Aula Magna 4

R-Mingle is Good Enough as a Paraconsistent Logic

Jon Michael Dunn
Indiana University


There is the famous saying: Do not let the perfect become the enemy of the good. I might say: “good enough.” In this spirit, I will examine the Dunn-McCall system R-mingle, exploring how it is (in the terminology of Arnon Avron) only a “semi-relevant logic” but still a paraconsistent logic. At issue is the theorem:

(p ∧ ¬p) → (q ∨ ¬q)

I shall discuss the merits of this system and its history, and compare it to Anderson and Belnap’s system R of relevant implication and to some other paraconsistent logics by Newton da Costa, Graham Priest, and others. I shall be evaluating these logics as “tools,” in the light of my recent work on “Humans as Rational Toolmaking Animals.”