21:06
@user21820 Admittedly yes, Godel's β is practically a miracle. That said, if we merely include exponentiation, I think the situation is much more obvious. There's scarcely a literate person on Earth who's unfamiliar with how finite strings encode numbers and vice versa; base 10. Peano excluded exponentiation as a primitive, but I think most people consider exponentiation as a fundamental part of arithmetic.
Using the language of arithmetic with exponentiation, the way we interpret finite strings and concatenation is pretty trivial. The reverse interpretation is a lot more complicated, at least in my opinion. Purely subjective though.
@user21820 Now they're saying that "there aren't" objects, and they "can only say what reality isn't, not what it is". I'm just thinking, you know, they're literally just describing an empty domain of discourse. It has a trivial theory, every existential is false and every universal is true. There's just nothing interesting going on there. Besides being trivial, it's an extremely unbelievable/untenable position to say nothing exists.
I'll just never understand why people do this. They have some crackpot theory, they realize it leads to a literal contradiction, and instead of saying "I guess my theory was wrong", they say "well I guess basic logic as we know it is totally incorrect and we have to reinvent everything from the ground up"
As if there was a fault in something so basic which nobody had ever noticed... instead of, you know, the thing they just made up
I suggested to them that there were other alternatives, like nonclassical logics which are better suited to the nuances of certain languages, or maybe they're just using alternative semantics about what "identity" means... but they insisted they were using ordinary semantics.
