Lesson 13: Category 5 — The Seventh Root

From the book Roots Outstretched by Rabbi Michael Avraham. Translated from Hebrew using gpt-5.4 (reasoning_effort=high, batch API).

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With God’s help

The Seventh Root: One Should Not Count the Fine Details of a Mitzvah (Commandment)

On Rationalism and Interpretive Empiricism

Our present essay deals with the seventh root, which states that different applications of the same mitzvah should not each be counted separately. This root belongs to the fifth category of roots, which deals with classification and categorization. So too do the next two roots, which are the last to be discussed in our series of essays. The previous root, which dealt with punishments, stood midway between the fourth and fifth categories, as we explained in the essay devoted to it.

By the very nature of this category, it seems that this root too concerns a purely technical principle, with no halakhic implications at all. The fine details of a mitzvah are, by all opinions, full halakhic requirements—that is, obligations of halakha (Jewish law). The discussion in this root concerns only the question of how these obligations are to be treated within the enumeration of the mitzvot. This is a question of technical classification.

And yet, as in previous cases, we shall see that here too the positions taken in the discussion rest on broader principles. These principles touch not only on halakha, but no less on methods of interpretation and their validity, and perhaps even on knowledge in general, scientific or otherwise.

In the introduction to our series, we already pointed out that Maimonides and Nahmanides differ in their basic approach to halakhic interpretation. We noted there that Nahmanides tends toward empiricism—that is, he adheres closely to the facts as they appear in Scripture and in rabbinic sources—whereas Maimonides tends toward rationalism, meaning that he places confidence in the conclusions of a priori reasoning, and at times even imposes them upon the sources. Here we shall see another expression of Maimonides’ rationalist approach. In this case, however, the empiricist pole is not represented by Nahmanides, but by other Rishonim (medieval authorities).

We shall conclude the essay with an appendix proposing a proof for the rationalist approach in the scientific context, and we shall see the implications of that proof for the interpretive questions discussed here.

A. Maimonides’ Method and Arguments in This Root

Introduction

Maimonides’ discussion in this root is quite lengthy. We shall therefore describe it without quoting it in full, and will try to focus on the points that will be discussed below.

Explanation of the Principle

Maimonides begins with a principled distinction between mitzvot and their laws. The first example he gives is yibbum (levirate marriage) and halitzah (the release ceremony):

The example of this is halitzah and yibbum. These are two positive mitzvot (positive commandments 216-217), and no one disputes this. But when we examine the law of these two positive mitzvot, and what follows from them according to the Torah’s premises, it follows that some women undergo halitzah and do not enter levirate marriage; some enter levirate marriage and do not undergo halitzah; some may either undergo halitzah or enter levirate marriage; and some neither undergo halitzah nor enter levirate marriage. The same is true of the men as well—that is, the brothers-in-law: some perform halitzah and do not enter levirate marriage; some enter levirate marriage and do not perform halitzah; some may do either; and some may do neither. Likewise, among the widows awaiting levirate marriage, some may undergo halitzah with one man and enter levirate marriage with another; some may undergo halitzah with both and enter levirate marriage with both. Some are permitted to their husbands and forbidden to their brothers-in-law, some permitted to their brothers-in-law and forbidden to their husbands, some forbidden to both, and some permitted to both.

Thus, the mitzvot of halitzah and yibbum are, by all opinions, two distinct mitzvot. Already here we should note that Maimonides does not explain why these two are not themselves merely fine details of a single mitzvah; see below on this point. Nevertheless, they have different applications in different circumstances, involving different categories of women.

If we were to count each of these detailed elements as a separate mitzvah, the number of items in tractate Yevamot alone would exceed two hundred mitzvot, though each of them is nothing more than a particular command or prohibition—for example, to say that this woman must perform halitzah under such-and-such conditions, or must enter levirate marriage under such-and-such conditions; or to say that this one is not permitted to that man, or that halitzah is impossible for her altogether, or levirate marriage is impossible for her. And so too with every mitzvah.

Here Maimonides determines that all these details are not to be counted as independent mitzvot. His proof is simple: if we counted them separately, the number of mitzvot would explode. Beyond this argument, he offers no further proof, and the point seems to him self-evident.

Immediately afterward he continues:

Since this is so, and since no one disputes it, the fine details of a mitzvah are likewise not to be counted even when they are written in the Torah. For just because Scripture explained that mitzvah in detail, or specified its conditions, we do not count every condition or every particular that is only a fine detail and say that it is a mitzvah.

In other words, with respect to yibbum and halitzah, no one disputes that they are to be counted as only two mitzvot and no more. The reason for this seems simple: only yibbum and halitzah themselves are explicitly commanded in verses of the Torah. Their details do not appear explicitly in the Torah, and therefore it is clear that they are not counted separately. On the dependence on the detail’s appearance in the Torah, see below when we compare this root to the ninth root. Maimonides now goes on to claim that from here it is also clear that even if the details are explicitly written in the Torah, they still are not to be counted as separate mitzvot. In other words, such details are not excluded from the count because they do not appear in the Torah, but because they are nothing more than manifestations of the same mitzvah.

Additional Examples

Another example of fine details of a mitzvah is the sliding-scale offering. One who defiles the Sanctuary or consecrated things must bring a type of sin-offering called a sliding-scale offering. A wealthy person brings a ewe or a she-goat; a poor person brings two turtledoves or two young pigeons; and a very poor person brings a meal-offering of one-tenth of an ephah of fine flour. We count these three detailed forms as one mitzvah, even though each of the three is written explicitly in the Torah. The same applies to an inadvertent sin of idolatry, where too there is a distinction in the required offerings, depending on whether the sinner is a priest, a ruler, or an ordinary Jew.

Another example is the obligation to punish an adulterous woman. On this Maimonides writes:

Included in this category also is what the Exalted One said: when a betrothed maiden commits adultery, she is punished by stoning (Deuteronomy 22:23-24), and a priest’s daughter by burning (Leviticus 21:9). This is only the completion of the fine detail of the law governing a married woman. And everyone I have heard of who counted the commandment erred by counting the married woman as one mitzvah, the betrothed maiden as another, and the priest’s daughter as another.

Here Maimonides states that all the enumerators of the mitzvot known to him erred with respect to this commandment. So this root is not accepted by the other enumerators of the mitzvot. With regard to details that appear explicitly in the Torah, it seems that the other enumerators do count them as independent mitzvot, and it is against this that Maimonides directs the present root:

This is not so, but rather as I shall explain. One mitzvah among the mitzvot—negative commandment 347—is the statement of the Exalted One, “You shall not commit adultery.” The received tradition explains that this prohibition warns against intercourse with a married woman. Scripture then explained that one who violates this prohibition is to be put to death, as it says, “The adulterer and the adulteress shall surely be put to death” (Leviticus 20:10). Scripture then completed the fine detail of this law and the conditions of this matter, stipulating that this phrase, “The adulterer and the adulteress shall surely be put to death,” is differentiated: if this married woman is a priest’s daughter, she is to be burned; if she is a virgin betrothed maiden, she is to be stoned; and if she is a non-virgin and not a priest’s daughter, she is executed by strangulation.

The basic mitzvah is “You shall not commit adultery,” which concerns a married woman. The Torah also explicitly prescribes the death penalty for adultery. Beyond that, the Torah specifies different applications of that punishment: a betrothed maiden who is still a virgin and committed adultery is punished by stoning; if she is a married Israelite woman who is no longer a virgin, she is strangled; and if she is a priest’s daughter, she is burned.

Maimonides now states that these are only details of one mitzvah, and therefore they must be counted as one mitzvah, not three:

The mitzvot do not multiply because the modes of death differ, for in all this we have not departed from the prohibition concerning a married woman. And they explicitly said in the Babylonian Talmud, Sanhedrin 51b: “All were included in the phrase ‘the adulterer and the adulteress’; Scripture singled out the daughter of Israel for stoning and the priest’s daughter for burning.” Their meaning is that the prohibition concerning a married woman includes everyone of whom Scripture says, “The adulterer and the adulteress shall surely be put to death,” but Scripture differentiated within this death penalty, assigning some persons to burning and some to stoning.

A distinction in punishment does not mean that these are separate mitzvot. This is one prohibition, and there is one obligation to punish the adulteress, though it has different applications. Here those applications are written explicitly in the Torah, and yet they are still counted as one mitzvah.

Another, somewhat different, example is the law of the unintentional killer:

If it were fitting to count a fine detail of a mitzvah merely because it is mentioned in the Torah, then we would have to refrain from counting “the unintentional killer goes into exile” as one mitzvah, for Scripture already specified this mitzvah in detail. We would then count as follows: the statement of Scripture, “If he struck him with an iron instrument…” (Numbers 35:16) would be one mitzvah. The second mitzvah would be, “If with a stone in the hand by which one can die he struck him” (Numbers 35:17). The third would be, “Or with a wooden instrument by which one can die he struck him” (Numbers 35:18). The fourth, “The avenger of blood shall put the murderer to death” (Numbers 35:19). The fifth, “If he thrust him in hatred” (Numbers 35:20). The sixth, “Or cast something at him in ambush” (Numbers 35:20). The seventh, “Or in enmity struck him with his hand” (Numbers 35:21). The eighth, “But if he pushed him suddenly without enmity” (Numbers 35:22). The ninth, “Or cast upon him any object without ambush” (Numbers 35:22). The tenth, “Or with any stone by which a man may die, not seeing him” (Numbers 35:23). The eleventh, “And it fell upon him and he died, though he was not his enemy” (Numbers 35:23). The twelfth, “The congregation shall rescue the manslayer” (Numbers 35:25). The thirteenth, “The congregation shall restore him to his city of refuge” (Numbers 35:25). The fourteenth, “He shall dwell there until the death of the high priest” (Numbers 35:25). The fifteenth, “But if the manslayer goes out, goes out…” (Numbers 35:26). The sixteenth, “After the death of the high priest the manslayer shall return” (Numbers 35:28).

If we did this with every mitzvah, the number of mitzvot would exceed two thousand, and the error is obvious. For all this is only the detailed law of the matter; the mitzvah that is counted (positive commandment 225) is the law of one who strikes a person unintentionally—the Torah instructed us to judge him according to these written details.

From Maimonides’ wording it is already clear that in this mitzvah all enumerators agree that it is only one mitzvah, and he uses it as proof for his position. Why, then, does Bahag agree here that this is one mitzvah, while dividing the punishments for adultery into three separate mitzvot?

A brief look shows that this example is indeed different. Here we are dealing not only with different applications of the mitzvah, but with the particulars of the mitzvah itself. To be sure, “in ambush,” “in hatred,” “with a wooden instrument,” and the like are different applications of the same mitzvah. But the death of the high priest and the law governing the case where the exile leaves the city of refuge are not different applications, but further legal particulars relating to this mitzvah. Are such particulars part of the present root? It is fairly clear that they are not, and we shall return to this below when comparing this root to roots 11 and 12. Maimonides apparently brings all of these here only in order to sharpen the problematic character of Bahag’s approach.

Parashiyyot: Bahag’s Solution to This Kind of Multiplicity

Later in his discussion, Maimonides notes that Bahag—the author of Halakhot Gedolot—was aware of these issues concerning the unintentional killer, and dealt with them by counting parashiyyot (scriptural sections):

God called them judgments, not mitzvot, as it says, “The congregation shall judge between the striker and the avenger of blood according to these judgments” (Numbers 35:24). The author of Halakhot Gedolot already noticed some of these matters and circled around them, counting sections section by section, saying in his enumeration: the section of inheritances, the section of vows and oaths, the section of the slanderer. And he counted many such sections. But he did not fully grasp this matter and did not attain it. Therefore, within those sections he counted things that he had already counted previously, without noticing it.

Bahag solved this problem differently—at least for mitzvot of this type, which contain many particulars and not only different applications. He treated the law of the unintentional killer as a section, gathering all of these particulars into one unit. On the idea of counting sections, see the appendix to our essay on the tenth root. Here Maimonides repeats his earlier charge that Bahag counted under “sections” certain mitzvot that had already been counted separately.

A Note on the Dispute over Conceptions of Punishment

In the previous essay, on the fourteenth root, we discussed different conceptions of punishment among the Rishonim. We saw there that some count the obligation to impose punishments as a mitzvah incumbent on the bet din (rabbinical court), as Nahmanides does. On that view, the duty to execute the adulteress rests on the court. According to such a position, one might indeed say that these are three different obligations, since these are three different forms of execution performed by the court. If, by contrast, these punishments are seen as consequences imposed upon the offender, then they are indeed different consequences, but the transgression is one.

And in fact, Maimonides’ argument here refers to the prohibition violated by those adulteresses, not to the punishment they receive for it. They all committed adultery and violated the prohibition concerning a married woman, and in that sense there is only one transgression here. Maimonides’ argument is directed against the notion that because the punishments differ, the violations must also be distinguished. But this itself depends on the question of the relation between the transgression and the punishment, and this is not the place to elaborate.

B. Defining the Scope of the Discussion

Introduction

After seeing Maimonides’ words, we must first determine and sharpen the scope of the present discussion—that is, to identify the kinds of cases addressed by the root before us. As we shall see, confusion about the scope of the discussion can lead to misunderstandings of Maimonides and of the other Rishonim on this issue.

The problem arises in light of the principles laid down by Maimonides in several parallel roots—9, 11, and 12¹—which at first glance seem very similar to the content of the present root. We shall try here to define the scope of this root by distinguishing it from those roots. Afterward we shall see an example of the implications of this delimitation.

Comparison to Roots 11-12

First, in root 11 Maimonides states: “One should not count the parts of a mitzvah individually, each part on its own, when their combination constitutes one mitzvah.” The example he himself gives is the four species on Sukkot. The mitzvah of the four species is indeed one mitzvah, but it is composed of four parts: palm branch, citron, myrtle, and willow. In such cases, one does not count each component as a separate mitzvah. The whole system describes the parts of one mitzvah.

In root 12 Maimonides lays down a similar principle: “One should not count the components of a labor among the labors one is commanded to perform, each component by itself.” His example is the building of the Temple, which is counted as one mitzvah even though it is composed of many parts. Together they make up the mitzvah of building the Temple—or perhaps the concept of a Temple itself, which we are commanded to build, but this is not the place to elaborate. The same applies to the sacrificial procedure for any offering, which is composed of several stages—slaughtering, receiving the blood, carrying it, sprinkling it, and so on—and all of them together are counted as one mitzvah. The difference between those two roots will be discussed in its place, when we come to them. But it also requires explanation how both differ from the present root. Seemingly, in all of them Maimonides says that the parts of a mitzvah should not be counted as independent mitzvot. Why, then, does he divide the discussion into three different roots?

The author of Lev Sameah, in his commentary on our root, explains the difference in scope. Those two roots deal with a mitzvah that is composed of parts, such that fulfilling the mitzvah requires performing all the parts together—as Maimonides says, “when their combination constitutes one mitzvah.” Here, by contrast, Maimonides is dealing with cases in which a mitzvah has different forms that appear in different situations, never all together. Some women or men perform halitzah and not levirate marriage; some perform levirate marriage and not halitzah. These are not parts that together create fulfillment of the mitzvah, or violation of a prohibition, but different ways in which the mitzvah appears in different situations. The same is true of the various forms of ritual impurity, of tzara’at (ritual skin affliction), of those with physical blemishes, and of the sliding-scale offering. All of them are modes of appearance of one mitzvah, not components that join together into its complete fulfillment.

To sum up: roots 11 and 12 deal with parts of the command and of the act of fulfilling it—or violating it—whereas the present root deals with branches of the command itself that are not parts of a single act of fulfillment, since each is realized in a different situation.

Comparison to the Two Parts of Root 9

In light of this formulation, the similarity to principles that are seemingly parallel to our root becomes especially problematic—namely, those appearing in the two parts of the ninth root. In root 9 Maimonides states that one does not count a mitzvah that is repeated several times in the Torah. The count is determined by the content, not by the number of appearances or verses in Scripture. In the second part of root 9 he discusses the opposite case: a general prohibition, a single prohibition that includes many matters. His example is “You shall not eat upon the blood” (Leviticus 19:26), from which the Sages derive several different prohibitions—see Babylonian Talmud, Sanhedrin 63a, and the parallel passage in the halakhic midrash Sifra (rabbinic legal exegesis)—such as the prohibition on eating from an animal before its life has departed, the prohibition on eating consecrated meat while the blood is still in the bowl before sprinkling, and the prohibition on members of the Sanhedrin who have sentenced someone to death tasting anything that day. Here too Maimonides rules that all of these are to be counted as only one mitzvah.

We already noted in our essay on root 9 that some objected that the two parts of that root contradict each other. From its first part it emerges that the count of the mitzvot is determined by contents, not by the number of verses. But from its second part the opposite seems to emerge: the count is determined by the number of verses, not by the contents—for there one finds different contents, all appearing in one command, and yet they are counted as one mitzvah. We explained there that according to Maimonides, two conditions are required for a mitzvah to appear in the count:
1. It must have independent content.
2. It must have its own explicit verse. See root 2 and our essay on it.

Now our root seems to present a similar principle. On the one hand, Maimonides is dealing here only with fine details of a mitzvah that appear explicitly in the Torah, for if they did not appear in the Torah there would be no reason even to consider counting them. As root 9 establishes, without an explicit command they are not counted as mitzvot. Thus, in our case, the three classes of adulteresses do appear explicitly in Scripture, and according to the second part of root 9 one might think they should be counted as three mitzvot, in keeping with the number of verses. On the other hand, according to the first part of root 9, one could say that they constitute a single content shared by all of them, as noted above, and therefore they should be counted as one mitzvah despite the multiplicity of verses.

To be sure, one might have treated each of them as expressing a different content. In our root: the betrothed adulteress, the adulterous Israelite woman, and the adulterous priest’s daughter. One might perhaps say that each has damaged something different. So too in roots 11 and 12, one might argue that slaughtering, receiving the blood, carrying it, and sprinkling it are each wholly different acts, not different expressions of one thing, and therefore each should be counted separately, since each has a different content and a distinct verse. This would seem to satisfy the criteria of both parts of root 9.

Here Maimonides, in our root and in roots 11-12, comes and determines that even a conjunction of contents can count as one content. In our root, there is one shared content that generalizes the three mitzvot—the prohibition of adultery—and that counts as one content. In roots 11-12, these are parts that each appear in the Torah with an explicit verse, yet their contents join together and are integrated into one content.

We thus learn that the three classification roots—7, 11, and 12—are all rules teaching us how to unify the contents of mitzvot that appear separately. Therefore, even if there are multiple verses for each part or detail, the content of them all is considered one content, and they are rightly one mitzvah. This is precisely the line that distinguishes the classification roots of the fifth category from the duplication roots of the fourth category.

We may now see an implication that clarifies the importance of this analysis.

An Illustration of a Misunderstanding of Maimonides Caused by Incorrect Delimitation

An example of the importance of defining the scope of the present root is Rabbi Daniel the Babylonian’s claim, in the letter to be mentioned below, that there is an internal contradiction in Maimonides’ own words. In negative commandments 8 and 9, Maimonides counts ov and yidoni—two forms of necromancy—as two separate prohibitions:

The eighth mitzvah is that He warned us against performing an ov. This is when one burns a certain incense and performs specific actions until it seems to him that he hears speech emerging from beneath his armpit in response to what is asked of him; this is one of its forms. This is the statement of the Exalted One, “Do not turn to the ovot” (Leviticus 19:31). The language of Sifra is: “Ov—this is a ventriloquist speaking from beneath his armpit.” One who violates this prohibition intentionally is stoned; if he is not stoned, he is liable to karet (spiritual excision), and if he sins inadvertently, he must bring a fixed sin-offering. This applies to one who performs the act himself and practices it personally. The laws of this mitzvah are explained in chapter 7 of Sanhedrin (Babylonian Talmud, Sanhedrin 53a, 54a, 65a, 67b).

The ninth mitzvah is that He warned us against performing the act of yidoni. This too is a kind of idolatry. It is when one takes the bone of a bird known by that name, places it in his mouth, burns incense, recites incantations, and performs actions until a condition akin to an epileptic trance attaches to him, sleep overtakes him, and he speaks of future events. They said there (Sanhedrin 65b): “A yidoni places the bone of the yidoa bird in his mouth, and it speaks on its own.”

Up to this point, these are two distinct mitzvot whose warning comes from one verse. Maimonides then raises a difficulty:

The warning concerning it comes in this language: “Do not turn to the ovot and to the yidonim.” Do not think that this is a general prohibition.

Maimonides asks why this is not a general prohibition, which ordinarily should be counted as only one prohibition. The difficulty is that both warnings are learned from one verse. True, both are mentioned separately in the verse, but the word of negation, which is needed to define a verse as a prohibition, appears here only once.

Maimonides explains:

For Scripture has already separated them in stating the punishment, saying “ov or yidoni,” and made each liable to stoning and to karet when done intentionally, as it says, “A man or woman in whom there is an ov or a yidoni shall surely be put to death…” (Leviticus 20:27). The language of Sifra is: “Since it says, ‘A man or woman in whom there is an ov or a yidoni’—we have heard the punishment; we have not heard the warning. Therefore Scripture says: ‘Do not turn to the ovot and to the yidonim.'” One who violates this prohibition inadvertently is also liable to a fixed sin-offering. The laws of this mitzvah are explained in chapter 7 of Sanhedrin (Sanhedrin 53a, 54a, 65b, 67b).

He explains that these are two mitzvot because the punishments of ov and yidoni are written separately in the Torah, and separate punishments divide the mitzvot, even if their warnings are not separate.²

Rabbi Yeruham Fishel Perla, in his discussion of the seventh root and following Rabbi Daniel the Babylonian, who also alludes to this point, asks: why does Maimonides write that punishments divide the mitzvot? After all, the punishments of the adulterous priest’s daughter and the adulterous Israelite woman are also written separately, and yet Maimonides claims in our root that they are to be counted as one mitzvah. If so, why are ov and yidoni counted as two?³ At the end of his discussion of this root, Rabbi Yeruham Fishel Perla argues that Rabbi Abraham son of Maimonides, in his reply to Rabbi Daniel in Maaseh Nissim, provides no answer to this difficulty, and he brings many other commentators who raised the same objection against Maimonides. He therefore concludes that there is no answer to the objection and, on that basis, rejects Maimonides’ position in this root.

But in light of what we said above, there is no difficulty here at all, and it is actually quite unclear what all these commentators wanted from Maimonides. Maimonides did not raise the case of ov and yidoni because they are fine details of one mitzvah, which would be the principle of the seventh root. His difficulty there is based on the second part of the ninth root, the case of a general prohibition. As we saw above, there is a major difference between these two roots. In the second part of root 9, Maimonides is dealing with a general prohibition, that is, a collection of prohibitions whose subject matter is different even though they are written in one verse. The same is true of negative commandments 8 and 9: their contents are different, and the only reason they would not be counted separately is that we lack separate verses for each of them, since both are written in one verse. In such cases, says Maimonides, if the punishments of each part are written separately, that counts as if there were several verses, and each can therefore be counted separately.

But the discussion in the seventh root concerns a situation where there is already a verse for each part of the mitzvah; the problem is not a lack of verses. What prevents them from being counted separately is only that their contents all join into one comprehensive content, as in roots 11-12, or are subsumed under one content, as in our root. In all such cases, it is obvious that punishments do not divide. Punishments cannot teach us that there are different contents here, because the contents combine into one. Separate verses of punishment can only cause the warning verse to count as multiple warning verses.

Summary

The subject matter of this root, then, is situations in which a set of laws that appears to share a common basis is written separately and independently in the Torah. Each appears as a different manifestation of the same common basis, and its distinctness is only the result of the situation or the persons involved in the act.

Maimonides argues that in such a case all of them are to be counted, despite their separate appearance in the Torah, as only one mitzvah. Below we shall see that at this point a dispute erupts among the Rishonim.

C. Pairs of Mitzvot — Commandments Built as Alternative Options

Introduction

As noted, Nahmanides makes no comment at all on this root, and it appears that he agrees with everything stated in it. Indeed, it is hard not to agree with the claim that one should not count parts of a mitzvah as independent mitzvot, if only because otherwise the number of mitzvot would rise into the thousands. At first glance, this seems to leave room only for local disputes—that is, disputes about one particular mitzvah or another, centering on whether the cases involved are merely fine details of one mitzvah or several different mitzvot.

That is indeed how the disputes surrounding this root appear. Yet when we examine the matter closely, we shall see that there is here a principled disagreement about halakhic interpretation of the Torah, with broader interpretive and even philosophical dimensions.

Alternatives in the Mitzvah of the Firstborn Donkey: Comparison to Levirate Marriage

The first difficulties raised by the principle established in this root are raised by Maimonides himself. As is well known, the law is that when the firstborn male of a donkey is born, it must be redeemed. If it is not redeemed, the Torah commands that its neck be broken. Maimonides counts these two mitzvot as positive commandments 81 and 82.

In positive commandment 82 he raises the following question:

A questioner may challenge me and say: why did you count its redemption and the breaking of its neck as two mitzvot, rather than counting them as one mitzvah and treating the breaking of the neck as one of the laws of the mitzvah, as you accepted in the seventh root? God knows that the inference would indeed require this, were it not for the language we found among our Sages indicating that they are two mitzvot. They said (Babylonian Talmud, Bekhorot 13a): “The mitzvah of redemption takes precedence over the mitzvah of breaking the neck, and the mitzvah of levirate marriage takes precedence over the mitzvah of halitzah.”

And just as the levirate widow stands ready either for levirate marriage or for halitzah, and levirate marriage is a mitzvah (positive commandment 216) and halitzah is a mitzvah (positive commandment 217), each one a mitzvah in its own right as mentioned, so too the firstborn donkey stands ready either for redemption or for breaking the neck; this is a mitzvah and that is a mitzvah, as we have said.

Maimonides asks why the mitzvah of breaking the neck should be counted as an independent mitzvah at all, when the mitzvah of redemption has already been counted. Seemingly, these are two details of one mitzvah, and according to the seventh root they should not be counted separately.

Maimonides’ assumption is that these are two manifestations of the obligation that falls on a person whose donkey has produced a firstborn opening the womb: if he wishes to redeem it, he must do so; and if not, he must break its neck. The basic obligation is not to leave it in his possession. He must choose between these two alternatives. These are different applications of one mitzvah, and according to the principle of our root they ought to be counted as one mitzvah with two manifestations.

It should be noted that above we already saw Maimonides treat yibbum and halitzah as two mitzvot, with the various details being the combinations of the two. He does not even raise the possibility of treating yibbum and halitzah as fine details of one mitzvah. But seemingly these too are just two applications—or alternatives—of the same obligation: if one wishes to perform levirate marriage, one does so; if not, one must perform halitzah. This is exactly the same structure as in the case of the firstborn donkey.

Below we shall discuss Maimonides’ answer to this question.

Alternatives in the Mitzvah of the Second Passover

There is another mitzvah in which Maimonides raises a similar difficulty for his own method: the mitzvah to offer the second Passover for one who was unable to bring the first Passover, counted as positive commandment 57. There he raises the very same question:

Here too a questioner may challenge me and say to me: why do you count the second Passover? This seems to contradict what you set forth in the seventh root when you said that the law of a mitzvah should not be counted as a mitzvah in its own right.

Let the questioner know that the Sages already disputed whether the second Passover has the status of compensation for the first Passover or whether it is an independent command stated on its own, and the halakha was decided that it is an independent command stated on its own, and therefore it is proper to count it separately.

Maimonides again raises the same kind of difficulty: why should we count the second Passover, offered by one who could not bring the first, as an independent mitzvah? Seemingly this is simply one of the laws of the Passover: if a person could not bring it, he is obligated to bring a second Passover. Here too there are two manifestations of one obligation, the obligation to bring the Passover offering, which changes according to the situation—whether he was impure or on a distant journey, or not. These are two alternatives for fulfilling the mitzvah of the Passover offering, and therefore, according to the principle of the seventh root, they would seemingly have to be counted as one mitzvah.

Unlike the previous case, here Maimonides says that the matter is subject to a Tannaitic dispute, and indeed one Tannaic sage holds that the second Passover is merely compensation for the first. According to that opinion, this mitzvah should indeed be counted as part of the laws of the first Passover. By contrast, according to Rabbi, who holds that the second Passover is a festival in its own right, and this is also the accepted halakha, it is clear that it must be counted separately.

Summary: The Relation to Alternatives

Up to this point we have seen three pairs of mitzvot, each pair constituting alternative ways of fulfilling what appears to be one mitzvah. Before explaining Maimonides’ position on this, we should ask ourselves why he connects these cases to the seventh root rather than to roots 11 or 12.

In light of what we said above, there is no difficulty here. Roots 11 and 12 deal with parts of a mitzvah such that every fulfillment requires all of them to be performed; together they make up the fulfillment of the mitzvah, as in the stages of offering a sacrifice. But in the seventh root we deal with different applications of the same mitzvah, each of which is realized on its own in other circumstances. Each one is a full fulfillment of the mitzvah under certain conditions.

The question of how to treat alternative applications therefore does indeed belong to this root. Below we shall see Maimonides’ approach.

The Tannaitic Dispute over the Second Passover and Its Relevance Here

In positive commandment 57 Maimonides mentions the Tannaitic dispute concerning the nature of the second Passover, and ties the manner in which it appears in the count of mitzvot to that dispute. The source is the sugya in Babylonian Talmud, Pesachim 93a:

The Rabbis taught: One is liable to karet for the first, and one is liable to karet for the second—these are the words of Rabbi. Rabbi Natan says: One is liable to karet for the first, but exempt for the second. Rabbi Hananiah ben Akavya says: One is not even liable to karet for the first unless he failed to perform the second. And they follow their own reasoning, as it was taught: A convert who converted between the two Passovers, and likewise a minor who came of age between the two Passovers, is obligated to perform the second Passover—these are the words of Rabbi. Rabbi Natan says: Whoever was subject to the first is subject to the second; whoever was not subject to the first is not subject to the second. What is the point of their dispute? Rabbi holds: the second is a festival in its own right. Rabbi Natan holds: the second is compensation for the first; it does not repair the first. And Rabbi Hananiah ben Akavya holds: the second is a remedy for the first. And all three expounded the same verse…

The law explicitly stated in the Torah is that if someone did not offer the Passover because he was impure or on a distant journey—that is, he was prevented on the fourteenth of Nisan—he must bring a second Passover. Seemingly, it is obvious that the second Passover is compensation for the first, a way of making up that original obligation.

Yet we find here that this conclusion is not agreed upon. The Sages indeed held thus, but Rabbi holds that the second Passover is a festival in its own right and not compensation for the first. The practical implication of the dispute concerns a minor for whom the first Passover was not offered because he was impure or the like, and who then showed signs of maturity between the two Passovers—for example, on the first of Iyyar. According to the Sages, he was not obligated in the first Passover. Therefore, if it was not offered for him, nothing happened, and there is nothing requiring completion. He is thus exempt from the second Passover. Only one who was obligated and failed to discharge that obligation, even under compulsion, must bring a second Passover. Rabbi, by contrast, holds that the second Passover is an independent obligation, a festival in its own right. Therefore that same minor who came of age on the first of Iyyar, once the date of the fourteenth of Iyyar arrives, is obligated like every adult in Israel to bring the second Passover, since he did not bring the first.⁴

How can Rabbi’s view be understood? Seemingly the Torah says explicitly that the second Passover is intended to complete the Passover offering for one who could not bring it under compulsion. How can one say that it is a festival in its own right, or that the offering is a renewed and independent obligation? Put differently: if it really is a new obligation, why is one who brought the first Passover exempt from it as well?

It seems that according to Rabbi, the second Passover is an independent obligation with its own purpose. One who offered the first Passover is exempt from it, but not because the second Passover is merely a makeup for the first. Rather, one who offered the first Passover apparently thereby achieved the purpose for which the second Passover is also intended.

Put more abstractly: according to the Sages, the first and second Passovers have the same aim; both are meant to achieve the same purpose. Therefore, if one did not bring the first, one must bring the second. According to Rabbi, by contrast, the mitzvah of bringing the first Passover has purpose A, while the mitzvah of bringing the second Passover has purpose B. Why, then, is one who brought the first exempt from the second? Apparently because, whether accidentally or not, bringing the first Passover also achieves purpose B, in addition to A. Therefore one who brought the first no longer needs the second. But one who did not bring the first, even if he brings the second, still lacks something, because he did not achieve purpose A, and that loss can never be fully repaired.

The conclusion is that according to the Sages, the failure to bring the first Passover is itself the cause obligating one to bring the second. Hence one who brought the first never became obligated in the second at all, not merely that he is exempt from it. According to Rabbi, however, the obligation of the second Passover falls on everyone for its own independent reason, not because he did not bring the first. Still, bringing the first Passover exempts him from the obligation to bring the second. According to Rabbi there is a relation of inclusion between the two mitzvot, in that the results of bringing the first contain within them the goals of the second.

We can now understand Maimonides’ words. According to the Sages, the two are indeed just two details of one mitzvah. But according to Rabbi they are two different mitzvot, even though there is a relation between them; they are not alternative applications of one mitzvah. Since the halakha follows Rabbi, who holds that the second Passover is a mitzvah in its own right, we rightly count them as two mitzvot.

A Halakhic Implication

And indeed we find echoes of this approach in Mishneh Torah, Laws of the Passover Offering 5:2, where Maimonides and the Raavad dispute whether impurity or a distant journey differ from other forms of compulsion and error:

How so? If one erred or was prevented and did not bring the first, then if he acted deliberately and did not bring the second, he is liable to karet; but if he also erred or was prevented regarding the second, he is exempt. If he deliberately did not bring the first, he nevertheless brings the second; and if he did not bring the second, even if that failure was inadvertent, he is liable to karet, because he did not bring the offering of the Lord at its appointed time and had acted deliberately. But one who was impure or on a distant journey and therefore did not perform the first—even if he acted deliberately with regard to the second, he is not liable to karet, because with respect to the first Passover he had already been exempted from karet.

The Raavad’s gloss: “If one erred or was prevented and did not bring the first, if he acted deliberately…” Abraham says: He taught this in accordance with Rabbi, while Rabbi Natan and Rabbi Hananiah ben Akavya disagree with him. /The Raavad’s gloss/ “Even if he acted deliberately with regard to the second…” Abraham says: Now he contradicts his own words. What difference is there between one who was impure or on a distant journey and then acted deliberately with regard to the second, and one who erred or was prevented with regard to the first and then acted deliberately with regard to the second?

Many, including Rabbi Yeruham Fishel Perla, who hints to this in his discussion of our root, have wondered about these words of Maimonides. What difference is there between one under compulsion and one who was impure or on a distant journey?

According to our approach, this can be explained as follows. For Maimonides, one who was impure or on a distant journey and did not perform the second Passover is exempt from karet, because in his view the karet pertains to the first Passover. By contrast, one who was under compulsion or merely erred with regard to the first and then deliberately failed to perform the second is liable to karet. This shows that impurity or a distant journey are not just ordinary cases of compulsion; they create a new and distinct obligation to bring the second Passover. Therefore one who fails to bring the second has violated only the second and is not liable to karet. But in cases of compulsion or error, the obligation is not really “second Passover” as a new obligation; rather, it is to go back and perform the first on the fourteenth of Iyyar, and one who deliberately does not do so is liable to karet.

The Raavad, by contrast, holds that exemption from the first generates obligation in the second, which is always a completion or consequence of non-performance of the first. Therefore, in his view, one is always liable to karet, because in both cases he failed to complete the first Passover. For the Raavad, the statement that the second Passover is “a festival in its own right” applies only to liability for karet—namely, that one who omitted the first under compulsion and the second deliberately is liable to karet, as if he had deliberately omitted the first. In other words, the Raavad does not see a different underlying cause in the first and second Passovers, whereas Maimonides does.

Comparison to Maimonides on the Firstborn Donkey and Levirate Marriage

We saw that with regard to the firstborn donkey, Maimonides asks why we count them as two mitzvot. This is what he writes in his answer:

God knows that the inference would indeed require this, were it not for the language we found among our Sages indicating that they are two mitzvot. They said (Bekhorot 13a): “The mitzvah of redemption takes precedence over the mitzvah of breaking the neck, and the mitzvah of levirate marriage takes precedence over the mitzvah of halitzah.”

And just as the levirate widow stands ready either for levirate marriage or for halitzah, and levirate marriage is a mitzvah (positive commandment 216) and halitzah is a mitzvah (positive commandment 217), each one a mitzvah in its own right as mentioned, so too the firstborn donkey stands ready either for redemption or for breaking the neck; this is a mitzvah and that is a mitzvah, as we have said.

From these words it emerges that this is indeed what simple reasoning would demand, were it not for the statement of the Sages. In other words, he argues that two alternative ways of fulfilling some mitzvah should really be counted as one mitzvah with two details. But specifically with respect to the firstborn donkey, the Sages stated explicitly that redemption and breaking the neck are two mitzvot.

Seemingly Maimonides himself admits that this talmudic passage stands in tension with his position in this root. Rabbi Yeruham Fishel Perla, and Rabbi Daniel the Babylonian before him, therefore argue against Maimonides that this talmudic passage provides no scriptural source indicating that these are two mitzvot. If so, the Sages evidently concluded this by reasoning alone. If that is the case, Maimonides ought to conclude from their words that whenever there are two such alternatives they must always be counted as two mitzvot. Rabbi Daniel writes, immediately after quoting Maimonides’ language on the firstborn donkey:

We cannot say that they, of blessed memory, were unaware of the methods of inference. If that is so, why should we not follow them in the way of inference and say that whenever Scripture decrees a division and differentiates the laws of the parts, that division should also be reflected in the count?

In other words, this talmudic passage itself contradicts Maimonides’ words in our root. Maimonides presents it as some sort of exceptional case, grounded in a scriptural decree as interpreted by the Sages. But Rabbi Daniel argues that there is no reason to see it as an exception. On the contrary, this itself proves the rule: where there are two alternatives, they should always be counted as two different mitzvot. If the Sages had no special source for this case, then the conclusion must be that this is simply their logical approach. We should not assume that they were ignorant of the methods of inference. Hence it must be generalized: every detail of a mitzvah that has its own distinct laws should be counted as a separate mitzvah.

As noted, Maimonides apparently understood that there is here a qualification of part of what he says, not a contradiction to the entire principle of this root. Therefore he does not infer from the distinction between yibbum and halitzah, or between redemption and breaking the neck, to all types of fine details of mitzvot. See below for an explanation of his view.

Rabbi Abraham son of Maimonides, in his reply to Rabbi Daniel, printed in the Frankel edition on this root, writes the following:

That the mitzvah of breaking the neck is a mitzvah in its own right apart from the mitzvah of redemption, and that halitzah is separate from yibbum, is a received tradition in their hands. Therefore one may not object that this runs counter to the methods of inference. For the reason is not their ignorance of inference, but rather as they said (Babylonian Talmud, Yevamot 76b; Keritot 15b): “If it is a received halakha, we accept it; but if it is only an inference, there is an answer to it.”

From his words it emerges that he partially concedes Rabbi Daniel’s point. Indeed, the matter is not self-understood to him. In light of the principle of this root, one would have expected to count only one mitzvah here. But we submit to the words of the Sages—”if it is a received halakha, we accept it”—while still not abandoning the logical principle itself, namely, that fine details of a mitzvah are not counted separately—”but if it is only an inference, there is an answer to it.” It seems that he understood that there is no internal logic here, only a kind of scriptural decree.

But as for Maimonides himself, it seems very likely that he had a logical explanation of these exceptions as well. Maimonides seems to regard the principle that such pairs of mitzvot are counted separately as a principle applying only to mitzvot that offer several distinct alternatives for fulfillment. Indeed, a closer look shows that with the first and second Passover, as with yibbum and halitzah, the picture is similar. In all these cases, a pair of alternatives for fulfilling some obligation is counted as a pair of separate mitzvot, not as one mitzvah with two details. It is unlikely that the identical pattern in all three pairs is mere coincidence. The conclusion is that there is here a broader and more principled qualification, built into Maimonides’ own view, of what he says in the present root. This is not merely a local scriptural decree, but a different type of detail that must be counted separately. What is the logic of this? Why, in such pairs, does Maimonides qualify his general position and agree that they should be counted as pairs of mitzvot rather than as details of one mitzvah? What is the inner logic of this sub-principle that qualifies the general principle of the present root?

Rabbi Yeruham Fishel Perla’s First Proposal

Rabbi Yeruham Fishel Perla, in his discussion here, apparently understood Maimonides to hold that two mitzvot that are conditional on each other must be counted as two mitzvot. These are not fine details of mitzvot but pairs of mitzvot. Fine details that are not counted separately would be cases like the punishments of the different adulteresses. There the details are not conditional on one another—if one was not performed, one does not then have to perform the other—but are simply different manifestations of the same law, namely the duty to punish an adulteress. In each case a different obligation applies, and this does not depend on the person’s own choice; he cannot choose between the alternatives.

But Rabbi Yeruham Fishel Perla’s words are not plausible as an explanation of Maimonides. After all, Maimonides explains the second Passover in terms of the dispute between Rabbi and the Rabbis. According to the Rabbis, who hold that the second Passover is compensation for the first, Maimonides agrees that it should not be counted separately. How is this different from yibbum and halitzah, or redemption and breaking the neck of the firstborn donkey? These too are conditional on one another. It follows that this cannot be Maimonides’ explanation, and the distinction does not hinge on whether the “details” depend on each other. We must therefore return to our question: why are these pairs not considered fine details of a mitzvah?

A Second Proposal for Explaining Maimonides

It may be that the key lies in Maimonides’ words about the second Passover, for there he explained his intent and tied it to a Tannaitic dispute. With regard to the second Passover, we saw above the logic behind the two views. One who sees the second Passover as compensation for the first will indeed count them as one mitzvah. The fact that in practice they are counted as two distinct mitzvot is only because the accepted halakha is that the second Passover is a festival in its own right, as we explained above.

If so, with regard to the firstborn donkey as well, it seems that in his question Maimonides assumes that these are two alternatives, one of which completes or compensates for the other—”if you do not redeem it, then you shall break its neck.” But after learning from the Sages, we understand that these are two independent mitzvot; one who redeems the firstborn donkey is simply exempt from breaking its neck. According to this logic, the breaking of the neck is not imposed only on one who failed to redeem; rather, one who redeems becomes exempt from it, exactly as we saw regarding the second Passover.

It seems likely that according to Maimonides this is also the case with yibbum. Halitzah is not an alternative compensation for yibbum, but a mitzvah incumbent on every levirate widow. If she enters levirate marriage, however, she is exempt from halitzah. Therefore these two alternatives are also counted as two mitzvot. This is precisely the comparison Maimonides himself makes in the words quoted above between the firstborn donkey and yibbum and halitzah.

Thus all these pairs, in their basic structure, ought to have been counted as fine details of one mitzvah according to the principle of the present root. When we see a halakhic structure consisting of a pair of mitzvot, such that only one who did not perform the first alternative becomes obligated in the second, our natural assumption is that the second is compensation for the first. Therefore, in principle, they should be counted as one mitzvah with two details. But where the Sages reveal to us that these are two mitzvot, they are evidently revealing that the relation between the two “details” is not one of compensation but of inclusion, as we saw regarding the Passover offering. Therefore they must be counted separately as a pair of mitzvot.

A Note on the Relation between the Three Pairs

It must be admitted that there is a difference between these three pairs. The first Passover is an absolute obligation, and only if one was prevented from fulfilling it does the obligation to bring the second Passover arise. By contrast, in yibbum and in the firstborn donkey, these are alternatives between which one may choose. True, it is preferable to perform yibbum rather than halitzah, and with regard to the firstborn donkey it seems at first that there is no preference for redemption over breaking the neck, though the sugya in Bekhorot 13a cited by Maimonides in positive commandment 82 shows that redemption is preferable. Still, in those two pairs the choice is left to the person to decide which of the two alternatives he wishes to adopt.

And indeed, one should note that Maimonides compares the case of the firstborn donkey to yibbum, but regarding the second Passover he explains it on its own and does not connect it to the other two pairs.

One might therefore wonder whether only with respect to the second Passover does Maimonides tie the manner of counting the mitzvot to the Tannaitic dispute over whether it is compensation or a festival in its own right. According to the Tanna who holds that the second is compensation, the two should be counted as one mitzvah. But even if there were a Tanna who held that breaking the neck is compensation for redemption, perhaps he would still agree that these are two separate mitzvot, because the person has a choice between them. In the Passover case there is no choice between the possibilities, and therefore, if one sees it as compensation, the two should indeed be counted as fine details of one mitzvah.

D. The Views of Rabbi Daniel the Babylonian and Saadia Gaon, and Their Disputes with Maimonides

Introduction

In this chapter we shall examine the positions of Saadia Gaon and Rabbi Daniel the Babylonian, both of whom disagree with Maimonides concerning the principle discussed in this root. Rabbi Daniel corresponded with Rabbi Abraham son of Maimonides, and their exchange appears in the book Maaseh Nissim. The responsa relevant to Sefer HaMitzvot and the roots were printed in the Frankel edition of Sefer HaMitzvot. Saadia Gaon’s position is presented here in light of Rabbi Yeruham Fishel Perla’s explanation of his method in this root.

It should be noted that most of the disputes between Rabbi Daniel and Saadia Gaon, as Rabbi Yeruham Fishel Perla presents him, and Maimonides are local disputes. The principle that fine details of mitzvot should not be counted is accepted by all. The question is only what counts as such details. Rabbi Daniel attacks Maimonides in particular commandments, and in Rabbi Abraham’s replies one always finds a local point of dispute about whether certain laws are to be classified as details of one overarching mitzvah or as independent mitzvot. At first glance these are merely collections of local disputes, and we shall therefore not analyze them all in detail here. In what follows we shall focus mainly on two principled points of disagreement, and in the next chapter we shall try to examine the relation between them and the philosophical-hermeneutic roots of the dispute.

The View of Rabbi Daniel and Saadia Gaon on Pairs of Mitzvot

Rabbi Daniel opens his remarks by saying that he does not agree with what is stated in the present root. If the punishments, or the laws—that is, the details—were uniform across all the various manifestations, then perhaps there would be room to count them as one mitzvah. But when the priest’s daughter who committed adultery is punished by burning, whereas the Israelite woman who committed adultery is punished by stoning, this proves that there are two different prohibitions. So too with the sliding-scale offering and the other examples brought by Maimonides. Above we already saw why, according to Maimonides, the change in punishments is irrelevant to the count of mitzvot.

Later in his discussion he argues that in the example of the sliding-scale offering there are two components of alternation: the wealthy person may choose between a ewe and a she-goat, and in addition there are two further levels of cheaper offerings. His claim is that where a person has the right to choose voluntarily among different options, one may perhaps treat them as one mitzvah, and therefore it is obvious that the ewe and the she-goat are merely details of one mitzvah. But when the law does not depend on him, but on his financial state, then in his view it is clear that the different possibilities should be counted as independent mitzvot. It should be noted that in the case of the second Passover too there is no element of choice; the matter depends on the person’s condition at the time of the first Passover—whether he was impure or on a distant journey. Thus the distinction we suggested at the end of the previous chapter appears explicitly in Rabbi Daniel’s own words.

Rabbi Daniel thus raises two distinctions leading to multiple counting: the absence of choice between the possibilities, and different punishments or laws among the manifestations. Rabbi Abraham, in response, argues that neither of the criteria raised by Rabbi Daniel is sufficient on its own to multiply the number of mitzvot being counted, and neither is the difference in laws on its own. Hence the most natural formulation of Rabbi Daniel’s claim would combine the two criteria: only different manifestations of a mitzvah that are characterized by different laws and in addition are not left to human choice would then be counted as separate mitzvot.

Rabbi Abraham, however, does not accept even this combined formulation. In his view it fails under the test of yibbum and halitzah, or the redemption and breaking of the neck of the firstborn donkey. In both pairs there is a human choice between the alternatives, and yet because the law is different, Maimonides counts them as two pairs of independent mitzvot. Of course, Rabbi Abraham is assuming Maimonides’ method. Rabbi Daniel could very well count each of those pairs as a single mitzvah. Below we shall see that Saadia Gaon indeed counts such pairs as single mitzvot.

The proof brought by Maimonides from the talmudic passage in Bekhorot 13a is not a special problem for these approaches. True, the passage there seems to show that yibbum and halitzah are two mitzvot, and likewise redemption and breaking the neck of the firstborn donkey, but that does not necessarily mean that they must be counted as two pairs of mitzvot. We have already seen a number of examples of distinct mitzvot that are nevertheless counted as one. For example, as noted in our essay on root 9, the prohibitions against taking neshekh and tarbit—two forms of interest—are two mitzvot. This emerges from the Talmud at the opening of the chapter Eizehu Neshekh, and this is also the ruling of Maimonides in Mishneh Torah, Laws of Lender and Borrower 4:1. Yet in Sefer HaMitzvot only one mitzvah appears—negative commandment 235. We see that the halakhic determination that there are two mitzvot does not necessarily have to be reflected in the enumeration of the mitzvot. So with respect to these pairs of mitzvot as well, one may say that they are indeed two distinct mitzvot in halakhic terms, but in the count of mitzvot they appear as fine details of a single mitzvah. This seems to be a possible explanation of Rabbi Daniel’s and Saadia Gaon’s approach.

Their View on Causality

Above we noted that according to Maimonides the three pairs are counted as separate mitzvot because, in all three, the relation between them is not one of causation. There is a relation between them—one who performed mitzvah A is exempt from mitzvah B—but not one of causation, meaning that non-performance of mitzvah A is not what causes the obligation of mitzvah B. When the details are linked by a causal relation—B is compensation for A—then even according to Maimonides the two details join into one mitzvah. When the relation lacks an element of causation, then according to him they are two mitzvot.

Rabbi Daniel and Saadia Gaon, by contrast, apparently do not distinguish between these kinds of relation. Whenever there is a relation between two mitzvot, whether causal or not, they regard them as one mitzvah. They are unwilling to distinguish among different kinds of relation between mitzvot. Thus Rabbi Yeruham Fishel Perla writes, in his discussion of this root, about Maimonides’ explanation of the second Passover:

These words are very puzzling to me. The question is certainly a powerful one, and his answer does not heal it and is not at all clear. What does it matter that the second is a festival in its own right and one is liable to karet for it just as for the first? Still, for the purpose of counting the mitzvot, according to what Maimonides laid down here, it is surely only one of the fine details of the mitzvah of the first Passover, and should not be counted as a mitzvah in its own right. For after Scripture obligated the first Passover and fixed its time on the fourteenth of Nisan, it returned and specified concerning this offering that one who at that time was impure or on a distant journey, or in other cases in which he did not perform the first at its time, should perform the second on the fourteenth of Iyyar. But those who performed the first at its proper time can never at all become obligated in the second.

Here he identifies the crux of the dispute. After all, there is still a relation between the first and second Passover even according to Rabbi, so why does Maimonides count them as two mitzvot? Rabbi Yeruham Fishel Perla refuses to recognize the distinction between a causal relation and some other kind of relation, as we explained above in Maimonides’ method.

He then mentions a reasoning similar to the one we ourselves suggested above for distinguishing among the pairs:

What difference is there between this and the sliding-scale offering, which Maimonides included under this root and regarded as fine details of one mitzvah? Indeed, the second Passover is much worse for this purpose than the sliding-scale offering. For with the second Passover it is certainly more fitting to say that it is only one of the fine details of the first Passover, since from the outset the main obligation rests on all Israel to perform specifically the first Passover. Only if some circumstance occurred that prevented a person from performing the first does the Torah say that the time of the Passover commandment has not yet completely passed, and obligate him to perform the Passover on the fourteenth of Iyyar. But there, in the sliding-scale offering, for the rich person the original mitzvah from the outset is only the rich person’s offering, and likewise for the poor and the very poor: for each, the offering that Scripture imposed on him is his mitzvah from the outset, from the first moment of obligation. Therefore it is fitting to say that each is a separate mitzvah in its own right.

He explains that the second Passover comes as a completion of the first, since ideally everyone is commanded to perform the first Passover. But in the sliding-scale offering, each obligation is directed to a particular person. There are not even alternatives one may choose between, and certainly none of them is a completion of the others.

So this dispute among the Rishonim concerns the notion of causality. Those Rishonim do not distinguish between a causal and a non-causal relation within a pair of halakhot, whereas Maimonides does make such a distinction.

Their View on Generalization

There is another important point to stress regarding the dispute between Maimonides and Saadia Gaon and Rabbi Daniel. Rabbi Yeruham Fishel Perla, in discussing Maimonides’ seventh root, explains that one must distinguish between two types of appearance of fine details of mitzvot in the Torah:

It is certainly clear that whenever a mitzvah is written in the Torah in general terms, and afterward Scripture explains in detail all its fine points and laws—even if those fine points and laws are each stated explicitly in separate verses—there is no doubt at all that they are not to be counted in the enumeration of the mitzvot as separate mitzvot. No one disputes this. But there are many particular mitzvot in the Torah, many of them each written in a separate section of its own, and nowhere in the Torah is there any general statement that includes them all together as one, even in a broad way. Yet Maimonides included them under this root and regarded them as fine details of one mitzvah, and decisively ruled that they should be counted only as one mitzvah.

In other words, one must distinguish between a situation in which the Torah itself subsumes the details under one general category—where all agree that only one mitzvah should be counted—and a situation in which the Torah contains no such explicit generalization, where Saadia Gaon disagrees with Maimonides.

This means that everyone accepts the root itself: everyone agrees that fine details of a mitzvah should not be counted separately. The question in dispute is whether we may decide on such a generalization ourselves, or whether only when the Torah itself says so may we infer that these are details of one mitzvah.

Yet toward the end of his remarks he notes that Saadia Gaon and the other Rishonim with him counted three mitzvot in the case of adultery, even though the Torah itself explicitly includes them in one general mitzvah:

At first glance, this is certainly a strong objection against our master the Gaon, Bahag, and those who side with them, for they counted the married priest’s daughter, the married Israelite woman, and the betrothed maiden each as a separate mitzvah. This appears clearly to run against the very foundation of the root before us, since in those three cases we have in the Torah a general mitzvah that includes them all together, and afterward Scripture explained in detail the conditions and fine points, distinguishing between the married Israelite woman who is no longer a virgin, the priest’s daughter, and the betrothed virgin. If so, according to the principle of this root they ought to be counted as one mitzvah, and yet they counted each one as a mitzvah in its own right.

Rabbi Yeruham Fishel Perla relies here on what Maimonides himself already noted, namely that these three cases are explicitly included by the Torah itself in one prohibition, and therefore everyone ought to concede that this is one mitzvah. Maimonides himself wrote earlier, as quoted above:

They explicitly said in Sanhedrin 51b: “All were included in the phrase ‘the adulterer and the adulteress’; Scripture singled out the daughter of Israel for stoning and the priest’s daughter for burning.” Their meaning is that the prohibition concerning a married woman includes everyone of whom Scripture says, “The adulterer and the adulteress shall surely be put to death,” but Scripture differentiated among them in the mode of death, assigning some to burning and some to stoning.

At the beginning of his remarks there, Maimonides brings a verse that includes those three cases under one transgression, adultery, and then even adduces an explicit rabbinic exposition stating exactly that.

So apparently these Rishonim dispute not only our ability to generalize on our own when the Torah does not explicitly do so, but the very principle of the root itself. Yet later Rabbi Yeruham Fishel Perla rejects that conclusion and explains the matter in terms of the change in punishment. We already answered that above and saw that, here, the change in punishment among these offenders should make no difference. He therefore concludes that the root itself is accepted by all, and the dispute concerns only generalization.

He then gives an example of a disputed case:

Consider the various forms of skin afflictions: each kind is written in a separate section of its own, including all the details and fine points of its impurity and purification—baheret on its own, se’et on its own, burns on their own, scalp afflictions on their own, and so on. Nowhere in the Torah is there any general statement that includes them all together. Yet Maimonides regarded them all as the details and fine points of one general mitzvah, and counted them (mitzvah 111) as one mitzvah that includes all the forms of human tzara’at.

He continues similarly with regard to the sliding-scale offering, which also appears in the Torah without an explicit generalization.

He then explains the root of the dispute—and this point is very important for what follows:

But our master the Gaon did not accept this reasoning at all, and his reasoning was well founded. In the enumeration of mitzvot we have only the language of the Torah. Since the Torah contains no single general mitzvah for all the appearances of human skin afflictions, but each of these kinds of affliction was assigned its own separate section in the Torah, there is no basis for saying that they are all merely conditions and fine points of one general mitzvah that is not written anywhere in the Torah. Shall we invent a general mitzvah that was not said to Moses at Sinai and is not written in the Torah, and then say that all these sections are merely the fine details of that general mitzvah which is not written? We therefore have no choice but to say that each of these appearances of human skin afflictions is counted as a mitzvah in its own right, just as they were said at Sinai and written in the Torah.

Saadia Gaon’s view is thus that where the details of a mitzvah appear explicitly in the Torah, and there is no general statement explicitly uniting them into one whole, those details must be counted as independent mitzvot. So there is agreement that fine details of a mitzvah are not counted separately, even when they appear explicitly in the Torah. The dispute concerns whether details that the Torah itself does not explicitly subsume under one whole may nevertheless be regarded as details of a single mitzvah. The crux of the dispute, then, is our ability to generalize the particulars in the Torah into a single whole on our own.

Another Note on Generalization

It seems that the dispute over generalization has deeper roots as well. Rabbi Daniel is an empiricist. That is, he bases himself on observational data—here, observation of the biblical text rather than of the external world, as in the scientific context. His classification is based on what he finds in the Torah itself. If the Torah presents separate mitzvot and does not itself include them under one heading, he does not generalize them on his own. For him those are the empirical facts, and he adheres to them. Maimonides, by contrast, is a rationalist. He works by force of reason and not only by empirical data. Therefore he is prepared to generalize on the basis of reasoning, even where the Torah itself does not do so.

At the beginning of this chapter we saw that Rabbi Daniel argues against Maimonides that fine details of a mitzvah whose laws differ, such as the punishments of the adulteresses, must be counted as separate mitzvot. Maimonides, by contrast, does not believe that a distinction in punishments necessarily indicates a distinction for the purpose of counting the mitzvot.

It seems that this dispute too is connected to the more basic difference between these two approaches. Maimonides is a rationalist, and therefore even when the facts point toward separation, he activates his reasoning and decides on that basis. He does not surrender to bare facts. Rabbi Daniel, by contrast, is an empiricist, and therefore where the Torah itself separates the details and assigns different boundaries to each, he adheres to the data of the biblical text and concludes that if the text distinguishes them, they must be different mitzvot.

Another example is Rabbi Daniel’s question: why do we not count the redemption of the human firstborn, the firstborn of a pure animal, and the firstborn donkey as one mitzvah? After all, they are all firstborns. What difference does it make that their laws differ? This seems very similar to the three adulteresses who receive different punishments even though their matter is one, namely adultery. Here too we see the same attachment to the text, despite the strong intuitive reason to distinguish between those two examples.

Summary: The Two Main Points of Dispute

We thus learn that although there is no dispute over the core of Maimonides’ words in this root—after all, no one suggests counting every fine detail of every mitzvah as an independent mitzvah—there are nevertheless several points that are indeed disputed, among them at least these two central ones:

1. Causality. Should mitzvot built as pairs of alternatives—yibbum and halitzah, redemption and breaking the neck of the firstborn donkey, and the first and second Passover—be counted as single mitzvot, as Saadia Gaon and Rabbi Daniel hold, or as pairs of mitzvot, as Maimonides holds? In light of our explanation above, the dispute may be formulated as follows: does one distinguish between different kinds of relations between mitzvot, causal and non-causal, or does any relation suffice to make them one mitzvah?
2. Generalization. In cases where the Torah itself groups the details under one obligation, everyone agrees that they are not counted separately. But when the “details” are written separately and there is no verse that groups them into one mitzvah, Saadia Gaon and Rabbi Daniel hold that we do not create such a generalization on our own, and therefore we have not one general mitzvah but a collection of separate mitzvot. Maimonides, by contrast, holds that even in such a case it is one mitzvah, and that we make the generalization by force of reason.

In the next chapter we shall offer a brief philosophical discussion as an introduction to understanding the dispute among the Rishonim with which we are dealing.

E. Causality and Induction: Science and Interpretation

Introduction

In the previous chapter we identified the two central disputes between Maimonides and Saadia Gaon and Rabbi Daniel, concerning generalization and causality. We also saw that Rabbi Daniel’s approach, and Rabbi Yeruham Fishel Perla’s explanation of Saadia Gaon’s method, is empiricist—based only on facts that emerge from observation—whereas Maimonides’ approach is rationalist, based on logical and intuitive considerations.

This pair of issues, causality and generalization, immediately evokes the questions raised by the Scottish philosopher David Hume, who also dealt with both and with the relation between them. Indeed, these are the two fundamental issues underlying the dispute between rationalism and empiricism in general philosophy as well. Hume’s discussion did not deal with interpretation, but with science and scientific inquiry. Yet, as we shall see below, there is a clear connection between his arguments and the controversy they generated, and the interpretive issues that concern us here.

This chapter therefore begins with a brief discussion of Hume’s arguments, as a basis for explaining the disputes among the Rishonim described in the previous chapter.

Hume’s Problems: On Generalization, Causality, and the Relation between Them⁵

At the beginning of the modern period, several major scientific breakthroughs took place, and science began its modern path. In the seventeenth century, the British philosopher David Hume raised several doubts about the foundational assumptions of the new empirical science, thereby threatening to undermine philosophically the very basis on which it rested—that is, the justification for the scientific method itself. The two central problems he discussed were the problem of causality and the problem of induction, meaning generalization. Reflection on those problems awakened Immanuel Kant from what he himself called “my dogmatic slumber,” and led him to develop his revolutionary philosophy. To this day these problems, in various forms, divide philosophers of science and generate differing views regarding the role of science and the justification of its methods. We shall now describe briefly, and in a schematic and superficial way because of limited space, the problems and the solutions that have been proposed for them.

The problem of induction is this: Hume asked what grounds our belief that things that have occurred repeatedly until now will continue to occur in the future. Does the fact that all massive objects we have thus far seen tend to fall toward the earth suffice to establish scientifically the claim—that is, the scientific law—that every object with mass must do so, including in the future? More generally, can one infer from a collection of particular facts that we have observed the existence of a general force in nature, such as gravity? Generalization is speculation with no anchoring in the observed facts, and therefore, Hume argued, it is unjustified.

Now, one possible answer to this question might rely on the principle of causality. A reasonable person assumes that the falls of the objects we have observed, like every other natural event, are subject to causality—that is, they did not occur without a cause. What is that cause? We call it the force of attraction exerted on them by the mass of the earth. Hence the natural conclusion is that so long as that mass continues to exist, massive bodies will continue to fall toward it. Thus induction might seem to be grounded in causality.

But Hume went on to argue that this is no real solution to the problem of induction, and here he raised the problem of causality. When I see an object falling toward the earth, I infer that the existence of the earth is the cause of its fall. Likewise, putting a branch into fire causes it to burn, and kicking a ball causes it to fly.

But such causal claims are not empirically grounded. In the phenomena we observed there is not even a hint that placing the branch in the fire was the cause producing its burning. At most one can say that this always occurs after that, meaning that there is a temporal sequence between placing wood in fire and its burning. At most one may perhaps say that the placing is a logically sufficient condition for the burning. But the active relation of causing does not emerge from observation as such. The same applies to every causal relation: observation of a kick to a ball does not show that the ball’s flight is a result caused by the kick. At most we can infer that after kicks, balls fly. The causing itself cannot be seen in any way, neither by the senses nor by instruments.

If so, the problem of induction cannot be solved by assuming causality, because the assumption of causality itself contains speculation similar to that found in generalization. One might perhaps say that this is the same problem from a different angle, as indeed emerges from Kant’s analysis of these problems.

Two Possible Conclusions: Empiricism and Rationalism

Hume’s questions assume an empiricist approach. His assumption is that nothing that does not arise from observation can be valid. He showed that causality and induction are not based on observation, and from this it follows that the general laws of science are not valid.

Hume therefore concludes that causality, in the sense of real causal connection, is a human fiction and has no grip on reality. That is because it lacks an experiential foundation. In his view these are merely inventions of human consciousness, which uses them to organize the world of phenomena. In the world as it is in itself, there is no basis for assuming that causal connections exist, and there is likewise no basis for assuming that the general law we have inferred really describes reality itself. It is merely our way of organizing facts. The only thing we can say about the world itself is the concrete facts we directly observed—for example, that the ball we played with yesterday did indeed fall toward the earth, or flew after being kicked. Generalizations and causal relations are statements about us, not about the world as it is in itself.

Another example is the law of gravitation. The empiricist claims that there is no “gravitational force” in reality, because no one can observe such a thing. There is a law of gravitation, describing the mutual effect of two masses on one another, but not a force that enacts that law. The force is a theoretical concept that is convenient for us to use, but it does not necessarily exist in reality. It is merely an elegant generalization, intended only for convenience.

So far we have spoken of theoretical generalization. By a similar line of thought Hume reaches a parallel conclusion regarding causality. He claims that causality is nothing more than a logical-temporal relation between event A and event B. Event A is a logically sufficient condition, prior in time, for event B. The claim that event A “caused” the occurrence of B is unfounded, and therefore we cannot infer it. A scientific theory may state: if A occurs, B will occur. But it cannot claim: because A occurred, B will occur.

But what if someone comes and says that he inferred the general law—performed the generalization—or the existence of a causal connection, from a priori reasoning without observation? Hume, as an empiricist, rejects this out of hand. Hence the vacuum that accepts as valid neither claims of causality nor generalizations, but only directly observed particular facts, is the result of Humean empiricism.⁶ We see that precisely his very high demand for empirical certainty for every claim leads him to an almost sweeping skepticism.⁷

How, then, can one answer Hume’s objections? Only by giving up his extreme empiricism. If we are willing to accept that there is a relation of causation between events even without directly observing that causation, then we can answer Hume by saying that although observation cannot serve as a basis for universal claims or for claims of causal relation, we nevertheless accept them on rationalist rather than empirical grounds. Rationalism is the only alternative to the empiricist vacuum.⁸ Immanuel Kant was the one who presented the rationalist position and thereby answered Hume’s objections. His arguments are not satisfactory, however; see Shtei Agalot ve-Kadur Poreah, especially the third section, and we shall return to this below.

For what follows, we should note that these determinations seem at first glance to lie entirely within the sphere of the philosophy of science. On the face of it, they do not really affect the actual course of science and scientific research. Science could adopt this definition of causality and continue its activity as before. One would merely say: we discover prior sufficient conditions for occurrences and phenomena, not their “causes.” Scientific activity could continue in exactly the same way as before Hume, even if the world of philosophy of science were to adopt his conclusions. At first sight, then, these approaches seem to matter only on the philosophical plane, not on the practical-scientific one. We shall see below that this is not quite accurate.

Science and Interpretation

The picture we described above concerns foundational questions in the philosophy of science. We saw that there are two basic approaches to the status of reason as against experience and observation: rationalism accepts generalizations and conclusions about causal relations even though they have no direct empirical basis, whereas empiricism refuses to do so.

In the world of interpretation there are very similar disputes, although they arose later and are not usually tied directly to Hume’s problems. These disputes concern the interpretation of literary texts and works of art, and later also of legal texts. Such questions constitute the field known as hermeneutics, the theory of interpretation.

Here too questions arise about the validity of generalizations and interpretive conclusions. They are formulated in terms of the possibility of reaching the author’s or creator’s intention, or the “true” meaning of the work or text. The basic claim is that all the interpreter has before him is the text or artistic object itself, and from that he tries to reach the author’s or creator’s intentions by means of generalization and by finding connections between different parts of the observed and interpreted object. But such interpretations can never be derived in a purely empirical way from the text; they always contain an element of the interpreter’s own reasoning and thought. Hence criticisms arise concerning the validity of such generalizations.⁹

In hermeneutics too there are two basic approaches. The empiricist approach adheres only to what emerges from the text itself, without speculative generalizations and connections. The more extreme versions of these approaches reached the conclusion, in the twentieth century, that interpretation has no meaning with respect to any “truth” that lies outside the interpreter himself. Generalizations are nothing more than statements of and about the interpreter, not about the work. In hermeneutics this position is known as deconstruction. Here too extreme empiricist demands lead to a vacuum. Opposed to them stand more “naive” approaches, whose common denominator is a degree of rationalism—that is, a willingness to accept generalizations and conclusions on the basis of a priori reasoning, even if they are not strictly derived from the text. According to the proponents of such views, we not only in fact accept such conclusions—as deconstructionists do as well—but we also believe that they are valid in some sense, whether with respect to the work itself or even with respect to the author’s intention.

We can now return and see that the disputes we described between Saadia Gaon and Rabbi Daniel, on the one hand, and Maimonides, on the other, revolve around these very axes.

Returning to the Dispute between Maimonides and Saadia Gaon

In the previous chapter we saw that there are two principled disputes between Maimonides and Saadia Gaon and Rabbi Daniel. The first concerns the main matter of the root itself: can one generalize several mitzvot that appear separately in Scripture and understand them as branches of one overarching principle? Maimonides said yes; Saadia Gaon and Rabbi Daniel said no. The second dispute concerned mitzvot that appear to depend on one another, such as the second Passover, which in its plain sense is compensation for the first Passover. Seemingly, then, failure to bring the first Passover is the cause of the obligation to bring the second.

In light of what we said above, we can see that these two disputes stem from one root. Maimonides’ confidence in the possibility of generalizing a collection of particular mitzvot that appear separately in Scripture expresses faith in the principle of induction. In the terms of the philosophical introduction above, Maimonides is a rationalist who trusts the generalizing intuition and accepts it despite its lack of direct empirical grounding.

Saadia Gaon and Rabbi Daniel, by contrast, are empiricists, and therefore they are unwilling to accept generalizations and causal connections that do not arise from direct observation. As we saw, this is precisely their claim against Maimonides: how can he make generalizations that have no anchor in the text? When the text itself includes the particulars under one heading, they too agree that these are parts of one mitzvah. But without such an explicit generalization, mitzvot that appear separately in Scripture will be interpreted by them as independent mitzvot. They adhere to the observational facts with empiricist devotion.

One can see in Maimonides’ own words a remark reflecting that this is indeed how he understood the possible dispute over what he says in this root:

Many have erred in this, counting everything they found written without reflecting on the root of the mitzvah, as opposed to its fine details or its conditions.

In this sentence Maimonides diagnoses the problem of those who erred in this root: they are unwilling to “reflect,” that is, to understand intellectually the roots of the mitzvah, and thereby to see that these are the same roots found in other mitzvot. What prevents confidence in generalization is the unwillingness to examine the root of the mitzvah, since those roots are not a product of observation of the halakhic-biblical facts.¹⁰ Reflection here means rational thinking—that is, rationalism. Empiricists oppose such reflection as a tool of knowledge.

If we are correct about the first dispute, which concerns generalization, it seems that the second dispute, which concerns halakhic causality, stems from the same source. Maimonides, the intuitionist, is prepared to believe in a causing cause, and therefore he distinguishes between a logical condition for the occurrence of some event and the cause of that event. Maimonides, like the scientific rationalist, distinguishes between the statement, “If A, then B”—a logical condition—and the statement, “Because A, therefore B”—a relation of causation. Saadia Gaon and Rabbi Daniel, by contrast, remain attached to Hume’s empiricist approach and identify logical conditioning with causal producing, because causal connection is not a product of observation but of thought.

For them, the fact that the second Passover is brought only by one who did not bring the first means that non-performance of the first is the “cause” of the obligation to bring the second. In their view, cause is nothing but logical connection. Maimonides, by contrast, argues that it is indeed true that only one who did not bring the first Passover incurs the obligation to bring the second, but this is a logical condition and must not be identified with an active cause. According to Rabbi, whose view is the halakha, the second Passover is indeed brought only by one who did not bring the first, but that non-performance is not the cause of the obligation, only the logical condition for its taking effect. The obligation of the second Passover is an independent obligation that falls on everyone, except that performance of the first exempts one from it. The Sages, by contrast, hold that there really is a causal relation between the two mitzvot, but the halakha does not follow them.

Rabbi Yeruham Fishel Perla’s own formulation of his objection to Maimonides makes clear that this is indeed the point at issue:

These words—concerning the dispute between Rabbi and the Rabbis over the second Passover—are very puzzling to me. The question is certainly a powerful one, and his answer does not heal it and is not at all clear. What does it matter that the second is a festival in its own right and that one is liable to karet for it just as for the first? Still, for the purpose of counting the mitzvot, according to what Maimonides established here, it is only one of the fine details of the mitzvah of the first Passover, and should not be counted as a mitzvah in its own right. For after Scripture obligated the first Passover and fixed its time on the fourteenth of Nisan, it returned and specified regarding this offering that one who at that time was impure or on a distant journey, or in other cases in which he did not perform the first at its time, should perform the second on the fourteenth of Iyyar. But those who performed the first at its time can never become obligated in the second. What difference is there between this and the sliding-scale offering, which Maimonides included here under this root and regarded as fine details of one mitzvah?…

We see that the heart of Rabbi Yeruham Fishel Perla’s claim against Maimonides is the fact that one who performed the first at its proper time can never become obligated in the second. In other words, he treats a logical condition as equivalent to causation, and therefore as parallel to the sliding-scale offering. For him this objection admits of no answer, because in his view there is no distinction at all between a logical condition and causal production. Maimonides, by contrast, holds that while it is true that performing the first Passover prevents the obligation of the second from taking effect, this still does not show a relation of causation—that non-performance of the first is the cause of the obligation of the second.

The two cases parallel to the second Passover, as Rabbi Yeruham Fishel Perla himself notes in explaining Maimonides, are the mitzvot of redeeming and breaking the neck of the firstborn donkey, and yibbum and halitzah. There too the situation is similar. Maimonides holds that these are two mitzvot because there is no relation of causation between them. Failure to redeem does not cause the obligation of breaking the neck; it is only a negative logical condition for it. Failure to perform yibbum is likewise not the cause of the obligation of halitzah, but only its logical condition.

The remaining disputes between Rabbi Daniel and Maimonides, as they appear in the exchange of letters between him and Rabbi Abraham son of Maimonides, are similarly derived from the principled dispute between Maimonides and Rabbi Daniel as described here: a dispute between interpretive intuitionism or rationalism and interpretive empiricism. This is not the place to elaborate.

These matters join what we saw in the introductory essay, where we noted that Maimonides holds a rationalist position and at times imposes a priori logic upon the halakhic sources. Nahmanides, by contrast, usually protests against this and adopts a more empiricist approach, one more tightly attached to the facts in the sources of halakha.

An Example of Different Levels of Connection between Events: “It Began with Negligence and Ended in an Accident”

Our discussion so far implies that according to Maimonides, even according to Rabbi, whose view is the halakha, if there were two mitzvot linked by a causal relation and not merely by a logical condition, they would be counted as one mitzvah. This is the case with the first and second Passover according to the Sages. In the three examples we discussed, however, the relation is logical rather than causal, according to Rabbi, and therefore they are counted as two mitzvot. Thus Maimonides distinguishes here between logical relation and causal relation, just as the scientific rationalist does. Saadia Gaon and Rabbi Daniel disagree and do not distinguish between the two. For them, logical relation and causal relation are equivalent, exactly as the empiricists, such as David Hume, hold in the scientific context.

An example in halakha of a logical condition that is not an active cause may be taken from the talmudic sugya of “it began with negligence and ended in an accident.” The description here will be schematic and incomplete, only for purposes of illustration. The Babylonian Talmud, Bava Metzia 42a, discusses a bailee who hid a deposit in a forest hut used by hunters. Such a place is regarded as protected against theft, since thieves are not expected to arrive precisely there and guess that money is hidden there. But it is not protected against fire, because if a fire were to break out in the forest, the hidden item might burn. In the end, contrary to all expectation, thieves came and stole the deposit from the hut in the forest. This is called “it began with negligence”—because the bailee was negligent with respect to the possibility of fire in the forest—and “ended in an accident”—because what ultimately happened was theft, an event he was not expected to foresee. The amoraim dispute whether in such a case the bailee must pay the owner.

The Talmud in Bava Metzia 36b brings another case. A bailee left a barn door open, and the animal entrusted to him went out to the meadow and died there. Here too the situation is described as “it began with negligence and ended in an accident,” because leaving the door open is negligence with respect to theft, but the end was accidental, since the death was unrelated to the open door; it died naturally. This case is apparently lighter from the bailee’s point of view, because there was no connection at all between the negligence and the accident. The Talmud says: “What difference does the Angel of Death make whether here or there?” In other words, the assessment is that the animal would have died even if it had remained in the barn. In such a case there is no relation whatever between the negligence, the open door, and the accident, the death of the animal.

Rif’s view there is that even in such a case Abaye obligates the bailee to pay. Most of the other Rishonim, however, do not think so. They hold that if there is no connection between the negligence and the accident, everyone agrees that the bailee is exempt.¹¹

We thus find three kinds of relation between negligence and the damage suffered by the deposit:

1. The damage is a direct result of the negligence. For example, the barn door was left open and the animal was stolen. This is defined in halakha as plain negligence on the part of the bailee.
2. The damage is related to the negligence, but not directly caused by it. For example, the money was hidden in the forest and thieves reached it there. This is the case called in halakha “it began with negligence and ended in an accident,” and on it the amoraim disagree.
3. The damage is entirely unrelated to the negligence. For example, the barn door was left open and the animal went out and died naturally in the meadow. According to halakha, everyone agrees that this is a complete accident and the bailee is exempt.

This raises the question how the second case is to be classified. In what way is it different from the others? Why is it not identical to the first case of plain negligence? After all, there too there was negligence, and because of it the accident occurred. If so, it is not clear why the amoraim dispute this case. On the other hand, if we say that the negligence never materialized at all, and what happened in the end was a complete accident, since the negligence did not cause it, then how is this different from the third case, where everyone exempts?

One who obligates payment even in the third case—Abaye according to Rif—apparently grounds the liability in the negligence itself.¹² According to that approach, the bailee’s obligation to pay does not derive from the loss of the animal, but from the fact that the bailee was negligent. If the animal had not been lost, he would have fulfilled that obligation simply by returning it. But once the animal died, he must pay money because of his negligence. Therefore the bailee would be liable even when there is no relation at all between the negligence and the accident, and he is in no sense responsible for the accident itself.

On that view it is obvious why one should obligate payment in the second case as well. Even if we do not treat the case as one in which the negligence caused the accident, he would still be liable because of the negligence itself. But halakha does not follow Abaye in this way, and so it is clear that the negligence as such does not obligate the bailee to pay. He pays for the loss of the animal, not for the negligence. We therefore return to our question: why should he be liable in the second case? Is it identical to the first case? And if it is, why do the amoraim dispute it?

It seems that the definition of the second case contains precisely the distinction made above between a logical condition and an active cause. In the case of “it began with negligence and ended in an accident,” there is a logical condition between the negligence and the accident, but not a relation of causal production. Hiding the deposit in the forest did not halakhically cause the theft, because even after it was hidden there the deposit was still regarded by halakha as guarded against theft, and therefore the bailee is not responsible for theft. From a legal point of view, his negligence did not “cause” the theft. It is indeed true that had he not hidden it in the forest—the very act that was negligence with respect to the possibility of fire—the theft would not have occurred. The hiding is a logical condition for the occurrence of the theft, but not its active cause from a halakhic point of view. Put differently: it is a negative condition, not a positive cause. Non-hiding would have prevented the theft, but that is not the same as saying that the hiding caused it. This is exactly the same distinction we made above between the two conceptions of the relation between the first and second Passover.

The dispute concerning “it began with negligence and ended in an accident” is a dispute over whether a logical connection that is not causal suffices to obligate the bailee to pay. That is the difference between the first case and the second: in the first there is a causal relation between the negligence and the accident, whereas in the second the relation is only logical and not causal. Again, we are speaking here of halakhic-legal causality, not physical causality.

A General Look at the Different Approaches

Before concluding this chapter, we want to return to a point already mentioned in passing above. We saw that Maimonides, Nahmanides, and Saadia Gaon appear to hold consistent positions regarding the level of detail they grant to families of mitzvot in their respective enumerations. Nahmanides is the most “economical”: for him ritual impurity is not counted as a mitzvah at all, all sacrifices are counted as one mitzvah, and all punishments are one mitzvah. Saadia Gaon, by contrast, is the most detailed: the impurities are counted as mitzvot, the sacrifices are all counted, there are eleven kinds of tzara’at, and every punishment is counted separately. Maimonides stands between them and adopts an intermediate method: he counts each type of impurity as a mitzvah—for example, tzara’at is one mitzvah—each type of offering as a mitzvah, and likewise each type of punishment.

Such a picture is unlikely to be accidental. It seems that here too each thinker remains faithful to the kind of position described above. Saadia Gaon remains close to the text and therefore refuses to make any generalization. Nahmanides generalizes completely and says that if one is already generalizing, one should do so consistently and all the way. Maimonides follows a middle path: he does not detail everything, meaning that he does engage in some generalization, but his generalization stops halfway. He does not subsume all the different forms of impurity and all the offerings under one single whole, and that requires explanation.

Of course every generalization must decide where to stop. One may generalize all mitzvot into one mitzvah and say that they are all clauses of the general principle of serving God. One may group all positive commandments under love of God and all prohibitions under fear of God, as seen in the quotation from Rabbi Abraham son of Maimonides in our essay on the fourth root.

Maimonides, as an interpretive rationalist, takes upon himself the interpretive freedom to define the boundary of classification into families according to his own understanding. Saadia Gaon, with his empiricist method, adheres to the text according to rigid principles that determine that every mitzvah written separately is counted as a separate mitzvah. But Nahmanides too, although he appears to stand at the opposite pole, adopts a simple approach that gives little status to the interpreter’s intuition. Therefore he chooses to go all the way rather than stop midway, which is more speculative and looks somewhat arbitrary. In that sense Nahmanides, who is usually more empiricist in orientation, is not as far from that pole as one might think at first glance.

The Relation to the Views of the Rishonim in Root 2

At first glance, the most extreme expression of these general approaches seems to appear specifically in the second root. There we saw Maimonides adhering zealously to the text and ruling that anything derived by interpretation is not considered written explicitly in the text, but rather an extension of the text’s content. specifically Saadia Gaon, by contrast, like all the other Rishonim, is not strict there about adhering to the text, and rules that what emerges from interpretive derivation is also considered written in the text. These positions seem opposite to what one would expect in light of what was described in the present essay.

But the contradiction is only apparent. Maimonides’ position in root 2 does not deny interpretation or rabbinic derivation; it only defines their boundaries and the status of their results. As we explained there, Maimonides argues that analogical derivation by the hermeneutical rules is not interpretation of the written text, but an extension of the written text. We also saw there that Maimonides himself distinguishes between plain interpretation of the text, which counts as biblical law, and extension by means of the hermeneutical rules through which the Torah is expounded, which is not interpretation of the text, and therefore its results are not treated as biblical law.

Maimonides does not doubt the validity of laws learned through such derivation. He only determines that their formal status is lower, that of rabbinic law. He says this explicitly:

Perhaps you may think that I refrain from counting them because they are not true. Whether a law derived by one of those interpretive measures is true or not is not the reason. The reason is that whatever a person derives are branches of the roots that were explicitly said to Moses at Sinai, and those roots are the 613 mitzvot. Even if Moses himself were the one to derive them, they are not fit to be counted.

In our essay there we elaborated on the meaning of this claim, and this is not the place to repeat it.

In any case, if what we are saying here is correct, then Maimonides’ words there do not contradict his position here. There is no skepticism there regarding the results of interpretation. Hence even in root 2 Maimonides gives full credit to human derivation and interpretation of the Torah. If so, there too he expresses a rationalist position.¹³ The question of the formal halakhic status of laws derived by interpretation is another issue and does not bear on the rationalist-empiricist dispute.

Appendix: A Decisive Argument in Favor of Rationalism

Introduction

As we have seen, from the problems of induction and causality Hume concluded that scientific theory and general scientific law are nothing more than our own fictions, not claims about the world itself. In more recent forms, philosophers of science deal with questions of confirmation and refutation of scientific theories, and with criteria for choosing among theories. Yet many of the problems in these areas are only different reflections of the Humean problems.

Empiricism has led many philosophers of science to positions that Ze’ev Bechler¹⁴ calls “actualism”: belief only in the actual, meaning what is present before our eyes. Actualism is a consequence of empiricism, which affirms the exclusivity of experience. Hence anything that is not directly and purely logically derived from experience is not acceptable as a claim about the world.

The more “naive” approach, which treats the laws and theories of science as claims about the world, reflects rationalism. A rationalist outlook is willing to regard conclusions that are not logically derived from directly observed facts as conclusions about the world. In Bechler’s terminology, such approaches are called “informativism.” They believe that theories contain information about the world beyond the specific facts on which they are based.

Thus the empiricist-rationalist dispute on the general philosophical plane is reflected in practice by the actualist-informativist dispute on the scientific plane. Extreme empiricism leads to actualism; rationalism leads to informativism. In what follows we shall identify these two levels and will not distinguish between empiricism and actualism, or between rationalism and informativism.

But the question remains: where does the ability to know things not learned from experience really come from? Hume’s questions are excellent questions, and some answer is required in order to ground a rational rationalism.¹⁵

In this appendix we shall try to propose such a basis, though a more detailed description appears in the book Et Asher Yeshno ve-Asher Einenu. We shall offer a statistical proof for rationalism, though not a full philosophical grounding for it. Such a grounding is described in Shtei Agalot ve-Kadur Poreah and its sequels.

The Actualist-Informativist Conflict

As noted, actualism is the view that scientific laws and scientific theories are not really claims about reality, but about the scientist or the scientific community. According to actualism, a theory is nothing more than a convenient and useful arrangement of the total body of scientific facts in the relevant field. On this approach, the added value that a theory has beyond the collection of particular empirically observed facts does not contain any information about the world. The theoretical entities are therefore merely useful fictions that serve us within the language science develops in order to organize the known facts. Actualism sees a scientific theory as nothing more than the set of particular empirically known facts included within it.

Informativism, by contrast, is the approach—some would call it naive—that sees science as a process of progress and accumulation of knowledge about the world. According to this approach, scientific theory makes claims about the world itself. Its proponents hold that theoretical entities may exist, though not necessarily. There may be erroneous theories, or phenomenological theories that do not purport to make claims about the world but merely offer a convenient description of a set of facts defining a scientific field. Informativism regards scientific theory as a claim about the world, containing empirical content beyond the specific empirical facts directly known to us by observation, which form the basis from which the theory arose.

This dispute also affects one’s understanding of the role and status of experiment and its results. According to actualism, scientific experiment is not a means of progressing toward a theory that more fully corresponds to reality, but a means of gathering one more scientific fact belonging to the field, which the builder of the theory will have to take into account and include in his fictional structure. A successful experiment is merely confirmation that the fictional language currently used by the scientific community does not yet need revision. For actualists, the failure of an experiment is not a refutation of a claim about the world, but the addition of one more fragment of information that forces us to change our language, and sometimes our theoretical entities as well, or to construct a different theory so that it can include this information too.

According to informativism, by contrast, the theory makes claims about the world, and therefore the scientific experiment is a testing stone for the theory’s validity. If the experiment succeeds, this confirms the claim that the theory does in fact correctly describe the world. If the experiment fails, then the theory has been refuted. In that case it can no longer serve us or provide an adequate description of the world, and a different theory must be sought that will fit the entire body of facts, including the latest one.

This schematic description includes under each of its two wings many shades and sub-shades of different positions in the philosophy of science, but it will suffice for our purposes.

Is This Dispute about an Empirical Question?

These two approaches understand the world, and especially science, differently. Actualism, the result of empiricism, sees the world as a collection of particular facts. Laws are subjective, or inter-subjective, constructions carried out within the scientific community, but certainly not descriptions of the world. Even if one were to assume that in principle there are such general laws in reality itself, we have no way of discovering them by empirical means. Empirical observation enables us to discern only particular facts, not general laws. Informativism, the result of rationalism, by contrast, sees particular facts as diverse expressions of general laws of nature. Science aims to approach as closely as possible a full description of those laws, which constitute a description of the world itself.

It follows from all this that the dispute is not merely philosophical in the narrow sense; it concerns the factual reality outside us.

We must now ask whether there is an empirical way to decide such a factual question. It is usually assumed that there is not. At first sight, both approaches seem to belong wholly to the theoretical-philosophical realm and not to the empirical-scientific realm. They deal only with meta-science and with the meaning of the scientific process, not with its content and method. Earlier we already noted that these conceptions seem to have no effect on the actual conduct of scientific research.

Put from another angle: on the face of it there seems to be no practical difference between the two approaches, and both describe the scientific process in exactly the same way. Both the actualist and the informativist say that science should generalize the facts known to it and do so by means of theoretical entities and a theoretical structure that unites them into a coherent whole, and then test itself by performing experiments that examine the theory’s predictions. If the experiment succeeds, the structure remains in place; if it fails, we are forced to replace the theory.¹⁶ The difference between these two approaches seems to concern only the meaning of this process, not its form or characteristics.

A good example of this is the criterion of simplicity and generality in theory choice. It is usually accepted that the simplest and most elegant generalization is the correct one.¹⁷ Some see this as the criterion of the most general theory—the one that explains the greatest number of particulars in the most economical way—and therefore the most efficient and elegant one.¹⁸

But it is obvious that the fact that a theory is the simplest possible is no guarantee of its empirical validity. Why should we assume that simplicity in the terms of our thought is a fitting measure for the way reality itself behaves? The actualist therefore says that simplicity is indeed a relevant criterion for adopting a theory within the scientific community, but only because simplicity guarantees that the theory will be efficient and useful, even if not true; and usefulness is precisely what the actualist asks of a scientific theory. The informativist, by contrast, sees the criterion of simplicity as a guarantee of truth, since for him the theory describes the world and not merely the way scientists think about it. And here the empiricist question arises once again: what is the justification for such a “mystical” notion?

Thus both approaches use the same methods, and even the same criteria for choosing among alternative theories, such as simplicity. Hence it seems that there is no practical difference between them, and the questions over which they disagree lie only in the philosophical sphere.

It is therefore unsurprising that these two approaches have continued to clash throughout history, as Bechler describes, without any clear resolution. The temporary swings of the pendulum in this dispute are the result of intellectual fashions more than of arguments, and certainly not of experiments. The usual conclusion is therefore that the decision between these two positions is not subject to any empirical test. It is not surprising that even Bechler, throughout his entire book, offers no argument or test that would decide in favor of informativism and against the actualism he so despises.

The Reasons for the Dispute

We have seen that the actualist-informativist dispute concerns reality, and that its roots lie in the philosophical dispute between empiricism and rationalism. We also noted that Hume’s arguments are indeed strong arguments, and as far as we know history has not provided convincing explanations that could philosophically justify rationalist informativism.

It is fairly clear that a large majority of scientists—certainly among those personally known to us—adhere to the more intuitive informativist approach. They see science as discovering reality rather than creating detached theoretical constructions. A considerable portion of philosophers of science, by contrast, tend to one degree or another specifically toward the actualist direction. What leads these thinkers toward a position so far from ordinary intuition? If there are in fact no empirical facts that oppose the informativist intuition, then why turn away from it? It seems that the reason for adopting actualism indeed does not lie in the factual realm but in the philosophical one. There is a philosophical difficulty that accompanies informativism, and because of its philosophical character, most scientists are probably not even aware of it. This difficulty is concentrated in the pair of problems raised by David Hume and in their later transformations.

Kant, who tried to cope with the Humean difficulty, recast those two problems as what he called the question of the synthetic a priori. The explanation he proposed is discussed at length in the first two books of the quartet, where one can see that it provides no real answer to Hume’s claims.

As far as we know, the history of philosophy offers no alternative to Kant’s answer. For our purposes, that means that there is no other philosophical foundation for informativism. There is no explanation or convincing basis for the conception that regards theoretical entities as real entities, and theory as a set of claims about the world.¹⁹ Rationalism thus seems trapped in a theoretical impasse, a road with no exit.

A Statistical Proof of Informativism

Here we wish to argue that the actualist-informativist question is in fact empirically decidable. We shall offer a statistical consideration that proves informativism.

Let us take Newton’s second law as an example. It states that there is a direct relation between the force acting on a body, F, and the acceleration it develops, a; in other words, F = m × a. The proportionality constant is the mass of the body, m.

Now suppose we want to test the relation between force and acceleration experimentally. We perform five experiments on a body of mass m and measure its acceleration for five different values of force acting upon it—say, forces 1 through 5. The results of the experiment are represented as five small open circles on a graph.

Insert graph here (attached in the appendix file).

The five results lie on a straight line, so the natural generalization—the elegant and convenient one—is to draw the solid line whose slope equals the mass of the measured body. Accordingly, in such a case the scientific community decides that the relation between force and acceleration is linear, with the mass as the proportionality constant. The law of nature we have found, or confirmed, is a direct proportionality between force and acceleration.

But it is a simple mathematical fact that there are infinitely many other ways of generalizing these five results, all of which fit all five. In other words, there is an infinite number of curves that can pass through those five particular experimentally measured facts, that is, the five given points on the graph. The number of possibilities is not merely very large, but infinite, indeed uncountably infinite. Just as an illustration, one such possibility is drawn as a dashed line on the graph above, and of course there are infinitely many more.²⁰

How are we to choose among these different possibilities? What is the result of the experiment—or, in other words, what is the correct law? As noted, science will always choose the simplest among them, namely the straight line. We already saw that the actualist explains this by saying that it is simply the most convenient option, and we adopt it until it is refuted. In his eyes this is not a claim about the true relation between force and acceleration, but only an efficient arrangement of the five particular facts already known to us. The informativist, by contrast, will say that the straight line is the correct possibility, one that probably also describes the world itself appropriately. This is the correct law yielded by the experiment.

Unlike the actualist, he will also tend to think that a future experiment will confirm this law. Of course, the informativist too will agree that a future experiment could refute the thesis, and therefore he sees it as a conditional fact that depends on future empirical results.

As noted, whether actualist or informativist, the next stage of the inquiry will be to perform another experiment, at another force value, and measure the acceleration there as well—say points 6 and 7 on the graph. If the experiment “succeeds,” meaning that the acceleration at those points also lies on the straight line, the theory remains in place—conditionally true according to the informativist, or convenient and useful according to the actualist. If the experiment fails, meaning that the result does not lie on the straight line, the theory is replaced. The new law will be the graph of the simplest curve that passes through the six empirical facts now known to us, the original five plus the last measurement.

Up to this point the procedure seems identical according to both approaches, and therefore there seems to be no methodological disagreement. But now let us ask a question that is empirical, though not itself straightforwardly scientific: what is the a priori probability that the next result, the sixth, will in fact fall on the present graph, the straight line? Here, surprisingly, the answer depends on whether we start from the actualist or the informativist point of view.

Let us begin with the actualist perspective. As noted, there are infinitely many possible generalizations of the five given points, and the straight line is only one curve chosen arbitrarily, according to actualism, from among them all. There are also infinitely many possible results for the future experiment; all values are a priori possible. Hence the chance that the next result will also fall on the straight line is exactly zero, inversely proportional to the number of possibilities.

One must remember that according to the actualist, the five known points are of no help at all in identifying the general law of nature or the “correct” curve. The curve conveniently describes only the results already measured, and says nothing about the future. The actualist regards this as a tentative generalization until the next experiment. The different curves connecting the five known points yield different predictions for the future experiment; see the dashed and solid lines on the graph. According to the actualist, all such curves are in principle equally possible, and their chances are equal. He chooses the straight line only because of its simplicity. Thus, in his view, the five known results give us no clue whatsoever about the correct curve, and therefore no clue about the result of the next experiment either.

Even if we insist that every future result must lie on some graph admitting a continuous and respectable mathematical description—an assumption totally unreasonable from an actualist point of view—the number of possible results is still infinite. One can see this in the following way. Choose an arbitrary value of acceleration and mark it as some point above or below the measured force value. Now connect that point to the five known points, as if all six results had been obtained in an experiment. True, there are infinitely many ways to connect these six results, just as in the case of five, but we can choose one of them—for example, the simplest. The resulting curve of course coincides with one of the possible generalizations of the five original experimental results, while also passing through the hypothetical sixth result. This can be done for every chosen value of acceleration at point 6.

The conclusion is that, a priori, a future experiment measuring acceleration at the sixth force value—point 6 or 7—can yield any value whatever. In the absence of information about the future result, we assign equal probability to all these possibilities. Therefore the chance that the sixth value will be exactly the value predicted by the straight line is precisely zero: one divided by the number of possibilities.

The informativist, by contrast, sees the straight-line generalization as the preferred one. Not necessary, since a future experiment may refute it, but certainly the best candidate yielded by the first five experiments. He sees it as describing actual reality, not merely as an efficient and convenient tool for arranging the five facts already in hand. In his eyes, the straight line is a proposed description of reality as it has appeared to us so far. Therefore he will not be surprised to discover that the next experiment, the sixth, yields the predicted result and also falls on the straight line.

The point is that the statistical consideration from the informativist perspective is different. For informativism, the infinitely many possible outcomes—the different curves that pass through the points—are not equivalent to one another, even a priori. Therefore the statistical weight of each is not equal to that of the others. The simple possibility is preferred, that is, more correct, because for informativism simplicity is a claim about the world. The simple generalization is chosen because it is truer, not merely because it is more convenient. Since it is not chosen arbitrarily, the informativist does not assign zero probability to the success of the next experiment.

We should note that we have still not justified this strange position, but for the moment we are treating it as a hypothesis to be empirically tested against the actualist hypothesis. The philosophical justification of this puzzling informativist assumption will be discussed below.

So far we have described a statistical consideration, but we have not yet indicated its empirical side. How does one empirically test and decide between actualism and informativism? The success or failure of any one particular experiment poses no problem for either side. After all, some result must emerge in the experiment even according to the actualist, and the probability of any particular result is zero, as in every case of a continuous range of equally likely possibilities.

To decide the issue, let us ask: is it really true that, statistically, in the history of science up to the present, the number of successful experimental results testing theoretical hypotheses is very small, with statistical weight zero? Is it really true that science almost never succeeds in conducting an experiment that fits its theoretical predictions? If that were so, then even in the twenty-first century we would still be in total scientific darkness. Every scientific generalization would be refuted by every experiment performed to test it. After all, there is no a priori chance that a generalization chosen by us arbitrarily, solely because of its simplicity and convenience, will also survive the next empirical test. The consequence of actualism should therefore have been that science would never have managed to formulate even a single law of nature that stood up under any empirical test, or a single scientific language capable of fitting any body of facts without changing after each and every experiment. According to actualism, almost all experiments in the history of science should have failed; the number of successes should have statistical weight zero.

From such a perspective we would not be allowed to get into a car or an airplane, because the experiments on which the laws of physics underlying those technologies are based, and the experiments of the technology itself, would have no foundation. There is no chance that the generalizations produced by those experiments will withstand the next test we are about to perform now—namely, the flight. This is just another consequence of Hume’s problem of induction. According to actualism, the airplane was built on the basis of generalizations which, apart from their theoretical simplicity, have nothing whatever to do with actual reality.

But the historical fact is that there is a non-zero percentage of experiments that do succeed in confirming the theories they test. Not all experiments succeed, but the statistical weight of successful experiments is certainly not zero. This solid fact constitutes a statistical proof against actualism. From an actualist point of view there should be no chance of seeing a successful experiment, not even one, in any scientific field.

In sum: the fact that not all scientific experiments fail, and that there are a number of scientific theories that do stand up under some empirical tests, is itself a clear empirical-statistical proof against actualism. Of course many experiments do fail. But even without attempting a statistical estimate of how many such experiments there are—which is obviously a very complex question—it is clear that the proportion of successful ones among all experiments is not zero. It is enough for our purposes that science genuinely progresses, meaning that theories gradually recover and fit more empirical details, rather than constantly being replaced without any order or progress. For the proof offered here, that is sufficient.

With this, actualism ceases to be a live philosophical alternative. This decision is empirical, and as such it ought to be accepted by empiricists such as Hume. It is a mistake to think that this is merely a matter of philosophical interpretation that cannot be decided by scientific tools.

The Philosophical Justification of Informativism

Even after we have empirically proved the informativist position, the philosophical difficulty noted above still remains. How can we explain the fact that a priori generalizations, made in what appears to be an arbitrary fashion—that is, selecting one generalization out of infinitely many possible forms—do in fact succeed in predicting future experimental results with a significance different from zero? The particular empirical facts gathered by direct observation—in the example above, the first five measurements—cannot themselves justify the generalization we chose. There are countless other generalizations that fit the same body of facts, such as the dashed line on the graph, and we reject them for a priori, not empirical, reasons. So how are we to explain the fact that our generalization, which has no empirical basis, survives future experiment?

This is in fact a mirror image of the Humean-Kantian problem of the synthetic a priori: how can we make general or causal claims about the world by means that are not learned from observation or experiment? But now we are already standing before a fact, not merely before a rationalist aspiration. As we saw, our ability to make justified generalizations, though never absolutely certain ones, is a statistical fact and not merely a wishful hope. We empirically and unmistakably observe that our capacity to generalize withstands testing. In other words, we have some human ability to penetrate through the facts we observed and find the more correct general theory. This is not a shot in the dark, but a real human capacity.

If so, one can no longer ignore the fact that we possess such a capacity. Hume’s question—how do we know that our generalization is correct?—is answered here by the discovery that we do in fact have such a capacity. That is a fact, and even if we do not understand it, we cannot dismiss it as false.

A rational person, as distinct from a rationalist, should first acknowledge facts as facts, whatever their nature, and only afterward seek a reasonable explanation for them. Denying facts merely because they sound mystical may be rationalist in some sense, but it is certainly not rational. As we saw, in our case such denial does not stand up to empirical reality.

All that remains for us, then, is to seek a theoretical justification for this fact, not to ask whether the fact is true. The question we must now face is not whether informativism is correct rather than actualism. The right question is: how does it happen that informativism actually works?²¹

In the first two books of the quartet, a possible direction for explaining this remarkable phenomenon is sketched. It involves giving up the sharp distinction between cognition and thought. We cannot elaborate here, nor is that necessary. It is enough for us to recognize that we are confronted with the existence of a human capacity to generalize the facts we observe. As a result of this capacity, the general law—the result of generalization—or the theoretical claim, such as the existence of a causal relation between events, is not arbitrary, though of course it is never certain.

Returning to the Disputes in Interpretation

We now return to the dispute among the Rishonim over interpretation. Above we noted that the dilemmas forming the axes of that dispute are very similar to those at the center of the philosophical-scientific dispute. In both cases the great question is whether we possess the ability to generalize and to determine the existence of a causal relation, even though neither the generalization nor the causal relation is directly observed by us. We saw that in the scientific context the answer is decidedly yes. We do not have a satisfactory explanation of how this works, but we have established that this capacity demonstrably exists.

If we now ask whether we possess such capacities in the interpretive domain, we have no reason to assume that we do not. Here too we can examine halakhic, legal, aesthetic, and similar facts and draw different conclusions from them by means of generalization, or find different kinds of relations, such as causal relations, between parts of the interpreted object. The empiricist hesitation, grounded in the exclusivity of sense-perception and direct observation, is no longer self-evident.

True, in the interpretive sphere we do not have a simple way to receive feedback on our generalizations. We have no independent route to know whether we generalized correctly or whether our generalization is mistaken.²² But in science we do have a way of testing our generalizations, and from that we learn that this capacity really exists in us. From this one may infer with considerable probability that there is a parallel capacity in acts of interpretation as well. The philosophy of science thus helps confirm our confidence in our rational ability to draw conclusions.

This is the basis of Maimonides’ optimistic rationalism, which trusts its own conclusions and allows itself to formulate generalizations even where they do not appear explicitly in the Torah. His halakhic-interpretive reasoning is nothing other than the use of the human capacity for generalization and interpretation, the existence of which—at least in the scientific context—we have proved above.

Footnotes

See also the discussion at the beginning of Shtei Agalot ve-Kadur Poreah, and in greater detail in the second section of Et Asher Yeshno ve-Asher Einenu.

There we also noted that in the world of thought, the pole of din corresponds to binah, while the pole of hesed belongs to hokhmah. Binah is understanding one thing from another; that is, it deals with the laws of logic, in other words analytical thought. Hokhmah, by contrast, is the totality of truths that are not logical derivations but the results of intuition—or perhaps hokhmah is the very power of intuition that yields such truths. In our present terminology we would call this rationalism: confidence in common sense, that is, intuition, and not only in logic and direct observation.

But there is a very basic mistake in this argument. Postmodernism, which is an expression of actualist empiricism, as M. Avraham argues in his quartet, does not see generality as a criterion of truth at all. The dispute is itself about precisely that point—whether generality or elegance is a criterion of truth. One therefore cannot use an argument that treats generality as a measure of truth as a tool for deciding the dispute.

For a similar consideration, see Ludwig Wittgenstein, Philosophical Investigations, translated by G. E. M. Anscombe, sections 143-245, in the discussion of rule-following. He shows there, in much the same mathematical manner, that there are infinitely many possible ways to continue any given series of numbers, and each has its own mathematical logic. His conclusion is that no series of numbers has a uniquely simple or natural continuation in any objective sense.