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Ayn Rand Society 2005 - Paper 1
James Lennox’s paper was on “Axioms and Their Validation” (AV).
Allan Gotthelf’s was on “Concepts and Essences” (CE).
Fred Miller’s was on “Values and Happiness” (VH).
Robert Mayhew’s was on “Literary Esthetics” (LE).
In the present communication, I would like to tell you a little about the first paper and to point to earlier, published works in which a comparison between Aristotle and Rand has been made concerning the nature of philosophical axioms and how they are validated. I hope to write messages soon concerning each of the other three papers composed for the 2005 meeting of the Society.
Professor Lennox first presented Rand’s views on axiomatic concepts, then Aristotle’s view on axioms and their validation. He then briefly compared their views in this area.
Lennox stressed that Rand draws her philosophic axioms so as to be highly abstract, yet to be based on concretes given in perception. As is well-known to readers here, Rand’s axiomatic concepts are existence, identity, and consciousness. It was incumbent on Rand to explain “how these concepts, the most abstract of all concepts, are related to the perceptually given” (AV 4). Rand’s answer: The axiomatic status of these concepts derives from the character of their referents. The facts identified by these concepts are directly perceived, and they are fundamental givens implicit in any knowledge or proof procedure. As readers here know, the truth of these identifying concepts cannot be proven, but their axiomatic status can be shown by showing that they are presupposed in any attempt to deny them.
On Rand’s view, these axioms are implicit in every state of awareness of any sentient animal. For humans the axiomatic facts of existence, identity, and consciousness are “perceived or experienced directly, but grasped conceptually.” Explicit conceptual identification of these axiomatic facts provides an ever-present widest conceptual context for all one’s conceptual constructions concerning reality.
Aristotle’s indemonstrable starting points for knowledge are the principle of non-contradiction and the principle of excluded middle. These principles are presuppositions of all demonstration. Aristotle says “we come to know the primaries [of a special discipline such as geometry] by induction; for that is in fact how perception produces the universal in us.” He seems to think the same faculty of reason enables us to know both the starting points of a special discipline and the fundamental principles of demonstration, which are non-contradiction and excluded middle. [Note from SB: For more on this, see Leonard Peikoff’s (1985) “Aristotle’s Intuitive Induction” in The New Scholasticism 59(2):185-99.]
For Aristotle these two principles identify fundamental facts of reality. Because these are the most fundamental facts about reality, cognizance of them is required to comprehend anything of the more special characters of things. Aristotle knows one cannot prove the truth of non-contradiction or excluded middle, but because these truths hold in every area of knowledge, one can always show their merit by showing the dissolution of thought that follows on their denial.
Both Rand and Aristotle see philosophical axioms as explicit identifications of fundamental facts of reality. Lennox goes on to observe that, also for both these philosophers, “anyone who knows anything and anyone seeking to prove anything has grasped, at some tacit level, these fundamental facts. Both insist that any attempt to deny such fundamental truths is self-refuting” (AV 13).
An obvious difference between Aristotle and Rand on philosophic axioms is in their selection of which facts are the axiomatic ones. Rand does not select non-contradiction and excluded middle as the most basic facts of reality. Beneath both of these, Rand sees the fact of identity: to be is to be something specific. That difference between Aristotle and Rand is a harmonious one. Lastly, Lennox sees Rand’s axiom of consciousness—that anyone who makes claims implicitly affirms their own consciousness of existence—as propounded also by Aristotle.
Earlier works on Rand and Aristotle concerning philosophic axioms and their validation are these:
Douglas Rasmussen (1973). “Aristotle and the Defense of the Law of Contradiction”
The Personalist (Spring).
Douglas Den Uyl and Douglas Rasmussen (1984). “Ayn Rand’s Realism” in
The Philosophic Thought of Ayn Rand.
Leonard Peikoff (1991). Chapter 1 of Objectivism: The Philosophy of Ayn Rand.
Tibor Machan (1992). “Evidence of Necessary Existence” Objectivity 1(4):31–62.
———. (1999). Chapter 2 of Ayn Rand.
Fred Seddon (2005). “Implied Axioms” in
Rebirth of Reason http://rebirthofreason.com/Articles/Seddon/Implied_Axioms.shtml
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