Why A=A Is Not Enough: The Law of Identity Presupposes Identity

The law of identity is traditionally treated as one of the fundamental principles of logic: A = A It is commonly assumed that this principle secures object stability, prevents conceptual substitution, and provides the basis for coherent reasoning. This paper argues that the law of identity by itself does not determine whether two objects are identical. Every practical application of identity requires the prior selection of a comparison mask: a subset of properties relative to which the comparison is performed. As a result, identity judgments are not absolute but mask-relative. Different masks may produce different identity results for the same objects, including both false-positive and false-negative identity judgments. The law of identity therefore functions not as an autonomous detector of sameness, but as a formal operation applied within a chosen system of properties. The paper develops a mask-relative account of identity, formulates the Mask-Relative Identity Principle, and shows how many classical philosophical puzzles arise from treating mask-dependent identity judgments as absolute.