Timeline for Supervenience in mathematics
Current License: CC BY-SA 2.5
27 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 14, 2014 at 21:46 | answer | added | Pablo Lessa | timeline score: 0 | |
| Oct 14, 2014 at 13:42 | answer | added | Hans-Peter Stricker | timeline score: 3 | |
| Jun 23, 2011 at 18:56 | answer | added | Gyorgy Sereny | timeline score: 2 | |
| Jan 9, 2011 at 3:15 | comment | added | KConrad | Hans, I meant my previous comment only as a small joke and put the smiley face at the end to indicate that. Nevertheless, it really is true that when reading Qiaochu's comments and the responses to it that I thought about "brickiness". | |
| Jan 8, 2011 at 22:18 | comment | added | Hans-Peter Stricker | @KConrad: That's a little bit unfair, since Feyman's question was to show the vainness of some sort of concept (in this case "essential object"), but I suppose that the concept of "supervenient property" isn't vain. | |
| Jan 8, 2011 at 21:51 | vote | accept | Hans-Peter Stricker | ||
| Jan 8, 2011 at 17:23 | comment | added | KConrad | This discussion reminds me of the question of whether a brick is an essential object (SYJMFeynman, p. 70). Have the philosophers figured that out yet? :) | |
| Jan 8, 2011 at 16:15 | comment | added | Qiaochu Yuan | @Joel: fair enough. What I meant was that I did not see the point of talking about supervenience if philosophers did not even agree about its meaning outside of mathematics. That is, I did not see this as a philosophical question about the foundation of mathematics but as a philosophical question, one part of which might have something to do with mathematics, and people didn't seem to agree about which part or how. And that seemed off-topic to me. But I defer to your expertise in the matter. | |
| Jan 8, 2011 at 15:35 | answer | added | gowers | timeline score: 16 | |
| Jan 6, 2011 at 15:49 | comment | added | Joel David Hamkins | Well, I'm sorry you feel that way. I view philosophical questions about the foundations of mathematics, particularly those involving a technical concept, as on-topic for MO. My objection to your remark above is that there are dozens of competing precise proposals for the meaning of supervenience. Perhaps the situation is like the use of the terms "explicit" or "canonical", often used on MO in vague ways, even though these terms have a variety of competing precise formulations. But these terms, like "supervenience", have a mathematical nature that can be usefully discussed by mathematicians. | |
| Jan 6, 2011 at 15:19 | comment | added | Qiaochu Yuan | @Joel: all the more reason for this discussion not to take place on MO, then! | |
| Jan 6, 2011 at 14:12 | comment | added | Joel David Hamkins | Qiaochu, there is a huge philosophical literature debating the precise meaning of the term; entire conferences are held on the topic of supervenience. | |
| Jan 6, 2011 at 14:00 | comment | added | Qiaochu Yuan | I don't see the point of having this discussion until someone provides a clearer and more precise definition of supervenience. | |
| Jan 6, 2011 at 13:46 | comment | added | Joel David Hamkins | I am saying that supervenience (which as a philosophical term has numerous senses and no universally agreed crisp meaning), is usually not taken to imply that there is not a direct reduction, but rather is meant to encompass both the situation where there is a direct reduction and where there isn't. | |
| Jan 6, 2011 at 13:33 | comment | added | Hans-Peter Stricker | If there were no cases of non-reducability, supervenience would be equipollent to reducability. Supervenience was introduced because of assumed cases of non-reducability, and these are the interesting ones (and of course the ones I had in mind). | |
| Jan 6, 2011 at 13:19 | comment | added | Joel David Hamkins | According to my understanding of how supervenience is used in the philosophical literature, this question is incorrectly suggesting that supervenience implies that there is not a strong reductive relation, whereas the uses I have seen are merely that we take X to supervene on Y if there is a necessary logical reduction of X features to Y features, whether or not there is a direct strong reduction. That is, instances with a strong reduction would be taken to be (trivial) instances of supervenience. | |
| Jan 6, 2011 at 13:10 | comment | added | Hans-Peter Stricker | @Daniel: I guess this is a good point! | |
| Jan 6, 2011 at 13:07 | answer | added | Joel David Hamkins | timeline score: 20 | |
| Jan 6, 2011 at 13:05 | answer | added | Todd Trimble | timeline score: 7 | |
| Jan 6, 2011 at 12:59 | comment | added | Daniel Moskovich | What about the answers to mathoverflow.net/questions/10993/… ? Isn't it supervenience if you can prove an equivalence abstractly (and so definable in terms of low-level properties) but not calculate anything? | |
| Jan 6, 2011 at 12:52 | comment | added | darij grinberg | Okay. A polynomial in $n$ variables $X_1$, $X_2$, ..., $X_n$ over an infinite field $k$ is uniquely characterized by knowing all its values (of course, when we say this, we assume that we know which points it takes which value at, and not just the multiset of its values). Still a polynomial is not "defined" by its values (it can be defined as a function, but this definition sucks since it behaves strangely for finite fields). | |
| Jan 6, 2011 at 12:43 | comment | added | Hans-Peter Stricker | @Darij: Can you give an example that is a bit "easier"? | |
| Jan 6, 2011 at 12:39 | history | edited | Hans-Peter Stricker | CC BY-SA 2.5 |
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| Jan 6, 2011 at 12:14 | comment | added | darij grinberg | Disregarding the quote in your post, which provides more of an example for how philosophers' language could profit from some clarity or at least some well-defined terminology, the notion of "supervenience" as defined in Wikipedia has plenty of applications in mathematics. For example, Tannaka duality is about in how far an algebraic group is determined by its category of representations. | |
| Jan 6, 2011 at 11:58 | answer | added | gowers | timeline score: 9 | |
| Jan 6, 2011 at 11:37 | history | edited | Hans-Peter Stricker | CC BY-SA 2.5 |
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| Jan 6, 2011 at 11:32 | history | asked | Hans-Peter Stricker | CC BY-SA 2.5 |