[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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