Some Aspects of ‘Identity’

On the Validity of the Principle of the Identity of Indiscernibles

Abstract

The Principle of the Identity of Indiscernibles (hereafter the PII) states that if any individuals exactly resemble each other, then they are necessarily identical. Intuitively, the PII seems valid, but Max Black attempted to refute it by introducing the possibility of a symmetry universe in which two iron spheres c and p can resemble each other exactly. This counterexample (hereafter BU) seems easy to rule out using a weak discernibility strategy (hereafter WD) according to which c, being spatially separate from p and not from c itself, is not indiscernible from p. WD, however, leads to ‘the presupposition problem’, because obtaining c as spatially separate from p presupposes the distinctness of c and p. In this discussion, I will give an outline of a defense of the validity of the PII that evades the presupposition problem through the elucidation of some aspects of ‘identity’.

In my view, ‘identity’ has two aspects: one is simply self-identity as a universal monadic property (hereafter identity-1), and the other is identity as an equivalence relation entailing indiscernibility (hereafter identity-2). The basis or ground for identity-1 obtaining with regard to an individual x can be called the individuator for x, but it is no wonder that the individuation and articulation of c and p are prior to or ground for obtaining c as spatially separate from p. So far as the PII is concerned with identity-1, it may not be valid. However, we can characterize identity-2, following David Wiggins’s lead, in terms of what is called the sortal dependency of identity-2 and the extended Locke’s Principle (hereafter ELP), according to which, for any sortal concept F, x falling under F is identical with y falling under F if and only if x is the same F as y, and x is the same F as y if and only if a) x and y share F and b) x is not spatially separate from y. If ELP is valid, we can regard BU as merely a general case to which WD is applied. And if the Wigginsian idea of the sortal dependency of identity-2 is also right, there is no longer a presupposition problem. I hence conclude that the PII is valid to the extent that it is concerned with identity-2.