Believing

Abstract

Leibniz’s Law or the principle that no two objects have exactly the same properties is one of the few philosophical principles that enjoy a general acceptance among philosophers in some form or other. The principle states that for any objects x and y, x is identical to y if and only if for any property P, x has P if and only if y has P. Some philosophers hold that this principle is true provided that the range of the second-order quantifier is restricted in certain ways, that is, that only certain properties can replace P in the right-hand condition. Others want to restrict the range of the individual variables to individual objects only and exclude such items as properties or sets. However, I find that Leibniz’s Law in its unrestricted form is true, but another principle closely associated with Leibniz’s Law does require some modifications. This other principle that Leibniz also held concerns the substitution of terms in sentences or statements. This principle, which I shall call ‘Leibniz’s Substitution Principle,’ holds that expressions that denote the same thing can be substituted one for the other in sentences without loss of truth.