In addition to the paragraph in “For the New Intellectual” quoted above, Rand wrote the following in Atlas Shrugged:
The choice is still open to be a human being, but the price is to start from scratch, to stand naked in the face of reality and, reversing a costly historical error, to declare: ‘I am, therefore I’ll think’. (1058)
Proof presupposes existence, consciousness, and a complex chain of knowledge: the existence of something to know, of a consciousness able to know it, and of a knowledge that has learned to distinguish between such concepts as the proved and the unproved.
When [an interlocutor] declares that existence must be proved, he is asking you to prove it by means of nonexistence . . . .
When he declares that an axiom is a matter of arbitrary choice and he doesn’t choose to accept the axiom that he exists, he blanks out the fact that he has accepted it by uttering that sentence . . . .
[In addition to its other features,] an axiom is a proposition that defeats its opponents by the fact that they have to accept it and use it in the process of any attempt to deny it. . . . Let the witchdoctor who does not choose to accept the validity of sensory perception try to prove it without using the data he obtained by sensory perception . . . . (1039–40)
Tibor Machan observes in “Evidence of Necessary Existence” (1992):
Whereas Descartes claimed to discover the cogito as his starting point simply by examining his ideas until he found one that is rationally undeniable, Rand holds that we somehow learn her axioms from experience. It is only after we draw the axioms from experience that we show that they are rationally undeniable. (35)
David Kelley writes in The Evidence of the Senses (1986):
Consider, for example, the first Meditation. Descartes begins by seeking any grounds for doubting the truth of his ideas—i.e., for doubting that they stem from and correspond to reality. The first such grounds he finds—sensory illusions and dreams—are actual occurrences, and in these cases we know that reality is not what it seems. For that reason, however, these occurrences could not raise the general question whether reality exists beyond our ideas; to identify an experience as an illusion, one must have enough knowledge of the objective facts to know that he is misperceiving them. Descartes therefore rests his case for universal doubt on the hypothesis that an evil demon may be deceiving him about everything. But what sort of ground for doubt is this? Illusions and dreams actually occur, but demons do not—the hypothesis is pure invention. As such, it would be completely subjective and could not provide an objective reason for doubting anything. Then why does Descartes suggest the hypothesis? It can only be as a way of concretizing a possibility he has already accepted: that everything we are aware of exists merely as the representational content of our ideas, ideas that do not, because they are modes of consciousness, depend on anything outside consciousness and could therefore be put into our minds by an evil demon even if there were nothing outside consciousness. In accepting this possibility, Descartes is clearly presupposing the theory of ideas presented later in the Meditations. (15)