more from Alan Musgrave

### Single Idea 10065

#### [catalogued under 5. Theory of Logic / C. Ontology of Logic / 3. If-Thenism]

Full Idea

If we identify logic with first-order logic, and mathematics with the collection of first-order theories, then maybe we can continue to maintain the If-thenist position.

Gist of Idea

Perhaps If-thenism survives in mathematics if we stick to first-order logic

Source

Alan Musgrave (Logicism Revisited [1977], §5)

Book Reference

-: 'British Soc for the Philosophy of Science' [-], p.124

A Reaction

The problem is that If-thenism must rely on rules of inference. That seems to mean that what is needed is Soundness, rather than Completeness. That is, inference by the rules must work properly.