Single Idea 10012

[catalogued under 5. Theory of Logic / D. Assumptions for Logic / 4. Identity in Logic]

Full Idea

Complete proof procedures are available not only for quantification theory, but for quantification theory and identity together. Gödel showed that the theory is still complete if we add self-identity and the indiscernability of identicals.

Gist of Idea

Quantification theory can still be proved complete if we add identity

Source

Willard Quine (Philosophy of Logic [1970], Ch.5)

Book Reference

Quine,Willard: 'Philosophy of Logic' [Prentice-Hall 1970], p.62


A Reaction

Hence one talks of first-order logic 'with identity', even though, as Quine observes, it is unclear whether identity is actually a logical or a mathematical notion.