3 ideas
10792 | The substitutional quantifier is not in competition with the standard interpretation [Kripke, by Marcus (Barcan)] |
Full Idea: Kripke proposes that the substitutional quantifier is not a replacement for, or in competition with, the standard interpretation. | |
From: report of Saul A. Kripke (A Problem about Substitutional Quantification? [1976]) by Ruth Barcan Marcus - Nominalism and Substitutional Quantifiers p.165 |
10245 | One geometry cannot be more true than another [Poincaré] |
Full Idea: One geometry cannot be more true than another; it can only be more convenient. | |
From: Henri Poincaré (Science and Method [1908], p.65), quoted by Stewart Shapiro - Philosophy of Mathematics | |
A reaction: This is the culminating view after new geometries were developed by tinkering with Euclid's parallels postulate. |
10269 | Mathematics eliminates possibility, as being simultaneous actuality in sets [Putnam] |
Full Idea: Mathematics has got rid of possibility by simply assuming that, up to isomorphism anyway, all possibilities are simultaneous actual - actual, that is, in the universe of 'sets'. | |
From: Hilary Putnam (What is Mathematical Truth? [1975], p.70), quoted by Stewart Shapiro - Philosophy of Mathematics 7.5 |