A question regarding the contradiction between choice and knowledge

In my book The Science of Freedom, I described the Newcomb Paradox (it’s also on Wikipedia). There I explained why foreknowledge does not go with free will on a conceptual-analytical level. The paradox was created by us, and therefore it does not help to talk about how the process is different for God. We think in our own language and concepts. Thus, you cannot explain that there is a round triangle by claiming that for God, the triangle does not contradict the circle. For us, it contradicts and we cannot talk about it (and not even say that for Him there is no contradiction. This is also a statement for us). If you have the book at hand, please check it out (because everything is explained well there). If not, write to me and I will try to explain here. —————————————————————————————— Asks: Hello, Honorable Rabbi, first of all, thank you very much for the quick reply. Unfortunately, I don’t have the book within my reach, but if it’s too much trouble to explain, I can’t ask you to do so.
The problem is that it seems that this explanation is indeed found in our language and concepts. The explanation is both scientific and not fully transcendental, all that is required is an understanding of the fact that time is also a dimension beyond which God is. Once this understanding is fully achieved, it seems that it does not contradict our language and concepts either – the possibility that a cause can look at time without being dependent on it and thus know the future but at the same time not contradict the course of time does not seem so far-fetched. You have probably heard of the familiar parable according to which when a person looks at a filmed film in which people made decisions, he can know what the decisions were even before they were made in the film, even though in reality the people filmed definitely made those decisions. —————————————————————————————— Rabbi: I have indeed heard of the parable, but it is not helpful. I have copied the relevant passage from the book here: Newcomb’s thought experiment: In the previous chapter, we discussed the idler argument, according to which a determinist is supposed to be idle and not act to achieve any goals. We illustrated this by using a person with infinite predictive power who writes on a piece of paper the grade that a student will receive on a future test. Since the grade that appears on the paper is necessarily correct (because the prophet has absolute and certain predictive power), there is no point in studying for the test, since the grade is predetermined. In the Newcomb problem, we find ourselves in a very similar situation (actually identical). Here too, two people are involved: the voter and the prophet. Two boxes are placed in front of the voter: one is open and contains $1,000, and the other is closed and contains $0 or $1,000,000 (the voter does not know which of the two options). The voter must decide whether to take the contents of both boxes together, or only the contents of the closed one. This is where the prophet comes into play (we assume that his predictive ability is perfect). He knows in advance and with certainty what the voter will do, and accordingly he prepares the contents of the closed box the day before the voter makes his decision. Since the prophet is interested in giving a reward to those who are content with little, he adopts the following tactic: if the voter is going to take both boxes, he makes sure that there is no money in the closed box at all. But if the voter is a person who is content with little and is only going to take the closed box, the prophet makes sure to reward him by having a million dollars inside. The voter himself knows all this. He knows the prophet’s abilities, and also his strategy. What the voter does not know is only one detail: what the prophet predicted regarding his now expected election (since he himself is not a prophet), and in any case he does not know what the prophet put in the closed box. The question is what strategy should the voter adopt? Ostensibly, he should take only the closed box, since that way 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, now the box is already closed in front of him, and what is inside it was already determined yesterday and will not change if he acts differently. If so, why should he not take, along with the closed box, 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). So, it seems that taking both boxes is the winning strategy in any case. But if the prophet is truly omniscient, he will make sure that in such a case the closed box is empty. So, when the voter takes both, he will win only $1,000, meaning he chose incorrectly. At the time this paradox was published, “Newcomb mania” was born, i.e., a phenomenon of people’s addiction to thinking about it. Philosopher Robert Nozick, in his 1969 article, where he introduced the Newcomb paradox to the public, reports that almost everyone has a clear position on the question, and almost everyone also thinks that anyone who holds the other position is a complete fool. But there is certainly no consensus on the question of which position is correct. I think I am no exception in this regard. I also have a clear position on this question. However, for our purposes, it is more important to emphasize that the assumption that such a prophet exists contains a disguised deterministic position. In the libertarian picture, there can be no talk of such a prophet, since it is impossible to know with certainty in advance what the voter will decide. If the information does not exist now, how is it possible for someone to know it with certainty? “Knowing information that does not exist” is an expression that has an internal contradiction; a prophet who predicts in advance the decision of a person who freely chooses is an oxymoron. This is not a question of the quality of his predictive ability. Predictive ability is defined where the information exists in principle, that is, it can be derived from current circumstances. However, in the libertarian picture, the information does not exist at all now, and therefore no one, no matter how high his predictive ability, will ever be able to predict the future (we saw above that even God himself cannot do this). In contrast, in the deterministic picture, the difficulty remains. There, there is an assumption that the information does exist. Even if no one can reach it (because it is very complex and complicated; unfortunately for the prophet, there is no computer powerful enough to predict this), the information exists. Therefore, there is no fundamental obstacle to the existence of a prophet who knows it. This is a supercomputer, which may not actually exist now, but the concept does not contain a contradiction (since the computer knows information that really exists). Therefore, in essence, this argument is a thought experiment conducted according to the determinist assumptions (just as Einstein conducted a thought experiment according to the Newtonian assumptions, and thus refuted them). This suggests that Newcomb’s paradox is actually an a priori argument against determinism, since if determinism is correct then the information does exist and such a prediction is possible on a principled level. If so, according to him, it follows that even though the contents of the closed box are already fixed and will not change, it is still better for the voter to forgo taking the open box and settle for the closed box. Taking the open box with another thousand dollars would supposedly “remove” a million dollars from the closed box. If so, according to the determinist, the voter must make a clearly irrational decision (not to take the thousand dollars placed in front of him), or alternatively he must believe in a causal effect back in time (that taking the box will retroactively change its contents). Which proves, in a nutshell, that determinism is clearly implausible.[1] Some have sharpened the difficulty by extending Newcomb’s problem to a glass box. If the closed box is made of glass, the voter sees what is inside it. If he sees that there is a million dollars inside, he understands that the prophet predicted that he would take only that one. So now he will take both boxes to earn another thousand dollars, contrary to the prophet’s prediction. If he sees that it is empty, then it is clear that the prophet predicted that he would take both. So to upset the prophet, he may decide to take only the closed one. In any case, his actions are the opposite of what was predicted. This is essentially proof that there cannot be a prophet who predicts the choice in advance. Alternatively, an action contrary to the prophet’s prediction would simply miraculously change the contents of the closed box, and then the prophet’s predictions would come true. However, in such a case, we have indeed saved the possibility of prophecy (=determinism), but at the cost of adopting a view that allows causal influence backward in time, from the future to the past. But this extension is problematic, since according to the deterministic assumption the voter cannot change his choice. Even if there is nothing in the box, he is forced to take both boxes, and vice versa. Ostensibly, this is also the solution to the original difficulty, but a closer look reveals that this is not the case, as we will immediately see. Further clarification of Newcomb’s paradox On the surface, this experiment does not seem to provide an argument against determinism, but at most proof that freedom of choice is incompatible with determinism (an argument against compatibilism). The determinist should not be alarmed by this difficulty, since in the deterministic picture the voter has no possibility at all of freely choosing between the two options. He will really do what the prophet predicted, since he has no other option. In fact, this is the obvious derivation from the deterministic worldview, and it shows that it is possible to remain a decent, or at least consistent, determinist. But further observation reveals that the determinist’s difficulty remains. Our problem is not what the voter would do in such a situation, but what is right for him to do. This is a mathematical question about strategy, which belongs to game theory, and not a question about the psychology of the voter or what will actually happen. Even in the deterministic picture, which holds that none of us have freedom of choice, the question can be asked: Assuming that some creature in some imaginary world has freedom of choice, what would be more right for him to do? There is no answer to this question, and this is the very problem that arises in the deterministic picture. The determinist may be able to escape this by claiming that the question is not defined. Freedom of choice is something that has a contradiction at the conceptual level, and therefore, from his perspective, it is impossible to ask even the hypothetical question (what is the right strategy?), let alone the practical question (what would you do in such a situation?). But this is an unreasonable claim. For the sake of the discussion, I am willing to accept that freedom of will is difficult to understand. I am also willing to assume for the sake of the discussion that such freedom may not exist for any creature (including man) 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 just a physical problem, is a very unreasonable and unfounded claim. It seems that this is too heavy a price to pay for stubborn adherence to the deterministic dogma.[2] This can be phrased a little differently. The determinist also does not deny the rationality of man, that is, that he 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 a kind of mechanical calculation that is forced upon us. However, if this is the case, the difficulty with his method remains: in our case, there is a prophet who knows in advance what will be chosen, and given this information, it is clear that the voter is also supposed to use it to “calculate” his decision rationally. But what is that rational decision that he must make (deterministically)? Ostensibly, he must only take the closed box to win a million dollars. On the other hand, as a rational person, he knows that the prophet cannot change the contents of the box after the choice, and therefore it is clear that it is better to take both boxes together. So, in order to solve the problem, the determinist now needs to take one step back and declare that the person is forced to act irrationally. And is the determinist willing to deny human rationality? If so, it is not clear to me why he takes so seriously the considerations that lead him to the determinist position itself. Perhaps he is also forced to these conclusions even though they are illogical?! The connection between fatalism and idleness As noted above, some have drawn a connection between Newcomb’s paradox and the idler’s argument.[3] In the idler’s argument, as mentioned, there is a note on which is written his score for the exam that will be given the next day. From this, the idler concludes that there is no point in studying because the score is already predetermined. Now we can see that in a deterministic world he has two options: either to do nothing, that is, not to act to achieve any goals, or to assume that studying for the exam will retroactively change what is written on the note, that is, to adopt a view that allows for causal influence back in time. In such a situation, if our idler is rational, he will do nothing. Alternatively, he can give up the rationality of the idler, that is, to act even though there is no reason to do so. We also saw above that determinism leads to giving up the view of man as a rational being. The connection to logical determinism Logical determinism points to a mechanism that is seemingly similar, but in fact completely different. Yesterday there was a note on which it was written whether or not there would be a naval battle. From this the logical determinist wanted to draw the conclusion that the occurrence of the naval battle was necessary, that is, it could not but have occurred. Our answer was that the occurrence of the naval battle is what writes the note retroactively. What is written on it a thousand years ago was determined at the time of its occurrence now. Why is this possible in the context of logical determinism (also according to the libertarian), while it is not possible in Newcomb’s prophet? Why can’t the determinist claim here that taking both boxes will retroactively change the contents of the closed box? The difference is very simple. In Newcomb’s context, it is a note containing information, or a box containing money. Such a note cannot be written before the event (which is why I stated above that there is no such prophet). But above I explained that the truth value of a claim is not information. The truth value of the claim “Tomorrow there will be a naval battle” has always been true, but that does not mean that the information about the occurrence of the naval battle tomorrow has always existed. As I explained, a truth value is our logical definition, and not information or a realistic fact. As such, it is atemporal or supratemporal. But information and the presence of money in the box are not supratemporal. Therefore, the truth value of a claim that describes an event can be created retrospectively, but information about an event is created only when the event occurs and not before. The connection to theological determinism If indeed Newcomb’s paradox proves that there cannot be such a prophet, it should also be seen as proof that, despite his omnipotence, it is impossible for God himself to know in advance what any person will choose in the future. To see this, we need only introduce God himself as a prophet into this game, and let him organize the closed box in light of his knowledge of the future (God is also omnipotent, and therefore we must add here the restriction that he accepts upon himself not to change the contents of the box after he organizes it. Alternatively, he can give the information to some person, the one who functions as a prophet, and he determines the contents of the box according to the information he has). This would of course raise exactly the same problem. That is, even God himself cannot know what the future choice will be. As mentioned, this is not fundamentally possible, and therefore it does not indicate a flaw in his omnipotence. He simply “cannot” do the impossible. Just as he cannot create a circular triangle, or a married bachelor, so he cannot know information that does not exist. If so, Newcomb’s argument also constitutes evidence against theological determinism. It is impossible to reconcile our freedom of choice with divine foreknowledge. God’s omnipotence makes no difference in this matter. The meaning of rejecting theological determinism is that the assumption that God knows everything in advance is false. This does not contradict the assumption of His omnipotence, as mentioned, since foreknowledge of an event that depends on choice contains a contradiction, like a circular triangle. The inability to produce contradictions or to act in a way that contains a contradiction is not a real inability (it is a logical, not a physical inability). Here we again see the paradox of this assumption from another angle. Indeed, it is true, Newcomb’s paradox undermines all sorts of evasive claims about God’s knowledge of the future. The obvious conclusion is that He does not know the future. If so, Newcomb’s thought experiment refutes both physical determinism (as long as the assumption of human rationality is maintained), logical determinism, and theological determinism. [1] An experiment could be proposed in which the experimenter uses brain signal scans to predict the subject’s choice in a Newcomb experiment situation. Below, in Chapter Fourteen, I will quote Ariel Furstenberg from the Hebrew University about how they are currently working on developing such experiments. [2] The seventh chapter is devoted to proving the feasibility of free will, that is, to showing that it does not involve a conceptual contradiction. In a footnote there I noted that this proof casts a serious doubt on the determinist’s ability to defend against Newcomb’s paradox as presented here. [3] See also Ron Aharoni’s book, The Cat Who Isn’t There, Magnes, 2009. —————————————————————————————— Asks: Thank you very much Rabbi, I read the piece and it was definitely interesting and enriching. After a long discussion, I came to the conclusion that I am convinced by your argument, but I was not convinced why the determinist should be idle and passive. This makes sense when it comes to a student who doesn’t like studying for a test anyway, but one could bring up a parable that reverses the direction – if a prophet were to tell a person that in a month he would die and that there was nothing to be done about it, it seems to me that the average person would not idle away and do nothing, but on the contrary, he would make the most of the time he has left. People who suffer or do not enjoy their lives will certainly behave like the student who knows what grade he will receive in advance, but what about people who are satisfied with their lives? It seems that an active determinist is definitely possible. —————————————————————————————— Rabbi: There is no obligation on the determinist to be what he is, since he is what he is. It is not in his hands. It is about psychology, not norms. But everyone’s psychology is different. —————————————————————————————— Asks: I think the matter is understandable.
Just one last question on the subject, if it’s okay, you argued in the book Two Carts and a Balloon that there is a meaning to believing in this contradiction because it is not purely logical, meaning that it is not like believing in a round triangle or a married bachelor. In the passage you included, you actually argued that this is indeed a logical-analytic problem (you compared it to these beliefs). Did your opinion change between writing the passages, or am I missing something here?
Thank you very much and have a good day. —————————————————————————————— Rabbi: I have been debating this point for quite a few years now. There seems to be a logical contradiction here (as Newcomb shows), but it is not really a direct conceptual contradiction. The bottom line today is that I tend to think that it is not possible to believe in both. —————————————————————————————— Asks: The truth is that it seems that in such a case the Maimonides’ explanation “His knowledge is not like our knowledge” really applies. In 2 Egalots you invalidated his answer by asking “What about knowledge as we know it? After all, this is the knowledge we are talking about when we mean the concept of knowledge,” and indeed it seems that such knowledge is not possible, but knowledge that is beyond us, that is not subject to the limitations of our logic, does exist. You claimed that it cannot be spoken of and therefore is irrelevant, but we see that it can indeed be spoken of – knowledge as we know it and without our limitations. Although we are unable to grasp how this is possible, that is precisely the point.
In other words, we really have no way of knowing what knowledge is beyond the limitations of cognition and thinking. But from the words of Chazal in Tractate Avot, “Everything is expected and permission is given,” and from the words of other sages who, according to the argument of the descent of generations, are much more connected to the Torah and to God on an intuitive level, it seems possible to trust their words.
Of course, ultimately there is no way to talk about 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. —————————————————————————————— Rabbi: 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). It is about something else that for some reason is also called knowledge. What do I care about that?! After all, what I call knowledge he does not have. Knowledge that is not subject to the limitations of our logic is a collection of empty words. You could just as well say that it might have blah blah blah blah. It has exactly the same content as what you are saying here. It’s not that we don’t understand how it’s possible, but we understand that it’s not possible. There’s a difference between not understanding and understanding that it’s not possible. The sentence in Pirkei Avot, “Everything is predictable,” does not necessarily mean this, and even if it did, I think it is wrong. The sages were not endowed with thinking beyond logic, if only because there is no such thing, and also because they were human beings like you and me. Of course, if the mere knowledge that blah blah blah or that every cat with bat horns possesses a triple virtue that is much more important than the amount of water in the ocean is enough for you, and that calms you down in some sense – then I have no argument with you. Each to their own ways of calming down. But if you’re trying to argue that this claim has any cognitive significance, I think you’re making a grave mistake. —————————————————————————————— Asks: I understand what you’re saying. You’re probably right, I need to think about it more.
Thank you very much for your time and investment, it’s really not obvious and you helped me a lot to understand.
Strong and courageous. —————————————————————————————— Rabbi: happily. —————————————————————————————— my father: Hello Rabbi,

Newcomb’s paradox speaks of a prophet who is part of the world, and more than that – tries to predict events that he himself influences using his abilities. How does this lead to the inability of a god external to the world to predict events internal to it (let’s put aside his intervention in events for a moment)? —————————————————————————————— Rabbi: Newcomb is not talking about anyone, neither inside the world nor outside it. He is denying the possibility that there will be something or someone who will know the future if there is free choice. That is all. It does not matter at all who that someone is or where he is. Note 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 knowledge exists outside the world and he has no ability to convey it to anyone in the world, then what have you gained? You have deprived him of a much simpler ability than to possess knowledge about a future choice (simply telling someone what he knows). —————————————————————————————— my father: I do not deny him this ability. I argue that prophecy cannot include the prophet himself (who performs his actions according to it), but only the system that is external to him. If he chooses to intervene in it based on his knowledge, it is obvious that it will change, but he has the ability to know how.

In this case, the prophet knew that if he acted as in the paradox, the man would react accordingly, and therefore he would not do that but something else (for example, something that would not allow anyone to know that he was involved in the matter). —————————————————————————————— Rabbi: I didn’t understand. I will comment on the sentences I did understand.
1. Prophecy does not include the actions of the prophet but only the actions of man (what he chooses).
2. Even if so, then you are essentially saying that God cannot know what He Himself does and therefore does not know what man will choose. Well, then that is what I am saying (that He does not know). Where is the argument? —————————————————————————————— my father: God can predict that a person will choose A if the conditions are A, and B if the conditions are B. Since God determines the conditions (whether there will be A or B), there is certainly no meaning to the predictions, since this would leave him without the ability to choose. If that’s what you meant, then there is probably no argument 🙂 —————————————————————————————— Rabbi: No. That’s not what I meant at all. I’m saying that God cannot predict that if the conditions are such that I will (freely) choose A. In my opinion, this is proven by Newcomb’s paradox. —————————————————————————————— my father: Okay.
So either I don’t agree that it’s derived from the paradox, or I don’t understand it. Feel free to classify me as one of Nozick’s complete fools 😉 —————————————————————————————— Rabbi: ???
I have no interest in assigning anyone to any category. If we have a disagreement – that’s perfectly fine, and it certainly doesn’t mean you’re one of Nozick’s fools or his wise men.
But if you have an objection to what I said, I would be happy if you presented it. I want to learn and see if I’m wrong. —————————————————————————————— my father: This was of course a joke. As a matter of fact, I will try to explain how I see things. Newcomb’s paradox actually describes the following case:
1. The voter has two alternatives, A and B.
2. The prophet predicts the alternative that will be chosen
3. The prophet acts on the basis of his prophecy and changes the reality that faced the voter.
4. The voter knows about 3
5. There is ambiguity about the choice

Sections 3-4 make the prophet part of the events. Once he determines the contents of the closed box based on his prophecy, and the chooser knows about it, the prophet’s own free choice has entered the picture and inevitably disrupted the predicted course of events. Any other option would imprison the prophet within his own prophecy, which is certainly not possible (because his free choice would be negated).

In conclusion, I do not see here any denial 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 only exists if a conflict is created between the prophet’s prophecy and his own choices. —————————————————————————————— Rabbi: I still don’t understand. Where is the problem with the description I offered of Newcomb’s case? Explain to me exactly at what point you disagree.
I’m talking about a prophet who decides to intervene in this particular way and even informs the voter about his policy. After all, God can intervene and can also inform about it, right? So I propose to conduct such an experiment. That’s all.
At most, you can conclude that if God knows, He cannot intervene, but then again you have limited Him and gained nothing. —————————————————————————————— my father: The problem in my opinion is in the sentence: “He knows in advance and with certainty what the voter will do, and accordingly he prepares the contents of the closed box the day before the voter makes his decision.” As soon as a perfect prophet did such a thing, the predicted future would change and he would automatically receive a new prophecy accordingly (and he would probably realize that he would not be able, in this case, to utilize his prophecy in the way he had planned). —————————————————————————————— Rabbi: Why does the preparation of the box affect the voter? What affects him is the prophet’s statement to him, and not the preparation itself, of which he is completely unaware.
Therefore, when the prophet prepares the box, he knows that the voter knows and that is what he must take into account. After he takes this into account, he knows what the voter will do and now he prepares the box accordingly. There is no problem here.