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Full Idea
The whole of the theory of numbers belongs to logic; or rather, it would do so, were it not, as pure mathematics, pre-logical, that is, even more abstract than logic.
Gist of Idea
Mathematics is close to logic, but is even more abstract
Source
Charles Sanders Peirce (The Nature of Mathematics [1898], IV)
Book Ref
Peirce,Charles Sanders: 'Philosophical Writings of Peirce', ed/tr. Buchler,Justus [Dover 1940], p.148
A Reaction
Peirce seems to flirt with logicism, but rejects in favour of some subtler relationship. I just don't believe that numbers are purely logical entities.
| 14789 | Experience is indeed our only source of knowledge, provided we include inner experience [Peirce] |
| 14782 | Philosophy is an experimental science, resting on common experience [Peirce] |
| 14783 | Logic, unlike mathematics, is not hypothetical; it asserts categorical ends from hypothetical means [Peirce] |
| 14784 | Ethics is the science of aims [Peirce] |
| 14786 | Some logical possibility concerns single propositions, but there is also compatibility between propositions [Peirce] |
| 14785 | The world is one of experience, but experiences are always located among our ideas [Peirce] |
| 14787 | Self-contradiction doesn't reveal impossibility; it is inductive impossibility which reveals self-contradiction [Peirce] |
| 14788 | Mathematics is close to logic, but is even more abstract [Peirce] |