display all the ideas for this combination of texts
2 ideas
9916 | Convention, yes! Arbitrary, no! [Poincaré, by Putnam] |
Full Idea: Poincaré once exclaimed, 'Convention, yes! Arbitrary, no!'. | |
From: report of Henri Poincaré (talk [1901]) by Hilary Putnam - Models and Reality | |
A reaction: An interesting view. It mustn't be assumed that conventions are not rooted in something. Maybe a sort of pragmatism is implied. |
19226 | We now know that mathematics only studies hypotheses, not facts [Peirce] |
Full Idea: It did not become clear to mathematicians before modern times that they study nothing but hypotheses without as pure mathematicians caring at all how the actual facts may be. | |
From: Charles Sanders Peirce (Reasoning and the Logic of Things [1898], I) | |
A reaction: 'Modern' here is 1898. As a logical principle this would seem to qualify as 'if-thenism' (see alphabetical themes). It's modern descendant might be modal structuralism (see Geoffrey Hellman). It take maths to be hypotheses abstracted from experience. |