🚀 go-pugleaf

In article <1992Nov19.195642.15296@ucthpx.uct.ac.za> gavan@elc.mth.uct.ac.za (Gavan Tredoux) writes:
>mclean@itd.nrl.navy.mil (John McLean) writes:
>: From cmitchell@falcon.aamrl.wpafb.af.mil ()
>: >My question is: WHY is the implication relation defined as it is?
>
>[some reasons]
>
>There are logics that don't allow this paradox of
>material implication - relevance logics, where the antecedent
>and consequent have to be relevant to each other for the
>implication to hold. Of course there are a million and one
>ways of doing this.
>
>Primary strength of classical logic: there's only one.

This is true for intuitionistic logic as well, which has only one
implication up to logical equivalence.  A->B is the weakest
interpretation of this implication for which modus ponens remains
sound, that is, the weakest C such that A&C |- B.  Assuming only the
cut rule and A|-A, this uniquely determines A->B up to logical
equivalence, where logical equivalence of A and B means A|-B and B|-A.
This definition may seem less paradoxical than the classical definition
of A->B as "~A or B".
-- 
Vaughan Pratt	  		A fallacy is worth a thousand steps.