Thursday, August 7, 2008

A theory about counterpossibles

I suspect that non-trivial per impossibile counterfactuals, true subjunctive conditionals of the form "pq", where p is impossible and the conditional is not simply said to be true on account of the falsity of p, are in a way like poetry: They tell us things that are hard to express in more ordinary language and that, moreover, have a deeper resonance with us, and are more plausible, when put poetically.

But we can, I think, give a sufficient condition for the truth of a counterpossible: if the material conditional "if p, then q" is true in virtue of a fact explanatorily prior to or independent of not-p, then pq holds. This condition seems to me to also hold in the case of ordinary counterfactuals. Thus, the laws of nature are explanatorily prior to or independent of ordinary non-nomic facts. Thus, if it is a law of nature that if something is a raven, then it is black, we can say that if there were a raven in this room, it would be black, because the conditional "if something is a raven, then it is black"[note 1] is explanatorily prior to or independent of the absence of ravens from this room.

In particular, when the consequent of the material conditional is true and explanatorily prior to or independent of the antecedent, the subjunctive conditional holds trivially. For instance: "Were God not to have commanded respect to parents, there would (still) be a duty to respect parents." Here, the corresponding material conditional holds in virtue of the consequent's holding, and the consequent is (or so the asserter of the conditional claims) independent of or explanatorily prior to God's commanding respect to parents.

I don't know if the condition I have given is necessary for a conditional's truth. But at least sometimes, I think, we use a per impossibile counterfactual precisely to express a claim about explanatory priority or independence.

Here is a seemingly different sufficient condition for the subjunctive conditional pq. If the material conditional "if p, then q" is more strongly necessary than not-p, then pq holds. The idea of grades of necessity is perhaps best introduced by example: nomic necessity is stronger than practical necessity; metaphysical necessity is stronger than nomic necessity; narrowly logical (or conceptual?) necessity is stronger than metaphysical necessity.

We can combine the two conditions. Suppose that the material conditional "if p, then q" follows with a necessity of grade n1 from some fact F, and this fact F is (a) explanatorily prior to or independent of not-p, and (b) the truth of not-p is not necessary with a necessity of grade n1, then the subjunctive pq holds. I don't know if this is a necessary condition for a subjunctive to hold. Maybe it is.

16 comments:

Enigman said...

I don't know how relevant this is, but we seem to regard absolute (or context-independent) moral laws as fixed for all possible worlds. When we consider a possible world, we rigidly apply our ethical intuitions to it. (That is perhaps why fiction is good at showing us what our true ethos is.) If so then it would always be true, that were X otherwise then M, where M is any absolute (or fully generalised) moral fact of this world, and X is anything at all. So my guess is that such an approach could (seem to) falsify not just D.W. metaethics, but any metaethics?

Mike Almeida said...

But we can, I think, give a sufficient condition for the truth of a counterpossible: if the material conditional "if p, then q" is true in virtue of a fact explanatorily prior to or independent of not-p, then p→q holds.

I can't see how this would give sufficient conditions for the truth of a counterpossible. The explanation required would be one that explained why q obtains or occurred on the condition p, given some laws or something else independent of p and q. But there is nothing that an impossible state of affairs (or event) p could explain, no matter what it is combined with. Impossible states of affairs could contribute to the explanation of nothing since they do not obtain in any world.

Alexander R Pruss said...

Mike:

I am not asking for p to be a part of the explanation, but rather for an explanation of the material condition p→q, or, equivalently, an explanation of (not-p or q).

For instance, when p=q, an explanation of (not-p or q) is easy: it holds in virtue of the law of excluded middle. This is true even in the special case where p is metaphysically necessarily false. Hence, the counterpossible p→p holds non-trivially in those cases where not-p isn't a truth of logic.

Mike Almeida said...

You're going to have to say more or point me to a paper. Let's actually consider a counterpossible. Take 'if God were evil, then he would command evil things'. That's a canddiate for a true, non-trivial cf. But how again? And if you use material conditionals in your explanaiton of how that it true and non-trivial, explain how these are relevant.

Alexander R Pruss said...

This counterpossible doesn't satisfy the sufficient condition for truth. I also don't think it's true, since an evil being might not command anything, or might command good things while having made creatures that will disobey him, etc.

But take a true counterpossible.
(C1) If x were a body of water that is H3O, then x would have hydrogen atoms in it.

Now, consider the corresponding material conditional:
(M1) "If x is a body of water that is H3O, then x has hydrogen atoms in it."
Now this is narrowly logically equivalent to:
(M2) "x is not a body of water or x is not H3O or x has hydrogen atoms in it."
But (M2) is a narrowly logical consequence of:
(M3) "x is not H3O or x has hydrogen atoms in it".
However, (M3) is a definitional truth, holding by definition of H3O. Therefore, (M1) follows from (M3) with narrowly logical necessity, and (M3) is a definitional, or conceptual, truth. Consequently, (M1) is conceptually necessary. Moreover, the antecedent of (M1) is not conceptually impossible, but only metaphysically impossible. Thus, by my second sufficient condition, (C1) is a non-trivial counterpossible.

Does this example help?

Enigman said...

If God were evil, then he would command evil things.

Were God evil, he would have some will (since otherwise he would not be a person) and it would be an evil will (according to the antecedent) so the conditional cannot be false for the reasons given by Alexander, not if 'will' might replace 'command' (and that the former should replace the latter follows from such cases as Abraham, as mentioned in a comment on the previous post).

But even so, the counterfactual (with 'command' replaced by 'will') equivocates.

It might not be a counterpossible, as it might mean that, had God's will been other than it is (as it might have been, as it is a perfectly free will), then he would have willed different things. That would seem to be true.

But the antecedent could also be the case of God's will being counter to his will, in which case it is counterpossible, as God's will is perfectly free (so that there could be no such inner conflict) and Divine Will metaethics is true (so the good is by definition God's will). Then the counterfactual is trivial, and it hardly seems to matter what we say of its truth.

Mike Almeida said...

Alex, that example does help. The worry I have is that material and strict conditionals license strengthening antecedents. That's why M2 is a consequence of M3. But justifying counterfactuals in general this way will get the wrong results.

1. If x were a golden retriever then x would not have gold-colored fur.

That's false. But consider the material conditional.

2. x is a golden retriever only if x does not have gold fur.

(2) is equivalent to,

3. x is not a golden retriever or x does not have gold fur.

(3) is entailed by,

4. x is not a golden retriever or x is not a green-furred golden retriever or x does not have gold fur.

But (4) is equivalent to the conceptual truth,

5. x is a golden retriever that is green-furred only if x does not have gold fur.

So, (1) should come out true. But (1) is false. Where does my counterexample go wrong?

Alexander R Pruss said...

Mike,

(4) does not entail (3). The middle disjunct in (4) is satisfied if x is a golden-furred golden retriever, while neither disjunct in (3) is satisfied in that case.

Alex

Mike Almeida said...

Yikes. A bit more cautiously, now. Suppose Smith's baseball is a white object that was painted green.

1. If x were a white object that was painted green, then x would look white. (false)

I mean, "look white" under normal conditions. The material conditional is in (2),

2. ~X is white v ~X is painted green v X looks white (under normal conditions).

(2) is entailed by (3),

3. ~X is white v X looks white (under normal conditions)

(3) is equivalent to the conceptual truth in (4).

4. X is white only if X looks white (under normal conditions).

Mike Almeida said...

There might be a simpler one.

1. Were the liveliest person in room to kill himself, he would be lively. (false)

The material conditional for (1) is equivalent to (2).

2. ~(x is the liveliest person in the room) v ~(x kills himself) v x is lively.

(3) entails (2),

3. ~(x is the liveliest person in the room) v x is lively.

(3) is equivalent to the concpetual truth in (4).

4. x is the livelist person in the room only if x is lively.

Time to get some work done. But this is an interesting problem.

Alexander R Pruss said...

Mike:

The tenses in your last example are confusing. Let me vary it:

(*) "Were the liveliest person in the room to be dead, he would be lively."

The material conditional "if x is the liveliest person in the room, then x is lively" is a conceptual truth. Thus so is the strengthened "if x is the liveliest person in the room and dead, then x is lively". Hence, by my sufficient condition, (*) is true.

I bite the bullet. (*) is true, in the way that "If x were a square circle, then x would be a circle" is non-trivially true, but "If x were a square circle, then x would be a triangle" might be only trivially true.

Mike Almeida said...

I don't see any problem with the tenses. This counterfactual is not a counterpossible. This is why you can't offer an explanation for why it should be true that has an analogue with the square-circle example. It should come out false. Here's another that should come out false, and it too is not a counterpossible.

1. Were X the fastest runner on the track to kill himself, X would be the fastest runner.

In the closest worlds in which the fastest runner kills himself, he is not a runner at all. So, he is certainly not the fastest runner. But (1) comes out true for you. Since (2) is a conceptual truth,

2. x is the fastest runner only if x is the fastest runner.

Alexander R Pruss said...

What's interesting about your counterfactuals is that if you're right about them, they seem to be counterexamples to any view like Lewis's. For on any view like Lewis's, if p entails q, then p → q. But of course that the fastest runner on earth kills himself entails that he is the fastest runner on earth.

I think the right way to see your counterfactuals is not to see "the fastest runner on earth" as wide-scoped and then understood in a Russellian way, so that the right reading is:

(There is a unique x such that x is the fastest runner on earth) and for all x, if x is the fastest runner on earth, then (were x to kill himself, x would be the fastest runner on earth).

This claim is false, and unproblematic for my theory, I think.

Mike Almeida said...

No, defnitely, it has to be read de re, otherwise it comes out true. I'd have to think about whether this matters to your view, or how your view manages de re counterfactuals.

Mike Almeida said...

A counterexample would have to go in the other direction. Is there some reason why an ordinary, true counterfactual with no conceptual relation between antecedent and consequent does not constitute a counterexample. 'If kangaroos had no tails, they would topple over', for instance. Or would you just reject the generalization of your account to these sorts of counterfactuals?

Alexander R Pruss said...

On reflection, I don't know what to say about the kangaroo case. Kangaroo tails and bipedality evolved in an interdependent fashion. I am tempted, thus, to say that if kangaroos had no tails, they'd be non-bipeds or have better balance (and wouldn't foll over). This conditional fits with my account. Let F be the claim that animals that readily fall over don't evolve and bipeds without tails and without a particularly good sense of balance fall over. Let p = kangaroos had no tails, and q = kangaroos are non-bipeds or have better balance. Then "if p, then q" follows from F with some sort of "biological necessity", and F is prior to not-p.