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 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.

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]

Objections to the Axioms (Part 1)

Previous: The Order of the Objectivist Metaphysics

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.

The Order of the Objectivist Metaphysics

Previous: The Metaphysically Given as Absolute

With the final principle of the Objectivist metaphysics articulated, we can now see the structure of this branch of philosophy.

The Basic Axioms, and Their Corollaries

We begin with the metaphysical axiomatic concepts and axioms, which I’ve already discussed in my essay on the axioms (the others will be discussed in the following essays on sense-perception and free will):

The Metaphysically Given as Absolute

Previous: The Primacy of Existence

The Objectivist view of metaphysics ends with the principle that alternatives to facts of reality are impossible and unimaginable.  These facts, which Ayn Rand called the “metaphysically given,” necessarily exist.  Man-made facts, on the other hand, are conditional, not necessary.  Due to this, metaphysically given facts are absolute.

The Primacy of Existence

Previous: The Law of Causality (Cause and Effect)

Objectivism is named for one of its key concepts that it emphasizes and upholds—the concept of “objectivity.”  Ayn Rand said this about objectivity in part: “It pertains to the relationship of consciousness to existence. Metaphysically [by the nature of reality—my comment], it is the recognition of the fact that reality exists independent of any perceiver’s consciousness.”[1] In general philosophy, this “recognition” is a position called “metaphysical objectivity”; in Objectivism, it is known as the “Primacy of Existence.” 

Like the law of causality, it is a law inherent in existence, and it describes the precise role of consciousness in relation to existence.  It is the most important principle in Metaphysics, and is a further corollary of the axioms and the law of causality.  I will describe how one could reach the primacy of existence from experience.  Then I will explain the opposition to this view, the primacy of consciousness.  Afterwards, I’ll explain a process for reaching generalized knowledge like the axioms without using strict induction, using the process of Aristotle’s that has been named “intuitive induction.”  Lastly, I’ll answer an objection about the mind’s control over the body in light of the primacy of existence.

The Law of Causality (Cause-and-Effect)

Previous: On Axiomatic Concepts and Axioms

Causality is something inherent in reality; it is an inescapable law of existence. In Objectivism, it is the first principle of Metaphysics after the identification of the basic axioms. I will give an inductive investigation of sorts into how this law can be formed. Afterwards, I will show why it can’t be an induction strictly speaking, and is rather a self-evident corollary of the Law of Identity.

Inducing Cause-and-Effect

Causality, or cause-and-effect, is the view that the world is lawful, orderly, or uniform in its operations. To understand what this means, we’ll have to revisit a number of concepts I discussed previously in my essay on axiomatic concepts and axioms.

On Axiomatic Concepts and Axioms

Reaching the Axioms

All topics and all fields of research have a beginning or starting point. Philosophy may be the most abstract field that we study, but it is no different. Whether they admit to them or deny them, all philosophies rest on a set of axioms, or starting points. Axioms are self-evident propositions that indicate the bases of all knowledge and are at the base of all statements and claims. Philosophical axioms must be accepted in order to make any statement or claim to knowledge of any subject, because philosophy is the backdrop for all other areas of study. Aristotle was perhaps the first individual to discuss the importance of axioms, and Objectivism is the most recent philosophy to emphasize their role in knowledge.