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Recently the question Do Complex Numbers Really Exist? was closed as "subjective and argumentative". I voted to close, because the way the question was asked invited two philosophical questions, and set them up in the worst way.

I'd hate, though, for us to have a general rule that philosophical questions are considered to be bad in this way, not least because I know someone very smart who ran into serious difficulties studying mathematics because of philosophical concerns.

Is there a good way of tackling these questions? Would a question along the lines of Are complex numbers quantities? have worked out better?

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  • $\begingroup$ I see a real danger in philosophical questions. They are (by nature) subjective and argumentative. Hopefully they could be reworded/re-asked to become more concrete in nature, so that the issue can resolve itself. $\endgroup$ – Justin L. Jul 21 '10 at 20:13
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    $\begingroup$ They are (by nature) subjective and argumentative - They need not be, if people put their own opinions on the backseat and concentrate on the nature of the arguments and the prior literature for them, as actual philosophers (usually) do. I'd like to have a criteria for which philosophical questions should be closed, and which contribute to the mission of this site. And ideally not all/none. $\endgroup$ – Charles Stewart Jul 22 '10 at 7:48
  • $\begingroup$ I tend to disagree. Without philosophical differences and differences in opinions you lack diversity and innovation. When people stop questioning and challenging things without any motivation of opinion then everything else becomes a get in line and follow orders humdrum slavery. I challenge everything and anyone including Einstein if he was still alive! $\endgroup$ – Francis Cugler Mar 3 '17 at 9:26
  • $\begingroup$ The fact that someone should have to stop and reword their question to suite others is a means of having to validate your own questions and opinions and it strips away the simple fact and truth of Freedom of Speech! $\endgroup$ – Francis Cugler Mar 3 '17 at 9:28
  • $\begingroup$ @FrancisCugler: I agree with the point about diversity, but some kinds of philosophical questions are problematic, ie. they generate bad answers. $\endgroup$ – Charles Stewart Mar 10 '17 at 16:30
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On MO, people tend to be fairly restrictive about philosophical questions -- they're generally closed mercilessly and swiftly. I'd say this is too strict for the present site, though, since the intended audience is different; however, the point remains that we're not running a discussion forum here. And, as we've come to see on MO, if we let "soft" questions run too wild, they tend to take over the site (because more people like to comment on them), potentially crowding out more specific questions.

It's kind of like on high school forums: I was fairly active on one a while back, and there used to be a fair bit of intellectual discussion until games started taking over the site, driving most of us who'd prefer to talk about serious stuff away until it became a ghost town.

Soft and community wiki questions are sort of analogous to these games. In moderation, they're fun and build a sense of community. In excess, they reduce the prominence of specific questions and weaken the site.

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    $\begingroup$ I think there's a risk here, but note that SO, with a far higher traffic than MO, is much friendlier to soft questions and is far from overwhelmed by them. It should, I think, be easier for the site to start tough and loosen up than move the other way. $\endgroup$ – Charles Stewart Jul 21 '10 at 19:36
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Indeed, I think Are complex numbers quantities? would have worked out better. I recall many requests for askers to reword their questions over at MO when it began - with strong threats to close the question if it is not reworded. Often times another member would even rephrase the question themselves in order to make it into a more serious or more answerable question.

It would be a shame to discourage philosophical questions.

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    $\begingroup$ Agree. Not a fundamentally bad question, could be fine with some rewording. $\endgroup$ – Larry Wang Jul 21 '10 at 12:40
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I have reworded not just the title but also the description along the lines you suggest, to make it less contentious, although I would have preferred the original wording for the following reasons.

I asked this question not because I don't have plenty of answers myself but because I thought it was typical of the kind of question that many future visitors to this site would want to ask, even in the way it was worded, and this week we are trying to build up a stock of questions and answers that future visitors will find interesting and helpful.

I have been disappointed to see the kind of responses there have been from a subset of the people who have contributed. To the kind of person we hope will visit this site in future, these responses would have come across as a real put-down.

This kind of thing has happened all too often at MO, and this site is supposed to offer an alternative to that. People with harsh, purist and superior attitudes should stay over at MO and not promote these attitudes here.

The answer I eventually accepted was produced very quickly (within an hour, I think) and was friendly, helpful and encouraging. It saw beyond the philosophical ambiguity in the question and gave what was really being asked for. This is the kind of response we need to see here.

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    $\begingroup$ I agree with you on everything but the original wording of the question. It is the type of phrase that I hate to hear as a walk-in tutor because it reflects a very shallow consideration of the real issue as to why the asker is confused. "Do they exist?" means that the asker has taken the existence of everything else for granted - so their issue with complex numbers is only with the word "imaginary" and not any concept of how they operate. Each of us should have thought about this question more carefully yesterday and simply requested a rephrasing. $\endgroup$ – Tom Stephens Jul 21 '10 at 13:38
  • $\begingroup$ I essentially agree with you that those of us on MO (including myself) shouldn't try to export our customs from there over here. But the reason I wasn't a fan or your question wasn't that I don't like it when people ask questions about complex numbers -- or why they're used -- but that the question was titled "Are complex numbers quantities?," which feels a bit too sujective. "Why are complex numbers useful?" would have been, in my opinion, a better question. $\endgroup$ – Akhil Mathew Jul 21 '10 at 13:48
  • $\begingroup$ @Akhil Actually, the original title that caused all the heat was "Do complex numbers really exist?" I see now that was real bait to a lot of people, but it's a question I've heard, with that exact wording, many times. The new wording pretty much presupposes the answer, unfortunately, but I see no good alternative. $\endgroup$ – Neil Mayhew Jul 21 '10 at 13:53
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    $\begingroup$ I think 'do complex numbers really exist' is an accurate reflection of what someone genuinely confused about the topic might ask. If someone starts typing their own, identical question, and sees the list of similar-looking questions pop up, there is a much better chance they will click on your question if it has the 'Do complex numbers really exist?' title. 'Why are complex numbers useful' is also a good title. I think the current one is the worst of the three. $\endgroup$ – Larry Wang Jul 21 '10 at 14:22
  • $\begingroup$ @Tom, @Akhil, @Kaestur, @Charles: I have changed the title back to the original, added a rider on the question as suggested by Charles in the comments, and added an answer of my own that reflects what I was originally asking for. Thanks for all your help with this. $\endgroup$ – Neil Mayhew Jul 25 '10 at 16:13
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I think phylosophical question may be fine to a certain extent. But this particular question sounds really bad. The only sensible answer I can see is to make the original poster realize that in mathematics natural numbers, let alone real numbers, are not any more "real" than complex ones.

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