February 24, 2007

Foreknowledge, Free Will, and the Grandfather Paradox

Compatibilism is belief in actions that are both free and determined. Usually, one hears such phrases as "what I will to do, I must do" (I think Hume phrases it something like this) or "I am free to act according to my nature." The idea is that human beings have determinate natures and they act as their natures determine. They are free because nothing outside determines their actions.

Theories that posit a more robust freedom of the will are called "libertarian" (no relation to the political theory referred to in my tagline). Usually one hears phrases like "I am free because I might have done otherwise." (Of course, if actions were completely random, that wouldn't be freedom either, so I believe that libertarians must posit a type of action that is neither free nor determined.)

Foreknowledge is often considered to be a problem for the latter type of free will. In order for it to be possible for there to be knowledge of something, there must be a fact of the matter about it, and even the existence of such a fact (a fact about what I will choose which is already the case before I choose it) has often been thought problematic. This is often solved by simply saying something about how it is my future choice that is the truth-maker for this fact. In an eternalist framework (one that views all times as existing equally, and does not give a priveleged position to the present), it seems unproblematic that my future choice should make something true now. In fact, if we take relativity seriously enough, then it isn't really that different from, for instance, a choice I made while in Greece making some fact true here in the U.S. Certainly that is unproblematic!

A further objection arises in terms of someone actually knowing the truth-value of the fact (especially me knowing what choice I will make before I will make it, through some other means than deciding). It is thought that this will interfere with free will since someone knowing the fact "pins it down" as it were. However, if eternalism is true, the fact is already "pinned down" - that future time exists, and in that future time, I make the choice. Still, it seems that my knowledge could interfere with my freedom in this sort of case.

The foreknowledge of God is considered to be a special case which is somewhat easier to get out of: since God exists atemporally, he witnesses all moments simultaneously, and so he simply observes me making my future choices. But why should foreknowledge had by an agent within time be any more problematic than this?

Consider the "Grandfather Paradox" as a famous example. Here is David Lewis's formulation of the problem:

Consider Tim. He detests his grandfather, whose success in the munitions trade built the family fortuen that paid for Tim's time machine. Tim would like ntohing so much as to kill Grandfather, but alas he is too late. Grandfather died in his bed in 1957, while Tim was a young boy. But when Tim has built his time machine and traveled to 1920, suddenly he realizes that he is not too late after all. He buys a rifle; he spends long hours in target practice; he shadows Grandfather to learn the route of his daily walk to the munitions works; he rents a room along the route; and there he lurks, one winter day in 1921, rifle loaded, hate in his heart, as Grandfather walks closer, closer,....
- David Lewis, "The Paradoxes of Time Travel," American Philosophical Quarterly, 13

To make the problem worse (although I don't think Lewis mentions this in his paper), we can imagine that these events occur before Tim's father was conceived, so that if Tim succeeds in killing Grandfather, Tim will not be born. Now, this is not only a problem for time travel, but a problem for human foreknowledge in general. That is, suppose we, with Tim, are in the year 1985 (since that is clearly when time travel was invented). We know, and Tim knows, that Tim didn't kill Grandfather in 1921. From Tim's perspective, 1921 is in the future as well as the past, since he will soon travel back to 1921. But Tim also knows that in 1921 he didn't kill Grandfather and, therefore, it is also true from his perspective that in 1921 he won't kill Grandfather, since 1921 is both past and future to Tim. But why should it follow that Tim can't kill Grandfather? Libertarians are already committed to the proposition that didn't does not entail couldn't have and won't doesn't entail can't, so why should they be troubled that Tim didn't and won't kill Grandfather in 1921? We have already posited that there is a fact of the matter. Why should Tim's possession of that fact change the situation?

Perhaps the concern is something like this: suppose that Tim goes through the same reasoning we have just gone through, and determines that he didn't and won't kill Grandfather, and therefore doesn't try. Further suppose that we have the correct theory of truth-conditions for counterfactuals (including counterfactuals of freedom - suppose that these have truth-values), and, on this theory, the statement "if Tim had tried to kill Grandfather, he would have succeeded" is true. Then we seem to have at best a case of circular causation, and maybe even worse difficulties. Consider an explanation of why Grandfather didn't die. It might go something like "although Tim could have killed Grandfather had he tried, he did not attempt to kill Grandfather because he knew that he didn't kill Grandfather." Or we could condense it into the even worse sentence "Tim chose not to kill Grandfather because he knew that he didn't kill Grandfather." Let C represent "Tim chose not to kill Grandfather" and D represent "Tim didn't kill Grandfather." It is now the case that (according to libertarians) C is the truth-maker of D, but D is the reason for C. What a headache!

But is this really worse than circular causation? I'm not sure. And, honestly, circular causation doesn't bother me too much anyway. It's not any worse than an infinite chain of causation, both of which are fine if there is a sufficient reason outside the chain or circle for why the chain or circle is. However, in this case, it doesn't seem that God can be invoked as the reason, because then we would no longer have libertarian free will (either God would be the truth-maker for C and not Tim alone or, worse, God would be the truth-maker of D and not Tim's free choice).

Might libertarians escape through their denial of psychological determinism? That is, Tim's knowledge that he didn't and won't kill Grandfather doesn't actually prevent him from trying in any deterministic way, so perhaps he might still have tried, and succeeded, and then it would have been eternally true that Tim killed Grandfather - but then Tim would not have been born, would not have built a time machine, would not have killed Grandfather, etc. Perhaps, however, this is only an argument against (one dimensional) time travel. Perhaps if we remove the causal problem it will work.

However, libertarians don't want to deny that our beliefs, etc., influence our choices, so it seems that we would still have a circularity problem. Perhaps a degree of uncertainty solves the problem. That is, I think it is very unlikely - say, probability .05 - that I will ever audition to be a television actor. I think this based on my plans, decisions, etc., in the present. But suppose I somehow gain additional information that makes it very likely - but not certain - that I will audition as a television actor in the future. It seems to me that whether this help will depend on its source. If someone I believe to be very skilled in such matters tells me, based on extensive psycho-analysis, that I am highly likely to make such a choice, this is not very problematic. But if I get a message from the future, that may be more problematic. We may have the circularity problem again.

But consider Tim once more. Suppose Grandfather is not his grandfather, but my great-grandfather (my grandfather not having been born in 1921). Tim doesn't know that he didn't and won't kill Grandfather, but I do. This doesn't seem to suffer from the same problem of explanatory regress. However, we must then ask the question of whether I am free to tell Tim what I know.

These are serious problems, but I'm not convinced they are unsolvable. We are walking along our epistemic boundaries here, and mind-bending difficulties here and there are to be expected.

The reason I am interested in these problems, is that it seems like detailed knowledge of brain states, etc., might provide the kind of information that runs into these difficulties. Then again, it could simply be that between the Uncertainty Principle of quantum mechanics and the limits of our ability to gather and process information (we can only know so much about a person's present brain states, and to then figure out what stimulus the person will experience in enough detail to make predictions may be impossible for humans) may make it impossible for us to reach this kind of knowledge. If there are no temporal beings capable of gathering and processing enough information to do this sort of thing, then the theoretical possibility of such a thing is probably unproblematic.

Posted by Kenny at February 24, 2007 1:47 PM
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Comments

The uncertainty principle is almost certainly irrelevant here. You, presumably, are going to say that the brain states are determined by the flow of electrons (or even larger particles) in the brain, and yes, there is uncertainty in the position and velocity of the electrons- but it is TINY. Keep in mind that physicists who believe that electrons don't HAVE determined positions and velocities within the uncertainty bounds still do nuero-physics without problem. Furthermore, what does any SINGLE electron do? Not much. To be activated, a cell typically needs to receive quite a few electrons, enough that experimental neuro-biophysicists tend to measure current. So, even if we only know with 99.9999999999999999999 (I got sick of typing 9's but you get the idea)% certain that each electron is on a collision course with this receptor, by the time that you account for the number of electrons typically released and the number of electrons needed to be received, the uncertainty will be negligible. The nuerophysics papers I've read didn't even need any correction factors for it. The scale just doesn't work.

The best qm is can do, I think, is to give you mechanism so that you can say that even if Tim is shoots the gun at his grandfather in the right trajectory, etc, since he can't control the collapse of the wave function, it COULD be that the bullet (for example) tunnels through grandfather. You could argue that it's also possible, no matter what action Tim does, that the laws of physics will conspire such that he fails because of something he cannot control. So then all his actions can be free, because he CAN do them, but they don't determine the outcome. But, of course, you don't like that whole collapse of the wavefunction and loss of causality, so you won't do this.

Posted by: Lauren at February 24, 2007 4:29 PM

The tunnelling idea, etc., wouldn't help anyway, because we could expand the thought experiment by supposing that we, in the future, know more. I had supposed that the brain was complex and sensitive enough (on a small enough scale) that uncertainty would matter, but perhaps not. The real point is that, even if it were in principle possible for someone to predict behavior through observing brain states, it might still be impossible for humans to do this, even at a very high state of technological advancement.

Posted by: Kenny at February 24, 2007 5:06 PM

Know more what? You'd have to know how to control the collapse of the wavefunction. Even ignoring that the probabilistic interpretation of qm, many of those who do accept some other deterministic form would say that, because you need a nonlocal variable, we cannot CONTROL that nonlocal variable, whatever it is- otherwise it wouldn't just be that the wavefunction collapses faster than light, but that physical changes propagate faster than the speed of light, and that has problems with relativity. Yes, you could expand the thought experiment by giving humans this knowledge, but your justification for doing it would be relatively weak.

Granted, I don't really like the idea of the laws of nature "conspiring" in this way- it makes a bunch for problems for the statistical interpretation, for one thing- but I'm trying to point out that if qm WAS going to be involved in this discussion, it'd probably be here, in to what extent can Tim's actions actually affect whether or not his grandfather is dead or alive. (Schroedinger's cat, anyone?)

I know you're trying to say that "it might still be impossible for humans to do this"- I'm pointing out that qm isn't going to do this for you, you'll still need something else. There's only so much you can solve by waving your hands and saying "quantum mechanics" :-)

Posted by: Lauren at February 24, 2007 5:28 PM

What I'm saying is that the possibility that some highly improbable quantum fluctuation occurred in 1921 doesn't affect the thought experiment. For instance, at one pont in the discussion, I stipulated that we knew that the statement "if Tim had tried to kill Grandfather, he would have succeeded" was true. In order to get out, it seems as if you might have to say that the people in 1985 couldn't know the relevant fact, and it's not clear why it wouldn't be at least possible for them to know it.

Posted by: Kenny at February 24, 2007 5:41 PM

I thought that the collapse of the wave function was just a gimmick to make Shroedinger's equations work. Under Heisenberg's matrix algebra approach, one does not have to posit any collapse.

Posted by: Anthony D'Amato at March 14, 2007 11:12 PM

The short answer to your question is: In some sense, yes, there is no wave function collapse in Heisenberg's matrix algebra (alone). This is because there is NO wave function to collapse. However, the discontinuity in behavior because of a measurement is still in matrix mechanics.

The long answer is this:
Like all physics theories, quantum mechanics is about things we can observe in the world. That is, if I make this sort of measurement, what result(s) do (can) I get. Quantum mechanics differs from classical physics in that it often gives a variety of answers here, for example, one could measure spin +1/2 OR spin -1/2 for an electron, but fundamentally it's about measurements.

Now, there are several different ways of doing this. These ways are mathematically equivalent, but alone have different (although not contradictory) interpretations, which makes certain formulations easier to use in certain circumstances. Early in quantum mechanics, there were two major formulations- Schrodinger's wave mechanics, and Heisenberg's matrix mechanics. To get the possible values from Schrodinger's wave mechanics, one solves Schrodinger's wave equation, a differential equation. To get the possible values from Heisenberg's matrix mechanics, one finds the matrix corresponding the hamiltonian, and solves something called an eigenvalue problem. They give equivalent results.

Now let's say you take a system in a superposition of states |x> and |y>, which is true in wave and matrix mechanics (I'm using Dirac notation). Let's say you take a measurement of the system, and get X. If you keep repeating the measurement, you keep getting X. There's been a change in the system, such that instead of being in a superpostion of |x> and |y>, it's now only in |x>. The question is, how is this dealt with and explained in matrix and wave mechanics, respectively?

In wave mechanics, we talk about the "wave collapsing". This means that there was one wave equation that described the initial state, but after measurement, there's only "part" of it. (Ignoring normalization). Wave mechanics works to predict the possible values we measuring in an experiment, and their relative probabilities. However, there's a "law" of wave mechanics, that says that, after an observation, if no further observations whose operator does not commute with the operator of the first measurement has been made, if the initial observation is repeated, then the same result will be measured. For shorthand, we call that the "collapse" of the wave function.

Now let's consider matrix mechanics. For simplicity, let's put everything in the basis of the eigenvectors. What happens is before the measurement, your matrix describing the system will have multiple elements, such as
[a1
a2
a3].
However, the matrix after the measurement will only have ONE entry (in the eigenvector basis), and the others will be zero. So it might look like:
[a2
0
0].
So, the discontinuity is still there- making a measurement requires a change in the mathematical formalism, regardless of whether one is using matrix or wave mechanics.

So why do we only hear about "wave collapse" instead of "spontaneous matrix change" or something? Well, a physical theory involves more than just mathematical formalism. It is requires an interpretation, some sort of connection to the "real" world. In matrix mechanics alone, this interpretation is not there- we just get results, but there's no meaning to the mathematics used to get them. We don't know the meaning of the matrices used to get them. But when we compare it to wave mechanics, we see that the matrix
[a1
a2
a3]
corresponds to the wave function, so that when the matrix "collapses", it's the same as the wave function collapsing. However, since our understanding of what the parts of matrix mechanics means is from comparing it to wave mechanics, by itself one could say there is no wave function collapse, only a "matrix" collapse. However, the discontinuity is there, all the same.

I hope this answers your question.

Posted by: Lauren at March 15, 2007 1:16 AM

it is impossible to go back in time, it is possible to go forward,however this does not do anyone any good, for anyone example.

1. you cant get back
2. you dont know whats in the future(an astroid may have destoyed the earth the minute you left)
3. you cant control how far into the future you will go
it is a matter of going faster than the speed of light , which in current astro,time ,quantum physics is not possible, its called the TWIN THEORY and it has been proven that it works, (TWO ATOMIC CLOCKS WERE PLACED ON TWO SEPERATE PLANES ,ONE GOING WITH THE ROTATION OF THE EARTH,ONE AGAINST) Guess which one was faster??? The times were off ever so slightly, but they were still off. FIGURE THAT ONE OUT!!!!!!!!!!!!!!

Posted by: Anonymous at August 19, 2009 9:49 PM

Generally I don't learn article on blogs, however I would like to say that this write-up very forced me to try and do so! Your writing style has been surprised me. Thanks, quite great post. you may like the .pdf piece written by : Scott Tucker on quantum computation

Posted by: Scott Tucker at July 17, 2012 1:15 PM

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