The Theory of Relevance, Formal Fallacies of Relevance, and Relevant Logic

Nicholas Ferenz (Czech Academy of Science)

19 April 2024, 16:00 (Lisbon Time – WET)

Faculdade de Letras de Lisboa

Sala Mattos Romão [C201.J] (Departamento de Filosofia)

Abstract: Relevant logics are logics with a conditional connective that represents, in the object language, various sorts of entailment relations. These entailment or implications each necessitate restrictions on grounds of relevance. In Entailment vol. 1, Anderson and Belnap note certain (formal) fallacies of relevance that should not be theorems of any (propositional) relevant logic. The area of first-order relevant logics is comparatively underdeveloped both philosophically and mathematically. In this talk I develop an account of formal fallacies of relevance, drawing on the Sperber and Wilson’s Theory of Relevance in linguistics. In short, formulas that are formal fallacies of relevance require too much cognitive effort to establish relevance over every context with every instance of the formula. This account of formal fallacies of relevance have the advantages of (i) implying a core semantic property of relevance in propositional logics (namely the Variable Sharing Property), and (ii) divorcing the definition of relevance from that of (the) truth (values). I then turn to first-order logics, where I apply the framework to a selection of formulas and outline future goals.