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Full Idea
In my personal opinion, predicativism is the best version of conceptualism that we have yet discovered.
Gist of Idea
The best version of conceptualism is predicativism
Source
David Bostock (Philosophy of Mathematics [2009], 8.4)
Book Ref
Bostock,David: 'Philosophy of Mathematics: An Introduction' [Wiley-Blackwell 2009], p.259
A Reaction
Since conceptualism is a major player in the field, this makes predicativism a very important view. I won't vote Predicativist quite yet, but I'm tempted.
| 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] |