Leibniz's 1686 Views on Individual Substances, Existence, and Relations Hector-Neri Castaneda The Journal of Philosophy, Vol. 72, No. 19, Seventy-Second Annual Meeting American Philosophical Association, Eastern Division. (Nov. 6, 1975), pp. 687-690. Stable URL: http://links.jstor.org/sici?sici=0022-362X%2819751106%2972%3A19%3C687%3AL1VOIS%3E2.0.CO%3B2-4 The Journal of Philosophy is currently published by Journal of Philosophy, Inc..
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the 'only if' part seems plausible, the 'if' part seems incredible. Again, I offer an explanation. T h e explanation turns on certain interesting doctrines Leibniz held concerning abstractions and accidents. After considering whether (b) is a consequence of (a), I suggest that we take the conjunction of (a) and (b) (actually, the conjunction of their refined versions) as that from which the notable paradoxes are affirmed to follow. I begin with what would appear to be the easiest case, i.e., the identity of indiscernibles. It turns out that a surprising number of metaphysical doctrines are required to reach the identity of indiscernible~in the powerful form accepted by Leibniz. I close with a consideration of a "paradox" not stated in paragraph 9. It is this: an individual substance is indivisible. For Leibniz this amounts to the claim that if x is an individual substance then there is no entity y such that y is a proper part of x . I t is easily seen that this doctrine yields a number of the paradoxes cited in paragraph 9. Here the temptation is to offer an explanation via Leibniz's analyses of extension, force, and material phenomena. But Leibniz thought that this doctrine was a consequence of the conjunction of (a) and @). Consider this remark from a letter to Arnauld: Substantial unity requires a complete, indivisible and naturally indestructible entity, since its concept embraces everything that is to happen to it.2
I make an effort-alas, not altogether successful-to Leibniz had in mind here.
explain what
ROBERT C. SLEIGH
University of Massachusetts at Amherst
LEIBNIZ'S 1686 VIEWS ON INDIVIDUAL SUBSTANCES,
EXISTENCE, AND RELATIONS *
UIDED by a principle of charity, Leibniz scholars often adopt the Athenian approach: assuming somehow that Leibniz propounded a coherent system of views, they pick, choose, and juxtapose passages from anywhere in the Leibnizian
G
2 T h e Leibniz-Arnauld Correspondence, edited and translated by H. T. Mason (Manchester: U~iversityPress, 1967), p. 94. * Abstract of a paper to be presented in an APA symposium on Leibniz, December 29, 1975. Robert C. Sleigh will be co-symposiast; see this JOURNAL, this issue, 685-687.
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corpus, regardless (inter alia) of dates, to piece together those views. Here I follow the Darwinian approach: * taking systematic unity and harmony of texts not as axioms but as theorems of historical scholarship, I subject unitary passages, mainly from the Discourse on Metaphysics and from the General Inquiries about the Analysis of Concepts and T r u t h (both of 1686) to radical exegesis and theory-complementation, letting confusion and development appear as they may. This must precede pairing of the Discourse with Leibniz's developmental correspondence with Arnauld. Substances, which underlie individuals like people and mountains, are for Leibniz primary reality. Each substance S has just one complete concept C(S). This is the set, or conjunction, or fusion of all of S's properties. Leibniz oscillated between (A): S is just C(S) cum existence, and ( B ) :S is not composed of C(S) at all. (A)is simpler and fits Leibniz's general metaphysics better. On neither view is existence a predicate. In the Discourse and the General Inquiries the concept of existence is a special irreducible copula, or connexion d u sujet et d u predicat. Existence itself is the truth (irreducibly knowable by experience) of propositions with such copula. These glorious insights became, unfortunately, warped under Leibniz's idea of a general logical calculus.~ Leibniz's views on relations ground other metaphysical views of his: the mirror thesis; the pre-established harmony among substances; monadism (that existence and the states of every finite substance are absolutely independent of the existence, but not of the states, of every other finite substance); mentalism; etc. Some commentators balk at monadism, arguing that, e.g., "a perceives b" or "a is taller than b" implies analytically that b exists. In a universe of discourse (like Leibniz's) containing nonexisting individuals, for every relation R such that R(a,, . . . , a,) implies the existence of each a* ( i = 1, . . . , n), there is a relation sh-R that holds iff R holds, but does not imply the existence of any a,. Thus, Leibniz presupposed the Pure Relation thesis: every ordinary rela1 Described in my "Leibniz's Concepts and Their Coincidence Salva Veritate," N o h , V I I I , 4 (November 1974): 381-398. 2 See my "Thinking and the Structure of the \tTorld," Philosophia, IV, 1 (January 1974): 3-40, on consubstantiation. 3See General Inquiries, and also my "Leibniz's Syllogistico-propositional Calculus," Notre Dame Journal of Formal Logic (forthcoming), and "Leibniz's Concepts . . . ," op. cit.
tion that analytically involves the existence of its relata is analyzable into a pure attributive relation, an sh-relation, and existence. Leibniz's monadism stem6 from his opposition to the analyticsynthetic distinction-before its formulation! For Leibniz relational facts (constituting the Pre-established Harmony) were irreducible, whereas relations were (because of his sweeping monadism) reducible to monadic properties. Yet he said little about this reduction. That he needn't have said much can be appreciated now, after the development of quantificational logic made it feasible to segregate the ontology from the logic of relation^.^ Three Leibnizian passages often juxtaposed are: (i) a text, doubtlessly before 1684, analyzing "Paris loves Helen" as "Paris loves, eo ipso Helen is loved two propositions collected in a compact one"; (ii) a 1714 fragment of a letter to Des Bosses: "as regards relations, one thing is paternity in David, another sonship in Solomon"; (iii) a passage from Leibniz's 1716 Fifth Letter to Clark discussing three ways of viewing [three propositions expressed by?] "L is greater than M : (a) "L is greater-than-M"; (b) "M is shorter-thanL"; (c) as a genuine relational fact involving M and L on equal footing.
...
The analysis envisioned in (i) treats relational propositions as molecular, built up from monadic propositions by the connective eo ipso. This places the reduction burden on the implication principles governing eo ipso. (The best and very illuminating attempt of this sort, Milton Fisk's "Relatedness without Relations," makes, unfortunately, all relations symmetric.) (ii) claims only that "David is Solomon's father" includes two "things," which very likely are not propositions. So the reduction burden shifts to the formation principles for atomic propositions, as in my "Plato's Phaedo Theory of Relations" (op. cit.). Text (iii) describes an important ambiguity not fully recognized by current logical or linguistic theory.7 According to (iii), the inSee my "Plato's Phaedo Theory of Relations," Journal of Philosophical Logic, 4 (August 1972): 467480, reprinted in Mario Bunge, ed., Studies in Exact Philosophy (Dordrecht: Reidel, 1973). 6 See also my "Relations and the Identity of Propositions," Phibsophicnl Studies (forthcoming). 6 Nods, VI, 2 (May 1972): 139-151. 7 See "Thinking and the Structure of the World," op. cit., for a treatment of 4
I,
this ambiguity.
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ternal modifications grounding relations (iii c) are relational properties containing relata. On view (A) above, these internalized relata may be complete concepts. On both (A) and (B), substances, or their representations in substances, somehow include each other, thus violating something akin to the set-theoretical axiom of regularity (Harry Teichert). This complexity strengthens the value of the reduction in "Plato's Phaedo Theory of Relations" (op. cit.) which illuminates (ii). Perhaps (iii c) should be interpreted as (ii). HECTOR-NERI CASTAREDA Indiana University OUTLINE OF A THEORY OF T R U T H
*
I. THE PROBLEM
E
VER since Pilate asked, "What is truth?" (John XVIII, 38), the subsequent search for a correct answer has been inhibited by another problem, which, as is well known, also arises in a New Testament context. If, as the author of the Epistle to Titus supposes (Titus I, 12), a Cretan prophet, "even a prophet of their own," asserted that "the Cretans are always liars," and if "this testimony is true" of all other Cretan utterances, then it seems that the Cretan prophet's words are true if and only if they are false. And any treatment of the concept of truth must somehow circumvent this paradox. The Cretan example illustrates one way of achieving self-reference. Let P(x) and Q(x) be predicates of sentences. Then in some cases empirical evidence establishes that the sentence ' ( x ) (P(x) > Q(x))' [or ' (3.) (P(x) A Q(x))', or the like] itself satisfies the predicate P(x) ; sometimes the empirical evidence shows that it is the only object satisfying P(x). In this latter case, the sentence in question "says
* T o be presented
in a n APA symposium on Truth, December 28, 1975. Originally it was understood that I would present this paper orally without submitting a prepared text. At a relatively late date, the editors of this JOURNAL requested that I submit a t least a n "outline" of my paper. I agreed that this would be useful. I received the request while already committed to something else, and had to prepare the present version in tremendous haste, without even the opportunity to revise the first draft. Had I had the opportunity to revise, I might have expanded the presentation of the basic model in sec. III so as to make it clearer. T h e text shows that a great deal of the formal and philosophical material, and the proofs of results, had to be omitted. Abstracts of the present work were presented by title a t the Spring, 1975, meeting of the Association for Symbolic Logic held in Chicago. A longer version was presented as three lectures a t Princeton University, June, 1975. 1 hope to publish another more detailed version elsewhere. Such a longer version should contain technical claims made here without proof, and much technical and philosophical material unmentioned or condensed in this outline.
