Talmudic logic
Hello Rabbi,
I am interested in Talmudic logic (as well as your other books) and have read some of the books and articles you have written or participated in writing, as well as other materials.
I was impressed that the field placed a huge emphasis on studying the 13 Midots, but I saw almost no discussion of the more basic and elementary Shekla and Terya of the Gemara.
For example, I began to do a schematic analysis of Tractate Sukkah. The first question that appears there in the Gemara is: ‘Who hates Gabi Sukkah is a religiously invalid act, and who hates Gabi Mebui is a religiously valid act?’
Several procedures of reformulation can be performed on a question, until a contradiction is reached. (Even if there is no explicit contradiction here, any question can be expressed in a certain way as a ‘contradiction’)
I did it this way:
- A sukkah that is more than twenty cubits long is considered an invalid statement (Naton, Mishnah).
- A turn that is more than twenty cubits is called a Tikanta (given, Mishnah)
– 2.1 Conclusion: A turn that is more than twenty cubits is invalid (Section 2 + semantics)
- Conclusion: The ruling on the sukkah and the edifice of more than twenty cubits is the same (sections 1, 2.1)
- Conclusion: The language in the Sukkah and in the narration is different. (1, 2)
- Equal law entails equal language ((a priori?) assumption)
- Conclusion: The language in both cases should be equal (3,5)
Contradiction between 4 and 6.
From this summary, it is of course easy to arrive at more formal notations. In my opinion, there are several advantages to presenting things this way –
A. It will be possible to show ‘prototypes’ of excuses and thereby establish a quantitative statistical study concerning the Talmud itself as well as its interpretation (for example, perhaps the Rashba will mainly consider questions of type 6 and 7 and the Ritva questions of type 2 and 9, etc.)
B. During the permutation process, it will be possible to separate the serious logical factors involved from the other assumptions (usually, mainly semantic, as in the example here in 2.1).
C. Also, the mere presentation of things in this way sometimes helps to reach clearer and more pointed distinctions. For example, in our example, the Gemara makes excuses in two ways:
Excuse A:
‘A sukkah from the Torah is not permissible, but from the rabbinate it is permissible’
In other words – the conclusion in (3) is not valid. The law may seem equal from an external point of view, but it is not entirely the same law, since here the law is from the Torah and here from the Rabbis. Therefore – it is not appropriate to apply to the present case the assumption that an equal law entails equal language. (in section 5).
Excuse B:
“And I have given you a mother in the Torah, give me a sign, who is a Sukkah (who is a woman who has given birth) a sign, and give me a sign, because I do not have a birth certificate, give me a sign.”
In other words, the assumption in section 5 is not valid in all cases (and therefore, in our case, is simply false, because every claim applies to all cases). Contrary to the previous excuse, according to which it is inappropriate to apply assumption 5 to the defendant, because the hearing was interrupted earlier (we are not talking about equal laws at all), according to this excuse, it is definitely correct to carry out this move. Nevertheless, since assumption 5 is false, we do not reach 6 anyway and the contradiction is avoided.
It can be said that the difference between the excuses is when we ‘step out’ of the move that leads to contradiction. (By the way, I think that with a little effort, this discussion could also be formalized.)
In my humble opinion, this is a useful discussion that may also open doors for further future research. If possible, I would be happy to hear whether there are already discussions in this field and your opinion on it.
Thank you very much in advance,
Hello.
In the future, I will thank you for contacting me through the website. It is much more convenient for me.
1. There is no domain. What people do is the domain.
2. Even what I and my colleagues have done, a small minority of it deals with the qualities of the sermon. See the Talmudic Logic series, only the first two books out of 13 are on the qualities of the sermon. We certainly deal with other aspects of the Gemara as well.
3. What you are presenting here is a formulation of the usual course of action. It has value under two conditions: A. If you succeed in finding patterns that repeat themselves and constitute a skeleton for the logic of Talmudic negotiations. B. If you see that formalization is beneficial beyond what we would know without it (there is a phenomenon of formalophilia, where people see value in the very act of switching to formal writing without it actually being beneficial).
4. The benefit of the formalization (3b) can be of two types: 1. Benefit for the simple and beginner learner. Didactic aid in learning. 2. Benefit for the advanced learner, such that it reveals conclusions and patterns that 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) and not the development of didactic aids for the learner.
In your words here, I did not see any significant benefit of type 2. Perhaps didactic (type 1), and I doubt that too.
Leave a Reply
Please login or Register to submit your answer
