A recent proposal by Dr. W. H. McCrae, cosmologist and mathematician, to the effect that decisions between such cosmogonies as those of Hoyle and of Gamow are experimentally impossible by virtue of a general cosmological indeterminacy principle, is here examined and elaborated upon. Some comments on the “antinomies” in Kant's “Critique of Pure Reason” are made in reference to this principle as well as to the Heisenberg indeterminacy principle. If McCrae's principle is accepted, we will have moved a long way toward Kant's conclusion that a logically consistent understanding of an underlying “ultimate reality” is outside the confines of science—whatever one may think of Kant's own line of reasoning.