Rabbi Eliezer Berkovitz
1. Logical inferences
As we have already shown, interpretative exegesis was primarily applicable when “new cases” arose in life —- cases which the law-maker could not have specifically solved previously, but which nevertheless had to be decided in the spirit of the Teachings. But how could the spirit of the Teachings be determined so that it would not simply be viewed as an individual’s subjective opinion of the Teachings, but rather so that it must be seen as the objective — and hence also valid — intention of the Teachings? There was only one way of making sure of this: inferring from the known to the unknown X. But since the Teachings never manifest themselves in the form of concepts, but instead as individual cases, in which they determine action or behavior, conclusions had to be drawn from one individual case to another individual case — or, to use the terminology of logic, from one particular to another particular. How did the Talmud proceed here? We will illustrate this by means of an example.
a) In Tractate Pesachim (66a), it says: It came to pass once that the eve of the Festival of Passover fell on the Sabbath, and it was not known whether the Passover sacrifice could be offered on the Sabbath, since the offering is associated with certain types of labor otherwise forbidden on the Sabbath. Neither the Bible nor the Oral Teachings contained any provision about this, but this case too had to be decided on the basis of the Teachings. Now Hillel taught: We know that the daily sacrifice must be offered on the Sabbath too. Of the daily sacrifice it says: it shall be offered “in its due season.” But of the Pesach sacrifice it also says: it is to be given “in its due season.” However, this justifies my inferring: Just as “in its due season” for the daily sacrifice means: even if this time is a Sabbath, so the same expression for the Pesach sacrifice will mean: “in its due season” — even on a Sabbath. Reduced to a logical formula, the reasoning runs as follows:
The daily sacrifice supersedes the commandment relative to the Sabbath
The daily sacrifice is similar to the Pesach sacrifice (because of the similarity of the wording determining the time in the Bible)
Hence the Pesach sacrifice supersedes the commandment relative to the Sabbath.
All this amounts to is a logical inference by analogy, where the formula is as follows: M = P; S and M are similar to each other; therefore S = P. Since inference by analogy in the Talmud is almost exclusively based on identity of the expression in the Biblical text, its name in the Talmud is “g’zerah shavah,” that is, an “analogous expression” or verbal analogy (cf. Sifra, beraita of R. Ishmael).
However, no inevitable — that is, completely reliable — conclusions can be reached on the basis of similarity. All that analogy can do is to substantiate with probability the similarity between M-like S and M-equals P. Analogy always justifies a supposition only. However, it is not possible to decide about issues in the Teachings on the basis of suppositions. The theory of probabilities can only be a method of science, not a satisfactory method of the Teachings. Whether or not the Pesach sacrifice can be offered on the Sabbath must be categorically known. Which is why the Talmudic verbal analogy (inference by analogy), the “g’zerah shavah” — a decision of law — requires further safeguards. Probability should prevail. How can it do so? Logic replies as follows: The probability inferred on the basis of analogy can become applicable on the basis of those experiences which confirm it. But the role that (empirical) experience plays in science is occupied in the Teachings by tradition. This is the reason behind the principle that the Talmudic inference by analogy applies only when it is confirmed by a tradition. Generally this involves the “g’zerah shavah” having been handed down from generation to generation, from teachers to students.
Or, as Hillel puts it: “Nobody may independently draw up a conclusion by analogy,” meaning: Nobody may make decisions of law on the basis of a verbal analogy if unsupported by any tradition (cf. Pesachim 66a). This is not a dogma, but the scientific consequence of the analogy. Analogy can only produce a probability; but probability cannot be an answer to questions of the Teachings.
b) Hillel also shows us another way to decide the above-cited question about the Pesach sacrifice. We can disregard verbal inference. The assumption is: We know that the daily sacrifice supersedes the Sabbath commandment. We know that, while the punishment of karet (= excision or premature death) applies to any omission of the Pesach sacrifice, this punishment does not apply to omission of the daily sacrifice. The law-maker must have attached greater importance to the offering of a sacrifice to whose omission the karet penalty is applied, than to the offering of a sacrifice for whose omission this harshest of punishments was not specified. Hillel now teaches the conclusion: If the offering of the daily sacrifice, for whose omission no karet penalty is imposed, already supersedes the Sabbath commandment, then how much more must the Pesach sacrifice, whose omission is punished with karet, supersede the Sabbath commandment. Reduced to a logical formula, this can be expressed as follows: Because of the relationship between the different nature of the penalties in the case of omission, the following is established:
The offering of the Pesach sacrifice exceeds in significance the offering of the daily sacrifice
The offering of the daily sacrifice is so significant that it supersedes the Sabbath commandment
Therefore, the Pesach sacrifice also supersedes the Sabbath commandment.
In the Talmud this conclusion is known as “kal va-homer” (a fortiori); originally in the sense of “(deduction) from a minor to a major case in terms of religious law,” or to put it more generally: “From the particular to the more comprehensive particular,” so that one might say: What A contains must also be contained by the more comprehensive A1. Unlike the verbal analogy of the gezerah shavah, this conclusion is mandatory; consequently, it needs no other confirmation than that of logical necessity. Kal va-homer is always applicable even if unsupported by any tradition. Or, as the Talmud puts it: “Everyone has the right to infer a kal va-homer on his own.” (ibid.)*Adolf Schwarz, whose basic work we followed in the section’s presentation of “logical inferences” and “exegetical rules,” although we differ from him on all essential points concerning the “inferences” (at this juncture we can only report on the exegetical rules on the basis of Schwarz A., “Der Hermeneutische Syllogismus in der Talmudischen Litteratur", Israelitisch-Theologischen Lehranstalt, Vienna, 1901) holds that kal va-homer is equivalent to a syllogism. This is not correct. There are countless syllogisms in the Talmud, but never in the form of kal va-homer; on the other hand there are a number of kal va-homer which can only be reduced to a syllogism with great difficulty. In my experience the nature of the kal va-homer has been correctly explained only by my esteemed teacher, Dr. I.I. Weinberg, Rector of the Hildesheimer Rabbinical Seminary in Berlin, who has re-established the a fortiori inference in kal va-homer. The special wording of the kal va-homer can be ascribed to the fact that the conclusion at the same time contradicts a possible objection to the identity to be inferred, that is, always in how it is shown: the point on which A and A1 differ from each other only strengthens the inference on the basis of identity, since the present in A, on which the identity is based, must — on the basis of the properties which are cited as differing — be present in A1 to an even greater degree.
c) Another case should enable us to gain an insight into the nature of a third exegetical rule. In the Bible we have four basic types of damage accompanied by liability for damages or liability to make good a loss. 1. A goring ox. 2. A pit which is dug or left open in the public domain. 3. An ox that grazes on someone else’s field. 4. A fire which starts out in a hearth and spreads. In the concise, catchy and graphic language of the Oral Teachings, they are designated by means of the terms: 1. The horn, 2. The pit, 3. The tooth, 4. The fire (cf. Bava Kama, Mishna 1:1). In defining the nature of these kinds of damage, it is determined that all damage caused by physical objects can be reduced to these four basic types. The tractate of Bava Kama (p. 6a) discusses the following question: Some-one had placed “his stone, his knife, his load” on a roof; they fell down during a normal wind (which should therefore have been foreseen), causing damage to something. Is the owner who laid them on the roof liable for damages or not? No decision was available in such a case, whether in the Bible or in tradition. An attempt is now made to determine to which group of damages the falling object belongs: 1, 2, 3, or 4. However, it turns out that this case cannot be placed anywhere; for in its nature it is not identical with 1, nor with 2, 3, or 4. However, although 1, 2, 3, and 4 also differ from each other, nevertheless in all four cases, the owner or party responsible is liable for damages. However, if the same applies to 1, 2, 3, and 4, the reason cannot be the points on which they differ (unequal causes having unequal effects), but rather the points on which they correspond. The “common factor” (ha-tsad hashaveh) to be found in them is: All four “are in the habit of causing damage, and must be guarded” — and this is therefore the cause of the provision: “The owner or party responsible is liable for damages.” The conclusion drawn from this is: Everything that has the property of “being in the habit of causing damage and needing to be guarded” carries with it, in the case of damage, an obligation on the part of the owner or the person responsible to pay damages. However, these properties apply also in the case in question to the “stone”; the owner or person responsible is therefore liable to pay damages. Reduced to a clear, logical formula, the conclusion can be worded as follows:
The “horn,” the “pit,” the “tooth,” the “fire” have the property: “they are in the habit of causing damage, and must be guarded”
The “horn,” the “pit,” etc. require the person responsible for them to pay damages.
Everything which has the property of “it is in the habit of causing damage and must be guarded” requires damages to be paid.
The “stone” has the property: “In the habit of causing damage and must be guarded”
Therefore, the “stone” requires damages to be paid.
However, this conclusion is simply the combination of an induction and a syllogism. The first part, the induction, is the well-known Aristotelian progression from the particular to the general. However, once the general is obtained, it can be used to infer an unknown particular from the general, as a super-proposition to the familiar syllogism: all M is P, S is M, therefore S = P. (The reader trained in logic will be able to recognize independently the importance of this combination for the disclosure of the relationship between induction and syllogism.) In the Talmud, this combined conclusion is called “binyan av” (basic rule, law or precedent); “av = father” means the type, the kind, the general as such, and “binyan = building” is what builds up the type, namely the particular with the distinguishing feature, as a result of which it is classified under the av. First an inference is drawn from the binyan particular to the general av, then back from the av to a previously unknown particular.
The task of ruling on new cases using the laws of logic and in accordance with the spirit of the Teachings has ben brilliantly solved by these three principles for inferring from the known to the unknown: The verbal analogy in the g’zerah shavah, the a fortiori inference (based on identity) of the kal va-homer which at the same time disproves a possible objection, and lastly the inference of the binyan av, deduced from induction and syllogism. Independently of Aristotle, and centuries before him, the scientific thinking of our great masters reached a level on a par with the greatest logicians of all times.
