The Proof of the Existence of the Intellect Separate from the Imagination and Education Toward It – Note (3) | Part I Chapter 73 (16) | Guide for the Perplexed 171 (Auto Translated)

Intellect and Imagination – Demonstration as Education of the Soul

Opening: Positioning the Remark in the Rambam’s System

Now we are studying. This is already the third lesson on this remark. I have many more investigations to examine in this, but I’m not sure I’m ready for it now. Let’s just review what we studied and see what we can say, yes?

What we saw is that there is here a remark that I claim is one of the main foundations of epistemology apparently, but actually the epistemology here depends on ontology, on the metaphysics of the Rambam and of his entire school of thought, his entire academy. And therefore the entire path of service of God, the entire matter of apprehension of God according to the Rambam, truly depends on understanding this thing.

And this is the matter of intellect and imagination. Yes, and here is the place where the Rambam clarifies what the difference is between intellect and imagination, and he also gives it a kind of proofs. I think there is here a deep investigation, the Rambam himself is going to say that there is here a deep investigation, that he intends something doubtful and not entirely clear.

The Methodological Question: Demonstrations or Education?

There is here a deep investigation which is, in what sense are these proofs proofs, and in what sense are they a kind of education. And there is also a deeper investigation whether there is a difference between these things, yes?

The Conventional Distinction: Education versus Demonstration

Because we are very accustomed, I’ll explain now something fundamental. We are very accustomed to discourse that distinguishes between education and proofs, yes?

What is Education?

There is such a thing that I educate you or habituate you or open your mind, your intellect, your heart, your life to see something, to behave in certain ways, to make present certain truths, to be open to certain ways of thinking or to certain ways of behaviors, this is what we identify as education.

And yes, there are for example especially mystics who bring this education into the head, yes? Into the brain, into the consciousness or knowledge of the person, yes? Everyone agrees that there are educations regarding habits, yes? Regarding actions, regarding deeds, perhaps even regarding feelings, regarding emotions, yes? We are also relatively accustomed to think that there are no educations regarding emotions, but it’s easier to understand that there is education in this.

Knowledge as Detached from Education

And less in the matter of, in what are called noetic matters, yes? In matters of intellection, in matters of knowledge, that belong to the question of knowledge, we are accustomed that this is not a matter of education, but a matter of seeing, discovering or learning. We don’t think about it in terms of education, and whoever speaks about knowledge in terms of experience, of education, he is usually identified as not a rationalist, not a philosopher, identified as a kind of, yes, yes, mystic.

A believer that if you fast from Sabbath to Sabbath, then you discover some truth, yes, some knowledge, and there is here truly, we identify here some crossing between categories that is not legitimate, yes? Fasting might educate you to be less ostentatious, less lustful or something like that, but how will it give you knowledge, yes? Knowledge, we, those of us who still remember that there is such a thing as knowledge and rationality, we think that there is some way to receive knowledge, because the truth is we have too little understanding of what this actually means, but we are accustomed to think that this is something very separate from education, yes?

Whoever claims that he will be educated and will arrive at knowledge, we say, okay, this is mysticism, this is perhaps a certain definition of what certain people call mysticism. Knowledge, when they claim it is knowledge, yes? When the skeptics, the doubters, think that this is not knowledge at all, perhaps it’s only a feeling or only some habit, that is received through education, through certain experience.

The Problem with the Modern Conception of Demonstration

Demonstration as External Action

And what about proofs? We are very accustomed to proofs as a kind of thing that doesn’t change at all the person who studies it, yes? We say, prove to me that there is such a thing as a soul, prove to me that there is, here we are dealing exactly, prove to me that there is such a thing as intellect separate from imagination, yes? Is there such a thing? We are looking here for a proof, yes? Looking for some case where we can see that this kind of proof or this kind of learning, this, this kind of intellect, works only in a faculty, yes? Only in another power, which is completely another power, which is called intellect, and we make for it a proof supposedly.

And then, as if, our naive thought is that the proof is something that happens completely outside the person, yes? That happens completely as if on paper, yes? Like they write mathematical proofs on paper, that it happens there supposedly, the action, yes?

The Active Intellect – The Intellect is Not Passive

This is what the Rambam began here with the word the active intellect, yes? The intellect does something. We are accustomed to a very strange conception that the intellect doesn’t do anything, the intellect is passive. The action of the intellect, which is to say an action of proving something, an action of discovering something, of joining, yes, making synthesis, making analysis, all kinds of actions that the intellect does, we are accustomed that this supposedly happens on paper, yes?

Example: Artificial Intelligence and the World to Come

To such an extent that we have doubt whether a computer that has a calculator sufficiently sophisticated that can also calculate words, called AI, whether it can, whether it thinks, yes? Yes, as if thinking is something that happens, yes, it could be that even according to the truth there is such a doubt, but not the doubt that most people have. As if thinking is something detached, and therefore from this also derives what everyone at this time knows as the distinction between rationality and mysticism, that rationalists are cold people, yes, because their action, what they do is some thing that happens on paper outside the soul, people don’t understand at all.

Yes, I saw today, yesterday someone asking, sorry that I keep returning to the same sermons, but I think this becomes clearer each time. I saw yesterday someone asking that the Rambam claimed that the World to Come, the survival of the soul, is only intellection, and in the age of artificial intelligence this is very difficult, because after all the intelligence has all the knowledge.

And the Rambam wouldn’t even begin, this question doesn’t even begin. He would answer, yes, this is imaginative thinking and this is thinking that completely misses what intellect is, if you are accustomed to think that intellect is an action, the action of intellect, say the action of demonstration, is an action that happens on paper, then yes, perhaps you can put this also in a computer, and you don’t need the computer, also the book in which are written proofs for the existence of God will go to the Garden of Eden according to the Rambam.

The Rambam never thought such a thing, because the action of the intellect doesn’t happen outside the thinking person or the intellecting soul. Yes, this wondrous thing, that is difficult for us to give it words, how can it be that there is such an action that happens in the thinking person, in the soul of the person, and therefore we say that this is a kind of different soul, yes, and so on.

Demonstration and Love and Fear – The Central Problem

So but, and I return to where I was, when I want to open for a person the consciousness, the capability to think, meaning to intellect, then I don’t only need to look for a proof, supposedly, as we imagine proof, a person remains the same thing, the question is whether he can arrange his arguments in a necessary way or something like that, yes?

What is Demonstration Anyway?

I already don’t know how to think, it’s difficult for me here because I don’t even know how people imagine, how people understand the concept of proving something, yes? They read arguments on the internet, is there a God? I have a proof that there is a God. I discovered a new proof for the existence of God, and then people are supposed to read this proof and become believers in the existence of God? Something doesn’t make sense to me there, even if there is, not only I, every romantic, every religious Jew or religious person says, what, how does the proof, yes, perhaps the proof helps in some very external argument, if we need to win in an argument of claims, and there are strange people who care about rational arguments, not normal people, only a certain kind of people, then perhaps it helps that you have a proof.

Religious God – Love and Fear

But no one becomes the kind of person who has love, connection, love and fear. People ask what is the difference between believing in God, believing, let’s say, people say this is some natural force, the force behind nature, not a natural force, but another force. So okay, how do we get from this, people ask, to a religious God, what does religious God mean? People err and say a God who intervenes in the world, this is not related. Intervention is anyway a terrible word and not good and I don’t think this is the matter.

God, in my opinion, is a God toward whom there is a relationship of love and fear. Yes, this is called God. A God that is not loved and feared is barely God. Yes, and there are many levels of love and fear. There is fear that is what they call awe, that you understand how far He is and therefore how can you even love Him, this becomes a problem, but this is still, there is here, I don’t only say, that is to say, I don’t mean only an emotional connection, yes? An emotional connection is a connection to something imaginary, a connection to this thing that we are dealing with.

The Gap Between Demonstration and Love

And therefore, very simply, it is very difficult for people to see how it can be that by my reading some proof, I will begin to love and fear, yes? That I will have love and fear, I don’t want to translate this because all translations destroy. I have love and fear for this thing that I proved, whoever proves that there is some basic atom or some basic field in the world, he suddenly receives a relationship of awe, of love. How does this even happen? What is the connection between these things?

And this is truly, according to our conception of proofs, I don’t really know what our conception of proofs is, how this, what this is supposed to be. I have no idea, I think something very basic is missing here in how people today commonly think about this, because I don’t know what it is.

The Thesis: Among the Ancients, Demonstration is Education

But one must note the ancients have a conception of demonstration that is itself a conception of education of development of the soul yes the soul the subject this thing that grasps reality that is opened to it through this opening that is called

Demonstrative Proof as Internal Transformation of the Soul

The Fundamental Distinction: Necessary Demonstration versus Rhetoric

The Nature of Demonstrative Proof

There is here some thing that our tool, our tool of knowledge is such a thing that is drawn or connected with necessity to a thing that it recognizes as necessary, yes? This is actually the distinction between demonstrative proof, what the Rambam calls demonstrative proof, necessary demonstrative proof, and non-necessary rhetoric, yes?

Because after all we have, one can easily convince the soul, the human subject to be drawn after something that is presented before it as sweet or as attractive or all kinds of such imaginative ways, and in all these attractions exists a certain freedom, yes? Freedom, I mean here freedom in the bad sense, yes? There exists a possibility not to be drawn, yes?

The Degree of Freedom in Rhetoric

You, yes, one can speak, one can discuss all kinds of low lusts, supposedly, you put before the cow the sweet thing, then she is always drawn after it, but a person is more complicated and has more degrees of freedom. I can show you how beautiful is the angel or something like that, and in the form of rhetoric, yes, in a non-necessary form, in a form of, yes, this is very beautiful, this could be, this seems, this, when I say seems, I mean seems in a psychic sense, yes, this is possible.

And you, and there are people who are drawn after this, yes, and therefore this is how religious rhetoric actually works, it presents before people possible things, things, and tries to make them attractive, yes, it tells a beautiful story, and a person can choose to be drawn after the beautiful story or not to be drawn.

“Doesn’t Speak to Me” — The Lack of Necessity in Rhetoric

Doesn’t speak to me, they say, yes? Doesn’t speak to me, this is what they call the subconscious, yes? It’s not that people, it’s difficult for a person to grasp why he is drawn after certain stories and why he is not drawn after other stories, but we can see at least that not all people are drawn after the same stories, after the same things that are presented before them in imaginative language, in emotional language, as things that are worthy to be drawn after, things that are good for you, yes? The person doesn’t always identify it that way.

Which shows us that there is here some lack of receptivity, yes? There is here some certain excessive degree of freedom, yes? You, that is, it’s not real, yes? When I say degree of freedom, that is, between you and the thing, and the object that you relate to, yes? The Rishonim would say cleave to it, this thing that you look at, that you love, that you fear from it etc., there is air in between which is this thing called I want, which is this thing called I love and I chose to love.

Because after all there are other people who see the same thing and don’t love. It could be that it’s difficult for me to follow the thing that allows me to choose and love this and not love that, okay. So this is a problem of the self-awareness of the person. Many people don’t grasp what motivates them, what causes them to love certain things, and it could be that truly these are natural things, this is not free choice in the sense that I can choose this way or that way, but this is worse than free choice, yes? This is something free, and therefore I speak about a degree of freedom.

The Problem with Imaginative Belief

Yes? There is here some something chaotic here, there is some lack of necessity, meaning lack of causal sequence, lack of sequence between the thing and my love for it, yes? And this is actually the problem with imaginative belief. Imaginative belief is belief that could have been otherwise. If it could have been otherwise, this means that my soul is not truly connected to this thing that it loves. It is connected, but within this degree of freedom.

The Process of Intellectual Education

The Prerequisite: Purification of the Soul

Whereas when I present before the soul a demonstration, that is, I lead the soul, this subject that has this capability, not only subjects have this capability, there needs to be some process of purification, a process of purity, a process of education of character traits, yes? Until a person becomes intellectual at all, until he discovers his intellectual part that is even affected by demonstrations, yes?

The Trait of Stubbornness as an Obstacle

Apparently we have a trait that doesn’t occur elsewhere, stubbornness, yes? Stubbornness is that a person can, they can prove to him that one and one is two, and he’ll say, but I think it’s three, and jump on me. That is, and he, he doesn’t have the, actually he doesn’t have the intellect, this person is not intellectual at all, he doesn’t have this capability, which is not a capability of free choice, one can ignore it, as I say, the trait of stubbornness, but the capability that the intellect has is not that I choose to believe and agree, later we’ll speak about loving, that one and one is two.

The Necessity in Demonstration: “Imposes Itself Upon You”

This is something that we say, this imposes itself, imposes itself upon you. Sorry. We say, this imposes itself upon you, but of course the word imposition is not a good word, because it sounds like something that forces you, and usually when they say imposition, they mean something against your nature, like you force something that wants to fall, like the ball that wants to fall, because there is gravitational force or something like that, and you force it to go up, this is not imposition of that kind.

But this is the opposite, one can describe this as the most love, this is love or attraction in which there is no degree of freedom, there is no chaos in it. This is a thing that when the intellectual soul sees a demonstration, then it is drawn after this thing that is shown to it in an essential way, in a way of this is I, this is the I that is the part that grasps necessary truths, it doesn’t have a little perhaps air, it doesn’t have freedom to say but perhaps it’s not so.

Automatic Cleaving Without Air in Between

If you have freedom to say not so, because truly the demonstration is not a necessary demonstration, this is a problem of the demonstration or a problem of your accessibility to the thing or a problem of the thing itself. But when the soul sees the things themselves, then it simply becomes cleaving to this thing, it recognizes this thing, one can even say loves this thing in a necessary way.

Summary: Demonstration as Transformation

The Intellectual Capability for Cleaving

So there is some capability, in summary, there is here some capability of the soul to be drawn after demonstrations when they are good demonstrations and when you have the time and the quiet hour and all the psychic and character conditions to see the demonstration, to see the thing, and then happens some automatic cleaving, not automatic in the sense of not passing through the rational intellect of the person.

The Highest Human Action

So this is actually the most human action, the most free choice one can say, free choice in the sense that expresses what he truly wants, that is not forced upon himself, upon you from outside. And this sounds to people like a contradiction, because when we imagine choice, we usually imagine choice within the world of possibilities, and then they say, but if there is no other possibility, then this is not choice.

But if one thinks about choice in a more positive sense, as something not forced from outside, then this is the thing least forced from outside. Because one cannot here convince, one cannot here make manipulations. This is the thing that is simple, the power to identify or to be drawn after true things, it is drawn after the truth.

To Be Drawn After Truth Because It Is Truth

This is what the Rambam calls in another place to do, but to be drawn after truth because it is truth, yes? And the question why should I have such an interest, because this is an interest that the intellect has, this is not an interest that the other parts of the soul have, and this is the only interest that the intellect has, to see the truth, yes? So this is understood.

Application to Proofs of God’s Existence

The Preparation for Hearing the Proofs

So this is my sermon on demonstration as internal transformation, yes? When the Rishonim speak about proofs for the existence of God, yes? This is what is sought here, in all these chapters we are dealing with preparation, the last million to be ready to hear proofs for the existence of God.

The Aspiration for Union with God

They speak about an aspiration that the soul will unite with God, yes, the intellect, as much as possible to apprehend Him, to intellect Him, in a necessary and essential way, and not in a free choice way, yes? You want to connect yourself to this thing, to this object of cognition, not because I love, but because it is so.

The Connection to Chapter 68: Union of Intellect and Intelligible

And then it is understood, if one understands that this cognition is a transformation of the person from something that doesn’t know this truth to something that does know this, then first of all it is understood that this is eternal etc., but also understood that yes, this is eternal because this is connected, this is almost more on the side of the intelligible than with the intellector, or there is a union of the intellecting intellect and the intelligible, as written in chapter 68, and then the knowledge of God is at least something divine, if not God Himself, there are here deep discussions.

Why This Is Not Something “Cold”

But this also at least shows us why this is not something cold, yes? Because one can discuss whether this is something warm in the sense of emotional warmth, yes? Whether this causes my blood to boil, or all kinds of such bodily reactions that belong to bodily love. But it is clear that one cannot imagine this as something external, as something that… what does it obligate me? This is much more than obligating you. To obligate is when you can not be obligated, this simply cannot be otherwise.

Demonstration as Religious Experience — Separating Intellect from Imagination

Introduction: Two Paths to Knowledge of God

This is my description, of my attempt to describe demonstration as religious experience, the proofs for the existence of God. Here we are accustomed to hear that there are parallel tracks — there is the Kuzari, Rabbi Hasdai Crescas, everyone spoke this way. This is a very ancient conversation, that spoke about parallel tracks of proofs for the existence of God and of experience of God, of what they call today the religious experience.

And this is all made possible because, and this is explicit, and the Kuzari truly explicitly has a Kalamist conception of proofs, and truly within this conception the proofs are not very useful except to convince your intellect, of yourself or of others, but this still works in the story of arguments and counter-arguments etc.

The Rambam: Demonstration as Necessary Experience

But the Rambam is one of those who believe in the intellect as an independent faculty, so they think that the proof for the existence of God is simply the necessary experience of His existence. Whereas any other proof can be denied, can be denied, as we know from reality. To have the strongest religious experience does not obligate that a person won’t deny it tomorrow. Whereas to believe, to intellectually grasp it, it’s not that it’s already impossible to even talk about this conversation of whether to deny. It’s like a person debating whether to deny that one plus one equals two, and much more than that. One can be stubborn, one can be wicked in many other senses, but one cannot deny.

The Irreversibility of Intellectual Apprehension: The Intellect That Becomes Actual

And therefore, this returns to the conversation about the enrichment of the soul, and this is the only eternal thing. Therefore the Rambam says that whoever knows, whoever merited to intellectually grasp God once, can never forget it. This is called that his intellect became actual, and it’s impossible, there’s no way back from this.

And people are mistaken when they hear this, because I don’t know, why can I forget? Because on the contrary, experiential, emotional things have much more lasting effect on the soul. Of course, even that gets worn away, but people think that intellectual apprehensions or proofs are forgotten a second after learning them.

Intellectual Apprehension as Transformation of the Soul

But this is because they don’t grasp it as a transformation of the soul, that it will be accessible to the intelligible thing in a necessary way, which is the definition of knowing something in the form of proof. This is the level of Moses’ prophecy, separate from the other prophets, that Moses was standing to learn it, he was a normal person, and saw it in a necessary way.

And it’s like you never — and I imagine this for people who have difficulty grasping what kind of intellectual apprehension there is that by its definition cannot be forgotten — so it’s almost like we all learned as very small children, the concept of what Piaget, the psychologist, called Object Permanence. We learned that when we close our eyes, things in the world don’t disappear. And very much, this was violent. As small babies, they don’t know this, they cover their eyes and think that father also disappeared, but at some point they learn this, and it’s part of our physical model of the world. It’s not something that came — perhaps Plato would say it’s built in, it’s innate within us — in any case it’s part of our model that we have of the world, and it’s unforgettable, impossible to forget. It’s not that we need to do work of bringing it to the heart, because it’s so abstract or something like that.

Let’s return to where you were. This was a very general introduction to the matter of proofs.

The Three Proofs for the Separation Between Intellect and Imagination

What I wanted to do with this, and I have doubts whether this works in the course I’m thinking now, but what I want to do with this is like this. Yes, have I already lost everyone? Have I lost you? This is already possible. What, is this completely clear, right? Yes, David, very good. Okay.

Now, what I want to say is like this, because I have very great doubts, and if I ever have time and strength to get into this — the Rambam here gave us three proofs for the separation between intellect and imagination.

The Examples: Two Directions of Collision

One proof, two proofs, two types of things that the imagination thinks are impossible, but the intellect compels us to accept that they are possible. The example of the person standing on the other side of the world, and the example of lines that approach forever and never meet. These are two examples that seem impossible to us, and the intellect says they are not only possible, but simply that’s how it really is.

And afterwards, I haven’t read this yet, but afterwards he also gives — maybe we read last week, I don’t remember — the opposite example of things that the intellect thinks must be, sorry, that the imagination says must be, and the intellect says cannot be, which is that God would be corporeal.

The Logical Structure of the Proofs

This is really a strange example. Three examples, and because of this we have two examples on one side — two things that the imagination says cannot be, and the intellect says can be, not only can be, but really exists — and the opposite example of something that the imagination says must be, and the intellect says cannot be.

So this leads us to the conclusion that there is a third thing. Yes the proof, I said the proof with the conclusion already, but the Rambam also said it, but actually it’s supposed to work like this: I say, you don’t have these problems, and then you say, but where did I err, where is the mistake? Why is it really like this?

And the answer, the solution to this perplexity — how can it be that it was so clear to us that this cannot be or that this must be, and in the end it turns out that it cannot, it yes must be or that it cannot be or that it can — is because we were speaking from different faculties. At first when we said cannot be or must be, it was, the imagination said it, and afterwards when we noticed that it must be or that it’s impossible, the intellect said it. This is really a very interesting answer to this problem.

Critical Evaluation of the Proofs

And I think there’s also a question here, and therefore I prefaced all this, there’s a question of how good these proofs are. Maybe I’ll still manage in a moment to speak a bit about these proofs and see how good they are.

The Philosophical-Analytical Question

But I noticed, when I speak about good proofs, I’m trying to make a proof as if I’m writing an article of analytic philosophy, and there really are articles that spoke exactly about this question, only in contemporary language — they don’t call it imagination, and there’s in this itself a history and an interesting conversation.

But I think as if, is it true that this proves that there is some other thing, that there is an intellect that is not the same thing as imagination, and now we can enter into debate whether this proves, whether this proof is valid or not.

Problems in the Choice of Examples

But, and really, also separate from this question, this is one question, separate from this question, there’s also a question of the choice of examples here. The examples here are not examples, it’s not clear that they are the best examples. Later we’ll see, Descartes and others, I think Descartes, had a better example for the second point of mathematics, who also wanted a conversation that the intellect is something separate in this way.

And also the opposite matter, this is a strange example. This is the example of almost the thing we’re asking, is God corporeal? It’s almost, I think it’s almost a dialectical proof of the Rambam, that he intends to speak about the Kalam, who also admit that God is not imagination, that God is not corporeal, so he says, but according to the imagination He must be corporeal.

The Experience is More Important Than the Proof Itself

But what I think is that more important than the question of whether these proofs are good and how good they are and one can debate about this — the experience in these cases of at least in the Rambam’s generation, in his study hall, that he and his friends and his students experienced this collision between what seemed to them necessary because of the first thought, because of the imagination, and afterwards saw that it’s also in a necessary way, that it’s not true — this experience opened people and it can still open people, perhaps with other relevant examples.

The Proof as Transformation

Not because these examples are written proofs, but because in order to experience, in order for this transformation to happen to you of opening to something else, of developing this capability of what today they perhaps call abstract thinking, but it’s much more than that — one needs to speak, one needs to experience this in things that are very important to you, in things that are very basic to your worldview, and suddenly discover in a very necessary way, that one cannot escape from it, that they simply are not true, and the opposite is true.

The Required Contemplation: “You Became a Different Person”

And then you contemplate, there’s a contemplation here that he requires you to do, contemplate, begin from this that he heard something, the sciences were elevated, the habitual wisdoms, the educational sciences, the sciences of mathematics and astronomy, that you should see, remember, when you learned this, how you became a different person. You became a different person, a different person in terms of intellect, just as the imagination distinguishes between people who have different bodies, you are supposed to distinguish.

This, the Rambam brings this verse, you became a different person, about a prophet, about King Saul, it is written, when he prophesies with Samuel, that you suddenly, in this moment, received — the Zohar would call this, you received a discerning soul (neshamah). Until now you only had spirit (ruach) and soul (nefesh), suddenly you received neshamah.

Central Claim: The Irreversibility of the Experience

And because I see, and then, if, even if someone will refute, then I want to claim something very interesting, that I’m doubtful whether it’s true, but in my experience it seems true.

Now, even if someone will come and claim and refute the proof, discover that this is a less good proof, one can debate about the proof — it’s not clear that he can turn back the wheel and give this person, remove from him this neshamah.

A bit in analogy, I’m constantly using, I’m doing the very strange thing, and using an analogy from mysticism in order to understand philosophy.

The Value of Proof Beyond Its Logical Validity — The Intellect as “Software” Installed in the Soul

The Proof as Educational Tool: Acquiring Intellect Beyond Logical Validity

I think, if I understand, if I’m correct, that these proofs, because they clothed themselves in very present things, very basic to people’s worldview, and very much showed him in his educational process that he’s not right — that there is some other thing that shows you what’s right, and not your imagination — that this gives you the possibility to understand what intellect is. Now you understood what I’m talking about.

Now, tomorrow someone will come and say the proof wasn’t good, one really needs to use another proof, there is, yes? But once you were educated, you received this intellect, this is more important than the matter of whether the proof is good.

The Correct Conclusion Even When the Path to It is Problematic

Yes, this is what I wanted to claim and I have historical examples of such things, for example, that the proof is not good, but what I gained — what I gained in the soul from this proof — is indeed true. It must be that the conclusion is correct without the path to it being correct. If the conclusion is not correct then really, and I became attached to some imagination, this doesn’t begin at all.

But if I did arrive at some thing that afterwards, after I pass through the course of this proof, I see it in another million places — not that I see it only, one can see it only in the example of this proof — I will use half the day with intellect and half the day with imagination every day, and I see a million questions for this distinction, yes? It’s not that this is the way.

The Four Proofs of the Rambam for the Existence of God: What They Teach Us

When we speak about proofs, come, one can speak about proofs for the existence of God, which is a bit like this. When you say there are 30 proofs — I don’t know, okay, there are only, how many proofs does the Rambam have? Four proofs for the existence of God, yes?

What does this mean? Does this mean that God is not found in the world except in these four places, except in these four paths? God is not found, that is, He is not seen — found in the sense of present, of known — He is not known, not found within the world, except through. This is actually what you’re saying, yes? From the point of view of the one who grasped the proof that there is a God, before this you don’t know there is a God. But why don’t you know? Because you didn’t see Him, yes?

The Chemical Analogy: Separating Components as an Example of Proof

It’s like if we use such a chemical analogy, yes? The chemical analogy will show us why this is not correct. So like this, ostensibly someone will ask, and therefore, what? Really, if we write, then your eyes were opened, and something else, and then you saw it everywhere, and in many forms. This happens with things that have tradition, we see, and then also with the opening of the eyes, and this was software, still the thing already, yes.

Example: Separating the Components of Air

I’ll think of an example. Let’s say, we have chemistry, yes? Chemistry is to discover the components of the composite things we have. We breathe air, but if you do some certain experiment, you can separate the oxygen from the carbon in the air, and then you discover that there is a certain concentration — sorry, a certain concentration of oxygen and all the other components that are in the air, and they’re not just one thing, they’re composed of all these things, yes?

Now, where — and I did the proof through some tool that does some chemical move that allows me to make this separation, and this is a proof, yes? What is the proof that air is not one thing but composed of 30 things? It’s that we have a device that allows it to separate this, yes?

The Proof Does Not Limit the Proven to One Place

Afterwards, now, after we separated it, we don’t intend to say that the air is found, these parts are found only within this separation device. We know it everywhere, and use it to explain a million other things that are not through this proof for this division. Although perhaps really, and if we discover that there is some problem in the proof, that we separated it incorrectly, it could be that we really have a problem.

I don’t know, but still, in any case, whoever believes — how do I say — if there is a good proof or another good proof, it doesn’t matter, but that we achieved this knowledge, that we know the world like this, it is still true. I’m not only assuming it’s true, it could be that it’s not true, and if I have an error then I’ll say, right, that this is an error. But assuming it’s not an error, let’s say we discovered another proof, and really the first proof was mistaken, because we had a problem with the measuring device or something.

What I mean to say is: when we make a proof, we don’t intend that the only place available is through this proof. In chemistry this is perhaps a bit true, that is, this material in isolated form really exists only in my separation device and doesn’t exist in the world. But afterwards, when I look at all the world in the world that has this thing within it, and not in isolated form, this is what I claim — I don’t claim it’s found only there.

Application of the Analogy: The Intellect Operates Everywhere, Not Only in the Proof

In the same sense, whoever claims he has a proof for the existence of the intellect, that it is separate from imagination, he doesn’t claim that the intellect operates only within this proof. He claims that the intellect operates in another million cases. The opposite — he claims every proof in the world works only through the intellect.

Searching for Good Examples: The Separation Between Intellect and Imagination

But when we search for good proofs, we’re actually searching for good examples. We’re searching for places where — and it could be that usually it’s too mixed really. This is really a very fundamental Aristotelian question: to what extent can one separate the intellect from the imagination, because usually they really operate very well together. Therefore my example of separation is not such a bad example.

But if I have one example that proves to you, that as it were opens your eyes, or separates for you the intellect from the imagination, and here you saw in isolated form what is the operation of the intellect and what is the operation of the imagination, and how they are not the same thing at all — afterwards, that someone else will say this works or this doesn’t work, what am I saying? You simply forgot. This is what I want to claim.

The Importance of Example Quality: Why We Need to Update Examples in Philosophy

And therefore it’s also, according to what I’m saying, it matters. Therefore, when we engage with examples, with proofs of this type, it matters very much if this is a good example, yes? And its goodness, the quality of the example, can be not only pure intellectual quality — there can be in it also imaginative quality, one can say a bit.

That is, when I began — there needs to be something very basic for you, or something common, something you know from your regular life experience, because otherwise you don’t manage to see it in a good way, and everything becomes something. And therefore I think it’s very important to update the examples in philosophy.

When standing in ancient philosophy, they encounter an example — sometimes a mathematical example, sometimes a physical example etc. — and if it’s within something we don’t know, then yes, theoretically I can look at the commentators and say, yes, here he means this matter. I say, no? Does this work?

Discussion: Is This a “Way of Looking” or Truth?

The Critical Question

Does this make sense what I’m saying? Like it’s true. If it — I hear how much if it works, then it works. If in the glass there is this, then it’s for the whole world. But if in the glass there is there, that you see it in the whole world, when you think in this way under the unit like this, it doesn’t make it true. The truth, I understand, like…

Yes, correct. According to capable of yes, or like, there’s what to do with it.

The Software Installed in the Soul

But I think because of this, therefore I prefaced all this thing, that this — it’s like this, it installed for you some, what do you call it, some software, yes? In our generation already, no? Like, when I see something in a certain way, I see it everywhere, even if it’s…

Even if it’s not true?

Yes. Something like that, but it’s not true.

Right, right. This is really dangerous.

And therefore if it is indeed true…

No, but then it becomes a way of looking and not truth. Maybe it is truth, but… it’s already…

Examining the Concept “Way of Looking”

Yes, this is too modern already. What’s the question? The sense of the concept of way of looking is a concept we use without thinking, so we need to think what it means. It could be that we’re equal that it indeed exists in all kinds of concepts.

It could be that ways of looking are really forms existing in the world. That is, from such a Platonic point of view, then these are not ways of looking that exist within the souls of people. There is reality.

No, and also if you say, if someone says, people today look at everything in a materialistic way or something like that, then you say need to look at the matter — this is true, because they really identify in the world only this part. And if you have a view that it’s formal parts or something like that, it’s not a way of looking — it’s a way of looking.

Updating Philosophical Examples and the Problem with the Rambam’s Proofs

The Need to Update Examples as a Condition for Reviving Philosophy

That is, from such a Platonic point of view, yes, then these are not ways of looking that exist within the souls of people. There is reality. Yes, no, and also if you say, if someone says, people today look at everything in a materialistic way or something like that, then you say, this is true, because they really identify in the world only this part. If you have a view that it’s formal parts or something like that, it’s not a way of looking, it’s a way of looking in the same sense that the device that shows you the parts, the telescope or microscope or something like that, is a way of looking, yes? It’s a way of looking that reveals to you, that enables you to see these types of existing things, yes? That it’s a way of looking, that it depends on your experience device or your measurement, doesn’t mean it doesn’t see real things.

Right. But therefore I, yes, yes, therefore, like, because I, I, like, tried to look at this as something of, of, that transforms the type, the person, yes? Therefore I, I began to say that for example it matters very much if the examples are relevant examples, yes?

Examples as Key to Philosophical Understanding

I think a large part of what I want to do, which is to update philosophy or revive it, is to update the examples. Why? Because if what we’re reading here, yes? Come let’s say, for example, we’re reading here, that the Rambam uses this example of the round world, yes, actually. The round world, and there are people on both sides and they don’t fall, yes? We’re very accustomed, we’re far too accustomed to this matter.

And another week you’ll submit about what you said before, about like, that we close our eyes and still things exist. Yes. After all there are people who will tell individualism, for example, exactly. They’ll say, you don’t see anyone, I think there are people who understand this. Right, but in principle, if we lived in a world, yes, like. Yes.

When the Example Works Despite Inaccuracy

But on the other hand, and therefore I’m saying, but when it can be the opposite, it does work. If I give you examples that are very present in your worldview, and I show you how from this to arrive at something, yes, at an intellect here, in the example, and then tomorrow you discover that this isn’t the best example, yes? It might not be a proof. Indeed one can explain this thing, one can explain without assuming there is a separate intellect, yes? This is actually my problem here.

Reaching the Destination Is More Important Than the Path

Still, you discovered from this a separate intellect, historically, yes? Even though tomorrow, and I’m of course assuming there really is a separate intellect, yes? If it’s a real mistake, then what I’m saying doesn’t help. But if it’s correct, then tomorrow I’ll come to you, I’ll come to you and say, say, yes, I was wrong, or we had a mistake in the details here, yes, we need to interpret this a bit differently, we need to state the proof in a different way etc., but this is comparable to someone who reached the destination by the wrong path, yes, but he arrived.

Once you’ve arrived, it matters less how you arrived. It matters a lot here, because we want to arrive, because I started with this that the proof is something that compels you to arrive. Good. Whoever remains with the proof, then nothing remains for him, and no proofs remain for retirement. Yes, you need to arrive, yes. If you arrived, and yes you arrived in a necessary way, it was just something inaccurate, or something incorrect in the example, or something like that, then it might still work, and there won’t be this problem here.

So this is what… I thought as an introduction to this whole thing.

Two Ways to Understand “Impossible for the Imagination”

Now, if we have a bit, wait, I’ll repeat the thing, there’s just, I want to understand, to understand what problem I have, yes? I’m just, at least I’ll ask the question. Afterwards we’ll talk about the third proof, maybe the third side that the Rambam brings.

Presenting the Problem: What Is Difficult to Imagine?

He gave us here examples that are like this. Let’s take the first example, and I have here the question. There is, if you tell a person, yes, and the Rambam wastes a lot of words trying to let us picture this thing, which is supposed to be impossible according to the imagination, yes? He says, take, yes, a circle, not a circle, a globe, yes? The largest sphere, and understand that its extremities, they must be, yes?

What he’s actually doing is apparently a proof, yes? This is what I want to talk about here, yes? Because there are two ways here, and here I think I’m right in this conclusion. There are two ways one can understand the explanation here, the problem here, yes?

There are things that are difficult to picture, difficult to imagine, yes? And it’s perhaps impossible because, or it’s impossible, or it’s at least very difficult to make a picture in the mind, an imaginary picture, yes? Fantasy, which is really a duplication of a picture of possessions inside the mind, it’s very difficult to make a picture of them, yes?

And now, now, what kind of things are difficult to make a picture of in the mind? That’s the question.

First Way: A “Resolution” Type Difficulty — An Internal Problem of Imagination

I can think of very complicated things or very detailed things. There are people who find it difficult in general to imagine things in their mind, that’s what research today says, that there’s a lot of distinction between people in this. But, what’s easy to imagine and what’s difficult to imagine? It’s difficult to imagine very detailed things or very, there are people here who will say, it’s very difficult to imagine things far from the mind, like some imaginary creature that no one has ever seen, that is very large and a million times larger and more complex than what you’ve seen. So this is a certain difficulty in imagining, or one can say, something very detailed, some picture that you only see in mathematics books, and you need graph paper for this, in order to draw it correctly, because it’s simply very difficult, you can’t do it in your head, you use paper, yes, graph paper.

Why do you use graph paper? Because it’s impossible. If there were someone whose mind had a more detailed processor so to speak, you had a more successful drawing ability, it might be that you could draw it in your mind and do all the calculation in your mind, yes, as they teach in mathematics, which is through imaginations, yes, through these figures, these drawings. It’s simply difficult, yes.

The Analogy to Mathematics on Paper

Even when we calculate, yes, we need to think about it like this. Even when they teach us in school to do mathematics, through the manipulation of, what do you call it? The symbols on paper, yes? Even the numbers. Why is it easier for us to do this on paper than in our mind? What’s actually happening here? Yes, there’s at least a sense in which it’s more difficult, for the very simple reason that the… what do we call it? The resolution of, of human imagination, of this graphics processor, yes? The graphics of my mind, it has, it’s weak graphics, it can’t do, it’s very difficult for me to imagine myself doing these manipulations on the numbers.

When I see it before my eyes it’s easier for me, even though in many respects I draw much worse than what I imagine. I can imagine in my mind very interesting drawings, and it’s much more difficult for me to imagine, much more, sorry, it’s difficult for me to draw them, but with the same kind of shapes that mathematics uses, I have some difficulty. It’s difficult for me to imagine it, but it’s easy for me to write it on paper and then see sharply how the calculation will work.

The Possibility of Improving Imagination

There really are people who practice this. I’ve seen courses on mental mathematics, that work on all kinds of memory techniques, or imagination, how you can do basic mathematical operations even with long numbers and so on, how to do them in your mind. But the problem, yes, besides the fact that there are all kinds of tricks for how to shorten calculations and such things, but there’s also a lot of simply associating it with some imaginary picture, yes, something like that, and then it’s all problems of imagination, yes, internal problems of imagination, yes, like one can go to a guided imagery course, and become a better mathematician, if you apply their techniques, to the problem of calculating, of imagining complex things, yes, or very fine things, that have resolution, that require high resolution, such things, yes?

Is this kind of problem understood?

The Hint to Descartes: A Second Possible Way

Therefore, for example, I thought about this and we need to discuss it. For example, Descartes claimed he has a proof for the existence of the intellect, and separate from the imagination in something very analogous to the proof.

A Fundamental Distinction Between Intellect and Imagination: Analysis of the Proof

Descartes’ Argument as a Starting Point — The Thousand-Sided Figure

Is this kind of problem understood? Therefore, for example, I thought about this and we need to discuss it. For example, Descartes claimed he has a proof for the existence of the intellect, and separate from the imagination, in something very analogous to the proof here, and it’s that there’s a picture, sorry, figure, how do you say, the shape that has a thousand sides.

The shape of a thousand sides is mathematically very different from a shape of 999 sides. It’s very easy mathematically to think, and intellectually to think about the differences and see what this shape is, and give all kinds of calculations of its properties etc. But no one in the world can imagine a shape of a thousand sides. If you imagine it, it more or less looks to you like a circle in the end, yes? Because it’s simply very small.

And even if someone says, okay, I do imagine it, he can’t imagine, see in his mind the difference between this and the picture of 999. It’s simply impossible. Whereas to think about it, it’s simply terribly easy. I tell you, you don’t struggle at all to think the difference between them, but you struggle very much to imagine the difference between them.

The truth is that even if I put it on paper, you can’t see the difference, because it’s too small to see. And even if you say, okay, I’ll magnify it, every time you magnify, you can magnify perhaps 50 sides, but once you need to magnify everything, you can no longer see everything at once. So you don’t see the picture, the figure with a thousand sides. You see something that you believe, that you remember has a thousand sides, but you don’t see it. This is Descartes’ argument.

The Problem with This Argument: The Intellect as “Improved Imagination”

Now, even he doesn’t mean it this way, but I want to sharpen. If we understand this problem this way, then it turns out that the intellect is simply something with a stronger processor. One can simply imagine the intellect as imagination that has stronger graphics, yes, or has resolution, yes, or some ability to look, or short term memory ability they call it, yes, it can do, it can concentrate, yes, it has, how do you say, awareness, it can look at more complicated things.

We, we have, our senses and also our imagination have a terribly small limitation of how many things it can see at once, yes, concentrate on them, or some say it’s only seven items or something like that, really a very small number. Whereas the intellect doesn’t have this limitation. Once we learn to use this tool of intellect, we can calculate, see, pay attention to much more basic things, much more complicated.

I think the Rambam here wants to do something stronger than this, because this is a problem, because this is altogether a problem, a particular limitation. If there is, maybe there’s a computer that has better imaginative power. This is actually a weakness of imagination and not a fundamental limitation of imagination, yes? What we want here, the truth is that also Descartes in this argument, what we want here is to see another kind of perception, yes? Another kind of thing, not the same kind of thing at all.

What the Rambam Seeks to Prove: Things the Imagination Identifies as Impossible

And what is the other kind of thing we want to do? What we want is to show that there are things that the imagination says are impossible, yes? And then I encounter a bit of another problem, but I’m trying to explain.

The Example of the Elephant and the Eye of a Needle

The problem of the… for example, the problem of the drawing of two people at two ends of the world, standing in opposite relation to each other and neither falls, it’s actually a problem, not an imaginary problem. It’s not difficult to imagine this, I can easily draw such a drawing. There’s no problem here at all, no problem of drawing. This isn’t a good example at all. We’re very used to this drawing, yes? Therefore we don’t understand at all what’s difficult for the Rambam in this. But it’s not just this, also for the Rambam it would be very easy to draw this. Why? Imagine that people don’t fall. What, you’ll do something, yes?

What he means, or what he’s trying to mean, we need to think about this. What he’s trying at least to say, and I’m here asking if I need to think if this is a good proof, what he means to say is that there’s here a thing that you think imaginatively is impossible, impossible to imagine. Impossible to imagine not because I have lower resolution, but it’s like imagining, as someone said in the Gemara, yes? Dream about an elephant entering through the eye of a needle, yes?

This, I don’t know how to imagine this, because every time I start to imagine it I encounter a contradiction, yes? Either the elephant becomes small and then it’s no longer an elephant, or the needle becomes large and then it’s no longer. This is a very ancient example of an impossible thing, yes? Also in the New Testament they use this image, yes? An elephant entering through a very small hole or something like that.

This is something that the imagination identifies as impossibility, not as something, it’s difficult for me to imagine this. Imagine the processor, the best graphics person, he can’t make you a drawing of this, because he needs to make a drawing of things opposite to each other, yes?

The Logical Contradiction in Imagination: Two People at the Ends of the World

So this person who says, there can’t be two people on two sides of the world, both not falling, this is because he says, he has a calculation actually here. And therefore we need to be careful, to understand why this isn’t actually just a mistake, because I have, and therefore this leads me to the second side of a problem in the proof here.

But the Rambam wants to claim, that as long as you use your imagination, your imagination thinks there is such a thing as up and down, and they are, as I said, absolute. And we experience the world this way as if up and down are absolute.

Now, and he brings you a story, and therefore he elaborated so much in all this story of either the line cutting the circle is vertical or it’s not vertical, yes? This whole thing. He’s simply trying to show you that there’s a logical contradiction here, yes? Supposedly.

Formulating the Logical Contradiction

The logical contradiction goes like this: two things in opposite relation to each other can’t both be up. This is the logical proof he makes. Either one is up and the other is down, or both are down supposedly. Half of both are down, but something like that. Simply it can’t be that both are up, this is impossible, this is a contradiction. Even it can’t be that both are up is impossible. This is simply a logical contradiction.

Tell me how there can be two things in opposite relation both up. If it’s a bit tilted, okay? Then they’re no longer exactly opposite to each other, I can imagine that. But if they’re exactly opposite to each other, then it’s impossible, simply impossible.

He says, enlarge it as large as you want, yes? Precisely to show you, this isn’t a resolution problem, we need to enlarge it. This is a problem in your thinking ability, as if what you now identify as your thought, you can’t think it, you can’t only not imagine it, you also can’t describe it. How do you describe two things that are exactly in relation, opposite to each other, that one, that both are up? Yes? It’s simply a contradiction.

The Intellectual Solution: Up and Down as Abstract Concepts

And the truth is, what’s the solution to this contradiction? The Rambam claimed, and no, and here it might be that the way we grasp physics didn’t fall into this problem. But the Rambam claims that the answer to this, the true answer, yes, is not imaginary, one really can’t imagine this, yes? Yes, of course I can make a drawing of people on two sides of the world not falling, but I can’t think about this with my imaginative power.

The Answer: Both Are Up

What do I need to think, if I understand the answer? The answer is actually that both are up, that’s the answer. According to Aristotle, according to the Rambam’s worldview, both are indeed up, even though they’re opposite to each other.

Why? Because as he wrote here, each of them is up and down in relation to the other, yes? Combined, it’s simply a word for relation. Each of them is both up and down. So how can someone, how can a thing be both up and down? Yes, if we define down relatively, yes? If you’re above him, yes, you’re above him. If you’re below him, you’re also below him.

The Absolute Meaning of Up and Down

What is the absolute truth? The absolute truth is that up is a word for external and down is a word for internal, yes? In relation to… if we look at the whole world, we need to understand that up and down, that it’s true, that things in the world behave, most things, yes, that are made of earth and so on, tend to fall down. We’re not denying this, there is up and down in the world, but this up and down is something abstract, it’s something impossible to imagine. One can’t imagine how the true up of the world works.

The true up, which is really up, doesn’t work in a way that has on its opposite side down. This is something wondrous, yes? He claims, there isn’t on the opposite side of the true up unlike the imaginary up, yes? The upward direction of imagination indeed behaves according to the rules we’re used to, that the imagination of the ummah, that the opposite of up is down.

But truly, the opposite of up is also up. Yes? This is something, this is, this is how his proof works.

The Complete Proof: A Fundamental Distinction Between Intellect and Imagination

The opposite of up in the true existing world, which we know intellectually exists, we never saw this, so if we had to learn this we would say it’s impossible, but because we have proofs, and I won’t detail the proofs here, we know that the opposite of up is also up.

If you specifically insist on speaking relatively, then yes, the opposite of up is down, but also, it doesn’t answer from the point of view, yes, he says in relation. In relation to the second it’s indeed down, but in relation, truly it’s up, both are up and therefore both fall down and not that each one has—

The Dilemma in Proving the Gap Between Imagination and Intellect — Continuation of the Discussion

Is It an Imaginary Problem or a Logical Contradiction?

Each of them is up, because there is a true up. There is a true up, only that the true up behaves in a way that’s impossible to understand, impossible to imagine, only to understand. And this is how this proof works, yes?

Now, for us this is very difficult, because we’re used to thinking, okay, you simply made a mistake in your physics, yes? You didn’t make a mistake in the form of intellect, you didn’t succeed in discovering, inventing a new form, yes, a definition, a concept, that says that up is not the opposite of down, even though it is up, yes, it’s not that he says there’s no true up. There is a true up in the world, and things indeed fall down and not up, only that this up is encompassing and not up, even though it is indeed up, yes, things rise up, only that they actually rise to the encompassing side of reality.

The Methodological Dilemma

And we are as if very, too used, when we approach such things, to somehow replace our imagination. And we need to think what happened here. I simply repeated the proof how it makes sense, therefore I said, it might be that the core of truth is this isn’t a good proof, because it’s simply a mistake, yes? It’s an intellectual mistake, and this is what I said.

Or we say, and I have here a kind of dilemma in how this proof is supposed to work:

Either this is a problem in the resolution of the imagination, of the graphics of our imagination, and then it doesn’t prove anything, except that there’s such a limitation, and indeed when we put it on paper it’s easier for us etc.

Or is this an intellectual problem, right? After all, the thing that troubles me, the thing that makes it difficult for me to imagine up and down is not an imaginative problem, it’s an intellectual problem, it’s a logical contradiction. Up is the opposite of down, right?

The Example of the Asymptotic Line — The Logical Contradiction

Or it’s even stronger in the second example, right? To approach forever, to approach means that you arrive in the end. How can you keep approaching without ever arriving? Especially if it’s infinite, infinity. That means in the end there’s no limit to arrival. If there’s no limit to arrival, then you should arrive, right? And the answer is no. There is a way, yes, there is a way to say that… yes, but it sounds like a logical problem, it doesn’t sound like an imaginative problem.

Why This Example Is Stronger

And therefore I showed with this example of the… I think this example is even better in another sense. In this sense, and the second example, that he shows you that at least according to human thinking, it’s not that you had a mistake about how reality works and then you discovered that oh, there is no up and down.

No, after all he takes very seriously this naive thinking that there is up and down and he stays with it. Aristotle doesn’t say there is no up and down, we simply made a mistake and we need to replace our model of the world. He says, there is up and down, but up and down are defined in a different way and the different way is an intellectual way. We can think about it and we cannot imagine it, it’s not because it’s hard for us to imagine, because the moment we start to imagine it, we encounter this contradiction, which is a contradiction according to imagination and not according to intellect.

It could be that we’re too accustomed to modes of intellectual thinking, that it’s no longer a problem, but that’s how this proof is supposed to work, right? Is this understood?

Okay, it’s more understood this time, yes. I think you listened to it. I tried.

Discussion with Students — Clarifying the Point

Yes, because we look at the west as down in a spherical way according to our calculation with legs, right? In the end.

Yes.

So the moment that the head of the legs are upside down, then it’s like…

Yes, and the person on the other side of the world, indeed his head is up and his legs are down. Yes, exactly, but that’s it, but then, and you’re right, that there’s some kind of problem here of this, really like imagining, missile and crash. Like, I’m here, I have to imagine it, that I’m up and he’s down. Yes, and… actually that I’m here. But you need to explain to you something here, here that it doesn’t work like that.

Right, and what is the other side? You don’t want to say the word relative, but it’s not the word relative, it’s like that the…

The Problem Is Conceptual, Not Pictorial

Yes, it’s a problem of a type of concepts, one could say. It’s not a problem of drawing, but a problem of a type of concepts. There’s a type of concepts like this that sometimes cannot reach the truth because they’re limited in the way they work. And there’s another type of concepts that are from the intellect, that are closer to how reality really is, something like that. That’s what he’s trying to give you.

Back to the Line Example — The Problem Is Not Pictorial

And the same thing even more so with the problem of the line, right. The problem of the line is not that it’s impossible to draw it. Again, I can show you a picture of it, no problem. Okay, a problem of resolution, but you can see because you can see a picture of it. Infinite because it cannot be actually infinite, as we’ll see later. But I can show you a picture of this line that keeps approaching and never. At every section of it, at every section of it I can show you this. The closer it gets the harder it will be for you to see, like with 1999. Okay, so it’s simply a problem of my eyes so to speak, not a problem of my imagination.

Why not? Because the legs you…

I don’t know, actually, for example, to dream, it seems to me easy to dream it.

Okay.

Because it’s only a problem of memory, because you remember yourself all the time, but you travel, travel, travel, you’re always closer, closer, closer, and never close enough, what’s the problem? And I can also easily give you the mathematical formula, right? You simply cut in half each time the distance, and there’s no end to this thing, or something, simply make a fraction of the distance, right? It’s not so hard to give it a formulation. We’re very accustomed to formulations of this type.

The Logical Contradiction in the Statement Itself

I think what’s difficult is a kind of contradiction, a logical contradiction. I’m saying, something that approaches forever and never arrives, sounds like a logical contradiction. I cannot draw, not this line, it could be that it’s possible to draw the line. You cannot draw this statement. How do you say a distance that approaches forever and never arrives? We think, something that approaches in the end arrives, right? Okay, it takes a million years. After infinite years it never arrives? This sounds to us, it approaches in an absolute way so to speak, right? As much as it’s possible to approach it approaches and it doesn’t arrive. That’s the problem, right?

The Solution: “Don’t Imagine — Think”

And the answer is, really, don’t think, yes, really when you do mathematics of infinity, of calculus, which actually, yes, in the end is based on this, they tell you don’t imagine it, yes, simply calculate it, yes, and then the Rambam actually thinks, simply calculate it and don’t understand, yes, install for yourself in your head a new program that says, yes, I’ll give you the proof, and yes, and for this you need the proof, yes, he also for this didn’t bring the proof, but there were proofs of, what was his name, this Apollonius, right? who gave a proof within the conic section, how it must be that it will never approach, that it will never arrive, and he shows you this with your eyes.

The Difference Between Imaginative Seeing and Intellectual Seeing

I show you this, but you cannot see it in your imagination, you can see it in your intellect, right? That’s what’s important. It’s not that you can do the manipulation of the calculations. That’s how we teach mathematics, especially in such topics of infinity, right? You can do the operation of calculation without understanding it. No, you can understand it, but not in the same way, not with the same connection, not with the same faculty that you understood the question, right? That’s actually the argument here at least.

Okay, that’s it for this topic. Okay.