Wolfgang Schwarz

Modal knowledge, counterfactuals and counterpossibles

Carrie, Joe and Brit have recently commented on Williamson's proposal that modal knowledge is based on counterfactual knowledge. I share their suspicion, partly for the reasons Carrie mentions: the mere fact that statements about necessity and possibility are equivalent to counterfactuals doesn't tell us that the route to knowing the former proceeds via the latter. In fact, the assumption that we have a special cognitive faculty for knowing counterfactuals already seems odd to me. After all, we don't have special faculties for knowing indicatives or negations or conjunctions.

I know that I'm not sleeping and that dolphins don't eat strawberries, but I don't know these facts by employing my negation faculty; rather, I know the first by introspection and the second by testimony. I would even say that the fact that I'm not sleeping is the very same fact as the fact that I'm awake (ignoring the possibility that I'm dead or in a coma). The fact that it's raining is the same as the fact that it's not not raining. Facts (the kind of things we learn) don't have a logical form. Just like conjunctions and negations, most conditionals express ordinary facts about us and our world. Those facts can equally be expressed without conditionals, though it is controversial exactly how. No doubt they can also be expressed as conjunctions and disjunctions and negations. All this is irrelevant to how we know them. That rather depends on what the facts are about (dolphins? my own mental states?) and how the information has reached us.

Joe and Brit also complain that Williamson's account relies on the equivalence of and , and therefore on the assumption that all counterfactuals with impossible antecedent are true. On this issue, I side with Williamson. He has a few good arguments in defense of it in his book (Philosophy of philosophy). Here are three more.

First. (Some of what Williamson says goes in the same direction.) Whenever we have a proof from A to B, it is intuitively correct to say that if A were the case, then B would be the case. This holds for all classical proofs, including proofs using disjunctive syllogism ("if either p or q were true, but not p, then q would be true") and proofs by reductio ("assume p; then ......; and then ~p; so if p were true, then ~p would be true; so p is false"). It follows that every counterfactual with a logically false antecedent is true. But if uttered out of the blue, some of these sound quite bad: if I haven't shown you the lengthy derivation of ~p from p, it is infelicitous to say that if p were true, then ~p would be true. (And there are good pragmatic explanations why.)

Second. In most cases where a counterfactual with impossible antecedent sounds false, other sentences sound equally bad, even though they, too, come out true on most accounts:

1. If the square root of 23409 is divisible by 3, then it is prime. [indicative]
2. From the assumption that the square root of 23409 is divisible by 3 it follows that it is prime.
3. Necessarily, if the square root of 23409 is divisible by 3, then it is prime.
4. It is a priori that either the square root of 23409 is divisible by 3 or it is not prime.
5. It could not have turned out that water is anything else but H2O. [I take it that if it could have turned out that p, then it could have been the case that p.]
6. Necessarily, if water is H4O, then water molecules contain only two H atoms.
7. It is impossible for water molecules to a) have the form H4O and yet b) contain hydrogen atoms.

If one accepts these -- or most of them -- as true, I see little motivation for insisting that the corresponding counterfactuals are nevertheless false. One could surely try to argue that all of these sentences are false. But I would not like to be in that position.

Third. Many counterfactuals with impossible antecedent really express falsehoods; but what is expressed isn't what is literally said.

1. If I were you, I'd stick a deckchair up my nose.
2. If it had turned out that water is XYZ, it would have turned out that water is H2O.
3. If you had proven that Fermat's theorem is false in 1982, I would have given you a million Euros.

What we have in mind when we say "if I were you" is not really a counterfactual situation in which I am you, contradicting the necessity of non-identity. Rather, it is a situation where I am more or less in your position in some relevant respect. Most people I've asked readily acknowledge this. But if the antecedent is re-interpreted in this way, it is no longer impossible, and the (re-interpreted) counterfactual is indeed false.

A similar story can be told about the other two examples. As for the water case, what we consider arguably aren't situations where water is really XYZ; we only mean situations where the watery stuff in our rivers and lakes is XYZ, or where "water" turns out to denote XYZ. (This is the story Kripke has told, for reasons that have nothing to do with saving the standard analysis of counterfactuals.)

In the case of Fermat's theorem, the envisaged situation might only be one where you've produced a sequence of mathematical statements with a conclusion that looks very much like the negation of Fermat's theorem, and where other people applaud you and say that you've proven the falsehood of Fermat's theorem, and so on. All this is clearly possible. (Indeed, "prove" has a non-success reading on which the fact that something is proven doesn't entail that it is true: this is the reading on which proofs can be invalid and fallacious.)

Brit worries that

the subjunctive mood is a common way in which to refute one's opponents in philosophy (perhaps the most common way), and so, if counterpossibles are true (per definition), philosophy isn't as deep and interesting as one would have thought.

I don't see why this would follow. It's not that if counterpossibles are true per definition, then all counterpossibles suddenly become uninteresting or trivial. What becomes trivial is only that if P were the case then Q would be the case given that P is necessarily false. But it is often far from trivial to see that P is necessarily false. In philosophy, it is generally much easier to establish the conditional than the necessary falsehood of the antecedent. And exploring what would be the case if some philosophical position were correct really seems much more interesting to me in cases where I'm not already absolutely sure that the position is (necessarily) false. At least for me, almost all cases are of this kind: there is hardly any philosophical position of which I am absolutely sure that it is false. Moreover, even if I am absolutely sure that your position is false, and therefore that all counterfactuals with it in the antecedent are true, I can hardly use this when arguing against you ("if your theory was right, there would be penguins that can hop over the moon: that's ludicrous!"). You would rightly complain that I haven't established the truth of these counterfactuals yet. I would first have to convince you that your theory is necessarily false. And if I could do that, say by deriving a contradiction from it, I think the complaint would lose its force. Once you accept that it logically follows from your theory that 1 = 0 and that penguins can hop over the moon, would you still reject that if the theory were true, these things would also be true?