[FOM] re elevant logic and paraconsitent logic
Mark Lance
lancem at georgetown.edu
Wed Mar 1 11:48:51 EST 2006
Joseph Vidal-Rosset wrote:
"Reading this paper from Priest and Tanaka :
http://plato.stanford.edu/entries/logic-paraconsistent/
(1) I feel uneasy with logical systems accepting "true contradictions"
(paraconsistent logics), but
(2) I willingly accept the idea of a system like IR where neither
(p & ~p)-> q nor (p & ~p) -> ~q are not valid deductions and where
paradoxes of material and strict implication are avoided."
There is no mathematical reason you have to accept paraconsistency
just because you accept relevance. Nor do you have to give up bi-
valence. There are many relevant systems, of various strengths which
accept bivalence, and imply no contradictions. Greg Restall -- at
Melbourne University -- has some papers on the issues, arguing
against the Priest position. (I think they are online.) The only
real connection is that if you accept true contradictions, you had
better use a relevance logic since you don't want to be committed to
everything. But there is no connection the other way. Priest, et
al, argue for paraconsistency, but the arguements are independent.
RL just makes it somewhat less obviously hopeless to do so. (to
betray my own views on the matter.) I've discussed interpretations
of relevant entailment that don't give any aid and comfort to
paraconsistency in several papers which can be found at my website --
homepage.mac.com/abuemma
Mark Lance
Georgetown University
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