Thursday, May 20, 2010

Counterfactuals with possible antecedent and impossible consequent

I used to think the following principle was certainly true, if → indicates subjunctive conditionals:

  1. If pq and p is possible, then q is possible.
Obviously, (1) holds on Lewis-Stalnaker semantics. More generally, it holds on any semantics whose picture of counterfactuals is that the antecedent selects one or more worlds in which it holds and the conditional is true if the consequent holds at these, or most of these, worlds.

But there seems to be a counterexample to (1). Suppose God promised to do A, and did A. Moreover, suppose that the circumstances are such that he is obligated to keep this promise (none of the defeaters for the duty of promise-keeping, if there can be any, apply; the promise has not been annulled by promisee's release; etc.). The following appears true;

  1. Had God not done A (or something better), he would have done something wrong.
(The parenthetical is if you believe that you can always fulfill a promise by doing something whose value dominates the value of what you promised.) Here, the consequent is impossible: God cannot do wrong. But the antecedent is possible: it is possible that God not have done A or anything better. After all, A may be a positive action with respect to a creature, while it is possible that God not have created anything.

The argument against (1) does not apply on views of counterfactuals on which relevant background assumptions automatically get imported into the antecedent. For part of the background here will be that God made the promise, and that the circumstances were such that he was obligated to keep it. But views like the Lewis-Stalnaker view, on which (a) there is no importation of background assumption, but (b) rule (1) holds, will have a problem here.


Mike Almeida said...

I can't the problem for LS. (2) is false. Clearly, the world in which God does something wrong cannot be among the closest worlds in which he fails to do A. It is in general false that antecedent admitting worlds in which the impossible happens are closer to the relevant world W than antecedent admitting worlds in which nothing impossible happens. The impossible, as one might imagine, makes for great dissimilarity. The closest world in which he fails to A is a world in which he did not make a promise to do A, or he is let off, or something of the kind.

Jonathan D. Jacobs said...

Context seems to require backtracking, which is allowable on the semantics even if it's not the standard resolution of vagueness of comparative similarity. Hence the closest worlds are worlds in which God does not do A and he did not promise to, not worlds in which God does not do A and He promised to.

Alexander R Pruss said...

On a closeness of worlds account of counterfactuals, (2) is false. But I was using the truth of (2) to argue against closeness accounts. :-)

Here's one way to support (2). Imagine God thinking whether to do A. "If I do A, then .... But if I don't do A, then I'll be breaking a promise without sufficient justification. So, I should do A."

Jonathan D. Jacobs said...

The truth value of 2 on closeness account is dependent upon context. If the context requires holding fixed that God promised to do A, then 2 is true on the closeness account, just trivially so. So to be a counterexample, you need it to be, not just be true, but non-trivially so. Right?

Alexander R Pruss said...

On Lewis's standard account, context enters only into determining the closeness relation. But no closeness relation allows you to get close to impossible worlds.

But you can have a closeness account on which context also determines the class of worlds that count. In that case, one can keep fixed the past, and then you do get (2) trivially. But you also get:
3. Had God not done A, he would have done what is obligatory.
And I don't want that.

Jonathan D. Jacobs said...

Let me try this way: Either we're allowing backtracking or we're not. If we allow backtracking, then the closest worlds are worlds where God does not promise to A, and so 2 is false. If we disallow backtracking, then it looks like the closest worlds are impossible, and hence 2 is true trivially, since the consequent is true in all of the closest, possible antecedent worlds.

So 2 is either false or trivially true.

Am I missing something here?

Alexander R Pruss said...

I think we shouldn't allow backtracking, and we should say (2) but not (3). On the triviality reading, we should say both (2) and (3), so that won't do. This means that either we should evaluate counterfactuals with respect to impossible worlds as well as possible ones, or else counterfactuals are not to be evaluated in terms of worlds.

If (2) were false, it could not figure in divine deliberation. If (2) were trivial, it could not substantively figure in divine deliberation. But (2) could substantive figure in divine deliberation--indeed, it could be God's reason for doing A.

Jonathan D. Jacobs said...

Ok, now I get the dialectic.

Do considerations like "That would be morally wrong" enter into divine deliberation? I really have very little in the way of developed thoughts regarding ethical theory, but on the face of it, I would have thought that God's deliberations would involve the truthmakers for the fact that it's wrong, whatever those are. Is the thought that moral realism requires basic facts like moral wrongness?

Alexander R Pruss said...

To be honest, I don't know what enters in God's deliberation. But the point is that we aren't really mystified by (2), and we take it to have a non-trivial content, as indicated by (3). Now, maybe, in the final analysis of divine willings, things like (2) won't be needed.

Another case would be something like this. Suppose, contrary to fact, that Molinism is true. God has given great powers to the friggles. Moreover, he has already issued them an irrevocable promise that he's not going to restrict their exercise of their powers. They have freedom. Now, God is trying to do decide between creating plum trees and creating apple trees, and there is a Molinist conditional: Were God to create plum trees, a friggle would cause an innocent to suffer for eternity. The friggles are really powerful--they can do that. However, it could be that divine goodness is incompatible with an innocent's suffering for eternity. If so, then we have a Molinist conditional--and a non-trivial one--whose consequent is impossible.