Roderick Fitts Posted July 26, 2015 Report Share Posted July 26, 2015 Question: “Are Axioms Proven or Merely Assumptions?” “Are first principles or the axioms of logic (such as identity, non-contradiction) provable? If not, then isn't just an intuitive assumption that they are true?[...]”[1] The axioms are neither “proven” nor “assumed.” (In the Objectivist view of axiomatic corollaries, Aristotle’s “Laws of Thought” are corollaries of the Existence axiom. And more specifically, the Law or Principle of Non-contradiction and the Law of the Excluded Middle are restatements/corollaries of the Law of Identity, which is a corollary of “existence exists.”[2] So I’ll consider this question as broad enough to encompass any first principle, including the Objectivist axioms.) I’ll make several points about why this can’t be the case when speaking of actual axioms. Continue...Link to Original Quote Link to comment Share on other sites More sharing options...
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