There is a metaphysical principle about the identity of individuals which is the subject of frequent controversy. The principle I am referring to asserts that any individuals, x and y, are identical only if they share all of their properties in common. Expressed formally, The Principle of Identity is
This principle is traditionally known as 'Leibniz's Law, and also as the 'Principle of the Indiscernability of Identicals'; the latter expression is descriptively more accurate, 1 though the weight of customary association has established a strong connection between the former expression and the principle. In what follows, the principle will be referred to systematically as The Principle of Identity.
The Principle of Identity has always appeared as an important stumbling block to those who would espouse materialism in the form of the Identity Theory. This is because the Identity Theory asserts an identity between certain items -sensations and brain processes -which appears to be falsified by the fact that there are characteristics which sensations have which brain processes do not have, and by the fact that there are characteristics which brain processes have which sensations do not have. In other words, given The Principle of Identity, as well as well-known facts about sensations and brain processes, the Identity Theory of Mind must be false. This objection to the Identity Theory is known as The Property Obfeetion, and is stated more formally as follows.
The Property Objection:
1 The Principle of Identity. (assumption) 2 Sensations are identical with brain processes. 2 (assumption) 3 There is some property, F, such that some sensation has F, but no brain process has F. (assumption)