1 Works are cited in the text by the following abbreviations: Adam, AT=C. and Tannery, P. eds., Œuvres de Decartes, 12 vols. (Paris: Vrin 1964-76)Google Scholar; Cottingham, CSM = J. et al., trans. and eds., The Philosophical Writings of Descartes, 3 vols. (Cambridge: Cambridge University Press 1984-91)Google Scholar; Dickoff, DJ = J. and James, P. trans. and eds., Arnauld, Antoine The Art of Thinking (Indianapolis: Bobbs-Merrill 1964)Google Scholar; Gerhardt, G = C. ed., Die Philosophishen Schriften von Gottfried Wilhelm Leibniz, Zweiter Band (Berlin: Weidman 1879)Google Scholar; Mason, M = H. trans. and ed., The Leibniz-Arnaud Correspondence (Manchester: Manchester University Press 1967)Google Scholar. Passages are cited by volume number, if applicable (except for CSM III, which is cited as CSMK to acknowledge A. Kenny’s contribution to the volume), and page. At the time of this writing, the best translation of the Correspondence is M. It is based on the text in G. References to both these works will appear in this essay.

2 As we shall see, the Leibniz-Arnauld debate parallels the contemporary debate between ‘actualists’ and ‘possibilists’ regarding the status of counterfactuals and possible worlds. For a wide-ranging discussion of recent developments, see Lewis, D. On the Plurality of Worlds (Oxford: Basil Blackwell 1986)Google Scholar, Ch. 1 and 3. Lewis employs different terminology.

3 Leibniz and Arnauld (New Haven: Yale University Press 1990)

4 This letter was addressed to Ernst, the landgrave of Hessen-Reinfels, but intended for Arnauld’s eyes. Sleigh gives a full account of Ernst’s role as intermediary in the correspondence (Leibniz and Arnauld, 15-25).

5 Parkinson’s reconstruction follows the quoted passage. I am not sure whether it is less involved or less obscurely expressed than the original, but I am sure that it does not do full justice to Arnauld’s argument.

6 Though he makes it out to be Leibniz’s: ‘For it seems to me that according to you the possible Adam (whom God chose in preference to other possible Adams) was linked to all the selfsame posterity as the created Adam; since he is, in your opinion, so far as I can judge, merely the same Adam considered now as possible and now as created’ (G 29; M 28).

7 Some commentators, for example R Adams, ‘Predication, Truth and Transworld Identity in Leibniz,’ in Bogen, J. and McGuire, J. eds., How Things Are (Dordrecht: Reidel 1985) 235-83CrossRefGoogle Scholar, take it for granted that Arnauld takes over enough of the Leibnizian framework so that he can be regarded as affirming transworld identity. I am suggesting that Arnauld would have rejected most of the framework necessary for stating a clear thesis regarding transworld identity. For Cartesians, the relevant question always instead concerns concept identity.

8 Adams in ‘Predication, Truth and Transworld Identity’ thinks it is clear that Leibniz denied transworld identity, but that this position cannot be demonstrated from concept containment or any other features of Leibniz’s system. His interpretation is convincing. Sleigh’s important clarification and development of the distinction between superintrinsicalness and superessentialism (Leibniz and Arnauld, esp. 67- 72) gives Leibniz a way of avoiding fatal necessity without directly invoking possible world machinery. Also see Mates, B. The Philosophy of Leibniz (New York: Oxford University Press 1986), 137-51Google Scholar.

9 The relevant text is the 13 May 1686 letter (G 30-1; M 29-30).

10 In some cases, we will be able to conceive as possible things which God will create, but has not yet created. The epistemological barriers to doing so might be overcome by Biblical prophecies, for example.

11 I am now arguing that this interpretation of the text is plausible. It will become clear in what follows why this interpretation is required by the doctrine of divine simplicity.

12 Descartes addresses worries (put forward by Arnauld) about whether this picture entails in an unacceptable way that God depends on himself in the Fourth Replies (at AT VII 235-45; CSM II 164-71).

13 This is the point of Descartes’s discussion at AT VII 221-7; CSM II 155-9 in the Fourth Replies. Again, it is significant that Descartes wrote this in response to Arnauld’s objections to the Meditations.

15 In the Correspondence, Leibniz takes an oblique shot at this ‘Cartesian’ doctrine. In the draft for the 4/14 July letter Leibniz wrote,’ And for the objection that possible things are independent of God’s decrees, I grant it where actual decrees are concerned (although the Cartesians do not agree) …’ (G 40; M 43). In the actual letter, it is strengthened thus, ‘[T]he most abstract specific concepts contain only necessary or eternal truths, which do not depend upon God’s decrees (whatever the Cartesians may say of it, and you yourself do not seem to have heeded them in this matter) …’ (G 49; M 54-5). I am arguing that Arnauld did heed the Cartesians because he was one of them, at least with regard to this issue. In the Correspondence, he lets Leibniz’s parenthetical remark pass.

16 Descartes does not confine the doctrine of divine simplicity to his later works and correspondence. It plays an important role, for instance, in the Third Meditation (AT Vll 50; CSM II 34), and in the Second Replies (AT VII 137; CSM II 98).

17 I think that the ‘argument’ Arnauld is referring to is the one distinguishing abstract or specific concepts from individual concepts. Everything demonstrable from an abstract concept (for example, that of a sphere) is, in a sense, necessary. An individual’s properties had better not be necessary in the same sense on pain of fatalism. In what follows, I shall argue that Arnauld can, nevertheless, agree that everything that will ever happen to an (actual) individual can be affirmed of that individual and is therefore, in a special way, included in God’s concept of that individual.

18 There is a sense in which they probably contain more: see Sleigh’s discussions of Leibniz’s notion of primitive properties (Leibniz and Arnauld, 48-50, 70; ‘Truth and Sufficient Reason in the Philosophy of Leibniz,’ in Hooker, M. ed., Leibniz: Critical and Interpretive Essays (Minneapolis: University of Minnesota Press 1982) 209-42, at 215-16)Google Scholar.

19 Descartes’s theory is complicated by his implicitly distinguishing concepts of substances from the concepts of things — a more inclusive class. One clearly and distinctly perceives a substance by perceiving its essence, but non-substances are clearly and distinctly perceived only in special circumstances. Jarrett, C. ‘Leibniz on Truth and Contingency,’ in New Essays on Rationalism and Empiricism: Canadian Journal of Philosophy Supplementary Volume 4 (1978) 83-100Google Scholar, has a good argument that Descartes intended Definition IX as a left to right entailment and not as an identity statement.

20 As the next quotation shows, Arnauld thought it immaterial in this context whether we are considering what is true of a thing or true of the idea of the thing.

21 I want to emphasize that in the Cartesian system clear and distinct perceptions are always of what is actual. In La Logique Arnauld wrote, ‘A true idea is an idea whose object is an existing object. If the object of an idea is not an existing object, then the idea is false— at least in one manner of speaking’ (DJ 41). Neither Descartes nor Arnauld says enough about how clear and distinct perceptions of mathematical essences like that of a triangle fit into this scheme. Descartes’s doctrine in the Fifth Meditation might seem to be that we could have true ideas of triangles even if they did not actually exist, so there is considerable tension in the texts. I believe the tension can be neatly resolved, but doing so requires material tangential to the concerns of this essay.

22 Leibniz and Arnauld, 58-70; 89-94, at 93, emphasis added.

23 This apt phrase is from Leibniz and Arnauld, 94.

24 I cannot here reproduce Sleigh’s deft deployment of the distinction between the intrinsic and the essential. He argues that even though superintrinsicalness (the doctrine that all of an individual substance’s properties are intrinsic to it) along with other Leibnizian principles entails superessentialism (the doctrine that all of an individual substance’s properties are essential to it and, hence, necessary), Leibniz was convinced that the two could be separated in a way that avoided objectionable necessary truths about individuals. See Leibniz and Arnauld, Ch. 4, esp. 67-72.

25 This is shown, for instance, in the 4/14 July letter (at G 54-5; M 61), and in the draft for that letter (at G 45; M 49).

26 Sleigh clearly explains Arnauld’s generally overarching concern with theological matters (Leibniz and Arnauld, Ch. 3).

27 I thank Nicholas Jolley, Steven Nadler, Calvin Norrnore, Marleen Rozemond, and R.C. Sleigh, Jr., for helpful advice.