volume 19, no. 42 he Principle of the Identity of Indiscernibles (henceforth: october 2019 PII) — the principle that no two numerically distinct things T are perfectly alike — features prominently in Leibniz’s meta- physics. Leibniz uses it when he discusses atoms, the vacuum, the nature of space and time, and the nature of individual substances, to name just a few of its applications. Despite its centrality to his philo- sophical system, however, it is surprisingly difficult to determine what Is Leibniz’s Principle of the modal status Leibniz ascribes to the PII. On the one hand, there are many occasions throughout his philosophical career where he says or implies that scenarios with numerically distinct indiscernibles are im- Identity of Indiscernibles possible. This suggests that he endorses a necessary version of the PII. On the other hand, there are several key passages — in particular in (but not limited to) his correspondence with Samuel Clarke — where Necessary or Contingent? Leibniz seems to say or imply that scenarios with numerically distinct indiscernibles are possible (albeit not actual). This suggests that he en- dorses a merely contingent version of the PII. Thus, Leibniz’s attitude towards the modal status of the PII appears to be inconsistent. How should we deal with this apparent inconsistency? Can it be resolved? And if so, what is Leibniz’s considered view? In short, what is the mod- al status of Leibniz’s PII? Given the unclear and seemingly contradictory textual situation, it is unsurprising that there is no consensus among commentators on what Leibniz’s view is. Some argue that he endorses the necessary ver- sion of the PII throughout his philosophical career, including the late Sebastian Bender correspondence with Clarke.1 Others are so impressed by the mixed textual evidence that they read Leibniz as having no consistent view Humboldt-Universität zu Berlin on the issue.2 Recently, however, a third view has gained in popularity, 1. This interpretation goes all the way back at least to Russell 1992 [1937], 65 (Russell also explicitly acknowledges though that there is a prima facie ten- sion in Leibniz’s texts that requires to be settled). Other proponents who con- sider Leibniz’s PII a necessary principle include Rescher 1967, 48; Broad 1975, 40−41; Frankel 1981; Jolley 2005, 86; Futch 2008, 147; and Rodriguez-Pereyra © 2019 Sebastian Bender 2014, chapter 9. This work is licensed under a Creative Commons 2. See, for example, Chernoff 1981, 137, who writes: “Any attempt to interpret PII, as it appears in the correspondence with Clarke, as a unique principle that Attribution-NonCommercial-NoDerivatives 3.0 License. accords with all of Leibniz’s relevant remarks is doomed to failure.” Similarly, <www.philosophersimprint.org/019042/> Cover and O’Leary-Hawthorne argue that different arguments lead Leibniz sebastian bender Is Leibniz’s PII Necessary or Contingent? according to which at least the mature Leibniz rejects the necessity of 1. Leibniz’s PII 3 the PII. It has been argued, in particular by Julia Jorati and Martin Lin, In this section, I will briefly explain what Leibniz takes the PII to say, that reading Leibniz as defending a merely contingent version of the bracketing the question of what modal status he ascribes to the prin- PII not only fits the texts better, but also makes the most philosophical ciple. A standard contemporary formulation of the PII goes as follows: sense. In this paper, I will argue against this view. Contrary to many recent (PII) F(Fx ↔ Fy) → x = y (If, for every property F, object x has F if and only if object y has F, then x is identical to y.)4 commentators, I claim that Leibniz is firmly committed to the neces- ∀ sity of the PII. In particular, I will argue that he subscribes to a mod- In other words, if x and y share all their properties, then x and y are ally robust version of the PII even in his correspondence with Clarke, identical. Leibniz is not a fan of this way of putting the PII. He typi- and that the recent attempts to refute such a reading are unsuccessful. cally avoids quantification over properties and prefers instead to state On the face of it, my interpretation of the Clarke correspondence may the principle in terms of resemblance, difference, or indiscernibility.5 come as a surprise, since Leibniz there appears to tie the PII to God’s Here are three representative passages from three different periods of wisdom, which would make the PII contingent. A detailed analysis of Leibniz’s career: the relevant passages, however, will reveal Leibniz’s deep and ongo- ing commitment to a modally strong version of the PII even in these [N]ever will be found two eggs, or two drops of milk, or very late texts. two leaves, or two animals, and in general two things so The paper is structured as follows: Section 1 briefly explains how similar that after an accurate examination, no difference 6 Leibniz understands the PII, independently of its modal status. Sec- can be noticed. (Letter to Casati in 1689, A 2.2.289) tion 2 surveys several arguments for the contingency of Leibniz’s PII and shows why they are not conclusive. Section 3 argues for the neces- [A]ll substances are of different natures, and […] there sity of Leibniz’s PII, with a special focus on the correspondence with are no two things in nature that differ in number alone. Clarke. Section 4 responds to three objections that might be raised (Letter to De Volder on 21 January 1704, G II 264/LDV against my interpretation. Section 5 concludes. 291) [T]here are not in nature two real, absolute beings, indis- cernible from each other. (LC 5.21) to different views about the modal status of the PII. They conclude that “it is not surprising that Leibniz vacillates between more and less modally com- mittal ways of speaking in connection with PII” (Cover and O’Leary-Haw- thorne 1999, 212). Anja Jauernig, who carefully analyses many of Leibniz’s 4. This formulation is taken from Forrest 2016. The converse of the PII is the arguments for the PII, refrains from making a judgement on the modal status Indiscernibility of Identicals: if x is identical to y, then, for every property F, of the PII (see Jauernig 2008). Stephen Steward, in a review of Rodriguez- object x has F if and only if object y has F. Leibniz endorses both. Pereyra’s recent book, takes a similar view and concludes “that the modal status of the PII is far from settled” (Steward 2015, 118). 5. On this point, see Rodriguez-Pereyra 2014, 22−25. 3. See Della Rocca 2015; Mugnai 2016, 379; Jorati 2017; and Lin (unpublished 6. For a thorough discussion of this letter, see Rodriguez-Pereyra 2014, chapter manuscript). 6. philosophers’ imprint – 2 – vol. 19, no. 42 (october 2019) sebastian bender Is Leibniz’s PII Necessary or Contingent? By stating the PII without mentioning (the sharing of) properties or should keep in mind, I will for the most part deal with Leibniz’s PII as it accidents, Leibniz remains faithful to his nominalist framework, ac- applies to the fundamental entities of his mature metaphysics, namely, cording to which “everything, apart from individual substances, is a (simple) individual substances, or monads. Whatever the mature Leib- mere name.”7 While he generally does not seem much bothered by niz takes the ontological status of eggs, leaves, and other bodies to talk of accidents,8 there are many passages where he makes clear that be, it is clear that all of their features are ultimately grounded in, or all there really is are individual substances and their modifications or constituted by, the fundamental entities of his ontology. Hence, what- affections.9 Presumably, Leibniz thinks that speaking of accidents is ever qualitative difference there may be between your breakfast egg acceptable, as long as one does not reify them and take them to be and my breakfast egg is ultimately due to whatever differences there entities over and above individual substances.10 Given that accidents are in the two distinct sets of monads that constitute or ground each do not constitute an ontological category distinct from substances for of the two eggs.14 Furthermore, it is quite plausible that the reverse is Leibniz, it makes sense for him to avoid formulations of the PII which also true and that each difference in the grounding entities leads to a presuppose that there is something (properties or accidents) which difference in the grounded entities. Therefore, if the PII as restricted to substances have in common or share. Stating what one wants to state monads turns out to be necessary (or contingent), then presumably (in this case, the PII) in terms of similarity or difference instead is of the unrestricted version of the PII, ranging over all things — including course a typical nominalist strategy. eggs, leaves, etc. — is necessary (or contingent) as well. What is the scope of Leibniz’s PII? It is clearly pretty wide. In just One should expect that the PII, if it is necessary, applies not just the three passages quoted above, Leibniz includes in it “eggs,” “leaves,” to actual substances but also to merely possible ones, i.e., mere pos- “animals,” “drops of milk,” “substances,” “real beings,” and “things.” In sibilia. This is true, if understood correctly. Leibniz’s official position is other texts, he also states that the PII ranges over (besides many other that possibilia are ideas or concepts in the divine intellect.15 While the entities) “individuals,”11 “beings,” and “monads.”12 All of this suggests PII presumably applies to such ideas as well — it would be quite odd that Leibniz’s PII has the widest possible scope and applies to any if God had two numerically distinct but indiscernible ideas of Peter in thing, and any kind of thing, whatsoever.13 While this is something we his mind — this is not the case that raises questions about the modal status of the principle.