I was reading this post in the latest edition of the Philosophers’ Carnival on conditionals and free will…I don’t have anything to say about the main topic of the post so I thought I would comment here…
What caught my eye was someone in the comment section who said that material implication ‘–>’ is not meant to capture ‘if…then’ in English rather it is merely a “convient way to combine negation and disjunction”…It is true that material implication is defined in terms of negation and disjunction but so is ‘&’ and in fact all of the truth functional connectives but that doesn’t mean that they do not attempt to capture the meaning of the English words. The truth conditions for ‘–>’ are meant to capture at least on of the things that we mean when we say ‘if…then’. Consider,
(1) if Santa is fat then Santa is jolly
The truth table definition of material implication says that this sentence is true when both antecedant and consequent are true and also when they are both false as well as wehn the atecedant is false and the consequent is true. The only time the sentence is false is when the antecedant is true and the consequent is false. So the claim is that these truth-conditions do not capture ‘if…then’ in English. Even the author of the post expresses some suprise that these turn out to be the truth-conditions for ‘if…then’.
But, what we mean when we say (1), and the reason why people intuitively accept Modus Ponens as a valid argument form, is that if it is true that santa is fat then it will also be true that Santa is jolly. The natural way to see if this sentence is true is by finding out whether Santa is fat or not and whether he is jolly or not. Now suppose that Santa in fact turns out to be neither fat nor jolly, does common sense expect (1) to be false? I don’t think so. (1) says that on the condition that Santa is fat he will be jolly as well, so if he is not in fact fat the condition doesn’t hold, but (1) could still be true because it might be true that if Santa were fat then he would be jolly. So the falsity of ‘Santa is fat’ is compatible with what the sentence says still being true counter-factually. But suppose that Santa turned out to be in fact fat but decidely NOT jolly. Then the sentence would be false because the relation that it asserts is shown not to hold. So it seems to me that the truth-table meaning of ‘–>’ does capture the meaning of ‘if…then’ in English.
It seems to me that the reason why the truth-conditons are suprising to people who see them for the first time is that it makes them realize that some sentence’s truth conditions depend on how the sentence behaves modally in opposition to the naive view that all sentences simply depend on how the world actually is for their truth. To put it a bit technically it forces them to realize that the sentence is made true in this world because it is true at some other possible world. It is NOT because these truth-conditions clash with what we take the meaning of ‘if…then’ to be…This, incidently, seems to me to be more evidence that there is something wrong with Williamson’s argument against the distinction.
These truth-conditions capture one of the meanings listed for the English conjunction ‘if”; that there are other uses of the conjunction doesn’t seem to matter.