> > > 2) Do you agree that choosing a number from a set with more than 1 > > element means writing or speaking or at least thinking the name of the > > number? > > No. The use of logic and axioms is justifiable as > representations that formalize mathematical practice.
The practice must not become unpracticable by logic.
> They are normative ideals against which mathematical > practice is measured.
Logic and formalization *describe* practice, they cannot change it.
> Your question applies to the faithfulness of those > representations. What is "nameable in principle" may > not be materially nameable.
Here is the question whether something can be chosen, not whether it can be "in priciple" chosen. > > > 5) Zermelo's AC requires that uncountably many names can be written, > > said or thought. > > No. Zermelo's AC requires that one name can be written > with certainty. > > "the cartesian product of non-empty sets is non-empty"
You could with same ease write: Fermat's last theorem can be violated with certainty. What would be the difference? > > > 6) In this respect it resembles the statement that a second prime > > number triple beyond (3, 5, 7) can be found, perhaps even infinitely > > many. > > My unfamiliarity with number theory,
Of six successive naturals, at least two are divisble by 3, one of them necessarily being an odd one. Therefore there cannot be another prime triple. But since you refrain from arguing and adhere to provably false claims, if given the form of axioms, you could also accept this one.