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.

Yes, I would accept that rewording. You are right, there are some.

Pat Hayes

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Received on Wednesday, 29 November 2000 17:22:25 UTC