‘The Common Denominator’ and ‘Conceptual Construction’ (Column 347)

Contents of the Article

With God’s help

‘The Common Element’ and ‘Conceptual Construction’

Introduction

In the previous column I dealt with inferences of the ‘common element’ type. We saw there three possible situations:

1. The ordinary case: when there is a common element shared by all the primary categories and the derivative (Figure 1 there).
2. There is a common element only to the primary categories, and it is not found in the derivative (Figure 2 there). In such a case the inference is refuted.
3. There is no common element even among the primary categories (Figure 3 there).

I explained that the resemblance of the third type to inferences of the ‘common element’ is merely external. There is no common element here, and the rule is learned only for those derivatives that resemble one of the primary categories. The result is a union of sets of prototype inferences from one text, from each of the source categories.

As I wrote at the end there, in this column I will try to identify a fourth type of learning from two sources, which at first glance appears identical to the third type, that is, one in which there is likewise no common element shared by all the primary categories. As we shall see here, in certain situations one can nevertheless use the two primary categories and draw from them conclusions broader than what is contained in them themselves. For reasons that will become clear below, I call such situations and such inferences ‘conceptual construction’.

The Common Element in the Laws of Shabbat

In the previous two columns I mentioned that in the discussion of the prohibited labors on Shabbat we do not find a derivative that cannot be learned from a single primary category, one that requires two primary categories to teach it by way of the common element. But there is nevertheless one exception in the context of the labors of Shabbat, which on its face looks like a derivative of two different primary categories.

The Jerusalem Talmud (Shabbat, chapter Klal Gadol, halakhah 2) brings the following statement:

If one spits and the wind carries it off, he is liable for winnowing; and anything that depends on the wind is liable for winnowing.

The Jerusalem Talmud rules that a person who spits on Shabbat and the wind scatters the spittle is liable to bring a sin-offering for winnowing. So too was this ruled in __Or Zarua (part 2, sec. 59) and in __Rokeach (sec. 62), and also in Rema (Orach Chayim, end of sec. 319), who writes:

One who spits into the wind on Shabbat, and the wind disperses the spittle, is liable for winnowing.

The continuation of the Jerusalem Talmud, where the generalization appears, that anything in which the wind is involved is liable for winnowing, is not cited here. Some commentators explained that the wind breaks the spittle into tiny pieces (see, for example, Korban Ha-Eidah on the Jerusalem Talmud there), meaning that there is here something akin to the labor of grinding. But many have already noted (see Chayei Adam in __Nishmat Adam__ rule 15, sec. 1, and R. Akiva Eiger, responsum 20; see also in the book __Menuchat Ahavah __part 2, ch. 7, note 13) that this explanation is extremely forced. The labor of winnowing is throwing grain together with chaff into the air so that the wind separates them, and the kernels fall back down once separated from the chaff. The Gemara says that it belongs to the family of the labor of selecting, together with sifting. See Shabbat 73b: ‘Winnowing is the same as selecting, the same as sifting.’ Beyond that, this certainly does not fit the Jerusalem Talmud, for it generalizes to any labor involving the wind.

Therefore some emended the Jerusalem Talmud so that its intent was to say that one is liable for ‘throwing’ and not for ‘winnowing’. See the glosses of Arukh Lechem by Maharikash (end of sec. 319) and Responsa Yechaveh Da’at (part 6, sec. 25). Again, if so, the generalization there is unclear. Other commentators explain that the Jerusalem Talmud intends to impose liability for throwing, that is, for moving an object four cubits in the public domain, and not for winnowing. They emend the text of the Jerusalem Talmud, and again the generalization requires explanation (perhaps they delete that as well, but then this really is far-fetched). Beyond that, in the words of the Rema this explanation is impossible, since his reading is that one is ‘liable for winnowing’.

Now in __Bi’ur Halakhah__ there he cites in the name of R. Menashe of Ilya, one of the disciples of the Gra (end of sec. 319, s.v. ‘disperses’):

And in the book Alfei Menashe he explained that the intent of the Jerusalem Talmud is a case of carrying four cubits in the public domain by means of the wind, and winnowing is mentioned only by way of example. That is: just as in winnowing, although the wind assists him he is nevertheless liable, so too with one who spits, where the transfer is accomplished by the wind, he is likewise liable. And this is correct.

It seems that R. Menashe of Ilya interprets the Jerusalem Talmud, like the above Acharonim, as referring specifically to the public domain, and what it imposes liability for in the case of spitting is throwing four cubits in the public domain (presumably the Jerusalem Talmud would likewise impose liability for transfer from a private domain to a public domain and vice versa). However, unlike those Acharonim, he does preserve the reading ‘winnowing’ in the Jerusalem Talmud, and does not change it to ‘throwing’. His claim is that the labor of winnowing was brought only as an example for the case of spitting.

From his words it emerges that spitting is a derivative of two primary categories: winnowing and throwing (carrying four cubits in the public domain).^[1] From the labor of winnowing we learn that a prohibited labor, indeed any labor, and that is the generalization there, when done with the aid of the wind is considered as though the person did it, and therefore carrying four cubits in the public domain, which is certainly a prohibited labor, is prohibited even if it is done by means of the wind. It should be noted that this also appears to be the conclusion of the __Bi’ur Halakhah __itself, as emerges from the end of his words, and it clearly seems that this is the most plausible interpretation of the Jerusalem Talmud. It answers the difficulties and also explains the generalization: for any labor aided by the wind one is liable, and this is learned from winnowing.

This is a unique example of a derivative learned from two primary categories. At first glance, then, we have found here a case of learning by way of the ‘common element’ even in the context of the labors of Shabbat. Before we continue discussing this, let us note something about this conclusion from a dispute among the Rishonim in the sugya in Bava Kamma 60a.

Winnowing and the Wind’s Assistance

In the sugya in Bava Kamma 60a, they discuss damage caused with the aid of the wind, damage that resembles fire. The Gemara there states that the damager is exempt, and raises a contradiction between the law in damages and the law of winnowing on Shabbat:

The Rabbis taught: If he stoked it and the wind stoked it further, if his own stoking was enough to make it blaze, he is liable; and if not, he is exempt. Why? Let it be like winnowing, where the wind assists him!

We see that with respect to damages, if a person intensifies a fire with the indispensable help of the wind, he is exempt for the damage caused by his property, that is, the fire. But with respect to the labors of Shabbat he is liable for the labor of winnowing, which is done with the assistance of the wind.

The Gemara there offers four resolutions to this contradiction. What interests us is the last of them, proposed by Rav Ashi:

Rav Ashi said: When we say ‘winnowing and the wind assists him,’ that applies only with respect to Shabbat, for the Torah prohibited purposeful labor; but here it is only indirect causation, and indirect causation in damages is exempt.

Rav Ashi explains that in the labor of winnowing on Shabbat one is liable because on Shabbat the Torah prohibited purposeful labor. But in damages there is no importance to the fact that this was purposeful labor, and so long as another force was involved one is exempt.

What is purposeful labor? The accepted explanation (see column 345) is that his intention was realized. That is, if a person performs some act indirectly, for example with the help of the wind, and from the outset he planned to make use of the wind and his plan was fulfilled, the wind’s involvement does not exempt him. His intention was realized, his plan came to fruition, and therefore he is liable. By contrast, in damage caused by one’s property there is no rule of purposeful labor, and so there the involvement of the wind exempts because it is only indirect causation.

The Rishonim there disputed the meaning of Rav Ashi’s words. Rashi there writes:

Purposeful labor: his intention was fulfilled, for he wants the wind to assist him.

From his wording it appears that this is a general principle valid for all the labors of Shabbat, namely that, unlike in other areas of law, even one who performs a labor indirectly is liable on Shabbat, because his intention was realized.

By contrast, the Rosh in his rulings there (ch. 6, sec. 11) writes:

And we do not say that, although the wind assisted him in making the fire, it is as though he did it alone, just as with winnowing and the wind assisting him, where we regard it as though he performed the labor alone. For there the Torah prohibited purposeful labor; even though it is only indirect causation, the Torah nevertheless made him liable in this case, since the essential manner of performing this labor is by means of the wind. But here it is only indirect causation, and indirect causation in damages is exempt.

The Rosh explains that the fact that the wind assists exempts only in labors like winnowing, whose normal manner is to be done by means of the wind. His words imply that in labors that are not ordinarily done with the aid of the wind, even if the person planned to make use of the wind and his intention was realized, he would not be liable. In other words, according to the Rosh this is not a general principle but a special law concerning winnowing, and it cannot be learned from for other labors.

We can now see that R. Menashe of Ilya’s derivation regarding spitting seems plausible, indeed almost necessary, according to Rashi’s understanding, which holds that there is a general principle throughout the labors of Shabbat that when a person plans to make use of the wind he is liable. But according to the Rosh this is a special rule of the labor of winnowing, and it cannot be learned from for our case. Here the liability is for the labor of throwing and not for winnowing, and in throwing the ordinary manner is not aided by the wind, although one could dispute that, and then R. Menashe’s words would fit even according to the Rosh. See more on this at the end of the column. What underlies their dispute? Is the logic of an inference from two sources not agreed upon by all? To understand this we must enter more deeply into the logic of the inference.

Is This Inference ‘The Common Element’?

Let us now look at the derivative of spitting, which according to R. Menashe of Ilya is learned from winnowing and throwing. Is this an inference of the ‘common element’? At first glance yes, for this scheme can be presented exactly as we saw in the previous column:

We try to learn spitting (C) from throwing (A).

We refute: what distinguishes throwing is that no wind is involved (x).

We learn spitting (C) from winnowing (B).

We refute: what distinguishes winnowing is that it is a labor of separating food from waste (y).

And so the rule returns: we learn from winnowing and throwing together to spitting.

The resemblance to inferences of the ‘common element’ seems perfect, since the derivative spitting is learned from the two primary categories winnowing and throwing, and cannot be learned from either of them alone. To see that this is an illusion, ask yourselves: what is the shared characteristic, the common element, of winnowing and throwing, which they share with spitting? In other words, can this inference be presented by means of Figure 1 from the previous column? What would the characteristic z be in this case?

It is quite clear that there is no characteristic common to winnowing and throwing.^[2] Therefore this inference resembles the type presented in Figure 3 in the previous column, and not the one in Figure 1. But in Figure 3 we saw that the result of the inference is a union of two or three prototype inferences from one text, that is, each primary category teaches separately and the derivatives are the sum of the derivatives learned from all the primary categories. There is no fusion there between the primary categories that yields a new derivative that cannot be learned from one of them. But in our case the inference is clearly different: we saw that the derivative, spitting, cannot be learned from any one of the primary categories, winnowing and throwing, separately, but only from both together.

‘Conceptual Construction’

From this it is clear that this exceptional example as well is not an inference of the ‘common element’, but another kind of inference, which I shall call ‘conceptual construction’. We construct the derivative, spitting, by means of a synthesis between the two primary categories, winnowing and throwing, and infer from this that the rule P that applies to them, liability for prohibited labor on Shabbat, will also apply to the derivative. How is this done? To understand it, let us return to Figure 3 and analyze it differently.

It is clear that the basis of the liability in spitting is throwing and not winnowing, for we already noted above that the essence of the labor of winnowing is separation, like selecting, and that does not exist at all in spitting. What is done in spitting is clearly the throwing of something in the public domain. When there is liability for spitting, it is solely on account of the labor of throwing. But in spitting there is a side problem that does not allow us to learn it from throwing alone, because the spitting is done with the help of the wind, without which the spittle would not travel four cubits, whereas in ordinary throwing this happens by the person’s own force. Therefore we need the second primary category, winnowing, to remove the difficulty, the refutation, by proving in general that the assistance of the wind does not exempt in the labors of Shabbat.

To explain this further, let us again consider the parallel to Figure 3 from the previous column, only this time we will draw it with two primary categories, as in our case. The numbering continues that of the previous column:

Figure 4: A basic scheme of conceptual construction. A and B are the primary categories and C is the derivative. In parentheses appear the characteristics of each of the primary categories and of the derivative, where an overline indicates that the characteristic does not exist in the primary category or in the derivative. This figure is identical to Figure 3 in the previous column, except that it has two primary categories rather than three.

Let us now identify the variables in the figure. The two primary categories are A, winnowing, and B, throwing. The derivative is C, spitting. The characteristic x that exists only in A is that this is a labor of separation. The characteristic y that exists only in B is that there is no assistance from the wind. Both of these are, of course, characteristics that contribute to prohibition, stringencies, and neither exists in the derivative, which does involve the wind and is not a labor of separation.^[3] Notice that what does not enter here is the resemblance between spitting and throwing in terms of the content of the act, both concern moving something four cubits in the public domain. At that level an asymmetry is created between the two primary categories, because in terms of the nature of the labor the derivative clearly resembles only B, which is the essential primary category, and not A, which is a non-essential primary category whose role is merely to neutralize a characteristic that is a side obstacle to the inference.

The Logic of ‘Conceptual Construction’ and Its Relation to ‘The Common Element’

How are we to understand the logic of an inference of ‘conceptual construction’? At first glance there is here an elimination of the characteristics x and y, that is, a demonstration that neither of them is relevant. Exactly as I described in the previous column with respect to Figure 1: from A one can prove that a prohibited labor need not be a labor of separation. From B one proves that a labor need not be done without involvement of the wind. Hence spitting, which is not separation and does involve the wind, is also liable. But there is a difference between Figure 4 and Figure 1, for in Figure 1 there is a common element z shared by the two primary categories and the derivative, whereas here there is not.

Therefore it is more accurate to present this inference as a synthesis of the two primary categories. First, we define the inverse of the characteristics we defined above, and now we combine the inverted characteristics of the two primary categories and fuse them to create a new derivative. On this view, the inverted characteristic of A is the involvement of the wind, which we will denote by . The inverted characteristic of B is that this is not a labor of separation, but rather a labor of transfer, or change of place in the public domain, and we will denote it by . If we look at Figure 4 above, we must treat the negation of the characteristics, the letters with the overline, as new characteristics. In the original figure the notation was by an overline, whose meaning is that the characteristic does not exist in the primary category or in the derivative. Here, by contrast, the notation is by negation, whose meaning is that the inverted characteristic itself functions as a characteristic of the primary category or of the derivative.

We can now see that the derivative is a combination of the two inverted characteristics of the primary categories, and : spitting is a labor that is not separation, but transfer, and that is performed with the wind. The inference is not built on the common element shared by the primary categories and the derivative, but דווקא on the different sides, the inverted characteristics, found in the primary categories; when these are joined together, fused into one, they create the derivative, which possesses both inverted characteristics. That is why I called this ‘conceptual construction’, for we construct a new derivative concept out of the two concepts of the primary categories. In other words, if ‘the common element’ is built on the intersection of the characteristics of the primary categories, an intersection that leaves only z, the common element that exists in both, then ‘conceptual construction’ is built on the union of the inverted characteristics of the primary categories, which leaves in the derivative both inverted characteristics, each primary category contributing one inverted characteristic to the derivative.

Applications of This Algorithm to the Three Previous Cases

If we apply this algorithm to the case of the blessing over benefit that was presented in the previous column in Figure 1, we could derive from the two primary categories, vineyard and standing grain, that the inverted characteristic unique to vineyard, namely that it is not obligated in the dough-offering, and the inverted characteristic unique to standing grain, namely that it is not obligated in gleanings, are fused and together create derivatives that are obligated in neither the dough-offering nor gleanings, and yet still require a blessing before one derives benefit from them. One can see the equivalence between the inferences, except that ‘the common element’ deals with the intersection of the ordinary characteristics, whereas ‘conceptual construction’ deals with the union of the inverted characteristics.

If we apply this to the case of the refutation based on a stricter aspect that was described in the previous column in Figure 2, we obtain that the two primary categories do not have the inverted characteristic (), and therefore nothing can be learned from them for any derivative that lacks the characteristic w, that is, that has . Therefore this is a refutation.

Now let us apply this to the case described in Figure 3, the owner deals with the carcass. The result will be a union of three groups, each of which is defined as a combination of two inverted characteristics out of the three. The three characteristics there were: uncommon damage, damage that occurs of itself, and damage caused by one’s property. The three inverted characteristics are: common damage, damage that does not occur of itself, and human-caused damage, that is, not damage caused by one’s property. We now create all the fusions of these inverted characteristics. Each type of derivative is created from the fusion of a subset of the inverted characteristics, and therefore the derivatives learned are the union of the three pairings of the inverted characteristics together with the intersection of the three inverted characteristics: {, ()() ,() ,()}. Each of the items joined here is a conceptual construction of a subset of the inverted characteristics of the primary categories.

To understand this better, note that the result obtained in the case of Figure 3 is the union of the groups of the three original characteristics: {(x), (y), (z)}. We explained in the previous column that this is the result of joining the three prototype inferences. Is there an equivalence between that and the result of the conceptual construction described here, which, as noted, is represented by an identical figure? Not always. It depends on whether the only characteristics relevant in this context are those three, or whether there are additional relevant characteristics. In other words, are there situations in which there is a damager and a carcass but none of those three characteristics, or not. If there are such situations, then they will not be included in the inference of Figure 3, but they will be included in the inference of ‘conceptual construction’ described in Figure 4. Those situations are the practical difference between these two kinds of inference, which, as stated, are represented by an identical figure.

Now I remind you that in the previous column we saw such situations. These are the thief and the robber. These are relevant situations, there is a damager and a carcass, and we saw there that they are not described by any of those three characteristics, and therefore one cannot learn from the three primary categories that with respect to a thief and a robber too the owner deals with the carcass. But the inference of ‘conceptual construction’ could indeed yield those cases as well. We saw above that the result of ‘conceptual construction’ in this case is a union of four groups of derivatives, each of which is a fusion of a subset of the original inverted characteristics. We saw above that the ‘conceptual construction’ of the three inverted characteristics of the three primary categories is the last term in that union. Hence ‘conceptual construction’ can indeed produce the thief and the robber as derivatives.

I will note that later in the sugya in Bava Kamma, there on 11a, there is brought the view of R. Elazar, which was not accepted in practice, that one appraises even in the case of a thief and a robber, meaning that in those cases too the owner deals with the carcass. He apparently performs a conceptual construction, Figure 4, between the three sources and not a prototype inference, Figure 3. In practical law this was not accepted, meaning that in practice they make there an inference of the type of Figure 3, as I explained in the previous column.

The question that remains for us to clarify is when one decides to perform three prototype inferences and when one performs an inference of ‘conceptual construction’. Remember that we are dealing with the very same situation described by exactly the same figure, and as we saw, the two inferences sometimes yield different results. If so, how does one decide which logic to use? Here I find it hard to give a general answer. It will probably depend on how we relate to the meaning of the characteristics that appear in the figure. If it is more correct to see them as positive characteristics and their absence as the absence of a characteristic, then one uses the logic of ‘prototype inference’. But if it is more correct to see the inverted characteristics as positive characteristics, then one makes an inference of ‘conceptual construction’.

In the case of the sources for the rule that the owner deals with the carcass, it is apparently more correct to view the positive characteristics as the essential ones, and therefore in practice they use there an inference of ‘prototype inference’. By contrast, in the case of spitting presented above, it is more correct to see the inverted characteristics as the relevant characteristics. The meaning of this is that the Jerusalem Talmud, according to R. Menashe of Ilya, assumes that the involvement of the wind interferes with the application of the rule, and not that for the rule to apply there must be no involvement of the wind.^[4]

Let us now examine another example in which one can see the difference between the two inferences described in Figures 3 and 4.

Another Example: ‘The Common Element’ in Damages

In the previous two columns, and also above here, I mentioned the fact that in damages we do indeed find inferences of the ‘common element’ from two primary categories to a derivative. Those cases are brought one after another in the sugya in Bava Kamma 6a-b. Here I will examine only the first one, and through it we will look into the logic of those inferences.

The Gemara there discusses why the Mishnah at the beginning of the tractate presents the common element of the primary categories of damages. The different cases of the ‘common element’ in damages are brought as the answer to that. I will quote here part of the first case, which focuses us on the important points:

What does their common element come to include?^[5]

Abaye said: It comes to include his stone, his knife, and his load, which he placed on the top of his roof and they fell in an ordinary wind and caused damage… But then after they came to rest… they do not resemble a pit. What distinguishes a pit is that no other force is involved in it; can you say the same of these, where another force is involved in them? Fire will prove it. What distinguishes fire is that its way is to move and cause damage. A pit will prove it. And the rule returns.

The two primary categories from which this is learned are pit, damage caused by something lying in the public domain, like a pit, which we shall denote B, and fire, a damager that moves with the help of the wind, which we shall denote A.^[6] The derivative, C, is objects, his stone, his knife, and his load, that were lying on the roof, an ordinary wind came and knocked them to the ground, and while they were lying there an ox passed by and was damaged by them.

Again the structure of the inference is as follows:

We try to learn C from B.

We refute: B has a unique characteristic (x), namely that no other force is involved in it.

We try to learn C from A.

We refute: A has a unique characteristic (y), namely that its way is to move and cause damage.

And the rule returns: we learn from A and B together to C.

Here too the unique characteristics exist only in one primary category and not in the other primary category nor in the derivative.

To understand which figure is the relevant one for describing this inference, 1 or 4, we must ask ourselves whether there is a shared characteristic, z, that exists in both primary categories and in the derivative. At first glance yes, for that is exactly what the Mishnah says: all of them are my property and their safeguarding is upon me.^[7] It is no accident that the Gemara presents this example as an inference of the ‘common element’, thereby explaining the end of the Mishnah, which deals with the common element of the primary categories. This example comes to show us that there are derivatives learned from the common element of two primary categories and not from one primary category alone. If so, at first glance the relevant figure for this inference is Figure 1.

A Dispute Among the Rishonim

However, in the Rosh there one sees otherwise. At the beginning of his comments he brings this example:

And we conclude that we derive his stone, his knife, and his load, which he placed on top of the roof and which fell into the public domain in an ordinary wind and caused damage after coming to rest, from pit and from fire.

Immediately afterward he brings a dispute among the Rishonim that places this diagnosis under a question mark. To understand it we must first note that each primary category of damages has special lenient laws, exemptions. In the case of fire damages, the damager is exempt from paying for damage to concealed items, those not visible to the eye. In the case of pit damages, the damager is exempt from paying for damage to utensils, and to a person. We must now ask ourselves what the laws, the relevant exemptions, will be for the derivative C, his stone, his knife, and his load that fell into the public domain and caused damage. Will we impose liability there for damage to utensils? And what about damage to concealed items?

In my understanding, three opinions are brought in the Rosh there, although people usually distinguish only two:

1. Some of the great authorities wrote that one is liable only for what both are liable for, and exempt from damage to utensils and from the death of a person, like a pit, and from concealed items, like fire, since they come by way of the common element and we give them the lesser, more lenient side of both.
2. And some were uncertain about the matter.
3. And it seems to me that they have all the laws of a pit…

After that he brings proofs from the Gemara for position C.

What are these three opinions and what is the difference among them? The first opinion is that the derivative C has all the exemptions of the two primary categories, it is exempt both for concealed items and for utensils. The logical reasoning for this opinion is understandable and almost self-evident. If we want to impose liability for damage to concealed items, we could learn that only from one primary category, pit, for fire is exempt for concealed damage. But one cannot learn the derivative from one primary category alone, and therefore we cannot learn liability for concealed damage. The same is true of damage to utensils, for only fire is liable for them, while pit is not.

The second opinion is uncertain, but it is not clear between what and what. If no further detail is given, it is reasonable that the uncertainty is between position A and the opposite position, that the derivative C has no exemptions at all. What is the logic of that? It is usually explained as follows: first, we learn from the two primary categories that the derivative too is a category of damage that requires payment. We now have a sweeping obligation to pay. At the second stage we want to examine whether to exempt for damage to concealed items or for damage to utensils. But neither can be learned, because each such exemption exists only in one of the primary categories and not in the other. I remind you that to learn about the derivative we need both primary categories. Therefore we have no way to learn the exemptions, and we are left with full liability without any exemptions whatsoever.

But that explanation needs completion. At first glance the original learning in the Gemara, which requires two primary categories, is learning whose purpose is to apply a stringency to the derivative: both primary categories have stringent characteristics, and therefore to learn the stringency, that he must pay for the damage, we need both of them. But the learning of the exemptions is learning of a leniency, exemption from payment for concealed items or for utensils, and here perhaps there is room to learn from only one of the primary categories. How do we know that two primary categories are required even when one wants to learn a derivative leniently?

But on closer inspection one sees that this is true of lenient derivations as well. After all, each of the primary categories also has a unique lenient characteristic, that is, a characteristic that gives a reason not to pay, which exists only in it and not in the other primary category and not in the derivative. The lenient characteristic is the inverse of the stringent characteristic of the other primary category. The pit has the inverted characteristic that its way is not to move and cause damage (), and fire has the inverted characteristic that another force is involved in it (). But the derivative too has both of those inverted characteristics, just as in Figure 4.

It seems that we have reached an inference of ‘conceptual construction’, that is, that the derivative is a synthesis of the inverted characteristics of the two primary categories, exactly as in Figure 4. In the case discussed above, spitting, there were no consequences to this, because in the prohibited labors of Shabbat the only question is whether one is liable or exempt, and there is no discussion there of additional special lenient rules for the various primary categories. Likewise in the rule that the owner deals with the carcass, the only question was whether the owner deals with it, and there were no additional lenient laws for the injured party. But from here it appears that the בעלי שיטה ב hold that if the primary categories have special leniencies, then the derivative created from their ‘conceptual construction’ will not have the leniencies of either primary category.

Yet it is still not so simple to claim that, for even if this is ‘conceptual construction’, from a logical standpoint it is still possible to learn each of the two leniencies by a prototype inference from the primary category relevant to it, to learn the exemption for concealed items from fire and the exemption for utensils from pit. Perhaps those who hold this view assume that these primary categories also have additional lenient characteristics that do not exist in the derivative, for example: fire has the lenient characteristic that its initial formation was not for damage, unlike pit and unlike his stone, his knife, and his load, and pit has the lenient characteristic that one would not expect a wind to come and create damage from it, and therefore it requires less guarding.^[8] Perhaps that is why one cannot learn the halakhic leniencies to the derivative, but this still requires further thought.

The third opinion, which is the one the Rosh himself accepts, is that the derivative C receives all the laws of pit and not the laws of fire. This is a surprising opinion, because it breaks the symmetry between the two primary categories. On what is it based? It should be remembered that in learning by way of the ‘common element’ the two primary categories have identical and parallel standing, and therefore there is here a hint that the Rosh does not see the logic here as that of the ‘common element’.

His Stone, His Knife, and His Load: The View of the Rosh

If we look at the different damaging agents under discussion, we will see that the situation here fully overlaps with what we saw above regarding spitting. It is clear that the objects lying in the public domain are, in terms of the manner of damage, completely a pit, just as spitting is completely throwing. In terms of the nature of the damage, his stone, his knife, and his load in the public domain are static, and therefore this derivative has nothing in common with fire, which damages while moving. Exactly as spitting has nothing in common with winnowing, which is a labor of separation. Therefore it is clear that these objects are in essence a pit, and that is their essential primary category, just as throwing is the essential primary category of spitting. But there is here a side deficiency that interferes with learning them from pit, because their coming into being was with the help of the wind, whereas a pit is dug by a person without the help of an external factor. That is what fire is used for: it shows us that even a damager that is aided by the wind obligates payment, the wind is not an exempting factor. This is exactly as we proved from winnowing that the involvement of the wind does not exempt from liability on Shabbat. In other words, the side primary category of fire serves here, just like the side primary category of winnowing in that other case, to remove a side obstacle, the involvement of the wind, that could disrupt the inference from pit or from throwing. Therefore it is not correct to relate to fire as a second primary category from which the damager is learned. It takes no part in the learning itself, but merely removes a side obstacle to the learning, exactly like winnowing.

The conclusion is that the derivative C in this case is created by the ‘conceptual construction’ of pit and fire, and not by an inference of the ‘common element’ from both of them. I fuse the involvement of the wind, the inverted characteristic of fire, with the damage of an object lying in the public domain, the inverted characteristic of pit, and that fusion creates the derivative: his stone, his knife, and his load that flew off the roof and caused damage after coming to rest in the public domain. This derivative is damage caused by an object lying in the public domain in whose creation the wind was involved. According to the Rosh, the parallel to Figure 4 is complete.

Again, the advantage of the present case over spitting is that here one can see a halakhic consequence of the fact that this is ‘conceptual construction’ and not ‘the common element’: if we were learning by way of ‘the common element’, then the conclusion would be like position A brought in the Rosh, the ‘some of the great authorities’, namely that the derivative has the two types of exemption of the primary categories. But because this is ‘conceptual construction’, the derivative has only the exemptions of the essential primary category, the pit. The second primary category is not really a primary category at all, for there is nothing in the manner of its damage that resembles the manner of damage of the derivative; it merely removes an obstacle in the learning. According to this proposal, if there were special lenient laws for throwing that did not exist in winnowing, they would pass over to the derivative, spitting. But if there were special lenient laws for winnowing that did not exist in throwing, they would not pass over to the derivative.

But note that one can easily point to such consequences. The prohibition of carrying out does not apply on a Festival day, but the prohibition of winnowing does. This is a leniency that exists in the labor of carrying out, and throwing, but not in winnowing. Would the prohibition of spitting apply on a Festival day? According to our approach, clearly not. Spitting is essentially throwing, only aided by the wind, and therefore it is not prohibited on a Festival day. The fact that in the course of the inference we made use of the labor of winnowing is not because there is something of winnowing in spitting, but only in order to neutralize a side obstacle, the involvement of the wind. By the same token, it seems that if there were a special lenient rule in winnowing that did not exist in throwing, and I cannot think of such a rule, it would not pass over to the derivative.

I will only note that the wording of the Gemara in Bava Kamma 6a very strongly reinforces the Rosh’s conception. Notice that the formulation there strongly resembles the standard formulation of ‘common element’ derivations, but it is cut off in the middle: there is the attempt to learn from pit and it is refuted. There is the attempt to learn from fire and that too is refuted. But then the Gemara says laconically: ‘And the rule returns.’ That is all. And what about the standard ending: ‘This is not like that, and that is not like this; the common element between them is that both are such-and-such; so too his stone, his knife, and his load, which are such-and-such, is liable to pay’? None of that appears there, and the reason is that in truth this is not a learning of ‘the common element’, but of ‘conceptual construction’. As stated, there is no common element to pit and fire and the derivative.^[9]

A Final Note: Is There a Contradiction in the Rosh’s View?

We noted above that the Rosh sees the involvement of the wind as a matter specific to winnowing. According to his view, if some other labor is done with the involvement of the wind, the person will be exempt. At first glance the Rosh appears to disagree with everything I have said here, for he should have learned from winnowing to all the other labors that the involvement of the wind does not exempt. Thus, for example, if we were discussing plowing with the aid of the wind, we should have learned from plowing and winnowing that he is liable, and according to the Rosh we have just seen, in Bava Kamma 6a, this would even have all the laws of plowing, and not the laws of winnowing. But according to the Rosh on 60a it emerges that one does not impose liability for plowing with the aid of the wind. If so, not only does the matter depend on the dispute between Rashi and the Rosh regarding winnowing and the wind’s assistance, but there is an internal contradiction in the Rosh’s own doctrine.

But that is a mistake. The Rosh himself on 60a explains that winnowing is a special labor because its ordinary mode of performance is with the aid of the wind. Therefore, according to him, one cannot learn from it to other labors done with the aid of the wind that one would be liable for them, since in those other labors the wind is not the ordinary mode of performance. Therefore the Rosh באמת will not impose liability for plowing with the aid of the wind, but that does not contradict his view at the beginning of Bava Kamma regarding the ‘conceptual construction’ of two primary categories, where he imposes liability for winnowing by means of the wind. One performs ‘conceptual construction’ only where it is possible to learn from the assisting primary category to the derivative. It is true that according to the Rosh it should follow that the Jerusalem Talmud’s law is incorrect, or at least that R. Menashe of Ilya’s interpretation is incorrect, for according to him spitting is a derivative of carrying, the essential primary category, and winnowing is only an assisting primary category, which neutralizes the involvement of the wind, and therefore one cannot learn from winnowing to carrying. In winnowing the ordinary mode is by means of the wind, whereas in carrying it is not. If so, the Rosh probably would not accept the ruling of R. Menashe of Ilya, but there is no reason to assume that he disputes the very logic of ‘conceptual construction’, which he himself teaches us in the sugya of ‘the common element’ in damages.

True, in the damages inference one does learn from fire that the involvement of the wind does not exempt in all the primary categories, and there they do not make this depend on the fact that the wind is the ordinary mode of the damage. At first glance the Rosh should have objected to this inference, arguing that fire ordinarily goes by means of the wind and pit does not. But that too is not a difficulty against him, for in damages there is no importance to the question whether the ordinary way of doing this is with the aid of the wind or not. Only with the labors of Shabbat is it important to us how they were done in the Tabernacle, for that is what determines the prohibited labors. In damages there is no such rule.^[10]

1.

Footnotes

1. However, the Rishonim disputed whether carrying and throwing are a primary labor or a derivative. See Ramban on Shabbat 73a, who wrote that carrying four cubits is a derivative. Ritva there was uncertain about this. Maimonides, Hilkhot Shabbat 12:8, wrote that carrying four cubits is like taking out from a private domain to a public domain, and in 12:10 he wrote that passing and throwing are derivatives. If throwing is a derivative, then spitting is a derivative of a derivative, and I will discuss that concept later.
2. One could sharpen the point by suggesting that both are types of creation, and in column 345 we linked that to the dispute between Rashi and Tosafot Rid. But carrying and taking out are inferior labors, and ostensibly there is no creation in them. To say that all of them are human actions is too broad, for on that basis one could prohibit every human action.
3. It is enough that it be different, but here it is even more deficient than winnowing, for there is no change in the object apart from a change of its location.
4. At first glance these two formulations are logically equivalent. But that is not precise. This is not the place to enter into that, and to understand it one may look at my essay on the sixth root in the book Yishlach Sharashav (there I dealt with the question what the difference is between commanding us to put on tefillin and forbidding us to be without tefillin, and I showed that this is not really a logical equivalence). It is also worthwhile to see the analysis of the Raven Paradox (see also in the responsa here), which is also connected to the matter.
5. I occasionally use this Gemara here to demonstrate the Talmud’s opposition to positivism. The Mishnah brings four examples of categories of damage that appear in the Torah, and then includes them under a general rule: ‘their common element is that they are your property and their safeguarding is your responsibility…’. Instead of rejoicing that the Mishnah has done us a favor by giving us the rule and not only the examples, and perhaps even asking why examples are needed if we have the general rule, the Gemara wonders why the general rule is needed if we have examples. The Talmud places much greater trust in analogy based on examples, a casuistic approach to law, as in the British system, the common law, than in deduction from general laws, a positivist approach characteristic of German law, Bundes law, and continental law in general, which is based on Roman law.
6. A mnemonic to help follow the discussion below: A marks fire and B marks pit. The notation follows the first letter in the original names of the damaging agents.
7. The addition that they are your property is according to the Rif’s reading there.
8. This is merely an example whose purpose is to sharpen the logic. Usually this is presented as a stringent characteristic, but one can debate that.
9. I have begun to check a bit whether this formulation appears in the Talmud in places that are not ‘the common element’ but rather ‘conceptual construction’, and so far it does indeed seem so. True, even when it is ‘the common element’ it does not appear in a perfect form, because the Gemara abbreviates formulations, but as far as I have checked it is never abbreviated in this way.
10. Moreover, if his stone, his knife, and his load were lying on the roof, then their way is to fall in an ordinary wind. But one may reject that, for precisely because of this we should have inferred that it is not a pit, because in the case of a pit its way is not to come into being by means of the wind. And there is still more to analyze here.