Identity (philosophy) - Metaphysics of Identity

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.

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.