Re: Equality and subclass axioms

At 01:34 PM 11/26/00 -0600, pat hayes wrote:
>Oh yes it does. It arises if we allow disjunctions (which are logically 
>equivalent to implications, as Im sure you know) and negations; it arises, 
>in fact, whenever it is possible to express any kind of contradiction. The 
>only way to avoid it is to make it impossible for anyone to ever disagree 
>with anyone else, by for example only allowing positive logic (no 
>negations.) The problem with logics this weak is that it is very difficult 
>to draw useful conclusions in them.

I've been cogitating a little about a related issue.  Would you accept a 
rewording of the final sentence above:

   The problem with logics this weak is that they are very limited in the
   range of useful conclusions that can be drawn.

?

I think there are _some_ useful conclusions to be drawn from logics without 
negation, etc.

#g

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Graham Klyne                       Content Technologies Ltd.
Strategic Research              <http://www.mimesweeper.com>
<Graham.Klyne@mimesweeper.com>
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