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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 Ref
-: '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]
| 10054 | Arithmetic and geometry achieve some certainty without worrying about existence [Descartes] |
| 10055 | Mathematical proofs work, irrespective of whether the objects exist [Locke] |
| 10056 | At bottom eternal truths are all conditional [Leibniz] |
| 14783 | Logic, unlike mathematics, is not hypothetical; it asserts categorical ends from hypothetical means [Peirce] |
| 21493 | Pure mathematics deals only with hypotheses, of which the reality does not matter [Peirce] |
| 24137 | Mathematics is just accurate inferences from definitions, and doesn't involve objects [Nietzsche] |
| 10053 | Geometrical axioms imply the propositions, but the former may not be true [Russell] |
| 10064 | Quine quickly dismisses If-thenism [Quine, by Musgrave] |
| 10066 | Putnam coined the term 'if-thenism' [Putnam, by Musgrave] |
| 10061 | The If-thenist view only seems to work for the axiomatised portions of mathematics [Musgrave] |
| 10065 | Perhaps If-thenism survives in mathematics if we stick to first-order logic [Musgrave] |
| 17620 | Critics of if-thenism say that not all starting points, even consistent ones, are worth studying [Maddy] |
| 22291 | Deductivism can't explain how the world supports unconditional conclusions [Potter] |