Objections to the Axioms (Part 4)

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]

Objectivism says that there is a certain order to know the axioms, not that there's a certain order to prove them one after the other. The philosophy does not say that one axiom logically leads to the next one. The axioms are not meant to prove themselves, and they are not designed to prove the other axioms. They are outside of proof as such and are at the base of the concept "proof." Some axioms are deemed basic, while others are derivatives but still axioms. Certain ones are hierarchically higher than others, while others are on the same level in comparison to these higher axioms.

Certain Axioms as Implications of More Basic Axioms

For instance, the Law of Identity is a basic axiom, and the Law of Noncontradiction (LNC) and the Law of Excluded Middle (LEM) are corollaries of that law.[4] All things possess identity, which can be restated as the LNC (which is the negative statement of Identity) or the LEM (identity in relation to the existence or non-existence of any given thing). The Law of Identity is hierarchically higher, and the other two are on the same level beneath it. The statement "A is A" means that it's never the case that something is both A and not-A at a given time and respect, the LNC, and that it's always the case that something is either A or not-A at a given time and respect, the LEM/Either-Or. As should be clear, even discussing one of the laws implies the others, and it certainly is a peculiarity among the axioms.

Rand noted how recognizing certain axioms implies others in For the New Intellectual,

Existence exists—and the act of grasping that statement implies two corollary axioms: that something exists which one perceives and that one exists possessing consciousness, consciousness being the faculty of perceiving that which exists.[5] 

There she claims that understanding the existence axiom implies that one can readily understand the consciousness and identity axioms. She follows that line with 2 more axiomatic statements concerning consciousness:

If nothing exists, there can be no consciousness: a consciousness with nothing to be conscious of is a contradiction in terms. A consciousness conscious of nothing but itself is a contradiction in terms: before it could identify itself as consciousness, it had to be conscious of something[…][6] 

Connecting the fact of existence and the fact of consciousness implies that consciousness as such would not exist without things external to it that would allow it to be conscious. The axioms also preclude exclusive, exhaustive self-consciousness à la solipsism or (to a lesser extent) Cartesian doubt: external awareness precedes self-awareness, the self needs something external to differentiate it from those external things.

Axioms as Pre-Logical and Non-Circular 

The discovery and validation of the axioms are technically pre-logical because the axioms are the foundation for the field of logic itself. The axioms are not reached by inductive or deductive argument, and are the preconditions for issues like inductive or deductive validity. (This should be readily understood, since we are discussing principles like the LNC and the LEM.)

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.

References

[1]: The objection was suggested by Facebook friend and fellow student of philosophy, Francesca Ford.
[2]: Leonard Peikoff, Objectivism: the Philosophy of Ayn Rand, p. 18, PDF version.
[3]: Leonard Peikoff, Understanding Objectivism: A Guide to Learning Ayn Rand's Philosophy, p. 152, Kindle Edition.
[4]: Nathaniel Branden, Vision of Ayn Rand: Basic Principles of Objectivism, Lecture 3: Logic and Mysticism, p. 66
[5]: Ayn Rand, Galt’s Speech, For the New Intellectual, p. 124.
[6]: ibid.