identitiesneither

Identitiesneither is a neologism used in philosophy and logic to describe a class of identity statements that can be neither true nor false under certain semantic frameworks. The term blends identity theory with the idea of indeterminacy, signaling that some claims of sameness resist a definitive truth value in non-classical logics or in contexts with incomplete information.

The concept arises in discussions of how to treat identity in non-binary logics, such as three-valued logics or paraconsistent systems. In these frameworks, the equality predicate can take a third value beyond true and false, often labeled indeterminate or unknown. Under such semantics, an assertion of sameness, such as “a = b,” may be designated as identitiesneither when a and b lack determinate referents, or when the available information does not resolve whether they denote the same object.

Identitiesneither is not widely standardized in formal literature, but it is used as a descriptive label to discuss limitations of classical identity judgments in several areas. It has potential applications in the philosophy of language, formal semantics, and computer science, particularly in models that must handle incomplete, vague, or non-existent referents.

Related concepts include the ordinary notion of identity or equality, indeterminacy in truth-value assignment, and non-classical logics that admit gaps or gluts in evaluation. The term serves as a concise way to reference cases where identity claims resist conventional true/false classification.