The Contingency of Leibniz's Principle of the Identity of Indiscernibles

Abstract

The Ohio State University Leibniz's famous Principle of the identity of indiscernibles (Pii) states that no two things are exactly alike. The Pii is commonly thought to be metaphysically necessary for Leibniz: the coexistence of two indiscernibles is metaphysically impossible. This paper argues, against the standard interpretation, that Leibniz's Pii is metaphysically contingent. in other words, while the coexistence of indiscernibles would not imply a contradiction, the Pii is true in the actual world because the Principle of Sufficient reason rules out violations of the Pii. God could have created indiscernibles but he did not because he is wise and does nothing without a sufficient reason. Because it is plausible that all Leibnizian possible worlds are unified by a wise plan, this means that the Pii is true in all possible worlds. God could create indiscernibles, but the resulting creation would not be a world. To argue for this conclusion, the paper carefully examines Leibniz's mature account of metaphysical contingency. it shows that for Leibniz, only states of affairs that imply logical contradictions are metaphysically impossible. next, it argues that the coexistence of indiscernibles would not imply a logical contradiction; it would merely imply what Leibniz calls a "moral absurdity," that is, a violation of the Principle of Sufficient reason. This means that the Pii is true contingently and-since God can do whatever is metaphysically possible-that God can create two things that are exactly alike. 1. See for instance Gonzalo rodriguez-Pereyra's recent monograph on the Pii (rodriguez

Leibniz on Innocent Individual Concepts and Metaphysical Contingency

“…What is undeniable is that different readings of the PII have central consequences for metaphysics of modality. For example, Jorati (2017b) argues that, for Leibniz, the PII is metaphysically contingent partly because it depends upon the PSR which is also metaphysically contingent. Cover and Hawthorne (1999, Ch.…”

The Modal Status of Leibniz's Principle of Sufficient Reason

“…There is a great deal of disagreement over whether Leibniz was committed to the absolute possibility of indiscernibles. Many commentators think that Leibniz was indeed committed to their absolute possibility (Russell 1900: 55–56; Vinci 1974: 100; McRae 1976: 110; Chernoff 1981: 135; Carriero 1995: 21n68; Vailati 1997: 117, 125; Lodge 2010: 25; Lin 2016: 450; Jorati 2017). Other commentators deny this (Parkinson 1965: 132–33; Broad 1975: 40–41; Jolley 2005: 86; Rodriguez-Pereyra 2014: 118–26).…”

“…This text has split commentators into two camps. Some think that it shows that Leibniz genuinely believed that indiscernibles are possible (Russell 1900: 55–56; Vinci 1974: 100; McRae 1976: 110; Chernoff 1981: 135; Carriero 1995: 21n68; Lodge 2010: 25; Lin 2016: 450; Jorati 2017: 912). Others think that Leibniz is simply conceding that they are possible for the sake of argument without believing so himself (Parkinson 1965: 132–33; Broad 1975: 40–41; Jolley 2005: 86).…”

“…Some commentators do think that passages such as this support the absolute necessity of Leibniz's theory of truth and therefore of the PSR as well (Couturat 1901: 208–10; Jauernig 2008: 214; Rodriguez-Pereyra 2014: 82). Other commentators have expressed doubts over whether Leibniz's theory of truth as it is expressed in such passages is indeed absolutely necessary (Carriero 1995: 21n68, 23–26; Jorati 2017: 921n53). In what follows I will join the latter group in expressing doubts concerning the absolute necessity of Leibniz's theory of truth.…”