Timeline for Top-down mathematics, or "Where it all begins"
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 23, 2021 at 8:41 | comment | added | François Brunault | Actually it has been translated in English: Conversations on Mind, Matter, and Mathematics, Princeton University Press. | |
| Mar 23, 2021 at 8:22 | comment | added | François Brunault | @AndrejBauer You're welcome. If you are interested, there is a book "Matière à pensée" (well it's in French) which is a conversation between Alain Connes (platonist) and Jean-Pierre Changeux (materialist biologist). | |
| Mar 22, 2021 at 20:34 | comment | added | Andrej Bauer | @FrançoisBrunault: thanks, that makes your comments clear(er) to me. I can appreciate them as a thorough non-Platonist. | |
| Mar 22, 2021 at 14:56 | comment | added | François Brunault | @AndrejBauer Sorry if my comment was not clear. By "first cause" I meant "first cause in mathematics", in other words "true foundations". In this context, a platonist may believe in a first cause which is not accessible to us. In my opinion, the parallel with theology is not irrelevant, as one refers to an entity beyond our senses. In both cases, a first cause is a belief so (a) it should not be perceived as a scientific or universalizing claim, and (b) it makes little sense to give scientific arguments to prove or disprove it. But discussing this would lead us far from the original question. | |
| Mar 22, 2021 at 14:22 | comment | added | Andrej Bauer | @FrançoisBrunault: I am not sure how to read your comment. The two interpretations that come to mind are (a) that it is beneficial for us to pretend that there is a First cause that we aspire to (isn't that intellectual dishonesty?) or (b) that there is a First cause but not within our material world (where then, and what evidence of its existence is there?). Could you clarify a bit, please? | |
| Mar 21, 2021 at 18:57 | comment | added | Andrej Bauer | @TimothyChow: kudos for appropriate Latin phrases. | |
| Mar 21, 2021 at 16:24 | comment | added | Hollis Williams | ''A number of mathematicians are platonic and this helps them doing mathematics'' As an example, if I remember rightly from reading 'The Road to Reality' by Roger Penrose, he explicitly states at the beginning that he is a Platonist (I might be misremembering). | |
| Mar 20, 2021 at 17:46 | comment | added | François Brunault | Mathematics is a human activity and philosophical considerations necessarily enter the picture. A number of mathematicians are platonic and this helps them doing mathematics. So I would not say that desiring to find the first cause (or a first cause) is necessarily flawed, inasmuch as it stimulates research. Desiring something does not mean that the thing is reachable, we can try to get closer. The mistake is to assume that this first cause actually exists within our material world. | |
| Mar 20, 2021 at 12:56 | comment | added | Timothy Chow | I agree. In my experience, one of the biggest stumbling blocks people have (and I mean not just undergraduates but also professional mathematicians) when they approach the study of logic and set theory is a tacit expectation that they have to suspend all their mathematical beliefs in order to avoid "circularity." A proof that they would unhesitatingly accept when it comes out of the mouth of, say, a number theorist is suddenly rejected when it comes out of the mouth of a logician. I have to explain that formal logic can clarify mathematical reasoning but cannot justify it ex nihilo. | |
| Mar 20, 2021 at 8:31 | history | answered | Andrej Bauer | CC BY-SA 4.0 |