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I have always tended to assume that any of my more philosophical questions about mathematics would off-topic for Math.SE. As such, I have tended to restrict (or try to restrict) my questions to those of a more purely technical nature. However, when posting my most recent question I realized that there is a tag whose tag-wiki suggests that, in fact, philosophy of mathematics questions are on-topic for Math.SE.

Given that Philosophy.SE is a fairly small community (at least in terms of active members) and that the active members who can respond to somewhat mathematically sophisticated questions are even fewer, this was encouraging to find. It seems that some of these questions would receive much more attention, and mathematically informed answers, on this SE.

Which brings me to my question. What sort of questions within the philosophy of mathematics would be on-topic for this SE?

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    $\begingroup$ I think asking for positions in the hilosophy of mathematics or its history is fine, "philosophizing" is not. "Do real numbers exist?" is a bad question, or at least off-topic, "What are the main positions in the philosophy of mathematics on the ontological status of real numbers?" is fine as a question. $\endgroup$ – Michael Greinecker Apr 8 '13 at 8:28
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    $\begingroup$ I have always assumed that this tag related to the intersection of mathematics and philosophy. This is stuff relating to the foundations of mathematics (I think it is perhaps described by the label "logic"?). For example, Bertrand Russell was a philosopher but his work has implications for mathematics. I read a book on logic once which said that maths was the act of proving stuff while logic was the theory of the proofs themselves (and logicians are often in phil. departments). Anyway, the works of Kurt Gödel, Bertrand Russell and their kin are what I had always assumed this tag was for... $\endgroup$ – user1729 Apr 8 '13 at 10:34
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    $\begingroup$ That's a philosophical question maybe the tag [philosophy] should be added. $\endgroup$ – Rudy the Reindeer Apr 8 '13 at 17:37
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    $\begingroup$ We know that "subjective and argumentative" questions are off topic. But questions asking for an answer (and not for a discussion) could be on topic. This applies regardless of whether the question is about philosophy or number theory. $\endgroup$ – GEdgar Apr 11 '13 at 13:36
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Try viewing the questions tagged with this. Expecially the highly-voted ones. Then note here whether you think they are on-topic for math.SE.

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    $\begingroup$ A quick look makes most of them (starting with #1) totally off topic in my untrained eyes... $\endgroup$ – vonbrand Apr 8 '13 at 14:47
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    $\begingroup$ @vonbrand Only if mathematical philosophy and foundations are off-topic, which is not true. $\endgroup$ – Math Gems Apr 8 '13 at 15:34
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    $\begingroup$ "Do complex numbers exist", "Do I have to believe in axioms", ... give me a break. $\endgroup$ – vonbrand Apr 8 '13 at 15:53
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    $\begingroup$ @vonbrand Have you never read Penelope Maddy's Believing the axioms? See also this related MO question. I think that many of the answers to the question Do complex numbers exist? will be very helpful to many of our readers (esp. high-school students and mathematical laypersons). $\endgroup$ – Math Gems Apr 8 '13 at 17:58
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    $\begingroup$ I would say most of these are actually on-topic. Some of the questions are naive, such as "do complex numbers really exist?" but that doesn't imply they are off-topic. Also many of the questions are actually interesting, such as the ones discussing ultrafinitism and intuitionism. $\endgroup$ – Cheerful Parsnip Apr 9 '13 at 15:17
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    $\begingroup$ @GrumpyParsnip: Given that the question of which sense complex numbers can be said to exist in stumped bright minds for centuries, I think it's a little harsh to call it naive. It's a good and interesting question, on-topic on MSE, and rightfully tagged (philosophy). $\endgroup$ – Henning Makholm Apr 9 '13 at 18:42
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    $\begingroup$ @HenningMakholm: Fair enough. We do agree that it is an appropriate question. Maybe I should have said that the question seems naive rather than that it is naive. $\endgroup$ – Cheerful Parsnip Apr 9 '13 at 19:33
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    $\begingroup$ Most are clearly on-topic. I consider the question in the title of the first one meaningless, at least without a lengthy explanation of what is meant here by exist, but the question actually found in the body of the post is perfectly reasonable. The goal question is terminally silly, but even it isn’t really off-topic. $\endgroup$ – Brian M. Scott Apr 10 '13 at 21:24

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