Abstract
This paper gives an account of Anderson and Belnap’s selection criteria for an adequate theory of entailment. The criteria are grouped into three categories: criteria pertaining to modality, those pertaining to relevance, and those related to expressive strength. The leitmotif of both this paper and its prequel is the relevant legitimacy of disjunctive syllogism. Relevant logics are commonly held to be paraconsistent logics. It is shown in this paper, however, that both E and R can be extended to explosive logics which satisfy all of Anderson and Belnap’s selection criteria, provided the truth-constant known as the Ackermann constant is available. One of the selection criteria related to expressive strength is having an “enthymematic” conditional for which a deduction theorem holds. I argue that this allows for a new interpretation of Anderson and Belnap’s take on logical consequence, namely as committing them to pluralism about logical consequence.
Highlights
Tradition has it that relevant logics are inherently paraconsistent; that is they don’t license the inference from the premise set {A, ∼A} to B for arbitrary A’s and B’s
This paper has provided a systematic account of the selection criteria Anderson and Belnap appealed to in giving what they argued to be a more adequate theory of entailment
These criteria were categorized into three groups: the modal properties, the relevance properties, and the properties pertaining to expressive strength
Summary
Tradition has it that relevant logics are inherently paraconsistent; that is they don’t license the inference from the premise set {A, ∼A} to B for arbitrary A’s and B’s. In the prequel to this paper, Non-Boolean Classical Relevant Logics I, I presented a. 173 of Neckam’s De Naturis Rerum, here requoted from Read The quote is from ch. 173 of Neckam’s De Naturis Rerum, here requoted from Read (1988, p. 31)
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