The Role of “Nafka Minot” (Column 481)

In column 479 I discussed the purpose of Torah study and the relationship between study and halakhic rulings. I argued that, on the one hand, study is not merely a means to know what to do (i.e., an instrument for observance), and on the other hand, study should culminate in a practical conclusion. My claim was that the requirement for study to be conclusive does not make it instrumental to practice; rather, this is the proper form of study: proper study should end with practical implications.

One implication of such an approach is that we may discuss non-realistic situations or non-realistic nafka minot (practical differences). The Talmud contains several such cases—some situations that cannot occur at all (a “flying camel”), and others whose realization is extremely uncommon (placing a bill of divorce in the hand of a bound and sleeping slave). It seems to me this indicates that practical cases are presented as the conclusion of the study rather than as an instruction for what to do in practice (see on this in volume 11 of the Talmudic Logic series, on the Platonism of the Talmud).

In this column I wish to touch a bit on the concept of nafka mina—that is, the importance and function of practical implications in our study, and also in scientific research (after writing I noticed substantial overlap with column 404, but I decided to leave the discussion as is).

A nafka mina for betrothing a woman

There is a common yeshiva quip: one student senses that his friend is advancing a claim X (asking, answering, distinguishing), but in truth it’s just words with no practical consequence, so he asks: “Lemai nafka mina?”—what practical difference does it make? The other replies: “A nafka mina for betrothing a woman,” meaning: if a man betroths a woman on condition that X is true, then the question becomes whether she is betrothed or not.

What’s the problem with such a nafka mina? It turns every question into a halakhic/Torah question worthy of discussion in the beit midrash. Even the question of whether there are at least three fleas in this room is a nafka mina for betrothing a woman. The expression “a nafka mina for betrothing a woman” has become a way to mock statements lacking practical implications—and perhaps lacking meaning.

This quip has roots in the Talmud and the Rishonim. For example, Noam asked me a few months ago about nafka minot cited in Chagigah 6b:

Rav Chisda inquired: How is this verse written—“And he sent the young men of the Children of Israel, and they offered burnt offerings of sheep, and they sacrificed peace-offerings to the Lord—bulls” (i.e., were the olot sheep) or perhaps both were bulls? What is the practical difference (nafka mina)? Mar Zutra said: for the division of cantillation; Rav Acha the son of Rava said: for one who says, “Behold, it is upon me to bring an olah like the olah that Israel offered in the wilderness”—were they bulls or sheep? Teiku (unresolved).

The Gemara is uncertain whether the burnt offerings offered in the wilderness were bulls or sheep. To the question “what practical difference does this make?” it gives two answers: for the division of the verse (whether there is a pause after “olot”), or for one who vows “It is upon me to bring an olah like what Israel offered in the wilderness.” The second answer is essentially the “nafka mina for betrothing a woman,” since it too turns any question into a Torah question.

Another example appears in the Ran on Sanhedrin 15a. The Gemara there discusses the rule “As the owners’ death, so the ox’s death”—that an ox that killed a person is judged by twenty-three judges, just like a person who killed a person. In that context the Gemara asks: “How many judges for the ‘Sinai ox’?”—that is, with how many judges were the oxen judged that approached Mount Sinai and were liable to death (“both the flocks and the cattle shall not graze facing that mountain”).

The Ran, in his novellae there (15b), asks:

“And if you will say: Why derive anything from this—whatever was, was? One can answer: ‘Expound and receive reward.’ Alternatively, a practical difference emerges for one who vows: if he says, ‘I am a nazir if the death of the Sinai ox required twenty-three (judges),’—if it did require twenty-three, he is a nazir; if not, he is not a nazir.”

Again we see the “nafka mina for betrothing a woman.”

What is going on here? I suspect the Ran was actually joking—and perhaps the Gemara as well. But if so, the question remains: does such a question have meaning? Is there value in engaging it?

The meaning of such nafka minot

Note that in both cases, the option resembling the “nafka mina for betrothing a woman” is brought second, and in both a more serious option appears first: in both cases the aim is to understand what the Torah says. Remember: every exegetical question about the Torah lacks a practical difference. Where did Jacob—or Abraham—go? Why did Moses flee Egypt? What was the name of Aaron the Priest’s wife? What is the genealogy from Adam to Noah? All these are questions without practical consequence, yet people engage in them (those who choose to waste time on them—unlike me) because they clarify the meaning of the verses. That is Torah study (to be precise: low-quality bitul Torah), even if it is not the study of halakhah.

Notice that the questions raised in the Gemara in Chagigah and Sanhedrin are also exegetical questions about the Torah: whether they offered bulls or sheep, and with how many judges the ox near the mountain was judged. Moreover, from the “Sinai ox” case one might glean insights regarding the halakhic principle “as the owners’ death, so the ox’s death,” which could then have actual halakhic ramifications. If so, it is quite possible that the second nafka mina cited in Chagigah and by the Ran is presented as a mockery of the questioner: there is a simple reason these questions have value—they clarify the text—so one who hangs importance solely on practical implications is answered with: it’s a nafka mina for a vow or for betrothing a woman. In that case this is truly a joke in the modern sense described above.

By the way, in Brisk it is customary to brush off such “lemai nafka mina” challenges to lomdish inquiries. Someone presents two sides of an analysis, and the local wise-guy asks for the practical difference; to blunt his teeth one answers: “A nafka mina for betrothing a woman.” The point is that the sides have clear meanings and the question is understandable even without a practical difference. Moreover, the retort claims that the value of engaging in the inquiry—and of Torah study in general—is not confined to practical consequences; there is value in the intellectual clarification itself. This brings us back to column 479, where I argued that study has intrinsic value, and its role as an instrument for clarifying halakhah is only an enabling means, not the mitzvah of Torah study itself.

Nafka mina as a criterion for meaning

But the fact remains that in the Talmud—and in the beit midrash generally—we certainly do discuss practical differences for various claims. It’s hard to ignore that searching for a nafka mina is an important part of study. A nafka mina can clarify the different sides of a dispute or inquiry; even if it is not essential for the value of study (which exists even without it), it is certainly worthwhile to seek practical differences to sharpen our understanding.

Sometimes, however, one feels we must find a nafka mina because without it the discussion truly lacks meaning—not merely value. Sometimes people debate two sides of a Talmudic inquiry, and the sense is that both sides are saying the same thing in different words; there is no real difference in meaning. In such a case, a nafka mina is essential to show that there are genuinely two sides. By the way, in such a case the “nafka mina for betrothing a woman” will be of no help at all, for if there is truly no difference between the sides, there will be no practical difference for betrothal either. Here that line is certainly a joke, and effectively means the inquiry has no meaning.

An example is the inquiry mentioned in column 404: is Shabbat deferred (dechuyah) or permitted (hutrah) in the face of danger to life? I argued there that there is no nafka mina between the two sides; if I am right, it is doubtful the inquiry has meaning at all. Not necessarily because the sides are equivalent (saying the same thing in different words), but because the “deferred” side is false: there are not truly two sides—clearly Shabbat is permitted in the face of danger to life, not merely deferred. Note that if this is so, then there is indeed a difference in meaning between the sides, except that one of them is simply incorrect. One might try to claim there is no difference in meaning, since if Shabbat is “deferred” in the face of danger to life, the act is permitted; whether or not that claim holds, it already undermines the very difference in meaning between “deferred” and “permitted.”

By the way, in philosophical literature there is often a sense that many questions or claims lack meaning, and that proposed distinctions are merely two formulations of the same thing (see, for example, column 223 on “the French and their helpers”). In such cases it is very important to look for a nafka mina to sharpen the difference between the options—if there is one.

Between consequences and meaning: logical positivism

Note that the logical positivists held that a statement that cannot be tested by experiment is meaningless—that is, on their view, lack of practical consequences is identical to lack of meaning. But this is clearly nonsense. There are quite a few statements with no practical consequences, and it is hard to deny that they have meaning. In practice, there are many claims we cannot test empirically, such as: “There are exactly 103 billion ants in the universe.” There is no practical way to refute or confirm this. Does it have meaning? Clearly yes. One could reply that here the impossibility of testing is merely technical, not essential—but still, there is no way to confirm or refute it.

Beyond that, the claim “One ought not waste time” is a claim that cannot be empirically confirmed or refuted; in fact every value claim is like that. Is it reasonable to say such claims are meaningless? Carnap thought so (he called them pseudo-statements), but that is empty semantic pilpul (does this judgment itself have meaning? can it be confirmed or refuted?). In short, we must distinguish between statements that lack practical implications and statements that lack meaning.

What bothered the positivists about statements without practical consequences was that they cannot be empirically refuted or confirmed; they somehow identified a claim’s scientific status with its meaningfulness. But a more moderate and stronger criticism of such claims is available: if a claim has no practical consequences, it lacks meaning because it says nothing. Here “practical consequences” are the point, irrespective of empirical testability. For example, a value claim does have practical implications: “One ought not waste time” implies—don’t waste time. It cannot be tested empirically and is therefore unscientific, but it certainly has meaning.

And what about the claim “God exists”? Assuming we are speaking philosophically (deistically) and not religiously (theistically), it has no practical consequences. Does it have meaning? Certainly. Why? Because it has factual implications—namely, that there is a God. It asserts the existence of something in reality. In that sense, every proposition has meaning, since it states something about the world. Meaningless sentences are not propositions: contradictions (e.g., “this sphere is a square circle”) or nonsense (e.g., “virtue is triangular”) are meaningless. And what about questions like “What time is it?” They are not assertions about the world and do not point to a particular fact, yet clearly they have meaning. In this case the meaning is not something in the world to which the sentence points, but what occurs in my mind and leads me to answer the question—what I grasp when I hear it (that one is asking me for certain information).

Empty distinctions in science: on teleology

In the fourth conversation (part two) of my book HaMetzi HaRishon (The First Being) I discussed the dual formulations that exist in much of physics between causal and teleological formulations. It begins with Aristotle, who held that a stone falls to the ground because it “strives” to return to its natural place. I do not assume Aristotle thought stones have aspirations and make calculations; rather, the law of nature is that the stone moves with the goal of returning to its source—perhaps its Creator arranged it so.

Consider Fermat’s principle as an alternative formulation of the laws of geometrical optics. For example, Snell’s law links angles of refraction and refractive indices of different media and describes the path of a light ray crossing from one medium to another (e.g., water to air) and refracting. Instead of all this complexity, Fermat proposed that the ray always traverses the path that brings it to its destination in minimal time. It turns out this description is entirely equivalent to the standard description in geometrical optics. Likewise for the description of a body’s trajectory (position and velocity as a function of time) under a force: one can describe it via forces and accelerations or via energies and potentials. These, too, are equivalent descriptions.

Equivalent descriptions in physics mean that the same phenomena can be described in two entirely different languages, and the outcome of calculations in one language will not differ from those in the other. So which is correct? Both are. Yet one may still ask: does the light ray “calculate” minimal time (a teleological description), or does it simply refract when passing between media (a causal description)? Physics cannot answer that. From its standpoint they are the same claim in two different languages, because physics translates every claim into its practical consequences (predictions), and in this sense the consequences are the same—therefore the claims are the same.

Nevertheless, one might argue: if the light ray acts teleologically, then there is likely some intelligent agent controlling it (or having set things up that way), for the light ray surely does not make purposive calculations. From my remarks it follows that there is a consequence to this difference, even though scientifically they are the same claim. This demonstrates that while it is very useful in science to identify a claim with its observational consequences (which underlies Popper’s criterion of scientific status: empirical falsifiability), that identification is not complete. Outside the scientific domain, such claims are not necessarily identical. The emptiness of this scientific inquiry exists only on the empirical-scientific plane; it is not true that the meanings of the two sides are identical.

Another example is the dispute between the Copernican (heliocentric) view—that the earth revolves around the sun—and the Ptolemaic (geocentric) view—that the sun revolves around the earth. More than once (see column 112, here, and in brief here) I argued that in this case matters are even more extreme, since it is not clear we are dealing with two distinct claims (or descriptions) at all. When one observes the solar system from the earth’s frame, the sun revolves around the earth; from the sun’s frame, the earth revolves around the sun. But a change of reference frame does not produce a different claim; at most it is a different linguistic description of the same claim. It’s like the parable of those arguing about how to describe an elephant: one says it has two very close legs and two eyes; the other says it has two far-apart legs and one eye. The first looks from the front, the second from the side; both are describing the same thing (though here each is giving only a partial description, and thus there is a real—albeit illusory—dispute).

In the dispute between geocentrism and heliocentrism you will not be able to produce a nafka mina (a practical consequence distinguishing the descriptions). Here, unlike the previous example, this is not due to the limitations of empirical science but because these are actually identical claims. The question “Lemai nafka mina?” in this case truly hides the assertion that this “dispute” has no meaning; it is two different descriptions, equivalent to the very same picture.

I find this very amusing, because many self-styled know-it-alls (scientists or “scientismists”) explain to us, with great relish and certainty, that those (religious people) who cling to Ptolemy’s geocentric description are primitive—unaware that Copernicus already showed it to be false. This is of course nonsense. Copernicus merely found a more convenient coordinate system for describing the solar system; there is nothing inherently truer or falser in it than in the geocentric description that preceded it.[1]

[1] My claim of “no difference between the descriptions” concerns kinematics (the theory of motion). On the dynamic level (forces and accelerations) there is a difference between these descriptions, but I do not wish here to enter questions of fictitious forces, inertial frames, etc. A layperson who does not view this scientifically has kinematic descriptions in mind, and therefore my discussion here is the one relevant to him.