I’ve been having a fantastic time in my philosophy of math course this term. It’s incredible how deep and how long these debates have been running. Cantor, Frege, Russell, Hilbert, Heyting, Gödel, Quine, and on and on!
I forget which book is the source of this, but I recall Smullyan writing about (I hope I have it roughly right) asking a child whether they could prove something they knew about mathematics or logic, and the child replied "What is a proof?"
Smullyan said that this was--if you took it literally--an incredibly deep question.
“What is a number? Do numbers exist?”
I’ve been having a fantastic time in my philosophy of math course this term. It’s incredible how deep and how long these debates have been running. Cantor, Frege, Russell, Hilbert, Heyting, Gödel, Quine, and on and on!