The Logic of Kal Va-Chomer: B. Exceptions (Column 736)
The Logic of Kal Va-Chomer: B. Exceptions
In the previous column I examined the assumption of relevance that hides behind kal va-chomer (a fortiori) arguments. In its light, I explained the logical flaw in an a fortiori pilpul that is based on only two data points. In this column I will look at additional examples in which the Sages themselves perform a kal va-chomer based on two data points.
Exit and Entry
In Parashat Shemini, the Torah discusses the entry of Moses and Aaron into the Tent of Meeting and their exit from it (Leviticus 9:22–23):
“And Aaron lifted up his <hand> hands toward the people and blessed them, and he came down from offering the sin-offering and the burnt-offering and the peace-offerings. And Moses and Aaron went into the Tent of Meeting, and they came out and blessed the people; and the glory of the LORD appeared to all the people.”
Upon exiting they blessed the people, while nothing is stated about blessing upon their entering.
In the Sifra (Shemini, Parasha 1) this serves as the basis to learn that they also had to bless the people upon entering:
“‘And Moses and Aaron came into the Tent of Meeting’—why did Moses and Aaron enter together? To teach Aaron the procedure of the incense. Or perhaps they entered for some other matter? I will reason: Descending (y’ridah) requires a blessing, and entering requires a blessing. Just as the exit (apparently it should read: descent) is of a kind with the service, so too the entry is of a kind with the service. From where do we know that entry requires a blessing? It is logical: If exit—which does not require washing—requires a blessing, then entry—which does require washing—certainly requires a blessing. Or the reverse: If entry—which does not require a blessing—requires washing, then exit—which does require a blessing—certainly requires washing. No! Do not say entry, for there one goes from profane to sacred; but say exit, for there one goes from sacred to profane. The reversal is nullified, and we return to the reasoning: Descending requires a blessing, and entering requires a blessing. Just as the descent is of a kind with the service, so too the entry is of a kind with the service. Therefore, why did Moses enter with Aaron? To teach him the procedure of the incense.”
This argument relies on an additional assumption, namely that entry requires washing. We thus have a table with two data points, just as we saw in the previous column:
| State/Action | Washing | Blessing |
| Exit | ? | 1 |
| Entry | 1 | ? |
Naturally, two possibilities arise for filling the lacunae cells: in the first a fortiori we learn that entry requires a blessing. Immediately thereafter the argument is raised in the opposite direction—that exit requires washing.
As we saw in the previous column, at first glance these two a fortiori arguments contradict each other. In a fortiori #1 we assume as a datum that exit does not require washing; yet the conclusion of a fortiori #2 is that exit does require washing. And conversely: in a fortiori #2 we assume that entry does not require a blessing, while the conclusion of a fortiori #1 is that entry does require a blessing. The conclusion of one undercuts the premise of the other, and vice versa. On the other hand, we saw that even if both cells are filled with “1,” there is no real contradiction, for at most we have two independent generalizations (binyanei av), and the resulting table is indeed consistent.
Ultimately, the Sifra does see a contradiction here and decides between the two opposing possibilities on conceptual grounds: going from profane to sacred (entry) more properly requires washing than going from sacred to profane (exit), and therefore it is clear that entry requires a blessing. Consequently, it is more reasonable to return to the first a fortiori and conclude that entry requires a blessing (and to remain with exit not requiring washing).
Uncertainty vs. Irrelevance
Two empty cells do not always express irrelevance. Sometimes the empty cells result merely from uncertainty, not irrelevance. In the argument about the doorpost and the tassel (tzitzit) discussed in the previous column, it seemed that the problem was irrelevance; however, in our case (exit and entry) the parameters are clearly relevant, and the issue is uncertainty alone. We do not know whether the lacuna the Torah left indicates obligation or exemption. Therefore the Midrash ultimately decides in favor of the first direction: washing is not relevant when going from sacred to profane; hence that cell should clearly be filled with “0.” That is, the Midrash concludes that this cell is not a lacuna (in which case “X” would be appropriate) but should be filled with “0.” Once we assume that exit does not require washing, the case reverts to a regular “middot-based” a fortiori with three data points.
In other words, the Midrash itself takes for granted that relevance exists here. In this it differs from the doorpost case; hence here there arises an initial thought (hava amina) to reverse the a fortiori. For that reason they are unwilling to accept a result of two binyanei av that would fill the entire table with “1,” and in the end they choose only one of the two directions.
This is evident from the very wording of the Midrash. It presents the matter as a doubt about which direction to take and presumes there is a contradiction between the directions. Where the problem is irrelevance, there is no room to formulate both directions (the “reversal”) and to deliberate between them. As we saw previously, in a situation of irrelevance we are not unsure which is correct; we know with certainty that neither is valid.
Can There Be Irrelevance with Three Data Points?
We saw that with only two data points, the natural conclusion is irrelevance. Yet it is possible that there are two data points and still relevance (and then we search for a value to fill another cell). Note that when a third datum is actually found—or when we begin with three data points—it becomes clear that relevance exists. When the upper-right cell is filled with “0,” this indicates an exemption: the rule is relevant to that state, but there is an exemption. Thus, for example, washing upon exit from sacred to profane is certainly relevant; washing makes sense there. But reasoning suggests that there should not be an obligation—since we are descending from sacred to profane and washing is triggered only when ascending to the sacred. The conclusion is therefore an exemption (“0”) rather than irrelevance (“X”).
As we saw, finding the additional information returns us to a regular “middot-based” a fortiori grounded in three data points. In such a case, the variables are generally fully relevant, and the a fortiori can be performed. A case of a three-datum, “middot-based” a fortiori that expresses not lack of knowledge but irrelevance (and thus cannot be performed) is very rare—though in principle possible. For example, if exit were entirely irrelevant to washing while entry were relevant to blessing. In that case, even if the third datum (that entry requires a blessing) were known, one could still not perform an a fortiori to learn that exit does not require washing.
How then can we know whether we are dealing with irrelevance or with lack of information? As stated, only by conceptual reasoning (sevara). Note that as long as we have not determined the nature of the table’s absences (irrelevance or lack of information), we cannot perform an a fortiori. The upshot is that every regular, “middot-based” a fortiori rests on the exegete’s a priori reasoning that relevance exists. This is not a purely technical formalism; it is the product of an a priori conceptual analysis of relevance.
Let us now turn to another example of a two-datum a fortiori.
Another Example of a Two-Datum A Fortiori: Berakhot 21a
There are a few examples in the Talmud of a fortiori derivations based on two data points. One well-known and clear example appears in the Babylonian Talmud, Berakhot 21a. The Gemara states:
“R. Yehuda said: From where is the obligation of Grace after Meals (Birkat Ha-Mazon) from the Torah?—as it is said (Deut. 8): ‘And you shall eat and be satisfied and bless.’ From where is the obligation of the blessing over Torah study before it from the Torah?—as it is said (Deut. 32): ‘For the name of the LORD I will call; ascribe greatness to our God.’”
Up to this point we learn two data points from the Torah: one blesses for food after eating, and one blesses for Torah before learning. The data table is as follows:
| Action/State | Before | After |
| Food (bread) | ? | 1 |
| Torah | 1 | ? |
It is now natural to try to complete the two missing entries via a fortiori. We have seen that relying on two data points is problematic, and even if one proceeds, one should choose a single direction. Yet here the Gemara proposes to learn both missing entries together:
“R. Yohanan said: We learn the blessing after Torah from the blessing after food by a fortiori; and the blessing before food from the blessing before Torah by a fortiori. The blessing after Torah from the blessing after food: if food, which does not require a blessing before, requires a blessing after—then Torah, which requires a blessing before, surely requires a blessing after. And the blessing before food from the blessing before Torah: if Torah, which does not require a blessing after, requires a blessing before—then food, which requires a blessing after, surely requires a blessing before.”
Apparently, the Gemara assumes relevance between the rows and columns despite having only two data points—just like the a fortiori above. Conceptually, there certainly appears to be relevance between blessings before and after, both for Torah and for food.[1] It is sensible to bless both before and after on both Torah and food. This is likely the reason the Gemara attempts a two-datum a fortiori here. However, in this case there is no conceptual reason that would lead us to choose only one direction (unlike the washing/blessing case). Therefore, the Gemara fills both lacunae. We end up with a table full of “1”s:
| Action/State | Before | After |
| Food (bread) | 1 | 1 |
| Torah | 1 | 1 |
Seemingly we received a binyan av table, but the Gemara learned both entries via a fortiori. That is very problematic, for if both are a fortiori arguments, they contradict each other: each assumes the third datum is “0” and concludes that the fourth is “1.” Yet the third datum for the first a fortiori is the fourth for the second, and vice versa.
The Refutation (pircha)
In the end, the Gemara rejects both a fortiori arguments by presenting refutations: a stringency of Torah and a stringency of food:
“There is a refutation: as to food—there is enjoyment; as to Torah—it is eternal life! Moreover, we learned (Mishnah): one blesses after food but does not bless before it! Refuted.”
The resulting table differs from the initial one in two respects: two “refutation” columns are added, and the lacunae are filled with “0” (not “1” as above):
| Action/State | Before | After | Enjoyment | Eternal Life |
| Food (bread) | 0 | 1 | 1 | 0 |
| Torah | 1 | 0 | 0 | 1 |
Why are two columns needed, when only one of them (enjoyment) is actually a refutation?
If one wishes to construct a data table like the first two columns, where the hierarchies are reversed (the columns are independent), then necessarily there will be one parameter with respect to which food is more stringent (controlling the blessing after), and another parameter with respect to which Torah is more stringent (controlling the blessing before).
Thus one can say that the Gemara is not truly adding “refutation columns,” but rather defining the model’s parameters for this table: α—enjoyment (present in food but not in Torah), and β—eternal life (present in Torah but not in food). In other words, the table is 2×2 cells, not 2×4 as I drew above:
| Action/State | Before | After |
| Food (bread) | 0 | 1 |
| Torah | 1 | 0 |
Note that the lacunae here are filled with “0” and not “1.” In place of the columns I deleted, we can now use the two parameters revealed by the Gemara to write the model for the final table:
| Food has stringency α (enjoyment).
Torah has stringency β (eternal life). To obligate a blessing before something, it must be associated with eternal life; to obligate a blessing after something, it must involve enjoyment. That is: A blessing after requires α. |
Rashi here, however, presents these refutations as two column-refutations applied to the two a fortiori arguments above:
“There is a refutation—of both. When you seek to learn Torah from food, there is a refutation: as to food—there is enjoyment. And when you seek to learn food from Torah, there is a refutation: as to Torah—it is eternal life.”
That is, two column-refutations are indeed required, because both a fortiori arguments are column-type: one was an a fortiori regarding the blessing before, learning food from Torah; the other, an a fortiori regarding the blessing after, learning Torah from food. We refute the first with “eternal life” and the second with “enjoyment.” Such a situation can occur only when the table contains just two data points and we wish to fill the other two.
The Difficulty
Still, a difficulty remains: how could R. Yohanan adopt a double a fortiori based on two data points, when the two stand in direct contradiction? As we saw, each direction seemingly refutes the other. Note that had the Gemara not raised its two refutations, R. Yohanan’s two arguments would apparently have stood.
In light of this, perhaps we can read the Gemara’s own refutations as indicators: the Gemara indeed intends to reject each of R. Yohanan’s a fortiori arguments by means of the other. The rejection of the first is by virtue of the second, and vice versa. However, a rejection by virtue of some rule must always point to a stringency grounded in conceptual reasoning. For example, the rejection that there is no explicit verse requiring a blessing after Torah indicates that Torah is, in this respect, lighter than food. But then we may ask: why is it lighter? That is what the Gemara explains by saying that Torah is “eternal life”—though its intent is to refute the a fortiori.
The problem is that, if so, it is unclear why the Gemara assumes that both a fortiori arguments are refuted. Seemingly it would suffice to refute one and leave the other intact. Perhaps in this case the Gemara had no way to decide which to retain (“since they are balanced, let both fall”), and because neither is certain we have no basis to establish either of the two novel rulings.
A Proposed Resolution: Rashi’s Remark
Rashi seems to sense this difficulty, and therefore he interprets R. Yohanan’s words in a way slightly different from the plain implication:
“‘Which does not require [a blessing] before it’—that is, we have no explicit verse requiring a blessing before food. ‘Requires [a blessing] after it’—as it is written: ‘And you shall eat and be satisfied and bless.’ ‘Torah which requires [a blessing] before it’—as stated above.”
That is, Rashi attributes food’s “leniency” relative to Torah not to an actual exemption from a blessing before eating, but to the lack of an explicit verse mandating it. According to Rashi’s proposal, the entry “0” we placed in a cell as a working assumption does not indicate legal exemption but the absence of an explicit verse. The assumption is that even if, in practice, food is obligated in a blessing before it, the very fact that there is no explicit verse is itself a leniency.[2]
Rashi’s suggestion indeed eases the difficulty, but it does not fully resolve it. On this reading we have filled both cells with “interpretive 0” but “halakhic 1.” Even if food requires a blessing before and Torah requires a blessing after, those obligations are not explicitly written in the Torah (unlike food-after and Torah-before). Hence they are lighter rulings. But halakhically, in both cases, the obligations stand by virtue of the a fortiori. This yields a further difficulty: suppose we put “interpretive 0” in the “food-before” cell and, via a fortiori, fill the “Torah-after” cell (which had “interpretive 0”) with “halakhic 1.” What now? Torah-after still remains lighter than food-after, since the obligation is not written explicitly. In other words, the hierarchy that Torah is stricter than food does not truly hold; and similarly in the opposite direction for the a fortiori about food-before.
A Reformulation of the Difficulty—For Any A Fortiori
In fact, the difficulty amounts to this: the table that results once both of R. Yohanan’s a fortiori arguments are applied is inconsistent. His table looks like this:
| Action/State | Before | After |
| Food (bread) | (0,1) | 1 |
| Torah | 1 | (0,1) |
Here “(0,1)” indicates the rule exists in principle but only by virtue of a derivation; it is not stated explicitly in the Torah. That is, “0” interpretively (not in the text), but “1” halakhically (by a fortiori).
We can now immediately see that the datum for “food-before” does not support the a fortiori from which “Torah-after” is concluded (at least as framed above): the reason is that, when we seek to learn “blessing after Torah” by a fortiori, we rely on the generalization that Torah is stricter than food; but according to the conclusion, Torah is lighter than food—since, in the end, “after” the obligation to bless is lighter for Torah ((0,1)) than for food (1). Even if the obligation exists, it is not written explicitly; whereas for food-after it is.
Upon further reflection, this problem appears in every a fortiori—even one with three data points. Consider a regular table (Table 1 from the previous column) applied here:
| Action/State | Before | After |
| Food (bread) | 0 | 1 |
| Torah | 1 | ? |
Let us assume for discussion that there truly is no Torah-level obligation to bless before eating (as in fact the halakhah says; blessings of enjoyment are rabbinic). We now perform an a fortiori and learn that there is an obligation to bless after Torah. But again, that obligation is learned via a fortiori and not written explicitly; thus the lacuna cell will not contain “1” but “(0,1).” Therefore, the assumption that Torah is stricter than food, inferred from the left column, does not actually hold regarding “after” blessings (the right column). Recall: “1” is stricter than “(0,1).” The result of the a fortiori does not change this; it actually demonstrates it. After performing the a fortiori, Torah is still not stricter than food; and if so, the a fortiori itself collapses (for the generalization that served as its basis collapses).
Another Proposed Resolution: A Fortiori as a Textual Rule
It seems that to address this we must distinguish two distinct stages in the derivation. When we examine the scriptural data alone, the picture is that the learned rule is stricter than the teaching rule. But according to the conclusion, it turns out to be less strict. Therefore, we must understand a fortiori as a textual rule, not (only) a logical one. When we consider the biblical text alone, the learned rule appears stricter. True, that is not their real halakhic relationship—after the a fortiori the reverse relation also comes into being—but that is the picture reflected in Scripture itself. That textual picture instructs us to derive the learned rule from the teaching rule by means of a fortiori. Once the learned rule is obtained, the true halakhic relationship is revealed (beyond the interpretive-textual one): the teaching rule, explicit in the Torah, is stricter than the learned rule, which arises only by derivation. But it is the relation as reflected in Scripture that governs the a fortiori.
There is no escaping the conclusion that the a fortiori of the middot is a textual device rather than a strictly logical one. Put differently: the “leniency” and “stringency” operative in a fortiori are not the actual halakhic leniencies and stringencies, but those that emerge from the biblical text alone. In other words, the “(0,1)” value in a lacuna cell is not a value between 0 and 1 (like 0.5). It is a pairing of 0 with 1 on two different planes: interpretively it is 0; halakhically it is 1. Cells that express rules stated explicitly in the Torah contain only a single number because there the interpretive and halakhic values coincide. Needless to say, “(1,1)” and “(0,0)” are simply 1 and 0 respectively. Likewise, “(1,0)” is impossible (for what is written in the Torah certainly holds halakhically—aside from pathological cases of a derivation that uproots or overrides a verse).
I will sharpen the picture by means of a diagrammatic description. On this proposal, a fortiori proceeds in two layers: Layer A gathers the relevant biblical data and records them in a table on Transparency A. Layer B performs the a fortiori inference based on those scriptural data. The midrashic inference generates new halakhot. These halakhot emerge from the derivation and are thus not present in Scripture itself; therefore we record them on Transparency B, which overlays the first. The full halakhic picture is the combination of what appears on both transparencies: the scriptural-textual and the midrashic-halakhic. However, refutations of a fortiori or data used by it cannot belong to Transparency B; they belong exclusively to Transparency A.
Answering the Difficulties
This picture answers the two questions raised above:
- The data on Transparency B are halakhically valid, but they are not scriptural. Therefore they cannot be used to refute the hierarchical relations in the table. This is why the result of the a fortiori does not refute the a fortiori itself. The conclusion that Torah requires a blessing after is not a “0.5”-level obligation that would undermine the assumption that Torah is stricter than food; it is a composite “(0,1),” which refutes nothing. In sum: a fortiori is also a tool of scriptural interpretation, not merely a logical inference. For this reason one cannot refute an a fortiori by arguing, “As for what you seek to learn—its halakhah is only derivational.” Such a refutation belongs to Transparency B.
- If we adopt this picture, then the problem with R. Yohanan’s double a fortiori disappears as well. There, too, only the true halakhic relationship would be contradictory, while what governs the a fortiori is the scriptural relationship—not the ultimate halakhic one. Scripturally, ‘Torah-after’ and ‘food-before’ are absent.
Thus, Rashi’s suggestion in Berakhot—to treat the absence as “not explicit in Scripture” rather than as a halakhic leniency—is not unique to a two-datum a fortiori (like R. Yohanan’s). On our approach, in every a fortiori the leniency and stringency are determined by textual appearance (the scriptural plane), not by the final halakhic ruling (the halakhic plane). Rashi’s proposal therefore resolves all the difficulties.
Implications and Sources for This Proposal
According to this, a fortiori is not merely logical reasoning but also a textual-interpretive tool. This can explain why the Torah transmits the a fortiori measure within the broader system of exegetical rules (middot). It is important to note that there are other types of a fortiori, those based on a single datum plus reasoning rather than on three data points (all biblical a fortiori are of this kind—for example: “Behold, the children of Israel have not listened to me; how then shall Pharaoh hear me?”; likewise all “within two hundred is a hundred”-type arguments). The logical reasoning of a fortiori exists in all such inferences. The middot-based a fortiori (the one conveyed with the exegetical rules) is specifically the sort based on three halakhic data points—a textual tool. Therefore, it requires the Torah’s authorization and revelation to legitimize its use. In the former types we rely on their inherent reasoning.
On this approach it is also easy to understand the tannaitic view that we do not perform a fortiori from a law given to Moses at Sinai (halakhah le-Moshe mi-Sinai; see Mishnah Nazir 56b, and this is the halakhic ruling).[3] Since a law of this sort is not written in the Torah, R. Eliezer (in that Mishnah) holds that the a fortiori cannot apply to it, for it is not a general logical rule but a textual-interpretive one whose force pertains only to what is in Scripture. It is likewise explained in several places that one does not refute an a fortiori on the basis of a halakhah le-Moshe mi-Sinai.[4] These principles clearly indicate that the Sages viewed a fortiori as a tool addressing biblical textual interpretation, not necessarily a logical device. This also seems to emerge from the sugya of “learning from what is itself learned,” for if the product of an a fortiori is not part of the biblical text, it makes sense that one should not build an additional a fortiori on its basis (see more in the article Middah Tovah, 2005, Parashat Pekudei), though this is not the place to expand.
There is an interesting source implying that a fortiori is a textual measure rather than a logical one. See the Hiddushei ha-Rashba to Bava Kamma 2b s.v. “aval be-mehubber,” and the explanation in R. Baruch Ber Leibowitz’s Birkat Shmuel, Bava Kamma, §2, and this is not the place to expand. Another source suggesting that a fortiori is not a logical rule appears in the Brisker Haggadah (in the commentary to “Who knows thirteen?”). See my critique there in the article Middah Tovah, 2005, Parashat Bereshit, where I explained the logic of that inference.[5]
A Different Two-Datum A Fortiori: Harlot’s Hire and an Object of Worship (Asherah)
About seven years ago I was asked in a responsum about a sugya in Avodah Zarah 46b. In the course of the discussion I explained to the questioner that this is another two-datum a fortiori:
“Rava said: A fortiori! If a harlot’s hire (etnan), which is permitted when detached for ordinary use, is prohibited when attached for sacred use—since it is written, ‘You shall not bring the hire of a harlot or the price of a dog’—there is no difference whether detached or attached; then an object of worship (ne’evad), which is prohibited when detached for ordinary use, surely is prohibited when attached for sacred use. Rav Huna the son of Rav Yehoshua said to Rava: Or the reverse: If an object of worship, which is prohibited when detached for ordinary use, is permitted when attached for sacred use—as it is said, ‘Their gods are upon the mountains’—and not ‘the mountains are their gods’—there is no difference for ordinary use or sacred use; then a harlot’s hire, which is permitted when detached for ordinary use, surely is permitted when attached for sacred use…”
Here three axes are in play: etnan vs. ne’evad; detached vs. attached; ordinary use (hedyot) vs. sacred use (gavoah). But the last two are really one axis: detached-for-ordinary vs. attached-for-sacred. We have the following table (1 = prohibited; 0 = permitted):
| Action/State | Detached for ordinary use | Attached for sacred use |
| Harlot’s hire (etnan) | 0 | 1 (?) |
| Object of worship (ne’evad) | 1 | 0 (?) |
From the Gemara’s perspective, the entries in the left column are not decisive (the question is whether, when the Torah speaks generally, we make no distinction between detached and attached, or whether we may still be speaking only of detached; hence the question marks). The sugya then offers two opposing a fortiori arguments, seemingly like Berakhot regarding Torah and food. But note that it is not quite the same: the first a fortiori seeks to fill “1” in the “object of worship—attached for sacred use” cell; the second seeks to fill “0” in the “harlot’s hire—attached for sacred use” cell. That is, the two a fortiori arguments address different cells in the right column: the first aims to be stringent regarding the object of worship; the second, to be lenient regarding harlot’s hire.
It is no surprise that the sugya subsequently states:
“He said to him: I argue toward stringency, and you argue toward leniency. Between stringency and leniency—we prefer the stringency…”
This is a comparison between an a fortiori toward stringency and one toward leniency, and is thus not our topic. The rule there is: when we have two possibilities—learning to stringency and learning to leniency—we choose stringency. By contrast, in the cases we saw earlier, both a fortiori arguments lead to stringency: one in the upper-right cell and the other in the lower-left cell. There, the stringency/leniency preference is inapplicable, and thus there is no rule telling us which inference to make. That is the subject of this entire column.
Summary and Conclusion
As I explained in response to Tirgitz in a comment to the previous column, in that earlier piece I concluded that when a table has only two data points, we infer that there is no relevance between the variables and therefore no a fortiori may be made. Accordingly, I rejected the a fortiori obligating a doorframe in tzitzit and a garment in mezuzah. In this column we saw that sometimes relevance does exist even with two data points (as with food and Torah, or blessing and washing).
Therefore the overall conclusion is slightly different: when the table has only two data points, the presumption is non-relevance and an a fortiori may not be made—unless one provides conceptual reasoning (sevara) that relevance exists (as with Torah and food). In such a case, the burden of proof lies on the one who claims relevance. By contrast, in a regular a fortiori based on three data points, the starting point is that there is relevance (since the Torah itself assigns a rule regarding both rows or both columns); there the burden of proof lies on the one who claims non-relevance. See more in my discussion with Tirgitz there.
[1] One could discuss whether, from the mere fact that the Sages instituted a blessing before enjoying food, it follows that the obligation is relevant to the state prior to eating. It could be countered that perhaps on the Torah level it is not relevant at all—but that is unlikely. It is reasonable that the difference between rabbinic and biblical obligations is quantitative rather than qualitative; what is wholly irrelevant biblically would not be instituted by the Sages either. Presumably, the Sages merely lowered the threshold of obligation relative to the Torah.
For a discussion of this from a very different angle, see Daniel Weil, “The Logic of the Sages’ Completions and Greek Logic,” Higayon 1. On the contrast between the Sages’ reasoning and Greek logic (in response to that article), see also M. Avraham’s response, “What Is a ‘Chalut’,” Tzohar 2, and this is not the place to expand.
In any case, since here we are dealing with the biblical plane, later rabbinic enactments are not probative. The question is how the Sages themselves reached their conclusions (that relevance exists). This point arises in every rabbinic enactment, for they always legislate where the Torah was silent; therefore they must ask in each case whether relevance exists and the Torah merely set a higher quantitative bar, or whether the Torah indicates irrelevance—in which case there is no room even for a rabbinic ordinance.
[2] See a similar consideration in R. Elchanan Wasserman’s Kuntres Divrei Soferim, §1 n. 20: what the Torah states explicitly is more stringent than what it merely alludes to by exegetical methods. There are several sources for this among the Rishonim as well, and this is not the place to expand.
[3] See numerous sources collected in Encyclopedia Talmudit, s.v. “Halakhah le-Moshe mi-Sinai,” around notes 191–213.
[4] See Encyclopedia Talmudit there (around notes 203–213).
[5] There I also discuss an a fortiori based on a single assumption; in any case that is a logical a fortiori, not a middot-based one. There the relevant plane is assuredly logic.
Discussion
A. In the previous post, in note 1, you mentioned that there are cases where one may derive a kal va-chomer from a law that is itself learned from a derashah and is not written explicitly in the Torah. (And here, in the paragraph beginning “According to our approach,” I did not understand how you rejected that.) In the past it was also mentioned that objections are made from things learned by derashot; in Yevamot 5a: “What about a nazirite, who can be released by annulment?” And it is well known that “the laws of releasing vows are suspended in the air,” meaning that release from a vow is at most based on a derashah, and nevertheless they make a refutation from it. Therefore one can only say either that with two data points this is really a binyan av (as I recall some have written, though you rejected that because the Gemara calls it a kal va-chomer), or that the two kal va-chomers operate in parallel, so each is unaware of the other but is aware of all the other products of derashot. Responsa called Be’ur Kal Va-chomer.
B. The issue of relevance that you introduced should apparently apply to a binyan av as well and not only to a kal va-chomer. That is, even in a binyan av, which is basically one datum, one should require relevance; and according to the explanation you added in this post, one must appeal to reason. I think your words amount to the claim that in every binyan av one must identify the reason for the law (the common factor among all the source cases and the derived case); it is not enough to point to the fact that two subjects have the same law and transfer it to a third subject, but rather one must find a common factor among all three subjects and claim that it is the reason for the law in the two source cases. Is that correct? [This is the explanation of Maharam Schiff and Penei Yehoshua in Ketubot 32 regarding the objection of “a stricter side,” because they did not find a common factor between the two source cases.]
Nice.
A. It requires further thought when yes and when not. But the very discussion points in the direction I suggested. There are derashot that for various reasons are considered an unpacking of the plain meaning of the verse (supportive derashot according to the Rambam, and more).
B. A binyan av is not one datum but three (except that all three are 1). Beyond that, even in a kal va-chomer one does not explicitly look for and define the common factor (the relevance); one simply assumes there is one. The same is true in a binyan av. Even in learning by the common factor, they do not always present the common factor explicitly. Sometimes the common factor is halakhic (some law exists in both), and not an essential property of the source cases themselves.
A. I didn’t understand. They make an objection from the release of vows, which is “suspended in the air,” and you say that this is a supportive derashah? Even if so, here you are taking the position that one neither derives nor refutes a kal va-chomer from a law given to Moses at Sinai. And what about the rule that something learned by kal va-chomer can itself teach via kal va-chomer in matters other than sacrificial law? Why go to such strong claims when it would be enough to restrict oneself to the smaller claim that the two derivations operate in parallel and simply do not recognize one another? As I recall, you agreed with that in the past as well.
B. Why three? For example (in a mah matzinu): “Just as with vows the father annuls his daughter’s vows and the husband annuls his wife’s vows, so too with naziriteship the father annuls his daughter’s naziriteship and the husband annuls his wife’s naziriteship”; “Just as a brother’s wife enters levirate marriage, so too a wife’s sister should enter levirate marriage.” Here too I understand you to be claiming that relevance is required, grounded in reason (and it indeed exists). A halakhic common factor, namely that both have some shared law different from the one being learned, is certainly an important common factor (at the very least as an indication), and I did not understand why you brought that up.
Here there is direct reasoning against the relevance. That does not establish the post’s claim that everywhere one needs direct reasoning in favor of relevance (or an indication from the three data points).
A. Yes, release of vows really does look very much like a supportive derashah. After all, it is “suspended in the air,” so how did they arrive at it? Presumably there was a tradition that vows can be released, and they attached it to that biblical hint. You are right that learning from something already learned applies only in sacrificial law, and even there not in every combination of two hermeneutic rules, but still there is a hint here in the direction I suggested. Why there are limitations is a good question, and I did not get into it.
B. Even in a kal va-chomer there is an inference built on one datum, but that is a biblical kal va-chomer. A Talmudic kal va-chomer (a hermeneutic one) is mostly built on three. “All the more so” is usually a Talmudic inference with the character of a biblical kal va-chomer. I claimed that only a kal va-chomer built on three data points is a hermeneutic rule. The others are just plain reasoning. Here I claimed that the same applies to binyan av. When you make an analogy between two things, that is not a hermeneutic rule in the full sense. Ordinary reasoning does that all the time. Therefore I claimed that a hermeneutic binyan av is built on three data points. And indeed relevance is required there too. Otherwise, from a doorpost and tzitzit I would make a binyan av and obligate a garment in mezuzah and a doorpost in tzitzit at the same time.
As for the common factor, that is a shared law, whereas I am talking about a shared characteristic (the parameters alpha and beta represent characteristics, not laws). I expanded on this in my articles on non-deductive logic.
But this is a nice example of the principle itself, that relevance is required, even with three data points (against your own claim, where you denied this).
Beyond that, it is quite hard to define when there is reasoning against relevance and when there is merely no reasoning in its favor. Is there a difference between those two? The line is not sharp.
Tirgitz, on second thought it seems that in fact you are mistaken.
After all, you see here that even in a case of three data points, when there is reasoning against relevance that negates the kal va-chomer. That implies that when there is no such reasoning, the very existence of three data points creates a presumption that there is relevance. So you are not right. One does indeed see here that the existence of three data points presumes relevance unless proven otherwise.
At this point I deny only the default assumption that any two things are irrelevant unless proven otherwise, and I maintain the default that they are relevant. With or without three data points. Reasoning against relevance is the proposal of an explicit and plausible model of what is required for betrothal, what is required for a Hebrew maidservant, and what intercourse has that money does not—why is that not sharp?
To be sure, the explanation of an inapplicable objection is not clear to me either, but in any case how do you explain it? I have no tool to search right now, so all I have is the Halikhot Olam, which brings Bava Kamma 88 to derive by kal va-chomer that a slave is disqualified from testimony: “Testimony comes by kal va-chomer from a woman: if a woman, who is fit to enter the congregation, is disqualified from testimony, then a slave, who is not fit to enter the congregation, is all the more so disqualified from testimony.” And they refute: “What about a woman, who is not fit for circumcision—would you say the same about a slave, who is fit for circumcision?” And Tosafot there wrote: “Even though circumcision is not applicable—this is still a refutation.”
A. But my question was: after all, you also do not derive a kal va-chomer from a law given to Moses at Sinai, so likewise not from a supportive derashah.
B. As for the common factor, I recall that you argue that a shared law is an indication of a shared causal characteristic, so I wrote “at the very least as a sign”—isn’t that so?
As for the derivation from doorpost and tzitzit, I suggested objections: what about a house, which is obligated in a parapet, and what about a garment, which is forbidden in sha’atnez. So in my view that example collapses entirely. And my assumption is that in any other example you bring there will likely be an objection, because every subject has something unique; and if not, then indeed we would learn it. And we would not be able to learn simultaneously that a house requires tzitzit and is forbidden in sha’atnez (and that a garment requires mezuzah and a parapet), because one does not do that simultaneously.
Consider, for example, a doorpost and mezuzah. Quite apart from our previous debate (that both serve as reminders and appear in the Shema), the feeling is that there is no connection at all, and everyone immediately laughs when they hear this kal va-chomer. That is even before they notice that there are only two data points here and that one could make the reverse kal va-chomer. Why do they laugh? Because it is obvious to them that there is no relevance. But there is no conceptualized argument for this. Just a feeling that there is no reason to say there is relevance. Is that a case where there is a reason, or where there isn’t? This is an example of why the boundary is not sharp.
An inapplicable objection is indeed something puzzling. I do not accept it, and prefer to leave it unresolved. I could even have suggested an explanation here. There is some sort of objection (in the sugya in Hullin, 115?) where they distinguish between a binyan av and a kal va-chomer. That is something close to weak relevance. But an inapplicable objection is something totally lacking in relevance, and I do not accept that such a thing exists.
A. I didn’t understand. A supportive derashah is a derashah that supports the law that comes from Sinai. Here we are talking about a kal va-chomer that creates a new law on the basis of a halakhah given to Moses at Sinai.
B. Indeed. But there is no conceptualization here of the shared characteristic. I explained that this is what underlies the objection of “a stricter side.”
As I wrote to you in a parallel thread, go and see: people immediately laugh when they hear the kal va-chomer obligating a doorpost in tzitzit. It is obvious to them that there is no relevance. They are not thinking about objections, and not even about the fact that there are only two data points here and that one could make the reverse kal va-chomer. This is an intuition of irrelevance.
A. Apparently I am missing something. You say that release from vows is a law given to Moses at Sinai. And you say that one does not make objections (or derive a kal va-chomer) from a law given to Moses at Sinai. But the Gemara makes an objection from release from vows.
B. You explained the objection of “a stricter side” as the objector hiding behind the claim that perhaps different halakhic characteristics stem from some mysterious shared factual characteristic that does not exist in the derived case. But I proved in the past that this nice explanation is not correct, and if the topic comes up again I can lay out my arguments again.
A. You are assuming that “suspended in the air” means utterly source-less. I am not sure of that. What I suggested is that we have here a supportive derashah, meaning a derashah that explains that this is the intent of the verse itself, and therefore release of vows is indeed written. This is certainly true according to the views of the other tannaim there in Hagigah (beyond the first tanna). So at least one can say that when they object that release of vows is subject to annulment, that is according to the other views.
Where did you prove that my explanation of the objection of “a stricter side” is incorrect?
I wrote about the objection of “a stricter side” under post 346 and in another place on the site that I do not remember. I will summarize my arguments. The two hard difficulties are: (1) in Sotah 29, a later generation objects with “a stricter side” even though the derived case also has its own stricter side; in that situation the objector has no basis to think that the factual characteristic shared by the two source cases does not exist in the derived case. (2) In Ketubot 32a they object with “a stricter side” according to Ulla, whereas in Bava Kamma 88a Ulla himself learns by a common factor with halakhic objections and does not object with “a stricter side.” There are also softer difficulties there (though in my view the soft one is stronger than the hard one).
And in the context of relevance, it now becomes clearer to me: it comes out that with “a stricter side,” you accept, according to the objector who is defending himself, the hypothesis that there is relevance (a shared factual characteristic) between two subjects that have different halakhic characteristics. But here you hold a general position (which the objector using “a stricter side” would also have to accept) that the default is that there is no relevance. So it turns out that for one who objects with “a stricter side,” the default of irrelevance is not independent but serves only to fend off arguments; and to the same extent one may assume relevance in order to fend off arguments. Correct?
What stricter side does the derived case have there? That it is invalid for ordinary food? According to that, whenever we are dealing with a kal va-chomer one could not invoke the objection of “a stricter side,” since the derived case too has a stricter side (quite apart from my explanation). I assume that once the kal va-chomer is rejected, the Gemara assumes that the stricter side is not relevant.
The fact that in some place they do not object with “a stricter side” proves nothing. After all, Ulla does object that way. So irrespective of my explanation, you have a difficulty on him from his own statements. Apparently there is some specific reason why there he does not object with “a stricter side,” or these are two different amoraim according to Ulla, or something like that.
As for the default regarding relevance, indeed. A mere possible hypothesis is enough to reject an inference.
That is indeed my claim: according to your explanation, one cannot object with “a stricter side” against a common factor that began as a kal va-chomer. This is specifically connected to your explanation; according to the explanation of Maharam Schiff and Penei Yehoshua in Ketubot 32, one can object there with “a stricter side,” because they did not find by reasoning a common denominator among the three subjects that would be the reason for the law. The stricter side in Sotah there needs to be especially well grounded, since Rabban Yohanan ben Zakkai foresaw that a later generation would come and object with this stricter side and declare it pure, and when Rabbi Akiva came and found a verse to declare it impure, Rabbi Yehoshua exclaimed: “Who will uncover the dust from your eyes, Rabban Yohanan ben Zakkai!”
And the difficulty from Ulla too is of course only according to your explanation, because only according to your explanation does the objection of “a stricter side” depend on whether the objections are halakhic or not. That is, someone who objects with “a stricter side” in one place harms himself and nullifies all the Talmud’s derivations by common factor that are built on halakhic objections (from what I remember when I tried to check, almost all the ones I saw are like that), including Ulla’s derivation in Bava Kamma 88 before the Gemara replaces it.
A. I don’t know what the Penei Yehoshua and the others explained. But as I said, there can always be a local explanation (from what I understand from you here, that is exactly what the Penei Yehoshua and Maharam Schiff did there). My explanation is, in my opinion, very sensible and compelling, so one needs strong evidence to reject it.
B. I do not understand why Ulla’s contradiction is not difficult for you. I do not see why one should not explain that he has a local reason there not to object with “a stricter side.” In any case one has to come to that.
There really is a difference in point of departure. In my opinion, your elegant explanation is possible in itself, but not “very sensible,” for two softer reasons.
One reason is that, in my opinion, even as an objection according to one opinion, it is very hard to defend oneself behind the pair of claims: there is a shared factual characteristic in the two source cases (which generates different halakhic characteristics), and it does not exist in the derived case.
The second reason is that the main empirical basis of the explanation is that in every one of the four places where they object with “a stricter side”—not including the side of altar / karet / transgression—the objections are halakhic and not factual. In my view this empirical basis is not enough, because there are very few occurrences of the objection of “a stricter side,” while on the other hand, from what I managed to check and see, a clear majority of all the Talmud’s derivations use halakhic objections. In particular, according to this, those who object with “a stricter side” would have to overturn the system in all the many sugyot that make a common factor with halakhic objections and draw conclusions from it.
Therefore my starting point is that ordinary evidence is sufficient, and one does not need strong evidence. And in addition, in my view the proof from Sotah is indeed strong, and I do not see in your words any resolution of it. Maybe there is a hidden characteristic, maybe there is a local explanation here, and maybe a local explanation there—what kind of method is that? When the matter comes up, we can discuss it.
The explanation of Maharam Schiff (Ketubot 32b, Tosafot s.v. “for they have”) and the Penei Yehoshua is not affected by the question whether the derived case also has its own stricter side. And it too is a general explanation like yours, only narrower in nature, depending on whether one finds a plausible common factor among the source cases and the derived case that would be the reason for the law. But in your explanation, the whole power of the objector to suggest that perhaps the hidden factual characteristic that exists in the two source cases (according to his suggestion, the same factual characteristic in both) does not exist in the derived case exists only because the derived case does not likewise have its own stricter side; otherwise this is just adding characteristics with no basis whatsoever, and one could refute any derivation in the world that way. Yet we see that the objector stands by his objection even when the derived case also has a stricter side.
With Ulla I do not understand your claim. Only according to your words, one who objects with “a stricter side” in one place does so everywhere the objections are halakhic. Yet we see that in two places where the objections are halakhic, in one he objects with “a stricter side” and in one he does not. Not so according to Maharam Schiff’s explanation: one objects with “a stricter side” where one cannot find a common factor between the source cases and the derived case. Therefore, aside from checking that in those places where they object with “a stricter side” it is indeed hard to find a common factor, all that remains is to verify that in all the other places where they do not object with “a stricter side,” there is in fact a common factor between the source cases and the derived case. And I think that this claim of his—that one needs to find a common factor—you also accept in any event, as emerged from your words in the sugya of the owners dealing with the carcass in 346, and so the Penei Yehoshua wrote there as well. In any case, I am not responsible for their explanation.
I find it hard, with my sins, to get into this any further. I will only note that the claim that there is no common side to the source cases that is absent from the derived case is an unreasoned claim. It is an okimta with no trace in the language of the Gemara. My explanation is a general explanation for all these cases by virtue of the very structure of a common factor with halakhic objections, without assuming additional ad hoc and unreasoned assumptions.
As for Ulla, I do not understand your claim. After all, I answer exactly what they answer (that there is no common factor there that is absent from the derived case), but only with regard to the difficult place. They assume ad hoc for all the places where they object with “a stricter side” that there is a relevant common side. By contrast, I assume such an ad hoc assumption only for the place where he does not object, in order to resolve a difficulty. That seems far more reasonable to me.
But as I said, it is hard for me to get into this any further.
Rabbi, if you could arrange for your articles to be printer-friendly I would appreciate it (I read many of them on Shabbat and print them out). It’s a headache to print—you can try it yourself and see why, especially this article.
Precisely for that reason, in articles like these we attach a PDF, and you can print that.
There isn’t a PDF, but there is a print button at the bottom of the page. For me it prints fine. You just need to switch to light mode before printing.
All I see here is a print button where everything is laid out nicely, but all the text is really faded.
I don’t see such an option. Do you mean printing with a black background for the whole article? Because if so, that works, it’s just a crazy waste of ink.
It appears at the end of the menu, on the opposite side from where the “Home” button appears.
Thank you very much, works great. I thought you meant the print settings, not a button in the site’s header.
I just added something that causes it to switch to light mode automatically before printing.
(Also regarding the previous post)
If in the sugya of “tooth and horn” all the data belong to the same field (= a one-parameter table), and given the simple assumption that the injured party’s courtyard is more stringent in its laws than the public domain, then seemingly a deductive conclusion follows:
B>A
a,b €A. a,b €B
aA<bA
Conclusion:
aB<bB
(B = the injured party’s courtyard. A = the public domain
a = tooth. b = horn.
€ = epsilon)
Here the assumptions are trivial (unlike the generalization assumption you proposed in the previous post), and one can approach the biblical text with them as such. Then, even though they are not explicitly separated out in the text, it would not be absurd to use them as a clear datum for this purpose, such that the result would count as deductive (at least from the trivial assumptions, even though they are not written).
If this is correct, then the result of one of the ‘kal va-chomers’ (straight or reverse) would indeed count as Torah law. (And then indeed one could not maintain the other side of the kal va-chomer as well.)
If so, my main question is: why here is the assumption that the datum in the sugya of ‘sustenance and Torah’ is 0,1 and not 1? Why indeed is the result of a kal va-chomer not considered Torah law (in the sense that it is a trivial conclusion), but rather of a lower status than an explicit verse?
I’m not sure I understood your point, but if I did, there is a common mistake here. Every kal va-chomer contains a generalization, and therefore it is not deduction. The generalization is: from a relation of stringency in one domain, to assume that the same relation of stringency holds in all domains. I explained this in the post.
Right.
But when the intermediate assumption (the generalization)
is present in the text, then it is indeed deduction.
Now, what happens in a case where it is not explicitly written, but is trivial (your proposal for the ‘generalization’ assumption is indeed not trivial, so I suggested another model: that the injured party’s courtyard is more stringent than the public domain, which is a trivial assumption)—what prevents us from regarding the result as a full Torah law?
It is no worse than our own reasoning that wearing square black leather boxes on the head and on the hand is Torah law, even though these are not explicit in the text.
If the stringency of the injured party’s courtyard were trivial by reasoning, there would be no need for the data about tooth and foot in the two domains. It would be a kal va-chomer with reasoning on the basis of one datum: if horn is liable in the public domain, it certainly is liable in the injured party’s courtyard. The Gemara uses those two data points in order to derive the generalization that the injured party’s courtyard is more stringent than the public domain. That is a generalization like any hermeneutic kal va-chomer based on three data points.
Why?! It is enough to say that the stringency of the injured party’s courtyard implies that tooth is liable there.
Therefore one needs the datum showing that horn is more stringent than tooth (in the model I proposed above, the picture is detailed).
*implies only
I’m sorry, but I do not understand what you are claiming.
I don’t see the ‘Reply’ box after the rabbi’s response, so I am replying here:
Forgive me. I will be more precise.
Assume that all the data belong to the same semantic field.
And we come to assume that the injured party’s courtyard is more stringent than the public domain; the basis for this is that tooth, which is exempt in the public domain, is liable in the injured party’s courtyard (that is, once these are explicit data we naturally assume that the injured party’s courtyard is more stringent than the public domain).
Now after these two assumptions (the second based on two data points in the public domain and the injured party’s courtyard),
we also find the assumption that horn is more stringent than tooth.
Now it follows that horn is liable in the injured party’s courtyard.
That is, given the above assumptions, it comes out that tooth in the public domain swallows up horn in the injured party’s courtyard.
If that is indeed so, I am not prevented from treating this result as Torah law even though it was not explicitly written, since it is implicit in the simple assumptions, similar to almost every Torah law where we come to the text with our simple assumptions and give the final interpretation the status of Torah law (I gave above the example of tefillin).
From your words in the post it seems that you do not hold this way, but rather that the result does not have the status of an implicit Torah datum.
The upshot is that if we are dealing with the hermeneutic rule of kal va-chomer, then since ‘leniency’ and ‘stringency’ are matters of logic, the statement in the post that “the rule of kal va-chomer is a textual and not a logical rule,” or something like that, seems at first glance to be an oxymoron. That is, what gives us the right to feed Torah and sustenance into the same table? And what gives us the right to determine that one of them is more stringent, if we are dealing only with the explicit text and not with its real-world meanings?
Put differently: how can there be a hermeneutic rule whose very meaning undermines itself? For at the first stage we treat the explicit text as more stringent relative to what is not explicit, and then surprisingly a result is supposed to emerge that is not written because it is more stringent. Seemingly, either way: if we are working on the biblical plane, then nothing can be learned (and the contradiction proves it), and if on the halakhic plane (= explicit data with real-world meaning), then as I said before.
If there is no reply box, you need to go back up until you encounter a box for the first time, click it, and reply. It will appear at the end of the thread.
As for your claim itself, I still do not understand it. If the generalization that the injured party’s courtyard is more stringent than the public domain is created from the laws of tooth and foot, then it is a generalization. If it is reasoning, then they would create it even without those two laws. I do not understand what it means to say that it is reasoning created from the laws.
Apparently I am missing something. If
1. the table is one-parameter
2. tooth is liable in the injured party’s courtyard and exempt in the public domain.
3. Intermediate conclusion: the injured party’s courtyard is more stringent regarding tooth
4. horn in the public domain is liable
5. Intermediate conclusion: horn in the public domain is more stringent than tooth in the public domain
Conclusion: horn in the injured party’s courtyard is more stringent than tooth in the injured party’s courtyard, and therefore liable.
The generalizing assumption is assumption 1.
But it is trivial because it is a simpler state relative to a two-parameter table.
Without assumption 2 I could not learn that horn is liable in the injured party’s courtyard, even if the table were one-parameter.
Maybe it can be modeled this way (after the assumptions):
Tooth has liability-strength 1
Horn has liability-strength 2
The public domain has liability-strength 1
The injured party’s courtyard has liability-strength 2
So the most liable case is horn + the injured party’s courtyard = 4 strengths of liability. So given that any case of 3 and below is liable, then 4 would also be liable.
What brings them all into the same ‘field of numbers’ is the assumption that they are indeed like this, namely one-parameter.
Where am I going wrong?
I will answer one more time and that’s it. The conclusion after 5 does not follow from all your assumptions. You simply do not write the generalization, but it is there.
The claim that a one-parameter model is simpler is a conclusion, not an assumption. But you cannot take it as a rational assumption that turns the argument into deduction. Every non-deductive argument is based on considerations like Occam’s razor in various forms.
All right, it’s not clear.
What about the continuation of my remarks from my first response (today),
from the section “The upshot of the matter”
?
The fact that we are operating on the textual plane does not mean that we ignore meanings. This is not mere empty formalism. We ignore the relations of stringency of the result, but the data in the text are measured against one another in terms of relevance and stringency.
I thought I would manage to ignore it; apparently not. So with fear and reverence I return once more to my first question, only since the rabbi’s time is precious I will put it simply. In addition, even a yes/no answer alone would help. :
According to the other commentators (excluding Rashi), as I understand it, carrying out the kal va-chomer does not undermine its assumptions, because the assumption that Torah is more stringent than sustenance remains in the result. Isn’t that so?
I’ve lost you. I too wrote that carrying out the kal va-chomer does not undermine its assumptions. After all, the Gemara does it. True, in the conclusion it is rejected. I explained that there is a difference between the textual plane and the plane of stringency, and apparently that is what Rashi means. So who are the other commentators, and what are they saying? I am really not following.
Excellent.
(I thought this was clear; now I understand that it wasn’t. So I note that all my remarks above concern the stage before you divide into two planes—textual and halakhic.) So in a ‘stringent and lenient’ argument, to make it easier, even according to Rashi does carrying out the derivation not undermine its assumptions?
Suppose, in the sugya of escorting a sotah: according to R. Yehudah they trust the husband, because if in the case of a menstruant, where the prohibition is karet, they trust him, then all the more so in the case of a sotah, where the prohibition is only a negative commandment. Here the ‘leniency’ for the husband is not written in the Torah, but its status really is lenient (which is the simpler state).
I am assuming (necessarily) that the state of ‘exempt’ is the simpler state. And that is the point of distinction in my remarks between a kal va-chomer and ‘stringent and lenient.’
Put differently, one can formulate ‘stringent and lenient’ like this: if in a place where there is explicit text the Torah exempted, then in a place where there is no explicit text, all the more so it is exempt.
Meshekh Chokhmah, Devarim 17:11 (Parashat Shoftim):
“It seems possible to give an intellectual explanation for why one does not derive a kal va-chomer from rabbinic law [see Yadayim]. For the example given in Torat Kohanim derives by kal va-chomer that on Sukkot one should be obligated in matzah, and in Kiddushin (4b) they derive from a maidservant who is not acquired through intercourse (but is acquired through money): if that one, which is not acquired through intercourse, is acquired through money, then this one, which is acquired through intercourse, is it not all the more so acquired through money? And likewise in tractate Derekh Eretz (Rabbah, chapter 1): if I am forbidden with a married woman, is it not all the more so that I should be forbidden with her daughter, etc.; see there. For a kal va-chomer has no place in deep rational analysis, since according to the nature of the subjects, the opposite may be required for one who understands the depth of their rationale [an example of this is Berakhot 23b: ‘This matter should come as a matter of reason and not as a matter of kal va-chomer,’ etc.]. Rather, the thirteen hermeneutic principles were handed down from Sinai, through which they judge, compare, and derive. And the Creator, blessed be He, who is infinite, knew that in order to remove the possibilities of error into which human reason may fall when it does not know the depth of the Supreme understanding, He revealed an extra word or a hint so that we should not come to error. And everything that has no explicit instruction in the Torah is learned through these thirteen principles. Not so with rabbinic laws, which human reason, with the Holy Spirit resting upon it—even if it attained the truth—cannot encompass all that we might learn in all sorts of foreign ways and remove errors by means of an extra letter or unusual word; this is difficult for finite human reason. Moreover, they were transmitted orally, where it is impossible to be precise about the words. Therefore they said: one does not derive a kal va-chomer from rabbinic laws [and this also gives some reason why one does not derive a kal va-chomer from a halakhah given to Moses at Sinai]. And likewise in tractate Derekh Eretz, the kal va-chomer of R. Yose ben Tudai would have been correct if the prohibition of a married woman were due to kinship. But the prohibition of a married woman is because she is the wife of another man. And the prohibition of one’s wife’s daughter is not a prohibition for some other reason, but because he has already married her mother and is forbidden with a woman and her daughter—this is the cause of her prohibition, and she is not called by the title ‘the daughter of his wife,’ but rather ‘a woman and her daughter.’ Therefore a sister’s daughter is permitted, and so on. So according to deep reasoning there is no kal va-chomer here at all, and in the Torah the opposite is explicit. Therefore Rabban Gamliel excommunicated him. This is correct; analyze it carefully.”
And R. Moshe Kazis writes at length similarly at the beginning of Bava Kamma.
It seems that the Meshekh Chokhmah is speaking about cases where there is direct reasoning against the kal va-chomer (anti-relevance). See Yaakov’s remarks above, who brought the derivation also mentioned in the Meshekh Chokhmah—that a woman is acquired by money by kal va-chomer from a maidservant—and the discussion beneath it. I do not have the words of R. M. Kazis; could you please quote them?
By the way, in the previous post I asked: if there really is a kal va-chomer that is rejected by force of reasoning (a presumption of irrelevance, or even a claim of anti-relevance), then we should expect to find such an occurrence explicitly in the Gemara, where they reject a kal va-chomer that way, and also that they would disagree about a certain kal va-chomer as to whether the reasoning rejects it or not. And from the fact that we still have not seen such an occurrence brought (for Torah law), a suspicion arises that the idea may be doubtful. The words of the Meshekh Chokhmah seem to answer this: that even against erroneous derivations, the Holy One, blessed be He, took care to write in the Torah a source for a derashah to exclude the mistaken derivation, lest we err. So in practice one can derive a kal va-chomer mechanically and ignore this problem—that perhaps the kal va-chomer is not sound in reasoning itself. This does answer what I asked, but seemingly it also neutralizes the whole novelty, because it comes out that there is no practical difference to the claim that one can reject a kal va-chomer by force of reasoning (even anti-relevance).
It seems to me that there is an example in the Ramban of irrelevance even in a kal va-chomer from three laws. The Gemara in Kiddushin (4b) proposes a kal va-chomer: if a Hebrew maidservant, who is not acquired through intercourse, is acquired through money, then betrothal, which is effected through intercourse, all the more so should be effected through money.
Hebrew maidservant Betrothal
Intercourse 0 1
Money 1 ⟸
In the end the Gemara refutes this, but the Ramban challenges the very kal va-chomer:
“It is difficult for me, for this is not because intercourse is a leniency, but because her acquisition is not for any marital bond.”
That is, he objects that intercourse is relevant only to betrothal and not to a Hebrew maidservant, since intercourse is meant to create a marital acquisition, whereas a Hebrew maidservant is not acquired for marriage but for servitude. Therefore, the fact that a Hebrew maidservant is not acquired through intercourse does not show that it is ‘harder’ to acquire her, since this mode of acquisition is simply not relevant to her at all. And indeed the Ramban answers that one really could have refuted it this way, but the Gemara nevertheless preferred to say that even if we wanted to learn it by kal va-chomer, it could still be refuted.
And one should note that the rule that a Hebrew maidservant is not acquired through intercourse does not itself stem from this reasoning that acquisition by intercourse is inapplicable to her, so that this would really be a kal va-chomer from two laws. Rather, this rule is learned from a verse (Kiddushin 9b): from the verse “When a man takes a woman and has relations with her,” the Gemara excludes and teaches that specifically betrothal is effected through intercourse, and a Hebrew maidservant is not acquired through intercourse. If so, this turns out to be a kal va-chomer from three laws, which according to the Ramban can at least be refuted by the claim of irrelevance.