Causality: VII. Causality as an Internal Timeline (Column 466)
With God’s help
Disclaimer: This post was translated from Hebrew using AI (ChatGPT 5 Thinking), so there may be inaccuracies or nuances lost. If something seems unclear, please refer to the Hebrew original or contact us for clarification.
Introduction
In the previous column, I returned to a model described earlier, in which the time-axis is composed of two components: a static component and a dynamic one. The static axis is the first component of the causal relation, meaning the cause must precede the effect on that axis—though not necessarily on the dynamic axis (at least when we are dealing with meta-legal questions; in the physical plane it seems so). In this column I wish to conclude the series by relating to that internal time axis and its connection to causality. I will do so through two topics: (1) R. Shimon Shkop’s proposal for stopping loops in halakhah; and (2) the sugya of “coming as one” (ba’in ke’echad). I will then wrap up with a summary of the series’ findings and close the circle.
Stopping loops
I presented R. Shimon Shkop’s proposal for stopping loops in halakhah (since it was discussed there, I will only touch on it briefly here, to show the link to this series’ discussion of causality and time). The example was the case that opened our discussion in Gittin 90a: Reuven divorces his wife Leah on condition that she not marry Shimon. Leah then marries Levi and has children with him, divorces Levi, and subsequently marries Shimon—thus seemingly violating Reuven’s condition.
At first glance, this creates a loop that cannot be stopped. If Leah violated Reuven’s condition, her later marriage to Shimon nullifies Reuven’s get retroactively, so her intermediate marriage to Levi was invalid and the children from that union are mamzerim. But if her marriage to Shimon falls away (since she was still married to Reuven), then she never violated the condition, in which case the get from Reuven stands, her marriage to Levi is valid, their children are kosher—and so on ad infinitum.
R. Shimon Shkop (Sha’arei Yosher, Sha’ar 7, chap. 16, p. reish-nun-chet) addresses this difficulty and writes, in essence, that there is no possibility for a halakhic status to take effect if its very taking effect would retroactively uproot itself. A halakhic act that annuls itself cannot take effect at all. I called this the principle of consistency: we stop the loop by ruling that the self-uprooting effect cannot occur, and therefore Leah’s marriage to Shimon never takes effect; consequently she remains divorced from Reuven, is divorced from Levi as well, and the children from Levi are kosher—in short, the loop is halted.
In the earlier column I showed that this principle, by itself, is insufficient. Implicitly, R. Shimon assumes another principle: the sequence of events that, in reality, occurs “at once” is legally apprehended as a succession—as if one event follows another along a virtual internal timeline. In other words, the causal link between events renders them sequential (on an internal axis), even when (in the external, real timeline) they happen together.
Thus, halakhic analysis spreads the events across an internal time axis, and evaluates them as if they occur one after the other along that axis.
Visually applied to the divorce example: on the internal axis, the get from Reuven takes effect; afterward (on that axis) Leah’s marriage to Levi and her divorce from him take effect; then comes the (putative) marriage to Shimon. But since the very taking effect of the marriage to Shimon would retroactively uproot itself (by undoing the earlier divorce from Reuven), it cannot take effect at all—so the chain collapses before that event. The loop is halted without needing to actually “cut” anything in reality; the calculation is hypothetical on the internal axis, and once completed it “disappears” from the real-time axis.
(For a brief presentation of the loop-stopping idea see: https://mikyab.net/en/posts/1660; and within this series on causality and time, see: https://mikyab.net/en/posts/72990.)
Notice that in the real timeline, parts of the process “reach backward”: the (attempted) later marriage to Shimon, which would set the loop in motion, would retroactively undo the earlier divorce from Reuven; that would, in turn, undo the intermediate marriage to Levi; and so forth. All of this is motion back and forth along the real dynamic time axis. But according to R. Shimon’s second assumption, we lay out the whole loop onto the internal axis, arranging it in purely forward order by causality (like the static axis from the previous column). The causal ordering defines the internal axis and flows only forward. On the dynamic (real) axis, backward causation could be described; but on the internal (static/causal) axis, the order is strictly from cause to effect.
Conclusion: In halakhah, a causal linkage among events in a chain creates an internal timeline that orders them from cause to effect. This mirrors the temporal component of causality, but with a twist: the causal relation itself generates a “temporal” ordering—not that external time is a component inside the causal relation.
We will now see this in another sugya.
Prelude: the link to “coming as one”
Following the first column in the series, a reader asked me how the Talmudic rule of “coming as one” (ba’in ke’echad) fits my model. It seems to contain both a logical component (if you give the bill of release, the slave is released) and a physical component (the act of giving causes the release), but appears to lack a temporal component.
Indeed, the temporal aspect (on the ordinary dynamic axis) seems absent. But what we shall see is that the temporal structure is present internally—i.e., on the static/causal axis.
1) The rule of “coming as one”
The Mishnah (Gittin 78a) teaches: “If one throws a get to his wife and she is inside her house or her courtyard, she is divorced.” The Gemara asks: since “what a woman acquires, her husband acquires,” how can placing the get in her courtyard effect the divorce while she is still married (and thus has no courtyard of her own)?
Rava explains (Gittin 78b): “Her get and her hand ‘come as one’—so too here, her get and her courtyard ‘come as one.’” Ravina asks Rav Ashi: does a husband acquire the wife’s hand? Even if he acquires her labor, he does not acquire her body. Rav Ashi answers: Rava’s difficulty concerned a slave’s hand—for the view that a slave can be freed by his own document. The slave’s hand is like his master’s hand; nevertheless, his bill of release and his hand ‘come as one’. So too here: her get and her courtyard ‘come as one’. The upshot is that at the very moment of divorce/release, the woman’s (or slave’s) courtyard/hand is acquired to them such that the get can be acquired in it. The acquisition of the courtyard and the acquisition of the get are simultaneous.
The difficulty is obvious: each acquisition depends on the other, seemingly requiring precedence—so simultaneity should not help. It is as if we assert both “she first acquires a courtyard and only then acquires the get in it,” and also “she first acquires the get and thereby divorces, and only then the courtyard becomes hers.” How can both be true “as one”?
Some Acharonim (e.g., Ketzot Ha-Choshen 139:6) limit ba’in ke’echad to bills of divorce and slave-release—cases where no act of kinyan is needed, merely delivery. They propose that the delivery creates the “hand” (domain) and thus immediately effects the divorce; once divorced, the courtyard is her “hand,” and all is well. Others, however, object that even here some form of acquisition of the get is required, and simultaneity still seems problematic.
Other Acharonim (e.g., Keẓot, Kehillot Ya’akov to Gittin 8; Chidushei Rav R. Reznik; Ahiezer to Gittin; Chazon Ish O.C. 28:11; and Mishpatim Likkutim end §5) suggest models in two stages: the giving generates a hand/domain, which then acquires both the courtyard and the get within it; once the get is acquired, the divorce is effected. A different trend (see there) argues that the delivery removes the husband’s impediment, enabling her to acquire—so the obstacle was lifted, and she could now take possession.
The problem with all these explanations
What these approaches have in common is that they avoid true simultaneity by decomposing the process into two stages that occur one after the other, so the dependencies work out. But the Gemara’s language suggests literal simultaneity—ba’in ke’echad—and the forced readings are difficult.
An alternative: causality as an internal timeline
Or Gadol (siman 53) writes that ba’in ke’echad is a special Torah novelty. From the Torah’s establishing that a woman/slave can acquire their get, it is clear that the problem did not trouble it; it treated the process as two events that “come as one.”
In light of the framework developed above, this can be understood as follows: halakhah sometimes views a causal chain of events that happen in a single external moment as spread out along an internal time axis. That, I suggest, is precisely the Torah’s novelty here: the get/hand (or courtyard) and the divorce form a causal loop—each supports and stabilizes the other. Externally they occur at one instant, but because there is a causal relation between them, halakhah “lays” them out along an internal axis, “straightening” the loop forward and backward into a line set by the causal relations. Thus, each is prior to the other in the relevant sense—not in external time, but on the internal, causal axis.
Put differently: the acquisition of the courtyard is (internally) prior to and causes the divorce, and the divorce is (internally) prior to and causes the acquisition of the courtyard. This is a causal circle that, at the external level, is compressed into one instant; but internally it is ordered by causality.
I discussed two logical structures of such paradoxes (see Column 195): the Escher-type paradox (two hands drawing each other) and the anti-paradox. Here, as in Escher’s picture, each hand depends on the other and should only appear after it. On the ordinary time axis this cannot occur. But if there exists an internal timeline wholly contained within one external instant, then it can occur—just as we saw earlier with R. Shimon Shkop’s consistency principle.
(For my earlier column on this point and related discussions, see: https://mikyab.net/en/posts/61239, https://mikyab.net/en/posts/75264, https://mikyab.net/en/posts/75462; and on Zeno’s arrow and modern physics, see: https://mikyab.net/en/%D7%9B%D7%AA%D7%91%D7%99%D7%9D/%D7%9E%D7%90%D7%9E%D7%A8%D7%99%D7%9D/%D7%97%D7%99%D7%A6%D7%95-%D7%A9%D7%9C-%D7%96%D7%99%D7%A0%D7%95%D7%9F-%D7%95%D7%94%D7%A4%D7%99%D7%A1%D7%99%D7%A7%D7%94-%D7%94%D7%9E%D7%95%D7%93%D7%A8%D7%A0%D7%99%D7%AA1 and https://mikyab.net/en/posts/9327. For the reader comment mentioned above, see: https://mikyab.net/en/posts/75264#comment-59893.)
Note: Must a cause necessarily precede its effect?
We have been assuming that a cause precedes its effect (the first component of the causal relation; see Column 459). But that assumption is not trivial. Already the ancients argued that some causes and effects must be simultaneous. Suppose B is a sufficient condition for A. Then if B occurs, A must occur as well. If there is a moment A exists and B does not, B would not be sufficient—contradiction. Hence A and B must obtain together. A classic example: fire and the light it emits in the place of the fire itself. Where there is fire, there is light, and there is no moment of fire without light.
Maimonides, Millot ha-Higgayon ch. 12, writes that there are several kinds of precedence: in time, in nature, in rank, and in cause. The sun’s rising is “prior” to daylight as a cause, even though they occur together in time. The priority here is metaphorical with respect to external time; it expresses a causal ordering, not a temporal one.
We can illustrate with Newton’s second law, F = ma. It is customary to interpret the force as the cause of the acceleration. The equation is simultaneous: at each time t, F(t) = m·a(t). If the force changes with time, the acceleration changes at the same moment. Thus, cause and effect appear together. How, then, do we speak of temporal priority? And if all effects appear the instant their causes do, how can there be extended causal chains?
In field theory, physics offers a more accurate description: a mass generates a gravitational field that propagates through space-time; influences travel at finite speed. The relation is then continuous, not point-wise simultaneous. We should think of a continuous chain of causal influence along the axis, not of discrete instants of “cause” followed by “effect.” As in Zeno’s paradoxes, speaking of an isolated “instant” is misleading; reality is a continuum. On such a continuous description, the cause precedes the effect, but not as a single instant; rather, as an extended process.
Closing the circle
This way of speaking also reshapes the earlier claim about temporal precedence. On the internal axis defined by causality, all the events that “happen at once” externally can be arranged one after another by their causal order. Temporal precedence, in Maimonides’ sense, is not merely a metaphor: there is priority, but it is internal/causal, not external/temporal—even when, in the external sense, the events are simultaneous.
Summary: the end is tied to the beginning
At the outset of the series, we identified three components of causality—temporal, logical, and physical. Let us close the circle with a concise formulation:
Let event (A, t_A, T) occur at time t_A relative to timeline T, and event (B, t_B, T) at time t_B. To say that A is causally related to B means that three requirements are met:
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Temporal component. On the relevant axis we must have t_A < t_B. On the dynamic (external) axis this need not hold (at least in meta-legal or “abstract” planes), but on the internal/static (causal) axis we require t_A < t_B.
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Logical component. A ⇒ B (implication): it cannot be that A occurs and B does not; if A, then B.
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Physical component (production). A → B (causal production): A produces B (not merely correlates with it).
If any component is missing, there is no causal relation. For example, if the influence runs backwards on the external axis, or if A is only necessary but not sufficient for B, or if there is no productive link—at most there is correlation, not causation.
(As noted in response to a comment on the first column: when the causal relation does obtain, the logical and temporal components are also present—but causation adds something beyond them. See: https://mikyab.net/en/posts/75264#comment-59835.)
Links referenced in this column (with English-site prefix):
(Non-Mikyab link preserved as is: OneDrive lesson notes:
https://onedrive.live.com/view.aspx?cid=395204ec53f39ce0&page=view&resid=395204EC53F39CE0!1679&parId=395204EC53F39CE0!573&authkey=!AN6Tk6Jkb1l3UOw&app=Word)
End of Column 466.
It is certainly possible that I got confused, but it seems that you said two different things here:
1. The progress of cause and effect is on an internal time axis, while on the real axis they are simultaneous
2. There are time differences between the cause and effect on the real axis as well, but the progress is continuous
Which is correct?
These are two different stages of the argument. In stage A, I assume simultaneity on the true axis. In stage B, I refine it and say that it is not really simultaneity but a progression in sequence.
I understand. Thank you.
“You have nothing that is not preceded by its inscription. Like a bird, before it flies it spreads its wings and they make a shadow, it looks at the shadow and takes off its wings and flies” (Agnon, Ido and Einam)
On Shabbat, I thought that even in calculating chametz on Pesach after the cancellation, there is a similar circularity. The Gemara says that one checks chametz to see if a nice gloss is found and counts it as Pesach. And here the question arises, so what does it matter? After all, he canceled the chametz before Pesach. So why does counting chametz on Pesach cancel the cancellation of the chametz and obligate him to be seen and not found?
It could be said that the very act of counting chametz reveals that at the time of cancellation, the chametz was not really canceled. But that sounds absurd. After all, at the time of cancellation, you really canceled it and counted it as dust. And so I thought that perhaps there really is an internal timeline here. Counting chametz during Pesach excludes it from the invalid chametz that was canceled before Pesach and obligates you even though at the time you canceled the chametz. I don't know if this is a good example.
In the Great Feast of Unleavened Bread, 5752
Hello Rabbi,
I am not on the subject, but according to my recollection, the Rishonim say that the fear is that he will find a beautiful gluska and come to eat it without noticing that it is Passover. Or that he will commit a sin because of ‘bel yara’ in the moments of hesitation after finding it, when he will hesitate and look for a solution that will not require the elimination of the gluska, and in these moments of hesitation he will find a transgression against ‘bel yara’.
With the blessing of ‘Hag HaMatzat Dititzat’, Yaron Fish’l Ordner
I think that in our day the abolition that considers chametz to be ’ofra dare’ It requires burning it, after all, what kind of ‘balbuste’ would allow a ‘aphra da'ara’ to roam around in the cupboards or on the floor? In ancient times, the entire floor of the house was ”aphra da'ara’ and no one was moved, but today, ‘aphra’ in the house is ‘not to be seen and not to be found’ all year round. 🙂
And there was a story about a woman who found a worm in her soup, and presented the problem to her husband. The old man began to analyze the issue aloud and began to favor the explanation that the worm had been crushed and thrown away. As soon as the woman heard the option that a crushed worm was roaming around in the soup – within a second, the contents of the pot reached the toilet. Is it conceivable that a woman in our time would allow a ‘Afra Dara’ to be found on the floor of her house or in her closets? God forbid, God forbid, and God forbid again…
There it is clear that the intention is that the retroactive cancellation did not have a cancellation. When he cancelled, it did not occur to him that he had such excellent chametz; if he had known, he might not have cancelled it. If you would like to see an interesting example of a retroactive mechanism in the law of chametz, see my article on validity.
In the opinion of the Rabbi Moshe G. B.
Ramda and Rid – Shalom Rav,
To Rashi, the concern as I wrote that his opinion had come to him, that is, when he finds it, and during his hesitation, it will be binding on the B. I think that the first to disagree with him (Ramban added) had his opinion come to him, that is, that there was a prohibition in the B., that the glossa is not automatically invalidated as fragments because it is important. It is explained at the outset that the concern is for a glossa that he knew about its existence but forgot at the time of its removal, and according to him, its opinion arose in the past. It seems that both for Rashi and for those who disagree with him, this is not a retrospective declaration of opinion.
All of this appears on the surface from what I saw briefly, in the response of Rabbi Y. N. Epstein (Havel Nahaltou 11,11) and in the statement of Rabbi Y. C. Rimon, a leaven that is not known (on the Torah of Mount Etzion website) and the reader will read, and will find beautiful glosses in it 🙂
With greetings, Hillel Feiner-Glossinos
In line 2
… We were at the time when…
As he wrote (I can't remember his name anymore due to the many aliases) it seems in Rashi that this is not a retroactive declaration of opinion. In advance, he abolished the chametz, including the proper glosses. Now that he has found it, his consideration of the glosses turns it back into chametz that is binding on him. And again the question arises, so what does that mean? After all, he has already defined it as the dust of the earth?
Rather, it must be said that his consideration of the chametz acts as a parallel reason for the abolition of the chametz and gives it the status of chametz even though he abolished the chametz.
This is not retroactive, but rather he is not thinking of abolishing Gloska, but rather he does not think he has one. The mechanism you are proposing is a condition from now on, and I do not see why such a condition would be appropriate here.
I may not have fully understood the last argument, but even if we assume that there is a precedence between the cause and the circumcision on the internal timeline, what is the actual proposal? For the sake of this matter, receiving the get is the cause of the divorce, which is the cause of receiving the courtyard, which makes receiving the get possible. But even such a description does not really solve the problem. After all, a logical process is not circular, and therefore receiving the get is not possible without her owning the courtyard - which she does not have when the husband comes to her. Simultaneity does not help in this situation, but only an assumption that her owning the courtyard precedes receiving the get, and we do not have that.
I didn't understand what was difficult. I explained that there was a circle here and it could be stopped according to the principle of R”S. The logical move here is definitely circular, and that is exactly the problem.