John Mikes wrote:
> Isn't logical inconsistency = insanity? (Depends how we formulate the
> state of being "sane".)
As Bertrand Russell pointed out, if you are perfectly consistent you are either
100% right or 100% wrong. Human fallibility being what it is, don't bet on
being 100% right. :-)
In classical logic, an inconsistency allows you to prove every propositon. In
para-consistent logic the rules of inference are changed (e.g. by restoring the
excluded middle) so that an inconsistency doesn't allow you to prove everything.
Graham Priest has written a couple of interesting books arguing that all logic
beyond the narrow mathematical domain leads to inconsistencies and so we need
have ways to deal with them.
> Simplicity in my vocabulary of the 'totality-view' means mainly to "cut"
> our model of observation narrower and narrower to eliminate more and
> more from the "rest of the world" (which only would complicate things)
> from our chosen topic of the actual interest in our observational field
> (our topical model).
> Occam's razor is a classic in such simplification.
And so is mathematical logic and arithmetic. But if one can reconstruct "the
rest of the world" from these simpler domains, so much the better that they are
> John M
> On 8/18/08, *Bruno Marchal* <[EMAIL PROTECTED]
> <mailto:[EMAIL PROTECTED]>> wrote:
> On 18 Aug 2008, at 03:45, Brent Meeker wrote:
> > Sorry. I quite agree with you. I regard logic and mathematics
> as our
> > inventions - not restrictions on the world, but restrictions we
> > place on how we
> > think and talk about the world. We can change them as in para-
> > consistent logics.
> I think it depends of the domain of inquiry or application.
> Para-consistent logic can be interesting for the laws and in natural
> language mind processing, but hardly in elementary computer science or
> number theory.
> Then recall that any universal machine, enough good in the art of
> remaining correct during introspection, discovers eventually at least
> 8 non classical logics (the arithmetical hypostases) most of them
> being near "paraconsistency" (by Godel's consistency of inconsistency)
> making the most sane machine always very near insanity.
> And so easily falling down.
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