Odd that this sentence:<p>> Whereof one cannot speak, thereof one must be silent.<p>did not get a citation. Perhaps its so well known among its target audience that none was considered necessary. Since HN appeals to a broader audience, I'll supply the missing citation: It's from Wittgenstein's Tractatus - the very last line in fact. The usage is apt - as far as I can tell, Wittgenstein was making the same point about the difficult - even impossibility - of making meaningful statements outside of a formal language.<p><a href="https://en.wikipedia.org/wiki/Tractatus_Logico-Philosophicus#Proposition_7" rel="nofollow">https://en.wikipedia.org/wiki/Tractatus_Logico-Philosophicus...</a>
This is great!<p>I'd love to read a similar explanation about surreal numbers. Are surreal numbers in N or not? How do we know? (In my limited understanding, they're not easily excluded.)
In Gödel's collected works vol. 2 one has the detailed argument by transfinite induction up to the first inaccesible ordinal. Interesting to have this as guidemap.