Bare conditionals, I argue, exhibit Conditional Duality in that when they appear in downward entailing environments they differ from bare conditionals elsewhere in having existential rather than universal force. Two recalcitrant phenomena are shown to find a new explanation under this thesis: bare conditionals under only, and bare conditionals in the scope of negative nominal quantifiers, or what has come to be known as Higginbotham’s puzzle. I also consider how bare conditionals behave when embedded under negation, arguing that such conditionals (...) often involve denial negation. One important conclusion that emerges from the discussion is that an account of bare conditionals that validates Conditional Excluded Middle is not warranted. By limiting the scope of the strict analysis Conditional Duality is also a way of maintaining such an account. (shrink)

Adams’ thesis is generally agreed to be linguistically compelling for simple conditionals with factual antecedent and consequent. We propose a derivation of Adams’ thesis from the Lewis- Kratzer analysis of if-clauses as domain restrictors, applied to probability operators. We argue that Lewis’s triviality result may be seen as a result of inexpressibility of the kind familiar in generalized quantifier theory. Some implications of the Lewis- Kratzer analysis are presented concerning the assignment of probabilities to compounds of conditionals.

This note relates the Lewis/Kratzer view of conditionals as restrictors to the philosophical debate over the meaning of conditionals.