century later. 17  Jevons in particular had a formative impact, in the 1930s, on Claude Shannon, the originator of information theory. In its turn, information theory has come to exert a powerful influence on prominent strains of analytic epistemology. 18  In his penetrating Implication and Linear Inference (London: Macmillan, 1920) and, earlier, in the 1911 revision of the volume of his Logic devoted to inference (esp. the Appendix to Chapter 1, “On the Relation of Symbolic Logic to the Theory of the Present Work,” pp. 40-49). 19  This is most evident in the field of information science. Cf., for example, Luciano Floridi’s declaration: “Information ‘can be said in many ways’”— the initial move in his effort to construe “information” as First Philosophy by characterizing as Aristotelian substance “factual or epistemically oriented

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porary scholars who do genuinely immerse themselves in the question of being (i.e., as First Philosophy) tend rather to be historians of philosophy than systematic metaphysical thinkers in the classical spirit. We shall see some of the consequences of this trend in the aporiai that render problematic, as an orientation in general, the analytic epistemology of the act of inference. At a minimum, epistemology recapitulates ontology on the level of reflective intelligence (spirit, Geist). But for that very reason epistemology itself can establish its being— and hence its status as a ground for making truth claims—only by exhibiting as its own reality (i.e., as the act of knowing) the act of being. (When an analytic philosopher of inference such as Gilbert Harman endeavors to distinguish inferential relational structures from inferential processes, ultimately by way of “a kind of psychologism,” he implicitly credits this fact.20) Contrary to the general impression of those many scholars who possess little more than a passing acquaintance with the names Lotze and Bosanquet, the latter were not reactionary thinkers. For all their traditional metaphysical proclivities, they were no less modern than the immediately succeeding generations of neo-realists, naturalists, logicists, logical positivists, and linguistic philosophers. Perhaps nothing so attests to the modernity of Lotze and Bosanquet as the ontological weight that they accord to the law of (non)contradiction, or identity,21 an emphasis with which, in Bosanquet’s case, we shall have occasion to take issue. For Bosanquet, “reality in all its form and phases can defend and maintain itself according to the principle of non-contradiction. It never depends for its relative logical stability upon approximation or correspondence or anything else.”22 At a minimum, Bosanquet’s thinking here is consistent with that of the very analytic epistemologists who largely broke with classical, non-mathematicized systematic approaches to logic such as his. These analysts labor under the shadow semantic information”; see The Blackwell Guide to the Philosophy of Computing and Information, ed. Luciano Floridi (Malden, Mass.: Blackwell, 2004), chap. 4 (“Information”). 20  Harman’s recourse to psychologism as an onto-epistemological explanatory principle of inferential process is speculatively otiose; see §2.3, below. 21  As the “law” of identity is a correlative of (non)contradiction, both are implied when I cite either. 22  Logic, Or the Morphology of Knowledge, 2 vols., 2nd ed. (London: Oxford University Press, 1911), vol. II, p. 291.

26 Inference and the metaphysic of reason of the reigning post-Kantian epistemological hegemony—at least so far as they operate on the assumption that the “horizon of cognitive intelligibility is defined by the principle of contradiction.”23 (Kant himself classed this principle as analytic judgment, and he faulted “the illustrious Wolff” and “the sagacious Baumgarten” for endeavoring “to find the proof of the principle of sufficient reason, which is manifestly synthetic, in the principle of contradiction.”24) 3 Following the mainly critical discussions of Part I, the second Part of this work (chapter 4) undertakes to trace the conceptual logic of the act of inference. This phase of the investigation proceeds by way of reflections on the being of knowing, and in effect repudiates what amounts to the ontological therapeutics of the analytic epistemologists. The conceptual logic of the relation of being and knowing that acquires definition through the course of the fourth chapter entails no the saltus metaphysicum—charges of such moves having inspired, at least in part, the later criticism and marginalization of Lotze and Bosanquet. The portrait of inference that emerges through chapter 4 is of a reflective process rather than anything that one might non-reductively define in terms of abstract rules of entailment or implication or validity. This is consistent with the Hegelian insight that serves as one of the lead epigraphs of this book: “In order to know die Sache, reflection is necessary….This is the meaning of the assertion that the true is the unity of thought and being.” [Um die Sache zu wissen, dazu gehört Nachdenken.... Diesen Sinn hat es, wenn wir sagen, das Wahre ist Einheit des Denkens und des Seins.] 25 Classically speaking, rules or norms of entailment involve the relation between “scientific” principles and conclusions, a relation that follows from the reason of inference, indeed depends upon it, but is 23  Stanley Rosen, G. W. F. Hegel: An Introduction to the Science of Wisdom (New Haven: Yale University Press, 1974), p. 18. 24  Prolegomena to Any Future Metaphysics, trans. Peter G. Lucas and Günter Zöller (Oxford: Oxford University Press, 2005), p. 77. 25  Lectures on the Philosophy of Spirit 1827-8, trans. Robert R. Williams (Oxford: Oxford University Press, 2007), p. 239 [Georg Wilhelm Friedrich Hegel: Vorlesungen über die Philosophie des Geistes, Berlin 1827/1828, ed. Franz Hespe and Burkhard Tuschling (Hamburg: Felix Meiner, 1994), p. 227].

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not identical with it.26 The onto-epistemological character of a route of inferential ideation proves to be the range or complex of what is, so far as intelligible, that comes to be (or become actual) as form—that literally is per-form. This cryptic observation, which it is the business of chapter 4 to unpack and illustrate, identifies the actuality of reflective intelligence as a distinctively ontogenetic act.27 Given the primary concern here with inferential concept formation, it makes sense to address the conceptual dynamic of discursive reflection on the plane of conceptual logic. Considering the idea of the reason of inference as act from this perspective, one finds a resource of unparalleled insight in what might initially seem a highly unlikely quarter: Hegel’s Logic. It turns out that the Doctrine of Essence (Wesen), which straddles the doctrines of Being and the Concept (Begriff) anticipates an onto-epistemological orientation to inference in decisive ways, this in the treatment of what Hegel denominates setzende Reflexion and its correlative Gesetztsein. What’s more, Hegel adduces this positing (setzen) in an analysis of essence that articulates a metaphysical logic of reflection and ground that virtually outlines the reflective itinerary of inferential concept formation. As operative on the cognitional level relevant to the act of inference—the level of “pure thinking” (reine Denken), which for Hegel is no less than die letzte Hauptentwicklungsstufe der Intelligenz28—this conceptual logic of reflection demarcates the living moments of inference with unerring fidelity. 26  Richard D. Mckirahan, Jr., discusses the bearing of the Aristotelian doctrine of causes upon scientific explanation. In the process, he spells out why one errs in thinking of formal cause—what I take to be the ground of the rule of sufficient reason in the act of inference—as what a fundamental principle is for some conclusion. Still, Mckirahan does single out formal cause, recognizing (as does the present writer) its ontologically grounding status: “It is best,” he finds, “to refuse to identify the relation between scientific principles and conclusions with any of the four ‘causes,’ while recognizing that the relation depends on the formal cause…”; see Principles and Proofs: Aristotle’s Theory of Demonstrative Science (Princeton: Princeton University Press, 1992), p. 230. 27  Cf., for example, the parallel observation on the ontogenetic element of inference by the philosopher of mathematics Arend Heyting (a student of Brouwer), p. 224, below. 28  Die Philosophie des Geistes, Enzyklopädie der philosophischen Wissenschaften im Grundrisse 1830. Dritter Teil (Frankfurt am Main: Suhrkamp,

28 Inference and the metaphysic of reason These substantial correlations with a phase of the Logik do not, however, render the onto-epistemology of inferential reflection outlined in my fourth chapter “Hegelian” in any systematic sense. To begin with, Hegel would insist that it is a mistake to invoke the doctrine of essence in a purportedly onto-epistemological analysis of inference, since the realization of essence in the Logic is a matter of pure ontology (i.e., metaphysical). Moreover, he would object that any such appropriation fails to credit the conceptual logic of those epistemological moments that properly belong at the more concrete stage of logical development—i.e., on the plane of subjective Geist—where the focus is on reflective judgment and inference.29 Hegel maintains that the doctrine of essence always already presupposes the structure of the self-conscious knowing that it anticipates. While this is consistent with the orientation to the reason of inference as explicated in the pages ahead, everything hinges on how one construes that Hegelian “anticipation,” two elements of which are at odds with the philosophy of inference sketched forth in the present essay. One is Hegel’s metaphysical privileging of the Begriff (and selfconsciousness for that matter30). The second is the teleological character that Hegel expressly ascribes to the principle of sufficient reason—the Grund—when the “ground” has the Begriff for its content.31 (This metaphysical architectonic is necessary, as Hegel sees it, since Sufficient Reason ultimately devolves exclusively from the Begriff, the

1986), §465z; [Hegel’s Philosophy of Mind, trans. William Wallace, Zusätze trans. A. V. Miller (Oxford: Oxford University Press, 1971)]. 29  Cf., Hegel’s Science of Logic, trans. A. V. Miller (Atlantic Highlands, N.J.: Humanities Press, 1993), vol. II, Section One, chaps. 2 and 3; [Wissenschaft der Logik II (Frankfurt am Main: Suhrkamp, 1986)]. 30  Karl Ameriks, for one, critiques “a thoroughly optimistic rationalistic monism” in German Idealists from Reinhold to Hegel. The latter, as Ameriks notes, identified self-consciousness as the ground for disclosing and expounding “an extraordinarily fulfilling and accessible—and in that sense ‘ideal’—underlying pattern to the way that all nature, culture, and history have developed”; see Ameriks, Kant and the Historical Turn (Oxford: Oxford University Press, 2006), pp. 213-15. 31  Cf., Encyclopedia Logic §121z.

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only mode of being whose “content” is fully determinate: i.e., as spirit (Geist) in and for itself.32) But one can follow Hegel only so far in this connection. The leading systematic implications that he draws from the conceptual logic of essence, or rather imputes to it—particularly those implications that concern Ground (Reason)—suggest, in terms open to fundamental debate, that rationality is parasitic on an architectonic exigency of the Absolute. Hegel astutely enough recognizes, with Leibniz, the originary status of the principle of sufficient reason. But his tendentious reinterpretation of the latter as final cause—as opposed to mechanical (efficient) cause—must give way, I shall urge, to a reading of Sufficient Reason as a matter of formal cause, at least with respect to the actuality of any given line of inference.33 Discursive, inferential thinking is essentially formal thinking; and the principal thesis that Part II of this essay seeks to substantiate is that the sufficient reason of inferential reflection is a formally articulated conceptual logic. 3 A main ambition of this book is to help prompt an orientational shift in how we conceptualize the reason of the act of inference. The emphasis throughout on the reason of inference as act signals the abiding concern with the speculative (vernünftig) onto-epistemological horizon of discursive thinking (Understanding) whose being is the act of inference.34 Discursive reflection is conceived here as composing a 32  Chapter 4, below, revisits these issues and reflects upon how, in the move from ground to existence, Hegel incurs a logically vitiating teleological suspension (or supersession) of the principle of sufficient reason. 33  See Blanchette, Philosophy of Being (§15.1), on the contrast between the extrinsic character of final cause and the intrinsic character of formal cause in the “communication among beings” (a contrast that is a feature of the context of the “communication” between remote fact—the nature of whose being one may have no notion—and reflective thought in human being). 34  Kant would certainly have repudiated any proposal to explain the character of Reason by way of a sufficient (formal) cause that defines acts of inferential reflection. As Henry E. Allison observes, “Kant notes that the traditional logical conception of reason as the faculty of drawing mediate inferences provides no insight into the nature of reason considered as a transcendental faculty with a real, that is, metaphysical use”; see Transcendental Idealism, rev. ed. (New Haven: Yale University Press, 2004), p. 308. At most Kant might grant that the present work proffers some sort of transcendental logic, albeit one that misguidedly takes its point of depar-

30 Inference and the metaphysic of reason unity whereby what “shows” as a premise does so by virtue of acquiring its determinate identity as a premise—which is to say the determination of thought—reflectively, through being ordered to a conclusion, vis-à-vis at least one other premise. The ontogenetic nature of this “show” (Schein) attaches to the very circumstance of one’s putting to thought, as a premise, some moment of significant fact.35 For this is how I realize the moment as significant, hence as eductor, of a living intelligence, the virtue of whose very act ture from what he insists is a syllogistically rule-governed mode of thought (inference). 35  By “fact” is understood any “what,” any thing-in-itself, as it is for us, i.e., as “this” or “that”—Dasein in the sense of Zugegensein—actually or potentially. To characterize the “what” and the “for us” as discrete or abstractable within the living act of reflective intelligence is to lose sight of the fact that neither Substance nor God, but the human being is, to employ the Thomist notion, our “primary analogate.” Put another way, to separate the what and the for us is to construe this reference to fact as a metaphysical dogma. It is to miss or ignore the fact that the what and the for us are essentially “one word,” such as is exemplified, in a different speculative context, by Buber’s Ich-Du. Finally, to confuse “fact” with “faciticity” in the act of reflection is tacitly to import an ungrounded principle of individuation (regardless of any imputed origin). On how the use here of “thing-in-itself ” differs from the Kantian notion, see §4.7a, below. One finds in Fichte a penetrating analysis of the onto-epistemological analogate of fact as it is for us (a circumstance that gives “truth” its meaning, indeed a circumstance that we affirm with the very idea of “truth”). In his later lectures on the Wissenschaftslehre, Fichte explicates a principle of “true seeing,” which we may inferentially posit, as a “light” that is not merely intentional, but the condition of the intentional that is qualitatively revelatory—as “genetic” knowing, in contrast with empirical knowing—of the very efficacy of fact for us. Fichte formulates his insight with the proposition, “light is an absolute ‘from’”; see The Science of Knowing: J. G. Fichte’s 1804 Lectures on the “Wissenschaftslehre,” trans. Walter E. Wright (Albany: State University of New York Press, 2005), p. 149. The present work is not an essay in general ontology—the formative constructive theme being limited mainly to the conceptual logic of the act of discursive intelligence; hence it does not pursue this theme of general metaphysics, nor does it venture into the metaphysics of substance. For a contemporary systematic ontology that rejects “substance” but approaches “fact” as a primary onto-epistemological moment, see Lorenz B. Puntel, Structure and Being: A Theoretical Framework for Systematic Philosophy, trans. Alan White (University Park, Pa.: Penn State University Press, 2008).

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of being is literally to invest fact (as significant) with a formative, an ideal character or shape (Gestalt) as a term of rational thought. Hegel would call this the function of intelligence as productive imagination (produktive Einbildungskraft).36 The show posited in this sense is not strictly analogous to visual phenomena. It has, rather, the character of the formal efficacy of actuality or manifestation (i.e., of a power37) as a reality of intelligence—indeed as perhaps the most significant fact of it. Grasped in this light, the show of premises in the positing that is peculiar to acts of inferential reflection has nothing to do with any “allegiance” to the “special superstition” that Gilbert Ryle identified with the “epistemology of ratiocination,” namely “that the theorizing operations which it is trying to describe ought to be described by analogies with seeing.”38 The principle of order that at once underwrites and marshals the premises (as premises) in any coherent act of inference is a constitutive element of them, not merely a regulative one. It is that which discloses what they are as ingredient in the formal, “objective reality”39 proper (in cogent inferences) to the concept of a rational conclusion. The latter is not as such properly reducible to an abstract concept but instead is concretely actual only as a living process, as forma formans.40 The reason of this act of inference betokens the “faculty” of the principle (of Sufficient Reason) that renders the reflective show of premises (the scheinen) intelligible as, in the first instance, determinately ordered to a formal totality—the conclusion, or meaning.41 The latter falls un36  Cf., Lectures on the Philosophy of Spirit 1827-8, p. 222. 37  For the Heideggerian, alētheic power. 38  Ryle, The Concept of Mind (New York: Barnes & Noble, 1949), p. 303. See §1.iii, below. 39  Cf., Kant, Critique of the Power of Judgment, ed. Paul Guyer, trans. Paul Guyer and Eric Matthews (Cambridge, Engl.: Cambridge University Press, 2000), §76. 40  In a way that speaks directly to what is at issue here, Ernst Cassirer discriminates between forma formans from forma formata as he delineates the metaphysical ground of his philosophy; see The Philosophy of Symbolic Forms. Volume Four: The Metaphysics of Symbolic Forms, ed. John Michael Krois and Donald Phillip Verene, trans. John Michael Krois (New Haven: Yale University Press, 1996), chap. 1 (“‘Geist’ and ‘Life’”), esp. pp. 17-20. 41  Hegel, as we shall see, delineates this with great precision, in his doctrine of essence, as a totality that is a ground.

32 Inference and the metaphysic of reason der the discursive “rule” of order. Unlike the doctrines of idealist logicians from Hegel to Bosanquet and Harold Joachim, this reading of inference harbors no metaphysical pretensions about any underlying general nisus toward an Absolute or Whole that informs the spiritual (geistig) trope that is inferential reflection (an act that putatively constitutes some stage or phase of the Absolute). The reason of inference explored in this study thus refers to considerably more than the “reasonable” or valid mediated judgment. It has to do, in the main, with the onto-epistemological provenance of the act of inference. This act is a discursive performance of reflective thought that, being ordered to some form, is determined in a formal manner. To appreciate the metaphysical implications of inferential thinking in these terms is to come into possession of a philosophical touchstone. For one thereby acquires a heuristic resource that enables one both to recognize and to probe the limits of the analytic illusion that one can rightly explain the rational character of discursive thought by invoking socio-linguistic norms and praxis or the (philosophical) psychology of reasoning or the axiomatized syntactic rules of a propositional calculus with its concomitant validation procedures. The appeal to reason in the present context brings with it grounds for radically challenging rationalistic theories, of whatever analytic stripe, that in any way counterpose the exercise of discursive thinking to “intuition” or “perception” or “sensuous apprehension.” One gets a fair sense of how far this emphasis on reason distinguishes the onto-epistemological orientation to inference from other approaches when one considers the pivotal issue that Gilbert Harman has raised relative to the modus operandi of many contemporary accounts. Harman remarks that it is futile to try to explain inference as logically definable, rule-governed cognition (whether deductive or inductive): “nothing in logic tells us which rules to apply in particular circumstance.”42 This is at bottom a metaphysical challenge, an unanswerable challenge for the many post-Kantian analytic epistemologists—the bulk of contemporary philosophers of inference. To know, for these epistemologists, is to justify appearances by unifying them under logical schedules of rules of entailment or norms of praxis. Harman himself tried to circumvent this aporia by an overt appeal to psy42  Cf. §2.3, below, for my critique of Harman’s doctrine. See also §2.5, for some remarks relative to Michael Williams’ reliance on Harman’s dismissive evaluation of linear inference.

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chologism without metaphysics. This strategy, however, brings with it its own problematic metaphysical assumptions—something Errol Harris would have been quick to point out, even if he would have been sympathetic to Harman’s motivation. An acute critic of the metaphysical short-sightedness that marks too many analytic epistemologies, Harris had this to say about the efforts of analytic thinkers to extirpate every trace of psychologism and metaphysics in the philosophical logic of discursive knowledge: Inference…is an operation of thought—though most contemporary logicians, anxious to purge their disciplines of all taint of psychologism, prefer to substitute for principles of inference rules of implication or entailment. Nevertheless, few would wish to deny that logic is concerned with concepts, with the relations between them, and between them and the entities of which they are concepts. Here, whether we like it or not, there is inevitable involvement with thought, for a concept is obviously a product of conceiving; and relations between concepts and that to which they apply inescapably implies the relation of conception to its objects. How we view that relation, moreover, is, or involves, a metaphysical theory. Indeed, logical theory and practice always do presuppose some concept of the structure of fact, which, when made explicit, is a metaphysic.43

The difficulty that accompanies the analyst’s proposed rules of implication or entailment is that no such axiomatic schedule, however systematically articulated, can be self-consistently, hence logically, complete (coherent) as an explanation, whether implicit or express, of inference as a living act of intelligence. The axiomatic appeal to rules, abstract concepts, to explain a process of cognition that is the very medium of concept formation—and concepts are no more than metaphorically the “content” of thought—cannot tell us44 how to apply those rules even to the most immediate context of implication or entailment in view, i.e., that explanation itself. One begins to appreciate the signal bearing that this has on the conceptual logic of inference once one recognizes that as a living act, the process of inferential cognition features a constitutive element of indeterminacy vis-à-vis its theme. This element is of decisive import in that it involves the meta43  Formal, Transcendental, and Dialectical Thinking: Logic and Reality (Albany: State University of New York Press, 1987), pp. 24-25. 44  Beyond a vicious circularity or futile appeal to a “bad infinite.”

34 Inference and the metaphysic of reason axiomatic meaning that vouchsafes the ultimate rationality of any particular rubric of implication, and hence conceptualization. Kant would class the formalism of concern here under “general logic,” which includes inference in the form of the syllogism. Hegel, on the other hand, would question such a move, charging that, as the logic of the understanding, inference so conceived “fails to recognize the relation” between, say, particular and universal or concept and conceptualized, “even when it has already been expressly posited.” 45 Indeed, as Hegel saw, “it overlooks the very nature of the copula in a judgment, which says that the singular, or the subject, is not just singular but universal as well.”46 What in the first Critique Kant takes as the capacity of transcendental logic “to tell us which rules apply in particular circumstances,” namely the faculty of the “unity of rules of understanding” (and hence of the logic of inference),47 is, as Henry Allison notes, a function of “principles that Kant connects with the use of reason.”48 Kantian Reason (Vernunft) is a faculty of principles that vouchsafes the rational unity of discursive rules of thought. Often overlooked, here, is that Kant identifies the unity of Reason itself not with the unity of possible experience but with the principle of sufficient reason, recognized as a (synthetic) principle that “makes the unity of experience possible” while it “borrows nothing from reason” (A306-07/B363-64).49 Kant recognized that it is the form of inference with which the “pure concepts of Reason” originate.50 He thus adumbrates a defining principle of the present work, which is that the Sufficient Reason of the act of inference is a matter of formal cause (i.e., an intelligible cause 45  The Encyclopedia Logic, §214. 46  Ibid. 47  Critique of Pure Reason, trans. Paul Guyer and Allen W. Wood (Cambridge, Eng.: Cambridge University Press, 1998), p. 389; (A302/B359). 48  Transcendental Idealism, p. 309. 49  Again, Lotze’s account of the principle of sufficient reason is consistent with this. 50  Cf., “…we can expect that the form of the syllogisms, if applied to the synthetic unity of intuitions under the authority of the categories, will contain the origin of special concepts a priori that we may call pure concepts of reason, or transcendental ideas, and they will determine the use of the understanding according to principles…” (A 321 / B378); see Critique of Pure Reason, p. 399 (boldface type in original, italics added).

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rather than a sensible cause).51 Specifically, Kant argued that the syllogistic logic of scientific cognition—the received formal paradigm of inferential thinking—contains “the origin” of “the pure concepts” of Vernunft.52 The formal character of this origin is limited, in Kant’s doctrine, to three syllogistic forms, those of the categorical, hypothetical, and disjunctive syllogism. Consequently, he saw in the syllogism “a judgment determined a priori in the whole domain” of the “function of Vernunft in its inferences” (A 321-22/B378-79). Here is how Kant summarized what he held to be the three-phase act of inference as syllogistic: In every syllogism I think first a rule (the major) through the understanding. Second, I subsume a cognition under the condition of the rule (the minor) by means of the power of judgment. Finally, I determine my cognition through the predicate of the rule (the conclusio), and hence a priori through reason.53

From the standpoint of Kant’s doctrine of inference as syllogistic, one can read Harman’s earlier-cited criticism as pertaining to theories of inference that fail explicitly to address the Reason of the act. Such unsatisfactory accounts lack, again from the Kantian orientation, a transcendental logic, and thereby fail to credit that “unity of rules” which alone can render intelligible the act of discursive reflection. Still, Kant’s explicit, traditional doctrine of the form of inference as syllogistic has unwarranted limitations, and this problematically 51  Cf., Critique of Pure Reason, pp. 534-37; (A535-41/B563-69). See also the Prolegomena to Any Future Metaphysics, trans. Peter G. Lucas and Günter Zöller (Oxford: Oxford University Press, 2005), §17, where Kant asserts that the “formal in nature is…the conformity to law of all objects of experience, and insofar as they are known a priori, their necessary conformity to law” (p. 103). By substituting for “nature” the idea here of “fact for us,” and for “law” the term “order,” one approximates a Kantian version of a key phase of the onto-epistemology of inference. 52  Cf., “…we can expect that the form of the syllogisms, if applied to the synthetic unity of intuitions under the authority of the categories, will contain the origin of special concepts a priori that we may call pure concepts of reason, or transcendental ideas, and they will determine the use of the understanding according to principles…” (A 321 / B378); see Critique of Pure Reason, p. 399 (boldface type in original). 53  A304/B360-61; Critique of Pure Reason, p. 390 (boldface type in original).

36 Inference and the metaphysic of reason constricts his view of how the rational inference (Vernunftschluss) expresses Reason (Vernunft).54 Of course Kant does not restrict Vernunft to syllogistic thinking—for example, Reason regulates the understanding by establishing the categorical imperative (not to mention God) as unconditioned grounds of the conditioned.55 But this merely evidences a metaphysic of Reason that sunders the relation between mediated judgment and understanding. The nineteenth century saw the classical syllogistic definitions of inference superseded;56 and this exposed the formal shortcomings of Kant’s conceptual logic,57 a cardinal facet of his doctrine of speculative Reason. The lesson here is that the philosopher of discursive thinking who fails sufficiently to consider the onto-epistemological dimension of the act of inference invariably operates with an inadequate conceptual logic. This issue in large part motivates the effort in chapter 4 to concentrate on the conceptual logic of inference. ii. Chapter summaries. Interrelated critical and constructive phases of discussion compose the core of the present investigation. Following this introductory chapter, chapter 2 assesses leading accounts that represent the broad spectrum of contemporary philosophies of inference. The sampling of diverse if exemplary analytic philosophies of inference that come in for assessment include those of Rudolf Carnap, Gilbert Harman, Robert Brandom, Michael Williams, and Bernard Lonergan. The critique will take as points of departure central position statements of each doctrine and evaluate those operating assump54  Cf., Graham Bird’s lucid explication of this difficulty, in The Revolutionary Kant: A Commentary on the “Critique of Pure Reason” (Chicago: Open Court, 2006), p. 603. The account of inference thought through in the present essay tracks well beyond the conventional doctrine to which Kant subscribed, i.e., that Reason is “the faculty for drawing inferences, and hence of completing sciences by means of syllogisms”; Allen W. Wood, Kant (Malden, Mass.: Blackwell, 2005), p. 77. 55  Cf. Mark Fisher and Eric Watkins, “Kant on the Material Ground of Possibility,” pp. 393-95. See also Karl Ameriks’ discussion of Kant on the “unconditioned,” in Kant and the Historical Turn, pp. 149-54. 56  In Lotze we shall find an example of a seminal nineteenth-century proposal to think beyond it; see §3.4.2, below. 57  Much as advances in geometry and physics disclosed shortcomings of the transcendental logic.

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tions from an onto-epistemological standpoint, the present work’s speculative frame of reference. This modus operandi will call attention to inconsistencies and contradictions in the doctrines of Carnap, Harman, Brandom, Williams, and Lonergan which evidence the need for the sort of critical metaphysic of inferential reflection that we shall undertake in chapter 4. This critical metaphysic, as was indicated at the outset, engages the problematic of inference in terms of the ways that reflective knowing is of being. Among the key distinctions operative through the ensuing critique of Carnap, Harman, Brandom, Williams, and Lonergan is the Kantian one between absolute and relative positing (Position oder Setzung). Given that discussions (let alone the application) of Kantian Position oder Setzung are marginal in current philosophical discourse, this introductory chapter concludes with a section devoted to clarifying something of the notion’s provenance and range of meanings. This should make intelligible the significant sense and implications of the regular references to onto-epistemological positing in chapter 2 and beyond. (The four sections of Appendix I provide the interested reader further reflections on the topic.) Following the second chapter’s critique of the epistemological philosophies of inference, chapter 3 shifts the focus of inquiry to the earlier, metaphysically contexted logics of inference worked out by Lotze and Bosanquet. Subtle analytic thinkers in the great tradition of the philosophia perennis, Lotze (in the 1870s) and Bosanquet (in the 1910s) were acutely sensitive to the risks of reductivist narrowing that they detected in the growing trend to mathematicize symbolic logic. And upon examining their treatments of inference, we shall discover that both philosophers articulated astutely nuanced, systematic explications of judgment that incorporate the ontological moment of reflective thought in ways that transcend on various fronts the speculative scope of the analytic doctrines grounded in analytic epistemology. To explore the thinking of Lotze and Bosanquet on inference, however, is invariably to find oneself in philosophical territory that extends considerably beyond the constellation of issues that have to do with the onto-epistemology of positing (as a moment of inference). Hence by contrast with chapter 2, allusions to “position” if regular are relatively infrequent in chapter 3, which includes forays into the metaphysics of form, relation, actuality, and implication. As pursued by Lotze and Bosanquet, the latter paths of inquiry yield il-

38 Inference and the metaphysic of reason lumining insights that at various junctures substantiate, as we shall see, the onto-epistemological approach to inferential reflection. Beyond that, Lotze and Bosanquet produced accounts of inference that do not incur the sorts of antinomies and heteronomies that chapter 2 brings to light in the more recent, epistemologically positive views. These virtues notwithstanding, however, the doctrines that Lotze and Bosanquet promulgate are not without systematic difficulties of their own, problems that will come in for comparative analysis vis-à-vis the onto-epistemological orientation that underlies the conceptual logic of inference detailed in chapter 4. With chapter 4, the constructive phase of the investigation commences. This second, culminating part of the inquiry explicates and integrates the defining elements of the onto-epistemology of inference that figure either tacitly or expressly at different points in Part I. Given that the leading concern throughout is with inferential concept formation, the fourth chapter considers the reason of the act of inference principally from the angle of conceptual logic, rather than from that of a logic that is either purely transcendental or conventionally formal. Such an approach to reflective thought eschews dichotomies between knowing and being that in one way or another undermine the rational coherence of the sorts of analytic inference theory critiqued in chapter 2. After spelling out the underlying rationale for an onto-epistemology of inference, the fourth chapter addresses the challenge of thinking through the formative structural and functional moments of the act of inferential reflection. Separate sections investigate each of three main components: onto-epistemological positing, conceptual logic, and the ground of sufficient reason (in inference) as formal cause. Beyond tracing in systematic outline the onto-epistemology of inference, chapter 4 shows how this speculative orientation is deeply consistent with scientific cognition (Erkenntnis) in the classic philosophical sense. The latter survived and continued to develop as a traditionally systematic science until the early twentieth century—only to be marginalized, if not attenuated, by a narrowing of analytic focus,58or simply dismissed by logical positivism, linguisticism, and other analytic schools. One of the few major twentieth-century thinkers who understood the value of philosophically scientific cognition 58  As witnessed in the waves of leading scholarship constellated around such themes as scientific realism, operationism, perception, explanation, confirmation, and the sociology of scientific theorizing.

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relative to its originating spirit in Enlightenment thought and classical philosophy was Ernst Cassirer.59 A self-described critical idealist, Cassirer is among the most distinguished neo-Kantian theorists of inference who possessed detailed mastery of the latest developments in both mathematicized logic and the exact sciences generally. And it is Cassirer’s philosophy of inference to which the present work’s orientation exhibits perhaps its closest historical and conceptual affinities. For that reason, after outlining that orientation chapter 4 devotes its penultimate section to identifying the signal correlations that betoken the affinities with Cassirer’s thought. Teasing out the parallels with Cassirer reveals the current of philosophical history to which the onto-epistemology of inference championed in this essay is most nearly aligned. To be sure, the philosophy of inference thought through here is not a neo-Kantian philosophy. Indeed, the comparison with Cassirer will bring to light, beyond the affinities, pivotal divergences that betray telling points of incommensurability between the two approaches to the conceptual logic of the reason of inferential reflection. The concluding section of chapter 4 sums up this book’s principal debts to Kant, Hegel, and Bosanquet, underscoring at the same time the issues over which it breaks with their views. The chapter and with it the investigation’s core discussion wrap up with some reflections on the thinking that distinguishes this essay in critical metaphysics from other philosophical approaches to the act of inference. The study ends with a word about the larger purposes that animate its call to rethink the philosophy of inference along onto-epistemological lines.

59  Paul Natorp and Heinrich Rickert are two other notable onto-epistemologists of scientific knowledge, while Whitehead (like Natorp strongly influenced by Plato) is perhaps the greatest thinker of the period who articulated a metaphysics of scientific cognition from a different philosophical stance than the neo-Kantians. The divergent applications of Kantian thought that one sees in Cassirer and the early Carnap reveals the metaphysical basis of the analysts’ scientism and their repudiation of Geisteswissenschaft (and hence philosophy of being) as genuine science. In this connection, see Michael Friedman, A Parting of the Ways: Carnap, Cassirer, and Heidegger (Chicago: Open Court, 2000).

40 Inference and the metaphysic of reason iii. Onto-Epistemological Positing and the Philosophy of Inference: The Kantian Legacy.60 As Kant initially characterized it and as later philosophers employed it, Position oder Setzung61 is manifestly an onto-epistemological concept. The standard translation, “positing” or “position” (taken in the active sense62) hardly captures the term’s subtle and all-important speculative connotations, references that stand in need of retrieval and renewed consideration, particularly in Anglophone philosophical discourse. Since the idea of onto-epistemological positing is one of the recurrent and unifying components of the critical and the constructive phases of discussion ahead, we need to get clear at the outset about the term’s philosophical pedigree as well as about the range of cognate speculative meanings that Position, Setzung, has accrued.63 3 Formative currents of the very culture of philosophical thinking during the European Enlightenment involved systematic investigations into how the nature and limits of reason relate to the acts of thinking that we identify as inference. An intellectual historian such as Louis Dupré would judge this development as evidence of the culminating 60  For more on the Kantian conception of Position and its relevant speculative implications, see Appendix I, below. 61  Cf., Kant’s original formulation, in Theoretical Philosophy 1755-1770, p. 119. 62  Interestingly, the OED identifies “position” as an antithetical correlative of “sublation,” citing a statement by Sir William Hamilton as an historical precedent for this association in English. 63  Appendix I, below, further details Kant’s conceptualization of “positing” and touches upon philosophically consequential implications of this often ill-understood thought-determination. Section ii of Appendix I considers its significance in contemporary philosophical history, touching upon Frege’s influential if controversial effort indirectly to exploit the Kantian notion in order “to explain how” the logical function of quantification yields “informative existence claims.” Appendix II is a commentary on W. V. Quine’s appropriation of “positing” as a speculative notion. A more recent treatment of “positing” in Kant and Brentano appears in Wayne M. Martin, Theories of Judgment: Psychology, Logic, Phenomenology (Cambridge, Engl.: Cambridge University Press, 2006), chap. 2. Martin’s analysis, however, is insufficiently developed in some key respects and consequently somewhat distorts the picture.

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or “full” restoration of the classical “principle of rationality,” whereby Enlightenment thinkers imposed the rules of the one science that the mind could indeed claim full authorship of and which depended on no external content, namely, mathematics. The mind thereby acquired an unprecedented control over nature, yet it ceased to be an integral part of it.64

Although it originally targeted concerns about the being of discursive intellection, this exploitation of the mathematic would eventually revolutionize formal logic and consequently the philosophy of inference. Such proved to be the case, at least, for those influential scholarly cohorts who shifted the grounding orientation of philosophical speculation from systematic ontology to alternative varieties of analytic epistemology. One result of this revolution was a proliferation of epistemologies of inference that fail satisfactorily to address, when they do not simply ignore, the onto-epistemological character of the integral relation that obtains between the act of inference and that which is not “mind.” What must count as some of the most deeply influential Enlightenment thinking that bears on this issue is Kant’s doctrine of Position oder Setzung. Notwithstanding a fundamental limitation65 and the fact that till now it has not played a role in the philosophy of inference (a field of inquiry to which it is, as we shall see, patently germane), Kantian “positing” constitutes a trenchant speculative instrument. This will be evident when in chapter 2 we employ it, along with other modes of analysis, to take the measure of some leading epistemologies of inference that wrestle with the above-noted problematic concerning the relation of inference to what is ontologically diverse from mind. (Beyond this heuristic value of onto-epistemological positing, we shall consider, in chapter 4, its constitutive function in the conceptual logic of inferential reflection.) Little remarked in the literature, though a recurrent topic in this investigation, is Kant’s distinction between absolute and relative pos64  Dupré, The Enlightenment and the Intellectual Foundations of Modern Culture (New Haven: Yale University Press, 2004), p. 16. The seminal premodern anticipations of this appear in medieval rational theology by the likes of Maimonides and Aquinas. 65  I.e., the categorical split between absolute and relative Position, discussed in this section and in §4.4.a; see also Appendix I, i, below.

42 Inference and the metaphysic of reason iting. Among the few recent treatments of this classification, perhaps the most distinguished is that of Manfred Frank, who in lectures dating from the late 1990s explicates Kant’s move to distinguish metaphysically discrete types of Position oder Setzung.66 Frank stresses that relative positing is for Kant the frame of reference for how we cognize “original Being.” As Frank puts it, “Kant draws a distinction not only between the terms ‘existence’ and ‘predication,’ but also shows that the original meaning of Being is first fulfilled within the context of predication” 67—the context, that is, of relative Position.68 This distinction between existence and predication becomes systematically established only with the “Copernican Revolution” of the first Critique. One finds it generalized there, in the Transcendental Dialectic, as a logical feature of Kant’s system. Kant onto-epistemologically inverts the relation in the traditional notion that a subject contains implicitly within itself all of its possible predicates. The subject in the logical proposition is a function of absolute position. It is “put” to thought, namely as in itself the unconditioned ground of all predicates 66  The Philosophical Foundations of Early German Romanticism, Lecture 3. 67  Ibid., p. 62. Studies that explore the continuity, on these grounds, between Kant’s pre-critical and critical phases remain few and far between. Eckart Förster’s Kant’s Final Synthesis constitutes one form that such an investigation can take. Heidegger offers a more original approach in “Kant’s Thesis about Being,” pp. 337-63. 68  In this connection, cf., Paul Natorp: “absolute positing, whether it be of being or not-being or any determination in thought, itself does away with thinking and determination, and…in the last analysis only relational [relative] positing can obtain. Positing means relating”; see Natorp’s discussion of the Parmenides, in Plato’s Theory of Ideas: An Introduction to Idealism, trans. Vasilis Politis and John Connolly (Sankt Augustin: Academia Verlag, 2004), esp. pp. 254-58. The onto-epistemological thrust of this view is clear when one recalls that Natorp follows Lotze in holding that “to be is to stand in relations.” At least with respect to the Idea of the Good, however, Natorp rejects Lotze’s standpoint on “the being of ideas” as signifying “a ‘validity’ understood teleologically,” i.e., signifying “the highest genus of being” taken as “practical necessity” (ibid., p. 201). Natorp is closer than Lotze to the present author’s orientation when he finds “even the claim that the idea of the good surpasses being does not directly refer to practical necessity’s going beyond (conditioned) being, rather it refers to the fact that the positing in thought as such logically goes beyond every specific positing in thought” (ibid.). For Lotze on “validity,” see p. 162, below.

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(conditions) of it.69 On the other hand, one posits predicates relative to their subject, as conditions of the subject—indeed as the only means by which we are able to conceive the subject. Kant’s inversion of the traditional view is apparent when he argues that the very unity of reason follows from the synthetic principle “that when the conditioned is given, so then is the whole series of conditions subordinated one to the other, which is itself unconditioned, also given (i.e., contained in the object and its connection).”70 This is a synthetic principle—as is, for Kant, the principle of sufficient reason—because although “the conditioned is analytically related to some condition,” the conditioned is not analytically related “to the unconditioned.” In other words, the absolute (or unconditioned) moment of position—the existence, the being, of the subject— “is given” with the relative (conditioned) moment. The latter, in the words of Henry Allison, “involves a metaphysical assumption concerning the reality of a complete set of conditions for every conditioned, a set that must be considered as unconditioned….”71 Although ignored by contemporary theorists of inference, the implications of Kant’s thinking here for the philosophy of inference are profound. For it means that given with the form that a particular line of inferential reflection takes is the virtual fact of the absolute or unconditioned ground of the whole extension of its sense. While the whole extension “can never be given as an object,” Kant nevertheless asserts its regulative efficacy as a fact. And this is itself an unequivocal assertion of what fact is for us. Yet for Kant, since the unconditioned can never be objectively given to us, the very ground of that efficacy is a transcendental illusion, albeit one that is an ineludible requirement of the logical use of reason.72 As onto-epistemological doctrine, this is rationalist dogma. It reflects the legacy of essentialist ontology (the 69  Cf., Adamczewski: “It would seem that ‘position’ yields ‘proposition’: I must posit, i.e., think something (setzen), in order to have it capable of logical analysis in the form of subject-predicate (Satz)” (“Kant’s Existential Thought,” p. 327). 70  A307-08 / B364, Critique of Pure Reason, p. 392. 71  Kant’s Transcendental Idealism, revised ed. (New Haven: Yale University Press, 2004), p. 312. See also Karl Ameriks, Kant and the Historical Turn (Oxford: Oxford University Press, 2006), pp. 138-40. 72  Details of Kant’s doctrine of the “Transcendental Illusion” are not a concern in the present context. For a detailed explication of the topic, see Allison, pp. 322-32.

44 Inference and the metaphysic of reason “bad” metaphysics). Indeed, one sees here something of the metaphysical groundwork of the epistemological hegemony that, as Kant’s own legacy, proved instrumental to the rise of contemporary analytic philosophy. In the first Critique, one learns that Being (and by extension the concept of Position) is a modal transcendental category. Modality sets the condition of possibility for our scientific knowledge of Being, namely as being possible, being actual, and being necessary. And it is scientific understanding (Verstand) that becomes, through the pure synthesis of transcendental apperception that determines its use, “the source,” as Heidegger observed, “of the original positing.”73 Hence, for Kant scientific understanding is the ground of Being as thinking.74 The transcendental synthesis is itself a function of the speculative Reason (Vernunft). This Reason connects representations (Vorstellungen) in originary inferential forms that engender “what we may call the pure concepts of reason, or transcendental ideas”; these pure concepts of Reason “determine the use of the understanding” (A321 / B378). It is with this train of transcendental-idealist thinking that Kant establishes that “original positing” (the concept of which is for him identical with the concept of Being) has its source in our scientific knowing, the understanding (Verstand). This is the passage of transcendental logic in view when, in the discussions ahead, I refer to the Kantian reduction of absolute positing to relative positing, and by extension the reduction of ontology to pure epistemology. In the quarter century following the second edition (1787) of the first Critique Kant’s proposal to restrict to the Verstand the horizon of what we may rationally understand of the Being of thinking sparked a legendary philosophical reaction—one that produced the remarkably fertile range of ontoepistemological “corrections,” amplifications, and systematic alternatives to Kantian transcendental epistemology. 3 73  “Kant’s Thesis about Being,” p. 349. 74  That said, one can adduce evidence that Kant, at least in the second edition of the Critique, admits of a non-categorial existence (being). Reiner Shürmann, for one, calls attention to revisions in the Preface, the Refutation of Idealism, and in other places where Kant “conjoins with existence as the second category of modality a notion of being that points elsewhere than toward the understanding” (Broken Hegemonies, p. 482). Evident here is some of the groundwork of the third Critique.

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The concept of Position/Setzung enjoyed such currency in German thinking toward the end of the eighteenth-century that, by the end of the nineteenth, the most distinguished editor of Kant denounced the Setzkrankheit that struck him as plaguing the period of German Idealism dominated by Kant and Fichte.75 In the case of Fichte, to cite only the most prominent example, exasperated readers complained of a philosopher who wrote “as if setzen were the only root verb in the German language.”76 But it didn’t end with Fichte. Far from falling into desuetude with the attenuation of German Idealism in the mid-nineteenth century, “positing” has persisted as a vital speculative thought-determination down to our own day. The diverse line of eminent German thinkers who employ the notion in philosophically material ways runs from Hegel, Herbart, Lotze (negatively77), and Brentano, to Natorp (who went so far as to propose Gegenstands-setzung as a means of redefining the Kantian doctrine of categories78), Husserl, and Reiner Schürmann.79 Although rarely singled out for investigation, particularly as a factor in the evolution of Kant’s thought,80 onto-epistemological Position is 75  Erick Adickes, quoted in Eckart Förster, Kant’s Final Synthesis: An Essay on the “Opus postumum” (Cambridge, Mass.: Harvard University Press, 2000), p. 76. 76  Martin, Theories of Judgment, p. 57. 77  On Lotze’s philosophically disclosive critique of the term, see §3.4.3, below. 78  Cf., also, Natorp’s onto-epistemologically Kantian use of “positing” in the following reading of Plato’s Idea of the Good: “it is not an ultimate logical principle, but the principle of the logical itself and in general, in which all specific positing in thought and hence all specific being—since being is nothing but the positing in thought—is ultimately to be grounded”; see Plato’s Theory of Ideas, p. 196. 79  Schürmann’s Broken Hegemonies features one of the latest comprehensively systematic use of Position as a technical speculative term. Position (the “thetic”) underlies Schürmann’s principal critical concept of “Hegemonies.” Schürmann, however, splits the sense of Position and Setzung in Kant’s thinking—a transparently tendentious expedient that is analogous to the early Heidegger’s procedure of egregiously adjusting the Kantian record in places to fit a thesis of his own. (Appendix I.i, below, identifies an instance of this.) 80  An example of this now-rare focus of analysis appears in Wayne Martin’s, Theories of Judgment, chap. 2.

46 Inference and the metaphysic of reason a speculative idea that was catalytic in the emergence and ascendancy of the analytic orientation in Western philosophy. Wayne Martin has recently traced this from the angle of Kant’s explication of logical judgment, and of how “Kant’s treatment of existential judgment as positing prompted the revisionist trend in nineteenth-century logic.”81 Most relevant here is Martin’s intention to “show how Kant’s own treatment of singular existential judgment as positing (setzen, qevs i~) led to the overthrow of the model of judgment upon which he had relied.”82 While Martin does allude to Kant’s initial (1763) explication of “positing,” he does not take up the pivotal distinction between absolute and relative positing (a lapse surprisingly frequent in commentaries on the text). This oversight is all the more puzzling in view of the salient treatments of Kant’s dichotomy or, better, binarism by the likes of Heidegger, Förster, and Manfred Frank—not to mention those by Johann Friedrich Herbart, Franz Brentano, and Moritz Drobisch, a trio of distinguished earlier thinkers whom Martin himself singles out for discussion. 3 The Anglophone student of thought gets something of the idea of Position in the words “positing” and “position” when they are understood in the active sense (the sense of ponere, antecedent to positus), as in to “put” (setzen) or “putting.” But the English verbs “put,” “posit,” “postulate,” “suppose,” and the like miss or obscure seminal ontoepistemological connotations that resonate in Position and Setzung as part of the German speculative vocabulary. (Contemporary analytic epistemologists typically think of “positing,” in conjunction with inference, as “supposing” or as an action on the order of laying a bet.83) The character of the referential disparity becomes manifest when once one takes seriously Kant’s 1763 observation—which was never annulled in his later thinking—that the concept of Position is identical with that of being in general (Sein überhaupt). This is an orientational, a metaphysical use of the word that the standard English translations reduce to nonsense. We see this, for example, in the principal translation of 81  Ibid., pp. 70-71. 82  Ibid., chap. 2. 83  Wayne Martin exemplifies this line of thinking when he suggests that when reflecting on Kant’s use of setzen, “it is useful to have in mind the mathematical sense of positing – as when I posit a number in the course of a proof ” (Theories of Judgment, p. 52).

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Lotze, a philosopher of inference who virtually rejected the speculative value of the term altogether. One hardly need be a Germanist to recognize in the English version of Lotze’s Metaphysik (initially prepared by T. H. Green, later edited by Bosanquet) the sharp disparity between “putting,” in anything like its standard acceptation, and the philosophical sense of setzen that Lotze targets in his opening chapter. Perhaps the most telling passage is one in which Lotze criticizes various ontological associations identified with Position oder Setzung:84 “Actual Being,” argues Lotze, “as distinguished from the mere validity of the thinkable, can never be arrived at by this bare Putting, but only by the addition-in-thought of those relations, to be placed in which forms just the distinction that actuality has over thinkability.” [Das wirkliche Sein, unterschieden von der bloßen Gültigkeit des Denkbaren, kann nie durch diese schlechthinnige Setzung, sondern nur durch Hinzudenken derjenigen Beziehungen erreicht werden, in welche gesetzt zu sein eben den Vorzug der Wirklichkeit vor der Denkbarkeit ausmacht.] 85 More recently, and consistent with Lotze’s rationale for dropping the term (for which he substituted Wirklichkeit), a leading Anglophone student of Kant, Allen W. Wood, is persuaded that “positing” serves merely a “semantic function.” But this would make Kant’s identification of Position with being “in general” an egregiously un-Kantian postulate. To read Position “semantically,” as signifying or referring to the “givenness” of an object, is to lose sight of what Kant himself initially took to be the ontological register of the act (something that both Manfred Frank and Heidegger fully appreciate86). 84  See Metaphysic in Three Books: Ontology, Cosmology, and Psychology, esp. pp. 42-45. 85  Ibid., p. 44 (translation modified) [Metaphysik: Drei Bücher (Leipzig: Hirzel, 1879), pp. 37-38]. 86  See Frank’s Philosophical Foundations of Early German Romanticism, Lecture 3; and Heidegger’s “Kant’s Thesis about Being.” Cf., the corroborating observation in Adamczewski’s tortured English: “The interrelations are complex, but they show that it would be wrong to equate positing and mentally entertaining or conceiving....this can be said: in a sense legitimate but not sufficient for Kant, ‘position’ of a mental entity as the inception of thinking enterprise [sic] is logically prior to ‘proposition’ as its explicit development—this is so with regard to any essence the human mind may contemplate or manipulate. In contrast to that, Kant understands ‘position’ with regard to existence, to an ‘object’ for a concept, about which more than one ‘proposition’ may be already available, if not posterior to, it is [sic] more

48 Inference and the metaphysic of reason Discussing the idea of Kantian positing and the theory of logical judgment in ways that are consistent with Wood’s reading of them, Wayne Martin discovers a difficulty with Kant’s theory of judgment when one assesses it from the perspective of positing understood in these terms. “What exactly does it mean to posit an object?”, asks Martin, as he reviews Franz Brentano’s Kant-inspired doctrine of the thetic judgment, what is involved in positing something?…when we attempt to go beyond…negative characterizations it is easy to slip into vacuous circularity….In positing Pierre, I claim that there is something which answers to my description of him. But such answers are obviously circular if they are meant to explain or define the positing involved in existential judgment. So where the synthetic construal of judgment left us with a research program (what sort of synthesis of concepts amounts to a judgment?), the characterization of judgment as positing threatens to leave us with an empty tautology: existential judgment is positing; positing is an assertion of existence.87

The suggestion here is that the critical Kant advanced beyond his early conception of judgment as Position. Kant, however, never defines the latter as bare assertion. How far any such association is from the mark becomes clear when one considers setzen as Fichte understood it. Arguably the greatest authority on Kant’s onto-epistemological employment of Position oder Setzung, Fichte is perhaps the subtlest expositor of the notion. In the Wissenschaftslehre, setzen stands as a moment of the original act [Tathandlung], which is by the same token “the first ‘fact’ of consciousness [Tatsache des Bewusstseins].”88 Manfred Frank points out that Fichte “presents the term ‘setzen’ as synonymous with original activity (ursprüngliche Handlung) and couples this with Kant’s definition of the intellect as something ‘whose concept is a deed (ein Tun),’”89 i.e., existential. Fichte declared that the self, no mere assertion, “exists because it posits itself, and posits itself because it exists. Hence self-positing and existence are one and the same. But the concepts of self-positing than what lies in the domain of essential thought. Yet this relation is not logical but ontological” (“Kant’s Existential Thought,” p. 328). 87  Theories of Judgment, p. 71. 88  Manfred Frank, Philosophical Foundations of Early German Romanticism, p. 65. 89  Ibid.

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and activity in general are again one and the same. Hence, all reality is active and everything active is reality.”90 This goes considerably beyond “the characterization of judgment as positing” to which Martin refers, above. Moreover, as understood in the context of Fichte’s metaphysics the formulation is anything but an empty tautology. Indeed, one finds that Fichte exploits the full measure of the onto-epistemological implications of Setzung as a speculative thought-determination. During the course of a Harvard lecture on Fichte, Dieter Henrich identified for his Anglophone audience the multifaceted associative range of “positing” as a philosophical term. Much of this range of senses proves to be distinctly illocutionary in character, a defining feature of Fichtean usage. “Setzen,” notes Henrich, “has a richness of connotations”: For instance, setzen brings to mind such words as “constitution” (Satzung). To posit implies to constitute something, to establish it originally as a state that comes into being by way of the establishment of its constitution. This contrasts with the idea of an already-existing state creating for itself a constitution. Another association with setzen is the word “law” (Gesetz); and still another is “investiture” (Einsetzung), in the sense of a ruler or a prelate being “invested.”91

Henrich could also have mentioned that in section 290 of the Fichte Studies Novalis explains “gegengesetzt” as expressing “the activity of the object [whose substance is the universal], whereby the opposite and thus the object itself emerges”; while entgegengesetzt “expresses the activity of the opposite, whereby the object becomes unmediated object and the opposite itself becomes mediated.”92 A decade after Novalis’s death, Fichte himself would come to identify Setzung with Bilden. As 90  Cited by Jere Paul Surber, “J. G. Fichte and the ‘Scientific Reconstruction of Grammar,’” in New Perspectives on Fichte, ed. Tom Rockmore and Daniel Breazeale (Atlantic Highlands, N.J.: Humanities, 1996), p. 66. 91  Between Kant and Hegel: Lectures on German Idealism, ed. David S. Pacini (Cambridge, Mass.: Harvard University Press, 2003), p. 233. Two later English-language analyses of Fichte’s use of “setzen” appear in Fichte: Historical Contexts/Contemporary Controversies, ed. Daniel Breazeale and Tom Rockmore (Atlantic Highlands, N.J.: Humanities Press, 1994): Robert R. Williams, “The Question of the Other in Fichte,” pp. 142-57; and Wilhelm S. Wurzer, “Fichte’s Parergonal Visibility,” (ibid.), pp. 211-19. 92  Novalis: Fichte Studies, translated and edited by Jane Kneller (Cambridge: Cambridge University Press, 2003), p.104

50 Inference and the metaphysic of reason Fichte employs it in the last phase of rethinking the Wissenschaftslehre, Bilden is a cognitional imaging (a moment of reine Denken) whose ontological “law”—Fichte refers to das Gesetz des Bildens93—“necessarily exceeds the empirical and logical operations of consciousness.”94 As Wilhelm S. Wurzer explains, “imaging is not a free play of images,” for Fichte, “but a law, notably, a command derived from the unique relation of the I to Being…a relation between an imaginal parergon and an ontological work of reflection.”95 This “law” is the very “ground or pure form of consciousness” that Günter Zöller sees Fichte making out as “an inferred condition, grasped in philosophical thought by means of abstraction from what is empirical in consciousness and reflection on what remains after such abstraction.”96 93  Johann Gottlieb Fichte, Einleitungsvorlesungen in die Wissenschaftslehre, die transzendentale Logik und die Thatsachen des Bewusstseins (Bonn: Marcus, 1834), p. 432; cited in Wurzer, p. 211. 94  Wurzer, “Fichte’s Parergonal Visibility,” p. 211. 95  Ibid., p. 216. This constitutes the final variations on the Wissenschaftslehre, the most germane features of which Fichte lectured on in Berlin as “Die Tatsachen des Bewusstseins,” in 1813, about a year prior to his death. For a volume that contains several essays that track and analyze the changes in Fichte’s doctrine, see After Jena: New Essays on Fichte’s Later Philosophy, ed. Daniel Breazeale and Tom Rockmore (Evanston: Northwestern University Press, 2008). 96  Fichte’s Transcendental Philosophy (Cambridge, Eng.: Cambridge University Press, 1998), p. 36, emphasis added. It is more than a little curious that Zöller omits the manifest influence on Fichte of Kant’s treatment of Position oder Setzung. In a section headed “Absolute Positing,” Zöller observes that in the Foundation of the Entire Wissenschaftslehre Fichte offers “no explicit justification” for choosing “the term ‘positing’ to designate the absolute, grounding dimension of knowledge or the I….Nor is there an explanation of the technical meaning of this term offered anywhere in the work.” Zöller then makes a most baffling claim: “Since there is also no direct precedent for the specific use of the term in transcendental philosophy before Fichte, it seems indicated to interpret Fichte’s use of “positing” functionally, as a coinage…” (pp. 45-46). A look at chap. III, §4 in the second book of the first Critique’s “Transcendental Dialectic” confirms that Kant did not drop his onto-epistemological use of “positing” in his critical period and before the Opus postumum. Given his intensive and direct interaction with Kant, Fichte no doubt knew this and Kant’s earlier treatments of “positing” at least as well as G. E. Schulze and Reinhold, the protagonists of the

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After Fichte, Hegel in the Logic invokes positing most interestingly in conjunction with the doctrine of essence. He points to Gesetztsein (“positedness” or “posited being”) as resulting from the movement of setzende Reflexion (“positing reflection”), the latter understood as a moment of essence. The determinate negativity of setzende Reflexion mediates simple immediacy, and thereby constitutes the first negation of Being. Essence (and by extension positing) thus sponsors Being itself, as Stephen Houlgate observes, since as “the pure negativity that has nothing outside itself which it negates….[essence] brings being into being.” 97 (Relative to the topic of inference, we shall see in chapter 4, below, that it is not necessary to follow the comprehensive metaphysical itinerary of the Begriff to discover in this phase of Hegelian logic a central passage of the conceptual logic that informs the ontoepistemology of inferential reflection.) In the twentieth century, Edmund Husserl, among the most influential heirs of idealist philosophy, adduced in Ideas I (1913) the concept of positing as a phenomenologically formative thought-determination. Husserl there characterized “negation” noetically, as “the ‘modification’ of some ‘position,’ the latter term signifying not a bare assertion or affirmation, but a ‘setting down’ (Setzung) in the extended sense of some form of belief-modality.”98 By the time of Experience and Judgment (1930), Husserl would have added “positing-as-now” (Jetzsetzung) to his list of associated meanings.99 Other German philosophers of the period stressed the crucial, metaphysical relation—the relation implicit in the present essay’s onto-epistemological orientation to inference— that Position oder Setzung formally indicates between ontology and 1792 debate to which Zöller traces “the emergence of the term ‘positing’ in Fichte” (p. 46). 97  “Why Hegel’s Concept Is Not the Essence of Things,” paper read at the Cardozo School of Law, Yeshiva University, New York, N.Y., March 2004, pp. 2-3. See Hegel’s Science of Logic, trans. A.V. Miller (Atlantic Highlands, N.J.: Humanities Press, 1969), p. 400. It is this sort of ontological reasoning that Lotze (no champion of Hegelian thought) repudiates. 98  Ideas: General Introduction to Pure Phenomenology, trans. W. R. Boyce Gibson (New York: Collier, 1962), p. 278; see also §§ 113, 117, 129, 11334, 136, 138, 140, and 147. 99  Experience and Judgment: Investigations in the Genealogy of Logic, ed. Ludwig Landgrebe, trans. James S. Churchill and Karl Ameriks (Evanston: Northwestern University Press, 1973), p. 383.

52 Inference and the metaphysic of reason epistemology. This twentieth-century onto-epistemological emphasis stands out with particular force in William H. Werkmeister’s descriptions of a) “change” and “substance” as Paul Natorp understood them, and of b) Cassirer’s construal of the result of quantum theory: a) Every change which occurs in a definite time and at a definite point in space must be representable as the univocal result of the continuously changing spatial distribution of a “substance.” “Substance,” therefore, is nothing “given” as independent or as existing in and by itself; it is “posited” as required by the “relations according to law” which describe observable changes.100 b) Just as in mathematics “point” and “straight line” are implicitly defined by the relations which govern them, so, in quantum mechanics, “atoms” and “electrons” are defined by the laws and relations of the system as a whole. The only difference between physics and mathematics is that the axiomatic assertions of mathematics are replaced in physics by hypothetical “posits” of such a type that their interrelations constitute the most complete system, the most comprehensive context, of the phenomena of experience.101

Cassirer viewed “symbolic forms” as “connected meanings” (Bedeutungszusammenhänge) that get realized by Setzung as a constitutive function of Geist. Cassirer found, moreover, that it “belongs to the essence of consciousness itself that no content can be posited in it without positing, at the same time, through this simple act of positing, a complex of other contents with it.”102 Late in his career Cassirer would make a systematically developed reference to onto-epistemological positing in his posthumously published study of the “Basis Phenomena.” These “phenomena” —the Ich-Phänomen, the Wirkens-Phänomen, and the Werk-Phänomen—he understood as metaphysical primitives “from which we must take our starting point in order to attain any access to ‘reality,’ and in which all that we call ‘reality’ is originally disclosed and opened up.”103 Cassirer’s Basis Phenomena are “‘prior’ to all thought 100  Werkmeister, “Cassirer’s Advance Beyond Neo-Kantianism,” The Philosophy of Ernst Cassirer, ed. Paul Arthur Schilpp (Evanston: Library of Living Philosophers, 1949), p. 768. 101  Ibid., p. 777. 102  Cf. Philosophie der symbolischen Formen, vol. I: Die Sprache (Berlin: Bruno Cassirer, 1923), p. 31. 103  The Philosophy of Symbolic Forms, Volume 4: The Metaphysics of Symbolic Forms, ed. John Michael Krois and Donald Phillip Verene, trans. John

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and inference and are the [ground (Grund)] of both.”104 The reference to positing occurs in a discussion of the third Phenomenon: “the sphere of works”—the sphere “of creations [which] provides the passage, the actual access, to the sphere of ‘objective’ being.”105 The “movement” of Action (the Wirkens-Phänomen) at once ceases and finds its “expression in a work [Werk].” This is an objectification of Geist, and, declares Cassirer, “the beginning of a completely new position—of that ‘position’ [Position] that only truly leads to an authentic consciousness of reality.” In a note, Cassirer makes it clear that he derives his usage of “position” here from Kant. Cassirer cites Kant’s denial, in the first Critique, that Being is a real predicate (A598/B626), and that Being (again, the concept of which Kant took to be identical with that of Position oder Setzung) “is merely the positing [Position] of a thing or of certain determinations in themselves.” The early Rudolf Carnap built on (and against) Cassirer in the process of developing his own systematic “constitutional theory”; and he can serve here as a final, if perhaps unexpected, exponent of ontoepistemological positing as it persisted in twentieth-century speculative thought. In the 1920s Carnap identified Ordnungssetzungen, “order-posits,” as the “basic relations” (Grundrelationen) by means of which preconceptual objects given in experience become constituted as objects of cognition.106 It comes as no surprise that for Carnap, “the constituted objects are only objects of cognition qua logical forms constructed in a determinate way.”107 Michael Krois (New Haven: Yale University Press, 1996), p. 137. 104  Ibid., p. 141. Cf., Zur Metaphysik der symbolischen Formen, ed. John Michael Krois with Anne Appelbaum et al. (Hamburg: Felix Meiner, 1995), p. 132. 105  Ibid., p.141. 106  The Logical Structure of the World (with Pseudoproblems of Philosophy), 2nd. ed., trans. Rolf A. George (Berkeley: University of California Press, 1967), §75; [Der logische Aufbau der Welt (Berlin: Weltkreis, 1928)]. 107  Ibid., §177 (Michael Friedman’s translation); see Friedman’s commentary on the context of Carnap’s reference to “order-posits”; in “The Davos Disputation and Twentieth-Century Philosophy,” in Symbolic Forms and Cultural Studies: Ernst Cassirer’s Theory of Culture, ed. Cyrus Hamlin and John Michael Krois (New Haven: Yale University Press, 2004), esp. pp. 232-33. See also Friedman, A Parting of the Ways: Carnap, Cassirer, and Heidegger (Chicago: Open Court, 2000), chap. 5.

54 Inference and the metaphysic of reason 3 The foregoing conspectus could readily have been extended to cover systematic speculative uses of Setzung at least through the writings of Reiner Schürmann.108 And a good many pages might well have been devoted to probing the philosophical history and tracing the ramifications of onto-epistemological positing with respect “thesis,” or the thetic—the perennial topic of philosophical debate alluded to at the outset of this Introduction. Yet if abbreviated and in some respects fragmentary, the preceding overview, in conjunction with Appendix I, should nonetheless equip the reader hitherto unfamiliar with the speculative notion of “position” to grasp what is in play (and what’s at stake) as the term figures both in the critical discussion of next two chapters and in chapter 4, this essay’s culminating, constructive phase.

108  See n. 79, above.

Chapter 2 Critique of Analytic Epistemologies of Inference: Carnap, Harman, Brandom, Williams, and Lonergan No logician has yet developed analogy and induction properly. Immanuel Kant, Logic The so-called problem of induction is the despair of philosophy. [For “key to the process of induction”] we must recur to the method of the school-divinity as explained by the Italian medievalists….We must observe the immediate occasion, and use reason to elicit a general description of its nature. Induction presupposes metaphysics. In other words, it rests upon an antecedent rationalism. Alfred North Whitehead, Science and the Modern World

2.1.1 Leading philosophical orientations to inference. A good deal of scholarly activity centers at present on the most basic issues that relate to the validity, justification, and purchase of formally logical, semantic, and probabilistic rules that pertain to how and why certain conclusions follow from one or more premises. Given the predominating constellation of analytic epistemologies that have for some decades enjoyed something of a hegemony in philosophical discourse on the topic, one might well question the need for, even the very concept of an extended onto-epistemological inquiry into the reason of inference per se (i.e., as act). The skeptic might well question the viability of any such metaphysical orientation as a standpoint from which to critique the ontological assumptions of received analytic epistemologies of inference. Indeed, the prevalence of game-theory and socio-linguistic semantics, neo-pragmatics, philosophy of mind, symbolic techno-logic, and other speculative regimes makes it likely that the analytically trained student of rational thought would be inclined simply to dismiss out of hand, as anachronistic or idiosyncratic, an onto-epistemological approach to inference. After all (so the charge often runs), metaphysicians typi-

56 Inference and the metaphysic of reason cally forfeit any claim to speculative legitimacy because they invariably propound some wooly-minded, apriorist ontology—one predicated upon an Absolute or a Whole or an essentialism that they implausibly privilege over calculative thinking, relativity, pragmatics, semantic commitments, epistemic beliefs, socio-linguistic norms, and so forth. This dismissive stance, insofar as epistemologists assume it toward the critical metaphysic that is true to the deepest-running disclosures of classical thought, is itself coming to seem historically idiosyncratic. One sees evidence that bears this out in, for instance, the growing criticism of the scientistic, empirically positivist, and ideologically narrowed thinking of those modernist philosophers, from the early G. E. Moore and Bertrand Russell to the Vienna Circle to the latest neopragmatists, who attempt to discredit or ignore the very orientation of synthetic, metaphysically developed systems of thought. The most fully realized doctrines of the latter sort—represented in the last century by thinkers as diverse as Whitehead and Karl Jaspers, Bernard Lonergan and Nicholas Rescher, and in the present by Lorenz Puntel1 —are not only keenly if critically appreciative of the most profound currents of the scientific spirit but also, in a number of signal respects, more subtle, far-reaching, and fundamentally cogent than the doctrines of their detractors. Moreover, if contemporary critical metaphysics does take its bearings from the ancient lessons of First Philosophy and the abiding insights of medieval and early modern systematic thought, it 1  Cf., A. N. Whitehead’s Process and Reality: An Essay in Cosmology. Corrected Edition. Edited by David Ray Griffin and Donald W. Sherburne (New York: Free Press, 1978); Karl Jaspers, Philosophy , 3 vols., trans. E. B. Ashton (Chicago: University of Chicago Press, 1969-71); Bernard Lonergan, Insight: A Study of Human Understanding (San Francisco: Harper, 1958); Nicholas Rescher, System of Pragmatic Idealism, 3 vols. (Princeton: Princeton University Press, 1994); Lorenz B. Puntel, Structure and Being: A Theoretical Framework for Systematic Philosophy, trans. Alan White (University Park, Pa.: Penn State University Press, 2008). Puntel has found Rescher’s magnum opus, for all its systematic pretensions, lacking on this score in three crucial respects: 1) “the interconnection (‘systematic interrelatedness,’ according to his [Rescher’s] Preface) presented…in the domain of philosophical topics and theories is only quite general and loose”; 2) “the generally pragmatic-idealistic perspective…is far too narrow to be appropriate for the immense task of systematic philosophy”; and 3) “Rescher’s theory lacks central components of a comprehensive theory of actuality as a whole, quite particularly as an ontology and a metaphysics” (ibid., p. 9n).

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nonetheless sharply repudiates the speculative lapses and elements of dogmatism that admittedly count as no small part of the Great Tradition.2 But it is precisely definitive discriminations of this sort that those who would reject the metaphysical orientation are prone to overlook or discount. What marks the historical shift away from the summary dismissal of what at bottom are systematic inquiries into the onto-epistemology of Reason is an ever more insistent and penetrating questioning of the moves to repudiate wholesale what loosely falls under the rubric of Idealism. One detects this historical shift in a growing plurality of contemporary voices calling for critical review of the often unspoken ontological assumptions informing leading currents of contemporary philosophy. John Heil, to cite a salient recent example, complains that analytic philosophers of mind who attempt to sidestep ontological issues too often implicitly adopt a substantive ontological scheme. Unacknowledged, the scheme works behind the scenes in a way that can be difficult to detect. In many cases, the scheme does most of the work in subsequent debate. This is so…in the vast literature on mental causation. Problems stem from commitments to ontological theses that rarely see the light of day. 3

2  A prominent example that infects systematic philosophy in the modern period is the massively influential post-Suàrezian essentializing of Being; cf. Oliva Blanchette, “Suárez and the Latent Essentialism of Heidegger’s Fundamental Ontology,” Review of Metaphysics 53.1 (1999): 3-19. 3  From an Ontological Point of View (Oxford: Oxford University Press, 2003), p. 249. The ultimate philosophical insight that, at the end of his book, Heil wishes to leave with his readers “is just that decisions about ground-level ontological matters determine the space of possibilities in the philosophy of mind—and, of course, in other domains as well” (p. 248). Heil is quite right, and nothing attests more forcefully to the continuing reign of the post-Kantian epistemological hegemony than that Heil finds it necessary to devote 250 pages of closely reasoned argumentation to defend such a thesis. Cf., Structure and Being, pp. 422-23, where Puntel discredits the “constructive empiricist” Bas van Fraassen’s contention that ontology is little more than “world play” that “is but idle word play”; see also Puntel’s remarks, in the Introduction of Structure and Being, on the onto-epistemological “fragmentarity” of analytic doctrines more generally.

58 Inference and the metaphysic of reason To the best of the present writer’s knowledge, no one has till now systematically raised this metaphysical issue with respect to the plurality of analytic philosophies of inference. 3 The balance of this section demonstrates how, by reflecting upon the reason of inference as act, one comes to discern speculative limitations and aporiai that hobble accounts rooted in analytic epistemology. These difficulties will be seen to justify on rational grounds the venture in the chapters ahead to think-through a more speculative “science” of the reason of inferential reflection. Most current philosophical treatments of the topic take as a settled starting point the idea that inference involves the movement of thought, or some literally thought-less mechanistic process of movement, that proceeds from one or more premises to a conclusion. Far too often, however, such doctrines drop the very notion of “movement” and the thought of “thought” (and with them what Joseph Maréchal called the “dynamism of spirit”), or translate them as “pattern” or “rule.” On this score, Bernard Bosanquet long ago noted that such omissions or transmutations constitute far more than a benign elision or shift in emphasis, but rather betray a fundamental speculative misstep. “The error consists,” observes Bosanquet, in taking out the active form of the inference—the intellectual function which the syllogistic or constructive arrangement expresses— and making this a mere portion of the content from which inference is drawn. In drawing the inference the intellectual function is inevitably active, and the principle expressed in the major [premise] is no justification of the activity of this function, but merely a content on which it operates as it would on any other content….4

One finds symptoms of this tendency in speculative theorists ranging from self-described “inferentialists” to mathematical logicians to philosophers of mind, thinkers who formalize their explanations in the conceptual currency of a broad spectrum of specialized sub-disciplines—socio-linguistics, axiomatics (logical, mathematical), game4  Logic, or the Morphology of Knowledge, 2nd ed. (Oxford: Oxford University Press, 1911), vol. II, p. 66 (emphasis added). Cf., Rudolf Hermann Lotze’s discussion of the contrast between “the logical act of thinking” and the “Thought itself…in which the process of thinking issues”; in Logic in Three Books: of Thought, of Investigation, and of Knowledge [1880], 2nd ed., trans. Bernard Bosanquet et al. (Oxford: Oxford University Press, 1888), vol. 2, §345.

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theory semantics, and others. Generally speaking, the concern is with one or more of three constellations of issues. a) The rationality of inference—inductive (ampliative,5 enumerative), deductive, subsumptive, semantic. b) Putatively originary, axiomatic inferential patterns— syllogistic, quantificational, sentential, probabilistic. c) The pragmatics of inference—conventional “implicature” (Grice), for example, and inferential rule use with respect to referential meaning, paradigmatically in conjunction with computer programming and artificial intelligence.6 Depending on orientational commitments (whether epistemological or purely formalistic), analytic epistemologists proffer explanations of inference that emphasize cognitional or formal elements. Rarely, however, do they introduce, let alone interrogate, the ontological facts that, systematically explicated, might correct for the (Kantian) epistemological bias of those preponderantly cognitionalist readings of inference that fail rationally to explain how inferential knowing noncircularly discloses the being that it constitutes. On the other hand, 5  “What is ampliative reasoning like?”—this, in Jaakko Hintikka’s view, is “the basic question of contemporary epistemology”; it is one that poses the “most general problem to which both the hypothetico-deductive approach and [Peirce’s] idea of abduction are attempted solutions”; see Hintikka, Socratic Epistemology: Explorations of Knowledge-Seeking by Questioning (Cambridge: Cambridge University Press, 2007), p. 40. 6  On “implicature” see Paul Grice, Studies in the Way of Words (Cambridge, Mass.: Harvard University Press, 1989). Grice falls back on John Cook Wilson to account for the actual “chains” of passages “of thought, or inference”: “any such chain of passages of thought or inference may be thought of, in line with Cook Wilson, as involving a chain of interrogatively subordinated questions in which an affirmative answer to an earlier question determines affirmative answers to later questions, and equally a negative answer to a later question determines negative answers to earlier questions” (pp. 77-78). Even discounting the implausibilities of this questionand-answer model of the reason of inference, one is left wondering about Grice’s reliance on Wilson in this connection (which is without qualification or justification). For Grice later rejects Wilson’s view on “how a state of mind”—in particular “taking for granted” (for instance that something in a “chain” of inferential thinking actually is an affirmative answer)—may “guarantee a particular truth-value on the part of its object” (ibid., p. 383). For a sense of the Ge-stell and empirical purport of inference studies in the fields of computer programming and artificial intelligence, see Lecture Notes in Artificial Intelligence 872, ed. S. Arikawa and K. P. Jantke (Berlin: Springer, 1994).

60 Inference and the metaphysic of reason theorists who champion more formalistically weighted doctrines prove least able satisfactorily to settle the cardinal issue of the knowing of being, namely how an axiomatic pattern charters what one knows when one credits, not the validity or mere self-consistency but the existential warrant or soundness of what one cognizes as fact. The more philosophically astute students of inference, such as those five whose doctrines come under review in the present chapter, attempt to integrate these two originary moments of the coherent discursive act of intelligence—but not without incurring serious speculative difficulties. A tacit epistemological bias undercuts the analytic epistemologist’s ability to establish or substantiate (or even so much as to propose) a rationally defensible onto-epistemological frame of reference. Absent such a metaphysically articulated context, one can never hope systematically to address the intermediation of knowing and being. One encounters reluctance, even outright resistance, if one presumes to confront the analytic inferentialists (as has the present writer) with metaphysical queries such as about the ontological warrant of the initial selection of the suppositions that they take as grounding axioms. Often as not, the cold look and polite dismissal also greet questions about the philosophical implications of their use of universal variables or quantification to make truth claims about facts.7 The “facts” meant here are the irreducibly embedded and relationally composed facts of a real existence to which one inevitably appeals, tacitly or explicitly, when ascribing meaning to particulars or possibilities or to abstractive thought itself. With respect to language, for instance, one major logic text calls the student’s attention to the circumstance that English has more than its fair share of irregular and idiomatic constructions. Consequently, advises the author, if one hopes to translate “an English sentence into logical notation”8—to recast it, that is, in terms of propositional functions and quantifiers—one must first ensure in each case “that the meaning of the sentence be understood.” This seemingly benign precept glosses over an expressly tendentious and reductive strat7  Regardless of whether one, in the first instance, apprehends those facts as intelligible in a symbolic or intentional or physical or ideal form. For discussion of Richard L. Mendelsohn’s recent analysis of the problems with Frege’s misleading appeal to Kant in attributing existential import to the quantifier, see Appendix I.ii, below. 8  Irving M. Copi, Introduction to Logic, 5th ed. (New York: Macmillan, 1978), p. 342.

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agem, 9 a methodological expedient that the logician had enounced a few pages earlier. There the student new to “philosophical” logic learns that if from a “grammatical” standpoint “the distinction between adjective and noun is of considerable importance” any such distinction “is without significance from the point of view of logic.”10 This is an egregiously apriorist contention. It amounts to an instruction stipulating the way that, for logical purposes, one is to understand the meaning of a sentence—but only after first being told all that the meaning of the sentence may mean, in the interest of ascertaining its validity in conformity (by way of “truth-functional” concepts and derivation rules) with a demonstrably self-consistent set of suppositions. As one might expect, what remains open to perennial debate among symbolic logicians is how one genuinely captures or preserves the meaning and nuances of a natural-language sentence11 submitted to an abstractive operation that elides essential, if implicit, grammatical and semantic distinctions that regularly outstrip the rational purchase of privileged regimes of abstraction and calculation. To abstract, as Whitehead somewhere remarks, is to leave out a part of the truth (something that if problematic in the present context is, of course, neither good nor bad in itself ). I would submit, consistent with a well-established current of philosophical criticism, that the “translations,” whose modus operandi symbolic logicians teach their students to take as philosophically authoritative, reflect insufficiently critical, which is to say insufficiently rational, narrowing elisions of truth to fact. Consider, by way of illustration, the textbook logician who teaches that the sentence “Socrates is mortal” is no different, logically speaking, than “Socrates is a mortal.” One appreciates some of the implications of ignoring the subtleties of the indefinite article’s denotative character in a natural language when one substitutes the grammatically identical and (semantically) equally plausible predicate “human” for “mortal.” If saying “Socrates is human” is “no different, logically speaking” than saying “Socrates is a human,” then one subscribes to a logic that operates with a semantically impoverishing translational ex9  One that strikes the philologically trained student of the literary life of a language as patently misleading. 10  Introduction to Logic, p. 342. 11  And thereby preserves the ground for determining that the logical notation faithfully symbolizes that meaning.

62 Inference and the metaphysic of reason tension, a logic blind to the fact that the indefinite article in English is far from categorically indefinite with respect to the class memberships it denotes. This is an elementary issue to which teachers of formal logic typically give short shrift. If one wishes to determine the meaning of a sentence prior to translating it into symbolic logic, one must have a prior intuition or grasp of (or “insight” into) the sentence as, in the first place, construable in accord with the axiomatic principles of a logician’s scheme of meaning. This must hold regardless of the logical sense and rational precisions of reference that may be challenged or sacrificed in the process of translation.12 Let me offer a second and closely related illustration, one that broaches issues of ontology and predication that will play large in the sequel. This example suggests the problems that arise when one privileges the calculative idiom of formal logic in codifying (natural) language meaning. In a recent text on philosophical logic,13 A. C. Grayling distinguishes the verb “exists,” read as a grammatical predicate, from its sense as a logical predicate (i.e., as “something that would count as a predicate in an interpretation of first-order predicate logic”). Grayling assures his readers that the notion “of a logical predicate is just the ordinary idea of a grammatical predicate, but in a special language” (emphasis added). This “special language” is insensitive to the signifying nuances of the article and dismisses as “without significance” the distinction between the adjective and the noun. Grayling doesn’t offer to justify how— outside of being self-consistent and making whatever gets translated consistent with it as well—the special language rationally qualifies, beyond mere self-consistency, to be the ground for determining the truth of propositions expressed in a natural language. Grayling’s assurance might well strike the philosophical student of language as playing fast and loose with the very idea of predication. At the least, Grayling’s assertion would be subject to fundamental qualifications by a philosopher such as Cassirer or Kant, for whom, as Cassirer observes, “the objective meaning of judgment [is] intimately related to the [natural]

12  Lotze (1817-1881) made essentially the same point in a critique of the original efforts of Boole, Jevons, and Schröder to recast formal logic in the image of a mathematical calculus. See §3.4.1, below. 13  An Introduction to Philosophical Logic, 3rd ed. (Oxford: Blackwell, 1998).

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linguistic form of predicative statement”14—not to the mathematically abstract symbolic form of a calculus. A look at the basic translation strategies of the so-called sentential and predicate doctrines of symbolic logic verifies the foregoing observations. Consider, for one, the license taken when the logician recasts declarative statements as hypothetical conditionals. This stratagem silently interjects the subjunctive mood—on teleological rather than semantic or logical grounds15—in deference to a dubious equation of the possible with the actual. In this connection, the logician generally counsels students that they will learn to confront challenges merely of “translation” or periphrasis when they wrestle with disparities of meaning between a grammatical predicate and alternative sets of quantifiers and variables that vie for recognition as the definitive logical code by means of which one may symbolize (natural) grammatical meaning. Here, though, as in the examples above, fundamental meanings get lost, distorted, or elided in the interest of the calculative elegance of a deductive symbol system. Symbolized predicate logic recasts for its own purposes the sense-bearing or the actual (wirklich) distinctions in natural-language grammar. And this gives the lie to the conceit of “ontological commitment” retailed in declarations such as the following: “To paraphrase a sentence into the canonical notation of quantification is, first and foremost, to make its ontic content explicit, quantification being a device for talking in general of objects.”16 14  The Philosophy of Symbolic Forms, Volume 1: Language, trans. Ralph Manheim (New Haven: Yale University Press, 1955), p. 314. 15  Ironically enough, this is the familiar sin of the dogmatic metaphysics that major thinkers since the Enlightenment have sought to repudiate. Cf. Lenn E. Goodman, who in a critique of Quine cites logicist thinking that proceeds “as though the prevalent conventions for formalizing the implication relation held some kind of legislative mandate over the usages of ordinary language and could single-handedly ban questions of relevance and ignore the critical nuances of the subjunctive mood”; see In Defense of Truth: A Pluralistic Approach (Amherst, N.Y.: Humanity Books, 2001), p. 118. 16  W. V. Quine, Word and Object (Cambridge, Mass.: MIT Press, 1960), p. 265. For broad-based, yet analytically keyed challenges to Quine on this and other facets of his thought, see Christopher Norris, On Truth and Meaning: Language, Logic, and the Grounds of Belief (New York: Continuum, 2006), esp. chaps. 2 and 4. Norris is critical of contemporary analytic

64 Inference and the metaphysic of reason 2.1.2 Problems with received philosophical definitions of inference. Contemporary philosophical definitions of inference collectively exhibit a variety of inconsistencies and contradictions. Some explain inference as involving induction and deduction; others restrict it to deduction, while still others reject both as contexts for elucidating the nature of inferential thinking. Concomitant with this bewildering mix of differing views, one finds in the literature uncritical shifts between, on the one hand, inference explained as an a priori pattern or as a product of thought and, on the other, inference defined as a cognitional process or act. This state of affairs is not merely the consequence of competing varieties of logicism. It reflects as well the competing formalisms and methodologies chargeable to the semanticism, neo-pragmatics, and mental-state theory that distinguish leading currents of analytic epistemology. Exponents of the most influential of such approaches commonly fail to investigate in any systematic way the onto-epistemological implications of their explanations and speculative procedures. The shortcomings, for example, of philosophy of mind, in this regard have recently been pointed out by Jerry Fodor, himself a prominent philosopher of mind: “it’s been the tradition in analytic philosophy to play ontologically fast and loose with the mental whenever it seems convenient to do so.”17 One of the principal critical contentions that animate the present study is that to investigate the onto-epistemology of the reason of the act of inference is to encounter the ineludible metaphysical presuppositions that inform the patterned suppositions (the articulated axioms or rules) that ground much contemporary philosophy of inference. Without systematically addressing the underlying rationale or metaphysical implications of their foundational premises and axioms, analytic epistemologists—in particular the champions of logicist, linguistic, neo-pragmatic, rationalistic-epistemological, and scientificempirical doctrine—only fitfully move beyond the plane of secondorder themes. These themes include the likes of formalisms ascribable to patterns of logical reasoning, semantics, normative beliefs, and jusphilosophy of language and logic along lines consistent with the purport of the present work. 17  Fodor, “What is Universally Quantified and Necessary and A Posteriori and It Flies South in the Winter?”, Presidential Address, American Philosophical Association, Eastern Division, Proceedings and Addresses of the American Philosophical Association 80.2 (November 2006): 13.

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tification (something frequently identified as constitutive components of the reason of inference). Such formalisms all too often prove, in the words of Oliva Blanchette, “of no consequence in the ontological order,”18 and hence merely derivative in their bearing on what inference is as an onto-epistemological act. One hardly has to resort to a neoThomist like Blanchette to find equally trenchant if more targeted critiques along these lines. The distinguished critical metaphysician and synthesizer of analytic and continental thought, Lorenz Puntel, observes the following by way of preface to a detailed refutation of the substance ontology that he demonstrates compositional semantics tacitly to presuppose or implicitly to entail: “In formal semantics, the usual practice is to understand all ‘entities’ like semantic structures as ‘abstract’ entities; the relation to ontology is generally left wholly unclear. Nevertheless, the usual interpretation involves a clearly ontological import in that the domain is characterized as ‘domain of objects’ or as ‘universe.’”19 Predictably enough, the foreshortened metaphysical horizon within which analytic philosophies of inference operate has licensed, if not stimulated, the proliferation of elaborately involved logical schemes of reasoning or appeals to conceptual norms and mental states (such as belief and commitment) that don’t come to terms with the originary issues in any definitive way. This concentration on second-order themes has engendered a host of ontologically anomalous, if technically virtuosic studies in predicate logic, applied semantics, and cognitive-scientific epistemology. These often present, as philosophically foundational, alternative modes of explicating the formative components of inference which, as we shall see, prove by turns inconsistent, fragmentary, self-contradictory, even adventitious. Some readers will no doubt be inclined to conclude that the charge leveled here against the speculative pretensions of contemporary philosophies of inference is at bottom hardly more than the complaint of a disgruntled traditionalist who nurtures an animus against analytic epistemology. To jump to any such conclusion, however, is radically to misconstrue both the spirit and philosophical purposes that animate this investigation. In fact, various of the complaints that target analytic inferentialists come from other analytic philosophers (such 18  Personal communication. 19  Structure and Being, p. 190.

66 Inference and the metaphysic of reason as Jerry Fodor, cited above). Indeed, it was Wesley Salmon, no enemy of analytic epistemology, who complained that analysts have not met the basic challenge to a satisfactory account of inference, namely “the problem of providing adequate grounds for the selection of inductive rules.”20 Salmon thus clearly recognized that one needs to inquire into the grounds of explanation per se in order effectively to address the problematic of inference. Unfortunately, his own proposal is a rationalistic commitment to the idea of rule-selection as the means of explaining inductive thinking—a solution that incurs a dubious apriorism21 and hence is itself symptomatic of the problem. More recently, Jaakko Hintikka, one of the deans of mathematical logic, had this to say about appealing to formal logic in explaining inferential thinking: a study of the inferences people are inclined to draw qualifies as a genuine logic only in so far as those inferences are based on the descriptive function of part of the logic in question.…In reality, the core area of logic is the one where all the valid inferences are based on the model-theoretical meaning of logical constants. Whether one wants to call what goes beyond this core area “logic” or not is a matter of intellectual taste [sic]. 22 20  “The Justification of Inductive Rules of Inference,” The Problem of Inductive Logic, ed. Imre Latkaos (Amsterdam: North Holland Publishers, 1968), p. 33. 21  An apriorism of the sort criticized by, for example, Karl Popper in Objective Knowledge (Oxford: Oxford University Press, 1979). For a recent critique of Popper’s own approach to induction, see Michael Williams, Problems of Knowledge: A Critical Introduction to Epistemology (Oxford: Oxford University Press, 2001), chap. 18. 22  The Principles of Mathematics Revisited (Cambridge, Engl.: Cambridge University Press, 1997), pp. 20-21. Hume’s classic challenge to the intelligibility of induction (itself an inductive generalization) has been defeated perhaps most forcefully, in view of the present discussion, by a mathematician who was, like Hintikka, a mathematical logician, but who was in addition a metaphysician of the first rank: A. N. Whitehead. Hume based his argument against the intelligibility of inductive thinking on an abstractive procedure that unjustifiably omitted constitutive elements (and with them the actual character) of concrete reality. This is an ontological criticism of Hume (and thus in line with the orientation here to the problematic of inference). Whitehead spells out this problem in the third chapter of Science and the Modern World: “It is impossible to over-emphasise the point that the key to the process of induction, as used either in science or in our

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3 One comes face to face with the practical implications of inference as a philosophical problem when one surveys a cross-section of prominent contemporary analyses of the concept. Telling inconsistencies show up even among statements that philosophers of recent times have made concerning just what it is that is under discussion when one refers to inference. The following passage from a respected monograph on The Structure of Scientific Inference illustrates the situation. The author, Mary Hesse, identifies inference with both inductive and deductive thinking: …the rules of induction are not actually well formulated, as those of, say, propositional logic or arithmetic are. Moreover there is no agreement about how they should be formulated.…With regard to inductive logic we are in a position which would only be paralleled in deductive logic if we imagine the multiplication table and the syllogism to be unformulated and controversial, and logical and arithmetical arguments to be carried on according to a variety of unanalyzed and mutually inconsistent procedures.23

Hesse aims here to demonstrate how different the aporia of inductive logic is from any difficulties with the notion of deductive logic. Although at first it may seem beside the point, the counterfactual analogy that she adduces is itself evidence of the larger problem. This is because Hesse bases it on an inference for which she can offer no idea of “rule” that applies univocally as a middle term establishing a rational link between inductive thinking (the act by means of which arises the very notion of a rule) and deductive logic. Absent such a mediating context of signification—of necessity an onto-epistemological context—one has no intelligible grounds for comparing the different ontic moments of a deductive logic with those of an inductive order of thinking. Hence, one can draw no parallel, even negatively. The intelligible frame of reference of any such possible parallel—the condition ordinary life, is to be found in the right understanding of the immediate occasion of knowledge in its full concreteness” (p. 44). Popper would later, though less convincingly, reject the idea that we even need to respond to Humean skepticism because rational thinking (and science in particular) proceeds by means of conjecture and refutation, not in accord with any formal “rules” of induction or postulated inductive “logic.” 23  The Structure of Scientific Inference (Berkeley: University of California Press, 1974), pp. 92-93.

68 Inference and the metaphysic of reason not only of its possibility but also of our ability to conceptualize it— transcends the limits of the assumed rational basis of the parallel that Hesse invokes. Hesse thus unwittingly illustrates the larger problem of inference in terms of the very grounds of her effort to emphasize one aspect of it by means of hypothetical analogy. One may discount Hesse’s implicit point about the need of an agreed-upon set of inductive rules that at least correlates with those that render mathematics a science, and even dismiss the entire notion of rules-based approaches to inference (such as Salmon’s). Still, radical challenges—pertaining, for example, to what is ontogenetically contextual and existentially relevant—confront the effort systematically to think the matter through in terms of analytic epistemology, or even properly to frame from any such standpoint the issues at stake in the problematic. Relative to these larger themes, an air of uncertainty informs the debate over whether or not one rightly describes deductive thinking as inferential. A theorist of the caliber of Rudolf Carnap confidently affirms that in the order of “deductive logic inference leads from a set of premises to a conclusion just as certain as the premises.”24 But then one discovers in the article on “Inductive Inference” in the Routledge Encyclopedia of Philosophy that deductive thinking does not even qualify as inference, at least as the notion is “traditionally understood.” No doubt Carnap merits greater credence than an obscure contributor to the Routledge Encyclopedia.25 Yet a half-century before the appearance of the encyclopedia, Bertrand Russell argued against classifying deduction as an act of inference. Russell lays out his position in the introduction to Human Knowledge: Its Scope and Limits (1948), his last volume of systematic philosophizing, and one in which he set out “to discover the minimum principles required to justify scientific inference.” Says Russell, “So far as deductive logic can show, any collection of events might be the whole universe; if, then, I am ever to be able to infer events, I must accept principles of inference which lie outside de24  “Induction and Statistical Probability,” in An Introduction to the Philosophy of Science, ed. Martin Gardner (New York, Harper, 1974), p. 20. 25  A designedly post-modern compendium of very uneven quality. That said, “inference” rated no separate entry even in the classic Encyclopedia of Philosophy published by Macmillan in 1967, although the second edition (2005) does contain an essay by Peter Lipton on “inference to the best explanation.”

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ductive logic.”26 Following Russell, one could never infer strictly on deductive principles the very manifestation, the concrete event, of logical thinking itself—i.e., the act of drawing deductive conclusions. More to the point, one could not infer on that basis the relations of any logical consequence in a deductive train of reasoning if what one deduces is an event (as must be the case in an event-ontology). Turning to Jaakko Hintikka’s Principles of Mathematics Revisited (1996), one reads that the “concrete manifestation” of logic as “the study of the relations of logical consequence” is “the ability to perform logical inferences, that is, to draw deductive conclusions.”27 What Hintikka affirms accommodates a significant implication of Russell’s position, namely that the ability to draw deductive conclusions, to perform an act of inference, need not have its ground in deductive logic. This is neither novel nor controversial. What is problematic is that both Russell and Hintikka purport to elucidate inference but fail to address how inference itself, let alone its rational relation to deductive thinking, gets definitively explained by invoking formal logic. Indeed, one could argue that this unresolved issue—the rational character of the act of inference (particularly inductive inference)—is what most radically exposes the axiomatically delimited nature of the rationality of contemporary formal logic. Gilbert Harman, whose philosophy of inference comes in for scrutiny in the third section of the present chapter, is among those who reject the very idea of deductive inference, at least as a rule-governed activity and insofar as any such rules decide how one acquires and discards beliefs. Championing a holistic approach to inference “as the way we represent the world,” Harman contends that deductive rules are actually “rules of entailment, not rules of inference.” (One could construe this as consistent with Russell and Hintikka if, risking what Kant identified as a dogmatic metaphysic, one were to distinguish the transcendent ground of the act of inference from the various deductive [or inductive] fields that are in effect theaters of inferential cognition. From such a standpoint, the expression “deductive inference” is at best a metonym for a cognitional act whose rules or principles “lie outside deductive logic.”) 26  (New York: Simon and Shuster, 1948), p. xii. 27  Ibid., p. 4, emphasis added.

70 Inference and the metaphysic of reason As for inductive reasoning, the difficulties philosophers encounter when they undertake to work it into a systematically coherent account of inference are due, says Harman, to “confusion about induction and deduction, arising out of the deductive model of inference.”28 But in a pointed critique of Harman’s inferential holism. Michael Williams argues that we have “no reason to deny that there is such a thing as deductive inference,” if only we steer clear of a radical holism.29 “Such inference,” contends Williams, “takes place in contexts in which certain commitments are so firmly set that we may justifiably add their perceived consequences to our stock of beliefs.”30 But it is precisely the character and cognitional authority of the “certain commitments” in question—whether conceptual, semantic, or otherwise normative— that are far from settled and that constitute flashpoints among competing accounts of deductive and inductive methodology and conceptualization. The onto-epistemological implications of these debates leave one skeptical of references, such as Hesse’s, to “rules” of inductive inference. Beyond Hesse, the skepticism would extend to any analysis that takes as its point of departure a version of the ubiquitous generalization that inference is at bottom “the process of drawing a conclusion from premises or assumptions, or, loosely, the conclusion so drawn” (Cambridge Dictionary of Philosophy). The orientational nature of the issues at stake in this matter, and the often-incompatible purport of the differing approaches that proceed implicitly or overtly on the strength of a version of this definition, betoken the deep-running tension along what amounts to a major fault line in contemporary analytic philosophy. 3 The foregoing observations give an idea of how unsettled the state of scholarship is on the defining issues of the problematic of inference. Before reflecting on that problematic in light of a critique of the ana28  Reasoning, Meaning, and Mind (Oxford: Oxford University Press, 1999), p. 30. 29  Williams also underscores the limits of Nelson Goodman’s analysis of inductive thinking. For Goodman’s widely discussed treatment of inference, see Fact, Fiction, and Forecast (Cambridge, Mass.: Harvard University Press, 1955), and the introduction to chapter VIII of Problems and Projects (Indianapolis: Bobbs-Merrill, 1972). 30  Problems of Knowledge, p. 216.

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lytic epistemology of inference, it will help briefly to look ahead to the onto-epistemology that frames the ensuing discussion. “It has been widely thought that all knowledge of matters of fact that we have not observed must be based on inductive inference from what we have observed”—thus Patrick Maher, author of an encyclopedia essay on “Inductive Inference.”31 Such a view fails to account for those occasions when we acquire knowledge of previously unobserved matters of fact, absent any reflectively cognitional process of drawing an inference from an observed fact. We often acquire knowledge of unobserved fact but rather through immediate or intuitive insight (or unmediated judgment) that a remarked fact prompts. Among the more curious examples of this phenomenon are those well-documented cases of idiots savants who display a marked inability to perform enumerative inference with any accuracy, but who enjoy astounding and virtually immediate arithmetical or, better, enumerative insights when prompted by a numerable fact. The clinical neurologist Oliver Sacks reports the case of twin brothers with an IQ of sixty who, given a date “any time in the last or next 40,000 years,” almost instantly report with unerring accuracy what day of the week it would be.32 Moreover, the twins could “tell you the date of Easter during the same period of 80,000 years” with the same speed and inerrancy. “When one recollects,” remarks Sacks, “how even Carl Friedrich Gauss…had the utmost difficulty in working out an algorithm for the date of Easter, it is scarcely credible that these twins, incapable of even the simplest arithmetical methods, could have inferred, worked out, and be using such an algorithm.”33 The twins reported “seeing” the previously unobserved matters of fact, and indeed Sacks notes that their eyes “move and fix in a peculiar way…as if they were unrolling, or scrutinizing, an inner landscape….although it has been concluded that what is involved is pure calculation.”34 (Among other things, this conclusion brings home both the hold and the limits of the discursive conception of “calculation” in conventional analytic thinking.) 31  Routledge Encyclopedia of Philosophy, ed. Edward Craig (London: Routledge, 1998). 32  The Man Who Mistook His Wife for a Hat (New York: Harper, 1990), p. 197. 33  Ibid. 34  Ibid.

72 Inference and the metaphysic of reason The episode reported by Sacks underscores a difficulty that genetic analytic epistemologies of inference are at odds over how to resolve: just which “sources of knowledge are non-inferential remains an issue.”35 One might well attempt to sidestep this dimension of the problematic of inference and its ramifications by shifting from a terminus-a-quo speculative line to a pragmatic tack—one ordered, via usage, to a terminus ad quem. “Inference to the best explanation” is a leading if embattled version of such approaches. Proponents of this explanation maintain that an act of inference is the thinking by means of which one concludes something to be “the case on the grounds that this best explains something else one believes to be the case.”36 The author of this statement leaves no doubt, however, that this way of construing inference incurs intractable problems of its own: “inference to the best explanation is plausibly involved in both scientific and common sense knowledge, but it is not clear why the best explanation that occurs to a person is likely to be true.”37 To understand what it is that licenses any such explanatory statements or hypotheses (cf., C. S. Peirce’s “abductive” inference38) to begin with, and “what consequences may be drawn from” the likelihood of their being true—this, according to Simon Blackburn is to identify inference. Blackburn maintains that inference thus effectively constitutes the very “project of analysis” as philosophers pursue it “in the classical 35  P. Lipton, Inference to the Best Explanation (London: Routledge, 1991), p. 4. 36  David Sanford, “Inference,” The Cambridge Dictionary of Philosophy, ed. Robert Audi (Cambridge, Engl.: Cambridge University Press, 1999). Puntel is a contemporary systematic metaphysician who reposes a great deal of faith in this approach to inference, albeit his concerns are strictly methodological in this connection; see Structure and Being, p. 453. 37  For a study in the philosophy of science that centers on an extrapolation from this fact, see Kyle Stanford, Exceeding Our Grasp: Science, History, and the Problem of Unconceived Alternatives (Oxford: Oxford University Press, 2006). 38  The idea, at bottom, that we infer a hypothesis, not from a rule nor because it yields a rule, but because it best explains a set of data; and abduction has been identified with the theory of “inference to the best explanation.” For a highly nuanced recent analysis of Peirce’s idea of identifying abduction with inference, see Hintikka, Socratic Epistemology, chap. 2 (“Abduction—Inference, Conjecture, or an Answer to a Question”).

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tradition.”39 But here again one encounters a basic challenge to formulating a sufficiently rational account of the act of inference—now in the context of post-Kantian (epistemological) “metaphysics”: “The problem that many authors find with this line of thought,” confides Blackburn, “is that the inferences in question do not seem to come in statement-sized bundles. The mental world is full of surprises and caveats….”40 Contemporary analytic philosophers commonly note how this fact renders inductive inference unsuitable as an instrument of analysis—as opposed to its value in, say, artistic creation. This is a formative pragmatic matter that reflects the daunting challenge of probing the nature of inferential reflection—probing not merely rational inferences in an abstractly circumscribed sense, but the very reason of the act of inference as an onto-epistemological reality. Just how one might proceed from the pragmatic issue of inference as an instrument of analysis to the metaphysical problematic that underlies it—this is something that such thinkers appear either unprepared or ill-equipped to address. 39  “Metaphysics,” A Blackwell Companion to Philosophy, 2nd ed. (Oxford: Blackwell, 2003), p. 78. Like too many recently published “authoritative” reference works in philosophy, this text is very uneven in quality and demonstrates egregious biases in favor of narrowing, intellectually parochial orientations. Blackburn’s essay on “Metaphysics” is a case in point. It condescendingly dismisses ontology (“some authors give the impression that metaphysics is the science of Being”) while featuring a bibliography marked by breathtaking omissions--ancient (missing is Aristotle’s Metaphysics, for example), medieval (no medieval text is cited), and modern (absent are references to the likes of Spinoza, Wolff, Hegel [the only work Blackburn lists is The Philosophy of Right!], Bradley, Whitehead). Kant himself, when not yet forty, censured approaches to metaphysics that, if in other guises, continue to appear in books and university courses devoted to various Anglo-American logico-analytic orientations. “The mania,” as he put it, “for method and the imitation of the mathematician [to which we would now add the linguist, neo-pragmatist, and information theorist], who advances with a sure step along a well-surfaced road, have occasioned a large number of such mishaps [unwarranted definitions] on the slippery ground of metaphysics”; see The Only Possible Basis for a Proof of the Existence of God, in Theoretical Philosophy 1755-1770, translated and edited by David Walford and Ralf Meerbote (Cambridge, Engl.: Cambridge University Press, 1992), p. 117. 40  “Metaphysics,” p. 78.

74 Inference and the metaphysic of reason 2.1.3 The metaphysical challenge to analytic epistemologies of inference. If the preceding section indicated the constellation of questions that motivate an onto-epistemological inquiry into the act of inference, it could nonetheless do little more than adumbrate the plethora of competing analytic definitions and explications of inference that an extended and systematic survey might feature. Regardless of comprehensiveness, however, any intellectually responsible critique of the field would need to acknowledge the foundational character of the difficulties that we have noted. A trenchant summary of these problems appears in an article on inference included in a recent Companion to Epistemology. After rehearsing the most widely respected contemporary theories, the author of the essay concludes with observations that make it quite clear just how foundational the problematic of inference is for analytic philosophy: Attempts to explain inferences by formal-logical calculations or derivations leave us puzzled about the relation of formal-logical derivations to the informal [e.g., “intuited”] inferences they are supposed to represent or reconstruct, and this raises questions about the sense of such formal derivations…. Aren’t informal inferences needed in order to apply the rule governing the constructions of formal derivations (inferring that this operation is an application of that formal rule)? Coming up with a good and adequate characterization of inference—and even working out what would count as a good and adequate characterization here—is a hard and by no means nearly solved philosophical problem.41

One can hardly overstate the decisive nature of the implications that these remarks have for philosophical analysis, particularly for analytic epistemology. The defining character of these controverted issues is most apparent to those many philosophers who would concur with Simon Blackburn that the task of the identifying of inferences is “in effect, the project of analysis.” A cardinal related matter that has a crucial bearing on the orientational cast of the present study concerns the extent that analysts cannot settle on what to make of the “informal” inferences (intuition, “seeing,” and so forth)42 that formal inferences putatively “represent or 41  Robert S. Tragesser, “Inference,” A Companion to Epistemology (Oxford: Blackwell, 2000), p. 206. 42  More precisely, non-formal cognitions identified as inference.

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reconstruct.”43 This in turn raises far-reaching general questions about formalization per se, most especially its relation to rationality. These issues justify, if indirectly, the propriety of the sort of systematically articulated metaphysical dimension of inquiry that we shall pursue in this work, namely one that is sensitive to the bearing of the ontological, in the classical sense of being as being, on the act of inference. Stanley Rosen astutely makes the case for just such a venture in a remark quoted in part above, as an epigraph at the head of this chapter:44 Formalization is an expression of a metaphysical thesis or position….it is the thesis that rationality is finally or ultimately a question of formal relations. The thesis comes to regard itself as metaphysically neutral when it forgets that formal relations have a being more fundamental even than the values of their variables. This forgetfulness is induced primarily by the redefinition of being as existence and the definition of existence on the basis of quantifiers, functional analyses of propositions, and variables as quantifiable and ranging over domains of objects. The formal symbolism thus assumes a cloak, not quite of invisibility, but of magisterial neutrality.45

One is witness to a telling concomitant of this situation in those practitioners of analytic epistemology (in logic, linguistics, philosophy of mind, and other sub-disciplines) who on occasion cross over into traditional metaphysical territory when probing inference. These thinkers pursue such excurses in “scientifically” metaphysical ways— i.e., along lines, that don’t exclude the formative onto-epistemological implications of their methodologically abstractive assumptions. Even so, the analysts typically encounter difficulties that make patent determinating limits of the analytic “project” when conceived as isolable (bracketable) from the philosophy of being as being. One purpose of the present essay—which makes no pretence of being a systematic work in First Philosophy—is to shed some light on why this is so. 43  Relevant here is the matter of so-called “unconscious” or “implicit” (Bosanquet) inference—a construct of reflective inferential thinking. 44  Lotze argued much the same point over a century earlier; and his theory of “relation” (Verhältnis), which Rosen unconsciously echoes, was an original and influential contribution. 45  “Logic and Dialectic,” The Ancients and the Moderns: Rethinking Modernity (New Haven: Yale University Press, 1989), p. 135.

76 Inference and the metaphysic of reason The venture to cast in relief the ineliminable metaphysical component of the philosophical inquiry into inference sharply challenges the limiting focus that one finds in major contemporary orientations to speculative thinking—and by extension to discursive thought at large. The doctrines at issue tend to restrict the “space of reasons” to rule making and pragmata,46 even as they bracket the disclosive claims and speculative authority of theoria, and this most problematically with respect to demonstrably material aspects of ontology. The present chapter, however, goes beyond the preliminary task of considering the analytic problematic of inference in light of relevant onto-epistemological factors. It also prepares the ground for investigating the metaphysics of inference along axes that transcend47 the formalistically circumscribed fields of operation generally that the preponderance of contemporary inferentialists have staked out. The larger purposes of this book if arguably of consequential philosophical moment are considerably involved, and this opening gambit can do little more than shadow forth what gradually emerge, through the broader course of discussion, as the principal features of the problematic of inference, viewed from within an onto-epistemological frame of reference. The overall picture will by turns deepen and evolve as the critical exposition shifts from assessing a range of paradigmatic contemporary doctrines to explicating the metaphysically grounded inference theory of Lotze and Bosanquet.48 46  In his highly regarded Elements of Analytic Philosophy (New York: Macmillan, 1949), Arthur Pap observed that anomalies to rule-governed inductive inferences are “of course, a practical, not a logically decidable question” (p. 455). But is logical praxis not itself practical? Even a cursory review of the history of logic reveals how logical thinking is saturated with practical judgments of all sorts (even if current symbology designedly obscures them or factors them out)—as for example, in the previously noted judgment that “the distinction between adjective and noun…is without significance from the point of view of logic.” 47  Historically (back mainly to Hegel and Kant) as well as speculatively; and with emphases on “essence,” for instance, and “sufficient reason.” 48  One should not confuse such thinkers with the scholars who currently claim the title of “philosophical logicians.” The former are sometimes referred to as “epistemological” logicians, but this is a reductive appellation. It betrays nothing so much as the post-Kantian epistemological hegemony that finds contemporary philosophers assimilating ontology to (or predicating it upon) the axiomatics or findings of a theory of knowledge or a

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At first sight, the diverse conceptual idioms and speculative programs of Rudolf Carnap, Gilbert Harman, Robert Brandom, Michael Williams, and Bernard Lonergan might suggest that the singling out for commentary of their particular doctrines of inference is merely adventitious. Indeed, from a purely technical standpoint other philosophers certainly could have filled the bill. Nonetheless, these five thinkers are of especial interest here because of the way that each addresses the idea of inference as a subject of pivotal orientational import. Moreover, with the possible exception of Williams,49 they consider the topic from speculative viewpoints sufficiently different from each other so as to provide, collectively, a sense of the broad spectrum of leading analytic epistemologies of inference. Carnap is a Vienna Circle logician and scientific empiricist. Harman is an ethical theorist, Quinean epistemologist, and philosopher of mind. Brandom is a self-styled neo-pragmatist and Sellarsian semantic theorist who in recent years has sought to appropriate Hegelian thought to his own systematic ends.50 Williams, who counts Sellars and to a lesser extent Brandom cognitive science that underdetermines the issue of Being. Such moves are in the tradition of Kant’s “characteristic tendency to convert ontological questions into epistemological questions” (Paul Guyer and Allen W. Wood, “Introduction,” Critique of Pure Reason, trans. Paul Guyer and Allen W. Wood [Cambridge, Engl.: Cambridge University Press, 1998], p. 25). 49  Williams’ philosophy of inference exhibits somewhat less originality than those of the other philosophers that I consider. The relation of his thought to that of Carnap, Harman, and Brandom, however, as well as his critiques of holism and linear inference that speak to certain larger themes of the present essay recommend an assessment of his doctrine as a unifying element of the critical phase of discussion here. 50  Tom Rockmore, for one, has raised serious questions about the legitimacy of Brandom’s pragmatic (and Hegelian) self-ascriptions; see “Brandom, Hegel, and Inferentialism,” International Journal of Philosophical Studies 10 (2002): 429-47. Rockmore’s more recent criticism of Brandom involves, however, a substantive error. “Brandom,” declares Rockmore, “depicts the process of cognition as one of bringing together identity and difference to yield determinateness in order, ‘in Hegel’s terminology, to “posit” [setzen] something determinate as, for instance, simply immediate being.’ This is obviously a slip,” says Rockmore, “since the term ‘posit’ is Fichtean, not Hegelian” (Hegel, Idealism, and Analytic Philosophy [New Haven: Yale University Press, 2005], p. 129). Although Brandom doesn’t state that he is applying the idea of onto-epistemological positing to the domain of pure thinking, he pretty clearly refers here to Hegel’s doctrine of essence, which

78 Inference and the metaphysic of reason (although never Hegel) as influences, espouses a problem-structured, contextualist epistemology grounded in social practices; he sharply distinguishes his thinking from that of prominent figures who have influenced it—most notably Harman, Rorty, and Quine. Lonergan is a preeminent neo-Thomist whose treatment of inference is singularly relevant here for how it transects contemporary analytic epistemologies and the speculative thought-determinations of pre-analytic metaphysics. We shall find Lonergan’s modus operandi most germane for the way it deepens critical insight into both traditions relative to the problematic of inference. Probing the inference theory of Carnap, Harman, Brandom, Williams, and Lonergan could easily run to five chapters. This essay, however, is ultimately constructive in aim, and so I’ve limited discussion primarily to what uniquely distinguishes each doctrine, and to those of their related position statements that are most material to the ontoepistemology of inference. The one exception is Lonergan, who situates his analytic inference theory within a comprehensively systematic onto-epistemology of “Insight.” Lonergan’s thinking invites more extended reflection in these pages because it articulates both formative continuities and telling disparities between contemporary epistemologists and the orientation of the earlier, metaphysically attuned philosophers of inference, Lotze and Bosanquet, to whose thinking I devote the bulk of chapter 3. 2.2 Rudolf Carnap. The most widely known of the five philosophers whom we shall consider in the present chapter is Rudolf Carnap, a Vienna-Circle luminary who counted Frege among his teachers. Carfeatures a uniquely Hegelian use of setzen. Cf., for example, the opening of Hegel’s discussion of “Die Lehre vom Wesen”: “Das Wesen ist der Begriff als gesetzter Begriff….” (Der Wissenschaft der Logik. Enzyklopädie der philosophischen Wissenschaften. Erster Teil. [Frankfurt am Main: Suhrkamp, 1986], §112); [The Encyclopedia Logic, trans. T. F. Geraets, W. A. Suchting, and H. S. Harris (Indianapolis: Hackett, 1991), p. 175]. For a definitive critique of neo-pragmatic efforts to appropriate Hegel, see Rolf-Peter Horstmann, “Substance, Subject and Infinity: A Case Study of the Role of Logic in Hegel’s System,” in Hegel New Directions, ed. Katerina Deligiorgi (Montreal: McGill-Queens University Press, 2006), pp. 69-84. Also see Brian O’Connor, “Hegel’s Phenomenology and the Question of Semantic Pragmatism,” Owl of Minerva 38.1-2 (2006-07): 127-43, a critique based on “Hegel’s notion of [ontologically transformative] progressive determination.”

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nap devoted considerable effort to explaining inductive reasoning from a technically analytic standpoint. The ultimate fruit of this line of investigation Carnap summarized in two relatively late essays: “Inductive Logic and Inductive Intuition”51 and “Induction and Statistical Probability.”52 The first sees Carnap rejecting attempts to formulate rules of inductive reasoning. The “essential point,” he argues, is rather to focus on the “determination of probability values”53—particularly empirically derived, statistical probability values, beyond those of abstract logical probability. In the second essay Carnap stresses that the “truth of an inductive conclusion is never certain.”54 And he settles for a logic of induction that identifies “inductive probability” not with statistical but with logical probability, “because in my conception this is the kind of probability that is meant whenever we make an inductive inference.”55 Carnap goes on to explain that by “inductive inference” he means “not only inference from facts [the empirical grounds of statistics] to laws, but also any inference that is ‘nondemonstrative’; that is, an inference such that the conclusion does not follow with logical necessity when the truth of the premises is granted.”56 He declares, in the 51  In The Problem of Inductive Logic, ed. Imre Lakatos (Amsterdam: North Holland Publishers, 1968). 52  In Rudolf Carnap, An Introduction to the Philosophy of Science, ed. Martin Gardner (New York, Harper, 1974). For an incisive detailed analysis of the rationality of Carnap’s earlier work on the problematic of (inductive) inference, see Ernest Nagel, “Carnap’s Theory of Induction,” The Philosophy of Rudolf Carnap, ed. Paul Arthur Schilpp (LaSalle, Ill.: Open Court, 1963), pp. 785-825. For a more recent, comparative critique of Carnap’s theory, see D. P. Chattopadhyaya, Induction, Probability, and Skepticism (Albany: State University of New York Press, 1991), esp. pp, xxi, 62-67, 94-102. 53  “Inductive Logic,” p. 259, emphasis added. 54  “Induction,” p. 20, emphasis added. 55  Ibid., p. 22. One should not confuse such logical probability with statistical reasoning. The latter, as Michael Williams explains, is “in its mathematical aspect…entirely deductive and owes nothing to the sort of ‘inductive logic’ proposed by Carnap. Statistical inference is not ‘probabilistic reasoning’ but ‘reasoning about empirical probabilities’” (Problems of Knowledge: A Critical Introduction to Epistemology [Oxford: Oxford University Press, 2001], p. 214). 56  Ibid., emphasis added.

80 Inference and the metaphysic of reason same passage, that inferences of this sort “must be expressed in degrees of what I call ‘logical probability’ or ‘inductive probability.’” Whether one thinks of probability statistically or as a theory of “partial implication” (which Carnap termed “inductive probability”57), the turn to probability theory in the effort to elucidate the character of inductive inference is far from original with Carnap.58 Moreover, it is an approach to inference that has long elicited sharp philosophical criticism.59 C. D. Broad, to cite a near contemporary of Carnap (and, like Carnap, an adept in mathematics), published a major paper as early as 1918, “On the Relation between Induction and Probability.”60 Broad finds that the “degree of belief which we actually attach to the conclusions of well-established inductions cannot be justified by any known principle of probability, unless some further premise about the physical world be assumed.”61 (He thus anticipates, and perhaps 57  Ibid., p. 32. 58  Cf., for example, Thomas Reid, “Of Probable Reasoning,” Essays on the Intellectual Powers of Man ([1785] Cambridge, Mass.: MIT Press, 1969), Essay VII, §III; and Bosanquet, Logic, pp. 169-71. 59  In his last lecture course (1915-1916), Josiah Royce had this to say about inductive inference and probability: “the conception that is really defined by the process of induction is the conception of probability, one of the profoundest and most problematic conceptions in the whole range of human thought—a conception to whose use the pragmatists [ James and Dewey] have contributed without recognizing what concept they were dealing with” (Metaphysics, ed. William Ernest Hocking, co-edited by Richard Hocking and Frank Oppenheim [Albany: State University of New York Press, 1998], p. 47). 60  The paper is not referenced by Carnap in either of his essays. 61  Induction, Probability, and Causation: Selected Papers by C. D. Broad, ed. Jaakko Hintikka (Dordrecht: Reidel, 1968), p. 16, emphasis added. This statement of Broad’s correlates with the view of Bosanquet (a philosopher for whom Broad nurtured the highest respect), who subscribes rather to a holistically systematic than to a linear (mathematically ordered) approach to inference: “…you cannot go straight from an enumeration of actual cases to a statement of chances. You must consider what sort of system the enumeration indicates” (The Value and Destiny of the Individual [(1913) Bristol, Engl.: Thoemmes Press, 1999], p. 302 n). Something not made explicit here by Carnap or Broad or Bosanquet is the relation between a plausible mode of construing inference and the reason of the act of inference per se—which can hardly be, in the first instance, the application of a proper means of representing or interpreting itself.

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partially motivates Wilfrid Sellars’ theory of a “material,” or natural law-like, inference that complements formal (deductive) inference.62) Broad’s insight moots what Carnap viewed as his singular contribution to inference theory, namely the distinction between statistical and logical probability. In what amounts to a refutation of Carnap’s strategy, Broad develops his observations on the ontic (“natural”) ground that demands systematic elucidation as the meta-analytic context of any philosophically coherent probabilistic explanation of inference: All particular inductive arguments depend on probability and only lead to probable conclusions whatever we may assume about nature. But unless we assume something about nature they give no finite probability to any law (a) because an indefinite number of alternative hypotheses which are not laws are as probable antecedently as the suggested law, and (b) because we are not equally likely to have met with any instance of the class under discussion, since it is quite certain that if there be an instance remote in space and time it could not have fallen into the selection which we observed.63

Broad here puts his finger on the difficulty that, as we shall see, would ultimately lead Carnap to desperate speculative measures. Indeed, Broad’s conclusion offers little encouragement to probabilistic theorists of inference in general: “The certainty of the most certain induction is,” asserts Broad, “relative or hypothetical, and the probability of the hypothesis is not of a kind that can be stated numerically.”64 Still, Broad himself went to considerable lengths formally to justify conditions under which one can assign a high degree of probability to an inductive inference (and in that respect explain it probabilistically). He ran into serious and proliferating onto-epistemological complications, however, in his efforts to relate Being to the technically involved mathematical logic of his justification. (Broad empirically refers the “ontological” extension of his theorizing to “nature”; and it is ultimately only with respect “to the belief that we really have got hold of the 62  Sellars was Robert Brandom’s teacher and a major influence on his philosophy of inference. 63  Induction, Probability, and Causation, p. 49. 64  Ibid., p. 51. Consistent with the epistemological tradition so decisively shaped by Kant, Broad tacitly construes hypothetical conditionals as, one and all, instances of “relative” Position. This verdict correlates with Salomon Maimon’s conclusion that “if (for every x) Ax then B” is a derivative form of a categorical judgment: namely, “The A that is x is also B.”

82 Inference and the metaphysic of reason general ground-plan” of nature—a telling expression of Santayanian “animal faith”—that he locates the “logical position” of the probability of inductive inference.65) Like Broad, Carnap inevitably encounters intractable difficulties on the onto-epistemological plane. Symptomatic of this are his uncritical shifts between references to inference per se and different modalities of inference, shifts (implicit in the passage cited immediately below) that effectively elide the ontological dimension of inference in the interest of analytical diahresis. The onto-epistemological aspect of the act of inferential thinking is what makes inference the sort of phenomenon that manifests entailments that we need to find some means to express—Carnap opts for the medium of mathematical logic66—even 65  Ibid., p. 51. See Georg Henrik von Wright, “Broad on Induction and Probability,” in Induction, Probability, and Causation: Selected Papers by C. D. Broad, pp. 228-72. This text contains later elaborations of Broad’s views on inductive inference as well as his reply to von Wright’s searching criticism. In the face of the latter Broad finds himself, at the end of his career, compelled to concede the following in the volume’s Preface: “One could not hope to have a fuller or fairer critical synopsis of one’s writings…” (p. ix). Alfred North Whitehead—for whom “connectedness is of the essence of all things of all kinds”—compellingly raises the metaphysical dimension (something that Broad merely adumbrates in his references to “nature”) that ineluctably attaches to any evidence, empirical or logical, which one might wish to adduce in an inductive inference. As Whitehead puts it, inferential “anticipations are devoid of meaning apart from the definite cosmic order which they presuppose”—and which must be articulated in any philosophically rational account. See Process and Reality: An Essay in Cosmology, Corrected Edition, ed. David Ray Griffin and Donald W. Sherburne (New York: Free Press, 1978), pp. 201-05. More than a half-century before Whitehead, Lotze declared that the “one supposition…of there being a universal inner connexion of all reality as such which alone enables us to argue from the structure of any one section of reality to that of the rest, is the foundation of every attempt to arrive at knowledge by means of experience, and is not derivable from experience itself. Whoever casts doubt on the supposition, not only loses the prospect of being able to calculate anything future with certainty, but robs himself at the same time of the only basis on which to found the more modest hope of being able under definite circumstances to consider the occurrence of one event as more probable than that of another” (Metaphysic, p. 4, emphasis added). 66  While still under the influence of Cassirer and the Marburg school, Carnap did adduce absolute onto-epistemological positing with his concept of Ordnungssetzungen, a notion adduced in the constructive phase of

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if we can’t finally demonstrate them discursively.67 One philosophically damning consequence of attempting this in received discursive terms is an indefinite proliferation of types of inference (something that F. H. Bradley had cautioned against68). “Induction,” states Carnap, is often contrasted with deduction by saying that deduction goes from the general to the specific or singular, whereas induction goes the other way, from the singular to the general. This is a misleading oversimplification. In deduction, there are kinds of inferences other than those from the general to the specific; in induction there are also many kinds of inference. The traditional distinction is also misleading because it suggests that deduction and induction are simply two branches of a single kind of logic.69

Beyond the “logic” of inductive thinking, Carnap tacitly recognizes that his controversial recourse to probability does not settle basic questions that concern inductive inference as an epistemological analogue to deductive thinking: “the epistemological situation in inductive logic,” observes Carnap, “is not worse than that in deductive logic, but quite analogous to it.”70 Although he doesn’t expressly state it, the present study (cf., chap. 4.2b, below). He identified these as “basic relations” in his early “constitutional system,” but not in connection with his later theory of inference. See The Logical Structure of the World (Berkeley: University of California Press, 1967), §75; [Der logische Aufbau der Welt (Berlin: Weltkreis, 1928)]. On the formative neo-Kantian elements of Logical Structure, see Michael Friedman, A Parting of the Ways: Carnap, Cassirer, and Heidegger (Chicago: Open Court, 2000), chap. 5. 67  Curiously, Carnap himself is quite aware of this, as he is that his late suggestions about resorting to intuition in order to settle matters “should not be taken as anything more than a few rough, preliminary hints” (“Inductive Logic,” p. 266). 68  Bradley observes the following in his late essay “On Inference”: “The idea of a complete body of models of reasoning, to be followed as patterns and faithfully reproduced to make and guarantee the individual inference, I set down as superstition. No such code of rules and examples could…warrant its own infallible application; and, in the second place, no collection of models could conceivably be complete, and so anticipate and prescribe beforehand the special essence of every inference”; see The Principles of Logic, 2nd ed., revised with commentary and terminal essays, corrected edition (London: Oxford University Press, 1928), vol. II, p. 618. 69  “Induction,” p. 19. 70  “Inductive Logic,” p. 266.

84 Inference and the metaphysic of reason the cognitional situation in both cases is inferentially articulated. But Carnap fails speculatively (dialectically) to work through the aporia71 (a fundamental one that arises in the philosophy of mathematics as well as in the philosophy of inference72). This is because he is unable, from within his (analytic) epistemological frame of reference, to posit onto-epistemologically, not the formal content of inductive or deductive logic but rather, in any given instance, the fact of it as meaning cognized in a living act of intelligence.73 Consequently, his ultimate explanatory recourse, so far as the concept of inference itself is concerned, is to adduce, as the passage cited above indicates, an indefinite variety of types. This in its turn leads to an expedient that Hegel, for one, would have censured as dogmatic and that Carnap himself admits his “friends warned me against,” namely invoking “intuition.”74 The “intuition” to which Carnap appeals not only falls beyond the pre71  He might have done better, perhaps, to conceive of an analytic of inference keyed to his early notion of Ordnungssetzungen, which he understood, onto-epistemologically, as a moment of what Kant identified as absolute Position. 72  Alexander George and Daniel J. Vellman call attention to it in their discussion of intuitionistic and classical mathematics, a critical comparison based on “what constitutes a proof of a logically complex arithmetical statement.” After spelling out the difficulty, however, they “choose not to pursue” the matter. See Philosophies of Mathematics (Oxford: Blackwell, 2002), pp. 105-06. 73  Cf., Hegel’s Lectures on the Philosophy of Spirit 1827-28, trans. Robert R. Williams (Oxford: Oxford University Press, 2007), §442. 74  Improbable as it might seem, the idealist logician Harold H. Joachim would have sided with the friends of Carnap on this matter (and against the likes of Stanley Rosen). “The intellect,” argued Joachim, “has no separate function of intuition, whereby it immediately apprehends—takes in at a stroke, or sees, without discursus of any sort—certain things or facts or simple self-evident items which are the elements of reality and knowledge” (Logical Studies [Oxford: Oxford University Press, 1948], p. 46). David Weissman, in a chapter on “Dialectical Cycles of Intuitionist Method,” analyzes Carnap as an intuitionist but limits his discussion to The Logical Structure of the World (1928); see Weissman’s Intuition and Ideality (New York: State University of New York Press, 1987), pp. 75-82. For a more recent and detailed discussion of “intuition” from the standpoint of a prominent analytic intuitionist who is a philosopher of mathematics and logic, see Charles Parsons, Mathematical Thought and Its Objects (Cambridge: Cambridge University Press, 2008), chap. 5 (“Intuition”).

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cincts of standard formal logic, but on pain of infinite regress cannot claim any affinity with Gödelian “rational intuition,” i.e., as a merely conceptual or meaning-theoretic connection. This is because the link that Carnap wishes to name is not one that inheres simply between two logically or formally independent sets of axioms.75 (Indeed, what Gödel has in mind presupposes the onto-epistemological factor that Carnap attempts to identify.) Interestingly enough, Carnap’s master, Frege, dealt briefly with the issue at the end of his career. In a posthumously published paper of 1924, Frege distinguishes between, on the one hand, judgments, which justify “the recognition of truth” and hence are a source of knowledge; and on the other hand, the grasping of thought, which is the bare “recognition of its truth.” The intractable problem here is how one justifies the grasp.76 In a comment on Tarski’s analysis of logical consequence, Stanley Rosen lucidly delineates the fundamental epistemological problem that the resort to intuition such as Carnap hazards, be it tacit or overt, poses in analytic science: There is nothing ambiguous in the conception of the task of science as the replacement of primitive intuitions by formal theories. The intuitions cannot be simply replaced by theories, because the function of theories is to explain, and so to be measured by, intuitions. On the other hand, intuitions cannot be precisely captured in theories. It is almost immediately evident that the relation between intuition and logic is dialectical.77

The resort to intuition is a dialectical move on Carnap’s part; but he had long abandoned, for linguisticism, anything approaching the conceptual logic that informs his onto-epistemological notion of Ordnungssetzungen in Logical Structure of the World (1928).78 Carnap 75  For a lucid and highly accessible treatment of Gödelian “rational intuition” (and of Gödel’s critique of the early Carnap), see Richard Tieszen, Phenomenology, Logic, and the Philosophy of Mathematics (Cambridge, Eng.: Cambridge University Press, 2005), chaps. 6.4-5 and 8.5. 76  Tieszen cites this difficulty in Phenomenology, Logic, and the Philosophy of Mathematics (p. 330), but his view that Husserl resolves the problematic by appeal to intuition, rather than merely shifts it to different ground, raises fundamental onto-epistemological questions in its own right. 77  Rosen, “Logic and Dialectic,” The Ancients and the Moderns, p. 119. 78  See n. 66, above.

86 Inference and the metaphysic of reason thus makes the dialectical move dogmatically instead of by appeal to fact79—by considering, that is, the onto-epistemological ground that makes intelligible the rational connection of intuition to his formal explanation of inference. To be consistent, Carnap must demonstrate that his heteronymous appeal to intuition holds for induction as well as for deduction. And indeed he sets about explaining his approach to inductive inference by adducing an intuitive plausibility that has persuaded few of his critics: “Although in choosing axioms for inductive logic we have to rely,” says Carnap, “on inductive intuition, the intuitive plausibility of an axiom may be more or less strong.”80 The very act of resorting to axiomatic theorizing to establish the truth, or to otherwise justify such intuitions as recommend the value or relevance of an inductive inference, is tantamount to supplanting intuition with theory. Rosen underscores this difficulty in his statement quoted above. One cannot plausibly replace intuition with formal theories; this is because the role of theories—theories of inductive logic, say, or of deductive rules—“is to explain, and so to be measured by, intuitions. On the other hand, intuitions cannot be precisely captured in theories.” Bosanquet, for one, long since identified the underlying onto-epistemological problematic at the heart of this matter. “There is no axiom,” he observed, “that warrants us in arguing directly from the reality of full experience to the reality of abstraction, and if we adopt this procedure we must do it on the special ground that what we exclude is ad hoc irrelevant, a contention which always leaves us exposed to some degree of risk.”81 Perhaps the most important classical analysis bearing upon these issues is Aristotle’s discussion in the Posterior Ana79  Beyond demonstrative reasoning, the onto-epistemological orientation to inference also involves dialectical reflection, with its direct appeal to particular fact. On the Aristotelian origin of this distinction in the philosophy of inference, see H. W. B. Joseph Introduction to Logic, 2nd ed. (Oxford: Oxford University Press, 1925), pp. 397-99. It comes as no surprise that Carnap’s appeal to “intuition” has a historical parallel in the mathematical formalist David Hilbert’s late move, in the words of L. E. J. Brouwer, to “consciously and in confesso [make] use of the intuition of natural numbers and complete induction” (ms, quoted in Brouwer’s Intuitionism, Walter P. van Stigt [Amsterdam: Elsevier, 1990], p. 280). 80  “Inductive Logic,” p. 266. 81  Logic, vol. II, p. 309. To his credit, Carnap discerned this risk and was clearly uncomfortable with it.

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lytics. Aristotle there reflects upon how the prereflective “grasp of the what-it-is” (to ti esti) is a sine qua non for determining the appropriateness of premises, and even the intelligibility of the move from premise to premise, in acts of theorizing or inference at large.82 Contrary to first impressions, invoking intuition is not a Kantian expedient on Carnap’s part,83 although he is after some extra-discursive substantiation of how we apprehend things in what we identify as inferential modes of thought.84 Carnap seeks this ground by way of what, in the first Critique, Kant, by contrast, distinguished as “cognition from principles,” namely “that cognition in which I cognize the particular in the universal through concepts” (A300/ B357). This is not an appeal to intuition. As Henry E. Allison observes, “principles in the strict or ‘absolute’ sense (if there be any) would yield synthetic cognition from concepts alone, without any appeal to intuition (A301/ B357-58). It is such principles,” explains Allison, “that Kant connects with the use of reason.”85 If less philosophically imaginative, Carnap’s friends were certainly more consistent on this score. Carnap, however, justifies his resort to heteronomy by declaring: “you have to appeal to deductive intuition, in order to teach ‘deduction.’”86 (Kant might have objected that so far 82  Cf., Posterior Analytics II. 5. See Patrick Byrne’s elucidation of Aristotle’s discussion, in Analysis of Science in Aristotle (Albany: State University of New York Press, 1997), chap. 6. 83  Cf. Carnap’s criticism of Kantian intuition, in “Euclid’s Parallel Postulate,” An Introduction to the Philosophy of Science, chap. 13. Carnap is closer, in his appeal to intuition, to Descartes than to Kant; as Brand Blanshard lucidly summarizes the Cartesian position: “Intuition is the insight that two properties are necessarily connected. Deduction is the insight that two or more propositions are necessarily connected….Deduction is merely intuition serially applied” (Reason and Analysis [La Salle, Ill.: Open Court, 1964], p. 71). 84  For an extended critique of the resort to intuition in speculative thought generally, one that includes a discussion of Carnap, see Weissman, Intuition and Ideality. 85  Kant’s Transcendental Idealism, revised ed. (New Haven: Yale University Press, 2004), p. 309. Recall that Reason, as Kant famously explains, “is the faculty of the unity of the rules of understanding under principles” (A302/ B359). 86  “Inductive Logic,” p. 266. Onto-epistemologically, the fatal if unstated assumption here is that one must at all costs “preserve a dualism between

88 Inference and the metaphysic of reason as learning involves understanding, the appeal must be rather to the process of reflective thinking, since “the understanding intuits nothing but only reflects.”87) Presumably, Carnap would pin his hopes on the student’s ability to intuit that, not just how, logical form justifies the validity of a paradigmatic instance of deductive inference. But then how could one plausibly abstract the element of intuition supposedly necessary for the very grasp of “deduction” per se from the techniques of justifying any particular form of deduction? And how would one do this without representing the mere idea of justification rather than the articulate fact? This Carnap doesn’t explain.88 Once he has resort to intuition, Carnap commits himself to a view whereby intuition— whether as unjustified belief or unexplained immediate knowledge that is non-propositional or ante-inferential—is an implicit and inexpugnable feature of how, as an act of intelligence, justification (of any form of deduction) succeeds in its own terms. And he would need to address Moritz Schlick’s challenge to intuitionism, a challenge that Schlick mounted just prior to the time that he convened the Vienna logical forms and the cognizing intelligence”—the result being that one “leaves the process of meaning itself unintelligible” (Rosen, The Limits of Analysis [New York: Basic, 1980], p. 233). Consider how Santayana dealt with this need to resort to an independent, prediscursive moment of knowing that existentially charters a discursive account, explanation, or definition as intelligible fact: “Only animal faith, trust in appearances, or experience in practical arts can justify” the “presumption” that “any material, visible, or imagined circle” can be “said to be a circle in the mathematical sense” (“Some Meanings of the Word ‘Is,’” Journal of Philosophy 21.14 [1924]: 370). 87  Prolegomena to Any Future Metaphysics, trans. Peter G. Lucas and Günter Zöller (Oxford: Oxford University Press, 2005), pp. 94-95. 88  Bosanquet calls attention to a statement of Locke’s that suggests the degree to which Carnap and those who share his analytic frame of reference are simply ill equipped to pursue a genuine science of inference. This is a failure one might lay at the doorstep of the hegemony of calculative and rule-governed models of sense-making—an orientation that fails to rationally engage the reason of the act of inference: “‘If we will observe the actings of our own minds,’ says Locke, ‘we shall find that we reason best and clearest when we only observe the connection of the proof, without reducing our thoughts to any rule of syllogism’” (Implication and Linear Inference, p. 105). Locke here anticipates by two centuries the sweeping repudiation of the tradition that identifies inference strictly with the syllogism.

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Circle and subsequently fell under the spell of Carnap, Wittgenstein, and others: Only so long as we consider immediate intuiting to be a necessary condition of knowledge, does the opposition of appearance and thing-in-itself coincide with that between the knowable and the unknowable. For to be intuitive is to be a content of consciousness, and in fact only ‘appearances’ are that; things-in-themselves, however, are by definition not contents of consciousness, and hence are wholly remote from intuition….if we could intuit them this would give us no direct help at all in knowing them.89

As a more recent analyst of deductive thought has put it, “the justification of a form of inference cannot derive from intuition of the validity of its instances.”90 If one cannot justify the form of deductive inference by recourse to an intuition of the validity of its instances, then it would appear bootless to adduce intuition as the epistemological ground of how one communicates to the uninitiated the idea of “deduction” when one introduces the idea merely through examples of formal procedures that exemplify it. These criticisms might leave Carnap’s position untouched, but only if one could “teach ‘deduction’” without appeal to “deductive intuition” when one teaches the student to derive the justification of a form of inference from particular instances. The irony in Carnap’s turn to intuition as an originary component of inferential modes of knowledge is manifest. The stratagem is used, after all, by the author of The Logical Syntax of Language (1937), a positivist and then logical empiricist who from the 1930s on held that the formal methods of natural science are the sole sources of knowledge, this rather than any unjustified true belief or faith in immediacy per se.91 89  Schlick, “Appearance and Essence,” Philosophical Papers, Volume I (19091922), ed. Henk L. Mulder and Barbara F. B. Van De Velde-Schlick, trans. Peter Heath (Dordrecht: Reidel, 1979), pp.. 283-84. 90  Susan Haack, “The Justification of Deduction,” in A Philosophical Companion to First-Order Logic, ed. R. I. G. Hughes, (Indianapolis: Hackett, 1993), p. 84. Although she does not directly criticize Carnap’s specific references to intuition, Haack, like the present writer, quotes Carnap on the analogous difficulties of satisfactorily explaining inductive and deductive inference. 91  Cf., The Logical Syntax of Language, trans. Amethe Smeaton (New York: Harcourt, 1937), p. xiii.

90 Inference and the metaphysic of reason Had the late Carnap revisited the writings of an earlier generation of idealist logicians he would have discovered that they had already exposed the systematic character of the aporia that put him at odds with his logical-empiricist friends. Consider the following observation of F. H. Bradley at the end of his career (and well into the era of mathematicized logic): The so-called ‘premises’ [of a proposition] by themselves certainly never are all that is really required for the conclusion. And the question is whether in logic what is really presupposed for each inference, always, or even ever, admits of a complete statement, and so avoids the implication of an unknown condition. And with this arises a ground of doubt as to how far in logic the claim of logic is made good.92

Perhaps what Carnap’s bid to incorporate intuition as the foundational epistemic moment in his account fails most fundamentally to establish is the intuitive warrant of the very “plausibility” to which he refers. He would need, at the least, to explain how his speculative move escapes the vicious circularity entailed when one presses the issue in the direction of intuition. As implausible as it might seem, however, Carnap’s instinct to invoke intuition does intimate a seminal philosophical insight. It is one, however, the purport of which only a more metaphysically attuned thinker could articulate. Consider, for example, Maurice Blondel’s critique of experimental science. “The relation between calculus and intuition,” observed Blondel, “between the intelligible determinism of facts and the sensible discontinuity of the data of observation escapes it [positive science] at the beginning, in the course, and at the ideal end of its development; and yet it lives by this very relation.”93 Nearly a century later, Rosen had this to say about the rational limits of analysis disclosed when the analytic epistemologist turns to intuition in order to justify, explain, or even communicate to the uninitiated how thinking progresses from premises to conclusions: Logicians are right to refer to intuitions of consequence, but they do not seem to me to take this point seriously enough. Perhaps the reason is their professional bias which leads them to assume that the imprecision of intuitions can always be replaced by the rigor of 92  The Principles of Logic, p. 601. 93  Action (1893), trans. Oliva Blanchette (Notre Dame: University of Notre Dame Press, 1984), p. 86.

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conceptual definition. I agree that such a replacement is possible. But the serious problem is quite different: how shall we justify the step from our intuitions to this or that rigorous definition.94

2.3 Gilbert Harman. Like Carnap, Gilbert Harman doesn’t approach induction and deduction as two branches of a single kind of logic. In fact he contends that they are not even “two kinds of reasoning….not two kinds of anything.”95 Since, as Harman sees it, “deduction is not a kind of reasoning,”96 he would certainly challenge Carnap’s postulate that deductive thinking features a plurality of kinds of inference. Harman argues that to think deductively in accord with a pattern of rules (of entailment)—specifically in accord with “certain relations among propositions, especially relations of implication and consistence”—is simply not to “reason deductively in the sense that your reasoning has the pattern of a proof.”97 Rejecting out of hand the very idea of deduction as inferential reflection, Harman draws a categorical distinction between argument and reasoning. He classifies rules of deduction as rules of argument: “they are not,” he insists, “rules of inference or reasoning.”98 The case of induction, however, is another matter. Unlike deduction, induction does not feature the sorts of apodictic rules or patterns of proof incorrectly taken to be constitutive of the very reasoning processes, the living acts of concept formation, that entertain them. Harman is thus able to regard inductive reflection as genuinely inferential. Yet beyond references to enumerative induction (e.g., “Given that all observed F’s are G’s, you infer that all F’s are G’s, or at least that the next F is a G”)99 and beyond inference to the best explanation (e.g., “Scientists infer that Brownian motion is caused by the movement of molecules”), Harman finds only confusion in theorists who aim to ar94  “Logic and Dialectic,” p. 126. 95  Reasoning, Meaning, and Mind (Oxford: Oxford University Press, 1999), p. 27. 96  Ibid., p. 27. 97  Ibid., p. 28. 98  Change in View: Principles of Reasoning (Cambridge, Mass.: MIT Press, 1986), p. 5. 99  Bertrand Russell’s position on inference centered on enumeration; see Human Knowledge: Its Scope and Limits (New York: Simon and Schuster, 1948), pp. xii & xiii.

92 Inference and the metaphysic of reason ticulate a definitive account of inductive reasoning by addressing the (Humean) “problem of induction.” He even questions “what the problem of induction is supposed to be.” As Harman sees it, “Premises in an argument are to be distinguished from the starting points in reasoning….The conclusion of an argument is not to be identified with the conclusion of reasoning in the sense of what you end up with or ‘conclude’ after reasoning.”100 Harman’s own proposal is that inductive reasoning works by way of a regulative ideal, namely some “best explanation” predicated upon the most coherent total view of the world.101 This dubious explanation has come in for severe criticism. As one skeptic has pointed out, “Harman’s argument would not apply with complete generality [i.e., count as a plausible general inference] if, by their very nature, some beliefs were ‘premises’ and others ‘conclusions.’”102 Criticisms aside, however, Harman’s account features a holistic element that is consistent in principle with the holism of the ontoepistemology of inference delineated in the present study, a holism that trades on the conviction that it is a mistake “to identify reasoning with proof or argument in accordance with rules of logic.”103 This insight, far from original with Harman (Bosanquet underscored this same point104), makes less surprising his contention that one errs in regarding deduction and induction as “different species of the same sort of thing.”105 The implications of these position statements involve Harman in a still more general concern about the relation of logic to 100  Thought (Princeton: Princeton University Press, 1973), p. 30. 101  See Thought, pp.161ff; and Michael Williams, Unnatural Doubts: Epistemological Realism and the Basis of Skepticism (Princeton: Princeton University Press, 1996), pp. 281-82. Williams, like other analytic epistemologists such as Popper, bends his efforts to the proper justification of inference, something that one can pursue while remaining indifferent to the rationally grounding, onto-epistemological dimension. See also Williams’ criticisms of Harman in Problems of Knowledge, pp. 214-15. 102  Williams, Unnatural Doubts, p. 282. 103  “Logical Reasoning,” Syntheses 60 (1984): 107. 104  Without finding it necessary to resort, as does Harman, to psychologism as an explanatory principle. See Bosanquet, Logic, vol. I, pp. 81-84 and vol. II, pp. 4-5. 105  Change in View, p. 6.

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reasoning, i.e., reasoning understood as “a procedure for revising one’s beliefs, for changing one’s view”: Should we think of logic as a science like physics and chemistry, but more abstract and with a wider application? Or should we think of logic as having a special role in reasoning, a role that is not simply a consequence of its wider application? This is a difficult issue and I for one am unsure how to resolve it.106

These questions notwithstanding, Harman considers inference a cardinal epistemological phenomenon: “Inference, conceived in the most general way, is a process that modifies the way we represent the world.”107 But he resists so much as entertaining the idea that one might define inference by recourse to inductive rules or arguments or logic, when “the principles of induction are not even known.”108 Accordingly, for Harman, what I end up with upon concluding a coherent argument—one that involves thinking through the principles of implication that compose inferential reasoning—is not a proof that establishes anything, but rather a “reasoned change in view.”109 Harman here makes a dialectical move—to the visionary—over against the predicational, relative positing. But as with Carnap, the strategy leads only to a heteronomy. This is perhaps inevitable in light of Harman’s failure to consider the systematic ontological entailments of either “view” or “change” as these relate to his “change in view” thesis. Limitations of this sort reflect a philosophically otiose practice chargeable to analytic epistemologists, particularly philosophers of mind such as Harman, a practice recently censured by one of their own in a previously cited remark: “it’s been the tradition in analytic philosophy to play ontologically fast and loose with the mental whenever it seems convenient to do so.”110 In any case, what distinguishes Harman’s approach is his repudiation of predicational accounts—i.e., views that conceive of inference as essentially the principled act or the route of reflection whereby I think 106  Ibid., p. 6. 107  Ibid., pp. 34-35. 108  Ibid., p. 19. 109  Ibid., p. 3. 110  Jerry Fodor, “What is Universally Quantified and Necessary and A Posteriori and It Flies South in the Winter?”, p. 13. See above, p. 64.

94 Inference and the metaphysic of reason that some S is P. Harman, by contrast, proposes a meta-cognitional strategy: I suggest that the only way we can discover what [the] principles [of inference] are is to discover what principles account for the inferences we actually make. Similarly, the only way to discover when a person makes inferences is to discover what assumptions about inference are needed to account for his knowledge….111

As Michael Williams observes, Harman recognizes a crucial point, namely “what may be inferred from what is never determined by logical relations alone.”112 But where to search for the requisite “assumptions about inference”? Like Carnap, Harman fails to bring to bear the sorts of speculative resources requisite even to detect, let alone ground, “the process that modifies the way we represent the world,” in any dialectical intermediation of (predicational) relative positing with existential positing (absolute Position). And as with Carnap, Harman too has recourse to a conceptually adventitious, discursively circular expedient—in this case invoking, as he confesses, “a kind of psychologism: the valid principles of inference are those principles in accordance with which the mind works.”113 But this simply won’t do. How could this very inference to psychologism—not to mention the counter-inference that this appeal entails a vicious circularity—not be some “principle” in accordance with which the mind works? The ontoepistemological status of such “principles”—how they bear on the fact that knowing is of being—this core philosophical issue Harman leaves unresolved. 2.4 Robert Brandom. By contrast with Carnap and Harman, Robert Brandom does not invoke an extra-discursive moment—intuition, principles of mind—in order to ground his approach in a Real that sponsors and that (as Hegel saw) reflectively comes to be, as truth, in 111  Thought, p. 20. 112  Unnatural Doubts, p. 282. 113  Thought, p.18. One finds Harman applying this dubious, or at least insufficiently developed, principle when he stipulates that while logical rules “are universally valid,” they “are not exceptionless universally valid rules of inference”; see Harman, “The Logic of Ordinary Language,” in Common Sense, Reasoning, and Rationality, ed. Renee Elio (Oxford: Oxford University Press, 2002), pp. 93-103.

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the discursive acts of inferential ideation. Still, Carnap and Harman recognize and respond, if only indirectly and problematically, to the ontological factor that points beyond the post-Kantian epistemological hegemony to the reality of the act of inference as the knowing of being. Brandom’s neo-pragmatic inferentialism, however, takes doing as an ultimate explanatory ground. His approach reflects a focus on normatively determined “commitments” and “entitlements” of semantic norms “implicitly acknowledged by those who participate in assertional practice.”114 Brandom develops a view that delineates and generalizes the idea of inference in light of issues and formulations that do not typically play large in the debates, such as we’ve sampled, over its deductive or inductive character. According to Brandom, No beliefs, judgments, reports, or claims—in general, no applications of concepts—are noninferential in the sense that their content can be understood apart from their role in reasoning as potential premises and conclusions of inferences. Any response that does not at least have an inferential significance—which cannot, for instance, serve as a premise in reasoning to further conclusions— is cognitively idle: a wheel on which nothing else turns….Awareness that reaches beyond mere differential responsiveness—that is, awareness in the sense that bears on cognition—is an essentially inferentially articulated affair.115

So far as they go, these general contentions seem true enough, although one could question whether they don’t uncritically conflate that which is significant for inference with the act, the articulation, of inference. To refer, moreover, to “concepts” either as discrete from their “content” or from the “role” that such content putatively plays in inferential reflection is tacitly to trade on an order of abstraction that orients a speculative line of thinking in view of which one essentializes analytic features of conceptualization in ways that factor out its metaepistemological significance. Brandom subscribes to what he terms “strong inferentialism,” by which he means, “inferential articulation broadly conceived is sufficient 114  Articulating Reasons (Cambridge, Mass.: Harvard University Press, 2000), pp. 196-97. 115  “Overcoming a Dualism of Concepts and Causes: The Basic Argument of ‘Empiricism and the Philosophy of Mind,’” The Blackwell Guide to Metaphysics, ed. Richard M. Gale (Oxford: Blackwell, 2002), p. 268.

96 Inference and the metaphysic of reason to account for conceptual content.”116 Concepts, something Brandom identifies “broadly” as “inferential norms,”117 are what “govern” the practices, for Brandom socio-linguistic practices, that generate rules establishing the “propriety” of both the premises and conclusions of inferences. Here we see what critics have identified as Brandom’s practice of conflating semantics and epistemology.118 While of interest as an anthropology or sociology of inference, Brandom’s doctrine, for all its complexity and synthetic virtuosity, does not address the ineludible elements of the metaphysics of meaning. Brandom’s philosophy of inference exploits the notions of speech acts, their “proprieties,” and “the rules for the asserting game, or the norms implicitly acknowledged by those who participate in assertional practice”—the latter being Brandom’s “pragmatic norms” directly off of which we read “semantic norms” that give meaning to inferences. Yet these notions express facts (i.e., are real in virtue of conceptualizing facts) that outrun our very ability to interpret meaning, establish norms, and determine “representational correctness.” And it is the “proprieties” of discourse per se, vis-à-vis the meta-discursive, metapragmatic realities of fact—i.e., the metaphysic of what is properly inferential—that calls for systematic treatment in this connection. Contrasting sharply with the onto-epistemological orientation to inference, Brandom’s inferentialism is beholden to the analytic semantic theory of language and to neo-pragmatism in ways that ground his detailed explication in what Kant understood as relative positing. This is clear in Brandom’s idea that as a matter of concept formation, inference is an expressive form of normative—for him, socio-linguistically relative—discursive practices. These practices are structured by the “game of giving and asking for reasons.” 119 As the foregoing 116  Ibid., p. 28. 117  “Reason, Experience, and the Philosophical Enterprise,” paper read at NEH Institute, St. Louis, Mo., June 1998, p. 15. 118  For sharp critiques of this practice, see Tom Rockmore, “On Semantics and Epistemology,” Hegel, Idealism, and Analytic Philosophy, pp. 133-38; also see Jerry Fodor and Ernie Lapore, “Brandom Beleaguered,” Philosophy and Phenomenological Research 74.3 (2007): 677-91. 119  Cf., “…the capacity to use concepts…is parasitic on the prosaic inferential practices in virtue of which we are entitled to see concepts as in play in the first place. The game of giving and asking for reasons is not just one game among others one can play with language. It is the game in virtue of

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observations suggest, Brandom considers the play, variously implicit and explicit, of linguistic meaning in the socio-historical pragmatics of discourse to be epistemologically orientational. Consequently, he reads “semantics and the understanding of rationality as two sides of the same coin.”120 What “can be offered as, and itself stand in need of, reasons”121—what serves, in other words, as the basis for understanding rationality—is, argues Brandom, “whatever can serve both as a premise and as a conclusion in inference.”122 On this basis, he construes semantic relations as, “to begin with,” inferential in the sense of constituting practices “of making claims that can serve as reasons for others, and for which reasons can be demanded, without using any specifically representational vocabulary. That is what,” concludes Brandom, “the model of discursive practice as keeping score on commitments and entitlements does.” 123 Unlike Carnap and Harman, Brandom is self-consistent in refraining from any appeal to an extra-discursive moment in his explication of inferential thinking. He makes a seamless transition from linguistic to practical actualities via an appeal to social norms, which he justifies as follows: We typically think about inference solely in terms of the relation between premise and conclusion, that is, as a monological relation among propositional contents. Discursive practice, the giving and asking for reasons, however, involves both intercontent and interpersonal relations. The claim is that the representational aspect of the propositional contents that play the inferential roles of premise and conclusion should be understood in terms of the social or dialogical dimension of communicating reasons, of assessing the significance of reasons offered by others.124

The “we” to whom Brandom refers in the first line of his statement would exclude those many philosophers of inference—including Harman, and arguably the late Carnap—who do not tend to think of which what one has qualifies as language (or thought) at all”; see “Overcoming a Dualism,” p. 13. 120  Articulating Reasons, p. 160, emphasis added. 121  Ibid., p. 165. 122  Ibid. 123  Ibid., p. 166. 124  Ibid., p. 166.

98 Inference and the metaphysic of reason inference solely in narrowly formalistic terms, whether of traditional syllogistic logic or of mathematicized symbolic logic. And while the relation between premise and conclusion marks the itinerary of inferential reflection in the onto-epistemological account that I shall outline in chapter 4, the conceptual logic of that relation would be an empty abstraction if one were to conceive it as exclusive of more originary considerations that are incompatible with the idea of “monological” relation. (Three such considerations come in for detailed scrutiny in chapter 4: the notion of inference as act, the onto-epistemological dimension of positing premises, and the character of the ground, the Sufficient Reason, of the act.) The radical limitations of Brandom’s influential if controversial thinking on inference become evident when one factors in the nonnormative ineliminable absolute aspects of inferential cognition. Brandom skirts round the ontological issue, the issue of absolute positing (Position), inherent in the act of inference. He focuses alternatively on context of use and on orders of propositional “correctnesses.” The context of use marks the pragmatic thrust of Brandom’s doctrine, which he details with much talk of “commitment…to the propriety of the inference from the circumstances to the consequences of application.”125 (In a recent footnote, Brandom identifies two frames of reference from the standpoint of which he declares it to be “an essential move to replace the undifferentiated notion of propriety with the more articulated distinction of two flavors [sic] of deontic status: commitment and entitlement.”126) Propositional correctness has to do with propositional structure— inferentialism for Brandom is, after all, “an essentially propositional 125  Ibid., pp. 28-29. For an analytic linguistic challenge to applying the idea of “commitment” to a normative semantics of inference, see Jerry Fodor and Ernie Lapore, “Brandom Beleaguered,” p. 684. 126  Brandom states that the first of the two frames of reference obtains when one extends (inferentially?) the “inferential approach” to “material inferential and incompatibility relations”—which for Brandom is to take inference “beyond its paradigmatic application to logical concepts.” The second context applies when one essays to account for “the inferential relations linking circumstances and consequences of application, even where these are noninferential circumstances or consequences”; see “Inferentialism and Some of Its Challenges,” Philosophy and Phenomenological Research 74.3 (2007), p. 658.

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doctrine.”127 The articulation of propositional structure purportedly reveals inference to be “primary in the order of explanation.”128 Brandom employs this last (classically resonant) locution to signal what he understands as a “top-down order of semantic explanation” that gives “pride of place to propositional contents.” But he regards an inferential explanation as a claim, which, in his words, “is to purport to state a fact” (emphasis added). Facts as “stated by true claimings,” i.e., inferences, “must be about objects” and “states of affairs.” These references to “fact” necessarily invoke the ontological order and with it, to use Brandom’s own language, the “commitment…to the propriety of [Brandom’s] inference from the circumstances to the consequences of application.” Thus when he declares that inference is “primary in the order of explanation” Brandom effectively brings into play not only the structure of explanation but also, if implicitly, the supervening order—the order of Being—that discloses the actuality (Wirklichkeit) of the meaning, and hence the philosophical (factual) cogency, of construing inference in terms of semantics and the socio-linguistic practices that express its “aboutnesses.” Upon encountering Brandom’s reference to “the order of explanation” philosophers such as Oliva Blanchette, who are attuned to the most enduring and penetrating ontological insights that distinguish the philosophical legacy of the Aristotelian and Thomist traditions, might well miss in Brandom’s talk of “the order of explanation” what is to be explained.129 Tellingly enough, however, it is not a systematic metaphysician like Blanchette, but dyed-in-the-wool analysts—Jerry Fodor and Ernie Lepore, for example—who have most persistently challenged the cogency of Brandom’s detailed claims and formulations on precisely this count.130 Brandom’s move to explain inference by invoking propositional structure (as opposed to positional order, such as the early Carnap 127  Articulating Reasons , p. 13. 128  Ibid., pp. 39-40. 129  Blanchette, personal communication. This telling omission betrays, from the perspective of systematic metaphysical thinking, the onto-epistemological Achilles heel of Brandom’s approach to inference as a philosophical problematic. Indeed, it betokens in principle the same systematic shortcoming in philosophical logic that thinkers from Bosanquet to Brand Blanshard to Errol Harris have criticized in analytic epistemologies from Russell through Quine. 130  Cf., “Inferentialism and Some of Its Challenges,” pp. 679-81.

100 Inference and the metaphysic of reason identifies with the notion of Ordnungssetzung) involves a fallacy of ontological inversion, in that it prioritizes propositional over existential—relative over absolute—Position. That Brandom’s thinking incorporates this fallacy, and by that token reduces being to being predicated, becomes manifest when he declares that his “inferential pragmatism is committed to a top-down order of semantic explanation.”131 The “top” for Brandom, that to which he accords “pride of place” are nothing other than “propositional contents.” On what grounds the predicative framing of “contents” earns its “pride of place” remains unexplained. It would appear, however, that the content served up by propositions, something intrinsically normative, is what for Brandom corresponds to the absolute Position, to unmediated being—i.e., to the essential and implicitly posited dimension of every particular proposition in a given domain (the critical Kant’s unconditioned ground of the conditioned). As distinguished from Carnap and Harman, Brandom expressly identifies himself with the Kantian tradition. While in certain respects this self-ascription may be uncontroversial, it does not obtain in the present connection132 for the reasons that Brandom intimates. Consider, for instance, his appeal to Kant’s authority in licensing the propositional cast of his semantic approach to inference: One of Kant’s epoch-making insights, confirmed and secured for us also by Frege and Wittgenstein, is his recognition of the primacy of the propositional….One of his cardinal innovations is the claim that the fundamental unit of awareness or cognition, the minimum graspable, is the judgment. Judgments are fundamental, since they are the minimal unit one can take responsibility for on the cognitive side, just as actions are the corresponding unit of responsibility on the practical side.133

What first strikes one in this passage is the issue of how to construe taking responsibility, on the cognitive side, for, say, a reflective (indeterminate) judgment. “The ‘emptiest of all representations,’” asserts Brandom (quoting Kant), “the ‘ “I think” that can accompany all representations’ 131  Articulating Reasons, p. 40. Jerry Fodor and Ernie Lapore sharply challenge Brandom’s top-down, bottom-up ordering; see “Brandom Beleaguered.” 132  In view, that is, of Kant’s classification of absolute and relative Position. 133  Articulating Reasons, pp. 159-60.

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expresses the formal dimension of responsibility for judgments.”134 One might question this contention in the case of reflective judgment, since in a reflective judgment the “I think” may be a representation that “by itself stimulates thinking so much that it can never be grasped in a determinate concept [einem bestimmten Begriff].”135 Exclusive of concepts determinate in nature, Brandom’s claim that “responsibility” is the criterion that charters the ground of judgment is itself a concept lacking rational determination—however ostensibly regulative he finds it for his own speculative purposes. Discounting this issue, even to consider Brandom’s inferentialism as no more than a point of reference for developing a systematic philosophy of inference presents difficulties. Perhaps most egregious from an onto-epistemological perspective is the absence of an ontological context of signification (something seen as well in Brandom’s construal of Hegel’s Logic136)—and this notwithstanding repeated references to pragmatic epistemological “commitments” that would presumably accord an existential warrant to the idiosyncratically invoked ethical concept of “responsibility.”137 Brandom’s socio-linguistic treatment of inference in the pragmatic register stands at a normative practical remove from the (conceptual) domain of analysis proper to the

134  Ibid., p. 160. 135  See The Critique of the Power of Judgment, trans. Paul Guyer and Eric Matthews (Cambridge, Engl.: Cambridge University Press, 2000), §49. 136  Stephen Houlgate has penetratingly criticized Brandom’s tendentious reading out the rational, metaphysical ontology of Hegel’s logic; see, “Hegel and Brandom on Norms, Concepts, and Logical Categories,” conference paper (read at Boston College, Chestnut Hill, Mass., March 2007). RolfPeter Horstmann argues that Hegel would have charged “the neo-pragmatic interpretation with misunderstanding his own philosophical project, for this interpretation conflates the process that describes the discovery of the ‘true’ categorical structure of reality through knowing and acting subjects in different historical contexts (for Hegel the phenomenological process, which certainly refers to specific social and historical phenomena) with the process that takes the constitution of this ‘true’ categorial structure as its specific object, with what one could call the ‘logical process’” (“Substance, Subject, and Infinity,” in Hegel: New Directions, p. 83). 137  Cf., for example, Making It Explicit (Cambridge, Mass.: Harvard University Press, 1994), pp.17 and 172-73.

102 Inference and the metaphysic of reason onto-epistemology of inferential reflection.138 He thus does not engage to articulate a conceptual logic ordered to the actualities of how, when I infer, I reflectively invest otherwise remote facts with an ideal character,139 namely by way of Position, whereby I “put” (setzen) significant facts to thought in the originary meaning-currency of “scientific” rationality that motivates commitment and informs justification and inspires belief. Simply stated, just as one cannot properly explain the reason of the act of inference by appeal to a priori patterns of deduction, so one cannot rightly reduce it to an account of cognitional “commitments” and mental states like “belief,” however consistent, normative, or socially sanctioned they may be. 2.5 Michael Williams. A scholar with acknowledged debts to Carnap, Harman, and Brandom, Michael Williams is a self-described “contextual” epistemologist who incorporates elements of their thinking in his philosophy of inference. This he does, albeit far from uncritically, in two chapters of his book on Problems of Knowledge (2001)140—a work puffed as a “masterly introduction to epistemology and an original contribution.”141 Although not as original as those of the three inferentialists considered in the preceding sections, Williams’ analysis of inference recommends itself for discussion here both for how it critically reflects the views of Carnap, Harman, and Brandom, and for its focus on “linear inference.” The concept of linear inference, beyond its intrinsic relevance in the immediate context, will reappear in chapter 3 when we investigate Bernard Bosanquet’s treatment of the topic. (Al138  As if being established by “commitments” the reason of inference were merely a matter of resolution or faith or of the ways that one might substantiate (rather than delineate) its reflective moves. Moritz Schlick approximates this same point in his explication of the “unity of consciousness,” of which the act of inference stands as the paradigmatic rational manifestation. He terms his formulation “a summary designation”: like the living act of inference, the unity of consciousness is not the sort of thing that one might substantiate as one would the discursive constructs that it sponsors. See Schlick, General Theory of Knowledge, trans. Albert E. Blumberg (La Salle, Ill.: Open Court, 1985), §17 (“The Unity of Consciousness”). 139  For more on “remote” fact, see Appendix V, below. 140  Problems of Knowledge: A Critical Introduction to Epistemology (Oxford: Oxford University Press, 2001). 141  Ernest Sosa, back cover.

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though he was no analytic epistemologist of inference,142 Bosanquet was the philosopher who initially brought the term “linear inference” to prominence in the literature.) While Problems of Knowledge treats a broad spectrum of issues that preoccupy contemporary epistemologists, Williams’ text concentrates upon—and by the author’s lights defeats—“radical” holism, coherence theory, and the use to which philosophers have put the distinction between linear and non-linear modes of inference. Given this trio of themes, the historically informed student of inference might initially suppose that Williams aimed to reestablish, at the outset of the twenty-first century, a serious critical engagement with the holistic approaches to the subject, which were originally formulated by such systematic thinkers as F. H. Bradley and Bosanquet. Williams, however, soon disabuses one of any such expectation. He is silent on Bosanquet and merely alludes to Bradley in a brief note.143 Williams’ first move is to contrast the holism of coherence theories with the discredited atomism of “foundationalist theories of justification.”144 He then argues that systematic coherentists (such as Bradley) are radically holistic and are thus themselves hopelessly foundationalist. In the orientation to inference that Williams himself champions, the operative epistemological assumption that first becomes apparent is that one can simply identify the idealists’ “coherentist approach to knowledge (and truth)” with a “coherence” understood as a theory of justification. To be “justified,” insists Williams, “a belief must fit into a justified system,” a system that is itself com142  Bosanquet explicitly repudiated any move to identify his philosophical logic, particularly his doctrine of inference, as epistemological. Cf., Logic, vol. II, p. 271, where he criticizes Dewey’s assertion (made with Bosanquet in mind) that “logic is supposed to grow out of the epistemological problem” of knowledge. Also see the Appendix of his published 1913 University of Manchester Adamson Lecture, The Distinction between Mind and Its Objects (1913. Bristol, Engl.: Thoemmes Press, 1990), pp. 51-60. 143  Cf., Problems of Knowledge, p. 126 n. 1. Such summary dismissal of idealist thinking on this subject only reinforces the impression of epistemological parochialism that Williams’ analysis conveys. Cf., for example H. H. Joachim’s influential critique of coherentism in The Nature of Truth (Oxford: Oxford University Press, 1906) and Bosanquet’s onto-epistemological refutation of Joachim’s charges, in the 1911 edition of his Logic (vol. II, pp. 288-92). 144  Ibid., p. 117 (emphasis added).

104 Inference and the metaphysic of reason posed of “suitable supporting beliefs.”145 Williams makes the case for this claim most explicitly in relation to his notion of “epistemic significance.” Epistemic significance is the cognitional purchase of the mental state of “belief ”—“belief ” apparently constituting, to Williams’ way of thinking, the primitive intentional mood of any system of thought. “Coherence” is the title of the first of the two chapters in Problems of Knowledge that concentrate on matters directly of concern here. Williams considers the concept of coherence principally from the angle of his mental-state epistemology of inference. It is from this epistemological reference point that he treats inferential cognition as, in the first instance, an issue of normatively attuned beliefs in conjunction with their correlative epistemic commitments. Williams’ talk of “commitment” echoes Brandom’s terminology, something particularly evident where Williams adduces the idea in representing deductive inference as something that occurs “in contexts in which certain commitments are so firmly set that we may justifiably add their perceived consequences to our stock of beliefs.”146 The social psychologism implicit in Brandom’s doctrine in this connection is apparent in Williams as well. “The Myth of the System,” the second of Williams’ chapters that is relevant here, finds him rejecting as foundationalist the coherentist, “‘non-linear’ conception of justifying inference.” Bradley, who rates no more than passing reference in a note,147 serves as Williams’ representative British idealist and stands charged with propounding the previously mentioned “coherentist approach to knowledge (and truth).”148 145  Ibid., p. 117-18 (emphasis added). 146  Problems of Knowledge, p. 216. See Articulating Reasons: An Introduction to Inferentialism (Cambridge, Mass.: Harvard University Press, 2000) p. 40, and §2.4, above. 147  Bradley’s name does not appear in Williams’ index. What’s more, Williams pairs it, idiosyncratically enough, with the younger, American idealist Brand Blanshard rather than with Bosanquet, the British originator of the term “linear inference” understood as a defining architectonic of the philosophical logic of inference. 148  Problems of Knowledge, p. 126 n. 1. The single entry on Bradley in Williams’ bibliography is the classic Essays on Truth and Reality (Oxford: Oxford University Press, 1914). This text contains nothing approaching the definitive, twenty-four page statement on inference that Bradley appended as a “terminal” essay to the 1922 edition of his Logic. Williams’ use of labels as a way of clearing ground for his analytic epistemology puts one in mind of Schelling’s mordant response to what he perceived as a similar practice

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Williams rejects what he describes as “radical” holism and the “myth of the system.” Further, he dismisses the very notion of distinguishing linear from non-linear models of inference. Censuring “radical” holism, system, and the value of discriminating linear from non-linear inference, Williams marshals arguments that find their ultimate justification in his mental-state epistemology of “belief-systems.” A belief system is not, he stresses, synonymous with the “total view” or “system of beliefs” that Harman thematized over two-decades earlier.149 Williams regards his own epistemology as contextualist in a way that is, to his mind, self-critical, practical, and empirically sensitive. More specifically, he champions an “anti-atomist” contextualism, which “insists that justification always presupposes a critical epistemic mass of contextually relevant beliefs,” rather than any holistic system (some mere “pseudo-totality”) to which coherence theorists subscribe.150 Resorting to the derivatively quantitative notion of a “critical epistemic mass,” Williams implicitly reads the “critical mass” in question as existential, i.e., conceptually on a par with the concept of being in general. He thus asserts a chartering principle or order, an absolute positing (in the Kantian sense that we’ve discussed) that grounds his own speculative inference, relative to which he refers the act of justification. A systematic philosopher of logic such as Bosanquet would flag as a speculative dodge Williams’ appeal to an ontologically anomalous “critical epistemic mass.” So far as the metaphor has a literal extension, one might well object that it refers to what is in effect a pseudo-systematic totality or principle of emergence, one predicated upon an unacknowledged metaphysical law having to do with the fact that masses become “critical.” This implicit totality is supposed to impart epistemic warrant to the implications of related beliefs when one undertakes to inquire into or to justify something as a source of knowledge. in Friedrich Schlegel: “Once one finds the right label for a system, the rest follows of its own accord, and one is spared the trouble of investigating its peculiarities with any greater precision”; see “Philosophical Investigations into the Essence of Human Freedom and Related Matters,” trans. Priscilla Haydon-Roy, Philosophy of German Idealism, ed. Ernst Behler (New York: Continuum, 1987), p. 221. 149  See Harman’s Thought, pp.161ff; and §2.3, above. 150  Problems of Knowledge, p. 167 (Williams’ emphasis); see also p. 35. For Williams’ correlative notion of “critical semantic mass,” see ibid., pp. 110, 142, 178.

106 Inference and the metaphysic of reason The nature of Williams’ grounding epistemological context is that of justified practical and conceptual commitments that he associates with belief systems whose constitutive relations refer reflexively to socio-cultural and historical worlds of norms. These worlds of norms compose each belief system’s context of epistemic signification. Right off, one observes that Williams’ modus operandi is sharply at variance with an onto-epistemological orientation. Bosanquet would likely have sized up Williams’ doctrine as a neo-pragmatic151 species of radical empiricism.152 For Bosanquet, the detail of whose inference theory we shall probe in chapter 3, “No history of opinion…no idiosyncrasies of mental organization, can come into court when the question of truth is raised.” His “one criterion of truth” does have a concretely epistemological cast, being “a fuller systematic cognition of the content of whose truth is in question.” Ironically, this is manifestly consistent with Williams’ attack on the idea of Truth, with a capital T. But there is a decisive difference, which involves the content or reality that one examines for its truth. In the world as Bosanquet the idealist envisions it, “reality…becomes truth when it takes ideal form” (emphasis added). Williams’ epistemology would have struck Bosanquet as perpetuating the “upside down” thinking that truth “depends on representing some151  Robert Brandom, John McDowell, and Wilfrid Sellars are among the leading neo-pragmatic protagonists of Williams’ philosophical milieu. 152  William James, recall, defined “empiricism” as placing “the explanatory stress upon the part, the element, the individual, and treats the whole [not as prior to parts in the order of logic, but rather] as a collection and the universal an abstraction.” He distinguished from Humean empiricism his own philosophical worldview as radical empiricism, for which “the relations that connect [individual] experiences must themselves be accounted as ‘real’ as anything else in the system”; see Essays in Radical Empiricism (New York: Dutton, 1971), pp. 24-25. For Williams, the relations are not ideal but social, normative, practical, historical—in short empirical, but indexed cognitionally to mind-states, i.e., epistemically significant beliefs and commitments. What James alludes to as the grounding experiences are apparent in Williams’ reference to “the phenomenology of everyday epistemic practices” that his contextualism “stays close to.” In a neo-pragmatic move (one, to be sure, that even a Bosanquet would accorded qualified assent), Williams repudiates an “epistemological realism” that subscribes to “generic sources of knowledge and of a fixed order of reasons” (Problems of Knowledge, pp. 254-55).

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thing outside it”153—something like a belief, a commitment, a justification, a linguistic or social norm. Another fundamental difference is that Williams links to normatively ordered belief systems any such “fuller” knowledge as he is willing to admit. This he does instead of associating the fuller knowledge with anything like an idealist system,154 the logical rationality of which derives its warrant from the correlative “fact that fuller cognition can compel every false judgment to expose itself as flat self-contradiction.”155 Turning to what Williams has to say about linear inference, one shifts to concerns that if important in Bosanquet’s thought are equally pertinent to the inferentialism of recent analytic epistemologists, Gilbert Harman in particular. It is to Harman’s views that Williams refers in his treatment of linear and non-linear inference. Harman, as we’ve seen, denies that deductive arguments involve inferential reasoning at all, since they merely call on one to trace some given rules of entailment.156 He opts, in effect, to isolate implication from the act of inference—proposing, as we noted, a dubious heteronymous doctrine that speaks to incompatible empirical and epistemological elements of his analytic orientation. Harman thus argues, on the one hand, for conceiving inferential reasoning as inductive thinking impelled by the goal of developing the “best explanation” of its data consistent with the most coherent total view of the world. On the other hand, he explains inferential thinking epistemologically by appealing to some unnamed grounding principles “in accordance with which the mind works.”157 Critical of Harman in other respects, Williams accepts Harman’s contention that any distinction between linear and non-linear inference is moot. Williams is consequently open to the same criticisms 153  Implication and Linear Inference, p. 148 n. 154  Such as Bosanquet’s, the cogency of which inheres in a metaphysical “systematic necessity of [non-contradictory] knowledge.” This reflects a position that Bosanquet states in one of his Gifford lectures: “thought has always the nature of a system of connected members, and is an effort to take that form, which we may call a ‘world’….[this alone] can satisfy the logical law that contradiction is a mark of unreality, or—the same law—that the truth or the real is ‘the whole’”; see The Principle of Individuality and Value, Lecture II (“The ‘Concrete Universal’”). 155  Bosanquet, Logic, vol. II, p. 247. 156  See §2.3, above. 157  Thought (Princeton: Princeton University Press, 1973), p. 18.

108 Inference and the metaphysic of reason as is Harman on this issue. According to the latter, there is no “such a thing as genuinely linear inference,” since, whether linear (as in formal deductive argument) or not, “nothing in logic tells us which rules to apply in particular circumstances.”158 A systematic philosophical logician such as Bosanquet would fault Harman’s sweeping assertion, not to mention Williams’ concurrence with it. Harman’s declaration would have struck Bosanquet as symptomatic of a covert metaphysical dualism irresolvable on purely epistemological grounds. Bosanquet might well have pressed Harman and Williams to explain how one can intelligibly speak of drawing “a conclusion from a mere and pure supposition” like an abstract logical rule. Logical rules are always given, whether tacitly or explicitly, with reference to a “partial system… as continuous with the real universe.”159 Absent this inexpugnable relational moment of logic, “you do not even know that reality is noncontradictory itself.”160 Logic thus always entails a real, an existential context, one that provides cues for practical judgment. This it does even as it substantiates its authority, on onto-epistemological grounds, as the formative instrument of rational thought. Sentential logic, for example, is ordered to a syntactic “complex” with which the logician operates as referring to a systematic reality that includes natural languages, such that familiarity with the logical syntax equips one to apply, as “marks” of reality (Merkmale), logical rules for symbolizing, in the logical code, sentences in natural languages. This objection notwithstanding, Bosanquet would certainly have agreed with Williams that deduction per se is something different from “the linear ideal of inference.” He himself identified it with “a series of terms connected by successive statements of conjunction [e.g., the sorites], called a chain of reasoning.”161 (The “true deduction” is 158  Problems of Knowledge, p. 130-31. Harman’s criticism speaks only to theories of inference that fail to account for the reason of the act—theories that, in the Kantian speculative idiom, fail to credit the “unity of rules” which alone can render intelligible the act of discursive reflection. I shall argue that the requisite unity is a matter of sufficient reason construed as a function of formal cause, and that this is what characterizes the reason of the act of inference. See §4.3, below. 159  Implication and Linear Inference, p. 5. 160  Ibid. 161  Moreover, Bosanquet held it “a mistake to apply the name of deduction to syllogism” (Implication and Linear Inference, p. 22). For a recent, ana-

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something that Bosanquet understood as thinking “which passes, for example, from the law of gravitation to particularization of the movement of the moon,” and as such, is “obviously a very different thing from a chain of reasoning of the type of the Sorites, which can never particularize its predicate.”162) 2.6.1 Bernard Lonergan: the metaphysician as analytic epistemologist of inference. A neo-Thomist with a Kantian epistemological bias,163 Bernard Lonergan is a preeminent, if controversial expositor of transcendental Thomism. Lonergan’s thinking effectively transects modern scientific rationalism and traditional metaphysics. His keynote inquiry into human understanding, Insight, is a massive systematic work that he presents as an organon of “insight into insight.” The modernist strain in Insight takes the form of its concessions to a derivatively Cartesian epistemological scientism, from the standpoint of which all philosophical roads lead ultimately to an act: “one’s own rational self-consciousness clearly and distinctly taking possession of itself as a rational self-consciousness.”164 Notwithstanding his commitment to lytically keyed comparative evaluation of Bosanquet’s doctrine of scientific inference, see Fred Wilson, “Bosanquet on the Ontology of Logic and the Method of Scientific Inquiry,” in Bernard Bosanquet and the Legacy of British Idealism, ed., William Sweet (Toronto: University of Toronto Press, 2007, pp. 267-95. 162  Implication and Linear Inference, p. 22. 163  Cf., Insight: A Study of Human Understanding (San Francisco: Harper, 1958), where Lonergan explains his reason for taking an epistemological approach to metaphysics. His aim is to advance “from a mere broad agreement in [Scholastic] metaphysics and epistemology to a precise and detailed agreement in both,” and this by attempting “to reach a fresh and fuller view of the relevant facts.” I take with utmost seriousness Lonergan’s explicit reservation about being “far from certain” that in carrying out this project by adopting a neo-Kantian epistemological frame of reference he has done so from “a correct perspective” (p. xxvii). 164  Insight, p. xviii. This replicates, at the level of self-consciousness (i.e., that of insight into insight), the act of insight simpliciter. In his first chapter, Lonergan describes the latter in terms of an instance of inferring the definition of a perfect circle from posited images of radii topped by a curve: “the insight is the act of catching on to a connection between imagined equal radii and, on the other hand, a curve that is bound to look perfectly round” (Ibid., p. 9, emphasis added).

110 Inference and the metaphysic of reason traditional metaphysics, then, Lonergan is a modern rationalist. And he promulgates a doctrine of formal inference that, if distinctive in being integrated within a meticulously articulated philosophical system, is nonetheless preponderantly epistemological, like those of Carnap, Harman, Brandom, and Williams. As such, Lonergan’s views on formal inference are deeply consistent with that of other contemporary analysts,165 and this despite the diverse character of their explanatory reasoning. What makes Lonergan of special interest here is that unlike other analytic epistemologists of inference, he incisively probes at various junctures the onto-epistemological dimension of inferential thinking—albeit not as part of his positive account of inference. One sees a salient instance of this when Lonergan censures Kant’s “failure to find the virtually unconditioned as constitutive of judgment and thereby to reach the universe of being.”166 If such a claim rightly applies only to cognitive judgment,167 Lonergan’s assertion nevertheless anticipates, and indeed substantiates, my own proposal to move beyond Kant in order to trace the onto-epistemology of the act of inference.168 Consistent with his claim, Lonergan maintains that as a form of judgment inference, at least deductive inference, “presupposes other [non-inferential]

165  His concern, for instance, with the “laws” of deductive inference is a case in point; see Insight, II.3. 166  Ibid., p. 482. For sympathetic readings of Kant on this score, see Karl Ameriks, Kant and the Historical Turn (Oxford: Oxford University Press, 2006), pp. 139-40; and Henry Allison, Kant’s Transcendental Idealism, pp. 311ff. 167  The synthetic aspect of (determinate) cognitive judgments merely adds concept to concept. Whereas, by contrast, reflective, aesthetic judgments involve syntheses that “go beyond the concept and even the intuition of the object,” syntheses that disclose things about one’s subjective state of mind vis-à-vis the form of what one apprehends (this taking place, after all, under the dispensation of the unity of one’s apperception). Crucially, aesthetically apprehended form is not a function of the reproductive imagination, but rather a conductive moment of something “virtually unconditioned.” See Kant’s “Analytic of the Beautiful,” in The Critique of the Power of Judgment; and Rudolf A. Makkreel, Imagination and Interpretation in Kant (Chicago: University of Chicago Press, 1990). 168  See §4.1, below.

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judgments to be true,” and that “the function…of the form of deductive inference is to exhibit a conclusion as virtually unconditioned.”169 The foregoing observation suggests that Lonergan recognizes the limits of Kant’s thinking for explaining or even orienting oneself to the onto-epistemology of inference. Lonergan is most illumining in this particular when he repudiates the notion of restricting “reason and its ideal” to “the dubious and merely supervisory” regulative (rather than constitutive) role that Kant assigns them in rational judgment.170 Yet for all that, Lonergan nonetheless operates largely in terms of Kantian speculative points of reference, even where his (Lonergan’s) thinking most closely approximates the non-Kantian conceptual logic of the onto-epistemology of inference.171 This is clear in Lonergan’s discussion of the “virtually unconditioned” prospective judgment172 (evidence for which one putatively grasps by way of “insight”). Beyond crediting the onto-epistemological aspect of the act of inference, Lonergan also underscores its disclosive aspects when he declares that acts of knowing “denote what is known in as much as one affirms.”173 It is evident, moreover, that Lonergan is alive to the pre-predicative, indeterminate (unbestimmt) moment of absolute Position that grounds what one might call this “revelatory” (aletheic) aspect of inference: “Once one has accepted definitions and postulates, deduction makes manifest the unconditioned that is to be grasped reflectively.”174 3 Despite significant affinities, two correlative facets of Lonergan’s thought strikingly display its distinction from the alternative currents 169  Insight, p. 281. 170  Ibid., p. 341. 171  This is a logic articulated in the essentialist (wesentlich) Hegelian terms that open up the onto-epistemological heart of the idea of “reflection.” It is a speculative route that Kant approaches only from the angle of judgment that is aesthetic rather than scientifically rational. See §4.5.2, below. 172  Insight, pp. 280-81. 173  Insight, p. 486. Like denying, agreeing, disagreeing, assenting and dissenting, the act of affirming is, for Lonergan, a mode of judging; and judgments (which may “contain” propositions) are “the final products of cognitional process” wherein, at some postulated primitive cognitional level, “the link between conditioned and conditions” exists “in a more rudimentary state” (p. 281; cf., p. 271). 174  Ibid., p. 484.

112 Inference and the metaphysic of reason of analytic epistemology that we’ve touched upon in Carnap, Harman, Brandom, and Williams. These are 1) the subjectively introspective (transcendental) posture of Lonergan’s speculative modus operandi175 and 2) the individualist character of his epistemology. 1) Lonergan’s speculative method involves expressly inviting his readers to attend to the mental acts in which they engage when they come to know anything. This appeal to subjective experience might well seem to the contemporary exponent of analytic epistemology something of a throwback if not to Descartes, then to the period of Fichte and Hegel. (Besides the famous performative strictures in Hegel’s prefaces, one recalls the precept with which Fichte, among the seminal influences on Hegel, opens his Wissenschaftslehre nova methodo: if you wish to achieve the “proper frame of mind for philosophy” you must “construct a concept of the I and observe how you accomplish this.”176) Such an expedient can appear oddly anachronistic for 1957, when Insight was published (and when Carnap was at the height of his influence). Yet Lonergan insists that he designedly employs sentences—“sentences on mathematics, on science, on common sense, on metaphysics”—whose meanings, whose “intention and significance,” one genuinely grasps only “by going…to the dynamic, cognitional structure that is exemplified in knowing them.” And he takes this structure as subtending thought at the highest level at which Insight occurs, the level at which the reader properly approaches the systematic exposition of Insight in his book—i.e., his “insight into insight.” 2) Underscoring the individualist character of his epistemology (which contrasts most radically with Brandom’s socio-pragmatic nor175  Cf. Giovanni Sala: “It is by no means a smooth-sounding slogan or a sly trick when Lonergan in his last great work [Method in Theology], for which Insight had laid the epistemological foundation, repeatedly reduced the conclusion of his intentionality analysis to the brief formulation: ‘Genuine objectivity is the fruit of authentic subjectivity. It is to be attained only by attaining authentic subjectivity’”; see Lonergan and Kant: Five Essays on Human Knowledge, trans. Joseph Spoerl, edited by Robert M. Doran (Toronto: University of Toronto Press, 1994), p. xvii. 176  Foundations of Transcendental Philosophy: (Wissenschaftslehre) nova methodo (1796/99), edited and translated by Daniel Breazeale (Ithaca: Cornell University Press, 1992), p. 110. Cf., New Essays on Fichte’s Later Jena “Wissenschaftslehre,” ed. Daniel Breazeale and Tom Rockmore (Evanston: Northwestern University Press, 2002), p. xi.

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mative epistemology), Lonergan argues that this highest cognitional plane is the locus of “the personally appropriated structure of one’s own experiencing, one’s own intelligent inquiry and insights, one’s own critical reflection and judging and deciding.”177 The individualist cast of Lonergan’s epistemological orientation thus stands from the outset in bold relief, contrasting with the more social and neo-pragmatic character of analytic epistemologies such as we saw in Brandom and in Michael Williams. (The latter, for instance, would found the authority of knowledge claims practically, on “knowledge-seeking [that] is always embedded in socially transmitted practices of inquiry.”178) Still more than either Lonergan’s introspective method or the individualist stamp of his epistemology, it is his metaphysical turn that puts Lonergan at odds with the general run of contemporary analytic epistemologies of inference. And it is just this dimension of his thinking that recommends him as a transitional figure in the present study; for, as already suggested, it exhibits phases that anticipate an ontoepistemology of inference as act—a way of grasping inference that is fundamentally at variance with those of the analysts. A prime example of a Lonerganian metaphysical assertion that foregrounds the speculative divide between himself and the analytic epistemologist is a claim, a loosely Maréchalian claim, about what the act of thinking contains. The “contents of cognitional acts,” declares Lonergan, “either refer to the known or are identical with the known, and so the dynamic structure of knowing is also the structure of proportionate being.”179 One 177  Insight, p. xviii. 178  Problems of Knowledge, p. 250. Cf.: “…by my standards Kuhn can be read as making important contributions to” what Williams identifies as “epistemology in the broader sense of ‘normatively significant philosophical reflection on issues concerning human knowledge’” (ibid., p. 243). 179  Insight, p. 486. Lonergan actually defines metaphysics “as the integral heuristic structure of proportionate being” (ibid., p. 483). By “integral heuristic structure,” he means “the anticipatory outline of what would be known by affirming a complete explanation of experience” (ibid.). And he defines “proportionate being” as “what is to be known by experience, intelligent grasp, and reasonable affirmation” (ibid.). But the attempt to arrive at “what is to be known by experience” seems problematic. This is because it, in turn, rests upon the principle of “proportionate being” in its status as the onto-epistemic dimension of what Lotze long ago described as “a universal inner connexion of all reality to that of the rest…the foundation of every attempt to arrive at knowledge by means of experience, and…not derivable

114 Inference and the metaphysic of reason would search long and hard in the writings of Carnap, Harmon, Brandom, or Williams to find anything approaching such a claim. When Lonergan identifies knowing with being, even if in structural terms, he invokes by that token a range of onto-epistemological values and implication that transcends the austerely technical focus and idiom of the Anglo-American analytic regime dominant not only when Insight appeared but also, to a great extent, half a century later. 3 I have suggested that although Lonergan is in many respects sui generis, one can view him both as an epistemologist of inference and as a philosopher who discerns and credits certain elements of the ontoepistemology of inference. Having distinguished his thinking from that of other analytic epistemologists, I wish to turn now to the principal feature of his metaphysical thinking that sets it apart from the onto-epistemology of inference traced in the present inquiry. This is his notion that the proportionate character of Being has a “structure” that is isomorphic with the “dynamic structure” of knowing. “Being,” declares Lonergan, “is proportionate or transcendent according as it lies within or without the domain of man’s outer and inner experience.”180 At first sight, Lonergan’s contention seems consistent with the view, defended in the present work, namely that the proportionality of the intelligible and the intellect is a function of how significant facts are for us. But Lonergan finds that the moment, phase, or aspect of Being, in its difference, which is proportionate to knowing (as opposed to transcendent from experience itself”; see Metaphysic in Three Books: Ontology, Cosmology, and Psychology [1879], trans. Bernard Bosanquet et al. (Oxford: Oxford University Press, 1887), p. 4, emphasis added. On another score, one might object that Lonergan’s view makes nonsense of a whole host of intentional attitudes that betoken the unknown, and that his formulation thereby empties “the dynamic structure of knowing” of most profound constitutive attunements that are the very energeia of that dynamic. As I reject the Kantian privileging of epistemology over ontology in the elucidation of rational cognitive life, I find Lonergan’s “dynamic structure of knowing” less persuasive than Joseph Maréchal’s “spiritual dynamism” as conducing to a properly metaphysical approach to inference, one that, in Thomist terms, recognizes the act of inference as a cognitional species of “objectifying” or “ontological” affirmation. That said, Maréchal’s linkage of dynamism to the absolute is rather more controversial. 180  Insight, p. 640.

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to it) is restricted to that which “lies within…the domain of man’s… inner experience.”181 This restriction to “inner experience” is consistent, not with any onto-epistemology of inference, but rather with the reigning epistemological hegemony that philosophers commonly, if not with complete justice, identify as mainly Kantian in origin, and by extension Cartesian. Lonergan confirms his allegiance to that hegemony when he asserts (dogmatically, it could be argued) that in the epistemological modality of “outer” experience—i.e., as a transcendent, not as a contingent fact—proportionate being is an isomorphism between knowing and the known.182 If Lonergan’s “outer” experience weren’t a transcendent fact—and that itself, on his account, one could not know—the very idea of transcendent Being would be a chimera. Still, one might maintain that what Lonergan offers here is a third possibility: “…what is neither necessary nor arbitrary yet intelligible and a value, is what proceeds freely from the reasonable choice of a rational consciousness.”183 But this appears merely to beg the question. Regardless of the “proportionate” character of the “being” to which Lonergan refers, when he asserts that knowing and the known are isomorphic, he makes an onto-epistemic move that, to recur to the Kantian distinction, effectively subsumes absolute onto-epistemological positing within relative Position.184 The known as a transcendent fact 181  Ibid., p. 640. 182  This isomorphism Lonergan holds to be something that we “invoke” as the fourth and final moment of a process—one that he finds articulable as a logical argument—of erecting “integral heuristic structure,” or metaphysic. The context of the move to invoke (in its metaphysical sense, positing) the isomorphism includes the following three moments: 1) “dialectical criticism” that “transforms one’s common-sense and scientific views to provide the secondary minor premise of the argument”; 2) a “cognitional theory” that “brings to light the four methods of possible inquiry”—classical, statistical, genetic, and dialectical—such as “to yield the principal minor premise”; and 3) “metaphysical understanding” that “unites the principal and secondary minor premises, much as a physicist unites a differential equation with empirically ascertained boundary conditions, to obtain the integral heuristic structure relevant to this universe” (Insight, p. 484). 183  Insight, p. 657. 184  Cf. Oliva Blanchette’s critique of Lonergan on this point, in Philosophy of Being, p. 315. Perhaps reflecting the influence of Blondel, Blanchette proposes that the isomorphism inheres “between knowing as the proper

116 Inference and the metaphysic of reason (i.e., for us) is a function of absolute onto-epistemological positing; yet being isomorphic with the act of knowing, it is identical and hence always formally reduced as graspable—as known—to relative Position, i.e., as an epistemologically conditioned moment. That Lonergan commits a methodological reduction of absolute to relative Position follows perhaps inevitably from his doctrine that “proportionate being” is something that one cognizes through heuristic structure alone. This view discloses problematic concomitants when Lonergan asserts, for instance, that the “transcendent sphere of being”—as distinguished from the “real” and “restricted” (possible-worldlike) sphere—is “known by us through grasping the virtually unconditioned,” which he posits as “formally unconditioned, absolute.”185 This direct insight expressly presupposes the “dogmatic” dichotomy between absolute and relative Position, and this is ultimately to identify absolute position with the relative positing that characterizes our activity of human being and the same human being as knower” (ibid.). This is in principle consistent with Fichte’s use of “setzen” and with the ontoepistemology of inference as explicated in the present work. To defend Lonergan on proportionate being, a doctrine that as Giovanni Sala notes is “the fundamental” element of Lonergan’s very “conception of metaphysics” (Lonergan and Kant, p. 129), one would need to defeat Blanchette’s challenge to his correspondence thesis (and by extension to Lonergan’s “rational conception of reality”). “Even if we grant,” remarks Blanchette, “that knowing is of being, as we do from the beginning, it does not follow that the heuristic structure of our knowing is of itself grounds for affirming a parallel structure in the reality of what is known or in what Lonergan refers to as ‘proportionate being’…” (Philosophy of Being, p. 315). In this decisive particular, Blanchette finds Lonergan’s thinking at bottom a transcendental dodge, implicitly operating under the dispensation of what has been called here the Kantian epistemological hegemony. 185  Method in Theology, 2nd ed. (Toronto: University of Toronto Press, 2003), p. 76. Lonergan sees himself as a “critical realist”; cf.: “to move beyond idealism to realism, one has to discover that man’s intellectual and rational operations involve a transcendence of the operating subject, that the real is what we come to know through a grasp of a certain type of virtually unconditioned” (ibid.). From an onto-epistemological standpoint, this “transcendence of the operating subject” is precisely what needs to be explained as a function of the reason of the inferential act, which cuts across Lonergan’s “spheres of being.” Lonergan propounds an absolutely posited “grasp,” an intuitive insight—which just is—regardless of the “intellectual and rational operations” that it putatively sponsors.

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rational grasp of the “virtual” (i.e., of the power of somewhat that lies beyond the sphere of that grasp). It thereby dubiously imputes the reception of form to what rather demonstrates its actualization, its reception, in the merely relative. None of the foregoing observations discredit Lonergan’s speculative penetration when he situates his own contribution to metaphysics, whatever its limitations, precisely on the fault line of Kant’s critical philosophy. And this even while Lonergan’s thinking here is arguably consistent with, if not an indirect legacy of, Kant’s insight that relative and absolute Position are at least in principle onto-epistemologically distinct ways to express Being.186 (The interested reader will find some reflections on this theme in Appendix III, below.) 2.6.2. Lonergan on inferential thinking: compared with Carnap, Harman, Brandom, and Williams. We next assess Lonergan’s main pronouncements on inference in a brief comparative review that will tie in with earlier phases of this chapter’s discussion. The focus is limited primarily to those elements of Lonergan’s account that relate directly to an onto-epistemological construction of inference as a spiritual (geistig) phenomenon—an orientation informed from start to finish by the ineludible metaphysical dimension of inferential reflection. Most contemporary analytic philosophers pay little more than lip service to onto-epistemological factors in their treatment of inference. Those, like the later Carnap and Gilbert Harman, who do address topics in the (classical) metaphysics of inference generally probe the bounds of discursive analysis without bringing to bear the dialectical reflection187 that would credit formative meta-analytic factors as something more than moments of the perennial speculative conundrums that dog rational thinking at its outer limits. One need merely juxtapose Lonergan’s systematic work on this score with the doctrines of Carnap, Harman, Brandom, and Williams to appreciate how Lonergan conceives of inference in light of a metaphysical context that extends far beyond the reflective scope of the leading contemporary epistemologists. To illustrate this in view of the broader frame of our critical discussion, and in a way that looks forward to chapter 3, the following series of comparisons links up the 186  See Eckart Förster, Kant’s Final Synthesis: An Essay on the “Opus postumum” (Cambridge, Mass.: Harvard University Press, 2000), pp. 77-78. 187  Cf., Rosen, “Logic and Dialectic.”

118 Inference and the metaphysic of reason critique of Lonergan with the earlier assessment of Carnap, Harman, Brandom, and Williams. We shall thus consider Lonergan’s position on three orientational issues that also figure prominently in the work of the other philosophers. The issues in question are a) the “problem of induction”; b) the inferential nature of inductive thinking as opposed to that of deductive thinking; and c) the appeal to a grounding, extradiscursive moment, an element of onto-epistemological primacy. a) Of central importance to how Lonergan frames the “problem of induction” is his strategy to distinguish between inference, on the one hand, and, on the other, the movement of “knowledge of a truth to belief in the same truth.”188 According to Lonergan, the latter involves knowledge “in one mind” becoming “belief in the same truth in another mind.”189 By contrast, “inference moves from knowledge of premises to knowledge of a conclusion in the same mind.”190 If not obviously at odds with Carnap and Harman, this distinction of Lonergan’s does radically challenge the socio-linguistic aspect of Brandom’s semantic inferentialism. Lonergan sees through and rejects semanticism (along with rules of syntax, i.e., rules that inform the predicate calculus) that either implicitly stands in for systematic metaphysics or effectively supplants it. This he does by dismissing analytical propositions as irrelevant grounds for “such a concrete deduction as Newton’s Mathematical Principles of Natural Philosophy.” He argues—and here Carnap’s early work (earlier refuted by Gödel, among others) is clearly a target—that analysts too often derive such propositions “by studying the rules of syntax and the meanings of words, and clearly that procedure does not yield an understanding of this universe.”191 Unlike Harman, Lonergan does not flatly renounce the idea of “the so-called problem of induction” (something that Whitehead, no less, declared to be “the despair of philosophy”192). But he finds “a law” at 188  Insight, p. 718. 189  Ibid., p. 718. 190  Ibid., p. 718. 191  Insight, p. 405. 192  “and yet,” continues Whitehead, “all our activities are based upon it”; see Science in the Modern World (New York: Free Press, 1969), p. 23. Whitehead recognized that “the key to the process of induction, as used either in science or ordinary life” lies in our properly grasping the absolute dimension of the concrete immediacies of each “occasion of knowledge” (p. 44). This is the very purport of the present investigation, although I approach

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work in inductive inference—a law that, as “an almost automatic procedure of intelligence,” constitutes the principle of how thought moves “from one particular case to another or from a particular case to a general case.”193 This Aristotelian law—“immanent and operative in cognitional process”194—is “that similars are similarly understood.” Lonergan identifies this venerable notion as “the heuristic premise” of logicians who argue from analogy. The latter is a mode of proof that “can yield a valid argument,” in his view, “only if the two concrete situations exhibit no significant dissimilarity.”195 The first thing to note here is that argument by analogy is hardly the only logical form of inductive inference (although Lonergan might reply that it underlies all the others as formal cause). The related form of induction by simple enumeration, for example, requires more than operating simply under the aegis of the principle that similars are similarly understood. It involves, in addition, some independent ground for understanding that some all of instances (a, b, c, …) that are similar in respect of x are on that count instances of y. The latter insight is a function of a principle of universal judgment that Aristotle would recognize as “a matter of art” rather than merely a perception of similarity among similars.196 the immediate, in inferential cognition as relative Position, hence as the negative moment of the wesentlich onto-epistemic dialectic that discloses the sufficient reason of Being in its differences in discursive thinking. The latter is conceived as ordered (to invoke the Thomist idiom) to an analogy of being, an analogy that is cognitionally determinate as forma formans. See §4.2, below. 193  Insight, p. 288. 194  A cognitional process that renders “sufficiently” evident a “prospective judgment,” grasped as “virtually unconditioned,” but whose sufficiency derives from the “link of the conditioned to its conditions and the fulfillment of the conditions” (Insight, p. 315). 195  Insight, pp. 175-76. 196  Cf., Metaphysics 1.1.981a5-12. Philosophical logicians have long offered fundamental challenges to the very idea that arguments from analogy have logical value at all. H. W. B. Joseph, a most acute if now-neglected philosophical logician, observes that the argument from analogy “is plainly not proof. As Lotze has pointed out, there is no proof by analogy. Many conclusions drawn in this way are afterwards verified; many are found to be false. Arguments from analogy can often be found pointing to opposite conclusions” (Introduction to Logic, p. 538). Cf., Lotze’s Logic, §214. Irving Copi provides a more recent summary of the issues from an analytic per-

120 Inference and the metaphysic of reason What reason does Lonergan adduce to substantiate his fundamental principle of acts of inductive thinking? “We appeal to analysis and we generalize,” he declares, “because we cannot help understanding similars similarly.”197 Lonergan might have persuasively qualified his account by recalling Aquinas’s notion that the similitude “of the thing known must be in the nature of the knower, not actually, but only potentially” (ST, Ia, q. 75, a. 1). As it stands, however, Lonergan’s petitio principii is not mitigated by the rider that this “law” of thought requires an antecedent “act of understanding,”198 for my act of understanding might betoken the “well known logical principle that although we can infer like effects from likes causes, we cannot conversely infer [inductively or otherwise] like causes from like effects.”199 As Ernst Cassirer long since remarked, moreover, this “law” of similars is at the very least one-sided. I may generalize, for example, on the strength of a relation of necessity that I apprehend between dissimilars, not because I “cannot help understanding similars similarly.”200 Lonergan’s proposals thus arguably contribute little to how one might understand that aspect of spontaneous and orientational (“rule-grounding”) reason (Vernunft) that distils, as it were, the unity of thinking and being. As I shall urge in chapter 4, this is a Reason whose essential (wesentlich) moment composes the formally articulated dynamic that realizes the onto-epistemological dimension of acts of inferential thinking. The formal composition in question, is an essential phase of inferential concept formation. It is elucidated by Hegel— whom Lonergan mistakenly dismisses for failing “to advance critical

spective; see Introduction to Logic, 5th ed. (New York: Macmillan, 1978), pp. 403-05. 197  Ibid., p. 288. By consulting Aquinas’s reply to the second objection in Q. v, a. 4, of the Commentary on the De Trinitate of Boethius, Lonergan might have gone some way toward establishing this axiom in terms of formal cause. 198  Ibid., p. 288. 199  Ernst Cassirer, The Philosophy of Symbolic Forms, Volume 3: The Phenomenology of Knowledge, trans. Ralph Manheim (New Haven: Yale University Press, 1957), p. 82. 200  Cf., Cassirer, Substance and Function, trans. Swabey and Swabey (New York: Dover, 1953), pp. 14-16.

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realism”201—when in the logic of essence he delineates the actualization (Wirklichkeit) of Setzung.202 The errors or confusions that as often as not attach to the act of inductive inference (as the “appeal to analogies”203 and consequent generalization) occur, says Lonergan, “because the particular case may not be properly understood.”204 Lonergan then reverts to his core conception of Insight to explain and resolve the “problem of induction”: “There must be a correct insight with respect to the basic situation.”205 This stipulation prompts questions about the nature of what might non-circularly constitute such a “correct insight” from the standpoint of the act of inference. According to Lonergan, it is a composition of cognitionally “grasping” correlations that yields relevant experiential and explanatory (pure) “conjugates.”206 The meaning of the correlations at issue is what gets expressed when one appeals “to the content of some human experience” or alternatively to some “empirically established correlations, functions, laws, theories, systems.”207 At bottom, Lonergan interprets acts of inductive inference as a “procedure of intelligence” that falls under the “law, immanent and operative in cognitional process, that similars are similarly understood.”208 While this implicitly and persuasively represents the reason of the 201  For Lonergan’s critical realist, “a verified hypothesis is probably true; and what probably is true refers to what in reality probably is so” (Method in Theology, p. 239); historical facts for the critical realist “are events in the world mediated by true acts of meaning” (ibid.). Lonergan sums up the metaphysical thrust of his critical realism by declaring that beyond any naïve realism, critical realism liberates us “to discover the self-transcendence proper to the human process of coming to know” (ibid.). Beyond the epistemologically biased idiom, one finds little here that is fundamentally at odds with Hegel’s teaching. 202  The logic of essence, as a moment of onto-epistemologically positing (i.e., on the level of “pure thinking”), is the show (Schein) of a living act of reflective intelligence. On the use here of this Hegelian term, see §1.iii (b) and (c), above, and §4.5.2, below. 203  Insight, p. 288. 204  Ibid., p. 301. 205  Ibid., p. 288. 206  On conjugates, see ibid., pp. 79-82 207  Ibid., pp. 79-80. 208  Ibid., p. 288, emphasis added.

122 Inference and the metaphysic of reason process of inductive thinking as an onto-epistemological logic of analogy,209 the appeal to a transcendental law of thought merely lends weight to Lonergan’s confessed uncertainty as to the correctness of a philosophical “perspective” that licenses his comprehensive study of human understanding, a study that proceeds “from knowledge” to metaphysics. He understands this “knowledge” as the product of a “cognitional theory” that “expands” from “self-appropriation of one’s own intellectual and rational self-consciousness” to “reach metaphysics only as a conclusion.”210 Lonergan founds his idea of “law” on the metaphysical notion that intelligibility, which “is either spiritual or material,” is “intrinsic to being.”211 By operating with such an idea as a presupposition from the outset, however (i.e., prior to “reaching” metaphysics), Lonergan can achieve metaphysical insight only on the strength of epistemological theory. One might object, however, that any such theory becomes a methodological liability vis-à-vis the originary metaphysical concerns that must be addressed even as one engages the problematic of beginning—the perennial and perhaps most consequential challenge confronting systematic philosophy. b) Like Carnap, and thus unlike Harman, Lonergan detects inference in deductive as well as in inductive reasoning. In a section titled “Concrete Inferences from Classical Laws”212 he examines a deductive order of inference—“practical inference”—whose form, he concludes, “is merely a clear illustration of what is meant by grasping a prospective judgment as virtually unconditioned.”213 Lonergan identifies three “conditions” of concrete scientific inference, a class of reflective thought that takes “practical” and “anticipatory” forms: “it supposes information 209  One might profitably extend this line of investigation by tracing the topic of analogy in medieval and classical treatments of inference, with special emphasis on Aquinas and Aristotle. For an investigation of analogy as “sameness-in-difference” in Aquinas (and indirectly in Aristotle), see John F. X. Knasas, Being and Some Twentieth–Century Thomists (New York: Fordham University Press, 2003), chap. 5. Knasas surveys the thinking of leading neo-Thomists on the topic (with special emphasis on Jacques Maritain, Joseph Owens, and Ralph McInerny). 210  Insight, pp. xxvii and 731. 211  Ibid., p. 617. 212  Insight, pp. 46-63. 213  See ibid., pp. 576-77, where Lonergan distinguishes insight from judgment.

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on some concrete situation; it supposes knowledge of laws; and supposes an insight into the given situation.”214 Particularly significant in the present context is that Lonergan adduces at this juncture the indeterminate (unbestimmt) epistemic concept of insight (understood as an event that can be thought and studied apart from determinate conditions215). This is just where Carnap, discussing the crucial case of the teaching of deduction per se, confessed that he needed to revert to “intuition” as a primitive explanatory principle. Lonergan contends that it is insight that enables one to select the appropriate law “for the inference” and, again, insight that determines the inferential “particularization” of the law.216 If insight is for Lonergan the pivotal cognitional act, and if such acts somehow “contain contents”217 that either “refer to the known or are identical with it,”218 then deductively to infer that

214  Ibid., p. 46. 215  Ibid., p. xxii. As an onto-epistemological contextualist, I would side with those Thomists—Blanchette, Norris Clarke, and Desmond Connell, among others—who find difficulties with the order of Lonergan’s method of procedure. The latter’s modus operandi is to progress from characterizing insight as an event of scientific epistemology—one that purportedly answers the question, “What is happening when we are knowing?”—to construing insight (based on inferences “from the structural and dynamic features of the scientific method”) as an event of metaphysically disclosive knowledge of proportionate being, knowledge that answers the question, “What is known when that is happening?” 216  Lonergan’s class of “anticipatory inferences”—the second “manner” in which concrete inferences “can be carried out”—applies to both deductive and inductive reasoning; cf., Insight, p. 47. 217  Discussing the content of act, Lonergan refers in this connection to “the noêma or intentio intenta or pensée pensée [that] may always be expressed with greater accuracy and completeness” (Insight, p. xxvi). Cf., “in every experience one may distinguish between content and act…” (ibid., p. 81). The explication of inference in chapter 4, below, finds the reason of the act of inference to be a reason of Wirklichkeit—of actualization. This is a dynamic wherein the onto-epistemological Position oder Setzung of “content” (a positing that is intermediatingly absolute and relative) is nothing less than the “content’s” formally realized articulation—its identity-in-difference—as it “shows” in the reflective life of discursive intelligence. 218  Insight, p. 486.

124 Inference and the metaphysic of reason something constitutes the particular instance of a law amounts simply to seeing219 that the particular refers to or reproduces “the known.”220 Two difficulties with Lonergan’s explication of inferential reflection stand out here. The first has to do with the consequences of asserting, on the strength of such perceived references or identification, that the dynamic structure of knowing is isomorphic with the structure of proportionate being. To postulate such isomorphism is tacitly to employ “insight” (at least in its character as medium of content or an intelligible container) as a non-analogous epistemological act. And this implicitly violates the order of inquiry that Lonergan propounds. Put in different terms, to see an isomorphism between the dynamic structure of knowing and the structure of proportionate being is in effect to represent a metaphysical orientation as a practical epistemological presupposition. A second and closely related issue is whether Lonergan’s recourse to insightful seeing is ultimately any more justified than Carnap’s appeal to intuition—even if it is far and away more rational and systematically integrated. To account for the being (or Existenz) of reason as wirklich—here the act of inference—Lonergan first (in his preferred order of reflective meditation) recommends cognitional process as insightfully delineating the structure of the isomorphism between knowing and known, rather than between the act of knowing and that of the being of the knower. This is arguably to accord “insight” an adventitious transcendental purchase that in effect constructs a metaphysic upon epistemology.221 A classical Thomist philosopher 219  This seeing is an active process, a cognitional grasping, and not the otiose gazing, intuiting, or “looking” of a mere conscious awareness that Lonergan repudiates; see Insight, pp. 320-21. 220  The present work’s concern on this head is with a conceptual logic that accounts for the form or “look” of facts as a constitutive moment in a scientific onto-epistemology of inference. Rather than the act of seeing as cognitional grasping, the onto-epistemology of inference evidences the positing of the particular as actualization of the intelligible, i.e., form, as analogously ordered formans, not as a container. Such positing is too concrete to admit anything approaching the form/content distinction (a distinction that one is led to reject in Hegel’s exposition of the notion of posited Schein). From this standpoint, acts do not properly speaking “contain,” rather they enact or prehend, in Whitehead’s vocabulary, the facts that they express—the psyche becoming in this sense the things that are. 221  And by extension upon possibility—the possibility that the cognitional process, as an activity of “seeking…correct understanding” of “the particu-

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like Blanchette would judge such a move to be a consequence of improperly claiming to enter “the analogy of being.”222 c) We saw, finally, that Carnap, Harman, and Williams (unlike Brandom) found it necessary to incorporate a heteronomy in their theorizing, specifically in their appeals respectively to principles of intuition, psychologism, and critical mass. The underlying motivation in each case was the imperative to square analytic working assumptions with the fact that at bottom inference somehow expresses an identity of rational intelligence and being. How does the case stand with Lonergan? A systematic philosopher in the great tradition, he elegantly addresses the relation of cognitional acts and ontology when he considers “whether the metaphysical elements constitute an extrinsic or an intrinsic structure of proportionate being.”223 The metaphysical elements to which Lonergan refers are “central and conjugate potency, form, and act.” This is not the place to trace the ramifications of these terms in Lonergan’s system;224 it will do for present purposes simply to observe that, true to his practical epistemological bent, Lonergan defines them all (heuristically) in terms of cognitional acts—the “differences of the metaphysical elements are differences in the process of knowing.”225 lar” solves, as Lonergan has it, “the problem of induction” wherever it arises (Insight, p. 301). Among other things, this follows Kant in restricting inference to relative Position (the domain of Verstand). Lonergan’s account here involves the dubious conception that in “fully explanatory knowledge,” one knows potency merely as “an intellectually patterned experience of the empirical residue [sic]” of proportionate being (p. 432). However, our grasp of dunamis is considerably more profound, one might find, than a rationalized perception of empirical data, regardless of how suggestive such data may be. Not all the actualization that refers onto-epistemologically to potency is reducible to empirical (i.e., a posteriori) experience. Lonergan’s own “Insight,” for example, “is a function not of outer circumstances but inner conditions” (p. 4). 222  Cf., Philosophy of Being, p. 119. 223  Insight, p. 499-502. 224  Lonergan takes potency, form, and act to be the three main elemental categories of metaphysics, metaphysics as he understands it constituting “an integral heuristic structure of proportionate being”—which boils down to whatever we know “by experience, intelligent grasp, and reasonable affirmation” (Insight, p. 431). 225  Insight, p. 499.

126 Inference and the metaphysic of reason The three metaphysical categories are thus, for Lonergan, three types (or “differences”) of cognition that are intrinsic to proportionate being. In other words, “potency, form, and act [do] not merely assign the structure in which being is known but also the structure immanent in the very reality of being.”226 Here one sees the metaphysical relation that Lonergan affirms between the cognitional act and being, being that manifests differences that are not merely different, but that are also analogous (with the “content” of Insight as the distributed middle term). But if Lonergan’s classical and Thomist speculative resources enable him to avoid the heteronomy apparent in Carnap and Harman and Williams, not to mention the neo-pragmatic socio-linguistics of Brandom’s doctrine, his treatment of formal inference betrays some radical onto-epistemological limitations (something evidenced in his act/content binarism). Perhaps no position statement of Lonergan’s makes this clearer than one that appears in his last major work and that attests to the shaping influence of contemporary analytic thinking in his philosophy: “the form of inference,” declares Lonergan, “is the ‘if-then’ relation between propositions”227—the “law” of thought complementing this is that similars are similarly understood. From an onto-epistemological viewpoint, however, the so-called “material conditional” fundamentally miscasts the formal character of the reason of the act of inference. Bosanquet long ago recognized as much, and at the outset of an entire volume devoted to the logic of inference he noted that acts of inference are acts of affirmation: 226  Ibid., p. 501. 227  Method in Theology, p. 71 n17, emphasis added; see also Insight, p. 315. Lonergan’s definition would have drawn fire even back in Kant’s day. (Kant, recall, included the categorical and disjunctive syllogisms, along with the hypothetical, as forms of Vernunftschluss.) Salomon Maimon, for example, rejected Kant’s conventional declaration that logic had attained the stage of a complete and perfect science; in the process, Maimon argued that the hypothetical conditional is a derivative and not a basic form of judgment—it being reducible, as he demonstrated, to a set of categorical judgments. See Frederick C. Beiser, “Maimon’s Transcendental Logic,” The Fate of Reason: German Philosophy from Kant to Fichte (Cambridge, Mass.: Harvard University Press, 1987), §10.8. As we shall see in chapter 4, Bosanquet showed how implausible it is to restrict inference to hypothetical judgments; see his Logic, vol. I, pp. 234ff.

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The ground per se [in an if-then, or hypothetical, judgment] is not affirmed of Reality, and so the consequent per se is not affirmed to be true. The moment that “If ” passes into “Because” you can omit the ground and affirm the consequent per se. But retaining the “If ” we cannot affirm the consequent. We cannot affirm upon mere supposition, nor can we infer without affirming.228

2.7 Summation. By contrast with the foregoing review of Lonergan’s metaphysically developed doctrine of inference, the critiques of Carnap, Harman, Brandom, and Williams were relatively straightforward. Discussing Carnap, we observed that the attempt to explain inductive (“nondemonstrable”) inference by appeal to probability theory—his distinction between logical and statistical probability notwithstanding229—was hardly alien to received thinking on the theme. It had been an expedient of mathematical logicists practically from the first major stirrings of the modern analytic movement in the nineteenth century. While probabilism persisted as a topic of lively debate among analytic epistemologists, the idea of inductive inference as ultimately resolvable into a probabilistically structured mode of logical reflection has faced unanswerable ontological and epistemological challenges from various quarters. Carnap’s most telling move, again, is his reversion to intuition as the grounding phenomenon of the act of knowing. Unavailing though it proved, the appeal to intuition correlates, as we saw, with the expedients that different contemporary theorists of inference resorted to as a means of addressing the ineluctable ontoepistemological factors ingredient in inference grasped, even tacitly, as the seminal act of the knowing that is of being. As we have seen, Kant’s distinction between absolute and relative Position230 is useful heuristically for revealing the formal limits of Carnap’s thinking on inference. It also helps to disclose the level at which other analytic epistemologists sidestep onto-epistemological elements that inform the reason of the act of inference. Harman’s decision, recall, was explicitly to turn to psychologism. Brandom appealed to an “inferential role” semantics that pragmatically expresses sociolinguistic norms. Williams introduced a derivatively quantitative idea 228  Logic, 2nd ed., vol. II, p.10. 229  Cf. Introduction to the Philosophy of Science, pp. 34-39. 230  Both of which play a defining role as intermediating moments of inference (as argued below, in chapter 4).

128 Inference and the metaphysic of reason as a core epistemological (and semantic) concept. The philosophies of Harman, Brandom, and Williams thus in effect invert the ontoepistemology of the thetic act. Hence they fail coherently to address the status of inferential knowing as of being. The problem is that they characterize inference in relative terms in isolation from the absolute Position to which, in their own accounts, inferential reflection ostensibly bears witness. Lonergan proved of special interest here as a systematic theorist of inference because he comprehensively engages both traditional (Thomist and classical) metaphysics and contemporary analytic modes of thought. He is hardly unique, of course, in this sort of endeavor. Indeed, it is not difficult to locate among more recent analytic thinkers other systematic defenses of “insight” as the “genuine basis” of inductive inferential knowing. One example appears in “Is It Possible to Justify Induction A Priori?”, a culminating section of Lawrence Bonjour’s widely known monograph, In Defense of Pure Reason: A Rationalist Account of A Priori Justification. 231 “The problem of induction,” argues Bonjour, arises in the first place…from viewing induction as a mode of reasoning or argument that claims to be rationally cogent, that is, one in which the (probable) truth of the conclusion is at least claimed to follow in a rationally intelligible way from the truth of the premises. But what does it mean for a conclusion to follow rationally, whether certainly or probably, from a set of premises? I submit that it can mean only that one who understands the premises is thereby in a position to see or grasp or apprehend… that if those premises are true, then the conclusion either must be true…or is probably true…, where this seeing or grasping or apprehending can only be a priori in character.232 The connection between premises and conclusion must be, one might say, intellectually visible. No empirical appeal of any sort can replace the need for such an a priori insight, since any such appeal would amount only to adding one or more further premises to the argument, from which the conclusion would still have to be seen to follow.233 231  Cambridge, Engl.: Cambridge University Press, 1998. 232  In evidence here are the speculative implications of Bosanquet’s reading of the hypothetical conditional with respect to the ground of inductive inference; see p. 314, below. 233  Ibid., p. 203.

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What sets Lonergan apart from mainstream contemporary inference theorists such as Bonjour is his range of investigation. His work bridges the divide between the philosophia perennis of the earlier philosophical logicians of inference and contemporary analytic epistemology that, depending on the version, evinces hegemonic epistemological biases that take the form of logicism, positivistic empiricism, or socio-linguistic pragmatism. What illustrates this transitional character of Lonergan’s thought with perhaps the most force relative to the onto-epistemological perspective is his “Canon of Relevance.” This is the section of Insight where Lonergan describes as a matter of formal cause what is effectively the sufficient reason that constitutes the reason of the act of (empirical) inference. (Lonergan’s thinking is consistent, in this particular, with the exposition of inference undertaken, below, in chapter 4.) This section, which appears in a chapter on “The Canons of Empirical Method,” is the third of a half-dozen sets of “rules” that Lonergan identifies as governing “the fruitful unfolding of the anticipations of intelligence.”234 According to Lonergan, the canon of relevance has to do with the circumstance that “pure science aims immediately at reaching the immanent intelligibility of data and leaves to applied science the categories of final, material, instrumental, and efficient causality.”235 Limited to a special class of inferential acts, the canon of relevance “aims at stating the type of understanding proper to empirical science.”236 Only applied science, in Lonergan’s view, concerns itself first and foremost with final, material, and “instrumental or efficient” causes— grounds of things, he argues, that lie “not in the core but on the periphery of [pure] empirical science.”237 Exemplifying as it does “the inner constituents of science itself,” applied science exhibits the sort of understanding that falls under the canon of relevance, in the context of which the field of empirical inquiry “primarily aims at reaching the intelligibility immanent in the immediate data of sense.”238 This intelligibility of sense data is intrinsically relational and consists in “realized 234  235  236  237  238 

Insight, p. 70. Ibid. Ibid., p. 76. Ibid., p. 77. Ibid.

130 Inference and the metaphysic of reason possibility.”239 Lonergan holds that this intelligibility to which the canon of relevance applies is formal cause in its classical sense. On that score he takes care to distinguish formal cause from misleading contemporary associations of it with mere logical form, and from thinkers who construe formal cause as “merely the heuristic notion of the ‘nature of…’, the ‘such as to…’, the ‘sort of thing that…’.”240 These are seminal observations, and with them Lonergan displays insight into the onto-epistemological ground of the reason of inference as we shall explore it in the constructive part of this study. Notwithstanding such trenchant reflections, however, two factors signal radical differences between Lonergan’s philosophy of inference and the reading of the reason of inference developed in the present essay. First there is the restrictive purview of the intelligibility to which Lonergan limits his account, i.e., the Kantian element in his epistemology. Second, he fails expressly to associate his canon of relevance with his articulated doctrine of formal inference. It is under the heading of “Heuristic Structures of Empirical Method” that Lonergan explicitly deals with the topic of inference as such, which he construes formally as the hypothetical conditional.241 Construed from an onto-epistemological standpoint, this treatment of inference betrays close affinities with the methodological spirit of the contemporary analytic epistemologists. These affinities cannot but stand in tension with Lonergan’s implicit subscription to formal cause as the very intelligibility of inference (hence as its ground), at least in empirical science. In light of this tension Lonergan’s inferentialism marks a cardinal transitional point of reference as in the next two chapters we come to grips with increasingly involved onto-epistemological concerns of doctrines and issues that elucidate the reason of the act of inference. 3 239  Ibid., p. 78. 240  Ibid. 241  Cf., Joseph Fitzpatrick: “What we find [in ‘The Form of Inference’—a 1943 essay] is Lonergan’s reduction of all the traditional scholastic figures of syllogism…to one form, which he calls the ‘the simple hypothetical argument’: If A, then B; but A; therefore B. For Lonergan that is the basic form of valid inference”; see Philosophical Encounters: Lonergan and the Analytic Tradition (Toronto: University of Toronto Press, 2005), p. 192.

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The phase of inquiry that commences with chapter 3 highlights both the penetrating insights and limitations of Lotze and Bosanquet, philosophers of an earlier milieu for whom the logic of inference is not to be prescinded from Being, whether one approaches the latter (analogously) as Reality or as the Whole. Lotze and Bosanquet each authored a double-volume logic that is “philosophical” in that it is fully integrated within a systematic metaphysic. Unfortunately for their reputations over the last century, Lotze and Bosanquet pursued their respective investigations of inference at just the historical moment that traditionally oriented speculative inquiries into logic faced a rising tide of formalistic challenges. The result was that within a few decades their contributions to the philosophy of logic were largely sidelined.242 Champions of mathematicized symbolic logic and the emergent schools of pragmatism, naturalism, neo-realism, and logical empiricism promulgated reductive but nonetheless widely influential refutations of idealist thinking, when they didn’t simply dismiss it as irrelevant. Predictably enough, by the third generation after their deaths Lotze and Bosanquet had faded to near obscurity in most leading philosophical circles. What makes Lotze and Bosanquet of particular interest in the present study is that they manage to integrate systematic accounts of the Whole, understood as the Absolute or Reality, with philosophies of logic that more or less accommodate the onto-epistemological dimension of inferential thinking. By contrast with the difficulties we observed in the analytic philosophies of inference, those that one encounters in the thought of Lotze and Bosanquet are not most interestingly elucidated, for present purposes, in light of the Kantian distinction of absolute and relative Position. While a number of core 242  One finds Lotze, in the late 1870s, defending systematic metaphysics from what he saw as the emerging movement of “mathematico-mechanical construction.” He speaks, in a concluding section of his Metaphysik (three books of which he lived to complete), “of that requirement which I believe we must lay on ourselves—the total renunciation of our desire to answer questions by the way of mathematico-mechanical construction” (Metaphysic, vol. II, p. 318.). This position reflects Lotze’s concern with certain implications of the scientific application of such “construction.” What worried Lotze was the possible discovery of unanticipated worlds of fact that might afford grounds of explanation that are at best only provisionally related to that scientific construction of reality which, if it led us to stumble upon such fact, we in any case take to be a privileged worldview.

132 Inference and the metaphysic of reason problems respecting the onto-epistemology of inference will claim our attention, we shall find that they relate less to the notion of Position oder Setzung than to a constellation of speculatively pregnant issues that call for evaluation along lines of assessment that will grow increasingly intelligible as the details of the onto-epistemology of inference emerge more fully into view.

Chapter 3 Inference and Ontology in Systematic Philosophical Logic …the detail which [the universe] presents in the form of cognition is true of the universe, although falling within it, because the universe, qua object of cognition, in its self-maintenance against self-contradiction in that form shows that it must take the detailed shape which it does take and no other, and to know is to endow it with that form….

Bernard Bosanquet, Logic (1911), Book II (Inference) …the concept of inference as the “life” of a subject unfolding itself before the thinker’s mind according to its own inner necessity, is applied, with direct reference to Hegel, to philosophical dialectic.

Bosanquet, Implication and Linear Inference (1920) 3.1 Orientational shift in turning back to Lotze and Bosanquet on inference. We turn, now, from the partisans of diverse analytic epistemologies of inference to the very different orientation of Rudolf Hermann Lotze (1817-1881) and Bernard Bosanquet (1848-1923), two major exponents of a more metaphysically referred mode of thinking on the topic. The endeavor in the pages ahead to distil and evaluate the accounts of Lotze and Bosanquet1 marks a shift in critical emphasis that will set the stage for the culminating, constructive phase of the book. The present chapter effects this transitional end by critically amplifying and developing of a number of seminal metaphysical themes in Lotze and Bosanquet that both inform and uniquely distinguish 1  The philosophy of inference expounded by Bosanquet’s better-known colleague, F. H. Bradley, might initially seem more worth assessing than that of either Lotze or Bosanquet. But Bosanquet early on assimilated and built upon the lessons of Bradley’s thought, while Bradley himself ultimately relied very heavily on the authority of Bosanquet’s mature thinking on inference—a point that Bradley repeatedly stressed. Bradley conceives the “essential nature” of inference as a processive “ideal self-development of an object”; see The Principles of Logic, vol. II, 2nd edition, revised with commentary and terminal essays (London: Oxford University Press, 1922), p. 597.

134 Inference and the metaphysic of reason the onto-epistemology of inference that the reader is invited to thinkthrough in chapter 4. Lotze and Bosanquet were speculative logicians in the great tradition of systematic philosophy who undertook extended investigations of inference, till their day a notion commonly understood as properly syllogistic in character. Consistent with their systematic orientation, they each correlated their findings with full-dress metaphysical doctrines that situate logical and epistemological matters within highly nuanced, historically informed philosophies of the being of meaning. That said, neither Lotze nor Bosanquet offers some long-overlooked philosopher’s stone that (to extend the metaphor) might translate the more relevant if “baser” logicist and epistemological suggestions of recent theories into the gold of a definitive onto-epistemological account. Nonetheless, the pages ahead will reveal how the penetrating investigations of judgment that these two philosophers undertook thematize ineluctable (and non-bracketable) metaphysical implications of inferential thinking. Later students of the topic have too often overlooked these implications, cast them in reductive terms, baselessly dismissed them, or simply ignored them. To attempt anything like a comprehensive overview of Lotze and Bosanquet on inference far exceeds what is practicable or requisite for present purposes.2 What does claim attention here is how they treat the idea of inference as a mode of logical thinking that is consistent with, if not integrated within, a systematic metaphysic. The concern, in effect, is with how Lotze and Bosanquet conceive the act of inference as a unique and irreducible composition of thought and being, or thinking being. A related matter of particular interest that ties in with a leading heuristic component of this inquiry as a whole is how Lotze and Bosanquet come to terms with the onto-epistemological implications of Kantian Position oder Setzung. Beyond the foregoing themes, the present chapter also considers the onto-epistemological place that Lotze and more especially Bosanquet accord the principle of identity, or (non)contradiction, as a metaphysical law—particularly as it bears on the notion of Sufficient Reason 2  Their major works in logic and in metaphysics, largely neglected by contemporary thinkers, are punctuated with observations and insights that betoken speculative incisiveness and subtlety of a high order (something well known to their colleagues, their many distinguished students, and a scattering of currently active thinkers).

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(a metaphysical concept that, if time and again “refuted,” regularly returns to bury its undertakers3). This consideration will look forward to the fourth chapter’s core topic: the reason of the act of inference, the defining moment of which is the fundamental principle (Grundsatz) of the act of inference. This metaphysical principle, I shall urge, is a species of Sufficient Reason ordered, in the first instance, to formal cause. As Whitehead observed, “All reasoning, apart from some metaphysical reference, is vicious.”4 Consistent with this insight, is a principle of sufficient reason that constitutes the metaphysical reference of a properly rational onto-epistemological orientation to the act of inference. Philosophers of inference too often misconceive sufficient reason, however, as implicitly a function of either efficient or final cause, if they bother with it at all. Many follow Kant, who accorded the law of contradiction (which he identified as analytic5)--and not that of Sufficient Reason (for Kant, a synthetic principle)—the status of “first logical ground” of the “something real” [Dasein], the “absolute possibility,” presupposed by all possibility in general and of each possibility in particular. (Kant himself implicitly substantiates the formal-cause view of Sufficient Reason maintained in the present work when he traces the origin of the concepts of Reason (the transcendental ideas) to the form—categorical, hypothetical, disjunctive—of the inference of Reason (Vernunftschluss). Even in the pre-Critical period, he astutely notes 3  For a recent defense of the principle of sufficient reason, one that attempts (with but mixed success, in my view, and without reference to formal cause) to bring to contemporary debates the classic thinking on the topic, see Alexander. R. Pruss, The Principle of Sufficient Reason: A Reassessment (Cambridge, Engl.: Cambridge University Press, 2006). Pruss omits what from an onto-epistemological orientation are key texts, for example Heidegger’s Principle of Reason. After meeting various challenges to Sufficient Reason, Pruss concludes his study with the following declarations: “The PSR is not merely tenable…but actually true. Besides the still unrefuted [sic] possibility that the PSR is self-evident, a number of arguments are available in favor of the PSR. Abstract Thomistic considerations involving the nature of existence lead to the PSR….The best explanation of why the PSR holds in everyday contexts is that the PSR is metaphysically necessary. Our epistemic practices become quite dubious in the absence of the PSR” (p. 322). 4  Adventures of Ideas (1933. New York: Free Press, 1967), p. 154. 5  Cf., Prolegomena to Any Future Metaphysics, trans. Peter G. Lucas and Günter Zöller (Oxford: Oxford University Press, 2005), §3.

136 Inference and the metaphysic of reason that the “formal element of possibility consists in agreement with” the “law of contradiction.”6) 3.2 Speculative standpoint of philosophical logicians. To move from the analytic epistemologies of inference promulgated by the likes of Carnap, Harman, Brandom, Williams and Lonergan to the Lotzean and Bosanquetian philosophies of inference is to cross an orientational divide. The philosophical logicians of an earlier epoch, classing inference as a variety or complication of judgment, saw it as ingredient in a domain of logical thinking that one could not bracket from fundamental ontology. As such, the domain of logic—the “morphology of knowledge,” in Bosanquet’s phrase—derived its cogency (understood as genetically articulated) and relevance explicitly from the “world hypothesis” or, quite as aptly, “the process of vision”7 of a systematic metaphysic. Hence, for all their differences, some of the most important of which we will review in due course, Lotze and Bosanquet understood formal or symbolic logic to be simply a special province in the logical domain of reason. The sampling of position statements listed below—Bosanquet on logic, truth, and reality—gives a fair sense of the character and degree of the reversion in the present chapter to a more expressly metaphysical phase of inquiry into inference as a philosophical problem8: The full meaning of propositions [for the philosophical logician] lies always ahead of fully conscious usage, as the real reality lies ahead of actual experience. (L, p. x) For logic, at all events, it is a postulate [for the philosophical logician] that “the truth is the whole.” (L, p. 2) Logic has neither criterion of truth nor test of reasoning. Truth is individual, and no general principle, no abstract reflection, can be adequate to the content of what is individual. (L, p. 3) 6  Cf., Theoretical Philosophy 1755-1770, translated and edited by David Walford and Ralf Meerbote (Cambridge, Engl.: Cambridge University Press, 1992), pp. 124-25; emphasis added. 7  The phrase is lifted from the writings of James—Henry, that is. 8  The statements are from Bosanquet’s Logic, Or the Morphology of Knowledge, 2 vols., 2nd ed. (London: Oxford University Press, 1911) [L] and Implication and Linear Inference (London: Macmillan, 1920) [ILI].

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Logic is little more than an account of the forms and modes in which a universal does or does not affect the differences through which it persists. (L, p. 3) Truth seems to me to have no meaning unless (1) it is reality*; (2) is in the form of ideas. [*“The phrase ‘it is about reality’ suggests that its quality depends on representing something outside it. But this is upside down; it is reality which becomes truth when it takes ideal form.”] (ILI, p. 148) You cannot have truth except as reality in ideal form. (ILI, p. 149)

Conscious usage and reality, the connection of propositions and actual experience, logical postulates about truth that invoke the Whole, logical truth as individual, the “persistence” of the universal, truth as reality in ideal form—most contemporary philosophical logicians would write off such formulations as lacking in intellectual rigor and as alien in both tenor and purport to more timely analytic thinking and defensible speculative positions. Bosanquet, however, was anything but a backward-looking Victorian idealist proffering a half-baked and superannuated Hegelianism. He was quite familiar with the growing movement to recast logic in the symbology of exact science, particularly as exemplified in the work of William Stanley Jevons in the nineteenth century, and in that of Bertrand Russell in the twentieth. In fact, Bosanquet added a nine-page appendix to the 1911edition of his Logic in order to consider, in a comparative critique with his own views, the innovations in symbolic logic that Russell introduced in his Principles of Mathematics (1903). (It was in the latter text that Russell reviewed Frege’s work from the Begriffsschrift to the first volume of the Grundgesetze.) The Bosanquetian position statements listed above do not issue from the pen of a thinker who, like F. H. Bradley, was incapable of independently confronting the emerging mathematicizing and settheoretical trends in formal logic. A word on Bradley is in order here, to make clear the rationale for concentrating rather upon Bosanquet’s doctrine of inference than upon that of his better-known colleague. Like Bosanquet, Bradley, in a chapter of Principles of Logic (1883, 1922), took to task Jevons’s mathematical, “equational logic.” In doing so, he closely followed Lotze, who also analyzed Jevons’s work, as well as the early innovations of Ernst Schröder. With Lotze, Bradley

138 Inference and the metaphysic of reason rejects both the idea that one can pass off logical propositions as equations and the method of substitution, particularly in its role in the so-called “indirect method” of exclusion in disjunctive propositions. While he clearly recognizes the originality and merits of the new approach, Bradley confesses himself unable to “form something like an estimate of its educational value and practical powers.”9 As he writes in the 1883 edition of his Logic (a two-volume opus that preceded by five years the first edition of Bosanquet’s own double-volume Logic): “no living Englishman has done one half the service to logic that Professor Jevons has done. No living writer, to the best of my knowledge, now Professor Lotze is dead, has done more.”10 Still, by 1922 Bradley virtually gives up any claim to have rightly assessed the “new system”: My eulogy [of Jevons] may perhaps on the whole be exaggerated…. Whether a student of logic, who is incapable of learning mathematics and has therefore to leave out of his theory a recognized part of the facts, should never have written on logic at all, or should later at least suppress all that he once wrote—I will not offer to discuss. And what should be his attitude towards a claim to base the principles of logic on mathematics, I once more hardly know…. I am of course unable to accept a claim made on behalf of mathematics to have rationally solved logical and metaphysical problems in a way unintelligible except to the mathematician…. It would have to be made by a man, who can meet on their own ground the non-mathematical logicians and metaphysicians…and can inspire the belief that he himself is somehow better able, even outside mathematics, to deal rationally with ultimate problems.11

(Bradley, who died in 1924, would doubtless have counted his speculative position to have been more than vindicated with the spectacular emergence of the mathematician and mathematical logician Alfred North Whitehead, as a world historical metaphysician. Whitehead, a reader of Bradley, concluded that philosophy “has been misled by the example of mathematics; and even in mathematics the statement of the ultimate logical principles is beset with difficulties…”12) 9  Logic, vol. I, p. 370. 10  Ibid., p. 386. 11  Ibid., p.388. 12  Process and Reality: An Essay in Cosmology. Corrected Edition. Edited by David Ray Griffin and Donald W. Sherburne (New York: Free Press, 1978), p. 8.

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By contrast with Bradley, both Bosanquet and Lotze (a remarkable polymath who was an adept at mathematical thinking, as he was at translating Sophocles’ Greek into Latin verse) kept abreast of the attempts to mathematicize (and mechanize) formal logic that began in the mid-nineteenth century. Lotze in fact appended an extended “Note on the Logical Calculus” to the second edition (1880) of his Logik, published a year before his death.13 He there calls attention to the sacrifice of logical sense in the efforts of George Boole (1854) and 13  Logic in Three Books: of Thought, of Investigation, and of Knowledge, 2nd ed., trans. Bernard Bosanquet et al. (Oxford: Oxford University Press, 1888), vol. I, book II, chap. 3. On Lotze’s recognition of “the full claim of mathematics to a home in the universal realm of logic,” see §112 of the Logic. For his more general reservations about “our desire to answer metaphysical questions by the way of mathematico-mechanical construction,” see Metaphysic in Three Books: Ontology, Cosmology, and Psychology [1879], trans. Bernard Bosanquet et al. (Oxford: Oxford University Press, 1887), vol. II, pp. 318-19 (“Conclusion”). That Lotze’s thinking remains highly relevant on a number of issues is borne out by the radical challenge that this concluding section of his Metaphysic would pose to a contemporary systematic metaphysician such as Alain Badiou. Badiou’s magnum opus, Being and Event (trans. Oliver Feltham [New York: Continuum, 2005]), takes as its founding metaphysical assumption the axiom that “mathematics, throughout the entirety of its historical becoming, pronounces what is expressible of being qua being”(p. 8). Lotze would take a dim view of this sweeping claim, and in reply would likely have offered some such observation as the following: “All those laws which can be designated by the common name of mathematical mechanics, whatever that name includes of eternal and self-evident truths, and of laws which as a matter of fact are everywhere valid,--all these exist, not on their own authority, nor as a baseless destiny to which reality is compelled to bow. They are (to use such [ontological] language [such non-mathematical discourse] as men can) only the first consequences which, in the pursuit of its end, the living and active meaning of the world has laid at the foundation of all particular realities as a command embracing them all” (Metaphysic, vol. II, p. 391). Hence, Badiou’s defining move—to identify mathematics with ontology such that the former is conceived as the metaphysically primitive discourse of being as being—is a speculative strategy that Lotze would have judged a quixotic effort to deduce, “in one universal conviction,” that which “is expressible of being qua being.” Lotze would brush aside as metaphysically groundless Badiou’s protestation that his system goes no farther than to extrapolate from “the difficult constraint of fidelity” that Badiou sees as holding between the discursive universe of mathematics and the meaning of being as being. (Lotze himself suggested that speculation on “the ground of that

140 Inference and the metaphysic of reason the young Schröder (1877) to mathematicize logic. Commenting, for example, on Schröder’s “admirable” text on the Operationskreis of the logical calculus, Lotze remarks that Schröder’s mathematically articulated formulations of logical proof theorems have “no significance beyond that of establishing that the whole calculus is consistent with itself.” He contends that one could establish the general applicability of the logical calculus as a whole only “when it has been directly shown that each universal proposition is only the transcription of a logical truth into the symbolic language that has been adopted.”14 Lotze also challenges Jevons (1874), whose efforts to quantify predication are, to Lotze’s mind, neither genuinely innovative in the history of logical thought nor philosophically defensible.15 What Lotze concludes about the new symbolic logic remains highly pertinent. “It is inevitable,” he observes, “that a symbolic method intended to make uniform provision for every case should purchase its suitability for the solution of one problem at the cost of a useless prolixity in its treatment of others and of manifold discords with the custom of language.”16 Decades after Lotze’s death, Bosanquet would demonstrate the implausibility of Jevons’s probabilistic approach to hypothetical inductive inference (in contrast with his own position based “on material and positive connections, which are only defined by negation”17). Moreover, near the end of his own career Bosanquet—who remained active through 1922—published incisive criticisms of Russell’s symbolic logicism and of G. E. Moore’s unwarrantably influential misconwhich is” be pursued not in the order of the mathematical universe of discourse, but rather in the discourse of “that which should be” [ibid.].) 14  Logic, vol. I, p. 278. For Lotze’s detailed argument, see ibid., pp. 27898. 15  Maimon’s Experiment in New Logic (1794), a text doubtless known to Lotze, contains examples of earlier thinking on quantification, which N. I. Styazhkin explicates comparatively in terms of contemporary logical symbolism; see Styazhkin, History of Mathematical Logic from Leibniz to Peano (Cambridge, Mass.: MIT Press, 1969), pp. 130-33. For a twentieth-century critique of “Quantification of the Predicate” by an analytically astute idealist logician who had an acute grasp of symbolic logic as pioneered by Jevons and as later developed by Russell, see H. W. B. Joseph, An Introduction to Logic, 2nd ed. (Oxford: Oxford University Press, 1925), pp. 222-28. 16  “Note on the Logical Calculus,” Logic, vol. I, pp. 295-96. 17  Cf., Bosanquet, Logic, vol. II, chap. V, §4.

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structions and “refutation” of idealism.18 In the above-cited appendix on the relation of symbolic logic to his system of philosophical logic, Bosanquet criticizes Russell for an “extreme use of the hypothetical proposition in illustrating the meaning of implications.” Such meaning Bosanquet finds to be properly inferential only in metaphysically holistic systematic terms, not in mathematically linear, logical terms.19 And he declares against Russell’s logical orientation (an orientation now familiar to anyone with a passing acquaintance with “sentential” and first-order predicate logic) that one “cannot say, I should urge, ‘If a donkey is Plato, it is a great philosopher.’ The hypothesis scatters your underlying reality to the winds, and what I should call the basis of implication is gone. In a real system, S qualifies P as well as P, S.”20 18  In his last years, C. I. Lewis, who knew Moore’s criticism and who was deeply versed in Bradley and Bosanquet, confessed that as he “left idealist metaphysics permanently behind” early in his career, he “had done so with the conviction that, if [its main] theses had not been proved, neither had they been disproved. Its critics had won a shadow victory by capturing ground it did not hold and failing to attack where it was strongest. And no successor philosophic movement strikes me as having anything like equal depth and breath. It remains one of the most profound and impressive answers to perennial philosophic questions, though now largely neglected and forgotten”; see “Autobiography,” in The Philosophy of C. I. Lewis, Library of Living Philosophers, Volume 13, ed. Paul Arthur Schilpp (La Salle, Ill.: Open Court, 1968), p. 12. 19  As Oliva Blanchette would state the case, “logical truth and ontological truth cannot be understood as opposed to one another…Logical truth makes sense only in relation to ontological truth….”; see Philosophy of Being: A Reconstructive Essay in Metaphysics (Washington, D.C.: Catholic University of America Press, 2003), p. 201. Bosanquet doubtless would have dismissed as metaphysically question begging the technical distinction between “validity” and “soundness,” as opposed to the older distinction between two sorts of validity: formal and material. 20  Logic, vol. II, p. 41 note c. Cf., F. W. J. Schelling: “Ancient, profound logic differentiated between subject and predicate according to what preceded and what followed [antecedens et consequens], and thereby expressed the real sense of the law of identity”; see “Philosophical Investigations into the Essence of Human Freedom and Other Matters,” trans. Priscilla HaydenRoy, Philosophy of German Idealism, ed. Ernst Behler (New York: Continuum, 1987), p. 224. Gilbert Harman might chalk up the radical disparity of interpretation between Russell and Bosanquet to the latter’s reading of

142 Inference and the metaphysic of reason What Bosanquet rejects is Russell’s use of extensional logic, which, in the words of Brand Blanshard, “abstracts from all that is asserted by propositions” and, by the rules of its game, “deals with those propositions merely as units of truth or falsity.”21 (Hegel had long since repudiated a post-Leibnizian anticipation of such abstraction, in which “the relationship of the syllogism is made capable of being subjected to a calculus.”22) Whitehead would have classed rather as a “verbal expression,” than a proposition, the hypothetical conditional upon which Bosanquet based his criticism of Russell; and he ultimately would have sided with Bosanquet as philosophical logician. “It is merely credulous,” cautioned Whitehead (famed coauthor with Russell of Principia Mathematica), “to accept verbal phrases as adequate statements of propositions. The distinction between verbal phrases and complete propositions is one

Russell’s universality claim for symbolic-logical rules as improperly stipulating that they are also “exceptionless universally valid rules of inference”; see Harman, “The Logic of Ordinary Language,” in Common Sense, Reasoning, and Rationality, ed. Renee Elio (Oxford: Oxford University Press, 2002), pp. 93-103. 21  Blanshard, Reason and Analysis (LaSalle, Ill.: Open Court, 1964), p. 138. The most distinguished American student of Bosanquet’s thought, Blanshard probingly analyzes this “memorable difference of opinion between Messrs. Russell and Bosanquet,” in The Nature of Thought (London: Allen and Unwin, 1939), vol. II, pp. 430-34. 22  Cf., Hegel’s Science of Logic, trans. A. V. Miller (Atlantic Highlands, N.J.: Humanities Press, 1993), pp. 685-86 [Wissenschaft der Logik II. Frankfurt am Main: Suhrkamp, 1986, pp. 379-80]. The proponent of the mathematicizing approach that Hegel had in view declared that it had the advantage of rendering the whole of logic mechanistic and hence teachable to the relatively uneducated. (This calls to mind the masses of contemporary college freshmen in introductory symbolic logic courses). Hegel brushes aside the modus operandi of such formalists, whom he sees as operating als ob in der vernünftigen Verbindung, welche wesentlich dialektisch ist, ein Inhalt noch dieselben Bestimmungen behielte, die er hat, wenn er für sich fixiert ist (ibid., p. 379, emphasis added). He concludes his passing reflections on the topic with the judgment that to claim “that by means of the calculus the whole of logic can be mechanically brought within the reach of the uneducated, is surely the worst thing that can be said of a discovery bearing on the presentation of the science of logic” (ibid., p. 686 [p. 380]).

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of the reasons why the logicians’ rigid alternative, ‘true or false,’ is so largely irrelevant for the pursuit of knowledge.”23 More than six decades after Bosanquet’s death, Errol E. Harris picks up and extends Bosanquet’s thinking on this issue, formulating what is in effect a Bosanquetian critique of the major post-Russellian developments in formal logic (Quine’s, among others). Harris betrays a close affinity with Bosanquet’s holistic, systematic orientation in contentions such as the following: “It may be alleged that there is no contradiction in asserting that a whale has gills and lays eggs, but this is specious. If these terms are understood as they should be in their proper context the very idea of a cetacean becomes a texture of contradictions.”24 Challenges to formal logic along these lines are of course well known to analytic philosophers, whose responses range from modest qualifications of their own views, to charges that idealists are prone to crippling lapses of logical acuity, to blithe dismissals of such criticisms on grounds that they reflect a different and longsuperseded approach to the nature of reason. Bosanquet operated with the traditional view of predication, which at a deep level informs the metaphysical centrality that he accords the law of (non)contradiction, or identity. Indeed, one would radically misrepresent Bosanquet by lumping him with the enemies of formal analytic speculation. He simply insisted that the formal spirit of the logic of analysis must correlate with systematically general, fully articulated metaphysical insight. (Although Bosanquet died before Whitehead produced major systematic works that speak truth to Bosanquet’s speculative instinct on this theme, he did live long enough to recognize in the younger philosopher’s pre- and post-Principia writ-

23  Process and Reality, Corrected Edition (New York: Free Press, 1978), p. 11. 24  Formal, Transcendental, and Dialectical Thinking: Logic and Reality (Albany: State University of New York Press, 1987), p. 225 n. 9. For an incisive, classically grounded ontological critique of predicate logic and quantification, see Stanley Rosen, The Limits of Analysis (New York: Basic, 1980), esp. chap. 3. Another recent critical assessment of logicist thinking in just this connection is Lenn E. Goodman’s analysis of Quine, in In Defense of Truth: A Pluralistic Approach (Amherst, N.Y.: Humanity Books, 2001), §5.6 (“Ontological Relativity”).

144 Inference and the metaphysic of reason ings, through The Concept of Nature, a philosophical spirit that was in some fundamental respects at one with his own.25) 3.3 Critique of philosophical logicians on inference. Chapter 2 argued the case for why the onto-epistemological inquiry into the reason of the act of inference needs to extend beyond the purview of analytic epistemology, whether in the guise of logical empiricism or the philosophy of mind or neopragmatic philosophical semantics. We noted, moreover, that if in many respects a model of transcendental Thomist metaphysics, Lonergan’s philosophy includes an explicit doctrine of inference that is markedly analytic in character. We saw that if this is evident in his treatment of inference under the heading of “Empirical Method” it is all the more so in his bid to define “formal” inference as the hypothetical conditional (if-then statement). Our critique of the different analytic efforts to resolve “the problem of inference” disclosed unreasonable limitations and inconsistencies that raise basic questions about a broad range of leading contemporary accounts. These difficulties, as we saw, appear in sharpest relief when the goal is to formulate a general explanation of inductive inference (the perennial thorn in the side of logicist theory). From the standpoint of intellectual history, perhaps the central underlying factor that radically limits the onto-epistemological purchase of the classes of inference theory championed by the likes of Carnap, Harman, Brandom, Williams, and Lonergan is the prevailing rational-

25  In his late correspondence, Bosanquet confesses the wish for another half-century of life in order to witness the developments in philosophy that he felt were augured by the early writings of Ernst Cassirer and Whitehead. However, Bosanquet’s effort, at the end of his career, to find an underlying philosophical unity in the prominent competing currents of idealism and realism must count as a failure, although it did inspire the likes of Wilbur Marshall Urban (cf., Urban’s Beyond Realism and Idealism [London: Allen & Unwin, 1949]). Bosanquet would have been sorely disillusioned by the subsequent rise, between 1920 and 1970, of logical positivism and empiricism, Heideggerian continental thought, neo-pragmatism, the more decadent and topical post-Husserlian directions taken by phenomenology, along with the pervasive influence of linguisticism and analytic logicism. Cf., The Meeting of the Extremes in Contemporary Philosophy (London: Macmillan, 1921).

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ist epistemological hegemony.26 This scientific “shape” of consciousness (Gestalt) traces back to classical antiquity and begins to come into its own as a cultural force in early modernity. It came into its own in our epoch only with the advent of the Enlightenment Zeitgeist, which was lent its defining philosophical impetus by Kant.27 This circumstance in large measure motivated the effort in these pages to employ, as a heuristic instrument, the seminal Kantian onto-epistemological notion of Position oder Setzung, specifically in light of Kant’s own formal distinction between absolute and relative “positing.”28 Adapting Kant’s binary classification to such critical purpose has served two main ends. The first has been to help establish a unified context for critically evaluating the diverse philosophies of inference that we reviewed in the last chapter. The second goal has been to establish how the ontoepistemological basis for addressing the problematic of inference as act outstrips the orientational limits of paradigmatic analytic epistemologies. The next several sections of discussion build upon the points established in chapter 2, even as they address the reason of inference as explicated in the systematic thinking of Lotze and Bosanquet, both of whom take up the topic as a theme of the philosophical (metaphysi26  This is a hegemony of intellectual culture whereby the understandable sense of things in themselves is legislated by the epistemology of schematically applied formal sets of primitive principles or abstract categories. The latter ultimately derive from forms of logical judgment, and are propounded as the condition of the possibility of rational meaning, whose content is determined by the concept’s role as a “predicate of possible judgments”— i.e., as a moment of predicative thinking. 27  Who, despite his protests to the contrary, was widely understood as having assimilated ontology to epistemology. Cf., for instance, §13, Note II, of the Prolegomena. 28  As noted in chapter 2, three of the most valuable contemporary discussions on this topic are Eckart Förster, Kant’s Final Synthesis: An Essay on the “Opus postumum” (Cambridge, Mass.: Harvard University Press, 2000); Manfred Frank, Philosophical Foundations of Early German Romanticism, trans. Elizabeth Millán-Zaibert (Albany: State University of New York Press, 2004), Lecture 3; and Martin Heidegger, “Kant’s Thesis about Being,” trans. Ted E. Klein, Jr. and William E. Pohl, in Pathmarks, ed. William McNeil (Cambridge, Eng.: Cambridge University Press, 1999) [“Kants These über das Sein,” in Wegmarken, vol. 9 of the Gesamtausgabe (Frankfurt am Main: Klostermann, 1976)].

146 Inference and the metaphysic of reason cally speculative) logic29 whose lineage stretches back to classical First Philosophy. 3 Recent decades have seen Anglophone analysts silently if ever more confidently co-opt the designation “philosophical” as properly applying to deductivist sentential and predicational regimes of formal logic. One need only open a leading contemporary logic text, such as A. C. Grayling’s Introduction to Philosophical Logic,30 to find that this historically significant semantic drift essentially obliterates the distinction between sharply circumscribed formalist thinking and broadly systematic, onto-epistemology. (The latter entails a thinking that never postpones the largest questions about the nature of meaning, being, actuality, relation, and so forth from any technical analysis or formulation of axioms). Grayling’s Introduction includes, for example, a section on “Logical Predicates and Ontological Commitments” that treats of “existence statements” by way of rehearsing competing approaches to grammar, the syntax of quantificational logic, and the reference—the ontological commitment—of logical terms31 “to objects in a given domain of discourse.” The logic of Being, in view of this methodological regime, is in effect a product of discourse. Beyond the debates over whether to restrict the very idea of inference to deductive thinking, analytic epistemologists generally find themselves stalemated when they encounter the necessity to identify and substantiate in self-consistent terms “the sources of knowledge that are non-inferential.”32 These sources, which we cognize as “existential judgments,”33 both legitimate and give an intelligible definition to their positive claims (logical, empirical, semantic) about the structure or axiomatics of an inferential mode of thinking. Such originary, 29  By which I mean speculative logic (Hegel’s, however problematic, being the paradigm) that is more onto-epistemologically attuned and broader based than formal logic, and inclusive of it. 30  3rd ed. (Oxford: Blackwell, 1997). To date, this widely influential text has been reprinted five times, twice in 2003. It is puffed as a “mainstay for students taking courses in philosophical logic” (back cover). 31  Such as variables bound by quantifiers. 32  P. Lipton, Inference to the Best Explanation (London: Routledge, 1991), p. 4. 33  See Desmond Connell, “Existence and Judgment,” the opening chapter of Connell’s Essays in Metaphysics (Dublin: Four Points Press, 1996), p. 22.

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onto-epistemological sources of knowledge are not discrete from but rather formally implicated in the very act of inference. And the epistemologists of inference commonly err when they assume that they can capture the logic of non-inferential sources of knowledge in abstract logical assertions based merely on the law of (non)contradiction, without due regard for the principle of sufficient reason. Such assertions derive their persuasiveness from the fact that their denial involves one in self-contradiction (i.e., from the fact of “validity”)—this in abstraction from determinations as to how properly they bear out the existential judgments (i.e., “soundness”) to which they putatively refer. The more penetrating analytic epistemologies of inference don’t shirk the challenge of somehow incorporating the grounding principle of the reason (Grundsatz) of the inferential act, which is to say the principle of sufficient reason. But the effort is typically fraught with crippling speculative difficulties. We earlier considered a salient instance of this in Carnap,34 who found himself apologetically invoking intuition—for him an “existential judgment”—as the onto-epistemological moment that grounds as fact the meaningful grasp of his (or any) logical assertions about deductive inference. This expedient led Carnap to acknowledge that he was going against the consensus his analytic colleagues. But he fully recognized what Desmond Connell has termed “the embarrassment created for logical analysis of the existential judgment which can hardly be a tautology because it asserts a fact, and can hardly assert a fact if to deny it involves one in a contradiction.”35 The aporia for purely analytic approaches is unavoidable if one sets out to explain inference, of whatever sort, as strictly a function of formal patterns or sets of rules or procedures. One facet of the difficulty involves the matter of how much light any such axiomatic guidelines or directions actually shed on inferential thinking. Just how far and how reliably do, for example, the rules of chess delineate the actuality (Wirklichkeit) of a given player’s inferential moves? A second problematic aspect concerns the relation between the very act of axiomatizing logic and the nature of what such postulation is held self-consistently to distill or map or re-present. 34  See §2.2, above. 35  Essays in Metaphysics, p. 22.

148 Inference and the metaphysic of reason Jaakko Hintikka remarks at the outset of his Principles of Mathematics Revisited that any “complete” axiom system requires no “new observations, experiments, or other input from reality. It suffices to study the axioms; you no longer need to study the reality they represent.”36 What first strikes one here is the uncritical shift from referring to “reality” per se to “the reality” (emphasis added) that a set of axioms represents. (What licenses the reduction from “reality” to “the reality” represented by a set of axioms? What sort of real is it?) Second, the term “complete” sharply delimits the aspects of reality that apply, for nothing eluding a particular theorist’s or school’s “observations, experiments, or other input” could count as real (unless the initial axiomatic inspiration were superhuman). Perhaps the most telling formal limit of axiomatics, judged from an onto-epistemological perspective, is that at some point both the derivation and application of rules or axioms is not rule governed or axiomatic. Notoriously, it is at such junctures that analytic epistemologies of inference get tangled in contradictions and inconsistencies. This arguably follows, in great part, from conceptualizing predicative cognitional acts in ways that tacitly dichotomize the absolute and relative dimensions of the being of knowing, or that reduce the absolute to the relative. Unexpectedly enough, we shall presently see this in Lotze (no friend of metaphysically otiose formalism), whose philosophy of inference runs into systematic difficulties that have their source in his well-known categorical split between formal thinking and reality. 3.4.1 Overview of Lotze’s thought and influence. Rudolf Hermann Lotze ranks as perhaps the culminating metaphysically attuned theorist of the logic of inference prior to the revolution in the field wrought by the likes of Frege and Russell.37 Lotze was an early process philosopher who understood Being as “really a continuous energy, an activity or function of things.”38 He attempted to synthesize, along highly suggestive and influential lines, a monistic idealism with a pluralistic 36  (Cambridge, Engl.: Cambridge University Press, 1998), p. 1. 37  Widely hailed the original thinker who single-handedly initiated the transformative emergence of symbolic logic as the new model of scientifically rigorous philosophical logic, Frege himself drew to some extent on Lotze’s work. (Some might argue that Christoph Sigwart (1830-1904) is as much a culminating figure as Lotze on this score.) 38  Metaphysic, §49.

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realism.39 Although by the end of his career Lotze approached the international celebrity status of the leading figures in the nineteenthcentury German philosophical pantheon, he left no school of epigones. Moreover, the many students of his who became distinguished thinkers in their own right often adapted to their divergent purposes, and without acknowledgment, such original elements of Lotze’s thought as his core doctrines of relation (Verhältnis) and validity (Geltung). On that count, it is hardly surprising, that Lotze faded for the most part to little more than an occasional reference or footnote in the defining twentieth-century studies of logic and metaphysics, epistemology and the philosophy of psychology. Indeed, the late John Passmore hardly exaggerated when he described Lotze as the nineteenth century’s “most pillaged source”40 of original philosophical ideas. Frege is a case in point. He garnered fame for, among other things, advancing the notion of the concept as a function. This is an idea that he likely encountered initially in the Introduction to Lotze’s Logic, which he is known to have read. Lotze cites instances of “thought, concept, judgment, and syllogism” that make “clear what is the surplus of work performed by thought over and above the mere current of ideas; it always consists,” he observes, ‘in adding to the reproduction or severance of a connection in ideas the accessory notion of a ground for their coherence or non-coherence.”41 On another point, Kai Hauser remarks that Lotze’s “discussion of different expressions having identical referents, foreshadows the distinction between sense and reference standardly associated with Frege’s Über Sinn und Bedeutung.”42

39  Cf. the synoptic account of his metaphysical system in a lecture series, published as Outlines of Metaphysic: Dictated Portions of the Lectures of Hermann Lotze, translated and edited by George T. Ladd (Boston: Ginn, Heath, and Co., 1884). 40  A Hundred Years of Philosophy (London: Duckworth, 1957), p. 49. Also see Paul Grimely Kuntz, “Lotze’s Relevance to Contemporary Philosophy,” part of the extended introductory essay to Kuntz’s edition (the first published edition) of Santayana’s doctoral dissertation: Lotze’s System of Philosophy (Bloomington: Indiana University Press, 1971), pp. 69-83. 41  Logic, vol. I, p. 6. 42  Hauser, “Lotze and Husserl,” Archiv fur Geschicht de Philosophie 85, Bd. S. (Berlin: de Gruyter, 2003), p. 160.

150 Inference and the metaphysic of reason Edmund Husserl, who was in many respects an unfair critic of Lotze,43 nonetheless announced that the latter’s brilliant interpretation of Plato’s doctrine of Ideas gave me my first big insight and was a determining factor in all further studies…. [Lotze was someone to whom the Logical Investigations owe] very much in the thinking out and thinking to conclusion which brought forth in all directions novel thought-constructions both in details and as a whole.44

Among other eminent German thinkers indebted to Lotze, Ernst Cassirer (an acute judge of historically seminal philosophical talent45) argued that Lotze’s notion of the “first universal”—if “correctly understood and interpreted”—provides “the key to an understanding of the original form of linguistic concept formation.”46 The Oxford philosophers Bradley, John Cook Wilson (who studied with Lotze), and Bosanquet (Lotze’s principal Anglophone editor and translator of the later Logic and Metaphysic) repeatedly acknowledged the formative influence of the German master. Typical is the following confession of Bosanquet’s that appears in the opening pages of his own Logic: “As I have often been led to express disagreement with Lotze…I ought to say that but for his great work on Logic the larger part of what I have written would never have come into my head.”47 43  See Stambovsky, “Husserl’s Logische Untersuchungen (§59) and the Marginalization of Lotze in Anglophone Philosophy,” Prima Philosophia 16.3 (2003): 261-78. 44  “A Draft of the ‘Preface’ to the Logical Investigations (1913),” ed. Eugen Fink, trans. P. J. Boussert and C. H. Peters (The Hague: Nijhoff, 1975), pp. 36 and 47. Bosanquet detected early on that Husserl tended to downplay and even distort the originality and value of Lotze’s thought and influence; see Implication and Linear Inference (London: Macmillan, 1920), p. 142. For an assessment of Husserl on this score, see Stambovsky, “Husserl’s Logische Untersuchungen (§59) and the Marginalization of Lotze in Anglophone Philosophy.” 45  For example, it was Cassirer who was largely responsible, as Paul Tillich noted, for establishing the current consensus among informed intellectual historians that Nicholas of Cusa, and not Descartes, should be counted as the first modern philosopher of the Western tradition. 46  The Philosophy of Symbolic Forms, Volume 1: Language, trans. Ralph Manheim (New Haven: Yale University Press, 1955), pp. 282-83. 47  Logic, Or the Morphology of Knowledge, p. vii.

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American philosophers who attended Lotze’s lectures and whose work resonates with his thought range from such estimable if nowobscure systematic thinkers as the personalist Borden P. Bowne and the many-faceted George Trumbull Ladd, to major figures such as William James and Josiah Royce. Finally, that a considerable fraction of Lotze’s output still speaks to contemporary speculative concerns becomes apparent upon a close reading48 of his published lectures on metaphysics, psychology, philosophy of religion, ethics and aesthetics—not to mention his multi-volume Logic and Metaphysic. (Lotze’s bid, for instance, to reject the analytic/synthetic dichotomy on grounds that anticipate Quine’s famous critique typifies Lotze’s engagement with issues of abiding speculative interest.49) Credited or no, however, philosophical stature alone is not the reason why Lotze figures in this book as one of two metaphysicians whose thinking intermediates, as it were, between analytic epistemology and the onto-epistemology of inference. Lotze’s special pertinence here is owing to his discursively analytic typology of inference—syllogistic, mathematical, systematic. This he elaborates as a moment of concept formation, but one determined metaphysically, which is to say, a moment determined by a universal principle that guides inferential translation of “a given coexistence of ideas into a coherence between their contents.”50 It is this thinking, in conjunction with the ontological purport of his repudiation of the term Position oder Setzung (in favor of “Wirklichkeit”), that reveals Lotze to be a defining transitional figure in the present inquiry, as we move from the critique of contem48  Few contemporary students of thought are likely to find congenial Lotze’s prose style, marked as it is by attenuated pacing, a generally diffuse manner of elaboration, and a tentative tone. Like Bosanquet’s, Lotze’s prosody—to which the translations and his own English are in the main faithful—has doubtless contributed to his continued relative obscurity on the philosophical scene. In the case of Bosanquet, Brand Blanshard (a noted stylist) reports a meeting with F. H. Bradley (a master of lucid philosophical prose) during which Bradley “made the certainly true remark that Bosanquet had lost some deserved recognition because of his unfortunate style”; see The Philosophy of Brand Blanshard, ed. Paul Arthur Schilpp (La Salle, Ill.: Open Court, 1980), p. 25. 49  Cf., Logic, vol. II, §§297 and 363, and Quine’s From a Logical Point of View, 2nd revised ed. (1961), pp. 36-37. 50  Logic, vol. I, p. 134.

152 Inference and the metaphysic of reason porary epistemological inferentialism toward an exclusive concern, in chapter 4, with the onto-epistemology of inference.51 3.4.2 Onto-Epistemological reading of Lotze on inference. The theory of inference is the subject of an appendix to the second chapter of Lotze’s Logic and the main focus of his third chapter. The appendix covers so-called “immediate inference,” a dubious notion under the heading of which Lotze describes the four forms of judgment that compose the Aristotelian square of opposition. Without the mediating moment that attaches to the two or more antecedent judgments in proper acts of inference, Lotze’s “immediate inferences” describe the classic quartet of simple judgments (all S are P, no S is P, some S are not P, some S are P). But the four are mutually dependent, the truth-value of each judgment is determined with respect to that of the three others, something that does entail some explanatory relational principle (or middle term): subalternation, for example, or contradiction. We thus infer the truth-value of one judgment as it correlates, says Lotze, with that of the other judgments.52 This is the intermediate structure that Lotze invokes to substantiate his idea of a transitional variety of cognizing, one that takes logical thinking from judgment to inference. One might well find it difficult, however, to grasp how a subalternation or contradiction that derives from four simple judgments is anything other than the component of an inference, a mediated judgment, and not a transition from judgment to inference. As for inference proper, Lotze supplies his broadest-ranging explicit definitions in declarations such as the following: The form of thought which combines two judgments so as to produce a third is, speaking generally, inference….53 Following Aristotle, we give the name of inference or syllogism to any combination of

51  While Lonergan was quite as metaphysically inclined as Lotze, the expressly epistemological bias of Lonergan’s approach to the formal character of inference—as exemplified by the hypothetical conditional—justifies including his inference theory, with those by the likes of Carnap, Harman, Brandom, and Williams, as one of a representative sampling of notable analytic approaches to the “problem of inference.” 52  See Logic, §§75-83. 53  Ibid., vol. I, p. 106.

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two judgments for the production of a third and valid judgment which is not merely the sum of the two first.54

Lotze argues that the two antecedent judgments (the premises) require a common factor, or middle term, that as “a proximate higher universal” makes the inferential combination possible (e.g., SM, PM, consequently SP).55 Following these generalizations, Lotze goes considerable lengths to explicate and illustrate the epistemological limits of the full range of traditional syllogistic forms and moods. He explains the syllogisms as paradigmatic “methods” by means of which we infer—whether by way of “subsumption” or “induction” or “analogy.” The “form of the premises,” in his view, is the factor that determines these methods, and he finds that we simply “have to take” them “as experience offers.”56 The forms of syllogistic, however, impress Lotze as being insufficiently specific fully to characterize inference, given the ontic intentionality of inferential reflection in “the living exercise of thought.”57 Anticipating Cassirer’s explication of scientific inference, Lotze finds in mathematical inference—inference by substitution, by proportion, and from constitutive equation—thought forms that more determinately exhibit the relation between things in their difference. These things prove mutually determinative by way of general principles of differentiation (or transformation rules), i.e., “under a common law.” At first sight, this line exposition might appear formally to set to rights the problematic Kantian legacy of an epistemologically positivist orientation to inference, one limited, for the understanding, strictly to predicative, relative positing (setzen). Lotze seems here elegantly to recast inferential thinking as a variably modulated conceptual medium that reconciles, without attempting “to fuse,” in Bosanquet’s words, “into an undiscoverable third” the incommensurable moment 54  Ibid., p. 114. 55  The position of the present work, and Bosanquet’s point of departure, is that the act of inference is strictly a mediated form of judgment. 56  Logic, §101. This understanding of the efficacy of form in inference is consistent with its role in the onto-epistemology of inference as thoughtthrough, below, in chapter 4. 57  Logic, §107. Concurring with Lotze, I would emphasize the living nature of the reflective process in the act of inference, a defining moment of inferential thought that the general run of contemporary analytic epistemologies of inference typically neglect or associate with psychologism.

154 Inference and the metaphysic of reason of absolute (existential) positing with predicative thinking (discursive reflection). There is, for instance, perhaps no more familiar mode of rational understanding than that realized when one grasps with concrete specificity a geometrical curve by means, say, of “inference from constitutive equations.”58 Notwithstanding Lotze’s insights in the foregoing observations, this route of analysis hardly addresses certain onto-epistemological issues at the heart of the reason of the act of inference—something of which Lotze himself was, in his own way, fully aware. He points out, for example, that the very “disparateness of marks” (i.e., variables) that transect inferential domains, such as from algebraic to spatial realms, leads beyond a mathematically linear ideal of inference to synthetically “systematic” ideal forms of thought—classificatory, explanatory, and dialectico-speculative thought. But Lotze keeps the “ideal” character of logical forms front and center, reserving systematic ontological concerns for “the idealistic philosophy to which [his logic] is intended to lead.”59 (Bosanquet, among Lotze’s closest Anglophone readers, would later undertake to combine the two dimensions in his holistic, systematic philosophy of inference.) The classificatory, explanatory, and dialectico-speculative forms of thought are not, for Lotze, types of inference.60 And after surveying the “mathematical forms” of inference—substitution, proportion, and constitutive equation—he expressly puts off, as beyond the bounds of his Logic, precisely those systematic metaphysical concerns that are arguably most germane to the onto-epistemology of inference, as Bosanquet in particular recognized. Speculative concerns of just this sort—the status, for instance, of formal cause vis-à-vis the rationality of inferential reflection—will emerge as core issues in the constructive phase of the present study, signally in connection with the principle of sufficient reason.61 Regarding the latter, Lotze himself offers a highly interesting analysis, main elements of which inform the onto-epistemology of inference. Yet if he acutely adumbrates significant features of how the “law” of sufficient reason operates in the onto-epistemologically articulated 58  59  60  61 

Logic, §117. Logic, vol. I, p. 198. Cf., Logic, §119ff. See chap.4, below.

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reflective logic of the act of inference, Lotze explicitly limits the fact of sufficient reason to the epistemological domain. He concludes that the law of sufficient reason is concerned as such strictly “with the merely thinkable which has no real existence in fact,” and that its office is “merely to show how, from the combination of two contents of thought, S and Q, the necessity arises of thinking a third, P, and this in a definite relation to S.”62 Lotze reserves for his Metaphysic and his lectures on ontology (subtitled, “Of the Coherency of Things”63) discussion of the onto-epistemological issues that bear on inference in ways that correlate with the orientation to the topic taken in the present essay.64 One discovers in the Metaphysic65 that they emerge, indirectly and by way of contrast, when Lotze takes up the principle of sufficient reason in definitively onto-epistemological terms. This he does with respect to the principle’s germ in Aristotelian metaphysics. Lotze identifies in Aristotle ontological speculation that trumps the received view associating sufficient reason with the “modest truth, that anything which is to be real must be possible.” Dismissing this notion, Lotze locates the origin of the “law” of sufficient reason in the Aristotelian insight that “all Becoming” is “characterized throughout by a fixed law, which only allows the origination of real from real, nay more, of the determinate from the determinate. We have here,” concludes Lotze, “the first form of a principle of Sufficient Reason [die erste Gestalt eines Satzes vom zureichenden Grunde], transferred from the connected world of Ideas to the world of events….the possible transition from duvnami~ to ejnevrgeia [den möglichen Übergang aus duvnami~ in ejnevrgeia].”66 What strikes one most forcefully here is Lotze’s working assumption that logic, which he understands as thought (ideation), is ontologically discrete from Reality.67 While he rightly enough sees Sufficient 62  Logic, §§62 and 63. 63  Outlines of Metaphysic, §§8-20. 64  These issues will come to the fore when we turn to Lotze’s telling rejection of Position oder Setzung as a metaphysical term of art. 65  §§42ff. 66  Metaphysic, §41 (emphasis added); [Metaphysik: Drei Bücher (Leipzig: Hirzel, 1879), pp. 89-90]. 67  There will presently be more to say about this formative distinction of Lotze’s.

156 Inference and the metaphysic of reason Reason as a completely general “law” that originates not in Leibniz, but with the beginnings of metaphysics, Lotze thinks of it as initially having been “transferred” from the domain of Ideas to that of events. And he speculates that this may indicate the momentous transition or extension of “the space of reasons” from the potential (dunamis)—the realm of mere thinking and speculation—to that of actualization (energeia) or the Real.68 Lotze evinces in all this a most acute philosophical instinct: turning to the Aristotelian ontology of duvnami~ and ejnevrgeia to find the ground of the principle of sufficient reason. But his tacit metaphysical dualism precludes the consideration of a possibility that is central, I would submit, to the onto-epistemology of the act of inference. Lotze appears not to consider that, in the very act of being that is the “transition” from duvnami~ to ejnevrgeia, one has the ground of Sufficient Reason itself; and that this ground shows, in the first instance (Prius), as a matter of formal cause, rather than as either motive cause or strictly final cause. That this onto-epistemological itinerary might structure the conceptual logic of the act of inference—this is not a notion that Lotze, given his metaphysic, would have been in a position to entertain, although it will turn out to be the central thread of the present essay’s argument in chapter 4. By thus treating Sufficient Reason, in the Logic, as no more than an epistemological principle Lotze is being true to a metaphysic that categorially distinguishes formal thought from reality. On this particular, Moritz Schlick in his brilliant, pre-positivist period cautioned that it is “misleading to proceed as Lotze does, in his well-known treatment of the problem [of “the relation of the logical to the real”], by opposing the formal and the real significance of the logical to one another.”69 (Lotze understands by “real”—the German, Real—“only things and events in so far as they exist and occur in an actual world of their own beyond thought.”70) Schlick accurately enough detects Lotze set68  Lotze devotes the third chapter of his Metaphysik, Book I, to the “Realen und der Realität.” 69  See “The Nature of Truth in Modern Logic,” Mortiz Schlick: Philosophical Papers, Volume I (1909-1922), ed. Henk L. Mulder and Barbara F. B. Van De Velde-Schlick, trans. Peter Heath (Dordrecht: Reidel, 1979), p. 95. 70  Logic, vol. II, p. 281. The section in which this statement occurs (§345) summarizes the meaning and distinguishes from each other three essential

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ting the formal significance of logic over against its “real” significance; and in light of this, one might with some justification charge Lotze with dichotomizing logic and reality, at least on onto-epistemological grounds. But Lotze’s thinking here is more nuanced than Schlick’s verdict suggests. This becomes immediately evident when one considers the logic/reality opposition in light of his Metaphysic (pure ontology), rather than from the standpoint of the Logic. While even in the Logic Lotze insists that the Formal “cannot stand altogether out of connection” with the Real, it is in the Metaphysic that he develops his insight into the nature of this connection, which he contends is “more” than “a relation in the ordinary sense of the term”: it is ideal. This for Lotze means that the relation between the Formal and reality has an ontological status that, if a product of living thought, is not just a moment of cognition or in any way limited to the Subjective. This ontologically singular relation—what Lotze denominates “a between” (Zwischen)71—arising in a reflectively thinking being, is parasitic on the act of thought. It “arises…as a perception immediately intelligible to thought,” but not, Lotze would insist, as “a directly perceptible content”72 (like a color) that one passively apprehends. Indeed, Lotze portrays the relation in question as “a mere memorial of an act of thought achieved solely by means of the unity of our consciousness.”73 By the same token, given Lotze’s definition of the Real, it “would be binarisms, contrastive modalities of “significance,” with which Lotze operates: Subjective/Objective, Formal/Material (sachlich), and Formal/Real. (Cf., “…we call the logical operations not Subjective merely but Formal because [of ] their characteristics though not the actual determinations of the matter [der Sachen] they deal with, yet on the other hand are Forms of procedure the very purpose of which is to apprehend the nature of that subject-matter, and which therefore cannot stand altogether out of connection with that which there has place” [ibid., p. 280].) 71  A most pregnant ontological conception that, in recent years, has found a champion in William Desmond. Desmond systematically develops the notion of “the between” (beyond any Lotzean restriction to human consciousness), casting it as “a logos of the metaxu”—the “metaxological”—that constitutes “a sense of the ontological” that properly characterizes “the transcendence of beings in relation to their being.” See Desmond’s Being and the Between (Albany: State University of New York Press, 1995), esp. chap. 5. 72  Cf., Lotze, Metaphysic, §268. 73  Metaphysic, vol. I, p. 190 [cf., Metaphysik, pp. 157-58].

158 Inference and the metaphysic of reason wholly futile” [ganz unausführbar], as he explains, “to try…to assign to this between [diesem Zwischen]…a real validity in the sense of its having an independent existence of its own apart from the consciousness which thinks it” [abgesehen von dem Bewußtsein, welches es denkt].74 3 Consistent with his derivatively Kantian metaphysical distinction between the logical and the Real, Lotze expressly declines to explore the onto-epistemology of inferential reflection in the Logic. He proceeds instead from an analysis of syllogistic and then mathematical inferences to an involved combinatory explication of “classification”—an exercise in practical conceptual analysis (where references to inference drop from sight). Lotze winds up his discussion with a meditation on the logic of scientific explanation, one that prefigures those of logical empiricists, such as Karl Popper, by many decades. The nearest Lotze comes to articulating a conceptual logic of inference is when he takes a dialectical turn from the logic of “systematic” inferential form75 to that of the “form of speculative thought.” The latter turns out to involve the act of reflectively entertaining systematically related “essential marks” (Merkmale)76 whose formal law comprises 74  Ibid. [Metaphysik, p. 158]. 75  “Judgment” being the “comprehensive” form; see Logic, chap. II. 76  Building a case for his functional orientation to the concept in scientific concept formation (as opposed to the traditional “logic of the generic concept”), Ernst Cassirer, critiques reductive theories of abstraction. In the process he argues that by explicating logical inference in terms of nonvariable Merkmale and by employing the idea of Thing (in contrast, for example, with “property” and “event”), Lotze propounds an antiquated and reductive orientation to scientific concept formation (cf., Lotze, Logic, §§53 and 316). “As long as we believe,” argues Cassirer, “that all determinateness consists in constant ‘marks’ in things and their attributes, every process of logical generalization must indeed appear an impoverishment of the conceptual content. But precisely to the extent that the concept is freed of all thing-like being, its peculiar functional character is revealed. Fixed properties are replaced by universal rules that permit us to survey a total series of possible determinations at a single glance. This transformation, this change into a new form of logical being, constitutes the real positive achievement of abstraction”; see Substance and Function [Substanzbegriff und Funktionsbegriff ], trans. William Curtis Swabey and Marie Collins Swabey (New York: Dover, 1953), pp. 22-23. While acknowledging the force of Cassirer’s criticism, Lotze might have replied that he never taught that inferential generalization produces “things.” Such abstraction, to Lotze’s way of think-

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the concept of a thing “sufficient to distinguish it from others and to show what it is itself.”77 We shall see that Lotze considers this grounds for rejecting Position/Setzung as a speculative term. His proximate target when repudiating the term was Herbart’s atomistic use of Position, which he condemned for failing to accommodate the cardinal ontological moment of relation—Lotze’s historically influential core metaphysical principle. Overall, Lotze characterizes dialectico-speculative thought as a cognitive process the final cause of which is the constitutive concept, or “logical Idee.” He distinguishes the logical Idee of an object from its “mere conceptual form in general.” For instance, the logical Idee of a “plant or organism, as its formative law,” contrasts with “the concept of it, which merely comprises the sum of the necessary marks and the form in which they happen to be [semiotically] combined.”78 To Lotze’s way of thinking, a speculative concept (what I should term a route of inference) has “for its starting-point the law which determines the order of all the other marks” that explain whatever the object of the concept happens to be. In other words, the law—something that Cassirer would interpret rather as a function79—is the formal ground that determines the order of the signs or figures or “semblances” that reing, involves rather objectification (cf. Logic, §§2 and 3)—every bit what Cassirer would term “a new form of logical being.” As Lotze would have put it, this “replacement,” in the case of perception, for instance, “gives to what is perceived a definite place in the world, which makes it something on its own account, and not a mere excitation of the percipient at the moment.” In the sentence that immediately follows, it becomes clear (even as Lotze problematically separates the Formal from the Real) that in this observation Lotze intends something that approaches to onto-epistemological positing: “In this lies the logical gain which always results when the particular content of a perception is replaced in the judgment by the universal of which it is an instance” (Logic §105). Lotze goes on to indicate how this abstraction reveals the logical insufficiency of Aristotelian syllogisms. 77  Logic, §130. 78  Logic, §129. 79  Like Cassirer, Lotze moved beyond Aristotelian inference to mathematical inferential form (which he also referred to as syllogistic). Cassirer, however, held that the mathematically derived concept of “function” supplies the key to a non-reductive account of scientific knowledge, while Lotze interpreted any such “universal rule” as operative strictly in terms of quantitative determinations.

160 Inference and the metaphysic of reason flectively compose the “reason upon which in thought the reality rests” (emphasis added). Articulated as an inferential, form-ordered composition of “marks” this logical Idee is, insists Lotze, neither “the intention of a reflective consciousness striving for fulfillment” nor is it “an active force which causes its results.” It is a fact that is neither psychologistically subjective nor a motive power extrinsic to the act of thinking. Rather, as Lotze sees it, the onto-epistemological profile of the inferential form of speculative thought is that of a reflective act that grasps “the conceived or conceivable reason, the consequences of which under certain conditions are the same in thought as those which must follow in reality, under the like conditions, from an intelligent purpose or a causative force.”80 This is the Achilles heel of Lotze’s explication of inferential thought. Lotze contends that inferential thinking attains to intelligible reasons whose “consequences” are somehow, “under certain conditions,” necessarily the same in thought as those that occur “in reality” as a result of final cause and efficient cause. The most serious concern that this formulation raises in the present discussion has to do with the factor of “cause.” Notice the types of causes that Lotze adduces, and to what they are restricted, when under certain dispensations they sponsor the identity, in both thought and reality, of “consequences.” These consequences flow from abstractly logical (as opposed to conventional81) “ideas” that one inferentially conceives, or may conceive, as reasons for things. In thought those “real consequences” take a purely “abstracted” form. “Activity,” observes Lotze, “whether intentional or unintentional, never produces anything but what is abstractedly possible to thought, and this becomes necessary to thought as soon as we affirm one of a number of related points [in an organism or logical system] upon which the rest depend.”82 In the sphere of thought, the ideal moment—always, for Lotze, relationally composed—grounds the ontological identity of the consequences that thought and “reality” share. As such, the ideal moment is not any “intuition of a reflective consciousness striving for fulfillment, nor...an active force which 80  Logic, §130. 81  Lotze likely would have dismissed as positivists the general run of logicians who operate under the illusion that they are “doing” ontology or, more generally, an enlightened form of “topical” metaphysics. 82  Logic, §130.

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causes its results.”83 Nonetheless, such final and efficient causes are what actualize “in reality” the very thing that we may entertain in the cognitional idiom of reflective thought. What does this all mean with respect to the act of inference construed onto-epistemologically? On Lotze’s understanding, when one follows the implications of a constitutive logical Idee one entertains a notion that is neither a final cause (an aim) nor an efficient cause (a motive impetus) in one’s reflective activity. Yet the character of those implications is, according to Lotze, identical (to that in thought) in the ontologically objective domain, i.e., “in reality”—and is identical precisely as a consequence of final cause (“intelligent purpose”) or efficient cause (“a causative force”) operative in that domain. The logical Idee is neither a moment of cognitive process nor a substance or power capable of efficient cause; and Lotze may hold it to be as ontologically neutral in this respect as he pleases. But what this account does not explain is the idea’s formative efficacy—a function of its articulate character or power as forma formans—in inferential reflection. The causes are all on the side of objective reality, leaving open the question of how such an idea84 is onto-epistemologically operative as a moment in the reason of the act of inference. Moreover, one cannot reduce all causes simply to mechanism or aim. This fact has a decisive bearing on the orientation to the act of inference that in the view of the present author more nearly captures the onto-epistemological truth of its reason, namely that formal cause is what in the first instance explains the forma formans of inferential ideation in its onto-epistemological context. Lotze goes to great lengths detailing the many formal varieties of inference,85 but his efforts in that particular do not touch this fundamental issue. Still, to relegate, as he does, final and efficient cause to the “objective” reality of the inferential act does seem right enough. What from the subjective attitude are relations, Lotze counts, in the realm of objective reality, as components of a thing’s intrinsic make-up. Those relations, besides being mentally framed about things, are also “really extant for things themselves”—such Ver83  Ibid. 84  Understood as a Lotzean Idee that is ontologically discriminable from any given psyche that reflectively entertains it, since different psyches can think it, so long as they are sufficiently similar in nature. 85  Kant, recall, restricted the range of Vernunftschluss to the categorical, hypothetical, and disjunctive syllogistic forms.

162 Inference and the metaphysic of reason hältnisse Lotze denominates “metaphysical objective relations.” But he thinks of such “metaphysical” relations in subjective terms with respect to the objects or “Things” that feature them; for he argues that the relations take the form of “a resistance” (rather an expression of a thing’s inner constitution than a discrete fact), “which things really offer to one another.”86 Even granting Lotze his metaphysical subjective/objective binarism, however, one sees that nevertheless he does not clearly distinguish the causal factor, the rational Grund in the act of inferring that would explain, without recourse to psychologism, the ordered play87 of a “real” idea on the subjective side of the equation.88 Lotze himself takes the following view of “real” ideas: “in so far as they are present in our minds, [they] possess reality in the sense of an Event,—they occur in us.” But the “content” of these ideas does not occur, nor does it “exist as things exist,” i.e., objectively. What then, in the act of inference, is the ontological status of that criterion that vouchsafes the fact that is identical (hence true) for both thought, and the wirklich being of objective reality? Lotze’s position on this is that the ontological status of such a “real” idea is Validity (Geltung), in the sense of what holds or counts. And there the matter ends. “As little as we can say how it happens that anything is or occurs,” declares Lotze, “so little can we explain how it comes about that a truth has Geltung.”89 Among the best known and most influential of Lotze’s philosophical working assumptions, “validity” is “underivable, a conception of which everyone may know what he means by it, but which cannot be constructed out of any constituent elements which do not already contain it.”90 86  Outlines of Metaphysic, §20. 87  An ordered play not typically confined to any particular rational subject. 88  Addressing this matter is a chief aim of chapter 4, where I identify sufficient reason as a principle of formal cause and indicate how it, rather than the law of identity, or (non)contradiction, is in the first instance the Grundsatz that constitutes the reason of the act of inference. 89  Logic, §317. For a probing recent discussion of Geltung, and of Lotze’s influence (and Heidegger’s critical analysis of it), see Daniel O. Dahlstrom, Heidegger’s Concept of Truth (Cambridge, Engl.: Cambridge University Press, 2001), §1.3. 90  Ibid. On Paul Natorp’s objection to Lotze’s asserting the onto-epistemological ultimacy of “validity,” see, above, chap. 1, n. 68.

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Notwithstanding his often illumining, metaphysically informed explication of the elements that compose the onto-epistemology of inference, Lotze insists on establishing logical thinking and reality as ontologically disjunct categories.91 One consequence of this is that his theory of inference does not effectively integrate with his consideration of the “Being of Things” (the theme with which he commences his Metaphysic) his best insights into inference. Lotze divides syllogistic inference92 into subsumptive, inductive, and analogical modes— which correlate respectively with disjunctive, copulative, and “remotive” premises. Suggestively, in the crucial case of inductive cognition, he concludes that inferential thinking is “guided…by the universal principle which dominates all its activity, the principle of translating a given coexistence of ideas into a coherence between their contents.”93 How one might systematically articulate this “principle” not merely in formal but also in conceptually logical, onto-epistemic terms, Lotze does not say. Here perhaps more than anywhere else in his discussion one detects that “premonitory influence of the idealistic philosophy” to which Lotze tellingly reveals that his analysis of inference “is intended to lead.”94 It is precisely from the idealist orientation, however, that one might find that Lotze fails to establish the essential (wesentlich) character of his “universal” principle’s ontological provenance, its ontically “negative” determinations in the reflective act of inference. This issue of negative determination is crucial in the conceptual logic of inference. And as it happens to be a topic that Hegel develops with profoundly searching insight as he explicates Essence (Wesen) in the 91  Cf., “…we regard the idea for which we are looking, neither as the intention of a reflective consciousness striving for fulfillment, nor as an active force which causes its results, but merely as the conceived or conceivable reason, the consequences of which under certain conditions are the same in thought as those which must follow in reality….it will nevertheless be better…not to use what is found only in the real world as a name for the mere reason upon which in thought the reality rests” (ibid., §131). 92  Apart from “immediate” inference (based, as we previously noted, on the square of opposition), this is the only form of inference, in his account, in view of which Lotze attempts to demonstrate a transition from judgment to inference. See “Appendix on immediate inference,” in Logic, vol. II, chap. 2. 93  Ibid., vol. I, p. 134. 94  Ibid., p. 198.

164 Inference and the metaphysic of reason Logic, when we undertake, in the next chapter, to think-through the onto-epistemology of inference we shall follow Hegel more closely than Lotze on this theme. Lotze sedulously worked out a finely nuanced and in many respects original philosophy of inference understood as the process whereby we develop “as much new truth as possible.” But his doctrine rests at defining points upon what is arguably little more than an epistemological article of faith. 3.4.3 Lotze on Position oder Setzung. Lotze explicitly addresses the onto-epistemological conception of positing, a topic ignored by the analytic epistemologists of inference whose theories we reviewed in chapter 2. (Bosanquet ignored it as well.) The three places in which Lotze comments on the notion in ways most relevant to the present discussion are “World of Ideas,” perhaps the best-known chapter of his Logic; the opening chapter of his Metaphysic (“On the Being of Things”); and in the first part of the published outlines of his lectures on metaphysics. Although he approaches Position oder Setzung from a different speculative angle than does Kant, Lotze, like his great predecessor, does not expressly link Setzung to his analysis of inference; and this notwithstanding the fact that his critique of the notion is, as we shall see, highly germane to the onto-epistemological issues that influence his thinking on inferential cognition. A passage from the Logic and another from the Outlines of Metaphysic make clear both Lotze’s understanding of the received philosophical conception of positing and his misgivings about what he took to be its speculative extension: We have undoubtedly a conception of affirmation or “position” in an extremely general sense, which meets us in various fields of enquiry, and for which languages… have commonly no abstract term which expresses it with requisite purity.…the very term “position”…suggests by its etymological form the entirely alien sense of an act, or operation of establishing [Setzung], to the execution of which that state of affirmation which we wish to express then seems to owe its being. (Logic, §316) [T]he definition, which represents “Being” as “Position without relation” [e.g., “God is”] is so imperfect that it comprehends precisely

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the opposite of that which is to be defined. (Outlines of Metaphysic, §11)

What Lotze most objects to is the implication that (absolute) “positing” in some way, exclusive of relations, establishes or shows how Being originates. The “Being” that figures in Lotze’s criticism is the specious, essentialist idea of a “pure” Being that is antecedent to the intrinsically relative, or relational, moment of actuality (Wirklichkeit). Kant, recall, identified absolute positing with neither abstract Sein nor “pure Being,” but rather with the concept of Sein überhaupt, as represented in a given Dasein in and for itself (an und für sich selbst), i.e., with all its predicates. Moreover, he would have rejected Lotze’s best-known innovation of according Relation (Verhältnis) the status of an ontological category that is indeterminate between the possible and the actual (wirklich).95 Indeed, the distinction between actual and possible is thinkable in terms of the very distinction that Kant sought initially to affirm with absolute and relative positing. He himself made it clear that he understood the notion of Wirklichkeit in just this connection: “Absolute possibility”—what Kant would ultimately denominate the Transcendental Idea—has its “first real ground,” he declares, in dasjenige Wirkliche that gives, “as by means of a ground, the internal possibility [to which the idea of Dasein is fundamental] of other realities.”96 For Lotze, the principal bone of contention regarding the speculative idea of “position” has to do, again, with a “pure Being” thought of in abstraction from the concept of Verhältnis. To Lotze’s thinking, those who entertain any such notion commit the fallacy that Whitehead (refuting Cartesian dualism a half-century later) classically named, “Misplaced Concreteness.”97 Lotze declares that his own final purpose is simply 95  Cf. Lotze’s Metaphysic, §81. 96  Theoretical Philosophy 1755-1770, pp. 124-25. 97  Lotze emphasized the processive and event character of Being in ways that strikingly anticipate Whitehead, as does his rejection of the subjectpredicate (for a relational) form of characterizing metaphysical truths, not to mention his general effort to work out a metaphysic that integrates idealism and realism; see Paul Grimely Kuntz, “Lotze’s Relevance to Contemporary Philosophy,” part of the extended introductory essay to Kuntz’s edition (the first published edition) of Santayana’s doctoral dissertation;

166 Inference and the metaphysic of reason to convey…the familiar truth that general concepts [das Allgemeinbegriffe] are not applicable to the real world in their generality [i.e., as “a Real without content”], but only become so applicable when each of their [identifying] marks [Merkmale], that has been left undetermined, has been limited to a completely individual determinateness [völlig individueller Bestimmtheit beschränkt]….”98

Lotze found that historically “Being” had come to designate: “only one kind of actuality, —namely the motionless existence of things, in opposition, for example, to the happening of events.”99 As an abstraction, the general idea of pure Being thus “does not,” to Lotze’s mind, “admit, as it stands, of application to anything real.”100 Hence it cannot “in reality be an antecedent or substance of such a kind as that empirical existence with its manifold determinations should be in any sort a secondary emanation, either as its consequence or as its modification.”101 It is “merely in the system of our conceptions,” concludes Lotze that the “definite forms” of existence supervene upon pure Being “as subsequent and subordinate kinds.”102 Had he considered Kant’s early distinction between absolute and relative Position, Lotze might have found that his repudiation of a totally abstract Lotze’s System of Philosophy (Bloomington: Indiana University Press, 1971), pp. 69-83. 98  Metaphysic, §8 [Metaphysik, pp. 35-36] (translation modified). I would submit that one must account for degrees of universality and degrees of formal determinateness in the very dynamic of the inferential thinking that is ordered to “determinate universals.” 99  Outlines of Metaphysic, p. 16. Santayana, who at Royce’s suggestion wrote his doctoral dissertation on Lotze, would later identify this order of actuality the Realm of Essence, something that Lotze would have categorically rejected as a discrete domain of being. That he would do so is manifest in one of Lotze’s most singular formulations as to the place of essentia in the ontology of “the course of Things” in general: “…nothing but this continuously advancing melody of event is the metaphysical place in which the systematic of the world of Ideas [die Systematik der Ideenwelt], the multiplicity of its harmonious relations [hence, for Lotze, its being], not only is found by us but alone has its actuality” (Metaphysic, vol. I, pp. 96-97, translation modified; [Metaphysik, p. 81]). 100  Ibid., p. 42. 101  Ibid. 102  Metaphysic, vol. I, p. 42.

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“pure Being” is neither inconsistent with Kant’s criticism of the Ontological Argument nor, in the final analysis, at odds with the move to identify the concepts of positing and being. Declaring that being is not a predicate, Kant makes out the Ontological Argument (as positing “God is”) to be an instance of absolute (existential as opposed to predicative) Position oder Setzung. He thus censures it as an “argument” that transcends the realm of any discursively intelligible (formally understandable) proof. But this is not because he regarded Being as a substance without definite determinations, a substance thinkable as something instantiated empirically in definite forms that are on that count subordinate ontological kinds. Rather, on the plane of the understanding (inferential thinking) the concept of being, per se, like that of positing in its purely absolute aspect, is for Kant what Lotze himself finds it, namely an incomplete thought, one Kant would ultimately classify as a transcendental illusion. It is the relative positing that discursively (rationally) substantiates affirmations and theses, and it is to relative onto-epistemological positing that Kant restricts the cognitional act of inferential (for him syllogistic) thinking. On the other hand, absolute position (whose concept, again, is for Kant identical with that of Sein überhaupt), whether it concerns a mere abstract universal or God, “contains” in potential all of the predicates properly attributable to its object as an intelligible entity. I am able to understand an object of absolute position, able inferentially to grasp it, only through relative positing. Just how is left unexplained in 1763. As William J. Richardson put it, “To be sure [Kant] senses some relation between an [absolutely posited] ‘is’… and the understanding that makes the [relative position of ] judgment, but he is at a loss to explain it.”103 Kant would eventually explain this onto-epistemological relation in terms of what Heidegger identifies as “transcendental predication,”104 i.e., in the transcendental logic, under the category of Modality in the synthetic unity of apperception. Kant’s distinction between absolute and relative positing, and his subsequent emphasis on transcendental epistemology which assimilates that pre-critical distinction, never led him to make the sort of onto-epistemological assumption that Lotze cites as the fatal error of thinkers who employ Position oder Setzung as a speculative notion. The 103  Richardson, “Kant and the Late Heidegger,” Phenomenology in America, ed. James M. Edie (Chicago: Quadrangle Books, 1967), p.136. 104  “Kant’s Thesis about Being,” p. 353.

168 Inference and the metaphysic of reason error is to consider the idea of such positing as either accounting for or explaining “how it is brought about that, in general, something is.”105 Thus that Kant himself never thought of Position in this light blunts the force of Lotze’s objection to the term, at least so far as Lotze has anything like Kant’s metaphysic of positing in mind. To be sure, Lotze does not name Kant when he discusses “positing,” and he never refers to Kant’s original effort, in 1763, explicitly to distinguish the absolute from the relative modes of Position. Indeed, the emphasis on absolute positing in Lotze’s discussion suggests that he had his critical sights trained rather on some Fichtean or Hegelian or (most likely) Herbartian adaptation of the concept.106 Still, Lotze does employ, in both the lecture Outlines and the Metaphysic, the original Kantian formulation (Position oder Setzung). And the statement below, drawn from the Metaphysic, pretty clearly pertains to Kant’s characterization even as it reflects the reductive version of the “positing” that Lotze censures: There are other terms which have been applied to pure Being [reine Sein], in the desire to make that which admits of no explanatory analysis at least more intelligible by a variety of signs. Thus it is usual to speak of it as an unconditioned and irrevocable [i.e., “absolute”] Position oder Setzung. It will be readily noticed that as so applied, each of these terms is used with an extension of meaning [Weite der Bedeutung] in which it becomes an incomplete thought [durch welche sie zu unvollständigen Gedanken werden].107 105  Outlines of Metaphysic, §8. 106  Given J. F. Herbart’s use of the notion and his atomism, Lotze’s complaint that the idea of “positing” fails to account for relation (to Lotze’s thinking the sine qua non of Being) indicates that at the very least Herbart is prominent among those proponents of Setzung toward whom Lotze directs his censure; see, for example, Metaphysic §§12 and 13. 107  Ibid., §10 (translation modified) [Metaphysik, p. 37]. Lonergan’s conception of the “virtually unconditioned” prospective judgment (evidence for which one grasps through “insight”) does “represent” a “complete thought,” and in a way that traces the conceptual logic of the act of inference. Unlike the orientation that I describe in chapter 4, however, Lonergan spells out his view pretty much in the idiom of the critical Kant (with no reference to Kant’s terminology of positing). That said, he certainly differs with Kant on some decisive points—rejecting, for instance, Kant’s restriction of “reason and its ideal” to a merely regulative role in rational judgment; see Insight, pp. 280-81 and 341.

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This “unconditioned and irrevocable Position oder Setzung” Lotze declares to be a mere “error of thought” when taken as “the ground of reality to all definite Being”—i.e., as Kant’s “absolute position.” (Kant contends, as we saw, that the “concept of position or positing is completely simple” and strictly identical with the concept of Sein in general.108 When Kant came to formulate the transcendental logic of the synthetic unity of apperception,109 he discovered that the scientifically intelligible ground of reality to all definite Being is transcendental— taking three modal categoreal forms: being possible, being actual, being necessary.) The rule-governed order of propositionally articulated predication that does present a “complete thought,” at least for discursive reasoning, is by contrast an act of epistemologically determinate, relative positing, and the only means through which the act of absolute positing occurs.110 Here, as with Kant—in, for example, his 108  See Appendix I, i, below. Manfred Frank determines that Position per se is for Kant “a uniform and original meaning of Being” of which Kant’s distinction of absolute and relative positing merely marks “existential and predicative…specifications” (Philosophical Foundations of Early German Romanticism, p. 63). On the other hand, Eckart Förster doesn’t see Kant as distinguishing a discrete “pure” or “original” Being apart from absolute and relative position as two fundamental “expressions” of it. Frank’s interpretation is more Heideggerian than Kantian (reflecting the influence of Heidegger’s seminal 1961 essay on “Kant’s Thesis about Being”). Had Kant entertained the notion of a primordial Being of which absolute and relative Position (the only orders that Kant identifies) are mere “specifications,” then he would have needed to distinguish those specifications from the “completely simple” concept of Position that is “identical” not with the concept of being (as even Förster translates the text), but simply with “Being in general.” 109  A time, argues Heidegger, when Kant dropped the überhaupt modifying the concept of Being that he identified with Position. 110  A defensible onto-epistemological explication of inference requires a conceptually logical account of the mutually actual (wirklich) moments of relative and absolute position. Kant goes no further than to assert that we posit the latter through positing the former and he ultimately treats the reason of inference as a matter of relative positing (i.e., as formally deductive and syllogistic). Cassirer opposes categorizing “the relationship between the ‘absolute’ and the ‘relative’” as that of “different metaphysical kinds of being.” He proposes instead to think of them rather as two “pure functions,” wherein what appears “to be a real opposition when seen [with Kant] from the standpoint of Being becomes merged.” To consider onto-epistemolog-

170 Inference and the metaphysic of reason briefs against the Ontological Argument—and as with the analytic epistemologists that he inspired, one encounters a diremption of the understanding from Being, something that any recourse to intuition or insight does not effectively resolve.111 Lotze, of course, doesn’t see it in quite that way, since the only “Being” that he credits is one that is relational, as opposed to a vacuously abstract “pure Being” (the very idea of which he peremptorily dismisses). It is in the process of demonstrating that no in intellectu specifications of pure Being can be a “complete” thought—much less specifications of the act of inference—that Lotze asserts that one cannot “speak of a Position oder Setzung in the proper [i.e., ontological] sense of the term without stating what it is that is put.”112 Moreover, the “what” of (absolute) positing or putting “must be put somewhere… in some situation which is the result of the setzen and distinguishes the putting that has taken place from one that has not taken place.”113 Here one sees Lotze privileging the principle of identity114 as a way of establishing an alternative account of Position oder Setzung. This account would comport more with an ontological theory that is consistent with the onto-epistemology of inference—a theory, namely, that in taking relative and absolute position as a unity, approaches the act of inference as a dynamic of thinking that self-disclosively articulates Being in its differences. Lotze contends that anyone who would use Position to refer “to pure Being”—anyone who, by implication, would think to take inference as pure disclosure (whether in the form of ical positing from the standpoint of Cassirer’s notion of “function” is to conceive it “from the standpoint of activity, of intelligent creativity,” such that the relation of absolute and relative becomes “a correlation and cooperation.” This is consistent with the character of positing as we shall trace it in the onto-epistemology of inference; see chap. 4, below. 111  The case is very different, of course, for the alternative line of Kantinspired speculative thinkers that runs back to Fichte and Jacobi. 112  Metaphysic, §10 (emphasis added). 113  Ibid., §10. 114  As does Bosanquet, who emphasizes the character of identity as identity-in-difference. Lotze puts greater emphasis on the relational nature of identity. My own view, delineated in chapter 4, is that a more satisfactory account must accord at least equal weight to the principle of sufficient reason as onto-epistemologically formative of the reason of inference.

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“intuition” or “insight”)115—“would…soon find himself pushed back again to a statement of relations, in order to give this Position or pure Being the meaning necessary to its distinction from the not-Setzung, the pure non-Being.” This is what follows when one resorts to the mere abstraction of “pure Being.” The latter, notes Lotze, expresses in effect “only the purpose of the person thinking to think of Being and not of not-Being, while on the other hand it designedly [geflissentlich] cancels the conditions under which” the absolute aspect of the absolute-relative equation (the equation of being and meaning in the act of inference) “can attain its [ontologically disclosive] end and not the opposite of its end.”116 This Lotzean critique ramifies to the heart of the present essay’s concern with the onto-epistemological facets of the act of inference. For when one operates with the idea of pure Being that is merely an abstraction, the defining principle of inference—the reason of the act (what invests it with the significance of intelligibility)—appears to be something “pure and simple,” and epistemologically discrete from discursive thinking: a pure intuition (as per Carnap), for instance, or an insight (Lonergan). Lotze pointed out that any such account employs a spurious ontology (which invariably generates fallacies of misplaced concreteness) and “leaves out of sight every relation constituted by the act.” He contends that the “definition, which represents ‘Being’ as ‘Position without relation’” is thus so far wrong “that it comprehends precisely the opposite of that which is to be defined,” i.e., Being—what is.117 “Actual Being, as distinguished from the mere validity of the thinkable, can never,” to Lotze’s way of thinking, “be arrived at by this bare act of [diese schlechthinnige] Setzung, but only by the addition-in-thought of those relations, to be placed in which forms just the distinction which actuality has over thinkability.”118 This is consistent with the Lotzean ontology, whereby “‘to be’ means ‘to stand in relations’”; indeed, Lotze rejects as

115  To take it as “absolute position” in abstraction from “relative position”— thus in a way that is the reverse of that of laws-of-inference theorists. 116  Metaphysic, §10, translation revised; [Metaphysik, p. 37]. 117  Outlines of Metaphysic, p. 20. 118  Metaphysic, p. 44; quoted with the German, on p. 33, above.

172 Inference and the metaphysic of reason metaphysical error the idea that, in this particular, “standing in relations” pertains to “that which exists previous to such relations.”119 3 Hermann Lotze thus renounced the prevalent use of Position oder Setzung as an ontological term. Yet, in a lecture outline on metaphysics, he does accord it a genetic onto-epistemological role that is consistent with the view taken here of its efficacy in the reason of the act of inference. Lotze imputes an ontogenetic role to Setzung by casting it as a formative cognitional moment in virtue of which we conceptualize any “actual thing.”120 Specifically, he associates Position with the “means” by which “the unity of “the quality of the Thing and “the idea of the Real”—the unity of this quality and this idea—“is formed into the conception of an actual thing, in antithesis to the bare thought of the same thing.”121 (The “quality of the Thing” is for Lotze “the essentia by which the Thing is what it is”; and by the “idea of the Real,” he understands “the substratum, or ‘stuff,’ in which this essentia is coined, as it were.”) 119  Outlines of Metaphysic, p. 19. What puts Lotze in the camp of the Kantian epistemologists—and by extension in that of the analytic epistemologists of inference—is his conviction (noted, above, in sec. 3.4.2) that “relation” is not merely a moment of objective reality. Lotze held that all relations belong to one of two “classes.” One class is purely “logical,” subjective or “unreal”: i.e., those relations (such as ‘similarity,’ ‘contrast,’ ‘larger’ or ‘smaller,’ and the like”) that “originate at the moment when our perfectly voluntary attention brings any two elements, or rather their mental images, into a contact with each other that is quite indifferent and unessential to the elements themselves.” The other class of relations is objective, or what Lotze also designates metaphysical relations. This second division of relations “expresses a proportion which is not merely constituted between things by our thinking in an arbitrary way, but which is really extant for the things themselves in such manner that they are reciprocally affected in this same proportion.” Lotze explains the difference of objective (“real”) relations from simply “logical” ones in the following way: “The merely logical relation of comparison…that of ‘contrast’ (of which, in itself, the things that stand in it do not need to take any note),—would become an objective or metaphysical relation, if it is understood as a resistance which things really offer to one another” (Outlines of Metaphysic, pp. 31-32). 120  Lotze defines “Thing” as that which “is required to be a subject, that can fall into states, and be affected and produce effects” (Outlines of Metaphysic, p. 37). 121  See Outlines of Metaphysic, §25.

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Regrettably, Lotze never applies these onto-epistemologically pregnant lines of thinking to his account of inference. But he doubtless would have resisted the idea of any such move on grounds that it confuses objective metaphysics (the Real) with “mere” logic. Still, his account of Position trades upon core elements of the conceptual logic of the act of inference. More particularly, what he calls the “quality of the Thing” is, I would submit, what shows as a premise in inferential reflection. Lotze recognizes, further, that onto-epistemological position unifies the essential quality of the Thing with the idea of the Real, the idea of what at bottom happens to bear the very impress of the quality. What show as premises thus posited in inferential reflection do so, I should urge, only so far as they happen to be ordered to a conclusion, the order or form correlating with Lotze’s “Real.” Position of premises sponsors, through a route of inferential reflection (regardless of length or complexity), an ideal unity: the conclusion—however vaguely it may be intimated initially by a significant fact. By the same token, Position sponsors as well the quality, precisely in virtue of that ideal unity, whereby the “show” of the moment has the character of a premise. For any coherent route of inferential reflection, the conclusion as ideal unity ultimately composes, to use Lotze’s words, “the conception of an actual thing, in antithesis to the bare thought of the same thing.” Considered thus, in light of the conceptual logic of inference, and notwithstanding the dubious metaphysical distinction of the “merely logical” (“bare thought”) from the Real, Lotze’s analysis of Position compellingly evidences, and in its way systematically substantiates, the onto-epistemological character of inference as an act of living intelligence. While one can find in Lotze the speculative groundwork for a conceptual logic that incorporates the idea of onto-epistemological positing, this metaphysical thought doesn’t play any explicit role, as we’ve noted, in shaping his doctrine of inference. The speculative point on this score that Lotze most wished to stress about Position is that one errs so far as one follows the likes of Fichte, Herbart, and others in construing positing as a grounding principle (Grundsatz) of pure ontology. In fact, Lotze made it his business at the outset of his own work of systematic metaphysics to refute the doctrines of those thinkers who associated Position oder Setzung with pure ontology. Not wishing to be identified with proponents of substantialist ontologies of “pure Being” who give pride of place to absolute Position, Lotze expressly

174 Inference and the metaphysic of reason rejects the term Position122 as a purely ontological principle, both in his Metaphysic and in his Logic. He employs in its stead Wirklichkeit (for the critical Kant, the second category of Modality), a term that, in view of his speculative ends, recommended itself as more philosophically cogent. Unaccountably enough, however, the sense of positing that Lotze censures does not appear to reflect the distinctions unique to Kant’s fully developed formulation, with which Lotze would have acknowledged himself to be in substantial agreement. Nevertheless, if he overlooked or underestimated the speculative subtlety of Kant’s initial onto-epistemological conceptualization of Position oder Setzung,123 Lotze’s treatment of inference certainly went far beyond the traditional syllogistic logicism to which Kant, even in the Critical period, mainly limits his own thinking on the subject. 3 Leaving the theme of Position, let me offer some concluding observations on the “problem of all inferential processes,” as Lotze understood it. This “problem” does not, to Lotze’s way of thinking, hinge on the specifics of the logic of the deductive patterns or rules that ideation methodically tracks through premises to a conclusion. Rather, like Gilbert Harman nearly a century later, Lotze dismisses as “quite immaterial” the relevance of such “methods” in addressing the speculative problem. The “method,” he argues, “will be determined by the form of the premises”; such forms, Lotze shows, “indicate a limit of knowledge.”124 And as for the form of the premises, “we have to take” them, he asserts, “as experience, internal or external, offers them.”125 This is a lesson from which many later thinkers might well have profited and it correlates with the present essay’s proposal, in chapter 4, to single out formal cause as the Sufficient Reason chartering the reason of the act of inference. 122  Largely, to be sure, as Herbart adapted it to an atomistic ontology. 123  Contrary to Lotze’s reading of the idea, Fichte, for one, construes the “thetical judgment [as] not predicatively grasped (even if it subsumes all potential predicates); its structure is not something-as-something or something-as-not-something” (Manfred Frank, The Philosophical Foundations of Early German Romanticism, pp. 65-66, emphasis added). 124  Cf., for example, Logic, §115, where Lotze illustrates how this is so with the “inferences of proportion.” 125  Logic, vol. I, p. 134, emphasis added.

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Lotze was convinced that the defining philosophical issue for “pure logic” doesn’t concern the details of alternative methods of deductive reasoning. Rather, he took pure logic to involve how through acts of inference, proceeding “from given data or premises,” we “develop as much new truth as possible.” By contrast with the positivistic epistemological regimes of later analytic inference theorists, such as the five earlier surveyed in chapter 2, Lotze ties the logical character of inference—conceived, again, as the cognitional effort to develop “as much new truth as possible” 126—to “the subordination of manifold elements [premises, data] to the unity of a universal.”127 This subordination, says Lotze, makes “the universal named equivalent to the individual[s] intended.”128 These observations intimate a move that is consistent with the explication of inference as we shall undertake it in chapter 4. It involves taking, as intermediating moments, the absolute and relative facets of positing that Kant distinguished. This avoids the kinds of onto-epistemological dualisms that crop up in analytic epistemologies of inference. Lotze, as we saw, apparently overlooked or undervalued Kant’s pivotal distinction, and he consequently operated without a speculative basis upon which to develop his reflections along these lines. (It is likely, in any case, that he would have dismissed the emphasis here on the conceptual logic of inference. It might well have impressed him as engendering a misconceived view that virtually reduces inferential judgment to a logic of the middle term.) 3.4.4 Summary of Lotze’s thinking that anticipates the onto-epistemological orientation. Prior to turning to Bosanquet, it will be well to sum up the elements of Lotze’s thought that significantly anticipate seminal aspects of the onto-epistemological orientation to inference. a) The “form of thought which combines two judgments so as to produce a third is, speaking generally, inference”—this, we noted, is Lotze’s most general, Aristotelian definition. Here is how this reads from the standpoint of the onto-epistemology of inference: What one judges to “show” as premises in inferential reflection “combine” in the 126  The form of the premises in each case determining the instrumental “method” of development. 127  Ibid., §101. This pretty clearly inspired cognate lines of reflection in Bosanquet. 128  Ibid, §105.

176 Inference and the metaphysic of reason sense that each such moment functions—that is, becomes determinate—as a premise vis-à-vis a mediating other (only) insofar as that act of reflection is properly ordered to a “conclusion.” How is one to conceive these premises in abstraction from the order that orchestrates the reflective act as a dynamism dedicated to the actualization of intelligible form? (Lotze would identify this principle of order as a terminus medias, which, he declares, bears “the name of concept.”129) Apart from their order in a route of thought, the premises have the character of initial, unmediated judgments; they are simple immediacies, and in that respect do not “show” as premises at all. The end or conclusion “produced” by way of the passage of inferential reflection may likewise assume the character of a simple immediate judgment. But one grasps the conclusion as a simple immediacy only if one entertains it as a discrete essence, prescinded from the composition, the living definition—a dynamic of forma formans—that realizes it. Lotze’s generic definition thus correlates with the onto-epistemology of the reason of inference explored in the present work, albeit in a loose and rather unillumining way. b) Lotze finds that inductive inference—notoriously the stumbling block of analytic epistemologies of inference—is, to repeat his observation, “guided…by the universal principle which dominates all its activity, the principle of translating a given coexistence of ideas into a coherence between their contents.”130 What Lotze fails to work out, however, is the way that this transformational principle might organize the conceptual logic of inferential reflection. The closest approach he ventures to this is indirect, namely in his analysis of inferential form understood as categorically discrete from the Real. But while Lotze would contend that such a principle of induction can have at best only an indeterminate relation to the Real, he keenly appreciates its pivotal role in inferential reflection. What Lotze refers to when he alludes to this “principle” is, from the perspective of the onto-epistemology of inference, the element of order rendered ideal, “spiritualized,” through the consciousness (however inchoate and tenuous initially) of significant fact. This order—be it mathematical, for example, or theological, psychological or aesthetic—imparts rational definition, in the form of the discursive articulation, to the very cognitional process that is dedi129  Cf., Logic, §§83 and 120. 130  Logic, vol. I, p. 134.

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cated to rendering it rationally intelligible (ideally explicit). And it is in virtue of this order that one marshals judgments as premises in the act of inference. c) Along with “classificatory” and “explanatory” thinking, Lotze includes a dialectico-speculative ideal of universal law at the boundary of what he classes as Systematic forms of inference.131 He regards dialectico-speculative strains of reflection as a form of thinking that is “not quite that of inference” as he had previously described it. Bordering on metaphysics, and hence the Real, it largely transcends, in his view, the concerns of Logic and with them the theory of inference. Nonetheless, Lotze’s initiative to identify the dialectical dimension of reflective thought in this connection looks forward to an aspect of an account of inference that correlates more nearly with the one developed in the present work: that of Bosanquet, who emphasizes the metaphysically systematic nature of inference properly understood. From an ontoepistemological viewpoint, it is dialectico-speculative currents of inferential thought that render even long-established routes of reflection susceptible of novel turns and transformative enlargements. This obtains in the conceptual itinerary of the inferential act, whereby, as I would urge, what “show” as premises, each dialectically reflected in a mediating other, grow determinate as ordered to a conclusion. No sublation occurs in this dialectic of essence (as Hegel himself recognized). Hence one finds no canceling or superseding of the show of significant fact that we idealize as a component of the dynamism toward a totality that is inference in its truth. An essential consequence of this is that the unique occasion of onto-epistemologically positing a somewhat, a somewhat that shows as a premise, remains a living value in the act of inference. What this means—so far as we are neither machines nor think in a vacuum—is that all of the distinctive complexity of motivation and sometimes-unprecedented cognitional character ingredient in one’s investing (onto-epistemologically positing) a somewhat as a premise may enrich, with novel or previously unsuspected implications, an otherwise normative path of inference. The inference is motivated by the significant fact that excited the search for a meaning in the first place. For example, the living process of an Einsteinian act of inference, entertaining the reflective show of premises ordered to a 131  This, recall, is the third category in Lotze’s tripartite typology—supplementing the Aristotelian syllogistic and the mathematical forms of inference.

178 Inference and the metaphysic of reason conclusion in a Newtonian route of inference, is prompted by significant fact to posit additional premises, as essential factors, ordered to previously unrealized, relativistic dimensions of the truth that constitutes the totality, or meaning, of the premises. Lotze was in his way acutely aware of this creative process as a formative component of the act of inference.132 This is apparent when he censures the severe practical cognitional limitations of the Aristotelian syllogisms, and of “all ordinary judgments of the form” S is P, for their failure “generally to satisfy the practical needs of thought as a living process.”133 (Statements such as this enable one to recognize the historically myopic scope of the thinking of an analytic epistemologist such as Robert Brandom, who with unwarranted confidence opines that we “typically think about inference solely in terms of the relation between premise and conclusion, that is, as a monological relation among propositional contents.”134) Following this critical remark, Lotze offers an observation that characterizes a circumstance borne out, as we shall find, in the conceptual logic of inference. “In the living exercise of thought,” declares Lotze, “we are seldom concerned… to determine a mark which belongs to a concept [Lotze’s middle term, my order] once for all, or in the circuit of which the concept is to be classed.”135 d) Lotze calls the final cause of dialectico-speculative thinking its constitutive concept, or “logical Idee.” As a constitutive concept, the logical Idee of anything contrasts categorically with the abstract “concept 132  Which he explained as “simply an inner movement of our own minds, which is made necessary to us by reason of the constitution of our nature and of our place in the world”; cf., Logic, §345. 133  Logic, §105. To survey Lotze’s analysis of mathematical and especially systematic inference is to realize that while Lotze may identify the inference with the syllogism in a general way, he does not restrict the former to any narrowly syllogistic form. Indeed, he argued that in S is P, “P can only attach to S either as a state which it passes through, or as an influence which it exerts, or finally as a permanent quality which belongs to it.” This observation, in conjunction with Lotze’s overarching definition of inference, as any combination of two judgments for the production of a third and valid judgment, points considerably beyond the classical syllogistic understanding of inference. 134  Articulating Reasons (Cambridge, Mass.: Harvard University Press, 2000), p. 166. See discussion of this passage, above, in §2.4. 135  Ibid., vol. I, p. 142.

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of it, which merely comprises the sum of the necessary marks and the form in which they happen to be [semiotically] combined.”136 As we saw, Lotze regards the logical Idee as the “starting-point” and “law” that “determines the order of all the other marks” that explain whatever the object of the concept happens to be. The logical Idee is thus the formal ground that determines the order of the signs or figures or “semblances” that reflectively compose the “reason upon which in thought the reality rests” (emphasis added). Discounting Lotze’s signature binarism of logic and Real, his reflection contains seeds of the view, detailed below in chapter 4, that a properly articulated conceptual logic of the act of inference discloses its Reason to be a matter of formal cause. e) Finally, we noted that Lotze’s reasons for rejecting Position oder Setzung as a speculative concept follow from a sound critical analysis of the vacuous essentialist conception of “pure Being.” His assessment, however, might well have yielded more pregnant developments in the direction of the onto-epistemology of inference if he had probed Kant’s early distinction between absolute and relative modes of ontoepistemological positing. What would have been most interesting is if Lotze had found a way to consider Kant’s binarism from a standpoint that supersedes the dichotomous approach to logic and the Real, namely from the orientation of the onto-epistemological insight that prompted him to postulate what he identified as “the between.”137 3.5.1 Bosanquet as a philosophical logician of inference. Bernard Bosanquet was arguably the most sedulous and incisive Anglophone student of Lotze’s metaphysically grounded logic and its extended investigation of inference. Under Lotze’s influence, Bosanquet worked out his own holistic, genetic account of logic as a philosophical science, which included a substantial volume devoted wholly to the logic of inference. Like Lotze and other metaphysically oriented philosophical logicians,138 he never took mathematicized formal logic for the normative modality of rational thought. He judged it, rather, a highly specialized, if “somewhat subsidiary” type of reasoning. 136  Logic, §129. 137  See n. 71, above. 138  A designation that includes such men as Bradley, Alexander, Whitehead, Dewey, Blanshard, and (in a more limited sense) Stanley Rosen and Errol Harris.

180 Inference and the metaphysic of reason While early in his forty-year career he was both a translator of Hegel and the chief editing translator of Lotze’s Logik and Metaphysik, Bosanquet, a self-described objective idealist, matured into an original and deeply insightful systematic philosopher in his own right. Indeed, his writings, particularly the set of Gifford Lectures139 and the late monograph on Implication and Linear Inference, 140 show him to be no mere epigone (and anything but a stodgy, backward-looking Victorian141). To attempt a fully developed summary of Bosanquet’s meta139  Published in two volumes: The Principle of Individuality and Value (1912. Bristol, Engl.: Thoemmes Press, 1999) and The Value and Destiny of the Individual (1913. Bristol, Engl.: Thoemmes Press, 1999). 140  London: Macmillan, 1920. Described by C. D. Broad in his fifteenpage review essay on the work as a “little book” whose “value is altogether out of proportion to its size” (Mind ns 29 [1920]: 323-38). 141  One example of Bosanquet’s unflagging appreciation of younger philosophical talent appears in Implication and Linear Inference, where he singles out the speculative virtuosity of the mathematician Alfred North Whitehead, prior to the latter’s emergence (after Bosanquet’s death) as a process metaphysician of world historical stature. Bosanquet also saw significant implications, for philosophical logic, in Husserl’s Jahrbuch for 1913 (notwithstanding the fact that he never fully mastered Husserlian phenomenology). Indeed, Errol Harris notes a revealing affinity between Bosanquet’s logical orientation and that of Husserl respecting the limitations of formal logic: “the ordinary logician,” observes Harris, “takes it for granted that a judgment made on primary evidence is the same as when it enters into a train of reasoning, overlooking the fact that its meaning-structure and significance are modified by such a transition, as well as by a movement from mere inference to positive assertion as truth. The mere form of statement expressing a significant judgment will not in itself serve as the premise of an argument, for in order that it may do so the grounds of connected fact on which its meaning rests must be invoked. What Husserl seems to be hinting at here is something like the doctrine expounded independently by F. H. Bradley and Bernard Bosanquet (and derived originally from Hegel) that in inference the judgment is being expanded and developed, as it is itself an expansion and development of the concept” (Formal, Transcendental, and Dialectical Thinking: Logic and Reality, p. 93). This synthetic feature of inference (onto-epistemological positing being a thetic act) is a core component of the account detailed, below, in chapter 4. The formal moment (or ground) constitutes the intelligible character of the ordered, dynamic unity (of the premises), which is at the same time the reflective process whereby the premises are delineated, vis-à-vis each other, as ideal moments of the very actualization of inference’s formal cause (its Reason).

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physical doctrine would far exceed what is possible or necessary here. Nonetheless, through the course of discussion in this section and in the two that immediately follow we will encounter cardinal features of his system that adumbrate the lineaments of the whole. It will do at this point simply to note that Bosanquet produced a deftly nuanced and, on occasion, uniquely penetrating contribution to British speculative idealism properly understood,142 which is to say as the “convergence of investigations towards some truly speculative attitude—free, concrete, penetrating, and widely appreciative….”143 His contribution to logic has lately been shown to be “a crucial step in the evolution of logic as a subject from being a completed body of knowledge to being the essence of philosophy.”144 Like other leading philosophical logicians such as Lotze, Bradley, and John Cook Wilson, Bosanquet thinks of inference in conjunction with judgment.145 So it is no surprise to find that in his book on the logic of Inference—the second volume of Logic, Or the Morphology of Knowledge (revised, 1911edition)—Bosanquet commences his opening chapter, “The Nature of Inference,” by differentiating inference from judgment (the topic of his first volume): Inference shares the essence of Judgment, but, at least qua explicit Inference, has in addition a differentia of its own. The essence of Judgment is the reference of an ideal content to Reality; the differentia of Inference affects the mode of this reference, and consists of 142  G. E. Moore is notorious as the prominent and unwarrantably influential misinterpreter of the movement, someone whose distortive representation contributed significantly to its eclipse for the balance of the twentieth century. Moore’s famous attack, “The Refutation of Idealism” (1903) is reprinted as the opening chapter of his Philosophical Studies (London: Routledge, 1922). Bosanquet sharply criticized the piece after it first appeared; and Moore himself ultimately confessed that he found it “to be very confused, as well as to embody a good many down-right mistakes”—faults that he deemed insufficient to prevent him from reprinting it in 1922. 143  Bosanquet, The Meeting of the Extremes, p. viii. 144  James W. Allard, “Bosanquet and the Problem of Inference,” in Bernard Bosanquet and the Legacy of British Idealism, ed., William Sweet (Toronto: University of Toronto Press, 2007), p. 86. Allard’s observation is true enough with respect to the historical significance of Bosanquet’s achievement, but it is as yet hardly reflected in the historical record. 145  A look, for instance, at chap. I, §3 of Kant’s “general” Logic confirms the traditional provenance of this association.

182 Inference and the metaphysic of reason Mediation. Inference then is the mediate reference of an ideal content to Reality.146

What “usually” distinguishes “Judgment” is the character of immediacy exhibited in an affirmation or a denial, neither of which can exhibit necessity. Ever the systematic thinker, Bosanquet argues that necessity involves mediation or inference. No isolated judgment qua isolated can have necessity. Every necessary truth must, in so far as it is necessary, present itself as the conclusion from an antecedent. In the idle controversy whether axioms are known a priori or ‘from experience’ this aspect of necessity is forgotten on both sides. 147

Bosanquet describes judgment “as the act of thought which is capable of truth and falsehood.” (For logic per se, “it is a postulate that ‘the truth is the whole’”; at the same time, however, logic “has no criterion of truth nor test of reasoning. Truth,” insists Bosanquet, “is individual, and no general principle, no abstract reflection, can be adequate to the content of what is individual.”148) Aware that judgment under this description is tautologous, Bosanquet contends that it nonetheless “tells us that we are to look for the differentia of judgment not in a mere mental fact, but in some further value with which the mere mental fact is invested.”149 Kantian Position oder Setzung is not part of Bosanquet’s philosophical lexicon (even negatively, as in Lotze). Yet to read as act that which Bosanquet terms “mental fact” is to recognize that the dynamic of thinking at issue in his account is in effect an onto-epistemological positing of the “further value with which the mere mental fact is invested”—a value that Lotze would have interpreted as a validity of the “mental fact.” Thought, as “mental fact,” thus constitutes for Bosanquet a formative relation to an ultimate, trans-cognitional “Reality.” This Reality exhibits universality, “special phases” of which we identify 146  Logic, vol. II, p. 1. Even in this brief statement, one sees why Bosanquet selected as the two epigraphs that appear at the head of the Introduction to his Logic a passage from Hegel’s Wissenschaft der Logik and a brief excerpt from Darwin’s Origin of the Species. 147  Logic, vol. II, p. 224. 148  Logic, vol. I, pp. 2-3. The individual in its difference, and hence its truth, is (rationally speaking) being as dialectic, and not a formally logical moment of the whole. 149  Ibid., pp. 67-68.

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as universal laws of connection that manifest themselves in logic. The onto-epistemological relation that Bosanquet understands as “mental fact” in this context has the status of a Grundsatz in his theory of judgment and its mediate species, inference. Bosanquet describes, from the standpoint of subjective experience, the Reality referred to by the act of judgment as, given for me in present sensuous perception, and in the immediate feeling of my own sentient existence that goes with it. The real world, as a definite organized system, is for me an extension of this present sensation and self feeling by means of judgment, and it is the essence of judgment to effect and sustain such an extension.150

From the perspective of interpreting “the Unity of Reality” as “the postulate of knowledge,” Bosanquet finds it “convenient” to distinguish three “degrees” of reality (separable only at a high level of abstraction). The first is reality as “a mechanical system through and through,” a “postulate” that gets “expressed in the so-called ‘laws of thought’ which find their most explicit form in the ‘Law of Sufficient Reason,’ or principle of Relativity.” The second degree is reality as “quasi-teleological”: “a mechanical system…adapted to the evolution and maintenance of life.” And the third degree is reality “as a mechanical system” that “is further adapted to, or includes as elements within its unity, the substantive purposes of human intelligence.”151 As a mental fact, Thought and the trans-cognitional, systematic Reality postulated by scientific knowledge together manifest a relation that has, in Bosanquet’s account, an ontological status. This relation transcends both thought and that real world that is, for thought, “a definite organized system.” This third, onto-epistemological element Bosanquet ultimately identifies as Implication, which he finds realized in the thetic moment of the act of judgment. Bosanquet expressly affirms this from both the subjective and objective sides of the equation. Subjectively, it is “by means of judgment” that the posited world is “for me an extension of this present sensation and self feeling.” From the objective standpoint, the act of position, implicit in what Bosanquet intends as “the essence of judgment,” is the means by which I at once effect and sustain the objectively real extension that evidences the being 150  Logic, vol. I, p. 72. 151  Logic, vol. II, p. 223.

184 Inference and the metaphysic of reason of thought as an organ “within the universe for ‘eliciting’ its reality in the form of truth.” Bosanquet concisely formulates this onto-epistemological principle in one of the culminating observations in the concluding pages of his Logic: “A necessary connection even between two given terms is a reciprocal inferential relation, implying a system beyond either, and not present in the apprehension of each alone or of both together.”152 This reflects the view that (mediate) “Inference must have three terms and no more”—terms that take the form of “two premises and no more, which assert relations between differences qua belonging to a single universal.”153 Every other conclusion that affirms one definite content to be a consequence of another definite content, is an activity only separated from Inference by the degree of distinctness with which its parts are analyzed. Every such judgment, and therefore ultimately every judgment, can by further reflection be expressed as a three-term [i.e., ‘explicit’] inference, and this is especially the case with what we called the true Immediate Inferences, Comparison, Abstraction, and the rest.154

The plane on which Bosanquet conceives his tripartite doctrine of inference would seem to exclude any meaningful distinction between, say, deductive and inductive reflection. He contends, however, that acts of inference do not advance knowledge through the formal patterning of judgments (as in generalization from particulars, for instance). Hence the difference between deductive judgment and induction has only a tangential bearing on Bosanquet’s level of analysis. Beyond rejecting the idea that the formal pattern of judgment has intrinsic epistemological efficacy, Bosanquet also repudiates the notion that inference extends knowledge by eliminating hypotheses.155 Bosanquet’s doctrine of inference is implicitly onto-epistemological, and in leading respects it is consistent with the thesis of the present work that inference is the signature act of discursive intelligence. For example, early in the volume on inference, Bosanquet describes “the fundamental activity of thought as the same throughout and as al152  Vol. II, pp. 321-22, emphasis added. 153  Ibid., p. 203, Bosanquet’s emphasis. 154  Ibid., p. 203. 155  Bosanquet’s Logic, like that of Lotze, has many illumining if unrecognized implications for a philosophy of science.

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ways consisting in the reproduction by a universal or a real identity, presented in a content, of contents distinguishable from the presented content, which also are differences of the same universal.”156 Allowing for some qualifications, this correlates with the character of inferential reflection as we shall trace it, below, in the body of chapter 4. One point of divergence is that thought, as we shall find, doesn’t “reproduce” but rather is actual onto-epistemological Position. The formal cause of what show (Schein) as premises is intelligible as such in a dynamic of reflective activity constitutively ordered to some “real identity,” or form. The actuality of the latter is simply that which shows as premises composed in a determinately ordered formation (the composition is always in actu, always in movement and by that token not actual, but only reductively intelligible, as static). This form-as-formation is the forma formans that constitutes the ordered play of the premises’ identity-indifference as moments of the complete inference. The inference is an extended act, a “perfection” of onto-epistemological “energy,” since the form or reason of the effort is that the fact rendered ideally determinate as the conclusion is not, prior to the act of inference, rationally intelligible to the thinker as a term of judgment.157 3.5.2 Bosanquet’s differences with Lotze on inference. Having considered the main lines of Bosanquet’s philosophy of inference, it will be helpful to summarize principal elements of his account that set in relief his independence from Lotze’s thinking. a) Bosanquet goes farther than Lotze when he categorically asserts that inference as a form of knowledge takes “no antecedent scheme.” This disqualifies the syllogism as the logical paradigm of inference, at least to the extent that it constitutes a formally prescriptive “set of schedules in one or other of which every argument can be written out merely by filling up the blanks.”158 The fixed formalism of syllogisms, for all their different figures and moods,159 contrasts radically with 156  Logic, vol. II, p. 14. 157  See chap. 4, below. 158  Ibid., p. 201. 159  One can consult a lucid, highly readable modern treatment of this topic in H. W. B. Joseph, An Introduction to Logic, 2nd ed. (Oxford: Oxford University Press, 1925), chap. 12. Joseph was an acute systematic logician who maintained an informed, critical distance from the mathematicization of logic.

186 Inference and the metaphysic of reason the “form of knowledge” that Bosanquet understands as “an active and constructive principle, to the workings of which no abstract type antecedently prescribed can be adequate.”160 Lotze, on the other hand, regarded the antecedent “form of the syllogism” to be of “purely subjective significance.”161 Although Lotze thus understood the syllogism to be an inferential form of “the logical act of thinking,” the distance from Bosanquet is perhaps not so far as this might suggest. For Lotze thought of each form of syllogism as sponsoring a variety of possible routes of inferential reflection, depending on the domain of reality— “the real ground of …validity”—to which one applies it.162 A more involved order of divergence from Lotze is seen in Bosanquet’s criticism of linear inference. Bosanquet charged that to identify the inference with the traditional syllogistic forms (or any derived therefrom) is to restrict inference exclusively to the subject-attribute relation, and hence to a limited, linear mode of thought. (Although this might suggest otherwise, Bosanquet had no wish to dispense with the syllogism in the philosophy of inference. In fact, he himself introduced an original development of the traditional syllogism, a modification that, as he put it, “has no repugnance to the genesis of constructive relations within the unity that is expressed in the inference.”163) Inferences are “linear,” explains Bosanquet, when they “stress… argument ‘downward’ or ‘upward,’” and either proceed “from indemonstrable premises,” or generalize “from recurrent particulars.”164 While hardly restricted to the syllogism, this paradigm, whatever the infer160  Ibid. 161  Logic, vol. 2, p. 277. 162  See, for example, Lotze’s discussion of alternative routes of reflection possible under the inferential form of the subsumptive syllogism as applied to mathematical truths (Logic, §344). 163  Logic, vol. II, p. 207. While it is not necessary for our purposes to go into Bosanquet’s painstakingly detailed analysis, it might be helpful to supply the summary that he provides of his conception of the syllogism. He describes the syllogism as “a subsumptive reasoned judgment depending upon the unity of differences within an individual subject, and making the intelligible ground of this unity explicit in various degrees, according to which the unity displays itself as a conjunction or as a coherence” (ibid., p. 206, the entire chapter, “Concrete Systematic Inference,” repays close study). 164  Ibid., p. 21.

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ential form that it invests, “is drawn from the analogy of the formal syllogism” and manifests “inherent vices” that “are far more widespread than most logicians have supposed.” Bosanquet detects these “vices” in even the “most convinced opponents” of the syllogism, “as well as in those very modern views [as of 1919] which insist on the one hand upon a priori principles of inference, and on the other, upon an Induction through repetition of occurrences in experience.”165 The principal “vice” in question is the narrow implicative “scheme” whereby “reasoning can only work by subsumption of new particulars under general connections borrowed from elsewhere.”166 (Subsumption, as Cassirer reminds us, is what pre-mathematicized, “traditional logic regards as the constitutive relation through which the universal is connected with the particular.”167) Whether an exogenous connection (i.e., one “borrowed from elsewhere”) in a route of inferential thought “is explicitly stated in a premise introducing a middle term, or whether the reasoning goes…‘from particulars to particulars’—this, asserts Bosanquet, is simply an “irrelevant” matter.168 It is not to the purpose here further to trace Bosanquet’s explication of linear reason; suffice it to say that instead of a linear orientation to the philosophy of inference, he opts for a more comprehensive, “systematic” view that adumbrates in onto-epistemological terms his metaphysic of the Whole. Bosanquet argues most insistently against limiting the ground of inference to fixed empirical or a priori rules or axioms, whether one construes the inference as intrinsically syllogistic in nature or as constituted by (Humean) “subsumptive induction” on the principle of similarity169 or enumeration. He is convinced that the traditional division of logical grounds of certainty into axioms at one end and particular data at the other, due to the predominant linear conception of inference, has done great injustice to the most

165  Ibid. 166  Ibid., p. 24. 167  Philosophy of Symbolic Forms, Volume 1: Language, trans. Ralph Manheim (New Haven: Yale University Press, 1955), p. 283. 168  Implication and Linear Inference, p. 24. 169  As we saw earlier, in chapter 2, this is a guiding law in Lonergan’s account of inductive inference.

188 Inference and the metaphysic of reason central and most exalted certainties of life, as well as to the commonest and most practical.170

At an earlier point in his discussion Bosanquet is more explicit about mistakes that follow from limiting understanding of the act of inference to any linear mode of discursive thought. “The linear scheme of inference,” he remarks, “naturally leads to a disruption of the theory of reasoning, and with that to an isolation of a priori principles from each other, and of the whole a priori world from the whole of that which is empirical—of certainty from value. And this I believe to be a profound philosophical error.”171 Never denying the constitutive role that assumptions or axioms play in inferential reflection, as in all rational thought, Bosanquet cites with approval Bertrand Russell’s observation that such points of departure betoken different degrees of self-evidence. Going further, Bosanquet concludes, rightly enough, that such degrees of self-evidence signify the onto-epistemological nature of premises. But he does not interpret this self-evidence as something that substantiates in a logically independent manner the propriety of any given premises either to ground and or to bear out the conclusion of an act of inference. Consequently, the self-evidence of premises, in its varying degrees, is for Bosanquet “simply degrees of implication in the whole system” of totality, a systematic developing whole to which “the natural expansion of experienced connections” tends.172 This systematic whole is for Bo170  Implication and Linear Inference, p. 96. 171  Ibid., p. 69. 172  Cf., Implication and Linear Inference, p. 67. The loose but unmistakable affinity here with Lotzean thinking is evident in the following paraphrase of a passage from Lotze’s late, densely Germanic, English-language account of his philosophical orientation and his criticisms of nineteenth-century theory of knowledge. From Lotze’s perspective: We can hope to acquire merely an approximate knowledge of the ground on which we stand, of the system to which we belong, and of the direction in which the motion of the great Whole carries us along. It is quite understandable that the human mind seeks at each new threshold of knowledge to construct a complete image of the world as a whole, an image that emerges with logical rigor from the novel cognitional standpoint that it has won. But one can never complete this task of progressively deducing the world’s manifold character from a single fundamental principle. As against this task, moreover, philosophy faces the more urgent and greater work of a regressive investigation that aims to discover and fix securely the principle that we are to recognize

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sanquet the “ultimate criterion” of implication. And implication is “the fundamental principle of inference.”173 Bosanquet defines “implication” in quasi-Lotzean terms as “the general name for the relation which exists between one term or relation within a universal, or connected system of terms and relations, and the others, so far as their respective modifications afford a clue to one another.”174 Correlatively, inference constitutes a systematic process—a “principle of progressive knowledge” based on implication, an activity of the living intelligence in which all of the terms undergo “transformation.” The most general sense in which such transformation occurs has to do with alterations of the character of that unity which distinguishes the connection of data and conclusion in inferential thinking. As Bosanquet expresses it, “in no inference do data and conclusion abide on the same level of unity….You begin with sporadic facts and you end up with a concentrated ‘plot’ and its ‘solution.’”175 Not only does this thinking go beyond the older, empiricist notion that laws are simply regularities,176 it “goes far beyond the limits of syllogistic reasoning,” although the syllogism “at its best” does exemplify, in its way, the act of inference. This is the case “when its linear aspect is least and it systematic aspect strongest,” when syllogistic reasoning thus transcends the narrowing, linear suggestion of the fixed formal relation of terms in the act of inference. b) Beyond the significant differences in emphasis relative to the syllogism in the philosophy of inference, a subtler and deeper-running and employ as the living principle that informs the construction and course of the world. (See “Philosophy in the Last Forty Years,” The Contemporary Review 37 [1880]: 135. Lotze published the twenty-page essay—the first of what were to be a pair [death preventing the second from appearing]— in a British journal, with the hope “to secure the favorable attention of my English readers.”) 173  Implication and Linear Inference, p. 9. 174  Ibid. 175  Ibid., p. 127. 176  For a recent assessment of Bosanquet’s philosophy of scientific inference, as compared with the doctrines of such contemporary scientific logicians as Fred Dretske and David Armstrong, see Fred Wilson, “Bosanquet on the Ontology of Logic and the Method of Scientific Inquiry,” in Bernard Bosanquet and the Legacy of British Idealism, ed., William Sweet (Toronto: University of Toronto Press, 2007), pp. 267-95.

190 Inference and the metaphysic of reason contrast between Lotze and Bosanquet emerges in their respective definitions of inference. Lotze, recall, asserts that inference is “any combination of two judgments for the production of a third and valid judgment which is not merely the sum of the two first.”177 Jettisoning the syllogistic subtext that, despite interesting developments beyond it, Lotze retained as an essential feature of his doctrine, Bosanquet works out his own idea of inference more with an eye to the onto-epistemology of judgment.178 He identifies mediation—mediation that takes the form of “the universal in its differences”179—as the factor that distinguishes inference as a distinctive species of judgment. Non-inferential judgment, by contrast, is a cognitional act whereby I directly refer the substance of something that I find intelligible to what is real—in Bosanquet’s language: “The essence of Judgment is the reference of an ideal content to Reality.”180 Expanding on his initial formulation of inference as the “mediate reference of an ideal content to Reality,” Bosanquet maintains that acts of inference indirectly refer “to reality of differences within a universal [the sort of universal, in the realm of knowledge, which determines the type of inference] by means of the exhibition of this universal in differences directly referred to reality.”181 Differences, as such, always concern 177  Logic, §83. 178  F. H. Bradley’s Logic, preceding Bosanquet’s, earned fame for rejecting the identification of inference with the syllogism, but Bosanquet was sharply critical of Bradley for not offering any account to replace it, such as the one that he himself eventually articulated (and which Bradley applauded). See James W. Allard, The Logical Foundations of Bradley’s Metaphysics: Judgment, Inference, and Truth (Cambridge, Eng.: Cambridge University Press, 2005), chap. 6. 179  In the conceptual logic of inference, as explicated below in chapter 4, this corresponds to the moment of form, taken as forma formans, which constitutes the intelligible character, that is to say the ordered character, of the dynamic that is the act of inference. Cf., Cassirer’s distinction between forma formans and forma formata, in The Philosophy of Symbolic Forms. Volume Four: The Metaphysics of Symbolic Forms, ed. John Michael Krois and Donald Phillip Verene, trans. John Michael Krois (New Haven: Yale University Press, 1996), chap. 1 (“‘Geist’ and ‘Life’”), esp. pp. 17-20. 180  Logic, vol. II, p. 1. 181  Ibid., vol. II, p. 3, emphasis added.

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a ground of distinction, a ground no less real than the differences.182 Inferential reference takes place in light of sponsoring implications that ramify systematically (rather than merely linearly) and ultimately to the Whole. One sees Bosanquet’s originality here, where his thinking outstrips the logical limits of Lotze’s analysis. The non-linear, systematic extension of implication (system being for Bosanquet the very “basis of inference”183) sharply distinguishes Bosanquet’s onto-epistemological orientation to inference from that of formalist analytic epistemologists. It follows from his working principle that the “entire content of the universal”—the universal grasped not as some hyperuranian form but as the “intellectual synthesis of difference” understood as a “connected system of terms and their relations”—is, “so far as recognized in the necessity that unites its differences,” the “true content of every inference….”184 From the standpoint of “implication,” Bosanquet restates his position in this way: “… it follows from the nature of implication that every inference involves a judgment based on the whole of reality, though referring only to a partial system which need not even be actual.”185 (Cf., Whitehead: “Every proposition must be considered with reference to the whole universe.”186) The idea that an act of inference refers “to a partial system which need not even be actual” correlates, as we shall find in the next chapter, with a defining onto-epistemological feature of the act of inference. In the onto-epistemology of the reason of inferential reflection, what Bosanquet calls the “partial system” proves to be the totality of the identity and distinction that composes the reflectively articulated show (Schein) of data in an act of inference. Bosanquet would sum it up thus: “the conclusion of inference is always the premises seen in a new light as a new whole.”187 182  Cf., ibid., vol. I, pp. 118-19. 183  Implication and Linear Inference, p. 9 n. 184  Logic, vol. II, p. 9. 185  Implication, p. 4. 186  From a transcribed Harvard lecture, in Lewis S. Ford, The Emergence of Whitehead’s Metaphysics: 1925-1929 (Albany: State University of New York Press, 1984), p. 311. 187  The Value and Destiny of the Individual, p. 24 n. 2.

192 Inference and the metaphysic of reason The systematic core of Bosanquet’s philosophy of inference is the idea that inferential judgment is grounded, at every turn (via implication), “on the whole of reality” in its differences. This reading of inference, which on its face evinces an intuitive plausibility, goes to the heart of Bosanquet’s objective idealism, with its roots in the best insights of Hegel and the classical tradition. In the event, however, its compelling rationality did nothing to preserve it from summary rejection by the middle of the twentieth century (as seen in leading logic texts188); by the beginning of the twenty-first, it had been relegated to virtual obscurity in the philosophical literature on inference.189 Was this due solely to the marginalizing impact of pragmatism, the new realism, logical positivism, and (later) scientific empiricism, along with the elevation of symbolic logic as properly philosophical logic? Perhaps. But one suspects that Bosanquet’s philosophy of inference would have had a different fate if like Ernst Cassirer—also an idealist, though of the neo-Kantian critical variety—he had demonstrated the significance of his doctrine by substantiating his systematic postulates more in phenomenologically190 conceptual terms than in propositionally formal ones (to which he most often resorts).191 188  Cf., for example, L.S. Stebbing, Modern Introduction to Logic, 2nd ed. (London: Methuen, 1933), p. x. See n. 219, below. 189  A neglect typified in the epistemological treatment of linear inference that we saw in Michael Williams’ Problems of Knowledge: A Critical Introduction to Epistemology (Oxford: Oxford University Press, 2001). Cf., §2.5, above. 190  In the Hegelian sense that Cassirer employed in his explication of the phenomenology of knowledge; see, The Philosophy of Symbolic Forms; Volume 3: The Phenomenology of Knowledge, trans. Ralph Manheim (New Haven: Yale University Press, 1957), p. xiv. 191  The following is a typical instance—First comes the assertion of a systematic position: “my mind,” declares Bosanquet, “does not come to me as a separable source that judges by connecting particulars ab extra. It comes to me as a full world which reshapes itself by its own impulse, involving, as it does so in certain respects more or less of a peculiar satisfaction which attends upon adequacy and coherence. So far from misrepresenting the world, my mind as a volitional or capricious being cannot in the least affect that reshaping by the world of its own meanings which is judgment.” Then follows, in the form of a hypothetical conditional, the demonstration of its significance, predicated not upon the conceptual but upon the purely formal character of a particular experience: “If I am in a motor collision I shall

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Since we shall ultimately return to Cassirer’s doctrine of inference for a comparative analysis (in §4.6), a brief word on how Cassirer differs from Bosanquet is in order here. The conceptual element of the metaphysic of inference, if left insufficiently worked out in Bosanquet, finds exemplary and influential development in Cassirer’s Substance and Function (1910). Cassirer’s expositional modus operandi is to substantiate his systematic assertions not only by articulating them in terms of (experiential and logical) form, but also by depicting them, at the same time, in the light of a properly scientific conceptualization.192 Although Cassirer was perhaps less successful than Bosanquet at formulating a coherent metaphysic of the real as the Whole,193 by probably be badly hurt. How am I to think otherwise? I only wish I could” (Implication and Linear Inference, p. 152). Too often, Bosanquet leaves the conceptual logic of such demonstration opaque, looking instead to linguistic use or “mental states.” Like Bosanquet, Cassirer is concerned to develop a philosophy of inference that transcends any split between thought and being, but he concentrates his efforts on the process of concept formation. 192  Consider this example of Cassirer’s systematic metaphysical extrapolation: “Just as the relational character of position and distance inheres in the individual point, so the character of a universal law inheres in the individual experience. The individual cannot be experienced save in connection with other spatial and temporal, near or remote elements; and this kind of connection presupposes a system of spatial and temporal positions, as well as a unitary whole of causal coordinations.” Like Bosanquet, who would claim that Cassirer here makes the case for Bosanquet’s own holism, Cassirer substantiates his metaphysical postulate by appeal to the form of experience. But note the prime emphasis on conceptual logic—i.e., fact accessible in the logic of functional (as opposed, say, to that of purely reflective) concept development—in demonstrating the cognitional purchase of form (an essential strategy not as fully developed in Bosanquet): “The fact a is only accessible to us in a functional form as f(a), f(b), y(g), in which f, f, y, represent the different forms of spatial-temporal and causal connection. The logical act of ‘integration,’ which enters in every truly inductive judgment, thus contains no paradox and no inner difficulty; the advance from the individual to the whole, involved here, is possible because the reference to the whole is from the first not excluded but retained, and only needs to be brought separately into conceptual prominence” (Substance and Function, pp. 248-49). 193  Cassirer’s speculatively pregnant if incomplete effort along this line involves his thinking on Basis Phenomena. See the posthumously collected work published as The Philosophy of Symbolic Forms, Volume 4: The Metaphysics of Symbolic Forms.

194 Inference and the metaphysic of reason contrast with Bosanquet’s work, his rigorously argued and historically grounded conceptual logic of scientific inference has never gone out of print, nor has it suffered the fate of simply being brushed aside by most later philosophers. c) Beyond their differences on the syllogism and the expressly metaphysical (indeed Hegelian) character of Bosanquet’s definition of inference, there is, in the present context, a still more material contrast between Lotze and Bosanquet. This one has to do with the explicit onto-epistemological route that Bosanquet takes to establish, by way of his doctrine of implication, the relation of inferential thought, of reason, to reality as a Whole (which, for the objective idealist, is simply the truth of thought). Lotze, as we saw, dichotomizes logical thinking and “reality” (the Real). The definition of inference with which Bosanquet operates in Implication and Linear Inference presupposes the book-length treatment that he accorded the topic in the earlier Logic, an opus of over seven hundred pages wherein he takes issue with Lotze on a number of matters, such as on the very nature of a priori knowledge.194 Nonetheless, Implication and Linear Inference concisely yet effectively articulates the epistemological dimension of his orientation, as well as making plain his reluctance to follow Lotze in associating the act of inferring with the notion of “new truth”195 in any strict sense. Inference, contends Bosanquet, “includes prima facie every operation by which knowledge extends itself. When, by reason of one or more things that you know, you believe yourself to have arrived at the knowledge of something further, you claim to have effected an inference.”196 Here questions arise that pertain to some of the core issues of the onto-epistemology of the reason of inference as we shall consider it in chapter 4. From this perspective, the first thing to ask relative to Bosanquet’s statement concerns the nature of the reason—i.e., the principle of reason—that intelligibly founds the knowledge of the “one or more things” to which he refers. For Bosanquet, that onto-epistemological principle is the 194  Logic, vol. II, p. 224 n. 3. Another salient point of disagreement with Lotze concerns how the disjunctive judgment relates to induction, analogy, and the subsumptive syllogism (cf., Logic, vol. II, p. 202). 195  Recall that Lotze does not simply equate inference to “new truth”; rather he sees the act as the means of developing novel truths from premises. 196  Implication and Linear Inference, p. 2.

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law of contradiction (as a correlative, or defining “complement,” of the law of identity197): Reality, the Law of Contradiction asserts, is a consistent unity; which is merely to say over again that it is unity. You cannot, that is to say, play fast and loose with reality. What is true at all, as the Law of Identity said, is true throughout Reality; but more than that, every such truth is double-edged, and carries with it throughout Reality consequences by which it affects and limits matters that are prima facie outside itself. To infer from ‘A is B’ that ‘A is not not-B’ means at bottom that A is determined by B in respect of C or D.198

Although never cited in the text, Leibniz is the historically proximate thinker upon whose shoulders Bosanquet here largely stands (as does every modern logician). But unlike Leibniz, he doesn’t pair the Law of Contradiction with that of Sufficient Reason as, together, the “two first principles of all reasonings.”199 Leibniz apostrophizes the “law” of sufficient reason, more appropriately I think, in the following terms:200 “This most noble principle of sufficient reason is the apex of rationality in motion.”201 Aside from being consistent with respect to noncontradiction and identity, such reason, particularly as it informs the act of inference must first and foremost be sufficient in an originary ontoepistemological sense, or so I shall urge in chapter 4. Bosanquet would doubtless reject out of hand any such contention. Getting clear about why he would is much to the purpose here, and it will repay the effort to look briefly at his treatment of the principle of sufficient reason, with a view toward his understanding how it bears on his theory of inference. Properly to appreciate Bosanquet’s reading of the principle of sufficient reason calls for getting, first, a sense of 197  Disputing Bosanquet on this issue, I shall maintain that in inference the “law” of Sufficient Reason is what has priority. 198  Logic, vol. II, p. 213. 199  Leibniz Selections, ed. Philip P. Wiener (New York: Scribners, 1951), pp. 93-94. 200  Terms that Heidegger, for one, took to be of utmost significance. Cf., Heidegger’s The Principle of Reason, trans. Reginald Lilly (Bloomington: Indiana University Press, 1996). 201  Leibniz Selections, p. 93. Pace Leibniz, in the domain of inference Sufficient Reason is, I submit, in the first instance, a matter of formal rather than of efficient cause.

196 Inference and the metaphysic of reason his attitude toward all of the traditional “postulates of knowledge.”202 When it comes to theory of knowledge, Bosanquet states his guiding systematic conviction—implicit in the extended quote, above—as a familiar idealist formula: “the truth is the whole.” He explains this, his “fundamental” logical principle, in the following way: The significance of judgment and knowledge as of experience in all its forms lies always on ahead, and not behind; that is to say, in attempting to discern the real reality which justifies any experience you must go forward from it to the more concrete and more complete, and not retire upon something from which an element has been withdrawn. 203

Bosanquet thus resists erecting a theory of inference on “any abstract principles [principles that expressly ‘omit’ part of Reality from the logic of reasoning] as points of attachment antecedently furnished upon which the truth of knowledge could be supposed to depend.”204 He is content, nonetheless, to accept a law such as that of sufficient reason as a “postulate, a general [characteristic] of known Reality, which it is convenient to state in abstract form in any systematic treatment of knowledge.” And this, as he explains, is “because [it is] interwoven in the whole texture of the real world.”205 Bosanquet divides all such principles into two complementary kinds, formal and material; and 202  Cf., “The Relation of Knowledge to Its Postulates” (Logic, vol. II, chap. VII). 203  Logic, vol. II, p. 301. 204  Ibid., vol. II, p. 208. On this matter, Bosanquet takes his cue from Locke; cf., §2.2 n. 88, above. One encounters this orientation, shortly after Bosanquet’s death (1923), in Whitehead’s thought on inductive inference. (A philosopher who evinced the deepest respect for Bosanquet, Whitehead was at once a preeminent metaphysical thinker and, unlike Bosanquet, a master of both mathematical and formally, i.e., symbolically, logical thought.) “It is impossible,” declared Whitehead in his 1925 Lowell Lectures, “to over-emphasise the point that the key to the process of induction, as used either in science or in our ordinary life, is to be found in the right understanding of the immediate occasion of knowledge in its full concreteness….We find ourselves amid insoluble difficulties when we substitute for this concrete occasion a mere abstract in which we only consider material objects in a flux of configurations in time and space”; see Science and the Modern World (New York: Free Press, 1967), p. 44. 205  Logic, vol. II, p. 208.

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he expressly contrasts the formal “law of sufficient reason” with the material “conception of a teleological whole.”206 As a formal postulate, the law of sufficient reason is “drawn from intelligence exclusively…. drawn from the character of experience merely as experience, existing no doubt solely for intelligence, but for that very reason not separable in its source or nature from any other source or nature which could be described as intelligence pure and simple.”207 Bosanquet thus holds that the principle justifying the very identification of an act of thought as inferential derives from experience that exists “solely for intelligence.” Any appeal, then, to Bosanquet’s definition of the law of sufficient reason necessarily invokes the conception of inference as ultimately based on “the demand of intelligence for the explanation of everything by something else.”208 He rejects “the operation of this law” in the scientific “construction of the would-be totalities of abstract time and space,” because in that context “it rests on the relations of parts in abstraction from the whole, or in other words, without the element of totality.”209 The “necessity” of Sufficient Reason is for Bosanquet is not “absolute” but rather “real,” by which he means “a necessity which is a ground rooted in a fact.”210 With respect to the idea of Sufficient Reason as a principle of thought that properly applies to the act of inference, Bosanquet’s thinking is on this head fundamentally consistent with the position of the present book that the rational coherence of inference is rooted in fact for us, and hence manifests at every turn the meaning of intelligence. 3.5.3 Bosanquet’s systematic philosophy of inference. It is in Implication and Linear Inference that Bosanquet spells out just how such an implied “system,” or what he otherwise refers to as “a whole of the relations and 206  Ibid., p. 209. 207  Ibid., p. 208. Bosanquet is in the main consistent here with Lotze (cf., the latter’s Logic, §62). He rejects, however, Lotze’s “placing the test of ‘selfevidence’ in an immediate recognition without any process of proof ”; as Bosanquet sees it, this is “to surrender altogether the rational character of knowledge” (Ibid., p. 225 n. 3). This position is consistent with the present writer’s brief against the plausibility of a notion such as “immediate inference,” as opposed to a simple or immediate judgment. 208  Ibid., p. 215. 209  Ibid. (emphasis added). 210  Ibid.

198 Inference and the metaphysic of reason properties of things,” relates to the act of inference. Describing inference as “the life of a ‘subject,’”211 he portrays the subject of an inference as a self-developing entity, one that when involved in an act of inferential reflection the thinker simply endeavors to follow.212 As a thinker, I select a “special line of development” that happens to seem promising or interesting. Each such special route inheres, says Bosanquet, “within a total necessary development” of a particular “inferential nexus.” As for the influence of the developing “whole” under the auspices of which the line of thought in question evolves, Bosanquet argues that when my “starting-place is in any way indicated to be the implicit whole itself in a certain phase,” I require no particular initial datum or premise to elicit and orchestrate reflection. In his view, we as thinkers simply elect one that “interests us at the moment as promising.”213 This account leaves one with questions about how the “indicated” implicit developing “whole” of the subject of the inference—whether it be an individual being or an abstract theme—continues to inform a given progress of inference (assuming, with Bosanquet, that it is ontologically discrete from the act per se). How does such a whole keep inferential reflection on track, as it were, given that acts of inference are as often as not fragmentary, aleatory, and more or less self-reflexive? Also not addressed is the related matter of what ensures that the act of knowing “on what basis [we] are inferring” is a reason sufficient, at least on occasion, to ensure in its turn that an act of reflection originating with a “premise or datum, however slight or simple,” remains true (relative to its differences) to the developing subject. While Bosanquet supplies a plethora of logical forms of thought that structure the rationality of inferential reflection, he does not offer a conceptual logic that enables one to grasp how the onto-epistemologically posited bases of an inference can grow conceptually determinate as the truth of a developing subject. To reply, as Bosanquet likely would, that the Whole is 211  Bosanquet understands “subject” here both “in the sense of an individual being and of a single theme” (Implication and Linear Inference, p. 105 n. 2). 212  Ibid., pp. 122-25. One can find the Hegelian provenance of this notion in the Philosophy of Spirit, §467z; see Hegel’s Philosophy of Mind, trans. William Wallace (Oxford: Oxford University Press, 1971); [Die Philosophie des Geistes. Enzyklopädie der philosophischen Wissenschaften im Grundrisse 1830. Dritter Teil (Frankfurt am Main: Suhrkamp, 1986), pp. 285-87]. 213  Ibid., p. 121.

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ultimately the premise in every inference does not explain how on the plane of concept formation form, whether of the Whole or of anything else, operates as the principle of sufficient ground, not merely of the structure but of the very being of thinking. In sum, while Bosanquet gives us insightful and critically detailed analyses of the forms of judgment and of the real ground of formal thinking, he does not work out a conceptual logic that would with equal persuasiveness elucidate how, on the onto-epistemological plane of inferential concept formation, reason is the form of thinking as being. Bosanquet generally takes the lead from Hegel in rejecting anything like a Kantian phenomenal/noumenal dichotomy. Championing a logic that is both formal and transcendental and for which the Whole is always the unit of value,214 Bosanquet, like Hegel, properly employs discursive thinking (understanding) as a reflective instrument in the scientific explication of what Kant early on distinguished as diverse onto-epistemological domains: those of absolute and relative Position. Again, however, Bosanquet never sufficiently developed a conceptual logic that would articulate the onto-epistemological purchase of his logic of judgment (and inference) on the plane of reason. Consequently he employs understanding within a metaphysical frame of reference that effectively casts an otherwise rationally cogent exposition as in the service of a holistic vision that risks giving the impression of superimposing an exogenous (some might argue, a supererogatory) speculative notion. Not only does this make Bosanquet’s philosophy of inference an easy target for the analytic epistemologist, it runs counter to his philosophical orientation, not to mention his intent, which is after all to demonstrate215 how to grasp the ways that inferential thought attains to truth by transcending its premises. This problematic aspect of Bosanquet is perhaps most apparent, at least respecting the doctrine of inference, when at the end of his career he defines inference “in its essence” as “the self-development of a single subject.” The self-development in question is operative in accord with an a priori, primitive principle: implication. The metaphysical nature 214  Cf. what Bosanquet takes to be the role of “complete logic”: namely, “to trace and master the thinking function which elicits in ideal shape at once the nature of reality and its own” ideal shape (Implication and Linear Inference, p. 161). 215  In ways that Carnap, for example, and Harman singularly failed to do; see §§2.2 and 2.3, above.

200 Inference and the metaphysic of reason of implication is something that Bosanquet sees as causing “every inference”—however partial or imperfect—to involve “a judgment based on the whole of reality.”216 A younger American contemporary of Bosanquet, the idealist Josiah Royce, described in his earlier works the only creature imaginable (at least to the present writer) that might be capable of such a judgment, namely a Universal Consciousness. At any rate, one cardinal metaphysical issue remains far from settled after considering Bosanquet’s theory of inference: whether the appeal to implication properly—which is to say rationally—addresses the Whole/ Part problematic as it pertains to the act of inferential reflection, at least in its self-reflexive modalities as Beisichseiende des Seins. This aporia relates, as well, to the very itinerary of inferential reflection—a main thread of the probe, in chapter 4, into the ontoepistemology of inference. For Bosanquet, so long as the inferential “procedure” that follows an initial perception or idea is governed by “the unity of the ‘subject’—the interrelation of circumstances round a common center,”217 the often apparently adventitious or trivial nature of the starting premise or datum has little bearing upon the ontoepistemological economy of the act of inference. Bosanquet does recognize the importance of a beginning, but from his objective idealist stance the factor that is still more significant in any route of inferential thinking is the developing Whole with which, in the act of inference, one uniquely enters into union (as a particular “phase”): If you had no premise or datum you could find no starting-place. But, on the other hand, you might say that in a sense you need no special datum, when your starting-place is in any way indicated to be the implicit whole [of reality] itself in a certain phase….You have, you may say, no single datum, because the developing [objective] whole is itself in union with you, and is, indeed, in so far as it comprises particular terms and relations, itself your total premise and datum.218 216  Implication and Linear Inference, p. 4. Although he disagreed with the systematic conclusions that Bosanquet reached from the implicatory articulation of inductive inference, H. W. B. Joseph importantly credited “implication” as “connexion of fact, not of mere thought, or statement” (Introduction to Logic, p. 333 n. 1). 217  Ibid., p. 124. 218  Ibid., pp. 121-22, emphasis added.

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This thoroughly discredits the old charge of subjective idealism that lesser thinkers have leveled at Bosanquet. On the other hand, one misses an articulated conceptual logic that might help to illumine the onto-epistemological rationality of the formal efficacy that is the Whole from the standpoint of the act of inference understood as a living phase and occasion of it. This need appears all the more acute (and confirmed by the later if misconceived charge of a fatal vagueness219 in Bosanquet’s thought) when Bosanquet refers to “the implicit whole” (where implication is simply an a priori “relation of content to reality as a whole”). The same need for conceptual logic is felt when he refers to phases of that “whole,” and to a whole construed as the “total premise and datum” of every inference. 3.5.4 Summary of Bosanquet’s doctrine of inference relative to the ontoepistemological orientation. As a prelude to exploring the conceptual logic of the onto-epistemology of inference, the phase of inquiry anticipated by this essay’s introductory chapter and the critical discussion in the two chapters that followed, this concluding sub-section enumerates leading elements of Bosanquet’s account that bear directly upon the reason of the act of inference as we shall presently engage to think it through. a) Bosanquet identifies “the ‘mediate’ reference of an ideal content to Reality” as the moment that differentiates inference from other forms 219  Perhaps the most fundamental of such criticisms is the sort that L. S. Stebbing levels in the second edition of her widely known Modern Introduction to Logic (London: Methuen, 1933). Her verdict is categorical: “Neither Bradley, nor Bosanquet, nor any of this school of Idealist Logicians, has ever succeeded in making clear what exactly is meant by the principle of identity-in-difference upon which the metaphysical logic of the Idealists is based” (p. x). Stebbing cites H. H. Joachim’s early (1906) attack on coherence theories (their failure on their own operating assumption—coherence—to be true as such), which led him to determine that the idealist logics of Bradley and Bosanquet end in “shipwreck.” In the 1911 edition of his Logic, however, Bosanquet systematically refutes Joachim’s criticism in a way that reflects the onto-epistemologically arbitrary scope of what formalist logicians such as Stebbing would count as the horizon of coherent philosophical thought. See Logic, vol. II, pp. 288-92. For a sharp critique of Stebbing’s questionable grasp of identity-in-difference as it varies from the mathematical to the logical domain, see H. W. B. Joseph, “A Last Plea for Free-Thinking in Logistics,” Mind ns 43 (1934): 315-20.

202 Inference and the metaphysic of reason of judgment. While in conjunction with this Bosanquet introduces a dubious notion of “true immediate inference,” his reference to the factor of mediation in this connection rightly characterizes the sine qua non for distinguishing inference from judgment. (Hence this moment of differentiation is an essential element of the challenge mounted here to the concept of unconscious or pre-reflective inference.) b) Inferential judgment manifests a “mental fact” that is “invested” with value that evidences, in Bosanquet’s view, a nomological relation of logical thought to a trans-cognitional Reality. Bosanquet contends that this relation composes the “special phase” of Reality that we identify as universal laws of connection. A crucial implication of conceiving inference along these lines is that it makes plain the need to get clear about the onto-epistemology of inference in a way that elucidates inferential reflection as an act that is as much a sponsor as a bearer of values (i.e., as an act that features onto-epistemological positing). Another key implication of Bosanquet’s doctrine is that to infer in any cogent sense shows not merely as a psychological process or the cognitional realization of some fixed rational pattern or scheme, but beyond that as a disclosive, onto-genetic living activity that is only insofar as it reflectively idealizes—i.e., actualizes as being for spirit (Geist)—significant if otherwise remote matters of fact.220 (For the phenomenological epistemologist this correlates with intentionality as the prime constitutive moment of consciousness.) The act of inference is thus never purely “mental” in any sense that refers to some category or existential order that is logically discrete from being or “Reality.” The present work’s effort to explicate the onto-epistemology of the act of inference thus eschews talk of mental states and mental facts. c) “A necessary connection even between two given terms is a reciprocal inferential relation, implying a system beyond either, and not present in the apprehension of each alone or of both together.”221 This thesis is among Bosanquet’s signature metaphysical postulates (and puts one in mind of Kant’s famed argument for the synthetic status of the proposition 7 + 5 = 12222). It highlights the systematic character of his philosophy of inference, underscoring in the process the 220  For further reflections on “remote” fact, see Appendix V, below. 221  Logic, vol. II, pp. 321-22. 222  Prolegomena to Any Future Metaphysics, trans. Peter G. Lucas and Günter Zöller (Oxford: Oxford University Press, 2005), p. 74.

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factors of “self-transcendence” and “implication” that are linchpins of his doctrine. The onto-epistemology of inference, as we shall find in the next chapter, does not credit, for threat of regress, the reflectively articulated relation between two terms (premises)223 as something that is itself identifiably inferential in a passage of reflective thought. Rather than self-transcendence of either premises or thinker, what will be seen to occur in cogent acts of inferential reflection are moments of formal realization (Wirklichkeit), articulated as an idealizing of significant fact224 as meaning. Such moments are in effect primitive onto-epistemological occasions wherein remote facts disclose—thereby come to be (through premises properly ordered to a conclusion)— their significance for us. And this, insofar as our living act of intelligence, spirit (Geist), invests them with ideal definition, whereby—to the extent that they are effectively put as terms of discourse—they assume their truth formally, in the consummately evolved cognitional reality of reflective spirit. From this perspective the concept of “implication” acquires explanatory value to the extent that one construes it from within the horizon of a conceptual logic. It is here, however, that we encounter speculative limits in Bosanquet, who does not approach conceptual logic with anything like the systematic penetration with which he explicates such purely formal dimensions of logical thought and of “Reality” as “measurement and individuality,” “enumerative induction,” and the architectonic of the Whole. d) Bosanquet’s metaphysical position that inferential thinking is intrinsically systematic (not merely linear), and that in any given instance it refers to a “partial system which need not even be actual,” correlates with the onto-epistemology of the reason of inference. As we shall find in chapter 4, the specific order that sponsors225 the progressive, mutually determinating show of premises that conduce to a conclusion may express an aesthetic or theological or psychological or political—virtually any—form of intelligible being. This ideational expression occurs in routes of reflection that are incommensurate with merely linear exercises in applying the rules of mathematics or 223  A relation of mutual determination sponsored by the moment of order in terms of which they show as premises in the first place. 224  By way of premises reflectively ordered (and rendered determinate thereby) to a totality, which as a conclusion is their truth. 225  And in turn is rendered actual [wirklich] as a formative moment of Geist.

204 Inference and the metaphysic of reason symbolic logic. (This says nothing, of course, about how properly defined or valid the systematic integrity is of any given form of being as entertained within the fallible, radically limited purview of particular inferential acts.) For all that, an act of inference may appear to some degree linear from the side of its ordering moment. But it is arguably only in terms of conceptual logic that one properly grasps and explicates it, that is to say, as an act of knowing that is of being—this as opposed to some act of following or applying the laws of perspective, say, or a set of transformation rules. The conceptual logic of the act of inferential reflection thus at bottom manifests the reason of the cognitional process not structurally, not psychologistically, but ontoepistemologically. Notwithstanding the significant correlations between Bosanquet and the orientation to inference articulated in the present book, however, the account presented in chapter 4 does not invoke anything like the notion of a metaphysical Whole that Bosanquet has in mind when he refers to his philosophy of inference as systematic.226 e) More consistent with the onto-epistemological philosophy of inference is Bosanquet’s emphasis on the transformative efficacy that distinguishes the process of inference as a living act of concept formation. For Bosanquet inferential cognition constitutes a “principle of progressive knowledge” whereby the terms of thought undergo transformation. To repeat his most concise description of the itinerary of inferential thinking: “You begin with sporadic facts and you end up with a concentrated ‘plot’ and its ‘solution.’” This identifies transformation as an element of scientific thinking, and in a way that foregrounds Bosanquet’s preoccupation with the objectifyingly formal aspect of inferential conceptualization, as distinguishable from its conceptual logic. 226  That intelligence refers to the whole remains central to systematic metaphysics is seen, for example, in the thinking of Lorenz Puntel, who links orientation to the whole to the subjectivist idea of intentionality (as opposed to Bosanquet’s objectivist notion of “implication”). “Thinking and willing,” declares Puntel, “are unambiguously intentionally structured: both involve directedness or orientation toward…, [sic] and ultimately toward anything and everything, toward the universe in the most comprehensive sense—in brief, toward being as a whole”; see Structure and Being: A Theoretical Framework for a Systematic Philosophy, trans. Alan White (University Park, Pa.: Pennsylvania State University Press, 2008), p. 278.

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3 As we shall see, the determining transformative moment in the onto-epistemology of inference differs significantly from what Bosanquet has in mind. James W. Allard has summed up Bosanquet’s concept of the process of inferential knowing in a way that foregrounds the most salient differences: The temporal process of inference is the transformation of judgments into a form in which their grounds are more explicit. It has stages marked by Bosanquet’s versions of the ‘three figures of syllogisms.’ The process begins with noting the circumstances under which a conjunction occurs, finding a law covering its occurrence, and exhibiting that law as a ground for the judgment.227

From an onto-epistemological orientation, the transformative aspect of inferential reflection does not restrict itself to syllogistic figures, nor does it extend to the activity of “finding a law” that the act of inference incorporates as a means of exhibiting its own ground. The transformative moment of inference has to do, rather, with pre-reflectively apprehended remote facts, whose significance for the thinker impels the Position of what, under a given set of circumstances, show as premises, and by that token, as always already ordered moments of implication in a reflective process. The act of inferential reflection simply is the transformation (specifically, the actualization [Wirklichkeit]) of otherwise “tacit” facts, by which is meant facts prior to their translation (in virtue of their intelligible significance for us) into ideal articulations of living intelligence, i.e., as moments of conceptual thinking. This reading of inference substantiates the seminal onto-epistemological relation, briefly noted in chapter 1,228 between the act of inference and the difficult fact noted for all time by Aristotle, namely that knowing “somehow” becomes that which it knows. The upcoming chapter, the second Part of this inquiry, undertakes, among other things, to think through what this means as the reason of the act of inference. After explicating this approach to inferential knowing as being through the greater part of chapter 4, we shall consider, in a penultimate section (§4.6), how this orientation to inference compares to the Marburg School doctrine that Ernst Cassirer presents in his analysis of scientific inference. Like Bosanquet, Cassirer was an idealist—al227  “Bosanquet and the Problem of Inference,” p. 84. 228  See, above, §1. iii (e).

206 Inference and the metaphysic of reason beit of the neo-Kantian “critical” rather than the neo-Hegelian “objective” variety. Also like Bosanquet, Cassirer accorded significant weight to the transformational element of inferential cognition. One sees this in the opening sentence of a section in Substance and Function titled, “Induction and analysis, ‘compositive’ and ‘resolutive’ methods” (part of a chapter that Cassirer devotes to “the Problem of Induction”). As Cassirer puts it, “The first result claimed by the inductive ‘concept,’ in the strict sense of this word is that it transforms the manifold of observations, which at first appears as a mere unrelated coexistence of particular elements, into some fixed serial form.”229 Cassirer’s modus operandi is to concentrate upon the dynamism (a term he would likely reject230) of the conceptual logic of induction. His neo-Kantian proclivities, however, render some of the grounds of his theory sharply at variance with the analysis of inference that will preoccupy us in the first four sections of chapter 4. Still, Cassirer’s thinking on the topic reveals a grasp of the reason of inference that is considerably closer in purport to the view at the heart of the present work than is Bosanquet’s (with its dual emphases on knowledge-forms and pure ontology). Given that nearer affinity, the comparative treatment of Cassirer’s analytically attuned onto-epistemology of inference will highlight in the figure of Cassirer a seminal modern development of philosophical and, more broadly speaking, intellectual history within and against which the present work may properly be judged.

229  Substance and Function, pp. 252-53. 230  Not least because of its Maréchalian associations with the absolute, something to which my use of the term in the present work is not committed either way.

Chapter 4 An Essay in the Onto-Epistemology of Inference …the suspicion forces itself upon us that in Kant’s determination of being as positing there prevails a kinship with that which we call Grund.

Martin Heidegger, “Kant’s Thesis about Being” (1961) Setzen fällt eigentlich erst in die Sphäre des Wesens, der objektiven Reflexion; der Grund setzt das, was durch ihn begründet wird....

G. W. F. Hegel, Wissenschaft der Logik With a true conception of form we can [in the act of ] recognizing the growth of implication in wholes freshly constituted ad hoc….observe the nature of reality establishing itself as a central identity of ideal determinations, among data previously disconnected for our apprehension. And though we can recognize the “form” by introspection, we cannot antecedently prescribe the conclusion, because the form is the spirit of the matter, and the matter is inexhaustible.

Bernard Bosanquet, Implication and Linear Inference Modern philosophy prior to Hegel terminates in a crisis with respect to form. On the one hand, modern philosophy cannot rid itself of the classical conception that Being and Knowing are united in their actuality by a formal structure. On the other hand, the manifest difference between formal structure and self-consciousness is immediately knowable but not knowable conceptually or analytically.

Stanley Rosen, G. W. F. Hegel 4.1 The need of an onto-epistemological approach to the reason of the act of inference. The body of chapters 2 and 3 constituted the first, critical Part of this inquiry. Chapter 2 identified a set of onto-epistemological aporiai discernible in the broad spectrum of leading analytic epistemologies of inference. The third chapter ultimately discovered some

208 Inference and the metaphysic of reason different though far from unrelated problems in the systematic philosophical logics developed by Lotze and Bosanquet; notwithstanding these objections, however, we noted the various points at which Lotze and Bosanquet distinguish, elucidate, and substantiate elements of an onto-epistemological approach to inference. As we turn now to the mainly constructive phase of discussion, it should be clear that the challenge of how to grasp inferential reflection as a living act of intelligence (or reflective spirit) is anything but a technical matter concerning arcane definitions that refer merely to a subclass of logical judgments (i.e., mediated ones). Indeed, the orientational nature of the difficulties exposed in the critical chapters suggests that we need to rethink the reason of the act of inference along more radically fundamental, onto-epistemological lines—namely, in the acute Thomist formulation, as “seeking some adequation to factual being.”1 The present chapter amounts to an effort to address just this task—an essay that if original in some key respects, is nonetheless far from unprecedented in its signal philosophical claims. What follows, then, details no methodology, nor does it delineate a techne. Rather, it explicates an orientation to the reason of the act of inference as to Being itself2— something that it undertakes primarily in terms of the conceptual logic of inferential reflection, grounds which emerged in the critical discussions of the preceding two chapters. Before outlining the specific topics to be explored in this second Part of the inquiry, let me say a word about some of the practical considerations that recommend the taking up of such a seemingly abstruse philosophical project in the first place. Reductivist or mutually inconsistent understandings of discursive knowledge impact educational, socio-political, and even scientific thinking and norms in ways that have far-reaching disciplinary, practical, and broader cul-

1  Let me be clear here: to associate with the Thomist maxim this effort to rethink inference onto-epistemologically is merely to cast as the object of this essay the achievement of a more fundamentally adequate measure of truth to fact in this field of inquiry. Invoking “adaequatio” to “factual being” thus does not attach to the onto-epistemological orientation per se (which harbors no latent dualism). 2  There is no pretense in these pages of propounding a system pure ontology.

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tural implications.3 To appreciate this is to recognize the true scope of the problematic of inferential thought for contemporary intellectual culture. Perhaps what most dramatically attests to the pressing nature of the issues at stake is that competing sociolinguistic or probabilistic, symbolic logical or psychologistic or semantic regimes of discursive thinking and its practical purchase come with no warrant, beyond instrumental efficacy, as to any thinking’s ontological authority. Symptomatic of this are the disputes that fuel national debate over the ontological legitimacy of competing evolutionary and creationist acts of inference. One can see this as well in the ongoing disputes over the ontological legitimacy of competing inferences—political, semiotic, materialist, and other species of inferences—as to the very nature of “information” in the Information Age. In all this the nature of discursive reason itself remains, for the analytic epistemologist, rationally indeterminate with respect to praxis in every field of intelligent action. (Gilbert Harman, as we saw, tacitly affirms as much when he denies that deduction, or following logical rules of any sort, constitutes reasoning.4) The consequences of this rational indeterminacy ramify, I would argue, to the most basic level of calculative rationality, which is to say the apperceptive plane on which we unreflectively employ inferential thinking merely to cast intelligible facts as objective terms of practical, instrumental knowledge. 3 The thinking-through of the onto-epistemology of inference that structures the present chapter commences with a synoptic statement (§4.2) that presents in a preliminary way the leading themes of the analysis. This is followed by a general account of the act of inference (§4.3). The next section (§4.4) summarizes the three interrelated core components of the account, namely a) the moment of “positing” (Position or Setzung) in the act of inference, b) the reflective itinerary of its conceptual logic, and c) the formal ground that is the Reason, quite literally the raison d’être of inferential reflection. On the heels of this 3  Cf., Myth and the Limits of Reason, Revised Edition (Lanham, Md.: University Press of America, 2004), where I identify and explicate mythemically figured critiques of reductivist modes of discursive reason in the domains of religious, psychosocial, national-cultural, and psychobiological experience. 4  See §2.3, above.

210 Inference and the metaphysic of reason overview comes an extended section that considers the trio of elements at close range (§§4.5.1-4.5.3). Prior to the chapter’s concluding section, the discussion shifts from constructive explication to a comparative exposition of Ernst Cassirer’s critical-idealist approach to scientific induction (§4.6). This denouement in advance of the coda serves as a means of stepping back, immediately following the extended exposition of the onto-epistemological account so as to situate it historically and conceptually in more systematic detail than could be usefully done in the earlier chapters. Cassirer’s seminal Marburg School philosophy of inference masterfully incorporates formative moments of both analytic and continental thought; and it does so in ways that illustrate something of the philosophical lineage of the effort in these pages, which is to elucidate the reason of the act of inference by explicating, onto-epistemologically, its conceptual logic.5 The chapter’s closing section (§4.7) sums up this study’s debts to Kant, Hegel, and Bosanquet; in the process, it enumerates the respects in which the present work breaks sharply with their systematic doctrines. The discussion ends with a review of what it is that distinguishes this inquiry overall as an essay in critical metaphysics. In a brief coda, I say a word about the more general significance of this venture to rethink the philosophy of inference from within an ontoepistemological frame of reference. 4.2 Synopsis of the onto-epistemological orientation to inference. Three mutually integrating moments are at the core of this account of the reason of the act of inference: 1) onto-epistemological positing, 2) an essential (wesentlich) conceptual logic of inferential reflection, and 3) the idea of formal cause as the principle of the sufficient reason that grounds the reason of inferential reflection. The synopsis that follows offers a preliminary sketch of the role that these components play in the onto-epistemology of inference. The overview consists of six brief statements. a) A general description of inference from the proposed standpoint. 5  I say “something of the philosophical lineage” because the orientation here, while it exhibits some close affinities with Cassirer’s neo-Kantian thought, stops short of subscribing to anything like Kantian transcendental logic.

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b) Some reflections on the idea of inference as act. c) A word about onto-epistemological positing and the essential dialectic of inferential reflection. d) Some remarks on the reflective “show,” the Schein, of premises that, as premises in a coherent act of inference, are formally ordered to a conclusion. e) Assertion of the principle of formal cause as the sufficient reason of the act of inferential reflection; this cause being—in the dynamism of discursive thinking toward a conclusion—the determinating actualization, the forma formans, of the “show” of premises; the premises in composition, each with a mediating other, as determinately (formally) ordered to a totality that is the conclusion of the inference, its meaning. f) Lastly, a brief comment on validation and the inferential process.

a) General definition. Every judgment is an intentional act of “assessive” cognizance. It is an act that, in its turn, we may assess for correctness or erroneousness—for its probability, its truth in a supervening context, its necessity. One prime class of judgments includes our immediate, unreflective acts of intelligence such as intuitions or immediate judgments or epiphanies or other unmediated cognitions. The act of inference, by contrast, exemplifies a second principal class of judgments. To infer is to judge in a way that is at once mediated, explicitly reflective, and discursive, a way that as the late Frege put it, “justifies the recognition of truth.” Of course, not every intelligent judgment takes the form of discursive, inferential reflection—most, pretty clearly, do not. Many would reject the move to classify inference in these terms. Indeed, it seems natural enough to think of unmediated judgments as inferences, for instance when one unreflectively “sees” a whole circle to follow from a perceived half circle. Proleptic cognition of this sort structures our conscious life. And as recent findings in neuroscience have borne out,6 we perform such judgments “without a thought,” or 6  The results of neuroscientific research prove consistent with the distinction I draw between immediate judgment and inference proper. The science that yielded results establishing the correlation was based on the following hunch: “the ease and speed with which we typically understand

212 Inference and the metaphysic of reason rather without thinking, without being reflectively alive in that connection. But to identify unmediated judgment as inference proper is arguably to betray a failure to discriminate pre-reflective cognition from the more evolved—the cognitionally “higher”—activity of inferential reflection. Unlike simple judgment, inference features a distinctive ontogenetic moment that has the character of a noetically perfecting, formative energy. The act of inference thus evinces the living actualization of thought (in Aristotelian terms, the manifestation of the energeia of nous7). And it always calls attention to itself as such, although inference is as often as not not self-reflective. Inferential thinking thereby discloses the onto-epistemological criterion for recognizing the difference between prediscursive and discursive thought in the first place. While prediscursive intelligence is ever potentially scientific and prosimple actions suggests a much more straightforward explanation” of how we grasp them than does some account of “a rapid reasoning process not unlike that used to solve a logical problem.” Over the period of a decade, scientists isolated and tested a class of brain cells, “mirror neurons,” that physiologically corroborate the philosophical move categorically to distinguish between immediate judgment and inference. These cells “appear to encode templates for specific actions.” (Although the researchers offer only vague speculation about the full range of the character of what qualify as such “actions” in human experience, it pretty clearly extends into the domains of symbolic form and of “virtual” entities, such as the perceived volume of a cube that a properly configured set of lines expresses two-dimensionally on a blackboard.) The scientists offer the following conclusions: “Much as circuits of neurons are believed to store specific memories within the brain, sets of mirror neurons appear to encode templates for specific actions. This property may allow an individual not only to perform basic motor procedures without thinking about them but also to comprehend those acts when observed, without any need for explicit reasoning about them. John grasps Mary’s action because even as it is happening before his eyes, it is also happening, in effect, inside his head….for neuroscientists, this finding of a physical basis for [immediate judgments] represents a dramatic change in the way we understand the way we understand.” See “Mirrors in the Mind,” Giacomo Rizzolatic, Leonardo Fogassi, and Vittorio Gallese, Scientific American, Special Section: Neuroscience, November 2006, pp. 54-61. This empirical work also bears out the epistemology of literary metaphor articulated by the present author two decades ago in terms of “participatory enactment” and “enactive envisagement”; see Stambovsky, The Depictive Image: Metaphor and Literary Experience (Amherst, Mass.: University of Massachusetts Press, 1988). 7  Aristotle, Metaphysics (1072b).

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vides what is in effect the basic noetic currency of discursive reasoning, the very distinction between unreflective cognition and the mediated, inferential sort discloses the grounds for our having come to enshrine the latter as the gold standard for the prosecution and deepening of scientific thinking. In this light, the idea of so-called “immediate” inference appears fundamentally problematic. This is hardly an original conclusion: “no inference is or can be really immediate”8—thus declared F. H. Bradley, consistent, so far, with an onto-epistemological view. As Bradley explained, “Unless there is a link of ‘why’ and ‘because,’ unless there is an ideal whole, and, through that, a necessary self-development, there is no inference anywhere at all.”9 At one with Bradley and with the onto-epistemological orientation on this score is Bernard Bosanquet’s definition, rendered in the speculative idiom his self-described objective idealism, namely that inference is “the mediate reference of an ideal content to Reality.”10 (Bosanquet does argue for what “might be called the true immediate inferences,” by which he understands “such processes as Recognition, Abstraction, Comparison, Identification, Discrimination.”11 But when he proceeds to explain these as “names of processes, of cases of the judging activity, in which one or other of its aspects asserts itself par excellence,” he defines such “cases” as complex forms of immediate judgment. The latter he tellingly ascribes to “Reason” as processes by means of which “Reason, armed with reflective ideas, breaks into concrete data in search of the unity of the universal.”12 Reverting to the agency of Reason in this manner enables Bosanquet to import—in an onto-epistemologically anomalous way—elements of conceptual logic proper to the act of inference. In other words, Bosanquet’s theorizing does not escape the underlying categorical diversity of immediate judgment and inference.)

8  The Principles of Logic, 2 vols., 2nd edition, revised with commentary and terminal essays, corrected edition (London: Oxford University Press, 1928), book III, part I, p. 430. 9  Ibid. 10  Logic, vol. I, p. 1. 11  Ibid., vol. II, p. 19. 12  Ibid., p. 21.

214 Inference and the metaphysic of reason b) Inference as act. Inferring from premises to a conclusion is a conscious action, an actualization (Wirklichkeit) of reflective intelligence that involves onto-epistemological positing. This originary cognitional positing13 is an operative component of discursive intelligence, which is the living process that reflectively assimilates facts that are immediate for experience with those that are remote. Remote facts are not in themselves predicable of a subject. (Rudolf Hermann Lotze, for one, contrasts what he recognizes as “remotive” judgments, for which S is neither q nor r, from both disjunctive judgments [S is either q or r] and copulative judgments [S is both q and r].14) Remote facts may show for us, however, as immediate determinacies (Hegelian scheinen: cf. Der Schein ist...selbst ein unmittelbar Bestimmtes15). Hence we judge facts, insofar as they are determinate—intelligible—through the posited, the thetic, mediation of formal order (Ordnungssetzung) that renders determinate the act of rational intelligence, in virtue of the show of fact for us. Put to thought in the thetic act, this mediating formal order—whatever the species of the form (mathematical, psychological, aesthetic, forensic, etc.)—is functional, operative, as an ontologically constitutive element of any premise as a premise in the dynamic of inferential reflection. It is thus that remote facts are actual in inferential thinking. Remote facts show (scheinen), articulated in our acts of inference, as premises ordered to some form of conclusion. From the standpoint of concept formation, the remote facts that show as premises in reflective thinking have been transformatively invested—onto13  The concept of which Kant held to be identical with nothing less than the concept of Sein überhaupt. From the Fichtean standpoint, this is “the highest Position,” and a concept of “the inner material content of knowing” construed as “only the negation of insight” that yet “arises only from it,” and which “in truth…is no negation.” Fichte stresses the existential character of absolute position as act; finding that although it is a concept, “in truth we in no way conceive it, but rather we have it and are it” (The Science of Knowing: J. G. Fichte’s 1804 Lectures on the “Wissenschaftslehre,” trans. Walter E. Wright [Albany: State University of New York Press, 2005], pp. 80-81). 14  See Lotze, Logic in Three Books: of Thought, of Investigation, and of Knowledge [1879], 2nd ed., 2 vols., trans. Bernard Bosanquet et al. (Oxford: Oxford University Press, 1888), vol. 1, p. 99. 15  See G. W. F. Hegel, Wissenschaft der Logik II (Frankfurt am Main: Suhrkamp, 1986), chap. 1, esp. pp. 19-21. Also see Robert M. Wallace, Hegel’s Philosophy of Reality, Freedom, and God (Cambridge, Engl.: Cambridge University Press, 2005), pp. 159-61.

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epistemologically posited16—with a determinate ideal sense that manifests some particular principle of order. In the crucible of the living, reflective intelligence, this ideal sense is consequently instinct with formal and ontic character and implication. In the dynamism of our reflective thought we thus, for better or worse (disclosively or confusedly), thetically “invest” facts with determinate ideal sense, which is to say formal meaning—mathematical, for instance, psychological, aesthetic, and so forth. This ideal sense, charged with formal meaning, is ontologically discrete from the conceptual logic that it uniquely instantiates, and that it bodies forth noetically. The formal sense of an inference is both originarily and through the very intellective activity that realizes it what Fichte denominated the Tatsache des Bewusstseins, the first fact of consciousness.17 This is what Hegel, rejecting the Kantian reference to “consciousness” as subjectivist, identified as infinite thought, thought as such—thought that “puts” facts to intelligent reflection, in the noetic currency unique to the actualization (Wirklichkeit18) that is spiritual (geistig) being. Take, for example, an act of religious witness or affirmation of faith: as a moment of reflective religious meditation it exemplifies, in its illocutionary actuality (i.e., its prayerful character), the ontic reality of the ideal sense that remote facts evince in showing, for the theophanically attuned witness, as ordered to the culminating ground of devotional reflection. To present a judgment as an “unconscious inference,” rather than as an immediate judgment sponsored by prereflective activity or antecedent occasions of thought or experience, is implicitly to re-present the reason of the act in question as a mode of mediated ideation. This 16  In the sense of Einsetzung (investiture); see Dieter Henrich’s list of terms associated with Setzung, in Between Kant and Hegel: Lectures on German Idealism, ed. David S. Pacini (Cambridge, Mass.: Harvard University Press, 2003), p. 233. 17  The moment, in Fichte’s view, that transcendentally grounds the concepts involved in the “self-positing” I’s originary expectation that it encounters “something corresponding” to the not-I. For a penetrating recent discussion of Fichte on this head, see Allen W. Wood, “Fichte’s Intersubjective I,” Inquiry 49.1 (2006): 62-79. 18  Lotze, in his Metaphysic (§3.4.3), thought it best to retire the term Position oder Setzung and replace it with Wirklichkeit. But I have appended the present note to the observation of a fact that indicates that such a move elides a crucial distinction between a cognitional function or power (setzen) and its formative efficacy (the self-realization of spirit).

216 Inference and the metaphysic of reason amounts to recasting the judgment in the image of a bona fide inference. (Inferential reflection is, on this account, strictly a consciously explicit act. Stated in the Hegelian idiom, it is a configuration of spirit, Geist, on the level of pure thinking, and realized not just in itself or for itself but only in and for itself.19 It is only thus that we are able reflectively to render in conceptual terms a world of otherwise uncognizably remote facts that are significant for us.) As a reflective act, inference is not properly cast as an immediate judgment. Those who identify prereflective mental acts as “inference” are, in the very process, exercising mediated judgment in a way that perforce reads back its own raison d’être into its object; and this without at the same time supplying rational grounds for distinguishing the putative “immediate inference” from a complexly articulated, an educated immediate judgment. The reason for this is that immediate judgments are an ineliminable ingredient of inference, and the mediated judgment that is inference is constitutionally incapable of accounting for them in its own discursive terms (i.e., terms that merely subsume immediate judgment, axiomatically, under the form of reflection).20 That all “scientific” thinking and teaching are referred to discursive, inferential thinking and knowing evidences the cutting-edge role that discursive reasoning plays in the self-reflective Bildung of human spiritual (geistig) life. So far as they are rationalizable, communicable, and potentially instrumental in rational thought, immediate judgments— intuitions (be they “pure” [Kant] or empirical or “rational” [Gödel]), epiphanic insights, “revelations,” and so forth—must “show” as formative moments of inferential reflection. In other words, they must be manifest as formally assimilated to acts of discursive intelligence. c) Onto-epistemological positing and the dialectic essence of inferential reflection. The modifier “onto-epistemological” refers to the guiding speculative principle of this orientation to inference, namely the irreducible composition of thinking and being that needs to remain front and center in any rationally and realistically cogent philosophy 19  Pace Hegel, however, the view here is that the onto-epistemological character of inference renders its actualization, which is its actuality (Wirklichkeit), something more than merely a form of subjective spirit. 20  What’s called for, I would submit, is a dialectical analysis that relativizes the defining moments of each mode of judgment to the ways that it is what it is in terms of the ways that it is other to its mediating other.

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of reflective thought. Viewed from this perspective, the act of “position” (Setzung) at issue here invests the presence of a significant fact (i.e., how it “shows” as put to thought21) with ideal actuality. As ideal, a significant fact is not something that I passively entertain by thinking. Rather, I prehend it in its implications as being for thought—and I do so by the very act of putting it to thought. In the act of inference I thus prehend a significant fact as a moment of reflection that constitutes at once its elucidation (Erläuterung) and its discursive, its ordered, “situation” (Erörterung). Onto-epistemological position thus renders explicit, in routes of inferential reflection (i.e., as setzende Reflexion), the what-it-is of some significant fact in its being for reflective thought, thought that (however imperfectly) ideally amplifies that fact and thereby develops it. Discursive thinking inferentially, reflectively, thus develops the being that it “positionally” sponsors by simultaneously elucidating and discursively situating it—Erläuterung und Erörterung haben, as Heidegger pointed out, “the character of reflection” [den Charakter der Reflexion].22 Inferential judgment is a reflective dynamic of living intelligence, and as such constitutive of inference as a process of concept formation. More particularly, this process is a dynamism toward totality and truth (in the very idea of which we affirm the circumstance that fact is for us). Moreover, the act of inferential reflection manifests a conceptual logic of essence that, for any coherent route of discursive thought, instantiates the reason of the act of inference. This logic—whether it takes the form of mathematical or psychological or aesthetic or forensic or any other mode of intelligible being—manifests the essence of facts that reflectively show as premises. The premises come-to-be determinate as such (so far as the facts admit) in being ordered visà-vis each other (i.e., “con-form”) to compose, more or less plausibly, a totality. When I am immersed in the reflective process, the premises do not stand as a composed conceptual totality, but instead logically conduce to a conclusion. As we shall see in §4.5.2, Hegel’s doctrine of essence provides a particularly pregnant context of analysis on this head. Indeed, one can trace the route of inferential conceptualization 21  Which is not to say that such “show” is reducible to presence; cf. John Sallis, Force of Imagination: The Sense of the Elemental (Bloomington: Indiana University Press, 2000), p.103; and chap. 4c (“Shining”). 22  “Kant’s Thesis about Being,” Pathmarks, p. 360 [“Kants These über das Sein,” Wegmarken, p. 470].

218 Inference and the metaphysic of reason from station to station in the phase of Hegel’s logic of essence that runs dialectically from identity through ground.23 That said, this is not a Hegelian theory of inference, the concern of the present investigation being limited to acts of intelligence that take place on the level of pure thinking (i.e., mediated being).24 The intelligible moments of the living cognition that is inference— namely, the essential (wesentlich) terms of discursive reflection—are not rightly taken as things in themselves. Nor are they particular mere appearances (Erscheinungen), i.e., some this or some that. Such apparent determination is a function of how it is that the identity of what shows as a premise in a given case does so in its differences from its counterpart(s). What shows as a premise does so in a relation to the mediating other or others always already ordered—howsoever tenuously or remotely, yet in so far invariantly—to an ideal totality or conclusion. Kant’s distinction,25 one doubtless familiar to Hegel, between show (Schein) and Erscheinung applies here: Schein being a nonillusionary appearance that is “simple self-relation”26 and hence neither true nor false, while Erscheinung is “mere” appearance, which may be determined to be true or false. How otherwise remote facts are for reflective intelligence—how, that is, the ways that such facts come to be as “ideas” in onto-epistemological position (setzen)—is their intelligible being. Intelligible being is a happening, an event that articulates reflectively in the act of ideationally prehending the differences of negation of immediacy. This ideational being of fact, in its difference (mediation), and as actual as a formative component of intelligent life, is neither thing-like 23  See Encyclopedia Logic, §§112-122. 24  Not that of the mere negation of being. 25  Cf., Metaphysical Foundations of Natural Science [1786], translated and edited by Michael Friedman (Cambridge, Eng.: Cambridge University Press, 2004), p. 94. 26  A self-relation that, as “passing into essence,” contains “within it being in general and its forms as sublated” [welche das Sein überhaupt und dessen Formen als aufgehobene in sich enthält]; cf., Encyclopedia Logic, p. 173. [Die Wissenschaft der Logik, Enzyklopädie der philosophischen Wissenschaften, Erster Teil (Frankfurt am Main, Suhrkamp, 1986), §111, emphasis added.] See also Wissenschaft der Logik II (Frankfurt am Main: Suhrkamp, 1986), chap. 1, pp. 19-21; and Wallace, Hegel’s Philosophy of Reality, Freedom, and God, pp. 159-61.

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nor illusionary, except when objectified as a discrete term of discourse. For when fact as idea gets thus objectified it is abstracted from its informing dynamic, it is no longer actual (as event). Hegel brilliantly depicts such objectification—the reduction from Schein to mere appearance—in a Zusatz appended to the lecture summary of the Doctrine of Essence in the Encyclopedia Logic. The record shows Hegel vividly rendering for his students this ontological moment by means of a remarkable theophanic analogy of being27: Just as God, the essence, is goodness, by virtue of lending existence to the moments of his inward showing [Scheinens] in order to create a world, so he proves himself at the same time to be the might that rules it, as well as the justice that demonstrates the content of this existing world to be mere appearance [Erscheinung], whenever it wants to exist on its own account.28 [Gott als das Wesen, so wie er die Güte ist, dadurch, daß er den Momenten seines Scheinens in sich Existenz verleiht, eine Welt zu erschaffen, erweist sich zugleich als die Macht über dieselbe und als die Gerechtigkeit, den Inhalt dieser existierenden Welt, insofern dieselbe für sich existieren will, als bloße Erscheinung zu manifestieren.29]

Mere appearance can of course evince a rich world of implication (as in the case, say, of a term that is an “implicit definition” in David Hilbert’s sense or one that is instinct with what Cassirer denominated symbolische Prägnanz). But insofar as such implication remains no more than tacit in the explicitation of the reflective thinking, it has no determinate bearing on the act of discursive reasoning—i.e., lacks, to recur to Hegel’s idiom, the “might” and “justice” of realized potential. (Absent supplementary acts of inference to render the tacit implications of its premise-terms explicit, such thinking readily loses touch with vital facts of its informing sources). Occurring as the onto-epistemological medium of discursive experience, it is the significant show (Schein) that is how any fact subject to 27  On the Thomist concept of analogy, see John F. X,. Knasas, “Analogy and Logical demands” and “Analogy as Supra-Conceptual,” Being and Some Twentieth–Century Thomists (New York: Fordham University Press, 2003), §§ 5.8 and 5.9. For a more detailed, systematic analysis see Blanchette, “The Analogy of Being,” Philosophy of Being, chap. 4. 28  Encyclopedia Logic, p. 200 (translation modified). 29  Die Wissenschaft der Logik, §131z.

220 Inference and the metaphysic of reason position in the act of inference30 is actual (wirklich). What shows as a premise, in the realization that is coherent inference, does so—its intelligibility as a premise hinges—upon the condition that, in its being posited, it manifests the character of being reflectively ordered, visà-vis at least one other premise, relative to some formally specifiable conclusion sponsored by that order. d) The reflective show (Schein) of premises that, as premises in a coherent act of inference, are formally ordered to a conclusion. The idea of “show” to which the German term Schein refers is seminal but in some respects elusive. In inferential reflection, onto-epistemologically construed, Schein is a rational determination or category. It is what Hegel understood as a unity of das Seiende—in light of which Geist “finds something existent in itself ”—and of das Seinige—“according to [which] spirit posits that something only as spirit’s own.”31 Robert M. Wallace finds that Schein is an untranslatable German word that implies a not-necessarily-illusory appearance of something and that lends itself to metaphors of “shining” and “reflection”—with the “given,” the “data” that both the idealisms of Leibniz, Kant, and Fichte, and the skepticism of Gottlob Ernst Schulze that criticizes those idealisms’ claims to knowledge, agree would be the basis of justifiable knowledge claims (if there were any justifiable knowledge claims) about the world. The connection is through the fact that both the ‘given’ and the ‘shine’ are dependent upon something other than themselves, not for their determinateness, but for their being.32

To consider premises in view of the onto-epistemological positing of premises in the act of inference is to see that they do not function merely as hypothetical suppositions (as they do, for example, on the

30  I.e., in terms of an Ordnungssetzung. 31  See translator’s introduction to Hegel, Lectures on the Philosophy of Spirit 1827-28, trans. Robert R. Williams (Oxford: Oxford University Press, 2007), p. 29. Cf. Enzyklopädie der philosophischen Wissenschaften. Dritter Teil. (Frankfurt am Main: Suhrkamp, 1986), §443; and Hegel’s Philosophy of Mind, trans. William Wallace (Oxford: Oxford University Press, 1971), pp. 184-85. 32  Hegel’s Philosophy of Reality, Freedom, and God, pp. 160.

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meta-discursive, noetic level of Plato’s Divided Line33). So far as one proceeds on the premise that such premises are merely hypothetically rather than thetically functional,34 one operates with a concept of discursive reasoning that reduces its authority, and by implication the authority of scientific rationality, to little more than an adventitious feature of the vocation of spirit (Geist) as witness of being. However, as properly ordered to a conclusion (no matter how ill-conceived initially), premises in the act of inference are never onto-epistemologically arbitrary or merely hypothetical. And they show as the “not-necessarily-illusory appearance” to which Wallace alludes—an “appearance” that is in fact presence (parousia). This essential show, this Schein, of facts as premises is of the “mode” that, in his Introduction to Metaphysics, Heidegger classes as Vor-schein, manifestation. (Vor-schein constitutes “the ground” of the “possibility” of the two other modes of Schein that Heidegger distinguishes, namely “luster and glow” and “mere seeming, the semblance (Anschein) presented by something.”35) What shows as a premise so ordered—and the moment of order is here no mere regulative function of the premise as such, but rather conditionally constitutive of it—may be any intelligible datum. It may be a number among others in a mathematical operation. It may be a “sentence” in a derivation of predicate logic. It may be a textual passage among others in an act of hermeneutic inference. It may be a piece of statistical evidence among others in mediated sociological judgment. It may be a Schillerian schöne Schein in an artistic inference. Whatever show as such manifest some specific character, which I can conceptualize in general as, to borrow Lotze’s term, the “thought-images” (Denkbilden) of ideas. Denkbilden are not independent of the living act of 33  The dialectic that determines the show of premises in a route of reflective cognition discloses (or, for the Platonist, “rises” to) the principle of order, the formal cause, which is the Reason of the act of inference. But if the conceptual logic of inferential reflection thus features an essential dialectical element, that moment is sublated in the formal logic of discursive thinking. 34  As “thetically functional,” a premise tacitly bears the thesis of the inference of which it is a component, namely the particular principle of order that the route of reflective thought, from premise to premise, brings to light as a whole. 35  See Heidegger, Introduction to Metaphysics, trans. Gregory Fried and Richard Polt (New Haven: Yale University Press, 2000), §4.2.

222 Inference and the metaphysic of reason intelligence. They are the ideal currency—numbers, for example, or texts or statistical data—of facts sufficiently general to be conceptualized in practicable abstraction (enumeration, linguistic inscription, quantification) and formal ordering (multiplication, say, a derivation rule, stylistic protocols, or actuarial principles). They are how facts can be for—how facts, in Whitehead’s onto-epistemological sense, can be “felt,” or prehended, by—a discursive intelligence. Such intelligence is an organismically evolved component of the very world36 that may show itself as the event of the significant facts, however imperfectly an intelligence reflectively posits them. e) Formal cause as the Sufficient Reason of the act of inferential reflection. The sufficient reason of a route of inference is the fundamental principle (Grundsatz) of the reason of the act. What articulates the sufficient reason that grounds an act of inferring is the reflective, mutually determinating show of premises ordered in composition as a totality. To put this in abbreviated terms and from a genetic frame of reference (rather than synchronic one): what articulates the reason of inference is the act in which the “position” (i.e., positing) of premises sponsors the show of premises as conducing to a conclusion. The very movement from the show of premises as formally, and in so far invariantly, ordered to a conclusion describes an ideal totality. That conclusion does not annul or sublate the premises, unless one takes it as a mere term in a supervening inference. In the process of division, for example, thirty divided by two divided by five ((30 ÷ 2) ÷ 5), each number is mediated by its other-in-order. The earlier numbers in the sequence are not annulled in the act of inferring, of mathematically formulating, the arithmetical functions that, synchronically, amount, as a totality, to the conclusion (the number 3); or that, diachronically, as thought-determinations, conduce to that conclusion. The number three is, in this inferential context of signification, a descriptive moment. It is not simply the isolated result—a contextless number that by itself constitutes no intelligible truth at all about what is, in being thought, in the inference (and consequently no truth about the significant fact that prompted and takes form in the “positional,” thetic act). I submit that it is the formal character, rather than any teleological element of the totality, that constitutes the sufficient, grounding reason (Grundsatz)—in effect, the Reason—of the act of inference. 36  For the Thomist, of the very act of being.

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This orientation to formal cause in acts of inferential cognition has seminal classical precedents to which I can do little more than allude here. Consider, for example, the following Aristotelian insight from the Posterior Analytics as explicated by Patrick H. Byrne: …knowledge of the what-it-is will be identical with knowledge of the cause (i.e., formal cause)….In this case, says Aristotle, the what– it-is is “immediate and a principle.”…both the fact and the what-it-is must either be supposed (hupothesthai) or “made apparent in some way” other than by means of a demonstration, if one is to have scientific knowledge.37

(Cassirer, for one, undertakes a modern critical analysis of cardinal Aristotelian precedents in his discussion of Aristotle’s “concept of form-cause,” wherein “the principle of form and the principle of reason coincide” for scientific concepts and philosophical knowledge.38) In a coherent act of inference, to entertain the formal cause, or the principle “received,” as it were, by what show as premises is literally to become a living exponent of the intelligible order—whether it be, for example, mathematical or semiotic, aesthetic or devotional: order that the premises reflectively realize as the totality or ground of a particular inferential cognition. Crucially, Aristotle distinguishes a contrasting holistic dimension of scientific knowledge that correlates with the holism of the approach to inference that I have been endeavoring to articulate. What he identifies is an onto-epistemological dimension wherein “facts have causes different from themselves,” facts that “appear as middle terms in demonstrations” (which paradigmatically include acts of inference). As Byrne goes on to explain about “facts” in this context, Knowledge of their [facts’] what-it-is is not expressed in the conclusion; yet the conclusion is what is demonstrated. Hence, their whatit-is is not demonstrated. Rather their what-it-is is “made clear…

37  Byrne, Analysis of Science in Aristotle (Albany: State University of New York Press, 1997), p. 159, emphasis added. 38  See Cassirer’s Logic of the Cultural Sciences: Five Studies, trans. S. G. Lofts (New Haven: Yale University Press, 2000), Study 4 (“The Problem of Form, the Problem of Cause”). Cf., §4.6, below, for an analysis of Cassirer’s theory of scientific inference.

224 Inference and the metaphysic of reason through a demonstration” (93b28).39 This means that it takes the entire demonstration, premises, conclusion, and their interconnections, to reveal what-a-demonstrable-is.

The Aristotelian thinking that Byrne distills here describes the holistic character of inferential reflection as understood in the present essay. The conclusion of a route of inferential thinking, a function of absolute positing, manifests its rational intelligibility coordinately through (i.e., in ideal composition with) the reflective determination of what show as the premises onto-epistemologically “posited” relative to it. This is deeply consistent, if only at the stage of pure thinking, with Hegel’s meaning when he finds that setzende Reflexion “ends up preceding,”40 as logically prior to, the Gesetztsein that it predicates. The conclusion to a cogent route of inferential thinking grows distinct concomitantly with the reflective explicitation of the premises as premises. In this process of resolution, the premises are, as such, informed by the order of a significant fact that they ultimately (systematically, not merely linearly) compose as a conceptual totality, and hence actualize reflectively—namely, as being that is articulable and articulate in the ontogenetic, ideal idiom of reflective intelligence. A little reflection will bear out the claim here that this ontogenetic metaphysic of inference is no speculative idiosyncrasy. Indeed, it, or something consistent with it, applies across the broad spectrum of discursive modes of thought. It is tacitly in play, to adduce a signal example from mathematical theory, in Arend Heyting’s classic “intuitionist” statement on the nature of the mathematical object vis-à-vis the implicitly ontogenetic character of acts of “human thought”: Even if they should be independent of individual acts of thought, mathematical objects are by their very nature dependent on human thought. Their existence is guaranteed only insofar as they can be determined by thought. They have properties only insofar as these 39  For an analysis of an acute Fichtean incarnation of this thought-determination relative to onto-epistemological positing, see Wilhelm S. Wurzer, “Fichte’s Parergonal Visibility,” in Fichte: Historical Contexts/Contemporary Controversies, ed. Daniel Breazeale and Tom Rockmore (Atlantic Highlands, N.J.: Humanities Press, 1994). 40  Houlgate, “Why Hegel’s Concept Is Not the Essence of Things,” conference paper (read at Cardozo School of Law, Yeshiva University, New York, N.Y., March 2004), p. 3.

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can be determined by thought. But this possibility of knowledge is revealed to us only by the act of knowing itself.41

f) Validation in the inferential process. Undertaking to determine the validity and soundness of an inferred notion may be a matter of immediate judgment, or of activities that involve further acts of inference ordered, dialectically, to more general universal conceptions or formative principles. (The Thomist has an onto-epistemological term—“primary” or “prime” analogate—for this most general of notions against which one may determine the validity and soundness of a judgment.42) In any case, one should not confuse the act of infer41  “The Intuitionist Foundations of Mathematics,” quoted in Roy Cook, “Intuitionism Reconsidered,” Oxford Handbook of Philosophy of Mathematics and Logic, ed. Stewart Shapiro (New York: Oxford University Press, 2007), p. 388. 42  While Thomist metaphysics is often incomparably penetrating and I have invoked it at various junctures throughout this study, the approach to the act of inference under discussion does not ultimately hinge on the Thomist philosophy of analogy despite several references to it that I find illumining strictly in an onto-epistemological context, as opposed to its classic onto-theological context in which the notion is ineliminably linked with Christian religious Mystery. This judgment is anything but idiosyncratic or parochial. Even discounting the range of secularly grounded conceptual issues raised against the idea as one finds tallied, for instance, in the Encyclopedia of Philosophy article on analogy, one finds opposition to the Thomist notion in Cusanus, for example. Consistent with Maimonides, Cusanus opted to substitute, for “analogy” of being, aenigmata—a view with which a thinker as recent as Emmanuel Levinas would have concurred. The standard gloss on “aenigma” that would have been familiar to Cusanus, one derived from the first book of Isidore of Seville’s Etymologiae, has it as an allegorical trope, one that differs, however, from the determinate character of standard allegorical signification—and by extension from that of analogical signification, whether proportional or attributive—in that “aenigma vero sensus tantum obscurus est, et per quasdam imagines adumbratus.” Spinoza also rejects the resort to attribution by way of analogy (as well as the negative theology of Maimonides on God’s attributes). He holds that characteristics attributed to God by way of analogy, whether equivocally or eminently, ineludibly involve a tacit anthropomorphism; see the Ethics, Proposition 17, Corollary II; and Letter 56, to Hugo Boxel. That the philosophy of inference, as the philosophy of (mediated) judgment, bears on Thomist metaphysics in formative ways is something that, to cite a recent example, John F. X. Knasas underscores in his study on Being and Some Twentieth-Century Thomists. Knasas argues that without

226 Inference and the metaphysic of reason ence per se with the endeavor to assert or assess the validity of a route of inferential reflection. The fact of validity and the indefinitely many general concepts and contexts of signification from the viewpoint of which one may determine validity in any particular case are secondorder matters at this level of analysis. Discussing induction in empirical scientific thinking, Cassirer makes the same point, albeit from the perspective of a neo-Kantian critical idealism with which I take issue at a number of points.43 “Constants of the second level” is what Cassirer denominates the formal conclusions of scientific inductions. What he has in mind specifically are “empirical laws of nature” that we grasp as the “apparent completion” of “the general [inferential] procedure” that involves “the gaining of particular ‘facts’ and the connecting of these facts into laws.”44 Consistent here with contemporary analytic thinking, Cassirer finds that determining the validity of an inferred law entails “the further process of knowledge” wherein “these ‘constants of the second level’ are resolved into variables.”45 4.3 The act of inference. An unmediated judgment is not an act of reflective thinking. It may be the fruit of long reflection, or won through the development of practical skills. It is an act of onto-epistemological position that develops significant fact into idea, renders it spiritually luminous. It thus invests fact (however suitably or inaptly) with explicit, consciously manifest sense and thereby realizes it as a compo“a philosophical elaboration of judgment as a grasp of a thing’s existence as a distinct actus,” the “development of Aquinas’ metaphysics would become unintelligible” (p. xxiv). If one correlates “significant” with “real” and “fact” with “thing” in the following statement of Knasas’ “elaboration of judgment,” the parallel with the present orientation becomes clear: “Since the real thing also genuinely exists cognitionally, the real thing of itself cannot be real. Rather, it is real by a distinct actus” (p. xxv). In the conceptual idiom of the present account, the distinct actus by which a fact is significant for reflective, discursive intelligence is the onto-epistemological Position, the concept of which Kant identified with the concept of Sein überhaupt. (Facts are, of course, implicitly significant for pre-reflective mentality as well.) 43  See §4.6, below. 44  Substance and Function, trans. William Curtis Swabey and Marie Collins Swabey (New York: Dover, 1953), p. 266. 45  Ibid., emphasis added.

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nent of rational cognizance. The otherwise cognitionally tacit remote facts that get invested with explicit sense in such acts of immediate judgment show as objectively ideal terms of discursive intelligence, when once they are incorporated in episodes of reflective cognition, i.e., in acts of mediated (properly inferential) judgment.46 The facts in questions, however, are not in themselves components of reflective thought—in themselves they lack the uniquely evolved ontological character, the “perfection,” engendered by the activity of reflective thought in relation to them. The act of reflection is the agent of their birth as forma intellecta,47 actualizing their potential for spiritual (geistig) articulation—as premises or ideal facts, facts for intelligence. Ernst Cassirer held it possible to “designate and define the scope of the human spirit” as a theater of culturally formative, conceptualizing energies. Such was the philosophical project that he pursued by explicating in alternative symbolic domains the “tension” that symbolic terms of thought feature when they show as premises in mediated judgments (inferences). This tension, he maintained, “is none other than that between potency and act, between the mere ‘potentiality’ of a concept and its full development and effect.” Cassirer rightly observed in this connection that the “progress from potency to act is the most difficult achievement of knowledge.”48 (It was by tracing the psychocultural progress of this difficult achievement in language, myth, and science that he worked out his systematic conceptual critique of objective spirit [Geist]. From Cassirer’s viewpoint the reason of the act of inference “refers no longer solely to the function of logical judgment but extends with equal justification and right to every trend and every principle by which the human spirit gives [symbolic] form to reality.”49) That which shows in a simply immediate judgment—such as “too salty,” or anger, or the shape of a leg, or the (for the speculative math46  On “remote” fact, see Appendix V, below. 47  Something that Aquinas saw: forma intellecta est universalis sub qua multa possunt comprehendi (De Malo, q. 6, a.1). Cf., Rousselot: Les intelligibles ne se trouve pas en acte hors de l’âme humaine…” (L’Intellectualisme de saint Thomas, p. 93). 48  The Philosophy of Symbolic Forms, Volume 3: The Phenomenology of Knowledge, trans. Ralph Manheim (New Haven: Yale University Press, 1957), p. 300. 49  See The Philosophy of Symbolic Forms, Volume 1: Language, trans. Ralph Manheim (New Haven: Yale University Press, 1955), pp. 79-80.

228 Inference and the metaphysic of reason ematical theorist) Pythagorean Theorem—functions no otherwise than as an ideal term of thought in any discursive effort to advance reflective intelligence or to pass on a practical skill—of baking, for example, or child management or artistic technique or geometry. The felt potency or tacit significance, the pro-determinate dunamis that in different modes attaches to unreflective terms of thought, purely in themselves, may insensibly limit the scope or restrict the development of inferential thinking. The shape of a leg, for instance, might elicit an erotic response that short-circuits the act of artistic reflection and thereby inhibits the acquisition or exercise of the independently valuable knowledge of technique. Hence the “given,” frequently hypnotic in its power, perennially threatens to co-opt reflective intellection, with all the challenges to scientific thinking that that entails. A completed logical or mathematical proof, the geometrical theory of gravity, an information system—these and innumerable other abstract formalizations are elegant, and in their way exhibit a formal beauty. This apart, moreover, from whatever acts of reflection render the remote facts, to which such formalizations attest, ideal terms of thought, and thereby actualize those facts in the currency of immediate judgment. The classic ascetic beauty exhibited by the ante-reflective show (Schein) of abstract form—forma formata—is cherished by the master in every domain of scientific (wissenschaftlich) thinking. This is the order of “show” that Hegel understood as “an immediacy which is not a something or a thing” but rather a presencing of “those manifold determinatenesses” of some fact which are unmediated, seiende, and mutually related as others. Schein, therefore, is itself immediately determinate. It can have this or that content; but whatever it has, it does not posit this itself, but has it unmediated. [Der Schein ist also selbst ein unmittelbar Bestimmtes. Erkann diesen oder jenen Inhalt haben; aber welchen er hat, ist nicht durch ihn selbst gesetzt, sondern er hat ihn unmittelbar.]50

Perhaps the most telling qualification that needs to be stressed relative to the Schein operative as a formative moment in the onto-epistemology of inferential reflection is that it does not properly “contain” anything: as parousia, it is its “content.” 50  G. W. F. Hegel, Wissenschaft der Logik II (Frankfurt am Main: Suhrkamp, 1986), p. 20.

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Thinkers often enough devote years of reflection—all too likely to prove little more than mere history to the scientific practitioner of a later day—struggling to clarify what, as immediate judgments, will become mere premise terms in subsequent (“higher”) acts of inference, acts of mediated judgment that they inspire. How pure thought-determinations show as terms of inference thus conceived exemplifies the ideal combination of abstraction and beauty that Hegel denominated as the “stage of beauty” that he understood to distinguished “Greek consciousness.” Heidegger explicates this familiar element of Hegelian historicism in a way that makes the connection manifest: The abstract is the first manifestation that remains purely with itself, the most universal of all beings, being as unmediated, simple shining [show]. But such shining [show] constitutes the fundamental trait of the beautiful. That which shines [shows] purely in itself indeed arose from spirit [Geist] as the ideal, i.e., from the subject, but spirit “does not yet have itself as medium (in order therein) to represent itself [reflectively] and upon which to ground the world.”51

One need not subscribe to Hegel’s philosophy of history to appreciate how spiritual (geistig) advance and practical self-transcendence transpire through the reflective show of discursive thinking—specifically through mediated judgments. These constitute inferential judgment, in which remote facts show as a “totality” of premises, ideal terms whose very determinateness as intelligibles—the ground of their distinction—includes their being reflectively ordered to some conclusion.52 The conclusion of an inference, which typically grows explicitly intelligible only as one thinks one’s way through to it, proves the principle of order in a route of reflection. As such, the conclusion is the intrinsic, formal cause (as distinct from the telos) of the judgment. This is the respect in which it evinces the rule of sufficient reason in the inferential act (i.e., its Grund)—therewith instantiating the reason of the act of inference generally. As formal cause in this sense of being 51  “Hegel and the Greeks,” in Pathmarks, ed. William McNeil (Cambridge, Eng.: Cambridge University Press, 1999), p. 328. 52  Kant would likely read this as a dubious effort to describe the genetic function of discursive thinking, contrasting it with what he would characterize as “the unity of the action of bringing different representations under a common one.” Cf., Critique of Pure Reason, trans. Paul Guyer and Allen W. Wood (Cambridge, Engl.: Cambridge University Press, 1998), A68/ B93.

230 Inference and the metaphysic of reason the sufficient reason, the conclusion is the principle of the premises as reflectively determinate in virtue of being intelligibly ordered (and thereby realized) in a totality that is their truth. From the standpoint of truth, the premises “end up preceding” their totality (i.e., as premises of a particular conclusion)—something Hegel had in view in the logic of essence, specifically in the relation of setzende Reflexion to its correlative Gesetztsein.53 Far from constituting a vicious circularity, this aspect of the conceptual logic of the act of inferential reflection illustrates the Aristotelian insight that, in the words of Patrick H. Byrne, “knowledge of the what-it-is will be identical with knowledge of the cause (i.e., formal cause)...In this case, says Aristotle, the what-it-is is [presentationally] ‘immediate and a principle.’” 54 All too frequently, one’s premises reflect false or faulty immediate judgments or, as subsequent analysis may reveal, judgments improperly ordered to a totality the truth of which constitutes their reason. But whether or not the premises of a given act of inference appropriately conduce to the formal cause that describes its initial impetus, as terms of living reflection they are nonetheless moments of onto-epistemological positing (setzende Reflexion). And this, whether or not they rationally occasion, as premises, my grasp of their intrinsic principle of determination. (One often enough comes to the “right” conclusion for the “wrong reasons.”) They are moments of positing that are indirectly relative to each other. More precisely, as reflectively articulated the moments of position are indirectly relative to each other under the form of some order—say, mathematical (e.g., rules of division) or aesthetic (as in rules of perspective) or logical (as in transformation rules) or legal (as in principles of probable cause)—to which they are directly relative. The premises in an act of inference are determinate so far as ordered to, hence formatively predicative of, a Totalität, a conclusion “for the sake of which”55 or, from a correlative viewpoint, “under 53  This is an element of the doctrine of essence that Houlgate elucidates with compelling acuity in “Why Hegel’s Concept Is Not the Essence of Things,” p. 3. 54  Analysis of Science in Aristotle (Albany: State University of New York Press, 1997), p. 159; see §4.2e, above. 55  Construed in the sense that in the conclusion one has, as Hegel puts it, “the immediate self-translation,” through “the self-movement of form” (der sich zur Wirklichkeit aufhebt), of “the inner into the outer”; see Encyclopedia Logic, trans. T. F. Geraets, W. A. Suchting, and H. S. Harris (Indianapo-

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the form of which”56 such identities as they assume are as terms of reflective discourse. If that were not the case, inference would have no factual basis; consequently, it would have no ground for its recognized role as the sufficient reason for the practical and intellectual authority that scientific peoples accord formal thought as the privileged means of mastering what facts signify. Facts of matter, truth, and spirit (Geist) at play in unmediated judgments are no more than merely potentially terms of scientific knowing. Those otherwise-tacit facts are commonly remote and show as explicit being, as practicable theoretical terms only in the energeia, which is to say the form, of rational intelligence. “Remote” refers here to what is beyond the horizon of simple sensation and other modalities of immediacy but that signifies, and is in this sense significant, for cognitive intelligence. By extension, facts that thus signify for Geist may be remote with respect to what is, or what may come to be, in virtue of living, reflective acts of intelligence. It is in this sense that the Pythagorean theorem, for example, is remote from a triangle drawn in the sand, just as the principles of the science of geometry are onto-epistemologically remote from the Pythagorean theorem itself when one takes the theorem as a premise-term in explaining that science. As a mediated judgment, the act of inference is reflective thinking and not an unmediated moment of cognitional life. The so-called “immediate inference,”57 a judgment predicated upon a single premise, is not a conscious or even an occult act of discursive reasoning—something recently substantiated empirically with the discovery of “mirror neurons.”58 Hence it is not rightly an inference at all. Rather, what some refer to as “immediate inference” are immediate, ante-deliberative judgments (cf., Kant’s “perceptual judgments”)—unreflective (which is not to say unintelligent or uninspired) cognitional deportments to fact. Whatever the complexities or subtleties of the fact in question, and whatever other acts of judgment might conduce to a lis: Hackett, 1991), §147; [Die Wissenschaft der Logik, Enzyklopädie der philosophischen Wissenschaften, Erster Teil (Frankfurt am Main, Suhrkamp, 1986), p. 288]. 56  As understood from the perspective wherein the conclusion is “the immediate self-translation…of the outer into the inner” (ibid.). 57  See §3.4.2, above. 58  See n. 6, above.

232 Inference and the metaphysic of reason particular immediate judgment, cognitive realization of this sort occurs without one’s having expressly to think one’s way through to it, reflectively, as a conclusion of a train of reasoning. Working through to the conclusion, i.e., the consummating truth, of a cogent inference commonly prompts me to deploy, in subsequent routes of inference, the resulting conception as a complex form of direct judgment, direct because within the new context the judgment is no longer a reflective act in its own right.59 The cognitional bearing of one’s grasp of fact, one’s deportment to fact—irrespective of whether that grasp is valid, verifiable, or true— takes many forms beyond simply asserting (“registering”) the assertible, for instance in affirming or in denying the predicate of a subject.60 I commonly grasp facts tacitly, without taking cognizance of the fact that I do so, in which case I am unreflectively aware of things, although aware of them in ways that may orient and inform judgment and motivate action. In other words, I habitually lose sight of the circumstance that, invariably, I implicitly assume a determinating cognitional bearing toward facts distilled as moments of conscious being. (This is the very antithesis of anthropomorphic projection “onto” fact as such, nor is it a reduction of fact to Geist.) Yet such modes of awareness—moods, fundamental attunements (cf., Heidegger’s Grundstimmungen)—typi59  An analytic epistemologist might describe this as the reaching of a new plateau of intellectual intuition. 60  Epistemological regimes that privilege subject/predicate syntax in the conceptualization of rational, onto-epistemological cognition impose a reductive syntactic frame of reference upon an act involving elements that outstrip formal linguistic categories. Cf. Lotze: “No real S can be subject and nothing more to a real P, which is its predicate and nothing more; in actual fact P can only attach to S either as a state which it passes through, or as an influence which it exerts, or finally as a permanent quality which belongs to it in the sense…in which we contrast the metaphysical notion of a Quality with the merely logical notion of a Mark [Merkmal]” (Logic, vol. II, p. 282). For a penetrating recent analysis of “the problem posed by predication on the level of first-order predicate language” that distinguishes “the semanticontological framework worked out and accepted” by the general run of analytic philosophers, see Lorenz Puntel, Structure and Being: A Theoretical Framework for a Systematic Philosophy, trans. Alan White (University Park, Pa.: Pennsylvania State University Press, 2008), pp. 193-95.

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cally play formative roles in the character, orientation, and development of reflective life. The act of judgment that some misleadingly refer to as an “immediate” inference, while ingredient in a cognitive process,61 is thus not, per se, formally an act of reasoning. Neither is so-called “unconscious inference.” As C. S. Peirce recognized, “conscious control of the [inferential] operation ought to determine the title of reasoning.”62 More recently, Gilbert Harman offers a comment that bears materially on the notion of immediate judgment as a discursively non-logical “production” or “inference ticket.”63 Alluding to a text of Wilfrid Sellars, Harman makes the following point: “Accepting an inference ticket that allows one to infer directly from the premise that something is copper to the conclusion that it conducts electricity is a way of treating the relation between copper and conducting electricity as a necessary or lawlike relation.”64 If one imputes the ontological value to “relation” that Lotze attributes to it, such that “to be is to stand in relations,”65 then one can see Harman’s contention as capturing, in onto-epistemological terms, the distinction between inferential reflection and immediate judgments. (The latter, again, are judgments that inform inferences and to which inferences reduce when, like dead metaphors, they are sublated as unreflective moments or terms of discourse in supervening acts of reflection.) I do not rely on “unconscious inference”—i.e., complex immediate judgment66 —to establish formally or rationally argue that I know something, nor to rationally verify truth, make sense of genuinely un61  What Blanchette describes as the “first act of intelligence”; see Philosophy of Being: A Reconstructive Essay in Metaphysics (Washington, D.C.: Catholic University of America Press, 2003), §2.1. 62  “Of Reasoning in General,” The Essential Peirce: Selected Philosophical Writings, Vol. 2, edited by the Peirce Edition Project (Bloomington: Indiana University Press, 1998), p. 22. 63  Though, as we saw, he fails satisfactorily to address the onto-epistemological character of inference; see, above, §2.3. 64  Harman, “The Logic of Ordinary Language,” in Common Sense, Reasoning, and Relativity, ed. Renee Elio (Oxford: Oxford University Press, 2002), p. 95. 65  See, above, §3.4.2. 66  A judgment that one might exercise in grasping, for example, the unity of sentence as the unity of a complex singular term.

234 Inference and the metaphysic of reason familiar data, develop research programs, nor to teach students how to think as engineers, accountants, biologists, logicians. As the consciously reflective, discursive act of intelligence, the mediated judgment that is inferential thinking is the gold standard of scientific (wissenschaftlich) reasoning. This is not to say that an act of inference is identical with or informed by the procedure of verifying it or teaching others to exercise it, or with any other context of articulating its character. Indeed, as Gilbert Ryle rightly stressed, “didactic expositions of arguments with their conclusions and their premises, of abstract ideas, of equations, etc., belong to the stage after the arrival and not to any of the stages of traveling thither.”67 An act of inference is a living function of spiritual life. It is unique in that it invests68 the remotest facts—the relation, say, of number to harmony, or the DNA sequence—with explicit determinations expressing the formative power (for Locke, a specific Quality) that such facts display, in consequence of their significance as meaning, namely as moments of the reason that constitutes our rational grasp of an intelligible world that is a universe. Cassirer would take this to be characterizing inference as “an authentic function of the human spirit,” which “does not merely copy but rather embodies an original, formative power.” This in an active “embodiment” that betokens, as Cassirer saw, “an independent energy of the human spirit through which the simple presence of the phenomenon assumes a definite ‘meaning,’ a particular ideational content.”69 The act of inference is thus not reducible to an analytic epistemology. It involves, rather, the onto-epistemological positing of things that, relative to each other in some form-ordered sense, stand as premises in a process of reflective reason. Regardless of whether they are true or verifiable or even more than minimally determinate, the premise-terms of inferences occur in the process of reflection as occasions of relative positing. They are (are real), and by that token show relative, vis-à-vis each to its other, to the conclusion to which they conduce in some rational (ordered) way—whether the route be, in those most general and hence least precise terms, deductive or inductive. The conceptual logic of inference thus properly unfolds on the plane of discursive thinking. At 67  Ryle, The Concept of Mind (New York: Barnes & Noble, 1949), p. 297. 68  Cf. Einsetzung (investiture), see p. 49, above. 69  The Philosophy of Symbolic Forms, Volume 1, p. 78.

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a murder scene, for example, the character of an empty wallet may show, reflectively vis-à-vis specific differences of other evidence, as a premise-term, determinate as such among others in virtue of being forensically ordered to a general conclusion about motive. The conclusion is the rationally explicit realization of an initial hunch. The hunch is the felt significance of some otherwise rationally unarticulated fact that informs the search for evidence. So far as the hunch proves to be formally realizable as a coherent forensic inference, it grounds the determination of each item (in its show, Schein, as a premise) as properly a moment in a route of inference that composes a rationally articulated (and perhaps definitive) account of the truth to which the evidence, as a totality, bears witness. It is hardly more than a dogmatic metaphysical presumption to predicate of this process an underlying general nisus toward some comprehensive, absolute totality that informs or motivates the spiritual dynamism or trope that is inferential reflection, and of which the latter constitutes an index and a stage or phase. Unlike the dialectic of essence, which in Hegel’s Logic is the negation of immediate being, the conceptual logic of the act of inference involves a principle of order that gives voice, as it were, to immediacy as such. On each occasion of inference, the order in play is the determinating70 form that constitutes the absolute position of the conclusion. (This position, this Setzung, is absolute with respect to the relative setzen of whatever premises reflectively conduce to the conclusion 70  This archaism captures the actuality of both the dynamic and directive character of those remote facts that, in their ideal being, are for reflective thought, as (“first”) intentional moments of the living act of intelligence. To revert briefly to pure ontology, the medieval formulation causa importat influxum quemdam in esse causati identifies, in the Thomist idiom, how remote facts are (participatively) for reflective thought. From this standpoint, the participatory moment of remote fact as communicated (as a power) in the show of premises in the act of inference manifests “the Pure Act of Being” for which “each and every manifestation of causal activity consists… in communicating something of its own being to the effect.” This holds regardless of how properly or how confusedly, in any particular instance, one entertains such premises as formally ordered to a conclusion. The mode of such participation is what it is that shows as premises in a given act of inference; as such, it is the essential character that defines the being, the what, that is at stake in any given act of discursive, inferential reflection. Cf., Etienne Gilson, The Elements of Christian Philosophy (New York: New American Library, 1963), p. 207.

236 Inference and the metaphysic of reason of a route of inference, and in that way formally realize it.) The order is thus the context whereby the show of the reflective identity-in-difference marks each premise as a premise. The conditionally constitutive status of order (form) for a premise as such—i.e., for a premise as “a pure category of meaning”—is axiomatic in the onto-epistemology of the reason of inference. Cassirer affirms this onto-epistemological fact, albeit from a neo-Kantian perspective, when he explicates the Reason that integrates “the world of intuitive objects and the relations prevailing between them.” As Cassirer states, We cannot explain the particularity and specific nature of the pure category of meaning, through which the relation of the perception of its object is constituted, on the basis of any sort of ontic determinations—whether of [efficient] causality, of identity or similarity between things, or on the basis of relations of the whole to the part. Here we must go back not to any attributes of given things, not to the image of already existing reality, but to the pure conditions under which a reality can be posited.71

The ontic determinations, including those that grow explicit in reflection—of what show as premises in inferential judgment (numbers, say, pieces of evidence at a crime scene or in scientific research on global warming)—do not of themselves explain their character as premises. Neither does their relation to their totality as a conclusion of a route of inference. The significant fact72 that prompts (or “empowers”) my being alert to, or the search for, what show as premises73—i.e., fact that thereby elicits scientific thinking—does so in the value-currency of forma intellecta that I onto-epistemologically posit as occasions of living, ontogenetic spirit (Geist). This value-currency is intelligible 71  The Philosophy of Symbolic Forms; Volume 3, p. 326. 72  This notion of “significant fact” has a correlate in Bosanquet’s objective idealism. Bosanquet identifies the “content of a judgment” as “always a significant idea,” by which he means “a recognized identity in differences.” He holds that the epistemological act of recognition charters the ontological character of a significant idea as an objective reference. This is consistent with the view of the present work, namely that what show as reflectively determined premises in the act of inference, being onto-epistemologically posited as ordered to a conclusion, sponsor a significant fact by rendering it ideal, i.e., “a significant idea.” See Bosanquet, Logic, vol. I, p. 90. 73  Or prompts one to be predisposed to take the Schein of particular experiences, items, or matters as premises.

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meaning, meaning self-reflectively grasped in terms of order that is the act or power of form—what Cassirer would term the “pure condition” (or Locke, the Quality) of form. What show as premises in an act of inference are hence unintelligible, as premises, so far as one prescinds them from their conditionally constitutive moment of order. Discursively rational, the factor of order in the relative positing of premises (namely, their being as ordered to an intelligible conclusion) renders the show of terms in an act of inference unintelligible, and untrue, if one deracinates them from the dynamic of discursive intelligence—if, in other words, one takes the terms as mere abstractions, simple immediacies. The inferential dynamic is the forma formans of the conclusion as onto-epistemologically intelligible, and hence of inference as a living act of intelligence—as opposed to a normative, cut-and-dried syntactic or mathematical or aesthetic or psychological assemblage of terms that one can put together (by rote memory, for example) without genuine understanding. The conclusion in an act of inference is a moment of absolute position (Setzung). But to think of it as a settled fact or idea is emphatically not to think of it as a defining moment of the reflective process that is the inferential act of knowing. What one does with a conclusion after the fact, so to speak, is to bracket it from the living context of its rational determination through the totality of relative positing that composes the premises reflectively ordered to it. Bosanquet employed an evocative simile when he described this process: No doubt we are apt to pluck off our conclusion like a fruit from a plant and carry it away for consumption. Practical life requires this procedure. But we must remember that from the moment of severance death has begun, and that he intellectual product can bear isolation far less than the material. The idea of an actual transition from data to result, so far as it is founded on this habit, is in science simply a pernicious blunder. The case in which the result is a systematic insight that includes the premises in a transmuted form does not of course fall under this censure. But this case is not as a rule contemplated by the traditional forms of inference.74

This case, however, is precisely what the present chapter has been considering from an onto-epistemological standpoint. If dialectically abstracted from its domain of actualization in the cognitional process that runs from premises to conclusion—if lifted, that 74  Logic, vol. II, p. 5.

238 Inference and the metaphysic of reason is, from the relative positing that marks the reflective determination of the premises formally ordered to the conclusion—the conclusion may serve as an immediate judgment or simply collapse as a groundless (hence irrational) immediacy, an abstract formalism.75 On the other hand, the conclusion of a route of inference regarded, say, from a Kantian transcendental frame of reference is an “object” (Gegenstand) that sacrifices its absolute dimension to the relative positing reflective of a determinate transcendental concept. Hegel, who never put the absolute and relative aspects of onto-epistemological positing logically at odds with one another (just as he never insulated the nature of verständlich thinking from vernünftig reflection), makes exactly this point in the course of a criticism of Kant.76 The Kantian Denkbestimmungen, observes Hegel, are also called “concepts” [werden auch Begriffe genannt] and hence to get a conceptual grasp of an object means nothing more than to grasp it in the Form of something Conditioned and Mediated [und einen Gegenstand begreifen heißt insofern nichts als ihn in der Form eines Bedingten und Vermittelten fassen]; so that inasmuch as it is what is true, infinite, or unconditioned, it is transformed into something Conditioned and Mediated, and instead of what is true being grasped in thinking, it is perverted into untruth.77

The mediation at issue here is not the living, mediating moment—the middle term—as it informs the conclusion of a given act of inference. Rather it is an exogenous concept—logically speaking, a premise “borrowed from elsewhere” (as Bosanquet would put it)—that schematically fixes the conclusion relative to a transcendental epistemology. Hegel’s critical insight here, I would submit, communicates the lesson to be drawn from the onto-epistemological “gap” in Kant’s transcendental epistemology,78 something that even the third Critique’s account of the reflective power of judgment never satisfactorily resolved. 75  Something “subject to analysis,” as Blanchette observes, “and nothing more” (personal communication). 76  One that was a virtual commonplace in the first decades of the nineteenth century. 77  Encyclopedia Logic, §62; [Die Wissenschaft der Logik, p. 148]. 78  See Eckart Förster, Kant’s Final Synthesis: An Essay on the “Opus postumum” (Cambridge, Mass.: Harvard University Press, 2000), chap. 3 (“The ‘gap’ in Kant’s Critical Philosophy”).

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The form of an inference’s conclusion, which can be virtually any object of reflective thought, is no Platonic idea. Rather, it is formal essentially, i.e., essential (wesentlich) form. Whether realized haltingly or swiftly, indeterminately or precisely, it is operative—perhaps as an inchoate impetus, perhaps as a clearly discerned end—throughout the reflective act as the effective (wirklich) moment, the energeia, that remote fact assumes as posited in the ideational currency of discursive intelligence. (Only as a term of discourse, as a forma formata, is the conclusion of an inference, operative as a direct judgment, properly viewed as a final cause.) The remote fact, in the discursive act of inference, comes to be as intelligible mediately. As inferred, the fact—whether logical or material or spiritual (geistig)—is something that is as it comes to be conceptualized. Inferential conceptualization proceeds through the ordered reflective dynamic of what show as premises, in a form-ordered play of identity-in-difference (the “fact called identity” being “perfectly inseparable from difference”79). Lotze touches upon this conceptual logic in comments on what he calls “an imperfect or growing concept.” Discussing the logic of concept formation, Lotze observes that we do not feel that we have got a perfect or fully developed concept, until the vague suggestion of some sort of whole has grown into the pervading thought that there is a definite ground [Grund] for the coexistence of these particular attributes [or premises] in this particular combination [or order] and to the exclusion of certain others,

79  Josiah Royce made this Hegelian point in his last lecture on “Identity and Identification,” in Metaphysics, William Ernest Hocking original editor, co-edited by Richard Hocking and Frank Oppenheim (Albany: State University of New York Press, 1998), p. 149. Harold H. Joachim, like Bosanquet, understood this cognitional process as the self-development of the subject or conclusion rendered discursively explicit through the reflective thinking that rationally articulates its sense: “…the explicandum constitutes itself in, is in large measure determined by, the intellectual discursus which explains it”; see Logical Studies (Oxford: Oxford University Press, 1948), p. 60. This seems to me to impute an unwarranted automatism to remote fact while concomitantly neglecting the ontogenetic power of reflective spirit (Geist)—or, better, Geist as an ontogenetic power—that synthesizes, from its unique standpoint, what such fact communicates, to engender an original spiritual formation.

240 Inference and the metaphysic of reason and that this ground [Grund] is an adequate one [i.e., the sufficient reason of the inferential dynamic].80

On this theme and, as it happens, with Lotze explicitly in mind, Cassirer offers an observation on concept formation that is consistent with the orientation to the reason of inference as we have been considering it. The “primary function of concept formation,” states Cassirer, “is not, as most logicians have assumed under the pressure of centuries-old tradition, to raise our representations to ever greater universality; on the contrary, it is to make them increasingly determinate.”81 (Bosanquet, as we saw, held that it is precisely inferential reflection, with implication as the middle term between judgment and “the whole of reality,”82 that unites such “ever greater universality” of “our representations” in an act that renders them “increasingly determinate.”) The ontogenetic moment of discursive intelligence—its poietic moment—is also a fact, one that becomes intelligible through every objective and practical substantiation of reasonable inferences that inform action in the world. Every act of inference is thus insofar an act of formal thought that betokens the onto-epistemological itinerary of discursive reason. That said, it is a misstep to lose sight of the cognitional circumstance “on the ground,” as it were, namely that most acts of inference are if corrigible, fragmentary, unverifiable, mistaken. What shows in the positing of something as a premise may not be the fact one takes it to be. As often as not, the premises of an act of inference are demonstrably mistaken, or the process of thinking suffers interruption, or the perceived order of the premises—a factor of their very show—is not formally coherent, i.e., not properly ordered, and hence insufficiently determined to a verifiably intelligible conclusion. Onto-epistemologically, the conclusion of an act of inference is the absolute Gesetztsein that, when approached in a posteriori linear terms, ends up following the reflective process in which it is constituted. The conclusion, from this standpoint, is an idea of order to which the reflective play of those facts that show as premises “con-form” (and are so far terms of discursive reasoning). The act of inference thus charters 80  Logic in Three Books: of Thought, of Investigation, and of Knowledge [1880], 2nd ed., trans. Bernard Bosanquet et al. (Oxford: Oxford University Press, 1888), §21. 81  Philosophy of Symbolic Forms, Volume 1, p. 280, emphasis added. 82  See p. 194, above.

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the rationality of predicates whose identity, manifest through differences orchestrated by the discursive order of reflection, formally compose (as a reflective episode of forma formans) a “totality” that is the idea’s—the conclusion’s—reason or ground in the inference. In other words, the act of discursive reflection composes the factual ground of what rationality is (the esse of rationality) with respect to a particular form of thought. There is a seminal classical precedent for this line of exposition, but given the limited parameters of the present inquiry it must suffice here merely to refer to a highly germane remark by Louis Dupré that adumbrates the Greek origins of this thinking. Dupré in effect sketches the classical provenance of the intellectual orientation of my approach to the reason of inference. The way that he does so clarifies the centrality of form, essence, and order in an ancient constellation of philosophical visions. These views held “in balance,” as it were, and thereby justified, “the simultaneous presence of unity and multiplicity, of order and chaos, of harmony and strife.” As he explains, If there was one belief Greek thinkers shared, it must be the conviction that both the essence of the real and our knowledge of it consists ultimately of form. Basically this means that it belongs to the essence of the real to appear, rather than to hide, and to appear in an orderly way….That appearance, however, derives not from our subjective perception of the real; it is the form itself that shines forth.… In sum, for the Greeks, the principle of form contains the definitive justification of the real.83

With the requisite qualifications respecting the ontogenetic thetic activity of knowing that is “of the real,” this classical view intimates the main lines of the explication undertaken here of the efficacy of form in the reason of inference. 4.4 Three defining moments of the onto-epistemology of inference. The present section offers a conspectus of three principal components that distinguish the onto-epistemology of inference introduced in the preceding section. These include a) onto-epistemological positing—the thetic element—of the act of inference, b) the reflective itinerary of the conceptual logic that articulates inferential reasoning, and c) the formal ground that is the reason of the act of inference, literally its raison 83  Passage to Modernity (New Haven: Yale University Press, 1993), p. 18.

242 Inference and the metaphysic of reason d’être. Following the summary observations, there follow three subsections (4.5.1- 4.5.3) that concentrate, one each, on these interrelated moments. The aim is to probe in detail the defining characteristics of each moment and to identify its formative philosophical implications. a) Onto-epistemological positing is what Kant and many distinguished thinkers who came after him understood in a variety of fundamentally related ways. Virtually all who employed this speculative notion recognized that it refers, at least in what Kant identified as its “absolute” dimension, to an ontogenetic, existential act. It is consistent with this constellated range of usage that the term functions here. Consequently, an existential dimension of position (Setzung) obtains in references to it that appear in statements that delineate the conceptual logic of the act of inference. As when I assert that the ontoepistemological positing of facts in inferential reflection is the act of investing (cf., Einsetzung84) their show with the spiritual character of premises reflectively ordered, as ideal terms, to a conclusion. “Positing” in this sense fundamentally transcends its standard Anglophone acceptations. The Oxford English Dictionary accurately enough lists the following as the chief definitions of “posit” in logic and philosophy: “Assume as a fact; put forward as a basis of argument; affirm the existence of; postulate.” (Interestingly, the OED singles out sublate as the opposite of “posit.”) While these meanings partially characterize inferential Position, none of them, as we noted at the outset of this inquiry, comes near to what Kant had in mind when he declared the concept of Position to be identical with the concept of Sein überhaupt. Indeed, the received English-language definitions of “posit” obscure the whole range of the term’s other onto-epistemological connotations that we surveyed in the introductory chapter.85 b) The second core element of inferential cognition is the reflective itinerary of its conceptual logic. It is Hegel, in my view, who elucidates this onto-epistemological trope with the greatest penetration as he explicates the dynamic of the “logic of essence.” By contrast with Hegel’s focus on the logic of essence per se, however, the concern here is limited to a reflective act of intelligence. Hence, my observations on the logic of essence rarely stray beyond its inherence in a special and highly developed phase in the Bildung of spirit, namely as it informs 84  See Dieter Henrich’s explication of speculative Setzung, cited above, p. 49. 85  See §1. iii, above.

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“pure thinking” (reine Denken). Hegel properly recognized reine Denken as the culminating stage in the development of intelligence (die … letzte Hauptentwicklungsstufe der Intelligenz86). As reine Denken inferential reflection cannot be unconscious or immediate judgment. This is because a defining feature of it (something per se notum) is that it always involves, beyond our simply “being thinkers,” our being as “knowing ourselves as thinkers.” One sees in this the most radically objective order or “shape” (Gestalt) of rational cognitional life—an order not to be confused with the subjectivist inward spiraling of self-reflection that is in reality its dialectical opposite. This Gestalt amounts to the paradigmatically Cartesian moment of the act of inference as a preeminently reflective act of intelligence. One can be “lost in thought” and yet be supremely cognizant of oneself as thinking. On the other hand, to be lost, or to “lose oneself,” in a film, say, or a novel or a fantasy typically involves, along with the suspension of disbelief, a displacement, in some measure, of the capacity—the part of what one is—that constitutes the reality principle, the ontoepistemological ground in Reason, that renders reflective intelligence significant. The form-ordered, reflective play of terms, as ingredient in the show (Schein) of premises, is the Scheinungsweise of reason in the act of inference. It is a function of positing reflection (Hegel’s setzende Reflexion) and is the originary, eidetic element of the movement of inferential reflection. The reference to “positing reflection” marks a turn, away from the implicitly dichotomous Kantian construction of setzen, to a loosely Hegelian conception. Hegel saw that “positing” has, in the context of reflection, an onto-epistemological character immune to the complications that follow the essentialist distinction of Sein (in acts of absolute Position) from predication (as relative Position), a distinction implicit in Kant’s transcendental logic. If I do not subscribe to Kant’s traditional explicit account of inference, and indeed abandon the Kantian orientation altogether where it stops short of onto-epistemologically integrating the absolute and relative dimensions of Position, this by no means signals acceptance of Hegel’s positive syllogistic doctrine of inference, which he expounds 86  Cf., Die Philosophie des Geistes, Enzyklopädie der philosophischen Wissenschaften im Grundrisse 1830. Dritter Teil (Frankfurt am Main: Suhrkamp, 1986), §465z; [Hegel’s Philosophy of Mind, trans. William Wallace (Oxford: Oxford University Press, 1971)].

244 Inference and the metaphysic of reason as a complex moment of the Begriff. Another marked divergence from Hegel has to do with his reading of Sufficient Reason as final cause. Such a reading, even if one grants legitimacy to Hegel’s Conceptual metaphysic, incurs a difficulty with respect to the unity of essence visà-vis the Begriff. As Alfredo Ferrarin astutely observes, “In the Logic of Essence all categories are the unity of existence and its condition posited reflectively,” but since the totality constituting the unity of essence is not a function of one moment sublating its antithesis, this essential unity (Grund, after all, being its truth) is “therefore defective” from the standpoint of the Begriff. 87 By contrast, the unity of essence that composes the ground in the onto-epistemology of inferential reflection exhibits no such teleologically bound defect. c) The third element of my account is one inextricably integrated with Position and the reflective itinerary of conceptual logic; but of the three, it has perhaps the broadest range of speculative ramifications. This is the principle of sufficient reason. If this study’s bid to appropriate speculative Position is ultimately at odds with Kantian transcendental idealism, its understanding of Sufficient Reason as the ground (Grund, cause) of inferential reflection is inconsistent, as well, with Hegelian absolute idealism. Dilating in a lengthy Zusatz of the Encyclopedia Logic upon the rational nature of the Grund that sponsors the totality of essence as a play of Scheinen in dem Entgegengesetzten88 (one that does not involve sublation89), Hegel introduces three conceptions of the principle of sufficient reason. Only one of these does he identify with the classic

87  Ferrarin, Hegel and Aristotle (Cambridge, Engl.: Cambridge University Press, 2001), p. 138. 88  Each essence having “its own determination only in its relation to the other: it is only inwardly reflected insofar as it is reflected into the other” (Encyclopedia Logic, §119). [“…jedes hat seine eigene Bestimmung nur in seiner Beziehung auf das Andere, ist nur is sich reflektiert, als es in das Andere reflektiert ist…”(Die Wissenschaft der Logik, p. 243).] We earlier noted Novalis’s understanding of entgegengesetzt as expressing “the activity of the oppo-site, whereby the object becomes unmediated object and the opposite itself becomes mediated”; see §2.5, above. 89  Short of the emergence of Existence, which features the self-sublation of Grund.

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formulation of Leibniz.90 The first rendering is formal in the sense of being empty of cognitional content, and pertains to the doctrine of essence, relative to which Hegel treats the category of Grund. Any such ground is merely a potential reason, i.e., “only the capacity to ground something.” Hegel dismisses the sufficiency of such abstractly formal ground as “otiose [Müßig] and tautological”—this because, in this matter, just as “all grounds are sufficient, so…no ground is sufficient as such.”91 Hegel contends that the second and third connotations of Sufficient Reason involve a Grund with a content determinate in and for itself (a concretely conceptual content), and hence as ground/reason proper to the plane not of essence but of the Begriff. He is doubtless on target when he condemns the view, to which “many people are still so attached,” that Leibniz’s doctrine of sufficient reason concerns merely efficient (mechanistic) cause—an aítion that Leibniz “rightly declared” to be “inadequate.” 92 It is as final cause—as the teleology of the Logic—that according to Hegel one correctly grasps Leibniz’s fundamental principle of sufficient reason in its non-trivial and non-reductive sense. Generalizing, Hegel thus construes “the simple meaning of the so-called principle of sufficient reason or ground” as, at each logical stage, the law “that things must essentially be regarded as mediated” [Dies ist dann auch der einfache Sinn des sogenannten Denkgesetzes vom zureichenden Grunde, durch welches eben nur ausgesprochen wird, daß die Dinge wesentlich als vermittelt zu betrachten sind].93 90  See Encyclopedia Logic, §121z (pp. 190-91) [Die Wissenschaft der Logik, pp. 250-51]. 91  Ibid., p. 190 [p. 250]. 92  Cf.: “It is very unjust to Leibniz to suppose that he contented himself [concerning the principle of sufficient reason] with something so lame as the formal principle of reason or ground [i.e., efficient cause]…where what is at issue is a cognition that comprehends. In this regard, Leibniz contrasted causae efficientes and causae finales, and required that we should not stop at the former but press on the latter. According to this distinction, light, heat, and moisture…must certainly be considered as causae efficientes, but not as the causa finalis of the growth of plants—the causa finalis being nothing else but the concept of the plant itself ” [welche causa finalis dann eben nichts anderes ist als der Begriff der Pflanze sebst] (Encyclopedia Logic, §121z; [Die Wissenschaft der Logik, p. 251], emphasis added). 93  Encyclopedia Logic, §121z [Die Wissenschaft der Logik, p. 248].

246 Inference and the metaphysic of reason Here I demur. At least on the conceptual plane of “pure thinking”— which is paradigmatically that of inferential reflection—it is reductive to privilege either efficient (agent) cause or, with Hegel, teleological cause as the defining moment of Sufficient Reason. To conceptualize Sufficient Reason, especially as it pertains to inferential reflection, in either of these terms misleadingly licenses approaches to acts of reflective cognition (taken as mediated judgment) that impute a problematically intrinsic or extrinsic character to the energeia of reason as cause (Grund) in the onto-epistemology of the act of inference.94 It is relative precisely to this that Hegel stands indicted of “intrinsicism” by those who interpret his ultimate appeal to the Begriff as, for example, an absolutely self-mediating actuality.95 (To be sure, Hegel might well have offered to rebut the charge by insisting that the Begriff doesn’t negate das Differente as an ontological absolute. The Begriff rather comes to be, he would urge, as the formal cause of the Different, the Idea within which, beyond abstract negation—which is always the negation of difference itself—das Differente gets posited absolutely for what it is.96) Instead of looking either to efficient or to final cause, one discovers (consistent with classical precedent97) that a properly onto-epistemological reading of inference discloses as formal cause98 that which defines, in the first instance, the principle of sufficient reason—what 94  Cf. Blanchette, who, in the context of explicating Aristotelian and Thomist thinking on the topic, provides a trenchant analysis of the excessive “intrinsicism” and “extrinsicism” that attach to misconceptions of “cause”; in The Perfection of the Universe According to Aquinas (University Park: Pennsylvania State University Press, 1992), pp. 157-61. 95  William Desmond, for example, understands Hegel in this way; see his Being and the Between (Albany: State University of New York Press, 1995). 96  Cf. Encyclopedia Logic [Die Wissenschaft der Logik], §242. By the same token, one could charge a philosopher such as Whitehead with “extrinsicism.” This for conceiving God as the primordial “actual entity” whose “unity of conceptual operations is a free creative act, untrammeled by reference to any particular course of things” and whose “primordial nature” is “the unconditioned conceptual valuation of the entire multiplicity of eternal objects”; cf., Process and Reality, Corrected Edition, ed. David Ray Griffin and Donald W. Sherburne (New York: Free Press, 1978), part I, chap. 3 and part V, chap. 2. 97  As in Aristotle’s Posterior Analytics; see chap. 1, iii e, above. 98  Not to be confused with material cause.

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Leibniz termed “the apex of rationality in motion.”99 Thus construed, Sufficient Reason, in conjunction with the law of (non)contradiction, constitutes, I would submit, the reason of the act of inference. It is formal cause that is operative as the onto-epistemological ground of inferential reflection understood as “essentially” (wesentlich) mediated judgment. If one considers it prescinded from any particular thoughtdetermination, the essential “form” in question here is the emptiest of abstractions, the merest notion of what Hegel denominates Schein. But in every actual occasion of reflective, mediate judgment, the formal character (the intelligible form)—of, for example, some forensically or aesthetically or logically, geometrically or theologically ordered elements of “aboutness”—shows as the substantial element of the dynamic, the forma formans, of a living route of inferential thinking (“rationality in motion”). This composition of ideal phenomena thereby exhibits a definite ontological reference.100 For what show (scheinen) are not mere appearances (Erscheinungen) so far as they com-pose, literally put together, a processually articulated totality that is the ground, the truth, of the very order of some actuality—be it forensic, aesthetic,101or logical, geometric or theological (e.g., a Thomist analogy of being102). Concretely realized in this way, a coherent inference 99  Leibniz Selections, ed. Philip P. Wiener (New York: Scribners, 1951), p. 93. 100  Cf. Whitehead: “The ontological principle can be expressed as: All real togetherness is togetherness in the formal constitution of an actuality” (Process and Reality, p. 32). 101  Cf., Schillerian schöne Schein. 102  To assess how the conclusion of an inference as an analogy of being squares with any “primary analogate” under which it falls is to wrestle with the problem of the truth or validity of inference—a second-order matter that is not a concern here, although a major topic of theorists who too often fail to think through the metaphysical ground of the issues at stake. In the language of Aquinas, my concern is with the act of inference as the perfection of the intellect: “Truth…can be present in sense, or in intellect knowing a meaning, as in a thing that is true; but not as the object known is in the knower, which is implied by the word ‘truth’; for the perfection of the intellect is truth as known” [Veritas quidem…potest esse in sensu, vel in intellectu cognoscente quod quid est ut in quadam re vera; non autem ut cognitum in cognoscente, quod importat nomen veri; perfectio enim intellectus est verum ut cognitum]; see Summa theologiae I, q. 16, a. 2 (quoted in Desmond Connell, Essays in Metaphysics [Dublin: Four Courts Press, 1996], p. 75). See

248 Inference and the metaphysic of reason is precisely its being the reflective Schein of premises properly ordered to the conclusion that they, as a totality, predicate, and insofar ground, in the act of reflective thought. This Schein is a Hegelian rational determination or category: a unity of das Seiende, in light of which Geist “finds something existent in itself,” and das Seinige, “according to [which] spirit posits that something only as spirit’s own.”103 4.5.1 Onto-epistemological positing. “…the suspicion forces itself upon us that in Kant’s determination of being as positing there prevails a kinship with that which we call Grund”—this Heideggerian remark serves as an epigraph at the head of the present chapter. It captures the sense of onto-epistemological positing in play as the thetic component of the reason of the act of inference. The statement directs attention to Kant’s original and radically significant move to identify the very concept of Position oder Setzung with that of being (Sein überhaupt). As the general course of the present inquiry has suggested, this early speculative insight of Kant’s ramifies considerably beyond the criticism of onto-theology wherein he initially introduced it. Indeed, it tacitly thematizes the metaphysical implications and efficacy of the act of inferential reflection.104 When once, in light of these implications, one grasps the position (setzen) of premises in routes of inferential reflection, one discovers that analytic approaches to the “problem Blanchette’s systematic treatment of “The Analogy of Being,” Philosophy of Being, chap. 4. Also see, John F. X. Knasas, “Analogy and Logical Demands” and “Analogy as Supra-Conceptual,” Being and Some Twentieth–Century Thomists (New York: Fordham University Press, 2003), §§5.8 and 5.9. 103  See translator’s introduction to Hegel, Lectures on the Philosophy of Spirit 1827-28, trans. Robert R. Williams (Oxford: Oxford University Press, 2007), p. 29. Cf. Enzyklopädie der philosophischen Wissenschaften. Dritter Teil. (Frankfurt am Main: Suhrkamp, 1986), §443; and Hegel’s Philosophy of Mind, trans. William Wallace (Oxford: Oxford University Press, 1971), pp. 184-85. 104  As we saw in §3.4.3 above, however, Lotze expressly rejects the notion of Position (exclusive of relation), although he had Herbart more than Kant in mind. A half century later Moritz Schlick, apparently missing the Kantian pedigree of the notion altogether, cites Lotze’s “excellent polemic against Herbart, who defined being as ‘absolute position,’ a formulation on whose meaninglessness we need waste no words”; see General Theory of Knowledge, trans. Albert E. Blumberg (La Salle, Ill.: Open Court, 1985), p. 183.

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of inference”105 all too often incur the antinomies and heteronomies engendered by a speculative thinking that fails properly to face the speculative implications (and the correlative conceptual logic) of its operative rational principles. Beyond its critical and historical value, however, Kant’s metaphysical conceptualization of Position prepares the way for a constructive effort, such as the present, which undertakes to rethink the act of inference from an onto-epistemological orientation.106 The critical phase of our investigation made it clear that in order rationally to conceive Position as a moment of the act of inference, one needs at once to recognize the absolute (existential) and relative (predicative) modes of it that Kant distinguished, and to look past the dualism that is at least consistent with Kant’s treatment of the notion—notwithstanding the onto-epistemological isomorphism implicit in his mature, assertabilist and referential conception of truth.107 While this might seem at best an arcane and marginal issue from the perspective of leading analytic and other epistemological trends in Anglophone philosophy, the speculative positing, the thetic, has seminal historical as well as conceptual relevance for analytic epistemology. Consider, for example, Frege’s dubious recourse to Kant’s authority in just this connection, namely with respect to Kant’s reference to Position in his criticism of the Ontological Proof. Like many in his wake, Frege imagined himself to be translating Kant’s thinking into symbolic logic by attributing an existential import—rather than a logically austere sense of abstract identity—to the idea of the quantifier. The reason, as Donald Davidson reminds us, is that Frege “wanted to be able to quantify over whatever predicates referred to.”108 Frege believed it consistent with Kant “to treat existence as a property of properties, not as 105  See chap. 2, above. 106  And this not least because Kant himself ironically enough restricts inference to the domain of analytic epistemology, in the form of the faculty of the Verstand. 107  On this score, see section III.B (“The Birth of Modern Reference”) of Carl J. Posy’s “Immediacy and the Birth of Reference in Kant,” in Between Logic and Intuition: Essays in Honor of Charles Parsons, ed. Gila Sher and Richard Tieszen (Cambridge: Cambridge University Press, 2000), pp. 155-85. 108  Truth and Predication (Cambridge, Mass.: Harvard University Press, 2005), p. 144.

250 Inference and the metaphysic of reason a property of objects.”109 Richard L. Mendelsohn calls attention to the telling, metalogical incoherency of this speculative gambit of Frege’s (a problem seen as well in more recent moves of certain ontological naturalists in mathematics who have proposed that finite cardinals are properties of properties110). Mendelsohn observes that Frege “offers no unified treatment of singular existence claims and general existence claims”111—a lapse hardly consistent with Kant’s modus operandi.112 This fundamental inconsistency is itself consistent with Frege’s notion that we are able to “obtain a basis for judging the epistemological nature of the theorem” (in general) because our “chains of inference do not have any gaps,” something that is possible, as Wilfried Seig observes, “only if inferences do not require contentual knowledge.”113 The idea of epistemically contentless inference is implausible, however, since the diremption of form from content in the act of inference (or of structure from meaning, in Gödel’s later extrapolation) can result only in a second-order inference about the first or in an impossible Platonism in the guise of an immediate judgment. Inference is irreducibly intentional. What about the variable, which “has” no determinate “content”? As with sets that are subsets of themselves, so the “content” of a variable in an act of inference is identical with its bound or unbound form. In other words, the content is whatever aspect of fact the variable “shows” of the reflectively articulated order that constitutes the intelligible whole of which it is a formative moment. 3 109  Richard L. Mendelsohn, The Philosophy of Gottlob Frege (Cambridge, Engl.: Cambridge University Press, 2005). 110  See Alan Weir, “Naturalism Reconsidered,” in The Oxford Handbook of Philosophy of Mathematics and Logic, ed. Stuart Shapiro (Oxford: Oxford University Press, 2007), p. 473. 111  Ibid., p. 118. The “claim,” remarks Davidson, “that predicates refer to anything at all can be given up without direct cost to Frege’s account of predication”—adding the rider that he does not mean to “say that other aspects of [Frege’s] philosophy would not have to be surrendered at the same time” (Truth ad Predication, p. 144). 112  For more on Mendelsohn’s critique, see Appendix I.ii, below. 113  “Mechanical Procedures and Mathematical Experience,” in Mathematics and Mind, ed. Alexander George (Oxford: Oxford University Press, 1994), pp. 74-75.

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As with the legendarily controversial distinction between Vernunft and Verstand, Kant failed persuasively to establish the onto-epistemological relation between the correlative concepts of absolute and relative positing. Hegel, on the other hand, while he never mentions the Kantian absolute/relative binarism, invokes reflective setzen in a sense, most germane here, that discloses the dialectical relation of absolute and relative Position. This he does in his conceptual logic, specifically in the doctrine of essence, where he tracks setzende Reflexion and its correlative Gesetztsein.114 In the process, Hegel unerringly traces the way that the onto-epistemology of inferential reflection involves the intermediation of absolute and relative modes of setzen. On the cognitional plane of the act of inference, the setzende Reflexion of essence is the relative, predicative, positing whereby I invest some otherwise tacit fact with ideal significance as a premise. This premise in my inference is indirectly relative to at least one other premise (inferences being acts of mediated judgment) and reflectively ordered to a conclusion.115 The logically concluding moment of the act of inference is positedbeing, Gesetztsein, a fact whose significant “power” (or quality) owes its explicit character to its determinating setzende Reflexion. As such, Ge114  Where reflection is Setzung as actuality of identity-in-difference in the determinate process of Becoming. The dialectical correlate of reflective negation is “quality.” For Hegel this is the negation of immediate Being as Fürsichsein in its infinite self-relation that is negative (der unendlichen und zugleich negativen Beziehung auf sich). This, being indeterminate, contrasts with reflective negation. See Encyclopedia Logic, §96; [Die Wissenschaft der Logik, pp. 203-04]. 115  Although he never satisfactorily worked out the connection, Kant himself insisted that it is through the relative positing that the dimension of absolute, or existential, Position oder Setzung is discursively intelligible. Interestingly, Kant’s thinking in this particular applies not only to the speculative use of pure reason, but to that of practical reason as well. One sees this in his dialectic of pure practical reason, wherein the idea of “highest good,” a moment of absolute positing, must be determined “practically— that is, sufficiently for the maxims of our rational conduct.” What confirms the character of the highest good as a moment of absolute position is that it constitutes, in Kant’s words, “the unconditioned totality of the object of pure practical reason,” relative to which we posit maxims that render the highest good intelligible as “the doctrine of wisdom.” See Kant’s Critique of Practical Reason, translated and edited by Mary Gregor (Cambridge, Engl.: Cambridge University Press, 1996), book II, chap. I.

252 Inference and the metaphysic of reason setztsein is like the “whole” in Aquinas’s classical analysis of whole and part:116 always already a component of the relative positing of premises, in their determination as ordered terms of discourse.117 This seeming paradox that marks the dynamism of the living act of inference, toward a conclusion that is its truth, is precisely what Ernst Cassirer, building on his teacher Georg Simmel, sees as distinguishing the “concept of Life” from “the concept of Being.” Cassirer puts it this way: The concept of Life is distinguished from the concept of Being in the older metaphysics and from its “ontology” by virtue of this one basic feature: it recognizes no substantiality other than that which consists of pure actuality alone….It is never at one with itself except by being beyond itself at the same time. The peculiar and unique act of erecting and breaking through its boundaries provides the only absoluteness we can attribute to its character.118

In the act of inference, the reflective Position of premises is ecstatic in this sense. The premises in the living process of inferential reflection are thus not discrete ideas. They are ideal moments that are substantial only so far as they are actual; and actual only so far as they show in 116  Aquinas’s argument, as John Wipple explains, is that what a given whole/part proposition means “would remain unknown to anyone who could not understand the notion of a whole.” And such knowledge of what that somewhat—that essence—termed a “whole” is need not extend beyond the fact that there must be a what that we identify as a whole. This is the case even if this whole is a simple essence that is not self-evident or, better, per se known to us. We have claim to genuine, if mediated knowledge of the whole so long as we can grasp it as uniquely distinguishable in itself—negatively, as it were, and a posteriori, by means of our materially composed understanding. Such understanding rationally cognizes by a process of abstracting from that which is more fundamental than we are able to master in acts of discursive, inferential thought. See John F. Wipple, The Metaphysical Thought of Thomas Aquinas: From Finite Being to Uncreated Being (Washington, D.C.: Catholic University of America Press, 2000), p. 389. 117  The analytic theorists who reject this line of thinking as viciously circular typically operate with a categorial substance ontology that ill-equips them properly to credit the ontogenetic dimension of knowing as being, to which an event or act ontology is most keenly attuned. 118  The Philosophy of Symbolic Forms, Volume 4: The Metaphysics of Symbolic Forms, ed. John Michael Krois and Donald Phillip Verene, trans. John Michael Krois (New Haven: Yale University Press, 1996), p. 9.

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being reflectively ordered to a totality that constitutes, in some formally intelligible way, a conclusion. The setzende Reflexion of what shows as a premise involves some other (another intelligible item, concept, affect, or sense) over against which it realizes its identity in difference, and hence to which it is indirectly relative. What the premise is directly relative to is an intelligible order that in the act of inferring one discursively educes (as an ideal term) from a significant fact. Before turning directly to the conceptual logic of inferential reflection, let me conclude this subsection with a word about a suggestive Thomist correlate that obtains here with respect to the setzende Reflexion of premises indirectly relative to each other and directly relative to order that the discursive, inferential act educes from significant fact. The two-aspect (direct/indirect) feature of relative onto-epistemological position in inferential reflection parallels a cardinal element of Aquinas’s logic of perfection. Oliva Blanchette has incisively summarized this element, one that Thomas casts in orthodox onto-theological terms. Aquinas, notes Blanchette, finds that the rational soul as spiritual soul has “a subsistence of its own, and hence [is] directly related to God’s creative act,” literally the rational soul’s induction.119 This metaphysical architectonic translates readily into the idiom of the conceptual logic of the act of inference: the onto-epistemological nature of the act of inference follows from the circumstance that what show as premises are posited directly, relative to an originary order. Each premise is what, as such, we put to thought indirectly (in its determinating differences) relative to what shows as the premise that is its co-relative other. Together, as a reflectively developed itinerary of thought, they discursively conduce to a totality, the “conclusion.” The conclusion is the truth that they compose, whatever sense it makes in context. The indirect relative positing that realizes the reflective nature of what shows as a premise vis-à-vis its mediating other in an ordered route of inferential thinking is something that Aquinas would explain as a function of the “composite” nature that uniquely stamps the subsistent, “substantial form” of spirit. Interpreted from the standpoint of conceptual logic, this composite nature—“educed,” as Aquinas would 119  Blanchette, The Perfection of the Universe According to Aquinas: A Teleological Cosmology (University Park: Pennsylvania University Press, 1992), p. 64.

254 Inference and the metaphysic of reason have it, “from the potency of matter”120—shows as the intentional character of rational spirit. 4.5.2 The conceptual logic of inferential reflection. Hegel’s doctrine of essence discloses with unexampled penetration main elements of the conceptual logic of the act of inference. And this section takes a critical look at those moments of Hegel’s thinking on the logic of essence which make explicit the reflective dynamic that animates the logic of inferential conceptualization.121 In light of the ways that it traces the reflective form of the act of inference, one might be tempted to read Hegel’s logic of essence as little more than a corrective to dualistic suggestions of Kant’s treatment of Position. To read it that way, however, would be to adduce it, along with the notion of “sufficient reason,” as a defining element of an onto-epistemological approach to inference—emphatically not Hegel’s intent, and a less defensible interpretive line than, say, the one that distinguishes Fichte’s much more widely discussed philosophy of Position and existence. On the other hand, if one considers Hegel’s Lehre vom Wesen not only as presented in the Logic, but also as he applies it in the systematically synoptic Philosophy of Spirit, specifically in the explication of das Denken (cf., §467), the appeal to Hegel in this connection takes an entirely different cast. What strikes one above all in Hegel’s treatment of das Denken—“the third and last main stage [following intuition and representation] in the development of intelligence”122— is how directly the logic of essence speaks to an onto-epistemological construal of the reason of inference. As Hegel insists, das Denken, “pure thinking,” alone, “knows that it…and not feeling and representation, is 120  Ibid. 121  Needless to say, the analysis here does not venture anything like a comprehensive textual critique of Hegel’s exposition, much less of its ramifications in his Logic at large. The Anglophone reader can find a close analysis of the elements of the Logic discussed here in Robert M. Wallace, Hegel’s Philosophy of Reality, Freedom, and God (Cambridge, Engl.: Cambridge University Press, 2005).(Wallace is a Hegel scholar and seasoned Germanist who has translated Hans Blumenberg’s three major tomes.) If less textually focused, Stanley Rosen has authored a more philosophically trenchant analysis of the doctrine of essence; see his G. W. F. Hegel: An Introduction to the Science of Wisdom (New Haven: Yale University Press, 1974). 122  Philosophy of Spirit, §465z.

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capable of grasping the truth of things….”123 It is not to the purpose to rehearse here Hegel’s account of thinking in any detail, but it pays to be clear about what he understands as the three orders of “pure thinking,” that is, of thought viewed as theoretical Geist (i.e., what Hegel takes to be the concrete, living act of intelligence). The first order, understanding (Verstand), is thinking that establishes formal identity or determinacy (of the individual) through a dialectic of mental representations (Vorstellungen). This thinking, understood along Kantian lines, manifests the truth of Being through thoughtdeterminations (Denksbestimmungen) for which “content is indifferent to form.” The second order is judgment (Urteil): “something not only subjective, but also objective.”124 Judgment is the formally conceptual order of thinking that regards its objects as relations (Verhältnisse), uniting otherwise abstract elements in such a way that the content appears as given.125 Formal reason,126 inferential understanding (formelle Vernunft, schließender Verstand127), is the third and culminating mode of pure thinking. Hegel finds that in schließender Verstand “thought supersedes the formal determination and institutes [setzt] at the same time an identity of the differences. It is on this plane of pure thinking—where die Intelligenz erkennt als denkend—that self-conscious knowing (“knowing ourselves as thinkers”) is, Hegel declares, “perfectly true.”128 The essential logic of this pure thinking-as- schließender Verstand further articulates with an onto-epistemological orientation to inference in three cardinal respects. a) It develops the link, by way of the logic of essence, between Position oder Setzung and Being. b) It discloses the reflective dynamic that is the essential character of the reason of inference. c) It incorporates a conception of Grund that reveals the bearing of the principle of sufficient reason on inferential think123  Ibid. 124  Lectures on the Philosophy of Spirit 1827-8, trans. Robert R. Williams (Oxford: Oxford University Press, 2007), p. 243. 125  Recall Kant on the inference of judgment; see his Logic, §§81ff. 126  Wherein “the content produces its form from itself ” (Philosophy of Geist, §467z). 127  Ibid., §467. 128  Cf., ibid., §§465-67.

256 Inference and the metaphysic of reason ing (notwithstanding the fundamental objections that one might raise respecting Hegel’s teleological reading of the principle129). These elements of the doctrine of thinking-Geist give force to a signal assertion of Hegel’s that makes unmistakable the centrality of the reason of inference in his system. At the stage of “pure thinking,” the stage at which cognition is inferential in character, “the Begriff,” Hegel declares, “is known as such.”130 This insight into the reason (Vernunft) of inferential reflection reveals as well the rational limit of the Hegelian doctrine of essence, at least from an onto-epistemological perspective. Hegel would doubtless object that such a charge betrays the limited speculative purview of the present study. He would see it as an abstractive reduction of “concrete thinking”—the very thinking “that comprehends its object.” He might further point to the treatment of the syllogism in his doctrine of Subjective Begriff as the properly concrete approach to inferential thinking in its relation to Being. By stopping short of pursuing the investigation into the domain of objective Geist, it is the present author, then, who would stand accused, from an orthodox Hegelian viewpoint, of propounding an insufficiently rational, indeed a not totally truthful, analysis of the act of inference. This orthodox line of criticism presupposes, however, one of Hegel’s most controverted working assumptions, namely that the Begriff, “in its comprehensive identity…is the fullest expression of the unity of thinking and being.”131 The systematic idealist implications of the present essay hardly extend to anything like absolute idealism. The defining unity of thinking and being is signally expressed, I have suggested, in the onto-epistemology of the act of inference. The selfconscious (self-thematizing) order of realization, which distinguishes perhaps the most definitively human dimension of inference, typically objectifies that expression in ever more developed and penetratingly disclosive terms—witnessing thereby what Karl Rahner would identify as the Beisichsein des Seins (what, with an eye toward the living dynamic of the self-reflexive event, I should term the Beisichseiende des Seins). Such orders of inference, however, do not constitute by that 129  See Encyclopedia Logic, §121z (pp. 190-91) [Die Wissenschaft der Logik, pp. 250-51]. 130  Philosophy of Spirit, §467. 131  Rosen, The Limits of Analysis (New York: Basic, 1980), p. 233.

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token objective moments of some Absolute fact of self-consciousness that most fully expresses the unity of thinking and being. So far, then, one follows Hegel in finding that the realm of pure thought is the “realm of truth as it is without veil and in its own absolute nature,” and even that “logic is to be understood as the system of pure Reason, as the realm of pure thinking.” Moreover, Hegel’s insights into realities betokening the ways that spirit in and for itself (ideality) is the truth of nature inform, from start to finish, the orientation to inference detailed in these pages. Hegel’s correlate of the nature/spirit relation, i.e., that the Absolute is the truth of spirit, holds only if one accedes to a prior correlation, for many a dubious one, as a middle term of the equation. A pair of hypothetical conditionals captures this correlation: if spirit is the truth of nature, the truth of spirit is the Absolute—correlatively—if the Absolute (as “essentially a result”132) is the truth of spirit, the truth of the Absolute is God (whose Concept Hegel articulates in the Logic). Like many students of Hegel’s thought, the present writer draws a line at the notorious claim that follows from this speculative axiom, namely that the content of the Logic of the Begriff “is the exposition of God as he is in his eternal essence before the creation of nature and of finite spirit” (daß dieser Inhalt die Darstellung Gottes ist, wie er in seinem ewigen Wesen vor der Erschaffung der Natur und eines endlichen Geistes ist).133 In any case, inferential thinking has a pivotal status, constituting an essential (wesentlich) and thus consequently134 a conceptual, self-defining phase in the logic of the philosophy of Geist. But the character of thinking in the logic of essence—always exclusive of how such thinking figures as sublated in the Begriff—remains for Hegel strictly preself-reflectively an sich, and by that token negatively “external” to the Idea. For all that, however, Hegel’s analysis of “Essence as Ground of Existence”135 is a profoundly illumining onto-epistemological anatomy 132  Cf., “Es ist von dem Absoluten zu sagen, daß es wesentlich Resultat, daß es erst am Ende das ist, was es in Wahrheit ist.... ” Phänomenologie des Geistes (Franfurt am Main: Suhrkamp, 1970), p. 24 [Hegel’s “Phenomenology of Spirit,” trans. A. V. Miller (Oxford: Oxford University Press, 1977), p. 11]. 133  Cf., Wissenschaft der Logik I, p. 44; [Science of Logic, p. 50]. 134  In the architectonic sense, not merely the temporal one. 135  Encyclopedia Logic, §§115-30.

258 Inference and the metaphysic of reason of the reason of the act of inference, and it prefigures the present approach in the respects that have been suggested. Certainly the most important anticipation is the all-important role that Hegel accords “setzen” and in the reflective character that he himself ascribes to “inferential understanding” as formelle Vernunft. (This reading sets in relief136 the dialectical correlate of Das Wesen als Grund der Existenz, i.e., the grounded determination of the unity of essence.) Two points forcefully attest here to the continuity on this score between Hegel’s doctrine and an onto-epistemology of inference. The first is the linkage between this part of Hegel’s Logic and the reason of “pure thinking” at the level of inferential—or reflective137—acts of intelligence. The second point is the formative onto-epistemological role that Hegel accords Setzung in the dynamic of reflection, most notably in the dialectical itinerary of “Essence as Ground of Existence.” Relative to the way that Hegel employs this pivotal thought-determination, a word should be said about a potentially misleading comment on the use of “setzen” in the Psychology section of his lectures on the Philosophy of Spirit. The comment appears as a note in Robert M. Williams’ introduction to his translation of the lately discovered Erdmann and Walter transcriptions of Hegel’s 1827 lectures on the Philosophy of Spirit. Williams rightly enough points out that setzen “is an operative term in German idealism,” although one might question whether it is for that reason that, as Williams opines, the notion “is rarely thematized [as we’ve seen that it has been by Lotze, Heidegger, Shürmann, Frank, and Förster] and clarified.”138 Williams informs us that Setzung 136  From the standpoint of construing Grund as, in the first instance, formal cause of the reason of inference. 137  I follow Bosanquet in taking properly inferential thinking as a type of judgment, whether deductive or inductive, that gets realized reflectively (not always self-reflectively) by way of a mediating moment. So-called “immediate” inference is judgment pure and simple, although it would be difficult to establish anything like a clear and distinct boundary that divides the latter from inferential thinking. The reason is that efforts to assess whether acts of un-self-reflective intelligence involve a mediating component invariably bring in train issues that have to do with how the mediated character of assessive thinking can effectively escape its own mediated condition-ofpossibility in critically representing (vorstellen) a target judgment as either mediated or unmittelbar. 138  Lectures on the Philosophy of Spirit 1827-8, p. 30 n.

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Subsequently [to what is not indicated] … has received a wide range of interpretations ranging from a modest and benign mentalcognitive act of reflection or consideration of an object to a strong metaphysical sense of producing and creating its object, as in the case of the intuitive intellect. In the Psychology, Hegel is focusing on theoretical spirit, i.e., cognition, and for the most part uses ‘posit’ in a cognitive rather than strong metaphysical sense.139

Williams’ admittedly loose portrayal of the “strong metaphysical sense” in which Setzung features in the thinking of German idealists, if open to qualification (particularly in the case of Hegel), is anything but a misconstruction. Still, I would argue that what Williams takes to be the “cognitive” extension of the concept is never, for Hegel, separable from its metaphysical (i.e., onto-epistemological) sense. At all events, Williams would certainly agree that in the Doctrine of Essence, in the Logic, the “benign mental-cognitive” meaning of setzen is, as Hegel would put it, “asleep” with respect to the likes of setzende Reflexion and Gesetztsein. 3 Among recent explications of the logic of essence, Stephen Houlgate’s “Why Hegel’s Concept Is Not the Essence of Things”140 is of especial interest as a masterly sketch, at once succinct and incisive, of just how Hegel thinks the notion of Setzung and, more to the point here, how he thinks with it.141 Hegel employs “position” in the foundational and multifaceted onto-epistemological sense, which ultimately, as operative on the plane of reflective thought, means that it expresses how, determinately, “something is so” through the geistig agency that is itself determined by the act.142 Houlgate’s explication is particularly helpful for outlining in brief compass what it is that Hegel contributes, on the plane of conceptual logic, to a properly rational grasp of the reason of inference. A further merit of Houlgate’s essay is that it elucidates 139  Ibid. 140  Paper read at the Cardozo School of Law, Yeshiva University, New York, N.Y., March 2004. 141  In The Opening of Hegel’s “Logic” (West Lafayette, Ind.: Purdue University Press, 2006), Houlgate offers a lucid, sustained account of his orientation to the Logic. 142  Cf. Hegel’s Lectures on the Philosophy of Religion, vol. III, ed. Peter C. Hodgson, trans. R. F. Brown, et al. (Berkeley: University of California Press, 1998), p. 212.

260 Inference and the metaphysic of reason Hegel’s speculative procedure along lines that enable one readily to pinpoint where the difficulties arise that prompt the present work’s turn to an alternative, Leibnizian, account of Ground (principium rationis sufficientis seu determinationis) as formal cause that constitutes the reason of inferential thinking, onto-epistemologically understood. The distinction most pertinent here that Houlgate stresses as he scrutinizes Hegel’s doctrine of essence is the one between setzende Reflexion and Gesetztsein.143 This distinction has a formative ontoepistemological bearing on the essential moment of inferential thinking (its reason), particularly in that the negativity of essence mediates the immediacy of Sein, and does so as “the movement” of setzende Reflexion, whose energeia is Gesetztsein.144 Moreover, as “definitive of all the categories of essence,” the relation of setzende Reflexion to Gesetztsein amounts to the onto-epistemological condition of possibility of Schein—the parousia of fact as dialectically “perfected” in reflective mediation or (on the cognitional plane of inference) in mediated judgment.145 It is precisely essential scheinen, in the determinating reflective process, that manifest “ante-predicatively” the predicative inherence of p in S. This showing manifests, by the same token, the correlative relation of S to p, in the act of inference, with the difference that S is the “integral,” as it were, of the premise or premises mediately predicated of it. For inference as mediate judgment, the “logic” distinguishing subject and predicate and middle term, whatever the ontological extension of each (universal, species, and singular), is, in the first instance, the work of essential negation—as opposed, for example, to the categorial move of subsumption. In the dynamic of reflective intelligence this logic 143  “Why Hegel’s Concept Is Not the Essence of Things,” p. 3. 144  This ultimately yields, for Hegel, a reprise of Being, but as Existence— reflected (mediated) Being—and now essentially sublated in the Concept. 145  To paraphrase Oliva Blanchette: “the reflection essential to any” process of inferring—when inference is once recognized as an onto-epistemological act, in which Being “makes itself known as truth”—such reflection “is an act in search of…how being shines forth in this or that representation.” I would submit that being “shines forth” as well in the “shine” (Schein) of premises in the onto-epistemological setzen (which is what distinguishes inferential thinking as wirklich) that is formally ordered to a determinate universal or, in Thomist terms, a primary analogate. See Blanchette, Philosophy of Being, §7.2.

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takes its inferential form as a distinctive, intrinsically communicative progress or order. The conceptual logic of inference thus exhibits a progression from premise to premise among mutually determinating, reflectively posited terms that as premises show, however tenuously, as always already ordered to, and in so far invariant vis-à-vis, some formal cause. Through the act of setzende Reflexion the thinker realizes a subject that “ends up preceding,”146 as logically prior, the Gesetztsein that it predicates. The predicate in its turn refers back reflectively to the subject in its being. This is the relation of posited form to order, as the form manifests the reason of a route of inferential reflection. “Showing in what is opposed” (Scheinen in dem Entgegengesetzten) is how Hegel depicts this essential component of communicative movement that on the plane of cognizing spirit, and as determinate in being presentationally ordered to a conclusion, articulates the ontoepistemology of acts of inference. It is one thing to make a case for the notion of the progressively determinate, reflective being of what show as premises in an inference; it is another, however, to contend that the show of premises ordered to a conclusion “ends up” preceding the conclusion, which is to say the truth, to which they conduce. Yet as thinkers from Hegel to Bosanquet and beyond have recognized, this is how finite truth is for the being of discursive intelligence. (Underlying this recognition is a tacit appeal to the foundational distinction of fuvs i~ and tevcnh, and the Aristotelian conclusion that the latter, for all practical purposes, is the paradigm or “prime analogate” for cognizing fuvs i~.) Through “ideal construction,” something that we do not construct, cogent acts of inference progressively realize and communicate the nature of significant fact as a finite whole with infinite implications, i.e., as a coherent perspective on or construction of truth.147 146  Houlgate, “Why Hegel’s Concept Is Not the Essence of Things,” p. 3. As Houlgate notes, “In the sphere of essence...there is no purely linear development: rather the active moment of positing only comes to precede (or to have preceded) the moment of positedness [Gesetztsein] when that positedness is actually being posited” (ibid.). My own claim, simply put, is that this dynamic, as operative on the plane of what Hegel termed reine Denken (“pure thinking”), is what from an onto-epistemological frame of reference animates the conceptual logic of inferential reflection. 147  See, Bosanquet, Logic, vol. II, chap. X. While elements of any number of idealist speculative systems are consistent with this reading of inference,

262 Inference and the metaphysic of reason Setzung, we have seen, has a profound range of commonly overlooked onto-epistemological connotations. One of the most salient in Hegel’s philosophical milieu was, as we have noted, Kant’s understanding of the concept as “identical” with the concept of Sein überhaupt. Another was Fichte’s notion that the act of setzen is “the first ‘fact’ of consciousness.” While a third sense of setzen features in Novalis’s understanding that gegengesetzt constitutes “the activity of the object [whose substance is the universal] whereby the opposite and thus the object itself emerges” for us. The foregoing meanings associated with onto-epistemological position—along with others enumerated in the introductory chapter (section iv)—are at play in inferential setzen. Subject and predicate, whether posited deductively or inductively, ontogenetically “show up” in each other (dialectically, Hegel would say148), yet “remain two quite distinct and [categorically] separate determinations.”149 Hence in the act of intelligence, identity and distinction, of whatever categorial determination or order, can cancel (sublate) each other only at the cost of extinguishing the essential “show.” And the latter spells the erasure of the act of inference, with a resulting collapse to prereflective immediacy (on the cognitive plane, prediscursive immediacy). At the level of Hegel’s Begriff, however, which supersedes that of essence proper, Hegel understands setzende Reflexion to be identical with its Gesetztsein; this follows the sublation of essential mediation and consequently negates the determining moments—the very reason, I would urge, of the act of inference as mediated judgment. Among the most revealing turns of Hegel’s thinking that puts it at odds with the onto-epistemology of inference as probed in the present chapter is his recourse to limiting, in the traditional manner, the form of inference to the syllogism. What’s more, he explicates the syllogism as onto-epistemologically parasitic on the logic of the Begriff. Hegel among the most deeply consentient with it is Whitehead’s view of “importance” as an “ultimate notion,” or principle, of the “assemblage” of concepts that properly precedes the formulation of systematic metaphysics. Cf., Whitehead’s Modes of Thought (1938. New York: Free Press, 1968), First Lecture (“Importance”). 148  Cf., Hegel’s Science of Logic, trans. A. V. Miller (Atlantic Highlands, N.J., 1993), pp. 685; [Wissenschaft der Logik II (Frankfurt am Main: Suhrkamp, 1986), p. 379]. 149  Houlgate, “Why Hegel’s Concept Is Not the Essence of Things,” p. 3.

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summarizes his speculative conception of the syllogism in an addition appended to an early section of the Encyclopedia Logic: If we take the syllogism [Schluß]… (not in the sense of the older formal logic, but in its truth), then it is that determination, in which the particular is the middle which joins [zusammenschließt] the extremes of the universal and the singular. This syllogistic form is a universal form of all things. All of them are particulars that join [zusammenschließen] themselves as something universal with the singular….In this way the Logic is the all-animating [allbelebende] spirit of all sciences…”150

Perhaps a more fundamental sign of Hegel’s divergence from the orientation to inferential reflection sketched forth here is his bid to read sufficient reason, or Grund, as final cause (i.e., as teleological) and thereby to represent it as a power of the Begriff. (Wherein ground 150  §23z 2; Die Wissenschaft der Logik, pp. 84-85. Also see Wissenschaft der Logik II (Frankfurt am Main: Suhrkamp, 1986), pp. 326ff; [Hegel’s Science of Logic, trans. A. V. Miller (Atlantic Highlands, N.J., 1993), pp. 643ff.]. The pertinence of Hegel’s doctrine of essence to the onto-epistemology of the reason of inference foreshadows the correlative relevance of his treatment of the “judgment of reflection” in the Doctrine of the Begriff. The reason for not pursuing that more developed route of conceptual logic as it relates to the approach introduced here is that Hegel limits the notion of inference at large to the syllogism (which is insufficiently nuanced, even “in its truth”) and to subjective Geist. (Cf., “…the mere determination of an object by predicates, when that is not at the same time the realization and objectifying of the Concept…remains something so subjective that it is not even the true cognition and determination of the Concept of the object—subjective in the sense of abstract reflection and uncomprehending (mental) representations” (Hegel’s Science of Logic, p. 706, translation modified) [die bloße Bestimmung eines Gegenstandes durch Prädikate, ohne daß sie zugleich die Realisation und Objektivierung des Begriffes ist, etwas so Subjektives, daß sie auch nicht einmal die wahrhafte Erkenntnis und Bestimmung des Begriffs des Gegenstandes ist,— ein Subjektives in dem Sinne von abstrakter Reflexion und unbegriffenen Vorstellungen (Wissenschaft der Logik II, pp. 403-04)].) Only when the Begriff moves beyond the “abstract reality” (wherein it determines itself into Schluß in individuality), only then—having sublated “by its own act its defect [Mangel] of being subjective”—is objectivity posited as inference; cf., Hegel’s Science of Logic, p. 710-11 [Wissenschaft der Logik II, p. 409]. Cf., James W. Allard’s brief overview of the main lines of Hegel’s account of syllogistic inference, in The Logical Foundations of Bradley’s Metaphysics: Judgment, Inference, and Truth (Cambridge, Eng.: Cambridge University Press, 2005), pp. 133-39.

264 Inference and the metaphysic of reason “is a property of the Begriff and of mediation by the Begriff, which is reason.”151 [cf., der teleologische Grund ist ein Eigentum des Begriffs und der Vermittlung durch denselben, welche die Vernunft ist.152]) Hegel goes beyond restricting sufficient reason to the Vernunft of the logical dynamic of essence manifest in a reflective play of Schein that composes a totality marking its rational term.153 In a reflective dialectic of Schein wherein the moments do not cancel their counterparts, Hegel ultimately discovers the curious sublation of mediation that marks ground as at once the immediate unity of the dynamic (reflective show) of essence and the distinction of identity and distinction.154 He goes on to locate the ontological upshot of the logic of essence in an existential immediacy of being for itself —taking the term “existence” as indicating a state of emergence (deutet auf ein Hervorgegangensein): “being that has emerged from the ground and become reestablished through the sublation of mediation.”155 I call the sublation of mediation in the doctrine of essence “curious” because, as previously remarked, Hegel sees in the principle of sufficient Grund the fact that “things must essentially be regarded as mediated” (die Dinge wesentlich als vermittelt zu betrachten sind); and, in its non-trivial and non-reductive sense, he understands the principle to be final (teleological) cause.156 The context of both of these imputed characteristics of sufficient Grund does not obtain at the (onto)logical phase of the doctrine of essence, although to recognize as much presupposes the begrifflich context in which they do obtain. The crucial implication here is that the move from essential ground to existence consequently entails an arational suspension of sufficient reason. As Houlgate observes, “the relation of grounding proves to be noth151  Hegel’s Science of Logic, p. 446 152  Wissenschaft der Logik II, p. 83 (emphasis in original). 153  Hegel would hold such reflective actualization to be operative in pure reason, although he doesn’t explicate it on that spiritual plane. Kant would have regarded such show Sinnleer—an empty concept—that belongs to pure thinking in the absence of intuition. 154  Cf. Encyclopedia Logic, §§ 122-23 [Die Wissenschaft der Logik, pp. 25254]; see also Hegel’s Science of Logic, pp. 474-78 [Wissenschaft der Logik II, pp. 119-23]. 155  Encyclopedia Logic, §123z. 156  Encyclopedia Logic, §121z [Die Wissenschaft der Logik, p. 248].

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ing but the emergence of the ground into being,” and hence, for Hegel, the principle of sufficient reason “gives way to the simple process of Hervortreten.”157 The onto-epistemological moments of the reason of inference assume a far different rational configuration. To see how, requires first recognizing that Hegel allows for the self-sublation (Sichaufheben) of distinction, and hence the sublation of mediation itself, in the logic of essence by way of Kantian absolute (existential) Position.158 One finds this where Hegel asserts that such positing is emergent Existenz, in the sense of the restoration of ante-predicative Being “inasmuch as it is mediated through the sublation of mediation” (insofern es durch das Aufheben der Vermittlung vermittelt ist).159 For Hegel, this amounts, as Kant would put it, to “the same as” Ground, in that, for Hegel, der Grund “does not remain behind existence” (bleibt nicht hinter der Existenz zurück), but is itself nothing other than “this self-sublation and translation into existence” (sich aufzuheben und in Existenz zu übersetzen).160 Hegel’s move has still deeper Kantian resonances—recall the passage from Kant’s early explication of Position oder Setzung: “If what is considered is not merely this relation but the thing posited in and for itself, then this being is the same as existence” (Wird nicht bloss diese Beziehung, sondern die Sache an und für sich selbst gesetzt betrachtet, so ist dieses Sein so viel als Dasein).161 Existential ground, for Hegel, is nur Grund insofern er Gegründet.162 The absolute positing of the selfsublation of distinction is something that Hegel tacitly assumes to be sufficient reason (i.e., teleologically163) to regard the self-sublation as, 157  Personal communication. 158  See Appendix I.i, below. 159  The Hegelian factor of its “emergent” nature is immaterial in this context. 160  Encyclopedia Logic, §123; [Die Wissenschaft der Logik, p. 254]. 161  Theoretical Philosophy 1755-1770, , translated and edited by David Walford and Ralf Meerbote (Cambridge, Engl.: Cambridge University Press, 1992), p. 119. Recall that Kant tends to use Dasein, Existenz, and Wirklichkeit interchangeably. 162  Cf. Hegel’s Science of Logic, p. 478. 163  Cf. Hegel’s contention that Leibniz appealed, in formulating the principle of sufficient reason, not merely to mechanical causae efficientes but more significantly to causae finales and that this substantiated Hegel’s own

266 Inference and the metaphysic of reason also, das Aufheben der Mittelung.164 And it is this that signally restores, now on the level of the Begriff (albeit only abstractly, as the truth of Sein and Wesen), the emergent immediacy of Sein as existence, so far as Being is mediated through the self-sublation of distinction that sublates mediation itself. What occurs here on the strength of a self-sublating moment of essence is arguably a metaphysical (ontological) leap—from ground as content (i.e., posited as essential) to ground as, by that token, also relation (with its formative conditions) that unifies Reflexion-in-sich und Reflexion-in-Anderes. This immediate unity is Existence, which emerges as the übersetzen of self-negating ground, the latter understood as at once the formal Einheit of identity and difference, and as real determination of that content.165 Hegel would protest that at the stage of essence, and hence prior to the concrete realization of the Begriff, ground neither has nor is content. My argument, however, is that this logic of essence is conceptually articulated in the reason of the act of inferential thinking, where it is illogical to violate the principle of sufficient reason by invoking or referring to “emergence.” At any rate, and as Houlgate affirms,166 Hegel regards neither the principle of sufficient reason nor “the relation of ‘grounding’” as “absolutely primary.” In the present context, I take a more Leibnizian view. 3 There should be little doubt at this juncture as to just where the orientation to the reason of inference introduced in this essay breaks with the speculative implications that Hegel draws as he delineates the logic of essence. The most notable difference has to do with his understanding of sufficient reason not as formal but as final cause and as a function of objective Begriff, which Hegel takes to be the formal cause of all thinking. (Die Logik Wissenschaft, declares Hegel, der absoluten teleological view of sufficient reason, and thus its origin in the objective Begriff. Indeed, Hegel makes it clear in his reading of Leibniz that the proper, non-trivial and non-reductive interpretation of the principle of sufficient reason involves the requisite account of the progression from mere grounds to the Begriff; see Encyclopedia Logic, §121z. 164  Encyclopedia Logic, §122. 165  Hegel might have objected here that this is to interpret the process one-sidedly and fails to credit the place of the Begriff. 166  Personal communication.

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Form ist.167) It should be equally obvious, however, that one encounters in the principal terms of Hegel’s analysis of essence unparalleled insight into the reason of inferential thinking. That said, there is no question but that from a fully consistent Hegelian position, it is simply a mistake to fancy that one appropriates elements of the Doctrine of Essence without incorporating the larger systematic logic of the begrifflich factors. This is because Hegel understood das Wesen als Grund der Existenz both to sponsor and to presuppose those factors, particularly in his doctrines of Judgment and der Schluß.168 Indeed, from an orthodox Hegelian perspective any partial adaptation of the System (concentrating, as in the present case, on formative elements of the moment of negation between Being and Concept) must be counted as little more than abstracting undeveloped logical moments of what is merely a facet of an intermediate level of development in the scientific logic of Geist. As already suggested, however, one has grounds for reservations about the metaphysical appeal to the emergence of Existenz (mediated Being), something that involves the sublation of mediation—and a concomitant suspension of sufficient reason. Hegel himself defined the principle of sufficient reason as the fact that we must regard things (Dinge) as essentially mediated. But this seems dubious given the previously noted Sichaufheben of distinction that constitutes a defining moment of the logic of essence. This skepticism reflects a tacitly critical stance169 that discerns “a possible inconsistency in [Hegel’s] way up to the more complete conception of the logic of judgment and reasoning.”170 The “possible inconsistency” at issue stands out in sharpest relief from the viewpoint of the onto-epistemological orientation that I have proposed in this work as the properly metaphysical approach to the reason of inference. The Hegelian aporia ultimately boils down to suspending sufficient reason in the face of the relations of a “grounding” that is bare emergence out of determinate conditions. 4.5.3 The formal moment. The sufficient reason, the cause, of an act of inference formally determines inferential reflection. It does so by or167  168  169  170 

Wissenschaft der Logik II, p. 267. See Hegel’s Science of Logic, vol. II, Section One, chap.3. One that as Blanchette has observed “is not amiss” here. Personal communication.

268 Inference and the metaphysic of reason dering, to some intelligible form (be it aesthetic or mathematical, theological or psychological), the reflective determination of what show as premises. The show of the mutually determinating premises describes a trope that, so far as it composes a properly ordered route of reflection, is an ideal presentational totality that gets expressed as a conclusion of a mediated judgment. Hegel termed the dialectically communicative character of this trope—albeit with essence alone in mind—a “showing within what is opposed” (Scheinen in dem Entgegengesetzten).171 Interestingly, one finds in Lotze reference to a use of “idea” that captures the sense in play here of such grounding ideal principles of order in their essential character. (The understanding of “principles” in this context is Aristotelian, i.e., principles “of scientific knowledge [epistēmē] by which we become aware of [gnōrizomen] definitions.” 172) The conception of “idea” in question—for example the law of the excluded middle173 or, in an entirely different thought domain, the idea of the holy—merely fixes, in Lotze’s language, “reciprocal relations of the manifold,”174 while being, in itself, “without properly representable object-matter.” Ideas posited in this sense, as executive moments of the reason of inference, literally compose what Hegel would identify as the “truth” of their concrete totality, namely the ground that is the sufficient reason for any particular route of inference that sponsors their Wirklichkeit (the “actuality” of the essential “show” of premise-terms reflectively ordered to the ideas). 171  Encyclopedia Logic, §240; [Die Wissenschaft der Logik, p. 391]. 172  Quoted in Byrne, Analysis and Science in Aristotle, p. xvi; see Aristotle: “Posterior Analytics,” 2nd ed., trans. Jonathan Barnes (Oxford: Oxford University Press, 1993), p. 5. 173  Which Hegel sees as the very principle of determinate understanding (der Satz des bestimmten Verstandes); Encyclopedia Logic, §119; [Die Wissenschaft der Logik, p. 244], although in the twentieth century intuitionists such as L. E. J. Brouwer and Arend Heyting challenged it in mathematics. 174  “Philosophy in the Last Forty Years,” The Contemporary Review 37 (1880), p. 139. This was to be the first (the introductory piece) of two articles that Lotze, writing in English, was to direct explicitly “to the favorable attention of my English readers.” His untimely death in July 1881deprived us of what promised to be a most interesting sequel, in which Lotze said that he intended to turn “without more ado, and with the desired freedom from scholastic forms, to those essential questions the discussion of which has at all times and not least in our own, awakened the lively interest of mankind” (p. 155).

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What further confirms that Lotze’s thinking in this particular substantially agrees with the view under discussion is his concept of “ideas” as “fundamental principles (Grundsätze), not fundamental notions (Grundbegriffe),” which “can be actual helps to the extension of our knowledge.” Lotze holds, however, that such ideas initially operate in us unconsciously.175 Here we part company. As a mediated judgment, the act of inference and, consequently, the reason of the act of inference are always reflectively articulated. Reflection being explicitation, mediated judgment and hence the reason of inference are thus actualizations of the fully alert, conscious intelligence, i.e., rational modes in which intelligent life unfolds as the realization of purely intelligible remote fact. (Those dream states in which one is to some degree conscious in a way that is explicitly and formally continuous with waking cognition, exhibit what one might classify as “oneiric” inference—merely an epistemological distinction.176) To determine as an inference a cognitional perception or insight or immediate judgment that is ante-reflective or unconscious is always itself the function of, and parasitic upon, a conscious act of inference, and one whose reason is projected as the formal cause of the intelligence that is the target of assessment. Suppose, however, that one were to interpret the ordering idea of an inference as a concept rather than a principle of conceptualization (as in Frege’s attribution of Kantian existential signification to quantification). In that case the appeal to formal cause as the sufficient reason of inferential reflection would incur a vicious circularity. The “form” ordering the premises would be reduced, along with them, to an abstract representation, or mere appearance (Erscheinung). Ontologically speaking, the formal cause that is the sufficient reason of a route of inference falls under, is dialectically ordered to, some more general principle or mode of being, some “primary analogate” of being. Consider, for instance, the deductive itinerary of cognition177 that determines how, through reflectively thinking axiomatized (ordered) patterns of identity and distinction, a set of “sentences” in sym175  “Philosophy in the Last Forty Years,” p. 143. 176  As distinguished from the onto-epistemological classification of judgments, for example, into immediate and mediated forms, the mediated form entailing the act of reflective onto-epistemological position. 177  An existential, processive act—and the only composite mode in which form subsists, or “has its being,” namely as a so-called “concrete universal.”

270 Inference and the metaphysic of reason bolic logic may show as inconsistent in light of a set of derivation rules. This route of reflective cognition, to the extent that it is cogent, is itself ordered to the intelligible form of the complete set of the derivation rules that belong to a given system of sentential logic. The version of sentential logic in question composes a notional complex that, in its turn, falls under the more universal formal logic, a formative principle that the logicist posits absolutely, i.e., the logicist’s “primary analogate.” Formal logic is thus analogous in this sense to the extent that logicians apply it systematically to every domain of inquiry as the paradigm of precision and discursive cogency. It stands as a primary analogate by constituting the context of signification to which every application of bona fide philosophical logic is, from the (symbolic-) logical point of view, properly ordered. As primary in this respect, formal logic stands as the ultimate frame of reference to which the contemporary analytic epistemologists commonly refer in judging the rational intelligibility of meaning. (Alternative speculative orientations abound, of course. Reiner Schürmann, to cite an original and interestingly relevant recent example, finds that it is the “hegemonic fantasms”—first ejn, later natura, and now, in the modern epoch, self-consciousness—that have functioned as the primary analogate in Western intellectual culture.178 An example of a more immediately germane and persuasive account of the relation of meaning and being is Oliva Blanchette’s largely Aristotelian and neo-Thomist metaphysic. Blanchette argues, metahistorically, that the human being is our most fundamental primary analogate.179) 178  See Schürmann, Broken Hegemonies, trans. Reginald Lilly (Bloomington: Indiana University Press, 2003). 179  Cf., Blanchette, Philosophy of Being, §4.4. From the Thomist standpoint, the contemporary analyst is at bottom a mere social constructionist, a mechanistic materialist, a scientistic empiricist, or some combination of these. Rather than the human being in general, I would identify the living reflective intelligence—akin to Rousselot’s intellectualisme—as the primary analogate. Onto-theologically speaking, this reflects the Maimonidean doctrine that the human is the image of God in virtue of its rational intelligence. Aquinas understands the latter as the formal cause of the body, and hence it constitutes in his view the distinguishing principle of his hylomorphic account of human being as embodied soul (cf., ST QQ 75-79). (The student of German idealism will find in Fichte’s later thinking—where the Absolute I gives way to the I as Erscheinung of the Absolute—some suggestive parallels to Blanchette’s view of human being as primary analogate.)

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Assessing the validity of the sentential deduction is a matter of finding out whether its form-ordered articulation is consistent with (properly ordered to) the derivation rules. Depending on the sentences, the rules at issue, and the thinker, this task of assessment can be a virtually immediate, non-inferential affair. At the other extreme, it might entail subsidiary acts of reflection that lead to reevaluating whether the notional complex comprising the system of sentential logic in play is itself properly ordered, or assimilated, to the grounding principles, the most general axioms, of formal logic (as to a “prime analogate”). The latter paradigmatically exemplifies how the exercise of rational intelligence creatively objectifies, in a discursive currency of reflective spirit (Geist), instrumentally powerful regimes of significant fact. Short of our actually putting them to thought in symbolic form, these dimensions of being hardly make themselves felt as such, and in any case remain always inaccessibly remote to less evolved acts of intelligence.180 The point of the foregoing example is to suggest how, from an ontoepistemological point of view, in deductive inferences “being makes itself present in [the form of the] actual exercise of judgment [in inference, mediated judgment], without confusing being with the actual exercise of judgment.”181 The matter concerns the propriety of the order of premises in an inference. The premises are moments of relative positing—and always, as such (i.e., as ordered), in solution as it were. If properly ordered, that is, if the inference is formally cogent, the premises reflectively bring to discursive life a logically articulated (i.e., analogous) fact, the conclusion, as a form of Sein überhaupt—in which, as Blanchette remarks, “we find the most fundamental analogy of all.”182 The reason of this act—the determination of its validity—is an issue of formal cause. Put another way, the mediating judgment involves the relative positing of reflectively determinate premises properly ordered 180  For more on “remote” fact, see Appendix V, below. 181  The paraphrase is based on a comment in Blanchette’s unpublished reply to David M. Hammond, from a session devoted to Blanchette’s Philosophy of Being. College Theology Society—Annual Convention, Catholic University of America. Washington, D.C., June 2004. 182  From the standpoint of Blanchette’s Philosophy of Being, the conclusion of a cogent act of inference, as an analogate of being (and no mere term of discourse), constitutes the Grund of the unity, activity, truth, and goodness of the order actualized and rendered determinate as the totality of premises that reflectively conduce to it.

272 Inference and the metaphysic of reason to (in the process of rendering discursively explicit) the formal cause of what “shows” as conclusion, which for conceptual logic is the ground of the premises. This act of discursive intelligence is not to be confused with any particular form of being that it may concern, a lapse apparent in those heirs to the Kantian legacy who relativize absolute positing and seek to ground inference—to establish its sufficient reason—by appeal to some extrinsic efficient or strictly final cause. Although one hesitates even to mention him in the same breath with post-Kantian analytic epistemologists, Hegel—who by contrast can be seen as absolutizing relative positing—illustrates the metaphysical risks incurred by having recourse to a teleologically defined notion of sufficient reason. (Hegel would of course vigorously protest that in his system—namely, the System—the final cause is anything but extrinsic to acts of reflective intelligence. Still one might nonetheless remain skeptical that the inversion of the inverted world of the analytic epistemologists is the Concept.) It is worth recalling here the aporiai that the analytic inference theorists encountered in their efforts to explain the ground of the act of inference in terms of efficient cause. Rudolf Carnap, for instance, felt compelled to invoke “intuition” as in effect the ontological guarantor of the novice’s grasp (of meaning) when taught the idea of a deductive inference in a step-by-step manner. While Gilbert Harman, to recur to another example, identified the “valid principles of inference” as “those [psychologistic] principles in accordance with which the mind works”183—the being of the working mind guaranteeing, to Harman’s mind, the validity of the principles. 4.6 The onto-epistemology of inference and Ernst Cassirer’s approach to inductive inference: correlations and contrasts. The philosophy of inference with which the present work has the closest affinities is that of Ernst Cassirer,184 the preeminent critical idealist of the twentieth century. And taking up Cassirer at this juncture will go some way toward establishing this essay’s place in the philosophical history of scientific cognition. What’s more, critically probing Cassirer on this theme will suggest how the present work taps into some particularly deep-run183  See §2.3, above. 184  Cf., Substance and Function, trans. William Curtis Swabey and Marie Collins Swabey (New York: Dover, 1953).

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ning currents of speculative thought that cut across the nominal analytical/continental divide. Cassirer’s neo-Kantian explication of inductive inference stands as among the most historically attuned yet keenly analytic expositions of scientific knowing published in the century of Einstein. In Substance and Function (1910), Cassirer develops an account of scientific induction that is dimensionally more metaphysically self-aware, articulated, and cogent than those of the analytic epistemologists that we reviewed in chapter 2. By the same token, his thinking is more epistemologically analytic in the contemporary sense than either Lotze or Bosanquet, the two exemplary metaphysical logicians discussed in chapter 3. What above all recommends Cassirer’s doctrine for comparative assessment here are some defining correlations with the present account which provide a context for grasping how the inquiry into the conceptual logic of the reason of inference that has preoccupied us through the balance of this chapter penetrates regions of thought that the modern philosophy of scientific cognition (Erkennen) has too often unwarrantably and to its own detriment bracketed or ignored. 3 Cassirer’s doctrine evinces the same onto-epistemological tenor as the conceptual logic of inference investigated in the foregoing halfdozen sections of discussion. In observations that confirm as much, Cassirer argues that the “new logical value” accruing to a scientifically empirical inductive inference gives to “the particular” something that “cannot be understood” by recourse to “the mere repetition and arrangement of particular observations.” Indeed, the “mere accumulation of elements,” notes Cassirer, “cannot entirely change their conceptual meaning; it can only render more distinct the determinations already contained in the elements.”185 These perceptions comport with defining features of the conceptual logic of inference onto-epistemologically construed. The conclusion, the totality or Gesetztsein, of any cogent act of inference invests the “particular” subject—an otherwise formally unrealized remote fact—with a conceptually originary onto-epistemological value. However, as for what show, in the reflective dynamic, as premises properly ordered to the conclusion—these I cannot grasp as such if I construe the scheinen as “the mere repetition and arrangement [in, say, empirical science] of particular observations.” What shows as a premise in a route of inference, while not mere appearance 185  Substance and Function, pp. 246-47, emphasis added.

274 Inference and the metaphysic of reason (Erscheinung), is an identity manifest only as an ideational event of being, i.e., reflectively in its mutually determinating differences with other premises that are intelligible as such (hence composed) exclusively in an ordered route of thought. It is by that very token, however, that I apprehend, rightly or wrongly, the order as conditionally constitutive of the premise. I thus know the premise, as premise, to be an always already ordered, and in so far invariant, element of the sufficient reason of some significant fact—as a moment, that is, of formal cause. Each determinate element in a process of induction, says Cassirer, must contain “a factor” that “raises it out of its limitation and isolation.” This factor is, as he puts it, “the real kernel of inductive procedure…by means of which we trace an empirical content beyond its given temporal limits and retain it in its determinate character for all points of the time series.”186 What Cassirer distinguishes as the kernel of inductive procedure correlates with the formal moment in the ontoepistemology of inference. Most notably, he himself identifies as the “gesetzliche Form” that to which every element of the inductive “logical process of integration” necessarily refers.187 Cassirer’s critical idealism reveals in this particular a deeper kinship with the onto-epistemology of inference as investigated in the present work than any other account of which I am aware. Perhaps the most salient correlation that Cassirer’s philosophy of inference exhibits with the orientation at the heart of this book concerns the metaphysical theme of being as knowing, in Cassirer’s words, “the old question as to the relation of thought and being.”188 Cassirer spells out a view of inductive thinking that explains “the system of empirical knowledge” in terms of “an original unity” that transcends the opposition of “thought and being” in the various speculative guises that that opposition assumes. Here we see a neo-Kantian reading of the conceptual logic that informs the onto-epistemological philosophy of the reason of inference. It is an account that like the one developed in the body of this chapter conceives of the idea of inferential reflection holistically and in terms of an engagement with fact that transcends any binarism thought and being. 186  Ibid., p. 247, emphasis added. 187  Ibid. 188  Ibid., p. 271.

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Another shared core theme is the ontogenetic component of inference that distinguishes it as an onto-epistemological act. Cassirer introduces this theme in commentary on the formal component of “all empirical judgment.” It is in relation to this that he calls attention to an “advance from the mere process of sensation to definite ‘objective’ assertions….that make possible the judgment of natural science.”189 Cassirer’s observation assumes an overtly onto-epistemological character when he refers to the empirically mediated judgment (of natural science) facilitated by this “advance” as a “new form of knowledge,” a knowing that “transforms the data of sense into a new mode of being.”190 Except for the invocation of “sense data,” Cassirer’s genetic doctrine of inferential reflection is, in this particular, at one with the view expounded in the preceding sections of this chapter. While Cassirer’s “sense data” may appear equivalent to what ontoepistemologically “show” as premises in inferential reflection, any likeness is superficial. The position (Setzung) that sponsors the show (Schein) of premises is unintelligible, on the plane of “pure” thinking, apart from how what show as premises in a reflective judgment are ordered as such (hence grounded as determinate) to compose an intelligible totality. (The latter is a conclusion that is the immanent significance and the formal truth of fact prehended by reflective intelligence and hence rendered luminous as idea, fact that is otherwise inaccessibly remote for cognition.191) How it is that what show as premises conduce to conclusions is not simply a matter of things given (data) to me, but rather the way that remote facts are ideationally significant for me, so far as I put them to thought. This fundamentally breaks not with Cassirer’s move to identify the “new mode of being” with inductive inference, but rather with his representation of how it features in acts of inferential reflection. Cassirer represents the new mode of being as simply that fact about fact, which is to say, the mere circumstance that significant facts are ideationally realized in the act of inference. By contrast, while crediting that aspect of inferential cognition, the pres189  Ibid., p. 242. 190  Ibid. (emphasis added). 191  When an act of inference lacks cogency, what show as premises are deficient in the intelligibility that attaches to premises properly ordered to a conclusion. In such instances, one cannot offer any rationally defensible explanation of how particular scheinen could be premises in a particular train of reflective thought.

276 Inference and the metaphysic of reason ent work frames the construal of this cognitional process in terms of an additional feature of inference: the nisus of actualization that in the route of inferential reflection marks the dynamism of premises toward a conclusion.192 In other words, I approach concept formation in the act of inference by way of the thetic moment of position (Setzung), whereby spirit acts to conceptualize fact by rendering as idea the significance of fact as form. 3 It should be clear that Cassirer’s analysis of scientific inference is a seminal historical and philosophical antecedent of the account thought through in these pages. If consistent with leading elements of Cassirer’s Marburg neo-Kantianism,193 however, the present inquiry into the reason of inference is no exercise in neo-Kantian philosophy. To foreground the nature of the differences, we turn next to the most significant features of Cassirer’s doctrine of scientific thinking that stand at odds with the onto-epistemology of inferential reflection propounded here. When Cassirer talks of the tracing of “an empirical content beyond its given temporal limits” (cf., p. 274, above), he tacitly ascribes a dubious spectatorial dimension to the act of inference. To postulate such a spectatorial dimension is to conceive the act of inference as the process of following the movement of a “factor” that “raises” the particular “out of its limitation and isolation.” While this efficient moment in Cassirer’s doctrine does find a corresponding element in the onto-epistemology of inference, what it corresponds to is not an autonomously growing relation to universal rules or regulative principles. Rather, this formative ingredient of Cassirer’s inferentialism can be seen in the order that is intermediatingly ingredient in what show for me as particular premises, and in virtue of which the premises reflectively conduce to a conclusion. Hence, unlike Cassirer’s particulars, the premises of a coherent act of inference are onto-epistemologically posited, I would argue, only relative to a conclusion, to which they are intrinsically and

192  Something that betokens the reality of what the Thomist would identify as the “proportionality” of the intellect and the intelligible. 193  Cassirer was manifestly an exponent of the Marburg School of neoKantianism at least through his publication of Substance and Function.

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properly ordered.194 They thus exhibit anything but “limitation and isolation” as particulars. The feature of Cassirer’s reading of induction that perhaps most starkly distinguishes it, systematically speaking, from the onto-epistemological orientation is one that explicitly aligns it with the transcendental and categorial architectonic of Kant’s critical philosophy. The feature in question is “the harmony” that he postulates “between theory and experience,” which for Cassirer underwrites “an ultimate constant standard of measurement of supreme principles of experience in general.”195 This standard is something that he finds exhibited in “those universal elements of form, that persist through all change in the particular material content of experience,” formal moments whose disclosure is the very procedure of inductive thinking. Cassirer names “space and time…magnitude and the functional dependency of magnitudes” as “established elements of such form, which cannot be lacking in any empirical judgment or system of judgments.”196 These and other “invariants of experience” constitute a priori elements “because and in so far as” they are “contained” as “necessary” premises “in every valid judgment concerning facts.”197 Cassirer takes it to be a logical imperative of “inductive procedure itself ” that scientific empiricism be critically guided and epistemologically chartered by the a priori categories. On this count, maintains Cassirer, “the critical theory of experience” would “constitute the universal invariant of experience,” a regulative invariant, to be sure. Granting as much, it follows that the “procedure” of inductive inference “directly” compares with the “procedure of the ‘transcendental philosophy.’”198 As such, the comparison traces back to Kant’s Copernican Revolution (along with the powerful if unintended impetus that it gave to the rise of the modern epistemological hegemony that dominates the spirit of analytic philosophy). And it obtains notwithstanding Cassirer’s critical decision to adapt the transcendental schematism of the understanding 194  However, this is something that in any given concrete instance I grasp and assess as a matter of discursive— scientific—knowledge only after the fact. 195  Substance and Function, p. 268. 196  Ibid., p. 269. 197  Ibid. 198  Ibid.

278 Inference and the metaphysic of reason to his own purposes. This he did by regarding a priori principles as exclusively regulative—hence jettisoning Kant’s notion of constitutive a priori principles (and the idea of a faculty of sensibility that is discrete from the understanding).199 3 Cassirer, for his part, might well have taken a dim view of certain elements of the present work’s analysis of the onto-epistemology of inference, such as the notion of Schein. He would likely construe the attention devoted to “show” as evidence that this account involves a dubious “descriptive” element. A reply to any charge of this sort would begin by reasserting that in inferential reflection an idea is something that may show, in virtue of the significance or importance200 that some remote fact has for me (an existential not a descriptive postulate), as a premise that grows reflectively determinate vis-à-vis other premise terms with which it is ordered. Moreover, what it is that shows in a thetic act of intelligence is prompted by that felt significance.201 In addition, the reply to the criticism would concede that the ontoepistemological sense of “show” at issue here would be vulnerable to the charge of descriptivism, but only if were reductively prescinded from its purely functional character in discursive reflection. The phenomenon of “show,” as purely the event of manifestation or presence, does not in itself describe or constitute a description of anything in particular. Nor does what shows202 in the process of becoming reflectively determinate, as premises (posited as) ordered to a conclusion, correlate with anything like a passive impression or intuition. The fundamental epistemological register of this “show” so far as I prehend it in itself, i.e., unthematically, is what Karl Rahner discriminates as 199  Cf., Michael Friedman’s discussion of Cassirer’s modification of the transcendental logic, in A Parting of the Ways: Carnap, Cassirer, and Heidegger (Chicago: Open Court, 2000), esp. pp. 116-17. 200  On Whitehead’s reading of “importance” as a metaphysical principle or “ultimate notion,” see n. 147, above. 201  “Feeling,” as Bosanquet somewhere puts it, is “the form of all contact with reality”—an insight that, systematically developed in Whitehead’s notion of “conformal feeling,” captures the implications of “felt” as used here. See Whitehead, Process and Reality, pp. 56 and 113. 202  Which is not a “content” of show, as if the latter were some sort of container or horizon.

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mitgewußt: “an unexpressed co-knowledge of being as the condition of every knowledge of single beings.”203 3 To sum up. We have noted certain of Cassirer’s philosophical commitments that are at odds with the onto-epistemology of inference outlined in the present study. These disparities follow from his talk of data of sense, his subscribing to the idea that determinations may be “contained in” the generative moments of inference, and his conceiving scientific inference as an act wherein one spectatorially traces a self-developing empirical content. Finally, Cassirer’s thinking bears the stamp of a neo-Kantianism that belongs to the same milieu of intellectual history as do the analytic epistemologists, one in which epistemology is the sovereign referent (or “hegemonic fantasm,” in Reiner Shürmann’s vocabulary204). Cassirer’s underlying connection, on this score, with contemporary analytic epistemologists of inference is confirmed in his championing of an epistemological orientation for which “the critical theory of experience would constitute the universal invariant of experience.” That Cassirer’s doctrine falls under the aegis of the Kantian epistemological hegemony is a fact that obtains despite his effort to cast this functionally determined “invariant of experience” as a regulative moment, rather than as the constitutive moment it would be in an orthodox Kantian transcendental regime. The foregoing points of contrast confirm that the analysis of inferential reflection undertaken in the body of the present chapter could hardly qualify as a development of Cassirer’s neo-Kantian philosophy of inductive inference. Nonetheless, the two views of discursive intellection do have marked affinities. These affinities are arguably at least as important, if not more basic, than the matters upon which the two philosophies of inference stand at odds with each other. As we saw, the points if agreement range from the explicit focus on the onto-epistemology of inference and the affirmation of the ontogenetic nature of the act of reflective thinking, to the holistic conception of scientific inference and the recognition that the “real kernel of inductive procedures” is a determinating process, one that is logically integrative. 203  Hearer of the Word, trans. Joseph Donceel (New York: Continuum, 1994), p. 26. 204  See Broken Hegemonies, trans. Reginald Lilly (Bloomington: Indiana University Press, 2003), pp. 6-16 ff.

280 Inference and the metaphysic of reason 4.7 Conclusion. This fourth chapter, and with it the body of the investigation as a whole, concludes by highlighting the routes of inquiry that compose the constructive phase of the essay. The overview is in two parts. The first (a) singles out the insights of Kant, Hegel, and Bosanquet that proved seminal to the inception and development of the present work; it then identifies in each instance the issues over which the view developed here breaks with their thinking.205 The second part (b) enumerates the speculative concepts and passages of thought that this study has made bold to exploit in pursuance of its leading aims. a) Kant. The influence of Kant’s metaphysical notion of positing (Position oder Setzung)—the concept that he held to be “identical with the concept of Sein überhaupt”—helped to shape this inquiry in three principal ways. First, Kant’s early move to identify the relation of the thetic act with being in general played large in the thinking that precipitated the decision to venture an onto-epistemological investigation into the act of inference. Second, Kant’s distinction between absolute and relative Position proved valuable as a heuristic for assessing the speculative limitations of contemporary analytic epistemologies of inference. Third, Kant’s classification of absolute and relative positing was helpful in getting clear about the conceptual logic of inferential intellection—particularly with respect to the construal of premises as a function of relative onto-epistemological Position, and to the conclusion as a correlative moment of absolute Position (toward which premises are ordered). Betokening a further, if less direct influence is the consistency between Kant’s thinking on positing and the working assumptions operative throughout this study which relate to “fact” as for reflective thought. As here understood, “fact” for the reason of the act of inference, is any “what”—any thing-in-itself—as it is for us, i.e., as “this” or “that” (Dasein in the sense of Zugegensein) actually or potentially.206 “Thing-in-itself ” denotes in this context that to which Kant refers when he employs the expression “in and for itself ” in his explication of 205  Although to enumerate my debts to every important influence on this study would far outstrip the bounds of a brief summation, the reader who has followed the discussion through from the outset will appreciate how much is owed here to other seminal thinkers, from Aristotle and Aquinas to Lotze, Cassirer, and Heidegger. 206  See the chap. 1, n. 35, above.

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the speculative idea of positing. Here is the key statement: “If what is considered is not merely this relation [of a characterizing mark to that which it refers] but the thing posited in and for itself, then this being is the same as existence” (Wird nicht bloss diese Beziehung, sondern die Sache an und für sich selbst gesetzt betrachtet, so ist dieses Sein so viel als Dasein).207 Heidegger’s comment on this passage substantiates the correlation that obtains here. The expression an und für sich selbst does not mean: “something in itself,” something that exists unrelated to a consciousness. The an und für sich selbst we must understand as marking the distinction from what is represented as this or that with regard to something else. This sense of “in itself ” is already expressed in Kant’s statement, in his saying that being “is merely the positing.” This “merely” sounds like a limitation, as if the positing were something inferior to the reality, i.e., to the substantiality of a thing. There “merely,” however, indicates that being can never be explained by what any given being is, i.e., for Kant, by the concept.208

The seminal influence of Kant’s thought, however, by no means renders the approach to the reason of inference set forth in the body of this chapter “Kantian” in any systematic sense. Kant himself never integrates his metaphysical thinking on Position with his formally logical teachings on inference (Schluß). His formal logic is traditionally syllogistic, and his doctrine of a three-phase act of syllogistic judgment209 amounts to a conceptual logic that is in principle inconsistent with the onto-epistemology of inference. As for what Kant designated “relative” and “absolute” Position, one must turn to later thinkers to find integrations of these elements of the act of inference that are not grounded in the synthetic architectonic of a transcendental logic. Finally, and 207  Theoretical Philosophy 1755-1770, translated and edited by David Walford and Ralf Meerbote (Cambridge, Engl.: Cambridge University Press, 1992), p. 119. See the fuller citation of this passage, below, in the Appendix I.i. 208  “Kant’s Thesis about Being,” trans. Ted E. Klein, Jr. and William E. Pohl, in Pathmarks, ed. William Mc Neill (Cambridge, Engl.: Cambridge University Press, 1998), p. 342. 209  See above, Introduction, p. 35. Cf., Graham Bird’s remarks on Kant’s restriction of inference to syllogistic logic The Revolutionary Kant: A Commentary on the “Critique of Pure Reason” (Chicago: Open Court, 2006), p. 603.

282 Inference and the metaphysic of reason in a way that coheres with the transcendental idealism introduced in the first Critique, Kant arguably relativizes the absolute moment of Position by identifying the Being of the thetic act not, certainly, as a real predicate, but as transcendentally predicative. Thus rather than referring to the substantiality (Sachheit) that distinguishes things in themselves (which if accessible to awareness are not, like appearances, discursively knowable), the concept of Being as identical with that of Position oder Setzung refers instead to objective fact (i.e., as Gegenständigkeit) determined transcendentally in three modalities, namely as being possible, being actual, being necessary. In an ontological critique of Kant’s transcendental logic, Oliva Blanchette indicates the systematic liabilities that follow from what I have identified as the (categorial) relativizing of absolute Position: Unable to conceive being in its transcendentality as anything more than a bare positing, [Kant] was also unable to think of any per se properties of being as anything else than abstract categories in the univocal predicamental order and, because it was impossible for him to increase the number of categories, there was only one thing for him to do, which was to dismiss [such per se properties of Being as the One, the True, the Good] as irrelevant in any scientific investigation except for what could be reduced to the scheme of the categories already established for scientific investigation, a scheme that could accommodate all sorts of physical or empirical sciences, that is, particular sciences, but not a more universal science of being as being, even as given in experience.210

Hegel. Hegel understandably enough reads Kant as ultimately putting “reason into the service of the understanding”—an inevitable consequence of holding, as Kant does hold, that pre-reflective, absolute Position (and thus existence) is intelligible only through a discursively conceptual relative act of Position. The result? Kant “himself fell prey,” as Hegel remarked, to the “discursive mode of reflection in that,” like the dogmatic metaphysicians whose speculative orientation Kant discredits, “he isolated contrary determinations from the movement which brings about their synthetic unity.”211 The consequence, something Hegel censured already in his early Differenzschrift, is a restriction 210  “Analogy and the Transcendental Properties of Being as the Key to Metaphysical Science,” The Saint Anselm Journal 2.2 (2005): 12. 211  See Karin De Boer, “The Dissolving Force of the Concept: Hegel’s Ontological Logic,” Review of Metaphysics 57.4 (2004): 794.

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of scientific thinking to an order of “isolated reflection” that did little more than evidence the hobbling grip that an empirically straitened estimation of the onto-epistemology of human understanding had on Kant’s philosophical imagination. The spiritual itinerary of Hegel’s doctrine of essence, as it runs from Identity to Distinction to Ground, delineates, at virtually a single stroke, the principal stations of the conceptual logic of inference ontoepistemologically conceived. What’s more, Hegel employs throughout his exposition of essence the speculative conception of positing, and his formulations of setzende Reflexion and Gesetztsein do not incur the metaphysical difficulties that attach to the latent dualism of Kant’s distinction between absolute and relative modes of positing. Hegel’s description of essence as the show (Schein) in reflection of identity in difference effectively articulates how what show as premises in an act of inference realize their determinate sense in being posited relatively to each other (as moments constitutively ordered to a conclusion). Another element of Hegel’s account of essence that, on the level of “pure thinking,” elucidates the conceptual logic of inference is the dialectic of identity and distinction. This is a dialectic that does not entail sublation, but eventuates instead in a dynamic totality. Such is the dialectic, as well, of premises that in a coherent act of inference, i.e., as properly ordered to a conclusion, reflectively212 manifest determinate meaning as a totality, without canceling out one another. A third count on which the conceptual logic of essence as detailed by Hegel correlates with that of the onto-epistemology of inferential reflection is the fact that the totality of identity-in-difference is the truth of essence as ground/reason (Grund). As a core feature of inference this moment of conceptual logic is pivotal to rethinking, in an onto-epistemological register, the efficacy of Reason (understood, with Hegel, as based on the principle of sufficient reason) in ways that challenge the scientific concept of discursive knowing operative in analytic epistemologies of inference. Despite significant debts, however, this study breaks with Hegel on certain defining issues. One major point of divergence has to do with his privileging of the law of identity (in the manner of the later philosophical logicians of inference). Hegel complements the law of identity with a teleological notion of sufficient reason, which he introduces 212  Both in themselves and for each other, as determined by the discursive order of the topic.

284 Inference and the metaphysic of reason in the remarks appended to his lecture-outline statements on Grund. Hegel consequently restricts the reason of inference, unwarrantably I would suggest, to “formelle Vernunft, schließender Verstand”—i.e., to thinking that dialectically supersedes Verstand and Urteil by positing die Identität der Unterschiede. A second marked divergence follows from Hegel’s conception of Sufficient Reason as a principle grounded in final cause, rather than in formal cause (at least on the level of “pure thinking”). Hegel would no doubt argue that he certainly does not reject the principle of form on the plane of Denken, which is the phase or level of Geist to which the conceptual logic of inference is restricted. Indeed, he would insist that it is precisely as formal thinking that, in inferential reflection, “thinking stands...in a completely free relation to the object” (steht das Denken… zum Objekt in einem vollkommen freien Verhältnisse).213 This is because at this stage of reine Denken, “the universal is…no longer a form external to the content, but the true form that produces the content from itself, the self-developing Concept of the matter.”214 The upshot of such assertions, however, sets in high relief the motive for perhaps the most fundamental split with Hegel here. The systematic implication of the wahrhafte Form “that produces the content from itself ” is, in his view, that the being of thinking—and hence the actualization of what I term “remote” fact in the reason of the act of inference—is a moment of der subjektive Geist. This is the case, for Hegel, at least insofar as it is taken in abstraction from his metaphysic of the teleology of the Begriff. The onto-epistemological orientation to inference as presented in this essay eschews any metaphysical teleology of fact or Concept. Nor does it credit the dogma (one that Kant would have identified as a dialectical illusion) that the absolute end of Reason is, as Hegel takes it to be, self-consciousness215—rather than, say, creation, or the open questioning that is Heidegger’s piety of 213  Die Philosophie des Geistes, p. 287; [Hegel’s Philosophy of Mind, §467z]. 214  “…das Allgemeine nicht mehr eine dem Inhalt äußerliche, sondern die wahrhafte, aus sich selber den Inhalt hervorbringende Form,—der sich selber entwickelnde Begriff der Sache” (Die Philosophie des Geistes, §467z). See Hegel’s Philosophy of Mind, §§465-67; [Die Philosophie des Geistes, pp. 283-87]. 215  Cf.: “Reason, which is spirit in and for itself, and of which spirit is conscious in its existence, is the concept [sic].” Lectures on the Philosophy of Spirit 1827-8, trans. Robert R. Williams (Oxford: Oxford University Press, 2007), p. 200.

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thinking, or even forma formans as the determining act of communication of being in thinking. Bosanquet. The debt here to Bosanquet’s thought generally pertains less to the particulars of conceptual logic than to how the onto-epistemology of inference is fundamentally more rational than metaphysically less developed analytic epistemologies. Following Bosanquet, “mediation” has been taken here to be the signal factor that distinguishes inferential judgment from immediate judgment, i.e., judgment that is not of itself an active occasion of reflective thinking.216 In addition, Bosanquet’s doctrine of truth as ideal form adumbrates the understanding here of the reason of the act of inference. Also, consistent with the present orientation to inference are the assumptions that inform Bosanquet’s criticism of philosophies that privilege symbolic logic as the definitive instrument for elucidating the nature of inferential reasoning. Finally, Bosanquet’s masterly critique of “linear” inference refutes reductivist, analytic epistemologies of inference in ways that recommend the onto-epistemological alternative. The limitations of Bosanquet’s doctrine that perhaps most strongly impel one to look beyond his philosophy of inference include, above all, his failure adequately to address the requirement of a conceptual logic necessary for properly working out the onto-epistemology of the reason of inference. Another formal shortcoming arises in conjunction with Bosanquet’s assertion of the familiar idealist shibboleth that the truth is the Whole. The problem on this head becomes apparent when he applies this notion axiomatically, if with all manner of detailed examples, to explicate the logic of inference by effectively hypostatizing “implication.” 3 b) It will be useful at this point simply to enumerate the concepts and passages of thought that this essay integrates in ways that set in relief the nuanced character and force of its philosophical claims, and that suggest the far-reaching implications of its principal objectives: • The essay exploits to critical and constructive ends the onto-epistemological thetic implications of the com216  On Bosanquet’s problematic effort to distinguish a category of “true immediate inference”; see §3.5.1, above.

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•

•

•

•

monly misrepresented and undervalued speculative notion of Position oder Setzung. It retrieves and unpacks some of the more pregnant implications of the unwarrantably neglected insights into the philosophy of inference left us by Lotze and Bosanquet. It cashes out Hegel’s thinking on position (Setzung)— in the forms of setzende Reflexion and Gesetztsein—and more generally on the logic of essence, as these bear upon the conceptual logic of inferential reflection. It adduces the principle of sufficient reason as ground (Grund) of the reason of the act of inference. And, most notably, it determines that from the standpoint of the conceptual logic of the onto-epistemology of inference the principle of sufficient reason is as seminal as the principle of (non)contradiction, of identity, when understood as a function of formal cause. It finds, in a comparative critique of Cassirer’s analysis of scientific inference (in “The System of Relational Concepts and the Problem of Reality,” Part II of Substance and Function), the most material historical and philosophical precedent of the onto-epistemological approach to inference.

Coda. Fichte, Schelling, and Hegel took inspiration from the questions that Salomon Maimon raised about Kant’s first Critique. The principal challenge centered on the Transcendental Deduction, specifically Kant’s grounds for establishing how synthetic a priori concepts correspond to experience (an issue still at play, beyond historical debate, in the philosophy of mathematics and mathematical logic). The influence of Maimon’s famed Essay on Transcendental Philosophy (1790) is widely acknowledged to have initiated the transition from Kant’s critical idealism to the metaphysically informed speculative idealism (both transcendental and absolute) championed by the generation of great systematic thinkers that followed him. Indeed, as Frederick Beiser has put the matter,

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To study Fichte, Schelling, or Hegel without having read Maimon’s Versuch is like studying Kant without having read Hume’s Treatise. Just as Kant was awakened by Hume’s skepticism, so Fichte, Schelling, and Hegel were challenged by Maimon’s skepticism. What shook them out of their Kantian slumbers was Maimon’s attack upon the transcendental deduction….Maimon’s defense of the metaphysical tradition in his Versuch began a new chapter in the history of post-Kantian philosophy. It marks the decisive transition from critical to speculative idealism.217

As it bears on the philosophy of inference, Kant’s legacy from the period of the three Critiques relates at best indirectly to his formal typology of inferences: those of understanding, reason, and judgment (inference for Kant being a matter of general, not transcendental logic). Moreover, in the speculative field of inference Kant’s critical legacy has faced no such transformative challenge as the idealists mounted against the Critical philosophy. Hence it is hardly surprising that the leading philosophies of inference in our time remain critical in spirit. Indeed, when stripped to their epistemological working assumptions the various symbolic-logical, semantic, neo-pragmatic, mental-state, and other post-ontological schools that set out to explain the act of inferential thinking reveal in different ways the legacy of Kantian ontoepistemological dualism218 between scientific thought and the deliver217  The Fate of Reason: German Philosophy from Kant to Fichte (Cambridge, Mass.: Harvard University Press, 1987), pp. 286-87. 218  The perennial charge of dualism targets various aspects of Kant’s transcendental doctrine. The difficulties that I trace, however, reflect a concern with the onto-epistemology of inferential thinking. Consequently, they center on the Kantian problematic of relating absolute (existential) to relative (predicative) positing, a matter that the Kant of the Critical period would have referred to the dialectic of speculative reason. Hence the objections that I raise in this connection are emphatically not to be construed as a version of the traditional dualism charge, of which I remain skeptical. Cf., Henry Allison’s incisive analysis and his refutation of the prominent lines of attack on the apparent dualism in Kant’s transcendental idealism, in Kant’s Transcendental Idealism, revised ed. (New Haven: Yale University Press, 2004), chap. 1. Also see Karl Ameriks, “The Critique of Metaphysics: The Structure and Fate of Kant’s Dialectic,” in Ameriks’ Kant and the Historical Turn (Oxford: Oxford University Press, 2006), chap. 6, esp. pp. 143-49. From the perspective of the doctrine of intuition, Carl J. Posy makes a case for onto-epistemological isomorphism at the heart of Kant’s notion of truth, in “Immediacy and the Birth of Reference in Kant,” in Be-

288 Inference and the metaphysic of reason ances of sensibility, the imputed dualism that Maimon219 censured to such great effect. It is with this in mind that, in chapter 2, I undertook to show how an onto-epistemological assessment of this dualism in leading analytic epistemologies of inference discloses contradictions and heteronomies that compromise their rational cogency.220 Fichte, Schelling, and Hegel addressed the problematic of deductive thought and experience by incorporating, as Maimon himself proposed, certain traditional metaphysical themes that Kant repudiated (the primacy of “Being,” for example, an issue that looms as the proverbial elephant in Kant’s critical “room,” his “space of reasons”221). tween Logic and Intuition: Essays in Honor of Charles Parsons, ed. Gila Sher and Richard Tieszen (Cambridge: Cambridge University Press, 2000), esp. section III.B (“The Birth of Modern Reference”). 219  See Paul Franks, “All or Nothing: Systematicity and Nihilism in Jacobi, Reinhold, and Maimon,” in The Cambridge Companion to German Idealism, ed. Karl Ameriks (Cambridge, Eng.: Cambridge University Press, 2000), pp. 105-10; also see Beiser, “Maimon’s Critical Philosophy,” The Fate of Reason, chap. 10. My view of Kant’s thinking on Position (throughout his career) is consistent with what Graham Bird terms a “revolutionary” reading of Kant, one that interprets him—Bird’s special focus is on the first Critique—as concerned at bottom with the metaphysics of experience. Henry Allison is among those—including the likes of H. J. Paton, Gerold Prauss, and Arthur W. Collins—whom Bird singles out as leading exponents of the “revolutionary” Kant. This approach stands opposed to differing versions of the “traditionalist” account that construes the Critical project as properly understood strictly in terms of the framework of a normative foundationalist epistemology. Besides criticizing this hermeneutic orientation in work of leading commentators such as Strawson and Paul Guyer, Bird finds it problematically at play in Wilfrid Sellars’ influential construction of the “myth of the given.” Not surprisingly, the “traditionalist” orientation is common in analytic epistemologists of inference. See Bird, The Revolutionary Kant, esp. chap. 10, §1.5. 220  One hardly has to resort, with Maimon, to “infinite understanding” in order to appreciate the need, given the onto-epistemological limits of Kant’s critical philosophy, for a richer notion of discursive thought. 221  This phrase, a virtual refrain in writings of a Sellarsian like Brandom, should be appreciated in context. Cf. the following passage from Kant’s Prolegomena §57: “…our reason sees so to speak around it a space for the cognition of the things in themselves, although it can never have determinate concepts of them and is limited merely to appearances.”

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A unspoken aim of the present study has been to prompt something of an analogous shift in contemporary thinking on the reason of inference. Reflected as it is, here, in an inquiry limited to the onto-epistemology of inference, this ambition is considerably more modest than Maimon’s. Still, any move in this direction would have potentially farreaching ramifications. At the very least, the challenge to received doctrine would impel students of inference to rethink the analysis (and praxis) of discursive reasoning. The critical and constructive phases of this investigation have thus sought to inspire a transformation in the way that we conceptualize reflective intelligence, this by motivating a turn from conceptually narrowing critical routes of explication to a broader and deeper-running path of philosophical science. 3 This book has had a more ambitious aim, however, than simply to proffer a novel critique of leading views in inference theory and to present, in their stead, the elements of an onto-epistemological alternative. Its larger purpose has been to exercise metaphysical thinking that establishes an orientation to the reason of inference, an orientation that discloses a more radically formal connection between reason and what it means to be—indeed, to be human—than is readily countenanced, or even understood, in an intellectual culture that has lost much of its grip on both. As Oliva Blanchette has observed on just this score, we inhabit a milieu wherein, with respect to the conceptual logic of our ubiquitous acts of inference, “the principle of non-contradiction is no longer seen as the flip side of the principle of identity formally reducible to being itself.”222 This circumstance follows nothing so much as the endemic dis-integration of the intellectual and general cultural order that, through its self-defining permutations, has underwritten at every turn the truth of that metaphysical dictum of Blanchette’s that serves as an epigraph at the beginning of this book—namely, knowing is of being. We struggle in our post-Enlightenment cultural epoch with a subtle yet spiritually enervating onto-epistemological alienation—a philosophical and spiritual pathology that, under the aegis of the postKantian epistemological hegemony, has become largely normative in both the human and exact sciences. Needless to say, the stakes in effectively meeting this challenge are high. For it is through the intellectual and historical trajectory of the diremption of calculative from 222  Personal communication.

290 Inference and the metaphysic of reason meditative thinking,223—the bracketing of rationality from intellectualisme224—that we stand to lose touch practically with civilized thought. And with the consequent, all-too-predictable resurgence of what Vico named la barbarie della riflessione,225 we face a genuine risk of losing touch as well with informing sources of our very humanity.

223  In the Heideggerian conceptual idiom. Cf., Discourse on Thinking [Gelassenheit], trans. John M. Anderson and E. Hands Freund (New York: Harper, 1966). 224  “By intellectualism,” announces the transcendental Thomist Pierre Rousselot, “I understand a doctrine that places everything of worth, all of life’s intensity, and the very essence of the good, identical with being, in the act of intelligence: everything else can be good only by participation in it” (Intelligence: Sense of Being, Faculty of God, trans. of L’Intellectualisme de saint Thomas, by Andrew Tallon [Milwaukee: Marquette University Press, 1999], p. 1). [“J’entends…par intellectualisme une doctrine qui met toute la valeur, toute l’intensité de la vie, et l’essence même du bien, identique à l’être, dans l’acte d’intelligence, le reste ne pouvant être bon que par participation” (L’Intellectualisme de saint Thomas, p. 1).] 225  Cf., The New Science of Giambattista Vico, trans. Thomas Goddard Bergin and Max Fisch (Ithaca: Cornell University Press, 1984), “Conclusion of the Work”; and Donald Phillip Verene, Philosophy and the Return to Self-Knowledge (New Haven: Yale University Press, 1997), chap. 1 (“The Barbarism of Reflection”).

Appendices Reason, considered as the faculty of a certain logical form of cognition, is the faculty of inferring, i.e., of judging mediately (through the subsumption of a condition of a possible judgment under the condition of something given).

Immanuel Kant, Critique of Pure Reason (A330/B386) Nor is it an intelligible contention, even if favoured by the language of Kant in dealing with practical philosophy, that Reason could be actual and operative otherwise than as completing and containing the understanding. That the understanding must have its rights is one of the cardinal principles of Hegel, which Lotze has but laboriously and ingeniously illustrated….

Bernard Bosanquet, Logic (1911), Book II (Inference)

I. Onto-Epistemological Positing i. Kant’s originary conception of Position oder Setzung. Kant initially introduced Position oder Setzung in The Only Possible Basis for a Proof of the Existence of God (1763). Manfred Frank points out that in that early work “Kant, for the first time, presented in a coherent way his thesis concerning the two meanings of the indefinite verbal expression ‘Being.’”1 While the notion of onto-epistemological positing appears in writings as late as those collected in the Opus postumum,2 it is in The Only Possible Basis that, not yet forty and largely under Alexander Baumgarten’s influence,3 Kant famously declares that existence is neither a predicate nor a determination of a thing. Something not to lose sight of, however, is that Kant qualifies this assertion in the following 1  The Philosophical Foundations of Early German Romanticism, trans. Elizabeth Millán-Zaibert (Albany: State University of New York Press, 2004), p. 61. 2  Cf., Immanuel Kant: “Opus postumum,” ed. Eckart Förster, trans. Eckart Förster and Michael Rosen (Cambridge, Engl.: Cambridge University Press, 1995), pp. 178 and 193. 3  Cf., for example, the contrast that Kant draws between Wolff and Baumgarten on the definition of “existence,” in Theoretical Philosophy 17551770, translated and edited by David Walford and Ralf Meerbote (Cambridge, Engl.: Cambridge University Press, 1992), p. 121.

292 Inference and the metaphysic of reason way: “the expression ‘existence’ is used as a predicate. And, indeed, this can be done safely and without troublesome errors, provided that one does not insist on deriving existence from merely possible concepts…”4 Hence Kant recognizes and, with the requisite proviso, accepts common usage. Kant argues that predication pertains only to the merely possible— i.e., to that reality or perfection which may or may not be. Again, he does concede that one may “safely” employ “existence” as a predicate, but only so long as one does not insist on deriving existence from merely possible concepts, as one is accustomed to doing when one wants to prove absolutely necessary existence….when existence [Dasein] occurs as a predicate in common speech, it is a predicate not so much of the thing itself [dem Dinge selbst understood as an “unanalyzable concept”5] as of the thought which one has of the thing.6

These distinctions of Kant’s have to do with language use and “can only be judged adequately in the light” of further reflections “of a subtler and deeper kind,” reflections that he identifies in the title of the second subsection of his essay’s opening discussion: “Existence is the absolute positing [die absolute Position] of a thing. Existence is thereby also distinguished from any predicate; the latter is, as such, always posited only relative to some other thing.”7 Heidegger lends some valuable insights here, but prior to turning to his explication of Kantian Position, it will be well to adduce the passage from Kant that Heidegger singles out in this connection, a statement that amounts to Kant’s baldest assertion on the meaning of onto-epistemological positing: Der Begriff der Position oder Setzung is perfectly simple and identical with being in general [Sein überhaupt]. Now, something can be thought as posited merely relatively, or…merely as the relation (respectus logicus) of something as a characteristic mark [Merkmal] of a 4  Theoretical Philosophy 1755-1770, p. 118. 5  Theoretical Philosophy 1755-1770, p. 119. In this essay, Kant maintains “that the whole of our cognitions ultimately resolves itself into unanalyzable concepts” (ibid.). 6  Ibid., p. 118 (emphasis added); Cf. Immanuel Kants Werke, vol. II, ed. Ernst Cassirer (Berlin: Bruno Cassirer, 1922), p. 76. 7  Ibid., p. 119.

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thing. In this case, being [das Sein], that is to say, the positing of this relation [die Position dieser Beziehung], is nothing other than the copula [Verbindungsbegriff] in a judgment. If what is considered is not merely this relation but the thing posited in and for itself, then this being is the same as existence.8 [Wird nicht bloss diese Beziehung, sondern die Sache an und für sich selbst gesetzt betrachtet, so ist dieses Sein so viel als Dasein.9]

Alluding to this definition, the Heidegger of the 1927 lecture course on The Basic Problems of Phenomenology10 rhetorically queries his auditors, “Does everything stand in the clear, or does it stand in the dark as a result of the statement that being equals position?…What does ‘position’ mean?”11 He then immediately identifies “a synthesis present in the experience of an existent” that involves “the addition of a predicate to a subject,” but one that is distinguished by the fact that it “is not the synthesis of predication.” This critical distinction Heidegger employs to foreground the onto-epistemological purport of Kant’s notion of “absolute” positing. As Heidegger explains, “in absolute position the object of the concept, the actual being corresponding to it [the “thought-reference”], is put into relation as actual to the concept that is merely being thought.”12 Kant holds “absolute position” to refer to the act of setzen, whereby existence, in Heidegger’s words, “expresses a relationship of the object 8  Ibid., p. 119. 9  Werke, vol. II, p. 77. Respecting this point (when it appears in the more developed epistemological context of the first Critique’s second edition), Heidegger stresses that the an und für sich selbst “does not mean: ‘something in itself,’ something that exists unrelated to a consciousness” (“Kant’s Thesis about Being,” trans. Ted E. Klein, Jr. and William E. Pohl, in Pathmarks, ed. William McNeill [Cambridge, Engl.: Cambridge University Press, 1998], p. 342). 10  Trans. Albert Hofstadter (Bloomington: Indiana University Press, 1988). 11  Basic Problems of Phenomenology, p. 45. 12  Ibid. (emphasis added). This is a far cry from the tacitly dualist, analytically epistemological explanation, such as the following one by Paul Franks: “To posit a thing absolutely or unconditionally is to undertake the relevant commitments by affirming that a particular thing of that kind exists in an actual spatio-temporal location”; see All or Nothing (Cambridge: Harvard University Press, 2005), p. 308.

294 Inference and the metaphysic of reason to the cognitive faculty.”13 By invoking absolute position here, however, Heidegger elides Kant’s essential discrimination between Dasein and Sein—“the difference between predicative and absolute being” (a distinction that Fichte, for one, “found it necessary to point [to] explicitly,” as Ernst Cassirer observed14). Kant regards Sein as identical to Dasein only when one is positing not merely relatively, predicatively (i.e., in terms of the possible), but absolutely as well. It is precisely “through” the positing of relation that we understand being as existence, as absolute Position. This follows from the claim that appears in a statement with which Kant offers “to sum up everything in a representation which is sufficiently subtle to avoid confusion”: “nothing more is posited in an existent thing [Dasein],” he declares, “than is posited in a merely possible thing (for then one is speaking of the predicates of that thing).”15 The difference is that “through” an existent thing one is onto-epistemologically positing more than through a merely possible thing, for positing through an existent thing [Dasein] involves the absolute positing of the thing itself as well. Indeed, in mere possibility it is not the thing itself which is posited; it is merely the relations of something to something which are posited in accordance with the law of contradiction. And it remains certain that existence is really not a predicate of a thing at all.16

Heidegger is careful not to confuse the Setzung (understood as the relationship of the object to the cognitive faculty) with Being per se: “Being [Sein], to be sure, is not,” he insists, “identical with positedness, but 13  Basic Problems of Phenomenology, p. 45. 14  The Philosophy of Symbolic Forms, Volume 1: Language, trans. Ralph Manheim (New Haven: Yale University Press, 1955), pp. 316-17. 15  Theoretical Philosophy 1755-1770, p. 121. 16  Ibid. (emphasis added). The implications of this statement can be seen as informing the judgment of James Collins that Kant “is not really satisfied with any purely thing-and-object-ordered conception of being. He directs philosophical attention to the positing act wherein being finds its proper meaning and ground. In our human experience there are different senses of to-be, precisely because there are different positing acts to signify the logical and the real, the transcendental and the experiential, bases of being. Kant’s recognition of these different component sources of the meaning of being…lies at the root of the several kinds of existential ontology”; see Interpreting Modern Philosophy (Princeton: Princeton University Press, 1972), p. 313.

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positedness is the how in which the positing of an entity assures itself of the being of this posited entity.”17 Even if betraying an essentialism here with respect to Position as act, Heidegger’s reading seems truer to Kant’s meaning than Manfred Frank’s recent gloss. Frank asserts that in absolute position “the content of intuition is…granted Being.”18 That said, Heidegger’s 1927 treatment of Position has severe limits of its own. Over the course of an extended critique, details of which are not material here, Heidegger faults Kant for an unclear and dubious “positive interpretation” of “existence [Dasein] as absolute position (perception [sic]), being [Sein] as position in general.”19 This criticism rests in good part on an inference of questionable relevance, one that Heidegger draws from Kant’s later, transcendental epistemology in the first Critique. After citing a statement from B273 in which Kant asserts that the “perception…which supplies the material to the concept is the sole character of actuality,” Heidegger argues that perception is, for Kant, what “intrinsically bears within itself the reach to actuality, the existence or, in our terminology, the extantness, of things. Thus the specific character of absolute position, as Kant defines it reveals itself as perception”20 (at least for the Heidegger of 1927 reading it back into the 1763 text). Had Heidegger included the sentence from the first Critique that directly follows the one he adduces, he would have needed significantly to qualify the categorical equation that he imputes to Kant, namely “actuality, existence, equals absolute position equals perception.”21 For after stating that for the mere, pre-perceptual concept (which signifies only possibility) perception is the sole characteristic of actuality, Kant, now (1787), as transcendental epistemologist, adds: However, one can also cognize the existence [Dasein] of the thing prior to the perception of it, and therefore cognize it comparatively a priori, if only it is connected [zusammenhängt] with some percep17  Basic Problems of Phenomenology, p. 50; [Der Grundprobleme der Phänomenologie, Gesamtausgabe, vol. 24 (Frankfurt am Main: Klostermann, 1975), p. 68]. 18  Philosophical Foundations of Early German Romanticism, p. 62 (emphasis added). 19  Basic Problems of Phenomenology, p. 55; [Der Grundprobleme, p. 77]. 20  Ibid., p. 46. 21  Ibid.

296 Inference and the metaphysic of reason tions in accordance with the principles of their empirical connection (the analogies).22

Problematic though it proves in its critical purport, Heidegger’s early grasp of Kant’s exposition is nonetheless exemplary for how it brings to light the onto-epistemological implications of “Position” instinct in Kant’s thinking, implications that inform my critique of contemporary epistemologies of inference (cf., chapter 2, above). Over thirty years after the lecture course on Der Grundprobleme, Heidegger would straighten out the order of development in Kant’s philosophy of positing. Indeed, in “Kant’s Thesis about Being” (1961) he would make it his particular business to concentrate on the evolution of Kant’s conception of Position from 1763 to 1787. The late Heidegger wished to underscore that Kant, in his critical period, understood the efficacy of the laws of thought, not least among them the “law” of (non)contradiction,23 in light of the transcendental unity of apperception: not until and only if all logic [including inference as Kant understood it] remains ordered into the place of transcendental apperception can it function within the critical ontology related to the given of sensuous intuition, that is to say, as the guiding thread of the determination of the concepts (categories) and the basic principles of the being of beings.24

Does this mean that Kant ultimately managed to delineate the intermediating absolute and relative moments of onto-epistemological positing in a conceptual logic that amounts to the reason of the act of inference? Heidegger appears implicitly to affirm as much when he observes that Kant’s “[t]ranscendental philosophy has its ground in logic,” which “is no longer formal logic, but determined by the original synthetic unity of transcendental apperception.” Kant himself put it this way in his “Open Letter on Fichte’s Wissenschaftslehre, August 7, 1799”: Formal, “pure” logic “abstracts from the content of knowledge, 22  B 273. The appeal to “empirical Verknüpfung” at this juncture arguably foreshadows later difficulties—what amounts to Hume’s revenge—with which Kant wrestles in the Opus postumum. 23  For Kant “the common principle of all analytic judgments”; see Prolegomena to Any Future Metaphysics, trans. Peter G. Lucas and Günter Zöller (Oxford: Oxford University Press, 2005), p. 72. 24  “Kant’s Thesis about Being,” p. 349.

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[and] the attempt to cull a real object of logic is a vain effort….If the transcendental philosophy is correct, such a task would involve metaphysics rather than [formal] logic.”25 The transcendental logic of Kant’s metaphysical epistemology is thus what charters the real sense of inferential (scientific) thinking—something that arguably ontologically complements, if indirectly, his formal treatment of inference (Schluß) as properly deductive and syllogistic. It is in the transcendental logic, observes Heidegger that, for Kant, “ontology is grounded.” While in Kant’s critical doctrine a transcendental logic is at bottom what objectively determines predicative thinking (and by that token relative positing), Kant relegates the absolute (the ontological) purchase of such thinking—its ground in Sein überhaupt—to nothing more than “the use of the understanding.”26 In this connection, we find Heidegger, with Kant’s Sein überhaupt in mind, raising the ultimate issue: “What…is called being such that it can be determined by way of representational thinking as positing and positedness? This is a question Kant does not ask….”27 ii. Onto-epistemological positing in Frege’s and Russell’s reading of Kant. It is worth calling attention to a significant development in the history of modern philosophy that relates directly to how Kant applied “positing” as an onto-epistemological term of art. The matter concerns the familiar debate about the way of conceiving “existence” as a predicate. Gottlob Frege and, through him, Bertrand Russell believed that in mathematicized logical theory the existential quantifier incorporates the sense of “existence” with which Kant operates in the first Critique, specifically in the famous section refuting the Ontological Argument (A 592-603/B 620-630). Two of the most fundamental objections to this highly influential view, both of which analytic philosophers themselves have articulated, focus respectively on existence statements and on the very ascription of existence. The former is the emphasis, for example, of a well-known critique by Wilfrid Sellars, who suggested “that the phrase ‘existential quantification’ should be dropped”: 25  See Kant: Philosophical Correspondence, edited and translated by Arnulf Zweig (Chicago: University of Chicago Press, 1967), p. 253. 26  “Kant’s Thesis about Being,” p. 349. 27  Ibid., p. 360.

298 Inference and the metaphysic of reason there is no general correspondence between existentially quantified formulae and existence statements. Only in those cases where the variable which is quantified is a variable of which the values are singular terms will a quantified formula be the counterpart of an existence statement. Nor is this all; not even all (so-called) existential quantification over singular term variables has the force of an existence statement.28

An unanswerable criticism of Frege’s move to associate existence ascriptions with the quantification function in formal logic recently appeared in Richard L. Mendelsohn’s Philosophy of Gottlob Frege. Mendelsohn, who concentrates on Frege’s philosophy of language and his metaphysical assumptions, reminds us that Frege is “widely credited with providing a precise interpretation in the language of modern logic of Kant’s…well-known declaration: ‘Being is obviously not a real predicate.’”29 Mendelsohn demonstrates, however, that the relevant passage in Kant does not support Frege’s (and Russell’s) contention that “existence” is rather a property of properties than a property of objects, i.e., not a first-order property. Frege, it turns out, confided to a colleague at Jena that he introduced this onto-logical innovation “in order to explain how there can be informative existence claims,”30 since first-order predicates lack, he felt, the informative character of such claims. (One finds among the last writings of Donald Davidson an incisive critique of Frege on just this point.31) Next to Kant’s own restriction of inferential (discursive) thinking to relative positing, Frege’s historically influential denial that existence qualifies as a first-order property must count as one of the defining, formally logical consolidations that in the domain of analytic philosophy reflect the modern epistemological hegemony—with its attendant speculative amnesia respecting “the priority of being in knowing.”32 28  “A Preface to Ontology,” in Science, Perception, and Reality (Atascadero, Calif.: Ridgeview, 1991), pp. 255-56. 29  Richard L. Mendelsohn, The Philosophy of Gottlob Frege (Cambridge, Engl.: Cambridge University Press, 2005), p. 100. 30  Ibid., p. 101. 31  See Davidson, Truth and Predication (Cambridge, Mass.: Harvard University Press, 2005), esp. pp. 144ff. 32  Blanchette, Philosophy of Being, p. 27. For Stanley Rosen, Frege would doubtless be one of the fathers of “the nominalist versions of Kantianism which predominate among analytic philosophers,” whereby “they reject, or

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Yet by identifying existence33 as a property of concepts rather than of objects,34 Frege ironically inverted Kant’s own priority. By this means, he effectively chartered the onto-epistemological consequences of Kant’s failure to respect an ineludible issue of First Philosophy—the metaphysical imperative of addressing being as being—that shadows the Kantian speculative enterprise. (This lapse is most apparent where Kant loses sight of the a priori dimension of knowing as of Being, i.e., as an act of absolute positing, when he undertakes to explain how logic35 functions “within the critical ontology related to the given of sensuous intuition….”36) Mendelsohn sedulously elucidates the grounds upon which “Frege thought he had captured Kant’s view, [as did so] many who followed.”37 The decisive element—one that Mendelsohn doesn’t take occasion to probe—turns out to be the formative role that Position plays in Kant’s thought, something that Frege either discounted or ignored. Mendelsohn sums up his chapter-long analysis of Frege on “Existence” stressing just this issue: Is there anything in our discussion that leads one to think Frege’s attribution of existential import to the quantifier, as opposed to any first-order predicate, correctly captures Kant’s view? The only piece of the passage [A598-600/B626-28] unaccounted for is Kant’s saying that we posit the object. But positing is not connected in any clear way with a particular linguistic or mathematical form. Frege’s suggestion should be abandoned completely.38 have forgotten, synthesis as unspeakable”; see G. W. F. Hegel: An Introduction to the Science of Wisdom (Hew Haven: Yale University Press, 1974), pp. 84-85. 33  What Kant, discussing absolute positing in the Ontological Argument, refers to as Sein überhaupt einerlei; cf. Kant, Theoretical Philosophy 1755-1770, p. 119; [Werke, vol. II, p. 77]. 34  Cf., Frege: “Affirmation of existence is indeed nothing other than denial of the number zero. Since existence is a property of concepts, the Ontological Proof of the existence of God fails in its aim”; see “The Foundations of Arithmetic,” §53, trans. Michael Beaney; in The Frege Reader, ed. Michael Beaney (Oxford: Blackwell, 1997), p. 103. 35  As syllogistic, relative positing. 36  Heidegger, “Kant’s Thesis about Being,” p. 349. 37  The Philosophy of Gottlob Frege, p. 123. 38  Ibid., p. 124.

300 Inference and the metaphysic of reason iii. Speculative implications of Kantian positing for the philosophy of inference. Among the more distinctive elements of the present study is the contention that Kant’s two modes of Position oder Setzung, absolute and relative, provide a philosophically and historically significant frame of reference for considering the intrinsically metaphysical scope of the very notion of inference. Kant’s classification motivates and implicitly substantiates the turn in chapter 3, above, to the two now mostly neglected yet metaphysically grounded treatments of inference by Lotze (held to be the first neo-Kantian) and Bosanquet. The early (1763) discrimination of absolute from relative positing had important and, in the event, highly controversial ramifications for Kant’s own later, “critical” speculation.39 Eckart Förster explores this very issue in his book on Kant’s Final Synthesis, and he does so along lines that bear directly on the aims of the present work. While undertaking to explicate the “Ether Proof and Selbstsetzunglehre” in Kant’s Opus postumum, Förster summarizes Kant’s account of “positing” or “position.” He locates Kant’s original treatment of the theme in the 1763 monograph on the Only Possible Basis for a Proof of the Existence of God, where Kant first contended that being is neither a real predicate nor the determination of a thing. It is there, as we have seen, that Kant introduces the core working assumption at the heart of what he understands by Position: “The concept of position or positing is completely simple and identical with that of being in general” (Der Begriff der Position oder Setzung ist völlig einfach und mit von Sein überhaupt einerlei).40 Förster’s investigation helps to establish both the viability and the import of this metaphysical positing as an instrument of critique for assessing contemporary analytic epistemologies of inference. This it 39  Ramifications that Fichte significantly attempts to address by appeal to thetic judgment. Alluding to the second note of Fichte’s Foundation of the Entire Doctrine of Science, Thomas M. Seebohm discusses Fichte’s concept: “A thetic judgment is a judgment that does not stand under the principle of the ground. It is, rather, the ground of everything grounded, including the logical principle of the ground”; see “Fichte’s Discovery of Dialectical Method,” in Fichte: Historical Contexts/Contemporary Controversies, ed. Daniel Breazeale and Tom Rockmore (Atlantic Highlands, N.J.: Humanities Press, 1994), pp. 35-36. 40  Quoted in Förster, p. 77; cf., Kant, Theoretical Philosophy 1755-1770, p. 119; [Werke, vol. II, p. 77].

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does by clarifying what might otherwise seem merely a tenuous connection between Kantian Position and an onto-epistemological concern with the reason of inference. Underscoring the ontological dimension that Kant ascribes to Position, not to mention the all-important relative/absolute distinction that Kant makes when introducing the idea, Förster detects in Kant the doctrine that we “express” Being in two fundamentally different ways: either in the copula in a judgment “x is p,” where the predicate is posited in relation to the subject;41 or in an existential proposition “x is (exists).” Kant calls the former the relative position, in which a further predicate is posited in relation to the subject. In the latter, the subject itself, with all its predicates, is posited outside the concept or the judger. This Kant calls the absolute position, or existence [Dasein].42

That the act of Position, at least in the relative sense, entails inferential judgment is evident. If I put to thought a predicate in relation to a subject, I necessarily infer the predicative, more precisely here the enunciative character (whatness) of the predicate. I perform this cognitional act by means of the character of the relation—operative as a middle term, or the ground of one—that I consciously represent, judge, to hold between x and p. In his Logic (§17) Kant himself explains “Judgment as such” to be “the presentation of the unity of the consciousness of several presentations, or the presentation of their relation so far as they make up one concept.”43 And in Reflection 6350, from as late as 1797, Kant writes: “In every judgment there is a subject and a predicate. The subject of the judgment, insofar as it can contain various possible predicates, is the object. The predicates are all dependent upon the subject….”44 41  Cf. Dieter Henrich on relation and judgment, in “Identity and Objectivity: An Inquiry into Kant’s Transcendental Deduction,” trans. Jeffrey Edwards, in Henrich, The Unity of Reason: Essays on Kant’s Philosophy, ed. Richard L. Velkley (Cambridge, Mass.: Harvard University Press, 1994), pp. 137-38. 42  Kant’s Final Synthesis, p. 77. 43  Emphasis added. See Logic: Immanuel Kant, trans., with an introduction, by Robert S. Hartman and Wolfgang Schwarz (New York: Dover, 1988), p. 106. 44  Quoted in Dieter Henrich, “Identity and Objectivity: An Inquiry into Kant’s Transcendental Deduction,” p. 153.

302 Inference and the metaphysic of reason (What contemporary scholars think of as deductive inference Kant would class “determinate” judgment. Inductive inference, on the other hand, he would explain as a variety of reflective judgments—not, like deductive inferences (i.e., syllogisms), “but only logical presumptions or empirical conclusions.”45 Kant would likely dismiss on grounds of heteronomy the contemporary notion of inference that includes both deduction and induction. He might direct those interested in inference to investigate instead how, as a species of subsumptive determinate judgment, inferential thinking mediates between Verstand and Vernunft, specifically in view of how the latter regulates the former. Kant assigns “immediate inference” [consequentia immediata] to the Understanding.46 He associates mediate, deductive inference with Reason.47) So far as Kant’s view of “judgment” remained fundamentally consistent, the statements drawn from the Logic and Reflections raise doubts about claims such as Manfred Frank’s, that absolute positing (which as existential, ontological, is ante-predicative) is per se a judgment. “In the judgment ‘A exists,’” argues Frank, “the content of intuition is not covered over with a concept, but is rather granted Being: the subject is posited as such without any characterizing additions.”48 This statement comports with Kant’s decision, in the first Critique’s second edition, to reject “the explanation that the logicians give of a judgment in general: it is, they say, the representation of a relation between two concepts.” But Kant doesn’t say that what we intuit—the subject of a judgment—is “granted Being” through the act of Position. Indeed, as Heidegger indicates, Kant is concerned rather with a more primordial, ontologically disclosive unity—“the originally synthetic unity” (of apperception)—“a unity with which and into which it connects the given manifold.”49 Kant explains judgment as “nothing other than the way to bring given modes of knowledge to the objective unity of apperception.” Directly addressing the issue of absolute Position, he stresses that in the “modes of knowledge” or “cognitions” the “copula is” serves to distinguish “the objective unity of given representations 45  46  47  48  49 

Logic, §84. Cf. Logic, §§41-55. Cf. Logic, §§56-93. Philosophical Foundations of Early German Romanticism, p. 62. “Kant’s Thesis about Being,” p. 348.

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[Vorstellungen] from the subjective” unity (B 140-42).50 Here we see the onto-epistemological pedigree of absolute Position as the ground of knowledge for inference, and in contrast to the predicative character of relative Position. Of course, not all knowledge is inferential. Since existence is neither a predicate nor a real determination—how can one intelligibly judge any relation to exist between x and “is”? —absolute Position (simply positing x to exist) does not in itself involve an act of inference, although it is involved in (i.e., obtains in each particular case through) the relative Position of an existent. Here is Kant’s thinking on the matter: …I maintain that nothing more is posited in an existent thing [in einem Existierenden] than is posited in a merely possible thing (for then one is speaking of the predicates of that thing). But more is posited through an existent thing than is posited through a merely possible thing, for positing through einem Existierenden involves the absolute positing of the thing itself [absolute Position der Sache selbst] as well. Indeed, in mere possibility it is not the thing itself which is posited; it is merely relations [Beziehungen] of something to something which are posited in accordance with the law of contradiction.51

It is from this standpoint that Kant dismisses as “obviously very indeterminate” Christian Wolff ’s definition of existence as “a completion of possibility.”52 For Kant positing in is positing what, while positing through is positing how. If, following Förster, one reads Kant as saying that absolute and relative position both express Being, albeit “in two fundamentally different ways,” then one is hard pressed to see how Kant can assert that the expressive efficacy of one way is a constitutive moment of the efficacy of the other. The issue becomes quite plain when one turns to what is among Kant’s most explicit definitions of onto-epistemological positing: 50  Critique of Pure Reason, trans. Paul Guyer and Allen W. Wood (Cambridge, Eng.: Cambridge University Press, 1998), p. 251. 51  Theoretical Philosophy 1755-1770, p. 121 (emphasis added); [Werke, vol. II, p. 80]. 52  Ibid.

304 Inference and the metaphysic of reason something can be thought as posited merely relatively, or, to express the matter better, it can be thought merely as the relation (respectus logicus) of something as a characteristic Merkmal [feature/mark] of a thing. In this case, Sein, that is to say, the positing of this relation, is nothing other than the Verbindungsbegriff 53 in a judgment. If what is considered is not merely this relation but the thing posited in and for itself, then this being [Sein] is the same as existence [Dasein]. 54

Statements such as this may give the impression of a categorical (ontic/ontological) dichotomy, even incommensurability, between relative and absolute Position. Kant himself, however, would go no further than to assert that if one were to conceive of the subject of the absolute position as somehow the theme of a possible judgment, then that subject would be objective so far as its Vorstellung “contains,” not an existential ground, but rather “the ground of the synthetic unity of a manifold of predicates.”55 iv. Kant and the privileging of relative positing. Fatefully, and pivotally for the ways that the present inquiry diverges from Kantian philosophy, Kant’s most influential critical legacy is a de facto assignment of epistemological primacy to relative positing. On the plane of scientific knowing and praxis, this means that for all intents and purposes absolute Position itself is taken as relative to the relative act of positing. Needless to say, this tacit assumption engenders a cognitional orientation that cannot rationally assimilate the fact of absolute Position as an originary expression of Being.56 The thinking that confines understanding to the relative positing thereby disregarding the ontological 53  The Cambridge edition editors translate this as “copula.” But I take it that Kopula is the precise German analogue to the linguistic term and that Kant wishes to emphasize the intermediary, that is, the onto-epistemological status (as opposed to a merely semiotic one) of the act of positing a relation that articulates “something as the characteristic mark of a thing” (Ibid., p. 119). 54  Theoretical Philosophy 1755-1770, p. 119. 55  Dieter Henrich, “Identity and Objectivity: An Inquiry into Kant’s Transcendental Deduction,” p. 153. 56  Cf., chap. 3, above, which traces ramifications of this in how Lotze views the identity of Position with a “pure” Being conceived as a vacuous abstraction; also, see Lotze’s Metaphysic in Three Books: Ontology, Cosmology,

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dimension that Kant himself associated with the doctrine of Position57 contributed mightily, if indirectly, to the verständlich rationality that distinguishes the general run of analytic approaches to the problematic of thought and reality in our own day. Having early in his career distinguished absolute from relative onto-epistemological positing (yet identifying the concept of Position as such with the concept of Sein überhaupt), the Kant of the first Critique effects a metaphysical reduction of absolute to relative position, at least with respect to pure Vernunft. As it pertains to our concern with inference, Kant refers to a “determination of things in themselves”—absolute position. This allusion, as Karl Ameriks has observed, “amounts to the thought of an unconditioned item or set of items corresponding to each” of Kant’s three forms of the inference of Reason (Vernunftschluss), “namely, an unconditioned, i.e., unpredictable, subject of categorical syllogisms, an unconditioned (i.e., first) item for ‘the hypothetical synthesis of the members of a series,’ and an unconditioned (i.e., exhaustive) source for ‘the disjunctive synthesis of the parts in a system.’”58 This amounts to reducing the onto-epistemology of scientific reason, for the act of critique, to the understanding—since for the latter, being itself is conceptually known strictly in terms of three “pure concepts of reason”: being necessary, being possible, and being actual.59 These transcendental ideas originate in the forms (categorical, hypothetical, and disjunctive) of the inference of reason. and Psychology [1879], trans. Bernard Bosanquet et al. (Oxford: Oxford University Press, 1887), §10. 57  And which Kant himself ultimately addresses in terms of practical reason and reflective judgment. 58  Kant and the Historical Turn, p. 139. Ameriks refers here to A323/ B379. 59  Heidegger would dispute this, insofar at least as he finds that the “ultimate determination of being as positing is accomplished for Kant in a reflection on reflection….the positing of the actual proceeds out of the bare concept of the possible, out into the outside, over against the insight of the subjective condition of the subject” (“Kant’s Thesis about Being,” p. 358). Although Heidegger finds it at play there, Kant never expressly identifies onto-epistemological positing with transcendental reflection. Still, Heidegger rightly sees “Kant’s thesis about being as pure positing” reaching “back to the determination of being as uJpocei`sqai [substratum (known only analogically)], and points forward toward the speculative-dialectical interpretation of being as Absolute Concept” (ibid., p. 363). Indeed, in

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II. W. V. Quine and Onto-epistemological Positing Among analytic philosophers, it is W. V. Quine who characterizes “positing” in a way that perhaps most closely approximates the speculative onto-epistemological extension of the term that traces back to Kant. Discussing “Posits and Truth,” Quine argues that we never fully determine the truths of “ordinary things.” This follows, in his view, from the circumstance that the truths about molecules, for example, are underdetermined as captured “by any ideal organon of scientific method plus all the truths that can be said in common-sense terms about ordinary things.”1 Quine’s point about underdetermination is implicit in the Kantian classification of positing as “absolute” and “relative,” the latter—a particular instantiation—always underdetermining the former. Quine himself develops this thought with a view to the conception of “positing.” Indeed, his observations on this theme hinge on what, in a metaphysical move with medieval antecedents, he postulates as an analogy between absolute and relative positing: Considered relative to our surface irritations, which exhaust our clues to an external world, the molecules and their extraordinary ilk are thus much on a par with the most ordinary physical objects. The positing of those extraordinary things is just a vivid analogue of the positing or acknowledging of ordinary things: vivid in that the physicist audibly posits them for recognized reasons, whereas the hypothesis of ordinary things is shrouded in prehistory….To call a posit a posit is not to patronize it.…Everything to which we concede existence is a posit from the standpoint of a description Hegel one finds the objection that I am raising here appearing as early as the Differenzschrift; see Karin De Boer, “The Dissolving Force of the Concept: Hegel’s Ontological Logic,” Review of Metaphysics 57.4 (2004): 794. The problematic of conceiving how to understand the bearing on each other of absolute and relative positing is a correlate of the perennial aporia concerning the intermediation of infinite and the finite. (As influential a figure in German thinking as Spinoza sought to explain it in terms of implication; see Manfred Frank, Philosophical Foundations of Early German Romanticism, trans. Elizabeth Millán-Zaibert [Albany: State University of New York Press, 2004], p. 69.) 1  Word and Object (Cambridge, Mass.: MIT Press, 1960), p. 22; Quine’s emphasis.

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of the theory-building process, and simultaneously real from the standpoint of the theory that is being built.2

Three parallels stand out here with the Kantian notion of positing, so far as it figures in the onto-epistemology of inference. One is the association of existence with positing. A second is Quine’s tacit acknowledgement that rational spirit (Geist) uniquely contributes to existence through the act of positing, something that he would have us credit “from the standpoint of a description of the theory building process.” Quine establishes what amounts to a third parallel with Kant when he insists that “a posit” is “real from the standpoint of the theory that is being built.” This reality is, as he would have it, “simultaneous” with the existence of what is posited as that existence shows in the articulation of a “theory building process” that sponsors the “posit.” These parallels might give the impression that Quine implicitly operates with a view of inference that is deeply consistent with—if it does not actually anticipate—the onto-epistemological orientation explored in the present study. But there are elements in Quine’s remarks that signal some defining differences from the onto-epistemology of inference investigated in the foregoing chapters. A first point has to do with Quine’s assertion of an analogy between our typically unreflective positing of “ordinary” physical objects and the positing of extraordinary objects, like molecules, by scientists. How precise is such an analogy? When I unconsciously acknowledge the existence of the refrigerator that I open in search of a snack, do I perform anything analogous to an appeal to “recognized reasons,” as does the scientist in positing the molecular structure of the appliance’s colored enamel surface? From the perspective of the onto-epistemology of inference, the first “posit” is an act of immediate judgment—not an occasion of reflective thought (i.e., inference). On the other hand, the positing of molecular structure by the scientist is a reflective act, a mediated judgment that exemplifies inferential concept formation. The only basis for postulating an analogy here is by appeal to a notion of judgment that includes the dubious idea of “unconscious inference.”3 A second respect in which Quine’s view of positing differs from the one that informs this investigation involves his claim that “a descrip2  Ibid. 3  Cf., pp. 215-16 and 233.

308 Inference and the metaphysic of reason tion” of theory building process is the standpoint from which “Everything to which we concede existence [hence Sein überhaupt] is a posit.” Quine does not indicate that any other kind of concept formation beyond theory building entails onto-epistemological position. Hence his account seems to suggest that so far as an act of reflective judgment—of inference—is not a process of theory construction, thinking would not involve positing anything. This would disqualify the idea that “extraordinary” aesthetic, devotional, emotive, and any number of other atheoretical orders of inference engage and realize formalizable aspects of existence in concept formation. Is the process of concept formation plausibly reducible in this sense to descriptions of theory construction? Finally, to contend that that “to which we concede existence” is “simultaneously real from the standpoint of the theory that is being built” poses two difficulties from the viewpoint of the onto-epistemology of the act of inference. On the one hand, it reinforces the idea that speculative positing is restricted to formal theory building. This idea seems open to question, however, unless one engages to subsume under the category of “theory building” other modes of mediated judgment, such as acts of purely musical, poetic, emotive, and psychological species of inference (about which we commonly build theories). On the other hand, this contention of Quine’s fails to shed any light on what, with respect to the act of position, “real” means as something that in any given instance gets determined in view “of the theory that is built.” What is the common onto-epistemological principle—the principle of identity—among the heterogeneous “posits” that we make in the process of constructing different theories, the intelligible ground that vouchsafes their all alike being real? To address an issue of this sort without appealing to such dubious mainstays of analytic epistemology as “intuition” calls for a critical metaphysical effort at working out an onto-epistemology of inference—such as the effort in the present work to explicate the act of inference from the angle of its ground in conceptual logic.

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III. Lonergan, Kant, and Cognitional Theory Consistent with Kant’s project in the first Critique, one might well read his treatment of the Ding an sich as a verständlich effort to conflate, if only methodologically, relative and absolute Position oder Setzung. Kant could be seen as doing this in the interest of clarifying how, for the understanding, “the original meaning of Being is first fulfilled within the context of predication.”1 When Lonergan specifies “the essential difference” that sets his doctrine apart from Kant’s, he implicitly underscores the ontological consequences of Kant’s conceiving of pure reason on the basis of relative positing—as opposed to absolute Position, wherein “the subject itself, with all its predicates, is posited outside the concept or the judger.”2 The eleventh chapter of Insight sets forth Lonergan’s version of “something similar to what a Kantian would name a transcendental deduction.”3 Lonergan’s aim is to establish his non-Kantian idea of “self-affirmation” as a constitutive moment “in the possibility of judgments of fact.” (This signals Lonergan’s declared primary concern “not with the abstract properties of cognitional process but with a personal appropriation of one’s own dynamic recurrently operative structure of cognitional activity.”4) Lonergan endeavors to go beyond the limits of Kant’s system of insight by addressing two familiar targets of criticism. One is that despite Kant’s conviction as to the defining efficacy of the “boundaries of sensibility,” the “distinction between considering a thing ‘as we cognize it’ and ‘as it transcends our cognition’ could…not yield determinate conceptions of what might be true of the thing as it is being considered or referred to in each way.”5 The second issue that Lonergan seeks to resolve in his approximation of a Kantian “deduction” is essentially the methodological context of the first, namely that Kantian “theory 1  Manfred Frank, Philosophical Foundations of Early German Romanticism, trans. Elizabeth Millán-Zaibert (Albany: SUNY Press, 2004), p. 62. 2  Eckart Förster, Kant’s Final Synthesis (Cambridge, Mass.: Harvard University Press, 2000), p. 77. 3  Insight: A Study of Human Understanding (1958. San Francisco: Harper, 1978), p. 339, emphasis added. 4  Ibid., p. xxiii, emphasis added. 5  Allen W. Wood, Kant (Oxford: Blackwell, 2005), p. 75.

310 Inference and the metaphysic of reason reaches its thing-itself [sic] by turning away from the thing as related to us by sense or by consciousness.”6 Lonergan interprets “self-affirmation…as a concrete judgment of fact.” It is a contingent fact, however, one established “not prior to our engagement in knowing, but simultaneously with it.” This element of Lonergan’s “cognitional theory” is something that he represents as improving on Kant because it “reaches its thing-itself by understanding itself and affirming itself as concrete unity in a process that is conscious empirically, intelligently, and rationally.”7 What warrant does Lonergan have for this claim? The ground of his insight is something that he secures not in the act of “demonstrating that one can know, but pragmatically by engaging one in the process.”8 Most significantly, he declares at this juncture that in “the last resort” one cannot “reach a deeper foundation than that pragmatic engagement.”9 Here, in bold relief, Lonergan affirms the defining modernist epistemological and Anglo-American coordinates of his thinking—elements in composition, as we saw (§2.6.2), with his formal doctrine of inference. Few would deny the persuasive force of the “realism” and the “action” that distinguish from abstract thinking a pragmatic engagement understood as self-affirmation “considered as a concrete judgment of fact.”10 But to propose pragmatic engagement as a foundational onto-epistemological moment, one that putatively settles the perennial Kantian debate over how I know the “thing itself ”—this is to incur some knotty speculative difficulties. For instance, the pragmatic can involve instrumental or irrational contingencies that might be incompatible with or even vitiate, on a given occasion of “engagement” in the process of knowing, the “contingent fact” that Lonergan declares to be the “ultimate basis of our knowing.”11 As for the action of engagement, Lonergan would need to square his postulate with the following Kantian view, enounced by Blondel, on the condition of the possibility of conscious initiative. “Conscious action,” Blondel observes, “finds its explanation and its total reason only in a principle irreducible to the 6  Insight, p. 338. 7  Ibid., p. 338. 8  Ibid., p. 332, emphasis added. 9  Ibid., emphasis added. 10  Ibid. 11  Ibid., p. 332.

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facts of consciousness as well as to sensible phenomena; it is conscious of its own initiative only by attributing a character of infinitude and transcendence to itself.”12

12  Action (1893): Essay on a Critique of Life and a Science of Practice, trans. Oliva Blanchette (Notre Dame, Ind.: University Press, 1984), p. 123.

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IV. The Challenge of Epistemological Critique to Bosanquet’s Inferentialism The fifth section of chapter 2, above, discussed the epistemologist Michael Williams’ critique of coherence theories and radical holism. Williams, we saw, raised objections to these two views that do not apply to Bosanquet either as a coherentist or a holist. Having briefly touched upon Bosanquet’s thought in that section and subsequently reflected at length, in chapter 3, on the defining elements of his philosophy of inference, we are in a position to appreciate how, in his own terms, Bosanquet would have defended himself against two criticisms that Williams levels at coherence theories. Although Williams never names Bosanquet, by the standard of Williams’ own passing if mainly secondhand references to British idealist and holist thought, Bosanquet would qualify as a prime target of his criticisms. The first objection “is that, since coherence reduces in the end to logical consistency, and since there is no limit to the number of consistent systems of statements, there is no limit to the number of ‘justified systems.’”1 Bosanquet, it turns out, had met just such an objection. Toward the end of the 1911 edition of his Logic is where Bosanquet, who restricts rational justification to the self-determinating limits of our experience, rebuts this “‘many-systems’ objection.” One gets a telling sense of the disparity in the caliber of philosophical thinking between Williams and Bosanquet by permitting the latter to speak to the issue with all of the understated authority of his own voice: Sometimes we are told that our criterion is mere formal consistency. This can mean nothing but that the critic has not thought the matter out to the bitter end. By coherence or consistency we mean the consistency, so far as attainable, of the whole body of experience with itself. Nothing less would satisfy the law of individuality or the necessity of non-contradiction. But in this interpretation of consistency comprehensiveness is obviously included.2

1  Problems of Knowledge: A Critical Introduction to Epistemology (Oxford: Oxford University Press, 2001), p. 214. 2  Logic, Or the Morphology of Knowledge, 2 vols., 2nd ed. (London: Oxford University Press, 1911), vol. II, p. 267.

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Ironically, Williams himself regards the appeal to “comprehensiveness” as “an important corrective to the emphasis on systematicity”3 The second of the two challenges that Williams levels—“the ‘isolation objection’”—urges that since coherence theory “makes justification supervene exclusively upon belief-belief relations, [it] fails to allow for empirical constraint: constraint by the world.”4 Bosanquet would have rejected outright the idea that one can reduce philosophical logic to talk of mental states (beliefs, commitments) exclusive of their actuality as “phases into which objective apprehension under certain conditions may fall.”5 Further, he would have charged the epistemological critic with compounded confusion for fancying that a system of objective idealism such as Bosanquet’s is out of touch with the world. If anything, the “isolation objection” might hold against subjective idealism. But even so, and allowing, as Williams explains, for “empirical constraint” on beliefs, its ‘corrective’ betokens the very vice that Bosanquet censured in repudiating the thinking of John Dewey (among others), whom Bosanquet quotes as supposing logic “to grow out of the epistemological problem” of knowledge.6 Dewey insisted on referring to Bosanquet’s philosophical logic as “a general logical theory”

3  4  5  6 

Problems of Knowledge, p. 120 (emphasis added). Problems of Knowledge, p. 119 (Williams’ emphasis). Logic, vol. II, p. 300. Logic, vol. II, p. 271. Decades later, Dewey was to criticize Bosanquet’s discussion of “comparison” along lines that reflect my own objection to Bosanquet’s onto-epistemologically privileging of the law of identity. Dewey, moreover, offers a contrasting account that can be seen as consistent in certain respects with my orientation to the reason of inference provided that, in remarks such as the following, one reads Setzung for Dewey’s “institution”: “[W]hat is meant by comparison is institution of selected facts on the basis of equivalent (similar) evidential force in a variety of cases which are existentially different, this determination being grounded only as the operations of observation involved in the selection eliminate, pari passu, other existential constituents as irrelevant to the problem in hand”; see Logic: The Theory of Inquiry (New York: Holt, 1938), p. 184. Missing from this description is an adequate treatment of the formal cause, the intelligible ground from which equivalence derives “evidential force”—its reason—and to which the act of comparison is as such ordered, in so far as it is an act of reflective intelligence (i.e., is inferential).

314 Inference and the metaphysic of reason and identified it with epistemology.7 Bosanquet was categorical on this point: in “Logic as I understand it…there is no epistemology in the sense supposed,” that is, epistemology as any “theory of cognition” with its vestigial dualism (as one sees, for instance, in Williams’s dichotomy of “beliefs” and belief-constraining empirical reality). Instead, argued Bosanquet, philosophical logic, in “analyzing the thought-world… holds itself to be analyzing the [very] structure of reality, the detailed and articulated responses by which the living body of experience exhibits its endeavor to approximate as a system of ideas to a non-contradictory whole.”8 The Whole to which Bosanquet alludes is no mere system of beliefs, but “the whole of reality” as it grounds every inferential judgment—regardless of how partial or lacking in actuality the “partial system” is to which that judgment refers.9 This whole is no “background system” to which one fits thoughts, or partial systems of thought. Rather, it is the immanent truth of each individual thing, attested, in Bosanquet’s view, by the very nature of implication itself. As such, “the whole is always the unit of value,” whose “form of truth is individuality, and cannot be reduced to specified combinations of premises or to reasonings under principles.”10 In his last major work, Bosanquet puts his case with a trenchant conceptual elegance: “Apprehend this partial system—so an inference from a supposition [a hypothetical conditional] says—as continuous with the real universe, and, reality being what it is, so and so must result.”11

7  See Bosanquet, Logic, vol. II, p. 271. Bosanquet’s logic is essentially ontoepistemological (cf., §§3.5.1-3, above). 8  Logic, vol. II, p. 271. 9  Even the “completest system” is, for Bosanquet, no more than the system of the moment, a system that you can test for further coherence (as an ideal rendering of “truth and reality”) only when “you are in a position to make it more complete” (Logic, vol. II, p. 267). 10  Implication and Linear Inference (London: Macmillan, 1920), p. 164. 11  Ibid., pp. 4-5.

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V. Reflection on the Reason of the Act of Inference Human discursive intelligence reflectively apprehends significant facts that are of unprecedented orders of remoteness, compared to those grasped by other cognizing creatures or to those evident as the manifest phenomena of nature at large.1 This human cognitional capacity evidences a penetrative power that transcends, dimensionally, the analogous visual power of the eagle, the gene’s miraculous power of biophysical memory, the very power of light to transect galaxies.2 In the living moment of the reflective act I grasp elements—“signifying” elements, “informing” elements—that are no more than mute potentials in the eagle’s sight and the gene and starlight, elements that prove to be facts of the world common to all three. Absent their being realized in the ephemeral dynamism of cognitional reflection, these facts are remote from any particular immediacy, although wholly immanent and, for the human thinker, potently significant. So far as they are unrealized as things that actually become what show in reflective intelligence, such remote facts are for me merely tacit (“passive”) ontoepistemological potentials of otherwise effectively actual (wirklich) matter, truth, or spirit (Geist). When remote facts actually show forth in routes of reflective thinking, they do so exclusively in a sponsoring thetic act. The latter establishes them as states of fact that are both in and of our thinking (hence no ideational form/content distinction properly obtains here). This thetic act is what a seminal current of German scholarship from Kant to Reiner Shürmann has treated as onto-epistemological “positing” (Position oder Setzung, in Kant’s phrase). It is unique to the reflective, inferential intelligence whose esse is to know, and whose knowing is in itself a synoptic fact and an originary form of being. This inferential luminosity of spirit, “announcing” the truth of the priority of act over potency, discloses the world as a universe of significance. 1  On the idea of “fact” referred to here, see chap. 1, n. 31. 2  From this standpoint, no such neo-Kantian ontological distinction is admitted as between Tatsachen der Natur and Tatsachen des Geistes (Dilthey), which so far as it actually obtains is a fact restricted neither to nature nor to human cognitional spirit.

316 Inference and the metaphysic of reason Those remote orders of facts that we have the ability to infer are hardly gifts exclusive to the scientific discursive thinker. Far from it. Great artists, for example, have always realized the worth of such orders of facts in ways that enable us more deeply to value every facet of lived experience and our fate in a world that eludes the understanding at every turn. For that reason the true masters of discursive thought keenly appreciate the artist’s work, cherishing the revelation of radically enhanced or previously unsuspected value as an impetus to develop the understanding and to recognize the disclosures of aletheic value as its reward. The artist may grasp the significance of facts—for aesthetic or moral or even reflective life-experience—without understanding them in the ascetically abstract terms of formal thought. It could hardly be otherwise given that the cognitional idiom of artistic intelligence is, in the first instance, visionary.3 The signal performances of artistic judgment are unmediated, pregnant with the unarticulated complication (complicatio) of remote fact perfected as vivid powers of presentational form4: in the telling sweep of a curve, for instance, the beguiling plangency of a melody, the epiphany of a dramatic image or gesture. Rather than primary concern with the instrumental explication (explicatio) of facts as such, the artist articulates the human implications of even the most remote facts as qualitative moments of being.5 The truth of those facts, rendered visionary in the work of art 3  “Visionary” in this sense is no figurative allusion or analogy parasitic on ocular vision. “Countless forms of this visionary aptitude exist”—so Dilthey, whose thinking on this theme correlates in some defining respects with my own. See “Poetry and Lived Experience,” trans. Christopher Rodi, in Poetry and Experience, Volume V of Wilhelm Dilthey: Selected Works, ed. Rudolf A. Makkreel and Frithjof Rodi (Princeton: Princeton University Press, 1985), p. 252. 4  For the Lockean, qualitative. Cf., Locke’s views on Quality as the Power to produce “the immediate object of Perception, Thought, or Understanding,” in the Essay Concerning Human Understanding, ed. P. H. Nidditch (Oxford: Oxford University Press, 1978), book II, chap. 8. 5  This is the artist’s orientation to the fundamental onto-epistemological question that Josiah Royce set himself to address in his socio-hermeneutic version of idealism: “The world is itself a world of fact—the question being what the idea of fact turns out to mean”; see Metaphysics, ed. William Ernest Hocking, Richard Hocking, and Frank Oppenheim (Albany: State University of New York Press, 1998), p. 242.

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(i.e., its Werksein), is what the artist thus makes accessible as actualities (Wirklichkeiten) in composition with the human spirit. The defining difference between aesthetic and discursive inference—ultimately more a matter of degree or emphasis than of kind— is that the former celebrates presentational experience as a disclosive power and enhances the vital nisus of the perceptual intelligence; whereas the latter, a function of form-ordered discursive reflection, perfects the understanding. The discursive genius thus cognizes intelligible facts in acts of inference that exercise and educate (bildet) the understanding. Any “felt”6 implications or intuitions of remote fact, so far as they have importance for the thinker (and the more remote an intelligible fact, the more universal its import), occasion mediated judgments, inferences, that reflectively realize fact as ideal, “intellected” form.7 This is the form instinct in the intelligibility of the actual, and the ground, or sufficient reason, of the act of inference—it is the logical principle of actualization (Wirklichkeit) and the coach of spirit.8 Speaking to the onto-epistemological ground of the philosopher’s motivation to explore these matters in a systematic and critical way is a remarkable passage from the Summa theologiae of Aquinas which identifies the context within which the student of nature or the arts might first come to grasp, and at various points think through, the philosophical problematic of the act of inference: “…beauty,” observes Thomas, “looks to the cognitive power….And since knowledge comes about through assimilation, and similitude looks to form, the beautiful properly pertains to the notion of formal causality.”9 6  “Feeling” understood here to be, as Bosanquet’s somewhere puts it, “the form of all contact with reality.” 7  Cf. Thomas Aquinas: forma intellecta est universalis sub qua multa possunt comprehendi  (De Malo, q. 6, a.1). 8  This human (rational) spirit, the Thomist would stipulate, itself possesses the proper amplitudo and extensio of form in order to be able to entertain fact as ideal in the first place. 9  I, q. 5, a. 4; see Thomas Aquinas: Selected Writings, edited and translated with an Introduction and notes by Ralph McInerny (London: Penguin, 1998), p. 350. I would submit, although this is not the place to argue the point, that the act of inference manifests the beautiful insofar as the act is true to its principle of sufficient reason, namely formal cause. (It is a “perfection” insofar as that which motivates it and that toward which it is properly ordered are good.)

318 Inference and the metaphysic of reason The intelligible order composing an inferential act of thought is not itself fact as given, but rather the what-it-signifies in ontogenetic, if fugitive exercises of reflective cognition. From this standpoint of evanescent intellection—the standpoint of coming to be and ceasing to be10—the order that informs an act of inference is something that I am alive to initially as felt significance (potential), albeit only inchoately conceptualized significance. It does not merely “dawn” upon me as the passive recipient of an idea,11 but rather calls forth efforts at ontoepistemological positing or, better, efforts at position that can realize, as intelligibly manifest and ultimately a totality, the formal moment that sponsors the itinerary of discursive thought.12 The coherent act of inference proceeds from premises to conclusion as the reflective determination of distinction. As an activity that answers the imperative formally to determine the rational and instrumental signification of fact, the coherent inference is thus irreducibly a dynamism toward a holistically articulated meaning. Through the completed route of ordered reflection of premises, the act of inferential judgment renders explicit a conclusion, a total conception. This inference, through the course of the reflective act, comes to be in the spiritual shape (Gestalt) of an emergent moment of cognition. As forma formans, the ordering principle of an occasion of inferential thinking is intrinsically dynamic and cognitionally instrumental. The thinker thus entertains facts as the very terms of understanding, not just as concepts or ideas for organizing experience. In the crucible of cognitional life facts thus come to life—the life of spirit—in the character of formal features of reality coming-into-being (gevnesi~ eji~ ojusian) invested with ideal meaning. By the same token, as Aristotle 10  Which, for the living intelligence, is coming to be and ceasing to be simply (wesentlich); while vis-à-vis the fact per se, it is secundum quid. 11  Gilbert Ryle, for one, speaks of inference as an operation whereby some subsistent, articulate meaning, the “force of an argument,” as Ryle has it, “does not flash, but only dawn, upon the thinker, much as the meaning of a stiff piece of Latin unseen does not flash, but only dawns, upon the translator”; see The Concept of Mind (New York: Barnes & Noble, 1949), pp. 299-300. 12  This correlates, as we saw above in chapter 4, with leading phases of Hegel’s logic of essence; cf. The Encyclopedia Logic, trans. T. F. Geraets, W. A. Suchting, and H. S. Harris (Indianapolis: Hackett, 1991), §128.

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and Hegel have taught, such features of reality are the constitutive, not merely regulative, values or powers of intelligence.13

13  Joseph Maréchal is an instance of a transcendental Thomist who sought to delineate this orientation by building on Kant (“the patient pioneer”). As Anthony M. Matteo explains in his book on Maréchal, “Kant recognizes the fundamental drive of the human intellect toward the absolute or unconditioned as the ground of the ideas of reason. But he maintains that, since the absolute is not an object of direct experience [a view that one discerns tacitly at play as early as Kant’s 1763 distinction between absolute and relative Position oder Setzung], and since the categories of the understanding can only legitimately synthesize experience-based data, the mind’s admitted dynamism toward the absolute can play a ‘regulative,’ but not a ‘constitutive,’ role in the cognitive process.” Maréchal undertook to “complete” Kant’s thinking by demonstrating “that this dynamism gives us access to the noumenal or metaempirical realm and has a ‘constitutive’ role in cognition, without appealing to an immediate intuition of the metaphysical absolute”; see Quest for the Absolute: The Philosophical Vision of Joseph Maréchal (DeKalb, Ill.: Northern Illinois University Press, 1992), pp. 88-89.

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index A absolute positing (Position [Ger.]), 19n, 20, 22, 42, 44, 50n, 64, 94, 98, 100, 105, 111, 116, 117, 128, 165, 167ff., 214, 224, 235, 237, 243, 248n, 251n, 265, 280ff., 292ff., 309. See also positing act of being, 25, 156, 222n, 235n act of inference (inference as act), 11, 13ff., 58, 64, 68, 69, 72ff., 80n, 95, 98, 102, 107, 108n, 110, 111, 113, 114n, 121, 123n, 124, 126, 127, 130, 134, 135, 144, 145, 147, 153n, 154ff., 161ff., 168n, 170ff., 185, 188ff., 195, 197ff., 211, 214, 217, 220ff., 226-241, 234ff., 246ff., 267, 269ff., 280, 281, 296, 303, 308, 315. See also inference; onto-epistemology of inference act/content binarism, 126 Action (1893) (Blondel), 9n, 311n Adamczewski, Zygmunt (“Kant’s Existential Thought”), 19n, 43n, 47n Adickes, Erick, 45n Adventures of Ideas (Whitehead), 17, 135 After Jena: New Essays on Fichte’s Later Philosophy (Breazeale and Rockmore), 50n “All or Nothing: Systematicity and Nihilism in Jacobi, Reinhold, and Maimon” (Franks), 288n All or Nothing: Systematicity, Transcendental Arguments, and Skepticism in German Idealism (Franks), 293n

Allard, James W., 181n, 198n, 205, 265n; The Logical Foundations of Bradley’s Metaphysics: Judgment, Inference, and Truth, 190n, 263n Allison, Henry E., 34, 43, 288n; Kant’s Transcendental Idealism, 29n, 43n, 87n, 110n, 287n Ameriks, Karl, 51n, 219n, 305; Kant and the Historical Turn, 28n, 36n, 43n, 287n, 305n “Analogy and Logical Demands,” (Knasas), 219n, 248n “Analogy and the Transcendental Properties of Being as the Key to Metaphysical Science” (Blanchette), 282n “Analogy as Supra-Conceptual” (Knasas), 219n, 248n “The Analogy of Being” (Blanchette), 219n, 248n Analysis of Science in Aristotle (Byrne), 87n, 223n, 230n, 268n analytic epistemology(ies) of inference, 5, 11, 13, 18, 55, 72, 74, 77, 113, 133, 136, 147, 148, 153n, 175, 176, 207, 280, 283, 285, 288, 300 anticipatory inference (Lonergan), 123n “Appearance and Essence” (Schlick), 89n apperception, objective unity of (Kant), 20 Aquinas, St. Thomas, 15n, 41n, 120, 122n, 226n, 246n, 252, 253, 270n, 280n, 290n; on formal cause, 270n, 317; on meaning, 247n;

336 Inference and the metaphysic of reason De Malo, 227n, 317n; Summa theologiae (ST), 247n, 317. See also Thomism (Thomist) Aristotle (Aristotelian), 24n, 27, 73n, 86, 87, 99, 119, 122n, 152, 155, 156, 159n, 175, 177n, 178, 205, 212, 223, 224, 230, 244n, 246, 261, 268, 270, 280n, 318; Posterior Analytics, 87n, 223, 246n, 268n Articulating Reasons (Brandom), 95n, 97n, 99n, 100n, 104n, 178n artistic intelligence (judgment), 316. See also judgment “Autobiography” (C. I. Lewis), 141n

B Badiou Alain (Being and Event), 139n la barbarie della riflessione (Vico), 290 The Basic Problems of Phenomenology (Der Grundprobleme der Phänomenologie) (Heidegger), 293, 294n, 295n, 296 Baumgarten, Alexander, 26, 291 Begriff (Hegel), 14, 15, 27, 28, 51, 78n, 101, 244ff., 256, 257, 267ff., 284 Being and Event (Badiou), 139n Being and Some Twentieth-Century Thomists (Knasas), 122n, 219n (“Analogy and Logical Demands,” “Analogy as Supra-Conceptual”), 225n, 248n (“Analogy and Logical Demands,” “Analogy as SupraConceptual”) Being and the Between (W. Desmond), 157n, 246n

Beiser, Frederick (The Fate of Reason: German Philosophy from Kant to Fichte), 286; “Maimon’s Transcendental Logic,” 126n; “Maimon’s Critical Philosophy,” 288n Beisichseiende des Seins, 200, 256 Beisichsein des Seins (Rahner), 256 Between Kant and Hegel: Lectures on German Idealism (Henrich), 49n, 215n Beyond Realism and Idealism (Urban), 144n Bird, Graham (The Revolutionary Kant), 36n, 281n, 288n Blackburn, Simon, 72, 73, 74; “Metaphysics,” 73n Blanchette, Oliva, 16, 65, 90n, 99, 115, 123n, 125, 238n, 253, 267n, 270, 271, 282, 289, 311n, 250, 251, 265, 268, 271, 272 WORKS: “Analogy and the Transcendental Properties of Being as the Key to Metaphysical Science,” 282n; The Perfection of the Universe According to Aquinas, 246n, 253n; Philosophy of Being, 23n, 29n, 115n, 116n, 125n, 141n, 219n, 233n, 248n, 260n, 270n, 271n, 282n, 298n; “Suárez and the Latent Essentialism of Heidegger’s Fundamental Ontology,” 57n Blanshard, Brand, 99n, 104n, 142, 151n, 179n; The Nature of Thought, 142n; Reason and Analysis, 87n, 142n Blondel, Maurice, 90, 115n, 310; Action (1893), 9n, 311n

3 index Bonjour, Lawrence (In Defense of Pure Reason), 128, 129 Boole, George, 24, 62n, 139 Bosanquet, Bernard, 21, 22n, 23ff., 32, 37ff., 47, 58, 75n, 76, 78, 80n, 92, 99n, 102ff., 114n, 126, 128n, 131, 133ff., 150ff., 164, 170n, 175, 177ff., 213, 214, 236n, 237, 258n, 261, 273, 278n, 280, 291, 300, 305n, 312ff., 317n; as philosophical logician of inference, 179-185; criticism of Dewey on epistemology; 103n, 313; on implication, 13, 24, 37, 88n, 128n, 134, 141, 183, 188ff., 199ff., 240, 285, 286, 314 ; on linear inference, 3, 102, 103, 104n, 108, 186, 285; on reason and inference, 185, 194, 196, 203; systematic philosophy of inference, 197-201 WORKS: The Distinction between Mind and Its Objects, 21n, 103n; Implication and Linear Inference, 24n, 88n, 107n, 108n, 109n, 133, 136n, 150n, 180, 187n, 188n, 191n, 193n, 194, 197ff., 207, 314n; Logic, Or the Morphology of Knowledge, 24n, 25n, 58n, 80n, 86n, 92n, 103n, 107n, 126n, 127n, 133, 136n, 140n, 150, 181ff., 190n, 191n, 194, 195n, 196n, 201n, 202n, 213n, 236n, 237, 261n, 291, 312, 313n, 314, 312n; Meeting of the Extremes, 144n, 181n; Principle of Individuality and Value, 107n, 180n; Value and Destiny of the Individual, 80n, 180n, 191n “Bosanquet and the Problem of Inference” (Allard), 181n, 205n “Bosanquet on the Ontology of Logic and the Method of

337 Scientific Inquiry” (Wilson), 109n, 189n Bowne, Bordon P., 151 Bradley, F. H., 24, 73n, 83, 90, 103, 104, 133n, 137ff., 141n, 150, 151n, 179n, 180n, 181, 190n, 201n, 213, 263n; Essays on Truth and Reality, 104n; Principles of Logic, 83n, 90n, 104n, 133n, 137n, 213n; “On Inference,” 83n “Brandom Beleaguered” (Fodor and Lapore), 96n, 98n, 100n “Brandom, Hegel, and Inferentialism” (Rockmore), 77n Brandom, Robert, 12, 36, 37, 55, 77, 78, 81n, 94-102, 104, 106n, 110ff., 117, 118, 125ff., 136, 144, 152n, 178, 288n WORKS: Articulating Reasons, 95n, 99n, 100n, 104n, 178n; Making It Explicit, 101n; “Overcoming a Dualism of Concepts and Causes,” 95n, 97n; “Reason, Experience, and the Philosophical Enterprise,” 96n Brentano, Franz, 40n, 45, 46, 48 Broad, C. D., 80ff.; Induction, Probability, and Causation, 82n; “On the Relation between Induction and Probability,” 80 “Broad on Induction and Probability” (von Wright), 82n Broken Hegemonies (Schürmann), 23n, 44n, 45n, 270n, 279n Brouwer, L. E. J., 27n, 86n, 268n Brouwer’s Intuitionism (van Stigt), 86n Buber, 30

338 Inference and the metaphysic of reason Byrne, Patrick H., 223, 224, 230; Analysis of Science in Aristotle, 87n, 223n, 268n

274; positing, 52-53; symbolische Prägnanz, 219; transformation of data of sense into new mode of being, 275; universal invariant of experience, 277, 279; C Werk-Phänomen, 52; Wirkenscalculative reason (rational Phänomen, 52, 53 indeterminacy of ), 209 WORKS: Logic of the Cultural canon of relevance (Lonergan), 122, Sciences, 223n; Philosophy of 123 Symbolic Forms, 20n, 31n, 52n, 63n, 120n, 150n, 187n, 190n, Carnap, Rudolf, 12, 22n, 36, 37, 192n, 193n, 227n, 234n, 236n, 39n, 55, 68, 77, 78-91, 102, 110, 240 n, 252n, 294n; Substance and 112, 114, 117n, 118, 122ff., 136, Function, 120n, 158n, 193, 206, 144, 147, 152n, 171, 199n, 272, 226 n , 272 n, 272, 276n, 277n; “The 278n; intuitive plausibility, 86; on System of Relational Concepts inference and probability, 79-82; and the Problem of Reality” on intuition in inference, 79, (Substance and Function), 286 83n, 84ff.; Grundrelationen, 53; Ordnungssetzung(en), 53, 82n, 84n, “Cassirer’s Advance Beyond Neo85, 100, 214, 220n Kantianism” (Werkmeister), 52n WORKS: “Euclid’s Parallel cause. See formal cause; efficient Postulate,” 87n; “Inductive cause Logic and Inductive Intuition,” Change in View: Principles of 79; “Induction and Statistical Reasoning (Harman), 91n, 92n, 93 Probability,” 68n, 79; The Logical Structure of the World (Der logische Chattopadhyaya, D. P. (Induction, Probability, and Skepticism), 79n Aufbau der Welt), 53n, 83n, 84n, 85; The Logical Syntax of Clarke, Norris, 123n Language, 89 coherence theory (coherentism, “Carnap’s Theory of Induction” coherentist), 103, 104, 312, 313 (Nagel), 79n Collingwood, R. G., 11 Cassirer, Ernst, 20n, 31n, 39, 62, Collins, James (Interpreting Modern 82n, 120, 144, 150, 153, 158, 159, Philosophy), 294n 169n, 170n, 187, 190n, 192, 193, complicatio, 316 205, 210, 219, 223, 226, 227, 234, 236, 237, 240, 286, 294; approach concept formation, 16, 27, 33, 38, 91, 96, 120, 150, 151, 158n, 193n, to inductive inference, 272-279; 199, 204, 214, 217, 239, 240, 276, Basis Phenomena, 52, 193n; 307, 308 concept of Life, 252; constants of the second level, 226; functional concept of Life (Cassirer), 252 “substructure” of exact knowledge, 158n, 193n, 279; gesetzliche Form, The Concept of Mind (Ryle), 31n, 234n, 318n

3 index The Concept of Nature (Whitehead), 144 conceptual logic, 12ff., 23, 26ff., 33, 36ff., 51, 85, 98, 102, 111, 124n, 156, 158, 163, 168n, 173ff., 190, 193, 198ff., 213, 215, 217, 221, 230, 234, 235, 239ff., 249, 251, 253, 254-267, 272, 273, 274, 280ff., 296, 308 conclusion (of inference), 11, 13, 26, 27n, 30, 31, 55, 58, 68, 69, 70, 79, 80, 81, 90, 92, 95ff., 108, 111, 118, 119n, 128, 150, 173ff., 182, 184, 185, 188, 189, 191, 203, 207, 211, 214, 217, 218, 220-224, 226, 229ff., 247ff., 248, 251, 252, 253, 261, 268, 271ff., 283. See also meaning; totality “Concrete Inferences from Classical Laws” (Lonergan), 122, 123n “The ‘Concrete Universal’” (Bosanquet), 107n conformal feeling (Whitehead), 278n Connell, Desmond, 123n, 147; Essays in Metaphysics, 146n, 147n, 247n constants of the second level (Cassirer), 226 “content” of thought, 33 Copi, Irving M. (Introduction to Logic), 60n, 119n  copula (copulative), 24, 163, 214, 301, 302; Kopula vs. Verbindungsbegriff, 304; Verbindungsbegriff, 293; Verhältniswörtchen, 20 (Kant) critical epistemic mass (M. Williams), 105, 125

339 critical idealism, 39, 210, 226, 272, 274, 286 critical metaphysic(s), 37, 39, 56, 65, 210, 308 critical realism, 121 Critique of Practical Reason (Kant), 251n Critique of Pure Reason (Kant), 18, 19n, 20n, 34n, 35n, 36n, 43n, 77, 229n, 281n, 291n, 303n Critique of the Power of Judgment (Kant), 31n, 101n, 110n Cusanus (Nicholas of Cusa), 150n, 225n

D Dahlstrom, Daniel O. (Heidegger’s Concept of Truth), 162n Dasein (Kant), 14, 135, 165, 265, 281, 292ff., 301, 304 Davidson, Donald (Truth and Predication), 249, 250n, 298 “The Davos Disputation and Twentieth-Century Philosophy” (Friedman), 53n De Boer, Karin (“The Dissolving Force of the Concept: Hegel’s Ontological Logic”), 282n, 306n deductive, 107, 108, 169, 234; inference, 59, 70, 81, 88, 89, 104, 110, 111, 122, 123, 147, 262, 271, 272, 297, 302; intuition (Carnap), 87, 89; logic, 13, 59n, 63, 67ff., 83, 84, 86, 174; principles, 69; thinking, 32, 67, 68, 70, 79n, 83, 89, 91, 118, 146, 175, 184, 258, 269, 288 The Depictive Image (Stambovsky), 212n

340 Inference and the metaphysic of reason Descartes (Cartesian), 21, 87n, 109, 112, 115, 150n, 165, 248 Desmond, William (Being and the Between), 157n, 246n Dewey, John, 80n, 103n, 179n, 313; Logic, 313n “Dialectical Cycles of Intuitionist Method” (Weissman), 84n Dilthey, Wilhelm, 315n, “Poetry and Lived Experience,” 316n Discourse on Thinking (Heidegger), 290n discursive intelligence, 30n, 123n, 184, 214, 216, 222, 226n, 227, 237, 239, 240, 261, 272, 315 “The Dissolving Force of the Concept: Hegel’s Ontological Logic” (De Boer), 282n, 306n The Distinction between Mind and Its Objects (Bosanquet), 21n, 103n Drobisch, Moritz, 46 Dupré, Louis, 40, 41n (The Enlightenment and the Intellectual Foundations of Modern Culture), 241 (Passage to Modernity) dynamism, 58, 114n, 176, 177, 206, 211, 215, 217, 235, 252, 276, 315, 318, 319n dunamis (dunami~), 14, 125n, 155, 156, 228

E efficient cause (causae efficientes), 15, 29, 129, 160, 161, 195, 245n, 265n, 272 Elements of Analytic Philosophy (Pap), 76n

The Elements of Christian Philosophy (Gilson), 235n The Emergence of Whitehead’s Metaphysics: 1925-1929 (Ford), 191n Encyclopedia Logic (Die Wissenschaft der Logik (Hegel), 14, 15n, 28n, 34n, 78n, 218n, 219, 230n, 231n, 238n, 244, 245n, 246n, 251n, 256n, 257n, 263, 264n, 265n, 266n, 268n, 318n energeia (ejnevrgeia), 14, 114n, 155, 156, 212, 231, 239, 246, 260 The Enlightenment and the Intellectual Foundations of Modern Culture (Dupré), 41n entailment, 82, 93. See also rules of entailment entgegengesetzt (Novalis), 49, 244n epistemic significance (M. Williams), 104, 106 epistemology of ratiocination (Ryle), 31 Erkenntnis (scientific cognition), 38 An Essay Concerning Human Understanding (Locke), 316n Essays in Radical Empiricism ( James), 106n Essay on Transcendental Philosophy (Maimon), 286, 287 Essays on Truth and Reality (Bradley), 104n esse, 235n, 241, 247n, 315 essence, 17, 47n, 76n, 89n, 176, 177, 217, 241; l’essence même du bien (Rousselot), 290; logic/doctrine of (Hegel), 16, 25ff., 51, 77n, 121, 163, 218, 219, 230, 235, 242, 244, 245, 254-268, 283, 286, 318n; of

3 index judgment (Bosanquet), 181, 183, 190; Santayana’s Realm of, 166 essentialism, 56, 57n, 295 “Euclid’s Parallel Postulate” (Carnap), 87n event(s), 68, 69, 82n, 121n, 123, 139, 155, 156, 158n, 162, 165n, 166, 218, 219, 222, 252n, 256, 274, 278 Exceeding Our Grasp: Science, History, and the Problem of Unconceived Alternatives (Stanford), 72n “Existence and Judgment” (Connell), 146n explicatio, 316

F fact(s), 11, 16, 30n, 31, 33, 43, 59, 60, 61, 70n, 71, 84ff., 96, 99, 115, 121n, 124n, 131n, 147, 155, 162, 173, 176ff., 202, 208n, 209, 214ff., 250, 251, 253, 257, 260, 261, 271, 274ff., 315-318; fact for us, 30n, 35, 114, 197, 280; of consciousness (Fichte), 48, 262; remote fact(s), 14, 29n, 102, 202n, 203, 205, 214ff., 227, 228, 229, 234, 235, 239, 269, 273, 278, 284, 315; Aristotle on, 223; Blondel on, 311; Bosanquet on, 189, 197, 204; Carnap on, 79; Cassirer on, 193n, 226, 277; H.W.B. Joseph on, 200n; Lonergan on, 309, 310 Fact, Fiction, and Forecast (N. Goodman), 70n The Fate of Reason: German Philosophy from Kant to Fichte (Beiser), 126n, 287, 288n

341 feeling, 254; Bosanquet on, 183, 254, 278n, 317n; conformal (Whitehead), 278n Ferrarin, Alfredo (Hegel and Aristotle), 244 Fichte, J. G. (Fichtean), 30n, 45, 48ff., 77n, 112, 116n, 126n, 168, 170n, 173, 174, 214n, 215, 220, 224n, 254, 262, 270n, 286ff., 294, 296, 300n; Wissenschaftslehre, 30n, 48, 50, 112, 214n, 296; The Science of Knowing: J. G. Fichte’s 1804 Lectures on the Wissenschaftslehre, 30n, 214n “Fichte’s Discovery of Dialectical Method” (Seebohm), 300n “Fichte’s Intersubjective I” (Wood), 215n “Fichte’s Parergonal Visibility” (Wurzer), 49n, 50n, 224n Fichte’s Transcendental Philosophy (Zöller), 50n final cause, 15, 29, 135, 156, 159ff., 178, 239, 244ff., 263, 266, 272, 284. See also teleology Fisher, Mark, and Watkins (“Kant on the Material Ground of Possibility: From The Only Possible Argument to the Critique of Pure Reason”), 19n, 36n First Philosophy, 22, 24n, 25, 56, 75, 146, 299 Fitzpatrick, Joseph (Philosophical Encounters: Lonergan and the Analytic Tradition), 130n Floridi, Luciano (“Information”), 24n Fodor, Jerry, 64, 66, 99; “What is Universally Quantified and Necessary and A Posteriori and

342 Inference and the metaphysic of reason It Flies South in the Winter?”, 64n, 93n; and Lapore, “Brandom Beleaguered,” 96n, 98n, 190n Force of Imagination (Sallis), 217n Ford, Lewis S.( The Emergence of Whitehead’s Metaphysics:1925-1929), 191n form, 12n, 13, 15, 27, 32, 34, 43, 58, 88, 106, 110n, 117, 122, 124n, 125, 126, 133, 135, 185, 186, 190n, 191n, 193, 199, 207, 212n, 214, 217, 227, 230, 234ff., 253ff., 261, 268ff., 284, 285, 299, 315, 317; diremption from content, 250; for Bosanquet, 25, 137, 207; for Hegel, 238, 263, 266-267; for Lotze, 158n, 173ff.; formcause, 223 (Aristotle); gesetzliche, 274 (Cassirer); substantial, 253; intelligible, 176, 247, 268, 270. See also formal cause forma formans, 15, 31n, 119n, 161, 176, 185, 190n, 211, 237, 241, 247, 285, 318 forma formata, 31n, 190n, 228, 239 forma intellecta (Aquinas), 227, 236, 317n Formal, Transcendental, and Dialectical Thinking: Logic and Reality (Harris), 33n, 143n, 180n formal cause, 15, 21n, 27n, 29, 34, 38, 108n, 119, 120n, 129, 130, 135, 154, 156, 161, 162, 174, 179, 180n, 185, 210, 211, 222-225, 229, 230, 246, 247, 258n, 260, 261, 266, 269, 270n, 271, 272, 274, 284, 286, 313n, 317n. See also Aquinas; canon of relevance (Lonergan) formal semantics (ontological criticism of ), 65

formalization, 17, 75, 228 formelle Grund (Hegel), 15 formelle Vernunft, 255, 258, 284 Förster, Eckart, 18, 19, 46, 169n, 258, 291, 301, 303, 309n; on Kantian Position oder Setzung, 301; Kant’s Final Synthesis, 19n, 42n, 45n, 117n, 145n, 238n, 300 The Foundations of Arithmetic (Frege), 299n Foundations of Transcendental Philosophy: (Wissenschaftslehre) nova methodo (1796/99) (Fichte), 112n Frank, Manfred, 19, 42, 46ff., 169n, 258; on Kantian Position oder Setzung, 42, 295, 302; Philosophical Foundations of Early German Romanticism, 21n, 47n, 48n, 145n, 174n, 306n, 309n Franks, Paul, 288n (“All or Nothing”), 293n (All or Nothing) Frege, Gottlob, 40n, 60n, 78, 85, 100, 137, 148, 149 (Über Sinn und Bedeutung), 211, 249, 250, 269, 281n (The Frege Reader (ed. Beaney)), 297-299; 299n (The Foundations of Arithmetic) Friedman, Michael, 218n; A Parting of the Ways, 39n, 53n, 83n, 278n; “The Davos Disputation and Twentieth-Century Philosophy,” 53n From a Logical Point of View (Quine), 151n From an Ontological Point of View (Heil), 57n function (Cassirer), 159, 170n, 277; of concept formation, 240

3 index

343

G

H

Gegenstands-setzung (Natorp), 45 Geist (spirit); 14, 17, 25ff., 52, 53, 117, 190n, 198, 202, 203, 215, 216, 220, 221, 227ff., 236, 239, 243n, 248, 255ff., 267, 271, 307, 315; subjective (Hegel), 28, 263n, 284 general logic (Kant), 34, 181n, 313 General Theory of Knowledge (Schlick), 22n, 102n, 248n George, Alexander, 250n (Mathematics and Mind); and Vellman, 84n (Philosophies of Mathematics) Das Gesetz des Bildens (Fichte), 50 gesetzliche Form (Cassirer), 274 Gesetztsein (Hegel), 27, 51, 224, 230, 240, 251, 259ff., 273, 283, 286 Gilson, Etienne (The Elements of Christian Philosophy), 235n Gödel, Kurt, 85, 118, 216, 250 Goodman, Lenn E. (In Defense of Truth), 63n, 143n Goodman, Nelson (Fact, Fiction, and Forecast), 70n Grayling, A. C., 62; An Introduction to Philosophical Logic, 62n, 146 Green, T. H., 47 Grice, Paul (Studies in the Way of Words), 59 Grund (ground/reason), 28, 53, 162, 207, 229, 239, 240, 244ff., 255, 258, 263ff., 271n, 283, 284, 286. See also formelle Grund Grundrelationen (Carnap), 53 G. W. F. Hegel (Rosen), 26n, 254n, 299n

Haack, Susan, 89n Harman, Gilbert, 12, 13, 25, 32ff., 55, 69, 70, 77, 78, 91-94, 95, 97, 100, 102, 105ff., 117, 118, 122, 125ff., 136, 141n, 144, 152n, 174, 199n, 209, 233, 272 WORKS: Change in View: Principles of Reasoning, 91n, 92n, 93n; “The Logic of Ordinary Language,” 94n, 142n, 233n; “Logical Reasoning,” 92n; Reasoning, Meaning, and Mind, 70n, 91n; Thought, 92n, 94n, 105n, 107n Harris, Errol, 33, 99n, 143, 179n, 180; Formal, Transcendental, and Dialectical Thinking: Logic and Reality, 33n, 143n, 180n Hauser, Kai (“Lotze and Husserl”), 149 Hearer of the Word (Rahner), 279n Hegel, G. W. F. (Hegelian), 13ff., 22n, 26ff., 39, 45, 49n, 73n, 76n, 77, 78, 84, 94, 96n, 101, 111n, 112, 120, 121n, 124n, 133, 137, 142, 146n, 164, 168, 177, 180, 182, 192, 194, 199, 206, 210, 214ff., 235, 238, 239n, 242ff., 272, 280, 282-285, 286ff., 291, 299n, 306, 319; Gesetztsein (positedbeing), 27, 51, 224, 230, 240, 251, 259ff., 273, 283, 286; logic/ doctrine of essence, 16, 25ff., 51, 77n, 121, 163, 218, 219, 230, 235, 242, 244, 245, 254-268, 283, 286, 318n; reine Denken (pure thinking), 27, 243, 261n, 284; Scheinen in dem Entgegengesetzten (showing in what is opposed), 244, 261, 268; setzende Reflexion (positing reflection), 27, 51, 217, 224, 224, 230, 243, 251, 253,

344 Inference and the metaphysic of reason 259ff., 283, 286; Sichaufheben (self-sublation), 265, 267 WORKS: Encyclopedia Logic (Die Wissenschaft der Logik), 14, 15n, 28n, 34n, 78n, 218n, 219n, 230n, 231n, 238n, 244, 245n, 246n, 251n, 256n, 257n, 263, 264n, 265n, 266n, 268n, 318n; Science of Logic (Wissenschaft der Logik), 14n, 15n, 51n, 142n, 182n, 207, 214n, 218n, 228n, 257n, 262n, 264n, 265n, 267n; Lectures on the Philosophy of Religion, 259n; Lectures on the Philosophy of Spirit 1827-8, 26n, 31n, 255, 258n, 284n; The Philosophy of Spirit [Mind] (Die Philosophie des Geistes), 17, 27n, 198n, 243n, 254, 256n, 258, 284n Hegel and Aristotle (Ferrarin), 224n “Hegel and Brandom on Norms, Concepts, and Logical Categories” (Houlgate), 101n “Hegel and the Greeks” (Heidegger), 229n Hegel, Idealism, and Analytic Philosophy (Rockmore), 77n, 96n “Hegel’s Phenomenology and the Question of Semantic Pragmatism” (O’Connor), 78n Hegel’s Philosophy of Reality, Freedom, and God (R. Wallace), 214n, 218n, 220n, 254n hegemonic fantasm (Schürmann), 220, 227, 270, 279 Heidegger, Martin (Heideggerian), 18, 19, 22n, 31n, 39n, 44, 45n, 46, 47, 53, 57n, 83, 144n, 162n, 167, 217, 221, 229, 232, 248, 258, 278n, 280n, 281, 284, 290n,

292ff., 302; on Kantian Position oder Setzung, 293-297 WORKS: The Basic Problems of Phenomenology (Der Grundprobleme der Phänomenologie), 293, 294n 295n; Discourse on Thinking, 290n; “Hegel and the Greeks,” 229n; Introduction to Metaphysics, 221; “Kant’s Thesis about Being” (“Kants These über das Sein”), 19n, 20n, 42n, 47n, 145n, 167n, 169n, 207, 217n, 281n, 293n, 296, 297n, 299n, 302n, 305n; The Principle of Reason, 135n, 195n Heidegger’s Concept of Truth (Dahlstrom), 162n Heil, John (From an Ontological Point of View), 57 Henrich, Dieter, 49, 242n; Between Kant and Hegel: Lectures on German Idealism, 49n, 215n; “Identity and Objectivity: An Inquiry into Kant’s Transcendental Deduction,” 301n, 304n Herbart, Johann Friedrich (Herbartian), 45, 46, 159, 168, 173n, 174n, 248n Hesse, Mary, 67 (The Structure of Scientific Inference), 68, 70 Heyting, Arend, 27n, 224-225 (“The Intuitionist Foundations of Mathematics”), 268n Hilbert, David, 86n, 219 Hintikka, Jaakko, 66, 80n; The Principles of Mathematics Revisited, 66n, 69, 148n; Socratic Epistemology, 59n, 72n

3 index History of Mathematical Logic from Leibniz to Peano (Styazhkin), 140n holism/holist, 69, 70, 77, 92, 103, 105, 141, 143, 154, 179, 193n, 199, 223, 312, 318 Horstmann, Rolf-Peter (“Substance, Subject and Infinity: A Case Study of the Role of Logic in Hegel’s System”), 78n, 101n Houlgate, Stephen, 16, 51, 101n (“Hegel and Brandom on Norms, Concepts, and Logical Categories”), 259n (The Opening of Hegel’s “Logic”), 260, 264, 266; “Why Hegel’s Concept Is Not the Essence of Things,” 224n, 230n, 259, 261, 262n Human Knowledge (Russell), 68, 91n Hume (Humean), 66n, 67n, 92, 106n, 187, 287, 296n A Hundred Years of Philosophy (Passmore), 149n Husserl, Edmund, 22n, 45, 51 (Ideas; Experience and Judgment), 85n, 144n, 149n, 150, 180 “Husserl’s Logische Untersuchungen (§59) and the Marginalization of Lotze in Anglophone Philosophy” (Stambovsky), 150n

I idealism, 44n, 45, 57, 116n, 141, 144n, 148, 165n, 201, 220, 258, 270n; absolute, 244; critical, 226, 274, 286, 287; objective (Bosanquet), 192, 213, 236n, 313; Roycean, 316; speculative, 181, 286, 287; transcendental, 21, 244, 282, 287n

345 Ideas (Husserl), 51n ideation(al), 155, 174, 203, 215, 218, 234, 274, 275, 315; inferential, 27, 95, 161, 239 “Identity and Objectivity: An Inquiry into Kant’s Transcendental Deduction” (Henrich), 301n, 304n Imagination and Interpretation in Kant (Makkreel), 110n “Immediacy and the Birth of Reference in Kant,” (Posy), 249n, 287n implication, 13, 24, 26, 33, 34, 37, 63n, 80, 91, 107, 114, 141, 183, 188ff., 215ff., 240, 285, 306n, 314 Implication and Linear Inference (Bosanquet), 24n, 88n, 107, 108n, 109n, 133, 136n, 150n, 180, 187n, 188n, 193n, 194, 197, 198n, 199n, 207, 314n implicature (Grice), 59 implicit definition (Hilbert), 219 “Importance” (Whitehead), 262n In Defense of Pure Reason (Bonjour), 128 In Defense of Truth (L. Goodman), 63n, 143n “Induction and Statistical Probability” (Carnap), 68n, 79 Induction, Probability, and Causation (Broad), 80n, 81n, 82n Induction, Probability, and Skepticism (Chattopadhyaya), 79n “Inductive Inference” (Maher), 68, 71

346 Inference and the metaphysic of reason “Inductive Logic and Inductive Intuition” (Carnap), 79, 83n, 86n, 87n Inductive reasoning, 70, 79, 92, 122, 123n inference: abductive (Pierce), 72; aesthetic inference, 214, 217, 247, 317; analytic epistemology of, 13; and probability, 59, 79-83, 127, 140, 209; as act, 27, 29, 58, 98, 113, 145, 211, 214-216, 229, 252n, 258, 261, 271, 275, 289, 308, 317; as mediated judgment, 20, 32, 152, 216, 225ff., 234, 246, 247, 251, 260, 262, 268ff., 307, 308, 317; enumerative, 59, 71, 91, 203; inferential ideation, 27, 95, 161, 174, 204, 215, 239; of reason (Vernunftschluss), 135, 305; reason of, 11, 14, 26ff., 32, 55, 58, 59n, 65, 102n, 130, 145, 169n, 170n, 176, 194, 203, 206, 222, 236, 240, 241, 254ff., 273, 274, 276, 281, 284, 285, 289, 301, 313n; syllogistic, 30n, 35, 36, 58, 59, 98, 134, 151, 153, 159n, 161n, 163, 167, 169n, 174, 177n, 178n, 186ff., 205, 243, 263, 281, 297; systematic, 178n, 186n; to the best explanation, 68n, 72, 91, 146n; totality in, 16, 31, 177, 178, 191, 203n, 211, 217ff., 229, 230, 235ff., 241, 244, 247, 248, 253, 268, 271n, 273, 275, 283, 318. See also concept formation; conclusion (of inference); ideation; inductive reasoning; problem of induction “Inference” (Sanford), 72n “Inference” (Tragesser), 74n Inference to the Best Explanation (Lipton), 72n, 146n inferential norms (Brandom), 96

“Inferentialism and Some of Its Challenges” (Brandom), 98n, 99n infinite thought (Hegel), 215 “Information” (Floridi), 25n Insight (Lonergan), 56n, 109ff., 168n, 309, 310n intellectualisme (Rousselot), 270n, 290 intelligence, 8, 11, 23, 27, 30-31, 33, 60, 84, 88, 119, 121, 123n, 173, 184, 189, 197, 203ff., 231, 233n., 234, 235n, 239ff., 254, 255, 258ff., 269, 270n, 271, 272, 275, 278, 289, 290n, 313, 315ff.; prediscursive, 88n, 212, 262 Intelligence (L’Intellectualisme de saint Thomas) (Rousselot), 227n, 290n Intermediation, 60, 94, 251, 306n Interpreting Modern Philosophy (Collins), 294n Introduction to Logic (Copi), 60n, 119n  Introduction to Logic ( Joseph), 86n, 119n, 140n, 185n, 200n Introduction to Metaphysics (Heidegger), 221 An Introduction to Philosophical Logic (Grayling), 62n, 146 intuition(ist), 32, 34n, 35n, 62, 74, 79, 83n, 84ff., 94, 110n, 123ff., 147, 160, 170, 171, 211, 216, 224, 225n, 232, 249, 254, 264n, 268n, 272, 278, 287, 288n, 295, 302, 308, 317, 319n; rational (Gödelian), 85; sensuous, 296, 299 Intuition and Ideality (Weissman), 84n (“Dialectical Cycles of Intuitionist Method”), 87n

3 index “The Intuitionist Foundations of Mathematics” (Heyting), 225n isomorphism between knowing and known (Lonergan), 115, 124; critique of, 115n

347

146, 147; hypothetical, 126n, 127; immediate/unmediated (direct, simple), 71, 176, 197n, 211ff., 225ff., 238, 239, 243, 250, 269, 285, 307; inductive, 193n; inferential (syllogistic), 175, 192, 202, 217, 227, 229, 236, 281, J 285, 301, 314, 318; logical, 46, 48, 145, 208, 227; Lonergan “J. G. Fichte and the ‘Scientific on, 110, 111(prospective), Reconstruction of Grammar’” 119, 119n (prospective), 122 (Surber), 49n (prospective),168n (prospective), James, William, 106n (Essays in 309, 310; mediated, 20, 32, 36, Radical Empiricism), 151 152, 216, 225ff., 234, 247, 251, Jevons, William Stanley, 24, 62n, 260, 262, 268ff., 275, 307, 308, 137, 138, 140 317; possible (Kantian), 145n, 291, 304; practical (non-Kantian), Joachim, Harold H., 32, 103n, 201n 76n, 108; rational, 111(Kant), (The Nature of Truth); Logical 168 n (Kant); reflective, 28, 101 Studies, 84n, 239n (Kant), 275, 302 (Kant), 305 Joseph, H. W. B., 24, 201n (“A (Kant); remotive, 214 (Lotze); Last Plea for Free-Thinking in thetic, 48, 300n Logistics”); Introduction to Logic, 86n, 119n, 140n (on quantification “The Justification of Deduction” (Haack), 89n of the predicate), 185n, 200n “The Justification of Inductive Rules judgment, 11, 13, 23, 26, 34ff., 40n, of Inference” (Salmon), 66n 45n, 51, 62, 85 (Frege), 107, 134, 136, 149, 153, 158n (Lotze), 159n (Lotze), 163n (Lotze), 167, K 168n, 175ff. (Lotze), 180n, 181ff. Kant, Immanuel (Kantian),11ff.; and (Bosanquet), 190 (Lotze), 196 onto-epistemological posting, 40(Bosanquet), 199ff. (Bosanquet), 53, 291-305; debts to, 280-282; 211, 215, 221, 240 (Bosanquet), doctrine of wisdom, 251n; double 255 (Kant), 258n, 263n, 267 comprehension of being 23n (Hegel), 277, 287 (Kant), 293 (Shürmann); dualism, 175, 249, (Kant), 294n, 301 (Kant), 314 283, 287, 288; judgment as such, (Bosanquet); aesthetic (artistic) 301; on being (Sein überhaupt), 110n, 221, 228, 316; analytic, 26, 11, 18, 46, 165, 167, 214n, 218n, 296n; Brandom on, 95, 100, 101; 242, 248, 262, 271, 280, 292, categorical, 81n, 126n; copulative, 297, 299n, 300, 305, 308; on the 214; deductive, 184; determinate, principle of sufficient reason, 43, 302 (Kant); disjunctive, 194n 135; Position oder Setzung, 11, 12, (Lotze), 214 (Lotze); empirical, 18, 19, 22n, 37, 40ff., 47ff., 123n, 275, 277; existential, 46, 48,

348 Inference and the metaphysic of reason 132, 134, 145, 151, 164, 167ff., 174, 179, 182, 248, 254n, 265, 280, 282, 291, 292, 300, 309, 315, 319n; pure concepts of reason, 34, 35n, 44, 305; transcendental ideas, 34n, 35n, 44, 135, 305; transcendental illusion, 43, 167; Vernunft (Reason), 34ff., 44, 120, 251, 255, 256, 258 (formelle), 264, 284 (formelle), 302, 305; Vernunftschluss (inference of Reason), 36, 126n, 135, 161n, 305; Verstand (Understanding), 44, 125n, 249n, 251, 255, 268n, 284, 302. See also logic: transcendental WORKS: Critique of Practical Reason, 251n; Critique of Pure Reason, 18, 19n, 20n, 34n, 35n, 36n, 43n, 77n, 229n, 281n, 291, 303n; Critique of the Power of Judgment, 31n, 101n, 110n; Logic, 55, 181n, 255n, 301, 302; Metaphysical Foundations of Natural Science, 218n; Only Possible Basis for a Proof of the Existence of God, 18n, 73n, 291, 300; Opus postumum, 19n, 45n, 50n, 117n, 145n, 238n, 291, 296n, 300; Philosophical Correspondence, 279n; Prolegomena to Any Future Metaphysics, 12n, 26n, 35n, 88n, 135n, 202n, 296n Theoretical Philosophy1755-1770, 18n, 40n, 73n, 136n, 165n, 265n, 281n, 291n, 292n, 294n, 299n, 300n, 303n, 304n; Werke (ed. Cassirer), 18n, 292n, 293n, 299n, 300n, 303n Kant (Wood), 54n, 309n Kant and the Historical Turn (Ameriks), 28n, 36n, 43n, 110n, 287n, 305n

“Kant and the Late Heidegger” (Richardson), 167n “Kant’s Existential Thought” (Adamczewski), 19n, 43n, 48n Kant’s Final Synthesis (Förster), 19n, 42n, 45n, 117n, 145n, 238n, 300, 301n, 309n “Kant on the Material Ground of Possibility: From The Only Possible Argument to the Critique of Pure Reason” (Fisher and Watkins), 19n, 36n “Kant’s Thesis about Being” (“Kants These über das Sein”) (Heidegger), 19n, 20n, 42n, 44n, 47n, 145n, 167n, 169n, 207n, 217n, 281n, 293n, 296, 297n, 299n, 302, 305n  Kant’s Transcendental Idealism (Allison), 43n, 87n, 110n, 287n Knasas, John F. X. (Being and Some Twentieth–Century Thomists), 122n, 219n, 225n, 248n knowing and being, 38, 60 Kuntz, Paul Grimely (“Lotze’s Relevance to Contemporary Philosophy”), 149n, 165n

L Ladd, George Trumbull, 149n, 151 Lakatos, Imre, 79n “A Last Plea for Free-Thinking in Logistics” ( Joseph), 201n law of (non)contradiction, 21n, 25, 26, 134ff., 143, 147, 162n, 247, 286, 294, 296, 303 Le Point de Départ de la Métaphysique (Maréchal), 17

3 index Lecture Notes in Artificial Intelligence 872 (ed. S. Arikawa and K. P. Jantke), 59n Lectures on the Philosophy of Religion (Hegel), 259n Lectures on the Philosophy of Spirit 1827-8 (Hegel), 26n, 31n, 84n, 220n, 248n, 258n, 284n Leibniz, G. W. F. (Leibnizian), 220; on the principle of sufficient reason, 195n, 245, 247, 260, 265n, 266 Lewis, C. I. ( “Autobiography”), 141n The Limits of Analysis (S. Rosen), 88n, 143n, 256n linear inference. See inference Lipton, P., 68n; Inference to the Best Explanation, 72n, 146n Locke, John (Lockean), 88n, 196n, 234, 237, 316n (Essay Concerning Human Understanding) logic: conceptual, 12ff., 23, 26ff., 33, 36ff., 51, 85, 98, 102, 111, 124n, 156, 158, 163, 168n, 173ff., 190, 193, 198ff., 213, 215, 217, 221, 230, 234, 235, 239ff., 249, 251, 253, 254-267, 272, 273, 274, 280ff., 286, 296, 308; general (Kantian) 34, 181n, 313; modal, 21; predicate, 62, 63, 65, 141, 143n, 221; sentential, 108, 270, 271; symbolic, 20, 24n, 37, 61ff., 98, 131, 136, 137, 140ff., 148n, 192, 204, 209, 249, 270, 285, 287; syllogistic, 35, 98, 174, 281; transcendental, 20, 23, 29n, 34, 35, 36n, 44, 126n, 167, 169, 210, 243, 278, 281, 281, 287, 297. See syllogism Logic (Bosanquet), 24n, 25n, 58n, 80n, 86n, 92n, 103n, 107n, 126n,

349 127n, 133, 136n, 140n, 150, 181ff., 190n, 191n, 194, 195n, 196n, 201n, 202n, 213n, 236n, 237, 261n, 291, 312, 313n, 314, 312n  Logic (Dewey), 313n Logic (Hegel): Encyclopedia Logic (Die Wissenschaft der Logik), 14, 15n, 28n, 34n, 78n, 218n, 219n, 230n, 231n, 238n, 244, 245n, 246n, 251n, 256n, 257n, 263, 264n, 265n, 266n, 268n, 318n; Science of Logic (Wissenschaft der Logik), 14n, 15n, 51n, 142n, 182n, 207, 214n, 218n, 228n, 257n, 262n, 264n, 265n, 267n. See Hegel Logic (Kant), 55, 181n, 255n, 301, 302 Logic (Lotze), 58n, 119n, 139, 140, 149n, 151ff., 174ff., 197n, 214n, 232n, 240n “Logic and Dialectic” (S. Rosen), 17, 21n, 75n, 85n, 91n, 117n “The Logic of Ordinary Language” (Harman), 94n, 142n, 233n Logic of the Cultural Sciences (Cassirer), 223n The Logical Foundations of Bradley’s Metaphysics: Judgment, Inference, and Truth (Allard), 190n, 263n “Logical Reasoning” (Harman), 92n The Logical Structure of the World (Carnap), 53n, 83n, 84n, 85 Logical Studies ( Joachim), 84n, 239n The Logical Syntax of Language (Carnap), 89 Lonergan, Bernard, 12, 36, 37, 55, 56, 77, 78, 109-130, 136, 144, 152n, 168n, 171, 187n, 309-311; canon of relevance, 122, 123; pragmatic engagement, 310;

350 Inference and the metaphysic of reason proportionate being, 113, 115, 116, 123n, 124ff.; Insight, 56n, 109ff., 168n, 309, 310n; Method in Theology, 112n, 116n, 121n, 126n Lonergan and Kant: Five Essays on Human Knowledge (Sala), 112n, 116n Lotze, Rudolf Hermann, 13, 22n, 23ff., 34n, 36n, 37, 38, 42n, 45, 47, 51n, 58n, 62n, 75n, 76, 78, 82n, 113n, 119n, 131ff., 145, 148-179, 180ff., 194, 197, 208, 214, 215n, 221, 232n, 233, 239, 240, 248n, 258, 268, 269, 273, 280n, 286, 291, 300, 304n; anticipations of onto-epistemological orientation to inference, 175-179; idea of the Real, 155-158, 159n, 162; the logical Idee, 159ff., 178, 179; mathematical inference; 153, 158; metaphysical objective relations, 162; on the logical calculus, 139-40; on Position oder Setzung, 164-174; on the logic of concept formation, 221; overview of thought and influence, 148-152; on the principle of sufficient reason, 154-156; remotive judgments/premises, 163, 214; Zwischen (“a between”), 157 WORKS: Logic, 58n, 119n, 139, 140, 149n, 151ff., 174ff., 197n, 214n, 232n, 240n; Metaphysic, 47, 131n, 139n, 148n, 155n, 157n, 158n, 163n, 164, 165n, 166n, 168n, 170n, 171n, 180, 215, 304n; Outlines of Metaphysic, 149n, 155n, 162n, 164, 165n, 166n, 168n, 171n, 172n, 287n; “Philosophy in the Last Forty Years,” 189n, 268n, 269n “Lotze and Husserl” (Hauser), 149n

“Lotze’s Relevance to Contemporary Philosophy” (Kuntz), 149n, 165n Lotze’s System of Philosophy (Santayana), 149n, 166n luminosity of spirit (Geist), 315

M Maher, Patrick, 71 Maimon, Salomon, 81, 126n, 140n, 286ff. “Maimon’s Transcendental Logic” (Beiser), 126n Maimonides (Maimonidean), 41n, 225n, 270n Making It Explicit (Brandom), 101n Makkreel, Rudolf A., 110n, 316n The Man Who Mistook His Wife for a Hat (Sacks), 71n Maréchal, Joseph (Maréchalian), 17 (Le Point de Depart de la Metaphysique), 58, 113, 114n, 206n, 319n mathematical inference (Lotze), 153, 158 Mathematical Thought and Its Objects (Parsons), 84n Mathematics and Mind (George), 250n Martin, Wayne M., 46, 48, 49; Theories of Judgment, 40n, 45n, 46n, 48n Matteo, Anthony M. (Quest for the Absolute), 319n McDowell, John, 106n McInerny, Ralph, 122n Mckirahan, Richard D., Jr. (Principles and Proof), 27n

3 index meaning, 31, 34-35, 42, 60, 66 (Hintikka), 82 (Whitehead), 84, 85, 88n (Rosen), 96, 102, 112, 121n (Lonergan), 139n (Badiou), 146, 169n (Frank), 171, 177, 178, 180n (Harris), 203, 211, 215 (formal), 234, 236-237, 247n (Aquinas), 250, 270, 272, 273 (Cassirer), 283, 309 (Frank), 318. See also conclusion “Mechanical Procedures and Mathematical Experience” (Sieg), 250n mediation/mediate(d), 20, 29n (Allison), 32, 36, 49 (Novalis), 51 (Hegel), 121n, 152, 153n, 90, 202, 214, 238, 260, 262, 269n, 271, 275, 285, 302, 307, 308, 317; inferential, 181-182; sublation of, 265-267 The Meeting of the Extremes (Bosanquet), 144n, 181n Mendelsohn, Richard L., 60n, 250, 298, 299; The Philosophy of Gottlob Frege, 250n, 298n, 299n Merkmal(e), 108, 158, 160, 166, 232n, 292, 304 Metaphysic (Lotze), 47, 131n, 139n, 148n, 155n, 157n, 158n, 163n, 164, 165n, 166n, 168n, 170n, 171n, 180, 215, 304n Metaphysical Foundations of Natural Science (Kant), 218n metaphysical “gap” (Kant), 238 metaphysical reference (Whitehead), 17, 135 The Metaphysical Thought of Thomas Aquinas (Wipple), 252n “Metaphysics” (Blackburn), 73n

351 Metaphysics (Royce), 80, 166n, 239n, 316n Method in Theology (Lonergan), 112n, 116n, 121n, 126n middle term, 67, 126, 152, 153, 175, 178, 187, 223 (Aristotle) , 238, 240, 253, 260, 301 Mill, J. S., 24 mirror neurons, 212n, 231 “Mirrors in the Mind” (Rizzolatic, Fogassi, and Gallese), 212n mitgewußt (Rahner), 279 modality (Kantian), 44, 44n, (Shürmann), 115, 167, 174 Modes of Thought (Whitehead), 262n (“Importance”) Modern Introduction to Logic (Stebbing), 192n, 201n Moore, G. E., 56, 140, 141n, 181n (Philosophical Studies) Myth and the Limits of Reason (Stambovsky), 209n

N Nagel, Ernst, 79n Natorp, Paul, 39n, 45, 52, 162n; Plato’s Theory of Ideas, 42n, 45n “Naturalism Reconsidered” (Weir), 250n The Nature of Thought (Blanshard), 142n The Nature of Truth ( Joachim), 103n “The Nature of Truth in Modern Logic” (Schlick), 156n neo-Kantian, 14, 22, 39, 52n, 83n, 109n, 192, 206, 210n, 226, 236, 273, 274, 276, 279, 300, 315

352 Inference and the metaphysic of reason neuroscience, 211, 212n 86n, 96, 106, 135, 175, 191, 205, 208, 210-226, 249, 255, 267, 277, New Essays on Fichte’s Later Jena 284, 307 “Wissenschaftslehre” (ed., Breazeale and Rockmore), 112n ontological proof (argument), 20, 167, 170, 249, 297, 299n The New Science (Vico), 290n The Opening of Hegel’s “Logic” Norris, Christopher, 63n (Houlgate), 259n “Note on the Logical Calculus” Opus postumum (Kant), 19n, 45n, (Lotze), 139, 140n 50n, 117n, 145n, 238n, 291, 296n, Novalis (Friedrich von Hardenberg), 300 49 (Fichte Studies), 244n, 262 order (as a principle of the act of inference), 16, 30ff., 35n, 72, 80n, O 102, 105 (M. Williams), 119n, 122 (Lonergan), 124n, 135, 166n, objective idealism (Bosanquet), 180, 169, 173, 185, 203ff., 211, 214ff., 192, 194, 200, 213, 236n, 313 228ff., 234ff., 243, 247ff., 260n, Objective Knowledge (Popper), 66n 261, 268ff., 283, 313n, 317, 318 O’Connor, Brian (“Hegel’s Ordnungssetzung(en) (Carnap), 53, Phenomenology and the Question 82n, 84n, 85, 100, 214, 220n of Semantic Pragmatism”), 78n Outlines of Metaphysic (Lotze), 149n, “Of Probable Reasoning” (Reid), 155n, 162n, 164, 165n, 166n, 80n 168n, 171n, 172n, 287n “Of Reasoning in General” (Peirce), “Overcoming a Dualism of Concepts 233n and Causes” (Brandom), 95n “On Inference” (Bradley), 83n Owens, Joseph, 122n “On the Relation between Induction Oxford Handbook of Philosophy of and Probability” (Broad), 80 Mathematics and Logic (Shapiro), “On Semantics and Epistemology” 225n, 250n (Rockmore), 96n On Truth and Meaning: Language, P Logic, and the Grounds of Belief Pap, Arthur (Elements of Analytic (Norris), 63n Philosophy), 76n The Only Possible Basis for a Proof of parergon(al), 49n, 50, 284n. See also the Existence of God (Kant), 18n, Wurzer 73n, 291, 300 parousia (being present, “presence”), onomata, 20 221, 228, 260 onta, 20 Parsons, Charles (Mathematical onto-epistemological orientation Thought and Its Objects), 84n (to inference), 11, 27, 32, 38, 51,

3 index A Parting of the Ways: Carnap, Cassirer, and Heidegger (Friedman), 39n, 53n, 83n, 278n Passage to Modernity (Dupré), 241n Passmore, John (A Hundred Years of Philosophy), 149 Peirce, C. S., 59n, 72, 233 (“Of Reasoning in General”) perfection, 185, 227, 247n (Aquinas), 253 (Aquinas), 292, 317n The Perfection of the Universe According to Aquinas (Blanchette), 246n, 253n Phenomenology, Logic, and the Philosophy of Mathematics (Tieszen), 85n Philosophical Correspondence (Kant), 297n Philosophical Encounters: Lonergan and the Analytic Tradition (Fitzpatrick), 130n The Philosophical Foundations of Early German Romanticism (Frank), 19, 21n, 42n, 47n, 48n, 145n, 169n, 174n, 291n, 295n, 302n, 306n, 309n “Philosophical Investigations into the Essence of Human Freedom and Other Matters” (Schelling), 141n Philosophical Studies (Moore), 181n Philosophies of Mathematics (George and Vellman), 84n “Philosophy in the Last Forty Years” (Lotze), 189n, 268n, 269n Philosophy of Being (Blanchette), 23n, 29n, 115n, 116n, 125n, 141n,

353 219n, 233n, 248n, 260n, 270n, 271n, 298n The Philosophy of Brand Blanshard, 151n The Philosophy of Gottlob Frege (Mendelsohn), 250n, 298, 299n The Philosophy of Spirit [Mind] (Die Philosophie des Geistes) (Hegel), 17, 27n, 198n, 243n, 254, 256n, 258, 284n The Philosophy of Symbolic Forms (Cassirer), 20n, 31n, 52n, 63n, 120n, 150n, 187n, 190n, 192n, 193n, 227n, 234n, 236n, 240n, 252n, 294n Plato (Platonism), 39n, 42n (Parmenides), 45n (Idea of the Good), 141, 150 (Ideas), 221 (Divided Line), 239, 250 Plato’s Theory of Ideas (Natorp), 42n, 45n Poetry and Experience (Dilthey), 316n (“Poetry and Lived Experience”) Popper, Karl, 66n (Objective Knowledge), 67n, 92n, 158 positing/position (Position [Ger.]), 11ff., 27, 31, 37ff., 40-54, 77n, 82n, 93ff., 105, 115, 116, 121ff., 145, 153, 154, 159n, 177ff., 202, 207ff., 220, 222, 224, 230, 234, 237ff., 248-254, 261n, 265, 271, 272, 280ff., 287, 291-309, 215, 318; Cassirer on, 52, 53; Fichte on, 49; Kant on, 11, 12, 18, 19, 22n, 37, 40ff., 47ff., 123n, 132, 134, 145, 151, 164, 167ff., 174, 179, 182, 248, 254n, 265, 280, 282, 291, 292, 300, 309, 315, 319n; Henrich on, 49; Hegel on (posited being, positing

354 Inference and the metaphysic of reason reflection), 27, 51, 217, 224, 230, 240, 243, 251, 253, 259ff., 273, 283, 286; Heidegger on, 293297; Lotze on, 164-175. See also absolute positing; relative positing Posterior Analytics (Aristotle), 87n, 223, 246n, 268n Posy, Carl J., 249n (“Immediacy and the Birth of Reference in Kant”), 287n potency, 125, 126, 227, 228, 254, 315 power, 31, 35, 117, 160, 161, 215n, 228, 234, 235n, 237, 239n, 251, 263, 315ff. pragmatic engagement (Lonergan), 310 “A Preface to Ontology” (Sellars), 298n premise(s), 13, 16, 30, 31, 55, 58, 64, 68, 70, 79, 80, 87, 90, 92, 95ff., 115, 118, 119 (heuristic), 128, 153, 163 (remotive), 173ff., 184, 185, 186 (indemonstrable), 187, 188, 191, 194, 198ff., 211, 214, 217ff., 227ff., 248, 251ff., 260, 261, 268ff., 280, 283, 314, 318. See also show presence, 23, 217, 221, 234, 241, 278 primary (prime) analogate, 225, 247n, 260n, 261, 269, 270, 271 The Principle of Individuality and Value (Bosanquet), 197n, 180n The Principle of Reason (Heidegger), 125n, 128n principle of sufficient reason, 11, 14ff., 21n, 26ff., 34, 38, 43 (Kant), 76n, 98, 108n, 119n, 129, 134, 135 (Kant), 147, 154-156

(Lotze), 162n, 170n, 174, 183 (Bosanquet), 195 (Leibniz), 196197 (Bosanquet), 210, 211, 222225, 229ff., 240, 244ff., 254, 255, 263-268 (Hegel), 269, 272, 272, 283, 284 (Hegel), 286, 317 The Principle of Sufficient Reason (Pruss), 135n Principles and Proof (Mckirahan), 27n The Principles of Logic (Bradley), 83n, 90n, 104n, 133n, 137n, 213n The Principles of Mathematics (Russell), 137 The Principles of Mathematics Revisited (Hintikka), 66n, 69, 148n probability and inference (Carnap), 79-82 problem of induction, 55, 92, 118, 121, 125n, 128, 206 The Problem of Inductive Logic (Lakatos, ed.), 79n Problems and Projects (N. Goodman), 70n Problems of Knowledge (M. Williams), 66n, 70n, 79n, 92n, 102ff., 113n, 192n, 312n, 313n productive imagination (Hegel), 31 Process and Reality (Whitehead), 56, 82n, 138, 246, 247n, 278n Prolegomena to Any Future Metaphysics (Kant), 12n, 26n, 35n, 88n, 135n, 202n, 296n proportionate being (Lonergan), 113, 115, 116, 123n, 124ff. Pruss, Alexander R. (The Principle of Sufficient Reason), 135n

3 index psychologism, 25, 33, 92n, 94, 104, 125, 127, 153n, 162 Puntel, Lorenz B., 56, 65; Structure and Being, 56n, 57n, 65n, 72n, 204n, 232n pure being, 165ff., 179, 304n pure concepts of reason (Kant), 34, 35n, 44, 305 pure thinking (reine Denken) (Hegel), 27, 50, 243, 261n, 284

355

59n, 65, 102n, 130, 145, 169n, 170n, 176, 194, 203, 206, 222, 236, 240, 241, 254ff., 273, 274, 276, 281, 284, 285, 289, 301, 313n. See also sufficient reason; Vernunftschluss Reason and Analysis (Blanshard), 87n, 142n “Reason, Experience, and the Philosophical Enterprise” (Brandom), 96n Reasoning, Meaning, and Mind Q (Harman), 70n, 91n quality, 172-173 (Lotze), reflection (inferential), 14, 16, 19, 178n (Lotze), 232n (Lotze), 23, 29n, 31ff., 51, 58, 73, 91, 95, 23quantifier4 (Locke), 237 102, 117, 124, 128, 153, 154, 161, (Locke), 251n (Hegel), 173, 175, 176, 184ff., 191, 198ff., 316n (Locke); of truth, 137 214, 216, 217, 220ff., 233, 235, (Bosanquet) 238ff., 251ff., 261, 263, 267, 269, 274ff., 284, 286, 317 Quantification/quantifier, 17 (Rosen), 40 (Frege), 59n, 60, 63 reflective dialectic, 264; intelligence, (Quine), 140n, 143n (critiques 25, 27, 30, 121, 214, 215, 218, of ), 146, 222, 249 (Davidson), 224, 228, 243, 258, 260, 270, 272, 269 (Frege), 297-298 (Sellars) 275, 289, 313, 315; judgment, 28, 101, 275, 302, 305, 308; thinking, Quest for the Absolute (Matteo), 319n 88, 214, 219, 226, 231, 239n, 279, “The Question of the Other in 288, 315 Fichte” (R. Williams), 49n Reid, Thomas (“Of Probable Quine, W. V., (Quinean), 40n, 63n Reasoning”), 80n (Word and Object), 77, 78, 99n, reine Denken (Hegel), 27, 243, 261n, 143, 151 (From a Logical Point of 284 View), 306-308 Reinhold (Karl Leonhard), 28n, 50n, 285 R relation(s), 17, 37, 129, 189, 200, radical empiricism, 106 255; absolute and relative positing, Rahner, Karl, 256, 278-279 (Hearer 251, 260; among propositions, 91 of the Word) (Harman); an imagined parergon and a work of reflection, 50 Reason (Vernunft), 34ff., 44, 120, (Wurzer); as Verbindungsbegriff in 251, 255, 256, 258 (formelle), a judgment, 293 (Kant); axiomatic 264, 284 (formelle), 302, 305; of logic and its re-presentation, 141; inference, 11, 14, 26ff., 32, 55, 58,

356 Inference and the metaphysic of reason basic (Grundrelationen), 53, 83n; being and predication, 18-19, 20; being and thinking, 21, 26, 256, 274; between concepts, 33-34, 302; between differences of a single universal, 184 (Bosanquet); between intuited objects, 236 (Cassirer); calculus and intuition, 90 (Blondel); characterizing mark and referent, 281; constitutive/formative, 106, 182, 187; construal of inference and the act of inference per se, 80; formal, 189; formal derivation and informal inference, 74; formalization and rationality, 75; implicational, 201-02 (Bosanquet); in posited possibility, 294 (Heidegger/Kant), 303 (Heidegger/Kant); induction and probability, 80 (Broad); inference and deductive thinking, 69; if-then, 126; inference and reality as a whole, 194; inference and the extra-mental, 41; inferential, 25, 98, 184, 201, 203; logic and reasoning, 92-93; logical, 94, 108; logical consequence, 69; meaning and being. 270; mediated judgment and understanding, 36; metaphysical, 51, 126, 162, 172n; object to cognitive faculty, 293-94 (Heidegger); of grounding, 264ff. (Houlgate); of necessity, 120; of terms, 191; ontological, 183 (Bosanquet); Lotzean ontological, 42n, 75, 149, 152, 155ff., 233, 248n, 268; part/whole, 197; posited form and order, 261; premise and conclusion, 97-98, 178; principles and conclusions, 26, 27n; setzende Reflexion and Gesetztsein, 230 (Hegel); subject/ attribute (predicate), 186, 301;

symbolic and philosophical logic, 141; thetic act and being, 280; thinking and thought object, 284 (Hegel); Verhältniswörtchen, 20 (Kant) relative positing (Position [Ger.]), 13, 19, 20, 23, 37, 41-42, 44, 46, 81n, 93ff., 100, 115ff., 123n, 125n, 127, 131, 145, 153, 165ff., 175, 179, 199, 224, 230, 234ff., 243, 249, 251ff., 271, 272, 280ff., 287n, 296ff., 309, 319n. See also positing remote fact(s). See fact remotive premises (Lotze), 163; judgments, 214. See also premise(s) Rescher, Nicholas, 56 The Revolutionary Kant (Bird), 36n, 281n, 288n Richardson, William J. (“Kant and the Late Heidegger”), 167 Rickert, Heinrich, 39n Rockmore, Tom, 77n, 96n (“On Semantics and Epistemology”) Rorty (Richard), 78 Rosen, Stanley, 20, 75, 84n, 85, 86, 90, 179n; G. W. F. Hegel, 26n, 207, 254n, 298n; “Logic and Dialectic,” 17, 75n, 85n, 91n, 117n; The Limits of Analysis, 88n, 143n, 256n Rousselot, Pierre, 270n; Intelligence (L’Intellectualisme de saint Thomas), 227n, 290n Royce, Josiah, 151, 166n, 200 ; Metaphysics, 80n, 239n, 316n rule(s), 13, 21, 27n, 30n, 32ff., 41, 49, 55, 58, 59, 61, 64ff., 83n, 86ff., 108, 118n, 129, 142, 147, 148, 153, 158n, 159n, 169, 174, 187, 203, 204, 209, 219, 222, 229, 230,

3 index 237, 270, 271, 276; of entailment, 26, 33, 69, 91, 107 Russell, Bertrand, 24, 56, 68, 69, 99n, 137, 140ff., 148, 188, 297, 298; Human Knowledge, 91n Ryle, Gilbert, 31, 234; The Concept of Mind, 31n, 234n, 318n

357

Schiller (Schillerian), 221, 247n Schlick, Moritz, 22, 88, 89 (“Appearance and Essence”), 156 (“The Nature of Truth in Modern Logic”); General Theory of Knowledge, 22n, 102n (“The Unity of Consciousness”), 248n Schluß (syllogism/inference), 263, 267, 281, 297 S schöne Schein (Schiller), 221, 247n Sacks, Oliver (The Man Who Schröder, Ernst, 24, 62n, 137, 140 Mistook His Wife for a Hat), 71,72 Sala, Giovanni (Lonergan and Kant), Schulze, Gottlob Ernst, 50n, 220 112n, 116n Schürmann, Reiner, 45, 54, 270; Broken Hegemonies, 45n, 270n Sallis, John (Force of Imagination), 217n Science and the Modern World (Whitehead), 55, 66n, 118, 196n Salmon, Wesley, 66 (“The Justification of Rules of The Science of Knowing: J. G. Inference”), 68 Fichte’s 1804 Lectures on the Wissenschaftslehre, 30n, 214n Sanford, David (“Inference”), 72 Science of Logic (Wissenschaft der Santayana, George, 88n (“Some Logik) (Hegel), 14n, 15n, 51n, Meanings of the Word ‘Is’”); 142 n, 182n, 207, 214n, 218n, Lotze’s System of Philosophy, 149n, 228 n, 257n, 262n, 264n, 265n, 166n 267n Schein(en), 30, 31, 121n, 124n, Seebohm, Thomas M., 300n 185, 191, 211, 214 (Hegel), 218 (Kant), 219 (Hegel), 220, Seig, Wilfried (“Mechanical 221 (Heidegger, Schiller), 228 Procedures and Mathematical (Hegel), 235, 236n, 243, 244 Experience”), 250 (Hegel), 247 (Hegel), 248 Sein überhaupt (Kant), 11, 18, 46, (Hegel), 260, 261 (Hegel), 264, 165, 167, 214n, 218n, 242, 248, 273, 275, 278, 283 (Hegel); as 262, 271, 280, 292, 297, 299n, simple self-relation, 218; that 300, 305, 308 contains “within it being in general self-positing (Fichte), 48, 215n and its forms als aufgehobene,” Sellars, Wilfrid (Sellarsian), 77, 81, 218n; reduction from it to mere 106n, 233, 288n, 297, 298n (“A appearance, 219 Preface to Ontology”) Scheinen in dem Entgegengesetzten Setzung (Position [Ger.]) / setzen. See (Hegel), 244, 261, 268 positing/position Schelling, F. W. J., 104n, 141n, 286ff.

358 Inference and the metaphysic of reason setzende Reflexion (Hegel), 27, 51, 217, 224, 224, 230, 243, 251, 253, 259ff., 283, 286 Shannon, Claude, 24n Shapiro, Stewart (Oxford Handbook of Philosophy of Mathematics and Logic), 225n, 250n show (onto-epistemological). See Schein(en). Sichaufheben (Hegel), 265, 267 Sigwart, Christoph, 24, 148n Simmel, Georg, 252 Socratic Epistemology: Explorations of Knowledge-Seeking by Questioning (Hintikka), 59n, 72n “Some Meanings of the Word ‘Is’” (Santayana), 88n space of reason(s), 76, 156, 288 Spinoza (Benedict), 73n, 225n, 306n spirit. See Geist Stambovsky, Phillip, 150n (“Husserl’s Logische Untersuchungen (§59) and the Marginalization of Lotze in Anglophone Philosophy”), 212n (The Depictive Image) Stanford, Kyle (Exceeding Our Grasp: Science, History, and the Problem of Unconceived Alternatives), 72n statistical reasoning, as contrasted with logical probability (M. Williams), 79 Stebbing, L. S. (Modern Introduction to Logic), 192n, 201n Structure and Being (Puntel), 56n, 57n, 65n, 72n, 204n, 232n

The Structure of Scientific Inference (Hesse), 67 Studies in the Way of Words (Grice), 59n Styazhkin, N. I. (History of Mathematical Logic from Leibniz to Peano), 140n “Suárez and the Latent Essentialism of Heidegger’s Fundamental Ontology” (Blanchette), 57n subjective Geist (Hegel), 28, 216n, 263n Substance, 52, 65, 161, 166, 167, 190, 252n, 262 Substance and Function (Cassirer), 120n, 158n, 193, 206, 226n, 272n, 272, 276n, 277n, 286 “Substance, Subject and Infinity: A Case Study of the Role of Logic in Hegel’s System” (Horstmann), 78n, 101n sufficient reason. See principle of sufficient reason Surber, Jere Paul (“J. G. Fichte and the ‘Scientific Reconstruction of Grammar’”), 49n syllogism, 34, 67, 194; Kant on, 35-36, 126n, 302, 305; Hegel on, 142, 256, 262, 263; Lotze on, 149, 152-153, 159n, 178, 186, 194n, ; Bradley on, 190n ; Bosanquet on, 88n, 108n, 185ff., 205; Lonergan on, 130n symbolische Prägnanz (Cassirer), 219 System of Pragmatic Idealism (Rescher), 56n “The System of Relational Concepts and the Problem of Reality” (Cassirer), 286

3 index

T Tatsache des Bewusstseins (Fichte), 48, 50n, 215 Tatsachen des Geistes (Dilthey), 315n Tatsachen der Natur (Dilthey), 315n teleology, 15, 245, 284 Theoretical Philosophy1755-1770 (Kant), 18n, 40n, 73n, 136n, 165n, 265n, 281n, 291n, 292n, 294n, 299n, 300n, 303n Theories of Judgment (Martin), 40n, 45n, 46n, 48n thetic act, 16ff., 45n, 48, 54, 180n, 183, 214, 222, 241, 248, 249, 276ff., 285, 315; judgment (Fichte), 300n thinking: abstract, 60, 61, 136, 147, 182, 263, 310; analytic, 22, 71, 126, 137, 226; calculative, 56, 88n, 209, 289-290; classificatory (Lotze), 177; concrete (Hegel), 256; deductive, 67ff., 83, 91, 118, 146; dialectical, 33n, 85, 86, 93, 117, 143n, 180n; discursive/ inferential, 18, 29, 32, 35, 36, 59n, 64, 66, 75, 82, 97, 107, 110, 117, 119, 120, 131, 134, 147, 153, 160, 163, 166, 167, 171, 189, 199, 200, 203, 204, 209ff., 221n, 224, 228, 229, 234, 247, 253, 256ff., 266, 267, 287, 298, 302, 318; explanatory, 177 (Lotze); formal, 29, 148, 199, 284; formalist, 196; inductive, 66, 67, 70n, 83, 107, 118, 120, 122, 274, 277; idealist, 44, 103n, 131; logicist, 63n, 143n; meditative, 290; metaphysical, 99n, 114, 281, 289; philosophical, 40, 312; predicative, 16, 145n, 154, 297; rational, 67n, 117; received, 127; reflective, 88, 214,

359 219, 226, 231, 239, 279, 285, 315; representational, 297; scientific (verständlich), 204, 208, 213, 216, 226, 228, 236, 238, 276, 283, 297; speculative, 76, 178, 249; syllogistic, 36, 167. See also pure thinking (reine Denken) Thomism (Thomist), 15, 30, 65, 78, 99, 109, 114, 119, 122n, 123n, 124ff., 135n, 144, 208, 219n, 222n, 225, 235n, 246n, 247, 248n, 253, 260n, 270, 276n, 290n, 317n, 319n Thought (Harman), 92n, 94n, 105n, 107n Tieszen, Richard (Phenomenology, Logic, and the Philosophy of Mathematics), 85n totality, 16, 31, 105, 177, 178, 188, 191, 197, 203n, 211, 217, 218, 222ff., 229, 230, 235ff., 241, 244, 247ff., 264, 268, 271ff., 283. See also conclusion Tragesser, Robert S. (“Inference”), 74n transcendental illusion (Kant), 43, 167 transcendental logic, 20, 23, 29n, 34, 35, 36n, 44, 126n, 167, 169, 210n, 243, 278n, 281, 282, 287, 297 transcendental phenomenology, 22n transcendental predication (Heidegger), 167 translation, 61ff., 151, 205, 230n, 231, 265 true seeing (Fichte), 30 truth, 16, 17, 25, 30n, 60ff., 79 (Carnap), 85, 86, 94, 103ff., 118 (Lonergan), 128 (Bonjour), 136-137 (Bosanquet), 139n (Lotze), 140, 141n (Blanchette),

360 Inference and the metaphysic of reason 142 (Blanshard), 161, 162 (Lotze), 164 (Lotze), 165n, 175 (Lotze), 177, 178, 180n (Harris), 182ff. (Bosanquet), 203, 208n, 211 (Frege), 217, 222, 230ff., 244, 247, 249, 252, 253, 254ff. (Hegel), 260n (Bosanquet), 261, 263 (Hegel), 266, 268 (Hegel), 271n (Blanchette), 275, 285 (Bosanquet), 287n (Kant), 306 (Quine), 314 (Bosanquet), 315, 316 Truth and Predication (Davidson), 249n, 298n

U unconscious inference, 215, 233, 307. See also inference understanding, 29, 34ff., 44, 87n, 88, 97, 109, 115n, 118ff., 129, 153, 154, 167, 170, 199, 237, 252n, 258, 268n, 277-278, 282, 283, 287, 288n, 291, 297, 302ff., 309, 316ff. unity of apperception (Kant), 20 (objective), 167 (synthetic), 169 (synthetic), 296 (transcendental), 302 (objective) “The Unity of Consciousness” (Schlick), 91n unity of rules of understanding (Kant), 34 universal consciousness (Royce), 200 Unnatural Doubts (M. Williams), 92n, 94n Urban, Wilbur Marshall (Beyond Realism and Idealism), 144n ursprüngliche Handlung (Fichte), 48

V validation (of inference), 32, 211, 225-226 The Value and Destiny of the Individual (Bosanquet), 80n, 180n, 191n van Stigt, Walter P. (Brouwer’s Intuitionism), 86n Vellman, Daniel J., and Alexander George (Philosophies of Mathematics), 84n Vernunftschluss (Kant), 36, 126n, 135, 161n, 305 Vico, Giambattista (The New Science), 290 visionary, 93, 316 von Wright, Georg Henrik (“Broad on Induction and Probability”), 82n Vor-schein (Heidegger), 221

W Wallace, Robert M., 218n, 221; Hegel’s Philosophy of Reality, Freedom, and God, 214n, 220, 254 Watkins, Eric, and Fisher (“Kant on the Material Ground of Possibility: From The Only Possible Argument to the Critique of Pure Reason”), 19n, 36n Weir, Alan, “Naturalism Reconsidered,” 250n Weissman, David (Intuition and Ideality), 84n (“Dialectical Cycles of Intuitionist Method”), 87n Werk-Phänomen (Cassirer), 52

3 index Werkmeister, William H. (“Cassirer’s Advance Beyond NeoKantianism”), 52 Werksein (of artwork), 317 Wesen. See essence “What is Universally Quantified and Necessary and A Posteriori and It Flies South in the Winter?” (Fodor), 64n, 93n what-it-is (to ti esti) (Aristotle), 87, 217, 223, 230 what-it-signifies (Aristotle), 318 Whitehead, Alfred North (Whiteheadian), 39n, 61, 73n, 124n, 142ff., 165, 179, 180, 191, 222; conformal feeling, 278n WORKS: Adventures of Ideas, 17, 135; The Concept of Nature, 144; Modes of Thought, 262 (“Importance”); Process and Reality, 56, 82n, 138, 246, 247n, 278n; Science and the Modern World, 55, 66n, 118, 196n “Why Hegel’s Concept Is Not the Essence of Things” (Houlgate), 33n, 44n, 211n, 239, 240n, 242n, 246 Williams, Michael, 12, 32n, 36, 37, 55, 70, 77, 78, 94, 102-108, 110ff., 117, 118, 125ff., 136, 144, 152n, 258, 259, 312ff.; Problems of Knowledge, 66n, 70n, 79n, 92n, 102ff., 113n, 192n, 312n, 313n; Unnatural Doubts, 92n, 94n; critical epistemic mass, 105, 125; epistemic significance, 104, 106 Williams, Robert R. (“The Question of the Other in Fichte”), 49n Wilson, Fred (“Bosanquet on the Ontology of Logic and the

361 Method of Scientific Inquiry”), 109n, 189n Wilson, John Cook, 59n, 150, 181 Wipple, John F. (The Metaphysical Thought of Thomas Aquinas), 252n Wirkens-Phänomen (Cassirer), 52, 53 Wirklichkeit (actuality as actualization), 47 (Lotze), 99, 121, 123n, 147n, 151 (Lotze), 165 (Lotze), 174 (Lotze), 203, 205, 214, 215, 216n, 230n (Hegel), 265n (Kant), 268, 317 Wissenschaftslehre (Fichte), 30n, 48, 50, 112, 214n, 296 Wittgenstein (Ludwig), 22n, 89, 100 Wolff, Christian, 26, 73n, 291n, 303 Wood, Allen W., 47, 48; “Fichte’s Intersubjective I,” 215n; and Paul Guyer, “Introduction” to Critique of Pure Reason, 77n; Kant, 36n, 309n Word and Object (Quine), 63n Wurzer, William S. (“Fichte’s Parergonal Visibility”), 49n, 50, 224n

Z Zöller, Günter (Fichte’s Transcendental Philosophy), 50, 51n Zugegensein (being-present), 30n, 280 Zwischen (Lotze), 157-158