What are the Fundamental Logical Axioms?

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Atran
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Hi, I've been recently reading about logic. Is there a list of the exact logical axioms underlying all axiomatic systems, postulates and mathematics?

Thanks...
 

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Atran said:
Hi, I've been recently reading about logic. Is there a list of the exact logical axioms underlying all axiomatic systems, postulates and mathematics?

Thanks...

The short answer is no. Russell and Whitehead tried to create (or discover) a formal logic for all of mathematics and essentially failed. The formalization of modern mathematics is based to a large extent on the Zermelo-Fraenkel axioms of Set Theory together with the Axiom of Choice (ZFC) and Peano's axioms of arithmetic.

http://mathworld.wolfram.com/Zermelo-FraenkelAxioms.html
 
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SW VandeCarr is certainly correct that there is no axiom system which is both correct and complete. This was proven by Kurt Godel in the 1930's. The mathematicians proceeded by just making up axiom system which looked correct and the started using them. They didn't care whether they are complete or not.

If you talk about logic, then the situation is quite different. There are axiom systems for logic which are both correct and complete. A good reference for this are the lecture notes of Lou Van den Dries: http://www.math.uiuc.edu/~vddries/ click on "Logic Notes" (you will need to be able to open DVI-files for this).
An axiom system for logic is described on page 38. But I don't think that it is known to be correct and complete...
 

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