# Maths branch of logics or vice versa?

Is it logics a branch of maths or vice versa?

From a the point of view of the definition of a logical system, logics is a 'calculus' which has axioms and rules as any branch of maths. However it seems that we are entitled to use logics rules in any branch of mathematics which will lead us to think that mathematics is inside logics.

For example, Godel's theorem is a theorem of logics or of maths? and if it's a theorem of maths, isn't it maths talking about maths? Then, is it legal that this theorem makes an statement about a 'flaw' in maths? Isn't it like a snake eating it's own tale?

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It depends on who you're asking. –  Asaf Karagila Apr 15 '13 at 22:07
"Logic" is a large subject. Mathematical logic is a branch of mathematics. A part of mathematical logic studies formal systems (which are mathematical objects) using the ordinary tools of mathematics. –  André Nicolas Apr 15 '13 at 23:02
You can do logic without mathematics, but you can't do mathematics without logic. –  Dan Christensen Apr 18 '13 at 4:35

## 1 Answer

I think from any perspective, we run into problems when we try to claim that the domain of either branch is a subset of the other. The intersection of the domains "logic" and "math" is hardly empty, but neither is their intersection entirely one domain of one or the other. And neither field is static; there is a dynamic interaction between the two, each enriched by and enriching to the other.

Why would we want to characterize "all that is math" as a part of "all that is logic", or vice-versa?

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Nice observations and I'd like to think that this generalizes to the whole of mathematics. +1 –  Amzoti Apr 16 '13 at 1:07