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Full Idea
Someone who believes that basic truths of mathematics are true in virtue of meaning is not absolved from the task of saying what the referents of mathematical terms are, or ...what mathematical reality is like.
Gist of Idea
If meaning makes mathematics true, you still need to say what the meanings refer to
Source
Philip Kitcher (The Nature of Mathematical Knowledge [1984], 04.6)
Book Ref
Kitcher,Philip: 'The Nature of Mathematical Knowledge' [OUP 1984], p.86
A Reaction
Nice question! He's a fan of getting at the explanatory in mathematics.
| 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] |