Ideas from 'Logicism Revisited' by Alan Musgrave [1977], by Theme Structure
[found in 'British Soc for the Philosophy of Science' (ed/tr ) [ ,]].
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5. Theory of Logic / C. Ontology of Logic / 3. IfThenism
10061

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

10065

Perhaps Ifthenism survives in mathematics if we stick to firstorder logic

5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth
10049

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

10050

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

6. Mathematics / B. Foundations for Mathematics / 3. 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
10063

Formalism is a bulwark of logical positivism

10062

Formalism seems to exclude all creative, growing mathematics

19. Language / B. Meaning / 3. Meaning as Verification
10060

Logical positivists adopted an Ifthenist version of logicism about numbers
