We choose this starting point because it is implicitly conceded even by those who would seek to deny it. To deny that reality exists is to assert, in effect, that "in reality reality does not exist"—that is, it is implicitly to acknowledge that there is a reality. People may claim that reality is an illusion; but the very notion of "illusion" requires a previously assumed reality with which that illusion is contrasted.

This kind of ultimate undeniability is characteristic of axioms, which we may distinguish here from postulates (although some use the two terms interchangeably). The term "postulate" is familiar to many from high-school geometry, where the postulates of Euclid give rise, through chains of deductive syllogisms, to more and more advanced theorems. Later mathematicians, however, recognized that Euclid's postulates (particularly his "fifth postulate") were not immutable, that they could be modified to generate other geometries, of equal mathematical validity and useful in other contexts ().