more from Stephen Read

### Single Idea 11024

#### [catalogued under 5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic]

Full Idea

For the realist, study of semantic structures comes before study of proofs. In higher-order logic is has to, for the logics are incomplete.

Gist of Idea

Semantics must precede proof in higher-order logics, since they are incomplete

Source

Stephen Read (Thinking About Logic [1995], Ch.9)

Book Reference

Read,Stephen: 'Thinking About Logic' [OUP 1995], p.229

A Reaction

This seems to be an important general observation about any incomplete system, such as Peano arithmetic. You may dream the old rationalist dream of starting from the beginning and proving everything, but you can't. Start with truth and meaning.