Q&A: Talmudic Logic
Talmudic Logic
Question
Hello Rabbi,
I’m interested in Talmudic logic (and also in your other books), and I’ve read some of the books and articles you wrote or took part in writing, as well as other materials.
I got the impression that the field places enormous emphasis on the study of the thirteen hermeneutical principles, yet I have hardly seen any discussion of the more basic and elementary give-and-take of the Talmud itself.
For example, I started doing this kind of schematic analysis of tractate Sukkah. The first question that appears there in the Talmud is: “Why is it that regarding a sukkah it teaches ‘invalid,’ while regarding an alleyway it teaches the remedy?”
One can carry out several formalization procedures for the question, until arriving at a contradiction. (Even if there is no explicit contradiction here, any question can be expressed in a certain way as a “contradiction.”)
I did it as follows:
- For a sukkah that is more than twenty cubits high, the wording used is “invalid” (given; Mishnah).
- For an alleyway that is more than twenty cubits high, the wording used is the remedy/correction (given; Mishnah).
– 2.1 Conclusion: an alleyway that is more than twenty cubits high is invalid (section 2 + semantics)
- Conclusion: the law regarding a sukkah and an alleyway above twenty cubits is the same (sections 1, 2.1).
- Conclusion: the wording regarding sukkah and alleyway is different. (1, 2)
- The same law entails the same wording (assumption (a priori?)).
- Conclusion: the wording in both cases ought to be the same (3,5).
A contradiction between 4 and 6.
From this schema one can of course also easily move to more formal notation. In my opinion there are several benefits to presenting things this way –
A. It would be possible to show “prototypes” of answers, and thereby establish quantitative statistical research relating to the Talmud itself as well as to its interpretation (for example, perhaps Rashba mainly raises difficulties of types 6 and 7, while Ritva raises difficulties of types 2 and 9, etc.)
B. In the course of the formalization process, one could separate the strictly logical factors in the argument from the other assumptions (usually semantic ones primarily, as here in 2.1)
C. Also, the very presentation of things in this form sometimes helps one arrive at clearer and sharper distinctions. For example, in our case, the Talmud gives two answers:
Answer A:
“A sukkah is Torah-level, so it teaches ‘invalid’; an alleyway is rabbinic, so it teaches the remedy.”
That is: the conclusion in (3) is not valid. The law may appear externally the same, but it is not entirely the same law, since here the law is of biblical origin and here it is rabbinic. Therefore, it is not relevant to apply to the case before us the assumption that the same law entails the same wording. (In section 5.)
Answer B:
“And if you wish, say instead: even in a Torah-level law it may teach the remedy; however, with sukkah, since its matter is more common, it taught decisively ‘invalid,’ whereas with alleyway, since its matter is less common, it taught the remedy.”
That is: the assumption in section 5 is not valid in all cases (and therefore for our purposes simply false, since every claim is about all cases). Unlike the previous answer, according to which assumption 5 cannot be applied to our case because the discussion is interrupted even earlier (they are not the same laws at all), according to this answer it is indeed correct to carry out this line of reasoning. Even so, since assumption 5 is false, one never arrives at 6, and the contradiction is avoided.
It can be said that the difference between the answers is at what point we “exit” the line of reasoning that leads to the contradiction. (By the way, it seems to me that with a bit of effort one could formalize this discussion too.)
In my humble opinion, as stated, this is a useful discussion that might also open the door to additional future research. If possible, I’d be glad to hear whether there are already discussions in this area, and also your opinion of it.
Thank you very much in advance,
Answer
Hello.
In the future, I’d appreciate it if you would contact me through the website. It’s much more convenient for me.
1. There is no “field.” Whatever people do—that is the field.
2. Even in what my colleagues and I did, only a small minority deals with the hermeneutical principles. See the Talmudic Logic series, where only the first two books out of 13 are about the hermeneutical principles. We certainly also deal with other kinds of Talmudic argumentation.
3. What you present here is a formalization of the ordinary line of argument. It has value on two conditions: a. if you manage to find recurring patterns that form a skeleton for the logic of Talmudic give-and-take. b. if you show that the formalization is useful beyond what we would know without it (there is a phenomenon of formalophilia, where people see value in the very move to formal writing even when it is not actually useful).
4. The usefulness of formalization (3b) can be of two kinds: 1. usefulness for the ordinary beginner student—didactic help in learning. 2. usefulness for the advanced student—something that reveals conclusions and patterns we would not have reached without the formalization.
We focused on benefits of type 2, since our goal was innovations in logic (import and export, as we explained in the introductions to the books), not developing didactic aids for the learner.
In what you wrote here, I did not see significant usefulness of type 2. Maybe didactically (type 1), though even about that I’m doubtful.