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In philosophy, identity, from Latin: identitas (“sameness”), is the exact sameness of things. According to Leibniz's law two things sharing every attribute are not only similar, but are the same thing. The concept of sameness has given rise to the general concept of identity, as in personal identity and social identity.
An entity can only be fully identical with itself. Any difference gives rise to a separate identity. Thus identity is whatever makes an entity definable and recognizable, in terms of possessing a set of qualities or characteristics that distinguish it from other entities.^{[1]}^{[2]} In layman's terms, identity is whatever makes something the same or different.^{[3]}
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Logic of identity
In logic, the identity relation (also called "equality") is normally defined as the binary relation that holds only between a thing and itself. That is, identity is the twoplace predicate, "=", such that for all x and y, "x = y" is true if x is the same thing as y. Identity is transitive, symmetric, and reflexive. It is an axiom of most normal modal logics that for all x and y, if x = y then necessarily y = x. That is, identity does not hold contingently, but of necessity.
Metaphysics of identity
Metaphysicians, and sometimes philosophers of language and mind, ask other questions:
 What does it mean for an object to be the same as itself?
 If x and y are identical (are the same thing), must they always be identical? Are they necessarily identical?
 What does it mean for an object to be the same, if it changes over time? (Is apple_{t} the same as apple_{t+1}?)
 If an object's parts are entirely replaced over time, as in the Ship of Theseus example, in what way is it the same?
The Law of identity originates from classical antiquity. The modern formulation of identity is that of Gottfried Leibniz, who held that x is the same as y if and only if every predicate true of x is true of y as well.
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