There are a number of questions on this site of the form, "How do I prove X in Y deduction system?" (especially Fitch). While this is a topic which arises (for good reason) in many philosophy classes and these questions generally seem accepted on this site, to me they're definitely more questions about mathematics rather than philosophy. The following questions are good examples of what I'm talking about: 1, 2, 3.

At present such questions seem to be considered appropriate for this site. My question is:

Do we actually want these questions, or would it be better to migrate them to math.stackexchange?

A couple notes:

  • Migration to math.stackexchange is not actually an option currently in the vote-to-close menu, so this would take some implementation.

  • A lot of questions of the above form would be closed on MSE (and I think should also be closed here) due to lack of context/effort shown. We definitely shouldn't flood MSE with questions which will just be quickly closed there. But that's a separate issue - I'm asking whether the general topic would be more appropriate there than here, so for the current purpose let's assume that the relevant questions are well-written and have all necessary context.

  • Finally, I'm talking only about questions of a very specific form here - again, of the form "How do I prove X in Y deduction system?," with no additional philosophical content (such as "... and does that accurately model the standard natural-language proof?"). So e.g. the following questions (regardless of whether they're appropriate for this site) are not examples of what I'm talking about: 1, 2, 3, 4.

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    Yeah, I am really not in love with these questions. Lack of effort means they're of almost no long-term value. Common pattern means they take up valuable space on the mainpage. Generally speaking they just convey the wrong idea about our community. – Joseph Weissman Feb 29 at 18:33
  • I'm not sure if I understand the idea that formal logic is a mathematical (as opposed to philosophical) topic. Granted, mathematicians should be able to handle formal logic with ease, though.. I mean, we don't stick basic physics or math in SE.Engineering just because an engineer should be able to handle those with ease. So, while I'd definitely accept the argument that mathematicians can do logic (and obviously use it heavily in research), what makes formal logic specially keyed to SE.Math as opposed to SE.Philosophy? – Nat Mar 1 at 8:17
  • Perhaps logic only becomes philosophical when it is applied to topics of life. The mechanics of formal logic applied to purely abstract terms are important to learn, but maybe they best belong somewhere else. But the moment you stop using x and y and apply it to intelligible arguments is when it belongs here? – curiousdannii Mar 1 at 13:01
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    @Nat While there are many philosophical things to say about formal logic and many questions in formal logic which bear on philosophy, I don't see how to construe questions specifically of the above form as anything but mathematical logic - that is, part of mathematics (one could also fold them into computer science - there's the natural overlap). Really they're just disguised questions of combinatorics: how to apply certain string manipulation rules. I'm not saying that this holds for all formal logic questions or even most, only questions specifically of the form "Deduce X in system Y." – Noah Schweber Mar 1 at 18:16
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    @curiousdannii I'd even say there are questions about formal logic which live entirely inside mathematics but are still appropriate here - e.g. the one about first-order logic in equality alone which I've answered - because of how they can impinge on philosophical questions. It's specifically problems of the form "Deduce X in system Y" phrased exactly thusly that I object to: I don't see that they have any philosophical relevance at all (they don't involve analysis of system Y or statement X in any meaningful way). (continued) – Noah Schweber Mar 1 at 18:18
  • I can imagine a possible exception - namely, where the deduction system in question is particularly "wild" so that understanding its basic inferences is actually philosophically significant - but for something "tame" like Fitch I just don't buy it. – Noah Schweber Mar 1 at 18:19
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    Perhaps we can finally open Logic.SE? – Yechiam Weiss Apr 18 at 11:07

My current opinion is the following:

While there is definitely some crossover between math and philosophy and some mathematics (especially mathematical logic) is relevant to philosophy, that doesn't mean that every mathematical question arising in a philosophy class is on-topic for this site.

In particular, while I don't know exactly where to draw the line, I do think that the questions referred to above are not appropriate here. They should either be migrated to math.stackexchange if they show sufficient context/effort, or closed (we should not migrate questions to MSE which we suspect will be closed there).

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Having answered a few of these questions on Philosophy.SE, and a few similar questions on Math.SE, I agree with you. "Prove a statement" questions are likely more at home on Math.SE, provided they meet minimum standards over there. In any event, they should be closed over here.

I write separately because I fear that, in a few months or years, users may unintentionally broaden this rule to cover other questions in the "general area" of logic, such as the following:

  • Why does Kripke choose to ignore issues of transworld identity in his semantics?
  • What sort of syntactic rules of inference arise if you replace Kripke semantics with David Lewis's counterpart theory?
  • Do any ethical systems actually use deontic logic?

The above questions are on-topic and should not be migrated. They say nothing about proving statements, their answers usually consist more of words than symbols, and they are, in some sense, "philosophically interesting" questions. In some cases, these questions are also on-topic at Math.SE (they do allow "soft" questions and theoretical questions), but questions may be on-topic in more than one place, and we usually allow the asker to choose where to ask in those cases.

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  • +1. FWIW the third is certainly off-topic at MSE; I think the first is somewhat dubiously on-topic for MSE, while the second is definitely on-topic for MSE. – Noah Schweber Sep 13 at 21:20

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