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Full Idea
Kant's intuitions have the Irrelevance problem (which structures of the mind are just accidental?), the Practical Impossibility problem (how to show impossible-in-principle?), and the Exactness problem (are entities exactly as they seem?).
Gist of Idea
Kant's intuitions struggle to judge relevance, impossibility and exactness
Source
comment on Immanuel Kant (Critique of Pure Reason [1781]) by Philip Kitcher - The Nature of Mathematical Knowledge 03.1
Book Ref
Kitcher,Philip: 'The Nature of Mathematical Knowledge' [OUP 1984], p.50
A Reaction
[see Kitcher for an examination of these] Presumably the answer to all three must be that we have meta-intuitions about our intuitions, or else intuitions come with built-in criteria to deal with the three problems. We must intuit something specific.
| 12421 | Kant's intuitions struggle to judge relevance, impossibility and exactness [Kitcher on Kant] |
| 16910 | Mathematics can only start from an a priori intuition which is not empirical but pure [Kant] |
| 16917 | All necessary mathematical judgements are based on intuitions of space and time [Kant] |
| 9830 | Bolzano began the elimination of intuition, by proving something which seemed obvious [Bolzano, by Dummett] |
| 17816 | Frege's logicism aimed at removing the reliance of arithmetic on intuition [Frege, by Yourgrau] |
| 9831 | Geometry appeals to intuition as the source of its axioms [Frege] |
| 12420 | If mathematics comes through intuition, that is either inexplicable, or too subjective [Kitcher] |
| 12393 | Intuition is no basis for securing a priori knowledge, because it is fallible [Kitcher] |
| 18061 | Mathematical intuition is not the type platonism needs [Kitcher] |
| 10244 | Intuition is an outright hindrance to five-dimensional geometry [Shapiro] |
| 8756 | Intuition doesn't support much mathematics, and we should question its reliability [Maddy, by Shapiro] |