A proof that ought implies can

Some actions are are things I can do immediately: for instance, I can immediately raise my hand. Others require that I do something to enable myself to do the action: for instance, to teach in person, I have to go to the classroom, or to feed my children, I need to obtain food. So, here is a very plausible axiom of deontic logic:

1. If I ought to do A, and A is not an action I can do immediately, then I ought to bring it about that I can immediately do A.

Now, say that I remotely can do an action provided that I can immediately do it, or I can immediately bring it about that I can immediately do it, or I can immediately bring it about that I can immediately bring it about that I can immediately do it, or ….

It follows from (1) and a bit of reasoning that:

2. If I ought to do A, then I remotely can do A, or I have an infinite regress of prerequisite obligations.

But:

3. It is false that I have an infinite regress of prerequisite obligations.

So:

4. If I ought to do A, then I remotely can do A.

A naive argument that ought implies can

It’s just occurred to me that there is a really quick argument for the ought-implies-can principle:

1. If you do the morally best you can in a situation S, you’ve done everything you ought in S.

2. You can always do the morally best you can.

3. So, you can always do what you ought.

I understand “the best” in the weak sense that if there is a tie for the best, then doing any tied action counts as doing the best.

There is one gap. While (2) is true for us in practice, it won’t be true in certain infinitary situations, such as Satan’s Apple. But we do not in fact find ourselves in such situations, so for us, ought does imply can.

Types of normativity

It is widely thought that our actions are governed by at least multiple types of normativity, including the moral, the prudential and the epistemic, and that each type of normativity comes along with a store of reasons and an ought. Moreover, some actions—mental ones—can simultaneously fall under all three types of normativity.

Let’s explore this hypothesis. If we make this distinction between types of normativity, we will presumably say that morality is the realm of other-concerned reasons and prudence is the realm of self-concerned reasons. Suppose that at the cost of an hour of torture, you can save me from a minor inconvenience. Then (a) you have a moral reason to save me from the inconvenience and (b) you have a prudential reason not to save me.

It seems clear that you ought to not save me from the inconvenience. But what is this ought? It isn’t moral, since you have no moral reasons not to save me. Moreover, what explains the existence of this ought seem to be prudential reasons. So it seems to be a prudential ought.

But actually it’s not so clear that this is a prudential ought. For a further part of the explanation of why you ought not save me is that the moral reasons in favor of saving me from a minor inconvenience are so very weak. So this is an ought that is explained by the presence of prudential reasons and the weakness of the opposed moral reasons. That doesn’t sound like an ought belonging to prudential normativity. It seems to be a fourth kind of ought—an overall ought.

But perhaps moving to a fourth kind of ought was too quick. Consider that it would be wrongheaded in this case to say that you morally ought to save me, even though all the relevant moral reasons favor saving me and if these were all the reasons you had, i.e., if there were no cost to saving me from inconvenience, it would be the case that you morally ought to save me. (Or so I think. Add background assumptions about our relationship as needed to make it true if you’re not sure.) So whether you morally ought to save me depends on what non-moral reasons you have. So maybe we can say that in the original case, the ought really is a prudential ought, even though its existence depends on the weakness of the opposed moral reasons.

This, however, is probably not the way to go. For it leads to a great multiplication of types of ought. Consider a situation where you have moral and prudential reasons in favor of some action A, but epistemic reasons to the contrary. We can suppose that the situation is such that the moral reasons by themselves are insufficient to make it be the case that you ought to perform A, and the prudential reasons by themselves are insufficient, but when combined they become sufficiently strong in contrast with the epistemic reasons to generate an ought. The ought which they generate, then, is neither moral nor prudential. Unless we’ve admitted the overall ought as a fourth kind, it seems we have to say that the moral and prudential reasons generate a moral-and-prudential ought. And then we immediately get two other kinds of ought in other cases: a moral-and-epistemic ought and a prudential-and-epistemic ought. So now we have six types of ought.

And the types multiply. Suppose you learn, by consulting an expert, that an action has no cost and there are either moral or prudential considerations in favor of the action, but not both. You ought to do the action. But what kind of ought is that? It’s some kind of seventh ought, a disjunctive moral-exclusive-or-prudential kind. Furthermore, there will be graded versions. There will be a mostly-moral-but-slightly-epistemic ought, and a slighty-moral-but-mostly-epistemic ought, and so on. And what if this happens? An expert tells you, correctly or not, that she has discovered there is a fourth kind of reason, beyond the moral, prudential and epistemic, and that some action A has no cost but is overwhelmingly favored by the fourth kind of reason. If you trust the expert, you ought to perform the action. But what is the ought here? Is it "unknown type ought"?

It is not plausible to think that oughts divide in any fundamental way into all these many kinds, corresponding to different kinds of normativity.

Rather, it seems, we should just say that there is a single type of ought, an overall ought. If we still want to maintain there are different kinds of reasons, we should say that there is variation in what kinds of reasons and in what proportion explain that overall ought.

But the kinds of reasons are subject to the same line of thought. You learn that some action benefits you or a stranger, but you don’t know which. Is this a moral or a prudential reason to do the action? I suppose one could say: You have a moral reason to do the action in light of the fact that the action has a chance of benefiting you, and you have a prudential reason to do the action in light of the fact that the action has a chance of benefiting a stranger. But the reason-giving force of the fact that action benefits you or a stranger is different from the reason-giving force of the facts that it has a chance of benefiting you and a chance of benefiting the stranger.

Here’s a technical example of this. Suppose you have no evidence at all whether the action benefits you or the stranger, but it must be one or the other, to the point that no meaningful probability can be assigned to either hypothesis. (Maybe a dart is thrown at a target, and you are benefited if it hits a saturated non-measurable subset and a stranger is benefited otherwise.) That you have no meaningful probability that the action benefits you is a reason whose prudential reason-giving force is quite unclear. That you have no meaningful probability that the action benefits a stranger is a reason whose moral reason-giving force is quite unclear. But the disjunctive fact, that the action benefits you or the stranger, is a quite clear reason.

All this makes me think that reasons do not divide into discrete boxes like the moral, the prudential and the epistemic.

'Ought' implies 'can'?

I am sick. Here's a heartening argument: Next week I have some teaching and I can't teach while sick. I ought to do the teaching. Ought implies can. So I will be well by next week.

One gap in the argument is that my doctor may tell me I'm not sufficiently infectious to be unable to teach. But that can't be all that's wrong with the argument.

Two applications of 'ought implies can'?

First application:
1. God ought to exist.
2. So, God can exist. (Ought implies can)
3. So, God exists. (By Ontological Argument)

Second:
4. It's an evil for a person to die.
5. If naturalism is true, people can't live forever.
6. Evils ought not be there.
7. So, people ought not die.
8. So, people can live forever. (Ought implies can)
9. So, naturalism is not true.

In the second argument, for 5 to be true, the "can" must be stronger than metaphysical possibility. Thus that argument requires a stronger ought implies can principle.

All that said, I am sceptical of 1 and 7. An impersonal "ought" not addressed to any person is weird.

The core of the second argument, however, can perhaps be rescued:
10. It's an evil for a person to die.
11. What is normal for a kind of being is not an evil.
12. If naturalism is true, it's normal for people to die.
13. So, if naturalism is true, it's not an evil for a person to die.
14. So, naturalism is not true.

Grounding inhomogeneity and analogy

I ought to respect innocent human life. So I ought not feed cyanide to the innocent. I ought to respect the legitimate intellectual autonomy of others. So I ought not force my students to believe all my metaphysical views.

So, some ought claims are grounded, in part or whole, in other ought claims, and sometimes in further non-normative claims (such as that cyanide kills). This is familiar in many other cases. Thus, it's a standard libertarian view about freedom that some exercises of freedom are only derivately free: they are free insofar as they flow from a character that was formed by other free actions.

It would generate a vicious regress to suppose that all free actions are derivatively free. (In this case, the impossibility of the regress is obvious from the fact that we've only performed finitely many actions in our history.) Likewise, it would be a vicious regress to suppose all ought claims are grounded in further ought claims.

So there are some thing that are derivatively obligatory and some that are non-derivatively obligatory. (The two categories might overlap. For if I promise to fulfill a non-derivative obligation, then that obligation is both non-derivatively obligatory and obligatory by derivation from the duty to keep promises.) Likewise for freedom and many other properties. The non-derivative cases may be brute and ungrounded, or they may be grounded in a different kind of fact (e.g., maybe non-derivative freedom is grounded in alternate possibilities or non-derivative ought is grounded in divine commands—I am not advocating either option as it stands).

Here is a maxim I find plausible: Properties that exhibit this kind of grounding inhomogeneity—sometimes being grounded in one kind of fact and sometimes either ungrounded or grounded in a different kind of fact—are in fact non-fundamental.

This may lead one to say that properties that exhibit this kind of inhomogeneity are really disjunctive. That (or the related suggestion that they are existentially quantified) may be true, but I think it isn't the whole truth. Maybe freedom just is the disjunction of non-derivative and derivative freedom. But it's not a mere disjunction, in the way that being red or cubical is. It's a disjunction between related properties. In the cases of freedom and obligation, the relationship here seems to me to be precisely that of Aristotelian analogy: there is a focal sense of freedom and obligation—the non-derivative case—and there is a non-focal sense as well.

Conjecture: When we are dealing with a somewhat natural property that exhibits grounding inhomogeneity, we are precisely dealing with a disjunction (or quantificational combination) between analogous more fundamental properties.

Aquinas' thinking on divine names fits well here. St Thomas thinks that when we predicate wisdom of God and Socrates, we do so analogically, because God's wisdom is God and Socrates' wisdom is accidental to him. But this difference is precisely a grounding inhomogeneity in the property wisdom, with God being the focal case.

Inferring an "is" from an "ought"

You tell me that you saw a beautiful sunset last night. I conclude that you saw a beautiful sunset last night. You are talking about Mother Teresa. I conclude that you won't say that she was a sneaky politician. You promise to bake a pie for the party tomorrow. I conclude that you will bake a pie for the party tomorrow or you will have a good reason for not doing so. I tell a graduate student to read a page of Kant for next class. I conclude that she will read a page of Kant for next class or will have a good reason for not doing so.

All of these are inferences of an "is" from an "ought". You ought to refrain from telling me you saw a beautiful sunset last night, unless of course you did see one. You ought not say that Mother Teresa was a sneaky politician, as she was not. You ought not fail to bake the promised cake, unless you have good reason. The student ought not fail to read the Kant, unless she has good reason.

All of these are of a piece. We have prima facie reason to conclude from the fact that something ought to be so that it is so. In particular, belief on testimony is a special case of the is-from-ought inference.

In a fallen world, all of these inferences are highly defeasible. But defeasible or not, they carry weight. And there is a virtue—both moral and intellectual—that is exercised in giving these inferences their due weight. We might call this virtue (natural) faith or appropriate trust. We also use the term "charity" to cover many of the cases of the exercise of this virtue: To interpret others' actions in such ways as make them not be counterinstances to the is-from-ought inference is to charitably interpret them, and we have defeasible reason to do so.

The inference may generalize outside the sphere of human behavior. A sheep ought to have four legs. Sally is a sheep. So (defeasibly) Sally has four legs.

I used to think that testimony was epistemically irreducible. I am now inclined to think it is reducible to the is-from-ought inference. Seeing it as of a piece with other is-from-ought inferences is helpful in handling testimonial-like evidence that is not quite testimony. For instance, hints are not testimony strictly speaking, but an inference from a hint is relevantly like an inference from testimony. We can say that an inference from a hint is a case of an is-from-ought inference, but a weaker one because the "ought" in the case of a hint is ceteris paribus weaker than the "ought" in the case of assertion. Likewise, inference from an endorsement of a person to the person's worthiness of the endorsement is like inference from testimony, but endorsement of a person is not the same as testimony (I can testify that a person is wonderful without endorsing the person, and I can endorse a person without any further testimony). Again, inference from endorsement is a special case of is-from-ought: one ought not endorse those who are not worthy of endorsement.

If is-from-ought is a good form of inference, the contraposition may-from-is will also be a good form of inference. If someone is doing something, we have reason to think she is permitted to do it. Of course, there are many, many defeaters.

It is an interesting question whether the is-from-ought inference is at all plausible apart from a view like theism or Plato's Platonism on which the world is ultimately explanatorily governed by values. There may be an argument for theism (or Plato's Platonism!) here.

The Miner Puzzle

Kolodny and MacFarlane give a neat puzzle.

The setup: ten miners are trapped in a shaft—A or B, although we do not know which—and threatened by rising waters. We can block one shaft or neither, but not both. If we block the correct shaft, everyone lives. If we block the wrong shaft, everyone dies. If we do nothing, only one miner dies. (Charlow)

The puzzle is that the following seem to be true:

1. The miners are in A or the miners are in B.
2. If miners are in A, we should block A.
3. If miners are in B, we should block B.
4. It is not the case that we should block A.
5. It is not the case that we should block B.

But assuming modus ponens for (2) and (3), the above claims are contradictory.

Some propose dropping modus ponens. But there is a much better solution. Claims (2)-(5) incompletely identify the relevant action types. Actions types should be identified, in part, by the reasons and intentions for them. Should Jones insert a knife into Smith's heart? The question insufficiently specifies the act. Inserting a knife into Smith's heart could be life-saving cardiac surgery or murder. The intentions and reasons matter. To decide what should be done, we need to expand the action descriptions. Here are some possible expanded descriptions:

6. block A because this has probability 1/2 of killing the miners in B.
7. block A because this has probability 1/2 of saving the miners in A.
8. block B because this has probability 1/2 of killing the miners in A.
9. block B because this has probability 1/2 of saving the miners in A.
10. block neither because that will save nine.
11. block neither because that we will kill one.
12. block A because that will save ten.
13. block B because that will save ten.

I am a reasons-externalist and I take "because" to be factive. Reasons-internalists will want to replace the "because" claims in (10)-(13) with "because you think".

The description "block A" is ambiguous between actions (6), (7) and (12). Once we disambiguate as above, we can say:

14. You shouldn't do (6) or (8).
15. You shouldn't do (7) or (9) if you can do (10) or (12) or (13).
16. If you can do (12), you should do (12).
17. If you can do (13), you should do (13).
18. If you can't do (12) or (13), you should do (10).

But what can you do? If you believe the miners are in A, you can do (12). In that case, you should do (12). If you believe the miners are in B, you can do (13), and so you should. If you have no idea where the miners are, you can't do (12), because it is not possible for you to act because of a reason that isn't available to you. For the same reason, you can't do (13), and so you should do (10).

Can we affirm any conditionals such as (2) or (3)? Not if "should" implies "can". For presumably the way to expand out the "should block" in (2) is not along the lines of (7) but along the lines of (12). And if "should" implies "can", then it is false that if the miners are in A, you should (block A because that will save ten), since you cannot in this case block A because that will save ten, as you are unable to act on that reason.

But suppose you deny that "should" implies "can". Then you can consistently say that:

19. If the miners are in A, you should (block A because that will save ten),

even though the action in the consequent is impossible to you. And then by (18), you can say:

20. Even if the miners are in A, you should (block neither because that will save nine),

since although the action in (19) would be the better one, it is not possible for you. And you are not culpable for failing to do the better action because you have an excellent exculpating excuse: you can't do it.

So we have different stories to tell depending on whether "should" implies "can", but they do not practically differ. Both stories agree that in the event that the miners are in A, you should block neither. The second version of the story also says that you should do something else, thereby placing you in a dilemma, but since that something else is impossible, you have a perfectly fine excuse for acting as you do.

But in any case, there is no real paradox.

So where do I stand with regard to (1)-(5)? Well, we need to have some rigorous disambiguation to the "should block". Here is one proposal. The statement "x should A" has the truth conditions "There is a relevant elaboration A* of A such that x should A*", where an elaboration of an action type is a narrower action type. Then if "should" implies "can", then (2) is false, because the only relevant elaboration of "block A" on which the consequent of (2) would be true is (12), and (12) is not doable in the situation as described, and the same goes for (3). And likewise (4) and (5) are both true, because it is not the case that there is an elaboration of "block A" or of "block B" that we should do.

If "should" does not imply "can", then (2) and (3) are true. But by the same token one of (4) and (5)—the one corresponding to where the miners are—is false.

Moreover, in either case, we can add:

21. You should block neither A nor B.

This may seem to contradict the "should" does not imply "can" statement that one of (4) and (5) is false. But "You should block A" is compatible with "You should block neither A nor B" at least if "should" does not imply "can".

I think Kolodny and MacFarlane would classify my answer as a subjectivist one, since I deny (2) and (3). Their main argument against the subjectivist is this scenario. Suppose the miners are in fact in shaft A. Then we can imagine this dialog. You say you should leave both shafts open because that will save nine. An adviser says: "No, you ought to block shaft A. Doing so will save all ten of the miners." The adviser is disagreeing with you. But how could she be disagreeing with you if your claim that you should leave both shafts open is true?

But on my above story, there is a straightforward way in which the adviser is wrong. How could one elaborate "block shaft A"? If the adviser is suggesting (6) or (7) as the action, then the adviser is giving poor advice, since (6) is wicked, and you shouldn't do (7) when you can do (10), so the adviser would be wrong to advise (7). The only thing the adviser could be reasonably advising would be (12). But unless you believe that the miners are in shaft A, action type (12) is not available to you. So the adviser is advising you to do something you can't do. I suppose there are occasions for remarks such as: "Well the thing you should do is to pay back the money you stole right away. It's really unfortunate that you gambled it all away." But such remarks are unhelpful and are not really advice (except maybe for future occasions). Moreover, in such cases the adviser should not be said to disagree with the claim that the agent should do the best of the courses of action that are in fact open to her.