Topics Logic

Question How can we ever talk about what would be? If a statement A is assumed, that's not actually true, then anything would follow since a conditional with a false hypothesis is always true. But anything (such as "P and not-P") can't be true. This seems to show that a statement that is not true would never be true to begin with. Thus, we can't talk about what would be, only what is. For example, I'm not driving to the store. But if I were, I'd also be swimming. Of course, though, I can't drive to the store and swim at the same time. This comes to show that so long as I'm not driving to the store, we can't ever discuss the situation where I am driving to the store, since that situation implies a contradiction.

Accepted:
September 22, 2011

Comments

Logicians have long distinguished between "indicative" and "subjunctive" conditionals. The terminology reflects a difference, in English, in the grammatical "mood" of the antecedent and consequent. So we have:

If Kennedy was not assassinated, he is living is Columbia.
If Kennedy were not assassinated, he would be living in Columbia.

The view to which you refer, that a conditional with a false antecedent is always true, has certainly been held, but only about indicative conditionals. So (1), on this view, is true if Kennedy was, as we all suppose, assassinated. But it is an entirely different claim that (2) is true simply because Kennedy was assassinated, and I know of no logician who has ever held that view. This is largely because some subjunctive conditionals, such as (2), are precisely intended to report on what would have happened had things been other than we know (or at least presume) they are. Since, as you say, it would be pointless to utter such conditionals, which are known as "counterfactuals", if their truth was always guaranteed by the falsity of the antecedent, we need a different account of what it is for such a conditional to be true.

What is involved in the truth of a counterfactual (or, more generally, subjunctive) conditional is, of course, an entirely different matter, one much discussed and debated. It's probably also worth noting that most logicians, and most linguists, would now reject the claim that natural language conditionals, even indicative ones, are "material", i.e., are true so long as the antecedent is false or the consequent is true.