Sola fide and evidential decision theory

Plausibly, there is a strong correlation between good deeds and salvation. Both are the fruit of God's grace. If evidential decision theory is correct, then the fact that good deeds correlate with salvation makes it rational to do good deeds. Thus, if evidential decision theory is correct, then it makes rational sense to do good deeds for self-interested reasons, even if the good deeds in no way causally contribute to salvation.

What conclusions could be drawn from this? Well, this means that even if sola fide were true, and good deeds in no way contributed to salvation, nonetheless it would be self-interestedly rational to do good deeds for the sake of salvation. This in turn means that those Protestants whose motivation for embracing sola fide is that the doctrine makes it not make sense to do good deeds for the sake of salvation either need to reject either evidential decision theory or their motivation for sola fide. Or one might draw a more ecumenical conclusion. If we all accept evidential decision theory, then our stance on the metaphysical question of sola fide need not affect our practices and motivations: Lutherans, Calvinists, Catholics and Pelagians can all consistently do good deeds for the sake of salvation.

The above argument would be particularly interesting if it turned out that causal decision theory requires indeterminism. For the above argument might give my Calvinist friends reason to reject evidential decision theory, and hence to embrace causal decision theory, and hence to reject determinism. (A Calvinist does not need to be a determinist. She could embrace the position that W. Grant Matthews attributes to Aquinas in a fairly recent issue of Faith and Philosophy.)

Newcomb and medical Newcomb

Leaving aside Egan's counterexamples to causal decision theory, which I need to think about more before I say anything, it seems to me that one way to view the debate between the causalist and the evidentialist is whether one should make the medical Newcomb cases or the standard Newcomb cases drive one's intuitions. Here is a reason to make the medical Newcomb cases drive one's intuitions: medical Newcomb cases are much closer to reality. While it is hard to imagine reliable prediction of choices, it is much easier to imagine factors that simultaneously affect behavior and other outcomes. Our intuitions are more reliable about cases that happen in worlds closer to ours, and medical Newcomb cases happen in worlds closer to ours.

In fact, medical Newcomb cases might very well happen in the actual world. Imagine the following story. There is a disease D that in its late stages horribly painful, incurable and fatal. In early stages it is very hard to detect. It has only one cure: regular jogging in early stages can cure it 20% of the time. This has resulted in the following evolutionary adaptation. Early stage sufferers from D are more likely to jog regularly. I am now trying to decide between regular jogging and regular biking. Suppose both are equally healthy in all other respects. Surely I should say to myself that jogging has the added benefit of reducing the risk of D, and go ahead and jog. But if I am an evidentialist, and the correlation between jogging and early stage D is strong enough, it can be the case that the expected value of jogging is lower than the expected value of not jogging. So evidential decision theory then leads me to act contrary to a very sensible evolutionary adaptation by avoiding the one and only thing that could cure D, and to do this in the name of avoiding D. That is perverse. (There is a way in which this case is a kind of reverse of the Egan cases. This fact may be important for figuring out what to do with the Egan cases.)

(Regular jogging is somewhat complex here, because it's a policy or habit rather than single act. We can replace jogging with eating unripe pears, or something like that.)

It would be quite unsurprising if there were such evolutionary adaptations. It would be surprising if there were actual Newcomb cases. It is more important for our decision theory to give us what are intuitively the right answers in these medical cases than in the standard Newcomb cases.

Charity and God

Last night, I led an Honors Colloquium on C. S. Lewis's Four Loves. Lewis's main point is that Affection, Friendship and Eros all run the danger of falling into a whole host of problems which he describes with great insight. There is only one solution: charity. It is charity that orders all the loves, keeping them faithful to themselves—keeping Friendship from usurping the role of Eros, keeping Affection from imposing on those close to one, keeping Eros from becoming a tyrant, and so on. Note that this is an empirically informed claim: it is informed by the universal human experience of the difficulties of love, and centuries of Christian experience in finding charity to be a remedy for these ills. Suppose that these quasi-empirical[note 1] claims are correct. Then we have the following plausible argument, which Lewis does not himself make in this book:

1. (Premise) Ordering one's loves in charity is a good solution to the ills of love.
2. (Premise) Ordering one's loves in a love for an imaginary being is not a good solution to the ills of love.
3. (Premise) Charity is a love for God.
4. (Premise) Either God is imaginary or God exists.
5. Ordering one's loves in a love for God is a good solution to the ills of love. (1 and 3)
6. God is not imaginary. (2 and 5)
7. God exists. (4 and 6)

This argument is closely related to this one.

Compatibilism and punishment

1. Necessarily, a punishment of x is only just if the occurrence of the punishment is at least partly explained by something x is culpable for. (Premise)
2. Necessarily, if x is guilty of having committed a horrific crime, x is unrepentant and unforgiven, and we believe on overwhelming evidence that x is guilty of the crime, then it is ceteris paribus just to punish x on the basis of the evidence. (Premise)
3. If compatibilism holds, it is possible to believe on overwhelming evidence that x is guilty of having committed a crime, without that belief or evidence being even partly explained by anything x is culpable for. (Premise)
4. If compatibilism holds, it is possible to justly punish x without the punishment being even partly explained by anything x is culpable for. (Premise, justified by 2 and 3 and some uncontroversial modal intuitions)
5. But the consequent of (4) is false. (By 1)
6. Therefore, compatibilism is false. (By 4 and 5)

The intuition behind (1) is that the punishment needs to be a result of the crime. Part of the intuition behind (2) is that what matters for justice is that the evidence be good, not what sort of evidence it is. But (3) observes that if compatibilism were true, we could have cases where our overwhelming evidence for a crime is the state of the world prior to the agent's coming into existence.

One might want to modify (1) by subjectifying it: justice only requires that one believe that the punishment would be a result of the crime. That's fine—the rest of the argument adapts to that version of (1).

This argument has an interesting consequence. It implies that one could not be criminally culpable for an action if that action follows with overwhelming probability from a prior state that one is not culpable for. This means that not only does the full causal determination of a wicked deed by an earlier state one is not culpable for take away culpability, but overwhelmingly strong probabilification will significantly decrease culpability.

The argument also rules out some Molinist views (I am grateful to Trent Dougherty for pointing out basically this)—namely those on which the truth values of the conditionals of freedom are never explained by the truth values of the consequents.

If I were a compatibilist, I think I'd deny (2). I'd insist that at least some of the evidence of the crime be explanatorily posterior to the crime. Not for epistemological reasons, but to ensure the "resultingness" of the punishment. This would, however, have the odd consequence that a person might become justly convictable by a piece of evidence that lowers the probability that she committed the crime. For suppose that all the evidence that has been given was about the state of the universe long prior to the defendant's crime, and that this evidence made it 99.99999999999% likely that the defendant committed the crime. We could now imagine a piece of testimony by an eyewitness to the crime that simultaneously defeats some of the evidence from the previous state of the universe and replaces it with slightly weaker evidence that is, nonetheless, explanatorily dependent on the crime, so that now the evidence makes it only 99.9999999998% likely that the defendant committed the crime. Since that's a probability high enough for conviction (at least in a non-capital case), and since now we have the explanatory connection requirement satisfied, it follows that this evidence which lowered the probability of guilt has made the criminal justly convictable.

Another sloppy way to define compatibilism

One might say:

1. Compatibilism is the doctrine that some deterministic world contains a free agent.

But some libertarians will agree with (1). For suppose, as many libertarians do, that choices are instantaneous, and suppose that simultaneous causation is possible. Then we can imagine a world that comes into existence at time t₀, and at time t₀ there comes into existence Fred, an agent who in the first moment of his existence freely chooses to do A, and suppose that the choice simultaneously effects the existence of a deterministic process that will lead to A. We can imagine that everything unrolls deterministically in this world from t₀ on, and that Fred is the only free agent in this world. Then this world contains a free agent, and that free agent's action is not determined, but nonetheless determinism holds. For determinism says that later states are determined by earlier states. It does not say that the initial states are determined by anything.

What this means, I think, is that we want to define compatibilism in something like this way:

2. Compatibilism is the doctrine that some deterministic world contains a free agent whose beginning is posterior to the beginning of that world.

Or, perhaps:

3. Compatibilism is the doctrine that some world contains an agent all of whose choices and actions are strongly causally necessitated but who performs at least one free choice or action.

(For "strongly causally necessitated", see the previous post.)

Incompatibilism

The following is a standard form of argument, but I've been trying to get to what I think is the most easily defensible, and least open to counterexamples, principle to base it on:

1. If x is responsible for an event E and E is causally necessitated without overdetermination, then x is responsible for at least one event causally upstream of E.

(Here, read "x is responsible for E" as "x is to some degree responsible for E".) Suppose now x is responsible for an event. Then unless x has an infinite history, there must be a first event x is responsible for. Let E be that first event. It follows from (1) that either E is not causally necessitated or E is overdetermined. Say that an agent is "like us" if the agent has a finite history that does not begin at the beginning of the universe's existence. Then:

2. Responsibility in an agent like us requires either (a) that the first event the agent is responsible for is overdetermined; or (b) causal determinism is false.

I think it is also plausible that:

3. Compatibilisms do not require overdetermination.

Given this, we can conclude that compatibilism (with respect to causal determinism) about agents like us is false.

It would be nice if we could handle the overdetermination option more neatly. Here is one way to do it. Say that an event E is strongly causally necessitated provided that it is causally necessitated, and if it is overdetermined, then each of the sets of overdeterming causes causally necessitates it. For instance, E's being strongly causally necessitated rules out the hypothesis that E is overdetermined by A and B, where A causally necessitates E while B causes E without causally necessitating E. If causal determinism holds, then every non-initial event is strongly causally necessitated. Then, we can replace (1) with:

5. If x is responsible for an event E and E is strongly causally necessitated, then x is responsible for at least one event causally upstream of E.

It follows from (5) (with some work) that if an agent like us is responsible for E, then causal determinism is false.

Responsibility

Suppose an action is necessitated by the agent's beliefs and motivational states. Under what conditions is the agent responsible for this action? Most people, compatibilists and incompatibilists alike (Frankfurt is an exception), will say that when the agent's psychological states in relevant respects came from brainwashing, then the agent is not responsible for the action. But of course brainwashing is not the only option here. Compatibilists have to work really hard to say what sorts of histories of the agent's psychological states exclude the agent's responsibility for the action resulting from the states, and there is always the worry that they missed out some particular freedom-cancelling effect.

Step back from the details of particular compatibilist proposals (I think the best one is Mele's compatibilist sheddability condition). What are compatibilists trying to rule out by giving their conditions? It seems to me that, even though they will deny this, what they are trying to rule out is cases where the necessitating psychological states are ones that the agent is not relevantly responsible for. Stipulatively, take an action not to be a psychological state. Then there is a simple principle that we should be able to agree on:

1. An agent is responsible for her action necessitated by the agent's psychological states if and only if the action is caused non-deviantly by the psychological states and the agent is responsible for relevant features of the psychological states.

If you don't think what I've listed is sufficient for responsibility, delete the "if and". My suggestion now is that what the compatibilist really should be searching for are necessary or sufficient conditions under which the agent is responsible for relevant features of the psychological states. Bracket the question whether the compatibilist is likely to be successful. We now have the following logical consequence of (1):

2. An agent is responsible for an action necessitated by the agent's psychological states only if the agent is responsible for some feature of these psychological states.

Now add the following principle, inspired by Galen Strawson:

3. An agent is responsible for a feature of a psychological state only if the agent is responsible for some action causally upstream from that psychological state.

From (2) and (3) we conclude that if every action of Sabina is necessitated by her psychological states, and Sabina has performed only finitely many actions, and there are no causal circles, then Sabina is not responsible for any of her actions.

A technical trickiness in the above is that maybe it's not correct to speak of an action as necessitated by psychological states. For it may be that an action also requires external causes: shooting an arrow requires also a bow. I suppose I could replace "action" by "choice" in the above. Or I could stipulate what I mean by "necessitated by psychological states" in such a way as to allow that there can be external enabling conditions.

Promises to non-existent people

The bindingness of promises after the death of the promisee is debated by philosophers, mainly I think because of the intuition that one can't owe anything to someone who doesn't exist (if I promise something to the Tooth Fairy, I don't need to keep to it). But in fact it seems quite obvious that it is possible to be bound by a promise to someone who doesn't presently exist. Sam is about to go on a trip, traveling until the beginning of next month. He has me promise to take care of his pet rat until his return. It surely does not matter for the bindingness of my promise whether Sam is planning on traveling by car, plane, donkey cart... or time-machine. But if he travels by time-machine to the beginning of next month, then as soon as he has departed it will be true to say that he doesn't presently exist. Yet, surely, he will be right to blame me for breaking my promise if five minutes after his departure I let his rat out to be eaten by the cats, possums and maybe snakes that roam our neighborhood.

If time travel is impossible, I can run the argument with gappy existence. Maybe you don't exist when frozen. Sam has himself frozen until next month. Etc.

Still, the idea that one can't owe something to someone who doesn't exist is plausible. If we are eternalists, we simply say that this principle holds when we talk about existence simpliciter, but not when we talk about present existence. Promises to those who currently don't exist may, however, make trouble for presentists.

Graduate school admissions

I wonder if it wouldn't be a good idea for US philosophy graduate schools to switch from the GRE to the LSAT. At Georgetown, before my time, my colleagues once did an informal study of what information available at admission-time correlated with graduate school success. They found only two statistically significant correlations:

1. scores on the analytic scale positively correlated with success; and
2. the number of undergraduate courses in philosophy that the student had taken negatively correlated with success.

I think (2) can be ignored. It could, for instance, be an artefact of the fact that the mini-study was done on admitted students, and admitted students with few undergraduate courses would probably have to be really good in other ways to get admitted, or would be less likely to have simply naturally drifted into graduate school as a continuation of undergraduate classes.

But (1) strikes me as important. And the GRE has eliminated the analytic section, replacing it with an analytic writing section. The analytic writing scores have low resolution (0-6, in intervals of 0.5). Anecdotal evidence suggests that differences in the analytic writing component do not correlate with the philosophical quality of the student—one knows of really impressive undergraduate students whose scores were pretty low, say 4. The LSAT, on the other hand, continues to have questions that test reasoning skills in the way the old analytic section of the GRE did, and even some that, from the samples that I've seen, combine logical reasoning with reading comprehension in a way that intuitively would very nicely reflect important aspects of philosophical abilities.

Furthermore, there are claims that I've seen that philosophy majors do better on the LSAT than other majors. This suggests that the LSAT is measuring something relevant to philosophy.

Alas, this is not a switch that any one Department can do on its own, and there may be university-wide policy problems. It would need to be done by the profession at large. Though, perhaps, some Departments could make the move of encouraging students to submit LSAT scores in addition to or, if the administration allows, instead of the GRE.

St. Augustine's alternative to the use-mention distinction

1. Man consists of three letters.
2. Man is a rational animal.

Both (1) and (2) are perfectly fine sentences of spoken English, and they are true. But we don't want to conclude from (1) and (2) that:

3. Some animal consists of three letters.

The standard contemporary solution is to say that "man" in (1) is only mentioned, while in (2) it is used, and in writing to distinguish by using quotation marks.

St. Augustine was aware of the difficulty, but his solution was, at least on its surface, different. He posited that the word "man" (or at least "homo") has two meanings. One of its meanings is something like rational animal, while the other meaning is something like the word consisting of the sequence of letters M, A and N. We have a systematic ambiguity running through our language: each word, in addition to its dictionary meaning, also means itself. (An interesting consequence which Augustine I think did not note is that each verb is also a noun.)

We could imagine accepting Augustine's solution, and then when necessary marking the distinction by the use of subscripts: man₁ is a rational animal and man₂ has three letters.

But perhaps we have accepted Augustine's solution? Instead of subscripting a "2", we superscript a quotation mark before and after when we mean the word, and instead of subscripting a "1", we leave the word unadorned. Thus, man is an animal, but "man" is not.

So, is there any difference between Augustine's proposal and the use-mention distinction? Maybe this much: Identifying the concept of the mention of a bit of language saves us from multiplying our vocabulary indefinitely by having to introduce the infinite set of nouns "'man'", "'a man sits'", "'a man sits or floats'", "'a man sits or floats or sits'", and so on.

But since "'a man sits'" surely is a noun denoting "a man sits", we still have introduced an infinite number of nouns. However, we did so by means of a quotation-functor which systematically takes any bit of language and returns a new bit of language denoting that bit of language. So all that the use-mention distinction comes down to is that sometimes bits of language are in the scope of a quotation-functor and sometimes they're not. And it is an accident of the quotation-functor of English, both spoken and written, that the sounds of the denoted bit of language are contained in the noun denoting the bit of language, and this accident we describe by talking of the "use-mention distinction". We could have had a different kind of quotation-functor, for instance using the Goedel number of a bit of language in golden ink to denote that bit of language, and forbidding the use of golden ink for anything else. And then it wouldn't make much sense to talk of use-mention. So the fundamental phenomenon here isn't use-mention, but meta-language.

Open theism and divine error

1. (Premise) If p is overwhelmingly probable on the balance of God's evidence, then God believes p.
2. (Premise) If open theism is true, then some of the propositions that are overwhelmingly probable on the balance of God's evidence are false.
3. Therefore, if open theism is true, God believes some falsehoods.
4. (Premise) God believes no falsehoods.
5. Therefore, open theism is false.

I think (2) is not that hard to argue for on the assumption that there will be infinitely many approximately independent free choices made in the future. Here is a plausibility argument for that assumption: at least some persons will live forever (this follows from divine goodness), and it is plausible that they will always be choosing freely (this follows from the value of freedom). To argue from this to (2), I will make the simplifying assumption that by law the choices are always between options A and B, and that the nth choice occurs exactly n years from now. For any prime number k, let p_k be the proposition that the choice made k years from now, or the choice made k² years from now, or the choice made k³ years from now, ..., or the choice made k¹⁰⁰ years from now will be A. The probability of p_k is 1−2⁻¹⁰⁰ given the setup. Then p_k will be overwhelmingly probable on the balance of God's evidence if open theism is true. But it is also all but certain that at least one of the propositions p_k, where k is a prime, is false. For they are independent, and given infinitely many independent propositions of probability 1−2⁻¹⁰⁰, it is all but certain that at least one is false. Hence some overwhelmingly probable proposition is false.
What about (1)? This is tougher. It is false that rationality requires us to believe everything that is overwhelmingly likely. We have to be careful not to clutter our minds with junk beliefs, because our minds are limited. But this concern does not apply to God. But, maybe, we could say that God should be very careful to avoid false beliefs. However, it would be a sign of irrationality, of an undue punctiliousness, to withhold belief simply because there is some tiny non-zero probability of the belief being false. God is not irrational. So God will believe what is overwhelmingly likely.

Towards a necessary being

Start with these premises:

1. It is a contingent fact that there are contingent beings.
2. No one can believe that there is nothing.
3. Necessarily, if p, then it is possible that someone believes that p.

It follows from (2) and (3) that:

4. It is not possible that there is nothing.

For if it were possible that there is nothing, then at some world there would be nothing, and it would follow by (3) and S4 that it is possible that someone believes that there is nothing, contrary to (2). But (4) is equivalent to:

5. Necessarily, there is something.

But by (1), there is a possible world with no contingent beings. Since (5) assures us that there is something at that world, it must be something necessary. Hence:

6. Possibly, there is a necessary being.

And by S5:

7. There is a necessary being.

We can do one better. Replace (2) with:

8. No one can believe there are no thinkers.

It follows from (3) and (8) that:

9. It is not possible that there are no thinkers.

By (1) it is possible that there are no contingent beings. Therefore:

10. Possibly, there is a necessary being who is a thinker.

And by S5:

11. There is a necessary being who in at least some worlds is a thinker.

That said, I don't know if (2) and (8) are true.

0.999...

Apparently, students often have a difficulty accepting that 0.999... = 1.  Here is a really neat paper explaining that maybe they are not being stupid.

Two kinds of responsibility

I hire Jack the mad brainwasher to capture a random Wacoite and brainwash the victim into burning up a local hardware store's stock of ramin dowels.[note 1] Jack captures Bob and brainwashes him into this, and as a result Bob promptly burns up the local hardware store's stock of ramin dowels. I am responsible for several things, notably:

1. my hiring Jack to fulfill such-and-such purposes
2. Jack's brainwashing the victim
3. the victim's burning of the dowels
4. the dowels' ceasing to exist.

Of these four things, however, only (1) is an action of mine. Items (2) and (3) are actions, but not my actions: I don't brainwash the victim or burn the dowels, but I have the victim be brainwashed and have the dowels burned. However, (2)-(4) are intended and foreseen consequences of my action, and indeed my hiring Jack to fulfill such-and-such purposes is my having the victim brainwashed and my having the victim burn the dowels. Thus, I am fully responsible for (1)-(4). But the responsibility involved in (1) differs in kind from that in (2)-(4). For in (1), I am responsible in a normal first-person-action sort of way. I am not merely responsible for the occurrence of Jack's being hired: I freely and with responsibility hire Jack. And it is by freely and with responsibility hiring Jack that I assume responsibility for (2)-(4).

Actions (2) and (3) are ones I am responsible for, but I am responsible for them in the way one is responsible for occurrences or events, and not in the way one is normally responsible in a first-person-action sort of way. And of course (4) is not an action at all. We might call my responsibility for (2)-(4) "event-responsibility", while my responsibility for (1) is "agency-responsibility". Observe also that Jack is agency-responsible for (2) and event-responsible for (3) and (4), while (unless there is some further backstory) Bob is not responsible in any way for any of (1)-(4).

Now, I think it plausible that agency-responsibility is intrinsically a different kind of responsibility from event-responsibility. For instance, event-responsibility does not essentially depend on my mental state during the event I am responsible for, but agency-responsibility does essentially depend on my mental state during the action I am agency-responsible for. I could be dead by the time the event I am event-responsible for occurs. There is even a little tense difference. If I am event-responsible for an event E at t₂, by virtue of an action of mine that I undertook at an earlier time t₁, the better thing to say at t₂ is that I was responsible for E. (This is particularly clear in backwards-causation cases. If in the year 2020 Smith sends a bomb backwards in time in a time-machine, and it explodes in the year 2009, in 2009 we could correctly say: "Smith is not yet responsible for this explosion." He will be responsible for it in 2020.)

Normally, I have agency-responsibility for my actions and event-responsibility for their consequences. But it is also possible for me to have event-responsibility but not agency-responsibility for my own actions. For suppose that the Wacoite that Jack randomly kidnaps happens to be me. I think I am no more agency-responsible for the burning of the dowels than Bob was in the original story. I am in exactly the same boat as Bob was. (We can even tweak the story so I am just as surprised as Bob was. For I could have my memory of my hiring Jack wiped as soon as I've hired Jack so that I wouldn't give my part in the plot away.) While the action of burning the ramin happens is done by me, it is not done by me in such a way that I would be agency-responsible for it. But I am event-responsible for it, exactly as I was in the case where Bob did it.[note 2]

If I am right about this, then some examples in the literature (e.g., in Randolph Clarke's response to van Inwagen's omission-centered versions of the Principle of Alternate Possibilities) in which one is responsible even though at the time of the action or omission one cannot act otherwise, where one is responsible for the action or omission because one is responsible for the impaired mental state that led to it, conflate two distinct kinds of responsibility. In cases where one's action or omission results from a severely impaired mental state that one has freely and responsibly produced, one may be agency-responsible for the production of the mental state, but one is only event-responsible for the action or omission flowing from the mental state. As far as one's responsibility goes, that action or omission could just as well have been done by a third party in whom one produced the mental state.

A more difficult question is about cases where with responsibility I produce a normal mental state that then constrains me to do something. Do I then bear only event-responsibility, or do I bear agency-responsibility? Do the souls in heaven bear agency-responsibility for acting rightly (as such) or only event-responsibility? (There is also the divine case, but I think divine simplicity complicates that case further, so it might go different from the souls-in-heaven case.) My incompatibilist inclinations based on the above discussion push me to thinking that even when one induces a normal mental state that determines an action, one only has event-responsibility for the resulting action. But the case in heaven might be different, because there could be miracles involved. It could, for instance, be the case that just as, plausibly, Christ's sacrifice of the Cross is really present at Mass[note 3], so too our graced earthly decision to follow Christ is present in our heavenly life and the heavenly decision to act rightly is numerically identical with our conclusive earthly decision.

Frankfurt, incompatibilism and finking

Some dispositions are deterministic, or nearly so. In normal conditions, in the presence of the trigger, they do their one thing. Sugar at room temperature in water dissolves. Some dispositions are indeterministic. The electron in a mixed up/down state sent through a magnetic field will go up or down; it might go up but it might also go down. We now know better than to try to define dispositions in terms of conditionals, unless perhaps we are fond of ceteris paribus or "normally" clauses, and even then defining dispositions in terms of would-conditionals is problematic. For the dispositions can be finked. Sugar is not such that it would dissolve at room temperature in water if there were a counterfactual intervener who would vaporize it as soon as it was dipped in water.

For exactly the same reason, to define a disposition as indeterministic by means of might-conditionals is problematic, and we should know better than to try. Let's say that flipping a coin has an indeterministic disposition to result in heads or in tails. But we can imagine Black, a counterfactual intervener who, as soon as the coin flies in the air, can tell which way it's going to land if it's not interfered with, and if it's not heads, he takes away the coin's disposition and makes it land heads. In the presence of Black, it's false that the coin might land tails. But the coin still has an indeterministic disposition in the presence of Black, even if it exhibits not even the least flicker of freedom (e.g., take the case where Black has access to divine middle knowledge about how the coin would go) and worries about counterfactual interveners should not talk us out of the useful notion of an indeterministic disposition.

The Principle of Alternate Possibilities (PAP) is closely analogous to a might-conditional characterization of an indeterministic disposition. And just as we now know we should not try to characterize indeterministic dispositions by means of "if ... might ..." (at least not without a dollop of "normally"), likewise we should not try to characterize freedom by means of "could have" or "might". But just as the realization that dispositions can be finked should not make us abandon the idea that some dispositions—say, quantum mechanical ones—are indeterministic, so too Frankfurt cases should not make us abandon the idea that something indeterministic is going on. It is reasonable in the face of worries about finking simply to take dispositions to be primitive, and in particular to take the notion of an indeterministic disposition with multiple outcomes (and maybe with probabilistic tendencies) to be primitive. And then it is reasonable to take it to be a necessary condition on a free choice that it is an exercises of an indeterministic disposition.

There are some pretty strong intuitions behind PAP—between Hume (inclusive) and Frankfurt (exclusive), compatibilists tended to feel the need to do justice to it, despite it being very difficult to do so satisfactorily. If a formulation of PAP can be given that is not subject to counterexamples and appears to capture a good deal of the intuitions behind PAP, there will be good reason to believe it. And I think there is such a formulation: The agent free to choose A in circumstances C has an indeterministic disposition to choose A or to choose something else in C. This seems to capture some of the intuition behind PAP, and also captures the intuition that some libertarians have that Frankfurt examples are missing something important. The down side of this formulation of PAP is that it directly denies that all dispositions are deterministic, and hence isn't going to be neutral ground. But that's fine. The neutral ground now shifts from PAP to the idea that "something like PAP is true".

Interestingly, fairly recently some compatibilists have started to try to rehabilitate PAP using dispositions (see, for instance, the references in this paper as well as this one). So the incompatibilist who makes this move will have to see if her proposed revamping of PAP is more plausible than the proposed compatibilist ones. But a revamping of PAP should be done, as PAP attempts to capture something central to our intuitions about freedom. And my point remains: to see Frankfurt examples as destroying the idea of alternatives as central to freedom is like seeing C. B. Martin's work as destroying the idea of dispositions.