Thursday, August 27, 2015

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] 

Friday, August 14, 2015

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).”

Tuesday, August 4, 2015

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]

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 exceptions.  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.

Objection: “Axioms are Empty Tautologies/Truisms”
            What, actually, do these axioms tell us?  Not very much.  At bottom, they are merely pretentious reformulations of several irrelevant truisms.  ‘Existence exists’ and ‘A is A’ are mere tautologies.  They tell us neither what exists nor what is A.  The second axiom asserting the existence of consciousness is simply a vague way of describing the indisputable fact that people are conscious of something.  But it fails to specify not only what that something is, but what consciousness is as well.
             It is these three cognitively empty truisms [The “Existence” and “Consciousness” axioms, and the Law of Identity] which, according to Peikoff, form the starting point and basis of the entire Objectivist philosophy.  […] Can anything be constructed from principles that are so destitute of specific empirical content? […] The problem with indefinite principles like the Objectivist axioms is that nearly anything, no matter how contrary to the facts of reality, can be inferred from them.  By including everything, they end up saying nothing.  As cognitive principles used to interpret the data of reality, they are cognitively worthless. – Greg Nyquist, Ayn Rand Contra Human Nature, p. 186.
The Meaning of the Axioms

So that there is no misunderstanding, I’ll state the meaning of the basic axioms that Nyquist mentions. 

The Existence axiom states that whatever exists does exist, “existence exists.”  The concept of “existence” includes every entity, action, attribute, and relationship.  Anything that has existed, exists presently, and will exist in the future.  This includes the fact of consciousness and its various states and powers, whether presently known or unknown.  The axiom underscores the fact that something exists, something as opposed to nothing.

The Consciousness axiom states that whatever is conscious is conscious.  “Consciousness is the faculty of awareness—the faculty of perceiving that which exists.”[1] (Perceiving here means “being aware of,” no matter what the state of consciousness.) The concept of “consciousness” includes every state and process of awareness one experienced, presently experiences, and will ever experience, and includes the faculties that one infers in other living things, past, present, and future.  The axiom underscores the fact that whatever exists that you are aware of, you are aware of it.

The Identity axiom or Law of Identity states that a thing is itself, whatever exists is whatever it is, the sum of its attributes or characteristics.  The concept of “identity” includes all the same referents as the concept “existence”; the difference in the concepts is of perspective, as “existence” differentiates something from nothing, whereas “identity” differentiates one particular existent from another.  The axiom or law underscores the fact that everything is something in particular, as opposed to something not specific (which means that it doesn’t exist).

Objectivism’s Rejection of Cosmology

Nyquist criticizes the axioms for not specifying what exists and what constitutes consciousness.  He seems to believe that this is some error or mistake on Objectivism’s part, but I disagree.  Ayn Rand was completely opposed to the branch of metaphysics known as “Cosmology.”  (Personally, I had never considered the validity of that subject until reading her scathing journal entry remarks about the field.)

In short, her view was that it was impossible for philosophers as philosophers to discover the ultimate properties or nature of reality, or of consciousness.  These are not the provinces of philosophy, but of science.  Without the instruments and experiments provided by scientists, it is not even possible to determine what the usual objects we deal with are made up of, let alone the underlying structures and things which make up all of existence and all of the faculties of consciousness.  (Compare the historical development of the atomic theory of matter with the “Atomist” theory of Epicurus (341–270))

She regarded all such cosmological arguments of past philosophers as “mystical,” because they were not logical arguments soundly combined with observations, but rather rationalistic deductions from supposed axioms or from what was observed in nature.  “Arrested empiricists” was her term for philosophers like Thales and Plato, who took some partial knowledge that they had, and tried to apply it to everything without any proper cognitive warrant.  (E.g., Thales’ idea that water was the ultimate substance, or Plato’s idea of the Form of the Good, the Form that gives rise to all the other Forms and thus to the material world as well, since the material objects “participate” or reflect the Ideas/Forms.)

I believe that all cosmological attempts must fail because the people arguing for these underlying elements or properties have no way to properly integrate everything they present without the crucial aid of science.  As Rand puts it,
[…]Unless you bring it back to the perceptual level, it’s not knowledge. That is what has to be kept in mind always in speculating about ultimate causes, which have to be discovered by some, at present, unknown means. You still always have to bring it back to your sensory-perceptual level, otherwise it’s not knowledge.[2]
We simply are not equipped philosophically to determine such a question, or even the nature of consciousness.  This is the thrust of her comment in one of her journal entries that: “‘Cosmology’ has to be thrown out of philosophy.”[3] It is an unwarranted attempt to explain something that philosophy as such cannot explain.  The discoveries of science will simply continue to explode the “discoveries” found by any future cosmologists, just as it has done in the past.

Rather than mystically deducing the “true” nature of reality, Rand proposed as axioms the principles she believed to be self-evident and inescapable, and left the question of the ultimate “stuff” of reality and consciousness to the scientists, where it belongs.

The Functions of the Axioms

While the Objectivist axioms do not serve the purpose that Nyquist wants, they do have important functions for the human mind.  I’ll quickly note them and their importance.

Axioms underscore primary facts, providing epistemological guidance.

The axiomatic concepts are converted into formal axioms as a statement.  The statements, such as “existence exists” and “a thing is what it is,” are presented as a base and as a reminder; the basic fact is repeated for emphasis.

Emphasizing a basic fact is Objectivism’s way of placing a check on the mind’s entire range of awareness.  Due to the fact of volition, we are capable of an error in thinking, or of lying to ourselves, or of believing something that was only imagined.  Objectivism also holds that using our conceptual faculty is our means of gaining knowledge and our basic means of survival; it is the means by which we live our lives successfully.  Conceptual errors and doubts can thus have disastrous effects on our thinking and lives (and philosophies). The identification and correction of conceptual errors is therefore a crucial need of the mind.

In this function, the axioms act as checks on a mind’s cognitive activities.  If a contradiction is reached in one’s thinking or some reasoning contradicts one of the axiomatic concepts that one knows, then one will know that a mistake was made at some point.  Essentially, it is the same purpose that Aristotle’s laws of thought serve in formal logic (i.e., The Law of Non-contradiction, the Excluded Middle, and the Law of Identity).  (What I mean is that any argument that violates Aristotle’s Laws is unsound.)  In this way, they provide epistemological guidance for a conceptual, fallible consciousness.

Axioms preserve the continuity of your thinking and your knowledge.

The human mind is capable of awareness of its own past, present, and projection of the future due to the conceptual level of awareness.  The conceptual level of consciousness can thus hold the total of the individual’s experience, “extrospectively, the continuity of existence; introspectively, the continuity of consciousness.”[4] The axiomatic concepts retain their respective fundamental facts independent of any particular moment of awareness.  The percepts and concepts a person is aware of can change countless times in a day, but the basic, primary facts always remain the same.  Thus, the axiomatic concepts serve as cognitive constants of one’s consciousness: whatever exists that you are conscious of, it will always be the case that something exists, it has an identity, and you are aware of something.

Axioms are the foundation for objectivity.

Objectivity is arguably the most important term in the philosophy of Objectivism (and the reason why it is named as such).  It has two interrelated meanings: “Metaphysically, it is the recognition of the fact that reality exists independent of any perceiver’s consciousness. Epistemologically, it is the recognition of the fact that a perceiver’s (man’s) consciousness must acquire knowledge of reality by certain means (reason) in accordance with certain rules (logic).”[5]

The axioms serve as the foundation for objectivity.  Their respective axiomatic concepts explicitly identify existence and consciousness, reality and the awareness of reality, the two basic components of objectivity.  Grasping the axioms leads to the idea of metaphysical objectivity, the independence of existence from consciousness (including the nature of any given consciousness): an axiomatic corollary which Objectivism calls the “Primacy of Existence.” This principle in turn provides the basis for epistemological objectivity, in that conceptual knowledge can only be gained by specific means (reason) using specific rules of thinking (logic); a man must adapt his reasoning to the facts of reality in order to know anything about it, not merely conclude whatever he wishes or feels.

Conclusion

This is basically what the axioms mean and some ways in which they are applied in the philosophy of Objectivism.  Nyquist demanded more from the axioms in his objection.  However, the whole philosophical discipline of cosmology is an ancient mistake that ruins the metaphysical theories of those who incorporate it into their views. 

Soon, I’ll answer another objection of Nyquist’s, and give a more complete picture of the structure of the Objectivist Metaphysics in the progress.

References

[1]: Ayn Rand, Introduction to Objectivist Epistemology, “Concepts of Consciousness,” p. 37.
[2]: Ayn Rand, Introduction to Objectivist Epistemology, 2nd edition, “Properties of the Ultimate Constituents.”
[3]: Ayn Rand, Journals of Ayn Rand, entry dated: 19 June, 1958.
[4]: Ayn Rand, Introduction to Objectivist Epistemology, “Axiomatic Concepts,” p. 57.
[5]: Ayn Rand, The Objectivist Newsletter, Who Is the Final Authority in Ethics?” dated: Feb. 1965, p. 7

Sunday, June 28, 2015

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):

Friday, June 12, 2015

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.

Friday, January 24, 2014

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.

Thursday, January 9, 2014

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.

Wednesday, January 1, 2014

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.

Saturday, August 25, 2012

Short Induction of "Man's Life as the Standard of Moral Value"

I’ve shown what I think needs to be shown for the principle that “life is the standard of value.”  That applies to all living things as such.  But humans are special, and it’s their special nature that brings in the necessity of morality.