An axiom is a statement that provides the basic foundation for other knowledge. It is a statement that cannot be proved by reference to any more basic statements, because it provides the most basic conceptual foundation of all proofs. A genuine axiom must be self-evident, because a statement that cannot be proved in any manner, yet is not self-evident, is simply an arbitrary assertion. And arbitrary assertions don’t constitute knowledge, but are just groundless fantasies or imaginings.
The philosophy of Objectivism has three axioms that it holds are implicit in any claim to knowledge of any sort. They are as follows:
“Existence exists.”
“Consciousness perceives existence.”
“An existent is itself.” (Often referred to as “A is A,” or the Law of Identity.)
These three metaphysical axioms form the fundamental base of Objectivism. A corollary of the Law of Identity is the Law of Causality, which states that an entity acts as itself.
“Existence exists.”
This first axiom states, in effect, “There is something, as opposed to nothing.” That something exists is perceptually self-evident, and is presupposed by every statement, action or thought. What does it mean to “exist?” The concept of existence is not reducible to any more fundamental terms. The term does not have a conceptual definition. (Any attempted definition must employ the concept of existence, and is thus circular.) The only way one can “define” existence is ostensively–that is by pointing out instances of “existence,” which are particular existents.
Note that this axiom does not say anything in particular about what exists, or how to find out what, in particular, exists. It does not even specify that a world of physical objects exists. All it says is that something exists.
“Consciousness perceives existence.”
In order to be aware that existence exists (and of any particular existents or facts), one must have consciousness, the faculty of perceiving existence. As with the first axiom, this is perceptually self-evident. In the act of perceiving that which exists, one implicitly confirms that there is something to perceive, and that one is perceiving it. (1) When one reaches the conceptual identification of consciousness, such that one can say explicitly, “Consciousness perceives existence,” this axiom can be stated equivalently in the form of a definition: “Consciousness is that faculty of an entity which perceives existence.” One’s own experience of one’s own consciousness (perception) is the self-evident basis (validation) of that axiomatic definition of consciousness. (2)
Note that this axiom directly implies that existence is, in some sense, independent of consciousness, since existence is the object of consciousness.
“An existent is itself.”
Every thing that exists, exists as something specific, not some indeterminate “nothing in particular.” Whatever an existent is, it is. It is itself and not something else. Something that has certain intrinsic characteristics cannot, at the same time, have the opposite characteristics. Contradictions cannot exist in reality. This, too, is perceptually self-evident. A rock that is very dense and that falls in the earth’s atmosphere, cannot simultaneously be a helium balloon that floats in the earth’s atmosphere. A conscious human being cannot simultaneously be an unconscious plant. (3) (4)
The Law of Causality
The Law of Causality is, in Ayn Rand’s words, “the Law of Identity applied to action.” It is a corollary of the fact that an entity is what it is, that that entity will act (or react) as what it is. (5) Whatever the nature of a particular entity, it is this nature that will determine what action(s) or reaction(s) is/are open to it in a given situation. An entity cannot act in contradiction to its nature.
It should be noted that this formulation of the Law of Causality does not require that an entity respond mechanically to an antecedent action of another entity. It does not require that an entity only be capable of one response in a given situation. Whether a single mechanical response is all that is open to the entity, or a vast range of possible responses/actions, is determined by the specific nature of the entity in question. In fundamental terms, the Law of Causality only links an action to the entity that performs it, not to the actions of other entities. (Put somewhat more technically: By the Law of Causality, not every action taken by an entity must have a set of prior actions that comprise a sufficient condition for it to occur. The only cause of the action that need be present in all cases is the entity that acts.)
If I stand on a rooftop and release a stone over the edge, it falls. This is the only response to the earth’s pull that is open to the stone in that situation: a simple response consistent with its nature as a stone. If I release a helium balloon over the edge, it rises. This is a very different response to the same situation that results from the different nature of the balloon. (The difference, of course, is a difference in the property of density possessed by the object.) If I am on that rooftop, and I attempt to push a man off the edge, he may push back, fight me, pull out a knife, attempt to run away, yell, or resign himself to being pushed off. His nature as a man opens up a vast array of possible responses not open to an inanimate object like a stone, or balloon. (6) (7)
Axioms are Validated Ostensively
Because the axioms are the most fundamental premises possible, they are implicitly presumed, not only in every claim to knowledge of any sort, but also in every attempt at proof. Any attempt to prove them conceptually must, itself, presume them. Thus, the axioms are too fundamental to prove using any other ideas as the basis of proof. The only way to validate them is by directly observing reality and recognizing the self-evidence of the axioms in that perception. This is the process of ostensive validation.
If one looks at the world around him he will see directly that there is something of which he is aware. That phrase in bold holds all three of the axioms in it. There is something (existence and identity) of which he is aware (consciousness.) To stress identity: everything he sees appears as some particular thing. (8)
The Rejection of Axioms is Logically Self-Refuting
Since the axioms are assumed in every claim to knowledge of any kind, any argument, any reasoning, and any thought, they are implicit in any attempt to deny their validity. (9)
If someone says, “I do not accept that existence exists” then one can show that that sentence can have no meaning if it is true (note the self-contradictory phrase in the bold italics): “‘I‘? To what are you referring when you say ‘I’? If nothing exists, there is no ‘I’ since there is nothing. ‘Do not accept’? This implies that it is possible to accept something, but that ‘you do not.’ But if nothing exists, then there is nothing to accept or reject. ‘Existence’? Since you say there is no such thing as existence, and this is the broadest possible concept, encompassing everything, you are left with nothing to refer to, at all, and no one to speak to, at all, including me.”
The denial that “consciousness perceives existence” is also self-refuting. To see why, we should recognize that, for each of us, our fundamental, primary experience with consciousness is our own. Your own consciousness is your fundamental standard of what consciousness is. It provides necessary material for the concept, such that before anyone can grasp the idea of consciousness outside of oneself, he must grasp that he is in possession of consciousness. (Indeed, if you did not possess consciousness, you could not form any concepts at all.) (10) Thus, denying that consciousness perceives existence is denying that your own consciousness perceives existence, and effectively stating that everything you perceive, and to which your concepts refer, does not exist. So any statement made by one who denies this axiom becomes meaningless and void, including the denial. “‘Consciousness?’ There is no such thing, if it is not that which perceives existence. ‘Existence?’ You claim to know absolutely nothing of anything that exists.”
The denial of the Law of Identity is self-refuting, as well. If anything can lack an identity, then contradictions can exist, and no knowledge whatsoever is possible. Anything could also be its opposite at any time, such that for any “true” statement, the opposite could simultaneously be “true.” A statement could be both true and false at the same time. In fact, without the absolutism of identity, the very concept of “identity” would be rendered meaningless: No one could ever know that anything is any particular thing, making identification of any sort impossible, including identification of the concepts of “identity,” “self,” and “disbelief.”
“Existence exists” Necessitates Material Permanence
“Existence exists” pertains to the universe as a whole, and the universe as a whole is simply the sum of everything in it. Thus, one can render the axiom as “Existents exist.” That is, one can apply the axiom to every single existent. (11) Matter, in the broadest, philosophical sense, refers to anything that is a physical entity or set of physical entities, without specifying any particular qualities, actions, relationships, or temporal changes. (Thus, philosophically, matter includes not only atomic particles, but also photons and the like.) When entities change, their qualities, actions and relationships can “come into existence” or “go out of existence.” Metaphysically, such changes are not “creations” or “annihilations,” but simply designate that the entities involved are changing. These changes are only “creations” and “annihilations” epistemologically; that is, they are creations or obliterations of instances/situations in which certain objective, human concepts apply. If, however, matter (broadly, i.e. entities qua independent existents) were to be created or obliterated, this would be a metaphysical creation or annihilation, and would violate the axiom that existence exists.
If an entity exists, then it exists in some form, permanently. It can change into something else, by changing its attributes, it can split into its parts, or converge to become part of something else, but it cannot change into nothing. (12) Saying that something changes into nothing literally does not make sense, since “nothing” does not designate a something that an entity can change into. “Nothing” only designates an absence where one is looking for–or considering the possibility of finding–a particular something; “nothingness” does not exist metaphysically, and is only defined in reference to those entities that do exist.
Are the Axioms “A Priori” Truths?
No. The axioms, like all other forms of knowledge, have their origin in sense-perception. The axioms are implicit in every perception and thus are not dependent on any specific observations, but they cannot be known at all apart from any perception; nor can they be regarded simply as features of human cognition, apart from the rest of existence that is being observed, (as Kant regarded such fundamentals.)
Naturally, the explicit identification of the axioms also rests on sense experience, in that the conceptual structure needed to arrive at the concepts “existence,” “consciousness” and “identity” is built on sense-perception, (in which the axioms are implicit.) (13)
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(1) By “implicitly” I mean taken for granted without being specifically identified consciously/conceptually. When someone accepts a premise implicitly, he generally acts as though that premise is true, without telling himself it is true in his conscious mind. See Introduction to Objectivist Epistemology, Exp. 2nd Ed.
(2) Note that this definition is not the equivalent of the claim that consciousness only passively perceives existence and does nothing else. Consciousness involves a great many activities, such as emotion and imagination. But the perception of existence is the fundamental activity that makes all others possible. Since definitions only consist of the fundamental characteristics of existents that enable them to be distinguished from other types of existents, not all the existents’ characteristics, this is a proper definition in its form. (Though it is not a definition in terms of more fundamental concepts, but an axiomatic/self-evident definition, since “perception” is “that which consciousness does with existence,” thus generating axiomatic circularity.) See http://aynrandlexicon.com/lexicon/definitions.html.
(3) This metaphysical Law of Identity is what underpins the logical Law of Identity and the Law of Non-Contradiction. Since everything in reality is something in particular, and conceptual consciousness (qua consciousness of reality) is the faculty of identifying that which exists, a consciousness cannot accept, as true, two mutually contradictory statements. Contradictions are strictly a phenomenon of conceptual propositions, not of sense-perception, or of reality.
(4) Please see Chapter 1 of Objectivism: The Philosophy of Ayn Rand (OPAR) for more on the axioms. This work is the primary source for this post.
(5) Note here that “entity” is slightly more specific than “existent.” See OPAR and/or this: http://aynrandlexicon.com/lexicon/entity.html for more on the distinction. Also, see http://aynrandlexicon.com/lexicon/causality.html Action, here, is used in the broadest sense. It includes any self-generated action on other entities, any reaction to other entities, and any internal change.
(6) Please see Chapter 1 of OPAR for more on causality.
(7) Of course Ayn Rand did not invent the Laws of Identity and Causality, nor did she claim to have. Plato was the first philosopher recorded to have stated the Law of Identity. Aristotle was the first philosopher known to have explicitly identified the Law of Non-Contradiction and types of causality. Parmenides had an axiom similar to Rand’s first: “Being is.” (Though what Parmenides took away from it is substantially different from Rand’s understanding, since he regarded all change as an illusion.) Ayn Rand’s primary contributions are to identify what, precisely, it means for something to be an axiom, how axioms can be validated, and her systematic and rigorous presentation/application of the axioms she identified as such. Here is an interesting discussion of the relationship of Ayn Rand’s metaphysics to Ancient Greek philosophy: Existence Exists, or the Modern Parmenides. (It should be noted that, according to Objectivism, Aristotle made a deep metaphysical error in postulating a consciousness that was only conscious of itself. Since this idea was confined to a distant, impersonal Prime Mover, it arguably had little impact on his effective philosophy of this world.)
(8) OPAR pg. 5
(9) Though the axioms are presumed as true in some way in every thought and statement, this does not mean that every set of one or more thoughts or statements reflects consistent adherence to the axioms. A statement may be self-contradictory, thus not conforming to the Law of Identity, but each side of the contradiction depends on the acceptance of the axioms (including identity) for whatever meaning it holds to the speaker. Indeed, insofar as the concepts that the person uses have any meaning whatsoever, they depend implicitly on the axioms (consciousness of reality) for that meaning. Otherwise, they would quite literally refer to nothing.
(10) For the Objectivist theory of concepts, see IOE. I also intend to write a future post on this, but certainly not in the kind of detail the book goes into.
(11) If “existing” were an attribute or action, this would not follow, and would be an example of the Fallacy of Division. But, despite the fact that, linguistically, “to exist” is treated as a verb, “existing” is not an action, but a primary fact. This logical step is the same in character as saying that ten equals ten multiplied by one. That is, if a total of ten things exists, then each one of those ten things exists.
(12) See http://aynrandlexicon.com/lexicon/matter.html
(13) I intend to write further on the issue of “a priori vs. a posteriori” and “analytic vs. synthetic” knowledge in a future post. For more detail on these issues, see IOE.
[Edited: 5-6-15: Added first paragraph.]
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“‘Existence exists’ Necessitates Material Permanence”
Doesn’t this equate matter with existence, as such?
I thought that…
“…this axiom does not say anything in particular about what exists, or how to find out what, in particular, exists. It does not even specify that a world of physical objects exists. All it says is that something exists.”
Also,
If the axioms are validated “ostensively” (by “looking at reality”), how does one validate the applicability of the axioms regarding that which he has not, or cannot, “look at”? How does one know that the axioms apply to *all* of reality, rather than only applying to that which he is looking at?
‘Doesn’t this equate matter with existence, as such?’
All true entities (independent, primary existents) are material. Consciousness is a process involving a relationship between material entities.
“…this axiom does not say anything in particular about what exists, or how to find out what, in particular, exists. It does not even specify that a world of physical objects exists. All it says is that something exists.”
There is a difference between what a statement (in this case, an axiom) specifies and what it logically necessitates. The axiom of Identity specifies nothing about what man is capable of. But once one has learned enough about man and the earth, one can see that the axiom of Identity necessitates any man’s inability to jump to the moon under his own power. So it is with material permanence, but at a much more fundamental level.
‘How does one know that the axioms apply to *all* of reality, rather than only applying to that which he is looking at?’
If I consider the violation of an axiom possible in reality at any point, then I have no basis for knowing whether or not the axiom is being violated right now, with what I am staring at. If axioms can be violated at all, then I can’t trust my perception at this instant, because “contradictory facts” may “negate what I am seeing.” But it is self-evident that I do see what I see, and not “what I see and not what I see at the same time.” It is self-evident in every perception that the axioms apply to reality; it is self-evident in perception as such.
So it is truly either-or: Either the axioms apply everywhere, or they can’t be regarded as applying at all. The first is self-evidently true, the second is self-evidently false.
But let me take another approach to the issue that might add clarity:
If the axioms are violated at any point, then a “contradiction would exist in metaphysical reality.” But all the instances from which I have formed the concept “contradiction” have been within a conceptual consciousness (most basically, my own.) Contradictions, by their essential nature and by definition, are purely a phenomenon of conceptual consciousness. To talk about “contradictions existing in metaphysical reality,” or in actual perception, is quite simply an illegitimate use of the concept “contradiction,” (i.e. it is to use “contradiction” as a stolen concept.)
Thus, it does not even make sense to speculate on the possibility of “contradictions existing in reality.” The words become meaningless sounds/letters in such a statement; cut off from their meaning in reality. Thus, talking about a “contradiction existing in metaphysical reality” is analogous to talking about an “unconscious, but morally evil rock.” (Of course, the whole concept of moral evil presupposes volitional consciousness. Likewise, the whole concept of “contradiction” refers to and presupposes the conceptual content of a consciousness.)
I don’t want to turn this into a “debate forum”, so the following questions aren’t meant for debate purposes, but clarification purposes so that I can more fully understand your / the Objectivist position more fully.
1) Does this mean that you / Objectivism accepts logical necessity (at least at times)?
2) Do you / Objectivism, hold then that the law of non-contradiction is entirely epistemological (or conceptual), and not metaphysical?
Thank you.
I’ll take 2) first: Yes, precisely speaking, the Law of Non-Contradiction is an epistemological law based on the metaphysical Law of Identity. Since everything is what it is, the fundamental epistemological guideline in dealing with reality conceptually is to avoid contradictions in identification. No question of contradictions actually comes up in sheer sense-perception of reality. I take Objectivism to be in agreement with me on this point. (I seem to vaguely remember Dr. Peikoff (?) mentioning that Non-Contradiction was epistemological in a recorded lecture. Not sure where it was.)
1) I’m not entirely sure what you take “logical necessity” to include.
If by “logical necessity,” you mean that the truth of one statement necessitates the falsity of any statement that contradicts it, then yes, Objectivism accepts this sort of logical necessity.
If you mean, “Does Objectivism accept deduction as a proper method of reasoning?” then yes, Objectivism accepts deduction with certain caveats.*
But if you take “logical necessity” to mean that the “logical” workings of a mind somehow push reality into doing certain things and not others–that is, if you take “logical necessity” as a form of the Primacy of Consciousness–then no, Objectivism doesn’t accept this sort of “logical necessity.” Logic derives from sense-perception of existence. Existence doesn’t “conform” to a prior logic.
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*One basic caveat is the matter of context. Most generalizations from which one might deduce (excluding basic axioms, which have no detailed content by themselves) hold as true only within a certain context. Most concepts are meaningful only within a certain context. Any proper deduction made from a contextual general premise will hold only within the premise’s context. Omitting the context omits information pertinent to the deductive reasoning. (For example, see Point 10 of The Morality of Rational Egoism: Short Notes.)
This is a major part of the problem with Rationalist philosophers who start in midstream with some “obvious” generalization and deduce consequences from it. They tend to omit the contexts of their concepts and generalizations. This leads to false alternatives, the Fallacy of the Stolen Concept, (e.g. “eternal happiness,” or “God’s purpose”) and general intellectual detachment from observed reality.
Another caveat is to avoid attempting deductions from arbitrary premises, or using arbitrarily defined concepts. Concepts and generalizations must first be formed or induced from sense-experience.
Thank you for a very interesting web site!
I do have a question regarding the axioms, specifically the Law of Identity. While I believe I grasp the axioms of existence and consciousness fully (as attempts at refutations lead to absurdities), it seems to me that the Law of Identity has a weaker axiomatic character, in that its validation is on continuous probation by the observational technology of human beings; it is an inductive postulate – not a true axiom.
A chair is a chair and a car is a car. These facts are validated every day by anyone who wishes to uses their senses. But this validation happens through empirical observation: for each new object one encounters, the law of identity validates itself. But isn’t there a theoretical possibility of encountering objects that stretch, or do not adhere to the law of identity as we hitherto know it?
For instance, what if identity is a cosmological property present as the likes of some energy field with fluxuating (meta)physical constants and magnitudes. In the part of the universe, and at the macro level, known to man, this property happens to be constant and hence we have induced what we call the Law of Identity. But e.g. as modern physics suggests, at the micro level the identity property has different characteristics than what we may observe directly through the senses.
I see that what I’m asking might be arbitrary, but I think this example is useful to resolve wether I am correct that the axiom of identity is less rigid than the other axioms, or if I misunderstand it / missed something.
Thanks again!
I’m glad you’re enjoying my blog.
But here’s where you misunderstand: Identity is not a property of entities. Just as I said that Existence is not a property of an entity, but the primary fact that it is there, so Identity is the primary fact that it is there. The Law of Identity is the Axiom of Existence considered from a different conceptual angle. (It’s being contrasted with different versions of fantasy/unreality. That is, reality is being protected in cognition from different conceptual errors.)
Thus, the Law of Identity is inseparable from the Axiom of Existence, and every bit as axiomatic. To be is to be something. To be something is to be.
The fact that you think of Identity as a property indicates that you may be confusing the Law of Identity with a statement about the temporal constancy and/or physical integrity of entities. The Law of Identity doesn’t say that things will continue to be what they are now, or that they cannot disintegrate. Neither an acorn that grows into a tree, nor a nucleus that disintegrates via internal processes is violating the Law of Identity. Nor would a field that caused things to behave strangely and unstably, violate the Law of Identity. Whatever something was at any given time, would be what it was. Period. (Since Identity is not a property, it can’t be changed or taken away from an entity.)
A distinction might be made between the axiom of consciousness, which states that “Consciousness exists” (or more personally, “I am conscious), and the axiom of the primacy of consciousness, which states that “Consciousness is objective, i.e. consciousness is consciousness of existence”. Does this help? David Tyson
Was there a first action within existence? I’m having trouble understanding that existence exists and has actions at the same time, because if it has always existed, what exerted any exitent to act, leading to a causality?
In your interpretation of Objectivism, is there any contradiction with Relativity, Quantum Mechanics, or Evolution?
Certainly not evolution: There’s no issue or conflict at all there, as far as I can tell.
The situation is somewhat different with Relativity and Quantum Mechanics, however. If, as many do, one interprets the principles of relativity and quantum mechanics to imply that one person’s reality is contradicted by another person’s reality, or that any entities don’t have a nature until “observed,” then yes, there’s a contradiction with Objectivism. No science, properly so called, can deny that there’s a single reality or that all entities have a particular identity at all times. Such self-contradictory conclusions are always the result of bad philosophy, not actual science. Science itself is predicated on the axiomatic Law of Identity. It requires one to be able to relate disparate entities and organize their interactions into principles.
A proper interpretation of relativity and quantum mechanics would hold that there is always one, objectively applicable description of reality and that all involved entities always have a specific identity at all times.