Saturday, July 25, 2015

Objections to the Axioms (Part 3)

Previous: Objections to the Axioms (Part 2)

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.

Sunday, July 19, 2015

Objections to the Axioms (Part 2)

Previous: Objections to the Axioms (Part 1)

This next objection is about the utility of the axioms.  

Objection: “Axioms Must Have Deductive Implications”
[...]A first principle is only useful and workable if you can deduce the rest of the worldview from it. You can't deduce anything from 'whatever exists exists'. You can't deduce any kind of epistemology (ie, how we know that whatever exists exists, how we know that we know, etc); we can't deduce any kind of metaphysic (ie, what is the nature of existence, what is the ground of existence, etc); and we certainly can't deduce any ethical or anthropological propositions (ie, what is right and wrong, what is the nature of man, etc).[...][1]

Monday, July 13, 2015

Objections to the Axioms (Part 1)

The axioms lay the proper foundation for a philosophy.  But for any statement or expression, there is almost always someone who disagrees.  Axioms are of no exception.  Of the people who are dismissive of Objectivism, I believe many are especially opposed to the Objectivist axioms.

Since I covered the metaphysical axioms of Objectivism in this series of posts, I’ll take the time to answer a series of actual objections to the axioms of the philosophy, and one objection to the idea of axioms as unprovable, originally answered by Aristotle.