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Full Idea
What we actually get by means of abstraction from things is the concept, and in this we then discover the number.
Gist of Idea
Abstraction from things produces concepts, and numbers are in the concepts
Source
Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884], §47)
Book Ref
Frege,Gottlob: 'The Foundations of Arithmetic (Austin)', ed/tr. Austin,J.L. [Blackwell 1980], p.61
A Reaction
And how do we 'discover' it, if not by a process of further abstraction? The concept of the moon (see Idea 8641) no more contains the number one than the actual moon does
Related Idea
Idea 8641 You can abstract concepts from the moon, but the number one is not among them [Frege]
| 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] |