equalidentical

Equalidentical is a term used in some philosophical, mathematical, or logical discussions to denote a notion that combines aspects of equality and identity. It is not a standardized term in mainstream literature, but it appears in discussions aiming to emphasize when two objects are not only equal in some sense but in fact the same object in every respect.

Conceptual foundations often contrast identity with equality. In standard logic, identity is the relation of numerical identity, usually written as x = y, meaning x and y are the same object. Equality, by contrast, often refers to a relation that permits substitutivity: if x = y, then any property or predicate applied to x yields the same result when applied to y. The phrase equalidentical is sometimes used to signal that equality is intended to collapse to identity, or to stress an extreme form of the Leibniz principle that any true property of one must be a true property of the other.

In programming and formal theory, similar distinctions appear between reference or identity equality (two references point to the exact same object) and structural or value equality (two distinct objects that share the same data). Some communities use “identical” to describe reference equality, which echoes the intuition behind equalidentical.

Usage and caveats: Because equalidentical is not a fixed technical term, its precise meaning can vary by author or context. Readers should consult the specific definition in a given text. The concept aligns with discussions about indistinguishability and the substitutivity of identicals.

See also: Identity (philosophy), Equality, Leibniz's law, Principle of the identity of indiscernibles, Reference equality, Structural equality, Substitution.