A Note on Two Theorems by Adams and McGee

Research output: Contribution to journalResearch articleContributedpeer-review

Abstract

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.

Details

Original languageEnglish
Pages (from-to)509-516
Number of pages7
JournalThe Review of Symbolic Logic : RSL
Publication statusPublished - 2009
Peer-reviewedYes

External IDs

Scopus 84989168229
ORCID /0000-0002-9962-2074/work/142234606

Keywords