more from Alan Musgrave

Single Idea 10061

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

Full Idea

The If-thenist view seems to apply straightforwardly only to the axiomatised portions of mathematics.

Gist of Idea

The If-thenist view only seems to work for the axiomatised portions of mathematics


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

Book Reference

-: 'British Soc for the Philosophy of Science' [-], p.119

A Reaction

He cites Lakatos to show that cutting-edge mathematics is never axiomatised. One might reply that if the new mathematics is any good then it ought to be axiomatis-able (barring Gödelian problems).

Related Idea

Idea 8752 Deductivism says mathematics is logical consequences of uninterpreted axioms [Shapiro]