Wiggins on Identity

Abstract

Consider the equivalence relations x is the same colour as y and x is the same shape as y, which can hold between material objects. (Anyone who thinks that relations thus expressed can only hold between colours and shapes-universals or abstract entities-can read 'has' for 'is'.) x may be the same shape as y but a different colour; and x may be the same colour as y, but a different shape. This shows that neither of these equivalence relations is absolute in a sense I shall define. An equivalence relation R is absolute iff if it is true that xRy, then, necessarily, for no equivalence relation S is this true: (Ez)((xSz V ySz) & xSy). That is, that an equivalence relation is absolute means that if it holds between any objects x and y, then, necessarily, there is no other equivalence relation in which either of these stand, which they do not stand in to each other. I call an equivalence relation 'relative' when it is not absolute. It is obvious that there are an indefinite number of relative equivalence relations. Classical identity itself is an absolute equivalence relation; its peculiarity is that it is strongly reflexive: everything has it to itself. The holding of a relative equivalence relation between x and y does not ensure that x is (classically) identical with y. No relative equivalence relation entails classical identity, for it will fail to ensure indiscernibility. If x is the same f as y, and y is a g, but x is not the same g as y-which means that being the same f as is a relative equivalence relation-then something will be true of x-that it is not the same g as y-which is not true of y. With the help of these notions we can get an insight into some of the problems discussed by David Wiggins in his book Identity and Spatio-Temporal Continuity.1