Representation and Non-Verbal Thinking: 1. Conceptual Representation (Column 379)

Michael,
You say: ‘The commandments are a representation of a more abstract idea, and the Torah exists on that plane.’
It’s easy to agree with such an approach regarding honoring one’s parents. Try applying it to the prohibition against deriving pleasure from slices of bread with cheese and sausage…
Whatever abstract ideas the commandments may represent, in everyday life observing them leads to foolish behavior, and sometimes cruel behavior.
Nissim

That is a misunderstanding of the whole matter. You have no way of knowing what those abstract ideas are, and certainly you cannot judge them in light of their garb. Even flower arranging can look, on its face, like foolish behavior, and yet one can learn Zen ideas through it. How is that different from the kata of not eating meat with milk?!
You cannot decide that this is foolish behavior without understanding what it is about. And as for cruel behavior, see column 15 (and at greater length at the beginning of the third book in my trilogy).

*

With God’s help, the Lord’s day, Bnei-San, 5780

And for those who have difficulty with non-verbal thinking, let us add a short verbal explanation.

The symbol of our method is the asterisk * – a central point sending out 5 rays in all directions: upward, sideways, and downward. The asterisk symbolizes the totality of the human being: the head, the hands, and the legs. The head – expresses the person’s intellectual capacity; the hands – his capacity to act and create; and the legs – expressing a person’s ability to choose his place in the world, his ability to leave the limitation of the ‘here’ and move toward new and unfamiliar places.

When a person builds himself as an ‘asterisk’ – all the layers of the person – thought, action, and movement – are connected to a central point, to the heart thirsting for a constant divine presence, which will guide the person to right choice in his thoughts, actions, and movements. The 613 commandments accompany a person in every step he takes and at every moment in time in which he finds himself. At every step and stage he is required to think: what does God require of me at this stage? And thus he ‘lives with God’ at every moment, connected and bound to his God and His guidance, and thereby connected to his central point.

With the blessing of ‘Spring Star’
Ching Chong Chi, man of La-Wing
The ‘Zen in His Mercy’ Institute, Kochav HaShachar

With God’s help, in Nisan 5780

To Nissim – greetings,

Immediately after the revelation at Mount Sinai, where the Ten Commandments were proclaimed to the people, God calls to Moses and commands him a system of commandments that constitute a specification and expansion of the Ten Commandments. Moses writes the ‘Book of the Covenant,’ makes a covenant with the people, and ascends the mountain for forty days to receive a complete explanation of the Torah. The ‘Book of the Covenant’ was repeated in shorter form following the breach of the covenant in the incident of the calf.

What is interesting is that both the first ‘Book of the Covenant’ (in the portion of Mishpatim) and the second ‘Book of the Covenant’ in Ki Tisa end with the commandment: ‘The first of the firstfruits of your land you shall bring into the house of the Lord your God; you shall not boil a kid in its mother’s milk.’ Man rules the world: he sows and brings forth fruit from the earth, and he rules over the living world and is even permitted to slaughter animals and eat them.

Man’s mastery over the earth, over animal and plant life – may lead him to pride, to the thought: I am the owner of the world, and who can tell me, ‘What are you doing?’ These commandments come to moderate that feeling of pride. He shall bring the first of the firstfruits of his land to the house of the Lord his God, and there he will say to the priest: ‘An Aramean sought to destroy my father, and he went down to Egypt,’ etc. There the successful farmer acknowledges that he began his ‘career’ as a humiliated and oppressed slave, and only by God’s grace merited to leave his bondage and settle in his good land.

Likewise, in exercising his superiority over the animal world – a superiority that permits him to eat both the flesh and the milk of animals – the Torah requires of him a bit of restraint and self-control. Do not devour ‘mother together with young.’ Enjoy, but with limitation. Know that you are not the master of the world. Even while eating, feel yourself a guest of the true ‘Master of the house,’ a guest who is not entitled to take ‘whatever comes to hand.’

It is worth noting that the final commandment in the Book of the Covenant, ‘You shall not boil a kid in its mother’s milk,’ provides excellent training for the hardest commandment of all: ‘You shall not covet.’ One who succeeds in restraining his appetite and not reaching for the ‘perfect steak,’ combining the tenderness of kid meat with the richness of milk – that marvelous delicacy with which the great host honored his guests, serving them ‘butter and milk’ together with ‘a calf, tender and good’ – the very culinary top of the top you will forgo, and thereby accustom yourself to living a life of restraint and self-control. As they say: ‘Hard in training – easy in battle.’

Regards, Yaron Fish"l Ordner

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… the asterisk symbolizes his being …

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… makes a covenant with the people and ascends the mountain …

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Man’s mastery over the earth …

Hi,
I didn’t understand whether your claim about the Torah as text and the two planes of representation (a kind of Platonism) is a factual claim or not.
Are you claiming that this is how the Torah is actually built? That the text is only an external expression of a deeper reality?
If your answer is yes, I didn’t find any argument for that in the column (beyond the views of Hazal or the author of the Tanya).

Wine and life according to the word of the master who speaks and acts. Very interesting. I’m not sure I understood exactly, so I’ll try to formulate it in somewhat different language, so that if it’s synonymous, all the better, and if not, please correct me. If there are two different representations, that means there is an additional level of abstraction, and the two representations are analogues in different domains. As in mathematics, where theorems have generalizations, each higher than the previous, and every theorem at a higher level of abstraction applies to more cases and domains, while the lower levels of abstraction are private cases of it; and when one rises in the level of abstraction, one can also project to domains that currently seem different (for example, the fundamental theorem of calculus < Green’s theorem < Gauss’s theorem < Stokes’s theorem). For example, a law in the Torah that the priest sees an affliction in a house, goes out, and quarantines it. This is a private case of the general principle of the prior presumption, and one can try to grasp that general principle intellectually. Now I understand that you are saying there is yet another stage, and that this principle itself is a private case of an even more abstract principle, and that abstract principle too, though it is a pure light, a polished light, is darkness relative to the principle above it, and so on. After taking the frying pans out of Yoreh De’ah and dealing with first-order abstract principles, these too can be taken out, and one can then deal with second- and third-order abstract principles and beyond. If I understood correctly, then on its merits this sounds reasonable to me, but essentially it is a claim that cannot be confirmed (with a somewhat conspiratorial scent) – that all our thoughts can be grasped at a higher level of abstraction/generalization, because whatever we attain, there may always be further levels above it.

With God’s help, in Nisan 5781

To Doron – greetings,

In several places the Torah defines the purpose for which it was given, and offers various aims that look like abstract ideals that are not at all easy to define verbally.

What, for example, is ‘a kingdom of priests and a holy nation’? What is ‘You shall be holy, for I am holy’? What is ‘to love the Lord your God and cleave to Him’? What is ‘you shall be My treasured possession’? What is ‘what great nation is there that has gods so near to it’? What is ‘May the Lord make His face shine upon you’? What is ‘May the Lord lift up His face to you and be gracious to you’? What is ‘He blessed the Sabbath day and sanctified it’?

Clearly, these descriptions express traits and states of mind to which the system of commandments seeks to lead a person, beyond ‘halakhic technocracy’ 🙂 And clearly, it is hard to give such states and dispositions an exhaustive verbal definition.

Regards, Othyphron Nefishtim Halevi

By the way, the Song of Songs is commonly interpreted as an allegory of the relationship between the Holy One, blessed be He, and Israel, but Malbim explains that it is not only an allegory that allegorizes a referent, but an allegory that allegorizes an allegory that allegorizes a referent. When I once thought about it, I came to the somewhat dry conclusion that I don’t understand what benefit there is in an allegory for an allegory, and that one can always go directly from the allegory to the referent. But I no longer had the strength to go over his commentary there very carefully (which in my eyes was a very beautiful work by Malbim, although I usually recoil from his commentaries) and try to see what we would lose if there were only allegory and referent. And I remained with the thought that this is merely an aesthetic matter: one does not compare a delicate thing directly to something too coarse. But from Malbim’s formulations there I got the impression that he thinks there is more in this hierarchy of representations than the aesthetic issue mentioned. [From what I remember, approximately and briefly, without commitment – Solomon loves a woman who longs for another wondrous lover. And this is an allegory that the body tries to seduce the intellect, which longs for intelligibles. And the Kabbalistic referent, on spiritual planes, is that many powers try to attain the community of Israel, which longs to connect with God.]

First, I am explaining the words of Hazal. I have no other source from which to learn about the essence of the Torah. This also follows from the importance they attach to study, which is not merely a means to know what to do. Therefore several later authorities explained (I cited two) that this is a way of cleaving to the Holy One, blessed be He. It is not plausible that this cleaving comes from dealing with oxen and thieves.

The continuation to infinity is your addition. Maybe yes and maybe no. But you are certainly right that these things cannot be directly examined by us. See my reply to Doron above.
I’m not sure that representation and instantiation are the same thing. Instantiation is like the relation between a theory and a model in mathematics. It is a private case of the general thing. Representation seems to me something slightly different, because it does not necessarily involve a move from the general to the particular, but from the abstract to the concrete, and the concrete too is a medium and not a representation of the thing itself. Think of the chair argument I gave as an instantiation of the logical syllogistic structure. It is not a representation of it but an instantiation of it.

As for a chain of allegories, sometimes the distance between the first allegory and the final referent is too great, and it would be hard to understand the connection, so one does it through a chain of closer links.

This is a big matter for me, and I wrote an entire scroll, but really it’s better first to ask questions. What is the relation between a priest and an afflicted house and the prior presumption? What is the relation between a one-dimensional theorem (the fundamental theorem of calculus) and its generalization to a two-dimensional theorem (Green)? What is the relation between a theorem (say, the fundamental theorem) and its application (to a concrete function)?

As for a chain of allegories, I’m looking for an example. For years I’ve been ‘planning’ to return to Malbim’s commentary there and see whether there is a convincing example there of the need for a chain of allegories, but laziness pushes the flesh aside. Because if nowhere else (that I’ve happened to encounter and remember) does anyone use a chain of allegories, then apparently it really is unnecessary.

With God’s help, in Nisan 5780

To Tola deGinta – greetings,

Without the allegory, which is a common and familiar situation, it is almost impossible to understand the referent. Has any ordinary person ever seen someone who, as Maimonides describes, contemplates the wonders of creation and is seized with an intense desire to know God, a desire that does not leave him, so that he is like one in love with a woman, continually preoccupied with love of her?

Many people experience the phenomenon of the ‘allegory,’ and they also display it strongly outwardly. Such love toward the Creator is attained by only a few elevated people, and their emotional state in the midst of that love is mature and ripe, where all the longing and ardor are internal and hardly revealed outwardly. Only on rare occasions does the inner ardor peek out. Were it not for that expression in the description of the love of God, and the words in the introduction to the Guide about the lightning that illuminates the human soul, I would get the impression from reading most of Maimonides that he was a cold rationalist devoid of feeling, with no sense at all of the storm raging inwardly in the heart.

In my youth I attended a lesson given by Prof. Yeshayahu Leibowitz in the Beit Yosef synagogue in Rasco on Maimonides’ explanation of the story of the Garden of Eden. One of the listeners, R. Shmuel Segal of blessed memory, remarked: ‘Well, after all, Maimonides was a rationalist.’ Leibowitz fixed his eyes on him and said: ‘Maimonides was a rationalist? Maimonides was a mystic.’ Leibowitz said it, and he was right.

But more than that, from the sages of Hasidism and Rabbi A. I. Kook one may learn that all the loves and desires in a person are nothing but a ‘derivative’ of the soul’s longing to cleave to its root, to the source of life. And especially the love of one person for another and the love of a man for his wife, in which a person senses the existential need to connect to something beyond himself.

Regards, Ami’oz Yaron Shnitzler

The Rebbe Menachem Mendel of Kotzk asked: if, above Yonatan ben Uzziel, every bird flying overhead would be burned – what about his teacher Hillel, who was presumably greater than his student? And the Kotzker answered that a teacher knows more than a student. The teacher knew how to keep the ardor inside, so that it would not burst outward.

You explain nicely that the allegory is taken from familiar things and is useful, but where is the explanation (and an example) of what a chain of allegories helps with, instead of a single allegory directly to the referent?

If one wants an example from mathematics, then a representation is the relation between a representative of an equivalence class (induced by some equivalence relation) and the class of which it is a member.

Even though the relation between the representative and the class is exactly the same as the relation between each of the class members and the class, and there is nothing special about the representative? When there is representation with respect to a certain operation, that means that operating on any two represented elements always yields the same result as operating on the two representatives. For example, the equivalence relation modulo 3 divides the integers into equivalence classes, and let us take, for example, the number 5 as a representative of the class ‘remainder equals 2’ with respect to the operation ‘addition modulo 3.’ Can you formulate in words the meaning of representation here?

With God’s help, in Nisan 5780

To Rabbi M. Abraham – greetings,

It seems to me that according to the author of the Tanya and Nefesh HaHayyim, not only reflection on the abstract idea underlying the halakhah, but also dealing with the technical details of oxen and thieves is part of cleaving to God. For their reason is that ‘He, blessed be He, and His wisdom and His will – are one’; hence clarifying the halakhic detail is really understanding that in such-and-such a situation, the wisdom and will of the Creator require such-and-such.

In the words of Nefesh HaHayyim in particular, this seems proven, since he says explicitly that contemplation of God’s greatness is supposed to occupy only a few minutes, after which one’s mind is given over for many long hours solely to the intricate halakhic discussion, literally. The student must be focused on the technical analysis before him, not on ideas and the upper sefirot.

The essential difference between one who cleaves and one who does not is the inner attitude while attending to the finest details. Thus there is a difference between a grocery employee (super-man in foreign parlance 🙂) who receives a ‘shopping list’ from some anonymous customer, and the loving husband who receives a ‘shopping list’ handed to him by his dear wife. The act is the same act, but the difference in inner feeling is abysmal.

Regards, Yaron Fish"l Ordner

An afflicted house is an example of a presumption. So it is an instantiation, not a representation. The principle of presumption is the logic illustrated through the afflicted house. Once we have conceptualized the notion of presumption, we no longer need the example of the afflicted house in order to learn it. It is like the example of chairs for the general inference (every X is Y and a is X, therefore a is Y).

Perhaps sorites is a good example of such a chain (of course not exactly the same thing). See Eruvin 51 and Middah Tovah, 5765, parashat Beshalach:
https://drive.google.com/drive/folders/0BwJAdMjYRm7IRmM4RGd0dG9zWU0
And the continuation from 5766:
https://drive.google.com/drive/folders/0BwJAdMjYRm7IRmM4RGd0dG9zWU0

Not for nothing is the heap paradox in English called the sorites paradox: https://plato.stanford.edu/entries/sorites-paradox/

It seems to me that a representative from an equivalence class is an instantiation or an application, not a representation in the sense I’m speaking about. The equivalence class itself is a representation of the equivalence relation that induces it. Something like Frege’s definition of the number n as the collection of sets that contain n elements. I never understood how that is a definition of the concept of number. That collection of sets is not a number but an equivalence class. I would call that a representation, not a definition.

This is basically the difference between induction and abduction. Induction is a move from an instantiation (a private example) to the general law. Abduction is a move from the private instantiation to a theory (not a phenomenological, descriptive theory, but an essential theory). The set of private cases is a representation of the law of nature. But the private case relative to the set of private cases is an instantiation, not a representation.
Now I think I elaborated on this in my book Ruach HaMishpat, where I distinguished between specification and instantiation.

With God’s help, in Nisan 5780

To T.G. – greetings,

What exactly Malbim means in his remarks about the necessity of a ‘chain of allegories,’ I am not sure I understand, so I will not take responsibility for conjecturing about the explanation of his words.

In any case, it also seems to me that one cannot understand a powerful emotional phenomenon through a single explanation, because the phenomenon is large and complex, many-sided and multi-hued, and sometimes those sides are opposed.

The allegory is well known of the dwarfs who found an elephant. Some of them would excitedly describe the solid pillars. Some the flapping sails. Some the great pipe spraying water. And some would describe the sharp, gleaming horns. Each grasps part of a large and complex picture.

Even the feelings between a man and his wife cannot be described by one allegory. The beloved, in his human sense, may at one and the same time be the simple youth from the desert, charming in his innocent simplicity, and at the same time also King Solomon, enchanting in his wisdom and his ability to solve intricate and complex problems.

And the beloved woman can also be the playful daughter whose games one enjoys, while at the same time one invests in paternal concern for her well-being and health. At times she is the mother who comforts and calms, and at times she appears as a sister with whom one can have an eye-level conversation, sometimes in admiring attentiveness and sometimes in arguments up to the heavens.

The mutual bond also includes longing and pain when they are not together, and also calm, because they know they can trust one another, even when a great distance separates them.

So if the human phenomenon of love between people is so complex and multifaceted – all the more so is this true of the Cause of causes and Reason of reasons, who on the one hand ‘no thought can grasp at all,’ and on the other hand whose wisdom and goodness, strictness and forgiveness are evident at every step.

It is the complexity that requires a multiplicity of allegories, and even after all of them we are still as far as heaven is from earth from full understanding.

Regards, Yismachah Fish"l Halevi Plankton

And beyond the philosophical insight that ‘He and His will and His wisdom are one’ – there is a further advantage in clarifying the halakhah, through which we find the right way to establish peace among people who are many and contentious, a peace founded on truth and justice. A judge who renders a true judgment according to its deepest truth is a true partner of the Creator of the world, for he brings the world to a sweet state, a state of peace and truth.

Regards, Yfa"or

‘And keep and do them, for this is your wisdom and your understanding in the sight of the peoples, who shall hear all these statutes and say: Surely this great nation is a wise and understanding people.’
‘And what great nation is there, that has statutes and ordinances so righteous as all this Torah, which I set before you this day?’
‘And this is the Torah which Moses set before the children of Israel. These are the testimonies, and the statutes, and the ordinances, which Moses spoke to the children of Israel, when they came out of Egypt.’

In our time, when people neither study nor observe the Torah and disparage its wisdom, it has become common to invent from imagination abstract ideas, most of them baseless, in order to explain the matter away.

From Rav Kook’s explanation of the uniqueness of the wisdom of the fear of God as compared to the other wisdoms, including apparently even the wisdom of the Talmud, in the other wisdoms the wisdom becomes knowledge that can be explained in a clear verbal explanation. Whereas the wisdom of awe cannot be explained in words, since one who has not himself undergone the emotional process does not really understand what is being discussed.

According to this distinction, one can understand the need, in the wisdom of awe, for allegories that bring one’s understanding closer to the required emotional process.

Regards, Yfa"or

I now recalled that this may also connect to the chain described in Middah Tovah, 5765, parashat Kedoshim: https://drive.google.com/drive/folders/0BwJAdMjYRm7IRmM4RGd0dG9zWU0
That’s even closer.

Michi,
Well, we are returning to an old argument of ours.
I argued in this framework in the past that the Torah, considered as a text (or as a body of knowledge in a broader sense), bears a character that you would call ‘analytic.’ Instead of positing a clear hierarchy that first and foremost grants primacy to the intuitive capacity in man, it places the language of the text, the wording that appears in the Pentateuch, at the center. On its view, the central mediating channel (and in practice also the only one) between man and metaphysical reality is the Torah itself.
Therefore my claim is not against the conception that there is an abstract essence behind the text. There may be. The claim is that the Torah does not permit us to think that.
I brought here in the past the ‘control group’ from the competing religious tradition – Christianity. In Christianity there are no ‘holy scriptures’ in the same sense as in Judaism, because its foundational text directs the believer first to his intuitive capacities (in Christian language this would be called faith, stirrings of the heart, or something of the sort), and only afterward brings the institutional social command into the picture.

To Tolginus

Yes. It is admittedly a somewhat subtle matter (I’m not sure that this distinction in Rabbi Michi’s terminology between instantiation and representation really exists. Anything that exists in an example of one of them can also, in some sense, be shown to exist in an example of the other). The assumption is that it will be hard for you to explain to someone who has not previously experienced an equivalence relation an operation between abstract equivalence classes (for example, adding the class of 5 modulo 7 to the class of 4 modulo 7, say; the set of equivalence classes forms a quotient group of the group of natural numbers with respect to addition). One has to use concrete examples in order to explain how equivalence classes can be added. In your example, for instance, let us add 5 and 7 and get 12, which is 0 modulo 3. And this represents the addition of 2 modulo 3 and 1 modulo 3, which equals 3 modulo 3, which is really 0 modulo 3; and these are all the equivalence classes of the equivalence relation modulo 3.

And on the matter itself.
There is no such thing as one thing being a true representation of another thing.
Either it is the thing itself or it is something else.
And if we are speaking of simulations, then there too there are many assumptions about the laws, as well as omissions and shortcuts.
The way to represent something truly is either to be the thing itself or to know all the laws governing the thing itself.

See my reply to Tolginus.

When one performs addition modulo 7, say, in order to explain to someone how the whole business works one must use addition of representatives from the classes. The abstract rules of addition of equivalence classes say nothing to someone who has not experienced the concrete rules of addition. And perhaps this is what the rabbi meant here in saying, ‘the equivalence class itself is a representation of the equivalence relation that induces it.’ Therefore this distinction does not seem sharp enough to me. Also, when one says that a particular is an instantiation of some universal, that also means that through it we grasp the universal (hold on to something of the universal). In the particular there is a reflection and appearance of the universal to which it belongs (one can see the universal through it). So in that sense it is also a representation of it. After all, that is the whole meaning of bringing an example in order to explain something. An example is a concretization.

In short, what I’m saying is that an element in an equivalence class is a concretization of the abstract entity that is the equivalence class to which it belongs.

Pearls are being handed out here, and I need more time. I’ll study everything you brought over the weekend. This topic is heavy for me, and I can’t exhaust it quickly. Today I went and got Kripke’s book, and it seems that my time has come to sit secretly on his rung. If anyone has a charm for slowing the hands of the clock, please let me know, and so may it be His will. By the way, in software they speak of the relation between inheritance and instantiation (Inheritance vs instantiation). Inheritance is abstraction, that is, reducing the number of properties and thereby increasing the range of applicability, and it deals with the dimension of properties and abilities. Instantiation is realization: one takes the properties as they are and pours into them specific values. (‘Human’ inherits from ‘Mammal.’ ‘Bezalel son of Uri son of Hur’ is an object of type ‘Human’).

By mistake I sent the message here instead of as a reply above to the references to the Middah Tovah articles.

A. By my nature, I think this is not a matter of explanation but of definition. In the quotient group one can define an addition operation between classes by means of the addition operation in the original group between elements of the classes. Maybe it really is connected to realism. I’ll think about it.
B. Representation is only with respect to a certain operation. For example, in your example the addition operation in the original group is blind to differences between different elements of the same equivalence class (just as height requirements for rides in an amusement park are blind to hair color). That is, there is no general relation of representativeness between an element in the class (a representative) and the class, but rather a property of a certain operation that it is blind to differences between different elements. If we take the quotient group from equivalence modulo 7 and try to apply exponentiation, then the representatives will represent nothing. For example, 9(2) and 8(1): if we take 9 to the power of 8 modulo 7 we get 4, which is not equal to 2 to the power of 1 modulo 7.

A. Of course there is an explanation. Definitions are not created out of nothing. They try to capture a basic intuition that precedes them. The explanation is supposed to convey the intuition to someone who does not have it.

B. The whole identity of elements in sets usually depends on some additional structure that the set has, such as an operation or a relation. Otherwise there are merely different elements, lacking character and color – lacking identity (that is not empty, meaning beyond the mere fact of their separate existence from others). If so, of course a different equivalence relation will color those elements differently.

B. Please elaborate further. For example, I form a quotient group by a certain relation (equivalence modulo 7 in your example) and then ‘to my surprise’ discover that one can use representatives with respect to a certain operation (such as addition modulo 7, or multiplication modulo 7, but not exponentiation modulo 7). What do you see here besides saying that ‘multiplication modulo 7 is blind to differences between elements equivalent modulo 7’?

In my book Et Asher Yeshno I defined this as the ‘degeneracy’ of concepts (like degeneracy of energy levels in physics).

Wonderful. We eagerly await the continuation of this column. And perhaps in this context you could explain Maimonides’ approach in the Guide according to your conception. I understood him exactly this way. Thank you!

??
Which Maimonides? Are you asking here for a general commentary on the Guide? 🙂

Why should one say anything more than: ‘Multiplication modulo 7 is blind to differences between elements equivalent modulo 7’? Once the equivalence classes have been formed (the equivalence relation being of course built on the natural operations of multiplication and addition), then their representatives are representations of the whole class, and that’s that. I don’t understand what is complicating this for you.

And in even shorter form, I claim that there is no such thing as a universal that is no more than the sum total of its particulars (particulars are not just gathered into random universals/collections. They have something in common that causes me to include them together in the first place. According to what criterion are they gathered?). In a situation where the universal is an entity in its own right, it is impossible to grasp it except through its particulars. Therefore they also constitute its representations.

A series on the Guide could be wonderful.

It seems that this is there all the way through.
What is the difference between the unity of intellect, intellection, and intelligible, and ‘embracing the king through his garments as though embracing the king himself’?

Or for example, the third interpretation of ‘and the form of the Lord he beholds’ – the true reality grasped by the intellect… and its meaning and explanation – he apprehends the truth of God. (Chapter 3). There is here an apprehension of the sign and of the thing itself, and an absorption into it, beyond understanding what the sign signifies.

So it seems to my limited mind. Perhaps I am mistaken.

Representation is only with respect to a certain operation, and therefore I do not see in it a statement about the (abstract and vague) connection between the representative and the class, but rather a (trivial) statement about the properties of the operation.

Indeed, the author of the Tanya relies on Maimonides’ reasoning that with the Holy One, blessed be He, He and His wisdom and will are one.

Regards, Yfa"or

The question is too general, and also not all that interesting. If you nevertheless want to discuss it, bring a specific quotation you are uncertain about and present a question for discussion.

In the articles Beshalach 5765–6 (files 16|70 in the folder) you dealt with the chain of derashot concerning the Sabbath boundary. The chain of derashot there is ‘place’ from ‘place,’ and ‘flee’ from ‘flee,’ and ‘boundary’ from ‘boundary,’ and ‘outside’ [‘let no man go out of his place on the seventh day’ – ‘and I will appoint you a place to which he may flee’ – ‘but if the slayer shall at any time go beyond the boundary of his city of refuge to which he has fled’ – ‘and the avenger of blood finds him outside the boundary’ – ‘outside the city, two thousand cubits’].
Everything is fine and interesting and gives good conceptual tools. But in those articles there is an overly formal treatment of this derashah. It seems the assumption is that by the same token one could have made a derashah like ‘In the beginning God created’ – ‘the first of the firstfruits of your land’ – ‘the firstfruits of the wheat harvest’ – ‘wheat and barley and vine’ – ‘and in my dream, behold, a vine,’ and learned that all creation is one great dream of God. And Hazal simply did not happen to do so because this was not a useful asmakhta, or it was not received in tradition. But plainly that is not so. In the derashah about Sabbath limits they are not merely learning words (‘semantic transitions’); rather, there is one single substantive content that runs like a thread through all the derivations, namely the clarification of the boundaries of ‘place’ through its alternative definitions.
The conception is that the Sabbath limit is not a special law in the laws of Sabbath, but a derivative of the general conception of city boundaries. Therefore one can learn from the boundaries of the Levitical cities (what is given to them) to the boundaries of the city of refuge (where the killer has protection) and to the boundaries of the Sabbath limit. The boundaries of the city of refuge define inside and outside – how far inward the killer enters when he flees, and how far outward, if he goes, the avenger of blood may exact vengeance on him. And those boundaries are defined as two thousand cubits. And just as the city is the killer’s ‘place,’ so the city is every person’s ‘place’ for every matter, and in particular for the matter of the Sabbath limit. This is a sensible interpretive derashah dealing entirely with the clarification of one concept of place through different definitions or implications of it: the boundary of place, where one flees to, what counts as outside, the area annexed to a city – all these are alternative definitions of the same concept itself, whose implications naturally pertain to the matter of the Levitical cities, the cities of refuge, and the Sabbath boundary. And so it is explained.

You burst through an open door. That is exactly why I referred you there, because one can understand that behind those analogies there are also substantive analogies. Therefore this is an example of a chain of analogies like the one you were looking for. If it were only a formal verbal comparison, it would not be an example of what you are looking for.

Ah. Though there is not a chain there (a line-configuration) but rather different implications from the center (an asterisk * configuration). The sphere of extension of place has different implications (where one flees, what counts as outside, what the boundary is, how much area is annexed, and the Sabbath limit), and each of them testifies to the sphere of extension. Now that one knows a numerical value for one of the implications, it testifies thereby to all the other implications of that same concept.

Only now do I realize that you made an analogy between allegory and analogy. In retrospect it’s a trivial analogy, but I hadn’t thought of it that way until now. Nice, thank you.
Now I also understand what you said, that each link in the chain takes one step and thus it is easier to identify that there really is an analogy. There is something like a common core in a chain of analogies: in all the links there is the essential component, but between two non-adjacent links the external difference is too great. So one makes a chain A-B-C. In A there is the essential component and also property 1. B has the essential component and also property 1 and property 2. C has the essential component and also property 2. In order to make an analogy between A and C, one passes through B.

Again :(. I wanted to thread this as a reply to your comment from today at 10:24.
It seems to me that if one waits too long before sending a reply-to-a-reply, then some session closes and the reply becomes an independent comment on the post.

Or else A has the essential component and 3 accompanying properties. B has the essential component and 2 of the accompanying properties (plus other unrelated properties). C has the essential component and 1 accompanying property (plus other unrelated properties). And D has the essential component (plus other unrelated properties). So in order to make it easier to accept the analogy between A and D, one passes through the chain.

In this context it is interesting to think about the melakhah of building on Shabbat. According to Rabbi Avraham Zev and the Steipler in Maimonides’ view, it is structured like this:

The primary category is building a house from bricks or wood – assembling parts that compose a hollow space (a structure).
Derivative A – a tent – creating a hollow space without assembling parts.
Derivative B: making cheese – assembling parts that does not create a hollow space.

There are two relevant parameters that compose the whole picture (two basic operations): assembling parts and creating a hollow space. Each of the two derivatives contains one parameter, but they are of course not similar to each other at all. They are derivatives of building because in each there is a different parameter of resemblance to the primary category. If so, between the two derivatives there is no chain (this is a star-configuration, according to your definition above: one center from which different branches emerge).

But it seems to me that the combination of assembling parts + creating a structure with a hollow space is not merely a combination of two properties. This combination creates a melakhah that has an overall meaning. Not every combination of two parameters creates a melakhah. For example, kindling fire and separating waste from food. These are two parameters with no connection between them, and they do not combine to create a complete whole composed of both. If so, when there is a melakhah composed of two parameters, this means there is some kind of connection between them.
(It somewhat recalls Borges’s description in his story Tlön, Uqbar, Orbis Tertius, which I cited in my book Shtei Agalot.)

In this sense there ought to be an affinity between the two parameters of the melakhah of building. And from here it follows that there is after all also some affinity between the two derivatives. You can see it better if you reverse the point of view: in each of the two derivatives there is some aspect of creating a structure, and therefore there is a similarity between them.
Notice that I reversed the direction of thought here, because now the structure is the parameter that generates the derivatives, each of which is a different species within the genus of creating a structure. Earlier we saw the structure as composed of the two parameters.

From this perspective one can nevertheless see a chain here: one makes an analogy between making cheese and creating a tent, but you will not see it unless you pass through building. This is in fact a continuum of different levels of building that appear in each of the melakhot, and they create a continuum of acts of building.

If you could please delete this comment, and I’ll copy it to the appropriate place. I thought that this time I had indeed made it a reply-to-a-reply.

The specific class too is only with respect to that particular operation. Under that operation, the representative represents the class.

What? The equivalence relation is equality modulo 7. The operation is addition modulo 7. There is a connection, but the equivalence class is not ‘aware’ of the operation at all. I can define an equivalence relation of ‘equality in shoulder width’ and divide all the people in the world by it, and then define an operation between two people: ‘how many floor tiles are needed so that there is room to stand them shoulder to shoulder,’ and it will be well-defined on the classes too (and therefore one can define an operation between the classes), even though measuring shoulder width and standing people next to each other are totally different things.

From Tolginus:
Wonderful. You are saying that the melakhah of building is the common denominator (which apparently exists) of its two parameters, and therefore the similarity between it and its derivatives is a core identity in the common denominator, not a partial similarity in some aspects. Core identity is transitive, and therefore it also exists between derivative and derivative. But partial similarity is not transitive (as if Sarah were to marry Adam and bear Cain, then Isaac and Ishmael would be half-brothers, Isaac and Cain half-brothers, but Cain and Ishmael not brothers at all. Or the segment 10-20 is somewhat similar to 5-15 and to 15-25, but those two are completely different from each other).
But at the end you formulated ‘a continuum of levels of building,’ and that means another idea that I still haven’t quite grasped. But I saw that in the article for parashat Kedoshim 5765 to which you referred me (file 30) there is something about a continuum and ‘if one says, I will study and then return [to sin], they do not grant him the opportunity.’

I think that in fact building is not in the middle of the chain between them, but rather a common factor that can mediate, like a binyan av in relation to its derivatives. Still, in order to understand the connection between derivative A and B, you need the help of the primary category. In that sense there is here a structure of the kind you were looking for (though, as noted, not a metamorphosis).

An incidental point. It seems there is an analogue of this also at the level of linguistic representation. At the level of linguistic representation, rhyme is an analogy. A full end-rhyme is transitive like the common denominator, where each rhymes with all the others – like setumah | ne’elamah | adamah | mehumah | neshamah. But in a more modern period an ‘imperfect’ rhyme developed that allows interweaving of rhyme in a way similar to the derivatives of building – like hifsid | hifsik | hitsik | hitsig. Each successive link is similar enough, but hifsid | hitsig is already too far apart. Such a rhyme is composed of three units: consonant-vowel-consonant (‘sid’ is s, hiriq, k), and if one matches only consonant and vowel and then only vowel and consonant, one creates a chain in which there is a gap between beginning and end. Obviously, if possible, to soften the transition it is preferable that the consonants too sound similar (s|ts, k|g).

Does a tree falling in a forest even fall in a forest at all?
Since the words ‘tree,’ ‘falling,’ and ‘forest’ merely denote our visual experiences, which are basically waves/particles of light striking our eyes and creating inwardly in our consciousness what we call an ‘appearance’ (in our case, a tree falling in a forest), then since when the tree fell in the forest there were no eyes there to see (nor ears to hear), not only did the tree not make a sound – it did not even perform a fall! Henceforth say: ‘A tree that fell in the forest and no one saw it – then it did not fall in the forest at all.’ Mark this well.

What is there to mark well? ‘Something’ happened in the world, and that something is such that if a detector of the human type had been there, then in his consciousness a sound would have been heard and an appearance of a fall would have been seen.

All right. Now I finally understand what you want. I was not speaking about a case like yours. One can always define whatever operations one wants on equivalence classes, except that then they will function merely as ordinary elements of some set. I was speaking about the standard case in which one defines some natural operation on the equivalence classes, a kind of inheritance or continuation of an operation that already exists on the elements of the original set. That is the interesting and non-trivial case. That is the fruitful definition in the context of equivalence classes. In such a case, the representatives of the classes are the representations of the classes to which they belong. By the way, even the case you brought is of course not accidental. The concept of length is what underlies both the equivalence relation and the definition of the operation, and makes it possible to define the operation on the equivalence classes.

Saidler,
A tree is a noun. In the world there are trees. Their appearance and attributes appear to us in different ways, and that indeed belongs to the subjective plane. But it is true that a tree fell in the forest. It is not true that it made a sound – it generated an acoustic wave.

I fear we still have not reached common ground. You are speaking specifically about a quotient group and not ‘just’ a quotient set (though that too is interesting and useful), but I still do not see the difference. I formulate it this way: all members of the class share a certain property, and it is the only property that a certain operation cares about, so that the operation simply cannot distinguish between different elements of the class, and that is all. I cling to the definitions like a weaned child with its mother. It may be that our whole ‘argument’ is a matter of terminology, and perhaps it will become clearer when the post on realism arrives.

To Rabbi Michi,
To say that ‘the word tree fills the role of a noun in language’ tells me nothing. Okay, it’s a noun – so what? Just because something is experienced through the sense of touch/sight, does that make it less existent in the world than things experienced through the sense of hearing? And if we were like bats, blind but with the ability of
echolocation, so that all the ‘objects’ we know and the words denoting them were experienced only through hearing? The criticism in my message above is not only of the specific example you gave at the end of the article; it is a criticism of the whole mode of thought throughout. The attempt in this column and in column 376 to enter into the thickness of the beam of philosophy of language and to speak of representation and non-verbal thinking, all without presenting or grappling with the hard problems of the relation between language and the world of experience, to bring Wittgenstein, Quine (in his article “On What There Is” he deals with related topics), or contemporary analytic philosophers like Bas van Fraassen (in his book The Empirical Stance he deals with related topics) – this seems to me very lacking.

It does not seem lacking to me at all, but perhaps I am mistaken. If you think something is lacking or that I am wrong, kindly make an argument. The claim you raised about the tree is incorrect, as I explained. Declarations or a list of names are of no help at all.

I still don’t know what is tangling you up. What Rabbi Michi calls ‘representation’ is called in my language a ‘manifestation’ (phase): for example, there is the pure substance water (dihydrogen oxide), and it appears (reveals itself) to our eyes in one of three manifestations (phases): solid (ice), liquid (water), gas (steam). The elements of an equivalence class are different from one another (because they are different elements), but each of them constitutes a ‘manifestation’ of the equivalence class for every natural operation or relation that you define on the quotient set and that is a natural continuation of the structure that the parent set had (operation or relation).

Correction:

‘…for example, there is the pure substance water (dihydrogen oxide), and it appears (reveals itself) to our eyes in one of three manifestations…’

I am really not tangled up. I am saying that certain operations are interested only in a certain property shared by all the elements of the class. That is all there is, and there is no representation of anything.
I don’t know whether it is worth bringing more examples, but I will give another one, again from a quotient set, because I insist that there is no principled difference between that and a quotient group (in which the operation on the classes is inherited from the operation on the elements and the output is also one of the classes).
Let us define that two numbers are in relation if the magnitude of the difference between them is divisible by 2π. Is this an equivalence relation? Yes. In every class the sine of every member is equal. One can now define a generalized sine function that takes an equivalence class and returns a number, namely the sine value of one of the elements in the class. Let us call this applying sine ‘to the class.’ Any element of the class can ‘represent’ it in order to know the result of the ‘generalized sine function’ on the ‘class.’ Does every number in the class represent something? It represents nothing. All that the elements of the class have in common is that the sine (or any function whose period is divisible by 2π) is periodic modulo 2π. Exactly the same thing happens everywhere there is ‘representation.’

To Tolginus, a reply I was asked to pass on to you from Shemaya:
Greetings!
Malbim, in his wonderful commentary on the Song of Songs, argues that Solomon described his personal life, together with his experiences of God’s revelations to him, through an allegory involving a wife beloved to him who is in love with a lover and flees from him in order to sport in love with that lover. So Solomon’s soul is beloved by his body, yet from time to time it flees to meet God. This is a description of five meetings of the wife and the lover, or on the level of the referent, of Solomon’s soul with God.
Malbim argues that despite his explanation, it still is not understood why this personal and private description should be included in the sacred writings, and therefore he reaches the conclusion that Solomon’s own life is itself nothing but an expression of the encounters of the whole nation with the glory of God throughout history. In this way, the song is removed from its private meaning to a broad national meaning.
So this is not an allegory for an allegory for a referent. Rather, it may be that King Solomon himself intended only to describe his own mystical experiences, and did so in allegorical form, but the sages of Israel who included this description in the sacred writings found in it a national significance.

Throughout the book, Malbim explains the earthly allegory (Solomon wants a wife who wants a lover) as parallel to the prophetic referent (Solomon’s body wants to conquer his soul, which wants prophecy), and then at the end of the book Malbim says that this referent itself is also an allegory for an even more secret referent (something wants to conquer the community of Israel, which wants God). I asked why one needs the mediation of the intermediate allegory, and I understand you to be answering that in fact, in order to reach the secret referent, one does not need the mediation of the intermediate allegory, and Solomon intended only the earthly allegory and the prophetic referent without the secret referent, and the secret referent was invented by those who came after him. That is of course fine, but it does not seem to me to touch on Malbim’s words. In any event, there is no practical difference as to exactly how Malbim interpreted it.
This is his language in the essay HaHarash VeHaMasger: ‘The interpretation which I called by the name melitzah (the prophetic referent) is the outer narrative of this exalted song, and it is truly the allegory, as I shall explain. And the interpretation which I called by the name mashal (the earthly allegory) is an outer shell… The melitzah is an allegory for the hidden secrets concealed in the holy song, and the mashal is an allegory for the allegory, a garment for the garment.’
By the way, the interpretation there really is wonderful and creative, but clearly its connection to the truth is tenuous. Malbim continues the traditional commentators in trying to interpret the Song of Songs as one continuous plot sequence (‘a dramatic interpretation’), and relative to Rashi and Ibn Ezra he innovates that there are three characters (Solomon, wife, and lover) instead of two, to explain the sudden flashes of references to Solomon here and there. But to me it is much more likely to interpret this whole book as fragments, scraps of scattered songs, as less traditional commentators concluded. Therefore when I put on my punctilious spectacles, I do not think that this interpretation is wonderful. It is simply beautiful, like a brilliant homiletic discourse or a historical fantasy story that succeeds in inserting itself among the hard historical facts.

Can the rabbi explain what that abstract Torah is – that is, what it means when we say that the Holy One, blessed be He, and the Torah are one? And why is there value in our consciousness encountering that abstract thing (the Torah)?

Any such explanation will require the characteristics of the Torah, meaning our language. From our perspective, that Torah is what appears in the Five Books. Therefore it is abstract.
The value lies in the encounter with the Holy One, blessed be He (devekut, cleaving).

How fortunate we are to have merited such a brilliant philosopher-rabbi in our nation!
A wonderful column. Just one question.
As I understand it, the rabbi argues that Kant’s distinction between phenomena and noumena is not a limitation of the one who grasps the phenomena (since that is his only tool for experiencing the noumenon in itself).

But as I understand it, the very fact that I do not grasp the thing in itself directly (I cannot do so without garments, i.e., phenomena) means that I truly cannot speak of it in itself. It follows that all my discourse is only about the phenomena, and this means there is a huge probability that I have missed so much of the noumenon.

So after all, the distinction between noumena and phenomena *is* a limitation of the one who grasps the phenomena! Since surely he misses so much in the thing in itself. (If we speak about Zen, one could say that whether one studies Zen through the sword or through archery, neither can ever speak of Zen in itself, but only of its garments. And garments, by their nature as garments, are partial by definition, relative to the larger picture.
And they cannot have a sharp argument about Zen in itself, but only about the sensation derived from the garment of Zen.)

The fact that we have no other way to grasp reality is not a limitation. That is what it means to grasp reality. Grasping is always bringing what is grasped into the grasper’s own tools. There is no meaning to the question of what the object’s ‘real’ color is, because it has no ‘real’ color. Color exists only in the tools of our cognition.
This does not mean that there is no possibility of error in perception. Of course there is. It only means that the error is not built in and does not necessarily derive from the limitation of phenomenon versus noumenon. Partial perception is certainly a source of error, but not because of the relation between phenomenon and noumenon, but because of the partiality. Theoretically one can grasp the whole phenomenon or part of the noumenon (if there were such a thing as ‘grasping noumenon’).

This is not called ‘representing.’ In English: represent. That is, presenting again.

When you do not know what is represented and have to decode it, this is not presenting again but a process of encoding and decoding.

According to your words about the Torah’s representations, it follows that you already know what is represented. And if so, then on your view one can throw the Torah in the trash and come hear from you what is represented.

With God’s help, the 9th of the 49th day of the count, 5780

To T.G. – greetings,

Indeed, regarding ‘In the beginning God created’ as well, there are derashot of Hazal that use different meanings of the word ‘beginning’ in Scripture, from which it emerges that ‘beginning’ is not only temporal priority but also priority in importance, such as ‘Israel is holy to the Lord, the firstfruits of His produce,’ and ‘The fear of the Lord is the beginning of wisdom,’ and the designation of the terumah as an ‘offering of firstfruits.’

From this insight that ‘beginning’ is also the part that is foremost in rank, Hazal explained ‘In the beginning God created’ in the sense of ‘by means of the beginning’ or ‘for the sake of the beginning’: that the physical world was created in order to actualize an idea, which is the ‘first thought’ for whose sake the world was created, and therefore they interpreted ‘beginning’ as the Torah or Israel – ‘beginning’ as purpose.

Regards, Ami’oz Yaron Shnitzler

Perhaps one may say that the beginning of the creation of reality is the gap between ‘heaven’ and ‘earth,’ between heaven, which expresses the ideal toward which one strives, and the earth, which is in a state of ‘astonishment and desolation,’ awaiting clarification and ordering that will implement the ideal in actual practice.

With God’s help, the 25th of Nisan 5780

Following what I suggested (in the last paragraph) that the distinction between ‘heaven’ and ‘earth’ symbolizes the gap between the ideal and its implementation in reality – one may say that on the second day it does not say, ‘And God saw that it was good,’ because on that day the partition separating the waters above the firmament from the waters below the firmament was created.

The first time the concept ‘not good’ is mentioned in the Torah is in the creation of man as an individual, of whom his Creator said: ‘It is not good for man to be alone,’ from which the conclusion is invited: ‘I will make him a help corresponding to him.’ Man was created in a state of ‘not good,’ in a state of loneliness, in order to create longing for a completing connection with his ‘other half.’

And so on the second day – on that day it seemed that the separating firmament had brought a total disconnection between the upper and lower waters. But the next day it became clear that this disconnection was not hermetic. The moment an additional separation was created between sea and dry land – the path was paved for the ‘water cycle’ that would bring about a connection of mutual fertilization between the upper and lower waters.

From the upper waters rain will descend to water the earth, its vegetation, and its inhabitants, and some of the water will flow to the sea and from there evaporate and return ‘upward.’ Later, on the fourth day, the changing of the seasons will arise, creating a cycle of rainy days in which the upper ones stream water downward, and hot days, when the evaporation of the sea’s waters upward is increased.

On the fifth and sixth days the animals will be created, drawing from the plants oxygen and nutrients, and contributing to the plants carbon dioxide and services of fertilization and thinning. The constant exchange of materials – brings about the continual preservation of balance in nature.

And on the sixth day man too will arrive, who will integrate within his being natural life together with directing spirit, and he will be entrusted with the proper management of the natural world, and at the same time with its cultivation and perfection, from a natural ‘field’ to a cultivated and tended ‘garden.’ And from ‘good’ the world will advance to ‘very good’ – goodness that goes on increasing.

Regards, Yaron Fish"l Ordner

In paragraph 1, line 1
… that the distinction between ‘heaven’ …

In paragraph 3, line 1
… that the separating firmament brought …

In paragraph 6, line 1
… man, who will integrate within his being …

A. In what way is an idea connected to heaven? It seems to me that this is quite a late terminology.
B. As for the rest of the interactions and cycles you described (the overall cycle of life in nature, in animate, vegetative, and inanimate realms, as the Lion King, may he live long, played so well) – I did not understand how you connected that with the integration of idea and deed.
C. At the beginning you said that man alone is not good, and at the end that man who adds idea to deficient nature advances it to the good. What is the sense of that?

To T.G. – a guten tag

A. ‘The heavens are the heavens of the Lord, but the earth He has given to the children of man.’ The Torah – the ‘idea’ – descends from heaven to earth so that man may implement it in the material world.

B. There is also mutual fertilization between the ideal and reality. For when one needs to implement the Torah under the conditions of complex reality – one encounters many problems and complications that require a person to deepen his understanding of the Torah in order to provide an answer to the complications of developing reality.

C. I spoke of three levels: A. ‘It is not good for man to be alone.’ B. ‘Good’ in the completing and fertilizing union between a person and his ‘other half.’ C. ‘Very good’ (‘very’ = ‘increase’), in the fertilizing union between developing spirit and natural reality, which tends toward inertia.

Regards, Tag [Tuvia al-Ghazali]

C. Indeed, I did not read carefully enough.

Sotah 17a: Tekhelet is like the sea, and the sea is like the firmament. And Rashi explained that tekhelet is not all that similar to the firmament, but rather similar to what is similar to it.

Thank you very much for the enlightening article.

A few corrections:
‘one of them’ – double space.
‘defined and to referred’ – should be ‘and not.’
‘strived therefore’ – should be ‘excess.’
‘the biblical text we received’ – should be ‘the scriptural’ (or ‘of Scripture’).
‘the boundary shin second’ – should be ‘between.’

Thanks much. Corrected.