Classical Logical Coherentism

Abstract Our usual explication of a logic through an axiomatic calculus is structurally foundationalist . Justification gets transferred by applying rules finitely many times from already justified sentences to new sentences in a linear-like fashion, by starting from a base of non-to-be justified sentences (i.e. the axioms). In contrast, this paper develops a coherentist approach to classical propositional logic , by explaining the fundamental notion of deducibility in terms of a primitive notion of logical coherence . This is done by introducing a calculus consisting of rules that capture the properties of classical consistency. The basic logical reasoning process explicated is that of constructing consistent sets of formulas. I show how to define classical deducibility in terms of the primitive relation of logical coherence. As applications, I use the coherence calculus to provide a non-semantic proof of the consistency of an axiomatic calculus for classical propositional logic, I show how the system avoids an impossibility result for semantic resemblance proven by Leitgeb, I show that the strategy of defining deducibility from coherence does not work for intuitionistic logic and I briefly compare my approach to the Simple Theory of Propositions put forward by Stalnaker and Fritz.