The Semantics of Conditionals
Dissertation, University of Notre Dame (1991)
In this dissertation a correct answer is sought to the question, 'When, in general terms, is an English conditional true?' The search was motivated largely by three apparent inadequacies in the most prominent proposed "semantics" for English conditionals. First, most such semantics counter-intuitively count as true all conditionals with necessarily false antecedents and/or necessarily true consequents. Secondly, no prominent semantics is designed to deal with "probabilistic" conditionals, conditionals like 'If he had fallen, he probably would have laughed.' Thirdly, most prominent semantics counter-intuitively count as true conditionals with antecedents which do not appear to be "appropriately relevant" to their consequences. ;In Chapter I, the common view is defended that English conditionals can be divided into two semantically-distinct classes, the "indicative" and the "subjective" conditionals, although the question whether these classes are actually distinguished by mood is left open. In Chapters II through IV, the "material implication" analysis, Ernest Adams' analysis, and the theories of Peter Gardenfors and Ken Warmbrod regarding "indicative" conditionals are all criticized. In Chapter V, a new semantics for "indicative" conditionals is developed. A "probabilistic" indicative conditional, as they're typically used, is true exactly when its consequent has the appropriate probability "on" the conditional's antecedent "relative to" the conditional's "intended background," and the antecedent is "appropriately relevant" to the consequent. A non-probabilistic indicative conditional is true when the conditional's consequent is certain "on" the conditional's antecedent, relative to the conditional's "intended background," and the antecedent is "appropriately relevant" to the consequent. ;In Chapter VI, consequences of this semantics for the logic of these conditionals are worked out. In Chapter VII, the semantics of David Lewis and Robert Stalnaker for "subjective" conditionals are criticized. In Chapter VIII, a new semantics for "subjunctive" conditionals is proposed, a semantics which is only a slight variation of the semantics given in Chapter V for "indicative" conditionals. Finally, in Chapter IX, new accounts of entailment and logical probability are proposed in order to yield intuitively-correct truth values for conditionals with necessarily false antecedents and/or necessarily true consequents.