- Gareth Evans's 1978 argument disproving the existence of indeterminate identity is discussed. On a simple analysis it appeals to the (invalid) contrapositive version of Leibniz's Law2; on a deeper analysis it presumes incorrectly that the formula '∇(x = a)' expresses a property (the property of being indeterminately identical with a).
- The proof is an RAA of the hypothesis that that formula expresses a property. This fact is not due to non-extensionality or to anything like the semantic paradoxes; instead it is akin to the "paradoxes" of naive set theory, due to the fact that identity is defined in terms of global quantification over all (worldly) properties.
- A test for whether a formula 'φx' expresses a worldly property is whether it satisfies the principle that joint (determinate) satisfaction and (determinate) dissatisfaction of the formula makes a "Definite Difference" in the identity of the objects in question; that is, that there are no objects x and y such that 'φx' & '!¬ φy' are both true, along with '∇x = y'.
- If a formula satisfies this principle, then an abstract, 'λxφx', constructed from it stands for a worldly property; otherwise we can either say that it does not stand for a property, or that it stands for a non-worldly "conceptual" property.
Footnote 1: Taken from "Parsons (Terence) - Indeterminate Identity: Analytical Table of Contents".
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