An Anti-Determinist Argument
Daniel Mullin

13 December 2013

We generally think that the past is settled and nothing we do in the present can change it (barring time travel or backwards causation). In other words, it seems irrational to direct our efforts toward trying to affect the past. For example, if an organism evolved a mutation that caused it to spend time and energy trying to influence the past instead of the future, it's reasonable to assume that the organism wouldn't survive very long. So far, so good.

However, a wrinkle in the assumption that it's irrational to direct our action toward the past is provided by Newcomb's Paradox. In this paradox, we are asked to stipulate an infallible (or near infallible) Predictor that can predict your actions. You're then presented with two boxes, Box A and Box B. Box A is transparent and you can see that it contains $1000. Box B is opaque, but you're told that it either contains $1,000,000 or nothing. You're then told that you can take both boxes or take Box B only. If the Predictor predicted that you would take both boxes, Box B contains nothing, but if the Predictor predicted that you would take Box B only, it contains $1,000,000.

Newcomb's Paradox is a common problem in decision theory, but it also pushes our intuitions about actions affecting events in the past. From Wikipedia:

The crux of the paradox is in the existence of two contradictory arguments, both being seemingly correct.

A powerful intuitive belief, that past events cannot be affected. My future action cannot determine the fate of an event that happened before the action.

Newcomb proposes a way of doing precisely this — affecting a past event. The prediction of the Predictor establishes equivalence between my choice (of renouncing the open box) and the content of the closed box, which was determined in the past. Since I can affect the future event, I can also affect the past event, which is equivalent to it.

Your 'solution' to the problem will likely depend on whether or not you think it's rational to try to affect something that's past and settled. After all, either the money is already there or it's not. Newcomb's Paradox is fun partly because it causes us to question this intuition, but in another sense, it can sharpen it (at least it does for me).

So let's say that our intuition that our actions can't affect the past survives Newcomb's Paradox. This intuition, if sound, has implications for determinism. If determinism is true, then all of our actions are determined by the prior causal history of the universe. A Predictor, in possession of all the facts about the universe, could in principle predict our future actions, much like in the case of Newcomb's boxes. The causal history of the universe, then, would be different depending on whether I chose both boxes or Box B only. But this also seems like a case of affecting the past, for the following reason.

Let's say I want the causal history of the universe to lead to my getting $1,000,000. Then I would choose Box B only. This seems to entail that my choice caused the past to be a certain way rather than another. But that doesn't seem possible. In fact, regardless of what choice I make, it doesn't seem like the past would change at all. Again, the matter has already been settled ex hypothesi. Thus, based on our intuition about the immutability of the past, it seems that we cannot coherently regard our actions as being determined by the prior causal history of the universe. This suggests that determinism is false.

Comments (9)

Daniel Mullin's picture

Daniel Mullin

Wednesday, May 1, 2013 -- 5:00 PM

To get the ball rolling on

To get the ball rolling on this one, I cross-posted a version of it on my personal blog. A reader posted the following comment:
Alternatively, and perhaps more naturally, this can be construed as an argument against free will (at least against the traditional, libertarian concept of free will, some compatibilist accounts of free will are compatible with determinism). I agree with your summary and analysis of Newcomb?s problem up to end of the second to last paragraph. However, I think the following sentence is incorrect: ?The causal history of the universe, then, would be different depending on whether I chose both boxes or Box B only.? The causal history of the universe is, ex hypothesi, past and settled, therefore the correct formulation is: ?whether I choose both boxes or Box B only is dependent on the causal history of the universe.? This is a variation of a basic premise of determinism, that the future is completely determined by the past.
So a determinist would interpret the following paragraph as follows: ?Let?s say I want the causal history of the universe to lead to my getting $1,000,000. Then I would choose Box B only.? The fact you chose box B only, a fact which the predictor was aware of before it occurred, is evidence that the causal history of the world is such-and-such. Therefor the determinist would argue that you have the explanatory priority backward in the next statement: ?This seems to entail that my choice caused the past to be a certain way rather than another.? Rather, the past caused you to make the choice that you did, the feeling that it was free is, on the standard determinist account, merely an illusion. The determinist would whole-heartedly agree that ? In fact, regardless of what choice I make, it doesn?t seem like the past would change at all. Again, the matter has already been settled ex hypothesi. ? But use this to draw the opposite conclusion, namely that based on our intuition of the immutability of the past, we cannot coherently regard our actions as being ?free?.
Any thoughts?

Hugh Millar's picture

Hugh Millar

Saturday, December 28, 2013 -- 4:00 PM

Sorry, I think the paradox is

Sorry, I think the paradox is just an illustration of how hard it is to accept determinism in the face of our everyday experience of free choice.  Alas, if determinism rules we don't actually have free choice, so we can stop agonizing about the consequences for the past world of our choosing one box or two.
The real question is how to reconcile these two apparently contradictory aspects of life - our experience of determinism in the laws by which the physical world runs, and our experience of free choice in our interior worlds.  The answer?  The contradiction is apparent rather than real, because the two experiences are orthogonal.  We see an external world when we look out, and an internal world when we look in.  An act of perception is a glimpse of the world out there *or* of the world in here, never together.  Nothing that we discover or infer externally has any  necessary implication for our interior experience.  The brain makes a good job of synthesizing, of course, but don't be misled.  We can recognize physical law in the world without giving up on our experience of free choice.  Both realms of human experience are equally valid.
I and Thou:  the above deals only with our individual experience of choice.  A tricky question remains about other people, who seem to inhabit the deterministic physical world but also claim to make free choices.  We'll maybe try to catch that later ...

M. Newton's picture

M. Newton

Saturday, December 28, 2013 -- 4:00 PM

Some thought experiments are

Some thought experiments are just for fun. Newcomb's is one such.
Once you grant a Predictor, you accept determinism.
But this scenario requires another genie, the one that takes note of the Predictor's prediction, and adjusts reality accordingly.  Predicting is not causing. It ought to be based on a knowledge of causation, of course. Doesn't this paradox remind one of the Ontological Argument for the existence of God?
I think we ought to use the term "free" more carefully. Specifically, we ought to always include "from ____." We ought always to say what something is free from, when we claim it is free. Then, we ought to require ourselves to show that what we say it is free from, it might not be free from. That keeps us in the realm of actual things and phenomena. Our intellectual powers are well tested within that realm, much less being supposed to succeed where the impossible and ill-defined are posited as a starting point.

Daniel Pech's picture

Daniel Pech

Thursday, February 27, 2014 -- 4:00 PM

My brain lacks the kind of

My brain lacks the kind of Predictor concept required to make this Newcomb's Paradox seem like a paradox to me. So, I see no difference between this thought experiment and one in which I get to place a million$ in an otherwise empty box B in the case in which you do not chose box B. This way, in the case in which you do chose box B, box B will be empty as required by Newcomb's version. Or, if I don't have a Million$, I can just not bother with box B, and the result for you will remain the same whether you chose box B or not.
There's a similar thought experiment, about omniscience, that seems as empty to me as Newcomb's one here. It says that in a game of 'chicken' with an Omniscient, all you have to do to win the game is simply to determine not to swerve aside at the last moment, determining simply to drive straight ahead, and ostensibly forcing the Omniscient to be the one to swerve aside (assuming that the Omniscient doesn't admit defeat at the outset in knowing your predetermination). Just the first two of several basic problems with this thought experiment is that we cannot actually know that a given entity against which we play this game is omniscient, and that, even if we believe that some such entity is omniscient, we cannot know whether an Omniscient knows how, in an entirely fair manner, to make us change our predetermination at the last moment.
Oops. "If you take box B only, then it contains a million$". Well, then I better have a milllion$ to give you for taking only box B. In any case, the problem I'm seeing (assuming it is a problem, and not some mistake on my part to understand the thought experiment) is that, given the variability of content of box B specified by the thought experiment, how did that million$ get in box B in the first place in the case in which you chose only box B? If box B has the option of being empty...
But, then, I guess we're dealing with your actual choice, not with...uh, whatever it is that, within the thought experiment, seems to allow that box B possibly can be empty. Anybody got a wrench? I think this paradox is leaking.

Lawliet.L's picture


Saturday, May 2, 2015 -- 5:00 PM

Considering the nature of a

Considering the nature of a paradox, the lack of conclusion in it, we might look for truth in what we know for sure.Since we are truly happy only when we accept determanism, it might be a hint of truth.

Walto's picture


Wednesday, May 20, 2015 -- 5:00 PM

My own sense of this paradox

My own sense of this paradox is that it shows that "rational" has two meanings.  There's a sense in which it is "irrational" to choose just one box, and another in which it's irrational to choose both.  But those who care more about the money than being sufficiently "sciency" about this matter, need not believe they are somehow affecting the past. They are simply making the bet that routinely produces the most money. 
That's the kind of "rationality" one wants one's financial advisors to exhibit, no? In addition, it's the kind of rationality that would make one prefer to allow oneself to be "cured" by a placebo.  When one is cured by a sugar pill, there's no reason to suppose that he or she has some theory about reverse causation: the same is true here.

sageorge's picture


Friday, February 12, 2016 -- 4:00 PM


First, determinism as a theory of how everything works is almost certainly false.  Outcomes of measurements at the quantum level appear to have a random aspect. Originally it seemed possible that so-called hidden variables might account for the varying outcomes, but theoretical work in the 1960s led to experiments since then, including ones being actively carried out now, that have eliminated almost all possibilities for hidden variables.  People and our brains, being big (compared to subatomic particles) and hot (compared to absolute zero) may be virtually exempt from quantum indeterminacy, but even so someone playing the Newcomb game could decide, let's assume deterministically, to put the decision about the boxes under control of a quantum process such as whether a particular radioactive decay happened or not within a certain time.  In that case the decision would be non-deterministic and radically resistant even to the fantastic predictive powers imputed to the Predictor.
However, the Predictor could stipulate that anyone who plays couldn't use such quantum processes in making the decision.  (The Player couldn't complain, having nothing to lose and an instant $1,000 to gain by foregoing all philosophical agonizing and just grabbing both boxes.)  Even if the Player does try to analyze the situation in order to maximize gain, I don't see a paradox. If the Predictor aimed to give away no more than $1,000, it will have set up the boxes after considering all the future (by hypothesis predictable) thinking of the Player.  The Player will try to psych out what the Predictor did in the past: "The Predictor thinks it knows what I will do, but I'm going to fool it by...", all to no avail since at the time the boxes were set up the Predictor already knew those exact thoughts would occur.  Perhaps the "It thinks I will do X, so I will respond by doing Y" could lead to an infinite loop or regress, but if the choice of boxes must be made in finite time, the Predictor knew exactly how many iterations of the loop will have taken place, and therefore knew what the box-decision will be.  The Player makes a completely free choice when that moment arrives (no guns pointed, no weird obsession against anything having to do with the letter "A" etc., making whatever thoroughly considered choice he wants ), but the Predictor, by hypothesis, knew when the boxes were set up what that choice will be, and placed the money accordingly.
The appearance of paradox in the story attached to the game comes, I think, from slipping in a random or supernatural basis for the Player's thinking, which contradicts the determinism implied in the Predictor's assumed powers.