If there any viable system in which you -can-
both derive, and find useful application for,
the equation 0=1 ?

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James Rose
Bruno Marchal wrote:
>
> At 13:40 26/11/04 -0500, Hal Ruhl wrote:
> >What does "logically possible" mean?
>
> A proposition P is logically possible, relatively to
> 1) a consistent set of beliefs A
> 2) the choice of a deduction system D (and then consistent
> means "does not derive 0=1).
>
> if the negation of P is not deductible (in D) from A.
>
> Concerning many theories, to say that a proposition
> (or a set of propositions) A is logically possible
> is the same as saying that A is consistent (i.e you
> cannot derive 0 = 1 from it), or saying that A has a
> model (a reality, a mathematical structure) satisfying
> it.
>
> Bruno
>
> http://iridia.ulb.ac.be/~marchal/