The Question of Knowledge and Choice 2 (Column 301)

With God’s help

Disclaimer: This post was translated from Hebrew using AI (ChatGPT 5.1 Thinking), so there may be inaccuracies or nuances lost. If something seems unclear, please refer to the Hebrew original or contact us for clarification.

In the column before last (the first in the series) I presented the contradiction between God’s knowledge of the future and our free will. I pointed out that the problem includes three components: divine knowledge, our free will, and the temporal relation between them (that the knowledge precedes the act). We saw that, accordingly, there can be four directions of solution: to give up the assumption that we have free will (determinism), to assume that God is beyond time, to claim that even if we accept these three assumptions there is in fact no contradiction, or to give up the assumption that God knows the future. In the previous column I examined the first two options and rejected them. In this column I shall discuss the third option, which is the trickiest of them all. I shall already say in advance that I tend not to accept it, but a shadow of doubt always accompanies me with respect to the arguments against it. In the third column I shall try to sharpen this point a bit more.

C. And Perhaps There Is No Contradiction?

As noted, the third proposal for resolving the difficulty claims that there is in fact no contradiction at all. One can adopt both claims, God’s knowledge and free choice, without changing our attitude to the time axis, and still there is no contradiction here. One way to do this is to examine the notion of “knowledge” as it applies to God. An example of this can be seen in Tam’s question on the previous column (ignore the unnecessary length). The claim is that we have no possibility of understanding God (“If I knew Him, I would be Him” – לו ידעתיו הייתיו), and therefore the term “knowledge” as it appears with respect to Him is not understood by us, and consequently cannot serve as a basis for a difficulty regarding our free will. Some will go further and say that God is beyond logic, and therefore they are not at all troubled by logical contradictions in our concepts concerning God.

I already addressed the second formulation in the previous column (and I shall return to it also in the next one). The logical contradiction is not in God but in us. If there is a contradiction between two claims that I make, I have no way of holding on to both. The statement that God is beyond logic is of no help, even if it were correct (and it is not), since the contradiction is in my concepts about Him and not in Him. Within my concepts there cannot be a logical contradiction. If I hold two contradictory beliefs, I simply do not believe both of them (I merely say both, lip-service only). Our beliefs are subject to the constraints of logic and of our thinking; if they transgress them, they lose all meaning for me.

Now I shall touch on the first formulation. Some hang this on Maimonides’ words in the halakhah brought in the previous column, where he writes:

We have already explained in the second chapter of the Laws of the Foundations of the Torah that the Holy One, blessed be He, does not know with a knowledge that is external to Him, like human beings, who and whose knowledge are two [separate things]; rather, He, may His name be exalted, and His knowledge are one. And the mind of man cannot grasp this matter in its fullness. And just as man has no power to apprehend and find the truth of the Creator, as it is said, “For man shall not see Me and live”, so man has no power to apprehend and find the knowledge of the Creator. This is what the prophet said: “For My thoughts are not your thoughts, and your ways are not My ways.” And since this is so, we have no power to know how the Holy One, blessed be He, knows all creatures and all deeds…

At first glance he seems to be saying that the concept of “knowledge” that we attribute to God is a notion whose meaning differs from the human notion that we use with respect to ourselves. Therefore it is neither necessary nor correct to see a contradiction between it and our free will.

The question that arises here, of course, is whether knowledge in the ordinary sense that we attribute to this notion (like human knowledge) exists in God with respect to the future. If yes – what, then, have Maimonides’ words helped? And if not – then, in fact, what he is saying is that God does not know the future. Therefore changing the meaning of the term “knowledge” with respect to God does not resolve the problem. The contradiction concerns knowledge in its ordinary human sense, and there the situation is: either He has it or He does not. If He has knowledge in some other sense, that is a different claim which does not touch our discussion. What remains to us is to interpret Maimonides as referring to the question how He attains knowledge of the future, or what the relation of that knowledge is to Him (in Maimonides’ language: “that He and His knowledge are one”), but as I explained in the first column, these questions are in no way relevant to the difficulty we are dealing with. However He came to have that knowledge, and however that knowledge relates to Him, if there exists in Him knowledge (in the ordinary human sense), and in fact we saw that it is sufficient that the information itself exists now, the contradiction with our free will remains in place.

We thus learn that what creates the contradiction is the assumption that there exists knowledge, in the ordinary and accepted sense for us, in God concerning the future. If He does not have that knowledge, He is not omnipotent and not perfect. And if He does have it, this does not sit well with our free will. The claim that He has some other kind of knowledge, not in the ordinary human sense, whether it is true or not (what does that even mean? Does such a sentence have any content at all? In my opinion, no), is of no significance for our question.

I shall recall here the conclusion from the first column, that the contradiction is not connected to God and His knowledge but to the very existence of the information. What confuses people here and leads them to hang the contradiction on someone’s knowledge of this information is the fact that if an ordinary person thinks he knows something about the future, there is nothing to prevent that from turning out to be wrong. Therefore a person’s knowledge does not contradict our free will. But God’s knowledge is necessarily true (it cannot turn out to be mistaken), and so if He knows what I shall do in the future there is no possibility that I will do anything else. Yet do not let this mislead you. There is no need for God at all in order to formulate this contradiction. What stands in opposition to my freedom to perform actions is the very existence of correct information. If that (true) information existed in a person, but it were known to us that this information is necessarily true, the same contradiction would arise. Thus what stands in opposition to our freedom is not the fact that someone knows what we shall do but the fact that the (true – it is not enough that someone thinks something about the future) information about what we shall do in the future already exists in the present.

In any case, the only way that remains open to us, if we wish to show that there is no contradiction between His knowledge and our free will (the third direction, which we are dealing with here), is to show that (true) knowledge in the present does not contradict freedom of choice in the future. This is irrespective of who knows it, how he attained that knowledge, what its relation to him is (whether it is external to him or not), and whether he does or does not have some other sort of “knowledge”. This approach maintains that the claim about a contradiction is based on a conceptual error: knowledge in the present, even if it were certainly true and even if it were in the hands of a human being (for example if it were given to him by God), does not contradict our freedom to choose freely in the future.

The Movie Theory

Some formulate this by means of the parable of a movie. Imagine Reuven watching a movie and seeing there Shimon weighing things in his mind, choosing and deciding, and performing various actions. Reuven knows what Shimon is doing, but his knowledge of course does not in any way affect Shimon. Instead of a movie we could just as well speak of knowledge of actions that were done in the past. There too my knowledge does not change anything regarding the events or the agents themselves. They act as they choose, and I know what they did. The claim is that God can watch “movies” of the future, but His watching the movie does not affect what happens in it. If a person were to choose differently, the movie that God would watch would be different, but God’s knowledge has no influence on what happens in the movie. On the contrary: the movie is the cause and God’s knowledge is the effect. Some have understood this as the suggestion of the Ra’avad in his gloss on the above-mentioned halakhah of Maimonides. Among other things, he writes there that God’s knowledge is “like the knowledge of astrologers, who know from some other power what the ways of this person will be” (we shall return to the Ra’avad’s words below).

Shatzal, in a comment to the first column (299), brought the words of the Rivash, who presents this formulation clearly (Responsa, §118):

But what seems to me to answer this question is this: that we are compelled to believe that man has free choice regarding his actions, in order to uphold the commandments of the Torah and their reward and punishment, as is explained in the Torah… And likewise we must believe that the knowledge of the Blessed One encompasses everything that a person will do by his choice before the thing comes into actuality, for we must not attribute any deficiency in His knowledge, Heaven forfend.

And this knowledge does not compel at all, for once it is assumed that man has free choice and it were possible for him to do the opposite – then when God knows that he will perform some particular act, He knows that he will do this by his choice and that it was possible for him to do the opposite. If so, this knowledge does not compel, for the knowledge is that he will perform that act by choice…

Therefore we say that man’s action does not follow from God’s knowing that act before it comes into actuality, but His knowledge follows from that act, which is done by choice and with the possibility of doing its opposite, even though He knows it before it comes into actuality. In this way man remains a being with free choice and the knowledge of the Blessed One remains complete without any deficiency and without depriving man of his free choice.

It is worth noting that it seems from the language of these early authorities that their words revolve specifically around God’s knowledge; this is not a general claim about foreknowledge that does not contradict free choice. But as noted above, this cannot be said only about Him. If there is a contradiction between foreknowledge and free choice, the fact that we are dealing with God does not rescue us from it. Those who follow this path must assume that there is in fact no contradiction between knowledge and free choice, independently of God.

Judith Ronen, in her sharp article “All is Foreseen and Permission is Given”,[1] offers a simple and very elegant logical formalization of this claim. I shall now present her schema for the benefit of readers who are not deterred by a bit of logical formalism (it is not particularly complicated).

A Short Background on Modal Logic

I shall begin with a brief introduction to modal logic. Ordinary logic deals with the truth and falsity of propositions (that is, the truth values of statements) and with the validity and invalidity of arguments. Modal logic, by contrast, deals with the necessity and contingency (= possibility, non-necessary truth, accidental truth) of propositions. There are propositions that are true but not necessarily true (contingent), and there are propositions that are necessarily true. Almost all the true propositions we know are contingent truths. For example, consider the proposition “There is light outside now”. This is indeed true, but it need not have been so. I can imagine another world in which it would not be so (if the earth had stopped and the sun had not yet risen, or in a universe with no sun and no light, and so on). It is important to understand: a sentence that describes a contingent truth is a true sentence (and not merely a possible one), but it is such that we can imagine a state of affairs in which it would not be true. In other words, that truth is not necessary (but only accidental). But as noted, there is also another type of proposition, one that is necessarily true. For example, every dog is either alive or not alive; every bachelor is unmarried, and the like.[2]

In modal logic we define, for convenience, a judgment whose meaning is “necessarily true”, and for clarity we shall express it here by the symbol □.

Now take the sentence “Moses is a bachelor”, and denote it as follows:

• A

The sentence “It is necessary that Moses is a bachelor” is formalized as:

• □A

Now note – and this is the basis of the argument that will follow – that since Moses is in fact a bachelor, sentence (1) is true (it is a contingent truth). In contrast, sentence (2) is not true, for sentence (1) is a contingent truth, that is, true but not necessary. Therefore to say that it is necessarily true is false. There may be a state of affairs in which Moses is not a bachelor, and thus sentence (2) asserts something false.[3]

The standard interpretation (= semantics) of modal judgments is given in terms of alternative (or possible) worlds.[4] According to this interpretation, to say that some sentence is necessary means that this sentence is true in every possible world we can imagine, however fanciful. Thus, for example, there is no possible world in which the dog is both alive and not alive, and so the statement “It is not the case that the dog is alive and not alive” is a necessary truth. According to this interpretation, a sentence is contingent if it is true in our world but we can imagine an alternative world in which it would be false. For example, “This dog is alive” is a contingent proposition, for although here before me in our world he is indeed alive, I can imagine a possible world in which this dog would be dead. This is a correct fact, but there is nothing that compels it, and therefore it could have been otherwise.

Let us now move to the sentence “Moses is not married”, and denote it as follows:

• B

Now consider the sentence “It is necessary that Moses is not married”. It is, of course, formalized as:

• □B

The analysis of this pair of sentences is similar to the previous pair. Moses, who is a bachelor according to the state of affairs in the world, is of course not married. Therefore sentence (3) is true. Not so sentence (4), which is false, because this state of affairs is not necessary. Although Moses is currently in fact a bachelor, there is no impediment to another state in which Moses would be married (and then, of course, he also would not be a bachelor).

Now consider the sentence: “If Moses is a bachelor, then Moses is not married”. It is formalized as:

• A → B

Note that from the content of the variables it follows that this sentence is necessarily true, not merely true. It is necessary that if Moses is a bachelor then he is not married.

Thus the sentence “It is necessary that if Moses is a bachelor then Moses is not married” is true. Its formalization is:

• □(A → B)

We have now reached the core of the argument. Consider the sentence “If Moses is a bachelor, then it is necessary that Moses is not married”. It may look similar, but its formalization will show that this is not so:

• □A → B

This sentence is not only different from sentence (6), it is false. An implication in which the antecedent is true and the consequent false is false. What is the difference between the two sentences? In sentence (6) the necessity concerns the derivation of B from A, whereas in sentence (7) the necessity concerns the sentence B on its own. For someone unfamiliar with the standard logical formalism (the meaning of material implication) this is a bit confusing. It is therefore important to remember here that the fact that Moses is a bachelor does not mean that he is necessarily a bachelor. After all, it is possible that he might have been married. Therefore, although he is a bachelor, it does not follow that he is necessarily not married. It is necessary that if he is a bachelor he is not married, but it is not true that if he is a bachelor then the state of his not being married is a necessary state in itself. We might perhaps phrase it in probabilistic terms: this is conditional necessity (on the existence of A, see sentence (6)) and not absolute necessity.

A Modal Formalization of the Movie Theory

Let us now assign a different interpretation to the propositional variables A and B and see what results. Let sentence A be “God knows today that tomorrow I shall choose X”, and sentence B be “Tomorrow I shall choose X”. From the very same analysis it follows that in this interpretation too sentence (6) is true, that is, “It is necessary that if God knows today that tomorrow I shall choose X, then tomorrow I shall choose X”. But sentence (7) is false, that is: even if God knows today that tomorrow I shall choose X, this does not mean that it is necessary that tomorrow I shall choose X (for I could have chosen not-X).

It is important to understand that absence of free choice means that it is necessary that I choose X (that is, that I am compelled to choose X), not merely that I will in fact choose X. Thus, although one can deduce from God’s knowledge what I shall do, one cannot deduce from this that what I shall do will be done necessarily, that is, a deterministic conclusion. Hence there is no contradiction between God’s knowledge and my free choice. This is Judith Ronen’s claim.

We must understand that this is a formalization of the movie theory. What this formalization teaches us is that although from “God knows today that tomorrow I shall do X” it follows that indeed tomorrow I shall do X, it does not follow that I shall do so necessarily. He watches a movie in which I do X, and therefore it is factually true that I shall do X; but determinism requires that I do so necessarily, and that cannot be derived from God’s knowledge.

Critique of the Argument: Back to the Interpretation of Alternative Worlds

At first glance this argument proves in a decisive way that there is no logical contradiction between God’s knowledge and free choice. In my book I pointed out several ways to attack this argument, but here I shall try to explain this simply, without resorting to complex arguments.

First, note that this claim is not true only with respect to God. It is also true with respect to a human being’s knowledge. We have no need here for anything in God’s unique properties; rather, any knowledge of anyone does not compel a certain action. Her claim is that there is no principled logical obstacle to knowing in advance an action that is bound up with free choice. Only the question of how one attains information from the future remains; we saw above that this is a different question. With regard to that, perhaps indeed only God can attain information from the future (or perhaps an expert astrologer as well). But Ronen’s argument shows that even the very existence of the information, regardless of who holds it and of his capacities, does not dictate the future action. In this sense she really does solve the problem without relying on the fact that we are dealing with God, as we saw we ought to do.

To understand the problematic point in her argument, let us examine this conclusion in terms of the alternative-worlds interpretation. What Ronen claims is that even if God knows that tomorrow I shall do X, it is still possible that I shall not do so. In terms of the modal interpretation, we must imagine a possible world in which God knows that I shall do X but I do not do it. But there is no such world, for the implication itself is indeed necessary. If God knows, then it necessarily follows that I shall indeed do it (but not that I will necessarily do it). Thus there is no possible world in which God knows that I shall do X but I do not do it. Therefore among the worlds in which God knows that I shall do X there is none in which I do not do it. Hence, in such a world, I have no possibility of not doing X.

This is a bit confusing, for Ronen too agrees that the implication is necessary. So where exactly is the disagreement? It seems to me that there is in her argument a conflation of truth value, which is atemporal, with the existence of the information contained in that proposition, which can indeed depend on time. To explain this, we must resort to another confusing argument, which goes by the name “logical determinism” (see on this in chapter four of The Science of Freedom).

Logical Determinism

The discussion begins with Aristotle, who dealt with the statement “Tomorrow there will be a sea battle”. He asked himself whether this statement is true or false. The truth value of a proposition is determined by comparing its content with the state of affairs in the world itself. Therefore, in order to determine the truth value of this statement, we must wait for tomorrow and see whether there will be a sea battle (in which case the proposition will turn out to be true) or not (in which case the proposition will turn out to be false). But the waiting until tomorrow is only due to our limitation. It has no connection to the truth value of the proposition itself. Therefore, if the truth is that tomorrow there will indeed be a sea battle, then the proposition is already true today, except that I do not yet know this. Comparing the content of the proposition with the state of affairs in the world (which can in fact be done only tomorrow) reveals to us that this proposition is true. If so, there is no reason to refrain from saying that it is already true today. The conclusion is that already today the statement “Tomorrow there will be a sea battle” is true, for the truth value of a proposition depends not on time but only on the comparison between its content and the state of affairs in the world. But if so, how is it possible that tomorrow someone will decide not to hold the sea battle? For already today the proposition is true, and if tomorrow there will be no sea battle it will turn out that the truth value of the proposition is false and not true. Here we have a logical proof of determinism.

The Polish logician Jan Łukasiewicz wanted to argue that logic with respect to propositions about the future cannot be binary (true or false). The truth value of propositions about the future is neither “true” nor “false”, but “unknown”. But I really do not agree with this, for as we have seen the truth value of the proposition is determined by that comparison, and therefore it is true or false already today, although I still do not know it. There are quite a few true propositions whose truth I cannot know. For example, the proposition “There are currently more than one hundred billion ants in the universe” is already now either true or false, even though I have no way of knowing this. The fact that I have no way of knowing it does not change the fact that the proposition is true (or false) if it matches the state of affairs it describes. Human knowledge is not related to the truth value of a proposition, and vice versa. Therefore, also with respect to the future, logic is binary, and every proposition about the future is either true or false, even if I have no way of knowing it.

The conclusion from all this is that there are only two truth values for propositions: “true” or “false”. The question whether I know this or not belongs to epistemology (theory of knowledge), not to logic. Therefore “unknown” is not a third truth value, for it is not a truth value at all. It is a description of a person’s cognitive state (sometimes temporary), not a statement about the truth of the sentence itself. The conclusion is that truth values are atemporal, that is, not dependent on time. If a proposition is true, then it is always true, from the Big Bang until the end of days. And likewise for a false proposition. What can change over time is only our ability to know this.

But even after all this, it is still clear that some logical trick cannot prove anything to us about the reality of the world. Logic is supposed to be empty with respect to facts. In other words, logic deals with the relations between propositions and not with the content of propositions. The content, that is, information about the world, must be learned from observation. A logical inference cannot teach us anything about the world. But the conclusion that the world functions deterministically is a factual claim (true or not) about the world. Note that this argument is what is called an “ontological proof”, that is, an argument that proves a claim about the world from conceptual-logical analysis (see in the first booklet here, and in the first conversation in the book The First Being). And indeed, this is exactly what the opponents of the ontological proof (rightly) claim. But as I argued there, it is not enough to point out that we are dealing with an ontological argument in order to reject it. One must identify exactly where the flaw is in the argument itself. If there is no flaw in the logical argument, then it itself shows that those who criticize it are wrong: here is an argument that proves a claim about the world from logical-conceptual analysis.

It seems to me that the flaw in the argument is the connection it makes between logic and the world. The fact that a certain proposition has a truth value at some time does not mean that the information exists at that time. This is only a logical statement and not a fact. The truth value of a proposition is a definition of logicians, that is, a description of how we relate to propositions, not a description of some fact. If I now know that tomorrow there will be a sea battle (let us assume from some reliable source), then indeed tomorrow there will be a sea battle. But if the truth value of the proposition “Tomorrow there will be a sea battle” is already fixed today, this does not mean that what will happen tomorrow is already fixed today. If tomorrow there is a sea battle, then already today the proposition is true; but if tomorrow there is no sea battle, then the truth value of the proposition is already today false. It may sound strange that the future can determine the truth value of a proposition in the past, but there is nothing strange about this. The truth value of a proposition is not information and not a fact (as we have seen, it is a definition of ours). Therefore there is no impediment to the future’s determining a logical definition of the past. There is an impediment to the future’s determining information in the past, for causality runs from past to future (this follows from the theory of relativity: information cannot travel faster than the speed of light, and certainly not from the future to the past – outside the light cone).[5] But the relation between a fact and the truth value of the proposition that describes it is not causal (but definitional).

Back to Judith Ronen’s Formalization

If we now return to Judith Ronen’s argument, I think its main problem is that it ignores the distinction between logical truth value and information. Even if already today the truth value of the proposition “Tomorrow I shall do X” exists, and this proposition is true, this really does not contradict my ability to do Y tomorrow. But this does not mean that if the information that tomorrow I shall do X exists already today, I will be able to do Y tomorrow. If God knows what I shall do tomorrow, there is no possibility that I shall do something else tomorrow (there is no alternative possible world in which this can happen). Hence, if God knows, I am indeed compelled to do what I shall do. The reason is that God’s knowledge is not merely the truth value of a proposition but information, and the existence of information contradicts the freedom to do otherwise in the future. The material implication used in logic expresses a relation between truth values of propositions (it is impossible that the antecedent be true and the consequent false), but not necessarily a causal relation between them.

We can perhaps see this as follows. Suppose I hypnotized some person to perform act X, and now he performs the act “of his free choice”. By this I mean that at the moment of action he feels that the choice is entirely in his hands. Has he really chosen freely? Compatibilists argue that he has. If a person is compelled to do something by his own nature, this is called his free choice. He chose, and nothing else (that is not himself) compelled him to do it. But at the beginning of my book The Science of Freedom I explained that this is a very implausible definition of freedom. Freedom is supposed to include the hypothetical possibility of doing otherwise. When you are compelled to do something, even if what compels you is your own nature, you still do not have the freedom to do or decide otherwise, and therefore it is hard to regard this as free choice.[6] When God knows in advance that I shall do X, then I really have no possibility of doing something else. Therefore it is difficult to regard this as an act done by my free choice. Of course, I could have done Y, and then God would also have known that I shall do Y, and all this is entirely possible. But under the assumption that God already now knows that I shall do X, I have no possibility of doing Y tomorrow. This is information (true) and not merely the truth value of a proposition.

We can see this from another angle, via Newcomb’s paradox.

Newcomb’s Paradox[7]

Newcomb proposed a thought experiment involving two people: a chooser and a prophet. Before the chooser lie two boxes: one is open and contains $1,000, and the other is closed and contains either $0 or $1,000,000 (the chooser does not know which). The chooser must decide whether to take the contents of both boxes together or only the contents of the closed one. Here the prophet enters the picture. We assume, for the sake of discussion, that his predictive capacity is perfect. He knows in advance and with certainty what the chooser will do, and in accordance with this he prepares the contents of the closed box the day before the chooser makes his decision. Since the prophet wishes to give a prize to someone who is satisfied with little, he adopts the following tactic: if the chooser is going to take both boxes, he already now ensures that the closed box will be empty. But if the chooser is a person satisfied with little and is going to take only the closed box, the prophet makes sure to reward him by placing in it in advance (already today) a million dollars.

The chooser knows both the prophet’s capabilities and his strategy (how he prepares the closed box). The chooser does not know only one detail: what the prophet has predicted regarding his expected choice now (for he himself is not a prophet), and consequently he does not know what the prophet in fact placed yesterday in the closed box. The question I pose to you is: given these facts, which strategy should the chooser adopt? At first glance he should take only the closed box, since that way he will win a million dollars. If he takes both, he will win only one thousand (because the prophet knows this in advance and then ensures that the closed box will be empty). On the other hand, at this point the closed box is already prepared before him, and what is in it was already determined yesterday and will not change now if he acts differently (the prophet is not a magician but only a prophet. He is omniscient but not omnipotent. He cannot change the contents of the box in the present). If so, why should the chooser not take, along with the closed box, also the open one with another thousand dollars? His taking the second box cannot retroactively change the contents of the closed box. What is in the closed box is there already, and now he merely adds another thousand dollars for himself. It seems that taking both boxes is the winning strategy in any case. However, if the prophet is truly omniscient he will ensure that in such a case the closed box will be empty. Thus, when the chooser takes both boxes, he will win only $1,000, that is, he chose incorrectly. If this does not happen, it contradicts the prophet’s omniscience.

In the period when this paradox was published, a phenomenon called “Newcombmania” developed, that is, people’s addiction to 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 opposite position is a complete fool. Yet there is definitely no consensus about which position is correct.

In the deterministic picture, this difficulty is clear. There is no obstacle there to thinking that the information already exists now. Even if no one can access it (because it is very complicated and complex; to the prophet’s sorrow there is no computer powerful enough to predict it), the information exists. Therefore there is no principled obstacle to the existence of a prophet who knows it. This argument is a thought experiment conducted according to the determinist’s assumptions, and it challenges them. In fact, it claims that the determinist is necessarily wrong, for his assumptions lead to a contradiction. Newcomb’s paradox is in effect an a priori argument against determinism, for if determinism is correct, then the information indeed exists and such a prophet is possible in principle. According to his view, it emerges that although the content of the closed box is already fixed and will not change, it is nevertheless better for the chooser to refrain from taking the open box and to make do with the closed box alone. Taking the open box with another thousand dollars would, as it were, “erase” a million dollars from the closed box. According to the determinist, the chooser must make a completely irrational decision (to forgo taking a thousand dollars lying before him), or alternatively he must believe in causal influence backwards in time (that taking the box will retroactively change its contents). This proves, from within, that determinism is utterly implausible.[8]

At first glance, the conclusion is that determinism is false, and we must adopt a libertarian conception. The assumption that there exists such a prophet covertly presupposes a deterministic position, for in the libertarian picture we cannot speak of such a prophet, since it is impossible to know in advance with certainty what the chooser will decide. If the information does not exist now, how can someone know it with certainty?

But Maimonides’ question assumes that even if we adopt a libertarian conception, there is no obstacle to knowing that future information, and therefore he wonders how it is possible that God (who plays the role of the prophet in this game) knows everything in advance and at the same time we have free choice (I remind you that the Ra’avad agrees with him). The bigger problem is that both Maimonides and the Ra’avad in their conclusion remain with both beliefs together: both divine knowledge and human free choice. At first glance this experiment proves that such a position is impossible. If man has free choice (that is, the world is not deterministic), then we cannot assume that the information exists in advance (that there is such a prophet). That assumption leads us to a contradiction.

In other words, the assumption that God knows in advance what I shall do (that there is a “prophet” as in Newcomb’s story) necessarily entails that I have no choice. It is impossible to say that God knows my deeds in advance and that nevertheless I have free will. This is a proof that Judith Ronen’s ontological argument (= formalization) is incorrect. The explanation of the precise error in it was presented above.

One might have argued that all this is correct if some human being could function as a prophet and know in advance what we shall do in the future. But God is not bound by these rules of the game. Yet this is again the same mistake. There is no obstacle to God’s revealing this information to some person, or to His preparing the boxes Himself and playing the game I described with some person. What would that person’s strategy be in such a case? We can repeat the entire argument and see that he has no strategy. We are again caught in the same loop. Therefore this argument attacks God’s knowledge as well, not only a human prophet’s knowledge. As I have already written here more than once, the fact that God knows the information, or that anyone knows it at all, is not relevant to the discussion. What creates the contradiction is the very existence of the information.

Some have sharpened the difficulty by extending Newcomb’s problem to a glass box. If the closed box is made of glass, that is, the chooser sees what is in it. Now imagine that he sees a million dollars in it and understands that the prophet predicted that he will take only it. Can he now not take both boxes, in order to gain another thousand dollars, against the prophet’s prediction? If he has free will he certainly can take the second box as well. So what will happen now? Will the box empty itself as if by magic? I remind you that the prophet is omniscient, not omnipotent. Similarly, if the chooser sees that the glass box is empty and then it is clear to him that the prophet predicted that he will take both. To annoy the prophet, he may decide to take only the closed one. Is this not possible? Under the assumption that he has free will this is of course possible. The claim that it is not possible forces us into determinism. The claim that it is possible says that there is no prophet who can know in advance what I shall do. Once again, the clear conclusion is that there is no way to reconcile foreknowledge with free will. We may perhaps save the possibility of prophecy and God’s omnipotence, but only at the price of adopting a deterministic view; or we may save free will but only at the price of foregoing divine foreknowledge.[9]

The Connection to Logical Determinism

Logical determinism points to a mechanism that seems similar but is in fact entirely different. Yesterday there was a note on which it was written whether or not there will be a sea battle. From this the logical determinist wanted to infer that the occurrence of the sea battle is necessary, that is, that it could not have failed to occur. My answer was that the occurrence of the sea battle is what “writes” the note retroactively. What is written on it a thousand years ago is determined at the time of the occurrence now.

Why is this possible (also according to the libertarian) in the context of logical determinism, whereas in Newcomb’s prophet it is not possible? Why can the determinist not argue here too that taking both boxes will retroactively change the contents of the closed box? The difference is very simple. In the context of logical determinism we are not dealing with information but with the truth value of a proposition, and as we have seen, that truth value can be determined retroactively from future to past (this is not a causal influence from future to past, but non-causal determination – a change in the content of a logical definition). By contrast, Newcomb’s paradox speaks of a note that contains information, or a box that contains money. Here we are dealing with a fact in the world and not merely a logical definition, and therefore it proves that such a note or box cannot exist before the occurrence itself. I explained earlier that the truth value of a proposition is not information but a logical definition, and therefore it is atemporal, that is, there is no obstacle to its being determined by a future event. But information such as the presence of money in a box is not atemporal. Information about an event is created only with the event’s occurrence and not before. Causality cannot function from future to past.[10]

Summary

The conclusion so far is that there is no way to maintain both beliefs together: if there is divine foreknowledge, then we do not have the freedom to choose in the future, and vice versa. This of course leaves us only with the fourth option that I described, which I shall discuss in the next column.

[1] In the collection Between Religion and Morality, edited by Daniel Statman and Avi Sagi, Bar-Ilan University, 1994, pp. 35–43. The matter is discussed in the fourth book in the series “Talmudic Logic”, Logic of Time in the Talmud (p. 50ff.).

[2] Note that I do not formulate this as “the dog is necessarily alive or dead”, for these formulations can be debated. There may be a state between life and death (brain death). But “alive or not alive”, “true or not true”, are necessarily true propositions. When there is a positive term that describes the opposite state, we must be careful not to see it as the full negation of the original term. “Dead” is not the precise negation of “alive”. “Not alive” is the more precise negation. In fact, we could have said the same regarding the pair bachelor–married (that is, to use bachelor–not bachelor). This is what I called elsewhere a synthetic a priori contradiction (as opposed to a logical, or analytic, contradiction), but I shall not go into this here.

[3] An interesting question is whether it is necessarily false, or contingently false, and this is not the place to expand.

[4] This interpretation allows us to analyze the modal operators in terms of the standard logical operators that deal with truth and falsity. See about this in the third book of the “Talmudic Logic” series, Deontic Logic in Light of the Talmud (chapter two, and applications mainly in chapter fourteen).

[5] Incidentally, this is what underlies the Talmudic topic of “bereirah” (see, for example, Gittin 25 and parallels). When a person says, “The get was written for that one of my wives who will go out first through the doorway tomorrow”, I have defined a woman on the basis of the truth value of a proposition and not on the basis of present information. The truth value of the proposition is also defined today, even though the event will only occur tomorrow. Therefore it is possible that such a statement will be effective, for the get was written for a well-defined woman (we shall know her concrete identity tomorrow). Although the information as to which woman this is does not exist today, the truth value of the proposition “Rachel will go out first through the doorway tomorrow” will only be known tomorrow; but when we know it, it will become evident retroactively. It will then turn out that already today this proposition was true.

[6] At the beginning of the second Ein Ayah lesson (section 114) and the third (section 115), I addressed this point in light of the Gemara in Berakhot 9a: “And they despoiled Egypt – against their will”, which according to one view is interpreted as against the Egyptians’ will (although “the Lord gave the people favor in the eyes of the Egyptians” and apparently they did this “of their free will”).

[7] See on this in chapter four of The Science of Freedom.

[8] One can propose an experiment in which the experimenter uses scanning of brain signals in order to predict the subject’s choice in a Newcomb-type situation. Below, in chapter fourteen, I shall bring the words of Ariel Poratstenberg of the Hebrew University about their current work on developing such experiments.

[9] One could perhaps save the contradiction if we were to speak of causal influence backwards in time. If the person decides to take the closed box when the prophet (or God) has prepared it full, then the prophet (or God) changes its contents retroactively and thereby realizes his prophecy. But even if such an influence were possible (I very much doubt it), this does not solve the difficulty. He still did not predict what would occur; he was forced to correct it. In other words, we have still proved that there cannot be a prophet who does not have the ability to act causally backwards in time. The possibility of such a prophet depends on an additional factor and is not possible in and of itself.

In my book there I raised several more arguments for and against, but for our purposes what has been presented here suffices. There I tried to prove by means of Newcomb’s paradox that determinism is false, and this requires several more logical twists. Here I am using the paradox only in order to prove that determinism does not sit well with free will (but is not necessarily false), that is, to reject the third proposed resolution discussed in this column, and for that what I have brought here is sufficient.

[10] Judith Ronen, in her doctoral dissertation (which was published as a book, The Fourth Dimension), which dealt with a logical-philosophical analysis of the possibility of parapsychology, argues that there is also causal influence backwards in time. According to her own view she remains consistent, but I do not accept this claim either, and for the very same reasons (in my opinion she again conflates the truth value of a proposition, which as we have seen can be determined retroactively, with information). This is not the place to expand on this further.