The Question of Knowledge and Choice 4 (Column 303)

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.

Once you have eliminated the impossible, whatever remains, however improbable, must be the truth.

(Sherlock Holmes, The Sign of Four)

In the three previous columns I examined four possibilities regarding divine foreknowledge of free choices. I reached the conclusion that the only possibility that exists is the fourth: God does not know. The motto of that column, which appears here as well, is meant to address the feeling that many experience upon hearing this conclusion. In this column I shall continue with the same motto and once again examine the question of whether the first three possibilities are indeed impossible. In fact, I shall focus here on the third and present some doubtful reflections about it.

Another Look at the Third Possibility

As I remarked at the end of the previous column, if one of the first three possibilities seems to someone correct in itself (that is, he does not see it merely as a forced escape route so as to avoid the fourth possibility), then of course one may adopt it. In my view they are implausible, and therefore I tend to think that the fourth is the correct one.

To round off the whole discussion, in this column I wanted nevertheless to examine the viability of the third-type possibility (the “movie theory”). In short, I still do not entirely rule out the possibility that there is no contradiction between knowledge and choice. This is a very delicate and confusing business, and for years I have been hesitant about whether the third possibility is indeed refuted or not (already at the end of Two Carts I raised doubts about this). Let me recall that at the beginning of the previous column, where I dealt with this possibility, I prefaced and wrote:

In this column I shall discuss the third possibility, which is the trickiest of them all. I shall already say in advance that I tend not to accept it, but I am always accompanied by a shadow of doubt with regard to the arguments against it.

In this column I shall try to explain that “shadow of doubt”, namely why I am not fully at peace with rejecting this possibility. In short, I indeed tend to think that it is not correct, but I am not certain of that.

Some of the arguments I shall present here were raised in the talkbacks to Column 301 (in various formulations). There were several discussions there that I had to cut off because the load on the site in those days was beyond my strength,[1] and therefore I could not continue to enter into details and subtleties in several parallel discussions. I apologize to the readers whose discussions were interrupted. I wrote to some of them that in the last column I would qualify my words, and indeed in what I say here you can find some of the counter-arguments that appeared in those talkbacks, which definitely helped me sharpen that shadow I mentioned. Here too the discussion will not be complete, and I shall merely describe the doubts without discussing them in detail (one of them alone requires philosophical and logical twists that are hard for me to carry out fully here).

Between Logical Contradiction and A Priori Contradiction

In the previous columns I distinguished between two kinds of impossibilities or contradictions: logical and physical. An impossibility is a claim that cannot obtain (logically or physically). A contradiction denotes a concept that is undefined (logically) or impossible (physically). A physical impossibility is a statement whose content contradicts the laws of physics, such as: the stone remained suspended in the air, the sea split in two, and the like. Correspondingly, a physical contradiction is a contradiction within a concept, for example the concept of ‘a stone that can remain suspended in the air’ (as opposed to the previous example, which was a statement; this is not a statement but a concept). A logical impossibility is a statement such as the triangle is round, this bachelor is married, or the diagonal of this square is shorter than its side. And correspondingly, a logical contradiction exists in concepts such as ‘round triangle’, ‘married bachelor’, and the like. I argued there that an expression that contains a logical contradiction is meaningless, and correspondingly a statement that contains such an expression or concept does not state anything (nonsense). However, this dichotomy is too rough. There is another category between these two types of contradictions, the logical and the physical, and it is important to pay attention to it: a priori contradiction.

At the end of my book Two Carts I distinguished between two kinds of non-physical contradictions/impossibilities (this is elaborated further in an unpublished article, here): logical contradiction and a priori contradiction.[2] A logical contradiction is a clash between two concepts or principles that directly contradict one another in terms of their very meaning, such as a round triangle. A circle is not a triangle and a triangle is not a circle, and therefore this combination is colorless and meaningless. By contrast, let us consider a concept such as ‘event without a cause’. David Hume taught us that the principle of causality is an a priori assumption and not the result of observation, and therefore asserting the existence of a causeless event is not a physical contradiction. But it is also quite clear that this is not a logical contradiction, since there is no principled bar to thinking about an event without a cause. It probably does not occur in our physical world, but in principle there is no logical impossibility here. An analysis of the concept ‘event’ does not reveal that it must occur by virtue of some cause. Thus, the expression ‘event without a cause’ contradicts a principle that we believe in a priori, but the conceptual combination ‘event without a cause’ is not meaningless. The question of whether such an event exists or not is a different question.[3] Contradictions or impossibilities of this sort I called there a priori contradictions/impossibilities.[4]

Thus there are two kinds of non-physical contradictions: logical contradiction and a priori contradiction. Why is this distinction important? Because I showed in the previous column that a physical contradiction does not bind God, whereas a logical contradiction does, but with respect to an a priori contradiction the situation is more complex. In the case of an a priori contradiction, the conceptual combination in question has meaning. It is not lack of meaning but lack of feasibility of actual realization. Regarding a concept that contains such a contradiction, one can perhaps claim that an omnipotent being can realize it. A concept or statement that contains an a priori contradiction has a well-defined meaning, but we have an inherent (a priori) inability to accept it, and therefore there may be room to speak of God being able to overcome such a contradiction. For example, it is quite clear that He can create an event without a cause (apparently even a human being can do that, at least when he chooses, according to the libertarian view). The creation of the world was probably such an event (regarding other miracles, there may be room to speak of the existence of non-physical causes).[5]

The Nature of the Contradiction between Divine Knowledge and Free Choice

In the previous column I quoted Maimonides in the Guide of the Perplexed, where he describes a situation in which one may hesitate as to whether some expression or statement constitutes a logical contradiction/impossibility or not. Eliezer raised the possibility that this is precisely the situation in our issue. Let us consider the concept of ‘divine knowledge of a future free act’, or the claim that God can know a future free act. Clearly these are not physical contradictions or impossibilities. The problem here is not the result of observation or of any scientific finding. The question is whether this is a logical or an a priori contradiction/impossibility. If I am correct in the conclusion of the previous column, then this is a logical impossibility, since it is a matter of ‘knowing information that does not exist’. How is that different from ‘a stone that the omnipotent cannot lift’, or from a ‘married bachelor’? But this is not necessarily accurate, because here the time axis may be important. The information does exist, for it will be generated at some point in the future and then it will exist. It does not exist now. Some would argue that if God can look at future information, then from His perspective the information does exist and there is no logical contradiction here. But one can formulate it differently: “God now knows information that does not now exist.” Here the problem is more severe, in two senses: first, if the information does not now exist, how can it be known now? And beyond that, once God knows it, it turns out that it does exist now (and we shall spare ourselves, for the sake of brevity, the predictable responses that His knowledge is not like ours and that He knows in a different way. I hope that by now it is clear that this is nonsense). In this formulation, is it not obvious that we are dealing with a logical contradiction?

One may raise the possibility that indeed God knows and the information really does exist now, but this does not contradict our free choice. That is, the information about a future choice does exist now (in the first column I already clarified that it is not very important whether someone knows it). This leads us to the claims in the second column that rejected the third possibility: that there is no contradiction between His knowledge and our freedom to choose. There I advanced several arguments in order to show that there is a contradiction, and now I shall present some doubts that I have regarding them.

Doubts Regarding Yehudit Ronen’s Formalization

Yehudit Ronen’s argument sought to show that there is no contradiction between these two assumptions. In brief, she argued that God’s knowledge entails that I shall do X, but not that I shall do it necessarily. She distinguished there between the claim: “It is necessary that if God knows that I shall do X then I shall do X”, which is true, and the claim “If God knows that I shall do X then necessarily I shall do X”, which is not true. She explained that determinism is equivalent to the second claim and not to the first.

My main objection to her argument was based on the possible-worlds interpretation. According to this interpretation, the term ‘necessary’ means “true in every possible world”. If something is necessary, one cannot imagine a world in which it does not occur. Hence, in every possible world it is true that if God knows that I shall do X, then I indeed do X.

In the talkbacks (see for example with Ariel here) the following claim was raised against me: even if in every such world I indeed do X, the important question is whether I do it necessarily. It is not enough to say that I do something in order to say that I necessarily do it. The whole point of Ronen’s formalization is precisely the distinction between these two situations. They argued that in such a situation there is no necessity in my actions, and therefore my challenge to her is mistaken. I replied that in order to clarify this we must apply the modal interpretation (of possible worlds) also to this very claim. To see whether, when I do something, I do it necessarily, we must examine the truth of the matter in all possible worlds. And indeed, assuming that God knows that I shall do X, then there is no possible world in which I do not do X. If so, it seems that the second claim is also true: if God knows that I shall do X, then necessarily I shall do it. And from here the deterministic conclusion does follow from God’s knowledge. Therefore, if we wish to preserve the assumption of our free choice, there is no escape from relinquishing the assumption that God knows in advance what we shall do in the future.

My shadow of doubt is that indeed there is a sense that even if in all possible worlds a person does X, there is room for the claim that the possible-worlds interpretation does not adequately capture the notion of necessity. According to what I have described here, there is in fact no difference between the two aforementioned claims, even though their formalization is different. Or, in different words: even if God knows that I shall do X, it is still possible that I would do Y, and then, of course, He would also know that I shall do Y. His knowing that I shall do X is not necessary, and therefore there may be a situation in which He knows that I shall do Y. In short, this whole business is confusing and seems somewhat dubious to me, although I am unable to put my finger on the precise flaw in my arguments. Asaf put it nicely and succinctly:

Perhaps I am not understanding or am missing something, but if He knows that I shall travel to Tel Aviv, does that not mean that He knows that I have freely chosen to travel to Tel Aviv? That is, He knows in advance what I shall choose freely, and although I could have chosen to travel to Haifa, I did not. Is there a problem with this way of thinking?

As I replied to him, this is precisely the movie theory that was discussed in the second column (he made this comment after the first column), but this formulation greatly sharpens the shadow of doubt that I am describing here. I cannot dispel the feeling that perhaps I have missed something here.

After the column was posted, Phil sent a talkback that convinced me that I was mistaken. I therefore added this passage to the column and updated it (I hope the site will not enter a loop of redirects). Phil wrote as follows:

According to your view, it seems that God does not even know what I chose in the past. For if He does indeed know, then according to the possible-worlds interpretation it follows that I had to choose that way. The argument is the same argument:

1. Today God knows that I chose X.
2. There is no possible world in which God knows that I chose X but in fact I did not choose X.
3. Conclusion: I had to choose X.

Although he himself suggested there a possible distinction between forward and backward causality, and I also answered him that this is the distinction, on second thought this is not correct. If the possible-worlds interpretation is applied to the claim that I did X yesterday, then he is indeed right: I did it necessarily. This is a good proof that this interpretation does not adequately capture the notion of necessity. This is a novelty in modal logic and is worth asking mathematicians and logicians about, but I am convinced.

What, then, is our situation now? Indeed, in the sense of possible worlds, it seems that God’s knowledge does not dictate my action. The question is whether the notion of necessity as defined here is really the relevant notion. It actually seems that I really do X of my own will, even though I did not, in fact, have the possibility of doing otherwise. This somewhat resembles the approach called compatibilism, that is, the claim that a person can be considered to act freely even though he has no other option. This is akin to the Talmudic discussion of compulsion and will (in footnote 6 in the second column I brought as an example the Talmudic passage in Berakhot 9 about “and they despoiled Egypt”). As long as this is what he himself wants and decides to do, he is considered free, even though he truly had no other option. I think that such a situation still does not deserve to be called free choice, but at this point I am really not sure of anything here.

Thus far I have discussed Yehudit Ronen’s argument, which shows that apparently there is no contradiction between knowledge and choice, and I suggested various ways to reject it (as stated, I am not sure what the conclusion is). By contrast, Newcomb’s paradox comes to prove that there must be a contradiction between God’s knowledge and our freedom to choose, and here we must examine the counter-arguments that were raised against me.

Newcomb’s Paradox

The paradox shows that if one assumes that the information exists, a contradiction arises, since there are two valid arguments regarding the chooser’s strategy, each of which leads to a conclusion opposite that of the other (either take only the closed box, or take both). In a follow-up challenge (here, at the end) Ariel also raised against this argument a claim similar to the one we saw above: it is indeed true that there cannot be a situation in which the prophet knew in advance that I would do X and yet I do something else, but the causal relation is not from the prophet’s knowledge to my action, but the opposite: from my action to the prophet’s knowledge. He argued that one should not rule out the possibility that the prophet knows in advance what I shall do and also takes into account my final deliberation, and therefore in the end there will indeed be a match.

I told him that he is presupposing here reverse causality, from future to past, and in my view this is unacceptable. Let me recall the distinction I presented in the second column between reverse causality with respect to information, which is impossible, and reverse causality with respect to logic, which is possible. Here we are dealing with reverse causality regarding information, and therefore it seems to me that it is impossible (see more on this below). Beyond that, as long as the prophet knows the information, regardless of the causal direction, I can still point to two contradictory strategies that stand before the chooser, and therefore his knowledge leads to a contradiction.

Phil too raised an argument of reverse causality, and he supported it with an argument similar to the one Ariel raised above, except that this time he applied it to Newcomb’s paradox: he wondered why the possible-worlds interpretation captures the notion of necessity. It may be that the chooser indeed does what the prophet predicted, but does not do it necessarily. To this I shall again say that I think this is impossible, because the possible-worlds interpretation is the correct interpretation of the term ‘necessity’, but the aforementioned shadow of doubt remains here as well. Beyond that, even if the chooser does not do it necessarily, I am not asking what he will do but what he ought to do. The question is what strategy he should adopt, not what he will actually do. In this sense there is a difference between Newcomb’s argument and Yehudit Ronen’s formalization.

Against Ariel and Phil I also raised the question of what they would say about the transparent-box experiment. There the chooser knows what the prophet has decided, and therefore he can decide to act contrary to the prophet’s prediction and turn it into a lie with his own hands. Abstention on the part of the prophet (which Ariel proposed) is not an option, for he is supposed to look at the future and say what he sees. After all, something will happen in the future, and he is supposed to see it. It was indeed argued that this is a situation in which the prophet’s own action influences the chooser’s decision, and therefore there is no room here to speak of a prophet who knows the future. I again argued that if the prophet simply observes the future and sees what will happen, this argument is not relevant to him. He will see what he himself will do and how the chooser will respond.[6] Therefore I do not see such involvement as a problem for my argument.[7]

Ariel Vinograd argued against me that one can formulate this very paradox also with respect to deterministic machines (this will apparently send them into a non-terminating loop). He concluded from this that there is nothing in this paradox that relates specifically to a being endowed with free choice. The very existence of such a prophet influences the future and therefore does not allow prediction or does not allow a winning strategy, even if the chooser does not possess free choice. If so, the root of the difficulty is not the contradiction between free will and the existence of the prophet. Such a prophet cannot exist regardless of the question of free will.

Now I think that if this is so, then my position is even better. If so, it is impossible that God knows what will happen in the future, regardless of the question whether we have free will. This is precisely my claim, and he only reinforces it.

But there I answered him that if we are dealing with a mechanical chooser, there is no problem whatsoever with the prophet’s knowing what this chooser will do. He need only examine the chooser’s software and see what it tells him to choose (and in the transparent-box case he must see what it tells him to do in each situation of the transparent box). Admittedly, one can also put this prophet into an impossible loop by instructing the mechanical chooser to act against the prophet’s prediction (in the transparent-box case, of course). And indeed, after some back-and-forth between us, Ariel Vinograd formulated the final difficulty as follows:

Or, more simply, in the version with the glass box. I instruct the software that if the glass box is empty, it is to take only it, and if the glass box contains a million dollars, it is to take both boxes. Thus in any case the software will foil the prophet’s scheme. We have reached the same paradox, and free choice will not help here (since a computer does not have it).

And to this I answered him:

I think you are making assumptions about the software that pull the rug out from under the question.

The chooser’s software knows that the prophet knows in advance what it itself will do. Therefore it will take what it is expected to take, unless it has the choice to do otherwise. That is what will happen, unless you introduce here a programmer who instructs it to do the opposite, but then you have already indirectly introduced either an assumption of choice [on the part of the mechanical chooser or of the programmer who created it] and/or the assumption that there is no software that knows in advance what I shall do. In any case, in my view the difficulty does not arise.

In other words, you have indirectly introduced here the assumption that the software itself is endowed with free choice or that the programmer has chosen the mode of operation for it. In either case, either no agent with choice is involved here, or such an agent is involved, and then the conclusion is that there is no such prophet. I think the problem cannot be formulated when dealing with a mechanical chooser.

And still, here too I have some sort of shadow of doubt. And I can only conclude with what I wrote to him there at the end of my message:

But I truly am not completely sure, and the whole thing somewhat confuses me (I apologize that I do not have time to deal with this seriously now; the pressure here is terrible). In any case, I shall qualify this argument at the end of the next column.

There is something elusive here that is playing tricks on me, and I am not entirely sure that my conclusion is really correct.

And again, a later addition to the column. After two days Ariel returned and argued against the transparent-box experiment with an argument that convinced me that I was mistaken here as well:

In the case of the deterministic prophet [in my view one can ignore the fact that this is a deterministic prophet. M.A.] and the transparent box – if from now on the opaque box is made transparent, there will be a very clear influence of the prophet on the chooser’s choice, and therefore the prophecy will fail. One must note that the prophet will still know exactly what will happen, but he simply will not be able to put into the box any amount that will come out right. The flaw is not in his knowledge, but in his ability to put money into the box or not to put money into the box, since he surely knows that if he puts the million into the box it will be chosen, and if he does not put it in, it will not be chosen.

As stated, I was convinced that the transparent-box experiment does not prove the impossibility of knowing. It is an experiment that cannot be carried out, which further strengthens the shadow of doubt that accompanies me with regard to the third possibility.

A Note on Reverse Causality and Time Travel

By way of a side remark, my entire discussion assumes that reverse causality is impossible,[8] and therefore that there cannot be information in the present about something that will be done freely in the future.[9] One can add here Yossi Potter’s claim from general relativity, where he proposed a physical possibility of reverse causality or at least of obtaining information from the future without influencing it. I argued against him that this information cannot be transmitted to the prophet (without fixing the future), and therefore we are still trapped in some inability on God’s part. If so, we have not gained much from this proposal. But of course, if he is right, then it is possible that God really does know the future (though even then there is some inability on His part). The fact that we have gained nothing does not mean that his proposal is wrong. The conclusion from his words is that the claim that God does not know is not necessary, even if as a result this information cannot be transmitted to human beings (and in fact cannot be transmitted to any point in time on our side that is located before the time of the act’s performance).

Perhaps I shall add another claim here. I wish to suggest that the theory of relativity deals with physical events. I am not sure that one may use it with regard to choice events. It may be that in a situation in which the information is generated in the future in a non-deterministic way (by a human choice) one is not allowed to apply the theory of relativity to it. Physics assumes determinism, and it may be that this enters in one way or another as a hidden assumption in the theory of relativity. I shall now bring some indication for this claim.

In Column 33 I discussed the deceptive nature of the concept of ‘travelling back in time’. I showed that it involves conceptual and logical difficulties and not only physical ones, and I proposed there a way to solve them (by assuming two time axes). Time travel gives rise to several paradoxes, and one of the best known among them is the ‘killing the grandfather’ paradox. Suppose that in some way one can travel back fifty years in time. I return to my father’s birthplace and a year before my father is born I kill my grandfather. Now my father cannot be born, and of course neither can I. But then, if we continue along the time axis another fifty years, I cannot exist. So who was it that travelled back in time? Seemingly this paradox proves that time travel is impossible. Time travel leads to paradoxes and is therefore impossible.

But note that this paradox is based on the assumption that I have free choice, and therefore I can decide to kill my grandfather. In a deterministic world I shall do what I am dictated to do, and therefore, by definition, I shall not kill him, and in such a situation the paradox, of course, will not arise. Perhaps this can be seen as a hint that the theory of relativity, and in particular time travel within it, cannot deal with beings endowed with free will (assuming there are such beings).[10]

Summary

I still tend to think that the most reasonable conclusion is that God does not know what a being with choice will do in the future (unless He removes its choice and determines the future Himself). Even if the adoption of far-fetched hypotheses of reverse causality in time or interpretations of the logical formalization and Newcomb’s paradox can in some way solve the problem (in light of the comments I have received, I am no longer at all sure that they cannot), it seems to me that the strain involved in them far exceeds the strain involved in the hypothesis that God does not know the future. As I showed in the third column, there is no principled problem with this claim. It does not in any way contradict the assumption of God’s omnipotence.

We must note that every proposal in this area leaves us with some inability on God’s part. In the worst case, we must all agree that even if He knows what will happen in the future, He certainly cannot both determine what will happen in the future and also grant us free choice. That is, our free choice deprives Him of control/ability at some level, at least practical control, even if not control in the sense of information. Therefore, the recoil from the thesis I have proposed here, as though it damages God’s omnipotence, has no substance. Logic will always “limit” His abilities (we saw in the third column that these are not really limitations).

Similarly, the silencing arguments raised against me, as if I am relying on my own gut feelings and on their basis coming out against positions accepted in the tradition for generations, have no substance for several reasons. First, in our tradition there are deterministic views, just as there are views that relinquish God’s knowledge (I have brought here only some of them). Second, just as all the sages who shape our tradition used their reason to propose positions and arguments on this issue, I see no reason why I, or anyone else, should not do the same. If everyone were to say only what accords with the tradition, different views would never have arisen. Third, it is completely unreasonable to tell me that even if my mind tells me something, I must subordinate it to tradition. First, because in my opinion there is no such tradition. There is a tradition that He is omnipotent, but regarding His knowledge of the future this depends on the question of whether it can indeed be derived from His omnipotence. In my view it cannot. But even if there were such a tradition, if this is what I think, then I must say it and propose it for discussion, and everyone will decide what to do with it. In particular, as I have written more than once, the claim of formal authority with regard to matters of fact (and the question of whether God knows or not is a factual question) is an oxymoron. If this is what I think, then this is what I think. And fourth and finally, the discussion of this question is far from being cardinal and consequential. On the assumption that we agree that a person has free choice, the question of whether God knows or does not know in advance what we shall do is marginal. Why should it be important at all? It is a theological question that is nice to play with, but the recoil from uttering “heretical” statements with regard to it seems very strange to me. In my eyes it is far more problematic to rule in the laws of Shabbat in a way that deviates from the accepted opinion, something that most great halakhic decisors do not hesitate to do.

In short, each person must think what seems to him most reasonable, regardless of whether it accords with the tradition. I have laid out the arguments and considerations (as well as the reservations) before you, and now everyone is invited to formulate his own position. Whoever has substantive arguments is invited to raise them in the discussion, but claims to the effect that one is forbidden to draw conclusions or forbidden to state them in public are cowardly nonsense. When substantive arguments and reasons run out, people move on to silencing techniques (“this is heresy”, “how can one reject the view accepted by all the great sages of Israel on the basis of gut feelings?”, “this shows lack of fear of Heaven”, and so on). Because such claims were raised against me in the previous columns, I decided to devote the next column to further discussion of the question of intellectual autonomy.

Thank you to all the intelligent commenters who helped me clarify this issue. I have learned from your words here, and it seems to me that now I am indeed exhausted but understand a little better what is going on here.

[1] That week I wrote four columns, all of which were packed with talkbacks to which I had to respond, in parallel to other questions that arose on the site, by email and by phone (there were several hundreds of them in those days), in addition to quite a few classes that I was giving every day. I am spelling all this out because I am uncomfortable about having cut off some interesting discussions. I would like to take this opportunity to apologize to the writers.

[2] This distinction was mentioned in footnote 2 of the second column.

[3] For example, an event of free choice is without a cause (in my book The Science of Freedom I argued that according to libertarianism its basis lies in teleological reason and not in cause).

[4] Strictly speaking, this is the synthetic-a priori, since if it were analytic then the a priori would be identical with the logical. My claim is that within the a priori there are two categories: the logical and the synthetic-a priori. I tried to see in these contradictions an indication of Kant’s thesis regarding the existence of an intermediate category between the physical and the logical (the synthetic-a priori).

[5] Incidentally, in the commentary attributed to Nahmanides on the Song of Songs (in the collected writings of Nahmanides, Schavel edition, vol. 2) he interprets the midrash in Pirkei de-Rabbi Eliezer, “From where were the heavens created? From the snow beneath His Throne of Glory…” as speaking of creation ex materia, for in his view creation ex nihilo is a logical impossibility. As is known, Maimonides in the Guide of the Perplexed apparently understood this midrash in the same way, and therefore wrote that he had never encountered a midrash so strange. I remarked on this in my article on Torah and science (see there around footnote 14. In the printed edition in Tzohar there is also a note by the editor and my response on the matter).

[6] This is not a prophet who calculates what will happen in the future, about whom one could claim that he gets into a loop in his calculation. It is a prophet who observes what will actually happen. Something will happen, and he is supposed to see it.

[7] This reminds me of an article by the economist Ariel Rubinstein, who argued that there cannot be an economic theory that accurately predicts everything that will happen in the future, since the very existence of the theory itself influences the decisions people will make. On this I wrote (to myself; it was not published) two claims: 1. One can speak of an economic theory that is not publicized. 2. One should not rule out the possibility of a theory that also takes into account its own influence on the market. In mathematics one defines the notion of a ‘fixed point’ of a function, where the value of the function equals the value of its argument: f(x=a)=a. If we define the ultimate economic theory T as a function G that takes into account all economic variables, including the effects of the theory T itself, then one should not rule out the possibility that it will still give the correct result: T=G(x,y,z,T). T is a ‘fixed point’ of the function G.

[8] I have already noted that Yehudit Ronen (in her doctoral dissertation) argued that there is no principled problem with such causality.

[9] Note that in this sentence I assumed a connection between the question of whether information about the future can be obtained and the question of whether, when such information exists now, it is still possible that I have freedom to choose. In the first column I explained that these are two different questions, and therefore the claims that God is above time and can obtain future information answer the first question but do not solve our question (which is the second). Now, after the conclusion of the third column, the two questions can once again be linked. If we have free choice, then it is impossible that God obtains in the present the information about the future. If He were to obtain it, we would not have choice. The conclusion from rejecting the third possibility (the movie theory) is that the second possibility as well (that God is above time) falls.

[10] Perhaps one can even say more than this. If I travel back in time, then my very presence there contradicts the reality that obtained then (for I did not yet exist at that time). Thus, regardless of killing the grandfather, such a situation itself is impossible. Seemingly, all that is possible, if at all, is merely to roll the time axis back to the same reality that existed then. But it is not clear in what sense this is time travel. Who is it that travelled in time? But this already takes us back in time to Column 33 and I shall not go into it here.