FOM: Re: twin primes again
V.Sazonov at doc.mmu.ac.uk
Sun Jun 25 10:54:24 EDT 2000
Joe Shipman wrote:
> The reason I used the twin prime conjecture rather than Goldbach's
> conjecture (Fermat's conjecture has been proven) is that the
> independence of the TPC from ZF would say nothing about whether it is
> true, while Goldbach's conjecture, if independent, must be true, because
> a counterexample could be finitely verified.
This well known trick seems to me rather doubtful because it is
based on an assumption (which is even impossible to formulate
rigorously) that each natural number (an illusory/imaginary
semantical object) can be denoted by a numeral (a concrete
syntactical object). I think that logicians (if not all
mathematicians) should be very sensitive and critical to any
such mixing of syntax and semantics.
I am afraid that so called "realists" in f.o.m. who declare
mathematical illusions as real things (in contrast to realists
in f.o.m. in the normal and natural sense of this word or term)
will hardly understand me.
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