The concept of relevance and the logic diagram tradition

Logica Universalis 4 (1):67-135 (2010)
What is logical relevance? Anderson and Belnap say that the “modern classical tradition [,] stemming from Frege and Whitehead-Russell, gave no consideration whatsoever to the classical notion of relevance.” But just what is this classical notion? I argue that the relevance tradition is implicitly most deeply concerned with the containment of truth-grounds, less deeply with the containment of classes, and least of all with variable sharing in the Anderson–Belnap manner. Thus modern classical logicians such as Peirce, Frege, Russell, Wittgenstein, and Quine are implicit relevantists on the deepest level. In showing this, I reunite two fields of logic which, strangely from the traditional point of view, have become basically separated from each other: relevance logic and diagram logic. I argue that there are two main concepts of relevance, intensional and extensional. The first is that of the relevantists, who overlook the presence of the second in modern classical logic. The second is the concept of truth-ground containment as following from in Wittgenstein’s Tractatus. I show that this second concept belongs to the diagram tradition of showing that the premisses contain the conclusion by the fact that the conclusion is diagrammed in the very act of diagramming the premisses. I argue that the extensional concept is primary, with at least five usable modern classical filters or constraints and indefinitely many secondary intensional filters or constraints. For the extensional concept is the genus of deductive relevance, and the filters define species. Also following the Tractatus, deductive relevance, or full truth-ground containment, is the limit of inductive relevance, or partial truth-ground containment. Purely extensional inductive or partial relevance has its filters or species too. Thus extensional relevance is more properly a universal concept of relevance or summum genus with modern classical deductive logic, relevantist deductive logic, and inductive logic as its three main domains
Keywords Alan Ross Anderson  Nuel D. Balnap  Gottlop Frege  Bertrand Russell  Ludwig Wittgenstein  W. V. O. Quine  Aristotle  Charles Sanders Peirce  relevance/relevant logic  entailment  logic diagrams  modus ponens  disjunctive syllogism  truth tables  truth-grounds  Venn diagrams
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DOI 10.1007/s11787-010-0014-1
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Word and Object.W. V. Quine - 1960 - MIT Press.
Posthumous Writings.Gottlob Frege - 1991 - Wiley-Blackwell.

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