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Published online by Cambridge University Press: 01 January 2020
Leibniz has enjoyed a prominent place in the history of thought about possible worlds. I shall argue that on the leading interpretation of Leibniz's account of contingency - an ingenious interpretation with ample textual support - possible worlds may be invoked by Leibniz only on pain of inconsistency. Leibnizian contingency, as reconstructed in detail by Robert C. Sleigh, Jr., will be shown to preclude propositions with different truth-values in different possible worlds.
1 See, for example, Adams, Robert Merrihew ‘Theories of Actuality,’ NoûS, 8 (1974) 211–31,CrossRefGoogle Scholar and Mates, Benson ‘Leibniz on Possible Worlds,’ in Frankfurt, Harry ed., Leibniz: A Collection of Critical Essays, (New York: Doubleday 1972) 335–64.Google Scholar
2 Sleigh, Robert C. Jr., ‘Truth and Sufficient Reason in the Philosophy of Leibniz,’ in Hooker, Michael ed., Leibniz: Critical and Interpretive Essays (Minneapolis: University of Minnesota Press 1982) 209–42Google Scholar
3 Leibniz himself clearly espoused the view that there are an infinity of nonactual worlds, any one of which God, without contradiction, could have decreed to become actual. AS Leibniz wrote to Arnauld,
I think there were an infinity of possible ways of creating the world according to the different plans which God might have formed and that each possible world depends upon certain principal plans or designs of God that are his own; that is to say, upon certain primary free decrees conceived sub ratione possibilitatis, or upon certain laws of the general order of this possible universe, with which they agree and whose concept they determine.
Discourse on Metaphysics, Correspondence with Arnauld, Monadology, trans. Montgomery, George R. (La Salle, III: Open Court 1980) 124.Google Scholar
4 See, for example, Arnauld: ‘God was free to create or not create Adam,’ Montgomery, trans., 73. Cf. Mates, ‘Leibniz on Possible Worlds,’ 344.
5 The concerns here by-pass the controversy over whether Leibniz legitimately could hold that Adam, say, had some of his properties contingently. For even if Leibniz's critics carry the day on that point, Leibniz could still maintain that there are propositions satisfying (C). For recent discussions with numerous references, see E.M. Curley, ‘The Root of Contingency,’ in Frankfurt, ed., 69-98, and Robert Merrihew Adams, ‘Leibniz's Theories of Contingency,’ Rice University Studies, 63 (1977) 1-42.
6 Discourse on Metaphysics VIII and XIII, Peter Lucas and Leslie Grint, trans., (Manchester, 1953), 13; 18-22. Leibniz: Philosophical Writings, Mary Morris and G.H.R. Parkinson, trans., (London: J,M. Dent 1973) 93-4; 96. Correspondence with Arnauld, Montgomery, trans. 110ff; 132
7 The following is a sketch of the interpretation offered by Sleigh in ‘Truth and Sufficient Reason in the Philosophy of Leibniz.’
8 ‘Leibniz on the Simplicity of Substance,’ Sleigh, Robert C. Jr., Rice University Studies, 63 (1977) 117.Google Scholar Also, Mates, ‘Leibniz on Possible Worlds,’ 339.Google Scholar
9 A number of writers have made similar points. E.g., see ‘Leibniz's Concepts and Their Coincidence Salva Veritate,’ Hector-Neri Castañeda, Noûs, 8 (1974) 393.
10 ‘General Inquiries About the Analysis of Concepts and of Truths,’ Logical Papers, Parkinson, G.H.R. trans. (Oxford: Clarendon Press 1966), 77.Google Scholar Leibniz counts propositions of the form ‘AB is A,’ as well as of the form ‘A is A,’ as identical propositions. (See Parkinson's introduction, xxxiv.) Also, see Morris and Parkinson, trans., 109.
11 The limiting proposition is known to God a priori: ‘ … it is God alone, who grasps the entire infinite in his mind, who knows all contingent truths with certainty.’ (See preceding note.)
12 ‘Individuals and Modality in the Philosophy of Leibniz.’ Mates, Benson Studia Leibnitiana IV/II (1972) 94Google Scholar
13 Leibniz would agree: ‘Now nothing is necessary of which the opposite is possible.’ (See note 17.)
14 David Lewis is the originator of counterpart theory. See ‘Counterpart Theory and Quantified Modal Logic,’ Journal of Philosophy (1968) 113-26
15 Benson Mates argues against applying counterpart theory to Leibniz; see his ‘Individuals and Modality in the Philosophy of Leibniz.’ esp. 110-13. Fabrizio Mondadori and Gregory Fitch argue for applying counterpart theory to Leibniz; see Mondadori's ‘Reference, Essentialism, and Modality in Leibniz's Metaphysics,’ Studia Leibnitiana (1973) 74-101, as well as his ‘Leibniz and the Doctrine of Interworld Identity,’ and see Fitch's ‘Analyticity and Necessity in Leibniz.’ Journal of the History of Philosophy, 17 (1979) 29-42.
16 Gregory Fitch, ‘Analyticity and Necessity in Leibniz,’ 41-2
17 For example, Leibniz wrote in Discourse on Metaphysics XIII:
although God always chooses the best assuredly, that does not prevent that which is less perfect from being and remaining possible in itself, even though it will not happen, for it is not its impossibility but its imperfection which makes God reject it. Now nothing is necessary of which the opposite is possible.
Peter Lucas and Leslie Grint, trans., 21-2. For a full discussion of complexities in this neighborhood, see Adams, ‘Leibniz's Theories of Contingency,’ 12ff. and 23ff.
18 Logical Papers, Parkinson, trans., 80. R.C. Sleigh, Jr. brought this example to my attention.
19 See the Leibniz/ Arnauld correspondence, Montgomery, trans., 73; cf. 108, 124. Also, Monadology, paragraph 53, Montgomery, trans., 262. Also, see Fabrizio Mondadori, ‘Leibniz and the Doctrine of Inter-World Identity,’ Studia Leibnitiana VII (1975) 21-57.
20 I am grateful to Robert C. Sleigh, Jr., David Benfield, Stanley Bates, Victor Nuovo, Michele LaRusch, and David Austin for helpful discussion and comments on an earlier draft of this article, which was inspired by Sleigh's magnificent lectures during his NEH Summer Seminar in 1981.