A very impossible world?

In a criticism of the Pearce-Pruss account of omnipotence, Scott Hill considers an interesting impossible situation:

1. Every necessary truth is false.

While the criticism of the Pearce-Pruss account is interesting, I am more interested in a claim that Hill makes that illustrates an interesting fallacy in reasoning about impossible worlds. Hill takes it that a world at which (1) holds is a world very alien from ours, a world at which there are "infinitely many" "false necessary truths".
But that's a fallacious inference from:

2. (∀p(Lp→(p is false))) is true at w

(where Lp says that p is necessary) to

3. ∀p(Lp→(p is false at w)).

Indeed, there is an impossible world w with the property that (1) is true at w and there is no necessary truth p such that p is false at w. Think of a world as an assignment of truth values to propositions. A possible world is an assignment that can be jointly satisfied—i.e., it is possible that the truth values are as assigned. An impossible world is an assignment that cannot be jointly satisfied. Well, let w₀ be the actual world. Then for every proposition p other than (1), let w assign to p the same truth value as it has according to w₀. And then let w assign truth to (1).

Non-triviality of conditionals

Here's a rough start of a theory of non-triviality of conditionals.

A material conditional "if p then q" is trivially true provided that (a) the only reason that it is true is that p is false or (b) the only reason that it is true is that q is true or (c) the only reasons that it is true are that p and q are true.

A subjunctive conditional "p □→ q" is trivially true provided that (a) the only reason that it is true is that p and q are both true or (b) the only reason that it is true is that p is impossible or (c) the only reason that it is true is that q is necessary or (d) the only reasons that it is true are that p is impossible and q is necessary.

For instance, "If it is now snowing in Anchorage, then it is now snowing in the Sahara" understood as a material conditional is trivially true, because the falsity of the antecedent (I just checked!) is the only reason for the conditional to be true. The contrapositive "If it not now snowing in the Sahara, then it is not now snowing in Anchorage" is trivially true, since it is true only because of the truth of the consequent. On the other hand, "If I am going to meet the Queen for dinner tonight, I will wear a suit" is non-trivially true. It is true not just because its antecedent is false--there is another explanation.

Likewise, "Were horses reptiles, then Fermat's Last Theorem would be false" and "Were Fermat's Last Theorem false, horses would be mammals" are "Were I writing this, it would not be snowing in Anchorage" are trivially true, in virtue of impossibility of antecedent, necessity of consequent and truth of antecedent and consequent, respectively. But "Were horses reptiles, either donkeys would be reptiles or there would no mules" is non-trivally true--there is another explanation of its truth besides the impossibility of antecedent, namely that reptiles can't breed with mammals and mules are the offspring of horses and donkeys.

A theory about counterpossibles

I suspect that non-trivial per impossibile counterfactuals, true subjunctive conditionals of the form "p→q", 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 p→q 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 p→q. If the material conditional "if p, then q" is more strongly necessary than not-p, then p→q 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 p→q holds. I don't know if this is a necessary condition for a subjunctive to hold. Maybe it is.

Evolution and moral knowledge

Consider this argument for moral scepticism (this formulation is based on a comment by Christian Lee). The existence of our moral beliefs can be given an evolutionary explanation which makes no reference to the truth of these beliefs, so that:
(*) If there were no moral truths, we'd still believe in moral truths.
This, the argument continues, is an undercutting defeater for our moral beliefs even if in fact there are moral truths.

I'm going to argue that at least on four metaethical views, (*) is false. But first note a complication. On many theories of morality, moral truths are necessary truths. But then (*) is a counterfactual with necessarily false antecedent and hence on Lewis semantics trivially true. However, this can't be how the evolutionary moral sceptic understands (*), since then (*) is going to be equally trivially true if one replaces moral claims with mathematical ones, and I take it that the moral sceptic isn't trying to argue for scepticism simpliciter. Rather, in the case of those theories of morality which make morality a necessary truth, the sceptic understands (*) to be a true per impossibile counterfactual. Now on to considering four moral theories.

1. Kantianism. On Kantian ethics, morality is very closely tied to practical rationality. If, per impossibile, there were no moral truths, there would be no practical rationality. If there were no such thing as practical rationality, there would be no agents or even potential agents. It is not clear whether on a Kantian view there could be any beliefs if there were no agents. If not, (*) is a false per impossibile counterfactual. Suppose that non-agents could have beliefs. Well, still, they wouldn't be our beliefs, because we really are agents, and being the sort of entity that has at least a potential for agency is essential to who we are.

2. Natural law. On natural law ethics, morality is grounded in the teleological features of our nature. If those features were other than they are, or if they were absent altogether, the nature would be significantly different, and the beings with that nature would be essentially different from us--they wouldn't be human. Thus, on natural law ethics, were there no moral truths, or even were the moral truths different from what they are, we wouldn't exist, and hence (*) is false.

3. Divine command metaethics of the divine-will variety. On this view, the right thing is what God wills us to (arbitrarily on some versions, or out of the goodness of his nature; the will in question is the antecedent will). Now, presumably God's deliberation as to what kinds of a universe to create was tightly intertwined with what actions, if any, he willed his creatures to do. It is very likely true that if there were no moral truths, i.e., if God had not willed any actions, then God would have created a significantly different universe (perhaps one in which finite agents would not have arisen), and similarly it is likely that if he had willed different moral truths, he would have set up evolutionary processes or intervened (or whatever is the right story about God's cooperation with evolution) to produce different creatures from the ones he had. In particular, it is unlikely that we would exist then, and hence (*) is probably false.

4. Divine nature metaethics. On this family of theories, the right is grounded in God's nature. For instance, the right may be imitation of God, or it may be a certain kind of participation in the Good which might be identified with God. But now consider the counterfactual. Were there no moral truths or were moral truths different, then God's nature would be different from what it is (e.g., it wouldn't be good). But God created us out of the goodness of his nature. Thus, likely, we wouldn't exist were God's nature different in moral respects from what it is. Hence, (*) is probably false, once again.

Note that on theories 2-4, I've also argued that the following variant of (*) is probably false:
(**) If moral truths were significantly different from what they are, our moral beliefs would be no different.