Infinite Cogitation

I finished David Foster Wallace’s book Everything and More: A Complete History of Infinite a few days ago. Something that might be interesting to the artists reading this blog is a kind of similarity between artistic and mathematical/philosophical perspectives- in fact, they even share some of the same terminologies. For instance, the “Formailist-v.-Intuitionist controversies of the early 1900s… we’re again back to metaphysics: the modern wrangle over math’s procedures is ultimately a dispute over the ontological status of math entities… Formalism seeks to make the abstractness of math both total and primary,” as in a theoretical proof, as opposed to Intuitionism, which promotes practical applications of not just numbers, but specifically integers (some Intuitionists apparently denied the existence of other numbers!) The most interesting thing about DFW’s book is that it culminates with Georg Cantor’s “proof” that there exist not only an infinity, but also infinities that are even greater in the most incomprehensible, abstract sense of innumerability. This yields some interesting paradoxes that seem to me to indicate that there is either a problem with math’s wording in its proof systems, or, maybe more simply, that there is a limit to how much we can understand or rationalize in the universe-which seems pretty obvious, actually.