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.


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.


[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.

Friday, August 17, 2012

Short Induction of "Life is the Standard of Value"

After reading chapter 1 of Peikoff's "Understanding Objectivism," I decided to give my own induction as to why and how life serves as the standard of value.

The principle that “life is the standard of value” is not a deductive conclusion in the philosophy of Objectivism: it is inductive.  It is an induction that arises from an analysis of value, of life, and of a standard, and observations of living organisms.  If someone doesn’t understand that, then they do not really understand what Rand meant when she wrote that “life is the standard of value.”

Thursday, March 15, 2012

Research Materials for Inducing Individual Rights (Founding Fathers)

I've decided to include a list of sites and books that helped me really understand and flesh out the theory of individual rights as the Founding Fathers understood it.

  1. The Jeffersonian Cyclopedia.  The quotes on the topic of "rights" were really helpful in quoting Jefferson in support of the points I made in this paper.
  2. Freedom Key's section, "About Rights." It has a good collection of quotes about rights, especially a few gems in particular by Jefferson, John Adams, and William Blackstone.

  3. The Founder's Constitution is the online version of a five-volume text on the historical context of the U.S.Constitution.  It has primary materials from the Founding Fathers, including letters sent amongst themselves, records of debates or meetings, and contemporary law cases.  I especially relied on the materials found in the sections, "Rights," "Republican Government,""Right of Revolution,""Popular Basis of Political Authority," "Equality," "Property," and "Epilogue: Securing the Republic."

  4. "Objectivism: the Philosophy of Ayn Rand," by Leonard Peikoff.  Despite having read Ayn Rand's books before reading this, I never considered the point that rights are inseparable and form a unity until I read Dr. Peikoff's discussion of them in chapter ten of the book, "Government."  The book is also my original source for the Samuel Adams quote about the rights of man being branches of "the duty of self-preservation."

  5. "John Adams," by Anne Husted Burleigh.  A republication of the biography Mrs. Burleigh wrote 40 years earlier, it is a very well-written work on the life of John Adams, and really gives you a sense of astonishment at the political victories this man accomplished in his life.  I'm still in the middle of finishing it, but I used the pages relevant to rights and the government to inform my essay.

  6. "The Leadership Assumptions of the American Statesmen During the Federal Convention and Ratification Debates, 1787-1789," the dissertation of Dr. Darin Layton Gerdes.  Chapter four features the assumptions and the conclusions of the Founders and others who participated in the Federal debates to ratify the U.S. Constitution.  These assumptions and conclusions centered around their ideas of "the nature of man," "the nature of power," "the nature of government," "the nature of people," and "the nature of society."  That chapter alone is great material for inducing many of the Founders' political principles from their personal context, such as inducing the corrupt nature of political power by examining cases where unchecked power led to needless violations of rights, destruction, and death.
Those were my sources for the essay.  I expect to use even more for my next essay, on republican government.

I may delve into this topic more deeply when I get the chance, so if anyone knows any works that would be really relevant, please let me know in the comments.

Wednesday, March 14, 2012

Induction of the Principle of Individual Rights (Founding Fathers)

Induction of the Principle of Individual Rights (Founding Fathers)

The Founding Fathers studied history, philosophy, economics, political science, and law, among other subjects.  They were all thinkers, and men of action.  In their own ways, they discovered the elements of two literally revolutionary ideas that they intended to finalize and put into practice for the first time on Earth: the principles of individual rights combined with a republican government.  With those two overarching principles in mind, they intended to change history, in a phenomenal way that has never been matched since.  I will focus on the principles and facts underlying the idea of individual rights, from the perspectives of American legends George Washington, Thomas Jefferson, John Adams, Samuel Adams, Patrick Henry, Thomas Paine, Alexander Hamilton, and James Madison, as well as lesser known Founders James Wilson and William Gladstone.