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Full Idea
Three simple objections to conceptualism in mathematics are that we do not ascribe mathematical properties to our ideas, that our ideas are presumably finite, and we don't think mathematics lacks truthvalue before we thought of it.
Gist of Idea
Conceptualism fails to grasp mathematical properties, infinity, and objective truth values
Source
David Bostock (Philosophy of Mathematics [2009], 8.4)
Book Ref
Bostock,David: 'Philosophy of Mathematics: An Introduction' [Wiley-Blackwell 2009], p.253
A Reaction
[compressed; Bostock refers back to his Ch 2] Plus Idea 18134. On the whole I sympathise with conceptualism, so I will not allow myself to be impressed by any of these objections. (So, what's actually wrong with them.....?).
Related Idea
Idea 18134 Predicativism makes theories of huge cardinals impossible [Bostock]
| 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] |