[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 :

(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 --  

Mark Lance
Georgetown University

More information about the FOM mailing list