display all the ideas for this combination of texts
4 ideas
| 12421 | Kant's intuitions struggle to judge relevance, impossibility and exactness [Kitcher on Kant] |
| 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?). | |
| From: comment on Immanuel Kant (Critique of Pure Reason [1781]) by Philip Kitcher - The Nature of Mathematical Knowledge 03.1 | |
| 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. |
| 17617 | Maths is a priori, but without its relation to empirical objects it is meaningless [Kant] |
| Full Idea: Although all these principles .....are generated in the mind completely a priori, they would still not signify anything at all if we could not always exhibit their significance in appearances (empirical objects). | |
| From: Immanuel Kant (Critique of Pure Reason [1781], B299/A240) | |
| A reaction: This is the subtle Kantian move that we all have to take seriously when we try to assert 'realism' about anything. Our drive for meaning creates our world for us? |
| 12458 | Kant taught that mathematics is independent of logic, and cannot be grounded in it [Kant, by Hilbert] |
| Full Idea: Kant taught - and it is an integral part of his doctrine - that mathematics treats a subject matter which is given independently of logic. Mathematics, therefore, can never be grounded solely in logic. | |
| From: report of Immanuel Kant (Critique of Pure Reason [1781]) by David Hilbert - On the Infinite p.192 | |
| A reaction: Presumably Gödel's Incompleteness Theorems endorse the Kantian view, that arithmetic is sui generis, and beyond logic. |
| 2795 | If 7+5=12 is analytic, then an infinity of other ways to reach 12 have to be analytic [Kant, by Dancy,J] |
| Full Idea: Kant claimed that 7+5=12 is synthetic a priori. If the concept of 12 analytically involves knowing 7+5, it also involves an infinity of other arithmetical ways to reach 12, which is inadmissible. | |
| From: report of Immanuel Kant (Critique of Pure Reason [1781], B205/A164) by Jonathan Dancy - Intro to Contemporary Epistemology 14.3 |