Reblogged: Objections to the Axioms (Part 4)

[Roderick Fitts]

Objection: The Axioms are Circular

The axioms rest on the law of noncontradiction for their validity, but the law of noncontradiction itself rests upon the axioms.[1] 

The Validity of the Axioms

The (basic) axioms do not rely on each other for their validity. Direct experience or sense-perception is the means of validating the basic axioms.[2] Derivative axioms like "self" and "volition" rely on the fact of the basic axioms and direct experience for their validity, but not the basic axioms themselves. Further, the basic axioms being part of the validation of derivative axioms does not mean that the derivative axioms are deductions from the basic ones, or logical consequences. In Objectivism, the material required to form the basic axioms of existence, identity, and consciousness are discovered simultaneously. Peikoff mentions in a lecture course that: "'A is A' is independent of consciousness for its truth, but it’s not independent of the existence of consciousness to be grasped."[3]

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[Plasmatic]

Roderick said:

What this means is that the axioms cannot be "circular": a circular argument is a proof in which one of the premises is repeated in the conclusion (albeit not always directly or obviously), such that the argument assumes what it is trying to prove. This is the logical fallacy of "begging the question," the petitio principii. The validations of the axioms are not arguments, but direct experience/sense-perception in the case of the basic axioms. The validations of derivative axioms are direct experience with prior knowledge of one or more of the basic axioms, as the derivative axioms are corollaries or new angles on self-evident facts. Since the axioms are the antecedents of the field of logic, their validations are outside of the realm of proofs and even fallacies like circularity.

I don't think it follows that the axioms are excluded from the category of circular. Dr. Peikoff accepts that the axioms are tautologies in the A-S article in ITOE. Also in the 1976 Lectures Dr. Peikoff says "all arguments presuppose them, including the argument that all arguments presuppose them". The validation of axiomatic truths as performed by any individual is not an argument, but the argument that one can only reaffirm the axioms by denying them is an argument. All truths are circular-tautologies. Edited August 17, 2015 by Plasmatic

[dream_weaver]

The distinction here is one of proof vs. validation. The petitio principii is a logical fallacy which would be disqualified in a valid proof. The process of validation is outside the realm of proofs.

 

You can find this example on Lecture 3 of Introduction to Logic at 2:34:50

 

#29 You ask me to give you a valid argument to prove the truth of the law of contradiction:

P1. Whatever is presupposed by all knowledge must be true.
P2. The law of contradiction is presupposed by all knowledge.
C: Therefore I infer that the law of contradiction must be true.

 

The structure of the reasoning is that X is true because X is true

You are assuming the point in issue, simply by making the argument.

 

Any attempt to prove the laws of logic would commit petitio.

Edited August 17, 2015 by dream_weaver

[Plasmatic]

Weaver said:

Any attempt to prove the laws of logic would commit petitio.

Sure, but the article says that "The validations of the axioms are not arguments[...]" instead of saying "The validations of the axioms are not" an attempt to prove them". My point is that one can affirm that axioms are beyond proof and still argue that they are tautologies. Edited August 17, 2015 by Plasmatic