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
Source
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]