FOM: Re: twin primes again

V. Sazonov V.Sazonov at
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.

Vladimir Sazonov

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