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ModalityMetaphysics, Logic, and Epistemology$
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Bob Hale and Aviv Hoffmann

Print publication date: 2010

Print ISBN-13: 9780199565818

Published to Oxford Scholarship Online: September 2010

DOI: 10.1093/acprof:oso/9780199565818.001.0001

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Modal Logic within Counterfactual Logic

Modal Logic within Counterfactual Logic

(p.81) 4 Modal Logic within Counterfactual Logic

Timothy Williamson (Contributor Webpage)

Oxford University Press

This chapter argues that claims of possibility and necessity are equivalent to claims involving counterfactual conditionals, and uses the equivalences to derive basic principles of modal logic within the logic of counterfactuals. The derivations employ weaker assumptions than corresponding derivations by Lewis and Stalnaker. They still use the principle that all counterpossibles (counterfactual conditionals with impossible antecedents) are vacuously true, but this principle is defended. The account is extended to quantified modal logic; de re modalities are equivalent to de re counterfactuals, which are usually considered unproblematic. An application is suggested to the epistemology of modality: the role of conceivability and inconceivability in the evaluation of claims of possibility and impossibility, rather than being regarded as problematically sui generic, should be treated as a special case of the role of the imagination in the evaluation of counterfactual conditionals, which is commonplace even for mundane, highly contingent counterfactuals.

Keywords:   conceivability, counterfactual, counterpossible, imagination, Lewis, modal logic, necessity, possibility, Stalnaker

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