LANCOG University of Lisbon
Generalised Tarski’s Thesis Hits Substructure
20 April 2018, 16:00
Faculdade de Letras de Lisboa
Sala Mattos Romão (Departamento de Filosofia)
Abstract: At the core of JC Beall and Greg Restall’s brand of logical pluralism is “Generalised Tarski’s Thesis”, according to which a relation of logical consequence is characterised by the fact that, in every “case” where every premise is true, so is the conclusion (with different specifications of “case” yielding different relations of logical consequence). I argue that the thesis implies that many philosophically interesting substructural logics (non-reflexive, non-monotonic, non-transitive, non-contractive and non-commutative ones) are not relations of logical consequence. I then diagnose the clash as due to the fact that the thesis is not sensitive to plurality in designated value, in connection between premises and conclusion, in premise occurrences and in models. I then extend the argument to the effect that the more general conception of logical consequence as necessary truth preservation clashes with substructurality. I conclude by sketching a proposal as to how we can still uphold a broadly semantic conception of logical consequence. Basically, given a substructural logic L, we can reinterpret truth-preservation conditionals with the notions of conjunction and implication available in L, and say that the fact that, in L, P,Q,R…S logically entail T is grounded in the fact that, in L, the conditional ‘If ‘P’ is true and ‘Q’ is true and ‘R’ is true… and ‘S’ is true, then ‘T’ is true’ is valid. On this proposal, contrary to the contemporary vulgate, it is logical consequence that is grounded in logical truth rather than vice versa.