January 29, 2007

On the consistency of Chisholm's axioms of epistemic logic


In the opening chapters of (Chisholm, 1977) and (Chisholm, 1982), Chisholm sketches an account of some basic concepts of epistemic justification in terms of the relation `P is more reasonable than Q' (suppressing references to epistemic agents and moments of time since they are not relevant for my purposes here), where P and Q are (roughly) propositional attitudes logically built from the primitives `believing p' and `withholding p', for any proposition p. In particular, Chisholm gives several axioms for the logic of this relation. My purpose here is to prove that these axioms are inconsistent.

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