Answer

In my book The Science of Freedom I described Newcomb’s paradox (there’s also an entry on Wikipedia). There I explained why foreknowledge is incompatible with free will at the conceptual-analytic level. The paradox arises for us, so it doesn’t help to say that with the Holy One things work differently. We think in our language and with our concepts. By the same token, you can’t explain a round triangle by saying that for the Holy One the triangle doesn’t contradict the circle. For us it does contradict, and we cannot speak about such a thing (we can’t even say that for Him there is no contradiction—because that too is a statement made in our terms).
If you have the book handy, please look there (because everything is explained well there). If not, write back to me and I’ll try to explain it here.
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Questioner:
Hello Rabbi, first of all thank you very much for the quick reply. Unfortunately I don’t have the book at hand, but if it’s too much trouble to explain, I certainly can’t ask you to do so.
The problem is that it seems that this explanation actually is in our language and concepts. The explanation is also scientific and not entirely transcendental; all that’s required is an understanding of the fact that time too is a dimension beyond which God exists. Once that is fully understood, it seems that it is no longer contradictory even in our own language and concepts—the possibility that a being can look at time without being dependent on it, and thereby know the future while at the same time not contradicting the flow of time, does not seem so far-fetched. You have surely heard the familiar analogy according to which when a person watches a filmed movie in which people made decisions, he can know what the decisions are before they are made in the film, even though in reality the people being filmed definitely made those decisions.
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Rabbi:
I have indeed heard that analogy, but it is of no help. I copied here the relevant passage from the book:
 
Newcomb’s thought experiment:
In the previous chapter we dealt with the lazy man argument, according to which a determinist ought to be idle and not act to achieve any goals. We illustrated this through a person with infinite predictive power who writes on a slip of paper the grade that a student will receive on a future test. Since the grade written on the slip must be correct (because the prophet has perfect and certain predictive ability), there is no point in studying for the test, since the grade is already fixed in advance.
In Newcomb’s problem we are in a very similar situation (in fact an identical one). Here too two people are involved: the chooser and the prophet. In front of the chooser are two boxes: one open, containing $1,000, and the other closed, containing either $0 or $1,000,000 (the chooser does not know which of the two possibilities it is). The chooser must decide whether to take the contents of both boxes together, or only the contents of the closed one. At this point the prophet enters the picture (we assume his predictive ability is perfect). He knows in advance and with certainty what the chooser will do, and based on that he prepares the contents of the closed box one day before the chooser makes his decision. Since the prophet wants to reward someone who is satisfied with little, he adopts the following tactic: if the chooser is going to take both boxes, he makes sure already now that the closed box contains no money at all. But if the chooser is someone who is satisfied with little and is going to take only the closed box, the prophet rewards him by putting a million dollars inside it.
The chooser himself knows all this. He knows the prophet’s abilities, as well as his strategy. The only detail the chooser does not know is what the prophet predicted regarding his present expected choice (for he himself is not a prophet), and therefore he also does not know what the prophet put into the closed box. The question is: what strategy should the chooser adopt? On the face of it, he should take only the closed box, because then he will win a million dollars, whereas if he takes both he will win only a thousand (because the closed one will be empty). On the other hand, the box is already closed in front of him now, and what is inside it was already determined yesterday and will not change if he acts differently. If so, why shouldn’t he take, together with the closed box, also the open one with another thousand dollars? After all, his taking the second box cannot retroactively change the contents of the closed box (our assumption is that the prophet is omniscient but not necessarily omnipotent). If so, it seems that taking both boxes is the winning strategy in any case. But if the prophet is truly omniscient, he will ensure that in such a case the closed box is empty. If so, when the chooser takes both he will win only $1,000—that is, he chose incorrectly.
At the time this paradox was published, a kind of “Newcomania” emerged, meaning a phenomenon of people becoming obsessed with thinking about it. The philosopher Robert Nozick, in his 1969 article in which he presented Newcomb’s paradox to the public, reports that almost everyone has a clear position on the question, and almost everyone also thinks that whoever holds the other position is a complete idiot. But there is certainly no consensus as to which position is the correct one.
It seems to me that I too am no exception in this matter. I also have a clear position on this question. However, for our purposes it is more important to stress that the assumption that there is such a prophet already smuggles in a concealed deterministic position. In the libertarian picture one cannot speak of such a prophet, because it is impossible to know with certainty in advance what the chooser will decide. If the information does not now exist, how can there be someone who knows it with certainty? “Knowing information that does not exist” is a self-contradictory expression; a prophet who predicts in advance a decision of a person who chooses freely is an oxymoron. This is not a matter of the quality of his predictive ability. Predictive ability is defined where the information exists in principle—that is, where it can be derived from the present circumstances. But in the libertarian picture the information does not exist at all now, and therefore no one, no matter how great his predictive power may be, could ever predict the future (above we saw that even God Himself cannot do this).
By contrast, in the deterministic picture the difficulty remains. There the assumption is that the information does exist. Even if no one can access it (because it is very complex and complicated; unfortunately for the prophet, there is no computer powerful enough to predict it), the information exists. Therefore there is no principled obstacle to there being a prophet who knows it. This is a supercomputer, which may not in fact exist right now, but the concept does not contain a contradiction (for the computer knows information that really exists). Therefore this argument is really a thought experiment conducted according to the determinist’s assumptions (just as Einstein conducted a thought experiment according to Newtonian assumptions and thereby refuted them).
From this it follows that Newcomb’s paradox is really an a priori argument against determinism, because if determinism is correct then the information indeed exists and such a prophet is possible in principle. If so, according to that view it follows that even though the content of the closed box is already fixed and will not change, it is still better for the chooser to forgo taking the open box and settle for the closed box. Taking the open box with another thousand dollars would supposedly “make disappear” a million dollars from the closed box. If so, according to the determinist the chooser must make a blatantly irrational decision (not to take a thousand dollars lying before him), or alternatively he must believe in causal influence backward in time (that taking the box will retroactively change its contents). Which in itself proves that determinism is patently unreasonable.[1]
 
Some sharpened the difficulty by extending Newcomb’s problem to a glass box. If the closed box is made of glass, the chooser sees what is inside it. If he sees that it contains a million dollars, he understands that the prophet predicted he would take only it. So now he will take both boxes in order to gain another thousand dollars, contrary to the prophet’s prediction. And if he sees that it is empty, then clearly the prophet predicted that he would take both. So to annoy the prophet he might decide to take only the closed one. In any event, his actions are the opposite of what was predicted. This is in effect a proof that there cannot be a prophet who predicts the choice in advance. Alternatively, acting contrary to the prophet’s prediction would somehow miraculously change the contents of the closed box, and then the prophet’s predictions would come true. But in that case we have indeed saved the possibility of prophecy (= determinism), but at the price of adopting a view that permits causal influence backward in time, from the future to the past.
But this extension is problematic, because according to the deterministic assumption the chooser cannot change his choice. Even if there is nothing in the box, he is compelled to take both boxes, and vice versa. Seemingly this is also the solution to the original difficulty, but a second look shows that it is not, as we shall now see.
 
A further clarification of Newcomb’s paradox
At first glance it seems that this experiment provides no argument against determinism, but at most a proof that free choice is incompatible with determinism (an argument against compatibilism). The determinist should not be alarmed by this difficulty, for in the deterministic picture the chooser has no possibility of freely choosing between the two options at all. He really will do what the prophet predicted, because he has no other possibility. In fact this is the natural outgrowth of the deterministic worldview, and it shows that one can remain an honest—or at least a consistent—determinist.
But further reflection shows that the determinist’s difficulty still remains. Our problem is not the question of what the chooser will do in such a situation, but what would be correct for him to do. This is a mathematical question about strategy, belonging to game theory, and not a question about the chooser’s psychology or about what will happen in practice. Even in the deterministic picture, which holds that none of us has free choice, one may still ask the question: assuming that some creature in some imaginary world does have free choice, what would be more correct for it to do? There is no answer to this question, and that itself is the problem that arises in the deterministic picture.
It is possible that the determinist could save himself by claiming that the question is not well-defined. Free choice is something that contains a contradiction at the conceptual level, and therefore from his perspective one cannot even ask the hypothetical question (what is the correct strategy?), and not just the practical question (what would you do in such a situation?). But this is an implausible claim. For the sake of the discussion I am willing to concede that free will is hard to understand. I am also willing to assume for the sake of discussion that perhaps such freedom does not exist in any creature (including human beings) in our deterministic world. But the claim that such freedom is not defined at all at the logical-conceptual level—that is, that it involves a logical problem and not merely a physical one—is a very implausible and unfounded claim. It seems that this is too high a price to pay for stubborn adherence to the deterministic dogma.[2]
It can be formulated somewhat differently. Even the determinist does not deny human rationality, that is, that a person makes decisions according to the best of his understanding and considerations. He only claims that this process does not express free choice and decision, but rather a kind of mechanical calculation imposed on us. But if so, the difficulty remains on his view as well: in our case there is a prophet who knows in advance what we will choose, and given this information it is clear that the chooser must use that too in order to “calculate” his decision rationally. But what is that rational decision that he must make (deterministically)? Seemingly he should take only the closed box in order to win the million dollars. On the other hand, as a rational person he knows that the prophet cannot change the content of the box after the choice, and therefore clearly it is preferable to take both boxes together. So in order to solve the problem, the determinist now needs to retreat one step and declare that the person is compelled to act irrationally. And is the determinist prepared to deny human rationality? If so, it is not clear to me why he takes so seriously the considerations that led him to the deterministic position itself. Perhaps he is compelled to those conclusions as well, even though they are illogical?!
 
The connection to fatalism and idleness
As noted above, some have pointed to the connection between Newcomb’s paradox and the lazy man argument.[3] In the lazy man argument, as mentioned, there is a slip of paper with his grade on the exam that will take place the next day. From this the lazy man concludes that there is no point in studying because the grade is already fixed in advance.
Now we can see that in a deterministic world he has two options before him: either to be idle, that is, not to act toward achieving any goals, or to assume that studying for the exam will retroactively change what is written on the slip—in other words, to adopt a view that allows causal influence backward in time. In such a state of affairs, if our lazy man is rational, he will do nothing. Alternatively, he can give up the rationality of the lazy man, that is, act even though there is no reason to do so. We saw above as well that determinism leads to giving up the view of man as a rational being.
 
The connection to logical determinism
Logical determinism points to a seemingly similar mechanism, but in truth one entirely different. Yesterday there was a slip of paper on which it was written whether or not there would be a sea battle. From this the logical determinist wanted to derive the conclusion that the occurrence of the sea battle was necessary—that is, that it could not but occur. Our answer was that the occurrence of the sea battle is what writes the slip retroactively. What was written on it a thousand years ago is determined at the time of the occurrence now.
Why is this possible in the context of logical determinism (even according to the libertarian), whereas with Newcomb’s prophet it is not possible? Why can’t the determinist argue here too that taking both boxes will retroactively change the contents of the closed box? The difference is very simple. In Newcomb’s context we are dealing with a slip of paper that contains information, or a box that contains money. Such a slip cannot be written before the event (therefore I stated above that there is no such prophet). But above I explained that the truth value of a proposition is not information. The truth value of the proposition “Tomorrow there will be a sea battle” has been true from all eternity, but that does not mean that the information about the occurrence of the sea battle tomorrow has existed from all eternity. As I explained, truth value is our logical definition, not information or a fact of reality. As such it is timeless or supratemporal. But information and the presence of money in a box are not supratemporal. Therefore the truth value of a proposition describing an event can come into being retroactively, but information about an event comes into being only with the event’s occurrence and not before it.
 
The connection to theological determinism
If Newcomb’s paradox indeed proves that there cannot be such a prophet, then it should also be seen as proof that despite His omnipotence, even God Himself cannot know in advance what some person will choose in the future. To see this, we need only insert God Himself as the prophet into this game, and let Him arrange the closed box in light of His knowledge of the future (God is also omnipotent, and so we must add here the restriction that He takes upon Himself not to alter the contents of the box after He arranges it. Alternatively, He can convey the information to some person, who functions as the prophet and determines the contents of the box accordingly on the basis of the information in his possession). This would of course arouse exactly the same problem. That is, even God Himself cannot know what the future choice will be. As stated, this is impossible in essence, and therefore it does not point to any defect in His omnipotence. He simply “cannot” do the impossible. Just as He cannot create a round triangle or a married bachelor, so He cannot know information that does not exist. If so, Newcomb’s argument constitutes a proof against theological determinism as well. It is impossible to reconcile our free choice with divine foreknowledge. God’s omnipotence changes nothing in this regard.
The meaning of rejecting theological determinism is that the assumption that God knows everything in advance is mistaken. There is no contradiction here with the assumption of His omnipotence, as noted, because advance knowledge of an event that depends on choice contains an element of contradiction, like a round triangle. Inability to create contradictions or to act in a self-contradictory way is not a real inability (it is a logical inability, not a physical one). Here again we see the paradoxicality of this assumption from another angle. Indeed, Newcomb’s paradox pulls the rug out from under all kinds of evasive claims about God’s knowledge of the future. The unavoidable conclusion is that He indeed does not know the future.
If so, Newcomb’s thought experiment rules out physical determinism (so long as one preserves the assumption of human rationality), logical determinism, and theological determinism alike.
 
 
 
[1] One could propose an experiment in which the experimenter uses a scan of brain signals to predict the subject’s choice in a Newcomb-type situation. Later, in chapter fourteen, I will cite Ariel Furstenberg of the Hebrew University, who says they are currently working on developing such experiments.
 
[2] Chapter seven is devoted to proving the feasibility of free will, that is, showing that it does not involve a conceptual contradiction. In a footnote there I noted that this proof casts serious doubt on the determinist’s ability to defend himself against Newcomb’s paradox as presented here.
 
[3] See also Ron Aharoni’s book The Cat That Isn’t There, Magnes, 2009.
 
 
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Questioner:
Thank you very much, Rabbi. I read the passage and it was indeed interesting and enriching.
After a long discussion I came to the conclusion that I’m persuaded by your argument, but I was not convinced why the determinist must be idle and passive. That makes sense when we’re talking about a student who doesn’t like studying for tests anyway, but one could give an analogy that goes in the opposite direction—if a prophet told a person that in a month he is going to die and that nothing can be done about it, it seems to me that the average person would not become idle and do nothing; on the contrary, he would make full use of the time he had left. Human beings who suffer or do not enjoy their lives would certainly act like the student who knows in advance what grade he will receive, but what about people who are satisfied with their lives? It seems entirely possible that there could be an active determinist.
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Rabbi:
There is no obligation for the determinist to be anything, since he is whatever he is. The matter is not in his hands. This is about psychology, not norms. But each person’s psychology is different.
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Questioner:
I think the matter is understood.
Just one final question on the subject, if that’s okay. In Two Carts and a Hot-Air Balloon you argued that there is some sense to believing in this contradiction, because it is not pure logic—that is, it is not like believing in a round triangle or a married bachelor. But in the passage you attached you argued precisely that this is indeed a logical-analytic problem (you compared it to those beliefs). Did your view change between the writing of the passages, or am I missing something here?
Thank you very much, and have a good day.
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Rabbi:
I’ve been wavering on this point for quite a few years. On the face of it there is a logical contradiction here (as one sees from Newcomb), but it’s not exactly a direct conceptual contradiction. Bottom line, these days I tend to think that it is not possible to believe in both.
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Questioner:
The truth is that in such a case Maimonides’ explanation, “His knowledge is not like our knowledge,” really does seem to work. In 2 Carts you rejected his answer by asking, “What about knowledge as we know it? After all, that’s the knowledge we mean when we use the concept of knowledge,” and indeed it seems that such knowledge is impossible—but there is a kind of knowledge beyond us, not subject to the limitations of our logic. You argued that we cannot speak about it and therefore it is not relevant, but we can see that actually we can speak about it—knowledge as we know it, but without our limitations. True, we are incapable of grasping how such a thing is possible, but that is exactly the point.
In other words, we really have no way of knowing what knowledge beyond the limits of cognition and thought is. But from the words of the Sages in tractate Avot, “Everything is foreseen, yet permission is granted,” and from other statements of the Sages, who according to the argument of the decline of the generations were much more connected to the Torah and to God at the intuitive level, it seems possible to rely on their words.
Of course in the end there is no way to speak of this knowledge and I will never be able to understand how it is possible, but for me at least the mere knowledge that it is possible is enough.
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Rabbi:
I disagree.
 
Maimonides’ “explanation” is not an explanation. To say that His knowledge is not like our knowledge is to say that He does not know (in our sense of the term “knowledge”). We are talking about something else that for some reason is also called knowledge. Why should I care about that?! Bottom line: what I call knowledge—He doesn’t have it.
 
Knowledge that is not subject to the limits of our logic is an empty collection of words. By the same token you could say that maybe He has blah blah blah blah. That has exactly the same content as what you are saying here.
 
It’s not that we do not grasp how it is possible; rather, we grasp that it is impossible. There is a difference between not understanding and understanding that something cannot be.
 
The sentence in Ethics of the Fathers, “Everything is foreseen,” does not necessarily mean this, and even if it does—then in my opinion it is mistaken. The Sages were not endowed with thinking beyond logic, if only because there is no such thing, and also because they were human beings just like you and me.
 
Of course, if for you the mere knowledge that blah blah blah—or that every cat with bat horns possesses a triple moral quality that is far more important than the amount of water in the ocean—is enough, and that calms you in some sense, then I have no argument with you. Everyone has his own methods of self-soothing. But if you are trying to claim that this assertion has some cognitive meaning, I think you are gravely mistaken.
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Questioner:
I understand what you’re saying. You’re probably right; I need to think about it more.
Thank you so much for your time and investment. It’s really not something to be taken for granted, and it helped my understanding a lot.
Stay strong.
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Rabbi:
My pleasure.
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Avi:
Hello Rabbi,

Newcomb’s paradox speaks about a prophet who is part of the world, and more than that—he tries to predict events that he himself influences by using his abilities. How does one derive from here the inability of a God external to the world to predict internal events within it (setting aside for the moment His intervention in events)?
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Rabbi:
Newcomb is not talking about anyone in particular, neither inside the world nor outside it. It rules out the possibility that there could be something or someone that knows the future if there is free choice. That’s all. It makes no difference at all who that one is or where he is located. Notice that the problem is not how he obtains the knowledge, but the very existence of such knowledge, in the world or outside it. Its very existence contradicts my ability to choose.
And if you say that the knowledge exists outside the world and he has no ability to convey it to someone in the world, then what have you gained? You have denied him an ability far simpler than possessing knowledge of a future choice—namely, simply telling someone what he knows.
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Avi:
I’m not denying him that ability. I’m claiming that prophecy cannot include the prophet himself (who acts on the basis of it), but only the system external to him. If he chooses to intervene in it based on his knowledge, it is obvious that it will change—but he still has the ability to know how.

In the present case, the prophet would know that if he acted as in the paradox, the person would respond accordingly, and so he would not do that but something else instead (for example, something that would not allow the person to know that he was involved in the matter).
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Rabbi:
I didn’t understand. I’ll comment on the sentences I did understand.
1. The prophecy does not include the prophet’s actions, only the person’s actions (what he will choose).
2. Even if so, then you are basically saying that the Holy One cannot know what He Himself does, and therefore He does not know what the person will choose. Well, that is exactly what I’m saying (that He does not know). So where is the dispute?
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Avi:
The Holy One can predict that the person will choose A if the conditions are A, and B if the conditions are B. Since the conditions (whether there will be A or B) are determined by the Holy One, clearly the predictions have no meaning, because that would leave Him Himself without free choice. If that’s what you meant, then apparently there really is no dispute 🙂
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Rabbi:
No. That is really not what I meant. I am saying that the Holy One cannot predict that if the conditions are such-and-such, I will (freely) choose A. In my opinion this is proven by Newcomb’s paradox.
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Avi:
Okay.
If so, then either I disagree that this follows from the paradox, or I don’t understand it. Feel free to classify me with Nozick’s complete idiots 😉
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Rabbi:
???
I have no interest in classifying anyone into any category. If we have a disagreement—that is perfectly fine, and it certainly doesn’t mean you are among Nozick’s fools or his wise men.
But if you have an objection to my argument itself, I’d be glad if you presented it. I want to learn and to examine whether perhaps I am mistaken.
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Avi:
That was of course said jokingly. As for the substance, I’ll try to explain how I see things. Newcomb’s paradox actually describes the following case:
1. The chooser has two alternatives, A and B.
2. The prophet predicts which alternative will be chosen.
3. The prophet acts on the basis of his prophecy and changes the reality facing the chooser.
4. The chooser knows about 3.
5. Uncertainty is created regarding the choice.

Sections 3–4 turn the prophet into part of the events. The moment he determines the contents of the closed box on the basis of his prophecy, and the chooser knows this, the prophet’s own free choice enters the picture and necessarily disrupts the predicted line of events. Any other possibility would trap the prophet inside his own prophecy, and that is certainly impossible (because his free choice would then be denied).

In conclusion, I don’t see here any refutation of the possibility of full prophecy. The prophet can know what will happen if he intervenes, what will happen if he does not intervene, and decide for himself whether to intervene or not. The paradox exists only if one creates a clash between the prophet’s prophecy and his own choices.
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Rabbi:
I still don’t understand. Where exactly is the problem in the description I proposed for Newcomb’s case? Explain to me at precisely which stage you disagree.
I am talking about a prophet who decides to intervene in this specific way and even informs the chooser of his policy. Surely the Holy One can intervene and can also announce that, right? So I am proposing that we conduct such an experiment. That’s all.
At most you could conclude that if the Holy One knows, He cannot intervene—but then again you have limited Him and gained nothing.
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Avi:
The problem as I see it is in the sentence: “He knows in advance and with certainty what the chooser will do, and based on that he prepares the contents of the closed box one day before the chooser makes his decision.” The moment a perfect prophet would do such a thing, the predicted future would change, and he would automatically receive a new prophecy accordingly (and would presumably understand that in this case he has no possibility of using his prophecy in the way he planned).
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Rabbi:
Why does preparing the box affect the chooser? What affects him is the prophet’s statement to him, not the preparation itself, of which he is entirely unaware.
Therefore, when the prophet prepares the box, he knows that the chooser knows, and that is what he must take into account. After he takes that into account, he knows what the chooser will do, and now he prepares the box accordingly. There is no problem here at all.