Single Idea 18108

[catalogued under 5. Theory of Logic / A. Overview of Logic / 5. First-Order Logic]

Full Idea

First-order logic is not decidable. That is, there is no test which can be applied to any arbitrary formula of that logic and which will tell one whether the formula is or is not valid (as proved by Church in 1936).

Gist of Idea

First-order logic is not decidable: there is no test of whether any formula is valid

Source

David Bostock (Philosophy of Mathematics [2009], 5.5)

Book Reference

Bostock,David: 'Philosophy of Mathematics: An Introduction' [Wiley-Blackwell 2009], p.152

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