Our philosophy … reduceth to a single origin and relateth to a single end , and maketh contraries to coincide so that there is one **primal** foundation both of origin and of end. From this coincidence of contraries, we deduce that ultimately it is divinely true that contraries are within contraries; wherefore it is not difficult to compass the knowledge that each thing is within every other.

— As translated by Dorothea Waley Singer (1950)

We debase the richness of both nature and our own minds if we view the great pageant of our intellectual history as a compendium of new information leading from **primal** superstition to final exactitude. We know that the sun is hub of our little corner of the universe, and that ties of genealogy connect all living things on our planet, because these theories assemble and explain so much otherwise disparate and unrelated information not because Galileo trained his telescope on the moons of Jupiter or because Darwin took a ride on a Galápagos tortoise.

— "A Foot Soldier for Evolution", p. 441

"Mathematics is a presuppositionless science. To found it I do not need God, as does Kronecker, or the assumption of a special faculty of our understanding attuned to the principle of mathematical induction, as does Poincaré, or the **primal** intuition of Brouwer, or, finally, as do Russell and Whitehead, axioms of infinity, reducibility, or completeness, which in fact are actual, contentual assumptions that cannot be compensated for by consistency proofs.

— Quoted in Hilbert's