This is closely related to, but I don't think a duplicate of, this meta-question.

Is it appropriate to ask questions about why, e.g., a constructive mathematician might believe classical mathematics to be illicit and why s/he might think that constructive mathematics is less objectionable?

I worry about the appropriateness of this question since the answer is likely to be philosophical, though certainly it would involve views about the "badness" of certain technical results.

At the same time, I worry that banning such questions would orphan them, since the philosophy stackexchange doesn't have anywhere near the number of mathematically informed users as Mathematics.SE.

What is the Mathematics.SE policy on questions of this sort?

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It is worth noting that this recent proposal got closed as a duplicate of MSE, giving the impression that people do think this is the right place for such questions. I agree, but I also agree with Qiaochu's answer, that such questions should be phrased in a very accurate way. –  Asaf Karagila Dec 30 '12 at 21:55
    
That is good information, and a good thing to refer any "math purists" to. It seems then, that mathematics.se includes philosophy of mathematics as its appropriate subject matter. –  Dennis Dec 30 '12 at 21:58
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Warily. Such questions could easily be "subjective and argumentative" ... In fact, haven't we had a few of those already? –  GEdgar Dec 31 '12 at 15:04
    
@GEdgar I don't take it that questions of the sort I have in mind are subjective and argumentative at all (at least if properly answered). These people (e.g., constructive mathematicians) have views about certain things (proper mathematical methodology, foundations of mathematics, etc.). The sort of question I have in mind (and the example I gave) is simply asking for an explanation of some view. The questionable part--- which I take it to be settled by Asaf's comment ---is that their view are philosophically (rather than mathematically) motivated. –  Dennis Dec 31 '12 at 17:57
    
I didn't mean anything about constructive mathematics, I mean questions about "motivations of a given mathematical point of view" may be subjective and argumentative. –  GEdgar Dec 31 '12 at 18:01
    
@GEdgar I was just using constructive mathematics as an example. I suppose I should clarify that a good question of this sort wouldn't be asking answered to speculate why, for example, Kronecker thought only the integers had construction-independent existence. A good answer to this sort of question would presumably include some sort of citations. –  Dennis Dec 31 '12 at 18:08
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I take it that the only way such questions could be subjective is if they ask for the personal views of people who answer. They could only be argumentative if phrased in such a way as to invite disagreement with the OP. Is this right? In fact, I'm starting to think it would be very difficult for most questions to be "subjective and argumentative". –  Dennis Dec 31 '12 at 18:12
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I would strongly discourage such questions: they will tend to evoke argument. –  Brian M. Scott Jan 1 '13 at 4:31
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3 Answers

If you really want to ask such a question, keep it as specific as possible. For example, cite a specific paragraph by such a mathematician and ask what considerations might have motivated the point of view espoused in the paragraph, or something like that.

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I think (good) questions of this kind would be very useful.

An example is Irrationality proofs not by contradiction (with its MO predecessor, http://mathoverflow.net/questions/32011/direct-proof-of-irrationality and a link to Andrej's blog entry, http://math.andrej.com/2010/03/29/proof-of-negation-and-proof-by-contradiction/).

Of course, a different issue is how to ensure the question is good, and will not simply attract uninformed speculation. An example is the question of whether mathematics is created or discovered. Though very interesting, reasonably informed answers tend to be sparse compared with others of a more anecdotal nature. (But I do not want to suggest that undue burden is to be put on the formulation of these questions.)

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I personally would be very interested in reading such questions and answers.

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And I would be strongly tempted to vote to close the great majority of them as not constructive. The exceptions would lie firmly on the history side of the history/philosophy divide. –  Brian M. Scott Jan 3 '13 at 15:45
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