Compatibilism and Prepunishment: A Response to Smilansky?

Posted by oisin on May 9th, 2008

I want to try out a thought here and get some feedback. In particular, I may have gotten some of the math wrong, but in broad outline I think the following argument against Smilansky has something to be said for it. If not, I trust someone will let me know(!).

Smilansky’s argument:

If compatibilism is true, then the world could be deterministic and agents could be free and responsible. In principle, we could come to know (presumably by deduction) that an agent X is going to commit a crime before s/he commits it. But there doesn’t seem to be any moral difference between knowing that X has committed a crime and knowing that X will commit a crime in the future. So, according to Smilansky, compatibilists can’t in principle object to prepunishment.

Smilansky thinks that this makes compatibilism a radical position.

*

There is long and interesting thread on this topic at The Garden of Forking Paths, with a link to the paper in which Smilansky makes his argument (“Determinism and prepunishment: The radical nature of compatibilism”).

I haven’t read the thread in its entirety, but I believe that the point I wish to make has not been thus far made.

Even supposing that there are no other reasons why compatibilists should not be committed to prepunishment, if we grant perfect foreknowledge of the future actions of agent X, obtained by deduction, I want to deny that compatibilists could be so committed. My point is broadly epistemic, but with a twist. It isn’t merely that it would be in practice impossible for us to acquire such knowledge, but that it isn’t at all clear that obtaining such knowledge is even in principle possible.

My aim:

I want to provide reasonable grounds for doubting Smilansky’s charge that compatibilism is committed, in principle, to prepunishment. Thus, my argument is supposed to be a compatibilist defence against Smilansky’s charge — even though I am, at best, only a partial compatibilist. Compatibilism may indeed be a weird position, or radical, and so on (as Smilanksy suggests), but not — or so I maintain — for the reason Smilansky gives in his paper, namely, that it is committed to prepunishment.

Assuming a deterministic world:

  1. Smilansky’s argument relies on the distinction between in practice possible and in principle possible.

  2. There are grounds for doubting whether this distinction can be maintained.
  3. If there is no coherent way to maintain the distinction, then some things may be impossible to deduce even in principle.
  4. If human behaviour is impossible to deduce in principle, then compatibilists need not (contra Smilansky) be committed to prepunishment, even in principle.

I’ve taken the following argument (to the effect that we should doubt whether the distinction between in principle and in practice possibility can be maintained) from personal correspondence with Joel Walmsley, with his permission. However, the details of the argument as I've stated it here are my own, and so I take responsibility for any flaws. Additionally, I’ve put Joel’s argument to an entirely different use than that for which he had originally intended it. I hope he doesn’t disapprove (too much)!

Support for 1:
“Smilansky’s argument relies on the distinction between in practice possible and in principle possible.”

  1. Self-evident from Smilansky’s argument.

Support for 2:

“There are grounds for doubting whether this distinction can be maintained.”

  1. Calculating the entire game tree structure for Xs and Os is both in principle and in practice possible.
  2. Calculating the entire game tree structure for international draughts is in principle possible, but in practice impossible (thus far).
  3. Calculating the entire game tree structure for chess appears to be both in principle and in practice impossible.

Support for 2a:

  1. The game Xs and Os has essentially 5,478 different legal positions (or 765 when rotations and reflections of positions are considered identical).
  2. Hence, the game tree structure of Xs and Os is (obviously) both in principle and in practice calculable (i.e., it’s easy to design a computer program to play perfect Xs and Os).

Support for 2b:

  1. The game international draughts has a game tree complexity of 1054.
  2. The number of atoms in the observable universe is about 1080.
  3. Hence, draughts has a game tree structure that is, prima facie, calculable in principle: there is enough space in the universe to perform such a calculation. If the universe were turned into a giant calculating device, there would be enough matter to map each node of the game tree structure of draughts onto an individual atom. (However, the game tree structure of draughts has thus far proven to be in practice incalculable; no computer program yet developed has managed to successfully calculate its entire game tree structure).

Support for 2c:

  1. The game chess has a game tree complexity of 10123.

    2. [Note: The game tree complexity of chess was first calculated by Claude Shannon as 10120, a number which is now known as the Shannon number.]

  2. The number of atoms in the observable universe is about 1080.
  3. There have been about 4.73 × 1017 seconds since the big bang.
  4. There is not enough matter in the universe to calculate the entire game tree structure of chess.
  5. Moreover, even if each atom could be reused multiple times, there is not sufficient time in the universe (i.e., since the big bang) to calculate the entire game tree structure of chess.

To see why, consider the following: Blue Gene/L — the fastest computer in the world — can perform about 2.8 × 1014 calculations per second.

Had Blue Gene/L been running at 2.8 × 1014 calculations per second since the instant of the big bang, it would have run 1.4 × 1033 calculations by now. But it would need to have run 10123 calculations in order to calculate the entire game tree structure for chess. So calculating the game tree structure for chess, while logically possible, is in practice impossible. Note the following: since it is logically possible, it seems perfectly natural for us to want to say that it is in principle possible.

But if there isn’t enough matter in the universe or time since the big bang for the most powerful computer yet built (even allowing — unintelligibly — that that computer would have to have been built before the big bang and have begun calculating at the very instant of the big bang) to calculate the game tree structure for chess, it’s difficult to see how the in practice/in principle distinction can be maintained: calculating the game tree structure for chess seems to be in principle, as well as in practice, impossible.

The essential idea here is this: logically chess and Xs and Os are on a par; it’s logically possible to play a perfect game in either case by constructing a giant branching tree structure representing all possible moves, and then selecting moves which force the game down a path that terminates with one’s winning. But practically they aren’t the same, because doing so with chess would require more time and space than the universe can provide (time being more important, since it isn’t re-usable).

Consequently, there are grounds for doubting whether the distinction between in practice possible and in principle possible can be maintained.

Support for 3:
“If there is no coherent way to maintain the distinction, then some things may be impossible to deduce, even in principle.”

  1. Objection: Even if Blue Gene/L couldn’t have performed such a calculation, surely we can imagine that some device or being could have managed it — for example, a Laplacian Demon or a Mathematical Archangel. Classically, such an intelligence — if it is given the positions and momenta of all the particles in the universe, along with all the laws of nature — is supposed to be able to predict (by deduction) all of the future states of the universe. Such a vast intelligence is supposed to do this by being the limit of the possibility of deduction. But s/he isn’t God — s/he’s just supposed to be able to carry out any deduction we could, only instantaneously. Therefore, a Laplacian Demon could (it seems) play perfect chess.
  2. Reply: Understood like this, it would seem that such an intelligence could solve the halting problem. Yet the halting problem (on Turing’s 1936 proof) is unsolvable in principle. So this indicates that there must be something wrong with the notion of a Laplacian Demon — the notion of such a being or intelligence can’t intelligibly be used to maintain the distinction between deductively impossible in practice and deductively impossible in principle.
  3. Conclusion: There is no coherent way to maintain the distinction; some things are impossible to deduce even in principle.

[Note: As Joel has pointed out to me in correspondence, there may be a different way to cash out the distinction that doesn’t encounter such problems. However, at present he doesn’t know what it is; at the very least, a Laplacian Demon or Mathematical Archangel won’t suffice. If a viable way could, however, be found to cash out and maintain this distinction, then my compatibilist defence against Smilansky’s argument might be in some trouble. But not yet, evidently!]

Support for 4:

“If human behaviour is impossible to deduce in principle, then compatibilists need not (contra Smilansky) be committed to prepunishment, even in principle.”

The question here is whether deductively calculating future human behaviour is relevantly similar, in terms of the complexity or the order of magnitude of difficulty involved, to deductively calculating the entire game tree structure of chess. I think it is. To see why, consider John Horton Conway’s Game of Life: This so-called “game” is actually a zero-player game, the evolution of which is determined by its initial state, which is in turn configured by the “player”. The player interacts with Life by creating an initial configuration and then observing how it evolves.

Life is played on an infinite two-dimensional grid of square cells. Each cell can be in one of two states at any moment: either ON or OFF. Each cell has eight neighbours located horizontally, vertically, or diagonally adjacent to it. Time in Life occurs in discrete units, called ticks. The state of the world in Life changes with the passing of each tick according to the following single, exceptionless law:

Each cell, in order to determine what to do in the next instant, counts how many of its eight neighbours is ON at the present instant. If the answer is exactly two, the cell stays in its present state (ON or OFF) in the next instant. If the answer is exactly three, the cell is ON in the next instant whatever its current state. Under all other conditions the cell is OFF. (Daniel Dennett, “Real Patterns”, p. 37)

I encourage anyone unfamiliar with Conway’s Game of Life to download it (multiple sources free online) and experiment. Various patterns emerge, such as the glider, and so on. But these shouldn’t detain us. My point here is just that the most efficient way to find out what a future state of a given initial configuration in Life will be is simply to run the game and see. (Even then, my computer gets hot and makes worrisome noises!) There’s no way to deductively calculate what any future state of an initial configuration of Life will be other than to run the configuration according to the law, and see.

It’s unimportant for my present concerns whether deductively calculating future states of the Game of Life is merely in practice impossible (as is currently the case with, for example, international draughts) or whether it is in fact in principle impossible (as is apparently the case with chess). If the Game of Life is analogous to chess, then it’s obvious that the complexity involved in trying to deductively calculate future human behaviour is many orders of magnitude more difficult than that of calculating the entire game tree structure of chess, and so deductively calculating future human behaviour is also in principle impossible. If the Game of Life is merely analogous to draughts, it’s nonetheless plausible to assert that human behaviour is analogous to chess (although the former involves many orders of magnitude more difficulty in terms of calculation).

The upshot is just that if we have reasonable grounds — as I think we do — for thinking that calculating the game tree structure of chess is in principle impossible, then deductively calculating future human behaviour is, if anything (and if it makes sense to say so), even more impossible, in principle.

If so, no one need be committed (contra Smilansky) to prepunishment, even in principle.

Does this work? Am I deeply — or even shallowly — confused?

Any comments (preferably helpful ones!) are welcome. Please give at least your first name (or a pseudonym) when commenting, otherwise I'll have no way to distinguish one “anonymous” commenter from another.

Thanks.

Anonymous on May 09th 2008

I like this argument - it seems to shift the force of Smilansky's objection from determinism as such to the ability to predict behavior as a consequence of determinism, a consequence that seems not to follow on your analysis. It feels like a strategically good move, but I also think that this is where you will encounter the most resistance.

The compatibilist might not take so much comfort from your defense, because ultimately, the response is that they are not committed to prepunishment, because that sort of prediction is impossible. I take it (and correct me if I am wrong) that the resistance to prepunishment is not based on worries about its computational viability, but rather about something ethically distasteful about prepunishment. And it think the "in principle" feature of the challenge is really meant to focus the issue on the seeming lack of an ethically grounded rejection of prepunishment from the compatibilist.

One way of viewing your argument is that the compatabilist couldn't be committed to prepunishment insofar as there is a certain level of detail or restraint in their imaginations - that they fully commit to the implications of this hypothetical predictive ability, and find that they are imagining something that is entirely impossible. (I take the denial of the distinction between in principle and in practice does something like this). But in my ethical imagining, I may just toss all the metaphysics out the window - I can still ask if I have any reason to object to prepunishment if I knew with 100% certainty that x was going to do some bad act. Perhaps I'll never be in that situation, but my imagination might not be worried about formulating a strategy for when that happens, but rather to find out what matters or not, and what I'll stand for and won't, and I'm not sure that whether something is even remotely possible matters in that kind of imagining. I suppose the tension here is whether or not my principled commitments are in any meaningful way bound by possibility. I suspect that they aren't, because I think these commitments are really just ways of making manifest my own values and reasoning, but I might just be a bit eccentric here, and I certainly don't have an argument to support that intuition.

But thinking about this, I think this argument could target Smilansky's claim that there is no moral difference between what x has done and what x will do. I take it that some of the motivation for prepunishment is the sense that if we could accurately predict x's bad act, in some (perhaps folk-psychological) sense it has already happened - the bad act is implicitly contained in the current state of affairs. But if something could not be predicted at all - then perhaps the future state isn't "implicitly contained" in the present state of affairs even in a folk psychological sense - it doesn't happen until it happens, and this in principle ability to predict does become a moral difference.

Anonymous on May 09th 2008

Oh, by the way, that comment was from Joe. I put "Joe's comment" in the subject, but I don't see that indicated anywhere in the post.

oisin on May 09th 2008

Hi Joe,

Thanks for commenting. I'll have to figure out just how people should add their names. I guess for the moment people actually have to write it in at the end of the comment — or put an initial, or whatever.

I agree that my argument is one that the compatibilist is unlikely to make - or, as you put it, the compatibilist is unlikely to take much comfort from my argument. However, that's exactly why I started out saying "Even supposing that there are no other reasons why compatibilists should not be committed to prepunishment, if we grant perfect foreknowledge of the future actions of agent X, obtained by deduction, I want to deny that compatibilists could be so committed." Many of the comments on The Garden of Forking Paths thread have followed something like the alternative line you suggest, namely, that there is something ethically distasteful about prepunishment, and so on. But I want to grant as much as I can to Smilansky: because I think that that makes for a stronger rebuttal of his position (and avoids anything even vaguely like begging the question) and because I share (to some extent) his intuition about prepunishment — that is to say, I am prepared to admit that if it were possible, even in principle (and certainly if it were possible in practice) to deductively predict future human behaviour, then I would be prepared to concede that we should perhaps consider prepunishment, at least in principle; I'd have no way to avoid that conclusion. But, of course, I want to argue that even conceding all this, it isn't possible, even in principle, to deductively predict future human behaviour, and so we don't need to be committed to prepunishment, even in principle.

As to whether our principled commitments are, or ought to be, in any way "bound by possibility", you said that you suspect they aren't, because you think that such commitments are really just ways of "making manifest" our values. I think something like this is certainly what motivates (at least some) compatibilist thinking. But I guess that I just have the opposite intuition. Even if my commitments are shaped by my values, I think that my values are (or, if they are not, then they perhaps ought to be — or at least I would like them to be) determined by what is possible. For example, I think that Santa Claus, God, and libertarian free will are all impossible, and I don't want my values to be shaped by these things, or my (false) belief in these things' being possible.

I suppose that's why I'm prepared to admit that if deductively predicting future human behaviour were really possible, even in principle, then I'd be compelled to admit that we should consider prepunishment, at least in principle. But if not, then not. (Of course, I have argumentative objections to any sort of punishment, which make it highly unlikely that I would actually accept prepunishment, but that's beside my present point.)

- Oisin

Anonymous on May 09th 2008

Oisin,

First of all, I like this argument. I haven't read Smilansky, so I can't give you really deep comments, but I think I can say a few things about what's here.

1. This is a really minor point, but I'm not sure what you have in section 2 is best described as an argument against the impossible in principle/in practice distinction. After all, it looks like you'd agree that computing the game tree for international draughts is possible in principle but not practice, while computing the Xs and Os tree is just plain possible. What section 2 looks like to me is an argument that some things are contingently impossible in principle. Computing the game tree for chess is impossible in principle because of accidental features of our bit of the universe--there could have been a bunch more atoms in the observable universe.

This isn't a problem for you, though--what you need is just that it's in principle impossible to do the kind of prediction Smilansky talks about. You don't also need to say we can't maintain the principle/practice distinction.

2. The bit about the Laplacean demon being able to solve the halting problem is a bit quick. Why can it do that? I guess you're thinking it's because turing machines are deterministic, so if the demon is supposed to be able to predict all future states of a deterministic system given its laws and initial state, it can do the same for a turing machine. But that might be taking the Laplacean demon's powers to be too general: after all, the halting problem is solvable for a suitably restricted class of allowable inputs. (Trivially: fixing the input is like restricting the class of allowable inputs to a singleton; and then a solution of the problem is a TM that just returns 1 or 0, depending on what that singleton is.) So maybe the Laplacian demon doesn't take all the universe's laws as inputs; maybe they're hard-wired into the demon. That might not be enough to make it unable to solve the halting problem, but then again it might.

Also: What Turing showed is just that no turing machine can solve the halting problem. You need the Church-Turing thesis to get from that to the claim that no computable function solves the halting problem, and then you need something more to get the claim that the halting problem is unsolvable (i.e., by any kind of intelligence). You'll lose a few people on that first step, and I think a lot more on the second.

3. I've lost track of the dialectic a bit, so I'm not totally sure where the following fits in, but your note at the end of section 3 had me thinking of this:

Suppose the universe continues infinitely into the future. Suppose also that as time goes by, the number of atoms in the observable universe doesn't change significantly, but that we keep designing better and better computers. Each year, they're more efficient, able to do more operations per second. Then for any problem of finite complexity, we'll eventually be able to compute a solution. With one computer of the computational speed of Blue Gene/L, it would take at least 10^123 / 10^15 = 10^108 seconds to compute the whole tree for chess, but that figure will be constantly shrinking as progress continues (and, maybe, as we build more copies of Blue Gene/L). Eventually, we'll be able to compute the tree as fast as you like.

Then at any given moment, there will be some problems that are impossible in principle to solve; but they will eventually become possible in principle to solve. (Practice might still be another story.) Then any problem of finite complexity will eventually be solvable in principle. (However, it is false that: eventually, every problem of finite complexity will be solvable in principle.)

If the problem of predicting human behaviour doesn't get more complex over time, then we should eventually be able to predict human behaviour.

One objection to this line might be that there might be a theoretical limit on how many operations a computer can perform per second. That would put a cap on the kind of progress I stipulated would continue infinitely; so some finitely complex problems would still be unsolvable.

4. What if the Laplacean demon can just predict the states of a system for the next n years? Then we don't have the halting problem worries: you can find a turing machine that'll determine the next n states of a given machine, or that'll determine whether a given machine halts after n or fewer steps.

Anyway, even with all the above, I still think you have an interesting point: determinism isn't enough for future states to be predictable in principle; the finiteness of our universe makes some really-big-but-still-finite problems unsolvable in principle. If anything is that complex, predicting human behaviour might very well be!

-Roger

oisin on May 10th 2008

Roger,

Thanks for your comments. You've made some immensely helpful and insightful remarks. I've been turning this idea over in my head (very) intermittently for quite a while now, and I just finally decided to throw it out into the blogosphere and see what happened to it.

On your first point, I think you are spot on — thanks. I agree, the second section is an argument to the effect that some things are contingently impossible in principle. And I also agree that making that amendment oughtn't to pose any difficulty for my argument.

On your second point, I'm strongly inclined to just defer to your greater familiarity with the halting problem (I'm a novice!). However, according to my limited understanding, Turing demonstrated that there simply isn't any mechanical procedure for deciding whether an arbitrary program will ever complete its computation and halt; that is, there isn't any set of instructions you can give the machine that will decide whether a given program will halt.

If, as you say, I need the Church-Turing thesis to claim that no computable function could solve the halting problem, and then something more besides to get to the claim that the halting problem is unsolvable for any kind of intelligence at all, then I suppose I may indeed lose everyone — including myself!

On three, I had (perhaps too briefly) considered this point.

In the first place, I'd like to maintain that there's something in principle (however contingently) impossible at present about calculating the tree for chess. Moreover, I don't think it's important for me that the chess tree remain impossible to calculate. I don't think my saying that involves any incoherence. But perhaps I'm operating with an eccentric conception of in principle; for example, it's been suggested to me that some people might take [in principle possible] to mean something similar to [logically possible], in which case my argument won't go through at all. I just think that calculating the tree for chess is so completely [in practice impossible] that it's also [in principle impossible]. Perhaps I should call this species of [in principle possibility] [in principle*]. In any case, I need the distinction between [logically possible] and [in principle* possible] to hold, but the distinction between [in principle* possible] and [in practice possible] to collapse.

As to the chess example, I only meant it to be illustrative. It's surely uncontroversial to maintain that calculating future human behaviour would be more difficult than calculating the tree for chess. And if chess is [in principle* impossible] to calculate, then it's plausible, to say the least, to maintain that human behaviour ought to be much more so. Even if we're eventually able to predict human behaviour by developing ever more powerful means of calculation, I suppose I could restrict my argument as follows: since we can't so predict in principle now (at least in my — non-logical — sense of [in principle*]), then we aren't currently warranted in being committed to prepunishment, since our being thus committed now would require us to be able to so predict [in principle*] now.

Does that work? Or is it too weak?

On four: If the Demon can predict the states of a system for the next n years, then yes, it would seem that we dispense with halting problem worries. And that might have the consequence for me that [in principle* possible] — even if such possibility isn't equivalent to [logically possible] — can be sufficiently distinguished from [in practice possible] for us to be able to say "Hey, it's in principle possible for us to predict future human behaviour; even if it's not practical at present for us to do so!"

In which case I'm not at all sure my argument goes through.

- Oisin

Roger (not verified) on May 11th 2008

Hi Oisin,

On 2: You're not wrong in your understanding of the halting problem. "Mechanical process" and "computable function" are, as far as we need be concerned, synonymous. What Turing proved was that no turing machine can solve the halting problem. The Church-Turing Thesis says, basically, that no mechanical process can do anything a turing machine can't do (and vice versa). I think most people believe the Church-Turing Thesis; at any rate, it's a perfectly respectable thing to rely on.

Where you might lose people is if you have to go from saying that no mechanical process can do X to saying that no intelligence can do X. But that's where things get murky and I have no idea what to think

On 3 and 4: What I was worried about in the "infinite progress" scenario is that it still seems bad for compatibilists if they have to say that prepunishment is a bad idea (in principle) now, but once we've made sufficient progress, it'll be at worst an impractical idea. If solving the problem of predicting human behaviour just requires a few more millennia of progress, that's worrying.

But I don't think this is an insuperable difficulty for your argument. I think you might well be able to argue that predicting human behaviour is, even in a deterministic world, a really, really hard problem, and make something work. I'm reminded of a story about a mathematician doing a computer proof of some theorem related to the four-colour theorem. This was a really complex problem he was working on, and he had to borrow time on a whole bunch of different gigantic supercomputers (or something like that). The interesting thing is, because of how much time he spent on such big computers (literally big, as in taking up a lot of space), the paper he wound up publishing included error calculations taking into account the chance of these computers interacting with cosmic radiation--and it was slightly significant!

What I'm thinking is that the prediction problem (if we can call it that) might be such a complex problem that in trying to solve it, we'd have to deal with things like quantum limits on how fast things can work (if there are such limits?) and how long the universe will last. And that seems plausible--especially if we're not talking about just one person. That would lead to the kind of in-principle* impossibility you're talking about. Now, it might be hard to argue for that kind of claim, but I bet it can be done; especially since chess is so complex--showing that there are other, easier problems that are plausibly hard enough to have to worry about the size of the universe makes it plausible that the prediction problem will never be in-principle* possible.

And I wouldn't worry too much about the n-years Laplacean demon. If it's not a turing machine, it's probably not something we can build. If it's some other kind of intelligence--well, maybe prepunishment makes sense for God(s)?

kmw (not verified) on May 12th 2008

dear oisin,

first of all, yes, as far as i know (and my logic is still very elementary) roger's point is slightly tricky: the fact that computable function / "mechanical process" does not readily map onto L. demons and g-dlike beings is because there are significant (mental/neural/???) assumptions -- specifically, that these processes are mechanical (note: i'm pretty sure that determinism does not entail that they are --- they could deterministically be soulful or something... i dunno)

that's realy minor though.

i have read smilansky's paper (the analysis one right -- "Determinism and prepunishment"). i think on prof. s's behalf, i could try the following important points:

first, i don't see the (explict or implicit) requirement to have a distinction between in practice / in principle. i think what you mean is that compatibilists in practice don't need to commit themselves to prepunishment but in principle they are committed to it. however, this distinction is unnecessary for his argument on my reading because all that he is trying to prove is the second conjuct; namely, in principle they are committed to prepunishment.

now your argument has two major steps: the first is to show that epistemically it is not possible "in principle" to gain access to future actions of humans (with the critical "at this given moment") due to the extreme complexity and limits to computing power. from this you conclude that there is no way that a compatibilist *could* be committed to the doctrine of prepunishment.

now, the face of it, that second step is a little tricky: simply because something cannot obtain, does not mean that one cannot have commitments about it. for instance, if i am committed (due to some ethical theory that i adopt) that, say all torturing of animals is wrong (*wink to roger*) and so logically find myself committed to all torturing of unicorns is wrong (being a good deducer like i am), then obviously i have commitments towards unicorns despite their not obtaining. analogously, i can have commitments towards "complete predictability" even if this does not obtain. so your claim about complete predictability as being even more complex than life misses the mark.

another way of making the same criticism is that smilansky says he is assuming complete predictability "for the sake of argument". if compatibilism and complete predictability obtained, then (he thinks) prepunishment follows. he is not committed to the claim that both obtain -- he is claiming that it is worrisome to think that this link exists!

that is, i think, the most important point. now on to the other major topic you discuss:

i think you are confusing this distinction yourself. one way we can try to reify the distinction is to interpret it via possible worlds (which is i think where roger was trying to push the conversation methinks). let us map "in principle" impossible to ~<> and "in practice" impossible to ~ in the actual world. i think that this would straighten things out. it would certainly be a robust distinction and we could characterize both your and his arguments. for instance we could say halting problems cannot be solve in principle (id est, in any possible world). on this interpretation, all of the questions you raise about computability are about the actual (given) world (i.e. about stipulating the atoms in the universe as nodes in a calculation). however, smilansky is concerned about any world in which determinism is true, so his concerns are not only "in practice" but "in principle".

in other words, they are theoretical implications of perfect predictability and compatibilism. they are not predicated on the given state of the universe.

i think that my comments have an interlinking focus: your (empirical, contingent) claims about predictability in the world do not diminish the power of an argument which uses perfect predictability only argumenti gratia.

oisin on May 12th 2008

Thanks for your interesting and useful comments.

Just a few quick thoughts (I'm currently very late night blogging, and I just read your comments a moment ago).

You say:

smilansky says he is assuming complete predictability "for the sake of argument". if compatibilism and complete predictability obtained, then (he thinks) prepunishment follows. he is not committed to the claim that both obtain -- he is claiming that it is worrisome to think that this link exists!

Yes, indeed; but what I'm trying to do is explore this apparent link and show how it might be weaker than we think - I don't know that I succeed, though.

one way we can try to reify the distinction is to interpret it via possible worlds

Yes; but as I mentioned (briefly) above, I want to distinguish between [logically possible] and [in principle possible]; if there is one type of [in principle possible] which is equivalent to [logically possible], then I want to say that there is a type of [in principle* possible] that is not equivalent to [logically possible]; rather, I think that some things are so wildly [in practice impossible] - because of contingent features of our universe - that they are in some way in principle impossible, i.e., [in principle* impossible]; there may be possible worlds in which those things are [in principle* possible]; but they're not our world.

I guess I'm assuming that makes a difference, but I may be wrong.

your (empirical, contingent) claims about predictability in the world do not diminish the power of an argument which uses perfect predictability only argumenti gratia

Yes, I agree; but I suppose what I want to say is just that compatibilists may have less reason to be worried by Smilansky's argument than might at first be supposed; as Roger put it, what I'm trying to say is something like "determinism isn't enough for future states to be predictable in principle; the finiteness of our universe makes some really-big-but-still-finite problems unsolvable in principle"; so although my (empirical, contingent) claims about predictability in the world may not "diminish the power of an argument which uses perfect predictability only argumenti gratia", I was hoping they might at least give us some pause; I suppose I just can't shake the intuition that if something is really, really, really [in practice impossible], then there's at least a sense in which it's actually in principle impossible, i.e., [in principle* impossible], at least in our world.

Anyway, these are useful comments and I'm worried that I might be grasping at straws now.

It's late for tonight: I'll look at this again tomorrow and see what I think then.

oisin on May 13th 2008

kmw,

I've just had a quick re-read of Smilansky's paper.

After giving a brief explication of both compatibilism and prepunishment, Smilansky makes the following two assumptions: (1) determinism, and (2) complete predictability.

Given both assumptions, Smilansky argues that compatibilism has no principled way to resist the temptation to prepunish.

The only reason, he says, that we ought not to prepunish is epistemic, i.e., that we "rarely have the required powers of prediction." (348) (There may also be pragmatic reasons, for Smilansky, but the main reason is the epistemic one.)

I want to challenge Smilanksy's second assumption, (2). In short, I think that we never have — nor could ever have — the required (i.e., deductive) powers of prediction.

What I mean is that there is a sense in which (2) is just not possible, in principle, in our world, given contingent features of our universe. And so either (a) there is little if any reason to assume (2) for the sake of argument; or (b) even if we do assume (2) for the sake of argument, little follows for the compatibilist. We simply can't have complete predictability of actual future human behaviour in our actual world; i.e., complete deductive predictability is [in principle*] impossible, I think, since it is unclear either (i) whether a being who is the limit of deduction could have it; or (ii) whether any being could have it, short of god(s) (whatever it/these might be).

In summary, my position is the following: I don't think that predictability is the only problem with prepunishment, but it is certainly one major problem with it, and it is not merely an in practice as opposed to in principle problem. Rather, complete predictability is so wildly in practice impossible for any deductive mechanism or intelligence in our world, due to contingent features of our universe, that it is in some sense in principle impossible too, i.e., what I call [in principle*] impossible.

So it's not clear in what meaningful sense (in our world) we're supposed to be in principle committed to prepunishment.

kmw (not verified) on May 13th 2008

heylo --- i wrote kmw for some reason, but i guess it's not clear that it's kian

so umm i'm kian

anyways

yes, i think the characterization of smilansky's paper you have provided in the above post is largely correct. if your claim is that compatibilists don't need to be so worried because deductive prior knowledge is not possible (in principle with all the asterisks required) then it seems it could be a bit more explicit in your initial post. i actually think that i understood that the first time i read it... and that lead to my point which is you are arguing against an assumption.

however, i think that smilansky has another response (based on the essay). he could answer that perhaps (altho he has not committed himself either way) deductive knowledge is not necessary. perhaps some "beyond a reasonable doubt" is sufficient ... (which of course is the standard used to judge people in the past).

so suppose we have a character "g.b." --- g.b. has a long history of failing to successfully run businesses, and has a family environment which has emphasized laissez-faire economics... in fact, he tells us that he intends to stop governmental interference in the market... we might not need to calculate every single movement he makes to conclude beyond a reasonable doubt that he wlll fail to manage the economics of a country.

smilansky's "rarely have the required powers of prediction" seems to lead me to this interpretation whereas the thrust of the article actually leads me to a stronger interpretation where it is deductive or at least g-dlike knowledge although i think he would resist either commitment.

however, i don't think he needs to retreat to this defence --- all he needs to say is that the intuition is with him that given complete foreknowledge and compatibilism, prepunishment should not follow!

further, i think there might be a slipperyness to your "in practice" / "in principle" dichotomy (and i would like to note here that neither phrase actually occurs in his paper). could you please define what "in practice" versus "in principle" versus "in principle*" means in the context of his paper? or is your contention that they all collapse, in which case i'm not sure why you introduce them initially.

oisin on May 13th 2008

Hi Kian!

Thanks for your comments.

  1. Perhaps I should have been clearer initially about my claim that compatibilists don't need to be so worried because deductive prior knowledge is not possible.
  2. I'm not sure that Smilansky can or would answer that deductive knowledge is not necessary, and that some "beyond a reasonable doubt" is sufficient.

    In the first place, I'm not sure he can, since he wants us to assume complete predictability — I understand this as meaning that deductive knowledge is necessary; surely that's the whole point of his asking us to assume determinism in the first place: in an indeterministic world we could have the sort of predictability that you (correctly!) say we could have about your character g.b.; we don't need either determinism or complete (deductive) predictability.

    In the second place, I take it that Smilansky is very unlikely to want to claim that "beyond a reasonable doubt" is sufficient here, on the basis that it is the standard used to judge people in the past; for Smilanksy, punishing people on the basis of compatibilist distinctions about free will and moral responsibility is "morally outrageous" (The Oxford Handbook of Free Will, Robert Kane (ed.), 2002, p. 496):

    ... once we grant the compatibilist that his distinctions have some foundation and are partly morally required, there is no further reason to go the whole way with him. There is no reason to claim that the absence of libertarian free will is of no great moral significance and moreover to deny the fact that without libertarian free will even a vicious and compatibilistically free criminal who is being punished is in some sense a victim of his circumstances. If we reflect upon the fact that many people are made to undergo acute misery while the fact that they have developed into criminals is ultimately beyond their control, it is hard to dismiss this matter in the way that compatibilists are wont to do... One chooses and acts, but this follows from who one is as a “given.” Any factor for which one is appreciated, praised, or even loved is ultimately one’s luck. That compatibilists are indifferent to such ultimate arbitrariness, shallowness, and injustice is morally outrageous.

  3. Also, I'm not sure what to make of the following (statement of yours):

    however, i don't think he needs to retreat to this defence — all he needs to say is that the intuition is with him that given complete foreknowledge and compatibilism, prepunishment should not follow!

    I took it that the intuition that he's trying to pump is that given complete foreknowledge and compatibilism, prepunishment should follow; and this shows that compatibilism is a radical position.

  4. As to [in practice/in principle]: I mean to say that there is a clear sense in which the game tree for draughts is in principle possible to calculate, although it is currently in practice impossible to do so; but in precisely the (contingent, etc.) sense in which the tree for draughts is in principle possible to calculate, it is not possible to calculate the tree for chess — even though it is clearly logically possible.

    I concede that Smilanksy does not use these terms, and moreover I concede that he does not explicitly state that his argument rests on a distinction between in practice/in principle (as I mistakenly characterized him as doing; thank you for the correction). However, I think that this distinction is relevant to his argument, along the lines I have suggested.

Does that help?

P.S. To lay my cards on the table: If anything, I agree with Smilansky that compatibilism is in some sense both unjust and a more radical position than we normally think; and I am anything but a full-blooded compatibilist! I only meant to test out what I thought might be a promising response which the compatibilist might make to Smilanksy. I think the comments so far have greatly helped me clarify what are the strengths and weaknesses of this response.

Thanks!

kmw (not verified) on May 18th 2008

right:

(1) yes, i think a slightly more explicit claim might help

(2) hmm, perhaps we are in some agreement here, but i would read this passage in similar terms (something like compatibilists' actions, namely blaming those whose choices are beyond their control, is unconscionable) but in the article he intends a different tack. i think he means in the article that IF a compatibilist claims that a given individual is responsible (for a past action), then there is no principled way to deny responsibility for future actions. so in the handbook / free will passage, he is simply saying that the antecedent of this claim is unconscionable (but he does not dispute that the compatibilist does assert it!).

(3) sorry, that was poorly written, but i meant that he intends to say in the essay that compatibilism + det. + predictability *should not* lead to prepunishment being permissible. of course, what he actually does is what you said just now, that these three *do seem* to lead to prepunishment being permissible. The tension between the first which is the intution and the second, which is what he endeavors to prove, leads to the issues.

(4) alright, i won't take issue with this distinction... but i still maintain that smilansky is not committed to perfect foreknowledge being either in practice or in principle possible. i think that all he requires is the tension generated by the intuition that any plausible theory does not entail prepunishment could ever be justified and the purported proof that compatibilism does entail that prepunishment could be justified.

cheers~

k

by the way, i'm now thinking that i might not go to oxford and attend amsterdam for logic! my, how things change... perhaps my mind is free after all.... =P

Jill fellows (not verified) on May 13th 2008

Hi Oisin,

Firstly, and a bit worryingly, this argument is familiar to me. But I cannot remember for the life of me where I've read something like it before. If I remember, I'll let you know. But I don't think that whatever I've read was dealing with the idea in exactly the same way, so I wouldn't worry about it too much.

I want to start with this quote, and then give you some rambling thoughts of my own. Maybe they'll help.

"But practically they aren’t the same, because doing so with chess would require more time and space than the universe can provide (time being more important, since it isn’t re-usable)."

This seems to commit you to the claim that what it means to be 'in principle' calculatable is for it to be in practice possible, or something like that.

The discussion is using three notions, logically possible, in principle possible, and in practice possible. You've shown why in principle possible, if defined differently from logically possible, cannot be maintained as separate from in practice possible. But could one claim that 'in principle possible' and 'logically possible' really meant the same thing? Of course, then we might be committed to saying that the halting problem is solvable in principle, which might be changing the meaning of 'in principle' far too much.

But I think there's something to this distinction between 'logically possible' 'in principle possible' and 'in practice possible' and perhaps even 'conceptually possible' (to throw in something I'm looking at right now). My hunch is that sometimes people might take 'in principle' to mean something similar to 'logically' and sometimes they might take it to mean something similar to 'in practice'. It all depends on whether the event whose possibility is in question is one that is being conceived of as taking place in our world (or in one very similar to ours) or in a world different from ours. If the former, then in principle is probably supposed to mean something like in practice. If the latter, it's probably supposed to mean something like logically possible.

So, if the former is being referred to, then your argument will go through. But if someone is taking 'in principle' to mean something more like 'logically' then your argument won't go through. In particular, cases of the Leplacian demon, or some other ideal knower, might be cases intended to demonstrate logical possibility, not really the possibility you're talking about. Even in our largely secular day, people still refer to god as a sort of logical benchmark.

On the whole, I think the argument is an interesting one, and I didn't see any major flaws. Hope this helped.

Jill

oisin on May 13th 2008

Hi Jill,

Thanks for that. Yes, I think you're right. I really do need the distinction between [logically possible] and [in principle possible] to hold up, and the distinction between [in principle possible] and [in practice possible] to collapse, or weaken. And I've argued mainly for the latter assertion, by proposing on the one hand cases that are clearly [in principle possible] although they are [in practice impossible], and on the other hand cases that are [logically possible] but which are so completely [in practice impossible] that they seem also to be [in principle impossible] in some sense. And I was hoping that this would also support the former assertion, namely, that the distinction between [logically possible] and [in principle possible] holds up, since we want to say that calculating the game tree structure of chess is [logically possible] but is so completely [in practice impossible] that it's also [in principle impossible]. But of course, as you say, I suppose someone is still free to stick to his or her guns and insist that [logically possible] and [in principle possible] are equivalent. In that case, the Leplacian Demon or Mathematical Archangel will simply be a logical device or benchmark for thinking about what is [in principle, i.e., logically, possible].

Again, many thanks for your (encouraging) remarks.

Oisin

Emma (not verified) on July 31st 2008

Hi Oisin, this is Emma,
Hope the Smilansky paper is going well - I've been following the comments on your blog with interest and can imagine that it will turn out to be a pretty good paper.

Since I first read your post I started thinking more about the distinction between in principle computable and in practice computable. I particularly liked how Roger's first post ended: "Anyway, even with all the above, I still think you have an interesting point: determinism isn't enough for future states to be predictable in principle; the finiteness of our universe makes some really-big-but-still-finite problems unsolvable in principle. If anything is that complex, predicting human behaviour might very well be!"

I wanted to think of a concrete example of a finite but unsolvable in principle problem. I eventually found this paper that applied complexity theory to perception, and in it is a neurobiological example of an unsolvable in principle problem, namely the "generic vision problem". This seemed like an example that may be useful to you.

First you need this distinction though (which you may already be familiar with), between tractable and decidable problems. A tractable problem is one for which we have enough time and space to actually carry out the computation; while a decidable problem is just one that can be modeled computationally (but which is not necessarily tractable). Then there is a further distinction with regard to tractability. Namely, tractability can be determined mathematically, i.e., in principle, so we can have problems that are "in principle tractable" or "in practice tractable." I propose that what you call [in principle* possible] is just what is known as "in principle tractable".

Therefore, interestingly, you can have an intractable problem that IS decidable, i.e. a problem that we can computationally model/simulate, but for which we don't have enough time and space to actually run the simulation, which means we can never compute its exact solution (At best, we can tweak the problem to get an approximate solution). Furthermore, some such problems are "in principle intractable" or in your own words [in principle* impossible] ! So, for example, an in principle intractable but decidable problem would be [in principle* impossible] but logically possible.

It seems that focusing on the distinction between decidable and "in principle tractable" is one way to raise your objection to the more general in principle/in practice distinction. As one computer scientist put it: "the fact is that some "computable in principle" functions are not computable in principle in any practical sense." (in other words, some decidable problems are not even decidable in any "in principle tractable" sense). I took the point of your three examples to want to raise such an objection, which relies on this finer distinction between decidable and "in principle tractable." Smilansky has a blanket notion of in principle possible. But you seem to want to say that some problems that are in principle possible, i.e. decidable or logically possible, may actually, more specifically, be "in principle intractable," or in your own words [in principle* impossible]. Furthermore, this does seem to collapse, or make less relevant, the distinction between [in principle* possible] and [in practice possible].

Here is the example itself, which may be more or less useful than the above distinction: Vision scientists are not yet sure whether human vision is decidable, i.e. can be computationally modeled. But they do know a smaller problem, generic visual search (which we studied at the end of Murat's class), is a decidable problem. More specifically, they know that unbounded visual search is intractable (and actually decidable too). While, bounded visual search is tractable (and so, of course decidable). Overall, they show that the generic unbounded problem of visual search is decidable but intractable, but if various bounds or approximations are granted then the generic problem can be reduced to a more specific bounded problem that is tractable by the visual system.

This might be helpful if you can argue that Smilansky's (wrongly) assumes that the problem of predicting human behavior is not only decidable but "in principle tractable", and this latter assumption is where the problem lies. For if the problem is general/unbounded enough, it may very well be decidable but "in principle INtractable" (as is the generic perception problem). In the case of prepunishment, the analogy is that even if we have a computational model of someone's behavior, unless it is also an "in principle tractable" problem, the specific verdict can never be computed (at best, by restricting the problem, only an approximate solution can be computed). Tsotsos concludes, "the brain is not solving the generic vision problem" because it cannot and never can, such a problem is intractable in principle. By analogy, Smilansky should not assume that we can solve the generic problem of predicting an individual's behavior in a morally complex situation, such a problem would not even be [in principle* possible] or "in principle tractable."

Here is the link to the article "Complexity constrains the architecture for visual processing" by J.K. Tsotsos.
http://books.google.ca/books?id=8nLPgE-n8bgC&pg=PR7&lpg=PP1&ots=GWdXVGqL...

In any case, I am interested to see how your paper turns out.

Best,
Emma