Saturday, March 15, 2008

Determination and Determinism

Why is the Two Envelopes paradox paradoxical? After some thought I've decided that I don't really know (so the following is less clear than I'd hoped it would be) but maybe the reason is related to our difficulties with such concepts as deliberation and probability. Perhaps we overlook (for some reason) something that we intuit easily enough in the case of, for example, Pascal’s Wager:
......Even were you totally unsure, whether or not there was a God, it would clearly be silly to act as though God probably existed just because (even if you did know that) the net rewards for doing so were very much greater than those for not doing so. Intuitively, such rewards are irrelevant if there is no genuine chance of whichever is not already the case (if it is not as if someone will toss a fair coin fairly, and give you those rewards on heads)—and that is, I think, reminiscent of the calculation (see my previous post) of the expected gain on exchanging your envelope (when only one of the ‘X’s in the equation for expected gain named the definite amount in your envelope). Such a distinction, between genuine and other chances, is obscure but apposite (cf. Denyer's 'proof,' below) because whenever we are thinking rationally we have already presupposed that our decisions might make a genuine difference.
......After all, with your original choice of envelope (which gave you the 50% chance of X = 1 and 50% chance of X = 2) there was no temptation to wonder how it could be that, whilst X = 3/2 is impossible, 50% of X (= 1) + 50% of X (= 2) = 3/2. And those chances were genuine (so to speak; and even if, counterfactually, your envelope had been given to you, via some deterministic mechanism, your epistemic uncertainty would have yielded a similarly quasi-genuine, if then entirely imaginary, chanciness). By contrast, the chances that seemed paradoxical, when focusing upon just part of what you know (when ignoring the parenthetical identities in the equation below for expected gain on exchange), could have measured nothing more than your ignorance about what was already the case.
......Regarding that possibility (that ‘could), it seems (as below) that simply to be rational is to have (rather obscurely) related presuppositions about what is possible—beliefs so obscure (so analytically dubious) that we might well overlook their import when a scenario encourages us to (and plausibly the way in which that happens within the two envelopes scenario is a clue as to how to analyse such beliefs). Similarly, we might presuppose that (certainly) 2 + 2 = 4, even those of us who think that a (Cartesian) demon, fooling us about such things, is not just possible (despite its inconsistency with 2 + 2 = 4) but is not necessarily unlikely. And if determinism is like that, if its nonexistence is a necessary presupposition of the practice of our rationality (for all that various determinisms are prima facie possible), then the fact that possible worlds are, in themselves, rather deterministic objects (whereas in no possible world is it false that 2 + 2 = 4) might help to account for why philosophers (who have tended to favour possible worlds analyses) have tended to find the Two Envelopes so paradoxical (cf. Pascal being a deterministic Jansenist, which might explain his view of his Wager).
......So maybe the answer (to why we find the two envelopes so paradoxical) has something to do with the following argument (inspired by Denyer's "Time, Action & Necessity") for free will (and against Stephen Law's most recent argument). Many Naturalists believe that there are, in reality, such relativistic particles and fields as are the subject-matter of physics, and that what the other subjects (biochemistry, psychology, politics and so forth) concern themselves with are really just relatively large chunks of that. Many Naturalists also believe that, given how much we know, from such sciences, it would be irrational to believe in such things as souls and revelations; and they think that it would, of course, be wrong to be irrational.
......Thinking is important (we can all agree, at least here). Coming to the right decision is important—it should not just be a random event, choosing what to think about the real world, of real people (many Naturalists are humanists too). One could be irrational, but that would be wrong. And thinking rationally (making a responsible decision on the basis of the evidence) cannot be something that you are bound to do, in a totally determined way, if it is something that you might neglect to do, could be at fault for not doing. Naturalists arguing against the possibility of religious knowledge are, in particular, very aware of the ‘ought’ in ‘thought;’ and ought implies can—there would be little point in arguing against irrational beliefs if believers are bound to believe as they do, as would be the case were the physics of their physicalistic minds deterministic.
......But the only alternative to determinism, in this physical universe (of which we know a vast amount, thanks to modern physics), is randomness; if there is another alternative, and if mind is reducible to physics, then it’s odd that we don't know about it in modern physics (which has even revealed to us the relativity of space and time). And how could mere randomness be the cause of the difference between a moral act (thinking properly) and an immoral act (thinking improperly); how could it be that we should try to get result A rather than B, if it is just random whether A or B? So (to end with my reply to Law) the very rationality that Naturalists are fond of opposing to religious knowledge presupposes something that cannot be either of the options (determinism or randomness) available to them, as physicalistic atheists; so that, according to their own scientific standards, all the evidence available to us, at any time, must be evidence between the major alternatives (such as some modern monotheisms).

18 comments:

Jeff said...

There are all kinds of interesting things that can be said about Pascel's intent for the wager, about the role of volition in belief, etc. Other people have said them better than I could, so I'll focus on something else, that I think is relevant.
Imagine a person lost something, standing on the border of an area lit by an overhead street light. If he recognized that there was only a 25% chance that the object fell into the lit area, he would be rational for choosing to do look in this area if it'd be impossible to find the object in the dark.
We follow this principle all the time. If it's a slightly breezy day and I've dropped a $20 I'll go back and look where I dropped it, on the remote chance it hasn't gotten picked up since I dropped it.
Of course, if there's a hurricane outside I won't go looking; or if it's a $1 bill. There are clearly a range of probabalities correlated with strengths of reward that these arguments only work with.
(It seems to me as the reward goes up we go through the effort for lessened chances.)
If a person's initial inquiry lead them to conclude that the probabality or reward were sufficient, they would engage in the action.
It would be rational to say "I'm only looking in the well-lit area" This does not mean that the person knows for sure that the lost item is here; it simply means that if it turns out the item went outside the lit area, they will never find it. To fail to look in the well-lit area simply because there is a possibility it fell in the dark area would be silly and illogical; a person would not be begging the question to only look in the lit area.
I can picture (but not quite describe) how all this applies to pascel's wager, Cartesian Demons and related skepticisms... It's a little more difficult for me to apply it to the examples listed. (Maybe Enigman can help?)
Bottom line: if there are two courses of events but one of those offers us no benefits, then it behooves us to assume the other is operating until we learn otherwise.

Enigman said...

Re your bottom line, what your previous argument justifies is not so much the assumption that the other is operating (you don't assume that the lost thing was 100% rather than 25% likely to be be in the lit area) as the consideration of such benefits, but only insofar as they're apposite (you do only look in the lit area, but also you believe that your chance of getting nothing by doing so is 75%)...

Suppose you have a lottery ticket for a prize of one trillion pounds, and a one in a billion chance of winning. The ticket is therefore worth a thousand pounds, but you might be rational to sell it for £800 (if you could use £800) just because winning nothing with it is a racing certainty.

Jeff said...

Interesting.
I'm sitting here trying to dust some old philosophy classes off from the cob webs of my brain. It seems like maybe these ideas are associated with "decision theory" and a guy named "Bayes" although perhaps that's me not remembering correctly.
At any point, one thing that somebody noticed is that the benefits of money are not linear for most people. A prize off 100 (pounds, dollars, whatever) is not necessarily twice as good as a prize of 50.
This becomes most clear with large sums: Would it be rational to to halve your chances at doubling a sum when the sum begins at 1 trillion?
Most people believe that at extreme ends of wealth, they could have as much quality of life as they want and doubling this sum would bring about a proportional change.
I make these observations to explore the issue of whether it works to divide the sum by the probality to determine cost when the pay off is money. (This principle might apply to other areas as well.)

jeff said...

oops. I meant to write "doubling the sum would NOT bring about a proportional change."

Doctor Logic said...

Enigman,

I think you are making the assumptions inherent in rational thinking a little too complicated.

To be rational, I have to assume that I know how to think rationally, and that certain things are true in my experience, specifically:

1) Non-contradiction, and, hence, truth and logic.
2) That my experiences (both mental and physical) should be taken as factual/axiomatic.
3) That past experiences (both mental and physical) are guides to future experiences, i.e., induction.

As you say, we rational thinkers assume rational thinking can make a difference (thanks to induction, btw). However, differences also get made in deterministic universes. If I deterministically reason to a conclusion about which envelope to open, I have made a deterministic difference. That is, a deterministic system that failed to reason would generally behave differently.

and ought implies can—there would be little point in arguing against irrational beliefs if believers are bound to believe as they do, as would be the case were the physics of their physicalistic minds deterministic.

Sure there is a point. Believers are no less deterministic when they change their minds than apples are when they fall off trees.

If a mind is a mechanism, and that mind is exposed to new arguments, it will change its thinking deterministically. Whether the mind is perfectly rational or partially rational, it will change as a function of new inputs. Indeed, I would say that rational thinking works to the degree that it is deterministic.

I have a question for you. You spoke about randomness being the complement of determinism in a physical universe. That's correct. Indeed, I would say it is true whether or not physicalism is the case. Your answer suggested there was some way randomness would not be the complement of determinism. How? If I say that a system is deterministic when the final state is determined by the initial state (or by constants), then the alternative is either randomness or that the final state is determined by the future (which would imply that the future is already fixed). I haven't gone through much of your blog yet, so if you've written about it before, please feel free to send me packing with a link to a prior post.

Enigman said...

Dr Logic, very good points, I think; but mine were only arguably too complicated, perhaps? After all, your (3) introduces obscure complexities (e.g. how much of a guide?), such as those Jeff mentioned (Bayesianism). Anyway, your final point is my problem (no previous posts sadly) as indeed, there does not seem to be any alternative to random or determined, not even logically.

But then, we do have prima facie evidence that there is something else, i.e. our experiences as we make our choices... An analogous situation is our personal experience of being a unitary subject, which seems, prima facie, to clash with physicalism. A soul is not a physical possibility, but that just means that physicalism might not be true (the evidence for that possibility being our direct experience, together with the obvious way to interpret physics)... Similarly, compatibilism may not be true.

Now, maybe compatibilism is coherent (I've yet to pick my way through it; and the amount of stuff there is to do, I may never do it) but even so, it is prima facie incoherent... So we've a prima facie impossibility (something other than randomness or determinism) but also a prima facie incoherence, and maybe together those just give us, at present, that libertarian free will is merely possible.

The question of whether that is an unnecessarily complicated possibility is an interesting one, I think; and again, an analogy may serve to show that the onus is still on those who assert that it is. The analogy is: David Lewis's Humean Supervenience! David Lewis asks, how can there be natural laws? It is analogous to, how can there be an non-random indeterminism. He then shows how we might do without such things in our theories. Of course, it is prima facie false!

Doctor Logic said...

Enigman,

I don't put a lot of stock in prima facie appearances. After all, prima facie, I ought to swap envelopes in the two-envelope problem. :P

As for the prima facie incompatibility between free will and determinism, I think we can chalk that up to human error.

Suppose I consider my decision to get married. The process implies that my decision has the ability to make a difference. It certainly does so, but that does not mean my decision isn't deterministic. At the start of my analysis, I will surely believe that my decision will cause (in the future) me to marry or not marry the lass in question. However, this does not imply that my process is non-deterministic. It only means that, having not done the analysis yet (or not being able to due to the large number of variables), I don't know the outcome.

However, I don't see any difference between this scenario and, say, my analysis of the likelihood of an avalanche. I know that the outcome of snowfall and sunshine will cause or not cause an avalanche to occur in the future. That my perspective reveals multiple possibilities is not an indication that the elements on the mountain are non-deterministic. It merely means that I lack the ability to predict it accurately.

Indeed, when I decide to marry, I do not exhaustively analyze my past, my DNA, etc. in order to rule out deterministic causation.

So I think the difference lies in the fact that in one case (decision-making) the agent of causation is largely internal, and in the other (avalanches), it is largely external.

Enigman said...

Dr. Logic, I think you do put a lot of stock in first impressions, because I think we all do; so I doubt your self-description, which may seem disrespectful of me - but similarly, I would have said that prima facie one need not swap envelopes, that it is only a misleading argument that says that one ought to, so perhaps we simply disagree on what is prima facie. And I think we might be able to chalk it up to human error, but there is surely something to be shown before we do (what first impressions can do is to assign the burden of proof). Your comparison of getting engaged with observing an avalanche fails to show much to me, aside from a poetic streak in you (I follow your argument - another might involve a hypnotised subject, whose impression of herself is that she is choosing). I cannot show that the world is indeterministic; but nor can I show that it contains ordinary objects subject to natural laws, but I assume that it does (as we all do, as aforementioned).

Doctor Logic said...

Enigman,

Sorry for taking so long to get back to you.

Maybe I can clarify what I mean by my not putting stock in the prima facie .

I think that intuitions (beliefs that are yet to be formally justified) are fine until we've had a chance to verify them. If philosophical analysis shows an intuition to be a delusion, then we ought not disregard our philosophical analysis in favor of the original intuition. IOW, I put no stock in the prima facie when formal analysis shows it to be false. I only put stock in my intuitions when I have no alternative but to do so.

We've shown that for phenomena that can be located in time, those phenomena are either deterministic or random (or some combination of the two). A third alternative is not logically possible. The debunking of an intuition doesn't get much stronger than logical disproof.

Now, whether the universe/multiverse is fully deterministic or deterministic-random might be impossible to say. It may not even be a meaningful question. However, the mythical third alternative is clearly ruled out.

Enigman said...

Hmm... logically, of course, the chair that you are sitting upon (if so sit you) does not exist - not as a logical object does it exist - and so I'm left wondering, in what ways does your logical refutation of the third possibility (of objectively responsible free will possessed by a non-physical object, so to speak) differ from such a refutation? The chair exists (maybe the language is at fault) and the third possibility exists, apparently.

Doctor Logic said...

Gosh, Enigman, I think you've lost me there!

Where's the logical argument that the "I'm sitting on a chair" is logically incoherent?

If you had such an argument, then you might have a parallel, but I'm not seeing it.

I'll say also that we have more than just an ironclad logical argument against the third option. We also have an explanation for the human intuition.

Suppose I say "I could have decided to eat the vanilla ice cream instead of the chocolate, and then I would have eaten vanilla instead of chocolate cream".

This is all pretty reasonable. However, it is just like talking about a counterfactual physical situation. For example, "San Francisco would have looked different if the San Andreas fault were 100 miles further East." This statement is true because SF would have been less impacted by Earthquakes. Yet we would not say that physics was indeterminate of free, simply because we can state this counterfactual.

The reason why statements about choices are similarly counterfactual is that my choice of ice cream flavor depended on what flavor I was in the mood for at the time of my decision. Alas, humans often forget this fact in their analysis. Replace vanilla with "dung" and it becomes pretty obvious. Could a person choose dung ice cream instead of chocolate? Only if they were in the mood for dung ice cream, which is counterfactual for most people.

What a person is really saying is this: "If I had been in the mood for vanilla ice cream, I would have chosen vanilla instead of chocolate, and eaten vanilla ice cream instead of chocolate."

There's nothing incompatible with determinacy in this statement because no one is saying that moods are non-deterministic. They are hard to predict, but that doesn't make them non-deterministic.

Yet, if we are blind to what we actually mean by our statements about free choice (because we neglect the mood dependence), then we'll think that our choices don't depend on anything while still not being random. That's a mistake, IMO. Moods are not random, they're just easy to overlook.

...in light of which I said...

Dr. Logic, no, moods are not random, but neither should rationality be based upon moods; I was not saying that choosing according to our moods could not be deterministic (there is a problem with physicalistic moods, prima facie, but that is different).

Your counterfactual about choice of flavour was surely as you said, about what would have been the case under different desires, and it was therefore like the geographical counterfactual, but had I said such a thing I could have meant that, with my existing desires, which were indifferent between those two flavours, I might have decided differently; I might have decided to allow different factors (cost, sociability, effect on the flavours of food I might eat later and so forth) to influence my decision, and it is not obvious to me that all such decisions could be compatible with determinism (the problem of physicalistic moods is related to this obscurity, I think).

(the chair of Theseus hardly exists as a logical object)

Doctor Logic said...

Enigman,

I might have decided to allow different factors (cost, sociability, effect on the flavours of food I might eat later and so forth) to influence my decision, and it is not obvious to me that all such decisions could be compatible with determinism (the problem of physicalistic moods is related to this obscurity, I think).

There are finely balanced physical systems that are deterministic, but which are difficult to predict because the initial conditions are complex. For example, lightning appears random to us. However, physicists of the 19th century were not led to propose that physics was non-deterministic just because we lacked the data and the ability to compute where the lightning would form, where it would strike, where it would fork, etc.

Of course we know that there are quantum effects at some level, so maybe there is some pure randomness. But would not the brain's selection of some criteria for choice be compatible with randomness if not determinism? I'm not seeing any inference to a third choice from cases where we are indifferent or teetering between one choice or another.

If randomness were involved in indifference, then, when I say "I could have decided another way," I mean something like "if that electron state had not decayed randomly when it did, I would have decided differently." It still seems counterfactual in the physical way.

Still, this all seems like a distraction. The argument against a third option is totally airtight. The only assumptions it makes is that events (like choices) are localized in time, and that it makes sense to ask whether events depend on past circumstances. The third option is intended to preserve human responsibility for the purposes of theology (human responsibility exists well enough for psychological and social purposes under determinism), but there's no rescue for theology if we can't even ask whether a choice depended upon circumstances.

So I said...

Consider a human choice. If initial physical conditions were exactly duplicated and the choice was made differently, then that would have to have been due to randomness in the system only if we also assumed materialism. Otherwise it could have been due to there being two different choosers. But the thing about souls is that if you had two of them then they would not be the same person, so such duplication cannot be extended to include them. So I don't see your airtight, ironclad argument; could you state it in a way that does not beg the question?

Without such an argument, if the same soul was put into physically identical worlds (same past and present) in succession, and chose differently in two of them, then that would not have to be due to something relevantly like physical randomness, would it? There is something irresponsible about such unthinking randomness, that is true, but there is something responsible about determining one's own future propensities in such a way. And that some of the observed properties of human responsibility are isomorphic to properties of a hypothetical deterministic physical system is obvious; where is the argument that they all are, which does not beg the question?

Doctor Logic said...

Hi Enigman,

I could not follow your last argument, but I can try to state my argument in a more general way.

I don't think my argument depends upon physicalism. For example, imagine that the human thinking system is not totally physical. The human makes a decision at time T in both the physical and non-physical realm.

Now, part of the man's decision depends on circumstances before and up to T in physical spacetime and "soulspace", including constants relative to the spacetime continuum. For example, if the speed of light is constant in our spacetime, and the man's decision depends only upon this, then, because the speed of light is fixed, his decision is determined.

Also, if the man is filled with some non-physical "goodness" prior to T, and his decision depends on this non-physical parameter, then his decision is fixed by that past state.

Assuming we cannot say that the decision depends on the future, then the remaining part of the decision depends on nothing whatsoever. It doesn't depend on the past, future or constants relative to the spacetime continuum or the non-physical dimension. That makes it random in the most fundamental way.

This randomness is present in both physical and non-physical space. For example, suppose that a man's non-physical goodness were neither dependent on the past nor a constant. In that case, his "goodness" is an utterly random quantity. His goodness depends on nothing.

I cannot find any way to break out of the logical dichotomy that the world (physical and otherwise) is deterministic + random as long as decisions are localized in time.

all that could be said...

But how does not knowing what else a choice could depend upon (e.g. because we cannot observe such personal creativity from the outside, to know about it in such an objective way) mean that the choice must, if not predetermined, be made at random? Your argument is very good, but, given how counter-intuitive its conclusion is, I would want it to be better before I accepted its conclusion (cf. Cartesian sceptical arguments, I suppose).

Doctor Logic said...

Hi Enigman,

Okay, one last comment, and then I'll leave you in peace. :P

It's not an issue of not knowing what the non-deterministic part of the choice depends upon.

I can account for all possible things by looking at the set of all things in time and all things outside of time. The things outside of time include universal constants and anything outside the spacetime continuum. Of those things in time, we can only depend upon the past and present, not the future (not without assuming the future already exists, and thereby assuming determinism).

We end up at fundamental randomness because the non-deterministic part of the choice literally depends on nothing (not unknowns, but an empty set). The set of stuff that is neither in time nor outside of time is empty.

this was not actually said...

...thanks for the simplification; I'll have to think about it some more. That way of looking at it (under which the set is empty) may be coherent. (Of course, maybe it is not - e.g. sets? all things? - and then we should not conclude too much from what it seems to show us.) What I'm saying is that that way of looking at it may not correspond exactly with the way reality is, to the extent that your conclusion is false. Therefore your argument is not airtight and ironclad. That air, such iron - those words, like all words, get their content from our experience of the world (of animals and such in 3-D space) around us, not from our theoretical model, however coherent and comprehensive it is. Our experience of rational choice is primitive. I'm not saying that it shows compatibilism to be false. I don't think it can do that. But it is certainly there, alongside the (actually rather inconclusive) evidence for physical closure, and such logical arguments as yours (which depend upon categories whose content comes from our experiences)... (was that :P a picture of you sticking out your tongue at me? gosh) ...but I agree that my position here is the burdensome one :c