Identity

Metaphysics

Metaphysicians, and sometimes philosophers of language and mind, ask other questions:

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• 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?

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.

Related Topics:
Gottfried Leibniz - Predicate

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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.

Related Topics:
Philosophy of mathematics - Predicate calculus - Leibniz's law - Equality - Mathematics - Equation - Variable

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More recent metaphysicians have discussed trans-world identity -- the notion that there can be the same object in different possible worlds.

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