1. It is obvious that any demand to conduct oneself according to the laws of logic is trivial, but raising awareness of this in the field of Jewish law is a new and refreshing approach, and also of enormous benefit, in light of the welcome proliferation of young men and kollel scholars engaged in Torah study. Their whole mode of thinking does indeed follow the laws of reason—but unconsciously—and therefore many mistakes usually crop up, alongside a failure to fully exhaust the material being studied. Those would be avoided if learners knew and were aware of the laws of reason. (I would send you a large selection of examples of logical mistakes even by famous rabbis and judges, but I trust that you know the phenomenon.)

2. More than that, I am fully convinced that if you did a small experiment and went around among learners, new and veteran alike, who are occupied with studying some Talmudic passage, and asked them how one should study, what they are “looking for” in their learning, and what their goal is, you would be surprised to find that you would have trouble finding an orderly work plan such as the one I presented (recognition that halakhic arguments at their source not only do not appear in their final and precise formulation, with clear definitions for all concepts, but that many halakhic arguments are hidden and need to be uncovered by inference, and all of this requires work. How trivial indeed). Of course everyone has a vague awareness of all this, and hence the dialectics, the discussions, and the arguments—but when the goal is blurred, the path looks accordingly.

3. I have no doubt that there is a great deal of novelty in this approach even for those who know the laws of logic, and instead of saying more, I will refer you to the writing of the first chapter on the “concept,” and I will send it to you when I finish.

(I will just note two of the central points in this chapter: 1. the need to look for the precise definition of every halakhic concept. That is, with concepts like “sukkah” or “leavened food,” with which we have no prior familiarity from everyday life, we will naturally be required to look for a definition for them, as with any encounter with a new concept. But with concepts like “minor,” “life,” “vegetable,” “bread,” and the like, which also exist in our ordinary world, we tend to assign them the meaning, if not the definition, commonly accepted by us, without noticing that this is a halakhic concept, and therefore its halakhic definition must be clarified. (As in the words of Birkat Shmuel, cited in the introduction to his novellae on Bava Metzia: “An ox that has no owner is not an ox,” by which he certainly meant that our normal definition of the concept “ox” does not include the concept of “ownership,” but in the halakhic context of a damaging ox, the concept of “ownership” is indeed part of it. [Although to be precise, in the laws of damages the exact concept is not “ox” but “living creature,” still the principle is the same: for us the concept of “ownership” is not part of the definition of the concept “living creature,” but in the context of primary categories of damages it is an inseparable part.])
And see Maimonides, Laws of Marriage 2:27: “It follows that all the terms whose meaning we have explained in these two chapters are twenty terms. And these are they: betrothal, forbidden relation, secondary prohibition, prohibitions by negative commandment, prohibitions by positive commandment, minor girl, maiden, mature woman, barren woman, adult woman, lower sign, upper sign, minor boy, one made a eunuch by the sun, one made a eunuch by man, adult man, androgynous, one of indeterminate sex, deaf persons, sound persons. Keep all these terms before you always, and let none of their meanings depart from your eyes, so that we should not need to explain each of them every time we mention it.”

2. There are many halakhic concepts that appear in more than one context, and one must be mindful that they do not always refer to a concept with the same definition. In fact, although the natural tendency is to think that in such concepts the definition is always the same, the correct approach in my opinion is to begin by assuming that it is a separate concept in each place, whose definition must be clarified, and only if there is evidence or strong reasoning may we accept that it is the same definition.
I will give an example: the concept “bread” appears in the context of “the obligation of Grace after Meals after eating it,” and in the context of “the obligation to separate challah from bread,” and one must clarify whether this is a concept whose definition is identical in both places. Only if we assume that it is, can we—in cases where a definition is given in one place (or a diagnostic feature in the definition)—transfer that to the other place. (See the novellae of Rabbi Chaim HaLevi on Maimonides, Laws of Leavened Food and Matzah 6:5, where he brings the law of dog-dough: when the shepherds do not eat from it, it is exempt from challah, by a scriptural decree from “your dough” and not dogs’. In his view there, this scriptural decree is part of the definition of the concept “bread,” and therefore it will also be valid in other contexts such as the obligation of Grace after Meals, or fulfilling one’s obligation with it on Passover. For even in “matzah” there is a law of “bread,” though of course not with an identical definition to other places, since “bread” that has become leavened is not “matzah”; and this too is one of Rabbi Chaim’s innovations there, that part of the definition of the concept “matzah” is the concept “bread”).

Another example, more basic and comprehensive: we know the concept of “acquisition” regarding property such as land and movable goods. Within it there are sub-concepts such as “acquisition by money,” “document,” “the intent of the buyer and seller,” and so on, all of which of course must be defined. On the other hand, we see that the Torah defines the “act of betrothal” as an “act of acquisition,” and beyond that, the modes of acquisition by “money” and “document” in betrothal are ones that also exist in the acquisition of land. And here the question arises: are these concepts identically defined? Birkat Shmuel on Kiddushin discusses this in many respects (half the book “sits” on this point). One by one he proves that the concepts of the buyer’s and seller’s intent are not identical; likewise the concept of money (according to many views, acquisition by exchange is considered a form of money, and nevertheless it does not help in betrothal, because it is not included in the act of taking, according to Birkat Shmuel). Elsewhere he shows that the concept of acquisition by document is different in betrothal, because its effect is not in “monetary acquisition” of the document itself as with acquisition by money (or acquisition by document in land), but depends on an “act of giving.”
I won’t go on at length, but I think the point is clear. Although the concept of “acquisition by money” in monetary law overlaps in many ways with the concept of “acquisition by money” in betrothal, each of them has a separate definition that one must pin down.)

It is hard for me to accept that there is nothing novel here, or at least no sharpening and emphasis of the correct approach to learning—especially since anyone who reflects a bit will discover that these ideas are the core of the distinctive method of Rabbi Chaim HaLevi Soloveitchik, and after him his student Rabbi Baruch Ber Leibowitz in his books Birkat Shmuel.

I would be glad to hear your opinion.

I’m sorry, but I still don’t see the novelty, and I also don’t see what is here that you wouldn’t find among systematic learners (not hasty ones) without a single drop of education in logic.
If you have one example in which you can show me an error by a good scholar (not a kollel fellow tossing out cute ideas), and that you can correct it by means of a logical tool that was unknown to him, that will show me the significance of what you are saying. Otherwise, for now I don’t see any connection here to logic. Everything you showed here, at least as far as I understood, is done by every good scholar, with no connection to logic. It is just a call for intellectual caution, not the use of logic.

1. It sounds as though you expect me to invent new laws of logic. To the best of my knowledge, none have been found in quite a few years.

2. My goal is to use the same old good laws of logic, which are (to the best of my knowledge): a. the existence of concepts, and the necessity of defining them. b. the ability to formulate and understand arguments, with recognition of the different kinds of argument (distinguishing assumption from compelled knowledge, positive and negative argument, analytic and synthetic, general and particular). c. the ability to make and understand inferences, with recognition of the kinds of inference (valid and invalid, necessary and probable).
All this while adhering to the laws of reason: the law of identity, the law of non-contradiction (open and hidden contradictions), and the law of the excluded middle.
In addition, sharpening and guidance on how to avoid in all this informal errors whose source is emotion and imagination.

Again I emphasize and say: I do not intend to invent new laws of reason, but only to show an application of all the above in the fields of Jewish law. (If you know of additional universal laws of reason, I would be glad if you would let me know of their existence.)

3. In addition to that, there is an internal functioning of halakhic laws of logic: scriptural decree, innovation, obviousness, reasoning, difficulty, resolution, proof (absolute, probable), doubt, dispute, error in judgment, error in an explicit Mishnah, and so on and so forth. And there is a need to define and clarify the precise content of all these.

4. In any case, if this does not seem to you to be the use of concepts of logic in Jewish law, what other logical tools do you know?

5. Regarding examples, there are so many; on another occasion I will send them to you. But they are all cases whose error becomes known through the above tools (vague definition, invalid inference, etc.). There are also cases that are errors in the sense of deviating from the Torah’s internal laws of reason, such as implausible innovations, and with God’s help I will deal with those too.

6. You do not have to respond. Everything I wrote was just to let off steam, but I am convinced of the importance and applicability of this approach, and I will pursue it.

There is a misunderstanding in your remarks of what I wrote. What I wrote was that if you want to interest me, you need to show me that the existing laws of logic actually help the Talmud student who does not know them. That is not the same thing as inventing new laws of logic. The background to my interest is that I have already seen quite a few compositions and articles that make similar claims, and in the end I saw no useful novelty there—meaning, nothing that an ordinary learner cannot do. Instead of talking about the matter, one should bring one example that demonstrates the benefit to the skilled Talmud student who does not know logic.

By the way, there certainly are new laws of logic. Not in basic logic, true, but today logic is far more branched out and developed. In our works on Talmudic logic, to the best of my judgment, we found new logics in that sense.

Much success.

1. Now you’ve completely confused me. This seems like an attempt to hold the rope at both ends. On the one hand you claim that “the need to define concepts and preserve the rules of inference is something trivial,” and that “every systematic scholar will maintain this intellectual caution,” and on the other hand you want to examine whether the “systematic scholar who doesn’t know logic” can be helped by the laws of logic. Well then, let us agree that that is exactly the person we are talking about: that “scholar who doesn’t know logic,” meaning that he is not aware of the laws of logic, among them for example the necessity of defining every concept (as in the examples I mentioned above), and likewise by our assumption he is not aware of the other basic laws of logic mentioned above. Such a person, although he will indeed seek to understand concepts, will not seek to pin them down in a fixed definition; he will not trouble himself to clarify the precise formulation of arguments, or at least to consider all the possible formulations; and when he needs to draw conclusions, he will sometimes fail both through invalid inferences, through failure to distinguish between necessary and probable inference, and through failure to fully extract the conclusions from a given argument.

And although in general even that “scholar who doesn’t know logic” will conduct himself according to the laws of logic, this will be done unconsciously, and therefore not professionally and not all the way through (and he will also fail in many informal errors).

2. You asked for an example of a logical fallacy. Well, an example of that (in my opinion) is from something I found in one of your posts.

“… But that is only in the realm of assumptions, because we have no way to judge them and distinguish between those that are rational and those that are not. But logical inference, that is, the move from assumptions to conclusions, can indeed be characterized in terms of rationality and irrationality. If a person derives his conclusions consistently from his assumptions and maintains consistency and systematicity in his way, one may say that he is a rational person. By contrast, a person who acts from the gut on the basis of feelings and does not maintain consistency is not rational. If so, rationality mainly characterizes the logical derivation of the conclusion from the assumptions, and not the assumptions themselves.
An interesting anecdote in this context is found in the responsa Igrot Moshe, Even HaEzer, part 1, sec. 120, where Rabbi Moshe Feinstein discusses someone insane in one matter (that is, a person who has one delusion, but in all other contexts conducts himself logically):

‘Now aside from this leniency, one may also discuss that he should not be considered insane at all because he thinks himself the messiah, just as one who worships wood and stone as idolatry is not considered insane, even though it is certainly a great folly to believe in wood and stone. Rather we say that he is sane and wicked, and we make him liable to death. So too one who considers himself the messiah—although it is a great folly—should not be considered insane; rather, his excessive pride has misled him into thinking that he is fit to be the messiah. And consequently one can argue even more that all his foolish acts that follow from his mistaken view that he is the messiah, which according to his bad opinion are the repair of the world, do not make him insane. For anything a person does on the basis of some calculated system and path that he holds in his mind—even if it is great stupidity—does not thereby make him insane, as is proven from idol worshippers, who performed many foolish acts, and all the ways of the Amorites mentioned in Sabbath page 67 are foolish acts, and yet they have the legal status of a sane person.’

He determines here that if that person acts in a way consistent with his assumptions (= rational), he is not insane, whatever his assumptions may be. He identifies folly here with irrationality in the sense defined above, that is, with inconsistency (by the way, I disagree with him about this).”

As I understand it, you are claiming that according to Rabbi Moshe, an insane person is someone whose behavior is inconsistent (irrationality as you defined it earlier), and with that you disagree.
In my understanding, that was not Rabbi Moshe’s claim; rather, he argued the other side of the coin. That is, in his view, the definition of the concept “insane person” (as one exempt from commandments and punishments) does not include a person with a foolish belief (that he thinks himself the messiah, or that he attributes divinity to wood and stone). And even if in addition he does other foolish acts, all of which follow from and consistently support that foolish belief, he still is not considered insane, since all his acts are directed toward that same belief.

It follows that Rabbi Moshe is not arguing that someone who behaves inconsistently is insane; rather, on the contrary: someone who holds a foolish belief and behaves foolishly (which should make him insane), because he behaves consistently with that belief, is not considered insane (and he proves this from an idol worshipper). And it does not follow from this that everyone who behaves inconsistently (as you wrote earlier, that an irrational person is one who behaves inconsistently) is therefore also considered insane. What can be inferred from his words is that someone who does 1. foolish acts, 2. inconsistently with any belief—about him one can say that he is insane.
Would even this definition of an insane person be unacceptable to you? What could be worse than a person who performs foolish acts inconsistently? (One can argue whether idolatry and messianism are foolish acts on the same level as other foolish acts, but that is already a different claim.)

All right, the discussion has become bizarre. So I suggest we stop here.
Two reasons: 1. Even if you found an error in my thinking (and you didn’t), what would that prove? Where is the missing logical knowledge? I happen to know the rules of logic quite well too (although it is certainly possible that I made a mistake. It happens to everyone). That of course proves nothing. I did not claim that scholars do not make mistakes, but that knowledge of logic does not necessarily prevent them. So here you have it: my knowledge of logic did not prevent the mistake (which, according to your view, exists in my words). 2. There is no error at all in my words. You are proposing two equivalent formulations and insisting that they are different.
But in any case, as far as I am concerned, I am done with the discussion. It is not focused and not useful.
All the best.