Bergen Logic Seminar: Confused Entailment
Keywords: • deduction theorem • entailment • modus ponens • relevant logic • substructural logic • naïve set theory
Priest argued in his Fusion and Confusion for a new concept of logical consequence over the relevant logic B, one where premises my be “confused” together. Priest claims that his approach represents a “return to the roots of relevant logic”. This paper puts that claim to the test. It is shown that Priest’s notion of logical consequence is in fact strictly stronger than that obtained for B using Anderson and Belnap’s conjunctive understanding of entailment, but also strictly weaker than the standard Hilbertian notion of logical consequence for B. It is shown that Priest’s notion of confused entailment is, although very weak, too much alike the Hilbertian consequence relation to truly be a relevant consequence relation. A suggestion is made for how to mend Priest’s notion which both makes it into a relevant one, but which also, unlike Priest’s, may be sufficiently weak so as not to trivialize naïve set theory.