display all the ideas for this combination of texts
3 ideas
| 3343 | Euclid's could be the only viable geometry, if rejection of the parallel line postulate doesn't lead to a contradiction [Benardete,JA on Kant] |
| Full Idea: The possible denial of the parallel lines postulate does not entail that Kant was wrong in considering Euclid's the only viable geometry. If the denial issued in a contradiction, then the postulate would be analytic, and Kant would be refuted. | |
| From: comment on Immanuel Kant (Critique of Pure Reason [1781]) by José A. Benardete - Metaphysics: the logical approach Ch.18 |
| 8737 | Kant suggested that arithmetic has no axioms [Kant, by Shapiro] |
| Full Idea: Kant suggested that arithmetic has no axioms. | |
| From: report of Immanuel Kant (Critique of Pure Reason [1781], B204-6/A164) by Stewart Shapiro - Thinking About Mathematics 4.2 | |
| A reaction: A hundred years later a queue was forming to spell out the axioms of arithmetic. The definitions of 0 and 1 always look to me more like logicians' tricks than profound truths. Some notions of successor and induction do, however, seem needed. |
| 5557 | Axioms ought to be synthetic a priori propositions [Kant] |
| Full Idea: Concerning magnitude ...there are no axioms in the proper sense. ....Axioms ought to be synthetic a priori propositions. | |
| From: Immanuel Kant (Critique of Pure Reason [1781], B205/A164) | |
| A reaction: This may be a hopeless dream, but it is (sort of) what all philosophers long for. Post-modern relativism may just be the claim that all axioms are analytic. Could a posteriori propositions every qualify as axioms? |