Equality and identity. Bulletin of Symbolic Logic. 19 (2013) 255-6. (Coauthor: Anthony Ramnauth) ► JOHN CORCORAN AND ANTHONY RAMNAUTH, Equality and identity. Philosophy, University at Buffalo, Buffalo, NY 14260-4150, USA E-mail: corcoran@buffalo.edu Two line halves are equal but not identical [one and the same]. Every line equals infinitely many other lines, but no line is [identical to] any other line-taking 'identical' strictly here and below. Knowing that two lines equaling a third are equal is useful; the condition "two lines equaling a third" often holds. But could knowing that two lines being [identical to] a third are identical be useful? The antecedent condition "two things identical to a third" never holds, nor does the consequent condition "two things being identical". The plural predicate 'are equal' as in 'All diameters of a given circle are equal' is useful and natural. 'Are identical' as in 'All centers of a given circle are identical' is awkward or worse. Substituting equals for equals [replacing one of two equals by the other] makes sense. Substituting identicals for identicals is empty-a thing is identical only to itself; substituting one thing for itself leaves that thing alone, does nothing. There are as many types of equality as magnitudes: angles, lines, planes, solids, times, etc. Each admits unit magnitudes. And each such equality analyzes as identity of magnitude: two lines are equal [in length] if the one's length is identical to the other's. Tarski [1] hardly mentioned equality-identity distinctions (pp. 54-63). His discussion begins: Among the logical concepts [...], the concept of IDENTITY or EQUALITY [...] has the greatest importance. Not until page 62 is there an equality-identity distinction. His only "notion of equality", if such it is, is geometrical congruence-having the same size and shape-an equivalence relation not admitting any unit. This lecture treats the history and philosophy of equality-identity distinctions. [1] ALFRED TARSKI, Introduction to Logic, Dover, New York, 1995.