Identity (philosophy)

In philosophy, identity, from Latin: identitas (“sameness”), is the relation each thing bears just to itself. [1] 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.[2][3] In layman's terms, identity is whatever makes something the same or different.[4]

## 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 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 and y, if x = y then necessarily y = x. That is, identity does not hold contingently, but of necessity.

Put in these terms (above), it can seem rather trivial, but the point, of course, is that the same number, object, or person, can have different "guises", and it is far from trivial if two or more guises refer to the same same number, object, or person. For example, 1+1=2 because '1+1' and '2' are different "guises" for the same number. Similarly, for personal identity over time, "me today" and "me yesterday" are different guises for the same person.

## 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 applet the same as applet+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.

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.

## Qualitative versus numerical identity

[citation needed]

Arbitrary 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 hand.

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.

## External references

General Information
• Stanford Encyclopedia of Philosophy: Identity, First published Wed Dec 15, 2004; substantive revision Sun Oct 1, 2006.
• Stanford Encyclopedia of Philosophy: Identity over time. First published Fri 18 March 2005.
• Stanford Encyclopedia of Philosophy: Personal identity. First published Tue Aug 20, 2002; substantive revision Tue Feb 20, 2007.
• Stanford Encyclopedia of Philosophy: Relative identity. First published Mon 22 April 2002.
• Erich Fromm Interview Excerpt. youtube.com.
Citations
1. ^ The Cambridge Dictionary of Philosophy, 2nd Edition, CUP: 1995
2. ^ Stanford Encyclopedia of Philosophy: Identity, First published Wed Dec 15, 2004; substantive revision Sun Oct 1, 2006.
3. ^ T. Thompson (ed.) and S. M. Black (ed.) (2006), Forensic Human Identification: An Introduction. CRC Press. ISBN 0849339545
4. ^ This includes operational definition that either yields a yes or no value for whether a thing is present in a field of observation, or that distinguishes the thing from its background, allowing one to determine what is and what is not included in it. Also see pattern recognition.
Books and publications

People
Friedrich Wilhelm Joseph Schelling, Baruch Spinoza, Karl Christian Friedrich Krause, Paul Ricœur, Gottlob Frege
General
Being, The Golden Rule, Personal identity, Shunyata, Pseudonymity
Identity
Recognition of human individuals, Cultural identity, Digital identity, Ethnic identity, Social identity, Reputation, Online identity, Identity theft, Counterpart theory

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