On Tue, Dec 09, 2003 at 02:25:07PM -0500, Stavros Macrakis wrote:
>
> HOWEVER, no matter how well Maxima does, it will never be able to detect
> all contradictions. So what do you do? Do you only allow assertions
> that Maxima can prove not to be contradictory? That would be far too
> restrictive (though it is of course desirable that it report on
> contradictory assertions *when* it detects them). For that matter, it
> is *useful* to allow contradictory assertions when pursuing a reductio
> ad absurdum argument. So it is not only *unavoidable* that Maxima will
> allow contradictory assertions, but actually *desirable* that it do so.
>
I am persuaded by this arguments. But until now I expected that a CAS is a
part of conventional mathematics (from textbooks, not Wulfram's Matematica).
Now I see that it is rather an instrument for doing mathematics, and not
the mathematics itself. Maxima, as I conclude based on my limited experience,
can be very powerful instrument, but it must be used with precaution.
Actually, it is normal if a programmer cares about everything (as in C/C++).
It would be nice if in the tutorial it would be clearly stated that certain
contradictory statements can coexist in the knowledge database, and give
examples of this. This would prevent confusions like mine.
Best regards and thanks to developers,
--
Alexander