structure for 'Mathematics'    |     alphabetical list of themes    |     expand these ideas

6. Mathematics / C. Sources of Mathematics / 10. Constructivism / c. Conceptualism

[maths is just a set of human concepts in minds]

8 ideas
We now know that mathematics only studies hypotheses, not facts [Peirce]
Abstraction from things produces concepts, and numbers are in the concepts [Frege]
Conceptualism holds that there are universals but they are mind-made [Quine]
Conceptualism fails to grasp mathematical properties, infinity, and objective truth values [Bostock]
The best version of conceptualism is predicativism [Bostock]
Conceptualists say we know mathematics a priori by possessing mathematical concepts [Kitcher]
If meaning makes mathematics true, you still need to say what the meanings refer to [Kitcher]
Conceptualist are just realists or idealist or nominalists, depending on their view of concepts [Shapiro]