[FOM] Platonism and Formalism (answer to Steve Newberry)
Vladimir Sazonov
V.Sazonov at csc.liv.ac.uk
Mon Sep 22 14:52:11 EDT 2003
Steve Newberry wrote:
>
> See my June 1, 2003 post Non-Arithmetical "Godel" Incompleteness.
>
> If you can show that both F,~F have finite realizations, then F is
> contingent, and unprovable in any consistent classical logic. The
> only other possibility for contingency is when F is n-valid and ~F
> is w-satisfiable. That case is the generalization of the G"odel sentence,
> and is recursively undecidable, but can sometime be resolved using
> a model-theoretic demonstration.
>
> Cordially,
>
> Steve
Sorry, I do not see how these considerations are related with
the discussion on Platonism and Formalism and even do not
understand them well. Hence, I do not know how to react.
To say anything, the fact that two sentences F and ~F may (each)
have a model (either finite or not), of course, implies that both
are unprovable in the classical logic. But I do not know what do you
mean by ANY consistent classical logic. We have essentially only
one classical first order logic (up to some reformulations).
Also, any logic - classical or not - is usually consistent.
I also do not understand "The only other possibility for
contingency..." because I do not know what do you mean
*precisely* by contingency. The informal meaning of this
English word is not enough for me to make any categorical
or even informal conclusions like those you do.
Vladimir Sazonov
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