Classical logical coherentism
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...
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| Format: | article |
| Publication Date: | 2026 |
| Country: | España |
| Institution: | Universidad del País Vasco |
| Repository: | Addi. Archivo Digital para la Docencia y la Investigación |
| OAI Identifier: | oai:dnet:addi________::1f8d2e7f9fcdea0e00fdbec961c678cc |
| Online Access: | http://hdl.handle.net/10810/79615 |
| Access Level: | Open access |
| Keyword: | coherentism maximally consistent sets logical consistency classical logic semantic resemblance philosophy of logic Boolean algebras |
| Summary: | 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. |
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