Types of Mitzvot: 2. Between Aseh and Lo Ta’aseh (Column 415)
In the previous column I discussed the obligation to fast on Yom Kippur. I dealt there with the prohibition (lo ta’aseh) on affliction on Yom Kippur, but I ended the column with a question about the positive commandment (aseh): Why is the commandment “to afflict yourselves” an aseh and not a lo ta’aseh? What this aseh imposes on us is not to eat—that is, an obligation of refraining from action—and at first glance that is precisely the definition of a lo ta’aseh (I cited there the Talmud that rejects the interpretation that this is a duty to do acts that bring suffering upon oneself; if that were the case, perhaps it could be defined as an aseh). This issue requires us to enter the general distinction between lo ta’aseh and aseh in halakha.[1]
Our starting point in this discussion is Maimonides’ words in the Sixth Root (shoresh) of his Sefer HaMitzvot.
The principle in Maimonides’ Sixth Root
The background is the principle Maimonides sets in the Ninth Root, where he explains that if there is a commandment—whether aseh or lo ta’aseh—that is repeated multiple times in Scripture, we count it as a single commandment. What determines the count is the content, not the number of times we were commanded about it. Against that background, we must read the Sixth Root, which carves out an exception for cases where there is a lo ta’aseh and an aseh with overlapping content. In such a case, the commandments are counted as two distinct mitzvot.
The heading of that Root is:
“The Sixth Root: When a commandment includes both a positive and a negative command, the positive aspect should be counted with the positive commandments and the negative aspect with the negative commandments.”
Already from the heading we learn there are two novelties: (1) We count the two commandments (contrary to the Ninth Root’s principle). (2) The lo ta’aseh is counted with the prohibitions and the aseh with the positive commandments.
Both points need explanation. The first creates an exception for the case of a lo ta’aseh and an aseh and rules that here we do count them as two. It’s not clear why this is so as long as the content overlaps. Why is this different from two prohibitions or two positive commands, which are counted as a single mitzvah? But even if we’ve carved out overlapping lo ta’aseh and aseh, why is it necessary to state that the lo ta’aseh is counted with the prohibitions and the aseh with the positives? Isn’t that self-evident?
Maimonides explains there as follows:
“It is clear that the nature of a command (tzivui) is different from the nature of a warning (azharah); they are two distinct notions—He commanded one and forbade the other. No one erred in this Root.”[2]
According to him, a command differs from a warning, and therefore they should be counted as two mitzvot. It is important to understand that we are not speaking of a case where there is a practical difference between the aseh and the lo ta’aseh, for that would not be a case of overlap. In such a situation, it is obvious we count them separately. Maimonides is addressing precisely a situation in which there is full overlap between the content of the aseh and the lo ta’aseh. He claims that from their very definition as a lo ta’aseh and an aseh we can understand that they are two different commandments, despite the overlapping content.
To the core difficulty: R. Yerucham Fishel Perlow’s (Rif”p) claims
I already mentioned in the previous column the words of R. Yerucham Fishel Perlow (=Rif”p), in his introduction to R. Saadia Gaon’s Sefer HaMitzvot, in his discussion of this Root (and also the Fourth). He explains there that in such situations Rasag counts one mitzvah and chooses between the two the one that more fully reflects the mitzvah’s content. Summarizing Rasag’s view, he writes:
“In any case it is clear that, according to our master the Gaon, the aseh and lo ta’aseh within a single mitzvah are certainly one and the same matter, since the essence of the mitzvah is one in both. Scripture wrote both an aseh and a lo ta’aseh only to increase the severity of the transgressor’s punishment; this has nothing to do with the count of mitzvot. Thus the mitzvah is but one; in counting mitzvot we consider only the actions we were commanded to do or refrain from doing. Unlike all other enumerators of the commandments—aside from the SeMaK—who also followed our master the Gaon to count an aseh and a lo ta’aseh within a single mitzvah as only one…”
Rif”p argues, in light of Maimonides himself in the Ninth Root, that two mitzvot with identical content should not be counted as two separate mitzvot. Thus, for example, the command to remember what Amalek did to us and the prohibition to forget it have exactly the same content. That is no different from two prohibitions to forget or two commands to remember.
Now the question arises in full force: All the Rishonim, except Rasag and the SeMaK, although they agree with the Ninth Root, nonetheless count an aseh and a lo ta’aseh in these cases—like Maimonides in this Root. What will they answer to Rif”p’s seemingly sound claims? We noted above that Maimonides himself sensed the difficulty and tried to explain his position by saying that a “command” and a “warning” are two different notions. Below we will elucidate these words, for the discussion here deals exactly with the distinction between lo ta’aseh and aseh, which is our subject.
Back to Rif”p on Rasag’s approach
Rif”p explains that Rasag chooses to count the mitzvah in which the essence of the mitzvah is explained more directly. It seems he means that we should examine the content of the command and see whether at its core it is an aseh or a lo ta’aseh. For example, in the mitzvah of building a parapet (ma’akeh) there is an aseh of “You shall make a guardrail for your roof” and a lo ta’aseh of “You shall not place blood in your house.” The practical directive is to get up and build a guardrail. That is, compliance with both of these mitzvot is via active doing, in the form of “rise and act” (=line"Ayin), and therefore they have the substantive character of an aseh. Indeed, if we examine Rasag’s Sefer HaMitzvot, we will see that ma’akeh is counted as a positive command (Aseh 77 in his count).[3] What about the lo ta’aseh and aseh regarding labor on Shabbat? There, the matter is more fully expressed in the lo ta’aseh and not the aseh, since both of these impose upon us an obligation of refraining from action; thus in their essence they are prohibitions.
It appears that Rasag understands the essential difference between an aseh and a lo ta’aseh in terms of the physical mode by which one fulfills or violates them: what is fulfilled through action (line"Ayin) and violated through omission (“sit and do not act” = vain"Tav) is an aseh; what is fulfilled by refraining and violated by active doing is a lo ta’aseh. According to him, the mitzvah’s nature does not depend on Scripture’s phrasing but on its practical character. On this view, resting on Shabbat is a lo ta’aseh, for its fulfillment is passive—by refraining (vain"Tav). Therefore, even if the Torah states there is also a positive command to rest, its intent is actually a lo ta’aseh and only the phrasing misleads us. Hence the Shabbat laws will be counted by Rasag as prohibitions, not positives. By the same token, “You shall not place blood in your house” is, in essence, a hidden aseh, since guarding against it is achieved by action (erecting a guardrail).
Two conceptions of the aseh/lo ta’aseh distinction
What we saw in Rif”p is the common conception of the difference between lo ta’aseh and aseh: a lo ta’aseh imposes a duty to refrain; an aseh imposes a duty to act. But that conception raises a difficulty regarding the Torah’s phrasing: Why does it sometimes describe lo ta’aseh-type mitzvot in active language reserved for aseh (e.g., to “rest” on Shabbat), and in some aseh-type mitzvot it uses passive language usually reserved for prohibitions (e.g., “Do not place blood in your house,” which on his view is really a positive command because it requires action)?
As we have seen, Maimonides and most Rishonim dispute this conception, for they count the command to rest on Shabbat as an aseh (even though it requires refraining) and “Do not place blood in your house” as a lo ta’aseh (even though it requires action). On their view, Scriptural phrasing determines the mitzvah’s character: active wording is interpreted as an aseh and prohibitive wording as a lo ta’aseh, regardless of the mode of fulfillment. In the previous column we saw that the duty to afflict oneself on Yom Kippur is phrased as an aseh (“you shall afflict your souls”), and therefore the Talmud and Rishonim assume it is an aseh and not a lo ta’aseh and seek a separate source for the lo ta’aseh.
Note that the very existence of overlapping lo ta’aseh and aseh already tells us that the definition cannot be based on performance. If the difference is performative (how one fulfills or violates—through action or omission), then an overlapping lo ta’aseh and aseh could not arise. If the content of the two commandments overlaps, that means they impose the same obligations, i.e., they are fulfilled and violated in the same way. But in such a case they would not be a lo ta’aseh and an aseh, but rather two prohibitions or two positives (depending on where the matter is more fully expressed)—precisely as we saw in Rasag’s approach.
The linguistic criterion
The Talmud scholar Aharon Shemesh, of blessed memory, in his article devoted to the distinction between lo ta’aseh and aseh,[4] notes two meanings that the aseh/lo ta’aseh distinction takes on in rabbinic literature (mainly among the Tannaim). He argues that in earlier literature, as well as in the Midrashim of the school of Rabbi Ishmael, the distinction is based on the mode of fulfillment: mitzvot fulfilled through active doing (line"Ayin) are aseh, and mitzvot violated through active doing (and fulfilled by refraining) are lo ta’aseh. There the governing criterion is performative.
By contrast, in the Midrashim of the school of Rabbi Akiva and in later strata of the Talmud we find a linguistic conception that ties the difference between the two types to the Torah’s phrasing (and not necessarily to performance). From this follows the possibility of a lo ta’aseh “without an act,” i.e., a prohibition violated by omission (=vain"Tav) and not by an active deed (=line"Ayin).[5] Here the linguistic criterion operates.
The partial nature of the foregoing description
In my article on Torah and science, I noted that such an explanation is characteristic of academic Talmud research: it suffices with describing and characterizing aseh and lo ta’aseh on a descriptive, scholarly level, and it engages less with questions of essence and rationale. Academics, like in the Brisker ethos, confine themselves mainly to “what?” questions and deal less with “why?”. But a traditional learner does not suffice with that. He asks himself why the Torah uses different formulations. It is not plausible that the distinction between aseh and lo ta’aseh is merely a result of wording and does not reflect some substantive layer distinguishing the two types. We must ask: if the practical content of the two mitzvot is the same, why does the Torah formulate them differently? Why are there cases where the Torah commands a prohibition in active phrasing while usually choosing the language of prohibition (“lo,” “hishamer,” “pen,” and “al”)? And similarly for aseh.
Moreover, different halakhic rules exist regarding aseh and lo ta’aseh. For example, an aseh overrides a lo ta’aseh. Another example: one must spend up to one-fifth of his assets to fulfill an aseh, whereas for a lo ta’aseh one must spend all his assets to avoid transgression. Another: considerations of human dignity (kavod ha-briyot) override certain aseh obligations but not lo ta’aseh,[6] and more. Do all these rules lack substantive basis? Is there no fundamental difference from which these halakhic consequences flow? It is very hard to accept that. Even if we say the Torah chose its phrasing specifically to teach us these consequences, that does not answer the difficulty. The question is: why are there such differences if the two are not essentially different in content but only in wording? What generates these halakhic differences?
These difficulties might seem to push us to the second conception, which sees the aseh/lo ta’aseh distinction as primarily practical. But that view is also problematic, as we saw. First, it does not match the halakhic facts—at least not according to Maimonides and most Rishonim. Beyond that, the Torah’s confusing and inconsistent phrasing remains unexplained. If so, we must search for a substantive difference between lo ta’aseh and aseh that is not necessarily rooted in how they are performed or violated (active or passive).
A substantive distinction between lo ta’aseh and aseh: Maimonides and associates
Our claim in that article is that an aseh is a verse that points to a state desired before the Holy One—i.e., a state the Torah commands us to achieve. The Torah commands us to build a guardrail because it wants the house to have a guardrail. By contrast, a lo ta’aseh points to an undesired state—i.e., a state the Torah commands us to avoid. For example, the Torah commands us not to place blood in our house because it does not want us to be in a state where the house lacks a guardrail.
Note that this is not a logical equivalence. The aseh to build a guardrail says the Torah wants the roof of a person’s house to be surrounded by a guardrail. By that definition the Torah does not directly invalidate a state in which the roof lacks a guardrail. The problem with such a state is only that it is not the desired state (of a house with a guardrail). It is not inherently problematic. By contrast, the prohibition of labor on Shabbat is a classic lo ta’aseh, because the Torah is not commanding rest but rather forbidding the state of performing melakha. The focus is on the undesired state, not the desired one. From the standpoint of the lo ta’aseh, the point is not that we enter the state of rest, but that we not be in a state of doing melakha. From the standpoint of the aseh to rest on Shabbat, there is an interest precisely in our being in the state of rest; the prohibition of melakha follows indirectly.
The Scriptural phrasing—positive or negative—indicates whether the mitzvah is an aseh or a lo ta’aseh, because it testifies to the Torah’s will: does it direct us toward a positive state or warn us off a negative state? The phrasing expresses the substantive difference between lo ta’aseh and aseh; it is not the cause of that difference.
The conclusion is that there are prohibitions that involve no act in their violation and positive commandments that involve no act in their fulfillment. These are exceptional cases. In all situations where there is both an aseh and a lo ta’aseh with overlapping content (the Sixth Root’s topic), such as Shabbat rest and guardrail, either the lo ta’aseh or the aseh is exceptional. In these situations the Torah tells us both that being in state X is desired (positive) and that being in state “not-X” is undesired (negative). Both norms are present; therefore there is no redundancy. This is why Maimonides and most Rishonim count two mitzvot in such a case.
Connection to the performative criterion
We can now understand why, even according to Maimonides, there is a connection to the mode of performance. Usually, when we are required to reach a desired state, it demands action, and so fulfillment is through doing (line"Ayin). Likewise, when we are required to avoid a certain state, fulfillment is through refraining (not entering that state). Hence the impression that the aseh/lo ta’aseh difference is performative.
But now you can see that while that is often the case, it is by no means necessary. There can certainly be cases where avoiding a negative state requires action, or where entering a positive state requires refraining. In Shabbat rest, the positive state is rest (and not merely that doing melakha is negative); therefore, even though fulfillment is by refraining (vain"Tav), it is an aseh. Conversely, “Do not stand by your fellow’s blood” is a lo ta’aseh because of the Torah’s phrasing, but that phrasing reflects a principle: being in a state where you do not save another is negative (and not merely that saving is positive—saving a friend in distress is apparently such a basic requirement that we are unwilling to consider the rescue itself “a positive state”). And yet, to avoid that negative state, what is required of us is action (jump into the river when he’s drowning or extend a rescue pole).
A logical problem
Thus far we have dealt with the substantive distinction: an aseh points to a desired state, a lo ta’aseh to an undesired state. But from this distinction a strong sense of a logical problem arises. Why is the statement “the roof must not be without a guardrail” different from “the roof must have a guardrail”? Seemingly, a double negation is logically equivalent to an affirmative statement. The command “It is forbidden for a roof to be without a guardrail” looks logically equivalent to “The roof must have a guardrail.” If so, again it is unclear whether our proposed difference between aseh and lo ta’aseh has a real basis. And if so, the question about duplication between aseh and lo ta’aseh returns: apparently it is total duplication, like overlapping between two prohibitions or between two positives.
“Stick” and “carrot”
However, this logical analysis is mistaken. To illustrate the difference between defining an aseh and a lo ta’aseh, let us define them as “carrot” and “stick.” When a person sits and does not build a guardrail for his dangerous roof, we can spur him in two ways: we can tell him that we expect him to build a guardrail—this is the “carrot” approach. We explain that the desired state (which he is not in), namely a roof with a guardrail, is better, and we thereby motivate him to attain it. Or we can tell him that his sitting idly with an unguarded roof is a disapproved state, and therefore he must leave that state—i.e., rise and build a guardrail. This is the “stick” approach. We strike him with the “stick” that declares his current state bad, thereby moving him to act (to reach a better, desired state).
The difference between the two formulations lies in the substantive content of the norm, or its purpose. What does the Torah want, really: that the roof be with a guardrail, or that it not be without a guardrail? Are these formulations equivalent? Intuitively, no. Is there a difference in implementation? Practically, both directives demand the same action (get up and build a guardrail), so it would seem there is no practical difference between them. That is why such a lo ta’aseh is, in essence, a “lo ta’aseh without an act.” But we will see that the difference manifests both practically and logically. We’ll now address those two planes in turn.
Practical ramifications of the distinction
One could have brought halakhic consequences that flow from the aseh/lo ta’aseh distinction itself. For example: if there is a positive mitzvah to build a guardrail and I did not fulfill it, I am not punished, for there is no punishment for neglecting an aseh. By contrast, if there were only a lo ta’aseh regarding a roof without a guardrail, then by not building one I would incur lashes.[7] Similarly, one could have brought ramifications regarding deference to considerations of human dignity (kavod ha-briyot)—which can override an aseh but not a lo ta’aseh—and the like.
But we are not seeking that kind of difference here, since all those are consequences of the difference, not the difference itself. Were there no substantive difference, it would be implausible that one is punished for a lo ta’aseh but not for an aseh, or that they differ regarding kavod ha-briyot. Those are results of an essential difference between these two types. It is implausible to see them as consequences flowing only from the Torah’s chosen phrasing. As I already clarified, we are seeking the root of these halakhic differences. There must be something essentially different between aseh and lo ta’aseh, from which these halakhic outcomes derive.
To demonstrate the difference itself, consider a person who was coerced (anus) and did not build a guardrail. If there were a positive mitzvah to build a guardrail, he failed to fulfill it. He is not punished—but that would be true even without coercion, for there are no punishments for neglecting an aseh. By contrast, if it were only a lo ta’aseh, then he certainly did not transgress it, since he was coerced. The core of the difference is the principle “onasa lav ke-man de-avad”—coercion can turn an act that was done into “as if it were not done,” but it cannot turn an act that was not done into “as if it were done.”[8]
Another example: someone who has no house at all. Is there any point to buying a house in order to become obligated in the mitzvah of ma’akeh?[9] If there were only a lo ta’aseh, there would be no point. But if it is a positive mitzvah, there is room to see value in buying a house so as to build a guardrail and merit a mitzvah. This holds even if we see ma’akeh as a conditional mitzvah (imposed only on one who has a house).[10] Still, if he buys a house, a positive mitzvah is credited to him. He fulfilled God’s will, not merely avoided transgression.[11]
Alternatively, suppose we have property of uncertain status—it’s unclear whether it qualifies as a “house” for this purpose. A doubt might arise whether to build a guardrail. There is perhaps room to argue that if there were only a positive mitzvah, the one who claims I am obligated (i.e., that this object is considered a house here) bears the burden of proof. To impose an obligation requires some argument; the default is no obligation absent proof. But if there were only a lo ta’aseh, then out of doubt I should be stringent and build a guardrail. Of course, even if I did not build one, no punishment would be imposed, since punishment also requires proof. But the obligation to build would exist even under uncertainty.
Between consequences and demonstrations
It is important to note that these examples are not consequences of the difference but demonstrations of it. They differ from the earlier “consequences” (kavod ha-briyot, financial expenditure, punishment) about which I argued they cannot serve as the explanation. The examples here illustrate the substantive difference between aseh and lo ta’aseh.
Now we can also understand the differences previously classified as consequences. Having grasped the essential distinction, we can explain its halakhic outcomes. Why is punishment specifically for lo ta’aseh and not for aseh? Because one who violates a lo ta’aseh is in an undesired state. He is wicked; therefore he deserves punishment. One who neglects an aseh is merely not in the desired state; in that sense he is simply not a righteous person, and thus he does not deserve punishment. The same with monetary outlay: to avoid being wicked, we must spend all our assets, for wickedness is a severe and fundamental defect. By contrast, the demand to be righteous is not as basic, and we are not required to attain it at any price; here one must spend only up to one-fifth. The same applies to kavod ha-briyot and other differences. Once we understand the essential distinction, we can also explain its halakhic consequences.
A clarification about the nature of negation: logical relations between norms
Even so, the task is not complete. We have seen that on the practical plane there are substantive differences stemming from aseh versus lo ta’aseh. But this still seems puzzling, since logically the statements appear equivalent: the directive to be in state X (an aseh, even if it requires refraining) and the directive not to be in not-X (a lo ta’aseh, even if it requires action) appear logically equivalent. It seems we are dealing only with double negation—but that should cancel out. How, then, can there be a substantive difference between two statements that are logically equivalent?[12] I will try to explain, at least briefly.
Consider the following phrasing, which is clearly a positive command: (a) “I command you to put on tefillin.” What is the logical negation of this statement? Seemingly it is the (lo ta’aseh) statement: (b) “I command you to be without tefillin.” But a closer look shows that (b) is not the precise logical negation of (a). The more precise negation is: (c) “It is not true that I command you to put on tefillin.” Yet that phrasing is not a command at all but a permission. It states only that there is no binding norm (neither obligation nor prohibition). Clearly, then, it is not equivalent to (b), which is a full-fledged norm. A parallel lo ta’aseh must be phrased as: (d) “I forbid you to be without tefillin.” Here too we have a norm, not the absence of one; thus it is not equivalent to (c).
In mathematical terminology (borrowed from operator theory), these two initial formulations are not equivalent. The mistake in seeing them as equivalent stems from assuming that negation and command are commutative operators. Applying negation to a command is not equivalent to commanding the negation of the original content. Therefore, in statements involving a command about a negation or the negation of a command, one must not swap the order of the command and the negation.
Incidentally, this is not unique to commands. Even in a factual statement, negation is not so simple (see more in my book Two Wagons and a Balloon, ch. 12). For example, negating the statement (1) “Moses is with tefillin” is not the statement (2) “Moses is without tefillin.” The more precise negation is (3) “It is not true that Moses is with tefillin.” The difference between the two negations appears clearly if we consider a situation in which there is no person named Moses at all. In that case, statement (1) is false—but statement (2) is also false. If there is a state of affairs in which both statements are false (or both true), then one cannot be the negation of the other. That is, between the two extreme states, which we can label (1) and (1−), stands an intermediate state 0 separating them. The negation of 1 is 0, not (1−)—or perhaps the union of all states other than 1.[13]
Returning to normative negation: phrasing (c) allows for an intermediate state (state 0) between the first two formulations, and therefore it differs from (b). Saying “It is not true that I command you to be with tefillin” means either “I command you to be without tefillin” (which is exactly (b)) or “I issue no command at all.” The minimal reading is the second; hence it is the more precise negation. For example, consider someone with no arms (to put tefillin on), or someone with no house (in the case of ma’akeh), or cases of coercion, or cases of doubt. In all such cases there is a difference between (b) and (c), which indicates they are not logically equivalent. We already noted this in the previous section.
We can now see that the positive command (I) “I command you to put on tefillin” is not equivalent to the lo ta’aseh (II) “I forbid you to be without tefillin.” Contrary to our initial assumption, there is no simple double negation here. Between the two negations stands the word “command,” which separates them, and since we cannot swap the positions of the command and either negation, the two negations in this statement do not cancel one another.
The conclusion is that there is no logical way to pass from the phrasing of an aseh to that of a lo ta’aseh using negation alone, and vice versa. The worlds of lo ta’aseh and aseh are two different worlds; they do not “speak” to each other and cannot be converted logically one into the other. One cannot formulate an aseh as a statement about the negation of an undesired state; such a formulation is, by definition, a lo ta’aseh. Likewise, one cannot formulate a lo ta’aseh without words of negation (by negating a statement of a desired state). Without the words of negation (“hishamer,” “pen,” “al,” “lo”), it is not a lo ta’aseh. You can now understand well Reish Lakish’s deliberation in Yoma regarding the lo ta’aseh of affliction discussed in the previous column.
Nozick’s paradox
Robert Nozick was a very well-known Jewish-American philosopher. Among his other exploits (the Newcomb paradox, about which I have written here more than once, was also published by him), he discussed the relation between tempting and extorting. When Reuven tempts Shimon, Reuven presents Shimon with two options: (1) If you do X, you will receive A. (2) If you do not do X, you will not receive A. For example, an employment offer X with salary A. This is entirely legitimate. By contrast, when Reuven extorts Shimon, the case seems very similar, yet it is illegitimate. In extortion Reuven presents two options: (1) If you do X, I will not take A from you. (2) If you do not do X, I will take A from you. For example, he demands that Shimon give him sum X, otherwise he will take Shimon’s car (A). This is forbidden extortion. Nozick asked: what is the difference between these two cases? In both, Shimon faces two options whose gap is A. Why, then, is the first legitimate and the second not?
Note that here too one could phrase extortion as temptation with negations: (1) If you do X, I will not give you (A−). (2) If you do not do X, I will give you (A−). That is, the amount is negative and the options are swapped. Seemingly, we could describe extortion as temptation with negation operators (negative amounts and inverted options), yet the meaning is different. Giving a person a negative amount is not giving a different amount; it is taking—which is an entirely different act. It is perfectly legitimate to give someone any sum for an action; it is not legitimate to take a sum for an action or inaction. Again, the “negation” here is not innocent; it transports us to an entirely different conceptual world: from giving we move to taking.
We can see the analogy to our topic as follows: there is a prohibition on extortion, and there is no prohibition on temptation. One cannot move from the world of prohibition to the world of permission by negations alone. Extortion is not temptation with a negative amount, and vice versa. The negation here performs a different operation (relevant also in the normative context), not merely changing quantities.
Put differently: there is a clear zero line separating cases of temptation from extortion. Positive amounts are not different from negative amounts merely in magnitude. The zero line between positive and negative cannot be crossed by negation alone. A positive amount is adding to you something to which you have no rights; a negative amount is taking from you something to which you do have rights—and that is forbidden. Things over which you have rights differ in essence from those outside your rights’ territory. So too with the states to which halakha relates: there are positive states (in which one should be) and negative states (in which one must not be). There is a sharp zero line dividing them. The relation between a positive and a negative state is not merely that one is more wanted; it is not a quantitative difference but a qualitative one. Therefore, a lo ta’aseh is not merely “more severe” than an aseh; it is essentially different. The relation is not merely stringency versus leniency but a difference in kind.
Explaining Maimonides’ two novelties
We can now understand the two novelties in Maimonides’ Root heading. Overlapping lo ta’aseh and aseh are counted as two mitzvot because the fact that they are lo ta’aseh and aseh says there is no true overlap between them. This is not like overlap between two prohibitions or two positives. We have seen that this is not merely different in content; the difference has practical halakhic implications. From this we can also understand his second novelty and why it is needed. He innovates that the lo ta’aseh is counted with the prohibitions and the aseh with the positives. It should now be clear that this is anything but trivial. According to Rasag, for example, even if we were to count two, on Shabbat we would count two prohibitions, and for ma’akeh two positives, because on the performative criterion there is no difference: Shabbat is a lo ta’aseh, ma’akeh is an aseh. Maimonides wishes to teach that the criterion is not performative; therefore, they are two distinct mitzvot—an aseh and a lo ta’aseh. Hence, in such a case we count two mitzvot (unlike Rasag). For the same reason, the lo ta’aseh is counted with prohibitions (even if it is violated by omission) and the aseh with positives (even if it is “violated” through action).
Back to the aseh of Yom Kippur fasting
We can now understand why the mitzvah of fasting on Yom Kippur is an aseh and not a lo ta’aseh. The Torah tells us that being in a state of fasting is a desired state. From the standpoint of this aseh, eating on Yom Kippur is not a directly negative act; it is problematic only because through it we are not in the desired state (of fasting). Therefore, it is an aseh.
However, according to most views (except Rasag, and perhaps also the SeMaK), there is also a lo ta’aseh on fasting on Yom Kippur, which we discussed in the previous column. Its meaning is that a state of eating is undesired (it is not merely a failure to achieve a positive state of fasting; non-fasting is itself negative). But note well: it is undesired not because we eat, but because we are not fasting (otherwise this would be an ordinary eating prohibition and could be phrased like ordinary eating prohibitions: “Do not eat”). The lo ta’aseh expresses that non-fasting is a negative state (and not merely not being in the positive state of fasting); but, as Reish Lakish shows, it is impossible to formulate this lo ta’aseh adequately (for wording like “Do not eat” would not express it well; it would be understood as an eating prohibition and not as a prohibition on non-fasting).
As we have seen, when there is both an aseh and a lo ta’aseh, the Torah tells us both that being in state X is desired (positive) and that being in state “not-X” is undesired (negative). The conclusion is that Yom Kippur fasting has both aspects: fasting is a positive state, and non-fasting is negative.
In the next column I will continue with a few further remarks on the aseh/lo ta’aseh distinction, and then we will enter the world of positive commandments.
[1] See this at length in the book Yishlach Sharashav, in the essay on the Sixth Root.
[2] In our article there (and briefly below) we noted that Rasag and the SeMaK likely did dispute the principle of this Root.
[3] In truth, the mitzvah of ma’akeh is broader than the prohibition “and you shall not place blood,” for a house lacking four by four cubits is exempt from a guardrail, even though obviously one must prevent danger. See Chazon Ish, Choshen Mishpat, Likutim §18:2, that the Torah removed our discretion to assess danger levels in the specific cases of ma’akeh, even though the danger is not necessarily greater than, say, climbing a permitted tree. This can explain R. Yehuda’s view, cited by the Mordechai (Halakhot Ketannot—Tzitzit §1544), that one who cannot make a guardrail is not obligated to demolish the house—just as one may wear a garment if he cannot attach tzitzit. It is difficult, though, since there is danger; apparently he refers to a case where the danger can be prevented another way or is not severe in itself. See also below, ch. 5, the first answer of Tosafot in Kiddushin; there too it seems the Ramban took it as full overlap.
[4] “On the Historical Meanings of the Terms Positive and Negative Commandments,” Tarbitz 62 (2003), nos. 1–2.
[5] Nonetheless, as he writes, this shift did not change the basic halakha that punishments (and sin-offer obligations) apply only to lo ta’aseh; therefore the rule was fixed that there is no punishment for a lo ta’aseh without an act (which, he claims, in earlier literature was called an “aseh,” and therefore it is clear there was no punishment).
[6] See our aforementioned article, ch. 6, where we discuss whether the distinction in the kavod ha-briyot sugya is between aseh and lo ta’aseh or between action and omission (line"Ayin/vain"Tav).
[7] I am ignoring here the ruling that there are no lashes for a lo ta’aseh without an act—both because this matter is disputed, and because there are cases in which lashes are given (for example, when one violates, through action, a lo ta’aseh that is in principle without an act, according to some Rishonim. See, for example, here, §3).
[8] See Jerusalem Talmud, Gittin 7:6 and Kiddushin 3:2, where R. Yohanan and Reish Lakish dispute this; some reverse the attributions. Compare Babylonian Talmud, Ketubot 2b–3a (the condition: “this is your get if I do not come”). In practice, the halakha follows that “coercion is as though it were not done.”
[9] See my essay Middah Tovah on Parashat Bereishit (2007), which deals with the distinction between fulfilling a commandment and attaining a state of exemption from it.
[10] And not a “kiyumit” mitzvah (a different definition). See the following columns.
[11] This is commonly used to explain the angel’s rebuke of Rav Ketina for not wearing a garment obligated in tzitzit—even though there is no actual obligation to do so. See Menahot 41a and Rabbeinu Yonah’s Sha’arei Teshuvah, Gate 3 §22: “Because he did not cherish in his heart the beauty of the mitzvah and its reward, to turn its obligation upon himself and take a four-cornered garment so as to put tzitzit on its corners.” Tosafot there, however, interpret the rebuke as due to seeking to evade obligation, not that one must “chase” obligation (hence some Rishonim concluded that in places where people do not generally wear four-cornered garments, there is no duty to wear one to incur obligation; see Tosafot, Shabbat 32b; Arachin 2b; and so wrote the Rosh, Mo’ed Katan 3:80).
[12] See also the end of our Middah Tovah essay on Parashat Yitro (and in the essay on Vayetze), 2007, where we detail normative versus logical negation.
[13] What is this like? If we wish to prove the claim that the current king of France is bald by way of negation: we look at the set of hairy people and find that none is king of France. Have we really proven our claim? The answer is no. At present there is no (current) king of France, and therefore of course we will not find him among the bald either.
Discussion
That is possible, but unlikely. If, once you examine it, there is a difference, why not count it? By the way, I noted in the article on the sixth or ninth principle that even according to the Rambam there are cases of double commandments that are not counted, yet are still considered two. For example, neshekh and tarbit: he writes that one transgresses two prohibitions, but counts only one.
A. What is the difference between a positive commandment and a prohibition? Aharon Shemesh presented a dispute (or a development) over whether they are defined by actions or by formulations. You tied the dispute between the Rambam and R. Saadia Gaon to this, and said that the formulations reflect a metaphysical difference. There is now a point that you explained, but I will still present the question.
Given that there is a great overlap between positive commandments and commandments of “arise and do,” once you separate the two completely, you need to explain how such a large overlap nevertheless came about. Why is eating matzah a positive state rather than not eating matzah being a negative state? If we look at states and not at actions, then there is no longer any reason to think there is any connection at all between the action/omission relation and the good/bad-states relation.
So you explained this (in the section “the connection to the performance criterion”) by saying that “usually, when we are required to reach some desirable state, this requires us to act.” I didn’t understand. Usually where? Usually in commandments, or usually in everyday life? If usually in commandments, that begs the question. If usually in everyday life, I don’t know whether that is true, and it also doesn’t seem likely that the way of the natural world should be relevant. The Gemara’s example of the sun and the shade illustrates well that a person wants not to be in the blazing sun; it makes no difference to him whether for that he has to walk into the shade or whether for that he has to remain in the shade. And besides, what does the natural order have to do with the metaphysical order?
By the way, when you also separated halakhah from morality (and there too moved the distinction to the metaphysical plane), one still has to explain how such a large practical overlap nevertheless came about. Though between halakhah and morality you sever the connection entirely, whereas between “arise and do” and positive commandments you do see a shared fundamental core. And it is about that core that I am asking.
B. If one was coerced not to build a parapet, you said that he did not fulfill the positive commandment and also did not transgress the prohibition, and this is an intermediate neutral state. Seemingly one should add that if he was coerced to build a parapet, then he also did not fulfill the positive commandment and also did not transgress the prohibition. But I learned from here that in your view he did fulfill the positive commandment [perhaps specifically if he wanted to build even were it not for the coercion]. But if so, that requires explanation: if entering a bad state under coercion (against my will) does not bring me into a bad state, then how and why does entering a good state under coercion (in line with my will) indeed bring me into a good state?
C. In terms of severity, do you see a difference between acting and refraining? Is someone who stood by complacently and did not press the button that would save his fellow less severe than someone who acted energetically and pressed the button that prevents his fellow from being saved? Is one who did not press the button that blocks medicine from his fellow less elevated than one who pressed the button that sends medicine to his fellow?
[In my opinion, on the moral plane one would need a third eye to manage to see a difference. So even if there is a halakhic difference, it still requires further investigation.]
D1. I thought of letting this point rest until I understood the previous points, but so be it.
You are looking for an essential explanation of the difference between a positive commandment and a prohibition that would be powerful enough to explain the halakhic differences between them. And you find the difference in the state under discussion—whether to bring about something positive or to avoid something negative. For example, that the showbread be arranged in its place is positive, and that the breastplate be on the ephod and not shift away is the prevention of something negative.
There is here a “simple” explanation with theoretical entities that explains the whole set of phenomena (and therefore there is good reason to assume that these theoretical entities do indeed exist). But what explains the appearances of the theoretical entities themselves? Without such an explanation we still remain in a kind of phenomenology. Why is a certain state positive and another state negative?
Perhaps you relate to this like the question why a physical constant has a certain value—and answer, thus His wisdom, blessed be He, decreed. But that is still not understanding. So what have we gained? Instead of wondering why a given positive commandment is characterized by such-and-such a set of halakhic properties (the properties of positive commandments), we now wonder why a given state is positive (rather than its complementary state being negative), and why a given state is negative (rather than its complementary state being positive). Are you looking for an explanation of the positive/negative choice in terms of ta‘ama de-kra, the rationale of the verse, or can the Torah in every commandment choose whether it will be a positive or a negative commandment and we simply accept it in silence?
Abduction without explanation is, of course, science par excellence (because in science one is interested only in knowing what will happen in such-and-such a situation), but to my taste this is not really Torah study. We know the laws even without this. And there is no understanding even with this. So what is there here? In another post you saw the construction of such a theory as the pinnacle of Torah study. And when I suggested that Torah study has a layer of “understanding,” unlike science, I seem to recall that you said there is no difference.
A. The continuation of the explanation regarding the relation to “arise and do” will come in the next post. In general, here I explained that entering a state requires action. Avoiding a state is usually by inaction. Here too I severed the two completely (as with halakhah and morality), and only explained why the impression of a connection is created (as there, because of the overlap).
It turns out that there is a not-insignificant overlap between the natural order and the metaphysical one. One may wonder whether this is accidental and how it came about, but that apparently is the situation. At least that is what emerges for me in order to explain the halakhic facts. If I am right in my explanation, then factually there is such an overlap. I do not see an alternative explanation for the disconnect between a positive commandment and “arise and do.”
B. Being coerced not to build a parapet sharpens the difference between defining a norm as a prohibition or as a positive commandment. If he was coerced, then he did not fulfill the positive commandment (that is, from the perspective of the positive commandment he did not fulfill the halakhah, but under coercion), but he also did not transgress the prohibition (that is, from the perspective of the prohibition he did fulfill the halakhah). When the coercion passes, he will have to put up a parapet. Likewise, if he was coerced not to put on tefillin, when the coercion passes he will have to put them on. But if there had been a prohibition against being without tefillin, then he would not have to go back and put them on.
As for being coerced to build a parapet, I do not see how you derived that conclusion from my words. As I said, my example was not dealing with comparing one who was coerced to build with one who was coerced not to build, but with the difference between formulation as a prohibition and as a positive commandment when one was coerced not to build.
As for the matter itself, if he was coerced to build a parapet, he fulfilled the commandment, but under coercion (will he not receive reward?). As I understand it, this is indeed parallel to one who was coerced not to build. The rule is that an act done under coercion is an act that was done, but non-performance under coercion is not performance.
C. You are comparing two equivalent transgressions. Pressing a button that prevents rescue is like not pressing a button. Both are “sit and do not act,” because the pressing caused non-rescue, not the death itself. If you want to compare, you should compare killing with failing to save. So there is no need for a third eye; in principle I agree with you. Though in my opinion there is some difference even in your comparison, that is another discussion. I was not talking about that.
D1. You are right that this is a phenomenological explanation, but it is better than no explanation at all. At least you can see from it that the accepted explanation (which ties it to the mode of performance) is incorrect. My claim is that there must be positive and negative states in some sense in order to explain these halakhic phenomena. Exactly like theoretical entities. Therefore, in my opinion this is not only phenomenological, though admittedly it is not complete. But that is true of every scientific theory as well: it is not completely phenomenological, but not complete either.
You are also wrong that we have gained nothing, because one may still ask why a certain state is positive or negative. Indeed one may ask that, but it is an entirely different question from the one I solved. The question I addressed was a difficulty—how can there be a difference between two commands with the same content? In other words, there is a contradiction here. The question now is a question and not a difficulty—why is a certain state positive or negative?
As I explained, there is definitely understanding here, even if not complete. Exactly as in science.
I answered this together with the answers to your questions in your previous message.
Thank you.
B. You wrote, “The rule is that an act done under coercion is an act that was done, but non-performance under coercion is not performance.” What does that mean?
D1. Before this, we thought there were commandments to which the Holy One, blessed be He, attached the label “positive commandment,” and others to which He attached the label “negative commandment.” You say no, no: rather, He attached the label “positive state” or attached the label “negative state.” How does such an explanation help if there is no hint how to judge whether a state is positive or whether its absence is negative?
D2. Does the rule that a positive commandment overrides a prohibition also stem from the model of positive and negative states?
That is a Hebrew translation of “onsa lav ke-man de-avid.”
Because now it is not an arbitrary label but an expression of two kinds of states between which there is clearly a difference. True, you have no criterion for determining which state is of which kind. So what?
In terms of states, “a positive commandment overrides a prohibition” means the following: you have two possibilities: (a) to enter a negative state and a positive state; (b) not to enter either of them. The question is whether the offset is complete, in which case there is no decision, or not. The rule says that there is a decision, and option (a) is preferable. The explanation is probably that not entering a positive state is a light transgression (= neglect of a positive commandment), but not entering a negative state is not a light commandment but rather a neutral state in itself. Therefore, in option (a) there is an offset and the overall utility is 0 (symbolically, of course), but in option (b) the overall utility is slightly negative.
But I suggest we leave this for the next stage, where I will deal with the various types of positive commandments.
Two comments on the paragraph “An Essential Distinction Between a Prohibition and a Positive Commandment: The View of the Rambam and His Camp”:
1) You wrote that a positive commandment is a verse pointing to a state that the Torah wants us to reach, and therefore the commandment is to have a parapet, and not necessarily the act of building a parapet itself. That is indeed correct regarding result-commandments, but certainly not regarding action-commandments, where the commandment is the very act itself, no?!
2) You also wrote, regarding a parapet, that the problem in the state of one who did not build a parapet is only that it is not the desired state (of a house with a parapet), and that this is not a problematic state in itself. But this is difficult for me, because while that is true in the case of an optional commandment—if you fulfill it, all the better, and if not, no great matter—in the case of an obligatory commandment, when you have not fulfilled it you are indeed in the negative state of neglecting a positive commandment!
Maybe I’m daydreaming, but in order to invent a distinction we could have said that positive commandments block destructive angels from harming the menorah in the heavenly Temple, while prohibitions clean the wings of the ministering angels. Now, why does a positive commandment override a prohibition? Because cleaning wings is self-evident and for that one gets no credit, but refraining from blocking the destroyers is a little bad. Why is there flogging for a prohibition? Because leaving dirt on the wings is very bad.
Like what you said: remaining neutral and not transgressing the prohibition is self-evident and not even a light commandment, but remaining neutral and not fulfilling the positive commandment is a light transgression. And for a prohibition there is flogging because the negative state is very bad.
1. A state can be active or passive. Even in action-commandments, the action is a state. If there is a positive commandment to build a parapet, the state can be the building of a parapet or the existence of a parapet. And if it were only a prohibition, then there would be no value in the building or the existence; rather, it would be avoidance of a state of non-building or non-existence.
2. I will address this in the fourth post.
Not leaving dirt on the wings, but putting it there.
The argument was expected, and apparently this time too it will remain as it is. 🙂
Leaving it—why putting it there? Keeping the prohibition cleans them, and violating the prohibition stops the cleaning.
Please enlighten me as to why this was expected. I asked about arbitrary entities (what is positive, what is negative) with arbitrary properties (entering the negative is very bad; not entering the negative is neutral; entering the positive is very good; not entering the positive is a little bad). What is that analogous to?
That is exactly what I corrected in your words. You distinguished between leaving and doing, but I wrote that this is not the distinction between a positive commandment and a prohibition. The distinction between a positive commandment and a prohibition is between leaving and putting there.
It was expected because several times already you have written that you do not see a difference between passive and active causation (killing or failing to save).
It has already been clarified, but I will write it out just to be safe, so that you can correct me if I am mistaken.
When I ask, I assume that I am choosing both the entities and the hierarchy and their properties. So I choose what it means to keep the prohibition (to clean) and to violate it (to leave dirt), and I choose what it means to fulfill the positive commandment (blocking) and to neglect it (allowing). Then I choose the hierarchy—violating the prohibition is very bad, enough for flogging. Keeping the prohibition does not excite us. Fulfilling the positive commandment is very good. Neglecting it is a little bothersome. Therefore there is flogging for a prohibition and more money is extracted for it. Therefore neglect of a positive commandment is worse than keeping a prohibition.
Whereas your answer is that this hierarchy is not an arbitrary choice but a natural consequence of identifying the entities as positive/negative. And this is basically “arise and do” versus “sit and do not act.” Therefore, after I have chosen the entities, it is no longer in my hands to determine the hierarchy; it is determined by judgment.
And one more small question, if you please. When you explain why there is flogging for a prohibition, do you mean that one is flogged for descending into a negative state (whereas one is not flogged for failing to ascend), or do you mean that one is flogged for being in a negative state (and therefore obviously one is not flogged for failing to ascend)? Is the punishment for the action or for the state? Prima facie, these are two entirely different kinds of punishment.
This topic is very precious to me and at the forefront of my thoughts, so please permit me to keep rubbing up against it a bit more, and I apologize for the quantity. Even if in your eyes everything has been ground up and repeated, I have not reached that point.
As an explanation of the halakhah, I now think your full structure is illuminating and reveals a truth. But as for whether all this is reasonable—here one already needs an external rationale.
At first glance, a demand to improve seems just as important as a demand not to deteriorate (for the issue of a positive commandment overriding a prohibition). And deterioration does not seem worse than lack of progress (for the issue of flogging and monetary loss).
But you also hold, regarding general plausibility, that this is indeed reasonable. You think that deterioration really is worse than lack of progress (therefore there is flogging for a prohibition). And you think that one does not deserve praise for not deteriorating, but one does deserve censure for not progressing (therefore neglect of a positive commandment and keeping a prohibition amount, overall, to something worse). That is already your extra-halakhic reasoning. And I am very uncertain whether you too distilled that from the halakhah, or whether it was already there with you from the outset.
By the way, similarly, I have always wondered at the custom of sellers giving a “discount” to friends. Conversely, I have never heard of a custom of buyers giving “appreciation” to friends. What is the difference between them? If by virtue of the discount I, as seller, granted you five shekels, why should you not alternatively grant me, as buyer, five shekels in appreciation?
According to what you explained in the paragraph “Returning to R. Perlow’s words on the view of R. Saadia Gaon,” it is difficult for me to understand why R. Saadia Gaon counts the obligation to afflict oneself on the Tenth of Tishrei, even though fundamentally it is a prohibition, since one fulfills it by refraining.
And now the question arises in full force: in the previous post you explained that “according to R. Saadia Gaon, the commandment to afflict oneself is indeed counted as a positive commandment because of the way it is formulated in the Torah, but essentially it is a prohibition, and therefore there is karet and a sin-offering.” So what determines whether to count something as a positive commandment or as a prohibition is the wording; but in this post the opposite emerges, namely that what determines it is the essence. True, this is when there is both the formulation of a positive commandment and of a prohibition, but I do not find it plausible to say that when there are two formulations what determines it is the essence, but when there is only one formulation what determines it is the wording itself. Why not say that what always determines it is the essence, and that would solve the issue?
Further on, you asked that according to the conception of R. Saadia Gaon and R. Perlow, why does the Torah describe certain prohibitions in active language reserved for positive commandments, and vice versa. But it seems that R. Perlow himself explains this when he writes, “And the Merciful One did not write regarding it a positive commandment and a prohibition except in order to magnify the severity of the punishment of one who transgresses it.” So what difficulty remains?
That seems right to me (though I am not sure I fully understood the matter of cleaning dirt and the like).
I explained above that there is no connection.
There are two kinds of prohibitions: a prohibition on an action and a prohibition on a result. As far as I am concerned, in a prohibition on an action, the negative state is the action; and in a prohibition on a result, the negative state is the result. In both cases this is being in a negative state, and for that one is flogged.
It is hard for me to assess whether this reasoning arose in me from the halakhah or not. My feeling is that it did not. It seems obvious to me as a matter of reason that there is a difference between drowning someone and failing to save him from drowning.
That mixes approaches. My explanation was stated according to the view of most of the Rishonim. R. Saadia Gaon disagrees with that.
Why, then, did he not write two prohibitions? When does one write two prohibitions (as in the case of interest), and when a prohibition and a positive commandment?
You say that one is flogged for being in a negative state, not for the transition into a negative state. Therefore it makes no sense to be flogged for remaining in a neutral state that avoided transition into a positive state. Does that mean that punishment is for atonement and not for deterrence and motivation?
That is not correct. In the paragraph “Returning to R. Perlow,” you explain that according to R. Saadia Gaon one must examine the essence of the commandment and see whether it is a prohibition or a positive commandment (which is not dependent on the wording). But in the previous post you proposed an explanation according to R. Saadia Gaon according to which the commandment to afflict oneself is counted as a positive commandment even though its essence is a prohibition. I have a sense of contradiction here, which raises the difficulty I mentioned in the last comment (why, according to R. Saadia Gaon, fasting is a positive commandment even though in essence it is a prohibition).
Not necessarily. A person who enters the negative state knows that he will be flogged for being there, and that deters him. So in my opinion the question of the purpose of punishment remains open. As I wrote in the article on punishments, I do indeed think that Torah punishments are not for deterrence (at least not only for deterrence), but this is no proof.
R. Saadia Gaon’s words are a puzzle in any case.
He says that one counts according to that by which the matter of the commandment is more clearly expressed, but it is not clear what he means. In the simple sense, he means the performance criterion. After all, his whole objection to the Rambam is based on the assumption that there is no essential difference between a positive commandment and a prohibition, only a difference of performance. So it seems likely to me that this is how he understood it.
But the question still remains why self-affliction on Yom Kippur is, in his view, a positive commandment and not a prohibition; for that I proposed a local answer. It is also possible that he understood fasting as active doing, because you create a state of affliction in your body (just as throwing a person into a river and holding him under is active murder, even though he dies from lack of oxygen and I am only causing it). But I do not have a systematic method for R. Saadia Gaon’s view.
So why is there no punishment for neglect of a positive commandment? Granted, if the punishment merely atones for the state, then punishment applies only to a negative state. But if punishment also tries to influence a person’s behavior, then why should one not punish for neglect of a positive commandment?
One can also ask why there are more severe and less severe punishments. Even if punishment is deterrence, there are still proportions. And for a positive commandment there is no punishment at all. Certainly if it is about atonement (= cleansing the sin; neglect of a positive commandment does not stain us).
1. In the paragraph “An Essential Distinction Between a Prohibition and a Positive Commandment,” you write at the outset that “there is no logical overlap here,” etc. In the last third of the post, are you only explaining this in greater detail, or from the paragraph “A Logical Problem” onward are you already presenting a different problem, and in the final third you are proposing an interpretation of that problem? Because after you wrote at the beginning “there is no logical overlap here,” etc., I did not understand the practical difference of the problem in the paragraph “A Logical Problem.” Is it the same problem?
2. I really tried to understand the difference between “implications of a distinction” and “demonstrations of a distinction,” and I did not understand. I would be very grateful for clarification either in different words or by means of a simpler example.
3. The negation of the claim “I am hungry” = “it is not true that I am hungry,” or simply “I am not hungry”?
1. The continuation is only elaboration. Here I explained it intuitively, and afterward I showed that there is no overlap on the formal logical plane and discussed the implications.
2. There are implications that cannot themselves serve as an explanation for the difference between a prohibition and a positive commandment. For example, the fact that for a positive commandment one parts with only a fifth of one’s money, whereas for a prohibition one parts with everything. For a positive commandment one receives reward, and for a prohibition punishment. That is not the difference itself, but an implication of the difference. Because there is a difference, the implication is that different sums are exacted. The difference between a positive and a negative state is the difference itself. Demonstrations of it are, for example, “it is preferable to perform a commandment oneself rather than through an agent,” coercion, when there is no house, etc. All these are expressions of the essential distinction that sharpen the distinction itself. The implications are derivative of the distinction.
3. In plain Hebrew it seems the same. But as I wrote, if I do not exist at all, then it is not the case that I am hungry, and it is also not the case that I am not hungry. But it is the case that “it is not true that I am hungry.”
With norms this is even clearer. There is a clear difference between “it is not true that there is a commandment to put on tefillin” and “there is a commandment not to put on tefillin” (a prohibition).
I would note even more than that: you wrote, “Therefore, even if the Torah indicates that there is also a positive commandment to rest on Shabbat, it really means a prohibition, and only the wording misleads us. Therefore the Shabbat prohibitions will be counted by R. Saadia Gaon as prohibitions and not as positive commandments.” But in truth, in R. Saadia Gaon’s Sefer HaMitzvot, resting on Shabbat is counted as a positive commandment. See positive commandment 34: “Guard the Sabbath—you, and your sons, and your servants, and your cattle shall rest on it.”
If so, that strengthens the difficulty I described above.
“The distinction between the two formulations of negation can appear clearly if we consider a situation in which there is no person named Moses in the world at all.” Of course, if you ignore the existential assumption of Aristotelian logic, you will have problems with the propositions. That is, there is an assumption of existence for whatever is designated by the terms appearing in the proposition, so Moses exists; and therefore, according to the square of opposition, two propositions are contradictory if and only if there cannot be a situation in which both have the same truth value. Indeed, the contradictory proposition (that is, the negation) of “Moses with tefillin” is “Moses without tefillin.”
The question whether the existential assumption is correct or not is irrelevant to the discussion, except perhaps to my example. That assumption is merely a convention (you may assume it or not). For my purposes here, it was enough to show that if one adopts that assumption, if only for the sake of discussion, a difference is created between the two types of negation. That already shows that these are two different types, regardless of whether you yourself actually accept that assumption or not.
More power to you for the article. Asking cautiously: couldn’t it be explained that R. Saadia Gaon meant that one does not count a positive commandment and a prohibition when their content is identical, rather than that they are not really divided into a prohibition and a positive commandment? In other words, perhaps the dispute among the Rishonim is about the method of counting, not about whether there really is a prohibition or a positive commandment here (you defined it as though according to R. Saadia Gaon there are two prohibitions or two positive commandments).