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] |
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] |