more from this thinker | more from this text
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.
Gist of Idea
We now know that mathematics only studies hypotheses, not facts
Source
Charles Sanders Peirce (Reasoning and the Logic of Things [1898], I)
Book Ref
Peirce,Charles Sanders: 'Reasoning and the Logic of Things', ed/tr. Ketner,K.L. [Harvard 1992], p.114
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.
| 19226 | We now know that mathematics only studies hypotheses, not facts [Peirce] |
| 8642 | Abstraction from things produces concepts, and numbers are in the concepts [Frege] |
| 1614 | Conceptualism holds that there are universals but they are mind-made [Quine] |
| 18140 | The best version of conceptualism is predicativism [Bostock] |
| 18138 | Conceptualism fails to grasp mathematical properties, infinity, and objective truth values [Bostock] |
| 18063 | Conceptualists say we know mathematics a priori by possessing mathematical concepts [Kitcher] |
| 18064 | If meaning makes mathematics true, you still need to say what the meanings refer to [Kitcher] |
| 8731 | Conceptualist are just realists or idealist or nominalists, depending on their view of concepts [Shapiro] |