Monday, April 21, 2008

The symmetric forking model of free will

Until very recently (the last hour!) I thought the following was quite a good model of what typically happens when a normal human agent x freely chooses between actions A and B: There are worlds wA and wB and a time t such that

  1. wA and wB coincide at all times earlier than t;[note 1]
  2. wA and wB have the same laws, and x is a normally functioning agent in both worlds in respect of the decision between A and B; and
  3. At all times later than t, it is true at wA that x has already freely chosen A, and it is true at those times at wB that x has already freely chosen B.
From (1), we can conclude that at no time earlier than t is the case at wA or wB that the agent has already chosen between A and B, but by (3) at all times later than t this is the case. Call (1)-(3) the Symmetric Forking Model.

It is, I think, prima facie plausible, at least to libertarians, that at least some normal human choices satisfy the Symmetric Forking Model.

However, it now seems to me that the following three propositions are incompatible (though we may need to tweak them slightly to get this result—I am just sketching this):

  1. The Symmetric Forking Model holds of some normal human's choice.
  2. There is a certain tiny but positive amount of time e such that a normal human cannot be aware of distinctions between events where the person gets to observe the distinction for an amount of time less than or equal to e.
  3. Necessarily, if one has freely chosen A, then one was aware of the choice of A as a choice of A.

Why are these incompatible? Well, start with the Symmetric Forking Model and form worlds w*A and w*B which coincide with wA and wB, respectively, up to time t+e, but where our agent x is miraculously made unconscious at time t+e. Then, by (5) (with a bit of handwaving), the agent in w*A cannot be aware of having chosen A and the agent in w*B cannot be aware of having chosen B. For the agent does not get to observe the difference between choosing A and choosing B before t, since the two worlds coincide up to t, and hence only gets to observe the difference between t and t+e, which by (5) will not be enough.

The plausibility of (5) and (6) is enough to make me have serious doubts about (4). On the other hand, I can also see how the plausibility of (4) might be seen as casting doubt on (6). I am in fact suspicious of (6), so I do not think it is absurd to hold on to (4) but reject (6), if there is good reason to hold on to (4).

One might think that libertarianism commits one to (4). But that, I now think, is false. For one might have a case where the alternative to making at t the choice to do A is not making another choice, but temporizing and taking longer to make up one's mind.

I think it is an interesting challenge for a libertarian to construct a model of free choice compatible with (5) and (6). I have some somewhat inchoate ideas in this direction. But that may be fodder for another post.

[Edited to rename "Forking Model" to "Symmetric Forking Model", to distinguish this model from a different model that hopefully will figure in tomorrow's post.]


Mike Almeida said...


It looks like your (1)-(3) leave no room for the action of making a choice. Before t no choice is made and after t the choice has already been made. If making a choice to A is also an action (along with performing A), then (1)-(3) cannot be right. You would want wA and wB to branch before t, if A/B are performed in wA/wB respectively at t.

Alexander R Pruss said...


I am not sure I understand. Presumably, on the forking model the action of choosing A happens either at t or on a time interval culminating at t. The time t is supposed to be the branchpoint between the world where one chooses A and the world where one chooses B.

That said, I am uncomfortable with thinking of the choice as a further action, because that threatens a regress.

philotheos said...

Perhaps we can deny (6). Something in place of (6) that might satisfy our intuitions might be:

(6*) Necessarily, if one has freely chosen A, then (if one reflects on whether A was freely chosen, then one is aware of the choice of A as a choice of A).

This would not be inconsistent with (4) and (5), since the antecedent of the conditional in the brackets not satisfied should the agent be made unconscious at t+e.

Independantly, it does seem to be the case that (6) is false. For we do seem to make free choices, of which we might not be aware of as choices, quite often. For we might not even be consciously thinking about the choice after the choice is made. (I take it that consciousness is a necessary condition of awareness as it is used here.)

Alexander R Pruss said...

I like the modification of (6).

It is a bit worrying, though, if one should be morally responsible for a choice one wasn't aware of making... I am willing to bite that bullet, but this ingestion of lead makes me uncomfortable.

Mike Almeida said...

I am not sure I understand. Presumably, on the forking model the action of choosing A happens either at t or on a time interval culminating at t.

It cannot happen at t, since t has no duration and choosing has some duration. And it cannot happen before t, since the worlds in which B and A are chosen are identical until t. There is no regress worry, since you can reasonably deny that though you must choose A in order to do A, you need not choose to choose A in order to choose it. There are good empirical reasons confimring this.

Enigman said...

Re philotheos, lack of awareness shouldn't be a logical problem, e.g. suppose one has acquired a habit, as a result of various choices. One remains morally responsible for the subsequent, habitual actions, to some degree?

Enigman said...

Does choosing take time? In ordinarily described choices (this hat or that) yes; but the elementary choices, those moments where the information is collapsed, where an option is just plumped for? Phenomenally such moments seem instantaneous (and the neurological evidence is arguably about something else entirely).

So I personally like the 1-3 model for the atomic choices; but since an unknown (fuzzily large?) number of them make up an ordinary choice, so such choices (as I think mike almeida has in mind) require time for choosing - but for them there would be different possible ways of choosing A or B, which would complicate the model in other ways too...

Alexander R Pruss said...


I see what you're getting at. Back in the day when I liked the symmetric forking model, I thought the following. We need to distinguish the event of choosing A from the event of choosing between A and B. The event of choosing between A and B can be entirely the same between the two worlds--the same considerations are in place, etc. And then you get divergence.

Suppose divergence happens at t. Then there are two ways I could identify the event of choosing A. First, I could simply identify it with the event of divergence. (This event might have zero temporal length or it might have limiting temporal length--think of the event of "starting to move".) Second, I could say this. The event E1 of choosing between A and B happens on some interval of times open at the upper end like, say, [u,t) (or (u,t), but the lower end won't matter for us). The event E2 of choosing A then is located temporally on the interval [u,t] which is closed at the upper end, and E2 includes E1 as a sub-event of itself, but includes the diverging.

Maybe you don't find this plausible. But for a libertarian there is, I think, significant reason to opt for a symmetric forking model. Let S be the set of times at which it is not yet determined (by the state of the world and the laws) that one will choose A. The libertarian is apt to say that at every time outside of S, the choice has already been made, since the libertarian thinks that it is only once the choice has it been made that it can be determined that one will choose A.

Now, let t be the supremum of the times in S. At every time before t, the choice has not been made, nor is it determined that A will be chosen. At every time after t, it is determined that A will be chosen, and hence the choice has already been made. Moreover, there is a world where one makes the other choice and where everything goes the same way in S, but then one doesn't choose A. If not choosing A counts as a choice of not-A (or maybe not-A-yet), which my next post on the topic will question, we surely have the requisite kind of divergence between worlds precisely at t.


Shouldn't it be the case that if we're not aware of the atomic choices, then we're not responsible for the atomic choices, and hence neither are we responsible for the larger choices which are only choices because of their composition from atomic choices?

Also, I am not sure habitual choices are literally choices. Nor am I sure that we can be guilty or innocent of them except in a legal sense, if they are literally habitual in the strong sense that we couldn't not make them.

Heath White said...

I think the contrast between two divergent worlds has to be that between choosing A and not choosing A, just on logical grounds. And it doesn't follow, from not choosing A, that you do choose anything else.

Also, I think (6) is probably false. I'm sympathetic with philotheos' (6*) but I have a few worries centering around the idea that a Christian is going to want to say that people freely choose damnation, hell, absence from God, etc., but it won't be true that they choose them under those descriptions. Probably some massaging to the idea of 'freely' is in order here.

All that, insofar as I'm sympathetic to the libertarian posiiton at all, which I only am on Mondays and Thursdays.

Alexander R Pruss said...


I am inclined to agree with you on the contrast, but it goes against the following argument:

a. You are only responsible (in the fullest sense) for your choices.
b. If you deliberated whether to choose A, could have chosen A, and without any determination or coercion (internal or external) you did not choose A, then you are responsible (in the fullest sense) for not choosing A.

I'm on the deck of a ship. You're drowning. I am deliberating whether to throw you a life preserver. (That I am actually deliberating about this might be my first fault, but never mind.) I could have chosen to do so. But instead I make no choice (and not because I am interrupted--I just make no choice). Surely I can be fully held responsible. But that goes against (a). To resolve the conflict with (a) one can argue that I've misdescribed the case: I have made a choice not to throw the life-preserver yet. So I always choose between A and at-least-not-yet-A.

Twas I Who said...

Shouldn't it be the case that if we're not aware of the atomic choices, then we're not responsible for the atomic choices...? We make the atomic choices, so we're responsible for them. We're aware of what we choose between (although not in the propositional way in which we are aware of it being the case that the cat is, or is not, in the hat, for example) because otherwise we cannot choose. We are hardly ever aware of the exact truth, about the objective situation, as such, and so social or legal ascriptions of moral responsibility are inevitably fuzzy and iffy... Habits are indeed analytically complicated, yet so easy to acquire! Sloth is one such, and yet it is a Sin. Still, I must look at your asymmetric model next...

Heath White said...


If you want to maintain that we are always choosing between A and not-yet-choosing-A, then I think we are making such "choices" constantly. At virtually every waking moment, there are all sorts of things I could, but choose not, to do. I'm not even sure I'm aware, in any interesting sense, of all the things I've chosen not to do.

This notion of "choice" is very far from the libertarian's ordinary phenomenological one. That raises my suspicions that either it's a bad analysis of libertarian choice, or libertarian choice isn't what it's ordinarily taken to be, or both.

Alexander R Pruss said...


I am uncomfortable with that, too.

But there does seem to be something right about the fact that I am fully responsible for the fact that five minutes ago I did not dance a jig in the street (it didn't occur to me). Moreover, the responsibility seems non-derivative. Is this a choice? It doesn't seem to be one. But if not, then we're responsible, in a primary sense, for something other than choices.

I really don't have a good story here. As I said, I used to accept the symmetric forking model, but I am now sceptical of it.

Enigman said...

One can be responsible for the actions of a pet dog that one has completely forgotten about (and if they are bad, then precisely because one has completely forgotten about it) of course, and one is a unity even if one is never aware of one's full extent; so why should one not be responsible for choices one makes (necessarily between objects (in the fuzzy logical sense) of which one is then aware) even were one never aware of making the choice.

One would be aware of the things chosen between, at the time, and one would actually plump for one of them, so to speak (and presumably be aware of that one in particular, although it may be forgotten about quickly enough and never recalled, in the swim of things), but why would one have to be aware of that as a choice (or recollect being aware of the things chosen)?

Even with habits, often one plumps for the habitual thing, or one is at least aware of one's general state which includes some awareness of having so plumped, and one lets it pass. Where even that is lacking, perhaps there is no choice, but there were choices necessarily (or it did not become a habit) so one is responsible, as in the pet dog case.

The idea of being responsible for not doing what one did not choose to do because one did not even make a relevant choice is a grey area, no? Suppose dancing such a jig would have, unbeknownst to you, led to many terrible things, so that you would have felt bad about not thinking more about it before so jigging. Could you then rightly feel good about your responsibility (whereas if the pet dog did bad things then you should feel bad about that of course)?

Alexander R Pruss said...

The pet case is an interesting case, but I think it's different. I think there is a difference between the kinds of responsibility that we have:
(a) for a choice
(b) for the intended effect of the choice
(c) for the unintended but foreseen effect of the choice. The responsibility for the dog's actions may fall under (c), or it may be a yet fourth kind of responsibility (it reminds me of the forensic theory of original sin that Reformed Christians have). But in any case it is different from (a).

The kind of case that I am thinking of involves a responsibility like that in (a), even though perhaps there is no choice made.

Consider this case. George sees Jennifer drowning. He hears her calls for him to throw a life preserver. He understands what is happening, but makes no decision about it, though he could have. He just stands there, thinking about the second version of Kant's transcendental deduction. (Variant: He starts to think about whether to throw the life preserver, but gets bored with the question, and before coming to a decision, he starts to think about Kant.)

Is this case logically coherent? Is George responsible in the (a) sense for having failed to make a decision to throw the life preserver?

I don't really know.

This is closely related to questions Michael Barnwell raised at the SCP Eastern Meeting concerning our responsibility for actions we apparently culpably failed to think about the consequences of, like that of the archer who shoots into the wood without thinking about the possibility of someone being there.