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Is logic a subset of mathematics or is mathematics a subset of logic? I have heard the former view, but is there any argument for the latter?

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Logicism: –  Doug Spoonwood Dec 7 '12 at 4:16
Perfect Thanks! –  vanattab Dec 7 '12 at 4:18

4 Answers 4

up vote 7 down vote accepted

Mathematical logic is a branch of mathematics. But mathematical logic is by no means all of logic.

There have been recurrent attempts, from Frege through Whitehead/Russell and others, to develop mathematics within what they thought of as logic. The attempts failed, we have moved on.

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[(logic) $\cap$ (math) $\neq \varnothing$] $\;\land\;$ [(logic)$\setminus$(math) $\neq \varnothing$] $\;\land\;$ [(math)$\setminus$ (logic) $\neq \varnothing$].

That is, the intersection of logic and math is clearly not empty, but I think it is also the case that neither one completely encompasses (contains) the other.

Also note:
Mathematical Logic is a branch of mathematics, and is also of interest to (some) philosophers.
Philosophy of Math is a branch of Philosophy, which is also of interest to (some) mathematicians.

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Nice answer, but every theorem can be rewritten using propositional calculus, for example. We can, of course, think of rules of inference as mathematical operations. –  glebovg Dec 7 '12 at 4:28
Thanks, @glebovg. Of course, I root for philosophy as overarching ALL. Every discipline is (or was at one time) the birthchild of Philosophy! –  amWhy Dec 7 '12 at 4:34

It is actually the other way around. Philosophy is the root of all sciences, including mathematics. You can think of mathematics as an application of logic.

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Also, you can think of both mathematics and logic as subsets of the Philosophy of Proof.

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