Talk:Logic/Mathematics

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How is logic a subcategory of mathematics? Surely mathematics is a subcategory of logic, or they are entirely separate!

Brianjd 08:26, Nov 6, 2004 (UTC)

I'm inclined to agree. Many people immediately think of mathematical logic, which is a sort of subcategory of math (and logic). Logic itself isn't though. I've taken it out of the discrete math category —siroχo 10:34, Nov 6, 2004 (UTC)

I answered the identical question on Talk:Mathematics, there. I would categorise logic in general as part of discrete maths, though not in the sense that discrete maths encompasses logic. Charles Matthews 10:53, 6 Nov 2004 (UTC)

Follwing text by Charles Matthews copied from Talk:Mathematics#Logic to consolidate discussion —siroχo

Formal logic is formally a subset of mathematics. Formalised mathematics is formally a subset of logic. Not everyone would agree that

logic = formal logic

or that

formalised mathematics = mathematics.

There is plenty of less-than-formal logic around, for example in philosophical logic. There is large amounts of non-formalised mathematics used in physics, engineering and so on. If you want a tight definition, you go to mathematical logic, which is one mathematical discipline (a few percent of mathematics, one could say). Definitely mathematical logic is a subcategory of mathematics.

Charles Matthews 09:29, 6 Nov 2004 (UTC)

The section Charles was referring to is Talk:Mathematics#Logic. I think that as far as Wikipedia categories go, logic and mathematics should be considered separate.

Brianjd 05:37, 2004 Nov 7 (UTC)

Doesn't make sense to me. Categories are often added in an overlapping way. And logic is also a major part of computer science. I think it has to be accepted that these three overlap in a quite complex Venn diagram. One way or another most of logic is covered by mathematics, computer science as it is now understood, and philosophy. About a century ago logic was for a while considered by some an autonomous discipline; but that really only lasted for about a generation. Charles Matthews 11:47, 7 Nov 2004 (UTC)

I most certianly agree that all three fields overlap in a complex venn diagram, but category wise they should be kept distinct, because of how differently each field is approached and studied for the most part. Certain pieces of each overlap, which is why I have added Category:Mathematical logic to Category:Mathematics. Also, Axiomatic set theory (the most logic-based part of math) is part of Category:Mathematical logic. There is way too much logic that is not part of math to categorize it as such. Also, mathematics is studied distinctly from logic in most cases. Including logic in the math category would be much like including math in the physics category. I won't address computer science here right now, because I haven't studied that categorization scheme very much yet. —siroχo 15:26, Nov 7, 2004 (UTC)

The way I've been handling the issue is just Charles Matthews's Venn diagram: ML is the intersection of Mathematics and Logic, Philosophical Logic of Philosophy and Logic, and Logic in Computer Science the intersection of Computer Science and Logic. It's not ideal from an intellectual point of view, but I think its convenience from an editing point of view is decisive. ---- Charles Stewart 09:19, 8 Nov 2004 (UTC)

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Doh! The main point is missing from what I wrote above: if something clearly belongs to a single one of these intersections, I just put it there, otherwise I allow topics to belong to several categories. In general, I think it's worse to err on the side of exclusion rather than inclusion, the exception being the main Logic category where I think material shoul be excluded unless it is either clearly elementary or of trans-disciplinary interest. ---- Charles Stewart 07:25, 10 Nov 2004 (UTC)

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The article Logic is already in Category:Abstraction. I think the category Category:Logic belongs there too. Brianjd 08:30, 2004 Nov 15 (UTC)

I've had some difficulty trying to figure out the point of Category:Abstraction; certainly the leader to that page is rather POV. Does Logic benefit from being regarded as a subcategory of Abstraction? Might not the other way around make more sense, seeing as abstractions are useless/inconceivable without the "grammar" of logic? ---- Charles Stewart 11:29, 16 Nov 2004 (UTC)

If that was done then philosophy would come under logic (though not directly), an idea that sounds a bit weird. But I can see no problem with it. Brianjd

Since the topic arises, I think that none of arts, mathematics nor philosophy are subcategories of abstraction, with much more confidence than I say logic is not. ---- Charles Stewart 02:19, 23 Nov 2004 (UTC)