Supervenience and counterfactuals

On typical functionalist views of mind, what mental states a physical system has depends on counterfactual connections between physical properties in that system. But we can have two worlds that are exactly the same physically—have exactly the same tapestry of physical objects, properties and relations—but differ in what counterfactual connections hold between the physical properties. To see that, just imagine that one of the two worlds is purely physical, and in that world, w₁, striking a certain match causes a fire, and:

1. Were that match not struck, there would have been no fire.

But now imagine another world, w₂, which is physically exactly the same, but there is a nonphysical spirit who wants the fire to happen, and who will miraculously cause the fire if the match is not struck. But since the match is struck, the spirit does nothing. In w₂, the counterfactual (1) is false. (This is of course just a Frankfurt case.)

Thus physicalist theories where counterfactual connections are essential are incompatible with supervenience of the mental upon the physical.

I suppose one could insist that the supervenience base has to include counterfactual facts, and not just physical facts. But this is problematic. Even in purely physical worlds, counterfactual facts are not grounded in physical facts, but in physical facts combined with the absence of spirits, ghosts, etc. And in worlds that are only partly physical, counterfactual connections between physical facts may be grounded in the dispositions of non-physical entities.

Natural event kinds and Frankfurt cases

Choices are transitions from an undecided to a decided state. Suppose choices are a natural kind of event. Then only the right sort of transition from an undecided to a decided state will be a choice.

Here, then, is something that is epistemically possible. It could be that a choice is a kind of thing that can only be produced in only one way, namely by the agent freely choosing. Compare essentiality of evolutionary origins for biological kinds: no animal that isn’t the product of evolution could be a lion. Of course, one can have something internally just like a lion arising from lightning hitting a swamp and one can have a transition from an undecided to a decided state arising from a neuroscientist’s manipulation, but these won’t be a lion or a choice, respectively.

If this is right, then it seems no Frankfurt story can make a choice unavoidable. For to make a choice unavoidable, an intervener would have to be able to cause a choice in case the agent wasn’t going to do it. In other words, there will be no Frankfurt argument against principle of alternate possibilities:

• If x chose A, then it was causally possible for x not to have chosen A.

This is rather flickery, though: it doesn’t require that x could have chosen non-A.

Acting otherwise and choosing otherwise

The traditional Humean compatibilist position, prior to Frankfurt's examples, is that a deterministic agent who is free could still have acted otherwise because

1. had she wanted to, she would have acted otherwise.

But the question relevant for determination of responsibility isn't whether one could have acted otherwise (uncontroversial Frankfurt cases, where Black acts only after the choice has been made, show that), but whether one could have chosen otherwise.

I wonder if a similar conditional-type of story can be told about the ability to choose otherwise? The obvious analogue to (1) is to say that

2. had she wanted to, she would have chosen otherwise.

But actually this condition is often false despite the agent being free. For it often, perhaps even always, happens in the situation of a free choice that the agent both wants to choose A and wants to choose B, but because she cannot go for both, she must choose between them. Suppose the agent chooses A. It is surely false that had she wanted to, she would have chosen B. For she did want to choose B, and did not—what better refutation is there of the subjunctive conditional than that the antecedent is true but the consequent is false?

But presumably in this case the agent didn't on balance want to choose B. So perhaps our compatibilist-friendly alternate possibilities condition is:

3. had she on balance wanted to, she would have chosen otherwise.

That may be true, but it is obviously a very weak condition. Perhaps even a trivial one. Indeed, we might reasonably say that what is constitutive of the agent's on balance wanting to choose A is precisely that she is such that given the choice she will choose A. If so, then (3) is trivially true in every case. And even if it's not trivially true in every case, it's going to be true in too many cases of freedom-canceling brainwashing to capture the alternate possibilities intuition.

It may be wiser, then, for the compatibilist to simply retreat from affirming any kind of alternate possibilities condition on freedom. But there is a cost to that.

(I am omitting consideration of the usual finkish objections (of which Frankfurt cases are one of the earliest examples) to conditional analyses. Maybe there is some way around those.)

Frankfurt and choices

Here is a picture of how choices work. Suppose a binary choice between A and B, and suppose what you choose is A. Then there are two events. There is a token of the event type c(A,B) of your choosing between A and B, and there is the token of the event type w(A) of your willing A (or of your "being set" for A). What makes it true to say that you chose A over B? It is not simply that a c(A,B) event happens and then a w(A) event happens. For instance, that a c(A,B) event happens and then a w(A) event happens happens is compatible with the hypothesis that first you're choosing between A and B, and then something external causes you to interrupt that process of choosing and forget all about B, and instead you embark on a process of choosing between A and C, and you choose A over C and hence a w(A) event happens. Nor is it true that you chose A over B provided that the w(A) event follows right after the c(A,B) event. For it could be that some external cause causes the w(A) event while suspending the causal effects of the c(A,B) event. Then you didn't choose A over B, because the choosing between A and B was causally irrelevant to your choosing A.

So, maybe we should rather say this: What makes it true to say that you chose A over B is that a w(A) event is caused by a c(A,B) event. That is close, but not quite right. After all, there could just be some weird causal chain on which a c(A,B) event causes an external cause to cause w(A), and that won't be a case of choosing A over B. We need to say:

• CHOICE: What makes it true to say that you chose A over B is that a w(A) event is caused by a c(A,B) event in the right way.

And as is ever the case in philosophy, we can't spell out what "in the right way" means.

Notice that in the above I said nothing about whether the causation between the c(A,B) event and the w(A) event is deterministic or not. The above story about choosing is one that both compatibilists and libertarians can adopt, though they will likely spell out "in the right way" differently. It is likely that libertarians will understand choice in such a way that the "in the right way" condition requires, among other things, that the causation be indeterministic.

So what's the point of this? Here is one point. Frankfurt proposes as a counterexample to the principle that if you are freely doing something then you could have done otherwise a case where a neurosurgeon watches what you're about to do. If you're about to do B, then he intervenes and makes you do A instead. But if you're going to do A, he doesn't intervene. You do A, and so he doesn't intervene. Surely you're free, but you couldn't have done otherwise.

Fair enough. But the libertarian really cares more about choices here. It is the choice in which you acquire primary responsibility. So, the libertarian can very reasonably retreat to:

• PAPC: If you freely chose A over B, then you could have failed to choose A over B.

But it is far from clear that the neurosurgeon case challenges PAPC in a way that does not beg the question against the libertarian. For the neurosurgeon would have to be able to ensure you to choose A over B, if you were about to choose B over A, in order for the story to work. But how could he do that?

One option would be to modify the c(A,B) event so that it deterministically causes a w(A) event. But the libertarian can reasonably say that a part of the "in the right way" condition in CHOICE is that w(A) is caused indeterministically by c(A,B). The other way would be to produce w(A) by means of some external cause, but then the w(A) event either won't be caused by the c(A,B) event or won't be caused by it in the right way, and so the agent won't be choosing A over B.

These considerations make it plausible that on the libertarian's view, no one can ensure you will choose A over B. And of course the claim that no one can ensure you will choose A over B is incompatible with determinism (since if determinism is true, someone could set up conditions before your conception such that you would have to choose A over B). And this, in turn, suggests that the libertarian can afford to say that to freely choose A over B is just to choose A over B.

I suspect that my above remarks are partly inspired by Richard Gale telling me that he thought Frankfurt and Locke showed you couldn't act otherwise but not that you couldn't choose otherwise. But I didn't manage in the above to show that if you freely chose A over B, you could have chosen B over A.

Mattering

Harry Frankfurt thinks that the only thing we can do is to see whether a given thing is one that we care about. Consequently, Frankfurt identifies what is important with what we care about. But the "consequently" does not actually all follow. For in exactly the same way we might argue that the only way of figuring out what really exists in physical reality is by examining what we perceive with our senses, and thus conclude, with Berkeley, that to exist in physical reality just is the same as to be perceived. We can say that the fact that we care about something is evidence as that it is important, just as the fact that we apparently perceive something by our senses is evidence that the object is physically real, without denying that I might care about something unimportant or have hallucinatory perceptions of unreal things.

Frankfurt counterexamples and compatibilists

Frankfurt counterexamples to the Principle of Alternate Possibilities (PAP) have worried libertarians. However, they should have also worried compatibilists. Traditionally, compatibilists have accepted PAP, but given it a counterfactual spin (see my previous post). Suppose Jones freely chooses to push button A. On the standard Humean analysis, this implies that were Jones to have chosen not to push A, he would not have pushed A. But a fairly crude Frankfurt case will provide a counterexample to this. Imagine Black stands by with his neuroscope and has a firm plan that if he sees Jones choosing not to push A, he will make Jones push A. Then it is true that were Jones to have chosen not to push A, he would still have pushed A.

Hence, Frankfurt cases are also counterexamples to the Humean version of PAP, and indeed are better counterexamples to it than to the libertarian PAP (standard Frankfurt cases are known to beg the question against many libertarians, since they require a sign that is nomically connected with the action in a way that many will not accept).

PAP is very plausible. So it is an important task not just for the incompatibilist but also for the compatibilist to find a version of it that survives Frankfurt counterexamples. Here is my hypothesis: A plausible PAP that survives Frankfurt counterexamples will still be sufficient for incompatibilist arguments once one plugs in a non-Humean analysis of "could have". If this is right, and if I am right that everybody needs a PAP, then Frankfurt examples do not in the end weaken the incompatibilist's case—just as before Frankfurt examples the question was whether the Humean analysis of "could have done" was right, so too this is the question after Frankfurt examples, once one correctly formulates PAP.

My own preferred PAP is flickery and fits well with the above remark: If x freely does A, then x could have failed to freely do A. Actually, it may be that the libertarian is in a better position than the compatibilist when it comes to formulating a PAP. For flickery PAPs like the above don't fit well with the Humean analysis of "could have done". Would the Humean want to say that "x could have failed to freely do A" means "were x not to have willed to do A, then x would not have freely done A"? But that's just a tautology and does no justice to the intuitions behind PAP.

In summary: Everybody who believes in free will—compatibilist or incompatibilist—needs PAP. Frankfurt examples affect both the compatibilist and the incompatibilist. It is a bit easier for the incompatibilist to find a replacement for PAP that survives the examples, but the replacement-finding task is one that both compatibilists and incompatibilists need to engage in. But the real question, as before Frankfurt, is how to understand "could have done" conditions.

Lewis, free will and miracles

Compatibilists like Hume accept the Principle of Alternate Possibilities (PAP): if x freely does A, then x could have refrained from doing A. However, they give a counterfactual spin to the "could have": x could have done A if and only if were x to have willed to do A, x would have done A.

Suppose now:

1. This Humean analysis of "could have" is correct.
2. Lewis's account of counterfactuals is correct.
3. Determinism holds.
4. On some non-initial occasion I could have done otherwise (in the Humean sense).

(An occasion is initial provided it happens at the first moment of time.) It follows from these that in the occasion mentioned in (4), I could have acted in such a way that a w₀-miracle would have occured, where a w-miracle is a violation of the laws of w, and where w₀ rigidly designates the actual world.

The argument is simple. Suppose on that occasion I did A. Let p be the proposition that on that occasion I did not do A. On Lewis's account of counterfactuals, I evaluate counterfactuals of the form "were p to hold, q would hold" by looking at worlds close to w₀ but where p holds, and in a deterministic case, these worlds match the actual world up to near the time of that occasion, and but depart therefrom in a way that goes against the laws of the actual world, i.e., in a way that is w₀-miraculous. Hence, "were p to hold, a w₀-miracle would occur" holds, and by the Humean analysis of "could have", it follows that I could have acted in such a way that a w₀-miracle would have occurred.

Frankfurt and free will

Here is a version of the Principle of Alternate Possibility that is immune to all of Frankfurt's counterexamples:

If x freely does A and Mr Black is nowhere near, x could have refrained from doing A.

An argument against psychological identity theories: accuracy and reliability of copying

According to the psychological identity theorist, if the contents of your mind (e.g., brain or soul) are copied into another mind (brain or soul), with the original mind destroyed, you will survive and come along with the copied contents. Now, plausibly, perfection is not needed in the copying. If one digit in the memory of your phone number is not copied over, and everything else is, then surely you will survive that, if you would survive any such copying operation at all. But some fidelity in copying is needed.

We can measure a copying operation in several ways. For any portion of the information to be copied (think of a 0/1 value or a continuously variable value, for instance), we can talk of the accuracy of the copying, which says how similar is the output of the copying procedure in fact was to the input, and the reliability of the copying, which is a measure of how likely it was that the output would have a given accuracy. (We can come up with various ways of quantifying this, but it doesn't matter.) Now, for a mind-copying to at all plausibly move a person from one mind to another, there has to be both overall accuracy and overall reliability. One won't do without the other. One could, after all, have very high reliability in copying, i.e., a high probability of accuracy, but be unlucky so that the the output is completely unlike the original. The psychological identity theorist would not say the person was moved then, since few of the memories and character traits would have survived. Nor would high accuracy with very low reliability transfer a person. Take a limiting case of low reliability where the output is entirely random and independent of the input. Nonetheless, one might be lucky, with the output by chance being just like the input. That wouldn't result in person-transfer, either. After all, if my mind is destroyed, and completely by chance a man arises randomly after lightning hits a swamp in Transylvania and that many by chance has the same mental states as I did, that man wouldn't be me.

So, we need both high accuracy and high reliability for person-transfer to occur. But now note that reliability is in part an extrinsic criterion. It measures the probability of accuracy. Suppose that you're undergoing a mind-content transfer procedure, and Dr. Black, the evil neurologist, after having starred in Frankfurt's Neurologist, XIII, happens to be sitting around in the lab. Now, almost all of the time when Dr. Black is in a lab when a mind-content procedure takes place, he hijacks the procedure, and ensures that while the subject's original mind is destroyed, the data transfered to the output mind in fact is a very poor copy of the subject--in fact, it is a copy of Dr. Black's vicious mind. This time, however, Dr. Black is distracted, and forgets to hijack the procedure, and only remembers once the operation is done. The reliability of the copying process is very low--Dr. Black was very likely to hijack it.

This leads to the following absurd conclusion. If person-transfer through copying of content is possible, then whether Dr. Black is in the room when the procedure happens determines whether the subject survives the procedure--even if Dr. Black in fact is distracted and in no way causally interacts with the process. Since this absurdity comes from psychological identity theories, we should reject psychological identity theories.

But what if one bites the bullet and says that whether Dr. Black is in the room when the procedure happens does determine whether one survives. Now I have a second move. What happens in copying is a causal process whereby an earlier mind causes a later mind to have the same content. The same thing is happening in us all the time. Our brain's having a certain neural state at t₁ (e.g., a state correlated with a belief that 2+2=4) will often cause that brain to have the same state at t₂. Our brains are always in a state of flux, and the brain's preserving of information is relevantly very much a process of copying. (Plato says something like this in the Symposium.) Suppose now that you live your ordinary life, but Dr. Black keeps on shadowing you, with his neurological equipment, and he keeps on planning to subvert your brain's data preservation processes, but whenever he is about to do so, by a very small chance, he is distracted and does not. In fact, Dr. Black does not interact with you causally. But his presence makes the reliability of the transmission of data from the past to the future in your mind be very low. By the same reasoning as above, it follows that the mere presence of Dr. Black kills you--even though he in fact does not interact with you.

Frankfurt and functionalism

We learn from Frankfurt counterexamples to the Principle of Alternate Possibility that we should not use counterfactuals and nomic modality to characterize intrinsic features of things. What Frankfurt cases show is that it is frequently possible to modify counterfactual and nomic modal properties of a thing, event or process without actually causally affecting the thing, event or process in itself.

This is a useful lesson. Here is one interesting application: standard functionalist theories of mind cannot be right. I will give the roughest sketch of the argument. Start with two observations:

1. Functional characterizations of a system depend crucially on the system's counterfactual properties. (An and-gate is a system of which it is true that it would produce a 0 given two 0's or one 0 and one 1, and would produce a 1 given two 1's, even if in the course of the system's functioning it is actually only fed one of these options.)
2. That a system exemplifies a functioning mind is an intrinsic property of the system.

Now, what we learn from Frankfurt cases is that we can radically alter the counterfactual properties of a system in just about any way we wish without actually causally interacting with the system, and hence without altering its intrinsic properties. It follows from this observation and (1) and (2) that whether a system exemplifies a functioning mind cannot be a matter of the system's functional characterization. (We can, for instance, make sure that a given logic gate could never have produced a different output from what it actually produced, because someone watching the system would have intervened and forced it to produce the output it actually produced, had this watcher seen the inputs being different. But if this were done, then this would not be an and-gate, as it would not have the counterfactual properties of the relevant kind of logic gate.)

I should say that there is a way out of this argument, and it is to embrace an Aristotelian functionalism that instead of characterizing functions counterfactually, characterizes them teleologically. But that is not what "functionalism" means in the context of the theory of mind. (One might also try to do the Aristotelian move and define the functionalism evolutionarily. But not hard to see that this fails [e.g., see this, or this, or just extend the argument here].)

Or maybe we could try to get out of the argument by supposing that we can cut a system away from its environmental context and characterize the functioning of the system by looking at how the system would function apart from its environment, thereby isolating the system from the kind of purely counterfactual interference that a Frankfurt-style watcher would impose on it. But that simply doesn't work. How does the human body work absent its environmental context? It simply dies, pretty quickly, when not supplied with air, food and water.

Of course one might try to define a notion of an appropriate environment and then calculate the counterfactuals relative to that. But if we are allowed to be completely free in choosing what environment counts as appropriate, then just about everything is up for grabs. And if there is an objectively appropriate environment for the system, then again we get some version of Aristotelian teleology, which is not what functionalism wants.