26 Mar '07 22:562 edits

I recently thought that I might’ve been using the term “axiom” incorrectly, so I looked it up. According to Webster’s New Universal Unabridged, it is:

1. a self-evident truth that requires no proof.

2. a universally accepted principle or rule.

3.

Could you give a brief and clear exposition on the role of axioms—and other foundational propositions—in logic, and the question of a logical system being incapable of proving all its axioms? Along the lines of your wonderful essay on deductive, inductive and abductive reasoning?

Thank you...

1. a self-evident truth that requires no proof.

2. a universally accepted principle or rule.

3.

*Logic, Math*a proposition that is assumed without proof for the sake of studying the consequences that follow from it.Could you give a brief and clear exposition on the role of axioms—and other foundational propositions—in logic, and the question of a logical system being incapable of proving all its axioms? Along the lines of your wonderful essay on deductive, inductive and abductive reasoning?

Thank you...