Objections to the Axioms (Part 6)

This will probably be my last response to the metaphysical axioms for some time.

A commenter raises the following issue:

It's often said that to deny axiom[sic] is to engage in self contradiction - and that wouldn't be a valid objection because in order to classify contradiction as an error one has to assume axioms to be true. I see circular reasoning in this answer against axiom deniers.[1] 

Objections to the Axioms (Part 5)

Objection: The Axioms Equivocate on Their Content

This objection concerns exactly what it is that the axioms are explaining and implying.  It highlights a seeming equivocation:

[…]In the Logical Structure of Objectivism, David Kelley makes the following observation:

Notice that neither [the axiom of existence nor the axiom of identity make] any specific statement about the nature of what exists. For example, the axiom of existence does not assert the existence of a physical or material world as opposed to a mental one. The axiom of identity does not assert that all objects are composed of form and matter, as Aristotle said. These things may be true, but they are not axiomatic; the axioms assert the simple and inescapable fact that whatever there is, it is and it is something.

Very well. Now consider what Rand draws from these very same axioms:

To grasp the axiom that existence exists, means to grasp the fact that nature, i.e., the universe as a whole, cannot be created or annihilated, that it cannot come into or go out of existence. Whether its basic constituent elements are atoms, or subatomic particles, or some yet undiscovered forms of energy, it is not ruled by a consciousness or by will or by chance, but by the law of identity. All the countless forms, motions, combinations and dissolutions of elements within the universe—from a floating speck of dust to the formation of a galaxy to the emergence of life—are caused and determined by the identities of the elements involved. 

In other words, she draws from these axioms: (1) that the universe is permanent and can neither be destroyed nor created; (2) the universe is not ruled by will or chance, but by the ‘law of identity’; (3) everything that happens is caused by the ‘identities’ of the elements involved. She also implies that the basic constituents of the universe, whatever they may happen to be, are non-mental (i.e., atoms, particles, or forms of energy). How does Rand draw all these things from these axioms when, according to Kelley [quoted earlier in the blog post] (who, in this instance, is being entirely orthodox) these axioms only assert that ‘something’ distinguishable exists?[1]

I’ll sum up this objection as: “Objectivism equivocates between axioms not specifying content (e.g. specific identities, specific actions), and inferences about reality that supposedly follow from the axioms (e.g. the universe cannot be created or destroyed, reality isn’t ruled by chance).”

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]