Some Notes on the Role of the Identity of Indiscernibles in Metaphysics

Abstract

The Principle of the Identity of Indiscernibles (PII) asserts that if putative objects x and y shareall properties P, then they must be one and the same entity. Since the usual formal rendering ofthe PII has the same formal structure as the Leibniz Identity, it may be unclear whether it canbe used to define identity and objectuality. As identity and objectuality are closely related, thisstudy aims to examine their relationship within the framework of formal ontology. Crucialfor the discussion are issues about type and range of quantification and the invariance ofthe identity predicate coourring in the PII. Ultimately, the analysis reveals that the appeal toPII is insufficient for providing both identity and objectuality. Some further considerationsabout how the PII sensitively constrains the range of available ontologies or metaphysics areformulated.