|Identity: Two objects are never identical. Identity is a single object, to which may be referred to with two different terms. The fact that two descriptions mean a single object may be discovered only in the course of an investigation.|
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Identity of classes: symbolic: PxEfxyx - Identity/Relation-in-Extension: PxPyEfxyyxy - Identity/thre-place predikates: PxPyPzEfxyzyxyz - so you can go on and on up - or down to zero-place predicates(propositions).
Identity / Prior: a "zero-place predicate": (0) Efy i.e. "If f then y and if y then f" (spelling Lesniewski: E = equivalent) - which is the case when f and y are the case, or not case when f and y are not.
Truth value / Prior: so we imagine the term "truth value" for what we describe as the same, if the condition (0) is satisfied.
Objects of thought Oxford 1971
Arthur N. Prior
Papers on Time and Tense 2nd Edition Oxford 2003