In a nutshell:
When are conditionals containing adverbial quantifiers true according to the David Lewis account? In particular, how are they to be judged if the situation in the antecedent never occurs?
In Adverbs of Quantification (1975), David Lewis proposed that adverbials such as always, mostly, rarely, sometimes, never and so forth are quantifiers that quantify over cases (as opposed to just time, for example).
So a sentence such as:
- I mostly go to the gym in my pyjamas
would be true if in most cases that I go to the gym I go in my pyjamas.
He then further proposes that when such adverbials appear in conditional sentences, the antecedent of the conditional functions as a restrictor of the adverbial quantifier. So in a sentence such as:
- Mostly, if on a Saturday morning I go to the gym, I go in a suit and tie
then we have a quantifier mostly that quantifies over cases restricted to cases in which I go to the gym on a Saturday. We can model the sentence like this:
- [Mostlycases : I go to the gym on a Saturday morningcases] I wear a suit and tie.
Assuming that I ever go to the gym on a Saturday morning this sentence is true if in a majority of such cases I wear a suit and tie. So far, so good (I hope).
Now I am a supremely lazy individual, and you are more likely to see me in Sainsbury's (a British supermarket) in my birthday suit on a Saturday morning than you are to see me at the gym. I assure you that neither has ever happened. What I want to know, therefore, is how David Lewis would regard my sentence:
- Mostly, if on a Saturday morning I go to the gym, I go in a suit and tie.
If this was a normal conditional without the word mostly, then this conditional would be true according to Lewis, because he subscribed to a material implication account of natural language conditionals. According to the material implication account of conditionals If P, Q is true whenever P is false or Q is true. So given that I never go to the gym on a Saturday morning the sentence above would be true according to such an account. However, Lewis rejects such an account when it comes to conditionals which have adverbials such as always, mostly, never and so forth. The reason is this:
- Mostly if students cheat in their exams, they get a B+.
In a sentence such as the one above, if we take the conditional to be a material implication then all that is needed for the sentence to be true is for the conditional to be true in a majority of cases. All that is needed for the conditional to be true in a majority of cases if the sentence is a material implication, is for most students not to cheat in their exams. If most students don't cheat in their exams but every single student that cheats gets an A+, the sentence would be true. So this is clearly not what we want.
For this reason, therefore, Lewis adopts his restricted quantifier account for such conditionals.
My problem is that I have been unable to find out (maybe because I'm missing something) how Lewis would treat conditionals like my Saturday-morning-at-the-gym one, given that I never go to the gym on a Saturday morning. Does anybody know?