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This "is structuralism quackery" thread has three votes to re-open and two votes to delete.
http://mathoverflow.net/questions/116201/does-bourbakis-and-grothendiecks-approach-to-mathematics-survive-today-clos
I don't think it deserves to be re-opened. I'm not so sure if it should be deleted. But this could be a borderline case people want to discuss.
Locked it. Open vs delete wars are not the right way to deal with this. This is the second one in a week!
I'll unlock after I see that this is going somewhere productive.
I voted to delete because of the votes to reopen.
Felipe and Bill, that's an abuse of the system, please quit doing that. Either let close/reopen battles happen or, if there is really good cause not to reopen, flag for moderator attention and ask us to lock the question closed.
I cleared all the votes to reopen and delete and then I unlocked. I hope that we can all work within the usual system norms after a fresh start.
I opined that even were the question to be improved (e.g., by removing the bit about 'quackery') it might still be too discussion-y to be a good MO question. This is despite the fact that I find the topic very interesting. (By the bye, part of me wonders at the accuracy of the image of Grothendieck as someone who likes to work with axiomatics; as I said in another comment there, the feeling I get is that choosing one's axioms is something that a "Grothendieck-type" might put off for a very long time indeed, until the time, or 'nut', was fully ripe.)
Words like "structuralism" have no place on mathoverflow. This term means something very different (and very stupid) in philosophy.
I agree with François that voting to delete because of votes to reopen seems like inappropriate use of one's power to delete.
Discussion of "mathematical structuralism" or "categorical structuralism" certainly could (and to some extent already does) take place on MO; see writings by Awodey and McLarty for what these terms might signify.
I did however feel that mention of Bourbaki wasn't pertinent to the question, which I took to be whether doing mathematics in the manner of a Grothendieck was still 'viable' (whatever that means exactly). I would feel that way all the more if "Bourbakian structuralism" were brought up.
The question just got significantly edited. For the record, I also consider the edited version as unsuitable, and feel even more convinced that it was right to close the original.
I agree with you, Gil, about the quality of the question, and I think your recommendation (7) is the critical one. But the recent edit at least has the virtue of making it clearer to me that the poster is someone young (in mathematics). It looks as though s/he has gotten an idea from Grothendieck that there are the 'clever' types like Serre who crack the nut by aiming the chisel judiciously and striking hard, and then there are other 'yielding' types (like Grothendieck) who let the nut soften in liquid for a long time, etc. -- a 'yin' approach, as it were. And the main question is which communities support the latter style. There are some seemingly confused ideas about structuralism and axiomatization thrown into the mix.
If that reading is correct, I can see why the underlying idea might be seductive. Unfortunately, this question (if I've understood it correctly) is almost certainly not right for MO (and unfortunately for JDH, I doubt the OP really wants to talk about structuralism in any sense of the word).
I agree with the general sentiment in Todd's reading of the question, and that the question should stay closed.
Just for the record, I wanted to say that I find high-level high-quality questions in the philosophy of mathematics to be on-topic for MO, and I would encourage you to post them on MO. Such questions are interesting and admit of knowledgeable answers that treat the topic with the same care and technical precision that our other mathematical questions and answers here do. In particular, I dispute the claim sometimes heard here that questions in the philosophy of mathematics are necessarily discursive and unsuitable for this site. I am disheartened when questions in the philosophy of mathematics that seem perfectly fine to me are closed, sometimes even with dismissive comments. Meanwhile, we have numerous experts in the philosophy of mathematics here, who are both interested in and able to answer such questions. Furthermore, I believe that the kind of questions I have in mind are enjoyed by a large segment of the MO community, even those who haven't particularly studied the philosophy of mathematics, and so I find that they really add value to MO.
But about "structuralism", and thanks Jon for bringing it up again. In the philosophy of mathematics this term is usually used to describe a position in mathematical ontology, by which one holds that what exists in mathematics is not mathematical objects, but rather mathematical structure, relations between objects. (e.g. see Daniel Isaacson's paper "The Reality of Mathematics..." for a great account of it). This is the view that it doesn't matter what the real numbers are really made out of, as objects, as long as they form altogether a complete ordered field, which is the structure that characterizes them. This philosophy of structuralism, of course, runs through the heart of category theory, and some use it to criticise set theory, although this is misguided in my view, since of course set theorists don't care what their sets are made out of either, as long as the set-membership relation has its characteristic properties, which is the relevant structure for set-theorists. In this sense, the philosophy of structuralism is pervasive in contemporary mathematics. Meanwhile, in the question and in the links you provide, it seems that the term structuralism is used differently, not as a matter of mathematical ontology, but rather simply as a mathematical methodology or attitude, a predisposition towards building theories rather than solving problems. But I'd like to learn more about the distinction, which is what I had meant in my comment.
Oh yes, that is what I would call structuralism. This seems to be very different from the theory-building use of the term in the original question, which was also a theme of the Gowers article.
@François: I considered the question as being very worthy of deletion, but ordinarily would not vote to delete because of the upvoted answers. However, the threat of this off topic question again appearing on the first page and pushing reasonable questions down forced my fingers to hit the delete button.
@bsteinberg: if you think it's a bad question, then why do you think it should be reopened? The number of upvotes seems like a very weak reason -- people can upvote for all kinds of reasons, many of them not good.
bsteinberg: You are not asked to make a binary choice between re-opening and deleting. The default (and what appears to be largely consensus in this thread) is to keep it as-is, which is simply closed.
I just deleted my (old!) comment
This question has two votes to delete. Not sure it is is a good idea to delete it. Perhaps, before a final vote is cast a meta could be created.
as it possibly contributed to this, while being (in view of the content of meta directly linked below it, obviously) obsolete.
@bsteinberg: There were no delete votes when you voted to reopen this bad question--François removed then, as he explained early in this thread. The only thing your vote to reopen accomplished is to increase the probability that the question will again junk up the first page.
By contrast I am virtually certain one has one vote to close and one vote to reopen.
This question now has 4 reopen votes ...
...since almost 24 hours.
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