Deducibility, Entailment and Analytic Containment

Abstract

The concept of entailment is often connected with deducibility: A is said to entail B iff B is logically deducible from A.¹ It has also been connected to the concept of containment in Kant’s sense of analytic containment: A entails B only if the meaning of B is contained in the meaning of A. But the concepts of deducibility and containment are two distinct concepts, and the failure to distinguish them leads to faulty attempts to merge them in formal systems. One such attempt is Anderson and Belnap’s system, E, in which a Fitch-type theory of natural deduction is modified to incorporate a certain sense of “containment”². Another is Parry’s system, AI, of “analytic implication” which began with a more restricted sense of containment but has usually been presented as a theory of deducibility (cf. Parry 33 and 72).