I can jump 100 feet up in the air

Consider a possible world w₁ which is just like the actual world, except in one respect. In w₁, in exactly a minute, I jump up with all my strength. And then consider a possible world w₂ which is just like w₁, but where moments after I leave the ground, a quantum fluctuation causes 99% of the earth’s mass to quantum tunnel far away. As a result, my jump takes me 100 feet in the air. (Then I start floating down, and eventually I die of lack of oxygen as the earth’s atmosphere seeps away.)

Here is something I do in w₂: I jump 100 feet in the air.

Now, from my actually doing something it follows that I was able to do it. Thus, in w₂, I have the ability to jump 100 feet in the air.

When do I have this ability? Presumably at the moment at which I am pushing myself off from the ground. For that is when I am acting. Once I leave the ground, the rest of the jump is up to air friction and gravity. So my ability to jump 100 feet in the air is something I have in w₂ prior to the catastrophic quantum fluctuation.

But w₁ is just like w₂ prior to that fluctuation. So, in w₁ I have the ability to jump 100 feet in the air. But whatever ability to jump I have in w₁ at the moment of jumping is one that I already had before I decided to jump. And before the decision to jump, world w₁ is just like the actual world. So in the actual world, I have the ability to jump 100 feet in the air.

Of course, my success in jumping 100 feet depends on quantum events turning out a certain way. But so does my success in jumping one foot in the air, and I would surely say that I have the ability to jump one foot. The only principled difference is that in the one foot case the quantum events are very likely to turn out to be cooperative.

The conclusion is paradoxical. What are we to make of it? I think it’s this. In ordinary language, if something is really unlikely, we say it’s impossible. Thus, we say that it’s impossible for me to beat Kasparov at chess. Strictly speaking, however, it’s quite possible, just very unlikely: there is enough randomness in my very poor chess play that I could easily make the kinds of moves Deep Blue made when it beat him. Similarly, when my ability to do something has extremely low reliability, we simply say that I do not have the ability.

One might think that the question of whether one is able to do something is really important for questions of moral responsibility. But if I am right in the above, then it’s not. Imagine that I could avert some tragedy only by jumping 100 feet in the air. I am no more responsible for failing to avert that tragedy than if the only way to avert it would be by squaring a circle. Yet I can jump 100 feet in the air, while no one can square a circle.

It seems, thus, that what matters for moral responsibility is not so much the answer to the question of whether one can do something, but rather answers to questions like:

1. How reliably can one do it?

2. How reliably does one think (or justifiably think or know) one can do it?

3. What would be the cost of doing it?

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.

The ability to do otherwise and brainwashing

Consider cases where an agent is brainwashed into having to choose A by having a set of desires implanted that are sufficiently strong to motivate her to choose A. Here's a rather rough argument:

1. In these brainwashing cases, there is no ability to do otherwise.
2. The relevant difference between these brainwashing cases and cases of agents in deterministic worlds is the history by which the agent came to have those desires.
3. The ability to do otherwise is independent of history.
4. So the relevant difference between brainwashing cases and cases of agents in deterministic worlds does not make a difference for the ability to do otherwise.
5. So agents in deterministic worlds are unable to do otherwise.

Of coure, if we replace "ability to do otherwise" by "freedom", the compatibilist, and many an incompatibilist as well, will dispute (3). But surely your ability to do otherwise depends only on how the world is now, not on how it used to be.

Basically, the point is that while compatibilists can perhaps get out of manipulation arguments by insisting that history makes a difference between cases of brainwashing and cases of determinism, since history makes no difference for the ability to do otherwise, manipulation arguments succeed for the ability to do otherwise, even if they fail for freedom.

There have been two kinds of compatibilists. The Humean compatibilist, well represented by Lewis, have held that determinism is compatible with the ability to do otherwise. The Frankfurtian compatibilist instead insisted that freedom does not require the ability to do otherwise. If my simple argument succeeds, compatibilists must be of the Frankfurtian sort.

Reverse Frankfurt cases

On standard Frankfurt cases, there is a counterfactual intervener who does nothing in the actual world, but who would prevent the action if one willed otherwise. I've been musing about reverse counterfactual interveners who do nothing in the actual world, but who would enable the action if one willed otherwise. For instance:

• Fred is sitting on the sofa watching The Good Guys. Unbeknownst to him, freak cosmic rays have just severed the nerve connections between his brain and his leg muscles. Fred knows the baby needs a change, but decides not to get up, and keeps on watching the show.

If that's the whole story, then:

1. Fred can't get up.
2. Fred is responsible for not trying to change the baby.
3. Fred is not responsible for his baby not being changed by him (since he can't change the baby).

But now add to the story:

• An alien monitoring Fred's thoughts would instantly reconnect the nerve connections as soon as Fred started trying to go change the baby.

The alien doesn't affect (2), of course. But does she affect (1) and (3)?

I have a hard time deciding whether Fred can get up with the alien in place. Consider:

• I don't try to run as fast as possible. But an alien is monitoring my thoughts, and were I to try to run as fast as possible, he would supercharge my muscles and the grippiness of my shoes and I'd run at Mach 3.

Can I run at Mach 3? There is something that I can do such that were I to do it, I would run at Mach 3. But maybe this doesn't make it be the case that I can run at Mach 3. Rather, maybe this just makes it be the case that I can do something that would make me able to run at Mach 3. After all, consider a very different case.

• I don't try to run as fast as possible. But an alien is monitoring my thoughts, and were I to try to run as fast as possible, he would make me able to speak Cantonese.

In this case, clearly I can't speak Cantonese, though there is something I can do such that were I to do it, I would become able to speak Cantonese. If this is like the Mach 3 case—and I am not completely sure of that—then in that case, I too can't run at Mach 3. And that suggests that even with the alien in place, Fred can't get up—though, again, I am not completely sure the Mach 3 case is like the Fred-and-alien case.

But perhaps the ability and responsibility don't line up. For I find it plausible that Fred is responsible for the baby not being changed by him in the case of the alien. After all, such double prevention things are not that unusual. To adapt Locke's example, you're at a party, and the host for security reasons locks the door but installs a doorman who will unlock the door who will open the door for anyone who wants to leave. It sure seems clear that if you stay at the party, you are responsible for that.

Maybe what happens is this. Assessment of outcome responsibility ("Is Fred responsible for the baby being unchanged by him?") tracks something like counterfactuals, while ability ("Can Fred get up?") tracks "internal features". The line between the two ways of tracking may not always be clear (I have some scepticism about how precisely defined counterfactuals are), but perhaps nothing of great moral significance rides on either one. For what matters morally for guilt and praiseworthiness is not what outcomes you are responsible for, but only what choices, what acts of will or failures to will, what tryings and failures to try, you are responsible for. Outcome responsibility does matter for the court system, especially but not only in civil cases, but that's mainly a matter of policy.

If that's right, then it does something interesting to some of the dialectics about alternate possibilities. For instance, Peter van Inwagen has argued that determinism and Frankfurt-style interveners would take away one's responsibility for certain outcomes. The compatibilist can embrace this conclusion. For the morally important question is about responsibility for one's will, not for outcomes. It could in principle be that we are responsible for no outcomes (if only because it could be that our acts of will have no outcomes), but we are responsible for our will.

But I don't know that this gets the compatibilist off the hook entirely. For something like an ability to try is important to assessing responsibility for a failure to try. And it is not clear that compatibilists have very good accounts of the ability to try.

Compatibilism, trying and trying hard

Some compatibilists—e.g., Vihvelin and Fara—think that something that merely blocks the possibility of your trying to do A but doesn't block your disposition to do A when trying to do A does not take away your present power to do A. Two examples of such blocks are (a) Frankfurt cases where you'd be counterfactually prevented from doing A and (b) being determined not to do A.

But there is an interesting family of cases where you can only do something when you try hard enough. For instance, you can run distance D in time T when you try really hard, and you can only try that hard when you know a bear is chasing you. In a case like that, even though you are disposed to do A when you try hard enough, anything that blocks you from the possibility of trying hard enough also blocks you from being able to do A. Thus the absence of a bear, or even just ignorance of the presence of the bear, blocks you from being able to running D in T.

So where trying hard to do A is needed for you to do A, anything that blocks your possibility of trying hard blocks your ability to do A.

Now, anything that blocks you from the possibility of trying also blocks you from trying hard. So in cases where trying hard to do A is needed to do A, determinism and Frankfurt cases block you from being able to do A.

So in cases where success requires trying hard, blocks to trying remove the ability to succeed. But why should this only be true where success requires trying hard? So in cases where success requires trying, blocks to trying remove the ability to succeed, too.

Ability and probability

You find a ticking bomb which will go off in five seconds. There is a pad on it, and if you enter the right five digit number in the time remaining you will defuse the bomb. You frantically enter "12345", "54321" and "91101", and none of these work. The bomb goes off. As it happens, had you entered 88479, a number that didn't occur to you, the bomb would have been defused. You surely could have entered 88479. Are you responsible for failing to defuse the bomb?

Of course not. But why not? You were in some sense able to.

In cases like this, a natural suggestion is one made by Gerald Harrison: you were unable to do it "because ... doing so is contingent upon something highly improbable happening, namely ... entering the right combination."

But I don't think this has much to do with improbability as such. Suppose I'm a habitual criminal and I come across a sure opportunity to steal a million dollars with almost no chance of being caught, and sure enough I avail myself of the opportunity. The probability that I refrain from this was nonzero, but it was very small—perhaps no bigger than the probability of entering the right combination in the above case. Yet despite the low probability, I am responsible.

Or vary the bomb case. There is time to enter only one combination. And you know it's either 12345 or 54321. You try 12345, and fail. You are not responsible for the failure to defuse, even though your defusing the bomb was not "contingent upon something highly improbable happening".

So why aren't you responsible in the two bomb cases? It sounds right to me to say that both in the original case and the bomb case you did your best, while in the criminal case, I failed to do my best. And neither the probabilities of success (low in the first bomb case and in the theft case, but moderate in the second bomb case) nor those of trying to do one best (high in the bomb cases but low in the theft case) seem to settle any of the cases either way.

This suggests the following principle:

• If you always tried to do the best you could as hard as you could, you are not culpable for the bad outcomes of any of your actions.

But if determinism rules out alternate possibility—as I think, pace Lewis and Hume and others—and if determinism is true, then we have always tried to do the best we could as hard as we could. For there never was anything else we could do, nor any other way of trying we could engage in.

The dispositional account of ability, the Principle of Alternate Possibility and compatibilism

The Principle of Alternate Possibility says something like:

• (PAP) If x freely does A, then x is able to do otherwise than A.

Michael Fara in a very interesting paper has offered an account of ability that makes PAP compatible with both determinism and Frankfurt examples. The clever move is to note that ability should not be tied to counterfactuals like

• Were x to try in circumstances C, x would do A

since such counterfactuals can be "masked" in Frankfurt cases, but to dispositions. More precisely:

• (DispAb) x is able to do B in circumstances C if and only if x has a disposition to do B when trying to do B in C.

The possession of a disposition to do B upon trying to do B in C is compatible with being actually determined to do A (where B is incompatible with A). And Frankfurt cases don't take away the disposition, but only mask the counterfactual. This is very neat.

Very neat, except that it runs into one serious difficulty. The definition of ability cannot be plugged into PAP. To plug it into PAP, we would need DispAb to define being able to do B. But DispAb doesn't define that. It defines being able to do B in circumstances C. And PAP has no mention of circumstances. In other words, PAP uses a two-place concept of ability—x is able to do A—while DispAb defines a three-place concept—x is able to do A in C.

Maybe this is much ado about nothing. While PAP doesn't mention circumstances, we should take it to say:

• (PAP') If x freely does (variant: chooses) A, then x is able to do (variant: choose) otherwise than A in these circumstances.

But now the problem is evident. For what are these circumstances in a Frankfurt case? Suppose we say:

1. The circumstances of deciding between A and B while there is a neurosurgeon who upon observing that you are about to try to do otherwise than A will prevent you from doing otherwise than A.

But you are not disposed to do otherwise than A when trying to do otherwise than A in circumstances (1). The details depend on how we spell out (1). Either the neurosurgeon manages to redirect your action towards A before you try to do otherwise or right after you have begun to try. If after, then it is clear that you are not disposed to do A in circumstances (1), since to have such a disposition you'd need to have a disposition to get past the neurosurgeon's control when you try to do otherwise, which you don't. If, on the other hand, the neurosurgeon is able to prevent the trying itself, then trying to do A in (1) is impossible, and Fara says you don't have dispositions whose activation conditions are impossible. (He needs this to handle cases where some psychological compulsion removes your ability to do B by making it psychologically impossible to try to do B.)

Of course, one might use coarser-grained circumstances:

2. The circumstances of deciding between A and B.

But that's too coarse grained. Suppose, for instance, that you are deciding between staying put and running off, while unbeknownst to you, you are tied down. That's a case where obviously you have no ability to do otherwise than stay put. Nonetetheless, you do have a disposition to do otherwise than A when trying to do otherwise than A in (2). For normally when you try to do otherwise than A in (2), you do succeed.

The above approach to figuring out what the relevant circumstances are is too ad hoc anyway. Obviously, one can specify the circumstances at varying levels of descriptive detail. We need a principled way to decide how much detail. The minimal level of detail is given by (2). We have already seen that that's too little. We presumably cannot include in the circumstances what the decision itself is—we get irrelevantly weird stuff if we ask what you are disposed to do in the odd circumstances of trying to do B when having decided to A. So that would be too much. Where can a principled line be drawn? I think the three most natural non-arbitrary options are:

3. The circumstances are all events that are causally prior to your decision.
4. The circumstances are all events that are not your decision nor causally posterior to your decision.
5. The circumstances are the complete state of the universe temporally just prior to your decision.

But now notice that given causal determinism, none of these three ways of specifying the circumstances is going to allow you to maintain PAP in a causally deterministic world. For each of them in a deterministic universe is sufficient, at least in conjunction with the laws[note 1], to fix what you're going to decide.

So all the non-arbitrary ways I can think of for spelling out the circumstances to plug the dispositional account of ability into PAP are not ones a compatibilist who wants PAP to hold can embrace.

But interestingly Fara's dispositional approach can help the incompatibilist! For those of us who think that causal (or at least explanatory) priority is the most important thing vis-a-vis freedom will, I think, be drawn to (3) as the right description of the circumstances. But the libertarian can say that in the neurosurgeon-type Frankfurt case, you do have the disposition to act otherwise than A when trying to do A in circumstances C satisfying (3). For the neurosurgeon's activities are not causally prior to your decision. (And if they were, then the Frankfurt case would make your action be determined by causal factors prior to your action, and that would beg the question against the typical libertarian.)

So, to recap, a non ad hoc filling out of the details in the dispositional account of ability (a) is incompatible with saving PAP on compatibilism but (b) can help the libertarian with Frankfurt examples.

Conditional analysis of ability

It's sometimes fun to beat a dead horse. Consider the classic compatibilist conditional analysis of ability:

• x can do A if and only if were x to choose to do A, x would do A.

A student in class today pointed out that then the indecisive Kirk in The Enemy Within can save the crew, since if he were to choose to do so, he would. But of course the point is that he can't (or at least wouldn't be able to if the condition progressed).

It gets worse:

• My pen can make a choice. For if it were to choose to make a choice, it would make a choice.
• A shark can entertain thoughts about moral duties. For if it were to choose to entertain thoughts about moral duties, it would entertain thoughts about moral duties.

The unavoidability of sin

Aquinas says that without grace we can avoid each individual mortal sin but not all mortal sin, at least not for a significant length of time.

On its face, this seems contradictory. After all, I can avoid the first mortal sin. If I avoid it, then I should be able to avoid the next one. And so on. And hence I should be able to avoid all mortal sin.

But this argument mistakenly agglomerates what one can do. For instance, suppose that there is a mine field with a thousand mines. I know how to defuse a mine, but I have an independent probability of 10% of slipping and detonating the mine. It's correct to say that each mine can be defused by me—being able to do this with 90% reliability is sufficient for this—but it is incorrect to say that I can defuse the whole minefield. It is appropriate to look at the minefield that one is to defuse and think: "This is an impossible task without help."

The person without grace is unable to presently control her future actions in favor of the good. Each individual action is in her power, but she cannot control them all at once. Hence she can rightly look with trepidation at her future moral life and say: "This is an impossible task without help."

But a virtuous person can control future actions in favor of the good en masse, by growing in virtue and resolving to do good.

Effort

A concept that I haven't seen much contemporary discussion of is effort. A jstor title search finds 18 entries, most notably an 1897 piece by Dewey. But there is very little recent material: There are a few interesting-looking pieces from the 70s (one on effort and desert, and two on effort and freedom of the will), and there is 2009 Business ethics piece on withholding job effort. The subject seems to have been largely neglected in recent times, though it was an active area of interest at the end of the 19th century (in addition to the Dewey piece, there is William James' 1880 Feeling of Effort.

So, if some graduate student needs a project in moral psychology or metaphysics, effort might be worth some attention. A dollop of history—thinking about conatus, say—wouldn't be amiss.

What made me think of the topic was struggling with wind in a canoe, and being struck by the idea that the feeling of effort or struggle, while unpleasant, does not seem to be classifiable as even prima facie evil.

Ability comes in degrees. I can easily lift a pound. With a moderate effort I can lift forty. And over that, effort significantly increases and ability peters out. There is some kind of a connection between ability and effort. Where ability is limited, at the edge of ability there seems to be a need for effort. So it may be that thinking about effort would help advance some of our understanding of ability, and hence of freedom of the will. But that's speculation. (On a connection with freedom, also see this and the responses in the above-mentioned jstor search.)

Here's an argument that has just occurred to me. The more effort of will, mind or muscle it would take for x to A, the less we blame x for failing to A. But the limiting case of increased need for effort is impossibility. So if Aing is impossible to x, for reasons of will, mind or muscle, then we will least, if at all, blame x for failing to A. This is a kind of principle of alternate possibilities. I am not that impressed with this argument. While the limiting case of increased need for effort is an impossibility of some sort, there may be sorts of impossibility that are not limiting cases of increased need for effort.

"Can"

I want to open a combination lock, but I don't know the combination. Can I do it? There is some sequence of numbers which I can enter, and which is such that if I enter them it will open. So it seems I can. On the other hand, I can't fly a plane. Yet there is a sequence of button presses and movements of levers which I can make, and which is such that if I enter them the plane will fly.
It seems, thus, that the thing to say is that there is something which I can do, which is such that if I did it, the lock would open, and would open as a result of what I did, but nonetheless I can't open the lock.
But now suppose that I try to open it. I enter a sequence of numbers at random. And I get lucky: the sequence is right, and the lock is open. But if what I said above is correct, then it seems that I should say: "I opened it, even though it wasn't the case that I was able to open it." And that sounds weird.
Dan Johnson suggested to me that "can" is context-sensitive, and the context shifts when you open it. Maybe I should say: "Yes, I was able to open it, given my luck"?
Or maybe the thing to say is this. The subjunctive conditional

1. Were I to try to open the lock, I would happen to enter the correct combination

is true at some worlds and not true at others. At the worlds where it's true, I can open the lock, by using the obvious method for opening the lock: trying. At the worlds where it's false, I can't open the lock. The world where I do enter the correct combination when I try to open the lock is always a world where (1) is true. If subjunctive conditionals have non-trivial truth values (which basically means: either Molinism or determinism holds), then some of the worlds where I don't try to open the lock are worlds where (1) is true and some of them are worlds where (1) is false. So at some worlds I can open it and at others I can't, and before I try, I can't tell which world I'm in. On the other hand, if subjunctive conditionals don't have non-trivial truth values, and my choice of numbers would be indeterministic, then in the worlds where I don't try, (1) is not true (either false or nonsense), and in those worlds I can't open the lock.

"Can" and the five minute mile

It used to be fashionable for compatibilists to analyze "x can A" as something like:

0. x would A if x wanted to

(or even worse: "x could A if x wanted to"[note 1]). Here's a sentence we can imagine a coach encouraging x by saying:

1. You would run a five minute mile if you really wanted to.

The coach might back this up by saying that she is sure that you would run a five minute mile when chased by a hungry bear. We should not take (1) to entail:

2. You can run a five minute mile.

To go from (1) to (2), we would need to know that you are capable of inducing in yourself, in the absence of a hungry bear, the kind of motivation that would be required for you to run a five minute mile. In other words, (1) only yields (2) if we suppose that you can get himself to "really want" to run. We all know that there are things that people in ordinary psychological situations can't do, but that they could do in motivationally extraordinary ones, and we do not attribute these things as abilities simpliciter to them.

I submit that for the same reason that (1) does not entail (2), (0) does not entail that x can A. Just as (1) raises the question whether you could get yourself to really want to, so too (0) raises the question whether you could get yourself to want to.

Objection 1: There is a difference between conditioning on "wanted to" and conditioning on "really wanted to". The latter condition requires a particular degree of desire while the former simply attributes the desire. One cannot infer "x can A" from "x would A if x wanted to with degree D", but one can infer it from "x would A if x wanted to".

Response: Actually, the "wanted to" in (0) has to say something about the degree of desire, or else "x can A" would not entail (0). For it can be true that x can A and x wants to A, but x does not A, because x does not sufficiently want to A. So the "wanted to" in (0) has to rule out, for instance, the case where x wants to A, but only just a little.

Objection 2: Claim (0) is a straw man. What really should be said is something like:

3. x would A if x wanted to A more than x wanted any alternative.

Response: But now the bear case comes back. For among the alternatives to running a five minute mile, for someone who does not habitually do so, there is the avoidance of severe exhaustion and pain. It could well be that only a threat like a hungry bear could make one want to run a five minute mile more than one wants to avoid these kinds of alternatives. And in that case, (3) could be true, because if one wanted to A more than one wanted any alternatives, that was because one's reason for Aing was at least as motivating as a hungry bear. But it could still be false to say that one could run the five minute mile sans hungry bear (or equivalent).

I should end by saying that I am not that happy with my response to (3). I fear it is finkish.[note 2]