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Is it math for studying logic or logic for studying math? I'm confused on what it really is.

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  • @Gordon Hey Gordon. I really appreciate this. Do you have a link to the book? I'm having difficulties getting it online. – asdfasfasdgf May 28 '20 at 2:18
  • Logic as used in mathematics or elsewhere is formalized and mathematical methods are applied to study it. But the result can then be fed back to analyze the uses of logic in mathematics and other areas. The former would be mathematical logic and the latter its applications. – Conifold May 28 '20 at 3:38
  • The relationship between math and logic is a colorful history. They complement each other. Math pedagogy can largely be seen as an exercise in applied logic, and they are inseparable at an axiomatic level because subitization and Boolean logic are both independent capacities of the mind. – J D May 28 '20 at 5:43
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    Crossley, What is mathematical logic, Oxford UP ( 77 pages) – user37859 May 28 '20 at 9:03
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Mathematical logic is a reasoning system that is sufficiently well-defined that it can unambiguously be applied to (for example) the control of complicated machinery- including things like trains and airplanes. This means that things like computers are ideal for its implementation.

As such, it is not designed for reasoning about things like for example ethical, psychological, or political issues- which cannot be managed on computers.

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  • This is really interesting. Thanks for the comment. It seems that Hilbert used this for meta-mathematics. Is it fair to say that mathematical logic has the primary application to meta-mathematical objects? – asdfasfasdgf May 28 '20 at 1:51
  • Like most of what I'm reading is applications of mathematical logic to meta-mathematics. – asdfasfasdgf May 28 '20 at 1:52
  • Like in literally almost every article that I read, it's all applied to mathematics itself. – asdfasfasdgf May 28 '20 at 1:56
  • As a recovering ex-engineer, my 12-step program does not touch upon meta-issues. – niels nielsen May 28 '20 at 2:01

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