Causality: VI. Different Mechanisms of Influence on the Past – A Halakhic Perspective (Column 465)

Introduction

In the previous column I discussed praying about the past, and we saw there that this concept is not well-defined. At the end of that column I noted that this is the fundamental problem that dictates the dependence of the causal relation on the time axis (why a cause must precede its effect). For this reason one cannot speak of causal influence backward in time—even with regard to the Almighty—since this is a logical problem rather than a matter of the laws of nature.

However, I cited what C. S. Lewis wrote: one can, in principle, speak of divine consideration—God making a decision at some moment in time while taking future prayers into account—since He can see the future. But in such a mechanism there is no causal influence backward. In that case, the decision made at any given time affects events from that time onward (and not backward), while taking future events into account. Such a description assumes only the ability to see the future, not causal influence backward. It is not a case in which event X occurred and later the situation suddenly changes and event X did not occur (or something else, Y, occurred). That is a conceptually undefined state of affairs.

Osmo’s Story

To sharpen this distinction, I return to the example brought by Richard Taylor in his book Metaphysics: the story of Osmo (see about him in column 299). Osmo, a schoolteacher in a Midwestern American town, enters a library one day and finds a book called… “The Story of Osmo.” He becomes curious and opens the book, and sees that it begins with Osmo’s birth, in exactly the place and at the time in which he himself was born. The names of the hero’s parents are identical to those of his own parents, and so it continues: kindergarten, school, college, marriage, and so on. The book contains an exact description of his entire life. At some point Osmo reaches the chapter that tells how Osmo enters the library and finds a book called “The Story of Osmo,” opens it and begins to read. He is, of course, thrown into great distress, and he flips ahead and sees that Osmo’s end is to die in a plane crash on a flight to New York. On the appointed day he flies to a completely different destination, but at some point the pilot announces that due to a strong storm they are changing course to New York. Osmo, in terrible panic, enters the cockpit and struggles with the pilot over the control yoke, and thus the plane crashes on its way to New York.

I brought that story there to show that it suffices that the information exists (even if no one knows it) to conclude that the future comes to us deterministically. But here I wish to illustrate through it that foresight of the future does not constitute inverse influence along the time axis. The paradox arises here because Osmo read the book, but one can imagine a case in which such a book sits in the library and Osmo does not read it at all; he simply boards a flight to New York and crashes. In that case the knowledge of the future is passive and plays no part in determining that very future. Such passive knowledge of the future can perhaps be granted here for the sake of argument (at least for events that do not depend on choice). The picture of causality excludes causal influence backward in time but not necessarily knowledge forward.

Nevertheless, I note that one can treat someone’s knowledge as an event that occurs in the world (in the knower’s brain). If he knows the future, then what is to occur influences the past, since the future event produces his knowledge in the present—that is, it constitutes a cause for neural processes occurring in him now. If so, it is quite doubtful to what extent the distinction between foresight and causal influence backward really holds water.[1]

In this column I will try to describe several mechanisms of causal—or seemingly causal—regard from the future to the past, and I will do so mainly through a halakhic prism.[2]

“Igla’i Milta LeMafre’a” (It Becomes Clear Retroactively)

There are situations that are undoubtedly different from inverse influence in time. The most trivial case is lack of knowledge about an event that has already happened. For example, if I am abroad and a son is born to me on day A. On day A I do not yet know his sex and perhaps not even the fact that a child was born to me. When I return to Israel on day B, I find out that on day A a son was born. It would seem that information about the past is now revealed to me, and this somewhat resembles influence backward along the time axis. But of course there is not a shred of paradox or problem here, since we are dealing with information that existed from the outset but was lacking for me at a certain time, and later I fill the gap. Nothing at all happens backward in time.

A less clear case is what Halakhah calls “igla’i milta le’mafrea”—it becomes clear retroactively. For example, an ordinary conditional case: a man divorces his wife on condition that it rains tomorrow (“al menat” or “me’achshav” conditions operate retroactively, in contrast to an “if” condition. See Rambam, Hil. Ishut 6:15–18, and elsewhere). If it rains tomorrow, it turns out retroactively that she was already divorced from today. Seemingly the rainfall is the cause of the divorce, and if so there is an “igla’i milta le’mafrea.” The later event shows that we had been living in error, and in fact she had never been divorced. But R. Shimon Shkop proved from several sources that this is not the correct understanding of a “me’achshav” condition, and I will return to this later on.

A situation better described by “igla’i milta le’mafrea” is what the Talmud calls bererah (retroactive designation). For example, a man writes a bill of divorce for one of his two wives (both have the same name). Since the get must be written for the sake of the woman being divorced, he states in advance that the get is written for the one who will be the first to exit the doorway tomorrow morning (see Gittin 25a). The Gemara makes this law depend on the dispute whether there is or is not bererah. If there is bererah—that is, if a future event can clarify a present situation—then this get is valid and can be used to divorce the one who exits first. But according to the view that there is no bererah, the get is invalid, because one cannot clarify a reality retroactively.

The view that there is no bererah is seemingly straightforward. It holds that the act of exiting the doorway cannot validate the get backward in time. That would be inverse causality. But the view that there is bererah, which validates such a get, requires explanation. How can a future event produce effects in the present? The simplest explanation is that the future event merely designates the woman for whom the get was written. Consider a scribe who writes a get for “Leah bat Shimon,” but he does not know her personally. Is that considered writing it for the sake of the woman being divorced? Certainly yes, for her name represents her; he writes the get for the woman characterized by the name “Leah bat Shimon.” The name is her designator. The designator may also be a characteristic of hers, some action she performed, or anything else that can define her unambiguously so that it is clear for whom the get was written. If so, there is no reason not to treat a future event or feature of the woman as a legitimate designator. I need to supply a feature that singles out a certain woman for whom the get is written. The feature here is: the one who will exit first tomorrow morning. That feature uniquely identifies one woman, and the get is written for her. True, we will not know who she is until the event occurs—that is, until tomorrow morning—but that is merely lack of information. There is no inverse causal influence here.

This can be sharpened based on what I explained in the first column (459) in the discussion of logical determinism. As we saw there, the proposition “It will rain tomorrow,” assuming that it indeed will rain tomorrow, is already true today. The truth-value of a proposition does not depend on time. The explanation is that a proposition’s truth-value results from comparing the content of the proposition with the state of affairs in the world that it describes. If there is a match between the content and the state of affairs, the proposition is true. It should make no difference if the state of affairs in question is future. That only means that we do not yet know that there is such a match, but the match certainly exists. We already saw above that the completion of missing information is irrelevant to our discussion and raises no difficulty or paradox.

If so, designating one woman out of two by means of one of her future events or features is a perfectly legitimate designation. We may not yet know which woman has been designated, but the designation is fixed and stable. There is only one woman who fits that description, and the question of who she is will become clear to us tomorrow. Just as I could designate her by her appearance, her height, her name, her place of residence, I can also designate her based on a future event that will befall her. When the event occurs, information that had been lacking in the past will be revealed to us retroactively. True, this is not the same case as merely filling in missing information (as in the example of the son who was born), since in that case the event had already occurred and only our knowledge of it was lacking. But essentially the two cases are quite similar.

One may wonder, then, why there is an opinion (which is in fact the halakhic ruling at least regarding biblical laws) that there is no bererah, i.e., that such a get is invalid. If it is mere designation, what is wrong with designating on the basis of a future event?! There are several possible answers. One might claim that within the requirement that a get be written “for her sake” there is a rule that the matter already be fixed and known (at least to someone, even if not to the scribe himself) at the time of writing. See a similar idea in Tosafot, s.v. le’eizo she’ertzeh, Gittin 24b. But Tosafot there make clear that this is a special law in the “for her sake” requirement of a get, whereas the Gemara’s discussion about the existence of bererah is a general one (not limited to gittin). It is therefore clear that the general dispute about bererah is not tied to the specific parameters of gittin (or any other particular area), but to a general question of retroactive clarification.

Still, the explanation I suggested for the view that there is bererah is quite reasonable, since it is merely designation. In other words, the view that there is bererah likens our case to the assignment of a logical truth-value to a proposition, which, as we saw, can also be done from the future to the past. The view that there is no bererah may hold that what is required is that the information itself already exist. Information about a future event certainly does not yet exist (see column 459). According to this view, designation based on non-existent information is not halakhically acceptable. In any case, there is no inverse causality here.

Thus, “igla’i milta le’mafrea” does operate in a certain sense backward in time (it is not identical to filling in missing information, as in the example of the son’s birth), but this is not inverse causality; it is merely the present decision’s taking account of a future event. This is similar to Lewis’s description in the previous column of the Almighty’s taking a future prayer into account. It is no wonder that people sometimes link the phrase “igla’i milta le’mafrea” to the question of whether something is “known in Heaven” or not. When we say “igla’i milta le’mafrea,” we are essentially saying that information was missing for us, since we cannot access future information. But the Almighty, who can access such information, is indeed equipped with it. His knowledge is an indication that this is merely the completion of missing information. By contrast, if we hinge divorce or betrothal on a future event that depends on human choice, it may be that according to all opinions we do not say that “it is known in Heaven” what will happen, and all will agree that the get is not a get (so it appears from Ramban, Gittin 25b). This is because an event that depends on human choice is not known even to God Himself.[3] In Yevamot 35b the matter is tied to “when Elijah comes” and reveals the future to us (i.e., what God knows), in which case it is a state of “igla’i milta le’mafrea.”[4]

Between Condition and Bererah

The Rishonim (see Rashi, Gittin 25a; Ramban 25b) raised the question: what is the difference between a condition (tenai) and bererah? They seem to be two identical mechanisms, and yet the laws of conditions are agreed upon, while regarding bererah there is a dispute, and the halakhah even rules that there is no bererah in biblical matters. Without entering the various opinions, I will present the simplest explanation. Bererah is always the designation of one alternative from two: one woman out of two for whom the get was written; one direction out of two upon which an eruv will take effect (see Eruvin 25); a pair of log measures of wine from a barrel that contains many log which will be terumah, and the like. In all these cases what is required is designation, and therefore, as I explained above, there is no problem with a future event serving as a designator for a present need.

By contrast, in a condition we do not have two objects but two possibilities of future occurrence. I divorce on condition that it will rain tomorrow. There is no designation of one object out of two, but the imposition of divorce dependent on some future occurrence that may or may not occur. Therefore, in a condition that makes a status take effect retroactively (“al menat” or “me’achshav”), one cannot explain that it is merely designation. Why, then, do conditions regarding the future operate (even retroactively) according to all views (including the one that denies bererah)?

This can be explained following R. Shimon Shkop, who brings several proofs that a “me’achshav” condition does not operate via an “igla’i milta le’mafrea” mechanism (see at length in his “Kuntres HaTenayim,” appended to his novellae on Gittin, §22). One of his examples is Rambam, Hil. Gerushin 9:11, who writes:

“This is your get from now if I do not come from now until twelve months.” We are not concerned that perhaps he came in secret, for it is not people’s way to come stealthily. If the set time was completed and he did not come, she is divorced. If he died within the twelve months—even though it is impossible for him to come and she will be divorced—she should not marry in a case of a levir until after twelve months, when the condition will be fulfilled.

A man divorced his wife “from now” if he would not return to her within twelve months. He died after two months, and seemingly it is already clear that he will not come anymore, and thus the law should be that she is immediately divorced. But the Rambam rules that in such a case she is forbidden to marry until the twelve months have passed. His glossators were puzzled by this: since it is a retroactive condition, i.e., if he does not come then the divorce takes effect from the moment the get was given, then the moment he dies it is clear that he will not come, and thus the divorce has already taken effect. Why, then, must one wait for twelve months to elapse?

The Maggid Mishneh (8:22 on Hil. Gerushin) explains that according to the Rambam the condition must be fulfilled in actuality:

“It follows that even though it is impossible for the condition to be nullified in any way—since once he has died he will certainly not come—nevertheless she is not permitted and we do not presume her divorced until it is actually fulfilled. And here too, even though it is impossible for the condition to be fulfilled in any way, since the husband has died, we do not presume the get to be null, such that she could undergo levirate marriage, until the condition is actually nullified; and it cannot be nullified in actuality since no time was fixed. Therefore she performs chalitzah and does not undergo yibbum. This is a wondrous precision that attests to our master’s insight. So it seems to me in his opinion.”

Even if it is clear the man will not arrive, so long as the condition has not been fulfilled in actuality (i.e., twelve months have actually elapsed without his arrival), she is not divorced.

R. Shimon Shkop explains that if a “me’achshav” condition were based on an “igla’i milta le’mafrea” mechanism, then the Rambam’s words would make no sense. The divorce takes effect from the time the get was given, but this is conditional on his not arriving. Until the condition is fulfilled we live in uncertainty, but that uncertainty is merely epistemic—ours. We lack information. When twelve months pass and he has not arrived, it turns out that she had been divorced retroactively; in other words, our missing information has been completed. If so, at the moment he dies we have full information, since we now know that he will not arrive. Why, then, should she not be immediately divorced retroactively upon his death?

We are compelled to say that the condition operates via a different mechanism. R. Shimon argues that the condition is not designation based on a future event (as we saw with bererah), but a causal mechanism that operates backward in time. The husband’s failure to arrive is the cause that produces the divorce, and therefore only from the moment the husband has not arrived has the cause been realized in actuality, and only then can it produce the effect—namely, the divorce that takes effect in the past. He brings several additional proofs for this view; this is not the place to expand.

At first glance this is very puzzling. We saw that causality cannot be defined from future to past (this is the first component of the causal relation; see column 459). If so, the condition’s mechanism includes a logical contradiction. One might distinguish between causality in the physical world and legal-halakhic causality. In the physical world there is a cause that produces an effect, and both are events in the world. A future event cannot produce an event in the past, i.e., it cannot change the past. Mai de-hava hava—what happened, happened. But in the legal sphere there is no barrier to defining that the future constitutes the cause of the past, and thus the status will take effect retroactively from the moment the future event produces it. The woman’s status—whether she is divorced or not—is a legal determination, and at the legal level there is no impediment to defining matters however we wish, so long as the legal ramifications are clear.

However, such a distinction can be accepted only if we assume that legal-halakhic status is not reality but a “floating” definition—i.e., a definition without a basis in reality itself. But if we assume that legal status reflects a factual, meta-legal, or spiritual reality, then inverse causality cannot be accepted even at the legal level. An abstract spiritual event, so long as it is a fact that occurred in reality (even if not in the physical reality), is subject to the same limits I described in the previous column. As we noted, inverse causal influence is not a problem of physics but of the concepts themselves. Therefore, if inverse causality is conceptually undefined, it is clear that it cannot exist in the legal-halakhic sphere either, and not only in the physical sphere.

“From Now Onward Retroactively”

R. Shimon Shkop consistently and systematically holds that legal-halakhic statuses reflect reality (spiritual reality).[5] If so, specifically according to his view it is unclear how a condition can be defined as inverse causal influence in time (see, for example, a brief discussion here). To understand this, we need another definition from R. Shimon Shkop’s school: “from now onward retroactively” (mi-kan u-lehabba le’mafrea).[6]

The example upon which R. Shimon bases his argument about this peculiar mechanism is the Rosh’s words in Nedarim. By way of preface: Halakhah is particularly stringent regarding temporary prohibitions—i.e., prohibitions that lapse after a set time (such as prohibitions on Shabbat or festivals, or prohibitions during a holiday or a given fast). For instance, such prohibitions are not nullified by a majority, and when they are rabbinic, their doubt is ruled stringently. The Rishonim explain that the reason is that there is no point in permitting them, since one can wait until the prohibition ends and eat them in full permissibility (“Instead of eating in prohibition, eat in permissibility”). This is called “a thing that has permissibility” (davar she-yesh lo matirin; see Beitzah 3b–4a, and elsewhere).

Now, the Gemara in Nedarim 59a defines a vow as a “thing that has permissibility,” since one can go to a sage to have it permitted and then eat in permissibility. The Rosh in his Piskei HaRosh there (6:3) brings the Yerushalmi’s difficulty:

“And thus it says in the Yerushalmi (ad loc.)… And these vows, how do we treat them—as a thing that has permissibility, or as a thing that does not have permissibility? It seems: do we treat them as a thing that has permissibility? But was it not taught there [Ketubot 74b] that the sage uproots the vow from its root? Meaning: since he uproots it from its root, it turns out that it was never prohibited at all, and it is therefore not a thing that has permissibility.”

The Yerushalmi wonders: how is a vow a “thing that has permissibility,” since if one goes to a sage who permits it, the permission takes effect retroactively (he uproots the vow from its root as if it had never been vowed). A “thing that has permissibility” is something that was prohibited and then at a certain moment the prohibition lapses. But with a vow, if one does not go to a sage, it remains prohibited forever; and if one does go, it was permitted from the start. There is no state in which the vow is a prohibition that at some stage has permissibility: either it is permanently prohibited, or it was never prohibited.

And the Yerushalmi answers:

“They said: he only uproots it from now on.”

He explains that the vow is uprooted from now on. But that is not legally correct, since the uprooting of a vow by a sage’s annulment certainly occurs retroactively. The Yerushalmi is certainly not disputing that.

The Rosh explains the Yerushalmi as follows:

“Meaning, the principal uprooting is from now on, for it was prohibited until now; and even though he uproots it from its root, in any case it was prohibited until today. Therefore it is considered a thing that has permissibility.”

This is a puzzling explanation, since after it is uprooted it turns out that it had not been prohibited even until now.

R. Shimon Shkop explains that the annulment of a vow operates “from now onward retroactively.” That is: from the moment a man vows, the vow takes effect, and he is obligated by it as prescribed by the Torah. After some time he goes to a sage who permits his vow, and the sage uproots the vow retroactively—as if it had never been. But this does not reveal retroactively that we had been living in error (it is not an igla’i milta le’mafrea mechanism). Rather, the permission is the causal factor that produces the outcome (uprooting the vow) retroactively. That is, if a man violated his vow, he is liable for lashes, and we would flog him. Even if he later went to a sage who permitted his vow, this only means that from the moment of annulment we will not flog him (even for a violation committed before the annulment). But if we already flogged him, he was flogged rightly.

We can sharpen this complex picture through a critique of an argument by Rabbi Shem Tov Gefen (a collection of his essays was published under the title Dimensions, Prophecy, and Earthliness). Gefen used Kant’s thesis that space and time are categories of our thought and perception, and do not exist in reality itself, to solve the problem of the age of the world. According to him, Kant’s view implies that before man was created there was no time (since time is merely a human form of intuition). Therefore, by definition, the age of the world can be at most the age of man (and from his claim it emerges that even the first five days of creation do not exist on the time axis).

That solution is charming and has a certain allure, but a closer look shows that it is nonsense. According to it, my grandfather, too, did not exist in time, since for me my time axis began when I was born (other people’s time axes are irrelevant for me, since time does not exist in reality but only “inside us”). Clearly even Kant does not deny the possibility of speaking about the distant past, before I was born and even before there was any human being on earth. He merely claims that this form of intuition arose with man (or, indeed, with me). But from the moment it arose, we can use it to describe and relate to earlier times. It is a kind of binoculars through which we look at reality—both that which will be and that which was. The moment those binoculars were created does not dictate the limits of their use. In R. Shimon Shkop’s terminology, we can say that the time axis operates “from now onward retroactively.” From the moment it is created, we can use it also for earlier times. In exactly the same way, from the moment the vow is annulled, now, from our perspective, there was no vow in the past and there was no violation of it. But all of this is only from the moment of annulment—and retroactively. Before the annulment, there was indeed a vow and indeed a violation.

The Problematic Nature of This Concept

Note that in the annulment of a vow we are dealing with inverse causal influence, for the annulment uproots a vow that was vowed in the past; whereas in Rabbi Shem Tov Gefen’s discussion we are speaking only about a way of viewing and not about a causal relation. Thus Gefen’s example is more similar to the truth-values of propositions on the logical plane, which are also assigned “from now onward retroactively” (once the event occurred this year, the truth-value of the proposition is retroactive), and this arouses no problem. Even so, the example nicely sharpens the concept of “from now onward retroactively.” In the case of vows we are dealing with inverse causal influence in time. We are changing the past by virtue of a future event. How can such a thing be, at least given R. Shimon Shkop’s assumption that halakhic effect (chalot) reflects a kind of spiritual reality? Is this not merely verbal cosmetics devoid of real content?

Of course, one could identify the case of vows with the truth-values of propositions or with the argument regarding the time axis, and say that there is no change in the past, but merely a different present viewpoint on the past. From now on I see the past differently, but (in legal terms) this is prospective, not retrospective. The past itself does not change; what changes is our perspective on it. From our standpoint now there was no vow, just as from our standpoint now the first living organism arose a billion years ago. But in “real time,” reality was different. This is essentially a change in our consciousness, not in reality.[7]

However, such a perspective effectively erases R. Shimon’s assumption that statuses reflect reality. On his view, the question remains: what was the reality that prevailed at that past time we are speaking about? On his view, a change in consciousness should reflect a change in reality itself. If we continue in R. Shimon’s path, a mechanism of “from now onward retroactively” cannot be merely psychological-subjective. How, then, can it be understood and defined?

Two Time Axes

In column 33 (and more extensively in the fourth volume of the Talmudic Logic series) I pointed out the conceptual difficulties that exist in the notions of time travel (and all the more so in inverse causal influence). I explained there that to use such notions consistently we must posit the existence of two time axes. There is a static time axis and a dynamic time axis that flows along it. In this model, when I speak of some point in time, I must define it in terms of these two axes. One can be on Sunday at the static-time point T₁, or at a different static-time point, T₂. We would describe the first event by the pair of numbers (Sunday, T₁) and the second by the pair (Sunday, T₂).

Thus, in this model, we must mark each time point as an ordered pair, where the left entry represents the static time (T) and the right entry the dynamic time (t). For example, when we speak about the time point (2,7), we mean Saturday from the standpoint of T = 2 (= Monday) on the static axis. One can be on that very same day at several static-time standpoints. The point (1,7) is that same Saturday, but now from the standpoint of T = 1 on the static axis. In the example of vow annulment above, suppose the person vowed on Sunday and the vow was annulled on Wednesday. When I ask about the status of the vow on Monday, that depends on whether I view it from the standpoint of Thursday (after the annulment) or from the standpoint of Tuesday (before the annulment). Therefore, the status of the vow along the time axis must be presented in terms of a two-component time axis: the static T describes the time from which I judge the situation, and the dynamic t describes the time being judged. Thus, for example, the vow at time (3,2) is prohibited, for I am viewing Monday (2) from the standpoint of Tuesday (3), which is before the time of annulment. But that same vow on that same Monday (2), at the point (5,2), is permitted, for I am viewing Monday from the standpoint of Thursday (5), which is after the annulment.

Returning to Kant: the subjectivity of time pertains only to one of the axes.[8] I can look at the day my grandfather was born—before I came into being—but I do so from my present standpoint (along the static axis). Once my static time is created, I have “glasses” with which I can look along the entire dynamic axis, including moments that preceded my existence.

We can now understand that any change in the world always occurs by virtue of a cause that precedes it along the static axis, even if it is later along the dynamic axis. I refer the reader to that column for the details. For our purposes, it is now clear that we can consistently define time travel, or even inverse causality. For example, one can speak of an event that occurs at time (1,5) and affects reality at time (4,2). An event that occurred on Thursday changes something on the prior Monday. But this is not ordinary time travel, which raises all the paradoxes and conceptual problems, since from the standpoint of the static axis the cause (which occurred at T = 1) did indeed precede the effect (which occurred at T = 4). Thus the first requirement of the causal relation (temporal priority; see column 459) is met. The temporal priority of cause to effect must be maintained along the static axis (T).

I do not know whether this model is applicable to the physical world. Various science-fiction authors and physicists who dealt with time travel and inverse causal influence have addressed this. But with respect to the abstract meta-legal world, in which we certainly define inverse causal influence (as with conditions), we have no choice but to adopt such a model; otherwise, we fall into a conceptual contradiction.

If we return to prayer about the past (from the previous column), we now see that perhaps it is possible to pray about the past in the most “brutal” sense of the term. I literally pray that Wellington will win or lose a battle that occurred two hundred years ago, except that my prayer is aimed at a point on the t-axis that precedes me by two hundred years, while on the T-axis it may be later than my present moment. The change would occur “from now onward retroactively.” This, of course, depends on whether we can apply this model to events in the physical world (to my mind, doubtful), or only to the meta-legal plane (as with conditions).

In the next column I will conclude this series by addressing that inner time axis and tying it back to the causal relation between events.

[1] Even God’s knowledge, which does not manifest in physical processes, suffers from a similar problem. There is still an event in reality, whose expression is spiritual. That does not make much difference. Below I will return to the distinction between physical reality and spiritual reality for this purpose.

[2] All these topics are discussed at length in the fourth book of the Talmudic Logic series, Logic of Time in the Talmud.

[3] According to this, God’s knowledge of the future pertains only to events unrelated to choice, which are determined deterministically by the present. Therefore one can also argue that God’s knowledge of the future is not drawn from the future but calculated on the basis of the present. This also solves the causal problem I noted above—namely, that the future event would be the cause of divine knowledge in the present—and therefore even God could not have knowledge of the future. See my comments on “He looked this way and that” in columns 32 and 302.

[4] Incidentally, there the Gemara does not hang it on the dispute about bererah, as many have already noted.

[5] See my essay “What Is ‘Chalot’?”, and at length in Shai A. Wozner’s book, Legal Thought in Lithuanian Yeshivot.

[6] On this, see Shiurei Rabbi Shmuel (Rozovsky), Makkot §Tekh, and more.

[7] Some have explained certain miracles relating to space and time in this way, such as “the sun stood still in Gibeon,” or “the Ark did not occupy space.” The claim is that the miracle did not change reality (which is logically impossible), but only our consciousness that views reality. From our standpoint time froze, or space contracted; but this did not occur in reality itself, only in our perception of it (in Kant’s terminology: in the phenomena, not the noumena).

[8] It is rather tricky to determine which of the two axes is the subjective one. I will not enter into this here.