On Sat, Jul 27, 2019 at 2:42 PM Lawrence Crowell < [email protected]> wrote:
*> I think that mathematics in general is not as rich if you work > exclusively in finitude. Fraenkel-Zermelo set theory even has an axiom of > infinity. The main point is with axiomatic completeness, and mathematics > with infinity is more complete.* I wonder If "more complete" just means more opportunity to write stories in the language of mathematics that have no plot holes but are nevertheless fictional; just as a fantasy novel by JK Rowling is still fictional even if she maintains perfect internal consistency within her story that is written in the language of English. For example take Euclid's proof that there is no largest Prime Number, it's a beautiful mathematical story and it has no plot holes, but is the story true? Unless it turns out we were very very wrong about General Relativity and Quantum Mechanics I don't believe the universe has the computational resources to calculate the 10^(10^9)^(10^9) prime number, not even if the universe is infinite in extent because it is expanding and accelerating. So if the word has any meaning how can the 10^(10^9)^(10^9) prime number be said to "exist"? John K Clark -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/CAJPayv1DyckEeJmJqcnsoC-MBDgMSAXNWL5gM_Pt4xn8%2BD96hw%40mail.gmail.com.
