Ramsey's Legacy (Mind Association Occasional Series)

MIND ASSOCIATION OCCASIONAL SERIES

RAMSEY’S LEGACY

MIND ASSOCIATION OCCASIONAL SERIES This series consists of occasional volumes of original papers on predefined themes. The Mind Association nominates an editor or editors for each collection, and may cooperate with other bodies in promoting conferences or other scholarly activities in connection with the preparation of particular volumes. Publications Officer: M. A. Stewart Secretary: B. W. Hooker

Also published in the series: Perspectives on Thomas Hobbes Edited by G. A. J. Rogers and A. Ryan Reality, Representation, and Projection Edited by J. Haldane and C. Wright Machines and Thought The Legacy of Alan Turing Edited by P. J. R. Millican and A. Clark Connectionism, Concepts, and Folk Psychology The Legacy of Alan Turing, Volume II Edited by A. Clark and P. J. R. Millican Appearance versus Reality New Essays on the Philosophy of F. H. Bradley Edited by Guy Stock Knowing Our Own Minds Edited by Crispin Wright, Barry C. Smith, and Cynthia Macdonald Transcendental Arguments Problems and Prospects Edited by Robert Stern Reason and Nature Essays in the Theory of Rationality Edited by José Luis Bermúdez and Alan Millar Leviathan After 350 Years Edited by Tom Sorell and Luc Foisneau

Ramsey’s Legacy Edited by

HALLVARD LILLEHAMMER and D. H. MELLOR

CLARENDON PRE SS

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OXFO RD

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Great Clarendon Street, Oxford, OX2 6DP Oxford University Press is a department of the University of Oxford. It furthers the University’s objective of excellence in research, scholarship, and education by publishing worldwide in Oxford New York Auckland Cape Town Dar es Salaam Hong Kong Karachi Kuala Lumpur Madrid Melbourne Mexico City Nairobi New Delhi Shanghai Taipei Toronto With offices in Argentina Austria Brazil Chile Czech Republic France Greece Guatemala Hungary Italy Japan Poland Portugal Singapore South Korea Switzerland Thailand Turkey Ukraine Vietnam Oxford is a registered trade mark of Oxford University Press in the UK and in certain other countries Published in the United States by Oxford University Press Inc., New York © the several contributors 2005 The moral rights of the authors have been asserted Database right Oxford University Press (maker) First published 2005 All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, without the prior permission in writing of Oxford University Press, or as expressly permitted by law, or under terms agreed with the appropriate reprographics rights organization. Enquiries concerning reproduction outside the scope of the above should be sent to the Rights Department, Oxford University Press, at the address above You must not circulate this book in any other binding or cover and you must impose the same condition on any acquirer British Library Cataloguing in Publication Data Data available Library of Congress Cataloguing in Publication Data Data available Typeset by D. H. Mellor Printed in Great Britain on acid-free paper by Biddles Ltd., King’s Lynn, Norfolk ISBN 0–19–927955–1

978–0–19–927955–5

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PREFACE

This volume contains revised versions of ten of the thirteen original papers given and discussed at the Frank Ramsey Centenary Conference, held in Newnham College, Cambridge, from 30 June to 2 July 2003. This conference, organised by the editors, was the first of three conferences held to commemorate the centenary year of Ramsey’s birth. (The other two were held later in the year in Paris and Vienna.) The Cambridge conference was generously supported by the Mind Association, the Analysis Trust, the Aristotelian Society, the British Society for the Philosophy of Science, and the Faculty of Philosophy, and the Centre for Research in the Arts, Social Sciences and Humanities, of the University of Cambridge. We are grateful to all these bodies, and especially to the contributors, and everyone who attended and helped us to organise the conference, who made it, we think, not unworthy of its subject.

H.L. D.H.M. Cambridge February 2005

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CONTENTS Notes on the Contributors

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Introduction HALLVARD LILLEHAMMER

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Ramsey’s Principle Resituated JÉRÔME DOKIC & PASCAL ENGEL

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Success Semantics SIMON BLACKBURN

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Ramsey’s Legacies on Conditionals and Truth DOROTHY EDGINGTON

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What is Squiggle? Ramsey on Wittgenstein’s Theory of Judgement PETER M. SULLIVAN

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Ramsey’s Transcendental Argument MICHAEL POT TER

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Ramsey on Universals FRASER MACBRIDE

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Empiricism and Ramsey’s Account of Theories PIERRE CRUSE

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Ramsey Sentences and Avoiding the Sui Generis FRANK JACKSON

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What Does Subjective Decision Theory Tell Us? D. H. MELLOR

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Three Conceptions of Intergenerational Justice PARTHA DASGUPTA

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References

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Index

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NOTES ON THE CONTRIBUTORS SIMON BLACKBURN is the Professor of Philosophy at the University of Cambridge, and a Fellow of the British Academy. His books include Spreading the Word, The Oxford Dictionary of Philosophy, Ruling Passions, and Think, and he has contributed widely to issues in the philosophy of language, epistemology, and metaphysics. PIERRE CRUSE currently lectures in philosophy at King’s College London. He is co-editor (with Dylan Evans) of Emotion, Evolution and Rationality. SIR PARTHA DASGUPTA is the Frank Ramsey Professor of Economics at the University of Cambridge and a Fellow of St John’s College, the British Academy, and the Royal Society. His publications include Economic Theory and Exhaustible Resources (with G. M. Heal), The Control of Resources, An Inquiry into Well-Being and Destitution, and Human Well-Being and the Natural Environment. JÉRÔME DOKIC is Directeur d’Études at the École des Hautes Études en Sciences Sociales, and a member of the Institut Jean-Nicod in Paris. He is the author of The Philosophy of Sound (with Roberto Casati), L’Esprit en mouvement, Qu’est-ce que la perception?, and Frank Ramsey. Truth and Success (with Pascal Engel). DOROTHY EDGINGTON is Waynflete Professor of Metaphysical Philosophy at the University of Oxford, and was previously Professor of Philosophy at Birkbeck College, University of London. She is best known for her work on conditionals, including a long survey article, ‘On Conditionals’, in Mind (1995). PASCAL ENGEL is Professor of Philosophy at the Université Paris– Sorbonne, and a member of the Institut Jean-Nicod. He is the author of The Norm of Truth, Davidson et la philosophie du langage, Philosophie et psychologie, Truth, and Frank Ramsey. Truth and Success (with Jérôme Dokic). FRANK JACKSON is Director and Distinguished Professor of Philosophy at the Research School of Social Sciences, the Australian National University. He is a Corresponding Fellow of the British Academy and his books include Conditionals, Perception, and From Metaphysics to Ethics. HALLVARD LILLEHAMMER is a University Lecturer in the Faculty of Philosophy at the University of Cambridge, and a Fellow of King’s College. He is co-editor (with Gonzalo Rodriguez-Pereyra) of Real Metaphysics.

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FRASER MACBRIDE is Reader in Philosophy at Birkbeck College, London. He has written several articles on metaphysics, the philosophy of mathematics, and the history of philosophy. D. H. MELLOR is Emeritus Professor of Philosophy at the University of Cambridge, a Fellow of the British Academy, and an Honorary Fellow of the Australian Academy of the Humanities. His books include The Matter of Chance, Matters of Metaphysics, The Facts of Causation, Real Time II, and Probability: A Philosophical Introduction. MICHAEL POTTER is Reader in the Philosophy of Mathematics at the University of Cambridge and a Fellow of Fitzwilliam College. His books include Reason’s Nearest Kin: Philosophies of Arithmetic from Kant to Carnap and Set Theory and its Philosophy: A Critical Introduction. PETER M. SULLIVAN is Professor of Philosophy at the University of Stirling. He has published numerous papers in the history of analytical philosophy, particularly on Frege and the early work of Wittgenstein. From 2003 to 2006 he is director of an Arts and Humanities Research Board project focused on the interpretation of Wittgenstein’s Tractatus.

Introduction HALLVARD LILLEHAMMER

Frank Ramsey’s brief publishing career lasted for eight years from 1922 to his death in 1930 at the age of 26.1 During this time Ramsey produced ground-breaking work in philosophy as well as mathematics and economics. The chapters in the present volume testify to the lasting significance of Ramsey’s work in each of these disciplines, with an emphasis on Ramsey’s ideas in the core philosophical areas of logic, metaphysics, and the philosophy of mind. TRUTH, SUCCESS, AND CON DIT IO NAL S The first two chapters in the volume concern an approach to the theory of representation known as success semantics (see Whyte 1990). In the first chapter of the volume, Dokic and Engel defend a version of this view according to which the truth conditions of a belief are the invariant conditions in the world that guarantee the success of any action based on that belief irrespective of the contents of the desires that motivate the action. They trace this claim, also referred to as Ramsey’s Principle, back to Ramsey’s analysis of belief in his 1927 paper ‘Facts and Propositions’. In this paper Ramsey writes (somewhat cryptically) that ‘any set of actions for whose utility p is a necessary and sufficient condition might be called a belief that p, and so would be true if p, i.e. if they are useful’ (p. 40). As understood by Dokic and Engel, Ramsey’s Principle has an apparently troubling consequence. If the truth conditions of beliefs are identified with the success conditions of associated actions, then the truth of all an agent’s beliefs entails the success of any associated action. This claim is problematic. On the face of it, failure to act successfully could be down to other factors than false belief, such as ignorance of relevant facts and the like. Dokic and Engel resist this conclusion. In doing so, they draw a distinction between implicit and explicit knowledge. On their view, actions are a source of implicit knowledge of their own success conditions. In acting successfully, an agent acquires the means to form explicit warranted beliefs 1 For details on Ramsey’s life and work, see the introductions to Ramsey (1978) and (1990), and Sahlin (1990). For electronic resources, see and . Ramsey’s writings, including work unpublished in his lifetime, are collected in Ramsey (1931, 1978, 1990, 1991).

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the collective truth of which guarantees the success of his action. Thus, my action of raising the glass puts me in a position to know that the glass was not glued to the table while I was acting. The action of raising the glass is itself a source of knowledge about the absence of any obstacles to the action of raising the glass. Most of the relevant beliefs comprising this knowledge will not be explicitly formed. Nevertheless, were they to be explicitly formed they would be justified by the experience of acting. According to Dokic and Engel, this avoids the apparent difficulty. On their view, Ramsey’s Principle should be understood as a claim about beliefs accessible to the agent, whether he holds them explicitly or not. It is this set of mainly implicit beliefs the truth of which entails the success of the agent’s action. Blackburn agrees with Dokic and Engel that true beliefs contribute to the success of an indefinite number of actions. But he rejects their claim that true beliefs are a guarantee of success when agents act. According to Blackburn, success in action is also sensitive to the agent’s environment and his other mental states. However, while he rejects Ramsey’s Principle as interpreted by Dokic and Engel, Blackburn does not reject success semantics. Instead, he puts forward a compositional version of success semantics, according to which a representational feature of a representing vehicle, such as a name or a predicate, refers to some entity if and only if actual and possible actions based upon that vehicle are typically successful, when they are, at least partly because of something about that entity. Blackburn calls this the Fundamental Schema. According to Blackburn, one advantage of the Fundamental Schema is that it retains the notion of success in action as fundamental to the theory of representation without thereby implying that true beliefs guarantee success in action. While avoiding the problem addressed by Dokic and Engel, Blackburn’s account runs into other difficulties. Perhaps the most serious objection is that success semantics can easily appear to presuppose what it tries to explain (see Papineau 1993). The explanation of the content of beliefs in terms of successful action is vulnerable to the charge that we can only understand what successful action is if we have an antecedent grasp of the satisfaction conditions of desires. Yet desire satisfaction is as much a representational notion as truth is. Blackburn’s response to this objection is that if the Fundamental Schema were intended as a reductive account of all representation, then its reliance on the representational character of desire would indeed refute it. However, the schema can also be thought of in a less ambitious way. According to Blackburn, for any representing vehicle (e.g. a belief ), the Fundamental Schema can be used to account for its representational power. In applying the schema, the representational power of other representing vehicles (e.g. desires) may need to be presupposed. But the representational power of these vehicles can then be explained by reapplying the Fundamental Schema. Thus, by means of a diachronic application of the schema to an agent’s overall mental economy, a plausible picture of what the agent believes and desires will eventually emerge. While

Introduction

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Blackburn admits that his epistemological solution to the problem leaves other, metaphysical, problems unanswered, he suggests that once the main problem is seen in its proper light the remaining metaphysical worries begin to disappear. Another influential and intriguing claim from ‘Facts and Propositions’ is that ‘It is, perhaps, also immediately obvious that if we have analysed judgement we have solved the problem of truth’ (p. 39). According to Ramsey, there is no separate problem of truth, but merely a ‘linguistic muddle’. Locutions involving the concept of truth do not introduce a new subject matter, but merely allow us to reaffirm what is being said or thought. Edgington’s chapter confronts this ‘minimalist’ account of truth with another of Ramsey’s influential claims, namely that indicative conditionals do not express genuine propositions. Taken at face value these claims conflict, because it is clearly possible both to affirm and to reject an indicative conditional such as ‘If I eat some pie, I will get a bellyache’. Drawing parallels with the later work of Quine and Lewis, Edgington argues that Ramsey’s view is entirely consistent on this point. While Ramsey was a minimalist about truth, he was not a minimalist about what it takes to be a bearer of truth. While, in a loose sense, indicative conditionals can be affirmed and denied, they cannot strictly speaking be negated. Disagreement about an indicative conditional is not disagreement about whether that conditional or its negation is true, but rather about the non-equivalent question of the conditional probability of the consequent given the antecedent. In her chapter Edgington traces the subsequent history of the analysis of indicative conditionals after Ramsey. She also draws attention to a number of features of conditionals as construed by Ramsey that support the claim that they do not express genuine propositions. RAMSEY, RUS SELL, AND WITTGE NSTEI N Two chapters in the collection concern the influence on Ramsey of Wittgenstein’s Tractatus, a work Ramsey was instrumental in translating into English. Sullivan’s chapter addresses Ramsey’s interpretation of the Tractatus analysis of judgement in his Mind Critical Notice of 1923, and his own elaboration of this theory in ‘Facts and Propositions’. The basic tenet of this theory is reasonably well understood. In order for beliefs to represent, they must share the structure and complexity of the facts they represent. In Wittgenstein’s words, ‘we have no co-ordination of a fact and an object, but a co-ordination of facts by means of a co-ordination of their objects’ (Wittgenstein 1922: 5.542). It is a corollary of this account that any reference to the subject (or ‘the soul’) in the analysis of judgement is otiose. Sullivan argues that Ramsey’s interpretation still provides the best clue to Wittgenstein’s account in the Tractatus, and that Ramsey himself ends up expounding a version of it. On this account, to report an agent’s belief is just to say how the representing elements of his mind are ordered.

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Sullivan goes on to consider an objection to the Wittgenstein–Ramsey analysis of judgement, namely that it is possible to know that an agent has a certain belief without knowing anything about the representing elements involved in it. In response, Sullivan argues that Ramsey (and possibly Wittgenstein) regarded his analysis as temporary, or merely schematic. The identification of the representing elements involved in judgement and their external relations to what they represent is a genuine matter of investigation, but one for the empirical science of psychology rather than a priori philosophical analysis. Potter’s chapter addresses the influence of Wittgenstein’s Tractatus on Ramsey’s treatment of infinity, and in particular on a transcendental argument for the Axiom of Infinity that occurs in two draft papers which Ramsey never published. According to this argument, our very idea of infinity proves its existence. The argument has four steps: (1) If the claim that there is an infinite number of objects is meaningful, then it is true; (2) If it is meaningful to say that there is an infinite number of empirical entities, then the claim that there is an infinite number of objects is meaningful; (3) It is meaningful to say that there is an infinite number of empirical entities; (4) Therefore, there is an infinite number of objects. Potter argues that Ramsey’s motivation for giving this argument presupposes a central element of the Tractatus theory of propositions. On this theory, propositions divide the way things could be into two classes. The truth value of a proposition is given by which of these classes includes the way things actually are. According to Wittgenstein, the different ways things could be must have something in common in order for this to be possible. It is this ‘something’ that Wittgenstein refers to as ‘objects’, and which Potter takes Ramsey to be inferring an infinite number of in his transcendental argument. Potter shows how Ramsey came to reject his transcendental argument after he adopted a new notation (known as ‘propositional function in extension’) that makes false premise (1) of his argument. Wittgenstein, however, refused to accept Ramsey’s new notation. Potter ends his chapter by asking whether the transcendental argument would go through if Wittgenstein were right and premise (1) restored. Potter argues that premise (3) of Ramsey’s argument is vulnerable independently of the coherence of propositional functions in extension. The question for Potter is not whether we can utter the claim that there is an infinite number of empirical things with the greatest confidence (we obviously can), but rather whether we can really understand it. If Wittgenstein was a major influence on Ramsey’s philosophical formation, so was Russell. In MacBride’s chapter this dual influence is explored in the context of Ramsey’s 1925 paper ‘Universals’. In this paper Ramsey famously questions the ontological distinction between universals and particulars. MacBride’s main concern is to defend Ramsey against a popular misconception that takes Ramsey’s argument in that paper to be that there is no universal–particular distinction because there is no subject–

Introduction

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predicate distinction. MacBride argues that Ramsey was not committed to either the antecedent or the consequent of this conditional, nor indeed to the conditional itself. In fact, Ramsey questioned the prospects of reading conclusions about ontological categories off from linguistic analyses, and was quite prepared to consider that the existence of universals might only be discoverable a posteriori, as argued by some contemporary philosophers, such as Armstrong and Mellor. By locating Ramsey’s paper in the context of the writings of Russell and Wittgenstein in the 1920s, MacBride provides a textual case for an interpretation of Ramsey as motivated by a commitment to a radically Humean metaphysics, in which Humean scepticism extends not only to notions such as causation or law, but also to the notions of particular and universal. RAMSEY SE NTENCES, METAPHYS I CS, AND CONCEPTUAL ANALYSIS In his 1929 paper ‘Theories’, Ramsey introduced what has later come to be known as the ‘Ramsey sentence’. In this paper Ramsey was concerned to explicate the relationship between the ‘secondary’ (e.g. theoretical) terms of a theory and the theory’s ‘primary’ (e.g. observational) terms. Ramsey’s highly influential proposal was that a theory’s secondary terms are analysable in terms of an existentially quantified formula in which all secondary terms have been replaced by bound variables, the resulting sentence including only primary terms plus the language of logic and mathematics. Cruse’s chapter traces the influence of the Ramsey sentence on twentieth-century empiricism, and goes on to defend the application of Ramsey sentences in accounting for what he calls theoretical concepts in the philosophy of mind. Adopting a modular approach to human cognition, Cruse defines a theoretical concept as one referring to something that is not represented by a perceptual module of information-processing (see Fodor 1983). According to Cruse, theoretical concepts so understood have their meaning fixed by their place in the theories in which they occur, as given by a Ramsey sentence in which the only singular terms remaining are ones expressing observational concepts represented by perceptual modules of the cognitive system. Cruse concludes that Ramsey’s account of theories can be used to defend a sophisticated form of concept empiricism. Jackson puts Ramsey sentences to a different use, namely a defence of conceptual analysis as a philosophical method. In his chapter Jackson attempts to answer the question why conceptual analysis is so hard. His answer is, roughly, that a conceptual analysis is a claim that there are two equivalent ways of picking out the same similarity patterns in the world. Thus, an analysis of ‘sibling’ in terms of the disjunction of ‘x is a brother’ and ‘x is a sister’ is correct if and only if ‘sibling’ and ‘x is a brother or a sister’ pick out the same similarity patterns in the world (which they do). Conceptual analysis is difficult because, according to Jackson, it is rarely

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obvious (as it is in the sibling case) that different terms put together in determinate ways carve out the same similarity patterns in the world. One fact which any account of philosophical analysis must explain is the ubiquitous nature of apparent disagreement on what constitutes a correct analysis of a concept like knowledge, say. For Jackson, this is where Ramsey sentences come in. According to Jackson, for a concept to have an analysis is for that concept to have a place in a network of terms for which we can give a Ramsey sentence in which terms expressing that concept have been replaced by bound variables. Yet for many terms, like ‘knowledge’ for example, it is implausible that all basically competent speakers locate the term in exactly the same network as each other. In other words, it is implausible that there is a single concept of knowledge that all competent users of the term ‘knowledge’ use that term to express. This does not rule out that there is a correct analysis, Ramsey style, for every candidate concept. It is this latter claim that Jackson wishes to defend in his chapter. DECIS ION THEORY, VALUE, AN D MEASUREMENT Two chapters in the volume address Ramsey’s contribution to theories of rational choice. Mellor’s chapter concerns the interpretation of subjective decision theory. In subjective decision theory rational choice is measured in terms of expected utility, as determined by how probable and valuable agents take the possible outcomes of relevant actions to be. In contrast to subjective decision theorists like Jeffrey and others, Mellor argues that subjective decision theory is most plausibly interpreted descriptively rather than normatively (see Jeffrey 1983). Mellor also argues that Ramsey interpreted subjective decision theory this way in his 1926 paper ‘Truth and Probability’. Mellor’s case against a normative interpretation of decision theory is based on his argument that an action’s maximising subjective expected utility is not enough to make that action the right thing to do. For example, whether it is right for me to stop smoking in order to avoid cancer depends on whether my smoking is in fact likely to cause me to get cancer and whether getting cancer will in fact be a bad thing for me. Thus, for decision theory to be normative, it requires an objective theory of both chances and utilities. Mellor’s case in defence of a descriptive interpretation of subjective decision theory consists in admitting that the theory has descriptively false consequences, but then claiming with Ramsey that the theory is nevertheless an ‘approximate truth . . . which . . . can, I think, still be profitably used even though known to be false’ ( Ramsey 1926c: 69). Further elaborating Ramsey’s analogy in his 1926 paper between subjective decision theory and Newtonian mechanics, Mellor claims that subjective decision theory is a theoretical idealisation the false consequences of which do not undermine its claim to be regarded as a constitutive truth about credences and subjective utilities as attributed to rational agents.

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Dasgupta’s contribution concerns the lasting significance of the approach to intergenerational justice taken by Ramsey in his 1928 paper ‘A Mathematical Theory of Saving’. In this paper Ramsey asks how much of its income a nation should save for the use of future generations. While this paper is not well known among philosophers, Dasgupta suggests that it could be among the dozen or so most influential papers in twentiethcentury economics. Ramsey’s approach to the issue of intergenerational saving was thoroughly utilitarian. Justice between generations is accounted for in terms of a notion of intergenerational well-being, this being the sum of each generation’s well-being, which is again the sum of individuals’ well-being within a generation. On Ramsey’s account, the optimal approach to saving is for each generation to act so as to maximise the well-being of all individuals in the present generation and all future generations equally, each successive generation knowing that the previous generation has done the same. It follows from this approach to saving that the well-being of future generations is not subject to discounting. Ramsey was aware of this consequence, the denial of which he claimed to be ethically indefensible. In his chapter Dasgupta shows how Ramsey’s utilitarian approach without discounting leads to both intuitively implausible and incoherent consequences in some possible worlds. Drawing on more recent work in economics, Dasgupta shows how Ramsey’s approach has come to be superseded by less overtly utilitarian models of measurement that do reasonably permit some discounting of future generations. These models adapt the mathematical techniques invented by Ramsey, and apply them to a more complex ethical domain than the narrowly utilitarian one envisaged by Ramsey. Dasgupta also argues that the contractarian approach to intergenerational justice taken by Rawls in his 1972 work A Theory of Justice does not represent any advance on Ramsey’s 1928 account.

Ramsey’s Principle Resituated JÉRÔME DOKIC & PASCAL ENGEL RAMSEY’S PR INC IPL E AND SUCCE SS SEMANT ICS Let us consider what may be called ‘Ramsey’s Principle’. It is the principle that ‘truth is the property of a belief that suffices for your getting what you want when you act on it’ (Whyte 1990: 149). When an action results in getting what one wants, i.e. when it leads to the satisfaction of one’s desires, the action is said to be successful. So, according to this principle, there is an internal relation between truth and success: (RP) True beliefs are those that lead to successful actions whatever the underlying motivating desires. Ramsey’s Principle should not be taken as a definition of truth. The conflation between RP and a theory of truth comes from the fact that one fails to distinguish truth (which can be understood in the minimalist sense ‘“p” is true iff p’) from truth aptness, i.e. whether p has truth conditions or not (Jackson et al. 1994; Engel 2002, 2004). RP is first and foremost about truth aptness. A fortiori it should not be confused with a pragmatist definition of truth. As is well known, Ramsey did not defend a pragmatist definition of truth, but argued instead for a version of the redundancy theory of truth.1 However, in ‘Facts and Propositions’ he exploited the idea that there is an internal relation between truth and success to suggest a pragmatist theory of the contents of at least some beliefs. The content of a belief is the conditions under which it is true. Now, even though Ramsey does not express himself in this way, we can derive from him the claim that a belief’s truth conditions are determined by its success conditions (Whyte 1990; Sahlin 1990: 70–2; Mellor 1991b: 21–3). RP
is an alternative formulation of RP which highlights this specific claim: (RP
) A belief’s truth conditions are those that guarantee the success of an action based on that belief whatever the underlying motivating desires. (Whyte 1990; Mellor 1991b; Papineau 1987, 1993) Ramsey’s Principle is often misunderstood. We cannot here deal with all the possible sources of misunderstanding, but two preliminary remarks are in order. The first is that truth conditions are not to be identified with the 1

23).

For the reasons why it is a only a quasi redundancy view, see Dokic and Engel (2002:

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results of action, which change according to the desire (or set of desires) involved. They are to be identified with the invariant conditions in the world that guarantee success whatever goal is pursued. According to Ramsey’s Principle, these conditions are nothing but the state of affairs corresponding to the belief or, more simply and less emphatically, the belief’s truth conditions. Typically, the truth conditions which RP promises to derive from the conditions of success of actions are not those of our actual actions, but they are the truth conditions of the beliefs which would lead to actions. (This disposes of the familiar objection to pragmatism that a number of our beliefs which are actually useful in such or such circumstances turn out to be false.) Second, RP, as stated above, applies to full beliefs, those which we are disposed to judge as true or false, period. A common mistake consists in supposing that it applies to partial beliefs—or to our subjective degrees of beliefs—as well. But if it did apply to these, RP would immediately turn out to be false, for the degree of our belief cannot guarantee the success of action. Suppose, for instance, that the degree of my belief that it will rain tomorrow is only 0.5. It can combine with a desire not to risk a wet picnic, which in turn can cause me to stay at home tomorrow. But we cannot say that it is part of the success condition of my staying at home that either it will rain tomorrow or not (Whyte 1990: 156). Could we say, however, that a sufficiently high degree of belief (say 0.6) could guarantee the success of our actions? Couldn’t we say that beliefs are more likely to be true when they lead to success more often than not, or even typically? Certainly such a relation seems plausible, given RP. But the high degree of partial belief does not warrant automatically the success of all the actions to which they lead. This may seem to be a threat to the correctness of RP, since most of our beliefs are partial ones, even if we do not hold them consciously. After all, did not Ramsey himself famously say that ‘all our lives we are in a sense betting’ (Ramsey 1926c: 79)? But this kind of objection rests upon a misunderstanding of Ramsey’s Principle. In order to assign any degree to a belief, one must be able to give a content to that belief, and RP tells us that this belief’s content or truth conditions are those which suffice for the success of the actions to which it would lead if it were a full belief. In this sense RP is presupposed by decision theory when it assigns degrees to our beliefs. The assignment of content to our beliefs through their success conditions is thus more fundamental than the assignment of degrees to these through the actions that we perform.2

2 Although we cannot argue for this here, this feature is closely related to the fact that the step of practical reasoning leading to action—what Searle (1983) calls the ‘intention in action’—is made through categorical judgements. See below, however, about the connections between knowledge and action.

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It is now customary to call ‘success semantics’ the philosophical project of deriving truth conditions from success conditions. According to many writers, Ramsey’s Principle should be supplemented by a teleological account of our beliefs and desires. Success semantics, they claim, is necessarily a ‘teleosemantics’, for the contents of our beliefs (and desires) are determined, at least in part, by their biological functions, including adaptative ones.3 RP seems to fit quite well in the teleosemantical picture. However, there is some controversy about the nature of the relationship between Ramsey’s Principle and teleology. There are at least four options:4 (a) The contents of beliefs and desires are directly defined by their biological functions or purposes. (b) Teleological considerations are relevant for explaining the normal functioning of the formation mechanisms of beliefs and desires, in particular their causal roles in the production of action. (c) Ramsey’s Principle needs a teleological definition of the satisfaction conditions of desires, from which it can derive a definition of the truth conditions of beliefs. (d) Ramsey’s Principle, in its absolute version, is in fact false. Truth guarantees success only in a normal context, and teleological considerations are needed to define what a normal context is (relative to the organism). The first option has been defended by Papineau (1987, 1993). According to him, beliefs have the biological functions of leading to success when they are true. This is what he calls their primary purposes, to be distinguished from their secondary purposes. For instance, the belief that one is not going to be injured in the ensuing conflict, though false, has the secondary purpose of getting people to fight effectively. Success semantics comes into the picture precisely to isolate primary purposes, since it equates the truth conditions of beliefs specifically with the conditions under which beliefs contribute to the satisfaction of desires. According to defenders of option (b), beliefs do not have biological functions from which one could directly read off their contents. For instance, Millikan argues that the content of a representation does not rest ‘on the function of the representation or of the consumer, on what these do’. There is no such a thing ‘as behaving like a representation of X or as being treated like a representation of X’ (1993: 89). Millikan introduces a distinction between the production and the consumption of representations in a cognitive system. She deplores, rightly to our mind, that most theories of 3 Sahlin (1990: 72) mentions this point about the famous chicken–caterpillar example given by Ramsey in ‘Facts and Propositions’. Defenders of teleosemantics include Millikan (1984), Dretske (1988), McGinn (1989), Papineau (1987, 1993), Jacob (1997 ). 4 We do not exclude that some of these options can be combined.

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representation almost exclusively focus on the production conditions of representations to the detriment of their consumption conditions. This is particularly true of ‘informational’ or ‘causal covariance’ theories, which try to define the content of a representation by reference to what causes the representation.5 In contrast, according to Millikan, the content of a representation is entirely fixed by the ways it is used in the cognitive system to which it belongs. Of course, one can invoke teleological considerations in order to deal with the conditions under which the representation is produced. For instance, one can suppose that one of the functions of the visual system is to produce representations that accord with reality, in other words, veridical representations. This function of the visual system, though, does not enter the definition of the content of a particular visual representation, which is determined by the way it is consumed, eventually by the kinds of behavioural control it can exert. Millikan nonetheless claims that other teleological considerations are relevant to defining the contents of our beliefs. The consumer part of a cognitive system has a biological function which has been selected for by evolution. According to Millikan, it is not directly the function of the consumer part which determines the content of a belief, for the use of a given belief can have an indefinite number of results, depending on the subject’s context and other propositional attitudes. Rather, the content of a belief is determined by the ‘Normal conditions’ of functioning of the consumer part. The phrase ‘Normal conditions’ is a term of art in Millikan’s account. The conditions under which a system is functioning ‘Normally’ are not necessarily those in which the subject is most often (this would correspond to the statistical sense of ‘normally’), but (roughly) those in which it exerts the function which it or its ancestors have been selected for in the past. Options (c) and (d) constitute quite different arguments for teleosemantics. According to (c), Ramsey’s Principle cannot get off the ground without an independent account of the satisfaction conditions of desires. RP defines the contents of beliefs in terms of the satisfaction conditions of the underlying motivating desires, i.e. of their contents. The partnership between RP and teleology should be understood as follows: success semantics is a theory of the contents of beliefs, and teleosemantics is an account of the contents of desires. According to (d), RP should be rejected in its absolute form. Truth does not guarantee success in every situation; at best, truth leads to success in a normal environment. RP should then be relativised to the context. Now, an 5 Roughly, informational or causal covariance theories define the content of a token representation by reference to the information it carries, or the information that any token of that type has the function of carrying. Such information is defined in its turn by the laws, most often causal, which link the referent to the production of a token representation. See Fodor (1990a); Jacob (1997 ).

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environment is ‘normal’ only if the agent has been adapted to it. The notion of adaptation is teleological, which means that success semantics must also be a teleosemantics. We cannot consider here all these options. In Dokic and Engel (2002) we argue, against (c), that one cannot have an independent account of the satisfaction conditions of desires. Moreover, it could be argued (Whyte 1993) against Papineau’s version that his distinction between normal or primary purposes of beliefs has the effect of making teleology redundant. RP just explains truth conditions in terms of the fulfilment of desires. But adding that desires must bring about ends which are favoured by natural selection adds nothing. Our argument here will be targeted specifically at (d): we shall claim that when the notion of adaptation is well understood, there is no need to relativize Ramsey’s Principle to circumstances. This leaves us with options (a) and (b). We cannot go into details here, but let us remark that, on either account, there is a sense in which teleological considerations play only a ‘pre-semantic’ role. Perry (1993) introduces the distinction between semantic and pre-semantic uses of context. In the case of the interpretation of utterances, context is used pre-semantically in order to determine the language, the words, and the linguistic meaning. For instance, the considerations that make a given proper name, say ‘Émile Ajar’, connected to a particular man, in the case in point Romain Gary, play a pre-semantic role according to Perry. In general, the considerations operating at the pre-semantic level do not have to enter the definition of the propositional contents of utterances, which is a semantic matter. Thus, it is not part of the meaning of the proper name ‘Émile Ajar’ that it has been introduced as a guise by Romain Gary. Similarly, although teleological considerations are relevant to determine the contents of our beliefs and desires, they play a pre-semantic role. Given an organism with beliefs and desires, i.e. given that their normal causal roles in an organism are in place, RP can be used to derive their truth and satisfaction conditions. Teleological factors are not part of the contents of our beliefs and desires. The success conditions of an action are facts which are coeval with the action; typically, in themselves they have nothing to do with the historical conditions in which our cognitive system has evolved. In this respect our defence of RP does not commit us to a form of naturalistic account of content (although we do not claim that it is incompatible with such an account). Perhaps the divergence between our understanding of success semantics and the various versions of teleosemantics can be formulated thus. Both success semantics and teleosemantics give sense to the familiar claim that ‘truth is the aim of belief’: truth is what our beliefs are directed to if our actions are to succeed. In this sense, both make room for the idea that truth is in some sense ‘normative’ for belief formation. According to Papineau, a teleosemanticist can perfectly account for this normative feature by arguing that the general fact that we value true beliefs simply flows from the very

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connection that success semantics postulates between true beliefs and the satisfaction of desires: If you act appropriately on true beliefs, then your actions are guaranteed to satisfy your desires, and indeed . . . this pragmatic connection [is] a crucial component in the analysis of truth conditional content . . . And this pragmatic connection does mean that there is always a species of derived personal value to truth in beliefs that are relevant to action, for such truth will always help you to find a way to satisfy whatever desires you have. (1999: 26)

Now Papineau emphasises the fact that, on this view, truth, as a value or a norm, is the external aim or goal of belief. On our view, however, Ramsey’s principle flows from an internal relation between the truth of beliefs and their success, and truth is the internal ‘aim of belief’.6 When an agent acts, and when his action is successful, the very fact that it is so implies that his beliefs are true. We could stress the contrast by saying that for the teleosemanticist truth is the distal, or external, aim of belief, whereas for success semantics as we conceive of it, truth is the proximal, or direct, aim.7 OBJECTIONS TO RAMSEY’ S PRINC IPLE FROM SITUATED COG NITIO N One of the (apparently) most damaging objections against Ramsey’s Principle is that it neglects the fact that human action is situated in a context. The principle implies that any failure of action is the result of some false belief on the agent’s part. For if all the agent’s beliefs are true, the action cannot but be successful. This would seem both to over-intellectualise action (by making it, when it fails, the product of false beliefs about it) and to overload the cognitive background of beliefs needed for any action. 6 On this internal reading of the aim of beliefs, as opposed to the teleological external one, see Engel (2004). The fact that success semantics allows us to account for the truthdirectedness of belief makes room for the normative dimension of belief. This point is also emphasised, although in a different way, by Simon Blackburn in his contribution to this volume. 7 In this sense, there is some truth to Horwich’s criticism of a principle which is close to RP ( Horwich 1998), which he claims to be trivial and merely a logical consequence of the fact that our actions presuppose true instrumental beliefs. According to Horwich, his own minimalist conception of truth has no difficulty in explaining the desirability of truth, for any instrumental belief of the form ‘ If I do A, then I will get result R’ will, if the action is successful, be true. Call such a belief D. Then an agent who wants to satisfy a desire to get R will want it to be the case that If I believe that D, then D, which, by the familiar equivalence principle, is equivalent to If I believe that D, then it is true that D. According to Horwich, generalising leads us to conclude that All our directly action-guiding (instrumental ) beliefs are true. Horwich concludes that there is no need to postulate an external and intrinsic goal of truth. We agree, but it does not make RP and success semantics trivial for that. On the contrary, we say that it allows for a substantial link between belief (and knowledge) and action.

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It is of course plausible that some failures can be traced to false beliefs. I try to drink from a particular glass because I believe that it contains something that will quench my thirst. If my belief is false and the glass is empty, I won’t get what I want. However, it is much less plausible, from a cognitive point of view, to suppose that any possible failure of an action corresponds to some false belief or representation on the agent’s part. Robert Brandom remarks that ‘ignorance is no less a threat than error to the positive guarantee of practical success that [Ramsey’s Principle] seeks to identify with truth’ (1994: 175–6). Suppose that I do not get what I want because the glass is glued to the table. According to Ramsey’s Principle, it seems that I should have the belief that the glass is not glued to the table, whose falsity explains the failure of my action. However, the fact that I tried to raise my glass shows at best that I did not have the positive belief that it was glued to the table, but it in no way indicates my having the negative belief needed to vindicate Ramsey’s Principle, namely the belief that it was not glued to the table. In general, there is no guarantee that, in every particular case of action, there is a plausible cognitive level intermediary between a general but trivial belief that there are ‘no impediments’ and a non-denumerable set of beliefs corresponding to each possible failure of the action. In the same vein, John Perry contends that Ramsey’s Principle in its absolute form amounts to ‘overburdening’ belief. He writes: let us first note how unrealistic it would be to suppose that the content of beliefs fix all of the circumstances relevant to the success of our action. Consider the force of gravitation. If I am in space or on the moon or in some other situation where gravitational forces are much diminished, the movement we envisage me making in the example will not lead to getting a drink; the water would fly out of the glass all over my face—or perhaps I would not even grab the glass, but instead propel myself backwards. If all possible failures are to be accounted for by false beliefs, the corresponding true beliefs must be present when we succeed. So, when I reach for the glass, I must believe that the forces of gravity are just what they need to be for things to work out right. (1993: 202)

According to Perry, the gap between action and success cannot be bridged by the agent’s cognitive state only (i.e. the set of her beliefs). At best, the truth of a belief guarantees the success of an action only relative to a normal context (for instance, on earth), whose identity conditions need not be known by the agent. Of course, Ramsey himself would not be much impressed by Brandom’s and Perry’s objections from situated cognition. If Ramsey’s Principle is relativised to circumstances, it becomes false by definition; any reference to a normal context should be blindly included in the belief’s truth conditions. However, even if this response is (as we think) correct, it does not go far enough. Brandom and Perry make appeal to our pre-theoretical intuitions about the contents of our beliefs. They argue that Ramsey’s Principle delivers truth conditions which are at odds with these intuitions. The

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principle would be strengthened if we could show that it is in fact compatible with them. RAMSEY’S PR INC IPL E RESITUATE D In the rest of this chapter we shall defend Ramsey’s Principle in its absolute form against the foregoing objections. Our defence is based on an analogy between knowledge and action. As a first and rough approximation, knowledge is the exclusion of alternatives incompatible with the subject’s claim of knowing. In a Cartesian-like epistemology, the subject must exclude all these alternatives, i.e. have knowledge that they are not the case. For instance, knowing that there is a glass in front of me requires knowing that my visual system is in good order, that I am not dreaming, etc., for these alternatives would certainly preclude my knowledge of the glass if they were the case. What is at stake here is a version of what is sometimes called a Principle of Epistemic Closure: (PEC) If I know that p, and q implies that I do not, I know that q is not the case. Here, q is an alternative with respect to my claim of knowing that p. I cannot be said to know that p if I do not know whether q is the case or not. So every piece of knowledge presupposes many other pieces of knowledge with their own sets of alternatives, which I must rule out in turn. A conception of knowledge based on PEC runs into familiar difficulties. For instance, I cannot know anything on the basis of perception unless I know that I am not dreaming or hallucinating. However, either the latter piece of knowledge cannot be established by perception at all, or it can be established by other perceptual experiences, which raises essentially the same problems. So perceptual knowledge is either impossible or circular. The ‘relevant alternatives’ view of knowledge has been proposed in response to these difficulties.8 On this view, knowledge is the exclusion of relevant alternatives only. What counts as a relevant alternative, and thus as knowledge, depends upon the context.9 To borrow an example from Austin, knowledge that a perceived bird is a goldfinch might depend, in some contexts, on whether there are other similar birds in fact present in my locality. It is then assumed that the alternative that I am dreaming is not relevant in ordinary contexts in which I claim to know that it is raining by looking out of the window.

8 9

Dretske (1970); Nozick (1981). These views are also usually associated with so-called contextualist solutions to scepticism. See e.g. the papers in DeRose and Warfield (1999).

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The relevant alternatives view in effect rejects the implication in PEC by relativising knowledge to circumstances. Some remarks of Michael Williams on epistemic closure suggest an alternative way out of the difficulties associated with PEC, which does not require making knowledge contextdependent.10 These difficulties arise from what we call a temporal interpretation of PEC. On such an interpretation, knowing that it is raining by looking out of the window requires that I first and independently acquire the knowledge that my eyes are in good order. On another, logical interpretation, my knowledge that it is raining and my knowledge that my eyes are in good order can have the same source, for instance my experience of looking out of the window. If I am in a position to acquire the former piece of knowledge, I am also and simultaneously in a position to acquire the latter piece of knowledge. In general, if I am in a position to acquire the knowledge that p, I am thereby in a position to acquire the knowledge that not-q, for any alternative q incompatible with my knowing that p. PEC, even on its logical interpretation, is still too strong. It neglects the fact that my knowledge that it is raining and my knowledge that my eyes are not in good order are not cognitively on a par. Typically, only the former piece of knowledge is explicit and based on direct evidence. I visually perceive that it is raining, but I do not perceive that my eyes are in good order. In order to give justice to the cognitive asymmetries between what I claim to know and what follows from my claim of knowing, two distinctions should be introduced, between implicit and explicit knowledge, and between direct and indirect justification. First, the knowledge that my eyes are in good order, or that I am not dreaming, is rarely, perhaps never, made explicit. The claim under 10 Williams (1991, ch. 8). In fact, Williams’s target is a different version of the Principle of Epistemic Closure, according to which if someone knows that p, and knows that p implies q, then she knows that q. PEC in the text is stronger than this principle, on two counts: it takes into account a larger set of alternatives (namely all alternatives incompatible with one’s knowing, which includes but is not restricted to the set of alternatives incompatible with what is known), and it does not require that the subject know that the alternatives are incompatible with her putative knowledge. Williams rejects the KK Principle (the principle that if one knows, one knows that one knows), which is a consequence of PEC. We cannot go into the discussion of this principle here. See in particular Williamson (2000). Actually Williams intends to defend a contextualist conception of knowledge, whereas our view about knowledge and action here is noncontextualist. Perhaps PEC should be modified to block the possibility of bootstrapping oneself into knowing that one knows. However, the principle that if someone knows that p, and knows that p implies q, then she knows that q, is too weak, for it neglects the possibility of reflective knowledge, such as the knowledge that I am not hallucinating based on my perceptual experience. If the neutralist conception of experience is rejected, it can be argued that my perception that p, which is essentially factive, is accessible to reflection or introspection, and thus can indirectly justify the belief that I am not hallucinating.

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consideration is only that if the subject were to form the corresponding beliefs, they would be justified by the very same experience which justifies her actual belief that it is raining. Second, the justification of the former beliefs need not be as direct as the justification of the latter belief. The exclusion of an alternative to the subject’s claim to knowing can be indirectly justified on the basis of her perceptual experience. Indirect justification can be inferential or reflective. One can gain knowledge that this is not fake rain by inferring it from one’s perceptual knowledge that it is raining. More controversially, one can gain knowledge that one is not dreaming by reflecting on one’s experience with a non-sceptical attitude. On such a view, PEC is essentially correct, but it needs a less misleading formulation in terms of implicit knowledge: (PEC*) If I know that p, and q implies that I do not, I at least implicitly know that q is not the case. In general, I have at least implicit knowledge that p if and only if I am in a position to acquire such knowledge, whether or not I exercise the inferential and reflective capacities needed actually to know that p.11 It seems to us that (PEC*) is consonant with Ramsey’s famous account of knowledge, when he says: ‘ We say “I know”, however, whenever we are certain, without reflecting on reliability. But if we did reflect, then we should be certain if, and only if, we thought our way reliable’ (1929b: 110). Here Ramsey rejects explicitly the condition (known as the ‘KK Principle’) that in order to know that p one needs to know that one knows that p. In Williams’s terminology the reliability conditions for a given item of knowledge do not number among the entailments of what is known (1991: 347).12 (PEC*) does not imply the KK Principle. The temporal interpretation of PEC is naturally associated with a neutralist conception of perceptual experience. According to this conception, perception is not a genuine source of objective knowledge. The best that I can learn from my experience of looking out of the window is that it seems to be raining. Perceptual experience is neutral with respect to the truth of the objective beliefs that are normally grounded on it, such as the belief that it is raining. Whether or not my belief is true, my experience remains in essence the same. In contrast, the logical interpretation of PEC is naturally associated with the rejection of the neutralist conception of perception, more precisely with what is sometimes called a ‘disjunctive’ theory of experience.13 When my 11 Compare Williamson’s (2000: 128) remarks about the distinction between knowing and being in position to know (neither of which, according to him, imply the KK Principle). 12 See Dokic and Engel (2002: 29). 13 Hinton (1973); McDowell (1982). However, see Williamson (2000, ch. 1) for doubts about some versions of disjunctive theories. What is important for our purpose is the rejection of so-called ‘conjunctive’ theories, such as the neutralist conception of experience.

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perceptual experience is veridical, the perceived fact that p manifests itself to me, so that the proposition ‘It seems to me that p’ is not the most precise characterisation of what is going on in my cognitive space. There is a real, cognitive distinction between a situation in which a fact manifests itself to me in perception, and a situation in which I am only under the impression that this is so. As a consequence, a transition from my experience of looking out of the window to a belief that I am not hallucinating would be warranted. In the terminology of Burge (1993), I am entitled to make such a transition, given that the occurrence of the experience implies the truth of the belief. We are aware that much more needs to be said about epistemic principles of closure. However, our aim in this chapter is not to defend a detailed epistemological outlook, but to point out an analogy between knowledge and action. The analogy we are interested in is between PEC and the following Principle of Pragmatic Closure: (PPC) If I am intentionally doing p, and q implies that I am not, I know that q is not the case. Here the phrase ‘doing p’ is used to imply success: just like knowing that p, doing p implies p. So q can be any alternative to the success of the action of doing p.14 PPC is not exactly analogous to PEC, for it does not state that in order to do p, I must do whatever is necessary to lift any obstacle to my making it the case that p. This would be utterly implausible, leading to permanent procrastination. PPC is not so obviously wrong. It states that if q implies the failure of my action of doing p, I must know that q is false. PPC is in fact a stronger version of Ramsey’s Principle, according to which the beliefs underlying a particular action should amount to knowledge, or at least should be sufficiently warranted. It is not enough that the agent holds the beliefs whose collective truth guarantees success; the action counts as intentional only if these beliefs are themselves epistemically well grounded. PPC is consonant with the spirit of Williamson’s (2000) claim that the place of belief and desire in the economy of mental life depends on their connection with knowledge and action and with the idea that knowledge is prior to belief in the understanding of action. Belief emerges only when mind is maladapted to world, just as desire emerges only when world is maladapted to mind. On this view, PPC is not just a variant of Ramsey’s Principle; on the contrary, the versions of Ramsey’s Principle formulated in terms of belief and desire are derived from the more fundamental PPC.

14 In the knowledge case, there is a distinction between an alternative to what is claimed to be known and an alternative to one’s claim of knowing. The analogous distinction in the action case is between an alternative to what is done and an alternative to one’s doing it. There are two different notions of success here—Ramsey’s being the former.

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As in the knowledge case, there is an issue about whether a relativization strategy is needed at this point. In particular, those who find PPC implausible might try to relativize Ramsey’s Principle to circumstances. I do not need to know that the glass is not glued to the table in order intentionally to raise the glass. I just have to try; if the circumstances are normal, the glass will be raised. My action still counts as intentional, even though, strictly speaking, it is the outcome of a joint collaboration with (benevolent) Mother Nature. The alternative option is to distinguish between a temporal and a logical interpretation of PPC. PPC won’t seem plausible if it is interpreted temporally, as if I should know that the glass is not glued to the table before and independently of my action of raising the glass. According to the rival, logical interpretation, I do not have to know that the glass is not glued to the table before acting; rather, my action of raising the glass puts me in a position to know that the glass was not glued to the table (while I was acting). Action itself is a source of knowledge about the absence of any obstacle to it. Such knowledge is not acquired before action; at best, it is a logical consequence of its occurrence. According to the logical interpretation of PPC, intentional action is a source of knowledge relative to a set of beliefs whose collective truth guarantees the success of the action. As with PEC, it does not follow that the agent is explicitly representing all possible obstacles to her action. Most of the relevant beliefs are implicit, in the sense that if they were to be formed, they would be directly or indirectly justified by the agent’s experience of acting. Normally, the agent does not form them, on pain of being distracted from what she’s trying to do. So, on the logical interpretation, the consequent of PPC should be qualified in the same way as that of PEC: (PPC*) If I am intentionally doing p, and q implies that I am not, I at least implicitly know that q is not the case. What is it about the experience of acting which can knowledgeably rule out the alternatives to my intentionally making it the case that p? To begin with, the fact that action is controlled by perception at the subdoxastic level is a source of knowledge about the agent’s orientation relative to the target of her action, the development of the bodily gesture, and many other parameters. Moreover, most of these parameters are not fixed in advance but change during the course of action, which is another indication that the corresponding beliefs cannot be explicit. Non-conceptual perception of affordances yields other beliefs which are instrumental in form, about what one can do and what would be the consequences of one’s doing it in the present circumstances.15 15 As Bermúdez (1998: 118) rightly says, ‘To say that affordances are directly perceived is precisely to say that instrumental relations can feature in the content of perception.’

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Can all the beliefs underlying an action be implicit? The answer might be positive for spontaneous actions, if they exist. Searle pointed out that there are actions which are not caused by any prior intentions, such as the spontaneous action of pacing about the room while reflecting on a philosophical problem (Searle 1983: 84). If these actions are genuinely intentional, they must be able to ground a set of beliefs whose collective truth guarantees success. However, none of these beliefs need to be formed before acting. The distinction between a neutralist and a disjunctive account of perceptual experience has an analogue in the action case. According to a neutralist conception of action, the best that I can do is try to move my body. Action is neutral with respect to its success conceived as the satisfaction of the underlying objective desires, such as the desire to raise my arm. Whether or not I succeed in actually raising my arm, I am doing essentially the same thing, namely trying to raise it. This conception is naturally associated with the temporal interpretation of PPC, for there is no physical action such that I can know in advance that there won’t be any obstacles to its success. Such knowledge is possible only for tryings to move one’s body, which in a sense cannot fail. In contrast, the rejection of the neutralist conception of action is in line with the logical interpretation of PPC. According to a disjunctive account of action, a particular trying is either a mere trying, which is a failed action, or a genuine (i.e. successful) action. So an action can have intrinsic success conditions which go beyond the mere trying to do something. The possibility is then open that one’s experience of acting, which is essentially psychophysical, is a source of knowledge about the action’s external success conditions. CONCL USION To sum up, Ramsey’s Principle in its absolute form is untouched by considerations about situated cognition. In particular, the objection of cognitive overload is answered by distinguishing between implicit and explicit knowledge. Ramsey’s Principle and the stronger Principle of Pragmatic Closure concern in fact all warranted beliefs accessible to the agent, whether or not she actually holds them. The agent must only have the means of forming a set of warranted beliefs whose truth guarantees the success of her action. However, the best argument in favour of Ramsey’s Principle is transcendental, in the sense that it embodies a condition of possibility of intentional action. Some of those, like Perry, who want to relativise the principle to circumstances invoke the agent’s adaptation to her environment in order to justify their claim that the agent does not act with a full awareness of all possible obstacles. Ironically, the objection of cognitive overload does not stand precisely because agents are normally adapted to

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their environment. Adaptation is not a purely external relation between an agent and its environment, as if the former happened to ‘fit’ the latter. Rather, adaptation manifests itself in the fact that action is normally a source of knowledge about its own success conditions. This is another aspect of the internal relation between knowledge and action which Ramsey much emphasised. Our actions’ success conditions reflect themselves in the subject’s cognitive state, if only implicitly, because the agent’s contribution and that of Mother Nature are so intertwined that it is impossible to tell them apart.16

16 The argument in this chapter derives from Dokic and Engel (2002). We would like to thank for their comments on this article and for their encouragements Hugh Mellor, Nils– Eric Sahlin, and Simon Blackburn.

Success Semantics SIMON BLACKBURN

How come we are so successful, unless we are hooked up right to the world? A good question, and one that suggests a way of thinking of our hook-up to the world. Success semantics is the result of that suggestion. It is the view that a theory of success in action is a possible basis for a theory of representation, or a theory of content or intentionality (throughout this chapter I shall use these interchangeably). At its most simple we can think of representation in terms of disquotation, as in the famous ‘Fido’–Fido relationship. Then the idea is that the disquotation of representation is explained or illuminated or even analysed by the disquotation of explanation, where whatever is represented explains something about the person representing it. And what it explains is primarily the success of the actions that the person bases upon the representing. The view is an heir to the pragmatist tradition. At the most general level, the idea is that we get our way, or flourish, or fulfil our desires or our needs because we get things right about the world. The contents of our sentences are then whatever it is that we get right. The ancestor of success semantics, as of so much else, is Frank Ramsey, who wrote that it is right to talk of a chicken’s belief that a certain sort of caterpillar is poisonous if the chicken’s actions were such as to be useful if, and only if, the caterpillars were actually poisonous. ‘Thus any set of actions for whose utility p is a necessary and sufficient condition might be called a belief that p, and so would be true if p, i.e. if they are useful’ (Ramsey 1927: 40). Ramsey did not develop the idea, and it may even be doubted whether his chicken was thought of in representative terms at all. Perhaps it was a primitive precursor of a representing agent. But the idea is too tempting to let lie. It was later picked up and paraphrased, by Jamie Whyte (1990: 147), in terms of the truth condition of a belief being that condition that guarantees the success of desires based on that belief. But the idea that the truth condition of a belief would be whatever guarantees success in action based on the belief meets trouble, because nothing at all guarantees such success. X’s belief may have the truth condition that Cambridge is north-north-east of London, and X may act on that belief, yoking it to his other belief that the way to travel north-northeast out of London is to take the first departure from Paddington. X lands

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up in Bristol, failing in his desire to get to Cambridge.1 This suggests that no fact guarantees success in action, because even when an agent apprehends a fact correctly, there may be an indefinite amount of other rubbish in her head, waiting to misdirect action based upon it. This is the familiar holism of the mental. And there may also be an indefinite number of things not wrong with the agent, as in this example, but wrong with the environment: unknown and unthought-of obstacles waiting to trip her up. Recently, Jérôme Dokic and Pascal Engel have attempted to protect the Ramsey–Whyte view against these difficulties. Their idea is to bring into view the whole range of actual and possible desires that might join with a given belief, and to suggest that true beliefs are those that lead to successful action whatever the underlying motivating desires. (2002: 46)

They quote approvingly Ruth Millikan, who says of percepts of the world: The same percept of the world may be used to guide any of very many and diverse activities, practical or theoretical. What stays the same is that the percept must correspond to environmental configurations in accordance with the same correspondence rules for each of these activities. For example, if the position of the chair in the room does not correspond, so, to my visual representation of its position, that will hinder me equally in my attempts to avoid the chair when passing through the room, to move the chair, to sit in it, to remove the cat from it, to make judgements about it, and so on. (1993: 92)

However, although Millikan is right that a false belief (here, a percept that does not represent a position correctly) stands ready to wreck an indefinite number of projects, it does not follow that a true percept similarly stands ready to guarantee the success of an indefinite number of projects, whatever the underlying desires. ‘Guarantee’ remains too strong. Taken strictly, the Paddington case alone falsifies the view that my saying about Cambridge ‘It’s north-north-east of London’ represents the fact that it does. For with this desire it failed to guarantee success, yet the formula requires that a truth condition guarantee success whatever the underlying desires. One kind of defence is that the theory works only for ideal agents, meaning ones who never believe anything false, and are (vividly) aware of any obstacle that may wait to trip them up. For such agents, perhaps a fact does guarantee the success of action based on a representation of it. But these are agents that have to be described in the first place in terms of representational successes—indeed massive, unqualified representational successes—so there will be a lurking circularity in approaching the issue by restricting the relevant agents in this way. I believe we have to recognize that a true belief will certainly aid an indefinite number of possible projects, but it can do this while guaranteeing 1

For non-English audiences: trains from Paddington go westward.

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none, and, realistically, we must still expect a failure rate, depending, as already indicated, on what else is in the agent’s head, and how cooperative the environment proves to be. In this chapter I try to show that we can do better, without in any way departing from the spirit of Ramsey’s position. Success semantics might be wedded to a theory of biological function, as in some versions of teleosemantics. But I regard that as an option, and one that we should not take. Suppose we want to say that a particular brain state in a frog represents the proximity of a fly (and not of any old small black thing). We could work in terms of some version of this: (A) The brain state represents the proximity of a fly = it is an adaptation, and evolution selected it because it is triggered by flies. Or we could work with some version of this: (B) The brain state represents the proximity of a fly = the state is involved in the genesis of action (behaviour) by the frog, and that behaviour is typically successful because of the proximity of flies. I shall argue in favour of approaches taking the second option. The second approach is equally a success-based approach, but it confines itself to the present, or at least the extended present in which we can talk of what typically causes what. It is by getting flies now that the frog flourishes. Evolution can stay in the background. It provides, no doubt, the correct explanation of the emergence of the system at all. But it leaves the content of any element in the system, such as the brain state, to hinge upon the kinds of behaviour in which it is implicated, and the kinds of function this behaviour has. This is an advantage. David Papineau, for instance, once defended the other choice, talking of the satisfaction condition of a desire as ‘the effect it is biologically supposed to produce’ (1987: 67). But this cannot generally be right, since many beliefs and desires have contents that are too late for any evolutionary process to have selected for them, and hence for any notion of biological purpose to apply. If Amanda wants a mobile phone, we cannot talk of this being an adaptation, nor of the ‘evolutionary purpose’ of her desire. Evolution has had no chance to act selectively on people who do or do not desire mobile phones. Of course, Amanda may be instancing some evolutionarily successful and much older strategy, such as acting like the rest of her group, or acting so as to attract a mate. But those are poor bricks out of which to build a theory of content, since desires, or beliefs, with almost any content can be seen in the same light. If Amanda can be said to instance such a strategy here, she presumably equally instances it when she wants a tattoo or a Britney Spears record. But these are different desires. There are many choices for a theory of content. It can take language as primary, or something else. It can take the individual as primary, or the language-sharing group or community. It can help itself to notions such as

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action, or it can regard them as too heavily involved with intentionality to be part of any explanatory project. It can be heavily marinaded in normativity, or it can try to make do without. It can be wedded to some kind of project called naturalism, or it can turn its back on any such motivation. It can take sentences, or sub-sentential parts, or larger units such as theories as primary. It can be presented as a kind of realism about the mental, or it can come in the spirit of an intentional stance or interpretative manual. It can put up with, or celebrate, indeterminacies and underdeterminations, or it can insist upon facts of the matter. My approach remains neutral on these issues for as long as possible. How long that is remains to be seen. What is the problem of content, or of intentionality or representation? It is usually expressed in terms of the mind’s relationship with external things and states of affairs: things and states of affairs that may or may not exist, or may be relatively near to the subject, or that may be far, in space and time. It is the fact that we can think of distant things, past and future things, or even just imagined things. Sometimes the problem is put as the problem that these thoughts, identified as they are in terms of things different from ourselves, cannot supervene upon brain states of our own. That by itself need not strike us as much of a difficulty. Many facts about ourselves would not be facts but for the relations we have with other things. But we like to be able to say what those relations are, and therein lies the problem. THE THEORY Any theory of mind that takes our representational or intentional capacities as something to be explained seems likely to work in terms of some kind of distinction between vehicle and content, and that is what I shall do. The vehicle of representation, or what Ramsey called ‘the subjective factor’, is usually thought of in terms of the sentence, identified by features other than those intrinsically connected with meaning. So it is contingent whether a sentence has the content that it does. This standard approach need not preclude a wider theory, according to which there might be or actually are other kinds of representational vehicles. For example, there may be nonlinguistic vehicles, or we might want to work towards a theory in which the whole person represents things, without there being anything as it were smaller to count as a specific vehicle at all. We come to say something about such extensions in due course, but for the moment it will do no harm to think in terms of sentences as paradigm representational vehicles. So consider a subject S. S gets about the world, and we suppose that some of her actions are successful. She achieves what she desires. And suppose some of her actions are based upon a vehicle V. It is not going to be easy to say exactly what that means, but at a first pass it may mean that it is because of an event whereby V becomes salient in her overall psychological state. Some writers like to think in terms of a sentence, such as V may be, entering S’s ‘ belief box’. Without being so literal, or geometric, we

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can use that as a model, again if only for the purpose of approaching a wider theory. A slightly more realistic version for humans might be that S gets into a state in which, were she to be asked why she is doing what she is, the answer would contain V as an ineliminable ingredient. As for what distinguishes one’s belief box from one’s entertainment box, containing vehicles of content which we entertain without believing, we should look to functionalism. We should concentrate upon force, meaning that a belief differs from a mere entertainment of a thought precisely in that beliefs are, as it were, in gear. They are playing a role in the machinery of agency. So for the moment we are to think of an event, which I shall call the tokening of a vehicle, precipitating a vehicle into that machinery. In order to come at the idea of V bearing a content (being a representation, having intentionality) we think in terms of explanation. What explains S’s success as she acts upon the belief expressed by ‘The university library is over there’? In the typical or paradigm case, she is successful because the university library is over there. She is not, on the other hand, typically successful because of the whereabouts of Heffers or Trinity College or Grantchester. Why were S and R successful in meeting this afternoon? Because they exchanged tokens of ‘Let’s meet at the university library’ and the university library was where they then went. Once more, it is their going to the university library, not their going past Heffers or through Trinity, that explains their successful tryst. Why was S successful in her shopping? Because she said ‘Can I have some haddock?’ and haddock was what she got. The properties of neighbouring halibut and cod are not typically relevant to the success of the actions based upon that tokening. We could at this point go directly for an attempt to describe the representative content of the whole vehicle, the sentence. We might try something like this: A vehicle V has the content p if and only if behaviour based on V is typically successful, when it is, because p. However, difficulties lie down that direct road. I have in mind difficulties connected with the utility of false belief, which can accrue in various ways. Consider, for instance, the vehicle ‘I am popular’. Psychologists say that this is a useful thing to get into your belief box. It promotes your ability to get on well, even if it is false (maybe, especially if it is false). So it will not be true that behaviour based on tokening this sentence is typically successful, when it is, because the subject is popular. Yet this is the content of the sentence. It would be possible to try to handle this kind of example as Dokic and Engel do, by bringing into view the variety of possible desires that might accompany the tokening. Then, while a false content explains occasional success, only true content could explain a general pattern of success across all these possible applications. I think this may work, although it takes us some distance from our actual evidence. We have no general access to the

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requisite patterns. We have to invent scenarios in which the tokening of ‘I am popular’ conspires with other desires to generate a whole pattern of actions, most of which are unsuccessful if, but only if, it is false. A different range of problems comes into view if we think of approximations. Behaviour based on tokening the standard expression of the Boyle–Charles gas law (Pressure times volume = constant times temperature) is typically successful, when it is, because of the truth of van der Waal’s equation.2 But the sentence does not express the same thing as that equation. Here expanding our gaze to take in possible but non-actual desires does not seem likely to help, since it will always be true that it is the more complex relationship between the magnitudes involved that explains success in relying upon the simpler relationship. In addition, there will be sentences that are too seldom tokened for there to be a typical way in which behaviour based on them is successful, let alone an explanation of any such pattern of success in terms of their truth. All in all, then, a direct approach looks unlikely to give us what we want. If we want to stay more closely to the evidence, the remedy must be to go compositional. We do not want to ignore the structure of the representing sentence. So let us look at reference first, and try what I shall call the Fundamental Schema: Suppose the presence of ‘a’ is a feature of a vehicle ‘a . . .’. Then ‘a’ refers to a if and only if actual and possible actions based upon the vehicle ‘a . . .’ are typically successful, when they are, at least partly because of something about a. Here we imagine a sentence containing a name. Actions are sometimes based upon it. When they are successful, this is typically at least partly because of something about some object. And that is the object that is referred to in the sentence. At this point we may wonder why ‘success’ is allowed to muscle its way to the front. After all, ‘a’ may represent something and then actions based upon a tokening that includes it would typically fail, when they do, at least partly because of something about whatever it represents. The university library being far from a mile away would explain why I failed to get there, acting on the tokening ‘The university library is about a mile away’. Perhaps ‘action semantics’ would be a better title than ‘success semantics’. I think this point is right, as far as it goes. But I also think that success in action is the fundamental notion: like Davidson and Wittgenstein I incline to think that failure only exists against a background of success. It is only because of our successes that the representational powers we have are adaptive, and

2 The more complex equation that corrects for the finite volume of gas molecules, and the attraction between them, which are ignored in the Boyle–Charles Law.

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exist in the first place. So I shall retain the title, while remembering that it is the place of representation in the overall life of an agent that is the focus. For any actual term, there will of course be a huge variety of possible sentences in which it may occur. So the pattern of success illustrated here for any one particular sentence can be enormously bolstered by thinking of other sentences alike in containing the term ‘a’—enough so that the credentials of the object a as the focus, the uniquely invariant explanans of a huge variety of doings, will be abundantly established. Some might worry that the ‘something about a’ introduces something suspicious and unscientific, such as surreptitious mention of facts.3 But that is just an artefact of the generality of the proposal. The fundamental schema collects together a pattern of explanation, and, as is often the case, to generalize in this way we need mention of truth or fact. But in any particular case, the explaining is done without anything suspicious of the kind. Why was John’s action based on tokening ‘The university library is about a mile away’ successful? Because the university library is about a mile away. In other words, the introduction of a vocabulary of fact or truth is necessary for theorists generalizing about the phenomenon. But it does not indicate any mysterious residue in the phenomena themselves. Before expanding this, and confronting objections, we should notice a few points. Some are obvious enough, but others deserve separate mention. 1. There is a disquotation in that the name, or other feature, of the vehicle mentioned is used in the sentence following ‘because’. It is in this sense that the schema reproduces the idea of representation as a vehicle– world relationship. 2. There is a ‘typically’ qualification corresponding to the fact that we want to tiptoe past deviant causal chains and the like. We gain our point of entry by thinking of the typical or normal case, just as we gain our point of entry to a causal theory of, say, vision by thinking of the typical or normal case. There may follow a choice about how seriously we should look on deviant cases. 3. There is an attempt to accommodate the thought that sometimes we refer to things which never enter into our action plans by expanding the explanatory range to actual and possible actions. I do not plan much on the basis of a tokening of ‘Henry VIII’, but were I to do so, or to have done so, and generated a class of successful actions, that would be because Henry VIII was one way or another. 4. The actions specified may or may not be those of the agent. A baby may say ‘biccy’, and the fact that the word signifies biscuits is certified by the fact that other people’s actual or possible actions based upon his saying are typically successful if, but only if, they involve biscuits. Things go well 3

This objection was urged upon me by Gary Kemp.

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just when biscuits are provided by someone else, in response. If the baby is at a stage where this is not so—for instance, the success rate is the same if cereal is provided—then reference is not so specific. Of course ‘biccy’ in the baby’s mouth may express desire rather than belief. But that is an advantage of the account: representation is different from force. 5. There is no necessary restriction to linguistic vehicles. The schema would apply, for instance, to maps. If a feature of my map of Cambridge is the presence of a big picture of a tower here, then that can refer to the position of the university library if actions based upon that feature of the map are typically successful, when they are, because of the position of the university library. Similarly, if we are moderately realistic about mental imagery, there is no principled objection to features of the imagery carrying intentional content. If we reify perceptions (I do not claim that we should, or even that it is permissible to do so), then elements of perceptions can carry content, referring to libraries, features, distances, and so on. 6. The schema speaks directly to compositionality. That is, its point of entry is a feature of a sentence, correlating with a feature of the world. Thinking intuitively, if we imagine an atomic sentence ‘Fa’, if one clause certifies the contribution made by the presence of ‘a’, another clause would certify the contribution made by the presence of ‘F’, in the obvious way (the presence of ‘F’ would refer to a property F if and only if actual and possible actions based upon the vehicle ‘. . . F’ are typically successful, when they are, at least partly because of something about the property F ). This compositionality is put into the shop window, as it were, because it is kinds of vehicles that correlate with kinds of explanations of success, and the ‘sub-sentential components’, or as I prefer to call them features of vehicles, identify the kinds. Of course, our standard model would be the presence of words in a sentence, but other features of vehicles could easily have content on this methodology. I believe this aspect is actually true to Ramsey, who introduced the chicken example only as a preface to considering other sorts of belief, that is, ones expressed in composite linguistic vehicles. 7. Although the point of entry is sub-sentential, there is no conflict with Frege’s insistence on the priority of the overall vehicle or sentence. That priority can be maintained provided the idea of action being based on a vehicle requires a whole or unified vehicle: something like a sentence. But in this sense, a picture could serve as a sentence. 8. Similarly there is no necessary conflict with a holistic view of language, for two reasons. Firstly, a feature may only be able to gain content, given this explanation, if it occurs in many different sentences, differently successful in different ways, provided there is a unifying thread in the explanation of those successes. This will be the various properties some thing has (if it refers to a thing) or the varying instantiations or lacks of them that some property has (if it refers to a property). And, secondly, it remains possible, for all that the schema implies, that an action can never be

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regarded as being based upon a single vehicle, but only on any given vehicle in conjunction with others. 9. The notion of ‘the’ explanation may worry some. In the simple, pointof-entry case, we imagine something like this. A person tokens a succession of vehicles, ‘The university library is over there’, ‘The university library is a mile away’, ‘The university library contains books’, and so forth. He performs acts based upon these tokenings and is successful in some typical ways. Then the idea is that there is no ‘total explanation’ of the success of the first that fails to include the position of the university library relative to the subject, or of the second that neglects its distance from the subject, or of the third that neglects the fact that it contains books. Although in particular cases we might choose to emphasize something else, these facts will merely have been suppressed. They would need to be cited in a full story. Equally, we might wish to stress the differential or contrastive nature of explanation in order to avoid the outcome that we are always referring to the presence of oxygen or the continuation of the gravitational field—things that are background general conditions of success. 10. The explanations in question need not be causal. Reference need not be confined to items that are causally anterior to the tokening of the vehicle. Actions successfully based on tokens such as ‘Tomorrow will be wet’, ‘Tomorrow will bring the examination’, and so on, may typically be successful because the day after their tokening is wet, or does bring the examination. In that case the day after the tokening is in good standing as the content or reference introduced by ‘tomorrow’ as an element of the vehicle. Abstract objects can be referents, in so far as (say) nineteen being one thing or another is the explanation of the success of action based on the vehicle ‘nineteen . . .’. Reference to complexes such as aggregates or species and kinds clearly follows on seamlessly. Actions based on the vehicle ‘Crowds are dangerous’ are typically successful, when they are, because crowds are dangerous, and similarly for sheep being tasty or water being wet. Indeed it is the very promiscuity of explanation, and its protean capacity for covering all kinds of topic, that largely explains the failure of causal theories and other attempted naturalistic reductions of semantic notions (there is a comparison here with similar frustrations in defining knowledge in other terms). 11. On the other hand, we could draw back at some putative cases of reference. Can one refer to non-actual possible worlds, for example? That will depend on how we can explain the success of actions based on putative mention of them. If such explanations can cite the way possible worlds are as the explanans of this success, then reference is saved. But if this is not so, then the referential credentials of the terms is put into question. I myself have grave doubts whether useful explanations of our propensity to modality can take this shape. If those doubts are well founded, then by the fundamental schema there is no such thing as reference to possible worlds.

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The schema does not solve our problems here, but it helps to pinpoint them. 12. The fundamental schema fleshes out the thought that our doings are successful because we are hooked up rightly to the world. This kind of formula may ring alarm bells, implying to some people an ‘Archimedean point’ or God’s-eye view whereby we Stand Above and Behind our own theories and applaud them for their real contact with Elements of the World. But this fear, whatever it amounts to, is in any event groundless. The explanation of our success that we give when we cite the university library being one way or another is not the offspring of some transcendental, Archimedean viewpoint. It is an explanation from within. It is no more mysterious than the way the university library blocks the view or costs money. These are things the library does, and there are others, and these are amongst them. The way it is in various dimensions sometimes explains the success of human doings, based on tokenings. (I should say myself that this ‘deflationist’ stance also explains what force there is to the ‘no miracles’ argument for realism about scientific theories. It is not that there is a metatheory, called realism, required to explain this success. It is that just as science explains pressures and temperatures, so it explains the successes of actions based on reference to those pressures and temperatures, and so on for the other theoretical elements of science.) 13. Many people hold that representation is somehow essentially normative, and that this normative dimension is, fatally, missing from naturalized accounts such as that of the fundamental schema. This is difficult terrain, but at least standards for normative assessment are closely implicated by the fundamental schema. For the notion of success is at the heart of the analysis. Where there is success there is also the chance of failure, either in a subject’s state, or in the way his signals are taken by others. It will not require any other source to give us all that is needed from a notion of correctness or incorrectness in representation. 14. The disquotation in the fundamental schema is one that we give. It is one we give when describing our own representations. So there is a sense in which, if it is the last word, we cannot stand outside our own skins— perhaps there is even a sense in which the early Carnap and others were right, that semantics is a very limited enterprise. But this does not mean that the proposal achieves nothing, or nothing more than a strictly modest or quietistic disquotational semantics does. It does not leave us with starkly irreducible notions like reference or predication, backed up, for all it tells us, by noetic rays. On the contrary, it naturalizes these notions by seeing them as applying to relational features of things we say to ourselves, or pictures, or anything else we give ourselves, responsible for our success as agents acting in a surrounding world. And so to difficulties. Some are easy to cope with, but others less so. The hardest, I believe, is voiced by Papineau. Papineau talks of Ramsey’s

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different suggestion, criticized above. But the present proposal is just as vulnerable to the objection. Papineau complains: ‘It explains truth for beliefs, only by assuming the notion of satisfaction, for desires. Yet satisfaction is as much a representational notion as truth, and so ought itself to be explained by an adequate philosophical theory of representation’ (1993: 70–1). So, for instance, consider our agent who wants a particular book, believes that the book is in the university library, and that the university library is in some direction from where he stands. Suppose all goes well. We can say that his success is explained by the book being in the university library, and the university library being where he expected. But his success is identified in terms of getting what he wanted, and that requires content or intentionality: he wanted a particular book, which he therefore had to represent to himself. If we cannot say that much about him, we have no reason, it seems, to talk of success at all. But to say that much requires some pre-existing representation, and that vitiates the proposal as a general account. Should this objection silence us? It does not falsify the fundamental schema, but only suggests a limit to its utility. Yet how severe is this limit? If we were trying to give a reduction of all intentionality at a blow, it would be serious. But perhaps we do not have to claim any such ambition. It remains true that for any particular representative feature of a vehicle, we can use the fundamental schema to give a truth condition or account of its representative power. That account only works, it is true, by imagining the feature embedded in the psychology of an active, desiring agent. And it is true that when we turn to the fact of desire, other representative powers will be implicated. But these in turn can be explained by a reapplication of the schema. Suppose the book our agent desired was Emma, and suppose his desire was activated by the tokening of a representative vehicle: ‘I must read Emma’. Then the fact that the term ‘Emma’ represents Emma is given, according to the fundamental schema, by the fact that actual and possible actions based upon the vehicle ‘Emma . . .’ are typically successful, when they are, because of something about Emma. Notice that among these examples of success we can number the very occasion under discussion: the agent’s success on this occasion arose because Emma was in the university library. Faced with this, it is not very clear how damaging Papineau’s problem is. But, in addition, we can approach it from a different angle. Papineau’s problem will probably seem most intractable if we think synchronically. We might imagine the simultaneous tokening of two vehicles, VB carrying the content of the belief, and VD carrying the content of a desire. And we perplex ourselves because ‘success’ underdetermines the identity of these two things together. ‘Success’ could consist in the belief having one content, and the desire a related content, or the belief having a different content with an accommodating difference in desire, and so on indefinitely. Underdetermination stares us in the face.

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But suppose we think a little more diachronically. We find out what baby wants by finding what brings peace. We could be wrong: baby may have wanted a biscuit, but be pacified by a rattle. But as the days go by, typical patterns emerge. If ‘biccy’ reliably correlates with pacification by a biscuit, we get one entry into our lexicon. If when baby seems to want a biscuit we direct his attention successfully by saying where it is, and the words we use become part of baby’s repertoire, then we take them to be representing wherever it is. And so it goes, entry by entry. But at the end of the process there is only one thing to think, sometimes, about what the emergent child believes and wants. And by then representative features of vehicles are available either to enter the function of pushing and pulling, the ‘desire box’, or the function of guiding the actions appropriate to the pushings and pullings, the ‘belief box’. This solves the epistemological problem. We play off macro behaviour and microstructure of vocabulary, and, just as with a crossword puzzle, clue at a time, fallibly, but eventually uniquely, a solution emerges. But does it solve the metaphysical or ontological problem? Does it tell us what representation is, or how intentionality is possible? Does it, for instance, make room for misrepresentation? I believe so. Consider misunderstanding first. Suppose subjects S and R want to meet, and S says ‘Let’s meet in New York’ and R hears ‘Let’s meet in Newark’. They will fail to meet. S intended R to token something with one kind of power, and he tokened something with a different kind. Instead of directing him to New York, the event set him off towards Newark. It is an event which reliably does that, because there is a feature of the vehicle (which might be ‘Newark is the place to go’), and actual and possible actions based upon the vehicle are typically successful, when they are, because Newark is the place to go. On this occasion, it is not, and action will fail. With falsity we imagine an agent whose tokenings of ‘a’ and of ‘F ’ generally slot into the fundamental schema so as to compel interpretations as referring to a, and to the property F, respectively. We suppose that the (syntactic) structure (or some other feature) of the vehicle ensures its indicative form. So the subject bases action on ‘Fa’, interpreted as a being F.4 In other words, he acts on the belief that a is F. Unfortunately a is not F. So either the subject will be unsuccessful, or his success will not be explicable in the typical, disquotational fashion. He is not successful because a is F, but in spite of a not being F. There is no principled difficulty about isolating such cases and saying the right thing about them.

4 Clearly, I am assuming that ‘concatenation’ in a simple atomic sentence as vehicle has the consequence that the vehicle represents whatever is referred to by the name term as having whichever property is represented by the predicate.

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If the theory allows misrepresentation to fall nicely into place, it is difficult to see what remains of the idea that it is at best epistemologically adequate, but failing on some metaphysical or ontological ground. However, another general problem looms. So far we have run representation and reference together, imagining that a theory of the latter, in terms of explanations of success, will automatically give us a theory of the former. But there are difficulties here, since obviously a subject can represent without referring. This is the problem of empty names (or predicates that fail to pick out properties, although historically that seems not to have been so worrisome). Johnny represents Santa Claus to himself (and success may attend his actions based on this representation). But his tokenings do not refer to Santa Claus, or to anything, since the explanation of his success does not consist in Santa Claus being one way or another. Johnny himself may suppose the explanation of his success to be the doings of Santa Claus, but he is wrong about that. Maybe the typical explanation of the success of Johnny’s actions, such as hanging up a stocking, are the doings of Johnny’s father. So can we avoid the result that his tokenings in fact refer to his father? We may not want to avoid it: it is no accident that when Johnny grows up, one way for his father to reveal the truth is to say ‘ I was Santa Claus all along’, or ‘It was me to whom you wrote all those letters’. If we want to avoid the interpretation, we can invoke several other features of the situation. Johnny’s friends all suppose one person to be the common reference of the name, but no one person explains their successes equally. Johnny’s conception of what Santa Claus is like is quite at variance with what Johnny’s father is like, and although that does not preclude reference, it at least counts against it. But there still remains the question: how are we to analyse the distinction between representation and reference that the case opens up? What we need to cope with this is the idea of Johnny’s mindset being appropriate to a Santa Claus world, although we do not inhabit such a world. We can do this if we use the notion of a dossier that Johnny associates with the tokening of ‘Santa Claus’: giving presents, visiting once a year, climbing down chimneys, and so forth. This dossier corresponds to beliefs Johnny has about what Santa Claus is like and what he does. The existential quantifications associated with those descriptions should not be problematic, for we have already suggested an approach to the general problem of misrepresentation. That he ties these quantifications together under the heading of Santa Claus gives us our understanding of Johnny’s mindset. It is inappropriate to the actual world, and its token ‘Santa Claus’ has no reference. But it does not show us a Johnny who is irrational or uninterpretable, and certainly not one whose tokenings fail of content, so that he fails to think at all. Johnny thinks, hopes, desires, is grateful, just as if Santa Claus were a real person. There is more to be said about fiction, and fantasy (I have imagined Johnny in the grip of a real mistake, not fantasizing about non-existents in

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full awareness that this is what he is doing). But I do not see that the phenomena will force any significant move away from the fundamental schema. Less global difficulties may remain. One intriguing worry might be that the theory falls into a mirror-image of one problem that afflicts a causal theory. Causal theories of reference do not easily allow reference to the future. Is it possible that success-based theories do not easily allow reference to the past? For after all, what causes success is a matter of what will be the case when the time to reap rewards comes, which will be the future. So, for instance, how can I refer to the present position of my car when it is the future position of my car that will explain my success or failure as I walk in the direction in which I am prompted by some tokening? There are two kinds of answer to this. One would point out that explanations cast a wide net, and we do not confine explanations to immediate or proximate explanations. True, it is whether the car will be in a place to which I walk that proximately determines my future success. But it is where it is now that explains where it will be (in the normal case, in which the car is stationary). The other kind of answer reminds us of the wide class of actual and possible actions. My actual actions, based on a tokening of the present position of the car, reap their rewards in the future. But possible actions based on the same tokening could have reaped their rewards now or in the past. Hence, there is a wider class of possible actions whose success would typically be, or have been explained in accordance with the fundamental schema, by facts about past or present objects. I have talked throughout of tokenings as events, in which a vehicle is somehow summoned into an active area of the brain or mind: a belief box or desire box implicated in the machinery of action. We may wish to point out that, as well as episodic events like this, there are ‘standing beliefs’, or for that matter standing desires, which may seem to be implicated in action but with no event of this kind taking place. To accommodate this idea, I take it we can expand our conception of what it is for action to be based on vehicles. We might think of some vehicles exerting a standing pull. The words ‘It is a bad idea to walk into a wall’ do indeed not have to go through my mind for me to act daily on the belief that it is a bad idea to walk into a wall. But the fact that it is that belief upon which I am acting has to lie somewhere. Presumably it lies in my being in a state both in which I am strongly disposed to avoid walls, and in which I am disposed to cite something like the belief mentioned as the rationale for my first disposition. In the habituated agent a tokening does not have to precede an action based on the belief that the tokening expresses. Similarly we can say that the batsman played the stroke as he did because he foresaw the flight of the ball. But we don’t have to think of an antecedent mental picture with elements representing that flight. It is enough that afterwards he could produce such a picture, either mentally or on paper or in any other way.

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I have talked in very simple terms of actions being based on tokenings, and some may be poised to object that this makes a mockery of the delicate space of reasons. Representational tokenings should not be thought of as pushing action in some hydraulic or mechanical way. Rather, they inject contents into the space of reasons, and whatever action emerges is only the resultant of operations within that space. But it is a mistake to think that the simplicity of the conception is inconsistent with the complexity of our reasonings. The simplicity of the conception is supposed to take some of the mystery out of representation or intentionality. It does require a notion of basing an action upon a tokening (or background disposition to token). Such ‘basing’ may become more complex than any simple two-factor, desire–belief, model suggests. Actions may turn out almost never to be based upon one tokening at a time. Standing beliefs and desires complicate things indefinitely. But at the end of the day there is such a thing as basing action on belief, and expressing belief in vehicles, just as there is such a thing as basing the direction of movement on a map. And this is all that is required to launch success semantics as a going concern.

Ramsey’s Legacies on Conditionals and Truth DOROTHY EDGINGTON I Two ideas associated with Frank Ramsey have been very influential, and further developed in recent years, one about conditional judgements, the other about truth. The two ideas can appear to be in tension with each other, for the former has a consequence which it has seemed hard to square with the latter. Philosophical descendants of Ramsey on truth have found it hard to be philosophical descendants of Ramsey on conditionals.1 It is this tension which I want to discuss and try to defuse. A footnote in Ramsey’s ‘General Propositions and Causality’ (1929a) has had a great impact on thinking about indicative conditionals since the 1960s. The idea it propounds has come to be known as the Ramsey Test. Here it is: If two people are arguing ‘ If p will q?’ and are both in doubt as to p, they are adding p hypothetically to their stock of knowledge and arguing on that basis about q . . . they are fixing their degrees of belief in q given p. ( p. 155)

Now there are proofs, the first due to David Lewis (1976), which appear to show that, on this way of thinking about conditionals, conditionals do not express propositions, evaluable in terms of truth. This came as a surprise to the interested part of the philosophical community. I think Ramsey would not have been surprised. There are numerous indications in the 1929 paper that he accepted that treating conditional judgements this way was not to treat them as expressing propositions. I don’t say that he had a proof to this effect, but I think he saw that the conclusion was correct. Ramsey is also a source of a family of views on truth called ‘minimalist’ or ‘deflationist’ or ‘redundancy’ theories: ‘It is true that Caesar was murdered’ means no more than that Caesar was murdered. The word ‘true’ has the useful function of enabling us to say things like ‘That’s true’, ‘Einstein’s Theory is true’, ‘Everything he said was true’. These locutions do not introduce a special subject matter of truth. They provide us with a way of affirming what was said, or Einstein’s Theory, or in the last case, of generalising—committing oneself to all instances of ‘If he said that p, then p’. As the names suggest, this is meant to be a thin and undemanding account of truth, compared to its rivals. It is hard to see how this minimalist 1

See, for instance, Blackburn (1986); Field (1994: 252–8).

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function can fail to apply to conditionals. If what you said, or one of the things that he said, or part of Einstein’s Theory, is a conditional, how can this use of ‘true’ (and mutatis mutandis of ‘false’) be disallowed? Hence the apparent tension. In the next three sections I discuss Ramsey’s idea about conditionals, its subsequent development, and its apparent incompatibility with treating conditionals as truth bearers. I then examine in more detail Ramsey’s conception of truth and its bearing on his treatment of conditionals. II Return to the Ramsey Test. What it proposes is that in assessing a conditional, we suppose that the antecedent is true, and consider what we think about the consequent, under that supposition. That sounds innocuous enough. The second part of the quotation is more specific about what this comes to: we are ‘fixing [our] degrees of belief in q given p’. This notion, ‘degree of belief in q given p’, was introduced in Ramsey’s earlier paper ‘Truth and Probability’ (1926c), and one of his ‘fundamental laws of probable belief’ is Degree of belief in ( p and q) = degree of belief in p
degree of belief in q given p. ( p. 77)

Substitute ‘probability’ for ‘degree of belief’, and you have a well-known law of probability, the term on the right being a conditional probability. There was nothing novel in this fundamental law of conditional probability, which was standard since the eighteenth century. What was novel in Ramsey’s 1926 paper was the interpretation of probability, and conditional probability, as partial belief, and partial conditional belief, the principles of probability yielding what he called a ‘logic of partial belief’ (p. 53). And what was novel in the 1929 footnote was the linking of ‘degree of belief in q given p’ with our ordinary, typically uncertain, conditional judgements expressed using ‘if’. A&B A&¬B ¬A

A ¬A FIG. 1

One way of explaining the idea is shown above in Figure 1, which shows two partitions: sets of exclusive and exhaustive possibilities. The probabilities of, or one’s degrees of belief in, the members of a partition (to the extent that they can be made precise) should sum to 100%, the degree of belief in a certainty. That is all there is to treating degrees of belief as probabilities. Coming to a view about A is comparing A and ¬A: seeing

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them as in competition for your belief. If you think that A is 4 times more likely than ¬A, that is to think that it is 80% likely that A. In coming to a view about B on the assumption that A, you ignore the ¬A-possibility—hypothetically eliminate it. Just focusing on the Apossibilities, you compare B to ¬B; that is, you compare A&B with A&¬B. If you think that A&B is 4 times more likely than A&¬B, you think it is 4 to 1 that B if A; that is, B is 80% likely on the supposition that A. Restricting attention to the A-possibilities, your degree of belief in B is 80%. For example, if you think it’s 80% likely that she will be cured if she has the operation, you think (she has the operation and is cured) is 4 times more likely than (she has the operation and is not cured). This way of looking at it is not the most basic way, for two reasons. First, you can have a degree of belief in B on the supposition that A without having a degree of belief in A (and hence without having degrees of belief in A&B and A&¬B). Ramsey noted this, considering conditionals like ‘If I do p, q will probably result’. He says ‘Here the degree of probability is clearly not a degree of belief in “Not p, or q” (i.e. the material implication) but a degree of belief in q given p, which it is evidently possible to have without a definite degree of belief in p, p not being an intellectual problem’ (1929a: 154). Second, to arrive at a degree of belief in A&B, one typically uses the notion of a conditional probability, according to Ramsey’s Test, and asks, how likely is it that A? And how likely is it that B if A? So the basic thought experiment is simply to assume the antecedent and consider how likely the consequent is, under that assumption (as Ramsey said). On reflection, that can be seen to be equivalent to judging that A&B is (say) 4 times more likely than A&¬B, even if you have no degrees of belief regarding the components of this comparison. To repeat the example, if I think that it is 4 to 1, or 80% likely, that she will be cured if she has the operation, I think (operation and cured) is 4 times more likely than (operation and not cured), even if I don’t have a degree of belief that she will have the operation, let alone that she will have it and be cured. In the passage just cited, Ramsey makes the point that it is our uncertain conditional judgements that make this approach essential. If I am sure that if I do p, q will result, there is no harm, he says, in considering this as belief in the material implication, that is, the disjunction ¬p or q (‘but it differs’ he says ‘from an ordinary disjunction in that one of its members is not something of which we are trying to discover the truth but something within our power to make true or false’). But when it is ‘If p, q will probably result’, this is not a degree of belief in ¬p or q, he says, but a degree of belief in q given p. ‘And our conduct is largely determined by these degrees of hypothetical belief’ (1929a: 154). Indeed, provided that the antecedent does not get zero, the probability of the material conditional and the conditional probability coincide in the case of certainty. Return to the partition on the right of Figure 1. If p(A&¬B) is

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0, p(A
B) and p(B given A) are both equal to one. There is only one other case in which they coincide: when the probability of the antecedent is 1. In all other cases, the material implication is more probable than the conditional probability, because it gets added probability from the case in which the antecedent is false. They come spectacularly apart when the probability of ¬A is high yet p(A&B) is low relative to p(A). For example, let p(¬A) = 90%, p(A&B) = 1%, and p(A&¬B) = 9%. p(A
B) = 91%; p(B given A) = 10%. And the latter, not the former, matches how we do assess conditionals. For instance, I judge that it’s 90% likely that Jane won’t be offered the job, 10% likely that she will, 1% likely that she will be offered and decline, 9% likely that she will be offered and accept. I think it’s 10% likely that she will decline if she is offered the job, while the probability of the corresponding material implication is 91%. This would appear to rule out that conditionals are material implications. If conditionals were material implications, we should judge them to be probable when the material implication is probable. But we don’t. Hence conditionals are not material implications (though they may harmlessly be treated as such in some contexts). It does not, of course, rule out that conditionals are some fancier sort of proposition. Nevertheless, it gives the shape of the stronger results to follow: for any proposed truth condition, it can be shown that the probability of its obtaining can come apart from the probability of consequent given antecedent. III In the 1960s Ernest Adams developed a theory of conditionals conforming to Ramsey’s footnote (Adams 1965, 1966). Most importantly, he developed a logic for arguments with conditionals among their premises or conclusion, whose rationale is as follows. First take an uncontentious classically valid argument without conditionals: one such that it is impossible that its premises be true and conclusion false. Ask this question: suppose I am close to certain, but not quite certain, that its premises are true. Then what should I think about its conclusion? It is easy to prove the following: it is impossible that the improbability of the conclusion should exceed the sum of the improbabilities of the premises (where improbability is one minus probability). Thus, arguments which necessarily preserve truth, necessarily preserve probability in the sense that there can be no more improbability in the conclusion than there is in all the premises together. So, in a twopremise valid argument each of whose premises gets a probability of 99%, the worst-case scenario for the conclusion is that it gets 98%. This vindicates the use of deduction from uncertain premises, provided that they are not too uncertain, and provided that there are not too many such premises. The only way that you can validly deduce an improbable— perhaps zero-probability—conclusion from highly probable premises is where there are a great many such premises, as in the Lottery Paradox. On

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the other hand, if you have just two premises but each is just 50% probable, the conclusion can get 0, for instance, ‘The coin will land heads; it will land tails; so it will land heads and tails’. This is all good stuff: an elaboration of the use of deduction under conditions of uncertainty. Now turn to conditionals. The truth-functional account does badly when we consider uncertain conditional judgements, as we saw above. Indeed, whatever plausibility it has comes from ignoring uncertain judgements. Adams’s view in the 1960s could be put like this: we don’t have a theory of the truth conditions of conditionals such that we believe them to the extent that we think they are probably true. But we do have an excellent way to assess their probability (or the degree to which they are accepted)—Ramsey’s way. So let us use the criterion of probability preservation (strictly, probability or conditional probability preservation) as the criterion of validity of arguments with conditionals. And a nice logic emerges. For example, modus ponens is valid: demonstrably, if p(A) is high and p(B given A) is high, p(B) is high. On the other hand, there are the counter-examples to strengthening of the antecedent, to transitivity, and to contraposition, which are now well known. ( Note: the logic is for sentences in which the conditional, if it occurs, occurs as a main connective. Not having truth conditions, we have no automatic treatment of embedded conditionals—a point to which I return.) Robert Stalnaker was also impressed by Ramsey’s footnote, and by Adams’s work. His project in the late 1960s was to fill the gap noted by Adams: to find a proposition such that the probability of its truth is measured in Ramsey’s and Adams’s way (see Stalnaker 1968, 1970). He was working in the framework of possible-worlds semantics, popular and exciting at the time through Richard Montague’s work. Plausibly, he was working with a richer notion of a proposition than was available to Ramsey. And he thought he had found the requisite proposition. He did find a proposition which generated a logic that agreed with Adams’s: this was a constraint on the success of his project—for propositions, necessary preservation of truth and necessary preservation of probability go hand in hand. Then David Lewis proved that the project must fail. There is no proposition such that, necessarily, the probability of its truth is the conditional probability of something given something. Conditional probabilities cannot be made to behave as unconditional probabilities, the latter being probabilities of the truth of propositions. There are now many ways of proving this result: thinking that B is probable on the supposition that A is not equivalent to thinking that something or other is probable, simpliciter.

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I shall try to give some indication of why this negative result holds. Let us try to construct the required proposition. Take two logically independent propositions, A and B. Suppose, then, that there is a proposition ‘If A, B’, which I shall call XA,B, or just X for short, such that necessarily, i.e. in all probability distributions, the probability of X = the probability of B given A. First we prove three entirely to be expected things about the logical shape of X: (1) X must be entailed by A&B; (2) ¬X must be entailed by A&¬B; (3) both X and ¬X are compatible with ¬A, i.e. neither X nor ¬X is entailed by ¬A.2 (1) If X were not entailed by A&B, certainty that A&B would not require certainty that X, i.e. there would be probability distributions in which p(A&B) = 1 and p(X) is less than 1. But if p(A&B) = 1, p(B given A) = 1, and therefore, on the assumption that p(X) = p(B given A), p(X) = 1. (2) If ¬X were not entailed by A&¬B, certainty that A&¬B would not require certainty that ¬X, i.e. there would be probability distributions in which p(A&¬B) = 1 but p(¬X) less than 1, so p(X) greater than 0. But if p(A&¬B) = 1, p(B given A) = 0, and so, on the assumption that p(X) = p(B given A), p(X) = 0. (3) If X were entailed by ¬A, then, given (1) and (2), X would be AB. But in general, p(AB)
p(B given A), as we saw above. If ¬X were entailed by ¬A, then, given (1) and (2), X would be A&B. But in general, p(A&B)
p(B given A). The logical relations between X, A&B, A&¬B, and ¬A are represented in Figure 2 below. (Please ignore for the moment the dotted line.) So far so good. We have a proposition of the expected logical shape. But—Result 1—it is simply and blatantly false that there is a proposition X of this logical shape such that in all probability distributions p(X) = p(B given A). Figure 2 shows a partition of four exclusive and exhaustive possibilities: (i) A&B&X; (ii) A&¬B&¬X; (iii) ¬A&X; (iv) ¬A&¬X. A probability distribution is any assignment of non-negative numbers to the members of a partition that sum to 1 (or 100%). Some such assignments will make p(X)—the sum of the numbers assigned to (i) and (iii)—equal to p(B given A)—the number assigned to (i) divided by the sum of the 2 I assume, for simplicity, that X is a classical, bivalent proposition, such that in any possible situation in which X is not true, it is false, i.e. ¬X is true. But the arguments that follow would go through just the same without that assumption, reading ‘p( X )’ as the probability that X is true, and ‘p(¬X )’ as the probability that X is not true. Even if it need not be false whenever it is not true, we would still show, in the same way, that there is no proposition the probability of whose truth necessarily equals the probability of B given A.

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numbers assigned to (i) and (ii), and other assignments will not. For instance, let the numbers assigned to the four possibilities be respectively 0.4, 0.1, 0.25, 0.25. Then p(B given A) = 0.8, p(X) = 0.65. The trouble is that p(B given A) depends solely on how probabilities are distributed among the A-possibilities; p(X) may be true or may be false if ¬A, and so it depends also on how probabilities are distributed among the ¬Apossibilities. But there are probability distributions which agree on the Apossibilities, hence agree about p(B given A), yet disagree on the ¬Apossibilities, hence disagree on p(X). A

B

X

(i)

¬B

¬X

(ii)

X

(iii)

¬X

(iv)

¬A FIG. 2

Perhaps Result 1 does not refute what Stalnaker intended. Perhaps his intention was that the holding of the equation p(X) = p(B given A) should be an additional constraint on probability functions: we are to add a new rule, which stipulates that the probability assigned to the conditional proposition X must always equal p(B given A). Stipulations have consequences, and this stipulation has unacceptable ones. You can make the stipulation for a single case in a single probability distribution, but it remains to be seen whether this clashes with the use we make of probability distributions, or whether one can consistently stipulate such a proposition for all conditional probabilities. Result 2: Lewis (1976) in effect showed that, given the stipulation, the only consistent place to divide p(¬A) into p(¬A&B) and p(¬A&¬B) is along the dotted line, making B equivalent to X and hence p(B) = p(X) in all probability distributions. For, being certain that B makes p(B given A) = 1 (provided p(A)
0). If B&¬X were possible, being certain that B would be consistent with having p(X) less than 1. Similarly, being certain that ¬B makes p(B given A) = 0. If ¬B&X were possible, being certain that ¬B would be consistent with having p(X) greater than 0. This conclusion is an absurdity. Conditionals are obviously not equivalent to their consequents. Stalnaker himself, in the wake of Lewis, showed—Result 3—that if the equation holds for given propositions A, B, and X, there can be other, more complex propositions in the same probability distribution, C and D—truth-

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functional compounds of A, B, and X—such that we cannot construct a Y such that p(D given C) = p(Y).3 I have given the following argument—Result 4 (see e.g. Edgington 2001). You have a distribution as in Figure 2. Then you rule out line (ii): you rule out A&¬B, no more, no less. This makes p(B given A) = 1. But it does not make p(X) = 1, because you have not ruled out the possibility that ¬A&¬X. And so it goes on. The source of the difficulty is, as I said above, estimating how likely it is that B on the assumption that A is an exercise which concerns only the A-possibilities, the possibilities in which A is true. Any candidate proposition X is true in some but not all ¬A-possibilities and so estimating it includes deciding how likely it is to be true if ¬A. Fixing it, on a one-off basis, so that p( X) = p(B given A) makes things go wrong elsewhere in one’s thinking. V Everyone finds the result puzzling. Two opposing philosophical attitudes find it particularly obnoxious or threatening: that of the ‘staunch truthconditional semanticist’, as for example Bill Lycan describes himself in his book Real Conditionals (2001), who does not want to forgo the virtues of explanations in terms of truth conditions; and that of the minimalist about truth, for whom truth is so innocuous that you shouldn’t be able to rule out its application to some bit of language to which it prima facie applies. I shall set aside the former, as not my present concern. Let us turn to minimalism about truth. Those who defend it take Ramsey’s remarks in ‘Facts and Propositions’ (1927) as a source. The aim of that paper is to give an analysis of judgement, belief, and assertion. And he says: But before we proceed with the analysis of judgement, it is necessary to say something about truth and falsehood, in order to show that there is really no separate problem of truth but merely a linguistic muddle. Truth and falsity are ascribed primarily to propositions. The proposition to which they are ascribed may be either explicitly given or described. Suppose first that it is explicitly given; then it is evident that ‘ It is true that Caesar was murdered’ means no more than that Caesar was murdered, and ‘ It is false that Caesar was murdered’ means that Caesar was not murdered. . . . In the second case in which the proposition is . . . not explicitly given we have perhaps more of a problem, for we get statements from which we cannot in ordinary language eliminate the words ‘true’ and ‘false’. Thus if I say ‘He is always right’, I mean that the propositions he asserts are always true, and there does not seem to be any way of expressing this without using the word ‘true’. But suppose 3 This proof of Stalnaker’s is published as a letter to van Fraassen in van Fraassen (1976: 303–4). The reasoning is reproduced in Gibbard (1981: 219–20), Edgington (1995: 276–7 ), and Bennett (2003: 71–3).

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we put it thus: ‘For all p, if he asserts that p, p is true’, then we see that the propositional function p is true is simply the same as p, as e.g. its value ‘Caesar was murdered is true’ is the same as ‘Caesar was murdered’. We have in English to add ‘is true’ to ‘p’ to give the sentence a verb, forgetting that ‘p’ already contains a (variable) verb. . . . . . . If we have analysed judgement we have solved the problem of truth. (pp. 38–9)

About the second case, Ramsey seems to be saying that it is only for syntactic reasons that we need to use the word ‘true’—to ‘give the sentence a verb, forgetting that “p” already contains a (variable) verb’. If our language were endowed not only with pronouns but with ‘prosentences’, the word ‘true’ would not be needed. ‘Everything he says is true’ is just a way of generalising over all instances of ‘If he said that p, then p’. In David Lewis’s words: The mention of truth lets us formulate generalisations that make long stories short, but the long stories made short are not about truth. [For example] ‘ Whatever the Party says is true’ is equivalent to an infinite bundle of conditionals ‘ If the Party says that two and two make five, then two and two make five’, ‘ If the Party says that we have always been at war with Eastasia, then we have always been at war with Eastasia’. And so on, and so forth. (2001: 279)

Philosophers are prone to generalise. Unsurprisingly, they enunciate many theses, some controversial, some not, using the word ‘true’. This formulation, according to the minimalist, comes just from the need to generalise. A rough shot at some of these: ‘True beliefs tend to facilitate the achievement of practical goals’ is equivalent to all instances of ‘If your belief that p is relevant to some practical concern, then you are more likely to get what you want if p’. ‘Beliefs obtained by certain methods of enquiry tend to be true’: if you arrived at p by suitable methods it is likely that p—more likely that p than if you arrived at p by astrology or crystal-ball gazing, say. ‘Beliefs aim at truth’: we try to believe that p only if p ; moreover, if we are trying to find out whether p, we also try to believe that p if p. Paul Horwich writes ‘The reason that the notion of truth is involved in logic is not that logic is about truth, but simply that logic makes precisely the sort of generalization that the truth predicate enables us to formulate’ (1990: 76). Even the so-called correspondence theory of truth, in its substantive form, according to which every truth is rendered true by the existence of some thing or things (states of affairs or whatever), Lewis argues, is not really a theory of truth at all—again, truth comes in because of the generality of the claim: ‘ It’s true that cats purr iff there exists some thing such that the existence of that thing implies that cats purr’, is equivalent to ‘Cats purr iff there exists some thing such that the existence of that thing implies that cats purr’. (2001: 279)

This, Lewis says,

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tells us nothing about truth. It is about the existential grounding of the purring of cats. All other instances of the truthmaker principle are likewise equivalent, given the redundancy biconditionals [of the form ‘ It is true that p iff p’ ], to this infinite bundle of conditionals not about truth but about the existential grounding of all manner of other things: the flying of pigs, or what-have-you. (2001: 279)

VI If truth is such a thin notion, can it be right to say that it doesn’t apply to conditionals (and other types of judgement where its application is controversial in philosophy, such as ethical judgements)? Doesn’t ‘Everything he said on that occasion was true’ fulfil its sole function when what he said was that today is Sunday, what you are doing is wrong, and if you keep on doing that you will be punished’? Can there be a case for denying truth to conditionals while still being a minimalist about truth? I shall cite a number of philosophers, including Ramsey, who would answer ‘yes there can’. And then I shall turn to some more signs of the nontruth-bearing behaviour of conditionals construed in Ramsey’s way. To be a minimalist about truth is not necessarily to be liberal about what it takes to be a bearer of truth. This point is argued by Jackson, Oppy, and Smith (1994). And here is Lewis to this effect: I take our topic to be, in the first instance, the truth of propositions. Sentences, or sentences in context, or particular assertions of sentences, or thoughts, can derivatively be called true; but only when they succeed in expressing determinate (or near enough determinate) propositions. A sentence (or . . .) might fail to express a proposition because it is ambiguous; or because it is vague; or because it is paradoxical or ungrounded; or because it is not declarative; or because it is a mere expression of feeling in the syntactic guise of a declarative sentence.4 Such a sentence (or . . .) is not a candidate for the status of truth simpliciter. But it might be a candidate for a related status such as truth on all or some of its disambiguations, or truth on all or most or few of its precisifications, or . . . make-believe truth. (2001: 276)

(Or, one might add, following a couple of examples from Hartry Field (1994), truth relative to a set of norms; truth relative to a frame of reference; or truth relative to a supposition.) For Lewis, clearly, minimalism about truth is compatible with stringent requirements on when a sentence or utterance is a candidate for truth. 4 Lewis adds a footnote here: ‘ When people in philosophy books go to the footy, they express their feelings by saying “Boo!” or “Hooray!”. Real people use a wider range of expressive locutions. Some of them have at least the superficial form of declarative sentences: “Leeds boot boys rule” or “Collingwood sucks”. A ( pompous) bystander might indeed respond to such a sentence by saying “That’s true” or “That’s false”, but calling it doesn’t make it so. Unless the sentence did after all express a true or false proposition, the bystander’s response would be just a piece of make-believe.’

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Ramsey’s view was similar. Ramsey did not say that there was no problem of truth, but no separate problem of truth—separate from the analysis of judgement. ‘Truth and falsity are ascribed primarily to propositions’, he also said (1927: 38). Much of ‘General Propositions and Causality’ is devoted to arguing that ‘Many sentences express cognitive attitudes without being propositions; and the difference between saying yes or no to them is not the difference between saying yes or no to a proposition. This is even true of the ordinary hypothetical’ (1929a: 147–8, my emphasis). Perhaps the presence of ‘cognitive’ in the above quotation is at first sight surprising. But there must be a good sense in which conditional statements ‘If you strike it, it will light’, ‘If Mary didn’t cook the dinner, John did’, express cognitive attitudes—express beliefs. Read Ramsey’s way, they do not express categorical beliefs about the way things are; but they express a conditional belief in the consequent, under the supposition that the antecedent is true. Ramsey stresses that disagreement about conditionals is not disagreement about whether a proposition p or its negation ¬p is true: If B says ‘ If I eat this mince pie I shall have a stomach ache’ and A says ‘ No you won’t’ he is not really contradicting B’s proposition … [ This example] asserts something for the case when the [antecedent] is true: we apply the Law of Excluded Middle not to the whole thing but to the [consequent] only. (1929a: 147–8)

That is, we both suppose that he eats the pie. Under that supposition, either he will get a stomach ache or he won’t, and we disagree about which, or their relative likelihoods; we have different views about the likelihood of (eating it and getting a stomach ache) relative to that of (eating it and not getting a stomach ache). And about a similar case, Ramsey says: ‘Before the event we do differ from him in a quite clear way: it is not that he believes [a proposition] p, we ¬p ; but he has a different degree of belief in q given p from ours; and we can obviously try to convert him to our view’ (1929a: 155). And then comes the famous footnote. The main business of this paper of Ramsey’s is to argue that judgements of causal law, also called variable hypotheticals, are not judgements about propositions: Variable hypotheticals are not judgements but rules for judging ‘ If I meet a
, I shall regard it as a ’. This cannot be negated but it can be disagreed with by one who does not adopt it . . . A variable hypothetical is not strictly a proposition at all . . . The difficulty comes fundamentally from taking every sentence to be a proposition. (1929a: 149, 159, 162)

So Ramsey’s position is like Lewis’s: minimalism about truth, combined with stringency on what it takes to be a bearer of truth. And another authority, famous for his minimalism about truth, Quine, in Methods of Logic:

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Now under what circumstances is a conditional true? Even to raise this question is to depart from everyday attitudes. An affirmation of the form ‘if p, q’ is commonly felt less as an affirmation of a conditional than as a conditional affirmation of the consequent. If, after we have made such an affirmation, the antecedent turns out to be true, then we consider ourselves committed to the consequent, and are ready to acknowledge error if it proves false. If on the other hand the antecedent turns out to have been false, our affirmation is as if it had never been made. (1974: 19)

One does not have to be a friend of propositions—as Quine is not—to find reason to doubt whether a given kind of sentence or utterance is a bearer of truth. It must be common ground that some sentences are not truth bearers; and syntax is too crude a device to determine which are. Sentences which are truth bearers have a certain kind of use, express a certain kind of mental state, with a certain kind of role. It is open to detailed argument, in cases of controversy, whether a given kind of sentence plays this role. I think we have to concede that, in a loose sense, anything which can be agreed with or dissented from, even ‘Leeds boot boys rule’, can have ‘true’ and ‘false’ applied to it. Call that super-minimalist or minimalissimo truth. Lewis said a pompous bystander might respond to such a remark with ‘That’s true’ or ‘That’s false’. It would be more pompous still to respond to this response ‘The concepts of truth and falsity do not apply to utterances such as these’. (It might even be dangerous.) But this is consistent with the view that there can be good and principled reasons for differentiating a class of sentences from that of truth bearers proper, because they lack significant features of the use of the latter. VII It would be nice to be able to state in an informative and illuminating way the necessary and sufficient conditions for being a truth bearer. I don’t know how to do that. In this section I draw attention to a number of further features of conditionals as construed by Ramsey which seem to differentiate them from propositions. 1. If we understand the ascription of ‘true’ to conditionals, we surely understand ‘not true’. And from the equivalence of ‘It is true that p’ and ‘p’, follows the equivalence of ‘It is not true that p’ and ‘¬p’. That is, we must understand the negation of a conditional. Now the Ramsey Test gives us no guidance as to what that means. Of course internal negation is unproblematic: suppose that A, and come to the conclusion that ¬B. But the whole conditional thought, as Ramsey said several times, is not, strictly speaking, the sort of thing you can negate. Some philosophers favourably disposed to the Ramsey Test stipulate that ¬(If A, B) shall just mean ‘If A, ¬B’. Others say that it shall mean ‘ If A, it may be that ¬B’. These are incompatible proposals: negations of conditionals are more readily acceptable on the second than the first. Both proposals are intelligible, because they reduce

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external negation to internal negation. But it is odd, if we understand conditionals as truth bearers, that controversy should persist about what it is for a conditional not to be true. 2. If conditionals are truth bearers, they should be the sort of thing you can suppose to be true; that is, they should go unproblematically into the antecedents of conditionals construed Ramsey’s way. Take any example of an uncertain conditional—for simplicity, take a balls-in-bags example: a certain proportion, say 70%, of the red balls have black spots. I am 70% certain that if you pick a red ball it will have a black spot. Is that a degree of belief that something is true? Well, if so, we can say: suppose it’s true; suppose that if you pick a red ball, it will have a black spot. Now it’s very hard to see what you are being asked to suppose. That you pick a red ball and it has a black spot? But the conjunction isn’t equivalent to the conditional. Sometimes we do utter and understand conditionals with conditional antecedents. But it has been argued that when we understand them, we understand them by ad hoc strategies which again reduce them to nonembedded conditionals. For instance, we look for some categorical statement which, in the context, we presume to be the ground, G, for the antecedent-conditional, and read the whole conditional as ‘If G, C’ (see Gibbard 1981: 234–8). Or we read it as ‘If you accept that if A, B, you must surely accept [such-and-such]’. Minimalism about truth typically claims that all there is to truth is captured by biconditionals of the form: it is true that p iff p. Applying this to the alleged case in which p is a conditional, ‘If A, B’, this tells us that if (if A, B) then it is true that if A, B; and if it is not the case that (if A, B) then it is not true that if A, B. We have just seen that it is not easy or straightforward to understand either the conditional antecedent in the first case, or the negated conditional in the second, hence not easy or straightforward to understand, via the biconditional, the application of truth to conditionals. This point is made by Michael Dummett (1991: 171–2). 3. Valid arguments which involve conditionals have some different properties from valid arguments which involve only propositions. I shall give two illustrations of this. First, for the latter, three criteria of the validity of arguments are equivalent: the necessary preservation of truth, the necessary preservation of certainty, and the necessary preservation of probability in the sense of Adams. Put the first aside (because for the minimalist it is non-explanatory). An argument such that certainty in the premises justifies certainty in the conclusion is also one such that there can be no more improbability in the conclusion than in all the premises together. For arguments with conditionals, the former can hold without the latter. Assuming the antecedents to have non-zero probability: if I am certain that if A, B, and certain that if B, C, I should be certain that if A, C; but I can consistently be certain that if A, B and almost certain that if B, C, yet have zero confidence that if A, C. This mirrors the radically different

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logical powers of ‘all As are B’ and ‘almost all As are B’. If all As are B and all Bs are C, all As are C. But we can have: all As are B, almost all Bs are C, yet no A is C, as in ‘All kiwis are birds, almost all birds fly, yet no kiwi flies’. Analogously: all my A-possibilities are B-possibilities, all my B-possibilities are C-possibilities, so all my A-possibilities are C-possibilities (the certainty case). But we can have: all my A-possibilities are B-possibilities, almost all my B-possibilities are C-possibilities, yet none of my A-possibilities are Cpossibilities (the close-to-certainty case). This helps explain why slight uncertainty can usually be ignored in propositional reasoning. It makes a difference only in pathological cases like the Lottery Paradox where there are very many premises; there is a smooth transition between the case of certainty and the case of near-certainty. And it explains why even slight uncertainty cannot be ignored in reasoning with conditionals; there is a sharp discontinuity in the inferential powers of certain premises (which we seldom have in reasoning about empirical matters), and near-certain premises. Second, an adaptation of a point made by Richard Bradley (2000). Consider the inference: it may be the case that A; it may be the case that B; so it may be the case that A &B. That is a really bad inference—a gross fallacy. Interpret ‘it may be the case that’ as the ascription of a non-zero probability. Again, a very bad inference! Indeed, if A and B each have probability at most 50%, or probabilities which sum to at most 100%, it is always consistent to assign a probability of 0 to A&B (where A and B are logically independent). Now consider: it may be the case that A; it may be the case that if A, C; so it may be the case that C. That doesn’t sound so bad: it may rain; the match may be cancelled if it rains; so the match may be cancelled. And interpreting ‘it may be the case that if A, C’ as giving the conditional a non-zero conditional probability, it is indeed right that if the premises get non-zero probability, so does the conclusion. If the probability of A is positive, and the probability of C given A is positive, the probability of C is positive. No propositional interpretation of the conditional gives this result. Again, we see that conditionals have different logical powers from propositions. 4. For some the most decisive argument against conditionals being truth bearers is the existence of no-fault disagreements. Ideally rational people, each on perfectly adequate grounds, can come to conflicting opinions about whether if A, B. For example, we both know from the state of play that Jack holds a queen or a king or an ace. I now pick from the pile the last king (the others have already been played). I now think ‘If Jack doesn’t have an ace he has a queen’. I totally reject ‘If Jack doesn’t have an ace he has a king’. You now pick from the pile the last queen. You think ‘If Jack doesn’t have an ace he has a king’. You totally reject ‘If Jack doesn’t have an ace he has a queen’. Neither of us makes any mistake and we have fully sufficient grounds for our respective judgements. If what we respectively accept and

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reject is a proposition, a truth bearer, it is hard to avoid the conclusion that one of us is wrong. (Examples like this are due to Gibbard 1981: 231–2.) We should not conclude that all conditional judgements are subject to no-fault disagreement. Examples like the above depend on the fact that the falsity of the antecedent is presently knowable, though not known by either party. (This does not, of course, cast doubt on our conditional judgements: we only said ‘if’.) Often, with future-looking conditional judgements, the truth value of the antecedent is not presently knowable; it has some chance of being true. And there may well be a presently best opinion as to how likely it is that C on the supposition that A, the chance of C given A. This may be 1 or 0, or it may be between 1 and 0, in which case it is not the chance that some proposition is true. 5. On the surface, supposing that A, and believing that B under that supposition, is a different kind of state from simply believing something. To think that there are conditional propositions as objects of straightforward belief is to reduce the former state of mind to the latter. Prior to detailed argument, it would seem reasonable to treat it as an open question whether this can be done. Lewis’s and other proofs show that the reduction cannot be carried out; the two kinds of state are irreducibly distinct, the former kind irreducibly hypothetical. It is not only beliefs for which the conditional–unconditional distinction needs to be drawn. There are also conditional and unconditional desires, the former irreducible to the latter, and conditional desires appear to be structurally similar to conditional beliefs: to desire that B is to prefer B to ¬B; to desire that B if A is to prefer A&B to A&¬B; there is no proposition X such that one prefers X to ¬X just to the extent that one prefers A&B to A&¬B. For instance, I have entered a competition and have a very small chance of winning. I express the desire that if I win, you tell Fred right away. I prefer (Win and Tell) to (Win and not Tell). I do not necessarily prefer (Win
Tell) to ¬(Win
Tell), i.e. ¬Win or (Win & Tell) to (Win & ¬Tell); for I also want to win the prize, and the most likely way for (Win
Tell) to be true is by my not winning. Nor is my conditional desire satisfied if I don’t win but in the nearest possible world in which I win, you tell Fred straight away. Indeed it would appear that every kind of speech act comes in a conditional and unconditional variety: there are conditional assertions, questions, commands, offers, promises, givings of permission, etc. The generality of this distinction adds further support to its existence for beliefs. VII I Consistently with the Ramsey Test, we may partially reinstate truth values for conditionals, and say that a conditional is true if it has a true antecedent and consequent, false if it has a true antecedent and false consequent, and has no truth value if its antecedent is false. All the problems with assigning

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truth values arise for the case in which the antecedent is false. If we do say this, we need to give up some cherished notions. It is no fault in a conditional that it has a false antecedent and hence is not true. It is no merit in a conditional that it has a false antecedent and hence is not false. Beliefs and assertions do not aim at truth. Rather, we want our conditional judgements to be true on the assumption that they have a truth value, true on the assumption that they are either true or false, i.e. we want the consequent to be true on the assumption that the antecedent is true. The probability of a conditional is not the probability that it is true, but the probability that it is true given that it is either true or false. This is equivalent to Ramsey’s idea. A minimalist about truth will not like this option, however, for it departs from the central tenet of minimalism. On this option ‘It is true that if A, B’ is not equivalent to ‘If A, B’. Ramsey’s own view, I have argued, is quite consistent: minimalism about truth combined with the denial that our hypothetical judgements behave like truth bearers.

What is Squiggle? Ramsey on Wittgenstein’s Theory of Judgement PETER M. SULLIVAN I At the age of 20, and fresh from his undergraduate studies in mathematics, Ramsey set about writing what would be his first substantial publication, his 1923 Critical Notice of Wittgenstein’s Tractatus (hereafter TL P). It is hard for modern students of that book, who negotiate its obscurities with generations of previous commentary to serve as guides, to appreciate the task Ramsey confronted; and, to the extent that one can appreciate it, it is hard not to feel intimidated by the brilliance of his success. His Critical Notice made Ramsey the first of Wittgenstein’s interpreters.1 In my view it makes him, still, the best. I want to illustrate that here by considering what light his remarks cast on a single passage of the book, in which Wittgenstein advances what might be called his theory of judgement. 5.54

In the general propositional form, propositions occur in a proposition only as bases of the truth-operations. 5.541 At first sight it appears as if there were also a different way in which one proposition could occur in another. Especially in certain propositional forms of psychology, like ‘A thinks that p is the case’, or ‘A thinks p’ , etc. Here it appears superficially as if the proposition p stood to the object A in a kind of relation. (And in modern epistemology ( Russell, Moore, etc.) those propositions have been conceived in this way.) 5.542 But it is clear that ‘A believes that p’ , ‘A thinks p’ , ‘A says p’ , are of the form ‘ “p” says p’ , and here we have no co-ordination of a fact and an object, but a co-ordination of facts by means of a co-ordination of their objects. 5.5421 This shows that there is no such thing as the soul—the subject, etc.—as it is conceived in contemporary superficial psychology. A composite soul would not be a soul any longer.

Part of what is going on here is well understood. This is, roughly, that a fact can be represented only by a fact that manifests in itself the structure of the fact represented, and thus that whatever represents a state of affairs has 1 Russell was too much a collaborator, I think, to be counted as first among Wittgenstein’s interpreters.

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to be complex in the same way as a proposition that might represent that state of affairs. That was first spelled out by Ramsey, and is now common ground amongst interpreters. Away from that common ground, though, interpretations soon diverge. In particular, they diverge even over such a seemingly basic question as whether Wittgenstein’s analytical proposal is intended to make clear the sense that propositional attitude statements have, or whether instead it is intended to make clear that they have no sense. I’ll suggest that this question and others that have seemed pressing to later commentators have done so because the focus and intention of Wittgenstein’s proposal have been misidentified, in ways that attention to Ramsey can correct. For the purpose of this illustration I’ll begin by contrasting the accounts of the passage offered by two of the best of later commentators on the Tractatus, Elizabeth Anscombe and Anthony Kenny. Although they wrote forty and thirty years ago, their discussions have not been surpassed. For Ramsey’s views I will draw on, in addition to the 1923 Critical Notice, his 1927 paper ‘Facts and Propositions’. Only the first of these is explicitly exegetical. In the second Ramsey is addressing the issues in his own right. Towards the end of this paper, though, Ramsey makes the following very suggestive acknowledgement: ‘In conclusion, I must emphasize my indebtedness to Mr Wittgenstein, from whom my view of logic is derived. Everything that I have said is due to him, except the parts which have a pragmatist tendency, which seem to me to be needed in order to fill up a gap in his system’ (1927: 51). This suggests a simple subtractive scheme for arriving at an exegesis from a non-exegetical treatment: X–Y = Z, where X = the total view of ‘Facts and Propositions’, Y = the ‘parts which have a pragmatist tendency’, so that Z = what Ramsey took to be the Wittgensteinian basis to which he was adding. The pragmatist theory of content that Ramsey proposed to fill the ‘gap’ is evidence of his genius as an original philosopher in his own right. What I want to emphasize about Ramsey as an interpreter is his recognition of the gap, or, in other words, his understanding of what kinds of issues and questions Wittgenstein’s account aimed to settle and which it left open. The pragmatist elements of ‘Facts and Propositions’ have more than one role. The most obvious but least important such role is to distinguish different attitudes—judgement, supposition, hope, expectation—towards, as we say, the same propositional content. This role I will ignore throughout the chapter. Wittgenstein’s ‘theory of judgement’, like Russell’s, is indifferent

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to such contrasts, so might be better called a theory of understanding (cf. Russell 1992: 107). The second and most important role is to make good a shortcoming in Wittgenstein’s account that Ramsey had already pointed to in the Critical Notice, extending this theory of understanding from elementary propositions to propositions in general. For much of this chapter (Sections V–VIII) I will be able to adopt the simplifying assumption that this is the role of Ramsey’s pragmatist innovations, so that removing these additions returns us to the elementary case. In the final section of the chapter, though, I will acknowledge a role that Ramsey rightly found for his pragmatist tendency in the elementary case too. II Anscombe’s reading of our passage has two main planks. The first is the common ground I’ve already sketched, but which she sets out more thoroughly and clearly in the following passage. ‘it is clear’, [Wittgenstein] says; and of course what was clear to him was that for anything to be capable of representing the fact that p, it must be as complex as the fact that p; but a thought that p, or a belief or statement that p, must be potentially a representation of the fact that p (and of course actually a representation of it, if it is a fact that p). It is perhaps not quite right to say that ‘A judges p’ is of the form ‘ “p” says that p’ ; what he should have said was that the business part of ‘A judges that p’ , the part that relates to something’s having as its content a potential representation of the fact that p, was of the form ‘ “p” says that p’ : ‘A believes p’ must mean ‘ There occurs in A or is produced by A something which is (capable of being) a picture of p’ . (Anscombe 1959: 88)

Summarizing this, we might say that on Anscombe’s analysis the gist of ‘A judges p’ is to be given in the pattern: (AA) A’s mental bits are configured thus and so, and the fact that they are so configured represents that p. As Wittgenstein told Russell (Wittgenstein 1995: 125), and as Ramsey seems to have known without needing to ask, it doesn’t matter at all what these mental bits might be. A thought is a type whose tokens have in common a certain sense, and include the tokens of the corresponding proposition, but include other non-verbal tokens; these, however, are not relevantly different from the verbal ones, so that it is sufficient to consider the latter. ( Ramsey 1923: 274)

Anscombe follows this recommendation in formulating the second plank of her reading, that what she takes to be the ‘business part’ of (AA), the part that follows the comma, is by the lights of the Tractatus a significant, bipolar proposition. She models this part of her discussion on the illustration Wittgenstein presents at TLP 3.1432,

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that ‘a’ stands in a certain relation to ‘b’ says that aRb ,

asking: What actually is that certain relation? There seem to be true and false answers to this question. Given the notational conventions she supposes in force, for instance, the following is true (where ‘^’ indicates concatenation): that ‘a’ stands to ‘b’ in the relation one establishes between names n and m by writing n^‘R’^m says that aRb, while the following is false: that ‘a’ is separated by one character from ‘b’ says that aRb. With different conventions different instances of the ‘business part’ of (AA) would hold. For instance, in the loose style that many of us adopt, one that tolerates either of ‘aRb’ or ‘Rab’ indifferently, we should have: that ‘a’ occurs in a three-character string also containing ‘R’ and ending with ‘b’ says that aRb. According to Anscombe’s reading, then, a specific instance of the pattern (AA)—or, as she puts it, some particular ‘interpretation’ of ‘ “p” says that p’, in which ‘ “p” ’ is replaced by a formulation of the representing fact that constitutes that proposition (1959: 90)—will be a contingent, bipolar proposition giving the content of a given report, ‘A judges that p’. III There are three obvious criticisms to be brought against Anscombe’s reading. Two are raised by Kenny, the third not. 1. The first questions whether the examples just given should persuade us that ‘ “p” says that p’ can be the form of a contingently true statement. To imagine a change from true to false in such a statement amounted, we saw, to imagining a change in linguistic conventions. On the conventions Anscombe supposes in force, the last example, that ‘a’ occurs in a three-character string also containing ‘R’ and ending with ‘b’ says that aRb, would be false; but with the laxer conventions I mentioned it would be true. The subject matter of this sentence must therefore be something that can remain the same while the conventions governing it are altered. It must be, in Wittgenstein’s terminology, a sign rather than a symbol (TLP 3.321– 3.322). But Wittgenstein seems to count it a mistake to ascribe any representational character to a mere sign. And if that is so, then the way Anscombe aims to provide for such a statement to be merely contingently true will, by Wittgenstein’s lights, prevent it from being a truth at all. Thus Kenny:

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‘ “p” says that p’ does not have true–false poles. For what appears within the nested quotation marks is either—as Anscombe understands it—a description of accidental features of the propositional sign, in which case the proposition is always false; or it is a description which identifies ‘p’ precisely as the proposition that says that p; in which case the proposition is necessarily true (and therefore, for Wittgenstein, a pseudo-proposition). (1984: 7)

This complements an earlier and simpler argument to the same conclusion: But ‘ “p” says that p’ must be a pseudo-proposition, since a proposition shows its sense and cannot say that it has it (TLP 4.022). ( Kenny 1973: 101)

Neither argument is altogether persuasive. The thought of TLP 4.022, that a proposition shows its sense, emphasizes Wittgenstein’s conception of the proposition as a standpoint of representation (TLP 2.173), a transparent medium through which we are presented with reality. Yet that conception seems not to preclude another straightforwardly empirical standpoint, one that focuses on the medium rather than looking through it. TLP 4.022 might be better rendered ‘A proposition shows the state of affairs that is its sense’, rather than ‘A proposition shows that this state of affairs is its sense’. Kenny would need the second, rather than the first, to argue that, since it is shown what sense ‘p’ has, it cannot be said what sense it has. As for the dilemma argument, it is certainly true that for Wittgenstein a symbol, and not a mere sign, is the proper bearer of meaning: that means, firstly, that only a symbol can have the kind of internal relation to reality that Wittgenstein takes to be involved in the philosophically important notion of meaning (TLP 3.31); and, secondly, that all manner of philosophical confusions result if that primary notion of meaning is imagined to attach to a mere sign (TLP 3.324). But again, accepting the priority of the meaning of symbols seems not to preclude, but to make possible, a secondary notion attaching to signs, when those signs are, contingently, the ‘visible parts’ of meaningful symbols (TLP 3.32).2 It was, Wittgenstein said, for the empirical science of psychology to determine what are the actual constituents of thought and the kind of relation they bear to things (1995: 125). Yet Kenny’s argument leaves to psychology no form in which to report its results. 2 A philosophical ascription of content aims at something with logical or epistemological consequences, consequences, for instance, for what implies what, or what is evidence for what; and no statement of the accidental properties of signs, or of their external relations to things, has such consequences. On the other hand, if on those grounds it is accepted that philosophy’s concern with content will issue in the statement of an internal relation, that the symbol ‘a ’ signifies a, that seems to make room for the statement of an external relation between the sign ‘a ’ and a, a relation that is, as it were, a product of the internal relation that interests philosophy and the contingent fact that the sign ‘a ’ is so used as to become that symbol.

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2. If that first criticism is inconclusive, a second seems more clear-cut. If there are genuine propositions of the pattern of (AA), and if Wittgenstein’s proposal is that ‘A judges p’ amounts to such a proposition, then the proposal does not solve, but simply replicates, the original problem. The problem was that ‘p’ misleadingly seems to occur as the argument of a nonextensional function in ‘A judges p’ (TLP 5.541). This second problem for Anscombe’s reading is that ‘p’ equally appears to occur as the argument of a non-extensional function on the ‘right-hand side’ of ‘ “p” says that p’. Whatever else it was supposed to achieve, Wittgenstein’s analysis was meant to remove that appearance. 3. The third criticism is simpler. Even if Anscombe is right that propositions of the pattern ‘ “p” says that p’ can be genuine contingent propositions, her proposal seems just to mislocate the contingency in the belief reports these propositions are supposed to analyse. Intuitively, ‘A judges p’ is a genuine contingent proposition because it is contingent how A’s mind is set: his mental bits are configured so as to think that p, but they might not have been so configured, and perhaps tomorrow they will not be. The contingency Anscombe argues for (and that Kenny denies) has to do instead with what significance, if any, attaches to A’s mental bits being configured in the ways they are. If that is contingent at all, it is so because it is contingent what mental language A ‘speaks’; but that is in the nature of a standing truth, one that will still hold tomorrow, when A changes his mind. IV Although the previous section casts doubt on some of his arguments, Kenny’s overall picture is, I believe, much closer to Wittgenstein’s intentions. Suppose that I think a certain thought: my thinking that thought will consist in certain psychic elements—mental images or internal impressions, perhaps— standing in a relation to each other. That these elements stand in such and such a relation will be a psychological fact; a fact in the world, within the purview of the natural sciences; just as the fact that the penholder is on the table is a physical fact within the purview of the natural sciences. But the fact that these mental elements have the meaning they have will not be a fact of science, any more than the fact (if it is a fact) that the penholder’s being on the table says that the cat is on the mat (if the appropriate code is in force). ( Kenny 1984: 8)

This section does not aim to challenge that picture, but only to question whether Kenny’s discussion can properly lead us to it. As we’ve already seen, Kenny denies that anything of the pattern ‘ “p” says that p’ can be a contingent truth. From that he concludes that ‘belief propositions must be pseudo-propositions’— or more precisely, they will be the conjunction of a genuine proposition and a spurious one. The proposition that Jones believes that grass is green will be a conjunction of (1) the proposition that certain mental elements in Jones’s mind are

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related in a certain way, and (2) the pseudo-proposition that their correlation in that way says that grass is green (1973: 101).

And this, Kenny contends, removes the original problem that Anscombe’s analysis merely relocated: if ‘ “p” says that p’ is only a pseudo-proposition, and ‘A believes that p’ is of that form, it is easy to see how propositions reporting beliefs are no exception to the rule that propositions can occur in other genuine propositions only as the bases of truth-functional operations. (1984: 7)

But, now, is the original problem, the appearance that ‘p’ occurs as argument to a non-extensional function in ‘A judges p’, really solved? That depends, I think, on what we take the original problem to have been: does it turn on the apparent non-extensionality of the argument-place occupied by ‘p’, or is the problem that the non-extensional place occupied by ‘p’ appears to be an argument-place? Kenny’s solution presumes the first. He is content to leave us with the appearance that ‘p’ does indeed occur in whatever analyses ‘A judges p’, while protecting the ‘rule’ of extensionality for ‘genuine’ propositions: on his account, one might say, ‘p’ does occur non-extensionally in a non-proposition. (Since ‘A judges p’ is not a genuine proposition, it has no truth value, so no truth value that varies independently of that of the contained proposition ‘p’.) If, on the other hand, the second formulation of the problem is the right one, we should expect a solution of it to reveal that ‘p’ does not occur as an argument at all in whatever genuine proposition replaces ‘A judges p’. And the history of our passage, which shows Wittgenstein to be concerned in the first instance to dispel the impression that ‘p’ has in a belief report an occurrence comparable to that of the name ‘b’ in ‘aRb’, suggests strongly that the second formulation is the right one.3 3

Some representative passages: In ‘a judges p’ p cannot be replaced by a proper name. This appears if we substitute ‘a judges that p is true and not p is false’. The proposition ‘a judges p’ consists of the proper name a, the proposition p with its 2 poles, and a being related to both of these poles in a certain way. This is obviously not a relation in the ordinary sense. (Wittgenstein 1961b: 95) When we say ‘A believes p’, this sounds, it is true, as if here we could substitute a proper name for ‘p’; but we can see that here a sense, not a meaning, is concerned, if we say . . . ‘A believes that “p” is true and “not-p” is false’. (1961b: 106) At this stage, note, Wittgenstein is content to leave the subject of a judgement as represented by a name. That stage is superseded in the notes dictated to Moore: The relation of ‘ I believe p’ to ‘p’ can be compared to the relation of ‘ “p” says p’ to p: it is just as impossible that I should be simple as that ‘p’ should be. (Wittgenstein 1961a: 119) In making that move Wittgenstein has strengthened his earlier contention, that belief is not a relation ‘in the ordinary sense’ to a proposition p, to the conclusion that it is in no sense a relation:

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Kenny opposes Anscombe’s view that what follows the comma in the pattern (AA) could ever be the form of a contingent proposition. But he shares with her the presumption that this is the ‘business part’ of the analysis. This shows up in his readiness to compress his ‘more precise’ statement, that a belief report conjoins an empirical psychological report (before the comma) with a non-empirical semantic commentary on it (after the comma), into the conclusion that belief reports are pseudo-propositions. The history just mentioned suggests, though, that we should look to find the ‘business part’ of the report before the comma. It must of course be some kind of shorthand for Kenny to describe a belief report as a conjunction of an empirical proposition and a pseudoproposition, a piece of nonsense. For one cannot conjoin a senseful ‘q’ with a nonsensical ‘r’. (One can pronounce one after the other, with ‘and’ between them, but that will not amount to conjoining anything with anything.) It would be natural to take this shorthand description to imply that the report reduces to the empirical proposition that is its first ‘conjunct’: adding the bit of nonsense doesn’t add anything. To suggest instead that the report reduces to its second ‘conjunct’ leaves us not so much with an account of what a belief report amounts to as with the contention that it amounts to nothing at all. (Kenny tries to soften the blow, holding that, while ‘ “p” says that p’ is a pseudo-proposition, it ‘is of course a correct pseudo-proposition: it is a thesis of the Tractatus’ (1984: 7). Here I think Anscombe is importantly right in focusing, not on the schema, but on its instances, for it is they that would be involved in analyses of given reports, ‘A judges p’. Whatever might be claimed for the schema, those instances would not be theses of the Tractatus, since they would relate to the peculiarities of A’s mental bits and their configuration.4)

The question arises how can one proposition (or function) occur in another proposition? The proposition or function can’t possibly stand in relation to other symbols. (1961a: 118) There are internal relations between one proposition and another; but a proposition cannot have to another the internal relation which a name has to the proposition of which it is a constituent, and which ought to be meant by saying it ‘occurs’ in it. In this sense one proposition can’t ‘occur’ in another. (1961a: 116) ( I rely here on the premise that any relation to a proposition p would be expressed in a proposition in which p occurred as relatum.) 4 This point happily allows me to avoid the general question, much discussed in recent work on the Tractatus, whether there is confusion in relying on the idea that a piece of nonsense might be ‘correct’.

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V Ramsey finds the business part of a belief report where several of our considerations have suggested it ought to be found, in the description of A’s mental set-up. The first passage of the Critical Notice to make this plain is not focused primarily on our passage, but occurs in Ramsey’s account of the picture theory; he is expounding the claim that ‘the representing relation’, the correlations between picture elements and objects, ‘belongs to the picture’ (TLP 2.1513). . . . this, I think, means that whenever we talk of a picture we have in mind some representing relation in virtue of which it is a picture. Under these circumstances we say that the picture represents that the objects are so combined with one another as are the elements of the picture, and this is the sense of the picture. And I think this must be taken to be the definition of ‘represents’ and of ‘sense’; that is to say, that when we say that a picture represents that certain objects are combined in a certain way, we mean merely that the elements of the picture are combined in that way, and are co-ordinated with the objects by the representing relation which belongs to the picture. ( That this is a definition follows, I think, from 5.542.) (1923: 271)

Ramsey is here concerned with two forms of statements. The first, a picture represents that certain objects are combined in a certain way,

shares with ‘ “p” says that p’ the shape: subject–verb–complement. Its subject seemingly refers to a representing item (a picture, proposition, or thought); its clausal complement then formulates the represented state of affairs. The second, the picture elements are combined in that way, and are co-ordinated with the objects,

begins by replacing the apparent reference to a representing item (“p” ) by the schema of a sentence that would state the representing fact; it then dispenses altogether with the clausal complement by which the represented fact would be formulated (‘that p’), and thus with the representational verb that introduces it (‘says’). Ramsey cites our passage as entailing that the first of these statements is defined by, or reduces to, the second. For that to be so, our passage must have the following implications: 1. No representational relation between ‘p’ and the possible fact that p figures fundamentally in what is asserted by ‘ “p” says that p’ (nor therefore in ‘A judges p’). 2. Nor is there in that statement any mention of, or formulation of, the possible fact that p ; i.e. the apparent occurrence of ‘p’ on the ‘right-hand side’ of ‘ “p” says that p’ (and therefore of ‘A judges p’) will, on a right account, simply disappear.

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3. The only correlation between thought or language and reality presumed in an account of judgement is the correlation between words (picture-elements, or mental bits) and objects. These implications give our passage a centrality in Ramsey’s reading of the Tractatus that few other commentators have recognized. He holds, firstly, that Wittgenstein here explicitly reduces the question as to the analysis of judgement . . . to the question ‘ What is it for a proposition token to have a certain sense?’ (1923: 274–5);

and secondly, that if we can answer [that] question we incidentally solve the problem of truth; or rather, it is already evident that there is no such problem. For if a thought or proposition token ‘p’ says that p, then it is called true if p and false if ~p. We can say that it is true if its sense agrees with reality, or if the possible state of affairs which it represents is the actual state of affairs, but these formulations only express the above definition in other words. (1923: 275)5

For all that he applauds Wittgenstein’s advance in clarifying the question, however, Ramsey is convinced that there is no generally satisfactory answer to it to be extracted from the Tractatus. Beyond the straightforward case of elementary propositions, he holds, Wittgenstein offers only an account of what senses there are for propositions to have, not an account of which propositions have which senses (1923: 275–7; 1927: 41). It is the main task of ‘Facts and Propositions’ to make good that shortcoming. In line with the subtractive scheme suggested in Section I, though, I will here be cutting away the pragmatist innovations of that work to expose its understanding of Wittgenstein; and I’ll have to be content if that leaves me only with a treatment of the simplest cases. The rationale for this indirect approach lies in the fact that Ramsey found the simplest cases so simple that he said very little about them—too little to make plain the implications 1–3 above.6 In the Critical Notice his whole account of elementary propositions is given in the following passage: 5 Because of implications 1–3, that is, any apparent mention of facts in an account of truth is no more than optional verbal decoration: We can, if we like, say that [a judgement that a R b ] is true if there exists a corresponding fact that a has R to b, but this is essentially not an analysis but a periphrasis, for ‘The fact that a has R to b exists’ is no different from ‘a has R to b ’. ( Ramsey 1927: 143) It is depressing to remember—when Ramsey had it right from the beginning—how often the Tractatus has been taken to offer (or even to represent a paradigm of ) a correspondence theory of truth. 6 Moore remarked in his Preface to Ramsey’s papers, ‘ But sometimes I feel that he fails to explain things as clearly as he could have done, simply because he does not see that any explanation is needed: he does not see that what to him seems perfectly clear and straightforward may to others, less gifted, offer many puzzles’ ( Ramsey 1931, p. viii). This is a case in point.

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According to Mr Wittgenstein a proposition token is a logical picture; and so its sense should be given by the definition of the sense of a picture; accordingly the sense of a proposition is that the things meant by its elements (the words) are combined with one another in the same way as are the elements themselves, that is, logically . . . Thus if ‘a’ means a, ‘b’ b, and ‘R’, or more accurately the relation we establish between ‘a’ and ‘b’ by writing ‘aRb’, means R, then that ‘a’ stands in this relation to ‘b’ says that aRb, and this is its sense. (1923: 275)

Here we have the common ground of subsequent interpretations sharply delineated, but what is distinctive in Ramsey’s reading is not yet prominent. Similarly in ‘Facts and Propositions’ atomic sentences are said to offer ‘no very serious problem’: If a, R, and b are things which are simple in relation to [a thinker’s] language . . . he will believe that aRb by having names for a, R, and b connected in his mind and accompanied by a feeling of belief. (1927: 41)

Pausing only to explain, as above, that a name for R will be itself a relation holding between the names for a and b, Ramsey scuttles along to confront ‘the more interesting problems’ posed by complex propositions. Because the moral for belief reports is not explicitly drawn in this simple context, we need to start with his account of more complex cases and work back. VI The major differences between Ramsey’s two discussions occur in parts that I intend to cut away, and that allows me to swap backwards and forwards between them. I’ll give priority to the account in the Critical Notice, drawing on ‘Facts and Propositions’ for comparisons and confirmation. This earlier discussion starts under the simplifying assumption that we have to deal with only one logical symbolism, so that apart from variation in the names used, there would be a rule giving all propositional signs which, in that symbolism, had a certain sense, and we could complete the definition of ‘sense’ by adding to it these rules. Thus ‘ “p” says that ~aRb’ would, supposing us to be dealing with the symbolism of Principia Mathematica, be analysed as follows: call anything meaning a, ‘a’, and so on, and call ‘a’ ‘R’ ‘b’,7 ‘q’; then ‘p’ is ‘~q’ or ‘~~~q’ or ‘~q
~q’ or any of the other symbols constructed according to a definite rule. (1923: 278)

Let’s first strip away from this all the complexities introduced by Ramsey’s attempt to deal with truth-functional complexity. That will allow us to drop the material about rule-generated equivalents of ‘~q’, at the same 7 The expression, ‘ “a” “R” “b” ’ might look to be simply a string of quotations, but what is intended is a proposition. Ramsey uses ‘ “R” ’ here, and I will use it in what follows, as a relational expression: it expresses the relation between names defined in the previous quotation from Ramsey (1923: 275).

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time swapping the example from ‘~aRb’ back to the elementary ‘aRb’. The result is: ‘“p” says that aRb’ is to be analysed: call anything meaning a, ‘a’, and so on; then ‘p’ is ‘a’ ‘R’ ‘b’. Now convert this—in a fashion Ramsey clearly anticipates later in the same paragraph—to an analysis of ‘A judges p’. We then have: Call that by which A means a, ‘a’, and so on; then ‘A judges aRb’ is to be analysed: ‘a’ ‘R’ ‘b’. The central feature I’ve aimed to preserve through this succession of cuts and simplifications is marked in Ramsey’s original statement of his proposal by the striking formulation, ‘then “p” is “~q” or “~~~q” [and so forth]’. This formulation embodies the idea, which grounds the implications 1–3 of the previous section, that to say what a propositional sign says, given an allocation of names, is just to say which propositional sign it is. Adapted to an account of belief in accordance with TLP 5.542, this central idea becomes: to report a belief is simply to report, in that identifying way, the occurrence of a belief token; or in other words, to say what A believes is simply to say how his mind is set. The same conclusion can be reached from the account in ‘Facts and Propositions’. If then I say about someone whose language I do not know ‘He is believing that not-aRb’, I mean that there is occurring in his mind such a combination of a feeling and words as expresses the attitude of believing not-aRb, i.e. has certain causal properties, which can in this simple case, be specified as those belonging to the combination of a feeling of disbelief and names for a, R, and b, or, in the case of one who uses the English language, to the combination of a feeling of belief, names for a, R, and b, and an odd number of ‘not’s. (1927: 44–5)

Again, strip away from this everything introduced only to deal with truthfunctional complexity (and thus the parts with a pragmatist tendency), and what remains is: To say of someone ‘He is believing aRb’ is to say that there is occurring in his mind a combination of names for a, R , and b.8 So again, we reach the conclusion that to report his belief is simply to say how his mental bits are configured. 8 Along with—if you must—a feeling of belief. Ramsey allows his reader the freedom to substitute for his talk of feelings ‘any other word . . . which the reader prefers, e.g. “specific quality” or “act of assertion” and “act of denial” ’ (1927: 144 n.). Suppressing the pragmatist tendency—and thus reassuming Wittgenstein’s indifference between believing, assuming, suspecting, denying, or whatever—I have preferred in the main text to substitute nothing for it.

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VII The account of judgement Ramsey finds in Wittgenstein is thus strictly parallel to the theory advanced by Geach in Mental Acts (1957, sect. 14).9 Geach speaks of Ideas of objects, where by an Idea is meant ‘the exercise of a concept in judgement’ (1957: 53). An Idea of a would thus be, in Ramsey’s way of speaking, a mental tokening of a name of a.10 Geach also introduces an undefined operator on relations ‘§( )’, pronounced ‘squiggle’, such that ‘if a relational expression is written between the brackets, we shall get a new relational expression of the same logical type as the original one. If “R” is dyadic, so is “§(R)”, . . . and so on’ (1957: 52). In Geach’s stark presentation ‘§( )’ is formally undefined, but the intention is clear: for A’s Ideas of a and b to stand in the relation §(R) will be for A to judge that aRb. Geach’s relation §(R) is thus Ramsey’s relation ‘R’: it is a mental tokening of a name of R.11 So, expressing Ramsey’s theory in Geach’s terms, we have: A judges that aRb =def I(a) §(R) I(b). Readers of Geach have naturally enough asked: What is squiggle? Its behaviour is in some respects unusual. It is, as Geach points out (1957: 53), clearly non-extensional: that §(cordate) I(a) will not amount to anyone’s judging that a is a renate. And its syntax is, to put it mildly, non-Fregean: what type of function is it that takes arguments of different types and delivers values of correspondingly different types? 12 9 Though Geach later acknowledges the influence of the Tractatus on his theory (1957: 101), he does not mention Ramsey at all in Mental Acts ; I take that merely to illustrate the minimal referencing conventions in vogue in 1957. 10 I am here bending, perhaps distorting, what Geach says. Geach’s Ideas are intrinsically general: they are Ideas of any knife, or of some spoon, rather than of spoon a or knife b (1957: 53–4); or they are Ideas simply of flash and bang, rather than of this flash or that bang (1957: 63). There are two reasons for this. The less relevant is the grinding of Geach’s customary axe, that name, and not proper name, is the fundamental syntactic category. The more relevant is his view that ‘there is more hope that an account designedly adequate for general judgements will turn out to be adaptable to singular judgements, than there is of the reverse adaptation’ (1957: 63). That reverse adaptation is of course Ramsey’s aim in the parts of ‘Facts and Propositions’ that I have cut out. I am similarly cutting out Geach’s scepticism about its prospects in translating his theory into an account of singular judgements. 11 Remember again that a name of a relation is itself a relation. As Geach makes plain elsewhere (1961), this is in harmony with Frege’s view that the name of a function is itself a function. Geach points out there that a name of a function can occur in a written expression when there is no ink-mark of it to impress itself on the eye, as the name of the exponentiation function occurs in ‘32 ’. Similarly a mental name of a relation can occur when there is no phenomenological ‘ink-mark’ of it to impress itself on the inner eye. 12 Geach in the previous section complains that Russell’s multiple relation theory ‘require[s] different relations of judging (differing as to the number and logical types of the terms between which they hold) for every different logical form of sentences expressing judgements’ (1957: 49), e.g. a triadic relation for ‘s judges that Fb ’, J(s , F , b ), and a tetradic

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If these are legitimate concerns, then they should spread to embrace I( ). No function delivers, for a as argument, the concept of a, or the mental name of a; for there is no such thing as the concept or mental name of a. And unless it is presumed, as in a Tractarian context it should not be, that all objects are of a single type, I( ) must float across types as freely as §( ). Geach seems untroubled by such thoughts. But do we really know what §( ), or I( ), is meant to be? VII I Surprisingly, in the face of very similar questions Ramsey shares Geach’s equanimity. Recall that the analytical proposal of the Critical Notice, quoted in Section VI, assumed that ‘we had only to deal with one logical symbolism’ (1923: 278). At some point that false assumption has to be lifted: so long as it is in force we have an analysis only of ‘A asserts p using such and such a logical notation’, not of the neutral ‘A asserts p’; and, as Ramsey says, to pass off the first for the second would have such effects as that ‘the evidently significant fact that Germans use “nicht” for not becomes part of the meaning of such words as “believe”, “think” when used of Germans’ (1923: 278). In the corresponding passage from ‘Facts and Propositions’, also quoted in Section VI, Ramsey illustrates how, in a simple case,13 the assumption can be lifted: the account there exploits the causal equivalence of the attitudes of believing ~q and disbelieving q to avoid having to make explicit reference to any negative particle. The two passages show that Ramsey’s concern to eliminate unwanted language-relativity from his analysis is focused solely on the language’s logical vocabulary. Surely, though, the point that motivates the concern is broader than that. ‘ But we may very well know that a Chinaman has a certain opinion without having an idea of the logical notation he uses’ (1923: 278), Ramsey says. Equally, one would have thought, one might know that without knowing what names he has for things; and certainly, if I ever know a Chinaman’s unexpressed opinion, I know it without having any notion at all of what mental bits are involved. If ‘ “a” “R” “b” ’, or the Geachian ‘I(a) §(R) I(b)’, is to give the content of my report of A’s judgement, then in it ‘ “a” ’, or ‘I(a)’, must function as my name of A’s name for a. But how am I to name that when I am not acquainted with A’s name, when in truth I have no notion what it might be? The Geachian formulation, in which, as we saw, ‘I( )’ and ‘§( )’ function exactly as Ramsey’s quotation marks, might prompt the thought that my names for A’s names are what Russell called ‘descriptive names’. But that relation for ‘s judges that a R b ’, J(s , a , R , b ). If we were to construe ‘§( )’ as any kind of functional expression, it would seem in hardly better shape. 13 For the importance of the qualification, see Ramsey (1927: 149 n.).

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thought would work only if I( ) and §( ) were functional, and we’ve seen that they are not. The suggestion would in any case not suit the Tractarian context. Most importantly, though somewhat vaguely, it would undermine the appeal of Ramsey’s analysis, which lies in the idea that my portrayal of A’s judgement pictures it precisely as it in turn pictures reality: if the apparent complexity in ‘I(a) §(R) I(b)’ were really operative, so that my judgement and A’s differed essentially in their multiplicity, then my report would no longer display how A’s mental bits are configured. Less importantly, though more concretely, complex terms such as ‘I(a)’ would on this account be, have no place in the language envisaged in the Tractatus. A natural response to the points just made would be to retreat to a generalization, so that my report would have the form
x, y,S: x names a . y names b . S names R . x S y, and this is indeed one of the ways in which Ramsey presented Wittgenstein’s analysis in his lectures.14 In the face of those points, though, this formulation can be only a temporary retreat, as can most easily be shown by reviewing the sign–symbol dilemma that structured the dispute between Anscombe and Kenny. The quantified variables the generalization employs cannot be supposed to range over symbols. That would raise again Kenny’s worries over whether its first three conjuncts are attempts to say what can only be shown. More definitively, in my view, this worry would now clearly 14 Ramsey expounded Wittgenstein’s analysis in his Lent Term 1925 lectures entitled ‘Foundations of Mathematics’. Notes of these lectures, taken by L. H. Thomas, read: The meaning of such a proposition as ‘A asserts a R b ’ is now analysed as (
‘a ’, ‘b ’, R 0 ): ‘a ’, ‘b ’ are in A’s mind . ‘a’ M a . ‘b ’M b . R 0M R . ‘a’ R 0‘b ’. In this analysis no facts occur and it does not presuppose a R b . (1925b: 40) ( It is explained that M represents ‘means’; that M is of different type from M; and that R 0 represents the relation that signs ‘a ’ and ‘b ’ have in ‘a R b ’.) Ramsey’s focus at this point in his exposition is most clearly brought out by his first comment on the displayed formulation (effectively embodying implications 1–3 of Section V above), that ‘in this analysis no facts occur’. Later in the notes Ramsey turns to the shortcoming in Wittgenstein’s account that he had identified in the Critical Notice and was to address with the pragmatist innovations of ‘Facts and Propositions’. The notes then read, very much in the vein of Anscombe’s analysis (see again (AA) in Section II above), and in apparent tension with the key point that ‘no facts occur’: We can reduce ‘A asserts p ’ to ‘p ’ says p just as before—in A’s mind there is a symbol ‘p ’ and ‘p ’ says p. ( p. 45) The apparent tension with the earlier point is, surely, no more than that—i.e. it is simply a consequence of Ramsey’s shifting his attention to a new point. In just the same way, I think, the fact that Ramsey was content to make that earlier point by means of a formulation of Wittgenstein’s proposal similar to that discussed in the text does not show that he would have accepted this formulation as adequate in every respect. Each of these two formulations is adequate to the point in hand at the relevant stage of Ramsey’s exposition. ( I am grateful to Michael Potter for reminding me of the need to square the points made in the text with Ramsey’s presentation of the issues in these lectures.)

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also afflict the fourth conjunct: while an arrangement of signs can be described in a proposition, the logical combination of symbols cannot (TLP 4.21ff.). Ramsey, in any case, is clear throughout that his analysis concerns configurations of signs. But that alternative now also seems to be unworkable. The retreat to a generalization was forced by the thought that I, as reporter, need have no notion of what verbal or mental signs A happens to employ. Equally, though, I have no notion of how those signs, whatever they might be, are connected with things. If the variables in this formulation range over signs, then the naming it speaks of is an external relation. What relation this is, just as much as what those signs are, is something for psychology to find out (Wittgenstein 1995: 125). How can I report that things stand in this relation if I have no notion what the relation might be? The question ‘ What is the naming relation?’ is the form now taken by the question ‘ What is squiggle?’. Our analysis seems both to need and to preclude an answer to it. IX Ramsey, as I noted, is no more fazed by the question than Geach is. He glides past the difficulties just outlined with the phrase ‘apart from variation in the names used’ (1923: 278), spoken in the tone of ‘apart from negligible details’. Those difficulties don’t worry him, I think, because they are irrelevant to the ‘formal standpoint’ (1927: 41) his discussion adopts. To make this clearer it helps to note an oddity of the way Ramsey introduces his quotational names for a judger’s names, his equivalent of Geach’s I-terms and §-terms. He says, ‘call anything meaning a, “a”, and so on’ (1923: 278, quoted in context in Section VI). You might compare that to an injunction ‘Call any elephant “Nellie” ’, to which a natural response is that it asks you to do something you cannot do: you cannot name an elephant ‘Nellie’ unless you know which elephant you are naming, and you don’t know that just by being told that ‘Nellie’ is to name any elephant. At any rate, that would be a reasonable response if it were supposed that ‘Nellie’ is to be really a name. It would, on the other hand, be an inept response if ‘Nellie’ were intended merely as the kind of dummy-name introduced in the course of a proof. (Compare ‘Let n be a real number between 0 and 1’. ‘ Which real number?’) Dummy-names like that are schematic in two ways: they achieve generality, and they cover ignorance. They are introduced on the back of premises enough to ensure that there is something of a relevant kind to be named, but not enough to make its naming really possible. Ramsey’s formulation seems suited only to introducing a dummy-name like that. If that is what it actually does, it will

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follow that subsequent analyses, which include these ‘names’, will inherit their schematic character.15 A modern reader expects to extract from Ramsey’s discussion an account of reports of belief, an explicit semantic explanation of how expressions function in indirect speech. To someone with that expectation Ramsey’s easy resort in the analysans to a device of quotation that is unexplained, and that threatens to be inexplicable, is bound to appear as a serious flaw in his account. But Ramsey’s concerns are different from this modern reader’s. He announces his target as ‘the logical analysis of . . . judgement’, not of reports of judgement (1927: 34, my emphasis). From the very traditional opening pages of ‘Facts and Propositions’, and the character of his engagement with Russell in them, it seems plain that Ramsey understood his problem very much as Russell did when he wrote: ‘The problem at issue is the problem of the logical form of belief, i.e. what is the schema representing what occurs when a man believes’ (Russell 1922: 19). The question for both of them is: What kind of thing is going on, or what kind of fact is it, when a man believes something? And Ramsey’s answer to that runs, for the atomic case: it is for him to have names of the things his belief concerns combined in his mind in the way he believes those things to be combined. It is not a fault in this answer that it presents the fact in question only by description, or that the names that would be involved in the fact are not actually named, but are mentioned only descriptively as names of such and such things. That complexity attaches only to the analyst’s characterization of the fact, and not at all to the fact characterized. The same holds, I think, when the analysis of ‘A judges that aRb’ is presented notationally by ‘ “a” “R” “b” ’, or by ‘I(a) §(R) I(b)’. Modern conceptions of what such an analysis is intended to achieve, of what questions it is supposed to answer and how, lead us to question how the terms in the analysans are supposed to work. So we ask, ‘ What is the semantics for quotation here exploited?’, or ‘ What relation is reckoned to hold between I(x) and x?’, or again, ‘ What is squiggle?’. Those questions miss Ramsey’s drift, since for him ‘ “a” ’ is not genuinely a complex term at all. It is just a stopgap, a stand-in for a name one is not in a position to know. I’m sure that’s how Ramsey thought of his Wittgensteinian analysis; and I’m sure he had Wittgenstein right in thinking of it that way. There is, though, a natural thought that suggests this cannot be the end of the matter. This natural thought, which I’m inclined to accept as correct, is that an expedient is only properly counted an expedient if it is temporary. It implies that one can brush aside questions about the complexity of such apparent 15 The point is not just that Ramsey’s analyses will be presented schematically, so as to cover in one go a range of propositions. That much would be true of ‘x is a bachelor =def x is male and x is unmarried’, a schema whose instances are full-fledged meaningful propositions. The consequence drawn above is that the instances of Ramsey’s analysis will have a schematic character.

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names as ‘ “a” ’ only if, in theory at least, those stopgap names could eventually be replaced by real ones. And to the question of what theory could meet that ‘in theory’ obligation, the only feasible answer is psychology. There are passages in ‘Facts and Propositions’ where Ramsey clearly envisages this kind of supplement from psychology.16 In those passages he is certainly going beyond anything said in the Tractatus, but I see no reason to hold that he is going against anything in Wittgenstein. What those passages envisage might now go under the title of a ‘naturalistic theory of content’, an empirical identification of a human being’s mental bits, and a description of their external relations to things. Wittgenstein would of course have thought it no business of a philosopher to supply such a thing. But the ‘gap’ for it is there, as Ramsey says; and perhaps noting that is more important than arguing over what to call people who try to fill it.17

16 With this point we abandon the simplifying assumption introduced in Section I, that the pragmatist elements of ‘Facts and Propositions’ can be cut away by limiting oneself to the elementary case: p. 45 of that article clearly envisages that a causal theory would extend to the names occurring in an elementary proposition. 17 Thanks to Alan Millar and Michael Potter for comments on a draft, and to participants at the Cambridge conference on Ramsey for challenging questions.

Ramsey’s Transcendental Argument M I C H A E L P O TT E R

One of the papers of Ramsey’s Nachlass which his widow, Lettice, sold to the Hillman library at Pittsburgh is a set of notes entitled ‘The Infinite’. Embedded in these notes is the following curious argument for the Axiom of Infinity: We can say that the idea of infinity proves its existence. ( Wittgenstein’s extra prop). But the sign
proves nothing. We can prove it this way. It is clear that there may be an
of atoms and whether there are or not is an empirical fact, and this possibility implies an
of objects, as it were to be the possible atoms. In this way it is clear that transcendentally taken the axiom of infinity is true, though empirically it is doubtful.

The argument occurs again in a slightly more finished piece of writing entitled ‘The Number of Things in the World’. But nothing like it is to be found in anything Ramsey himself actually published, and although both the pieces just mentioned are included in Galavotti’s selection of papers from the Nachlass (Ramsey 1991), the argument just quoted seems to have been ignored except for a brief discussion in my own book (2000). Yet it does seem to me to be a very interesting argument. So I want here to return to it in rather more detail than I had space for in my book and try to answer four questions about it: 1. 2. 3. 4.

What is the context of Ramsey’s argument? Why did Ramsey not publish it? When did Ramsey think of it? Does it have any merit independent of Ramsey’s own views? I

Let us begin, then, by getting clear about the argument itself. What is clear straight away is that the context Ramsey intends is the system of the Tractatus, in which he had been immersed since he prepared the first draft of its English translation early in 1922. So we cannot hope to understand Ramsey’s argument without first going some way into this context. Now it would be a brave man who confidently asserted what the key idea of the Tractatus is. (Certainly what Wittgenstein himself calls his key idea—that logical constants do not refer—is rather hard to present in a way that makes it anything like the lynchpin of the book.) But it is at any rate one of the key

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ideas of the Tractatus that the task of a proposition is not merely to say how things stand in the world but to contrast the way they do stand with other ways they could have stood but don’t. The job of a proposition, that is to say, is to carve up the ways things might stand into two classes: the proposition is then true or false according as the way things are is in one or other of these two classes. And Wittgenstein takes it that these different ways things might stand—possible worlds, to use the modern jargon—must have something in common, in order that they should be different ways our world could be rather than just wholly distinct worlds with nothing whatever to do with one another. The elements which different possible worlds have in common Wittgenstein calls objects. ‘Object’ is thus for Wittgenstein a technical term, referring to whatever it is that our language presupposes in order that it should be significant. We should grant one thing straight away: it is hard to be confident that the existence of objects really does flow from the key idea just alluded to. Certainly the existence of objects is one of the first claims of the Tractatus that Wittgenstein himself publicly renounced, and the only argument he ever offers for believing it—the argument for substance of Tractatus 2.0211–2—is notoriously brief and problematic. Nonetheless we must grant Wittgenstein’s claim for the time being if we are to be in a position to appreciate Ramsey’s argument, since it is a claim which Ramsey simply presupposes. And if we do grant Wittgenstein’s claim, it is easy to see that a great deal follows. It follows at once, for instance, that objects are necessarily existent, just because they are by definition what different possible worlds have in common. (And presumably, therefore, most of the humdrum things we knock against in our mundane lives are not objects in Wittgenstein’s technical sense, since it seems we can quite coherently express the possibility of their non-existence.) It follows, too, that there is no genuine relation of identity that can hold or fail to hold between objects: what changes in the transition between possible worlds is how objects are combined with one another to form atomic facts; what the objects are does not change, because they are the hinges about which the possibilities turn and hence are constant. But although there are according to the Tractatus no genuine identity statements, there are many propositions that are apparently of this form. What appear to us to be meaningful identity statements linking proper names actually involve disguised descriptions to be analysed by means of Russell’s famous rewriting device. But at this point there is a difficulty. Russell analyses g(the f ) as (
x): fx . (y)fy  x = y . gx , which still contains the symbol for identity. So if, as Wittgenstein claims, there is no relation of identity, the analysis is still strictly meaningless. Wittgenstein’s solution is to adopt a new convention for interpreting quantified variables: where one variable occurs in the scope of another,

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Wittgenstein assumes (unlike Russell) that the ranges of interpretation of the two variables do not overlap. Consider, for example, (
x , y)x Ry: for Russell this means that something is R-related to something; whereas for Wittgenstein it means that something is R-related to something else. This elegant notational device allows Wittgenstein to re-express the Russellian analysis of g(the f ) as (
x): fx . gx . ~(
x, y) . fx . fy. (In words: something is both f and g , and there are not two things which are both f.) Notice also that since which objects there are does not vary between worlds, how many there are does not vary either. And if how many objects there are does not vary between worlds, there cannot be a genuine proposition which expresses how many there are. The best we could do in this regard would be to say something which presupposes for its significance that there are a certain number of objects. If we did that, we would show but not say how many things there are. Now you might very well think that what I have just said is wrong and that there is in fact a way of saying how many things there are: you might think indeed that Wittgenstein’s own notation for avoiding the identity sign allows us to express exactly this. If fx is any propositional function, (
x1, …, xn) . fx1 . … . fxn apparently says that there are at least n things that are f. So if Tx is some propositional function which is true of every object of a certain sort (e.g. fx  ~fx), and if we let pn =def (
x1, …, xn).Tx1 . … .Txn , then pn seems to say just that there are at least n things. Seems to, but does not. What has always to be borne in mind is that Wittgenstein’s way of reading nested quantifiers is a device. We can invent all manner of such devices—all manner of combinations of signs—but whether any such combination succeeds in saying something significant depends on whether it carves up the ways the world could be into two classes, those in which it is true and those in which it is false. (This, remember, was part of what I earlier called Wittgenstein’s big idea.) And if there are not enough objects, his device will not say something false but will simply not say anything at all. Suppose, for instance, that there are only three objects a, b, and c. Then p2 says the same as Ta .Tb  Tb .Tc  Tc .Ta, which is a tautology, and p3 says the same as Ta .Tb .Tc, which is also a tautology. But what does p4 say? Nothing remotely similar to the preceding sentences is available. So we are forced to conclude that p4, despite appearances, is not a proposition at all but merely a jumble of signs without significance. More generally, the pattern is this. If there are n things in the world, the sequence

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starts with n ways p1, p2,…, pn of expressing tautology; but from then onwards the signs pn+1, etc., rather than being, as we previously thought, ways of expressing something false, are in fact ways of expressing nothing at all. Do not be too hard on yourself if you made the mistake, though: Wittgenstein says nothing in the Tractatus to guard against it, and when Ramsey went to visit Wittgenstein in Austria in September 1923, he evidently persuaded Wittgenstein how easy a mistake it is to make. (It may indeed be that Ramsey himself had made it.) For in Ramsey’s copy of the Tractatus, at the point where the text explains that one cannot say ‘There are 100 objects’ or ‘There are
0 objects’, Wittgenstein added an extra proposition intended to clear up the confusion (see Lewy 1967): ‘The proposition “there are n things such that . . .” presupposes for its significance, what we try to assert by saying “there are n things”.’ We may be sure, then, that even if Ramsey did not understand the point before he went to Austria, he certainly did when he returned to Cambridge to begin his first term of study as a graduate student in October 1923. This, then, is the Tractarian background. With it in place, Ramsey’s argument is quickly explained. Let q
0 be the claim that there are infinitely many empirical things (electrons, protons, or whatever). This may well, as a matter of fact, be false. But what is clear, Ramsey thinks, is that it is significant. And if it is significant, the sentence p
0 is also significant. But, as we have seen, the signs p1, p2,…, p
0 are all either tautological or meaningless. So in particular p
0 cannot be significant without being true. Since it is significant, therefore, it is true. But p
0 is just the Axiom of Infinity. (Or, more strictly, it shows what the Axiom of Infinity tries, illegitimately, to say.) So we may conclude that the Axiom of Infinity is true. II ‘The Number of Things in the World’ is not a finished article ready for publication: it launches into its subject far too abruptly to be that. Nonetheless, it is quite close to being in a suitable form for inclusion as a section in a longer article. Yet Ramsey never published it. Why not? There could be any number of mundane reasons for this, of course, but what I want to show here is that Ramsey’s paper ‘The Foundations of Mathematics’, which he published in 1926, contains the clues to a particularly straightforward explanation for his abandonment of the transcendental argument. That paper is nowadays famous principally (and for many readers, I suspect, only) for the distinction Ramsey draws between

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the set-theoretic and the semantic paradoxes. This distinction enables him to argue that a simple theory of types suffices to solve the set-theoretic paradoxes, leaving the semantic paradoxes to be solved at the level of meaning, with the advantage that the simple theory of types has no need of Russell’s problematic Axiom of Reducibility. But it is actually a little strange that this is nowadays seen as Ramsey’s principal achievement in the philosophy of mathematics, since the idea is not really his: the distinction between two types of paradox had already been made by Peano, as Ramsey knew, and the observation concerning the simple theory of types which he drew from it is not in itself especially deep. But ‘The Foundations of Mathematics’ does contain another big idea, and it is this other idea that may have led him to abandon his transcendental argument. We have already seen that Wittgenstein’s notation allows us to form the string of signs pn =def (
x1, …, xn).Tx1 . … .Txn , which seems to say that there are at least n things but, if there are not n things, is actually meaningless. Already in ‘The Number of Things in the World’ Ramsey notes that this lurking possibility that we are talking gibberish is very inconvenient, since ‘in making complicated signs, if we are not careful’, we shall involve such forms as this. He then argues that it would be far more convenient if we could give the string of signs a meaning and suggests that ‘the most suitable meaning to give it is that of contradiction’ (1991: 172). But this does not yet overturn Ramsey’s transcendental argument because, as he observes, p2 .~p3, for instance, is ‘not really the expression of a proposition “There are exactly two things”, and yet it is possible to treat it symbolically exactly as if it was’. Thus Ramsey’s position at this time remains that p2 ‘has no meaning (unless we define it arbitrarily to mean contradiction)’ except in the case in which there are at least two things. But what happened, and provides a sufficient explanation for Ramsey’s abandonment of his transcendental argument, was that he adopted a new notation which allowed him, as he thought, to define non-arbitrarily a sequence of propositions which switches from tautology not to meaninglessness but to contradiction. To explain Ramsey’s new idea we need to recall one more item from the theory of quantification in the Tractatus. One of the ways envisaged there of forming quantified expressions is to take a proposition p and replace some name ‘a’ in it with a variable x. The result is an instance of what Ramsey calls a predicative function. It is a symbolic notation whose role is to pick out a certain class of propositions, namely all those which are just like p except that they may have in place of ‘a’ some other name of the same type. As Ramsey points out in ‘The Foundations of Mathematics’, if fx is a predicative function, there is a clear sense in which fa says the same about a as f b says about b. The fact which obtains if fa is true has just the same structure as the fact which obtains if fb is true: the only

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difference is that the latter fact has b in it where the former has a. What Ramsey did was to introduce a quite different notation for picking out a class of propositions. A propositional function in extension (Ramsey 1925a: 215) is a notation
ex such that, for any name ‘a’ of the appropriate type,
ea expresses a proposition involving a. There is no longer any requirement that
ea should say about a the same as
eb says about b. What matters here is that this notion of propositional function in extension enables Ramsey to define a propositional function T(x, y) =def (
)
e x 
e y with the property that T(a,a) is a tautology and T(a,b) is a contradiction for any two distinct objects a and b. He can then define p2 to be the logical sum of all the propositions of the form ~T(x , y). Similarly pn can now be defined to be the logical sum of all propositions of the form ~T(x1,x2 ).~T(x2 ,x3 ). … .~T(xn
1,xn ). And p0 is the logical product of the propositions pn for all finite n. The result of all this is that with these new definitions Ramsey’s sequence p1, p2,…, p0 ,… goes from tautology not to meaninglessness but to contradiction, thus pulling the rug from under Ramsey’s argument. III Before we go on let us, as Ramsey would say, look around and see where we have got to. Ramsey’s transcendental argument is as follows: (1) If p0 is meaningful, it is true. (2) If q0 is meaningful, p0 is meaningful. (3) q0 is meaningful. So p0 is true. As we have seen, it is a sufficient explanation for Ramsey’s abandonment of the argument that he adopted a notion—that of propositional functions in extension—which makes premise (1) false. For Ramsey the point of the notion of propositional function in extension was that it was central to his attempt to show that mathematics consists of tautologies. His difficulty, however, was that although the notion was essential to his project, it vitiated his argument for something else that was essential, namely the Axiom of Infinity. He was therefore reduced to offering, in the last paragraph of the essay as published, what is little more than a rhetorical flourish: ‘The Axiom of Infinity . . . if it is a tautology, cannot be proved, but must be taken as a primitive proposition. And this is the course which we must adopt, unless we prefer the view that all analysis is self-contradictory and meaningless’ (1925a: 224). This is not satisfactory,

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and Ramsey knew it. About the same time as he was correcting the proofs of ‘The Foundations of Mathematics’, Ramsey delivered a paper to the British Association in Oxford in which he admitted that ‘there still remains an important point in which the . . . theory must be regarded as unsatisfactory, and that is in connection with the Axiom of Infinity’ (1926a: 241). Ramsey’s failure to find an argument for the Axiom of Infinity that is cotenable with his theory of propositional functions in extension is thus not peripheral but a mortal blow to his version of logicism. But can we date Ramsey’s argument? I think that we can, but to do so we need to continue the narrative a little beyond Ramsey’s return from his first meeting with Wittgenstein in September 1923.1 It is clear that Ramsey started on the work which became his famous article on ‘The Foundations of Mathematics’ soon after he had returned from Austria. He had told his mother in a letter written during the visit that he would ‘try to pump [Wittgenstein] for ideas for its further development which I shall attempt’, and this seems to be just what happened. We know that he was preoccupied for some time with issues arising from the Wittgensteinian notation for identity. In November 1923 he wrote to Wittgenstein (McGuinness and von Wright 1995: 191) about what he thought was a difficulty of expressing ‘Something other than a is f ’. Wittgenstein wrote back immediately with the answer fa..(
x, y) . fx . fy : ~fa (
x)fx , and Ramsey had to admit (McGuinness and von Wright 1995: 194) that he had not fully understood the notation. By the time Ramsey was ready to depart for his second visit to Austria in March 1924, he had made a breakthrough. In a letter to Moore in February of that year 2 asking for a reference in support of his application for an Allen Scholarship, Ramsey reported that ‘ I have got on W[ittgenstein]’s principles a new theory of types without any doubtful axiom which gives all the results of Russell’s one, and solves all the contradictions.’ What Ramsey is referring to here, of course, is his use of Peano’s distinction between types of paradox to argue for a simple theory of types without the need for reducibility. Ramsey must therefore have come upon this argument quite early in his graduate work. But he can hardly at this point have come upon his other big idea, propositional functions in extension. For he goes on to tell Moore that ‘ Wittgenstein and I think it wrong to suppose with R[ussell] that mathematics is more complicated formal logic (tautologies); and I am trying to 1 Ramsey’s notes on the Axiom of Infinity are certainly later than this since they refer explicitly to the ‘extra proposition’ which Wittgenstein wrote in Ramsey’s copy of the Tractatus during that visit. 2 Letter in Moore papers, Cambridge University Library.

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make definite the vague ideas we have of what it does consist of.’ And the whole point of the notion of a propositional function in extension in ‘The Foundations of Mathematics’ is that it is what Ramsey uses to show that mathematics consists of tautologies. ‘The Foundations of Mathematics’ did not appear in print until late in 1926, but almost all the work that went into it was done much earlier. After six months in Vienna (during which he had to field various complaints from his over-anxious mother that he wasn’t doing enough work and would have to answer to the trustees of the Allen Scholarship for misuse of their money) Ramsey returned to Cambridge in October 1924 and immediately took up a teaching fellowship at King’s College. It seems very unlikely that he would have had very much time for research during his first term in this post. Fellows of King’s were worked quite hard in those days and he would probably have had twelve hours a week of undergraduate supervisions to give in his first term. After his first term as a teaching fellow was over, though, he would have had a little time to write up the work he had done before and during his stay in Vienna in the form of an essay. We know from a letter he wrote to Lettice 3 (with whom he had at this point only just started a relationship) that he sent the essay to be typed on 31 December 1924. This was just in time for it to be submitted as an entry for the Smith’s Prize (a competition for dissertations by beginning graduate students in the Cambridge Mathematics Faculty) at the beginning of the Lent Term (i.e. mid-January) 1925. The essay did not win the Smith’s Prize, which went to a contemporary of Ramsey at St John’s College called Gerald Room.4 The following summer, however, Ramsey decided to submit the essay for publication. The impetus for this was the reforms imposed on the university by the Oxford and Cambridge Act of 1925. Until then the vast majority of the teaching staff at Cambridge did not hold office in the university itself but received their earnings by means of stipends from the colleges at which they held their fellowships, which they supplemented by charging a guinea for each student who attended one of their lecture courses. The new Act of Parliament led to the establishment of a reformed employment structure (which has survived in its essentials to the present day) in which the normal post for most of the university’s academic staff was to be the office of University Lecturer. Ramsey intended to apply for one of these newly created posts, but if he was to do so he needed some more publications. One product of this sudden need to publish was his paper ‘Universals’, which he wrote (apparently in something of a rush) and submitted to Mind in the summer of 3 4

Letter in Modern Research Archive, King’s College, Cambridge. Room’s essay was called ‘Varieties Generated by Collinear Stars in Higher Space’. It would of course make a good story if Room had sunk without trace, but in fact he had a distinguished career as a geometer, was a founding Fellow of the Australian Academy, and had the mathematics library at the University of Sydney named in his honour.

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1925. Another was that Ramsey decided to try to publish his prize essay. In those days before double-blind refereeing, however, he was worried that a journal which had not heard of him might reject it, so on 24 July 1925 he wrote to Russell 5 asking for a letter of support to be included with the paper so as to ensure that the journal editor took it seriously. Russell’s reply has not survived, but Ramsey submitted his paper to the Proceedings of the London Mathematical Society, with or without Russell’s testimonial: it must have been accepted in September or October of 1925, since we know that it was read at a meeting of the London Mathematical Society on 12 November 1925. As I have been unable to trace a copy of the prize essay in the form it was originally submitted as an entry for the Smith’s Prize, it is a matter of conjecture how much Ramsey altered it between then and when it was published, but circumstantial evidence suggests that any changes were very minor. Certainly by the time he corrected the proofs of the published article, in late July 1926, he had ‘thought of ever so many ways in which if I hadn’t been damned slack I’d have made it better. That always happens at least also with my Universals paper; I never write anything except in a hurry because it is pressing and then am too slack and selfsatisfied to improve it afterwards at my leisure.’ 6 And there are various places in which the published article betrays its origins as a prize dissertation. It starts with a table of contents, for instance, which is a little unusual in a paper of this length (forty-seven pages). What is at any rate clear is that the overall content of the published paper did not advance significantly beyond the prize essay. We know this because in the Lent Term 1925, immediately following his submission of the essay, Ramsey gave for the first time a lecture course entitled ‘Foundations of Mathematics’ and lecture notes taken by a student at these lectures survive.7 Ramsey included in this course a summary of his own work and included in this summary all the key ideas of the published paper. Where does all this leave the dating of our transcendental argument? As we have seen, Ramsey adopted the idea of propositional functions in extension some time between February and September 1924, most likely during his stay in Vienna. The transcendental argument must date from before this adoption. On the other hand, a set of notes entitled ‘Identity’, with which his notes entitled ‘The Infinite’ are closely related, make use of Wittgenstein’s translation of ‘Something other than a is f ’, which Ramsey did not receive until about the beginning of December 1923. All of this suggests that the argument dates from some time between January and September 1924. But the influence of Kant is also evident in the notes, not 5 6

Letter in Russell Archives, McMaster University. Letter to Lettice Ramsey in the Modern Research Archive, King’s College, Cambridge, quoted by kind permission of the Provost and Scholars of King’s College, Cambridge. 7 L. H. Thomas papers, Special Collections Department, North Carolina State University Library.

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only in the form of the argument itself, but in a contrast Ramsey draws between intuitive and discursive mathematics, and we know from his diary that Ramsey was reading Kant early in 1924. This makes it rather plausible that ‘The Infinite’ may well be what Ramsey is referring to in his diary entry for 28 January 1924: ‘ Wrote after tea some notes on formal logic (abstraction, identity, axiom of infinity).’8 IV The conclusion Ramsey was trying to substantiate, that mathematics consists of tautologies, is one to which Wittgenstein was fundamentally opposed. It was therefore important to him to object to some part of Ramsey’s theory. However, what he objected to was not so much Ramsey’s failure to provide a good argument for the Axiom of Infinity as the other part of his account, the theory of propositional functions in extension. Some of his objections to this theory are contained in a letter he dictated to send to Ramsey in July 1927 (McGuinness and von Wright 1995: 216–18)— just about the first evidence we have of Wittgenstein doing serious philosophy after his long sabbatical in Lower Austria. But Wittgenstein did not rest there: he returned to the issue in Philosophical Remarks (§120) and Philosophical Grammar (pt. II, ch. iii, §16), struggling to find a formulation which expressed his objection clearly. The issue of whether Ramsey’s notion of a propositional function in extension is coherent lies at the centre of deep difficulties in modern set theory on which I cannot arbitrate here. But there is at the very least reason to think that Wittgenstein may have been right (see Sullivan 1995). In which case it behoves us to return to Ramsey’s argument and ask, if we suppose that its first premiss is reinstated, whether its second and third premisses are likewise in good order. Ramsey’s second premiss, let us recall, was that if it is meaningful to say that there are infinitely many empirical entities (e.g. physical atoms or protons), then there must be some type of which it is meaningful to say that there are infinitely many objects of that type. Or, more briefly, if q
0 is meaningful, p
0 is meaningful. Is this true? There have of course been at various times scientists who have been physical atomists—who have supposed, that is to say, that the physical world is made up of irreducible entities of certain kinds. What these kinds have been has varied. At one time the irreducible entities were thought to be atoms (hence the name). During most of the twentieth century schoolchildren were taught that the world is made up of electrons, protons, and neutrons. Nowadays the fundamental particles are much more exotic. But at any of these stages in scientific development it would have been possible to 8

The diary is in the Modern Research Archive, King’s College, Cambridge.

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represent the world in such a way that the physically irreducible entities are also logical atoms, i.e. Tractarian objects. For anyone who did represent the world in this way the required link between q0 and p0 would of course be trivial. But the physical atomist is not forced to take this step. For in order to qualify as a physical atomist all one is required to believe is that the world is in fact made up of such and such fundamental particles, not that it must be. And a physical atomist who thought that the particles which are in fact fundamental might not have been would on Wittgenstein’s account have to represent the world in such a way that these particles are not Tractarian objects. So the fundamental particles of physics might not be Tractarian objects. However, Ramsey’s argument does not require them to be. Nor does it even require there to be any fundamental particles. For suppose that there are only finitely many Tractarian objects and finitely many elementary propositions. Since every proposition is according to the Tractatus expressible as a truth function of elementary propositions, it follows that, if we count propositions according to sense, there are only finitely many different propositions. But Ramsey’s point is that I can conceive of the possibility of saying ‘Here is a particle’ of infinitely many ‘here’s, i.e. of infinitely many possible utterances with different senses. This contradicts the supposition that there are only finitely many objects. But if this re-establishes Ramsey’s second premiss, it shifts the focus all the more acutely to his third, namely that q0 is indeed meaningful. Is this true? One worry we might have about this premiss concerns the Aristotelian distinction between the actual and the potential infinite: perhaps what we mean when we say that there are infinitely many physical things is only that for every finite number n there could be n physical things, not that there actually are infinitely many. But in fact this is enough for our purposes, since if the proposition qn that there are n physical things is meaningful, then the logical product of the qn for all finite n is also meaningful, and we can let that be our q0. The matter is rather delicate, however. We cannot be too liberal in our allowance of situations whose possibility we can represent to ourselves, for otherwise we fall into the opposite difficulty that the argument may prove too much. More precisely, if
is any infinite cardinal, it seems as though we can meaningfully (although perhaps falsely) say that there are
many physical things in the world. If so, then an argument parallel to Ramsey’s allows us to deduce transcendentally the proposition p
that there are
Tractarian objects of some type. But this is evidently very dangerous: in the simple theory of types which Ramsey was recommending it would in fact be inconsistent. If we are to block this inference to the existence of ever more objects, we need there to be a limit to the number of things our representation of the

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world allows for. What we presumably have to do here is to observe a distinction between what our current representation of the world allows as possible and what other representations are possible. Ramsey’s argument thus has to be that our current representation of the physical world already allows for the possibility that it is infinite. We could perhaps go further and say that the modern physicist standardly represents the world as having 20 points. But we do not already represent the world as having
possible locations in it for larger cardinals
. To allow for such a possibility—to make q
meaningful—would involve an enlargement of the number of objects in the world (or, to put it in more modern jargon, a change in our conceptual scheme). In order to keep this distinction, therefore, Ramsey has to maintain that (1) we understand at the moment what qn means for every finite n, but (2) there are larger cardinals
for which we do not at the moment understand what q
means. Towards the end of his manuscript of ‘The Infinite’ Ramsey puts the points as follows: The whole trouble with the infinite is that we cannot get at it directly. 3 we can get at at once by a tripartite symbol, that is by intuition (Anschauung) but we cannot make infinitely complex symbols. ( But we may have such in spatial images, yet I think never do for they are not infinitely differentiated, but perhaps the image of motion may be really useful.) . . . Hence at a certain point probably I think where we deal with infinities mathematics must cease being intuitive and become discursive. We must describe infinite cardinals in the manner of Cantor instead of seeing them as we can the finite integers. (1991: 181)

But when it is put like this, Ramsey’s original claim begins to seem dubious. Of course we can utter qn and think that we understand it. But we can just as well utter, and seem to understand, q
for some large cardinal
. The question in both cases is whether we really understand it. Suppose that there are in fact only n physical things in the world. Can I really in that case understand qn+1? The question, remember, is not whether I can envisage adopting a new scheme within which n+1 things are represented, but whether my existing scheme of representation already allows one to say (falsely, as we are supposing) that there are n+1. Or, to put the matter in Ramsey’s Kantian manner, how can I be sure that my understanding of large finite numbers is not already discursive rather than intuitive? At this point, though, we have arrived at one way of expressing the central concern which occupied Wittgenstein when he returned to Cambridge in 1929 to work once again with Ramsey on the foundations of mathematics, a collaboration that was cut short at the end of that year by Ramsey’s illness and death. It is rather striking that this concern, which occupied Ramsey so much at the end of his life, was already present in his notes for ‘The Infinite’, since, as we have seen, they are probably among the earliest things on the foundations of mathematics that he wrote.

Ramsey on Universals FRASER MACBRIDE 1. INTRODUCTIO N Is there a fundamental division of objects into two classes, particulars and universals? This was the question that Ramsey set out to address in his 1925 Mind paper ‘Universals’. After considering a variety of different arguments in favour of a fundamental division he came to the sceptical conclusion that there was no reason to suppose such a division between particulars and universals obtained. The theory of universals, Ramsey declared, was ‘nothing but a muddle’ (1925c: 30). ‘Universals’ has not received the critical attention it deserves. Despite the great burgeoning of interest in universals over the last twenty-five years and the fact that so many contemporary theoretical developments presuppose the existence of a fundamental division between particulars and universals, Ramsey’s views have received little or no attention.1 Why has ‘Universals’ been so neglected? Partly because many of Ramsey’s commentators have thought it possible to say simply, shortly, and decisively why the arguments of ‘Universals’ are mistaken. But Ramsey has been ill served by his commentators. They have failed to appreciate the significance of ‘Universals’ because they have treated its arguments in isolation not only from one another but also from arguments employed by Ramsey in other writings and the evolving views of Russell and Wittgenstein that influenced Ramsey. When placed in this wider context, it is evident that the arguments of ‘Universals’ cannot be so easily dismissed. It also becomes evident that ‘Universals’ continues to bear significance for contemporary debate. 2. WHAT THE COMMENTATORS SAY One of Ramsey’s main aims in ‘Universals’ was to undermine the view that the linguistic distinction between subject and predicate corresponds to a ‘difference in the functioning of the several objects in an atomic fact’ (p. 17). Indeed it is for a summary argument to this effect that ‘Universals’ is usually remembered. According to this argument the same object may ‘in a sufficiently elastic language’ be denoted by both subject and predicate 1 For example, ‘Universals’ receives no mention in either David Armstrong’s twovolume work Universals and Scientific Realism (1978) or his more recent A World of States of Affairs (1997 ). Hugh Mellor provides the notable exception to the rule, appreciating early on both the structure and significance of Ramsey’s views on universals. See Mellor (1978, 1980).

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expressions: given a sentence whose subject denotes an object t and whose predicate denotes an object t*, another sentence that ‘asserts the same fact and expresses the same proposition’ can be found where t* is denoted by a subject expression and t by a predicate expression. Ramsey offered ‘Socrates is wise’ and ‘ Wisdom is a characteristic of Socrates’ as a natural language example of two sentences so related (p. 12). He then concluded that no fundamental classification of objects could be based upon the distinction between subject and predicate. Ramsey expressed the argument in the following terms: Now it seems to me as clear as anything can be in philosophy that the two sentences ‘Socrates is wise’, ‘ Wisdom is a characteristic of Socrates’ assert the same fact and express the same proposition. They are not, of course, the same sentence, but they have the same meaning, just as two sentences in different languages can have the same meaning. . . . Now of one of these sentences ‘Socrates’ is the subject, of the other ‘wisdom’; and so which of the two is subject, which predicate, depends upon which particular sentence we use to express our proposition, and has nothing to do with the logical nature of Socrates or wisdom, but is a matter entirely for grammarians. In the same way, with a sufficiently elastic language any proposition can be so expressed that any of its terms is the subject. Hence there is no essential distinction between the subject of a proposition and its predicate, and no fundamental classification of objects can be based upon such a distinction (p. 12).

Despite its superficial clarity, this argument resists straightforward interpretation. The argument evidently relies on an underlying conception of propositions that enables a single proposition to be expressed by sentences that differ in the subjects and predicates they contain. This conception may have been as clear to Ramsey ‘as anything can be in philosophy’. But unfortunately ‘Universals’ contains no explicit guidance on the identity or character of propositions. Nor does it contain an account of the relationship between propositions and the sentences that express them and the facts they assert.2 Despite these difficulties in interpretation, Ramsey’s commentators have attributed to him on the basis of this argument the following three claims. 2 In his Critical Notice of the Tractatus Ramsey articulates a conception of propositions as types of linguistic or mental representations. And, at least in his 1925 paper ‘The Foundations of Mathematics’, he appears to endorse it (see Ramsey 1923; 1925a: 168–9). But in ‘Universals’ Ramsey appears to drift between a linguistic conception and one whereby propositions enjoy worldly constituents (compare Ramsey 1925c: 16 and 29). In his later ‘Facts and Propositions’ Ramsey adopts a multiple relation theory of belief that obviates the need to posit propositions and relates ‘mental factors’ directly to their worldly objects ( Ramsey 1927: 34–5). On the one hand, it is tempting to suggest that ‘Universals’ marks a transition stage in Ramsey’s thinking about propositions where his thought fluctuates between the alternatives provided by earlier and later theories. On the other hand, it may be that it is only Ramsey’s terminology that shifts and that Ramsey held one theory continuously through variations in expression. Unfortunately for reasons of space I cannot adjudicate between these different interpretations here.

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(1) There is no subject–predicate distinction. (2) There is no particular–universal distinction. (3) There is no particular–universal distinction because there is no subject–predicate distinction. His commentators have then dismissed ‘Universals’ by pointing to what they take to be the errors inherent in one or other of these claims. There have been identifiable generational differences in the criticisms that Ramsey’s commentators have brought to bear upon ‘Universals’. What I will call—by rough-and-ready standards—the first generation of commentators rejected (1). They based their contrary claim that there is a subject–predicate distinction upon the observation that whereas predicates may be negated names may not. For every predicate F, they claimed, there is another, its contradictory ~F, such that when each is attached to a common subject a the result is a pair of contradictory sentences (Fa and ~Fa); but there are no such contradictory pairs of names (Geach 1950: 474–5; 1975: 143–4; Anscombe 1959: 108; Dummett 1973: 63–4). The first generation of commentators adhered to a broadly Fregean conception of ontology. According to this conception it is the logical behaviour of the expressions that denote a thing that determines the ontological category to which it belongs. By contrast, the second generation of Ramsey commentators self-consciously rejected the Fregean conception (Simons 1991; Dokic and Engel 2002: 40–1; Lowe 2004a, sect. 3). Instead they adhered to an alternative conception that denies language the role of authoritative guide to ontology. According to this conception the categorial status of an entity is determined quite independently of the behaviour of expressions that denote it. Consequently, the second generation of commentators rejected (3) because the absence of a linguistic distinction between subject and predicate hardly provides—given the conception of ontology adhered to—a reason for supposing an ontological distinction between particular and universal to be absent too.3 This view of things is encapsulated in Peter Simons’s judgement on ‘Universals’: The supreme questionable presupposition of Ramsey’s paper . . . is that the logical structure of language is (or is meant to be) our infallible guide to ontology. Personally I consider it fundamentally mistaken to try to read important ontological or metaphysical theses out of logical or linguistic ones; it is one place where much of analytical philosophy, of which Ramsey is such a prime exponent, went wrong. It 3 ‘Universals’ may, of course, be criticised in other ways. Braithwaite (1926) and Strawson (1959: 160–1) argue that the particular–universal distinction may be understood in (roughly) spatio-temporal terms. MacBride (1998, 2001) raises a variety of considerations that speak against this line of criticism. Wisdom (1934: 208–9) responds to Ramsey’s scepticism about the particular–universal distinction by claiming that the identity of indiscernibles applies to universals but not particulars. Of course this does not exhaust the list of other ways in which ‘Universals’ may be criticised.

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is pleasing that modern realists about universals, such as David Armstrong have come to accept this, and have abandoned the bad old linguistic arguments. (1991: 159)

Unfortunately both generations of commentators have got it wrong. They have failed to interpret ‘Universals’ properly and consequently their criticisms miss their mark. They miss their mark because Ramsey did not advance any of the three claims (1)–(3) attributed to him. The first clue that their interpretations have gone awry arises in the sentence that immediately succeeds the above argument from ‘Universals’, a sentence that provides Ramsey’s own commentary on its significance: ‘I do not claim that the above argument is immediately conclusive; what I claim is that it throws doubt upon the whole basis of the distinction between particular and universal as deduced from that between subject and predicate, and that the question requires a new examination’ (p. 13). If we take Ramsey at his word, then we cannot expect to come to a proper appreciation of the position that he actually advanced without also examining the other arguments that Ramsey provides in ‘Universals’. 3. NEGATION, COMPL EX UNI VERS AL S AND NECESSA RY CONN EXIO NS Where did the first generation of commentators go wrong? They took Ramsey to deny that there is any logical distinction that obtains between subject and predicate. But Ramsey did not assert anything so strong. He sought only to cast doubt upon the assumption that differences that obtain between the linguistic expressions ‘Socrates’ and ‘is wise’ correspond to differences amongst the constituents of the proposition that ‘Socrates is wise’ expresses and the fact that makes the sentence true (if it is). Moreover, there is evidence to suggest that Ramsey would have treated with equanimity the observation that whereas predicates may be negated names may not. For Ramsey did deny that a predicate sign that contains a negation corresponds to a constituent of an atomic fact. He affirmed instead that predicate signs that contain a negation are to be treated as ‘incomplete symbols’. Incomplete symbols are expressions that—like definite descriptions conceived à la Russell—make a systematic contribution to the sentences in which they occur but do not do so by indicating a constituent of the propositions these sentences express or the facts that make them true (if they are). Once this move is made, it is no longer possible simply to read off a distinction between the constituents of atomic facts—between particulars and universals—from a distinction between expressions that can be negated (predicates) and expressions that cannot (names). The passage that supplies evidence for this interpretation occurs in the penultimate paragraph of ‘Universals’. In this passage Ramsey asserts that the possibility cannot be ruled out that there are atomic facts consisting of two objects of the same type. Ramsey then considers an objection:

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It might be thought that this would involve us in a vicious circle contradiction, but a little reflection will show that it does not, for the contradictions due to letting a function be its own argument only arise when we take for argument a function containing a negation which is therefore an incomplete symbol not the name of an object. (p. 29)

In this passage Ramsey is alluding to the class of paradoxes that Russell discovered in 1902 and that now bear his name. The most famous, the paradox of the class of all classes that are not members of themselves, arose from an examination of Cantor’s proof that there is no greatest cardinal number. However, it is a consideration of another version of what Russell called ‘the Contradiction’ that will most readily enable us to appreciate the significance of the above passage from ‘Universals’: ‘If x is a predicate, x may or may not be predicable of itself. Let us assume that “not predicable of oneself” is a predicate. Then to suppose either that this predicate is, or that is not, predicable of itself, is self-contradictory’ (Russell 1903, §101). Russell asks us to consider a function sign ‘not predicable of oneself’ that contains a negation. He then shows that a contradiction arises when this function sign is applied to itself (allowed to figure in its own argument position). Russell took it to be ‘obvious’ what conclusion to draw: ‘ “not predicable of oneself” is not a predicate’. Ramsey’s contention that function signs that contain a negation are incomplete symbols contains the germs of a related solution to the contradiction. It is because these symbols are not names but contribute to the sentences in which they occur in some different way that function signs containing a negation are not capable of selfascription. Unfortunately Ramsey does not elaborate, but what he appears to have in mind here is something like the following thought: when a function sign containing a negation appears to occur within an atomic sentence ‘(~F )a’ its semantic contribution is perspicuously displayed by a sentence in which the function sign and the negation are pulled apart and the negation assigned wide scope ‘~(Fa)’. It is because negation is resolutely assigned wide scope that function signs that contain negation are never genuinely self-ascribed and contradiction is thereby circumvented. Ramsey’s solution to ‘the Contradiction’ merits conviction only to the extent that there is independent reason to hold that function signs that contain a negation are incomplete symbols. Unfortunately the above passage supplies no reason of this kind, offering only the assurance that a ‘little reflection’ will suffice to show that these symbols are incomplete. In fact this situation is doubly to be regretted. It not only leaves us without the means to assess Ramsey’s solution to ‘the Contradiction’. It also leaves us without motivation for the claim that a distinction between the constituents of atomic facts cannot be read off the distinction between expressions that are capable of being negated (predicates) and expressions that are not (names). Fortunately, an argument that appears earlier in ‘Universals’ yields up some of the motivation missing.

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Ramsey begins his examination of the subject–predicate distinction by considering such sentences as ‘Either Socrates is wise or Plato is foolish’ (p. 13). Prima facie the subject–predicate distinction does not apply to this sentence or the proposition it expresses. But one might still contend that the distinction does gain application, the subject being any term, the predicate the complex remainder. For example, ‘Socrates’ may be taken to be the subject and ‘being wise unless Plato is foolish’ the predicate. If so, the predicate appears to be a name for a complex universal asserted to characterise Socrates. Ramsey seeks to discredit the theory that universals correspond in this way to complex predicates with a reductio ad absurdum: In order to make things clearer let us take a simpler case, a proposition of the form ‘aRb’; then this theory will hold that there are three closely related propositions; one asserts that the relation R holds between the terms a and b, the second asserts the possession by a of the complex property of ‘having R to b’, while the third asserts that b has the complex property that a has R to it. These must be three different propositions because they have different sets of constituents, and yet they are not three propositions, but one proposition, for they all say the same thing, namely that a had R to b. So the theory of universals is responsible for an incomprehensible trinity, as senseless as that of theology. (p. 14)

In this passage propositions, like facts, have worldly items as constituents (elsewhere in ‘Universals’ propositions take on a linguistic guise). Ramsey assumes that these propositions are distinct if their constituents are different. Absurdity results when this assumption is combined with the admission that complex predicates are names for complex universals. This is because more than one complex predicate may be isolated in a sentence of the form ‘a Rb’—predicates that may be represented by ‘
R  ’, ‘
Rb’ and ‘aR  ’. If these predicates are names of different universals, then the sentence ‘aRb’ expresses no less than three propositions—propositions that are distinct because they correspond to the three different collections of constituents (i)
R  , a, b, (ii)
Rb, a, and (iii) aR  , b. But this is absurd because ‘aRb’ says only one thing: that aRb.4 This argument can be generalised to rule out the possibility that negated predicates are names of complex universals (negative ones). This is because more than one predicate may be isolated in a sentence of the form ‘~Fa’— the complex predicate that may be represented by ‘~F
’ and the simple predicate ‘F
’. If these predicates are both names of universals, then the sentence ‘~F a’ expresses no fewer than two different propositions—one that denies that F
characterises a and another that asserts ~F
to do so. This too is absurd because ‘~Fa’ also says only one thing: that ~Fa.

4 Mellor revives a version of Ramsey’s argument against complex universals in his (1991a: 179). See Oliver (1992) and Mellor (1992) for a criticism and a defence of this argument.

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If this argument is effective, then it follows that neither relational nor negated predicates are names of complex universals. This supplies the missing motivation for Ramsey’s thesis that function signs that contain a negation are incomplete symbols. But this argument relies not only upon the assumption that propositions with different constituents are distinct but also upon the assumption that sentences—like ‘aRb’ and ‘~Fa’—say only one thing. And, unfortunately, Ramsey provides no explicit motivation for either of these assumptions.5 So if we are to understand Ramsey’s reasons for doubting that the distinction between particular and universal may be deduced from that between subject and predicate, then we must enquire further into the (implicit) grounds for these assumptions. It may appear, however, that Ramsey’s argument against complex universals does not rely upon any special assumptions. On one such interpretation the argument comes down to a judicious employment of Ockham’s razor. On this interpretation Ramsey is merely pointing out that there is no need to posit complex universals in addition to simple ones. This is because simple universals (and particulars) provide an adequate supply of constituents to construct the propositions our sentences express and the facts that make them true. So complex universals are nothing but an excrescence to our ontology. On a related interpretation, Ramsey’s argument depends ultimately upon the ‘robust sense of reality’ that Russell exhorted us to maintain when doing philosophy. This sense of reality can be seen to be at work when Russell argues that asymmetric relations (before, greater, up) are identical to their converses (after, less, down). Russell begins from the reflection that there is an important difference between ‘before’ and ‘after’, namely that ‘A is after B’ may not be inferred from ‘A is before B’. But, he continues, it may be inferred that B is after A, and so it would seem that this is absolutely the same ‘fact’ as is expressed by saying that A is before B. Looking away from everything psychological, and considering only the external fact in virtue of which it is true to say that A is before B, it seems plain that this fact consists of two events A and B in succession, and that whether we choose to describe it by saying ‘A is before B’ or by saying ‘ B is after A’ is a mere matter of language. ( Russell 1992: 85)

In this argument Russell appeals to our robust sense of reality to assure us that the external fact in virtue of which the sentence ‘A is before B’ is true admits of only A and B in succession. And certainly Russell has 5 Several of Ramsey’s critics have rejected these assumptions, arguing that the same proposition may admit multiple parsings where different parsings reveal the presence of different constituents (
R b on one parsing, a R  on another, etc.) but where the proposition nevertheless still says the same thing. See Moore (1962: 297 ); Anscombe (1959: 95); Geach (1975: 146); Dummett (1981: 264–6); Oliver (1992: 95–6). But unless we enquire into the underlying motivations that shape Ramsey’s argument we will be unable to assess the relative merits of endorsing or rejecting alternative views.

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intuition on his side when he makes this claim. Consider a situation in which a cup is on top of a saucer. Intuitively the cup’s being on top of the saucer is the same external state of the environment—the very same ‘chunk of reality’—as the saucer’s being underneath the cup.6 Similarly, it may be argued, looking away from everything psychological and concerning only the external fact in virtue of which it is true to say that aR b, it seems plain that this fact consists of just a, R , and b, and that whether we choose to describe it as ‘R holds between the terms a and b’, ‘a possesses the complex property of “having R to b” ’ or ‘b has the complex property that a has R to it’ is a mere matter of language. Consider a situation in which a cup is next to a saucer. Intuitively the holding of the next to relation between the cup and the saucer, the possession by the cup of the property being next to the saucer, and the saucer’s having the property that the cup is next to it, are the very same state of the external environment, a chunk of reality that consists of nothing but the cup and the saucer in adjacency. Whatever the intrinsic merits or defects of these arguments they cannot suffice as interpretations of Ramsey. It is critical to the structure of Ramsey’s argument that the admission of complex universals results in ‘an incomprehensible trinity’ of propositions. After all, the argument is intended to be a reductio ad absurdum of the assumption that complex universals exist. But neither of the interpretations offered makes sense of this. The trinity of propositions (or facts) that result from the admission of complex universals are—so far as these interpretations go—redundant or superfluous rather than incomprehensible. In order to understand why Ramsey should have thought that the admission of complex universals results in ‘an incomprehensible trinity’ it is necessary to appreciate the influence that Wittgenstein exerted upon him during the period in which ‘Universals’ was composed. In his Notebooks 1914–1916 Wittgenstein set out to investigate whether negative propositions correspond to negative facts. Raphael Demos had proposed that a proposition of the form ‘~p’ does not correspond to a negative fact, but rather corresponds to some true proposition ‘q’ that is incompatible with ‘p’ (Demos 1917). Russell was later to criticise Demos’s account on the grounds that ‘it makes incompatibility a fundamental and objective fact which is not so much simpler than allowing negative facts’ (Russell 1918: 213). Russell therefore admitted negative facts alongside positive facts to correspond to negative and positive propositions respectively. However, just as Demos’s account provides no explanation of the incompatibility of the propositions ‘p’ and ‘q’ but leaves this a brute fact of nature, Russell’s account likewise provides no explanation of the incompatibility of the positive and negative facts p and ~p. 6 See Fine (2000: 2–6) for a similar argument against converse relations. Williamson (1985) arrives at the same conclusion via linguistic considerations.

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When Wittgenstein came to reflect upon these issues, he found that fundamental incompatibilities of this kind offended against his Humean scruples. Just as Hume could not understand how there could be brute necessary connexions between causes and effects, Wittgenstein could not understand how brute necessary incompatibilities could obtain between positive and negative facts. At first Wittgenstein struggled to find a way to avoid such incompatibilities: The question is really this: Are there facts beside the positive ones? ( For it is difficult not to confuse what is not the case with what is the case instead of it.) . . . It is the dualism, positive and negative facts, that gives me no peace. For such a dualism can’t exist. But how to get away from it? ( Wittgenstein 1961: 25.11.14)

But Wittgenstein was soon to light upon an account of the role of ‘~’ and the other logical constants that obviated the need to posit a dualism of positive and negative facts, an account that addressed his Humean concerns. The account was to become the Grundgedanke of the Tractatus: 4.0312 . . . My fundamental idea is that the ‘logical constants’ are not representatives . . . ( Wittgenstein 1922)

It was the assumption that the negation sign contributes to the content of ‘~p’ that led Demos and Russell to affirm fundamental incompatibilities between propositions and facts. By both accounts ‘~’ combines with ‘p’ to produce a representation of a fact different from p—either a positive fact q that is incompatible with p or the negative fact ~p. A dualism of incompatible facts is thereby induced. To avoid this dualism Wittgenstein denied that the negation sign contributes to the content of the sentences in which it occurs. He proposed instead that both ‘p’ and ‘~p’ have the same content, but that they represent this content in different modes. On Wittgenstein’s account ‘~’ switches the mode in which the content is represented; what ‘p’ represents to obtain, ‘~p’ represents to be absent. The influence of Wittgenstein is evident in Ramsey’s 1927 paper ‘Facts and Propositions’. In this paper Ramsey endeavours to combat the idea that the logical constants are representatives of logical objects. Suppose, for the sake of argument, that the negation sign is the name of a logical object not. Then the sentence ‘~~p’ expresses a proposition that contains a constituent not that is missing from the proposition expressed by ‘p’. ‘p’ and ‘~~p’ therefore express different propositions (see Ramsey 1927: 43). But if they express different propositions, then it appears impossible to explain the fact that they are mutually entailing; the account that treats logical constants as representatives of logical objects leaves this a brute necessary connexion between distinct propositions. Ramsey concluded that the logical constants ‘must function in some different way’: I find it very unsatisfactory to be left with no explanation of formal logic except that it is a collection of ‘necessary facts’. The conclusion of a formal inference must, I feel, be in some sense contained in the premises and not something new. I cannot

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believe that from one fact, e.g. that a thing is red, it should be possible to infer an infinite number of different facts, such as that it is not not-red, and that it is both red and not not-red. These, I should say, are simply the same fact expressed by other words; nor is it inevitable that there should be all these different ways of saying the same thing. We might, for instance, express negation not by inserting a word ‘not’ but by writing what we negate upside down. ( Ramsey 1927: 42; cf. Wittgenstein 1922: 5.43)

Ramsey thus seeks to avoid brute necessary connexions by insisting that the conclusion of an inference must be contained in its premises.7 In this way Ramsey tries to ensure that the connexions between propositions are intelligible rather than brute. The underlying Humean concerns that shape Ramsey’s perspective reemerge later in ‘Facts and Propositions’ when he shifts his attention from the logical constants to the quantifiers. Frege and Russell had maintained that the universal and existential quantifiers denote higher-order properties. Their theory assigns quantified sentences the form ‘F( f )’: according to the theory a universal quantification ‘For all x, fx’ ascribes the higher-order property of universal application to the lower-order property f whereas an existential quantification ‘There is an x such that fx ’ ascribes the higherorder property of merely having application to f. Ramsey rejects this account in favour of Wittgenstein’s theory that ‘For all x, fx’ is equivalent to the infinite conjunction of all the values of ‘fx ’ (‘fa & fb & fc &...’) whereas ‘There is an x such that fx ’ is equivalent to their infinite disjunction (‘fa
fb
fc
...’). Ramsey endorses Wittgenstein’s account because It is the only view which explains how ‘fa’ can be inferred from ‘For all x, fx’, and ‘ There is an x such that fx’ from ‘fa’. The alternative theory that ‘ There is an x such that fx ’ should be regarded as an atomic proposition of the form ‘F( f )’ ( f has application) leaves this entirely obscure; it gives no intelligible connection between a being red and red having application, but abandoning any hope of explaining this relation is content merely to label it ‘necessary’. ( Ramsey 1927: 48–50)

In this passage Ramsey anticipates a difficulty—fashioned by contemporary Humeans—that has come to bedevil theories that conceive of laws of nature as the obtaining of higher-order relations. According to these theories, if it is a law that Fs are Gs then this is to be regarded as an atomic fact in which the higher-order relation of nomic necessitation obtains between the lower-order universals F and G. The difficulty such theories 7 Of course Russell would not have been swayed by this argument. In his dispute with Bradley he wrote: Such a view involves the assumption—implicit in many such arguments—that all inference is essentially analytic, that whatever can be inferred from a proposition is necessarily part of that proposition. This view appears to me to be erroneous, and to be connected with the theory of relations upon which most of my disagreements with Mr. Bradley depend. ( Russell 1910: 377 )

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encounter is that they fail to supply an account of the connexion between (i) its being a law that Fs are Gs and (ii) some particular a that is F being also G. For whereas (i) concerns a higher-order fact, the obtaining of a higherorder relation N between F and G (N(F ,G)), (ii) concerns lower-order facts, the distribution of the lower-order universals F and G over particulars like a (Fa,Ga). Since the higher-order and lower-order facts concerned are distinct, the theories in question are obliged to treat the necessary connexion between a law and its instances as brute (see Lewis 1983: 366).8 In the same way Ramsey accuses Frege and Russell of failing to supply an account of the necessary connection between, for example, (iii) something’s being F and (iv) a’s being F. For whereas (iii) concerns a higher-order fact, the inhering of the higher-order property of having application in the lowerorder universal F, (iv) concerns a lower-order fact, the inhering of F in a. Since these facts are distinct, Frege and Russell are obliged to leave the necessary connection between (iii) and (iv) entirely ‘obscure’. By contrast, Wittgenstein’s view avoids this difficulty. The necessary connection is rendered transparent because a’s being F is a constituent of the infinite disjunction Fa
Fb
Fc
... to which the existential quantification is deemed equivalent. How do the arguments from ‘Facts and Propositions’ illuminate Ramsey’s reasons for rejecting complex universals in ‘Universals’? These later arguments reveal an underlying Humean tendency in Ramsey’s thought, a tendency which can already be seen to manifest itself in his earlier argument against complex universals. According to this Humean interpretation of this argument, the trinity of propositions that Ramsey declares to result from admitting complex universals is ‘incomprehensible’ because it incorporates a commitment to the existence of brute necessary connexions. This Humean interpretation casts the argument against complex universals in the following terms. Suppose there are complex universals. Then the three sentences ‘R holds between the terms a and b’, ‘a possesses the complex property of “having R to b” ’ and ‘b has the complex property that a has R to it’ express propositions that contain different constituents (the complex universals
R  ,
Rb, and aR  ). Therefore, they express different propositions. However, these three propositions are mutually entailing: if it is true that R holds between a and b, then a must possess the property of ‘having R to b’ and b must have the property that a has R to it, and so on. But the theory of complex universals leaves this entirely obscure, providing no means of explaining the entailment; the entailment is an ‘incomprehensible’ necessary connexion between three distinct propos8 Of course Ramsey was later to reject theories of this kind on Humean grounds in his later paper ‘General Propositions and Causality’: ‘ But may there not be something which might be called real connections of universals? I cannot deny it, for I can understand nothing by such a phrase; what we call causal laws I find to be nothing of the sort’ (1929a: 160).

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itions. The only way to explain this mutual entailment is to insist that these sentences express the same proposition (recall Ramsey’s injunction: the conclusion ‘must be in some sense contained in the premises and not something new’ (1927: 42)). But if they express the same proposition, then the different predicates—‘
R  ’, ‘
R b ’, and ‘aR  ’—embedded in these sentences cannot refer to different universals. Such complex predicates must be incomplete symbols, neither representatives nor names of complex universals. It is noteworthy that it will not do to respond to this Humean argument that one and the same proposition may say three different things at once. This relieves the pressure upon the advocate of complex universals to explain the mutual entailment between three distinct propositions. But this response still leaves in place a comparable explanatory burden: the requirement to account for the tangle of necessary connexions that still obtain between the constituents
R  ,
Rb, aR  , a, and b even when they belong to a single proposition (the necessary connexions that oblige
R  to be instantiated if
Rb is, and so on). If this interpretation is correct, it is an underlying Humeanism that is ultimately responsible for not only Ramsey’s rejection of complex universals but also his claim that function signs that contain a negation are incomplete symbols. And it is because he denies that such signs are referring devices that Ramsey has no reason to suppose that the difference between signs that can be negated and those that cannot corresponds to a difference in the functioning of objects that make up atomic facts. Consequently, Ramsey may accept with equanimity the claim of the first generation of commentators that there is a subject–predicate distinction based upon the distinction between expressions that can be negated (predicates) and expressions that cannot (names). He may endorse this claim while still doubting whether there is a fundamental division of objects into two classes, particulars and universals.9 4. OUR KNOWLEDGE OF REL ATIONS Where did the second generation of Ramsey’s commentators go wrong? The second generation, recall, denied the third of the claims usually attributed to Ramsey: (3) There is no particular–universal distinction because there is no subject–predicate distinction.

9 See MacBride (1999, 2001) for further Humean arguments against the particular– universal distinction of this general kind. See also MacBride (2005), which seeks to show that Dummett’s and Geach’s arguments fail to demonstrate the necessity for a subject–predicate distinction based upon the distinction between expressions that can be negated and those that cannot.

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They denied this claim because they rejected the broadly Fregean conception that ties ontology to language. From this perspective the malady that afflicts ‘Universals’ is one of flawed conception. It presupposes that ontological distinctions are tied to logical or linguistic ones. This appears to set Ramsey at odds with much of contemporary ontology: Contrary to what one might call the classical stance in analytic philosophy, of which Ramsey in ‘Universals’ is one of the most brilliant representatives, much of contemporary ontology rejects the assumption that one can get at ontological issues through linguistic distinctions, and conversely that one can get rid of the latter through the former. ( Dokic and Engel 2002: 40–1)

It is perhaps not surprising that viewed from the perspective of its closing years the history of twentieth-century ontology should appear in this fashion. The last two decades of the century came to be dominated by a realist conception that divorces ontology from language (the philosophical systems of Mellor and Armstrong stand out as exemplars of this kind).10 However, other forces dominated the period that intervened between the analytic philosophers, such as Ramsey, and the modern realists, such as Mellor and Armstrong: the forces of ordinary language philosophy and the anti-realist programme that succeeded it. The contemporary revival of ontology is owed in no small part to the self-conscious attempt by modern realists to disentangle issues about meaning and ontology that ordinary language philosophy and anti-realism wove together, leaving it to fundamental science to settle a posteriori what there is. It is therefore entirely natural that a contemporary metaphysician should distinguish himself (or herself ) from his (or her) predecessors by the rejection of the ‘bad old linguistic arguments’ (Simons 1991: 159). However, this view of history does not do justice to the fact that the analytic philosophers—not only Ramsey but Russell and Wittgenstein as well—also came to doubt that reflection on language could determine a priori what there is. They too came to rely upon the a posteriori investigations of fundamental science to settle what exists. Moreover, this view of history leads the second generation of Ramsey’s commentators to misinterpret ‘Universals’, attributing to Ramsey a claim (3) and a conception of ontology to go with it that he did not hold. The awkwardness of attributing (3) to Ramsey should already be apparent from Ramsey’s discussion of incomplete symbols in ‘Universals’. For this discussion led Ramsey to the conclusion that neither complex relational predicates nor function signs that contain negation correspond to the constituents of atomic facts (complex universals). This move already distances ontology and language in one critical respect, enjoining a distinction between, on the one hand, what is merely a predicate and, on the 10

See Armstrong (1978, 1997 ); Mellor (1991b).

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other, the property (if any) that it denotes. Of course Russell had already drawn a distinction of this kind, remarking that there are ‘many abstract words which do not stand for single universals, e.g. triangularity and rationality’ (1924: 331).11 Russell made this distinction in the course of warning philosophers to guard against the danger of being misled by the vocabulary and syntax of ordinary language: ‘ The influence of language on philosophy has, I believe, been profound and almost unrecognised. If we are not to be misled by this influence it is necessary to become conscious of it and to ask how far it is legitimate. The subject–predicate logic, with the substance–attribute metaphysic, are a case in point’ (1924: 330). The subject–predicate logic and the substance–attribute metaphysic are a case in point because, Russell maintained, it is the uncritical assumption that all propositions must exhibit subject–predicate form that has duped philosophers into affirming the existence of attributes while denying that there are any relations. But here, as elsewhere, Ramsey was prepared to go further than Russell: ‘I shall argue that nearly all philosophers, including Mr Russell himself, have been misled by language in a far more far-reaching way than that; that the whole theory of particulars and universals is due to mistaking for a fundamental characteristic of reality, what is merely a characteristic of language’ (Ramsey 1925c: 13). Evidently Ramsey cannot be saddled with the assumption that there is any kind of straightforward or direct connection between the structure of language and the structure of reality. A further passage that significantly tells against the attribution of (3) to Ramsey is to be found in the sentence upon which ‘Universals’ concludes: ‘Of all philosophers Wittgenstein alone has seen through this muddle and declared that about the forms of the atomic propositions we can know nothing whatever’ (p. 30). If Ramsey indeed thought there to be no particular–universal distinction because there is no subject–predicate distinction, then it is entirely incongruous that ‘Universals’ should conclude upon the epistemic reflection that we do not and cannot know whether there is an ultimate distinction amongst the worldly constituents of the atomic propositions. It is only against the backdrop of Russell’s evolving views on universals that the significance of ‘Universals’ may be properly understood. In the second edition of Principia Mathematica (1925), Russell characterised the

11 This and related passages make Armstrong’s attribution to Russell of a ‘largely unthinking adoption of a one–one correlation between predicates and universals’ precarious indeed (Armstrong 1978: ii. 91). Russell is also to be seen carefully separating linguistic and ontological issues in his discussion of vagueness. He writes: ‘There is a certain tendency in those who have realised that words are vague to infer that things are also vague . . . This seems to me precisely a case of the fallacy of verbalism—the fallacy that consists in mistaking the properties of words for the properties of things’ ( Russell 1923: 85).

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particular–universal distinction in the following terms.12 After defining atomic propositions as propositions of one of the series of forms (A)

R 1(x)

R 2(x, y)

R 3(x, y,z)

...

Russell writes: Here R 1, R 2, R 3, R 4 ... are each characteristics of the special form in which they are found: that is to say Rn cannot occur in an atomic proposition R m(x1, x2, ... xm) unless n =m, and then can only occur as R m occurs, not as x1, x2, ... xm occur. Terms which can occur in any form of atomic proposition are called ‘individuals’ or ‘particulars’; terms which can occur as the Rs occur are called ‘universals’. ( Whitehead and Russell 1925, p. xix; see also p. xv)

Ramsey went on to offer the following gloss on Russell’s conception of the particular–universal distinction: [ Russell] says that all atomic propositions are of the forms R 1(x), R 2(x, y), R 3(x, y, z ), etc. and can so define individuals as terms which can occur in propositions with any numbers of terms; whereas of course an n-termed relation could only occur in a proposition with n+1 terms. ( Ramsey 1925c: 29; see also his 1926b: 31)

These passages raise a number of interpretative issues.13 Nevertheless, for the purpose of coming to a fuller understanding of ‘Universals’ we may, following Ramsey, isolate and abstract the following account of the particular–universal distinction from the second edition of Principia.

12 It should be noted that Russell maintained at one time or another a variety of other conceptions of the particular–universal distinction. Compare Russell (1911: 124; 1912: 53; 1919: 286–7 ). 13 For reasons of space I cannot offer a thoroughgoing reconstruction of the view Russell historically held in 1925. Instead I will confine myself to drawing attention to some of the interpretative issues that arise. Note first that Russell defines the particular–universal distinction relative to the occurrence of particulars and universals in ‘propositions’. Under the influence of Wittgenstein, Russell had adopted the view that propositions are types of mental or linguistic representations (see Russell 1918: 184–5, 196; 1919: 315–19; 1921: 240–2, 273-4; Whitehead and Russell 1925: 406–7 ). According to this view, it is the symbolic representatives of the particulars and universals that occur in the propositions that concern them rather than the particulars and universals themselves. This makes Russell’s 1925 claim to define the particular–universal distinction relative to the different ways in which particulars and universals occur in propositions puzzling—puzzling because particulars and universals do not occur in propositions. Second, contra Ramsey’s gloss, Russell does not simply define particulars ‘as terms which can occur in propositions with any numbers of terms’ and universals as n-termed relations that can ‘only occur in a proposition with n +1 terms’ ( Ramsey 1925c: 29; 1926b: 31). Rather Russell invokes the further idea that universals are items that not only occur in propositions with a fixed number of constituents but also occur in propositions in a certain distinctive manner; they are kinds of thing that ‘occur as’ relations. Unfortunately Russell does not make clear what it means to occur as a relation.

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Conceive of atomic propositions as worldly complexes—non-linguistic, non-mental items—that actually contain the constituents they are about. Then if the space of atomic propositions consists of the sequence of forms (A), particulars (x, y, z, ...) may be defined as entities that can occur in propositions with any number of constituents. By contrast, universals (R 1, R 2, R 3, ...) may be defined as entities that can only occur in propositions with n-ly many constituents (where n may be finite or infinite). Call those entities unigrade. Unigrade entities have a definite degree or adicity; they are either monadic or dyadic or triadic ... or n-adic. Entities that enter into propositions with differing numbers of other entities are not n-adic for any number. Call these entities multigrade.14 So whereas particulars are multigrade, universals are unigrade. Russell neglected to provide any direct motivation in Principia for the view that particulars are multigrade, universals unigrade. But this leaves one wondering from where his insistence derives that the space of atomic propositions exhibits the structure (A). If no assurance can be given that atomic propositions are one or other of the forms (A) depicts, then this conception of the particular–universal distinction can carry no conviction. For all that has been established so far the space of atomic propositions may exhibit an indefinite variety of other structures contrary to (A). For example, Russell has not shown that there is anything to prevent the atomic propositions from all exhibiting the same n-adic form. Nothing has been done to rule out the epistemic possibility that the atomic propositions are composed entirely of two constituents, (B)

R 4(x)

R 5( y) R 6(z) ...

or that they are composed entirely of three constituents, (C)

R 7(x, y)

R 8( y,z)

R 9(z,w)

...

Of course (B) and (C) are not the only structures that reality might exhibit contrary to (A). According to Ramsey ‘we cannot even tell that there are not atomic facts consisting of two terms of the same type’ (1925c: 29). It might be thought that self-predication of this kind will eventually result in a version of Russell’s paradox (‘a vicious circle contradiction’). But, as we have already seen, Ramsey endeavours to block the relevant version of the paradox by denying that negative predicates are referring devices. So far as Ramsey is concerned, we cannot then even rule out the epistemic possibility that the atomic propositions are composed as follows: (D)

f( f ) a(a) f(a) ...

Yet even if we restrict our attention to alternatives less radical than (D), it is evident that the mere possibility of (e.g.) (B) or (C) will serve to 14

See Leonard and Goodman (1940: 50).

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undermine the account of the particular–universal distinction Russell has advanced. For if either (B) or (C) obtain, then all the constituents of the atomic propositions will turn out to be unigrade (monadic in (B), dyadic in (C)), and the distinction between unigrade and multigrade will fail to characterise a fundamental distinction between two classes of objects. If the space of atomic propositions exhibits a structure other than (A), then Russell will have failed to put his finger on a convincing conception of the particular–universal distinction. In order to appreciate the theoretical underpinnings of the conception of the particular–universal distinction attributed to Russell, it is necessary to look back from the second edition of Principia (1925) to The Principles of Mathematics (1903) and Russell’s intervening debate with Wittgenstein and Bradley. In the Principles Russell sought to undermine the traditional logic that assumed propositions could only admit subject–predicate form. He endeavoured to do so by showing that many of the propositions of mathematics concerning ‘Number, Quantity, Order, Space, Time and Motion’ involve asymmetric relations. Russell then set about arguing that propositions involving asymmetric relations could not be reduced to the subject–predicate variety: We have now seen that all order depends upon transitive asymmetrical relations. As such relations are of a kind which traditional logic is unwilling to admit, and as the refusal to admit them is one of the main sources of the contradictions which the Critical Philosophy has found in mathematics, it will be desirable to make an excursion into pure logic, and to set forth the grounds which make the admission of such relations necessary. ( Russell 1903, §208)

Russell distinguished two ways in which relational propositions might be reduced to subject–predicate propositions. According to monadism, a relation between two terms is reducible to the properties of the terms taken separately (so a proposition of the form aRb may be perspicuously represented in the form Fa&Gb). By contrast, monism claims that the relation is a property of the whole that results from the two terms taken together (so a proposition of the form aRb may be perspicuously represented in the form R (ab)). It is because both kinds of reduction fail that Russell deemed the admission of asymmetric relations necessary. Russell’s reasons for rejecting monadism and monism are familiar. Nevertheless, bringing them to mind will help make sense of the conception of the particular–universal distinction under consideration. A thumbnail sketch: against the monadist, Russell argued that no property F of a term a that does not incorporate reference to another term b can imply a relation between a and b, while anything that does mention b cannot be a mere property of a; against the monist, Russell maintained that an asymmetric relation R cannot merely be a property of the whole ab (= ba) because this analysis provides no basis for distinguishing between the case where R

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obtains between a and b (in that order) and the contrasting case where R obtains between b and a (in that order) (Russell 1903, §§214–15). What is important to emphasise in the present context is that (B) corresponds to a form of monadism when x, y, and z are distinct monads, and to a form of monism when x, y, and z are one single thing. In the former case, reality consists of a collection of distinct particulars endowed with nothing but monadic features (R 4(x), R 5( y), R 6(z)). In the latter case, reality consists of a single particular x that also lacks relational features (R 4(x), R 5(x), R 6(x)). It is because (B) may be taken to correspond to a form of monadism or monism that Russell’s reasons for denying the credibility of monadism and monism are also reasons for dismissing (B) and thereby supply part of the missing motivation for endorsing (A). The other part—namely, a motivation for denying that (C) or its like might be necessary—emerges from Russell’s recognition that different propositions require the existence of relations of different adicities. For example, projective geometry requires a four-term relation to account for the order of points on a line (Russell 1903, §361). Russell’s conviction that there are genuinely monadic features in addition to external relations was grounded in assumptions about the character of the sense data with which we are directly acquainted (Russell 1992: 95–6). In this way Russell’s motivation for the conception of the particular–universal distinction outlined becomes bound up with the reasons that Russell provided for rejecting the traditional subject–predicate logic in favour of the new logic of relations. There remain, however, important gaps in Russell’s account of the matter. If his criticisms of monadism and monism are granted then it follows that relational propositions cannot be reduced to subject–predicate ones. But it does not follow that the admission of asymmetric relations is ‘necessary’ (Russell 1903, §208). Nor does it follow that (A) obtains. This is because it remains open that relational propositions may fail to be intelligible. It is this possibility that had exercised Russell’s idealist opponents who adhered to the traditional logic. The monist Bradley, for example, had long argued not—as Russell suggests in Principles—that relational propositions are reducible but that they are unintelligible: ‘a relational way of thought—any one that moves by the machinery of terms and relations—must give appearance, and not truth’ (F. H. Bradley 1897: 28). There is a further difficulty. Even if such propositions are intelligible, it does not follow that there actually exist the kinds or quantities of entities that are required to constitute such propositions. It is to this possibility that Wittgenstein drew attention in the Tractatus, stating that it could not be determined by logic or a priori means alone whether reality actually exhibited (A), (B), (C) or some other structure: 4.128 Logical forms are without number. Hence there are no privileged numbers in logic, and hence there is no possibility of philosophical monism or dualism, etc.

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5.553 Russell said that there were simple relations between different numbers of things (individuals). But between which numbers? And how is this supposed to be decided?—By experience? ( There is no privileged number.) 5.554 It would be completely arbitrary to give any specific form. 5.5541 It is supposed to be possible to answer a priori the question whether I can get into a position in which I need the sign for a 27-termed relation in order to signify something.

By 1924 Russell was prepared to make a dramatic shift in his position to fill the gaps Bradley and Wittgenstein identified in his argument. Instead of basing the admission of asymmetric relations on ‘pure logic’ Russell appealed to ‘empirical grounds’: If I am right there is nothing in logic that can help us to decide between monism and pluralism, or between the view that there are ultimate relational facts and the view that there are none. My own decision in favour of pluralism and relations is taken on empirical grounds, after convincing myself that the a priori arguments to the contrary are invalid. ( Russell 1924: 338–9)

But what are these ‘empirical grounds’? In contemporary ontology it has become commonplace to rely upon the a posteriori investigations of science to determine what properties and relations there are. In a passage that prefigures this development Russell declares: I do not believe, for instance, that those who disbelieve in the reality of relations can possibly interpret those parts of science which employ asymmetrical relations. Even if I could see no way of answering the objections raised (for example) by Mr. Bradley, I should still think it more likely than not that some answer was possible, because I think an error in a very subtle and abstract argument more probable than so fundamental a falsehood in science. ( Russell 1924: 339)

It is then the fundamental truths of science that provide the theoretical underpinnings of Russell’s conception of the particular–universal distinction. For it is science that ultimately provides Russell with the assurance that reality consists of the variety of atomic propositions (A) depicts. Hence Russell’s pronouncement in the introduction to the second edition of Principia: ‘Logic does not know whether there are in fact n-adic relations (in intension); this is an empirical question. We know as an empirical fact that there are at least dyadic relations (in intension) because without them series would be impossible’ (Whitehead and Russell 1925, p. xv). Against this backdrop the significance of Ramsey’s ‘Universals’ is thrown into relief. Ramsey did not seek to infelicitously draw ontological conclusions from linguistic premises, drawing the conclusion that there is no particular–universal distinction from the premise that there is no subject– predicate distinction. Rather—in agreement with Wittgenstein—Ramsey doubted whether it can be settled a priori (by reflection on language or otherwise) whether (A) or some other structure obtains. But—in disagreement with Russell—Ramsey also doubted whether even fundam-

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ental science can be relied upon to reveal a posteriori the structure of the atomic propositions. Ramsey’s denial that any fundamental classification of objects can be based upon the distinction between the subject of a proposition and its predicate is compatible with both these points: it is because the surface features of sentences—e.g. the subject–predicate distinction—cannot be relied upon to reveal the form of the underlying atomic propositions that neither the theoretical language of science nor the structure of ordinary speech can provide a sound basis for affirming the existence of a distinction between particular and universal. This interpretation is confirmed by Ramsey’s later reflections on ‘Universals’ in his paper ‘Universals and “the Method of Analysis” ’ (Ramsey 1926d). When I wrote my article [ ‘Universals’ ] I was sure that it was impossible to discover atomic propositions by actual analysis. Of this I am now very doubtful, and I cannot be sure that they may not be discovered to be all of one or another of a series of forms which can be expressed by R 1(x), R 2(x, y), R 3(x, y,z ) ... This I admit may be found to be the case, but no one can as yet be certain what atomic propositions there are, it cannot be positively asserted; and there is no strong presumption in its favour, for I think that the argument of my article establishes that nothing of the sort can be known a priori. ( Ramsey 1926b: 31)

Evidently Ramsey did not hold (3) that there is no particular–universal distinction because there is no subject–predicate distinction. He did not even hold (2) that there is no particular–universal distinction. Instead he maintained that the forms of language provide no guidance to the structure of reality. Far from advocating a position that has long been superseded by contemporary ontology, Ramsey anticipates its development in ‘Universals’. 5. CONCLUSION Ramsey did not hold any of the claims usually attributed to him; two generations of commentators have gone astray. Of course this does not settle what Ramsey really claimed and why he wished to claim it.15 Ultimately it will only be possible to come to a definitive judgement of the kind in the context of a fuller study that would address, amongst other things, the influence that other works of the period bore upon ‘Universals’. These include W. E. Johnson’s Logic (1921–2), A. N. Whitehead’s Principles of Natural Knowledge (1919) and The Concept of Nature (1920), and G. E. Moore’s (1923) polemic against G. F. Stout that Ramsey took to have ‘already sufficiently answered’ the view that properties are particular tropes.

15 I explore some further issues surrounding the interpretation of ‘Universals’ in MacBride (2004a,b). Hochberg and Lowe reply to some of the considerations raised in Hochberg (2004) and Lowe (2004b).

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Nevertheless, it is already evident that ‘Universals’ not only continues to bear significance for contemporary ontology but points beyond it. This may appear an unlikely claim to wish to make. Consider once more the conception of the particular–universal distinction that Ramsey isolated in the second edition of Principia. The campaign in favour of external relations and against monadism and monism appears to have long been fought and won. Speaking from a contemporary perspective, few would deny that there are external relations of different degree. And even if this cannot be known a priori, many are willing to affirm—as Russell did in 1924 and Ramsey came by 1926 to acknowledge—that a posteriori science provides a reliable guide to the existence of such relations. As a consequence few would seriously doubt that reality exhibits the kind of structure that (A) depicts. So unless life is somehow breathed back into a debate that appears to have been settled— the debate over the very possibility of external relations—it appears that Russell’s 1925 conception of the particular–universal distinction has been put upon a sure epistemic footing (albeit an a posteriori one). Yet even if it is granted that external relations exist, it does not follow that Russell’s conception of the particular–universal distinction is justified. Nor does it follow that Ramsey was mistaken in his scepticism about the distinction. For there may be other reasons to doubt whether (A) offers an accurate depiction of reality. There may be other universals that fail to be registered in (A)’s inventory. And if these universals are admitted alongside the ranks of n-adic universals that (A) records, Russell’s conception is thrown in jeopardy once more. For example, there may be multigrade universals (R m) that occur repeatedly in atomic propositions of the different forms (E)

R m(x)

R m(x, y)

R m(x, y,z)

...

Since different circles are formed from different numbers of objects or points, one might, for instance, conceive of the geometrical property form a circle as multigrade. But if there are multigrade universals—and this will need to be investigated—then the unigrade–multigrade distinction will fail to mark out the fundamental division of objects into two classes, the particulars and universals, into which Ramsey enquired.16 There is another respect in which ‘Universals’ points beyond recent debate. Contemporary forms of Humeanism restrict the diet of concepts to which their analyses apply to such notions as cause and law (consider, for example, the doctrine of Humean supervenience) seeking to avoid commitment to necessary connexions between distinct existences where these 16 Of course, one may question whether form a circle is truly multigrade rather than (e.g.) the monadic property of an aggregate or plurality. But (a) there appears to be no obligation to conceive of form a circle this way. Moreover, (b) there are other kinds of plausible examples of multigrade universals that cannot be so dismissed.

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concepts apply. By contrast, the arguments of ‘Universals’ point towards a more thoroughgoing Humeanism that applies even to such notions as particular and universal, perhaps the most fundamental categories of all.17

17 Thanks to Bill Demopoulos, Herbert Hochberg, Keith Hossack, E. J. Lowe, Mike Martin, Hugh Mellor, Kevin Mulligan, Stephen Read, and, especially, Alex Oliver for discussion. I am also grateful to Peter Sullivan for some last-minute suggestions. Thanks too to the audience at the Ramsey conference in Cambridge for helpful comments. I gratefully acknowledge the support of the Leverhulme Trust, whose award of a Philip Leverhulme Prize made possible the writing of this paper.

Empiricism and Ramsey’s Account of Theories PIERRE CRUSE 1. INTRODUCTIO N Suppose we propose a new scientific theory. Presumably we will do this because we want to explain some facts we already know about, and we will have a language to describe these facts that doesn’t get its meaning from our theory. This language we can call the ‘primary system’. However, typical theories also introduce new, or ‘secondary’, terms that are not in the primary system. These secondary, theoretical, terms tend to refer to things that are abstract and distant from observation. A plausible claim is that their meanings in some way derive from their connection with primary terms. The question arises how are we to understand this dependence. This, roughly speaking, is the question Ramsey considers in his 1929 paper ‘Theories’. Having introduced the primary–secondary distinction, Ramsey considers whether it is possible to regard secondary terms as defined in terms of primary—a natural suggestion given their lack of independent meaning. However, this turns out to be problematic. First of all, secondary terms will require very disjunctive definitions, which basically amount to lists of all the primary manifestations that each secondary concept has. If we needed these definitions, the theory would be pointless, since it would be simpler just to list its consequences directly in primary vocabulary. The second problem is that definitions of secondary vocabulary in terms of primary cannot cope with changes in the defining theory. Discovering a new manifestation of some secondary concept, for example, would entail alteration to the definitions of all the secondary terms in the theory, and thus to the meanings of all the theory’s terms. Somehow, then, it needs to be shown how secondary terms can function in a newly introduced theory without requiring that they be defined from primary terms, or at least, without requiring that whatever definitions are available are explicitly kept in mind by those who use the theory. Ramsey’s alternative proposal begins with the observation that The best way to write our theory seems to be this (

,  , ): dictionary . axioms. (1929c: 131)

In effect, Ramsey’s idea was that the theory should be assimilated to what was later dubbed its ‘Ramsey sentence’, the sentence formed by replacing the secondary terms in the theory with variables, then prefixing the resulting formula with a corresponding number of existential quantifiers. On this

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view, as Ramsey points out, propositions containing secondary terms are not seen as ‘propositions by themselves’, but rather as propositional functions, which only gain meaning when added within the scope of the existential quantifiers prefixing some particular theory. Secondary terms are not therefore names of properties or objects but are more like schematic names that stand for whatever happens to play some role in realizing the theory in which they occur. Terms can thus serve as abbreviatory devices allowing us to work out deductive relations between parts of theories without having to consider everything the theory says. However, in order to state the content of a statement within a theory we need to go back to what is asserted to exist by the entire theory in which it occurs—in other words, the Ramsey sentence. Thus, as Ramsey puts it, ‘the incompleteness of the “propositions” of the secondary system affects our disputes but not our reasoning’ (1929c: 132). In this chapter I propose to examine some of the arguments for and against Ramsey’s conception of theories. In particular, I will focus on attempts that have been made to defend empiricist conceptions of scientific theories, for reasons I will explain shortly.1 On balance, I think it is fair to say that the contemporary view is largely negative in this regard, holding that Ramsey sentences only ever promised to help doctrines that are now outdated, and even did that rather unsuccessfully.2 While I think that these criticisms are correct when aimed at existing applications of Ramsey’s view in this context, they undermine neither the view itself, nor the aim to use it to defend an empiricist conception of theories. In this chapter I will explain why this is, and propose a broadly empiricist framework in which, I will claim, Ramsey’s account is a successful explanation of the semantics of theories. 2. RAMSEY’S VIEW OF THEORIES AND EMPI RICI SM The first thing we notice about Ramsey’s view of theories is that it postulates a clear distinction between the semantics of ‘primary’ and ‘secondary’ terms. Primary terms are given independent meaning, and are assumed to refer directly to properties and relations in the world. Secondary terms, on the other hand, are given only derivative meaning, and stand for whatever plays some theoretical role, where the role is characterized wholly in terms of primary vocabulary. The immediate question that arises is 1 There are also non-empiricist views of theories inspired by Ramsey’s view, for example, Lewis (1970). However, I will restrict my attention in this chapter to versions of the theory that have aimed to defend some form of empiricism. 2 That the form of empiricism Ramsey’s account helps defend is defunct has been very widely argued; see e.g. Suppe (1971) for a summary of some of the main lines of argument. That Ramsey’s account doesn’t help defend it is pressed, for example, by Demopoulos and Friedman (1985), Ladyman (1998), and Psillos (1999).

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therefore why there should be any such distinction in the first place, and even if there is, why it should be of semantic significance. Ramsey, as far as I can see, didn’t commit himself on this question; he gives little explicit attention to the question of what sort of thing might count as a primary term. However, an obvious answer surfaced when it was noticed that Ramsey’s account might be used to defend empiricist conceptions of scientific theories. If you are an empiricist—especially of the positivistic variety—you will likely be worried by the following problem. If empiricism is true, then meaning is essentially connected to observation. In order for a term or concept to have independent meaning it must be an observational term, and refer to something directly observable. On the other hand, the empiricist stance involves a strong commitment to viewing science as the paradigm of meaningful discourse, in contradistinction to metaphysics, which is not genuinely meaningful. If both these claims are true, it follows that everything science says must be expressible using observational terms alone (plus logic and mathematics). The problem, of course, is that this doesn’t seem to be the case. Science is replete with theoretical terms like ‘electron’, which refer to things that are not by any stretch of the imagination observable. So either much of science is meaningless, or we have no way of explaining what is wrong with metaphysics. Neither conclusion is palatable to the positivist–empiricist, hence the problem. To solve it some way must be found of showing how the content of theories can be expressed using nothing more than observational terms, logic and maths. This is where Ramsey’s view of theories promises to help. Ramsey’s view of theories, as we have seen, does two things. First, it explains why theoretical terms are necessary to science. They are necessary because we need abbreviatory devices to work with theories—it would be hopelessly complicated to list all the primary consequences of a given theory every time we needed to use any part of it. Second, it entails that the meanings of secondary terms depend entirely on their connections with primary terms. If Ramsey’s account of theoretical terms is true, everything a theory says can be said in the primary system alone, using the Ramsey sentence. Thus, if we identify the ‘primary system’ with the language of logic, maths, and observation terms, and the secondary system with the language of theoretical terms, we are in a position to explain (a) why there are theoretical terms, and (b) how the content of theories is still entirely derivative from observational terms. Thus, we are in a position to make the role of theoretical terms in theories consistent with empiricism. 3. RAMSEY’S VI EW AND INSTRUM ENTALISM Unfortunately, this ostensibly neat resolution to the ‘problem of theoretical terms’ did not in the end satisfy many empiricists. The major difficulty is this. If you adopt Ramsey’s account of theoretical terms, you are committed

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to thinking that the content of a theory is given by its Ramsey sentence. But in fact few empiricists have found Ramsey sentences acceptable as representative of the content of scientific theories. Exactly why this is depends heavily on what wider epistemological position you are trying to use Ramsey’s view to defend. We can in fact find quite a spectrum of different views on this issue. To begin with, some authors (e.g. Hempel 1958; Scheffler 1961) considered the use of Ramsey sentences in defending a purely instrumentalist conception of theories. From this perspective it was regarded as problematic that theories seem to have ontological commitments to unobservable entities or abstract entities such as properties or classes, and Ramsey sentences were investigated as means to preserve the systematizing features of theories without these commitments. The motivating thought was that while it is easily demonstrable that the Ramsey sentence of a theory has all the same observational consequences as the original theory, it does not contain the theory’s theoretical terms, so should avoid its ontological commitments. Supposedly, then, the Ramsey sentence provides a ‘functional equivalent’ of the original theory. However, it was quickly realized that Ramsey’s view fails to provide what is needed here. Although Ramsey sentences do not contain theoretical terms, they nevertheless quantify over, and thus require the existence of, theoretical entities: as Hempel points out (1958: 81), the Ramsey sentence ‘avoids reference to hypothetical entities only in letter—replacing Latin constants with Greek variables—rather than in spirit’. Ramsey’s view therefore buys an explanation of the systematizing role of theoretical terms at too high a price for someone whose aim is to eliminate talk of theoretical entities altogether. A different, though related, attitude was taken by Carnap in his discussions of Ramsey’s view.3 As Psillos has recently argued (Psillos 1999, ch. 3), Carnap’s aim was not so much to come down in favour of a strong empiricism, but to defend a form of ‘neutralism’, on which both realist and empiricist viewpoints on the existence of theoretical entities were accommodated, and the debate between them shown to be cognitively insignificant. Carnap alighted on Ramsey sentences as a means to demonstrate this neutralism, the idea being that a realist and instrumentalist could agree to the Ramsey sentence of a theory, while disagreeing on what is now referred to as its ‘Carnap sentence’—the conditional of the theory’s Ramsey sentence and the theory itself. As the Carnap sentence is an analytic truth, Carnap argued, true or false as a matter of stipulation only, the question of whether to accept it is not a substantive one. Thus, since the realism– instrumentalism issue is (allegedly) just a dispute over whether to accept the Carnap sentences of theories, it too is insubstantive. However, as Psillos 3

See e.g. Carnap (1961, 1963, 1966).

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also argues (1999: 59–60), Ramsey’s view was never going to provide a genuine compromise between realism and empiricism, for much the same reason that it can’t sustain pure instrumentalism: the quantification it involves requires the existence of theoretical entities, and this on its own goes beyond anything an instrumentalist would be prepared to accept.4 Ramsey’s view of theories does not therefore seem to be genuinely neutral between realism and instrumentalism. 4. RAMSEY SENTENCE S AN D STRU CTURAL REAL ISM Ramsey sentences are therefore useless for the empiricist who wants to eliminate discourse about theoretical entities altogether. However, Ramsey sentences were used in service of a rather different version of empiricism by Grover Maxwell in a series of papers in the 1960s and 1970s (Maxwell 1966, 1970a,b). Maxwell was on the one hand convinced by arguments in favour of indirect theories of perception, entailing that the objects of direct perception, and thus direct reference, are entirely mental (mental events, on the version he puts forward). Thus, he held a very strong form of concept empiricism. However, he also thought there were compelling arguments to think that our theories make substantial assertions about an independently existing realm of physical, and possibly unobservable, objects, and in fact was one of the originators of many of the standard arguments in favour of scientific realism (see especially Maxwell 1962). Now this kind of empiricism also faces a version of the problem of theoretical terms: if we can only refer directly to the mental, how can we have theories that talk about the physical? Maxwell saw that Ramsey sentences give a way of answering this question. Maxwell’s idea was this. Suppose the content of a theory is given by its Ramsey sentence, formed by replacing all the non-mental terms in a theory with existentially quantified variables. In this case attributing knowledge of the theory to a subject only involves attributing to them the capacity to refer directly to mental events, since only mental events are referred to directly in Ramsey sentences. But since Ramsey sentences can quantify over unobservables, it also potentially involves attributing to them substantial knowledge of the unobservable; specifically, that there exist unobservable objects and properties which themselves have properties characterized using the observational vocabulary. In formulating this position Maxwell acknowledges his debt to the position defended by Bertrand Russell in The Analysis of Matter (1927). 4 Psillos goes on to argue that Carnap’s neutralism might be better understood rather as neutral not between realism and instrumentalism, but between ‘full’ realism—on which the existence of electrons, say, is asserted—and ‘Ramsey’ realism, which asserts only the Ramsey sentence of theories. This, however, is called into question by the argument of Newman (1928), which is discussed below. See Psillos (1999: 60–5) for further discussion.

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Russell, like Maxwell, believed both that there were incontestable scientific arguments for the view that the direct objects of perception are mental, and that we were able to infer via abductive arguments to the (probable) existence of non-mental causes for these percepts. Russell held that the ‘intrinsic characters’ of these non-mental causes were unknowable, but argued that this does not leave them entirely obscure, as we can invoke the principle that ‘differences in percepts imply differences in stimuli’ to attain knowledge of their ‘structure’ (Russell 1927: 226–7). This led him to propose that whenever we infer from perceptions, it is only structure which we can validly infer; and structure is what can be expressed by mathematical logic, which includes mathematics. (1927: 254)

Maxwell claims that the view he is defending, based on regarding the Ramsey sentence as giving the content of a theory, leads to a version of Russell’s conclusion: The Ramsey sentence refers to theoretical entities in exactly the same way in which any description refers—by means of variables, quantifiers, logical connectives, and descriptive terms whose direct referents are other than the referents of the description. This, incidentally, may be taken as an explication of the claim of Russell and others that our knowledge of the theoretical is limited to its purely structural characteristics and that we are ignorant concerning its intrinsic nature. (1970b: 188)

Maxwell’s idea seems to be as follows. The physical or unobservable world contains objects which instantiate various first-order, or ‘intrinsic’, properties. We can never be acquainted with any of these properties, and thus, we cannot come to know theories that directly refer to them. However, we can be acquainted with certain mental properties at a higher level of abstraction which those intrinsic properties themselves instantiate—these are ‘structural’, or ‘second-order’, properties—and we can come to understand theories which refer to these higher-order properties. Thus, we can come to know Ramsey sentences to the effect that there exist first-order properties which instantiate combinations of these more abstract structural properties. Because these existential propositions never refer directly to intrinsic properties we are left ignorant of the intrinsic properties, or ‘natures’, of unobservable entities and properties and can only attain knowledge of their structure: hence Maxwell referred to his position as ‘structural realism’. 5. STRUCTURAL REALISM AND TH E NEWMAN PROBLEM Although Maxwell’s use of Ramsey’s view of theories makes a virtue of the ontological implications of the Ramsey sentence, an objection which has been widely discussed in recent literature seems to show that even his version of Ramsey’s account is unlikely to be tenable. The objection had

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already been put forward to Russell’s ‘structural realism’ by the mathematician M. H. A. Newman shortly after Russell’s account had originally been published. Newman reads Russell as putting forward the view that the world consists of objects, forming an aggregate whose structure with respect to a certain relation R is known, say, [it has structure] W; but of . . . R nothing is known . . . but its existence . . . all we can say is there is a relation R such that the structure of the external world with respect to R is W . . . (Newman 1928: 144)

But Newman sees this as problematic since no important information about [an] aggregate A, except its cardinal number, is contained in the statement that there exists a system of relations, with A as field, whose structure is an assigned one. For given any aggregate A, a system of relations between its members can be found having any assigned structure compatible with the cardinal number of A. (1928: 144)

Given its premises, Newman’s argument is unexceptionable: as later commentators have verified, it is a theorem of set theory that a system of relations with any given set-theoretical structure will exist in any set, subject only to a cardinality requirement (see Demopoulos and Friedman 1985; Psillos 1999: 61–5; Ketland 2004). Thus, if the Maxwell–Russell claim is that all we know about the physical world is that there exist relations in it which have a certain structure, then their claim reduces to an extreme scepticism — we know nothing about the physical world bar its cardinality. As it stands, in fact, Newman’s argument does not quite hit its target. Russell (and Maxwell) did not claim that our knowledge of the world as a whole is only of its structural properties, as Newman alleges. Instead, it is only our knowledge of the ‘physical’ world that is supposed to be purely structural, while our knowledge of the phenomenal world goes beyond knowledge of pure structure. However, as Ketland (2004) shows, this does not solve the problem. The difficulty now is not that the theory amounts only to a cardinality claim, but that in an important sense the excess content the theory has over its claims about observables amounts only to a cardinality claim. In other words, it can be shown that, on this view, if a theory is true in the domain over which its observation terms range—if, in other words, it is empirically adequate—then it only takes a further cardinality requirement for it to be true, simpliciter. This is not quite the extreme scepticism that Newman claimed (as a whole theories are not true a priori), but it still allows far too little knowledge of the world to satisfy a realist. Another point we should make is that the Newman result does not explicitly rely on the claim that the referents of the observational vocabulary are mental, as Maxwell and Russell themselves claimed. What is important is simply that there is some sub-domain D of the universe of scientific discourse such that all we know of D is that, in it, there exist relations with a certain set-theoretical structure. One way of delimiting D is by drawing a distinction between the mental and physical realms, but another would be by drawing a more concessive observational–theoretical distinction which

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allows macroscopic physical objects, say, to count as observable. If the distinction is drawn in this way, the conclusion we arrive at is that no substantive knowledge of the unobservable part of the physical world is possible, a somewhat similar view to van Fraassen’s ‘constructive empiricism’ (see van Fraassen 1980 for an elaboration of this view).5 Needless to say, this is still a broadly anti-realist view of theories. Let us summarize the situation we have reached. We saw that the plausibility of Ramsey’s view of theories rests on the possibility of finding adequate reason to draw a distinction between the way ‘primary’ and ‘secondary’ vocabulary are interpreted. The reason we have considered is that primary vocabulary corresponds to observational vocabulary and secondary to theoretical. However, whatever its intrinsic merits, this assumption seems to lead the proponent of the Ramsey view of theories into deep trouble. If it is right, then we arrive via Newman’s argument at the conclusion that our knowledge of the unobservable is knowledge only of cardinality. But this is a rather bizarre half-way house acceptable neither to a realist nor to an instrumentalist. If we want to defend Ramsey’s view of theoretical terms, and use it to defend some form of empiricism, we therefore need to show how this can be done without committing us to the assumptions that lead to Newman’s argument. 6. AN ALTERNATIVE CONCEPT IO N OF OBSERVATIO NAL TERMS I want to respond to this problem by putting forward a version of Ramsey’s view of theories that I think gets round these problems. My proposal will be a version of the empiricist idea that theoretical terms have to have their meanings given in some way with reference to experience or observation. However, I think it is possible to hold a view that makes sense of this empiricist intuition without committing yourself to the kind of observational–theoretical distinction that the Newman argument requires to get off the ground.6 The conception of observational terms I am getting at was suggested by Grover Maxwell in 1962, before he (erroneously, as I have argued) went on 5 Van Fraassen himself would claim to be agnostic about knowledge of the unobservable, rather than positively sceptical, so this is not quite van Fraassen’s position. However, my point is merely that this is not a realist view. 6 An alternative response that has been proposed to Newman’s argument ( Psillos 1999, following Lewis 1984) relies on arguing that only natural relations count as genuine satisfiers of Ramsey sentences. It can then be argued that the relations that are guaranteed by Newman’s argument to satisfy any given Ramsey sentence will not in many cases be natural. However, I will not consider this response here since my focus is primarily on the use of Ramsey’s view of theories to defend forms of empiricism, and the anti-nominalist distinction relied upon here between natural and non-natural relations is avowedly non-empiricist.

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to defend ‘structural realism’. In talking about the prevailing positivistic conception of an ‘observational term’, Maxwell said, It seems to me that a large number . . . of theoretical terms could be explicitly defined wholly in terms of observation terms, but this would in no way avoid a reference to unobservable entities . . . [this] is an important oversight because philosophers today are devoting so much attention to the meaning of theoretical terms . . . while the ontological stomach-aches . . . concerning theories seem to have arisen from the fact that the entities rather than the terms were nonobservational. Implicit, of course, is the mistaken assumption that terms referring to unobservable entities cannot be among those which occur in the observation language. (1962: 15)

Maxwell is surely right. If we take an intuitive list of observation terms, it might include items such as ‘contiguous with’, ‘warmer than’, ‘larger than’, and maybe disposition terms such as ‘solid’. And we do seem to be able to use these concepts to make determinate assertions about the unobservable. We can understand what it is for two bacteria or two atoms to be contiguous with one another just as easily as we can understand the contiguity of two billiard balls. If ‘solid’ is translated in Lockean terms as ‘resistant to incursion by other objects’, then this can be true both of a table and of an atomic nucleus; and so on. We can sum this up by saying that the concepts we use to describe observable phenomena are often mixed, that is, their extension includes both observable and unobservable entities. This contrasts with prototypically theoretical concepts, which tend to be wholly non-observational—you can’t under any circumstances directly observe electrons, nucleotides, or quarks. If we adopt this version of Ramsey’s view, it is easy to construct a counter-example to the Newman claim that all empirically adequate Ramsey sentences are trivially true. Consider the predicate ‘is contiguous with’, and suppose that it is mixed, that is, that both observable things and unobservable things can be determinately contiguous (or incontiguous) with one another. Now consider the Ramsey sentence (

)(x)( y)(
x &
y
contiguous(x, y) & x and y are not observable). This sentence asserts the existence of a property that anything has if and only if it is unobservable and contiguous with something else unobservable. However, it clearly does not just make a cardinality claim. There is no reason why there should not be a domain in which no two unobservable individuals are contiguous. In such a domain the Ramsey sentence above will be false, and its falsity will not be a matter of cardinality. Thus, it does not follow from Newman-type considerations that all Ramsey sentences containing mixed terms are trivially true, or that they are statements only

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about cardinality.7 On the contrary, Ramsey sentences seem capable of sustaining a form of scientific realism. So is there any justification for drawing the distinction between observable and theoretical properties in this way? As I have suggested, I think the distinction corresponds more closely to the way one would intuitively draw the distinction, innocent of any theoretical presuppositions. However, I think there is also a stronger reason for thinking that a tenable distinction between observable and unobservable properties would count at least some mixed properties as observable. Assuming we identify an observational term as one that refers to an observable property, this would suggest that observational terms also count as mixed. One of the major contemporary reasons why one might want to draw a distinction between observation and theory in general arises from empirical claims about cognitive architecture. According to one influential theory, perception (along with other cognitive systems) is modular, in that it is subserved by domain-specific neural mechanisms that function largely independently of general belief-forming mechanisms (see Fodor 1983). A key point about the modular theory of perception is that modules are informationally encapsulated, in the sense that they only have access to a highly circumscribed number of the beliefs held by the subject in which they exist. Thus, they will form largely the same perceptual representations of the subject’s environment whatever wider theoretical beliefs they may hold. Modular theories of perception are important in the present context because they postulate a clear distinction between mental representations that are generated by perceptual mechanisms, and those that are generated by more general belief- or theory-forming mechanisms. Thus, they suggest how we might formulate a distinction between observable and unobservable properties. That is, we can say that a property F is observable if and only if it is possible that there is some object o such that a human perceptual module can form a representation that o is F. Whether the modular theory of perception is true is a controversial empirical issue, which there is no room to decide here. The following theory is therefore contingent on the way that 7 This relates to Ketland’s (2004) version of the Newman result as follows. Ketland shows that if a Ramsey sentence is empirically adequate, then (subject to cardinality constraints) it is true. In this proof, a theory is regarded as empirically adequate (following van Fraassen 1980) if and only if it has a model whose ‘observational reduct’ is isomorphic to the world’s observational reduct, where an observational reduct of a model is the model we get by removing from the model any individuals not in the union of the fields of the observational—i.e. unramsified—terms in our theory. However, if some of our theory’s observational terms are mixed terms, then the union of the fields of our observation terms contains unobservable objects. Thus, although it is true that given the way we have defined empirical adequacy, a theory’s empirical adequacy implies the truth of its Ramsey sentence, empirical adequacy fails to have its intended sense of ‘truth only about what is observable’. Rather, it requires the theory to be true about the objects in the extensions of the theory’s mixed terms, some of which objects are unobservable.

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this issue turns out. However, I think there is enough evidence for it that it is worth proceeding on the assumption that it is true (for further defence, see especially Fodor 1983, 1984). If the modular theory is true, exactly what does count as observable by this criterion is also an empirical issue. But, however this issue turns out, it seems very likely that at least some observational properties are going to come out as mixed. For a start, if there are perceptual modules at all, their function is surely going to be to produce representations of physical properties of a subject’s environment rather than just proximal patterns of stimulation. One of the major arguments for the claim that perception is modular is that it is obviously adaptive for an organism to have a mechanism which produces accurate representations of its immediate environment independently of what further beliefs it may hold, simply because its survival will depend on what is actually in front of it rather than what it thinks is in front of it (see Fodor 1984: 38). But if perception is to do this, it must at the very least succeed in producing representations of properties of the environment rather than just of proximal patterns of stimulation. Once you admit that external physical properties can be perceptually represented, there seems little reason to think that these properties cannot be mixed. For example, suppose for the sake of argument that the shapes of objects count as observable on the definition just given. Now a shape property such as square is, on the face of it, a mixed property, since it is just as meaningful to attribute squareness to an unobservable thing as an observable one. Denying this would involve claiming that in fact only the property square-and-observable-to-humans is represented, rather than squareness itself. But this just seems like unnecessary double-counting: we can explain why square objects are observable by the fact that they are observable and square, without the additional assumption that only their observable squareness is actually perceived. Without some strong reason to think otherwise, then, there is surely a strong default presupposition in favour of the assumption that at least some mixed properties can be perceptually represented. 7. THE SEMANTIC SIG NIFIC ANCE OF OBSERVATIO NAL TERMS I have argued, then, that formulating the distinction between observable and unobservable properties with reference to the informational encapsulation of perceptual mechanisms allows us to motivate the claim that a meaningful observational–theoretical distinction can be formulated that classes some mixed properties as observable. However, this doesn’t quite yet demonstrate that the distinction has exactly the semantic significance that Ramsey’s theory says it has. Ramsey’s theory, as we have seen, entails that, while primary terms are attributed referents directly, statements containing

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secondary or theoretical terms only get their meaning indirectly, and have to be rephrased as existential claims. In order to demonstrate this we need a further explanation of why the distinction between observable and unobservable properties corresponds to Ramsey’s semantic distinction between primary and secondary terms. One thing that isn’t going to work, I think (at least straight off), is Maxwell’s story about why the content of a theory should be identified with its Ramsey sentence. Maxwell’s view was essentially that because we could only use terms to refer directly to things that we are immediately perceptually acquainted with, Ramsey sentences represent the only way we could talk about the unobservable. The argument was therefore a kind of ‘transcendental’ argument, in the sense that it concludes that, since we do talk about the unobservable, and Ramsey sentences are the only way we could do this given our epistemic position, they must be how we actually do it. However, once we drop the requirement that we can only directly refer to sense data, as Maxwell held, the transcendental argument doesn’t seem as persuasive, simply because Ramsey sentences do not seem to be the only way of explaining how it is possible to have concepts that refer to unobservable properties. One alternative explanation, for example, is given by the causal– informational (CI) theory of intentional content, developed by Jerry Fodor and others (see e.g. Fodor 1987, ch. 4; 1990b; Dretske 1981; Prinz 2002). Ignoring certain niceties, the idea behind this theory is that the content of a concept is whatever in the world nomologically covaries with it, or reliably causes it to be tokened.8 Thus, my concept COW refers to cows because in nomologically possible worlds, I token the concept COW when and only when cows are present.9 I will argue below that the CI theory may well give a successful explanation of the content of observational terms. However, for the time being we can note that the CI theory suggests that the semantics of theoretical concepts might be accounted for in a way different from Ramsey’s. According to the CI theory what gives a theoretical concept like ELECTRON its meaning is not its role in the theory in which it occurs, but the fact that someone competent with it will be reliably caused to token it when and only when electrons are present (like any other concept, as the 8 One immediate problem with causal theories is whether they can account for the possibility of false applications of concepts—why do, say, horses on dark nights not fall under my concept COW, seeing as they are among the things that cause me to token it? Proponents of the CI approach to content generally add some further condition to the basic covariance idea to deal with this problem. However, what I have to say will only concern the basic causal covariance claim, so I will not discuss this problem further. 9 The CI theory is normally formulated in terms of concepts rather than terms. However, as I assume that Ramsey’s theory purports to explain the content of theoretical concepts as well as terms, I will formulate the issue with reference to concepts from now on. I will use small caps to represent concepts, so that ‘COW’, for example, denotes the concept of a cow.

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theory would claim). This, as Fodor has pointed out, leads to a form of concept empiricism, since the causal route between the presence of electrons and the tokening of the concept ELECTRON has to go through perception (see Fodor 1987: 119–23). In the case of observational concepts (the ones that refer to things represented by the perceptual module) we will automatically token them whenever their referent is present within the range of our senses, simply because we possess perceptual mechanisms that ensure that this is so. In the case of a theoretical concept like ELECTRON, however, there are no perceptual mechanisms that ensure we token the concept whenever its referent is present. Instead the tokening follows a more complicated causal path. First the presence of the electron causes some experimental manifestation which can be perceived. Then our perceptual faculties produce a perceptual representation of this experimental manifestation, so that we token the corresponding perceptual concepts. Finally, provided we possess an appropriate theory, we can then infer that an electron is present. Like Ramsey’s account, then, possession of the concept ELECTRON is explained with essential reference to theory and to observational concepts. However, unlike on Ramsey’s account, the meaning of a theoretical concept is not identified with its role in the particular theory in which it occurs, but with whatever this multi-stage causal path connects it to. As Fodor puts it: ‘the content of a theory does not determine the meanings of the terms whose connections to the world the theory mediates. What determines their meanings is which things in the world the theory connects them to. The unit of meaning is not the theory; it’s the world/symbol correlation however mediated’ (1987: 125). The situation therefore seems to be that there are (at least) two distinct ways in which we can understand the genesis of theoretical concepts. According to the Ramsey sentence story, we have a theoretical concept exactly when we have a theory which asserts the existence of something unobservable using observational primary concepts. According to the CI story, we have a theoretical concept exactly when we are reliably caused to token some mental state by the presence of some theoretical entity or property. The question therefore arises which of these theories is preferable. One way to answer this question is by looking at what each of these theories prohibits. If the Ramsey sentence story is correct, then we cannot be said to have a theoretical concept in a case where we do not possess a theory which asserts the existence of something unobservable using observational terms. However, if the CI story is correct, we cannot be said to have a theoretical concept in a case where we are not reliably caused to token the concept in at least some cases where its supposed referent is present. We can therefore look at whether these entailments are correct. Let us look first at whether there are cases in which a theoretical concept could be possessed in the absence of the sort of causal covariation that the CI theory postulates between concepts and their referents. In fact I think it is pretty clear that some theoretical concepts do have meanings despite

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failing to be reliably caused by the presence of their referents. The kind of case I have in mind is something like the concept of a superstring. Superstrings are postulated as part of a theory that attempts to unify certain fundamental physical forces. As I understand it, there are at the time of writing no currently known experimental manifestations of superstrings. Not only this, it may be that there are no possible observable manifestations of superstrings, at least of the sort that could be called ‘observing a superstring’ along the model of, say, observing a particle interaction in an accelerator.10 Suppose this is true. If it is, it is difficult to see how anyone’s concept of a superstring could be reliably caused by the presence of superstrings. If superstrings have no observable manifestations, there is no causal route via which superstrings could cause you to token the concept SUPERSTRING. However, there seems no reason to think that the concept SUPERSTRING lacks meaning. On the contrary, it seems that SUPERSTRING has a meaning precisely because superstring theories make determinate existential assertions, about the existence of minute spatial dimensions and the like, whose content can be stated independently of whether they can be experimentally tested. Thus, a very good explanation of why the concept of a superstring has meaning seems to be the one we would get from Ramsey’s theory.11 The same seems true of any concept that refers to something of which no observable manifestations are known. At this point, then, there is a preliminary case for saying that Ramsey’s theory applies more generally than the CI theory. Ramsey’s theory explains the content of a concept like SUPERSTRING, where there is no possibility of causal covariance between concept and referent. However, there seems no reason why the same type of explanation should not apply to a case like ELECTRON, where there is causal covariance. Adding the hypothesis that 10 Brian Greene (1999) describes the current situation (or at least, the situation as it was in 1999) as follows: Without monumental technological breakthroughs, we will never be able to focus on the tiny length scales necessary to see a string directly … As the Planck length is some 17 orders of magnitude smaller than what we can currently access, using today’s technology we would need an accelerator the size of the galaxy to see individual strings . . . If we are going to test string theory experimentally, it will have to be in an indirect manner. ( p. 215) It may, Greene says ( pp. 224–5), turn out to be possible to gain evidence of the presence of strings indirectly, via, for example, their cosmological implications. I am not sure whether this kind of observation would suffice for a CI explanation of the content of SUPERSTRING. But even if it would, it seems implausible that the contentfulness of the concept SUPERSTRING turns wholly on whether such observations turn out to be possible. 11 This is a criticism of the CI theory only if that theory claims that it is a necessary condition for the assignment of content that there exist appropriate causal correlations between tokenings of the concept and the presence of its referent. Fodor (1984) claims that this is only a sufficient condition, so this isn’t strictly a criticism of his theory. However, I take it that he would claim that it is actually plausible to assign content to theoretical concepts like ELECTRON using a causal theory, which I deny.

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there is causal covariance between a concept and its referent doesn’t make appealing to the Ramsey sentence of the theory in which a concept occurs any less of an explanation of its content, even if it now makes another explanation available. But if this is the case, then the CI explanation is threatened with redundancy, since the Ramsey-style account applies both in cases where the CI account applies, and in those in which it doesn’t. However, we should also ask whether there are any cases in which the CI theory could account for the possession of a theoretical concept but Ramsey’s theory could not. We might begin by noticing that in typical cases where the CI theory might apply, we are imagining the presence of a theory whose Ramsey sentence would contain enough detail to assert the existence of the supposed unobservable entity that is the referent of the concept in question. For example, consider the case of the electron, described above. According to the CI story in that case, we are able to token the concept ELECTRON precisely because we have a theory which entails that electrons cause certain observational effects. But then the Ramsey sentence of that theory must at least assert the existence of something that causes those observational effects. This kind of case cannot therefore decide which of the two theories is true. To decide between the theories we would have to think of a case in which there was causal covariance between a concept and its referent in the absence of a Ramsey sentence that asserted the existence of anything like that referent. What would such a case be like? In the case of electrons, say, we would presumably have to imagine someone who tokens the concept ELECTRON almost as a kind of reflex in the appropriate cases, without having an explicit conception of what is actually present when they are responding in this way. However, I doubt whether it is possible to conceive of the appropriate kind of case. Can we really imagine someone who is disposed to recognize the experimental manifestations of electrons without any sort of Ramsey sentence-type representation of what they are responding to? The problem with this supposition is that electron manifestations (cloud-chamber tracks, Geiger counter clicks, and so on) have nothing superficially in common. It is therefore difficult to see how someone could come to token the same concept in more than one of these cases without simply learning enumeratively to do so. But if they had been trained in this way—think ELECTRON in this kind of case, and in this kind of case, and . . .—we would be more inclined to say that they had a disjunctive concept of being a cloudchamber track, or a Geiger counter click, or whatever, even if electrons are in fact the causal source of all these things. One way to bring this out is by noticing that such a person would not be able to recognize new manifestations of electrons without being explicitly trained to do so. What is lacking is precisely the explicit conceptualization of the different phenomena as causal manifestations of the same kind of thing. Admittedly we could imagine that someone had a genuine causal sensitivity to electrons in the absence of a Ramsey-style theory if we

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supposed that they could actually perceive electrons. However, this would not demonstrate that causal connection in the absence of a Ramsey-style theory is sufficient for a non-observational concept to have content, since we would in such a case merely attribute to them an observational concept. Ultimately, as I suggested above, the proposed theory suggests that which are the observational concepts is essentially an empirical issue. However, the way that humans are constructed presumably prevents us from possessing an observational concept of an electron, so the case is merely hypothetical. In the case of theoretical concepts, then, I think there is a strong case for saying that, while a Ramsey-style account of theoretical terms can apply when the CI theory does not, the converse is not true, as there are no cases (given the way in which humans are constructed) in which we would attribute a theoretical concept on the basis of causal covariance in a case where no Ramsey-style account would apply. However, if this is true, it leaves us requiring some account of the semantics of observational concepts. It is in this context that I think that the CI theory is very plausible. One way to bring this out is by comparing what we would want to say when the causal covariance required by the CI theory is not present in the case of a theoretical concept and an observational concept. In the case of theoretical concepts, I have argued that this does not impugn the claim that those concepts genuinely have content. You can have a theoretical concept without any disposition to token it when its referent is present if you aren’t aware of any of its observable manifestations, provided you have a theory that describes its referent in observational (in this case mixed) terms. However, the same does not seem true in the case of observational concepts. Were someone to fail to be caused to token a concept such as SQUARE when squares were present in the optimal conditions, this would give us strong grounds for saying that they don’t possess the concept at all.12 This difference suggests that it is plausible to think that different conditions have to be met for observational and theoretical concepts to have content. In the case of observational concepts it is necessary and sufficient for possession of a concept that one is reliably caused to token it by the presence of its referent in appropriate circumstances. In the case of theoretical concepts, it is necessary and sufficient for possession of a concept that one thinks of it in Ramsey’s way, as abbreviating whatever plays a certain role in a theory. I will finally note that if the CI theory of content does apply to observational terms, this will give us further justification for thinking that observational terms can be mixed. The CI theory, as we have seen, explains 12 This is complicated slightly by the fact that someone might conceivably have a theoretical concept of a square, e.g. if they could provide a mathematical definition. However, assuming that we are talking about an observational concept of a square, I think the point holds.

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the content of a concept with reference to the state of the world that reliably causes it. But presumably the properties that are efficacious in causing us to token perceptual mental representations are going to be mixed properties such as squareness rather than truncated properties such as square-andobservable-to-humans. Square-and-observable-to-humans is too anthropocentric to count as a genuinely causally efficacious property. If this is true, there is no reason to deny that mixed properties can be observed. In summary, then, the theory I want to put forward is this. There are two kinds of concepts, observational and theoretical. Observational concepts are those which are represented by perceptual modules. They are concepts which we acquire in the absence of explicitly formulated theory, and their content is to be explained by their causal sensitivity to what they represent, along the lines of the CI theory. Theoretical concepts, on the other hand, are those that denote things that are not represented by perceptual modules. They should have their meanings explained using Ramsey’s method, with reference to their place in the theory in which they occur. But this requires that theoretical concepts ultimately can have their meanings specified with reference to observational concepts alone. Thus, if this theory is true, it suggests that Ramsey’s theory of theories can be used to defend quite a strong form of concept empiricism. 8. CONCLUSION I have argued that, despite extant objections, there remains a strong case for saying that an empiricist account of theoretical concepts based on Ramsey’s account of theoretical terms is true. For this claim to be defensible we have to be careful about what sort of empiricism we are trying to defend. First of all, it entails that we understand empiricism as an epistemological and semantic doctrine about how we acquire concepts, and not an ontological doctrine about whether ‘theoretical entities’ exist—a view we saw Ramsey’s view cannot help to defend. Second, empiricism must allow some mixed concepts to be acquired directly through experience, without allowing direct reference to theoretical entities. However, I have tried to suggest that there is justification for thinking that a form of empiricism is true that meets both these conditions. The form of empiricism I have in mind derives in the first instance from the claim that perception is modular, and uses this to define observational terms as those terms which refer to properties that perceptual modules can represent. I have argued that, if this view is true, there are strong reasons to think that observational terms so defined can be seen as getting their meaning directly, simply in virtue of being reliably caused by the things they represent. This strongly suggests that at least some observational terms are mixed, as required. However, I have also tried to argue that this explanation of content only plausibly applies to observational concepts of this form, entailing that we need a different explanation of how theoretical concepts

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acquire their content. The best account here, I claim, is Ramsey’s theory that the content of theories is always expressible as an existential claim in which only observational and logico-mathematical terms occur.13

13 The research for this chapter was carried out with the aid of a prix FSR at the Centre de Philosophie des Sciences, Université catholique de Louvain. Thanks to Jeff Ketland and Stathis Psillos, with whom I have had very helpful correspondence on the issues raised in this chapter.

Ramsey Sentences and Avoiding the Sui Generis FRANK JACKSON I Many philosophers say that the history of conceptual analysis is a history of failure. This is an exaggeration. The foundations of logic and mathematics contain many successful analyses. But you can understand why they say what they say. There have been many attempts to analyse knowledge since Gettier (1963) disturbed the ‘justified true belief’ conventional wisdom and we are still arguing the toss. And this is not an isolated example. The following seems a fair statement of the situation we find ourselves in. There are many important concepts—examples would include knowledge, intelligence, rationality, probability, pain, personal identity, life—which we appeal to in characterising elements of our world in the sense of classifying them: the intelligent are alike in a way that marks them off from the unintelligent, cases of knowledge differ from cases where we lack knowledge, pains differ from other feelings, and so on. But there are no generally accepted analyses of these concepts despite many attempts by many clever philosophers. To borrow from Steve Stich, in a contest between someone offering an analysis and someone searching for a counterexample, the smart money is on the person looking for a counter-example. Many view this situation with equanimity. In Knowledge and its Limits, Timothy Williamson records his view that most concepts are unanalysable, and is of the view that this is an interesting but unworrying fact (Williamson 2000: 77, 100). I am sure his attitude is widely shared. As against this, I think we should worry. This chapter divides into three parts. I start by saying why we should worry. I then suggest a way out. I finish by noting that the way out would not be available if Ramsey had not told us about the sentences named after him. II Much of language is a system of representation. What one or another sentence represents is the putative information about how things are that we use that sentence to convey. If you are wondering whether to turn left or right to find the coffee, a few words will give you the answer. If you are wondering what kind of animal is about to crawl up your leg, the sentence ‘It is a ferret’ will give you the far from glad tidings.

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The representational view of language has of course been controverted. In ‘Epistemology and Truth’, Donald Davidson argues as follows. The correct objection to correspondence theories is . . . that such theories fail to provide entities to which truth vehicles (whether we take these to be statements, sentences, or utterances) can be said to correspond. As I once put it, ‘ Nothing, no thing, makes our statements true.’ If this is right, and I am convinced it is, we ought also to question the popular assumption that sentences, or their spoken tokens, or sentence-like entities, or configurations in our brains can properly be called ‘representations’, since there is nothing for them to represent. If we give up facts as entities that make sentences true, we ought to give up representations at the same time, for the legitimacy of each depends on the legitimacy of the other. (1988: 184)

But surely maps and diagrams represent. People who use, and the people who create, the familiar map of the London underground take it for granted that it represents the relative positions of the stations, and they are right to do so. But once this is conceded, it is hard to see why we should make a big thing of the difference between maps and diagrams as opposed to sentences and words, for the job we do with maps can be done in many cases by prose, and in fact we often use words to assist people new to the map of the London underground to grasp its representational content. We might well have a debate about the right entities to be what a map or sentence represents—facts, events, worlds, sets of worlds, propositions, mereological sums, etc.—but that there is something to debate here should not, I think, make us think that it is open to serious doubt that maps and sentences (and thoughts if it comes to that) represent. III In order to use language to pass on information, we need to know what the relevant descriptive words stand for. In order to use Morse code or semaphore to pass on information, it is vital to know what the various configurations stand for. This is why we go to classes on Morse code and semaphore—or at least we did when those systems were still in general use. The same goes for words. For example, we need to know what the word ‘electron’ stands for in order to be able to use it as part of a system of representation for exchanging putative information about what our world is like, every bit as much as we need to know what the various arm positions stand for in order to use semaphore to exchange information. It would be very strange if we didn’t need to know what words stand for; we would be giving words special powers denied to other physical structures that we use to transmit information. IV I hope these remarks sound like commonplaces. Is it news that if you— potential giver and potential receiver of information alike—don’t know

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what a physical structure stands for, then that structure is not much use for passing on information? Did anyone need reminding about the value of going to classes on Morse code? But now we have enough to disturb equanimity about the problems for conceptual analysis. I will illustrate with the case of knowledge but very similar points apply to personal identity, pain, life, and all the rest. We use, and are justified in using, the word ‘knowledge’ to pass on information about how things are, especially concerning the epistemic states of humans. (Or at least we do unless some kind of expressivism about sentences containing the word ‘knowledge’ is correct.) In order to do this, we need to know, or maybe have true justified belief concerning, what the word ‘knowledge’ stands for. That’s the commonplace. But what does this knowledge come to? Let’s review some possible answers. V All we know is that the word ‘knowledge’ stands for the property it stands for. That’s all we can give by way of answer. But we know that speakers of other languages can pass on the very same information about what our world is like without using the word ‘knowledge’. It would be an extreme form of linguistic chauvinism to say to ourselves ‘How lucky we are to be English-speakers, because if we were not, there would be important information we could not pass on.’ Moreover, we would not accept this kind of answer from one who claimed to understand Morse code. Instead we would conclude that they did not understand Morse code. The reason, of course, is that knowing that a word stands for what it stands for is a trivial item of knowledge, whereas understanding a language is in general a highly non-trivial matter. VI We know the property the word ‘knowledge’ stands for. But the property is a sui generis unanalysable property. This means that all we can say by way of answer requires us to use the very word itself or some synonym. The property is distinct from the word or words we use to tell people about it, but we can do no better by way of words than to use the very words themselves. In this sense, knowledge is unanalysable. There are two problems for this answer. The first is that knowledge does not seem to be the right sort of property to be sui generis. What a person knows supervenes on enough information concerning truth, belief, justification, defeasibility, reliability, counterfactual dependence, flukiness, and the like. In all the surveying of possible cases prompted by Gettier’s paper, one thing we take for granted is that being a case of knowledge is a derivative or grounded property. It is a priori that no two cases can differ only in the fact that one is, and the other is not, a case of knowledge; in addition, there must be a difference in one or more of: how fluky the case is,

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the counterfactual connections between fact and belief, the degree and nature of justification, and so on and so forth. Exactly which items need to go into this list is controversial—we nearly all agree that truth and belief had better be there but quarrel about other candidates for inclusion—but it is not controversial that there is an illuminating list of knowledge-making properties. How so if knowledge is sui generis? The second problem is the threat of scepticism. We can agree that we have true justified belief on occasion, that we have true beliefs reached by reliable processes, that we have true justified beliefs which are nonaccidentally so and which have desirable anti-defeasibility properties, that sometimes we have true beliefs in situations where the possibility that they might be false has been excluded, that we have justified true beliefs not derived from false premises, and so on. We can agree, that is to say, that we have on occasion true beliefs that satisfy all the at all plausible constraints that have been suggested by the many who have sought an analysis of knowledge. But if knowledge is sui generis, none of these agreements amounts to agreeing that we have knowledge. How then can we ever be certain that we have knowledge by contrast with being certain that we have true justified belief, true belief reliably acquired, true belief with various antidefeasibility properties, etc.? We can put it this way. Let K1, ..., Kn be the sum total of all the sensible suggestions that have been or might be put forward as analyses of knowledge. Let knowledgei be knowledge analysed according to Ki . We can be confident that we sometimes have knowledgei for each i. The sceptical challenge is to provide a reason for saying that, moreover, we sometimes have knowledge itself—the allegedly sui generis unanalysable property distinct from all the analysable knowledgeis on the suggestion under consideration. I mentioned Williamson earlier as someone who views failures of analysis with equanimity. My sense is that he would confront the sceptical challenge by insisting that knowledge has an explanatory and predictive value that belief, for example, lacks, and this gives us good reason to accept knowledge as a feature of our world over and above one or another construction out of true belief and whatever. Knowledge earns its keep by playing important explanatory and predictive roles that cannot be handed across to the varieties of belief. However, the examples he gives are not especially compelling. Here is one (I think similar points apply to all the examples he gives—see Jackson 2002): How long would we expect a fox to be willing to search for a rabbit in the wood before giving up, assuming initially (a) that the fox knows that there is a rabbit in the wood, or ( b) that the fox believes truly that there is a rabbit in the wood? In (b) but not (a), the fox’s initial true belief may fail to constitute knowledge because the true belief is essentially based on a false one, for instance, a false belief that there is a rabbit in a certain hole in the wood. When the fox discovers the falsity of that belief, the reason for the search disappears. That will not happen in (a), because a true belief essentially based on a false one does not constitute knowledge. Thus,

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given plausible background conditions, more persistence is to be expected in (a) than in (b). In many such cases, lengthy persistence is better explained by initial knowledge than by initial true belief. ( Williamson 2000: 86–7)

The trouble with this example is that Williamson tells us the problem with the explanation in terms of (a) without mentioning knowledge. The problem is, to quote, that ‘the true belief is essentially based on a false one’. In consequence, the case gives no reason for favouring a knowledge story over a belief story with the defect remedied in terms that make no mention of knowledge and which Williamson himself provides. In terms borrowed from the final sentence of the quotation: in many such cases, lengthy persistence is better explained by initial true belief that is not essentially based on a false one than by initial true belief simpliciter. VII You are right that we had better know what ‘knowledge’ stands for and that it had better not stand for something sui generis. But this does not mean, as you seem to be implying, that there should be other words that we might use instead of the word ‘knowledge’, words that, suitably assembled, would play the same informational role. For perhaps we refer to knowledge via some guise G or other. We know what the word stands for—it stands for the property that is G—but we cannot, as of now anyway, say what the property itself is. But if this is right, we can state the circumstances in which someone will use the word ‘knowledge’. They will use it when they think something has the property which is G. The word ‘knowledge’ will be a good word for receiving and passing on the information that something has the property, whatever that property is, which is G, and that is what we mean here by a word standing for a property. So the suggestion itself delivers the words we need to do the informational job that the word ‘knowledge’ plays. Maybe when we learn which property is G, we will shift our use of the word ‘knowledge’ to that property, but that’s another question. VII I There are two things you might mean by saying that ‘knowledge’ stands for a sui generis unanalysable property. One is that it stands for the kind of property Moore thought goodness to be. You are right that we should reject this idea. The other is that although each and every case of knowledge can be fully described in all relevant respects in terms that do not include ‘knowledge’ or a near-synonym, there is no pattern capturable in these terms. This view involves no mysterious extra properties—each case is fully describable in terms that do not include ‘knowledge’—but because there is no pattern statable in terms that do not include ‘knowledge’ or a near-synonym, there is no question of giving an analysis of knowledge. Knowledge is a patternless infinite disjunction, as we might put it. There are three ways we might spell out this suggestion (which is of course modelled on some versions of autonomy theses about the relation of the moral to the non-moral, and of the mind to the physical). On one, the idea

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is that there is no pattern at all, not just no pattern in terms of the features of the disjuncts. This spelling-out raises serious questions about how we could have acquired the concept of knowledge and learnt to use the word, as cases where there is no pattern are cases where one cannot pick up a word by reflection on examples, and also raises serious questions about the utility of our talk of, and our concept of, knowledge. The more patternless a collection of items is, the less interest and theoretical value it has for us qua collection. And I think we should resist any suggestion that the applicability of the word ‘knowledge’ in itself creates the interest. To say that would go against our earlier point that we use words to tell about the world. The second way of spelling out the suggestion affirms that there is a pattern but not one capturable at the level of the disjuncts; it is not capturable in the terms of belief, truth, and the like—the more fine-grained features on which knowledge supervenes. But this is to return to the view that knowledge is an extra property, the view suggested by Moore’s view of goodness, the view we are supposed at this point in the discussion to be avoiding. Our topic here is not Platonism about properties or properties as the universals that serve to carve nature at its fundamental joints. For us, whenever there is a pattern unifying a set of items, there is a property in the wide sense of a way that things might be. What one then says, moving from speculative cosmology to analytic ontology, about whether we should think of this pattern in terms of a common relation that the items have to a universal, or in terms of resemblance nominalism, or in terms of an immanent shared thing which inheres in every item, or ... is another question. The third way of spelling out the suggestion affirms that there is a pattern at the level of the disjuncts capturable in principle in terms of the finegrained features but it is not capturable by us in these terms. Perhaps God can see the pattern at the level of the disjuncts but we cannot. But now it is unclear what we are supposed to be using the word ‘knowledge’ to stand for in the sense of that which we tell about when we use the word. If we come across a tribe that cannot detect a certain feature, we can be confident that they lack a word for it, or if they somehow do have one, their claims made using the word will be very unreliable. Obviously, we do not want to say that our situation with the word ‘knowledge’ is at all like this. Perhaps the suggestion is that we know that there exists a pattern at the level of the disjuncts and that creatures with special powers could articulate the pattern in the relevant terms, but all we can do is say, justifiably, that there exists a pattern. Experienced tennis players can tell whether a ball coming towards them will go out or go in with remarkable reliability. They know their judgement is triggered by a pattern at the level of direction, spin, velocity, height over the net, and the like, and that a brilliant cognitive scientist might find the pattern at this level after a lot of work. At the same time, the tennis players do not, and know that they do not, know what the pattern is at the level of velocity etc. Perhaps our use of the word

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‘knowledge’ is something like that. But the tennis example is patently not an example where we do not know or cannot say what unifies the disjuncts. What unifies them is their association with whether the ball lands in or out, and we all know that the information we pass around with the words ‘in ball’ and ‘out ball’ concerns where the ball is likely to land in relation to the lines, and, moreover, we can specify the relevant location without using the words ‘in’ or ‘out’ (so any suggestion that the property is sui generis is not to be taken seriously). There are, and we know that there are, two unifiers for the disjuncts. The one we cannot give with any exactitude is the one involving spin, height above the net, and so on; the other is in terms of where the ball lands, and that we can give and is the one experienced tennis players give putative information about when they say ‘in ball’ or ‘out ball’ in response to an approaching ball. IX The idea that we ask after the feature of the world that a word like ‘knowledge’ stands for in order to understand the information it serves to pass around is a hangover from an unduly regimented view of language. In some cases we did get together and agree to use one or another physical structure to stand for this, that or the other property. Morse code and semaphore are examples. But mostly we should think of words in terms of knowledge how and not knowledge that, as a matter of exercising abilities, especially recognitional ones, and not in terms of flagging features. The emphasis on recognitional abilities seems absolutely right, especially when one thinks of the tennis example above, but it does not address our problem. Our problem is, What information do we pass around by using words, the word ‘knowledge’, in particular? And it is not plausible that what we pass around is information like that we have recognitional abilities, or that we are currently exercising the ability that underlies our use of the word ‘knowledge’. That all pertains to how it is that we have the ability to pass around information using the word, not to the information we pass around. Likewise, one of the things we are able to recognise is similarity to one or another degree, and it is plausible that sometimes the information we pass around is to the effect that some item is, to some degree or other, similar to certain exemplars, but again what we pass around is that there is a similarity, not that we are recognising it. Of course we can pass around information about our abilities—as when we say that we can recognise Tony Blair in a photograph—but when we do, we use words that stand for the relevant recognitional features. Recognising Blair is something we tell about by using words we know stand for our acts of recognition. X This whole discussion is in the grip of an outmoded theory of reference. It is being assumed (presumed) that the reference of a word like ‘knowledge’ is given by a descriptive condition

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associated with the word. The talk of the property the word stands for is nothing more than the description theory in other words. What we learn from Saul Kripke and Hilary Putnam’s work on reference is that the reference, and hence what is being said about how things are, by the use of a word like ‘knowledge’ may be quite opaque to users of the word. The right theory of reference is an a posteriori matter, and this means that competent users of a descriptive word need not know what that word stands for. What a word stands for awaits the delineation of the right theory of reference and the discovery of the relevant empirical facts. For example, if the right theory of reference for the word ‘knowledge’ is that it refers to the property that stands in causal relation R 5 to users of the word, then to know what the word stands for we need to know both this and the property that stands in R 5.1 This is not the place to argue the theory of reference as such, but let me indicate why this seems to me to be a perverse moral to draw from recent work on reference. If what people are saying about how things are depends on something we philosophers know about but the folk do not, we had better hurry up and solve the theory of reference. The folk use words all the time to say how they take things to be and they would like to know what it is that they are saying about how things are. Should we put notices in the papers to warn them that they do not know what they are saying and ask them to watch out for the results of the next workshop on the theory of reference in the hope that it will settle the matter once and for all? I hope this will strike you as absurd. XI We find ourselves in the following situation. There are many words that patently serve the function of passing around information about what the world is like. This requires that, in coming to understand them, we grasp what features they stand for. For a few of these words, it is plausible that the corresponding features are fundamental features that cannot be thought of as complexes of more basic features. But mostly the features are not fundamental in this sense. To suppose otherwise is, as we’ve seen, to make a mystery of the way these features supervene on more fine-grained ones and to raise the bogey of scepticism. But this means that, provided we have sufficient linguistic resources, we should be able to identify the feature words like ‘knowledge’, ‘intelligence’, ‘life’, ‘personal identity’ stand for, using words other than the very words themselves; and do so not in the boring sense of using other words that are synonyms or near-synonyms, but in the interesting one which is what we have in mind when we offer conceptual analyses. We should be able to find illuminating alternative ways 1 Kripke (1980); Putnam (1975). I do not know if Kripke or Putnam would agree with this use of their work on reference but some certainly seem to draw the opacity moral from their work.

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of saying that something is known, is probable, is intelligent, is alive, is the same person as, and so on and so forth. Why then is it—conceptual analysis—so hard? XII If, as some hold, myself included, whenever linguistic structures S1 and S2 are alternative ways of saying the same thing about how the world is, then ‘S1 iff S2’ is a priori, we have the traditional connection between analysis and the a priori. But notice that we raised the puzzle simply in terms of the way language passes around putative information about how things are. There is a puzzle here independently of where one stands on the a priori. Some think that their robust rejection of the a priori means that they can think of the problems for conceptual analyses as ripples on a discredited backwater, but in fact there’s an issue for anyone who sees language as being like Morse code and semaphore in being a system of representation. XII I There is even an issue for wide-ranging expressivists. By wide-ranging expressivists I mean those who hold that very many of the terms philosophers have found hard to analyse, not merely the normative and ethical ones of classical expressivism, serve to express rather than report or describe. The issue for wide-ranging expressivists is not, of course, to capture the information putatively passed around by the use of the problematic terms. Their view is that there is no such information, and to ask after it is to misunderstand the role of the terms in our language. All the same, expressivists allow, have to allow, that the terms in question figure in language fragments that serve to make claims about how things are. For example, if ‘knowledge’ is a term that wide-ranging expressivists hold expresses rather than reports, they must allow that the sentence ‘The word “knowledge” in English serves to express an attitude rather than to make claims how things are’ serves to make claims about how things are. The question for them, accordingly, is what to say about the attitude in question. Is it sui generis, or is it subject to such and such an analysis, or ... ? Maybe wide-ranging expressivists have less trouble with these questions than the rest of us; maybe not. That’s an interesting question for another time. XIV My answer to why conceptual analysis is hard and why there is so much controversy takes off from a picture that underlies much of what I have said already. The world is a huge complex entity spread out in space and time. We make sense of it by finding patterns. If we did not discern patterns, we

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would be overwhelmed by the complexity. Finding patterns is a matter of carving out similarity regions, and we use physical configurations—maps, colouring conventions, and above all words—to tell about these similarity regions. Globes of the world once coloured the parts of the British Empire red. Here we have, first, the world. Second, those parts of the world that are alike in being one or another part of the British Empire—the similarity region is the scattered object that is the British Empire. And, third, the words and the colouring on the globes that serve to tell about that scattered object: where it is, its shape, how it waxed and waned. The same goes for more philosophically interesting examples. We can think of pain as a huge scattered object united by each element being a case of pain, of knowledge as that which unites in the relevant respect all the bits of the world that know such and such, of life as that which unites in the relevant way all the things that are alive, and so on. There are infinitely many similarity regions in space and time, especially when you bear in mind that anything that can be captured in a system of representation counts for our purposes, and that systems of representation carve out regions in logical space as well as actual space. We are not talking about carving nature at especially natural joints or anything like that, and we are talking about commonalities across possible worlds. This means that any system of representation that captures a good number of these regions has to be structured for the same reason that number systems have to be structured. We can tolerate a certain number of primitives, but, as everyone knows, after that we have to have a finite set of rules for operating on a finite list of primitives to form terms for the indefinitely many similarity regions (or numbers). Now a conceptual analysis is nothing other than a claim that there are two different ways of capturing the same similarity region, with the proviso that we are not interested in boring cases. The region carved out by the word ‘sibling’ is the union of the regions carved out by the word ‘sister’ and the word ‘brother’, and that is why we can analyse ‘x is a sibling’ as ‘x is a brother or a sister’. There is, therefore, no mystery about why conceptual analysis is sometimes hard. There is no reason why it should typically be obvious that different sets of ingredients put together in appropriately different ways carve out the same region. After all, in the main, the equations for the conic sections are not especially obvious, and they are cases where geometric and algebraic systems of representation carve out the same curves. Why should the situation be greatly different for representation by words and sentences? Another way of putting the point is to note that when we asked at the beginning rhetorical questions like ‘Surely we know what words like “pain” and “knowledge” stand for, otherwise we would not know what we were saying about how things are when we use them?’ to answer that of course we do is not to say that we know off the bat interestingly different ways of representing what we know in other words.

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XV This tells us why conceptual analysis is often hard, and perhaps is all we need to say about Moore’s famous Paradox of Analysis.2 But it does not tell us why there is so much disagreement, and why the smart money is on the counter-exampler. Finding the algebraic way to represent a curve that we already know how to represent geometrically may be tricky, but there is plenty of agreement once we’ve pulled it off. In order to explain the ubiquity of disagreement, we need a point about many concepts brought to our attention by many philosophers including Ramsey, and which famously played a central role in the arguments for materialism as a philosophy of mind in the hands of David Armstrong and David Lewis.3 I said we need to spot patterns if we are to make sense of our world. Very often the patterns we need, or which do the job best, form a theory in the sense of patterns that are identified by their relations to other patterns. They come as package deals, as David Armstrong likes to put it. What unites the husbands is that each has a wife, and what unites the wives is that each has a husband. Other familiar examples are the relation between force, mass, and acceleration in Newtonian mechanics, and the way belief–desire psychology finds patterns in the way we move through the world. It is, I take it, a contingent fact about the world we live in that many of the most useful patterns are package deal ones. In order to understand British politics, you need to understand the patterns picked out by terms like ‘cabinet’, ‘minister’, ‘backbencher’, ‘electorate’, and so on, and they make up a package deal. But this is a contingent feature of British politics. This gives us two sources of controversy when we come to do conceptual analysis. Both arise from the implicit nature of the package deals in the philosophically interesting cases. XVI The package deal that makes up Newtonian gravitational field theory has been written down. But the package deals that make up belief–desire psychology, rationality, being intelligent, knowing something, and so on have never been written down. Of course bits have been written down. Most accounts of rationality include clauses to the effect that one ought not believe contradictions other things being equal. Most accounts of chance include clauses connecting credences concerning chances of outcomes to 2

660).

But note that what we mean by analysis is not what Moore meant; see Moore (1942:

3 Armstrong (1968); Lewis (1966, 1970). The importance of Ramsey’s contribution is highlighted by Lewis.

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credences concerning outcomes simpliciter (see e.g. Mellor 1971). All accounts of knowledge make knowledge factive. But the absence of canonical statements means that two things can and do happen. One is that different people can have different theories without this being obvious. The other is that people can change their theories without noticing that they have. I think both are illustrated in the debate over the analysis of knowledge that started with the Gettier examples. The Gettier examples are often cited as one of the few examples of knockdown refutations in philosophy.4 But in fact there are three possibilities, only one of which is the knockdown refutation case. Case 1. Roderick and Alfred believe that the representational content they give to the word ‘knowledge’ is the intersection of the contents they give to the words ‘true’, ‘belief’, and ‘justified’. They are told about the Gettier cases and realise the error of their ways. Perhaps they explain that what tricked them is that they’ve always granted the link between knowing and its not being a fluke that one’s belief is true but thought that being justified rules out being right by fluke. The Gettier cases show this is a mistake. ( I have 90% credence that I am an example of case 1.) Case 2. Roderick and Alfred rightly believe at t that the representational content they give to the word ‘knowledge’ is the intersection of the contents they give to the words ‘true’, ‘belief’, and ‘justified’. They are told at t +
about the Gettier cases and immediately realise that there is an interesting epistemological state to be in that is distinct from true justified belief and which is in some ways superior. In the act of realising this, they switch, starting pretty much from t +
, their usage of the term ‘knowledge’ to this state they have only just discerned but without realising that they are making a switch rather than correcting an error. The fact that a change in usage has occurred is easy to overlook because Gettier cases are unusual and because of the lack of any explicit agreement. (I have a 10% credence that I am an example of case 2, or, better, that it is vague whether or not I am a case 1 or a case 2.) Case 3. Roderick and Alfred rightly believe that the representational content they give to the word ‘knowledge’ is the intersection of the contents they give to the words ‘true’, ‘belief’, and ‘justified’. They are told about the Gettier cases, are unconvinced, and become well known for articles defending the true justified belief analysis against Gettier and related cases. (I am certain that I am not an example of case 3 but I think that there are examples of case 3.) So why is there so much disagreement? Part of the answer is that there isn’t. What there is is an awful lot of apparent disagreement. Philosophers 4

Mea culpa, and thanks to David Braddon-Mitchell for making me rethink.

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enjoy argument. It is a bit of a let-down to be told that when Alfred insists that knowledge is true justified belief and Frank Plumpton that the justification clause should be replaced by a reliability one, we don’t necessarily have an interesting spat; we may have, rather, an interesting difference in what is called ‘knowledge’. I say an interesting difference because it would be a mistake to hold that it does not matter which patterns we pick out in our attempts to make sense of our world. Take, to illustrate, Newtonian mechanics: systems of particles’ being alike in regard to total mv 2, and being alike in regard to total mv 3 are equally patterns in nature, but it is a very interesting fact that the first is much more important than the second. Equally, it is a bit of a let-down to be told that one’s changes of opinion over time about which ‘ Beam me up, Scotty’ cases are cases where personal identity over time is preserved are not the result of the difficulties of discerning the real nature of a particularly difficult denizen of Quine’s museum (Quine 1969: 27) but are instead one’s possibly unnoticed oscillations between different concepts of personal identity, unnoticed because they are given by places in an implicit complex theory. So why is the smart money on the counter-exampler? There are many patterns, captured by places in implicit theories, that are of interest when we do epistemology: the pattern that links the designated notion with truth, justification, and belief; the one that inserts non-flukiness into the network; the one that replaces non-flukiness by lack of defeasibility by the true; the one that uses reliable connections in place of flukiness; and so on and so forth. It is, to one extent or another, vague as to which concept we use the word ‘knowledge’ for, and in practice it often does not matter—that which we are certain of is very often that which we arrive at by a reliable process and which is not true by accident. In consequence, it takes smart philosophers’ recherché examples to reveal that there are a number of candidate patterns. What the counter-exampler refutes is the view that there is a single, fixed concept which we all, or nearly all, use the word ‘knowledge’ for. It remains true, however, that for every candidate concept, there is an analysis, and that by giving the analyses of these candidates we can show how to avoid commitment to implausibly many sui generis properties. XVI I What’s all this got to do with Ramsey? Ramsey sentences tell us how having a place in a network can deliver an analysis in the sense of an account that reduces the number of unanalysable notions we have to admit in our account of what our world is like (Ramsey 1929c). The natural first thought on being told that some concept is defined by its place in a network is that vicious circularity threatens. Isn’t it circular to define C1 in terms of C2, and then turn around and define C2 in terms of C1? And defining C1 to Cn in terms of their places in a network looks suspiciously like this, except that more concepts are in play. But Ramsey

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sentences tell us that this need not be the case. To sketch the familiar story,5 let T(C1, ..., Cn) be the sentence that gives the network, with the ‘Ci’s thought of as names of the kinds corresponding to the concepts. If each Ci is defined by its place in T, then the content of T(C1, ..., Cn) is its Ramsey sentence, namely (
x1) ... (
xn) T(x1, ..., xn). For T(C1, ..., Cn) simply says that there are kinds standing thus and so to one another, which is what the Ramsey sentence says. But then to be Ci is to be that which is in the i-th place if such there be, for each i. That is to say, y is Ci iff (
x1) ... (
xn) [y has xi & T(x1, ..., xn)], where each xj is in Cj’s place in T. As the right-hand side of this biconditional contains no occurrences of any Cj, we see how a network story can avoid circularity, and how a network story allows us to reduce the number of sui generis concepts we need to admit. Without Ramsey’s insight, we would, I think, have had to embrace one of: language is not a system of representation; or it is, but it represents things as having implausibly many sui generis features and, in consequence, misrepresents a lot of the time and makes a mystery out of our supervenience intuitions. Ramsey shows us how to get out of a nasty dilemma.6

5 Best known through Lewis (1970). I omit the uniqueness requirement that Lewis includes, as indeed did Ramsey. The point at issue is independent of it. 6 I am indebted to many discussions with supporters and opponents, too many to list. My general debt to David Lewis’s writings on Ramsey sentences will be obvious.

What Does Subjective Decision Theory Tell Us? D. H. MELLOR 1. THE QUESTION By ‘subjective decision theory’, or ‘SDT’ for short, I shall here mean the common core of the subjective decision theories of Ramsey (1926c), Savage (1972), Jeffrey (1983), and others, ignoring differences of detail. This core theory bases an assessment of decisions to act on two features of the possible outcomes of alternative actions: how probable they are and how valuable they are—or rather, how probable and valuable we think they are as we make our decisions. For the probabilities and values which SDT invokes are not objective chances or values, if such there be. They are measures of how strongly, while deciding how to act, we believe in and desire various possible outcomes of our actions. This is why the theory is called ‘subjective’: in it, the values of these outcomes are just the so-called subjective utilities which they have for us in advance, and their probabilities are just the different degrees of belief, or credences, that we have in them. Although these features of SDT are contentious, I shall take them for granted in what follows, since what concerns me here is how we should read the theory, so understood. Should we read it normatively, as saying, rightly or wrongly, how we should act, or would act if we were rational; or descriptively, as saying, rightly or wrongly, how in fact we do act? Jeffrey and most other modern subjective decision theorists read it normatively, and take Ramsey to have done so too. I, like Blackburn (1998, ch. 6), think they are wrong on both counts: Ramsey read his theory descriptively, and was right to do so. The theory, as he presents it, is not normative: it is a descriptive theory that forms part of a functionalist account of states of mind. And that, I shall argue, is how we should read SDT; for only on this descriptive reading is it defensible. Since the issues that will concern us arise in even the simplest cases, those are all I shall consider. So suppose, for example, that I am trying to decide whether to stop smoking tobacco in order to avoid getting cancer: that is the intended end (call it E) to which my stopping smoking is a means (call it M). Suppose too that my nicotine addiction prevents me from smoking less, so that unless I stop smoking altogether I will carry on as before. This therefore is the relevant alternative to M (call it ¬M), just as my getting cancer is the relevant alternative to E (call it ¬E). Then SDT says that whether I will or should ‘do M’ (i.e. make M the case) depends on what, at the time and in the circumstances, are the utilities for me of the four

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possible upshots of my action—M & E, M & ¬E, ¬M & E, and ¬M & ¬E— and on what ( I now think) my credences in E and ¬E will be if I do M and if I do ¬M. Specifically, SDT says that whether I will or should do M depends on the expected utilities for me of M and of ¬M. M’s expected utility for me is the average of the utilities for me of M & E and of M & ¬E, weighted by what my credences in E and in ¬E will be if M is done; and similarly for ¬M. Then SDT says that I will or should do whichever of M or ¬M has the greater expected utility. That is, I will or should do M if M’s expected utility for me exceeds ¬M’s, and I will or should do ¬M if ¬M’s expected utility for me exceeds M’s. (If the two expected utilities are equal, SDT says nothing either way.) This is the principle of maximising subjective expected utility or, for short, the maximising expected utility principle, or MEUP. The question then is whether we should read MEUP normatively, as saying that we should maximise our expected utilities, or descriptively, as saying that we will maximise them. 2. THE RIGHT THING TO DO Before tackling this question, I must emphasise an important presupposition of either answer to it. This is that an action’s intended object, or end, can justify the doing of that action as a means to that end even if the action is neither certain, nor even thought to be certain, to achieve that end. This assumption is now fairly widely accepted. Most of us recognise that the increased probability of getting cancer if we smoke can make the desirability of not getting cancer justify stopping smoking even though some smokers do not get cancer and some non-smokers do get it. We accept therefore that there is a serious sense in which a probabilistic link between smoking and cancer can justify our stopping smoking even if we subsequently do get cancer. I shall express this sense by saying that, whether we get cancer later or not, stopping smoking is the right thing to do, or is a good idea, at the time. And as with this decision, so with many others, including important medical and political decisions, of whose consequences we cannot at the time be certain. Not all unwanted outcomes of such decisions show that they should not have been made, a fact which should be more widely recognised in our society than it is, and which I shall hereafter take for granted. Given this fact, it is part of the job of any decision theory to say what determines whether in this sense it is, or seems to be, a good idea at the time to do something, like stopping smoking, wholly or partly as a means M to some logically independent end E, like not getting cancer. If the decision theory is subjective, as SDT is, then what it tells us, rightly or wrongly, is what makes doing M seem at the time to be a good idea: since that, as the theory says, will depend not on how probable or valuable E really is with and without M, but on how much we now expect and want E with and

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without M. The question here is whether, if M seems in this sense to be a good idea at the time, it follows that it really is a good idea at the time. I say not. Consider first the probabilities involved. When doctors tell us to stop smoking in order to avoid getting cancer, they do not do so on the grounds that stopping smoking will raise our credence that we will not get cancer. They do so on the grounds that stopping smoking will raise our objective chance of not getting cancer. And I agree: doctors are right to take this to be the relevant probability. To see this, consider smokers who are ‘in denial’, i.e. who think they are no more likely to avoid getting cancer (E) if they stop smoking (M) than if they do not. Because (they think) their credences in E will be the same whether they do M or ¬M, then however much better (they think) E will be than ¬E, SDT will not tell them to do M, i.e. stop smoking: M will not seem to them to be a good idea, or the right thing to do. Yet given all the evidence for an objective if probabilistic causal link between smoking and cancer, most of the rest of us would agree that these smokers are wrong. Whether or not they admit it, if they want to avoid getting cancer, then stopping smoking is the right thing for them to do, whether or not they realise that it is, and whether or not their addiction allows them to do it. Similarly with utilities. Given the relevant subjective or objective probabilities, what makes it a good idea for me to stop smoking now in order to avoid getting cancer is not that I don’t now want to get that disease, but that getting it really will be very painful and life-threatening. Any smokers who were in denial about that, and carried on smoking because they thought having cancer would be no more unpleasant than not smoking, would be as objectively wrong as those who deny that stopping smoking will reduce their chance of getting cancer. (Hence, for example, the poster campaigns designed to make smokers realise just how dreadful having cancer is.) And because these smokers are wrong about this, since having cancer is in fact far worse than not smoking, their consequent decision to keep on smoking is equally wrong, as is SDT’s endorsement of that decision if it follows by MEUP from their subjective utilities and credences. And just as it takes more than subjective utilities to justify a decision in this case, so it does in many others. Take what Shakespeare says in his Sonnet 129 about ‘lust in action’, namely that it is An expense of spirit in a waste of shame . . . Enjoy’d no sooner but despised straight; Past reason hunted; and no sooner had, Past reason hated, as a swallowed bait, On purpose laid to make the taker mad: Mad in pursuit, and in possession so; Had, having, and in quest to have, extreme; A bliss in proof, and proved, a very woe; Before, a joy proposed; behind, a dream.

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In other words: the subjective utility of a seduction caused by lust is so much greater than its objective utility once achieved that even the seducer realises afterwards that the seduction, which seemed a good idea at the time, was in reality not a good idea, not even at the time. Unfortunately, as Shakespeare concludes, All this the world well knows; yet none knows well To shun the heaven that leads men to this hell.

These and many other examples that come easily to mind seem to me to show clearly that an action M’s maximising subjective expected utility is not enough to make M the right thing to do. Extra objective constraints are needed on the subjective credences and utilities that are MEUP’s input before it can tell us whether doing M really is the right thing to do. It is indeed debatable what these constraints should be, especially on subjective utilities. However, our two examples suggest that in many cases the constraints need only require how much we want something in advance to match how much we like it when we get it. But however that may be, these are not questions we need to settle here, since our business here is not to say what will suffice to tell us the right thing to do but with showing that and why SDT will not suffice to tell us this. That is the sense in which I say that SDT is not defensible as a normative theory. And in arguing this it will beg no present questions to assume, for simplicity, that the right normative theory is an objectified SDT, or ODT for short: i.e. a theory which still uses the formulae of MEUP to rank alternative actions, but does so with its input credences and subjective utilities replaced by their objective counterparts, namely chances and objectified utilities, whatever they may be. 3. BEING REA SONABL E I have said that all I mean by rejecting SDT as a normative theory is that it does not tell us what makes an action a good idea, the right thing to do, at the time. By this I do not mean that SDT cannot explain why we do what we do. On the contrary, that is just what a descriptive SDT does do— provided of course it is true, a proviso we shall return to in Section 4. Moreover, actions of whose aetiology SDT is true are not only thereby causally explained, by the subjective credences and utilities which cause them; those actions are also thereby rationalised, since credences and utilities which cause actions as SDT says are reasons for acting in a quite standard sense. We do not need SDT to tell us that if I stop smoking in order to avoid getting cancer, my reasons for doing this are my desire not to get cancer and my belief that I am less likely to get it if I stop smoking. All SDT does is to extend this basic idea of subjective reasons for action to cover degrees of desire and belief. Still, the fact that our credences and utilities can be the subjective reasons as well as the causes of our actions does not entail that the actions they

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rationalise are thereby made objectively reasonable, still less that, in the sense of Section 2, those actions are the right thing to do. Whether actions caused in accordance with SDT are reasonable depends on whether the credences and utilities which cause them in that way are reasonable; and while reasonable credences and utilities need not be right—i.e. they need not conform to whatever conditions ODT imposes—there must be some constraints on them. Not all the credences and utilities we can have are equally reasonable, and some are quite unreasonable. To take an extreme example, it would not be reasonable for anyone with good access to modern climatic data to have a high credence in snow in the Sahara, and drivers who did so, and as a result drove across the Sahara in cars with snow chains and no air conditioning, would be thinking and acting not just wrongly but unreasonably. In rationalising their action, SDT does not thereby show it to be reasonable: on the contrary, SDT shows precisely why the action was unreasonable, because the credence that caused it was unreasonable. On the other hand, credences can be wrong, in that they differ from the corresponding chances, and yet perfectly reasonable, having been reasonably based on freakishly misleading statistics. Thus ten fair coin tosses can all land heads, and seeing them do so may well give us a higher credence in heads than in tails on the next toss: a credence which is wrong, since the chances of heads and tails are in fact equal, but is still perfectly reasonable. So we cannot infer, just because an action is not the right thing to do at the time, that it, or the decision to do it, is unreasonable: it may or may not be. Or, putting it the other way round, it is no objection to a decision theory which is normative—in the sense of saying when an action is right—that there are many reasonable actions which the theory says are wrong. Finally, we should note for completeness that credences can also be both unreasonable and right: as when my conviction, in the teeth of all the epidemiological evidence, that I am immune to a current flu virus makes me expose myself to infection in ways that are quite unreasonable—but as it happens are also safe, since unknown to me or anyone else, I am in fact immune to the virus. Similarly with utilities. These too can be right or wrong, reasonable or unreasonable, in any combination. Suppose, to pick a different example, that your dentist asks if you will accept a slightly risky injection (M) to make a filling painless (E), and that whether you should let your dentist do M depends on how bad you would find the pain (¬E) if you had it. Suppose, moreover, that, as you’ve never previously had a tooth filled, it is only reasonable to let your dentist’s opinion of how bad ¬E would be determine its (dis)utility for you and thus your decision. Yet you may not be reasonable enough to take this advice, perhaps because of an unfounded fear, either of injections or of any prospect of pain, however mild. And as with credences, so with these utilities: whether you are reasonable or not, you may still be right or wrong: the pain, if you have it, might or might not be as bad as you fear.

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All this may suggest to defenders of a normative SDT that what matters in decision-making is not the sometimes unanswerable question of whether our subjective credences and utilities are right in my objective sense but whether they are right given our actual credences and utilities. But this statement of the condition is ambiguous. If it just means ‘given that these are our credences and utilities’, then no one will claim that it guarantees the rightness or reasonableness of decisions prescribed by SDT. For, as one of its advocates says, SDT ‘is as applicable to the deliberation of the ignorant and inexperienced as it is to that of the knowledgeable expert; and it is as applicable to the deliberation of a monster as it is to that of a saint’ (Eells 1982: 5). And no one will take a monstrous decision to be made in any sense more right or reasonable by being derivable by SDT from the monstrous agent’s appalling utilities and/or ludicrous credences; while if the condition means ‘given that our actual credences and utilities are right or reasonable’, then checking that it holds includes checking that our credences and utilities are right or reasonable, and we are no further forward. Nor is a normative SDT generally easier to apply to credences and utilities which we only know to be reasonable rather than right. This is because what makes credences and utilities reasonable depends on what makes them right, and the former is usually no easier to discover than the latter. Thus, in our last example, what makes it reasonable to accept a dentist’s advice about whether to have an injection is the fact that dentists know more than the rest of us about when dental work is painful. It is thus no easier to tell whether taking a dentist’s advice is reasonable than to tell whether it is right. Similarly with credences: what makes it reasonable to base our credence in the happening of events of a given kind on how often they happen is the fact that the greater their objective chance of happening, the more often they are likely to happen. This after all is the point of requiring clinical trials of any prospective new treatment for a disease: to provide reasonable estimates of the objective chances of recovery from the disease with and without the treatment; from which doctors and their patients can then derive corresponding credences, and thereby make reasonable decisions about whether or not to use that treatment. 4. THE CASE AGAIN ST A DESCR IP TIVE SDT I have used simple examples to argue that SDT is not defensible as a normative decision theory, because it cannot tell us when the actions to which it applies are right, or even when they are reasonable. In giving these examples, I have, however, tacitly assumed that something like SDT is a fairly accurate descriptive theory of how we actually make decisions. Why, for example, should you ask your dentist how painful a dental operation will be if not because your decision about whether to have an injection will be caused, roughly as SDT says, by your relevant credences and utilities. That is

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why you want these credences and utilities to be right, which you know they are more likely to be if you get them from your dentist. Similarly in other cases. Once doctors decide on objective grounds that the right thing for smokers to do to avoid getting cancer (E) is to stop smoking (M), they will try to make smokers believe that doing M will make E more likely. That is, they will try to raise the credences that smokers will have in E if they do M. And the obvious explanation of why doctors do this—apart from disseminating interesting medical information—is because they think that their smokers’ credences in E with and without M are what will in fact determine whether those smokers will do M when M is the right thing to do. This I believe is why, in general, we want to make adopting a means M to an end E seem like a good idea at the time just in case it is a good idea at the time; not because seeming to be a good idea is the same thing as being a good idea, but because making M seem a good idea only when it is a good idea will make us do M only when M is the right thing to do. If SDT does not tell us what people should do, it does at least tell us, rightly or wrongly, how to get people to do the right thing. That much a descriptive SDT can do. Given all this, why do Jeffrey and most other subjective decision theorists take their theories to be normative rather than descriptive? The main reason is that, read descriptively, SDT is false. Its most obviously false consequence is that it requires everyone to fully believe—to have credence 1 in—every necessary proposition and to fully disbelieve—to have zero credence in— every impossible proposition. We can see why SDT entails this by looking at how, in simple cases, it uses betting as a way of measuring credences. In particular, it measures our credence in a proposition A by the shortest odds we would accept for a bet on A’s truth if we were influenced only by how much we believe A and not at all, for example, by whether we want A to be true. In those circumstances, the more strongly you believe that a horse will win a race, or that a friend of yours will stop smoking, the shorter are the odds you will accept for a bet on those propositions, i.e. for a bet which you will win if the horse does win the race or your friend does stop smoking. Now one necessary assumption of this way of measuring credences is that, whether or not we want the proposition on whose truth we are betting to be true for some other reason, we do want to win the bet. If we did not care about winning the bet, we would also not care what odds we accepted for it. That is why SDT will not let us accept any finite odds for bets that we cannot win, such as bets on impossible propositions which, by definition, cannot be true. Hence the result, built into all versions of SDT, that our credences in all impossible propositions must be 0, and therefore that our credences in all necessary propositions must be 1. Note that this is not a trivial or dispensable consequence of SDT. It is essential if credences are to satisfy the most elementary rules of

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mathematical probability, for example that the probabilities of any proposition A and of its negation, ¬A, must add up to 1: since that will follow for credences only if our credence in the necessary proposition A & ¬A must be 1. How should we react to this and other obviously false consequences of SDT? The usual reaction is to retreat to a normative reading which makes SDT say not how we do act but how we would act if we were rational. But that reaction cannot really cope with this consequence of the theory. I suppose we might say that rationality requires us to believe all necessary truths whose necessity can be known a priori, i.e. by reasoning, so that a failure to believe, for example, any as yet unproved mathematical truth is really a failure of perfect rationality. But even that God-like standard of rationality cannot require us to believe necessary truths whose necessity can only be known a posteriori, like the allegedly necessary truth that water is made of H2O. Not even on Mount Olympus could this necessary truth have been recognised as such by pure reason. The fact is that, as a theory of our cognitive attitudes to propositions, including necessary and impossible ones, neither the descriptive nor the normative reading of SDT can make it fit all the facts of human psychology. Fortunately, however, this hardly matters, since we only need SDT to apply to states of affairs that we take to be not merely contingent in general but contingent in particular on our actions: either directly, when the state of affairs is a prospective means M, or indirectly, via its (possibly indeterministic) dependence on M, when it is a desired end E. But even here SDT, read descriptively, often makes false predictions, as experiments like those reported in Tversky and Kahneman (1982) have shown. People do sometimes act in ways which MEUP cannot explain on any consistent assignment of credences and subjective utilities, a fact which certainly counts against accepting a descriptive SDT; whereas there is a case for saying that, even if our credences in contingent states of affairs are not consistent in fact—for example, if our credences in A and in ¬A fail to add up to 1—they would be consistent if we were rational; and that supports a normative reading of SDT. One well-known argument for this normative conclusion, in the case of credences, is that unless our credences satisfy basic rules of numerical probability, we can be subjected to a Dutch Book: that is, to a combination of bets on which we are bound to lose money whatever happens. Thus if, for example, our credences in A and in ¬A do not add up to 1, there are combinations of bets on A and on ¬A, at odds which our credences in those propositions will make us accept, on which we can be made to lose money whether A is true or ¬A is. And since, as I have remarked, we must want to win bets if the shortest odds we will accept for them are to measure our credences at all, it does seem irrational to expose oneself in this way to a Dutch Book.

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And as for explicit bets, so for all actions to which SDT applies. For these too are bets, in an extended sense of betting: the sense in which, for example, stopping smoking to avoid getting cancer is betting that we will not get cancer if we do stop smoking. Here too, therefore, it seems irrational to act in ways that violate MEUP. So while the fact that we sometimes do act in such ways discredits a descriptive SDT, it seems not to discredit a normative SDT: on the contrary, since it is the normative SDT that tells us what is wrong with such actions. 5. THE CASE FOR A DESCRIPTIVE SDT That, in brief, is the argument for a normative and against a descriptive SDT. What can be said against this argument and in defence of SDT, read descriptively? I start with some quotations from Ramsey’s 1926 presentation of SDT. For although his successors have mostly taken Ramsey to have advocated SDT as a normative theory, I think, as I have said, that they are wrong. Ramsey took his SDT to be descriptive and gave good reasons for doing so, as we shall now see. First, Ramsey’s stated motivation for developing his theory, and the probability measure of belief which it provides, is that ‘it is not enough to measure probability; in order to apportion correctly our belief to the probability we must also be able to measure our belief’ (1926c: 62). In other words, we need to make sense of degrees of belief—credences—in order to explain how and why we should make those degrees match corresponding objective probabilities. And that we should do this is the only normative claim that I think Ramsey makes about credences. Next, Ramsey says that he proposes to base his measure of credences on ‘the theory that we act in the way we think most likely to realise the objects of our desires, so that a person’s actions are completely determined by his desires and opinions’ (p. 69). But this is, as Ramsey says, a ‘general psychological theory’, i.e. a descriptive theory which says, rightly or wrongly, that our desires and beliefs will in fact make us act in accordance with MEUP. How then can we defend this theory against the objections raised above, given that, as Ramsey himself admits, ‘this theory cannot be made adequate to all the facts’ (p. 69)? Ramsey’s defence of his descriptive SDT is that even if it is false, it still seems to be a useful approximation to the truth particularly in the case of our self-conscious or professional life, and it is presupposed in a great deal of our thought. It is a simple theory and one which many psychologists would like to preserve by introducing unconscious desires and unconscious opinions in order to bring it more into harmony with the facts. ( p. 69)

This why all Ramsey claims for his theory is

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approximate truth, or truth in relation to this artificial system of psychology, which like Newtonian mechanics can, I think, still be profitably used even though it is known to be false. ( p. 69)

And it is this comparison with Newtonian mechanics which I now wish to develop in more detail, to generate a fuller defence of a descriptive SDT, as follows. The reason Newtonian mechanics, like SDT, is false is that objects do not generally accelerate in precise proportion to the net forces applied to them, as Newton’s second law of motion says they do. For even neglecting relativistic effects, forces applied to objects often knock bits off them, thus reducing their effective inertial mass, while objects that accelerate in air generally drag some air along with them, thus increasing their effective mass. This means that different net forces will make any given object accelerate as if it had slightly different masses, i.e. that the mathematically convenient assumption that the masses of objects have precise values is a theoretical idealisation, an obvious falsehood which no one in practice either believes or needs to use. But this does not mean that ordinary objects do not have masses. All it means is that their masses, like their lengths, temperatures, and pressures, have interval rather than point values: intervals whose lengths can be conventionally indicated by the number of significant figures used to give those values. We all know this. No one thinks that saying an object’s mass is 75 kilogrammes means that it has a mass with a point value in kilogrammes that could be given to a million, or even to twenty, decimal places. All it means is that the result of dividing almost any of this object’s accelerations by whatever net force causes that acceleration will give a value for its mass in kilogrammes that lies between, say, 74.5 and 75.5. The important point here is that this assumes that an object’s mass, however imprecise, which is measured in this way, must still be related to its accelerations, and to the net forces on it, as Newton’s second law says. An object cannot have a mass which is not so related, since it is by this relation that masses are measured. This is not to say that an object could not fail to have a Newtonian mass: it could, and it would, if different net forces failed to accelerate it roughly in proportion to those forces. But then we could not explain its accelerations as the effect of net forces acting on its mass. So while there is an admittedly vague limit to how imprecise an object’s mass can be if that object is to have a mass at all, there is nothing vague, imprecise, or doubtful about Newton’s second law. That Newtonian masses and forces, when they exist, are related to accelerations as this law says they are is a constitutive truth of Newtonian mechanics. By this I mean what Davidson means when he says of length that ‘the whole set of axioms, laws or postulates for the measurement of length is partly constitutive of the idea of a system of macroscopic, rigid, physical objects’ (1970: 221), even though the lengths of objects can no more have absolutely precise values than their inertial masses can.

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Similarly, I say, in subjective decision theory, with credences, subjective utilities, and actions. Credences may never have point values, except where the theory requires them to be 0 or 1. In between, crediting anyone with a credence of, say, 0.67723 in any contingent proposition would be absurd; but no more so than crediting them with a mass of 74.66732896... kilogrammes. Yet as with mass and length, so the obvious imprecision of our credences does not mean that we do not have credences. All it means is that, as Levi (1980, ch. 9.8) insists, most of our credences, like the masses and lengths of most objects, have only interval values. There is of course a striking difference of degree: an object’s mass or length can often be truly stated to ten or more significant figures, whereas few if any credences can be truly stated to more than two—which I suspect is what Ramsey had in mind when he said of his theory that he had ‘not worked out the mathematical logic of this in detail, because this would, I think, be rather like working out to seven places of decimals a result only valid to two’ (1926c: 76). However, this difference of degree between credences and many physical quantities matters less than we might think, because most of the decisions we use subjective decision theory to explain are qualitative, like a decision to stop smoking. For most utilities, the relevant credences—that we will avoid getting cancer if we do smoke and if we do not smoke—need not have very precise values to explain, via MEUP, why we stop smoking. To say this is not to deny that, as with mass, there will be a somewhat vague limit to how imprecise our credence in any state of affairs A can be if there is to be such a thing as our degree of belief in A. Where there is not, that will be because many of the different possible subjective utilities which SDT says would combine with this credence to cause various actions would not in fact cause those actions. And when that happens, we cannot explain the other actions that occur instead as effects of that credence and of those utilities. Still, again as with Newton’s second law, this fact neither refutes nor renders imprecise the principle that, whenever we do have the relevant subjective credences and utilities, our actions will maximise our subjective expected utility. For as Blackburn (1998: 185) notes, just as Newtonian forces and masses cannot fail to be related to the accelerations they explain as Newton’s second law says, so credences and subjective utilities cannot fail to be related to any actions they explain as MEUP says: since it is this principle which, in SDT, gives credences and subjective utilities their measures. In short, just as Newton’s second law is a constitutive truth about Newtonian masses and forces, where they exist, so MEUP is a constitutive truth about credences and subjective utilities where they exist. This is my Ramseyan defence of a descriptive SDT, a defence and a conclusion which may indeed be made stronger still. For suppose our criterion for distinguishing actions from other events is that they can be explained by agents’ beliefs and desires or, more generally, as SDT says, by their credences and subjective utilities. If that is what it takes for an event to

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be an action, then it will be impossible for us to act in a way that is not caused by our credences and utilities roughly as SDT says. Any such apparently inexplicable actions will then show one of two things. Either they are caused by credences and utilities of which we are unaware, and even the agents may be unconscious (the possibility noted by Ramsey in one of the quotations above). Or these apparent actions are not really actions at all, but mere events, like the reflex movement of my foot when a doctor taps my knee. But whether or not this last claim is correct, two common responses to apparent actions that seem not to maximise subjective expected utility seem to me clearly mistaken. The existence of these apparently inexplicable actions does not show that the agents are irrational and a descriptive SDT is wrong. Nor, on the other hand, if we think the agents are rational, should we infer that SDT is normatively incorrect. SDT is normatively incorrect, but not for this reason. The real reason it is incorrect is, as I have argued, that it takes more than subjective credences and utilities to make it a really good idea at the time, and not just an apparently good idea, to adopt a means M to an end E.1

1 This chapter is derived from papers given to the Birkbeck College Philosophy Society in London on 18 March 2003, the Frank Ramsey Centenary Conference in Cambridge on 1 July 2003, Tokyo University on 7 October 2003, the Ramsey Conference in Paris on 24 October 2003, and the Durham University Philosophy Society on 6 November 2003. I am greatly indebted to all those who took part in the discussion of these talks.

Three Conceptions of Intergenerational Justice PARTHA DASGUPTA 1. INTRODUCTIO N How should we measure human well-being over time and across generations? In which way ought the interests of people in the distant future be taken into account when we make our own decisions today? In which ethical language should citizens deliberate over the rate at which their society ought to invest for the future? In which assets should that investment be made? What should the balance between private and public investment be in the overall investment that a generation makes for the future? Frank Ramsey’s paper of 1928 in the Economic Journal (‘A Mathematical Theory of Saving’) constructed a framework in which these questions can be asked in a form that is precise and tractable enough to elicit answers. Although very famous today, the article had no initial impact. In the years following its publication, a period now known as the Great Depression, the central economic conundrum in Western industrial countries was to find ways of increasing immediate employment. Factories and machinery lay idle, as did people. The policies that were needed then were those that would help to create incentives for employers to hire workers. This, however, was a short-term problem. With the emergence of post-colonial nations following the Second World War, long-run economic development became a focus of political interest. By the early 1960s Ramsey’s paper came to be acknowledged as the natural point of departure for exploring the normative economics of the long run. The number of trails the paper laid was remarkable. In academic economics it is probably one of the dozen most influential papers of the twentieth century. I don’t recall ever reading Ramsey’s article until preparing for the Centennial Conference on Ramsey. Classics typically don’t get read by us economists: we come to know them from subsequent developments of the subject and from textbook accounts. The paper has all the hallmarks of a classic and then some more. What has struck me most on reading the work is that it reads as though it could have been written last year. The techniques are thoroughly contemporary. Moreover, there is a self-conscious attempt at identifying a parsimonious body of assumptions that lead to the conclusions: the paper has no fat in it. Ramsey’s conception of intergenerational justice is grounded firmly on the Utilitarian calculus. In what follows, I first present an account of

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Ramsey’s formulation of the problem of optimum saving and sketch its most dramatic implications (Sections 2–4). As we will see, they look odd and are at variance with ethical intuition in plausible worlds. The theory is even incoherent in some worlds. Therefore, in Section 5 I explore one particular interpretation of a dominant alternative ethical theory, that of Rawls (1972), which defines just rates of saving to be the ones that would be ‘agreed’ upon by all generations behind a veil of ignorance—the hypothetical social contract. In keeping with Rawls’s reading of what members of a given generation would agree to be a just intragenerational distribution of resources, I take the Rawlsian principle of just saving to recommend maximising the well-being of the least well-off generation—the Difference Principle.1 I show that, in plausible worlds, the implications of Rawls’s theory are very odd and are at variance with both ethical intuition and actual, reflective practice. So, in Section 6, I turn to a formulation of the concept of justice among generations that was developed by a great twentieth-century economist, the late Tjalling Koopmans. Koopmans was moved to reformulate the problem of intergenerational justice because of the latent incoherence in Ramsey’s conception, mentioned above. Although Ramsey’s and Koopmans’s conceptions lie at different interpretative ends (Rawls would call the former ‘teleological’, the latter ‘intuitionist’), Koopmans (1960, 1972) showed that, mathematically, the two are very similar and that Ramsey’s techniques for identifying optimum rates of investment are usable in his own formulation (Koopmans 1965). In Section 6 I confirm that Koopmans’s formulation is sufficiently flexible to permit us to derive conclusions that do not jar against considered judgement. The common mathematical structure of Ramsey’s and Koopmans’s conceptions has been found to have wide applicability—so wide that within modern economics there is no rival formulation for evaluating the intergenerational distribution of benefits and burdens. Today, we economists who work on the concept of justice among the generations refer to that overarching mathematical structure as the Ramsey–Koopmans construct, even though the interpretation we give to that mathematical structure is the one advanced by Koopmans. It is a significant feature of Koopmans’s conception that the well-beings of future generations are discounted at a positive rate. This has been regarded by many to be cause for concern. In Section 7 I argue otherwise. In Section 8 I show, more generally, that the obsession in both the philosophy and economics literatures over the question of whether it is ethically justifiable to discount the well-beings of future generations has been misplaced. Koopmans’s formulation shows that there are at least two 1 Rawls (1972) uses the language of ‘primary goods’, not utility, nor well-being. At this point I am regarding well-being as an index of Rawlsian primary goods.

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ethical parameters that reflect considerations of intergenerational equity, the discount rate being one. There is, however, another parameter, that is in some sense dual to discounting, in that many of the demands made by considerations of intergenerational equity that can be achieved by manipulating the discount rate can also be achieved by manipulating the other parameter. That Koopmans’s conception insists on positive discounting would, therefore, seem to be of less moment than it has been taken to be. For ease of comparison among the formulations of Ramsey, Rawls, and Koopmans, I shall assume, until Section 9, that population is constant and that societies face no uncertainty. So, in Sections 9 and 10, I extend Koopmans’s formulation to include population change and uncertainty, respectively. The main conclusions are summarised in Section 11. 2. GENERAL FEATURES OF RAM SE Y’S FORMUL ATION In his 1928 paper Ramsey’s goal was practical: ‘How much of a nation’s output should it save for the future?’ In answering the question, he adopted a thoroughly Utilitarian posture. (For example, Ramsey used the term ‘enjoyment’ to refer to the content of someone’s utility.) The article embodies the sort of ethical deliberation Sen and Williams (1982) somewhat disparagingly called Government House Utilitarianism. But Ramsey’s article thrives today because Government Houses need ethical guidance that isn’t a prop for paid Officials to act in ways that are self-indulgent, but are, instead, impartial over people’s needs and sensitivities. We will see presently that, although Ramsey used the Utilitarian language, a generous reading of his paper suggests that much would be gained if, instead of ‘utility’, we were to work with the broader notion of ‘well-being’. The raw ingredients of Ramsey’s theory are individuals’ lifetime wellbeings. Now, intergenerational equity isn’t the primary concern of Ramsey’s: the Government House in Ramsey’s world maximises the sum of the wellbeings of all who are here today and all who will ever be born. The just distribution of well-being across generations is derived from that maximisation exercise. Of course, the passage of time is not the same as the advance of generations. An individual’s lifetime well-being is an aggregate of the flow of well-being she experiences, while intergenerational well-being is an aggregate of the lifetime well-beings of all who appear on the scene. It is doubtful that the two aggregates have the same functional form. On the other hand, I know of no evidence that suggests we would be way off the mark in assuming they do have the same form. As a matter of practical ethics, it helps enormously to approximate by not distinguishing the functional form of someone’s well-being through time from that of intergenerational wellbeing. Ramsey adopted this short cut and took it, in particular, that the method of aggregation should be summation.

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We assume that the demographic profile over time is given. The resource allocation problems Ramsey studied are those that arise when we try to strike a balance between the well-beings of present and future generations, keeping in mind that there is a corresponding set of allocation problems arising from the need to strike a balance in every person’s lifetime wellbeing. Parfit (1982) christened allocation problems involving the same demographic profile Same Numbers Problems. The thought is not that population size doesn’t change, but that the policies being studied are those that have a negligible effect on reproductive behaviour. 3. RAMSEY’S THEORY OF OPTIMUM SAVIN G Let t denote the date at which the saving problem is being deliberated. I shall use the symbol
to denote dates not earlier than t (that is,
 t). For notational ease, it helps to interpret the period between adjacent dates as the length of a generation. One can imagine that at the end of each period the existing generation is replaced entirely by its successor. This isn’t good demography, but it turns out not to matter. Every ethical consideration that emerges in this model makes an appearance also in worlds where demography is modelled better. Moreover, better models of demography would not raise any ethical issue that doesn’t appear here. Population size is assumed to be constant and the future is taken to be indefinitely long. I first consider a deterministic world. Later I relax these assumptions. In order to focus on intergenerational issues, I ignore matters concerning the distribution of intragenerational well-being. (If it helps, the reader could without loss of generality imagine that each generation consists of a single person.) So I let Ut denote generation t’s level of well-being. We may imagine that t’s well-being is an increasing function of t’s aggregate consumption, C (which I label as Ct ), but that it increases at a diminishing rate. Thus, we write Ut = U(Ct ), where the function U(C) satisfies the properties dU/dC > 0 (which we may write succinctly as U(C) > 0) and d2U/dC2 < 0 (which we may write succinctly as U(C) < 0). Being a Utilitarian, Ramsey regarded intergenerational well-being to be the sum of each generation’s well-being.2 2 It is an elegant feature of Ramsey’s formulation that he avoided specifying a subsistence rate. For technical reasons, he assumed that U has a least upper bound ( lub), but that the lub is beyond reach no matter how high is consumption. He called the lub ‘bliss’! U is assumed not to depend explicitly on time. This looks odd until we ask in which ways it is likely to change. The fact is, we don’t know. Certain obvious thoughts—for example, that the baskets of consumption goods and services that are needed today to attain a given level of well-being differ from those needed to attain the same level of well-being a hundred years ago—offer little reason for thinking that U depends explicitly on time. Admittedly, today’s necessities are different from necessities a hundred years ago. But the change could have come about because of shifts in the technology of consumption (e.g. if all others communicate over the telephone, one loses out in not using the telephone).

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From the vantage of generation t, let (Ct , Ct +1, ...) be a consumption stream, which is a sequence of aggregate consumption from t onward. Denoting intergenerational well-being at t by Vt , Ramsey’s theory has it that, Vt = U(Ct ) + U(Ct +1 ) + ... , which I write succinctly as 

(1)

Vt =  U(C), for t  0.3 =t

In words, intergenerational well-being at t is the sum of every generation’s well-being, starting at t. The theory regards bygones to be bygones. Let the present generation be t = 0. Generation 0 has inherited from its predecessors a wide range of capital assets, including not only manufactured assets (roads and buildings and machinery) and knowledge and skills (mathematics and the ability to do mathematics), but also natural capital (oil and natural gas, rivers and lakes, watersheds and wetlands, the atmosphere and the oceans, and ecosystems generally). Given this inheritance, generation 0 is able to identify the set of consumption streams (starting at t = 0) that are feasible. As Ramsey would have it, generation 0’s problem is to identify within the set of feasible consumption streams the one that maximises V0. The account in its entirety is as follows: Generation 0 has inherited from its predecessors a wide array of capital assets. Given this inheritance, it is faced with a feasible set of consumption streams. Call this feasible set
0. From generation 0’s vantage, a typical consumption stream reads as (C0, C1, ..., C, ...). Imagine now that (0, 1, ..., , ...) is that member of
0 which maximises V0. Ramsey’s theory calls upon generation 0 to consume 0. This simultaneously yields an investment decision (output minus what is consumed), which adds to, or subtracts from, the various capital assets generation 0 had inherited, which in turn determines the economic possibilities that are open to generation 1. Denote the set of feasible consumption streams for generation 1 to be
1. A typical member of
1 can be written as (C1, C2, ..., C, ...).4 The problem to be faced by generation 1 will be to identify that element of
1 that maximises V1. It is an interesting and important feature of expression (1) that generation 1 would identify the optimum consumption stream to be (1, 2, ..., , ...).5 3





is the summation sign, from t to infinity. Thus, in equation (1),  signifies dates that

=t

go from t to infinity. 4 Note that the first element of the sequence is generation 1’s consumption. 5 Looking backward, therefore, it would reason that generation 0 had ‘done the right thing’ by consuming 0. Note too that generation 1 would find it optimum to choose the level of consumption generation 0 had planned for it, namely, 1.

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Plainly, then, generation 1 would consume 1, invest accordingly, and pass on the optimum stocks of capital assets to generation 2. Denote the set of feasible consumption streams for generation 2 to be
2. A typical member of
2 can be written as (C2, C3, ..., C, ...).6 The problem to be faced by generation 2 will be to identify that element of
2 that maximises V2. It is an interesting and important feature of expression (1) that generation 2 would identify the optimum consumption stream to be (2, 3, ..., , ...).7 Plainly, then, generation 2 would consume 2, invest accordingly, and pass on the optimum stocks of capital assets to generation 3. And so on. The ethical viewpoints of the succeeding generations are congruent with one another. Each generation chooses its level of consumption and leaves behind capital assets that can sustain the subsequent stream of consumption levels that it deems to be just, aware that succeeding generations will choose in accordance with what it had planned for them. In modern game-theoretic parlance, Ramsey’s optimum consumption stream is a so-called ‘noncooperative’ Nash equilibrium among the generations. If expression (1) is the coin by which generation t interprets intergenerational well-being (for all t  0), and if every generation can be expected to choose ethically, then there is no need for an intergenerational ‘contract’. That it is not possible for the generations to devise a binding agreement among themselves is of no moment. 4. PROBL EMS WITH INFINITE HORIZON A ND NO DISCOU NTIN G Ramsey’s assumption that the future is infinite feels odd. We know that the world will cease to exist at some date in the future. So it would seem realistic to stipulate a finite horizon, say T periods, where the chosen T is large. The problem is that no matter how large T is, there is some chance that the world will survive beyond T. So, an alternative to Ramsey suggests itself: specify the capital stocks that are to remain at T for generations still to appear, and regard intergenerational well-being to be the T-period sum of well-beings and the size of the capital base remaining at T. There is a problem even with this formulation. If T and the capital base that remains at T are chosen arbitrarily, the consumption stream deemed the best could be sensitive to that choice. This means that T and the capital stocks at T should not be chosen arbitrarily, but should be based on our understanding of what lies beyond T (for example, the needs of those who may appear after T). But then, why not include their claims in the ethical 6 7

Note that the first element of the sequence is generation 2’s consumption. Looking backward, therefore, it would reason that generations 0 and 1 had ‘done the right thing’ by consuming 0 and 1, respectively. Note too that generation 2 would find it optimum to choose the level of consumption generations 0 and 1 had planned for it, namely, 2.

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exercise to begin with; why truncate the future into two bits? The route Ramsey followed, of regarding the future to be indefinitely long, is logically unavoidable; for, although we know that the world will not exist for ever, we don’t know when it will cease to exist. I want to leave aside for the moment the question whether Vt in expression (1) is well defined. (The infinite sum may not, after all, exist; see below.) The point to which I want now to draw attention is that in Ramsey’s formulation, as reflected in expression (1), future values of U are undiscounted. (Formally, Vt is symmetric in its arguments.) More than any other feature of his theory, it is this that has provoked debate among economists and philosophers. Ramsey himself wrote (1928: 261) that to discount later Us in comparison with earlier ones is ‘ethically indefensible and arises merely from the weakness of the imagination’. Harrod (1948: 40) followed suit by calling the practice a ‘polite expression for rapacity and the conquest of reason by passion’.8 What would Utilitarianism with positive discounting of future well-beings look like? Let  (>0) be the rate at which it is deemed desirable to discount future well-beings. Then, in place of expression (1), intergenerational wellbeing at t would be 

(2)

Vt =  U (
t ), =t

for t  0,where   1/(1+ ) < 1. In expression (2),  is the discount rate and  is the resulting discount factor.9 To some economists, Ramsey’s stricture forbidding the discounting of future well-beings reads like a Sunday pronouncement. Solow (1974a: 9) expressed this feeling when he wrote, ‘In solemn conclave assembled, so to speak, we ought to act as if the [discount rate on future well-beings] were zero.’ But there is a deeper problem with the stance. In such complex exercises as those involving the use of resources over a very long time horizon, in a world where investment in capital has a positive return (the latter reflecting an in-built bias in favour of future generations), it is foolhardy to regard any ethical judgement as sacrosanct. This is because one can never 8 Their position has been re-examined and endorsed by a number of modern philosophers; see Feinberg (1980) and Broome (1992). For wide-ranging discussions among economists on this question, see Lind (1982) and Portney and Weyant (1999). 9 The discount rate in expression (2) is constant. Arrow (1999) has appealed to agentrelative ethics to explore the consequences of using a variable discount rate. The variation he explored arises from the idea that each generation should award equal weight to the wellbeings of all subsequent generations, but should award its own well-being a higher weight relative to that awarded to the subsequent generations. In this chapter I am exploring the concept of intergenerational well-being, an essential ingredient in Government House Ethics. It is doubtful that agent-relative ethics would be appropriate for such exercises as Government House would be required to conduct.

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know in advance what it may run up against. A more judicious tactic than Ramsey’s would be to play off one set of ethical assumptions against another in not implausible worlds, see what their implications are for the distribution of well-being across generations, and then appeal to our intuitive senses before arguing over policy. The well-being discount rate may well be too blunt an instrument to settle questions of intergenerational equity. Consider, for example, the following ethical tension: (A) Low rates of consumption by generations sufficiently far into the future would not be seen to be a bad thing by the current generation if future well-beings were discounted at a positive rate. It could then be that, by applying positive discount rates, the present generation finds it acceptable to save very little for the future—it may even find disinvestment to be justifiable. But if that were to happen, the demands of intergenerational equity would not be met. This suggests that we should follow Ramsey and not discount future wellbeings. (B) As there are to be a lot of future generations in a world that faces an indefinite future and where the return on investment is positive, not to discount future well-beings could mean that the present generation would be required to do too much for the future; that is, they would have to save at too high a rate. But if that stricture were to be obeyed, the demands of intergenerational equity would not be met. This suggests that we should abandon Ramsey and discount future well-beings at a positive rate. The force of each consideration has been demonstrated in the economics literature. It has been shown that in an economy with exhaustible resources and ‘low’ productive potentials for manufactured capital assets, optimum consumption declines to zero in the long run if the future well-beings are discounted at a positive rate, no matter how low the chosen rate is (Dasgupta and Heal 1974), but increases indefinitely if we follow Ramsey in not discounting future well-beings (Solow 1974b). This finding was the substance of Solow’s remark (Solow 1974a), that, in the economics of exhaustible resources, whether future well-beings are discounted can be a matter of considerable moment. In recent years environmental and resource economists writing on sustainable development have taken this possibility as their starting point (e.g. Bromley 1995). On the other hand, if the Ramsey requirement, that future well-beings are not discounted, is put to work in a close variant of the model economy Ramsey himself studied in his paper, it recommends that every generation should save at a very high rate. For classroom parameterisations, the optimum saving rate has been calculated to be in excess of 60 per cent of gross national product. In a poor country such a figure would be unacceptably high, requiring the present generation to sacrifice beyond the call of

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duty.10 The real problem is that no one, not even Ramsey, could be expected to know in advance how to capture the right balance between the claims of the present generation and those of future ones. The issues are far too complex, especially in infinite horizon models. Unaided intuition is suspect. Rushing to Utilitarianism with no discounting can be treacherous. What the quantitative exercises in Dasgupta and Heal (1974) and Solow (1974b) tell us is that the long-run features of optimum saving policies depend on the relative magnitudes of the rate at which future well-beings are discounted and the long-term productivity of capital assets. In fact there is a deeper problem with Ramsey’s stricture that future wellbeings should not be discounted. Koopmans (1965) showed that consideration B can even overwhelm the stricture and render expression (1) incoherent. Zero discounting can imply that there is no best policy; that, no matter how high is the rate of saving, saving a bit more would be better. To see how and why, imagine a world where goods are completely perishable. Consider an economic programme where consumption is the same at every date. Now imagine that an investment opportunity presents itself in which, if the present generation were to forgo a unit of consumption, a perpetual stream of additional consumption µ (>0) would be generated.11 Suppose intergenerational well-being is represented by expression (1). Then, no matter how small is µ, future generations, taken together, would experience an infinite increase in well-being as a consequence of the investment, the reason being that µ ‘multiplied’ by infinity is infinity. So, for any level of consumption, no matter how low, a further reduction in consumption (possibly short of a reduction that brings consumption down to zero) would be desirable. As a piece of ethics, this is clearly unacceptable. Ramsey’s conception simply does not do. 5. RAWLSIAN SAV IN G In the philosophical literature the only rival to Ramsey’s Utilitarian principle of optimum saving is probably the principle of just saving in Rawls (1972). In fact, though, Rawls doesn’t have much of a theory of just saving. The first half of his second principle of justice, emanating from choice behind the veil of ignorance (the ‘original position’), alludes to a just savings principle (Rawls 1972: 302), but he gets nowhere with it (Arrow 1973; Dasgupta 1974, 1994). For example, he writes: 10 As a matter of comparison, it should be noted that saving rates in the United Kingdom and the United States are in the range 10–15 per cent of their gross national products. Interestingly, the fast-growing poor countries of the world in the 1970s (Taiwan, South Korea, and Singapore) routinely saved at rates in the range 40–5 per cent of their gross national products. 11 This means that the rate of return on investment is µ. The example has been taken from Arrow (1999).

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The parties do not know to which generation they belong . . . Thus the persons in the original position are to ask themselves how much they would be willing to save . . . at any given phase of civilization with the understanding that the rates they propose are to regulate the whole span of accumulation . . . Since no one knows to which generation he belongs, the question is viewed from the standpoint of each and a fair accommodation is expressed by the principle adopted. ( Rawls 1972: 287)

But this says nothing of import; it is merely a requirement of intergenerational consistency, namely, that each generation should find it reasonable to save at the rate that was agreed upon in the original position. But we are not told what could be expected to be agreed upon. If Rawls’s Difference Principle, which is all-important in the rest of his book, were applied to the saving problem, then for all consumption streams {C0, C1, C2, ..., C
, ...}, the Rawlsian Vt would be (3)

Vt = inf{U(Ct ), U(Ct +1 ), ...},

where ‘inf’ means ‘greatest lower bound of’. The problem with this conception is that if savings yielded a return, there would be no ethical motivation to save: a positive rate of saving, no matter how low, would mean that the present generation would be worse off than all future generations, an inequity that it could prevent by not saving at all! Rawls recognised the problem. So he altered the motivation assumption of individuals and wrote: The process of accumulation, once it is begun, and carried through, is to the good of all subsequent generations. Each passes on to the next a fair equivalent in real capital as defined by a just savings principle . . . Only those in the first generation do not benefit . . . for while they begin the whole process, they do not share in the fruits of their provision. Nevertheless, since it is assumed that a generation cares for its immediate descendants, as fathers say care for their sons, a just savings principle . . . would be acknowledged. ( Rawls 1972: 288; emphasis added)

One could take Rawls to mean by this that generation t’s well-being depends not only on its own consumption level, but also on its descendants’ consumption levels. Arrow (1973) and Dasgupta (1974) proved that if parental concerns extend only to a finite number of descendants, the Difference Principle either implies that no generation should do any saving (this would be so if the natural concern for descendants is ‘small’), or recommends a programme of savings and dissavings that would be revoked by the generation following any that were to pursue it (this would be so if the natural concern for descendants is not ‘small’). The latter would mean that Rawlsian savings policies are intergenerationally inconsistent. On the other hand, if parental concern were to extend to all descendants, the Rawlsian formulation would look similar to Ramsey’s (expression (1)), albeit with possible discounting (expression (2)). However, the infinite sum would now represent a generation’s well-being, not intergenerational wellbeing. Given that the Difference Principle is to apply, the Rawlsian recommendation would be that the rate of saving should be zero: any

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saving, whether positive or negative, would create inequity across the generations. In short, what Rawls has offered us is either mean-spirited (no saving at all) or intergenerationally inconsistent. So we must look elsewhere for a theory of just saving. 6. THE KOOPMANS CONSTRUCT In a classic article Koopmans (1960) adopted a different research tactic from that of Ramsey.12 Intergenerational well-being in Ramsey’s theory is the sum of well-beings (expression (1)). The ethical comparisons of infinite consumption streams in Ramsey’s theory is derived from the sum of wellbeings. In contrast, the primitive concept in Koopmans’s formulation is that of an ordering of infinite well-being streams.13 Koopmans’s tactic was to impose ethical conditions on such orderings and to determine, if possible, the form of their numerical representations. Intergenerational well-being in Koopmans’s theory is a numerical representation of an ordering of infinite well-being streams.14 An ordering is said to be continuous if, in an appropriate mathematical sense, well-being streams that don’t differ much are close to one another in the ordering. For an ordering to be monotonic, it is meant that a given stream of well-beings is regarded as being more just than another if no generation experiences less well-being along the former than along the latter and if there is at least one generation that enjoys greater well-being in the former than it does in the latter. Continuity is a compelling assumption. But even monotonicity is compelling, since it says that a just distribution of wellbeings should not be an inefficient distribution of well-beings.15 Imagine that the problem of intergenerational justice is being deliberated by generation 0. To see what the term ‘discounting’ means when the primitive is an ordering of well-being streams, consider two streams, {U0, U1, U2, ..., U
, ...} and {U1, U0, U2, ..., U
, ...}, that are identical except for the well-beings of generations 0 and 1, which are interchanged. Now 12 13

See also Koopmans et al. (1964); Diamond (1965). In a subsequent work (Koopmans 1972), the primitive was a consumption stream. But for ease of exposition, I report his earlier formulation. In order to avoid technicalities, I also cut corners in the account that I offer; nothing of moment will be lost by my doing so. To remind the reader, by an ordering on a set of objects, X, we mean a binary relation, R, among the objects that is reflexive (for all x in X, xRx), transitive (for all x, y, and z in X, if xR y and yRz, then xRz ), and complete (for all x and y in X, either xR y or yRx), where R is interpreted as, say, ‘at least as good as’ or ‘no less just than’. 14 Let R be an ordering of the elements of a set X. Let V be a numerical function on X. This means that V awards a numerical value to each element of X. We say that V is a numerical representation of R if, for all x and y in X, V(x)  V( y) if and only if xR y. 15 Even Rawlsian justice is efficient in the production and distribution of what Rawls called primary goods.

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suppose that U1 > U0. Positive discounting of future well-beings means that {U1, U0, U2, ..., U, ...} should be judged to be more just than {U0, U1, U2, ..., U, ...}. Diamond (1965) proved that if an ordering of infinite streams of well-being satisfies continuity and monotonicity, it must involve a positive discounting of future well-beings. If you think this result is stunning, you will find the following to be no less so. To motivate it, consider two further ethical assumptions, which Koopmans (1960, 1972) christened separability and stationarity, respectively. The former is familiar from expected utility theory, where it is applied to states of nature, rather than time. In the present context, it says that the ethically permissible trade-off between the well-beings of any pair of generations is independent of the well-beings of all other generations. The Stationarity Axiom, however, may be novel to philosophers; but it is merely a strong rendering of the idea that ethical principles should be universalisable. The axiom states that the ordering of a set of infinite well-being streams should be the same no matter which generation ranks the elements of that set. Generations should assume the same ethical perspective as and when they come on the scene: their time of arrival should not matter.16 Koopmans (1972) showed that if, in addition to continuity and monotonicity, an ordering on well-being streams satisfies separability and stationarity, its numerical representation is of the form 

(4)

Vt = G(U )(
t ), for t  0, =t

where   1/(1+  ), with  > 0, where G is a monotonically increasing function of U. Notice that the numerical representation of the ordering is not unique, because G is unique only up to a positive affine transformation.17 In 16

Formally, the axioms are: Intergenerational Separability: If {U0, U1*, U2*, ..., U*, ...} is judged to be ethically at least as good as {U0, U1*, U2*, ..., U*, ...}, then this judgement is independent of the reference stream ( U1*, U2*, ..., U*, ...), where the reference stream awards U1* to generation 0, U2* to generation 1, and so on. Stationarity: For all {U0*, U1*, U2*, ..., U*, U+1*, ...}, if {U0*, U1*, U2*, ..., U*, U+1, U+2, ...} is judged to be ethically at least as good as{U0*, U1*, U2*, ..., U*, U+1, U+2, ...}, then {U+1, U+2, ...} should be judged to be ethically at least as good as {U+1, U+2, ...}. In other words, the ranking of a pair of streams that are identical over the first  +1 generations should be the same as the ranking of the pair that is constructed by deleting the first  +1 periods’ well-beings from both and by bringing forward the subsequent well-beings by  +1 periods. But this can be shown to amount to saying that the perspective that ought to be adopted by generation  +1 is the same as the one that ought to be adopted by generation 0. 17 Thus, if expression (4) is a numerical representation of the ordering, then it would remain so if G were replaced by (a G + b ), where a and b are constants and a > 0.

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expression (4),
is the well-being discount rate. While expression (4) looks identical to Classical Utilitarianism with discounting (expression (2)), it is not. Even if U were to be interpreted as ‘utility’, G(U) should not be so interpreted: G is a monotonically increasing function of U. If, instead, U were to be interpreted more widely as well-being (as we are interpreting it here), the function G would reflect the manner in which different levels of well-being are traded off against one another in the ethical reckoning. This means that G is a measure of the extent to which intergenerational equity in well-beings is accommodated in the ordering, a matter to which I return in Section 8. It will be noticed that Koopmans’s axioms, on their own, are unable to determine the numerical value of
; nor are they able to specify the functional form of G (barring the fact that it is monotonically increasing). This open-endedness makes Koopmans’s formulation particularly attractive. The formulation ties down the concept of intergenerational well-being, but it doesn’t tie it down unduly; it leaves open the door for further ethical deliberations. In practical applications, Koopmans’s formulation allows us to conduct conceptual experiments. It possesses sufficient degrees of ethical freedom (in the choice of the number
and the function G) to iterate between the possible and the desirable to arrive at what Rawls (1972) called a ‘reflective equilibrium’. It is an agreeable feature of Koopmans’s theory that, as in Ramsey’s theory, the ethical viewpoints of succeeding generations are congruent with one another. Each generation chooses that policy it deems just, aware that succeeding generations will choose in accordance with what it had planned for them. 7. A POSSIBLE WEAKNESS IN KOO PMANS’S FORMULATION But there is a seeming problem with (4) as an expression of intergenerational well-being: it is vulnerable to what I earlier called consideration A. It is easy to construct possible worlds where Koopmans’s ethical axioms regard as most desirable a consumption stream that declines to zero in the long run (Dasgupta and Heal 1974). The question is whether we should find this troubling. I argue that we should not. Imagine that we adopted Koopmans’s formulation of intergenerational well-being (expression (4)), applied it to a deterministic model of production and consumption possibilities, and discovered that if the discount rate
is positive, the just consumption level will decline to zero in the long run, no matter how small
happens to be. Suppose it is also discovered that if
is sufficiently small (but not zero), the decline in consumption will begin only in the distant future—the smaller is
, the

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farther is the generation that will experience a lowering of consumption.18 Should Koopmans’s formulation be rejected on the ground that it recommends an eventual decline in consumption? Many would reject it on that very ground,19 but I have never understood why. Models of a deterministic world with an infinite horizon are mathematical artefacts. They are meant to train our intuitions about economic possibilities in a world with a long, but finite, horizon, when we are loath to specify the termination date, and are also loath to acknowledge that it as an uncertain date. The models must not be taken literally, because Earth will not last for ever. We cannot, of course, know now when Earth will cease to exist, but we do know that it will cease to exist by some date, say, 1012 years. (That’s 1 trillion years; and Earth is a bit over a mere 4 billion years old.) Suppose, for example, that we were to set  equal to 10
n per generation and were to choose n sufficiently large, so that the just consumption level in the kind of deterministic model I have been considering would have a turning point for, say, generation 1030 (that’s a billion billion trillion generations). Should we care that consumption in the model will decline for generations 1030 onward? I know of no reason why we should. On the contrary, justice would be ill served if all generations were asked to save for a posterity that won’t appear. As an articulation of the concept of intergenerational wellbeing, Koopmans’s theory would seem to be compelling. 8. ETHICAL DUAL ITY I noted in Section 6 that  is not the only free parameter in Koopmans’s formulation: the function G(U) is another. The two together determine the rates at which the well-beings of different generations are traded off against one another in expression (4). Now G is an increasing function of U, meaning that G(U) > 0. It can be shown that if equity in the intergenerational distribution of well-beings is taken to be a commendable feature of such distributions, then G(U) must be negative, which is to say that G must be a strictly concave function (Kolm 1969; Atkinson 1970). It is also easy to prove that, other things being equal, the greater is the concavity of G, the greater is equity favoured in the ethical theory underlying expression (4). I demonstrate below that there is a sense in which  and G are dual to each other, that aspects of the concept of equity among the generations that can be captured in the number  can also be caught in the function G(U). To see this, consider a world where the rate of return on investment is a constant, µ, per generation. We imagine that capital assets are productive. 18 As noted earlier, this has been shown to be the case in simple economic models involving exhaustible resources. See Dasgupta and Heal (1979, ch. 10). 19 For example, Heal (1998). Earlier, I called it consideration A.

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Therefore, µ > 0. As in Section 3, I assume that generation t’s well-being is an increasing function of its consumption level (Ct ), but that it increases at a diminishing rate, meaning that U(C) is positive and U(C) is a strictly concave function (U(C) < 0). Define H(C) = G(U(C)). Since G(U) is an increasing and strictly concave function also, it must be that H is an increasing and strictly concave function of C. Thus, H(C) > 0 and H(C) < 0. For expositional ease, I now focus on the question of equity among the generations in the distribution of consumption, rather than wellbeing. The theory of inequality measures has taught us that the correct index of the degree of concavity of H with respect to C is the absolute value of the percentage rate of change in H(C). Let  be that measure. Then we have (5)

(C) =
CH(C)/H(C) > 0.

(C) is called the elasticity of H(C). The theory of inequality measures has taught us that the larger is (C), the more equality-regarding is the concept of intergenerational well-being in expression (4). Since  is defined at each value of C,  is a local measure, which means that in general  is a function

of C. Now consider generation 0’s ethical problem. It has inherited from its predecessors a wide array of capital assets. Given this inheritance and the fact that the rate of return on capital investment is µ, it is faced with a feasible set of consumption streams, which, as in Section 3, I label as 0. From generation 0’s vantage, a typical consumption stream reads as (C0, C1, ..., C, ...). Imagine now that (0, 1, ..., , ...) is that member of 0 which maximises V0, where V0 is given by expression (4), with t = 0. Ramsey (1928), Koopmans (1965), and others have shown that the optimum consumption stream (0, 1, ..., , ...) must be a solution of the equation (6)

µ =  + (Ct )g(Ct ),

where g(Ct ) is the percentage rate of change in consumption between the consumption levels enjoyed by generations t and t+1. Equation (6) is fundamental to intergenerational ethics. It has a simple interpretation. µ is the rate of return on investment, meaning that it is, at the margin, the percentage rate at which consumption can feasibly be exchanged among successive generations, t and t+1 (t  0). The right-hand side of equation (6) can be shown to be the percentage rate at which, at the margin, it is ethically permissible to exchange consumption among the successive generations t and t+1 (see e.g. Arrow and Kurz 1970; Dasgupta and Heal 1979). If the two expressions were not equal, an appropriate reallocation of consumption between t and t+1 would increase V0. Therefore, the consumption stream deemed just must satisfy equation (6), and it must satisfy the equation for every t  0. In the language of social cost–benefit analysis, the right-hand side of equation (6) is the social rate at which future consumption

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ought to be discounted (in contrast to future well-beings, which are discounted at the rate ). There is an attractive class of functional forms of H(C) for which equation (6) simplifies enormously. Consider the form (7)

H(C) = B
C
(
1),

where B > 0 and  > 1.20 If H(C) satisfies formula (7), the elasticity of H(C), which is (C), is independent of C. In the economics literature, formula (7) is ubiquitous. As we see below, it offers a most instructive laboratory for conducting thought experiments. On using expression (7) in equation (6) and rearranging terms, we obtain (8)

g(Ct ) = ( µ
 )/ .

For vividness, imagine that  is chosen to be less than µ. Equation (8) tells us that, since the right-hand side is a positive constant, justice demands that consumption should increase at the exponential rate (µ
)/. Notice though that, as  and  are two free ethical parameters in Koopmans’s theory, that same growth rate would be implied by an infinite family of (, ) pairs. Presumably, a concern for equity in consumption among the generations would lead us to insist that g(Ct ) should not be too large. Otherwise, earlier generations would enjoy far lower consumption levels than later generations. Lowering the right-hand side of equation (8) would flatten the optimum consumption stream somewhat. But just as g(Ct ) would have a low value if, other things being equal,  were chosen to be nearly µ, the same low value would be realised if, other things being equal,  were chosen to be large. This is the sense in which  and  are ethically dual to each other. 9. POPULATION GROWTH As Earth is finite, changes in the size of population, when averaged over time, must be zero over the very long run. The base case we have been considering so far, that population size remains constant, is thus valid when the reckoning is the very long run. But for the not so very long run, population can be expected to change. What is the right concept of intergenerational well-being when population size is expected to change over time? Two alternatives have been much discussed in the literature. Both reduce to expression (4) if population is constant. After presenting them I introduce a third conception, which has been shown to be the natural one to 20 The constant B plays no role, in view of what was mentioned in note 16. I have introduced it, nonetheless, in case the reader feels that H(C ) ought to be negative for very low values of C, but positive for sufficiently large values of C.

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adopt when we try to formulate the concept of sustainable development (Dasgupta 2001). It too reduces to expression (4) if population is constant. One alternative is to regard the well-being of a generation to be the per capita well-being of that generation (with no allowance for the numbers involved) and sum the per capita well-beings of all generations, possibly using a discount rate. To formalise, imagine for simplicity that members of the same generation are awarded the same consumption level. Let U be the well-being of the representative person in generation . We then have (Cass 1965; Koopmans 1965) 

(9)

Vt =  G(U )(
t ), for t  0, =t

where   1/(1+  ), and  > 0. The other view is to regard intergenerational well-being to be the sum of the discounted flow of each generation’s well-being. Specifically, if N is the size of generation , then (Meade 1955; Mirrlees 1967; Arrow and Kurz 1970): 

(10)

Vt =  N  G(U )(
t ), for t  0, =t

where   1/(1+  ), and  > 0. Expression (9) regards generations, not people, to be the claimants. In contrast, expression (10) regards people, not generations, to be the claimants. Koopmans’s ethical axioms, when applied to the case where generations are regarded as the claimants, yield expression (9); they yield expression (10) if people are regarded as the claimants. Which is right? To answer, it pays to study the ways in which their recommendations differ. Imagine an economy consisting of two islands, with populations N1 and N2, respectively. People are assumed to be identical. A person’s well-being is denoted by U, which increases with consumption, but at a diminishing rate. There are a fixed amount of consumption services, C, that the government is to distribute.21 Let C1 and C2 be the amounts distributed to the two islands. We take it that, no matter how much were awarded to each island, the distribution of consumption within each would be equal. The economy is timeless. If numbers count, then analogous to expression (10), social well-being would be [N1U(C1/N1) + N2U(C2/N2 )] and the government would distribute C in such a way that consumption is equalised among all citizens.22 This is obviously the right allocation, because geographical differences are 21 22

The example is taken from Meade (1955: 87–9) and Arrow and Kurz (1970: 13–14). To prove this, simply maximise [N1U(C1/N1) + N2U(C2/N2 )] by suitable choice of C1 and C2, subject to the constraint C1 + C2 = C.

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an artefact for the problem in hand. On the other hand, if numbers don’t count, so that social well-being is taken to be [U(C1/N1) + U(C2/N2 )], the government should distribute less to each person in the more populous island,23 which is to say that the use of expression (9) discriminates against more numerous generations. This simply cannot be right. Extending this example to the case of a sequence of generations, we conclude that, of expressions (9) and (10), it is the latter that reflects the notion of intergenerational well-being. Expression (10) measures total (discounted) well-being. But there is another formulation of the concept of intergenerational well-being which is equally compelling. It is the average well-being of all who are to appear on the scene: (11)





=t

=t

Vt = (  N  G(U )(
t ) )/(  N  (
t ) ),

for t  0, where   1/(1+  ), and  > 0.

Notice that, since 

 N  (
t ) =t

is a positive constant, expressions (10) and (11) are numerical representations of the same underlying ordering of infinite streams of well-being. Koopmans’s axioms, when applied to the ethical sensibility that regards people to be the claimants, simultaneously yield expressions (10) and (11). This implies that, as conceptions of justice among the generations, there is nothing to choose between total well-being (expression (10)) and average well-being (expression (11)). A policy deemed to be just if expression (10) were used as the criterion of choice would also be judged to be just if instead expression (11) were used as the criterion of choice. In this sense, the two expressions would amount to the same. However, Arrow, Dasgupta, and Mäler (2003a,b) have shown that the two expressions would have different implications if they were used to decide whether a policy leads to an outcome where intergenerational wellbeing is sustained. In particular, it can be shown that expression (11) is the more natural formula to use in discussions of sustainable development (Dasgupta and Mäler 2000; Dasgupta 2001). Justice and sustainability are different concepts, serving different purposes. In the following section I use expected utility theory as the basis of choice behind Rawls’s veil of ignorance to provide an alternative interpretation of expression (11). 23 To prove this, simply maximise [U(C /N ) + U(C /N )] by suitable choice of C and 1 1 2 2 1 C2, subject to the constraint C1 + C2 = C.

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10. UNCERTAINTY How should uncertainty be accommodated? The theory of choice under uncertainty, in its normative guise, is called the expected utility theory. There is a large and still-growing experimental literature attesting to the fact that in laboratory conditions people don’t choose in accordance with the theory.24 But here we are concerned with normative questions. That the choices we make in the laboratory don’t conform to expected utility theory does not mean that the theory is not the correct ethical basis for evaluating the policy alternatives Government House faces. When applied to the valuation of uncertain well-being streams, probabilities are imputed to future events. The probabilities are taken to be subjective, such as those involving long-range climate, although there can be objective components, such as those involving the weather. Let Et denote generation t’s expectation. Imagine once again that population remains constant. Intergenerational well-being can then be expressed as 

(12)

Et (  G(U )(
t ) ), for t  0, =t

where   1/(1+  ), with  > 0. The function G(U) in expression (12) reflects the attitude to risk in Government House. The discount rate  in expression (12) can be given an additional interpretation. The time horizon has so far been taken to be infinity. But we know that Earth will become uninhabitable some time in the future, even though we don’t know when that will be. Consider those causes of extinction that are beyond our control. The simplest (though not the most plausible) way to formulate this uncertainty is to suppose that the date of extinction is subject to a Poisson process, which is to say that the probability of extinction facing any generation, given that extinction hasn’t occurred until its arrival, is constant. That constant is called the Poisson ‘hazard’ rate. It can be shown (Yaari 1965) that choice under uncertainty governed by a Poisson process is equivalent to choice in a world where there is no chance of extinction, but where future well-beings are discounted at the Poisson hazard rate. For example, suppose that for each generation t, conditional on Earth’s surviving until t, the probability of extinction is 0.001 per cent. Then, in evaluating well-being streams, one may pretend that extinction won’t occur, but add a premium of 0.001 per generation to the rate of discount on future well-beings. In expression (12), uncertainty in the date of extinction is included in . Extinction at some unpredictable date offers an additional reason why the future should be discounted. 24

See e.g. Bell et al. (1988).

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That the possible exogenous causes of Earth’s extinction are subject to a Poisson process really does stretch the imagination.25 It is much more plausible that the probability of extinction for generation t, conditional on Earth’s surviving until t, will be zero for many centuries, rising thereafter in the very long run. The discount rate that would correspond to such a stochastic process would be a function of time, not a constant. As an application of the use of expression (12), I now show that the maximisation of average intergenerational well-being (expression (11)) can be derived as the criterion for intergenerational justice if we were to appeal to expected utility theory behind Rawls’s veil of ignorance. The idea is to regard an economy at t to be a different economy from that same economy at t+1. Now suppose you were asked which of the two economies you would choose to inhabit if you did not know which person’s shoes you would occupy in either, but attributed ‘equi-probability’ to each position (Harsanyi 1955). I have qualified equi-probability, because it makes no sense when the future has no termination date. To give it sense we must suppose that the probability of extinction over the indefinite future is unity. We may then talk of equi-probability of the conditionals. Suppose for simplicity that the possibility of extinction is governed by a Poisson process, which is to say that the probability rate of extinction at t, conditional on Earth’s having survived until then, is a constant,
(>0). Imagine next that in this thought experiment your choice is based on your expected well-being in the two economies. Expected well-being in the economy commencing at t would then be given by expression (11). It will be observed that Vt +1 would be of the same form as Vt , with  commencing at t+1 in expression (11). You would choose between the two economies on the basis of Vt and Vt +1. Uncertainties regarding events in the very distant future are sometimes called deep uncertainties; the qualifier is taken to mean that it may not be possible to assign subjective probabilities to those events. This is another way of saying that, when there are deep uncertainties, it is difficult to know what one should choose, or how one should organise one’s thoughts regarding what to choose. Examples frequently mentioned involve environmental risks. People observe that it may not be possible today to estimate the risks of environmental catastrophes in the distant future, let alone to enumerate what they may consist of. Bewley (1989) has developed an account of uncertainty that offers a reason why we ought to be reluctant to undertake activities involving inestimable risks. He offers a reason why the status quo should assume a favoured status, which is the hallmark of what many refer to as the Precautionary Principle (e.g. Appell 2001). Bewley’s theory would appeal to someone who feels that it is easier to prevent 25 The Poisson process is often invoked by economists because of its simplicity—a large asteroid hitting Earth is a possible interpretation; but there is little else to commend it.

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environmental damage than to repair it subsequently. The theory gives expression to the demand that, in evaluating radically new technology (e.g. biotechnology), the burden of proof ought to shift away from those who advocate protection from environmental damage, to those supporting the new technology. But these are early days for such theories as Bewley’s. The problem is that they can be supremely conservative. Admittedly, even the expected utility theory can be made ultra-conservative if we adopt an infinite aversion to risk (which is to say that the elasticity of G
(U) in expression (12) is infinity), and imagine that the worst that can happen under any change in policy is worse than the worst that can happen under the status quo. But it is difficult to justify such an attitude: we wouldn’t adopt it even in our personal lives. At the moment we don’t have a theory, normative or otherwise, that covers long-term environmental uncertainties in a satisfactory way. These are some reasons why the expected utility theory remains a popular framework for evaluating policy options. In practical decision-making, though, short cuts have to be made. Simple rules of thumb are often followed in the choice of public policy, for example, setting interest rates so as to keep the rate of inflation from exceeding, say, m per cent per year. But the expected utility theory remains the anchor for reasoning about economic policies. If the probability of disasters under radically new processes and products are non-negligible, the expected utility theory recommends caution. The theory stresses trade-offs, it asks us to articulate our attitude to risk, and it forces us to deliberate on the likelihood of various outcomes. For the moment, it is the only plausible game in town.26 11. CONCLUSIONS In this chapter I have argued that the formal apparatus Frank Ramsey introduced to give shape to the question ‘How much of its income should a nation save?’ can be given a far wider interpretation than the one he gave to it. Ramsey’s ethics was overtly Utilitarian. Nearly five decades of work by economists working on the ethics of the long run has shown that that ethics will not do. It has also shown that, agreeably, there is a compelling ethical theory that has the same mathematical structure as the one invented by Ramsey. So, although Ramsey’s ethics cannot be accepted, the techniques he devised for evaluating the just rate of saving can be adapted for use in worlds that are ethically far richer than the one he considered.

26 Alternatives to the expected utility theory were much explored during the 1950s. See Luce and Raiffa (1957, ch. 3) for an axiomatic classification of such theories.

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INDEX

action 1–2, 6, 8–20, 22–36, 137–48 neutralist conception of 20 Adams, E. 40–1, 49 analysis 1–6, 44, 47, 55, 58–69, 72, 76, 99, 102, 123–35 Anscombe, G. E. M. 54–60, 67, 85, 89 Appell, D. 168 Armstrong, D. M. 5, 83, 86, 95–6, 133 Arrow, K. J. 155–8, 163–6 Atkinson, A. B. 162 atomism 81 beliefs 1–4, 8–20, 22–6, 29, 32–6, 38–9, 44–7, 51, 55, 58–64, 69, 84, 114–15, 123–8, 134–5, 140, 145–7 degrees of 9, 37–9, 47–9, 137, 145–7 Bell, D. E. 167 Bennett, J. 44 Bermúdez, J. L. 19 Bewley, T. 168–9 Blackburn, S. 2, 13, 21–2, 37, 137, 147 Braddon–Mitchell, D. 134 Bradley, F. H. 92, 100–1 Bradley, R. 50 Braithwaite, R. B. 85 Brandom, R. 14 Bromley, D. W. 156 Broome, J. 155 Burge, T. 18 Cantor, G. 82, 87 Carnap, R. 31, 108–9 Carnap sentences 108 Cass, D. 165 causation 5–6, 28–30, 35, 47, 70, 93, 103, 116–21, 139–41, 147 cognition 5, 14, 20

compositionality 2, 27–9 concepts 3–6, 65–6, 103–9, 113, 116–21, 123, 128, 133–5 observational 5, 117, 120–1 sui generis 125–31, 135–6 theoretical 5, 113, 116–21 conceptual analysis 123–36 conditionals 3–5, 13, 37–51, 108 counterfactual 125 indicative 3, 37 material 39 consistency 36, 81, 158–9 content 1–2, 8–14, 19, 22–6, 29– 36, 54–9, 62, 66–7, 70, 79, 91–2, 106–11, 116–21, 124, 134–6 causal–informational theory of 116–21 propositional 12, 54 contractarianism 7 contradiction 75–6, 85–7, 98 Cruse, P. 5, 105 Dasgupta, P. 7, 149, 156–8, 161–6 Davidson, D. 27, 124, 146 decision theory 6, 9, 137–48 descriptive 140–8 normative 142, 145, 160, 166–9 objective 140–1 subjective 6, 137, 138–48 Demopoulos, W. 104–6, 111 Demos, R. 90–1 DeRose, K. 15 desires 1–2, 8–13, 18–20, 22–9, 32–6, 51, 137, 140, 145–7 Diamond, P. A. 159–60 Difference Principle 150, 158 disquotation 22, 28, 31–3 Dokic, J. 1–2, 8, 12, 17, 21–3, 26, 85, 95 Dretske, F. 10, 15, 116 Dummett, M. 49, 85, 89, 94 Dutch Book arguments 144

Index economics 1, 7, 149–50, 153, 156– 7, 162–4, 169 Edgington, D. 3, 37, 44 Eells, E. 142 empiricism 5, 106–9, 112, 117, 121 Engel, P. 1, 2, 8, 12–13, 17, 21, 23, 26, 85, 95 Epistemic Closure, Principle of 15–19 epistemology 3, 15, 18, 33, 53, 57, 108, 121, 134–5 equity, intergenerational 151, 156, 161 ethics 7, 46, 131, 149–69 events 26, 31–3, 35, 47, 89, 109, 124, 142, 147 evolution 11, 24 expressivism 125, 131 extensionality 59 facts 1–6, 8–21, 23–5, 28–35, 53– 8, 61–2, 66–9, 71–5, 78, 81–2, 83–95, 101 atomic 72, 83, 86–7, 92–5, 98 Feinberg, J. 155 Field, H. 37, 46 Fine, K. 90 Fodor, J. A. 5, 11, 114–18 Frege, G. 29, 65, 85, 92–5 Friedman, M. 106, 111 functionalism 26, 137 functions 4, 10, 43 predicative 75 propositional 4, 45, 73, 76–80, 106 propositional in extension 4, 76–80 truth functions 41, 44, 59, 63–4 Fundamental Schema 2, 27–35 future generations 7, 150–2, 155–8 Geach, P. T. 65–8, 85, 89, 94 Gettier cases 134 Gettier, E. L. 123–5, 134 Gibbard, A. 44, 49, 51 Goodman, N. 98 Greene, B. 118 Harrod, R. F.

155

179 Harsanyi, J. C. 168 Heal, G. M. 156–7, 161–3 Hempel, C. G. 108 Hinton, J. M. 17 Hochberg, H. 102–4 Horwich, P. 13, 45 Hossack, K. 104 identity 72–3, 77, 80, 84–5, 123–5, 130, 135 infinity 4, 45–6, 71, 81–2, 92–3, 98, 127, 153–69 axiom of 71, 80 intentionality 18–21, 22, 25–6, 29, 32, 33, 36, 116 Jackson, F. 5–6, 8, 46, 123, 126 Jacob, P. 10–11 Jeffrey, R. C. 6, 137, 143 judgement 53–70 justice, intergenerational 7, 149–69 Kahneman, D. 144 Kant, I. 79 Kemp, G. 28 Kenny, A. 54–60, 67 Ketland, J. 111, 114, 122 knowledge 1, 6, 9, 13–21, 30, 37, 109–12, 123–35 Kolm, S.–C. 162 Koopmans, T. C. 150–1, 157–66 Kripke, S. A. 130 Ladyman, J. 106 language 5, 12, 25, 29, 44–5, 58, 62–7, 72, 83–5, 89–90, 95–6, 101– 2, 105–7, 113, 123–5, 129, 131, 136 linguistic vehicles 29 ordinary 44, 95, 96 laws 5, 27, 38, 47, 92–3, 103, 146– 7 Leonard, H. S. 98 Levi, I. 147 Lewis, D. K. 3, 37, 41–8, 51, 93, 106, 112, 133, 136 Lewy, C. 74 Lind, R. C. 155

180

Index

logic 1, 5, 13, 16–20, 38–42, 45, 50, 54, 57, 63–9, 71, 76–7, 80–1, 84–6, 91–2, 95–6, 99–101, 107, 110, 123, 132, 147 logical form 65, 69 Lowe, E. J. 85, 102–4 Luce, R. D. 169 Lycan, W. G. 44

Tractarian 81 observation 5, 105–21 Oliver, A. 88–9, 104 ontology 4, 33–4, 85, 89, 95–6, 101–3, 108–10, 113, 121, 128 ontological categories 5, 85 Oppy, G. 46 original position 157–8

MacBride, F. 4, 83–5, 94, 102 McDowell, J. 17 McGinn, C. 10 McGuinness, B. 77, 80 Mäler, K.–G. 166 Martin, M. 104 mathematics 1, 5–7, 53, 75–82, 99, 107, 110, 120, 123, 144, 147, 150, 153, 159, 162, 169 Maxwell, G. 109–13, 116 Meade, J. E. 165 meaning 4–5, 12, 23–6, 57–9, 63– 9, 72, 75–6, 80–2, 84, 95, 105–7, 113–18, 121 Mellor, D. H. 5–6, 8, 21, 83, 88, 95, 104, 133, 137 metaphysics 1, 5, 107 Millar, A. 70 Millikan, R. 10, 11, 23 Mirrlees, J. A. 165 Montague, R. 41 Moore, G. E. 53, 59, 62, 77, 89, 102, 127, 128, 133 Mulligan, K. 104

Papineau, D. 2, 8, 10–13, 24, 31–2 paradoxes 40, 75–7, 87, 98 Lottery Paradox 50 Parfit, D. 152 particulars 4, 83–6, 89, 93–100, 103 particular–universal distinction 97 patterns 5, 131, 133, 135 Peano, G. 75–7 perception 15–19, 109–10, 114– 17, 121 non-conceptual 19 Perry, J. 12–14, 20 pictures 29–31, 35, 55, 58, 61–3, 67 logical 63 Portney, P. R. 155 possible worlds 7, 30, 51, 72, 116, 132, 161 Potter, M. 4, 67, 70–1 Pragmatic Closure, Principle of 18–20 pragmatism 8, 9, 22, 54, 62–4, 67, 70 predicates 2, 5, 33–4, 45, 83–9, 94–8, 102, 113 complex 88, 94 primary system 105–7 Prinz, J. 116 probability 38–43, 49–50, 52, 123, 137–9, 144–5, 167–9 conditional 3, 38–41, 50 properties 29, 33–4, 64, 88–93, 96, 99–103, 106–17, 121, 126–30 higher-order 92, 110 Platonism about 128 propositions 3–4, 11–12, 18, 37, 40–51, 53–70, 72–81, 84–93, 96– 102, 106, 110, 124, 143–4, 147 atomic 96–103

names 34, 37, 56, 63–70, 85–9, 94, 106, 136 proper 12, 59, 65, 72 naturalism 25 necessity 1, 90–6, 99–100, 103 necessary connection 93 negation 3, 47–8, 86–95 Newman, M. H. A. 109–14 Newtonian mechanics 6, 133–5, 146 Nozick, R. 15 objects 3–4, 27–30, 35–6, 61–2, 65–6, 71–6, 80–7, 91, 94, 99, 102– 3, 106, 109–15

Index elementary 55, 62, 81 pseudo-propositions 57–60 Psillos, S. 106–12, 122 psychology 4, 32, 53, 57, 68–70, 133, 144–6 Putnam, H. 130 quantification 73–5, 92–3, 105, 109–10 Quine, W. v. O. 3, 47–8, 135 Raiffa, H. 169 Ramsey, L. 71, 78–9 Ramsey sentences 5, 105–22, 123–36 Ramsey Test 37–8, 48, 51 Rawls, J. 7, 150–1, 157–61, 166, 168 Read, S. 47, 104 realism 25, 31, 95, 108–14 Reducibility, Axiom of 75 reference 129–30 relations 57, 60, 65, 70, 90–2, 96– 103 asymmetric 89, 99–101 higher-order 92 representation 1, 2, 10–11, 14, 22– 36, 55–7, 61, 81–4, 91, 97, 114– 21, 124, 131–6 Room, G. 78 Russell, B. 3, 4, 53–5, 65–9, 72–9, 83, 86–103, 109–11 Sahlin, N.–E. 1, 8, 10, 21 Same Numbers Problems 152 Savage, L. J. 137 saving 7, 149–52, 156–9, 169 scepticism 5, 15, 65, 85, 103, 111, 126, 130 Scheffler, I. 108 Searle, J. R. 9, 20 semantics 2, 10, 12, 22–4, 27, 30– 1, 41, 60, 69, 75, 87, 106, 115–16, 120–1 success semantics 1, 2, 8, 10– 13, 22–36 teleosemantics 10–13, 24 Sen, A. 151 sense 54–63 Shakespeare, W. 139–40

181 signs 56–7, 63–4, 67–8, 71–5, 86– 91, 94–5, 101 Simons, P. 85, 95 Smith, M. 46, 78–9 Solow, R. M. 155–7 Stalnaker, R. 41–4 states of affairs 9, 25, 45, 53, 57, 61–2, 144, 147 Stich, S. 123 Stout, G. F. 102 Strawson, P. F. 85 success conditions 1, 8–12, 20–1 Sullivan, P. M. 3, 4, 53, 80, 104 Suppe, F. 106 sustainable development 156, 165– 6 symbols 56–7, 60, 63, 66–7, 72, 82, 86–9, 94–5, 117 incomplete 86 tautologies 73–7, 80 teleology 10–13 theories 5–6, 105–22, 124, 128, 134–5 instrumentalism about 108–9, 112 scientific 105 Thomas, L. H. 67, 79 transcendental arguments 4, 71– 82, 116 truth 1–8, 9–14, 17–20, 22–3, 27– 8, 32–4, 37–52, 56–9, 62, 108, 124–5, 128, 135 correspondence theory of 124 minimalism about 3, 8, 13, 37, 44–9, 52 redundancy theory of 8 truth aptness 8 truth conditions 1, 8–14, 41, 44 Tversky, A. 144 universals 4, 78–9, 83–104 complex 88–90, 93–5 multigrade 103 utilitarianism 7, 149, 151–2, 155–7, 161, 169 Government House 151, 155, 167

182

Index

van Fraassen, B. C. 44, 112–14 veil of ignorance 150, 157, 166–8 von Wright, G. H. 77, 80 Warfield, T. A. 15 well-being, intergenerational 151–8, 161–8 Weyant, J. P. 155 Whitehead, A. N. 97, 101–2 Whyte, J. T. 1, 8–9, 12, 22

7,

Williams, B. 151 Williams, M. 16 Williamson, T. 16–18, 90, 123, 126–127 Wisdom, J. 84–85 Wittgenstein, L. 3–4, 27, 53–9, 62– 70, 71–82, 83–101 Yaari, M.

167