>>12029702I think Wildbergers argument goes somehting like this:
Preliminary: Consider the polynomial expression . This can't be factorized over the reals (the factorization being ). We say, emphasis on the next sentence,
"this expression can't be factorized"
or
"this expression has no factorization"
Now consider N to be the number of particles in the observable universe or whatever. The number
is a product of a lot of seven.
Now the expression
"can't be factorized"
or one might go as far as saying it has no factorization. The arithmetic becomes meaningless.
This is similar (but a bit different, since Wildberger involves "the universe") to how some strong set theory axioms "practically meaningless":
The axiom of choice implies the well-ordering theorem that says any set can be well-ordered.
I.e. in ZFC you can "prove there exists" are well-ordering w of R. But you can also prove metalogically that no well-ordering of R could ever be syntactically stated. The axioms of set theory prove a non-constructive claim , the potential construction of which is provably impossible.
PS: I don't think Wildberger's take is very helpful.
