I think therefore I exist (from the liberal sciences)

I don’t think the cogito is necessary to understand the book. It is an introduction for illustration purposes only.
In any case, there is a detailed discussion of the cogito argument in the books of Abraham Zvi Brown.
The argument “I think” is necessary because even if you think you don’t think, it is still a thought. Either way, it turns out that you are thinking. In other words, when you say “I do not exist,” the subject of the sentence (the one who does not exist, and of course the one who is also saying it) must exist.

I didn’t understand the second part of your statement. Remember that Descartes begins his move by methodically casting doubt on everything. There is no body, so there is no point in talking about coordination between it and experiences and thoughts.
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Asks:
I don’t think “I don’t exist.”
When the thought “I think” appears, the thought “What is ‘I’?” appears, followed by thoughts that relate to all of my self-schemas, and followed by the thought (doubt) “Maybe these schemas don’t exist outside of the thought itself?”
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Rabbi:
I don’t understand. Where do these thoughts “appear”? Who is the owner of the thought within which everything takes place?
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Asks:

To the question – Where do thoughts appear? I will ask – What is a place? (“Where” asks about a place)
And to the question – who is the owner of the thought? I will ask – what is ownership?
I wasn’t talking about a thought within which everything is conducted.
In other words, you are imposing concepts of place and ownership on me, when I have never felt them. The assumption that there is place and ownership is based on matters that must first be proven. Instead of answering you that “I don’t think so,” I am breaking down the question into its components, and trying to understand the concepts.
It seems to me that the concept of physical place is intended for calculations, but no one experiences place. Place in spoken language is intended to convey a message like “go to the grocery store,” but here we are relying on the fact that there is something (the grocery store) that we do not sense. If we sensed everything, spoken language, which is not graphic, would not have invented the concept of “place.” Everything was “here” and in any case there was no “there,” and there was no difference between place and place.
The concept of “ownership” belongs to control and ethics, which we certainly need to prove, and which cannot be relied upon to prove my existence after I have called everything into question.
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Rabbi:
Just as an example. Here’s your first sentence:
To the question – Where do thoughts appear? I will ask – What is a place? (“Where” asks about a place)
I am now waiting for a definition of what “about”, “the question”, “where”, “appear”, “thoughts”, “I will ask”, “what is”, “place”. In fact, let’s start defining what “definition” is.
I suppose you understand that this is ridiculous. There are concepts that we use assuming that they are understandable, and there is no need to define them. When I think, everyone understands that the thoughts are going on inside me. The term place (which, by the way, I did not use. I asked “where”, and you transferred this to a discussion about place) here is of course broader than its geographical meaning. So what? Why does the geographical meaning seem clearer to you? On the contrary, it is just a particular case of location in its broad sense.
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Asks:
I challenged the terms of place and ownership not because I want to redefine language. The reason is that they seem misleading to me.

I will clarify further:
I do not understand what meaning there is in the fact that thoughts are “within me” or “mine” if it were not for the empirical coordination between them and the conduct of the body. I understand that there is an intuitive feeling that it is clear that thoughts are “mine,” but I analyze this experience of “mine,” and understand that it has no reality in itself (a bit like the course of a day when he claimed that we do not feel causality itself). This experience of “mine,” that thoughts are “mine” or “within me,” is created from the habit of experiencing coordination between the inner world and the outer world or the entire organism. Therefore, it is possible to say “the thought appears” and “there is a thought,” and it is not necessary to say “I think.” Only after the induction is activated can we say that I (the entire organism) am not a sensual imagination, and then say that the thought is “mine” in coordination with the entire organism, whose existence I have already received certainty about through induction.

I invite you to define what the “I” we are talking about is. Perhaps that will clarify a lot. In the book you wrote that it is the “thinking I” or the “spirit.” Needless to say, “spirit” is a very vague definition. The “thinking I” ostensibly assumes that there is an act of thinking, and that there is a difference between the I and thought (that the act of thought is in between them). Ontologically, these are terms that I find no reason to assume exist (I and the act of thought).

In a way, I also want to argue that proving the existence of things precedes naming them in language. What I mean is that I think the cogito is a play on words.

“Hey, what do you think?”
“No, I don’t.”
“So you exist because you think you don’t.”
“No, I don’t think so.”
“So how did you deny that you think if you don’t think?”
And so on, “correcting questions.”

But the basic premise of the “fixer” is that a “you” already exists. To such a question, one can either say “There is no such thing as ‘I’.” Or ignore it, or play the game. But it’s clearly just a word game. If I want to remove the sting through a philosophical discussion, I say “There is no such thing as ‘I’.” Or “Define ‘I’.” In any case, with the “fixer” there is a subtext that I already exist, and I don’t want to enter this game. And if I do enter, it’s not because I suddenly exist a moment later when I didn’t exist before the game. It’s just because from the very beginning I didn’t doubt everything with all my heart, and from the very beginning I had a vague idea of ​​my “I” (in my opinion, from an induction that we cannot free ourselves from, even if we delude ourselves that we doubt everything).
Is the sentence “This sentence is a lie” true or false? When you think it is true, does it suddenly become true, and when you think it is false, does it suddenly become a lie? not. It’s a play on words. When I make a claim, the subtext is that I’m making a true statement. So the claim means “True, that this statement is false.” Since a truth that is false is a logical contradiction, the statement makes no sense.

That’s why I’m asking for a definition. I want to hear the subtext.
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Rabbi:
I repeat that you are asking for definitions for basic things that have no definition. We perceive our self directly and there is no need or possibility to define it. The same is true for the fact that thought is done within me or by me. To the same extent, you cannot define concepts such as: existing, matter, definition, and the like. All of these are self-evident and do not require definition, nor can they be defined.
I also disagree with your assumption that the sense of self has no meaning and is misleading. In my opinion, it has nothing to do with coordination with the body.

Whether the organism is a sensual imagination or not is not our concern. The cogito is not concerned with the existence of the organism but with the existence of the thinking spirit.
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Asks:
You wrote: “We perceive our self directly and there is no need or possibility to define it.” If so, you don’t need a cogito. Not even an “I think.” According to you, there is simply “I” (which is the thinking self).
I personally don’t perceive anything that I could call “me” directly. Maybe I’m blind.
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Rabbi:
Indeed, this is the deep meaning of the cogito. Once you begin to use the tool of thought, you cannot conclude that you do not exist.
If you don’t experience “I” (which I find very hard to believe) then I think there is indeed some blindness here (unless I am wrong). But that is no longer a matter for philosophical discussion. I don’t know how to convey my experiences to others.