Godel’s theorem

Kurt Godel’s incompleteness theorem – the claim that every formal system of mathematics contains an undecidable formula and that a system’s consistency cannot be proven within the system – has been hailed as the mathematical equivalent of relativity and quantum mechanics, evidence, in the words of William Barrett, that “Mathematicians now know they can never reach rock bottom; in fact, there is no rock bottom, since mathematics has no self-subsistent reality independent of the human activity that mathematicians carry on.” Not so, claims philosopher and novelist Rebecca Goldstein in Incompleteness , her recent book on Godel. On the contrary, Godel not only believed in a reality “out yonder” (to use Einstein’s words) but believed that this objective reality include abstract entities like numbers. He was a thorough mathematical Platonist, and in fact his Platonic convictions led him to the theorem in the first place. Goldstein’s lucid book captures the drama and significance of what Godel always considered his “discovery” (not invention), and describes treats the logical, mathematical, and philosophical issues with remarkable lucidity.