FOM: consistency equals existence

Vladimir Sazonov sazonov at
Thu Feb 24 10:50:29 EST 2000

Dear Professor Robert Black,

You wrote:

> I am grateful to Vladimir Sazonov for his comments on my post of 18
> February. However, I must point out that I was there exploring the
> implications of positions which I would not necessarily want to adopt. In
> fact I am tempted by a realism/platonism so extreme that it would make
> Professor Sazonov's hair stand on end.

After your words :

"What I can't see is how the completeness theorem plays a role [in the
principle consistency equals existence - VS.] if we're not set-theoretic

you can say anything which looks like a Platonism. I understand that
you are usually working in (or construct) a formal system with
corresponding specific intuition which may have any flavor, say,
Platonistic. (A universe which contain "all" possible sets or anything
analogous.) This is a harmless (local) Platonism of any working
mathematician who has full rights to use ANY kind of intuition.
In my understanding, you are not Platonist. Real Platonist does not
see such distinctions as above.

Vladimir Sazonov

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