Ideas of Alan Musgrave, by Theme
[New Zealand, fl. 1993, At the University of Otago, NZ.]
green numbers give full details 
back to list of philosophers 
expand these ideas
5. Theory of Logic / C. Ontology of Logic / 3. IfThenism
10065

Perhaps Ifthenism survives in mathematics if we stick to firstorder logic

10061

The Ifthenist view only seems to work for the axiomatised portions of mathematics

5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth
10050

A statement is logically true if it comes out true in all interpretations in all (nonempty) domains

10049

Logical truths may contain nonlogical notions, as in 'all men are men'

6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic
10058

No two numbers having the same successor relies on the Axiom of Infinity

6. Mathematics / C. Sources of Mathematics / 7. Formalism
10062

Formalism seems to exclude all creative, growing mathematics

10063

Formalism is a bulwark of logical positivism

19. Language / A. Nature of Meaning / 5. Meaning as Verification
10060

Logical positivists adopted an Ifthenist version of logicism about numbers
