Re: If I were King... (fwd)

[Art Protin <protin@USL.COM>]

Folks,
    Iain Alexander seems to have said it better than I did:

> I'm not convinced there's a genuine problem here.
>
>> There is a problem with that. The simple logic of 'kanoi' is too
>> powerful. Any statement of the form "If <false statement> then <true
>> statement>." is true.
>>   If I were King, then pigs would fly.
>> is true because I'm not King. Swinish aviation is irrelevant.
>
> This is only half the story.  The speaker is not king at the present
> time, in the real ({ca'a}) world, but in the hypothetical world which
> we want to talk about, he is, and the truth of the statement once more
> relies on swinish aviation as you would expect.
>
> Straightforward predicate calculus and propositional calculus concerns
> itself with a simple world (model) where statements are either true or
> false.  It doesn't deal with complications like tense or hypothetical
> worlds, which are a vital part of language.  The truth of propositions
> varies with time, and we consider alternative realities with very little
> ceremony.  (I believe there are extensions to predicate calculus which
> (attempt to) deal with these issues, although I'm not familiar with them.)

I did have the please to be in the audience at an annual conference of
the American Association for Artificial Intellegence when one of the
great masters, I think it might have Gerald Sussman, did a presentation
on the applicability of a whole class of extensions to formal logic
and predicate calculus to real world problems.  The extensions had to
do with including time into the equations and trying to reasoning about
sequences of events.  The conclusion that was presented rather pointedly
was that there could not be any simple mechanism that would do the job
in general.  Any attempt to use equations of logic requires volumes of
equations that embody common sense rules about assumptions to make.
The assumptions are required to deal with the abstraction of the real
world into formula and what looks like a simple solution breaks down
because "equality commutes" but time does not.
    A conclusion that I drew from that talk was that the logic needed
by humans in order to function in the real world is probably noticibly
different from the mathematical logic built (if I remember correctly)
by, among others, Leibniz, Boole, & Church.  The dream of Leibniz is
probably unachievable.

    thank you all,
    Arthur Protin


Arthur Protin <protin@usl.com>
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