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A recent question: Calculus for Higher Order Logic has me wondering (and I honestly don't have a strong opinion on it either way).

We do answer a lot of questions with the logic tag here on philosophy.se. And one thing I like about those questions is that many of them are answerable. (Unfortunately, we also get some recurring questions about validity / soundness/ truth that should be marked dupe).

Many of the logic questions we answer are the sort one would encounter in a intro to logic course in philosophy. To me that makes those on topic. Similarly, we get some more advanced logic question about modal logic that are also commonly addressed in academic philosophy.

This particular question, however, seems different from those. This question reminds me of Introduction to Analysis and seems like something that gets rigorous treatment related to the ZF set and Peano arithmetic. Thus, it seems more like something one would learn as a fundamental in college math rather than a question about the nature of math (which would make it philosophy of math).

I'm not a specialist in philosophy of math nor do I have an advanced degree in math. Do we want to set some limits for questions about or in mathematical logic? Are they a better fit here or on one of the math-related SEs?

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    Logic is a tag in both math se and philosophy se (so modal logic problems for instance can be asked in both). Both tags have practically equivalent range, and the logic questions in both sites are similar, and would be on topic if cross posted.
    – Cicero
    Aug 17, 2015 at 3:03
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    That being said, despite Math Se having about 100 times more questions than Philosophy SE (474k vs 4.7k), it has only 7-8 times more logic questions (7484 vs 957), suggesting philosophy SE does get an unusually high number of logic questions compared to its size. Also, logic is the most popular philosophy tag, while being very low in the list for math se tags.
    – Cicero
    Aug 17, 2015 at 3:03
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    There is also a philosophy of math tag in math se, with a marginally higher traffic than that at philosophy se (422 vs 343), especially considering that math se has 100 times more questions. However, there not only is a disclaimer with the tag that philosophy se might be more appropriate, but there does appear to be a much lower tolerance for those types of questions in math se than philosophy se.
    – Cicero
    Aug 17, 2015 at 3:48
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    This being said, for the question you just linked, it would be accepted and decently upvoted, and have several answers if posted at math se, due to its more mathematical and less philosophical stance. However, it is perfectly appropriate for this site considering the type of questions that have been accepted.
    – Cicero
    Aug 17, 2015 at 3:49
  • Perhaps just as math se has a disclaimer for the philosophy of math tag, we should have a disclaimer with the logic tag suggesting that mathematical logic might be more suited for the math se.
    – Cicero
    Aug 17, 2015 at 3:54

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I have quite a strong opinion on this; it's not that I'm against logic, but for it.

There's definitely a distinction between philosophical logic and mathematical logic; and we should be encouraging the former, and the interplay of the two, as well as with language; but discouraging questions that are almost wholly mathematical; and I mean there in its degree of specialism - which the quoted question displays.

For example there are philosophical questions about what constitutes a proposition; what is predication or reference; questions on identity or equality; questions too of modality - I mean standard modal logic covers a number of modalities: intrinsic/extrinsic; possibility/neccessity and others; but without understanding their distinctions philosophically the abstract mechanism of axiomatic modal logic will just level the distinctions.

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