Round KW – The logical dimensions of the sermon as the foundation stones for non-deductive inferences

peace,
I apologize in advance for the length, I would be very happy if you still find time to read.
I recently read the rabbi’s two articles on the logical qualities of sermons. I understand that they were also published in a book in the Talmudic Logic series, but I do not have access to it, so I apologize if the answer to my question is there. One of the central claims that emerges from the model presented in the articles is that the rotation of the KV is not really meaningful. You showed how this conclusion is consistent with the issues of ink and the Gemara’s symmetrical treatment of row and column breaks.
But although we have not found such examples in the Gemara, as is known, there are several places where the Rishonim (mainly the Tosafot) twist the KV in order to escape a pirkha. For example, in the Sugiya Cholin (25):

El Rav Ada bar Ahavah to Rava: And if there is an earthenware vessel that is impure from its back, according to the law of the rabbinic period, and what of all the vessels that are not impure from being painted, are impure from being stained? An earthenware vessel that is impure from being painted is not subject to being impure from its back!

The additions there make it difficult to explain why not to paraphrase “What for all the tools, indeed, they have become the father of impurity,” and excuse “We did not use them because of the power of a workable tool, light and material, but because of the power of back and air,” and the latter there explain that he means the rotation of the KV. Apparently, the way you described the rotation in the model in the article, the rotation will not be of any use.
I think I have a solution to this question, I wanted to present it here and see how you think it fits with your model.
In my opinion, there is an inherent asymmetry between the rows and columns of the table (for convenience, I will define the columns as those on which the order relation is built). When I define an order relation between all vessels and pottery vessels, this relation should be maintained for each row I add to the table. When I add a row to the table, I am free to choose any relevant attribute of the vessels. The attribute could be “defilements from the air” or “defilements from the dirt,” but it could also be “becoming the father of impurity,” because this is an attribute of the vessels that we see as relevant to the issue of impurity.

In contrast, when adding a column to the literal, the restriction is much stricter. In the rotated literal, I define an order relationship between the places of impurity: air and back. The attributes that I choose in the rows are attributes of places of impurity: “impure in all vessels” or “impure in a clay vessel.” If we want to rotate the original section of the Tosafot, we get: “The father of impurity will prove that he is impure in all vessels and is not impure in a clay vessel.” But I cannot add this column to the table, because the attributes “impure in all vessels” and “impure in a clay vessel” are incorrect with respect to the subject ‘father of impurity.’ When I added a row, I was free to attach any verb I wanted to ‘father of impurity,’ and I chose the appropriate verb ‘becomes.’ But when I rotated the literal, I am bound to the verbs of the existing rows: ‘impure.’ When they say “the father of impurity defiles all vessels,” the word ‘defiles’ does not belong, or at least does not belong in the same sense that it belongs to air and back.
For that matter, this can be seen as a dimensional problem. The “units” in which the impurity of air in all vessels or of back in all vessels is measured are not the same units in which the impurity of the father of impurity in all vessels is measured. I cannot compare the values ​​of the ‘back’ column with the values ​​of the ‘father of impurity’ column, and therefore I cannot claim the order relationship between them “back > father of impurity” / “back = father of impurity”. The placement of the ‘father of impurity’ column in the table is incorrect. To allow for comparison, the units within each row must be uniform. This is in contrast to the units within each column, where there is no problem comparing subjects based on several attributes, each measured in a different unit.
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I don’t think this solution contradicts the model or the claims you presented in the article. I think the problem with the “rotation” you made in the article in the chapter on ink is that it’s not really a “real” rotation. When you “rotated” the Q&A – all you changed was whether you looked at the order relationship between the columns or between the rows. But the column and row headings remained the same headings.
If we rotate the KU in the same way you rotated it in the article, we get something like this:

Instead of discussing the order relationship between the vessels, we discuss the relationship between the places of impurity as actions (which actions operate on more than one vessel). In this way, the argument still stands, because the action of “becoming the father of impurity” really proves that it is not possible to conclude that actions operate on a clay vessel from the fact that they operate on all vessels. Or in terms of your model, it is possible to construct an order relationship between “becoming the father of impurity” and “impurity from the back” because the units in which each of their lines is measured are uniform: “success of an action.”
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This solution may seem like a linguistic-semantic trick, but I think there is a fundamental difference between the arguments here. When I claim that pottery vessels are more serious than all vessels, I expose myself to the rigors of all the existing properties of vessels. Not only properties of “will touching a certain place defile them” but also the property of “can they become the father of impurity.” This is a property of vessels.
When I twist the simple and the complex, and I claim that the place ‘Gev’ is more serious than the place ‘Avir’ – I evade the falsifications that are properties of the places ‘Avir’ and ‘Gev’ (such as “they become the father of impurity”), but at the same time I also expose myself to other falsifications that are properties of the places ‘Avir’ and ‘Gev’. If there were some halakhah in these places that was not related to types of vessels, I could refute it. Let’s imagine, for example, that Gev was not defiled by a worm, and Avir was. I would refute: “What about Gev, since it is not defiled by a worm.” This is a falsification of the simple and the complex that is twisted that cannot be refuted on the original simple and the complex.
I will conclude by saying that this explanation also explains when it is impossible to avoid a division by rotation. If the division has the same ‘units’ as the previous rows, and the units of the entire table are uniform, we can also place it as a column in the rotated matrix. For example: