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. If-Thenism
The If-thenist view only seems to work for the axiomatised portions of mathematics
Perhaps If-thenism survives in mathematics if we stick to first-order logic
5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth
Logical truths may contain non-logical notions, as in 'all men are men'
A statement is logically true if it comes out true in all interpretations in all (non-empty) domains
6. Mathematics / B. Foundations for Mathematics / 3. Axioms for Number / d. Peano arithmetic
No two numbers having the same successor relies on the Axiom of Infinity
6. Mathematics / C. Sources of Mathematics / 7. Formalism
Formalism seems to exclude all creative, growing mathematics
Formalism is a bulwark of logical positivism
19. Language / A. Nature of Meaning / 5. Meaning as Verification
Logical positivists adopted an If-thenist version of logicism about numbers