Timeline for Essential reads in the philosophy of mathematics and set theory
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
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| Oct 2, 2017 at 16:01 | comment | added | Peter Heinig | @ex0du5: likely you'll know this, and without any 'endorsement' whatsoever, yet it seems relevant to add to this a recent interpretation of Kant's logic using geometric logic (a subset of intuitionistic logic): Theodora Achourioti, Michiel van Lambalgen. A formalisation of Kant's transcendental logic. Review of Symbolic Logic, 4(2), 254-289. | |
| Nov 9, 2014 at 19:39 | comment | added | Christian Remling | Studying the philosophy of mathematics and completely ignoring Kant is like reading Dante while having no idea who Vergil was. | |
| Nov 9, 2014 at 19:36 | comment | added | Christian Remling | While today it is possible (even fashionable) to disagree with much of what Kant wrote about mathematics, his influence on the subject was tremendous. Brouwer, Hilbert definitely knew their Kant and were strongly influenced by his ideas. | |
| Jun 28, 2013 at 15:58 | comment | added | ex0du5 | I'm not saying it isn't instructive to learn from Kant the direction of much of that philosophy, but I wouldn't look to his work as being seriously defensible today. And I don't think it's purpose was to benefit mathematics either, simply to use it in a different programme. But if one wants to focus on the mathematical content of his work, I would recommend his Prolegomena before CPR. It is more focused on the examples of his philosophy, including much arithmetic, logic, and geometry. (And the occasional claim that the inverse-square law of forces is required by the area of spheres). | |
| Jun 28, 2013 at 15:53 | comment | added | ex0du5 | I'm not sure why your answer was voted down, but I do think that Kant is a horrible place to look for mathematical philosophy. In attempting to demonstrate the synthetic a priori, he uses basic mathematical statements that are now easily seen to not be a priori. His examples in Euclidean geometry are challenged by the fact that our geometry is apparently non-Euclidean. The logic of statements about the world appears to be a nondistributive orthomodular logic. Number relies on distinguishability, a much more troubling issue than Kant believed... (cont.) | |
| May 10, 2013 at 15:00 | history | answered | Jean Joseph | CC BY-SA 3.0 |