Exercising undue caution against over-application of the Law of Contradiction, Leonard Peikoff, in Objectivism: the Philosophy of Ayn Rand, managed to mangle the application of the concepts of "axiom" and "corollary" to not just one, but two issues: volition and validity of the senses.

In his discussion of causality (p. 15), Peikoff defines "corollary" as: "a self-evident implication of already established knowledge," and he clearly states that: "A corollary of an axiom is not itself an axiom." Makes sense, and couldn't be clearer, right?

However, in discussing volition, Peikoff first says: "The principle of volition is a philosophic axiom, with all the features this involves" (p. 70). Then, one page later, he blatantly contradicts himself: "Volition, accordingly, is not an independent philosophic principle, but a corollary of the axiom of consciousness."

Similarly, in discussing validity of the senses, Peikoff first says: "The validity of the senses is an axiom" (p. 39). Then, two paragraphs later, on the same page (!), he writes: "The validity of the senses is not an independent axiom; it is a corollary of the fact of consciousness." (Another booboo here is referring to validity of the senses as a corollary of a fact. Corollaries are implications not of facts, but of recognitions of facts, i.e., propositions, whether axiomatic or less general.)

Now, Rand was Peikoff's role model in many things, and it is possible that he took to heart her mangling of the discussion of architecture in "Art and Cognition" (The Romantic Manifesto, chapter 4)--thinking that if her example of applied logic was acceptable, then calling things "axioms" and "not-axioms" within mere paragraphs was acceptable, too. But in epistemology, as in ethics, two wrongs don't make a right.

REB