Beyond Zero and One (Andrew Smart) / quote 82 of 171
Penrose the mathematical Platonist
For all intents and purposes, Penrose is a Platonist when it comes to mathematical truth. This might seem at odds with his view that Gödel’s theorem shows that the mind in noncomputable. Penrose accepts the implications of Gödel’s theorem, which implies that human mathematical intuition is outside of the axioms; however, he believes that mathematics still forms the perfect laws from which the Universe derives its existence. Plato believed in an abstract world of ideal forms that was distinct from the physical world. For example, any actual sphere in the physical world is only an approximation of the perfect ideal sphere in Plato’s world. In one of Penrose’s other incredible books, The Road to Reality,45 he lays out his metaphysics of math in typical clarity and enthusiasm: Yet the Platonic viewpoint is indeed an immensely valuable one. It tells us to be careful to distinguish