[FOM] paraconsistent logic and computer science

Vladimir Sazonov Vladimir.Sazonov at liverpool.ac.uk
Sat Oct 13 20:12:34 EDT 2007

On 12 Oct 2007 at 11:09, Arnon Avron wrote:
>  On Fri, Sep 28, 2007 at 11:34:32AM +0200, Joseph Vidal-Rosset wrote:

> >  In what precise situations have we to allow $ p, \neg p \vdash q $ ?
> >  It is very difficult for me to understand what is a "true
> >  contradiction" and to admit "Dialetheism". I still believe that
> >  rejecting contradiction as false is a sane methodological position in
> >  science and in philosophy in general.

In http://cs.nyu.edu/pipermail/fom/2006-February/009746.html
it is presented a simple formalization of the vague "set" F of feasible 
numbers (a different from earlier formalization by R. Parikh and 
imposing a much more precise upper bound on F - the details in
the link above). But A & not A is derivable in this theory, however
it is in a sense formally (feasibly) consistent - not everything is
provable in spite of A & not A. (The underlying classical logic in
the form of natural deduction is restricted here essentially by
forbidding abbreviations of terms and allowing only intuitively
feasible proofs.) After some reflection on the meaning of the
sentence A, A & not A can be interpreted as "continuum is both
discrete and continuous" what looks intuitively plausible, say,
for pictures in computer display. Also think on the atomic structure
of the matter.

Is this formalization sane or not? It is what is possible to do
rigorously (formally/axiomatically) concerning the idea of
feasibility here. The alternative is to find a better formalization
avoiding (or explaining better) such kind of strange effects, or,
of course, to give up any attempts in favour of the "sanity".

By the way, I daubt that the above is related in any way
with the known approaches to paraconsistent logic.

Vladimir Sazonov

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