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Eric Kaun wrote:
>>Logic as a branch of mathematics most definitely requires axioms. --dawn
This is from http://en.wikipedia.org/wiki/First-order_predicate_calculus
--- Like any logical theory, first-order calculus consists of * a specification of how to construct syntactically correct statements (the well-formed formulas) * a set of axioms, each axiom being a well-formed formula itself * a set of inference rules which allow one to prove theorems from axioms or earlier proven theorems. There are two types of axioms: the logical axioms which embody the general truths about proper reasoning involving quantified statements, and the axioms describing the subject matter at hand, for instance axioms describing sets in set theory or axioms describing numbers in arithmetic. --- Now ultimately set theory is used for the foundation of everything in mathematics. So you use set theory to build your logical theory. You might ask how do you specify your set theory without using logic, otherwise you've got a chicken and egg situation. I'm not too sure what the answer is there, I think there is some kind of hand-waving appeal to "naive logic". Or maybe it is more rigorous, I don't know. Very philosophically interesting these questions of foundation though. Paul.Received on Fri Jun 18 2004 - 16:55:48 CDT