numerical identity

Identity (philosophy)

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. Or, in layman's terms, identity is whatever makes something the same or different. 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.

Logic of identity

In 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 iff 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. (These definitions are of course inapplicable in some areas of quantified logic, such as fuzzy logic and fuzzy set theory, and with respect to vague objects.)

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?

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.

Qualitative versus numerical identity

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 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.

See also

People: Friedrich Wilhelm Joseph Schelling, Baruch Spinoza, Karl Christian Friedrich KrauseGeneral: Being positive philosophy, The Golden Rule, Personal identity, Shunyata, Pseudonymity, ontological differenceIdentity:Recognition of human individuals, Cultural identity, Digital identity, Ethnic identity, Social identity, absolute identity, Reputation, Online identity, Identity theft, Counterpart theory

External articles and references

Books and publications

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

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