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The Tenth Premise in the Guide for the Perplexed — The Distinction Between Intellect and Imagination
Background: Critique of the “Pillar of Kalam Wisdom”
The tenth premise deals with the “pillar of Kalam wisdom” — the principle of possibility (admissibility), according to which everything that can be imagined is possible. The critique of this principle includes two parts:
1. First part: For the principle to hold, the Mutakallimun require their entire atomistic physics — the denial of the existence of causes in the world, the claim that everything is atoms and accidents, and hence that everything is possible.
2. Second part (focus of the discussion): The Mutakallimun determine that “whatever can be imagined is possible.” The fundamental debate is whether imagination is the criterion for possibility, or intellect. Indeed, there are more possible things than things that actually exist, but what distinguishes between possible and impossible is not imagination but intellect — which relates to proofs and true causes of things, in contrast to imagination which is incapable of proving or providing a reason for anything.
Just as the pillar of Kalam wisdom is possibility, so the pillar of the Rambam’s philosophical wisdom is the distinction between intellect and imagination. This distinction may also be the key to understanding the difference between ancient and modern philosophy — since modern philosophy is, in certain respects, a version of Kalam on this point.
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The Powers of the Soul as the Foundation for All Philosophy
The Rambam addresses “the person examining this treatise” and says: “And now, if you know the soul and its powers” — understanding the distinction between intellect and imagination is based on knowledge of the different powers of the soul.
The Philosophical Structure
The distinction between true causes and the way things appear (imagined, sensible) depends on there being different powers in the human soul. Every philosophical debate — epistemological, ontological — is ultimately a psychological debate, dependent on knowledge of the soul and its powers. Therefore the pillar of all philosophy is knowledge of the soul, as the ancients said.
Reference to Aristotle — The Book “On the Soul” (De Anima)
The Rambam refers to Aristotle’s book on the soul, in which the fundamental divisions of the powers of the soul are explained. Aristotle (and following him the Rambam) denies localization of the abstract powers — they have no “place” in the body (in contrast to Plato who located parts of the soul in the brain, heart, etc.). The distinctions are abstract and cannot be determined empirically.
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The Nature of the Distinction Between the Powers
The act of intellection and the act of imagination are completely different types of acts, belonging to different powers in the soul — not to the same power:
– Not everything that happens “in the head” is the same type of act — intellectual thought, imagination, hope, emotion — these are essentially different acts.
– The powers are distinguished from each other “like two human beings” — completely distant, not just distinctions within the same thing.
– The senses and imagination (“internal eyes”) divide things only when they are separate bodies; the intellect distinguishes between abstract things that do different things.
– In a Platonic analogy: imagination is a “theater” (lovers of sights and sounds), and intellect is “philosophy” — and these are not the same power at all, just as they are not the same people.
The Difficulty of the Distinction
The distinction itself is difficult to grasp, because we are accustomed to thinking of all internal operations as one type. The distinction itself is an intellectual operation — it cannot be seen with the senses, and one must be convinced of it intellectually.
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Imagination Does Not Distinguish Man
Fundamental point: Imagination is not what distinguishes man. Animals too (at least the “perfect” among them) imagine like humans. The power of imagination is capable of performing most of the operations that people mistakenly think are “intellection” — and therefore those people who live only in imagination “are truly not human beings.” The definition of man as “the image of God” (as already discussed in Chapter 1 of the Guide for the Perplexed) refers only to the intellectual capacity, not the imaginative. The power of imagination, like the vegetative power, may be necessary — but it does not define man.
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Three Operations of the Intellect
The word “intellect” appears three times in the Rambam’s text (according to Shem Tov’s count), and each appearance indicates a different operation:
First Operation: Distinction/Analysis (Analysis) Within Things
The intellect separates within one thing that the senses or imagination perceive as whole. The senses and imagination perceive whole things — composed of matter and form. The intellect discovers within them:
– Matter and form
– Four causes (as in Aristotle)
– Ten categories (substance and accident, different types of accidents)
All these are innovations of the intellect — things that the intellect distinguishes and discovers, not that the senses see.
Second Operation: Distinguishing the Universal from the Individual — and Therefore the Capacity for Demonstration (Proof)
The intellect distinguishes the universal matter from the individual matter. This is a critical distinction because:
– In the visible world there are no universals — one sees only particulars/individuals
– Demonstrations (proofs) operate only at the level of the universal, not at the level of the particular
– Demonstrative proof is always a syllogism from the universal to the particular, and it is necessary — not merely probable
Central distinction: There is an enormous difference between things that are “logical/probable” and things that are necessary. Most people do not recognize this difference — and the reason is that they think with imagination and not with intellect. Aristotle “taught people the ways of demonstration” — one of his greatest contributions (as the Rambam notes in the second part of the Guide for the Perplexed).
Third Operation: Distinguishing Between Essential Predicate and Accidental Predicate
Ostensibly this is included in the first operation, but the intention here is in opposition to the Kalam system:
– Kalam is built on the division of substance and accident, but their division is imaginative, not intellectual
– They imagine “substance” as a physical thing (atom), and accidents as its properties
– Therefore they deny the different types of accidents — they do not distinguish between quality, quantity, power, negation, etc.
– The reason: their distinction between substance and accident is not built on intellectual-theoretical observation but on imagination
Only true intellect distinguishes between essential predicate and accidental predicate — this is not a question of probability or mere “thought.”
Imagination as the Inverse of Intellect
Imagination does not perform any of these three operations. It operates inversely to the intellect — perceives things as wholes, does not separate universal from particular, and does not distinguish between essential and accidental.
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The Mechanism of Imagination — “A Copying Machine of the Senses”
Imagination as Internal Sense
The text: Imagination “will not apprehend except the individual composite in its entirety… according to what the senses apprehended.”
Imagination is a type of internal sense — it works only on what the senses have already absorbed. The senses perceive only individual particulars: we have never seen the species of horse but a particular horse, and not the species of man but a particular man. Likewise, one cannot see form separate from matter or matter separate from form — every sensible object is necessarily both together. Concepts like “form” and “matter” are theoretical-intellectual concepts that cannot even be imagined.
The Operation of Imagination: Limited Composition and Decomposition
Imagination is not only passive — it is capable of performing manipulations on the images it absorbed: decomposing and recomposing. For example, one can imagine a human head on a horse’s body. But this is only a composition of two existing images — there is no new creation or true analysis here.
The Distinction Between True (Intellectual) Analysis and Imaginative Analysis
– Intellectual analysis: Dividing an object into form and matter — distinguishing between different functions and definitions, not between visible parts. For example: a hand cut from a human body ceases to be a “hand” intellectually (because the hand is defined by its function within the organism, as discussed in Chapter 72), but from the perspective of imagination it still looks like a hand.
– Imaginative analysis: Division into parts that are still visible — two legs, two hands — a division that does not necessarily reflect the true structure of the thing.
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The Transition from Epistemology to Ontology — The Power is Defined by the Object of Perception
The Constitutive Principle
The text: “And all is body or a power from the powers of body.”
Imagination is limited to the corporeal not because of technical weakness, but because it is defined by the type of reality it perceives. Every perceptive power is defined not by the instrument with which it operates, but by the type of things it is capable of perceiving — this is an Aristotelian principle that Plato also agrees with.
When we say that “intellect is different from imagination,” the intention is not only that one thinks straight and the other crooked. The distinction is ontological — the intellect perceives the “universal matter,” that is, the “formal matter” (universal and formal are the same thing), while imagination perceives only the corporeal and its powers. Imagination does not “err” — it is simply a power that is defined by its very nature as perceiving only the bodily dimension of reality, and therefore is completely incapable of perceiving abstract parts.
Hierarchy of Perceptive Powers According to Type of Object
| Power | What it perceives | Limitations |
|——|————-|——–|
| Senses | Physical presence of objects — color, heat, touch | Limited to here and now; require causal activation (light → eye) |
| Imagination | Same corporeal objects + manipulations on them; “powers of bodies” like walking, actions | Somewhat freed from here-and-now but still limited to the corporeal |
| Intellect | The universal, the formal, the abstract | Transcends beyond the corporeal |
Note on Circularity
There is a certain circularity here: the distinction between intellect and imagination is based on the distinction between types of reality (corporeal/abstract), but the distinction between types of reality itself is an intellectual distinction.
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Imagination Errs Because It Perceives Only the Matter in Reality
The Ontological Reason for the Error of Imagination
The reason imagination is limited and errs is not only technical, but essential: imagination perceives only the corporeal-material part of reality, and in this part there truly is no necessity, no inherent order, and no distinction between possible and impossible.
Structure of the argument:
1. If one observes matter alone — there is no reason why a man with a horse’s head could not exist.
2. What negates such a combination is form — the logic, the logos — which necessitates that a man have a human head and a horse have a horse’s head.
3. Imagination has no access at all to the world of forms/intellect.
4. Therefore imagination errs regarding truth — not because of internal weakness, but because it belongs to the part of reality in which there truly is no demonstration and no necessity.
Key principle: Our powers are defined by the part of the world they perceive — not vice versa. Imagination is limited because it perceives matter, and matter itself lacks inherent order. All order derives from intellect.
Critique of Materialism
The belief that matter itself has structure and laws is problematic and inconsistent. Matter as such is not ordered — all order originates in intellect. Therefore, that we can imagine reality differently (without order) reflects a truth about the nature of matter itself.
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Imagination Composes, Intellect Separates — Inverse Operations
Ostensibly both do the same thing — decompose and compose. But in practice: the intellect separates and imagination composes, and these are completely inverse operations.
Example: Imagination takes a man and a horse, decomposes them into parts, and composes a man with a horse’s head and wings. The intellect says: there is in man a bestial power and a human power, and analyzes the relations between them. One is true and the other false.
The Term “False Invention” (الاختراع الكاذب)
The product of imagination is defined as “false invention” — a technical term meaning: something to which nothing existent corresponds at all.
Important distinction:
– Regular (non-false) invention: “I saw someone walking in the street yesterday” when it didn’t happen — possible but did not occur.
– False invention (fantasy): A man with a horse’s head and wings — cannot exist at all. This is true falsehood.
Imagination does not innovate anything — it only takes things that were seen and composes them in arbitrary combinations (“a bit of this from that”), like the example from Eight Chapters about an iron ship flying in the air.
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Imagination Cannot Serve as a Criterion (Test)
The Argument: Imagination is Forever Bound to Matter
The Rambam’s language: “And imagination can in no way escape in its apprehension from matter, even if it abstracts a form with the utmost abstraction.”
Meaning of the argument:
1. Imagination is always bound to matter — even if one tries to abstract (think of a horse without color, etc.), one is still thinking of a material particular, not of abstract “horseness.”
2. Matter is what creates individuals (according to Aristotle/Rambam) — and therefore imagination is always stuck at the level of particulars.
3. As long as one deals with individuals — there is no criterion for distinguishing between truth and falsehood.
4. Conclusion: Imagination cannot serve as a measure (test).
Connection to the Critique of Kalam
This is the heart of the dispute with Kalam: they took imagination as the criterion — “what I can imagine, can exist.” Imagination itself is capable of imagining impossible things (false invention), and therefore cannot serve as a test for actual possibility.
Application: The Existence of God and the Angels
Things that are not in matter (God, angels) — there is no way to imagine them. Most people who say “it is impossible to understand God” actually mean “it is impossible to imagine Him” — and this is trivial. The real question is whether it is possible to intellectually comprehend Him, and this is a completely different question. The problem is that most people have never learned to think about things that are not imaginative, and therefore remain stuck.
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The Role of Mathematics as “Purifying Wisdom” in the Ladder of Learning
The Problem: Why is Mathematics Required as Preparation for Metaphysics?
The Rambam establishes a ladder of sciences that must be traversed before studying divine science: logic, physics, mathematics (and astronomy). The need for logic is clear — it is the “instrument” (the Organon) for distinguishing between true and false argument. The need for physics is also clear — from it are taken the foundational premises for proofs of God’s existence (as discussed in Chapters 71-72). But what is the place of mathematics? It does not deal with the fundamental structures of reality (contrary to the Pythagorean approach), and mathematical axioms are not used to prove the existence of God.
The Answer: Mathematics as Practice in Abstraction
The answer is traditional (originating with Plato and Proclus): mathematics is purifying wisdom — not because of its content but because of its mode of operation. It trains a person to distinguish between imaginative thinking and intellectual thinking:
– Mathematics begins with symbols and diagrams (material representations), but mathematical thinking itself is not in the symbols — it is in abstract structures that are not physical at all.
– Mathematical proofs force a person to abandon imaginative intuition: imagination says “impossible,” but the step-by-step proof shows that reality necessitates otherwise.
– Children who do not succeed in moving from “two plus two in a picture” to abstraction — are stuck precisely at this point.
Plato required that whoever had not studied geometry not enter his Academy. Proclus compared mathematics to “purifying waters” — a purification ritual before seeing the divine. Even if one takes no formula from mathematics, the very practice in distinguishing between intellect and imagination — suffices to justify all mathematical study.
Connection to the Central Topic
The point connects directly to the discussion about the inability to imagine God. Most people have never learned to think about things that are not imaginative — they are “stuck” trying to abstract forms from material examples, and this will never suffice. Abstraction from a material example does not reach the truly abstract.
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Demonstrative Examples: Imagination Errs in Both Directions
The Rambam presents a principle: There are things that imagination rejects as completely impossible, but intellectual demonstration proves that they necessarily exist. The contradiction is resolved when one understands that the “impossibility” was only in imagination, while intellect operates according to true causes in reality, not according to pictures.
First Example: The Sphericity of the Earth and Two People at the Ends of the Diameter
The Imaginative Exercise
Imagine a large sphere — even the size of the all-encompassing sphere (the entire universe) — and draw a diameter passing exactly through its center. Two people stand at the two ends of the diameter, their feet on the straight line.
The Dilemma that Imagination Presents
The diameter is either lying on the horizon (horizontal) or not lying (vertical/diagonal). If horizontal — both should fall because they have nothing to stand on. If vertical — one above and one below, the lower one falls. In any case, imagination determines that it is impossible for both to stand.
The Intellectual Answer
It has been proven by demonstration that the earth is spherical and that people live on both sides of the sphere. Each of them is both “above” and “below” relative to the other. The fundamental error of imagination: the assumption that there are absolute “up” and “down.” In practice, “up” = toward the all-encompassing sphere, “down” = toward the center of the world. These are relative concepts, not absolute. There is no “down” in the Rambam’s universe — everything is circular.
The Significance
Imagination refuses to accept that there are no absolute up and down. This is not just a scientific error but a structural limitation of imagination: because imagination deals only with sensible things, it is incapable of grasping concepts that are the product of intellectual abstraction. People truly struggled historically to accept the sphericity of the earth — and even today there are things that physics necessitates and imagination is incapable of grasping.
Second Example: Two Lines That Approach Forever and Never Meet (Asymptote)
The Source
The book “Conics” by the mathematician Apollonius, second treatise. The Rambam read the book in Arabic translation.
The Description
Two lines — one straight and one curved (parabola/hyperbola) — emerge at a certain distance from each other. As they extend, the distance between them decreases, they approach all the time — but never meet, even if extended to infinity.
The Position of Imagination
Imagination rules that this is completely impossible: how can something approach forever and never arrive? The Rambam emphasizes: “It cannot be imagined nor fall within the realm of imagination at all” — not only is it difficult to imagine, but imagination rejects it entirely.
The Intellectual Proof
There is a clear logical-mathematical proof that such a line exists. Even in modern calculus we define “limit,” but changing the definition does not remove the difficulty of imagining — the distance is cut all the time but never reaches zero.
Why This Example is Better
This is a pure mathematical example, in which one can identify precisely why imagination fails: imagination deals with sensible things, and therefore is incapable of grasping abstract mathematical objects like an infinite process that converges but does not arrive.
Connection to the Problem of Actual Infinity
The difficulty of imagining parallel lines that never meet is related to a deeper problem: the problem of actual infinity. According to Aristotle, actual infinity is impossible — a topic that will be discussed in premises 11-12 of the Guide for the Perplexed. Although imagination is incapable of grasping this, the mathematical definition is valid — because it is correct in the abstract mathematical structure. One cannot “see” lines going to infinity, since infinity is a type of process and not an existing thing, and imagination is capable of perceiving only “snapshots” (static sensible states) and not processes.
The Common Conclusion of Both Examples
“The existence of what cannot be imagined and imagination cannot apprehend has been demonstrated, but it is impossible according to it” — there exist things that imagination rules are impossible, and yet they are real and proven.
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The Overall Conclusion: Imagination Errs in Both Directions
The chapter presented evidence from both directions against reliance on imagination:
| Direction of Error | Description |
|—|—|
| Imagination rejects, intellect necessitates | Things that imagination declares impossible but are actually necessary (for example: a God who is not a body, parallel lines, sphericity of the earth) |
| Imagination necessitates, intellect rejects | Things that imagination thinks must be but intellect proves are impossible (false invention — a man with a horse’s head) |
Since imagination errs in both directions — both when it rejects and when it necessitates — it is clear that another power is needed to distinguish between truth and falsehood, between the necessary and the impossible. This power is intellect, not imagination. This is the foundation on which the entire chapter rests, and it is the central critique of the pillar of Kalam wisdom.
Central Connections
– Guide I, 1 — Definition of “image of God” as intellectual capacity
– Guide I, 71-72 — Premises of physics as basis for proving God’s existence
– Guide I, 73 — Premises of the Mutakallimun and their critique
– Guide Part II — Aristotle taught the ways of demonstration
– Premises 11-12 — The problem of actual infinity
– Eight Chapters — Example of iron ship flying in the air as false invention
– Aristotle, De Anima — Powers of the soul and their division
– Aristotle, Organon — Theory of demonstration and syllogism
– Plato — Requirement of studying geometry; distinction between lovers of sights and philosophers
– Proclus — Mathematics as “purifying waters”
– Apollonius, Book of Conics — Example of the asymptote
📝 Full Transcript
The Tenth Introduction: The Distinction Between Intellect and Imagination
The Pillar of Kalam Wisdom and the Two Parts of the Rambam’s Critique
Okay, we are dealing here with a note that the Rambam wrote in the middle of the tenth introduction, which, according to how the Rambam presents it, is the pillar of Kalam wisdom, which is the matter of transference, yes, that possibility or that all things can be, everything that we can imagine.
And we learned that he has two parts of the critique on this. The first part is that he says that for this to be true, they need all their strange atomistic physics, and therefore this is connected to that, yes? The debate between them and the philosophers, whether there are causes for anything at all, is what allows them to say that everything is possible, because there are no causes and everything is atomism, atoms and accidents.
And a second critique, or second part of the critique, which is of course connected to each other, as we will reach at the end of the second critique, is that they say everything that is possible to imagine is possible, and the Rambam is going to argue, the fundamental debate he has with them is whether imagination is the measure, or the criterion for distinguishing what is possible, or the intellect. He argues, he admits to them that there are more things that are possible than existing things, than modes in which things exist in reality, but what distinguishes between what is possible and what is not possible is not imagination, not everything that is possible to imagine, but rather everything that is possible to intellectually grasp.
And the intellect is precisely this thing that pays attention to proofs, that pays attention to the causes of things, yes? This is separate from imagination which cannot at all prove, show, give a reason for anything. So this is actually the main argument.
The Need to Understand the Powers of the Soul
But for this he needs to appreciate, he appreciated for us here, to explain to us what actually is this distinction between intellect and imagination, what actually is this power called intellect and what is the power called imagination.
And as we presented this last time, this principle is actually, just as the pillar of Kalam wisdom is possibility, the pillar of the Rambam’s philosophy is the distinction between intellect and imagination. So a very important distinction, and it may be that in the end all of philosophy as a whole, the whole thing that we always love to deal with, which is the distinction between modern and ancient philosophy in some sense – modern philosophy is a version of Kalam in these senses. It depends actually on this point, and the Rambam here gives his clearest exposition of the difference between these two things, so we need to study this very seriously.
Address to the One Examining This Treatise
And he says like this, yes? Yes, I’m repeating what we already learned, and we will advance. He began with this and said, that first of all, he addressed the one examining this treatise, very important, he is not addressing everyone, he is addressing a person of the type who can examine this treatise, here the Rambam calls his book a treatise, that you need to know the powers of the soul, yes?
There is a very important distinction here, that the distinction between intellect and imagination, which is actually the distinction between the true causes of things, and the way they appear, which is not their true cause, things are not because of how they appear and because of how one can say the aspect, the imagined aspect of them, the apparent, the sensible aspect of them, but rather their intellectual aspect. And this depends on there being several powers in the soul of man, yes?
After all, we already said this last week. The whole idea of types of intellection, the whole idea of types of ways that people know reality, depends actually on the assumption of certain abilities, which can be called powers of the soul or parts of the soul, that enable man this access to reality.
Philosophy as Knowledge of the Soul
Therefore, ultimately, all philosophical debate, epistemological, ontological, all the debates ultimately are psychological debates. That is, debates that depend on knowledge of the soul and its powers. Therefore, in some sense, the backbone of all philosophy is knowledge of the soul, as the ancients said in all kinds of ways, and here too it comes out like this.
The Rambam not only wants to argue that there are fictitious things in reality and true things, or that there are true causes and untrue causes, but also, and mainly, this follows from this, that is, it doesn’t follow from this, it is based on this, it is based on the fact that there are in man powers completely different from each other, yes?
The Abstract Nature of the Distinction Between Powers
We are not accustomed to these distinctions, yes? Precisely, this type of distinction is precisely one of the things that the intellect does, and these are not things that can be seen and not that if we cut open a person’s head we will find there some one part of intellect and another part of imagination, not even in brain surgery or anything that neuroscience, for example, deals with finding physical correlations to such things. That’s not the point, this is all an intellectual distinction, yes? Yes, so this is not something that can be decided empirically.
These divisions are abstract divisions, and Aristotle even, and the Rambam following Aristotle explicitly denies that there is even a place for these powers within man. Here Aristotle and the Rambam following him deny that when we speak of the powers of the soul, especially these more abstract powers, the different powers of intellection, they deny that there is localization of these powers, say, as today they would say in different places in the brain, as Plato already said, that part of the soul, of man’s soul is in the brain, or in the heart, or in the kidneys, all kinds of such things.
Aristotle denies this because he wants to look at all these things from their abstract aspect. But this is an ability, yes? And this is an ability that relates to perceiving certain parts or different modes of perceiving the world, what we call depicting, perceiving the world.
The Different Powers as Different Types of Action
And when he wants to argue that there are, so I return to what I said, we are very accustomed to thinking that all the action of thinking, one can even say all internal actions – external actions, we divide them according to the limb in which they are done, according to the object they relate to, according to the manner of change they cause to the object etc., but how do we divide internal actions, that is things that don’t even create speech, the Rambam is very fond of this verse, “Commune with your own heart upon your bed, and be still, Selah”, yes, you don’t even need to say it, yes, completely internal actions, in the sense that they are not internal in the sense that they remain in the mind of, within the soul, yes, because then they would be fictitious actions, that don’t do anything, or in some sense don’t do anything external.
Actions that do relate to what is outside the soul, that’s why they are called intellection, at least intellection must be a type of perception, a type of seeing, because we love the analogy of seeing, but they are not things that can be seen, one cannot find the power of intellection, one cannot see that it does anything, with eyes and senses.
And therefore we are very accustomed to perceiving everything that happens, we say, inside our brain, yes, that’s how they taught us to say inside the brain, everything that happens inside the brain we perceive as one type of action, the same type of thing, yes, you can press this button, you can press that button, you can think in this way, you can contemplate in that way, you can imagine in that way, you can hope in that way, all kinds of such things.
Reference to Aristotle’s On the Soul
And the very fundamental argument here, therefore I return to this style, to this beginning, “I asked if you knew the soul and its powers”, yes, the very fundamental argument here, when he of course, when the Rambam says know the soul and its powers, he returns to De Anima, to On the Soul, to Aristotle, in which these divisions are explained in principle, and of course there are after him a thousand and one commentaries and disputes how to interpret even Aristotle, all the more so they bring in Plato and more disputes on these matters.
But the important thing that Aristotle already did, and that we, the Rambam refers to here, is to say that one can say such a thing, the type of action, yes, and therefore also this thing that acts this, that which is capable of acting this, the type of action that we perform when we think true intellection, is not the same type of skill, it is not the same type of action as when we imagine, or as when we, one can say, we would even say other internal things, like hoping, like what we feel.
These are different actions and belong to different powers in the soul, it’s not the same power, not everything that happens in my head, in analogy, we use this word in the head, not everything you attribute to the head will be the same thing.
And this helps us with many, with many problems this helps, this division, but this itself is something one needs to be convinced of, that needs to be seen intellectually, this is not something that can be seen, and also somewhat difficult to distinguish, yes, when he is going to say, when you make some combination in your brain about things you saw, or take apart things you saw, then it’s not the same action at all as the action he calls the action of intellect.
The Absolute Distance Between Intellect and Imagination
This is the first thing I wanted to emphasize, that we are dealing here with different powers in the soul, and the Rambam is going to say, he said here, “they are distinguished from each other exactly like two human beings”, yes? They are completely distant from each other, these are not just distinctions that we distinguish within the same thing.
It’s only that the eyes, the senses, and therefore also the power of imagination which is internal eyes, divides things only when they are separate bodies, yes? It can see one person, a second person. With the intellect, things that do different things, even though both the doing and the thing we anyway learn that they are different things that do this, they are abstract things, one cannot see them.
But they are completely different from each other, this is already the thing that is difficult for us to grasp, because we are accustomed, okay, these are all internal things inside the head, one has philosophy in his head, the other has theater in his head, yes? The Rambam argues to him, your head has a power of philosophy and a power of theater, yes, if we call imagination theater following Plato, who said these are lovers of sights and sounds, who thinks about theater, they are not the same people, yes? In Platonic language we even say not the same separate entity.
Part I Chapter 49 — Three Actions of the Intellect and Its Distinction from Imagination
Introduction: Distinguishing the Powers of the Soul — Intellect versus Imagination
But the Rambam following Aristotle uses the language: not the same power. It’s not the same power, not the same thing, not the same part in the soul that looks at theater, that enjoys it, that understands it — is the same power that looks at philosophy. They do two different things, and therefore why think they are the same thing? Only because you are confused, you don’t know the distinction. But if you study the distinction, which is itself intellection, you learn that they are different things. So this is the thing, the first point that I didn’t emphasize last time, I’m emphasizing it now, yes.
Imagination Does Not Distinguish Man
Afterwards, the Rambam began with this, and we already spoke about this last week, that imagination is not what distinguishes man, this is something very important, yes. Therefore it follows from this, if we know how to divide these internal powers into different things, we say: there is imagination and there is intellect, and the main thing we need to reach is to intellectually grasp what actually are these different actions, even opposite ones, as he says.
But first he gives us also a psychological introduction, that is of the doctrine of man. He says: everyone is accustomed to speak of man as a rational animal, a thinking animal, man is something that can intellectually grasp, a type of living being, a type of thing that can intellectually grasp – do not confuse this with imagination. That man can imagine is not interesting, this is not what distinguishes man. Also animals, he says, also animals, at least some of them, at least the complete animals, it doesn’t matter, many animals imagine also like man imagines, and to imagine means the same thing, the same power that is going to detail exactly what it is, that can do most of the actions that people think are intellection, yes, this is what…
And therefore those people are actually not people, yes, this is after all, this whole thing is actually in order to explain the fundamental thing in this whole book, that already from the beginning spoke about this, what is man? Man is the image of God, yes? Which is his intellectual ability, and not his imaginative ability – this is not man at all, this is an animal that also has it.
It may be that this is necessary, exactly as man needs his vegetative power, and without it you cannot live, and therefore you cannot think either, fine, this may be necessary, but this is not his definition as man.
Connection to Ethics and Prophecy
Now, so this relates to the matter of ethics, yes, to the matter of ethics or the doctrine of prophecy that speaks about how to be a complete man. A complete man is not one who has the vegetative power or the sensitive power or the best power of imagination, but rather the intellectual power. This is what is truly called in man, yes? The true definition of man is this intellectual power, which is completely a different thing from the other things, yes?
Three Actions of the Intellect
Now, what actually is the important thing he said about the intellect, yes? So I repeat the things and afterwards he brings a code on this. Let’s see how far we can get here.
He says like this: according to my count and the count of Rabbi Shem Tov, three main things are written here about the intellect. I saw that Rabbi Gershuni’s edition divides this differently, I think he is mistaken, because the word “intellect” is written here three times, and the Rambam, his sentences are precise.
First Action: Separation and Analysis — Distinguishing Parts Within a Thing
He says: The intellect, and this is because the intellect, what does the intellect do? The first thing the intellect does, is distinguishes. Distinguishes within one thing. We see, our senses, and therefore also our internal senses, that we can remember that we saw something etc., see only complete things, one can say things of matter and form, and also things that are composed in other ways, yes, one can understand, at least composed of matter and form, yes.
There are other compositions sometimes, but like all things that are beneath the lunar sphere, composed of four elements, but we can also see the moon which is not composed of four elements, so that’s not so important. And regarding this composition of the four elements, the main composition I’m speaking of is the composition of everything we see, everything we can see and therefore imagine, are things composed at least of matter and form, yes?
And not only this, but as the commentators hint here, we can also imagine between substance and accident and all the other ten categories, all the other categories, yes? We can say, this is a thing, and this is actually the third thing he says, so I’m not sure this is included in this, but we, as he says, imagination is a dividing power, it is a separating power – within one thing, sorry, the intellect, the intellect is a separating power, within one thing that the senses or imagination give it, it finds many things. It sees that there is form and matter here, primarily there are four causes for everything, as Aristotle said, there are three causes in another sense that Aristotle said, that is, there are ten categories, the substance and different types of accidents.
All these things are things that the intellect innovates, the intellect distinguishes. So this is the first thing. The second thing, is, and yes, he simply gives many verbs, many parts of this separation, but all these lines are parts of the intellect doing analysis, doing the analysis of things into their true parts. Okay.
Second Action: Distinguishing the Universal from the Individual — Foundation of Demonstrative Proof
The second thing the intellect does: “The intellect distinguishes the universal matter from the individual matter, and no demonstration can be verified except in universals.” So this is another very important thing. Intellect is the only place where there are proofs, yes? This actually returns, yes? This returns to logic, yes? To the organization, to Aristotle’s logic, which explains to us that proof is what the Rambam calls demonstration (mofet), yes?
Yes, demonstrative proof is always a syllogism that speaks about proof from the universal to the particular, yes, and this proof is necessary, yes, if indeed the thing participates in this universal, it necessarily has essential properties, yes, of this universal, there is no other way, this is not, this is not, this is not probable, yes, this is not probability.
The Distinction Between Necessary and Probable
The distinction is very important between things that are logical, probable and necessary, yes, this is Aristotle. The Rambam in Part Two says: Aristotle taught people the value of demonstration, this is one of Aristotle’s greatest gains, yes, of course one can find this also in Plato and earlier Sophists, but Aristotle did this very systematically and sharpened that there are necessary proofs and non-necessary proofs, yes.
Most people don’t know the difference in this, and the Rambam will argue that the reason is, or this leads to this, or this follows from this, that most people think with imagination and not with intellect. But the intellect is the only thing, sorry, demonstrative proof is the only thing that is necessary, that cannot be otherwise.
Why Only the Intellect Can See Demonstrative Proofs
And now, if we need to remember that the only power that can see this type of proof is the intellect. Why? Because after all in the world there are no universals at all, one cannot see universals. We see only individuals, complete individuals, and proofs don’t work on individuals, proofs work only at the level of the universal.
And therefore only the intellect that has this distinction, yes, this is another type of distinction, and this leads us to a more important topic, not only the first thing that the intellect knows the world as it truly is, yes, it knows it in its truth, as he said, yes, it knows the true parts, not the supposedly accidental compositions of things. And the second thing, that therefore the intellect can necessitate things, because it makes a second separation, besides the separation it makes within things, between their matter and form etc., but also makes a second separation between the universal matter and the individual matter, that is between the universal and the individual. And this is what enables the intellect to make demonstrations, because there are no demonstrations in the individual, only in the universal.
Third Action: Distinction Between Essential and Accidental Predication
And the third thing, that the intellect also divides, this is another type of division, he doesn’t call it division, but “by the intellect is known the essential predicate from the accident.” The intellect is the only thing that enables us to distinguish between substance and accident.
Seemingly this is part of the first thing, because in everything we see there are substances and accidents. I think the Rambam, apparently, I thought he apparently means here in contrast to the Kalam, yes?
Critique of the Mutakallimun’s Conception of Substance and Accident
We remember, all Kalam wisdom is built on a type of substance and accident. The problem is that their substance and accident is not something divided by intellect, but by imagination, yes? Because they imagine substance as something physical, yes? As an atom, which is really, that can be seen, well, maybe it cannot be seen because it’s too small, such things, but it’s a physical thing, they imagine it as the same physical thing, and the accidents are the properties of this.
And therefore all things with them are accidents, because they don’t have the distinction, for example, to say that quality is a different type of accident than quantity. They deny all these divisions, quantity they deny altogether, but quality and power and all kinds of different accidents of this they simply also negations, they deny the different types of accidents because their distinction, their substance and accident, is not built on the intellectual distinction, on the theoretical distinction of this, on the intellectual perspective of this, one can say, but rather on the imaginative distinction.
And therefore the Rambam says here: only the true intellect is what distinguishes between essential predicate and accidental predicate, this is not a matter of probability or thought etc.
Imagination as the Opposite of Intellect
And here there is something, so this is the definition of intellect, the intellect does these three things, and he explains imagination, yes? Imagination does the opposite, yes? “And imagination does nothing but actions” – imagination does none of these things.
If someone tells him you have after three…
Part I Chapter 73: Imagination versus Intellect — Mechanisms and Limitations
Three Actions of the Intellect That Imagination Cannot Perform
If someone knows that he can break something down to its truth, break it down into its true parts – imagination cannot do this. If someone wants to tell you that he has a distinction between substance and accident – imagination cannot do this. He explains why. Yes, this is also an action of why and also how. That is, there is here an explanation of the mechanism of why imagination is stuck in these things.
Imagination as a “Copying Machine of the Senses”
The Translation from Hebrew to English
He says this: The imagination can only apprehend the individual composite in its entirety. Imagination is simply a duplicating machine of the senses, according to what the senses have apprehended. So primarily, imagination is simply internal senses—sometimes they called it this, there are other internal senses that Ibn Sina spoke about, but in any case, one can call this a kind of internal sense.
That is, we can see, and the things we can see, we can perform various manipulations of the imagination, right? What does this mean? After all, we remember that the senses can only see individual things, right? As we said on the other side with the intellect a moment ago. You never saw the species of horse but rather the horse, and also not the species of man but rather the man.
The Basic Limitation: Matter and Form as an Inseparable Unity
And you also never saw the man, the Form of the man separate from his Matter, the Matter separate from his Form, right? Because everything we can see is necessarily matter and form. We cannot see either matter alone or form alone, right? One can even imagine this, because these are all theoretical concepts, they are all intellectual insights, they are all not things that can be seen.
Therefore, what we see, and therefore what we can imagine—and not only imagine passively, to close [one’s eyes], but also to perform manipulations, as he will say—is terribly limited, right? At least for one who believes that there is in the world, or at least in some sense that there is in the world, there are universals or there are parts, yes, true parts of things, our senses and imagination are limited, they cannot see this at all.
The Operation of Imagination: Limited Composition and Decomposition
And therefore, all in all, imagination knows complete things that it has seen, right? Or, okay, there is here yes some operation of the imagination, or it will compose the things scattered in reality and compose some of them to others. Here someone says, why? I can see a person and imagine only his leg. Okay, very good. He speaks only of composition, but of course, it will compose some of them to others, meaning that he has already divided them, right?
Example: The Man-Horse
You can imagine, as he will say in another moment, you can—you saw a man, a man, right? The particular of a man, you once saw a horse, and I say, okay, now I imagine a man-horse, right? That has the head of a man and the legs of a horse. Okay, all in all, you performed a manipulation on the image of the individual in your head, in your imagination. You decomposed it and composed it in another way. That’s all the imagination does.
The Transition from Epistemology to Ontology: The Fundamental Point
And what’s the problem? And here the Rambam arrives at his most fundamental point, at the end. And all is body or a power from the powers of body. Everything that the imagination can perform its manipulations upon, everything it can do, all its operation works only on corporeal things, on the bodies in the world, right?
So now we have transgressed a bit, one can say at this point, in this line, we transgressed from epistemology to ontology, right? That is, he is not only speaking about a certain limitation of the ability to imagine. The ability to imagine is, let’s say, not innovating new things, not composing, not decomposing things in the way that the intellect decomposes them, but rather decomposes them into parts that it can see, that it can still see, right? That it divides them not necessarily in a true way, right?
The Distinction Between True Analysis and Imaginary Analysis
I can also divide—what he means by a true way is that the analysis of all objects in the world into form and matter, for example, is because, it is an intellectual distinction, right? It’s not that there is one part that is matter and one part that is form, but rather these are different functions, right? These are different definitions. Whereas the division of the imagination is not according to truth, right?
It’s not that the man truly, right? Sometimes it is according to truth in some sense, right? I divide the man into two legs and two hands, which are things I can see, but specifically regarding the function of the legs, for example, there is here for example an intellectual distinction that we showed for example in Chapter 72—it’s not truly correct that a hand of a man is still a hand, right?
Example: The Severed Hand (from Chapter 72)
A hand that is a function within the man, that is operated by this matter of the hand, by this hand that I have. But when you cut a hand from a man, it ceases to be a hand from the perspective of the intellect, not from the perspective of the imagination, because the imagination does not see the function, right?
The Limitation of Imagination in Perceiving Processes
One can even say, although this may be less precise, but one can even say that imagination cannot see processes, right? You see processes, but only like a film, as you see one thing after another, and then you construct from this a process, and the process, the complete story, is already something that cannot be seen at once, and the imagination is also limited in time, it is also always in the here and now, right? Which is perhaps related to the fact that matter is like this, I don’t know.
The Ontological Reason for the Limitation of Imagination
But what I’m returning to, I’m returning to where I was—what the Rambam claims here is not only that the imagination has a lack of ability for true analysis, as I said. I wanted, I entered into this because I wanted to define what true analysis is as distinct from non-true analysis, the true that the imagination can do, right? Or that it can compose non-true things, right? I can connect, I can put the head of a man on a horse, okay, but after all in reality it’s impossible, or at least one who imagines this, he doesn’t imagine how it’s truly possible to do this. He simply composes two images that he has, why not? There’s nothing preventing him.
And this, now, this is all the intellectual problem, the epistemic problem of the imagination, right? But the Rambam gives this a reason, gives this a reason, and he says: The reason that the imagination cannot know if the man-horse that it creates can even be true, is because of something more fundamental.
The Aristotelian Principle: The Power is Defined by the Object of Perception
This returns to this matter of the different powers, which relate to different powers that exist in reality, right? And we will later see that there is here some circularity, but we of course understand that this division here of intellect and imagination, is not just to say, okay, sometimes a person thinks straight, sometimes he thinks crookedly. Sometimes he imagines, he thinks about something true that can be, sometimes he thinks about something that cannot be.
Or he has ways, he has some power. Let’s say, okay, let’s say he already has a power that can, that has a distinction, a power that distinguishes between true things and false things, and a power that doesn’t distinguish, he imagines what he wants, he is free, liberated, right? As Rav Salanter said, a person is free in his imagination.
More than this, because what truly distinguishes, according to Aristotle, also according to Plato, everyone agrees on this—what distinguishes between these two powers is not their ability, as if the tool in which they operate, it’s the opposite. What distinguishes them is the type of things they can perceive.
The Hierarchy of Perceptual Powers According to Type of Object
The Senses: Perception of the Sensible in the Here and Now
What we call sensibles, the sensible property, the sensible property of things in the world is precisely why we speak of senses as different from for example imagination, even this. Senses perceive that things in the world are present in the here and now, according to how senses work, through the causal operation that there is here light, so the light operates something on my eyes and then I see something, such things. But this must be now, for example, senses are also limited to the here and now. It’s impossible to sense something that was yesterday, it’s simply impossible.
And why? Because senses are not only a limitation of my power of sight, it also relates to a certain part in the world. There truly is in the world, this is what divides this at all, there truly is in the world the presence of physical objects that have color, which is what the eye sees, and they have volume, let’s say, not volume, some sensation, heat and cold etc., things that we can sense in them, the power of touch etc. etc. This is what I can see, this is what I can sense, right?
Imagination: Limited Extension Beyond the Here and Now
And the imagination that follows after the sense in this sense is also, as I said, truly can only see the here and now, or to compose—that’s it, this is already a bit more liberated, it can compose the here and now, but still it thinks only about what we call corporeal, or one can say not only bodies but powers from bodies, like the ability of man to walk, which is already a bit of a story, or the walking.
Or one can, sometimes we call powers from the corporeal things like the color of things—I don’t think these are cases, but power is actually directed to action, to the action of things, which is not exactly the body. Okay, I can imagine a story perhaps, in some sense, and still, what limits the imagination is that it cannot perceive the abstract parts in reality, right?
The Constitutive Limitation: Imagination is Defined by the Corporeal
It’s not that it has, it errs, it imagines, but rather it is such a power that is defined by the fact that it perceives the sensible powers or the bodily powers in reality, separately from the intellect, and this is what is very important.
When we say that intellect is something different from imagination, we are also saying that intellect perceives, as it says the universal matter—that is, the formal matter, universal and formal are the same thing. The intellect is not built on the fact that you see the man, right? Perhaps it begins from this and then there is some process of business that divides.
The Deep Reason for the Limitations of Imagination: Matter Itself Lacks Order
Because it perceives only the body in reality, and truly, in part of the body in reality there truly is no such distinction. What emerges, yes, if we think only about matter, only about bodies, truly there is no reason why there cannot be a man with a horse’s head.
What enables, what negates the man with a horse’s head is not the matter of human beings, it’s their form, it’s their universal, right? There is some logic, some logos, of some logic that necessitates that a man will have a man’s head and a horse, that doesn’t have an ox of a horse and they don’t compose together. But you, you have no access at all to this aspect, right, or to this reality, to this world of intellect, one can say. And therefore you truly err in relation to truth, right.
So I say this, all only in order to interpret this word, and all is body, all from the powers of body, this is not only because the imagination operates through images, but something more than this, that the reason that the imagination is limited and the reason that it errs, the reason that it cannot make demonstrations, the reason etc., is precisely because it truly belongs, it perceives the part of reality in which truly there is no demonstration, truly there is no necessity in anything, right?
Critique of the Modern Conception of Natural Laws
This is very different for example from a modern conception that if it already does recognize natural laws, it thinks that there can be natural laws on matter, right? Although this is truly not consistent, and the philosophers of the concept of natural laws are very perplexed by this, but we imagine as if the world is ordered and even on the material level, there is some strange belief of contemporary materialists, who think that there is material but this material has structure, but this is already not material, this is already not Aristotelian matter, and as we can see, we don’t imagine this in another way, and the reason we can imagine this in another way is truly, according to the Rambam, there truly isn’t this order in it, the order entirely derives from the intellect, right?
And therefore in a true sense matter is not ordered, right? Matter is not something that has intellect. Not only we, the foolish part of us cannot perceive this. The foolish part in the world so to speak is truly not like this, right? All these things are parallel and even a bit opposite. Our powers are defined by the part in the world that they perceive, because otherwise truly we don’t have, no one yet sees this distinction between intellect and imagination inside the head of a man. Okay? Is this understood? I’ll say this enough times, just so it will be understood.
Imagination Composes, Intellect Separates—Opposite Operations
Let’s continue, right? And he gives an example, right? Like, gives an example of the types of sophistries that the imagination does, right? In some sense it seems that both do the same thing, right? Both the intellect and the imagination decompose and compose, right? You decompose the… the imagination decomposes the man and the horse into parts and then composes them, and also the intellect says, man has an animal power and a human power, and then it says, ah, and the animal power is connected to the horse, right? Such things. But these are completely opposite operations, right?
And he gives an example of why they are opposite, because one is truth and one is falsehood, right? One is essentially not composition, the Rambam calls this one not, and therefore he doesn’t write here decomposition about the imagination, although as I mentioned, and also in other places, in the Rambam, in his sources, it is indeed mentioned like this. But the Rambam calls here, and because he wants to sharpen the distinction, he says, the intellect separates and the imagination composes.
The Example: A Man with a Horse’s Head and Wings
And he says, as the imaginer will imagine, someone can imagine a man, man, that is an individual of man, right, because he cannot imagine the species of man, and his head is a horse’s head and he has wings, and the like, right, like all kinds of true things that are exactly like this. And this is called the false fiction, to which no existent corresponds at all, right?
The Rambam says, I will give you the technical word for this thing. The technical word for this thing is false fiction, right? What does false fiction mean? Because there is fiction that is not false, right? That is, there is fiction like, for example, if I say, I saw someone walking in the street yesterday, and he precisely didn’t walk in the street, that same person. This is fiction, but this is not false fiction, this is possible fiction. It could have been, precisely this didn’t happen. This is not such an important lie, right?
Fantasy is a true lie, right? This is false fiction that cannot be, right? This is what he means, no existent corresponds to it at all. There is not at all in reality a man who has a horse’s head and wings. There are in reality all kinds of lies that I can say, okay, so they are small fictions. But fantasy is true fiction, fiction that cannot be.
The Mode of Operation of Imagination: Duplication and Combination
So this, and he gives, this is an example of the operation of imagination. The imagination, all it does is types of this thing. Of inventing a man with a horse’s head, or a horse with a man’s head, a man who can fly. It constantly takes, one can say, it doesn’t innovate anything, it takes things it has seen and it composes them some to others, like the Rambam’s example in Eight Chapters about an iron ship flying in the air. I know ships, I know birds, and I simply compose the properties, one can say, this is a power, to fly there is a power to fly, and I compose this power on a ship. This is very easy for the imagination. But this is not connected to anything real.
And this, and this, wait, and why is this not real? Because it’s not imaginary? What? Because it cannot be? Yes, because it cannot be. Yes, because it cannot be. Later the Rambam will note that there is here a contradiction, because he first says that imagination cannot see truths, and then he says, the things don’t fit because they, yes, the question is in what way, in what direction this goes. If here all in all reality is what distinguishes, not that there is imagination, right? That’s how it should truly be. The problem is that then someone else will say, no, there is, this does exist, and then you, again, you don’t have the distinction, but we’ll get to that. That’s the point.
Imagination Cannot Serve as a Criterion (Test)
The Bondage to Matter and to Individuals
And the Rambam gives the reason for this essentially, and the imagination cannot in any way escape in its apprehension from matter, and even if it abstracts one form to the utmost abstraction. As long as we think in imagination, we cannot be saved from matter at all. We can abstract, right? You can say, think not about the horse with its color, abstract it, okay, think about it without color, it doesn’t matter, you can perhaps, right? You can abstract it, you can think about… but you can never think about horseness. You always think about matter, and matter is also the thing that makes individuals, according to Aristotle, right? According to the Rambam at least, right? Because there are no individuals at all, there are only species from genera. Species and genera, right?
And therefore there is no test in imagination, precisely because of this reason, test he means criterion, therefore the imagination cannot be a measure, because the imagination cannot see at all the things that distinguish between truth and falsehood.
Imagination Cannot Explain What’s Wrong with Man-Horse
It can imagine, look, you ask this power, this is another way to see this, you ask this power called imagination, what’s the problem with man-horse? It cannot tell you what the problem is. It can say, I never saw this, okay, but not everything you didn’t see doesn’t exist, right? The Rambam admits this in general, not everything you didn’t see doesn’t exist. You never saw this, still not enough, right? The fool is satisfied with this. I never saw this, okay, so it cannot be.
So because it is in matter, and matter means individuality, matter means individuals, you can never hang above matter, you cannot imagine at all, right? And one can say this in another way. Our imagination is always duplication of things we saw and never saw.
Because you, there is as if another second thing, because you can never imagine a thing, what do you call it, an abstract thing, an intellectual thing, no matter how much you try, so therefore, and as long as you deal with individuals, with such things, there is no test here, no distinction, no criterion, and therefore the imagination cannot be a criterion, right?
The Connection to the Critique of the Kalam
This all returns to what he disputes, he claims that the Kalam took the imagination as a test, right? He thinks that the criterion for what can exist is what I can imagine, and the Rambam says, no, look, essentially, and this, apparently something happened, the false fiction is also a word they admit to, right? Because of this he uses this technical word, right? You admit that we can imagine impossible things? Perhaps not, this needs to be examined. But therefore you can see that there is no test in imagination.
Application: The Existence of God and the Angels
This line that matter cannot, sorry, the imagination cannot in any way escape from matter, the Rambam himself will bring us the example or this principle of the existence of the Name, or the angels, or things that are not in matter, that there is simply no way to imagine this.
There are many people who are stuck in this, I think, because they say, if it’s impossible to understand the Name, they mean it’s impossible to imagine Him. But to imagine it’s impossible many very simple things also impossible to imagine. The question is whether it’s possible to understand Him, to intellectually grasp Him, that’s already another question. But to say that it’s impossible to imagine Him is essentially trivial, right?
And because most people essentially never learned to think about things that are not imaginary, as the Rambam gives a bit of education for this, in another moment, they are stuck in this, they constantly try to abstract the form to the utmost abstraction, to abstract one form, yes, take an example and abstract it as much as you want, this won’t help you at all, that’s the point.
Examples of What is Prevented in Imagination but Exists in Reality
Okay, now he says like this, here there is something important.
The Role of Mathematics as a “Purifying Wisdom” in the Ladder of Learning
The Problem: Why is Mathematics Required as Preparation for Metaphysics?
He says today like this, and hear what the habitual wisdoms have benefited us, and how very good what we have taken from them from the premises. Yes, there are wisdoms called educational wisdoms in certain versions, or habitual wisdoms, the intention is to mathematics and astronomy sometimes. And these wisdoms, part of the Rambam’s ladder, he writes several times already in this book that there is a ladder of wisdoms until one reaches the divine wisdom. And it’s impossible to teach divine wisdom to one who hasn’t learned logic and physics and mathematics.
Part I, Chapter 73 – Continuation: The Need for Mathematics and Logic
And essentially there’s a question, the Rambam himself addressed this question in the earlier place where he spoke about it, I don’t remember right now where, what’s the connection between logic, you could say logic, but more than that in mathematics, which is all games and applications of logical things to all sorts of paradoxes, to all sorts of such problems. What’s the relevance of this to the divine science? Why do we place this as part of the ladder? We say, whoever hasn’t studied mathematics shouldn’t study metaphysics. Plato said, whoever hasn’t studied geometry shouldn’t enter his school, his house of study. And what’s the connection between these things?
The Need for Logic and Physics — Clear
There’s such a question in the air, it’s very accepted that this is one of the sciences we need to study as preparation, but apparently it’s also not an introduction. For example, if you say you need to study physics, that’s very understandable, as he already said in chapters 71, 72, physics is the place where we take the premises, the foundational assumptions, we prove, there is a God because there is physics and it must have order and must have an orderer, all sorts of proofs of this type. Okay, very nice.
You speak about logic, it’s very clear why logic is essentially the first study in this ladder, or one of the first studies, right? Because without logic you don’t distinguish between a true argument and a false argument and a fictitious argument and a rhetorical argument etc., so this is very important, or as they call logic an instrument, right? The Organon or the instrument for all the sciences, without studying logic one cannot study anything. Okay.
But Why Do We Need Mathematics?
But why do we need mathematics? Mathematics is, you could say, an application of logic to problems of numbers and patterns etc. Why is mathematics interesting, or even astronomy? Why is it interesting? Astronomy is very connected to mathematics.
So now the Rambam gives a very traditional answer, he didn’t innovate this answer, if we have time in the next lesson, and sometime we’ll work a bit on this, because there’s a very important matter here. The Rambam gives one of the very accepted answers to this question, and it’s that true, mathematics doesn’t deal with metaphysics. In metaphysics it’s clear that it deals with true reality, with things that truly exist, with God and the angels, with the general principles of the world. All sorts of definitions of metaphysics, it’s clear why this is important. Mathematics doesn’t deal with this, it doesn’t deal with the fundamental structures of the world, right, at least for those who aren’t Pythagorean, those who don’t follow Pythagoras, that’s not what people believe, that the world is fundamentally mathematics, the world is fundamentally Forms, not numbers. And it’s also not a science of necessary premises for anything. So it’s not that we use mathematical axioms to prove the existence of God, right, that’s not what happens. We use physical axioms, but not mathematical ones.
The Answer: Mathematics as a Purifying Science
So he has an answer. His answer is that mathematics is a purifying science, it’s an abstracting study, right? Whoever wants to be holy, meaning, we’re now constantly dealing with this matter that there’s something called intellect. Intellect is called abstract wisdom, right? An abstract capacity, whose operation, the operation of the intellect, the operation of mathematical calculation, is an abstract operation, it’s not acted upon by the imagination, it’s acted upon by the intellect, right, and therefore it also pays attention to the more basic structures of the world, right, it can, it at least trains a person to pay attention to the holy parts, right, those abstracted from the matter of the world.
Mathematics as Practice in Abstraction
And therefore mathematics is considered a purifying science, right, purifying I mean abstracting, right, whoever wants to merit the abstraction from corporeality, meaning, that he’ll be able to understand things that aren’t in body at all, so a way or introduction to this is to study mathematics. Because mathematics takes you from things that exist, it begins, you could say, it begins with triangles that are found in matter, even from diagrams, right, you make a diagram, it’s as if an example of this in matter, but the thinking of mathematics isn’t in its symbols, it’s in the thinking itself, in its structures, and these are non-physical things at all.
And mathematics is a very good place to show the difference between this and that, right, it’s not just that mathematics deals with the abstract, because then it wouldn’t be enough, because mathematics doesn’t deal with the most abstract and most important thing. But mathematics, therefore I call it a purifying science, following Plato, who spoke about how there’s the matter, which is as if the mixture, right, things are mixed, we have the purification itself, right, the abstraction, the abstract intellect itself, and we need some education, right, some learning, some way to get between this and that, to see clearly the difference between this and that.
Mathematics Shows the Difference Between Imaginative Thinking and Intellectual Thinking
And the Rambam says here, mathematics and astronomy, when thinking about the movements of the world etc. in such an abstract way, it’s the science that shows us most sharply the difference between physical thinking, imaginative thinking, and non-imaginative thinking, intellectual thinking, right? Why? This is very nice, right. Indeed you can see this, that there are children, they don’t succeed in crossing this. That is, they’ll understand that two plus two equals four in a picture, but the moment it reaches abstraction they won’t understand, because they don’t succeed in crossing this symbol.
Right, and mathematics, and even in astronomy, as he now gives two examples from astronomy and from mathematics, it can also force you to pay attention to this already everything, because there are proofs, what the proofs in mathematics do is they prove to you, you thought, you imagine that it must come out this way, and then I show you step by step that it can’t be this way, and how can it be, after all you’re still certain that it must be this way, because of your imaginative thinking, and then it forces you to exit from the imagination and say, but what can I do that it’s necessary, right? The step by step of proofs is supposed to take the person from within this impossibility to within this necessity, right?
Mathematics as a Mikveh — An Ancient Tradition
So therefore mathematics, Proclus says, mathematics is like the mikveh. Just, this is a Jewish example, but he says, it’s the purifying waters. When performing rituals of seeing the gods etc., so first one needs to immerse or do some purification. He says, mathematics among the sciences is the purification. And this is a very ancient saying. The Rambam essentially relates to this tradition when he says these things.
So this is what the Rambam says, and this is good, we, the introduction, right, as if. If you don’t take from mathematics the formulas and all these things, you take this introduction, that there is intellect separate from imagination, so for this it’s worth studying all the mathematics, just for this practice.
Mathematical Examples for Distinguishing Between Imagination and Intellect
Let’s study a bit more. And he says like this, Know, that there are things, when a person contemplates them, right, he says like this, Know, that there are things that when a person contemplates them with his imagination he cannot form them at all. You think about it in an imaginative way, I began, you say, I can’t picture this. Meaning, it’s apparently impossible. But it will be found, their imagination will be prevented. Your imagination says, this is impossible, because it’s as prevented as the gathering of two opposites. It’s as impossible as two opposites, it’s simply impossible.
But, and afterwards it will be verified by proof the existence of that thing which is prevented from being imagined, right? That it would be possible to imagine it, and reality brought it out, right? There are all sorts of things that as long as we think in what they call intellect, but it’s really imagination, we say impossible, I can really prove to you, I can almost draw for you the intuition that shows you that it’s impossible. I can’t imagine it. How to imagine it? If I start to imagine it, I see that it can’t work.
And afterwards we have a proof that forces us to agree to this, that it is indeed so. And then we have a contradiction, and as if the answer to this contradiction will be, okay, what was impossible was in the imagination, but intellect is something else, which doesn’t need pictures, it doesn’t work in pictures, it works according to reality, according to the true causes in reality.
And he gives an answer, such an example, and this, I’m already a bit tired in this lesson, so I’ll go over the examples quickly and we’ll return to them next time, because there’s something here I want to delve into. He gives a first example, and he tries to do the exercise, right? I actually did the exercise for children last week, and it works quite well. Only that we’re used in school not to think, but if you make this a bit exceptional, you do a bit of warning for it, right? You want them not to pay attention to what we’re talking about, so actually it works, I think.
If you imagine a large sphere, whatever size you want. Like he says, imagine for yourself, right? We’re now working in imagination. Imagine for yourself a sphere, no matter how large, even if you imagine it as the size of the sphere of the encompassing sphere, right? Let it be large.
Demonstrative Examples of the Limitations of Imagination: The Sphericity of the Earth and the Asymptote
The Imagination Errs with Certainty — Two Scientific Examples
The Rambam brings here two examples in which the imagination rules with absolute certainty that something is impossible — and in practice it turns out that it’s completely wrong, because the intellect and scientific proofs necessitate the opposite.
First Example: The Sphericity of the Earth and Two People on the Ends of the Diameter
The Imaginative Exercise
This is essentially the encompassing sphere, right? The whole universe, right? Like the stars, the whole thing. And afterwards imagine in it, right? We’re still imagining, a diameter passing through the point of its center, right? Make a diameter of the diameter of this sphere, exactly, right? Not a bit in the middle, not with width, right? A diameter exactly, exactly in the middle passes a diameter, right? And afterwards imagine two people standing on the two ends of the diameter, until the soles of their feet are and leave the diameter, right? Two people standing exactly equally on this diameter from the two opposite sides of the sphere. Right? And the diameter returns to the feet in one straight line, right?
The Dilemma the Imagination Presents
So now the Rambam says, I imagine this, and there’s something very interesting here, because it sounds as if I’m doing logic here, right? And I say, that is, the diameter will not be filled with wonder whether parallel to the horizon or not parallel. Right, this diameter is either, right, we have a completely straight line, right? So this straight line is either exactly, how do you say? Positioned. Right, what? We’re exactly in the same, well? Positioned. Right, positioned to the horizon, right? Meaning, one side is, as if, it’s exactly positioned on the horizon, or it’s not parallel, right? Right, or it’s perpendicular to the horizon, even a bit, no matter how much, right? There’s no third option, right?
And then you say like this, okay, so strip, let’s understand. Either… in short, either one side of this line is more up and the second side is less up, or both are exactly at the same height, right? So if it were parallel, both would fall together, right? A person can’t stand exactly in the middle, right? Right, he must fall, both must fall. And if it were not parallel, one of them would fall, he who was lower, and the other would stand.
Here there’s a segment of imagination, impossible, he’s trying to bring you the intuition, why this is simply impossible, because it’s really a contradiction in itself, it’s really a contradiction. Either this line is straight, and then both fall, because they, they have nothing, they can’t at all, they can’t stand straight, or one stands straight and the other falls. It can’t be that both won’t fall, it’s simply impossible, I can’t imagine it. Thus the imagination attains, this is what the imagination says, it’s impossible.
The Intellectual Answer: There Is No Absolute Up and Down
And the Rambam says, okay, what can we do that your imagination didn’t hit the mark? It has already been demonstrated by proof, we have necessary ideas, right? That the earth is spherical, that actually the world is such a sphere. This sphere is the world, right? And that the inhabited world is on the two ends of the diameter, and don’t say, okay, but there aren’t people on the other side because they would be falling. No, actually we know, it’s been proven by demonstration, or we saw, I don’t know, that there are people on both sides. Exactly one, two sides, no matter at which point, there are people who stand in exactly this relation to each other.
And every person dwelling at the two ends, his head is toward the heavens, and his feet are toward the side of the feet of the other, who is at the head of the other diameter. Two people stand in relation to the other person, on the other side, he stands where the head of the other person is, his head is where his feet are. If we look at one reference, which is essentially the mistaken assumption here essentially.
And in practice, and the fall of one of them is impossible at all and cannot be imagined. Imagined at all is not correct, it’s not just that he doesn’t fall, he can’t fall. Not only does he not fall, he can’t fall. And why? Because neither of them is up and one down, but each of them, one up and down, joins to the other.
The Fundamental Error of the Imagination
The Rambam says, why? And as we know, the desired answer to this is that we simply erred. Meaning, what was very clear to our imagination, that there is up and down, and people fall down, we didn’t have in our head the correct definition of up. We said, we thought that up is up, there is an absolute up, the answer is that there is no absolute up. Up and down are all relative to the center of the world. What we call up is essentially more toward the encompassing side, what we call down is toward the inner side, and therefore it’s not just that there’s no contradiction, our imagination, that we can’t, this is what he’s essentially trying to say, I think, we can’t imagine the fact that there is no absolute up and down.
And it could be that this is still true, even we today say, okay, because there’s gravity, it doesn’t matter what the mechanism is, right? We have a perceptual problem, at least according to the… it could be that if we speak about gravity, then we don’t need to say there’s no absolute up and down, but there are other reasons in modern physics to say this, it doesn’t matter. We have a problem that if you tell a person, there’s no up and down, he looks at you like you’re crazy and says, okay, there’s no up and down, but still people fall, right? Right, so it’s impossible that they both fall and don’t fall within the same thing.
And we have proofs, and we simply showed, we can’t escape from this that it’s simply not correct, our imagination doesn’t know correctly.
The Meaning: A Structural Limitation of the Imagination
And why? There’s some intellectual perception here, right, there’s a perception that can’t be imagined, that’s how I’m currently interpreting this passage, because otherwise, just a scientific error, and that’s not interesting. He says, it’s impossible to imagine that up and down won’t be absolute concepts. Right? And physics, the intellect forced us to understand that up and down are not real things. A person can be both up and down at the same time. Depending on whether you’re looking down relative to a person on the other side, or relative to the true down, meaning this down that operates when we fall, which is the center of the world at all, and not the absolute down of the universe or something like that. There’s no down at all in the universe of man, everything is round. And not in our university either, of course.
And this is something that the imagination simply refuses to accept, right? He brings below 11, which is… people really struggled to accept this, it’s not just a story the Rambam is inventing. For us, we’re so used to the earth being spherical and everything working this way, that we can’t grasp, that we can’t imagine it. But we can’t imagine it.
And here we… what? What? It’s worthwhile that yes, like such magnets, right. Right. But there are other things that are hard for us to imagine today. Right, I think that… there are black holes, I don’t know… Right, right, clearly our physics, we have things much harder for the imagination.
Second Example: Two Lines That Approach Forever and Never Meet
And there’s here, we need to think more about this parable, and what it’s supposed to show, and if it shows what it’s supposed to show, etc. Because it can’t just say, I’ll say what my problem is, and therefore I tried to solve it, and maybe it doesn’t solve. There’s the problem here, and then as if, it’s not enough to say people sometimes err. Clearly people err. He needs to invent here a force of a different type, that because it can only see tangible things etc., therefore it errs, right? There needs to be some therefore, because otherwise there’s nothing here that divides between intellect and imagination.
A Pure Mathematical Example
The second example is a bit better example, a pure mathematical example, that at least we, and this too we have, we learn this in school in a way that evades the problem, but it’s not clear that it evades. Let’s finish the second thing and then we’ll finish.
And likewise it has been demonstrated by proof, in the second treatise of the book of Conics, right? Conics is cones, conics, which is a book by Apollonius, Apollonius the mathematician, I forgot what they called him, one Apollonius, that the Rambam read his book, he wrote in Greek, he read in Arabic, and he spoke there that there is the emergence of two lines, there will be between them at the beginning of their emergence one distance, right? At one distance, and as they distance themselves that distance decreases and one of them approaches the other, and it’s impossible that they will ever meet even if they go out to infinity, and even though as they continue they approach, right?
He’s simply speaking about what’s called a parabola, right, or what do you call it, right, that a parabola sends, asymptotic lines, right. Lines that approach all the time and never arrive, right? And it can approach forever.
The Position of the Imagination: Completely Impossible
And this, what do you say, imagination, it’s simply impossible. How can it be that it approaches forever and never arrives? This sounds very impossible, but we have a clear logical proof that necessitates that there is such a line, right? And he says, and this cannot be imagined and cannot fall in the layer of imagination at all. Not only do we say there’s a contradiction here, I can’t imagine this at all. And the two lines are, one of them straight and one curved, as was explained there, right? Curved in a certain way, it’s calculated about this in a certain way, doesn’t matter, doesn’t matter now, it does matter.
The Common Conclusion of Both Examples
And in any case, behold it has already been clarified the existence, of what cannot be imagined and the imagination cannot attain, but it is prevented for it, right? So we have two examples of things that the imagination says, cannot be, right? This is something important. Not just that the imagination says, doesn’t exist, right? Imagine it in another way, right? These two examples are supposed to show something that the imagination says, impossible at all, that the Mutakallimun, for example, also agree that there are impossible things.
The Rambam says, no, as long as you’re using imagination, you don’t even know what’s impossible, because you would have also thought it’s impossible that, that the world is round and both sides don’t fall, and impossible that there would be two lines that approach all the time and never meet.
Modern Mathematical Explanation
I can force this on you scientifically, very easily, because we can say, the distance is constantly cut, but never reaches zero. And today in calculus we simply define, that’s what’s called, what do I call, the limit, and that’s it. But changing the definition doesn’t change the capacity to imagine it, right?
And therefore, here there’s apparently a better argument for something that sounds completely impossible, and also there’s apparently some real limitation of the imagination to grasp this. Because, you could say exactly because the imagination deals with tangible things.
Part I Chapter 73 – Conclusion: The Connection to Infinity and Conclusions
The Connection to the Problem of Actual Infinity
This comes to another problem of infinity, right? Because there’s a problem of infinity here, right? Because these lines, when they reach infinity, or they’re divided to infinity, and thus they don’t meet, there’s a question whether this can really be. And Aristotle at least holds it’s impossible, as we’ll reach, we’ll see in premise 11, 12, so in any case it belongs to the same problem.
Why the Mathematical Definition Is Correct Despite the Difficulty in Imagination
But if it really can’t be, then there really is here, but the mathematical definition is still correct. And why? Because it’s correct in the abstract mathematical structure, and it’s impossible to see this. You’ll look, you’ll never see this going to infinity, because infinity is not, you could also say infinity is a kind of process and not a kind of existing thing, and we can only imagine snapshots and not processes.
Summary of the Structure of the Argument of the Entire Chapter
In any case, so we saw two things that the imagination says are impossible and they’re actually necessary. Necessary, right?
And afterwards he brought two examples of, or at least one example, of something that the imagination thinks must be and the intellect says cannot be, right?
It’s the opposite, he brings examples from both sides, both from the side that there are things that the imagination negates and the intellect necessitates, and also things that the imagination necessitates and the intellect negates.
The Conclusion: The Intellect is the Faculty that Distinguishes Truth
And therefore the answer to this problem must be, that there is another faculty by which we distinguish truth from falsehood or the necessary from the impossible, and this is the intellect, not the imagination.
Okay, that’s the end of this chapter. There is a very deep inquiry here, and we will get to it even more.