| | Rand introduces her most fundamental axiom on page 1015 of Atlas Shrugged (hb). That is the assertion existence exists. As she introduces the axiom, she says that the moral code that she is overturning and replacing attempts to escape the axiom existence exists. She has already said that the code she means to overturn comes in a variety based on dictates of a supernatural being known as God (1011-12). One of the purposes of Rand's axiom existence exists is to foreclose the possibility of the existence of God.
In her later essay "The Metaphysical v. The Man-Made" (1973), she tells us that her axiom "existence exists" means that the universe exists independently of consciousness (24) and that the universe as a whole "cannot be created or annihilated, that it cannot come into or go out of existence" (25). She says that her fundamental axiom invalidates the question "If there is no God, who created the universe?"
Immediately after introducing he axiom existence exists in AS, Rand introduces axioms concerning consciousness, which are corollaries of grasping the statement existence exists. These are "that something exists which one perceives and that one exists possessing consciousness, consciousness being the faculty of perceiving that which exists" (1015). This characterization of consciousness and self-consciousness rules out the possibility of God as a mind existing before the existence of anything else. "A consciousness conscious of nothing but itself is a contradiction in terms: before it could identify itself as consciousness, it had to be conscious of something" (1015). In these strokes, not only God is swept away. Idealism (Berkleyian, transcendental, or metaphysical), Cartesian skepticism, and materialism (non-existence of mind) are also out of court. (See also, page 1027 and "For the New Intellectual" [1960].)
Readers here know that Rand articulated another axiom:
"To exist is to be something, as distinguished from the nothing of non-existence, it is to be an entity of a specific nature made of specific attributes. Centuries ago, the man who was---no matter what his errors---the greatest of your philosophers, has stated the formula defining the concept of existence and the rule of all knowledge: A is A. A thing is itself. You have never grasped the meaning of his statement. I am here to complete it: Existence is Identity, Consciousness is Identification." (1016) With this further statement of her axioms, Rand can go on to rule out radical indeterminacy of human nature and to portray the applicability of the law of non-contradiction to the real world known by ordinary experience and science (1016, 1037, 1040-41).
That is not all. With her full complement of axioms on the table, Rand puts them to the purpose of refuting the method of faith and revelation (1018, 1035-36), radical separation of human values from matter or mind (1029-30), supremacy of will or feeling over rational perception of reality (1036-37), skepticism concerning sensory perception (1036, 1040-41), skepticism concerning causality (1037), and skepticism concerning knowledge (1039-40).
On page 1040 Rand says that "an axiom is a statement that identifies the base of knowledge and of any further statement pertaining to knowledge, a statement necessarily contained in all others." She contends that anyone who denies the "axiom of identity" will be unable "to present his theory without using the concept of identity or any concept derived from it." Oh, I almost forgot another purpose to which Rand put her axiom of identity. She used it to bar the "negative way" of approaching God (1035). In Christianity that was an approach going back to Pseudo-Dionysius (c. 500).
Ten years later, Rand explicitly stated the general purposes of philosophical axioms. "Although they designate a fundamental metaphysical fact, axiomatic concepts are the product of an epistemological need---the need of a volitional, conceptual consciousness which is capable of error and doubt" (IOE 58). James Lennox reminds us that this was one of the purposes Rand gave for identifying philosophical axioms. I have compiled above several specific cases of Rand using her axioms for this purpose.
"Both Ayn Rand and Aristotle see axioms as grasps or explicit identifications of fundamental facts about being or, to use Rand's more typical wording, reality" (AV 13). Do Aristotle and Rand see philosophic axioms as serving the same purposes?
That is one of Joseph Rowland's main questions. I hope that thinkers reading here at RoR will contribute to this thread and supplement or correct that Jim and I are saying concerning Aristotle and Rand on axioms and to help find answers to the questions raised by Joe.
One of Aristotle's purposes in searching for axioms was to find out what is the most fundamental character of being (Metaphys. 982b11-28). I've always suspected that one purpose served by Rand's quests for fundamental elements in each area of philosophy was simply to satisfy her own curiosity. But unlike Aristotle and many other philosophers, I don't recall Rand ever acknowledging such a reason for doing deep philosophy. Could this difference concerning axioms contribute to Rand having arrived at axioms different from Aristotle's? I don't know, but see Fred Seddon's exchange with Roger Bissell here http://rebirthofreason.com/Forum/ArticleDiscussions/1339_11.shtml
I gather from Lennox's paper and more so from Tibor Machan's writings (those listed in my bibliography to this RoR article) that Aristotle used his axiom of non-contradiction to refute the Monism of the Eleatics, the Fluxism of Heraclitus, and the Paradoxes of the Megarians. I'm pretty sure Aristotle did not use his axioms to refute theism. Could someone help us out in this area?
It seems then that Aristotle, like Rand, used philosophic axioms as correctives for some big errors in philosophy. Lennox mentions a second purpose that Rand states for axioms. "It is axiomatic concepts that identify the precondition of knowledge: the distinction between existence and consciousness, between reality and awareness of reality, between the object and the subject of cognition. Axiomatic concepts are the foundation of objectivity" (IOE 57). The nature of consciousness and the distinction of subject and object seem to be not major concerns in ancient philosophy. Am I right in that impression? Could this be part of the reason Rand's axioms differ from Aristotle's?
Lennox draws attention to Rand's (1957) conviction that by welding identity to existence and identification to consciousness, she was completing the law of identity stated by "the greatest of your philosophers [Aristotle]." But I thought Aristotle's axioms were the principle of non-contradiction and excluded middle. Aristotle knew something of Rand's idea that to be is to be something specific, but did he know the traditional law of identity as it was received by Rand in her logic texts? When did the law of identity come into the texts? Leibniz said that the laws of identity and non-contradiction are the same law. Is that right?
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