The Proof-Theoretic Structure of Counterfactual Inference

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Counterfactual conditionals (i.e., constructions of the form 'if A were the case, then B would be the case') are ubiquitous in ordinary and scientific reasoning, and they are of central importance to philosophy. Typically, their logic and semantics is studied in terms of model-theoretic methods by appeal to possible worlds models, where the counterfactual logics based on the model-theoretic analyses usually extend classical logic. The main objective of the project is to contribute to the development of a proof-theoretic semantics for counterfactuals which is acceptable from an intuitionistic (or constructive) point of view. The project, thus, enters an almost unexplored area of research. It will be couched in a proof-theoretic perspective on counterfactuals which starts out from a methodological primacy of inference and proof. Roughly, on this perspective, the meaning of counterfactuals is explained in terms of the proof-theoretic structure of constructive counterfactual inferences which guide us, in a suitable structural proof system, from the antecedent of the counterfactual A to its consequent B. The project will be pursued building on the framework of subatomic natural deduction developed by the applicant in previous work. A main desideratum is the suitability of the intended proof-theoretic semantics for the analysis of counterfactuals in natural language.