Rabbi Yehuda and Scientific Nullification (full article)

In Zevachim 79, a brayta discusses cleansing a broken earthenware flask which had absorbed mei raglayim of a zav. The anonymous Tanna Kamma says that washing it three times with water will cleanse it and it will be ritually pure. However, washing it three times with mei raglayim of a non-zav will not. Rabbi Eliezer ben Yaakov says that even washing it with mei raglayim three times will thereby cleanse it. The underlying reality seems strange, but In antiquity — especially in ancient Rome — aged mei raglayim was used to clean and whiten textiles, because the ammonia formed in it works as a strong cleaning agent.

Who is the anonymous first Tanna in this brayta? The gemara suggests it’s Rabbi Yehuda (ben Illa), a fifth-generation Tanna in the 1st and 2nd century CE, based on the halachic position expressed in the Mishnah on Zevachim 78a – אֵין דָּם מְבַטֵּל דָּם. We’ll add that this works well with the explicit disputant, fifth-generation Rabbi Eliezer ben Yaakov II. Rabbi Yehuda’s well-known opinion is that nullification works with unlike substances (water and wine), but not with like substances (dam of a goat and bull). This is an interesting application of that principle, since one might otherwise claim that halachic nullification isn’t relevant, so much as whether the original material has been driven out by the cleansing process.

Atomists vs. Continuists

How does bittul, nullification, work? Does it operate via statistical likelihood, legal fiat, or scientific mechanism? I’d argue that different types of bittul fall into different categories. Here we focus specifically on liquids nullified in other liquids (lach belach), and we’ll posit that bittul operates physically.

Among ancient scientists, there was a debate between the Atomists and Continuists. Among the Atomists were Leucippus (mid-5th century BCE), Democritus (late 5th- early 4th), Epicurus (4th - 3rd), and Lucretius (1st century BCE, and Roman rather than Greek). The atomist view is fundamentally discrete. Everything is made of indivisible atoms moving in the void, and these atoms differ in properties like shape, size, arrangement and motion. And macroscopic qualities (such as hot, sweet, red) are emergent from how atoms are arranged and move.

The Continuists included Anaxagoras (early 5th-century BCE), Empedocles (mid 5th-century), Aristotle (late 4th) and the Stoics (3rd - 1nd century). I am simplifying and combining different theories, but they understood every substance as being composed of four elements or roots: earth, water, air, and fire. We can explain Empedocles as saying that every substance can be construed as a vector of four roots: (x_earth​, x_water​, x_air​, x_fire​), where each component is a fractional contribution. Aristotle agreed with the existence of four factors, but these were hot, cold, wet and dry. The elements were made of these, with fire as hot + dry, air as hot + wet, water as cold + wet, and earth as cold + dry. His vectors are not fractions of fire, water, etc., but of intensity of qualities, thus (q_hot​, q_cold​,q_wet​, q_dry​). Don’t worry that we’d say hot is the opposite of cold. Every substance had some hot quality and some cold quantity as part of it, so it is a four-dimensional vector. He actually also considered secondary factors like flavor, color, texture, and small as qualities that we could establish as part of this vector, but they would reduce to the four fundamental qualities. Later medieval Aristotelians added and explicitly mathematized many more qualities, including brightness, color degree, and hardness.

Explaining Bittul

Taking an atomist perspective, it is difficult to understand bittul of liquids from a scientific perspective. After all, even if you pour a cup of wine into a barrel of water and can no longer discern its presence, every atom is still present. It is be’ein. We would describe the bittul operation as experiential – can we humans discern it, and would we still call it wine or wine-like? Alternatively or relatedly, it operates legally - we declare that at this concentration or beneath this threshold, we no longer grant it the status of wine. Or there is a principle of rov, so we don’t care legally about the wine’s presence.

From a continuist perspective, bittul of liquids makes more scientific sense. In De Generatione et Corruptione I.10, Aristotle distinguishes between Aggregation, Alteration, and True Mixture (mixis). In Aggregation, two bodies lie next to one another – for instance, wheat and barley grains mixed together in a sack. The constituents remain unchanged and they retain their own qualities and forms. In Alteration, there is change in quality but not change in substance. Examples include water being heated still being water, milk souring and thus changing its qualities but remaining milk in substance, and metal being heated and therefore softening.

Finally, in True Mixture, two substances combine to form a new, uniform body in which neither original ingredient remains in its original state but both contribute “potentially”. Indeed, his example is mixing water and wine. In a mixture, the extremes are “reduced to a mean state” (mesotēs). He didn’t use vectors of numbers but imagine that we assigned easy to use numbers, with wine as (H = 0.8, C = 0.2, W = 0.6, D = 0.4), and water as (H = 0.2, C = 0.8, W = 1.0, D = 0.0). If we mix these two liquids in equal measure, then all that material assumes the average of these two vectors, with (H = 0.5, C = 0.5, W = 0.8, D = 0.2). And the milder wine-water taste is how we perceive that mixture. Similarly, say we mixed them in different proportions – 1 part wine to 3 parts water, then the resultant vector would be the weighted average, with Hot as 0.8 x 25% + 0.2 x 75%, Cold as 0.2 x 75% + 0.8 x 25%, and so on.

Dissolving vs. Proportionality

For Aristotle, this is true so long as one substance doesn’t vastly outnumber the other. If it does, he writes that “the effect produced is not ‘combination’, but increase of the dominant: for the other material is transformed into the dominant. (That is why a drop of wine does not ‘combine’ with ten thousand gallons of water: for its form is dissolved, and it is changed so as to merge in the total volume of water.)” In other words, Aristotle asserts that there is physical bittul, in which the wine no longer exists, and becomes water. There is no be’ein.

Plutarch (in 1st–2nd century CE) reported on the position of the Stoics. While Continuists, they disagreed with Aristotle. Discussing the wine and water case, they maintained that even in such non-proportional quantities, the effect was of combination. Chrysippus’ famous example is that a drop of wine can “coextend” through the whole sea. Rather than vanishing, the quantities in the vector are just incredibly diluted. I’d argue that the Stoic position, as well, can work as physical bittul. There is no be’ein, of atoms or molecules of wine present in this mixture. Rather, the water became more wine-like and the water became more wine-like, but this weighted average has so little wine-contribution, and is so water-like, that it is indeed water.

Understanding Chazal

Knowing the historical scientific background can help us understand certain halachic positions as well as halachic disputes, as different Sages may be grounded in different scientific theories. Above, we saw how bittul of liquids aligns with Aristotelian and Stoic science.

Similarly, different nullification laws apply in different circumstances. (See Rava on Zevachim 79a.) For instance, we distinguish between lach belach (liquids) and yavesh beyavesh (solids). As above, Aristotle also made this distinction, between Aggregation and True Mixture, with the latter only working in liquids. Solids retain their own identities, and can be picked apart with time and effort. Therefore, other purely legal principles of bittul, for instance following the majority, or legal and statistical principles of kol defarish meirubo parish, would instead apply.

Likewise, consider where the smaller liquid progressively drips into the larger liquid. Do we say that each drop progressively gets nullified (רִאשׁוֹן רִאשׁוֹן בָּטֵל)? This is Rabbi Yochanan’s position here in Zevachim 78a, as reported by Rabbi Chiya bar Abba, and elsewhere as by Rav Dimi. This corresponds to Aristotle who would argue for true nullification – increase in the dominant. Or, perhaps Rabbi Yochanan’s position is as reported by Ravin, that as the wine continues to drip its proportion increases past the nullification ratio, it reawakens (חוֹזֵר וְנֵעוֹר) and resumes its prior status. This would correspond to the Stoic position. Since the drop coextended through the entire mixture and was always present, once additional wine further modifies the quality vector, the wine can reassert itself.

Turning to Rabbi Yehuda, why would dam of a chaya and beheima not be nullified, just because they are the same min? If he were an Atomist, why should this be a distinction? (Yes, we could devise experiential or legal reasons.) If a Continuist, and further an Aristotelian Continuist, he would distinguish between True Mixture and Transformation towards the Dominant. If the two liquids are of essentially the same quality and the vectors are quite close in four-dimensional space, then nothing is dominant, and one would not transform.

Indeed, here is how Aristotle expressed the concept, which implications on min bemino, again in De Generatione et Corruptione I.10: “On the other hand (ii) when there is a certain equilibrium between their ‘powers of action’, then each of them changes out of its own nature towards the dominant: yet neither becomes the other, but both become an intermediate with properties common to both. Thus it is clear that only those agents are ‘combinable’ which involve a contrariety-for these are such as to suffer action reciprocally.” On min beshe’eino mino can involve bittul (transformation towards the dominant), instead of mixus.

Alternatively, within Stoic scientific theory, these quantity vectors always assume the weighted product, but enough of a shift would cause us to declare that all the material wine is no longer wine-like. Accompanying that physical shift, which we can call bittul, can be a halachic shift – it no longer carries its yayin nesech status. However, if we dilute forbidden wine in permitted wine, the vectors stay essentially constant. With no physical “nullification”, there is nothing for a halachic transformation / nullification to attach to.

This would also impact a discussion by Tosafot (on Zevachim 73a, s.v. רבי יהודה אומר) about which methods of nullification prevail when, in terms of like types. Rabbeinu Tam first suggests that Rabbi Yehuda only says that min bemino doesn’t nullify by liquids, not dry material; he then retracts. However, his original proposal is compelling, since physical nullification, or lack thereof, only occurs for liquids, while solids undergo aggregation. There’s more to explore, but hopefully this article can serve to shift our perspective as we analyze all sugyot regarding bittul,