Three-valued accounts of conditionals frequently promise (a) to conform to the probabilistic view that conditionals are evaluated by conditional probabilities, and (b) to yield a plausible account of compounds of conditionals. However, McGee (1981) shows that probabilistic validity, the conception of validity most naturally associated with the probabilistic view, cannot be characterized by a finite matrix. Adams (1995) indicates a further generalization of this result. Nevertheless, Adams (1986) provides a description of probabilistic validity in three-valued terms by going beyond the standard framework. Yet the language Adams considers is severely restricted: it does not contain compounds of conditionals. Thus, a natural question arises: Is there a plausible three-valued account of compounds of conditionals which agrees with probabilistic validity on the restricted language? In this note, I develop a general framework in which to address this question. The answer will be negative.
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