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In philosophy, identity (also called sameness) is whatever makes an entity definable and recognizable, in terms of possessing a set of qualities or characteristics that distinguish it from entities of a different type.[1][2] Or, in layman's terms, identity is whatever makes something the same or different.[3]
[edit] Logic of identityIn logic, the identity relation is normally defined as the relation that holds only between a thing and itself. That is, identity is the two-place 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, if x = x then necessarily x = x. [edit] Metaphysics of identityMetaphysicians, and sometimes philosophers of language and mind, ask other questions:
A traditional view 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. Leibniz's ideas have taken root in the philosophy of mathematics, where they have influenced the development of the predicate calculus as Leibniz's law. Mathematicians sometimes distinguish identity from equality. More mundanely, an identity in mathematics may be an equation that holds true for all values of a variable. Hegel argued that things are inherently self-contradictory and that the notion of something being self-identical only made sense if it were not also not-identical or different from itself and did not also imply the latter. In Hegel's words, "Identity is the identity of identity and non-identity." More recent metaphysicians have discussed trans-world identity -- the notion that there can be the same object in different possible worlds. An alternative to trans-world identity is the counterpart relation in Counterpart theory. It is a similarity relation that rejects trans-world individuals and instead defends an objects counterpart - the most similar object. [edit] Qualitative versus numerical identityArbitrary objects a and b can be said to be qualitatively identical if a and b are duplicates, that is, if a and b are exactly similar in all respects, that is, if a and b have all qualitative properties in common. Examples of this might be two wine glasses made in the same wine glass factory on the same production line (at least, for a relaxed standard of exact similarity), or a carbon atom in one's left hand and a carbon atom in one's right shoulder (perhaps true even for the most strict standard of exact similarity). Alternatively, a and b can be said to be numerically identical if a and b are one and the same thing, that is, if a is b, that is, if there is only one thing variously called "a" and "b". For example, Clark Kent is numerically identical with Superman in the sense that there is only one person (who happens to wear different clothes at different times). This relationship is expressed in mathematics with the "=" symbol, e.g., a = b, or Clark Kent = Superman. However in contrast to this, given that they are in fact the same individual person, they are not separate entities, "they" are merely a person that is both Clark Kent and Superman simultaneously, therefore a = a. Superman = Superman, and this Superman has a component to his personality that is also part of the individual identity. If they were indeed two separate people as the civilian Clark and the super-hero Superman then they would not equal each other as per the Law of excluded middle. It is then either Superman or Clark Kent, not both or neither. It is either the atom in the right or left hand, not both or neither. [edit] See also
[edit] External references
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