De Anima (On the Soul)
Lecture 151: Knowledge of Singulars and the Infinite

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We have a thought of it before. Whereas God would say, no, they're contrary. Basically, we know the effect before the cause, and the cause before the cause of the cause, and last of all, the first cause. Heisenberg, now the great physicist, says, when we begin our study, we never start at the beginning. And that's true, right? Water is known before hydrogen, even though hydrogen might generate water. And hydrogen is known before proton. Proton might be first to those three. That's why it's called to be first. But proton is not first in our knowledge, right? So it's just a reverse order. So it's a terrible mistake that Spinoza made. And then Hegel comes along, right? And since our mind knows things in a confused way first, right? And the general comes before the particular in the mind. He takes the most confused and general idea, the first thought of our mind, being, and He identifies that most confused thought with the one who said, I am who am. Terrible mistake, right? I mentioned how Thomas, you know, has a chapter just refuting that in this, from a kind of gentiles, after he shows, you know, the truth of the statement that I am who am, right? But Spinoza is influencing what? What's his name? Hegel, right? Yeah. You know, the historians have thought that they classify those guys who are tied up with geometry and procedure, right? Practically, like Descartes and Spinoza and Leibniz and even Hegel to some extent. They call them rationalists, right? As opposed to the English empiricists, right? Okay? So, two extremes. Different problems that they have. Okay. So, Thomas is saying, usually we know the effect before the cause, but when we finally come to know the cause, then we know why the effect was the way it was. Yes. Feinzak, right there, the student of Heisenberg, has a book there where he, he, he, you know, you first hear us tell us, this is about the order there, and then you're going, you know, from the extended body all the way down to the elementary particles, and then you kind of turn around, right, and try to see in terms of the causes you found, the reason why of the things you knew before. So they went from the periodic table of elements to quantum theory, which Niels Bohr applied to the atom. Then they began to see the reasons for the periodic table, why, you know, certain things repeated themselves, right, at certain intervals and so on, huh? So they were seeing the reason why of things they knew to be so, but they came to know the reason why afterwards, huh? So, big mistakes there for Descartes and Spinoza and Hegel. In some ways they're very gross, right? Yeah, but large, yeah. When Aristotle talks about, you know, when we do wisdom these days, when Aristotle talks about how one should determine the way of proceeding in any science, huh? He talks about those who want to proceed mathematically everywhere. And, of course, he's thinking of the Pythagoreans and people like that, huh? The guys who, you know, say the soul is a self-moving number and everything's mathematical. But, I mean, this same tendency dominates the, what, moderns, right, huh? And it's because mathematics is this, you know, clarity and certitude for us, and we wish to have that kind of clarity and certitude everywhere, but you can't. Aristotle would give the reasons why you can't. Anyway. Now, the second injection was trying to maintain that the point was placed in the definition of line, right? Actually, Euclid doesn't really say it quite that way, but he does go on to say the points are the limits of a line, right? Okay. To the second, it should be said that point is not placed in the definition of line taken in general, right? For it is manifest that in an infinite line, right, and also in a circular line, right, there is not a point except in, what, ability, huh? But Euclid defines a, what, finite straight line, right? And, therefore, he lays down point in the definition of line as the limit in the definition of the limited, okay? I don't remember Euclid doing exactly that, huh? You know? You know, that's what Thomas' text is there. I mean, what he does, Euclid, he defines point, and then he defines line, I think, as linked without breadth, right? And then you'll see that the limits of a line are point, you know? So there'd be less problem that way, huh? In the way the objection is saying, right? The unit, however, is the measure of number, right? That's the interesting thing, right? The unit measures number, but the, what, point doesn't measure a line. So I can see how many ones there are in three, or four, or five, or six, but I can't see how many points there are in this line as opposed to that line, right? Because there's an infinity of points in ability in every line, right? There's no such thing as a three-point long line and a five-point long line, right? Okay? And therefore, it is placed in the definition of number measured, huh? You define the number as a multitude, right? Measured by what? But it is not placed in the definition of the divisible, but more the, what? Reverse, right? Now, of course, through the modern mathematicians, they got us all fouled up, you know, because they talk about dividing the one into two halves or three, you know? And so I tell you, if students are out of their way of thinking a bit, huh? I'll say, well, what's... If I say, what's half of three, they'll say one and a half, right? Yeah. So I'll say, what's half of three points? Well, those things are one and a half points, right? And then I try to get them to see that the one is even simpler than the, what? Point. So if you can't divide the point, then you can't divide the, what? The one, right? I'm trying to show them that it's, what? Indivisible. And so it's not prior to divisible in definition, huh? But posterior, because you're going to try to explain it as something indivisible. They all get that idea that you can divide the one, right? Yeah. And the Greeks are very sure, you know, as I say, the Platonists sometimes would define the point as a one having position, right? And they saw that the point involved more than the one, huh? But if the one were divisible, then the one having position would be a fortiori, divisible, right? So, I mean, they're quite clear that the one is indivisible, huh? So I say, all the problems are getting into because they're kind of, you know, comparing the numbers to what? The continuous, right? And they'll, you know, go all graphed and there's minus ones and plus ones and so on, and you can divide like you divide the line, huh? But you're really talking about the continuous, and you're talking about half of the one. You're talking about one line or one loaf or whatever it is. But the one itself, the abstract one, that's simpler than the point. It can't be divided. They're so accustomed, you know, to this way of proceeding, you know, that you can't do much with them. Now, the third objection was based upon the idea that like is known by like, huh? But the indivisible is more likely to understand. To third, it should be said that the likeness by which we understand is the form of the known and the knower. And therefore, it is not by the likeness of nature to the knowing power. that something is known before, but by what? Fitting in with the object. Otherwise, sight would know what? Sound more than what? Color, yeah. Because sight doesn't have any color, right? But it does have a sound, you know? Okay. But it doesn't have any color. At least the center part, if it did, everything would look the same as that color. Okay? But notice in regard to the subjection, you see, some might say, you know, our reason, as we argued before, is something immaterial, right? And which is more like the immaterial? Material or the immaterial? Yeah. Therefore, man should know the immaterial things before material things. See? Well, you don't know things by what? Their likeness to your knowing power, right? But by your knowing power, having a likeness of the thing known in it. Okay? And the likeness of the thing known, in the case of our reason, is taken from the what? Images, huh? And therefore, so likeness is something material. So we know material things by this immaterial power, known as reason, right? Long before we even know there are immaterial things, huh? And in Aristotle, when he's taking a place there in the fourth book of natural hearing, he says, it's a common opinion among the philosophers that whatever exists is somewhere. If it isn't somewhere, it doesn't exist. I ask my students, would you agree with that? Oh, yeah. Whatever is somewhere. If it isn't somewhere, it doesn't exist. Of course, to be somewhere is to be contained in some place, and this is a property of bodies. So what they're thinking, really, is that everything is a body. And that's all it is. And that's the way the human mind begins, huh? You could say our mind is, what, left to itself, right? It's kind of almost naturally materialistic, huh? It thinks that only bodies and what is in bodies exists. I remember, you know, a conversation between my cousin Donald, who was trained in philosophy, with his mother, who was a pious Catholic, you know. He was trying to explain to her that God has no body. And she just couldn't buy this, right? See? And of course, you know, you think about your own soul, right, huh? You know? Where will my soul be after I die, huh? Where? See? Well, if you're taking where in the strict sense, it won't be in any place. It won't be in place anymore. And I'm so used to living in some place, you know? All my life, I'm in some place, right? My study is some place. My books are somewhere. My tea is somewhere. My bed is somewhere. My car is somewhere. I'm somewhere always, right? Well, my soul won't be anywhere, you know? And of course, we never think about images. Of course, that's why we kind of deceive my imagination to think, you know, that whatever he is must be somewhere. It isn't somewhere. It doesn't exist. Very hard for us to rise above that, huh? But notice, you can give the same objection then here to this, huh? And say, well, you wish. If our understanding is immaterial as it is, immaterial things are more like it. Therefore, you know them first, right? Yeah. But because our understanding, right, is a power of our soul, right? And our soul is the first act of a natural body composed of tools, right? Our reason's own object is the what it is of something, what? Material. Okay? And then we try to know something that is immaterial, like the word immaterial indicates, right? We tend to, if we know it at all, to know it, what? Negatively, right? So we say God is immaterial. He's incorporeal, right? He's not a body, huh? Okay? So we think about a body, but we negate it of God, huh? And that's the way our mind knows God in this life, huh? It knows what he is not. See, when St. John talks there in the first epistle, I think it's chapter 3, verse 2, something like that, in a way he's talking about the Vedic vision, we shall see him as he is, right? Okay? Rather than this via, what? Negativa, huh? Which we use so much in theology. So when you show God is simple, you're showing really that he's not, what? Composed, anyway. That he has no parts, and so on. That's why Thomas is, you know, always very clear about, you know, when you talk about the distinction between the Father and the Son and the Holy Spirit. You can speak of a distinction there, but you should not speak of a division, right? A division would imply that this is a whole, God is a whole, and these are the parts of this whole, right? You see? Because division, in the strict sense of the word, is a distinction of the parts of some whole. The Father, the Son, and the Holy Spirit don't, aren't parts of God. They're distinct in a much different way, huh? We'll take a little break here before we do, maybe do another first article in this next question, okay? What our understanding knows in material things, huh? And it's going to be followed by the one about what it knows, what? In itself, right? Which would be 87, and 88 would be what it knows, those things above it, huh? So the first question is, whether our understanding knows singular itself? And the great Boethius says, a thing is singular when sensed and universal when, what? Understood, huh? So when I see a chair there, and it's an individual chair, a singular chair, isn't it? But now when I understand what that is over there, it's a chair, it's now become something universal. Because what a chair is, is something common to all chairs, right? I see you, right? I'm seeing an individual singular man, right? What is this? It's an animal with reason, huh? It's a man. That's something universal, animal with reason, a man, right? So when I sense you, you're singular, right? When I understand what you are, an animal with reason, I'm understanding universal, huh? So what the reason knows directly is universal, what it is, something sensed or imagined, huh? But is it in some way able to come back to the senses, right? And know the singular? Well, as one of the objections we'll be pointing out, we form statements about the singular, huh? We say Socrates is a man, right? George Bush is a man, right? Okay? And you have to know both things to put them together, right? So if reason forms a statement, not only that man is an animal, but that George Bush is a man, let's say, he must, and some know the singular, too, right? But Sarah Stout says by kind of what, coming back upon its origin rather than directly, directly it knows what it is, huh? And that's something universal, what it is of the triangle imagined or the man imagined, right? To the first, thus one proceeds, it seems that our understanding knows singular, huh? For whoever knows some composition, something put together, knows the extremes put together. But our understanding knows this putting together. Socrates is a man, right? For it belongs to it or it's of it to form this proposition or statement. Therefore, our understanding knows the singular, which is what? Socrates, right? Moreover, the practical understanding, right? Directs us in doing something. But actions are always... about the what? Singulars, huh? So the dentist is fixing up my mouth, my individual mouth, right? Therefore, he knows singulars, huh? Moreover, our understanding understands itself, but it is something singular. Otherwise, it would not have some act, for actions belong to singulars. Therefore, understanding knows the singular. Moreover, what a lower power can do, so a higher power can do. But the sense knows the singular, therefore much more does the understanding know the singular. But against this is what the philosopher says in the first book of natural hearing, physics, that the universal by reason is known as singular by sense. Okay? Thomas says, I answer, it should be said that the singular in material things now. That's important that he's saying in material things. Our understanding directly and first is not able to know. Okay? That's what he's saying there. It's important in those two words or adverbs. Directe and what? Primo, right? What our mind knows directly is the what it is that something sense to imagine, right? And that's something universal. That's what knows directly and first, right? Now, the reason for this is because the beginning or cause of singularity in material things is individual matter. And we talked about that a little bit before, right? Why can you have many individuals of the same kind in the material world? Yeah. Because you have enough glass here that you're going to have all these little panes the same, exactly, right? Okay, and why can you have many chairs here all the same? Because you have enough metal, right? Or if there's wood, wooden chairs, because you have enough wood, right? So it's some kind of matter, wood or metal or glass, as subject to quantity, right? It enables you to divide it into many individuals of the same kind, huh? That's why you can have many individuals of the same kind in geometry too, huh? Because you have quantity there, huh? Okay. But our understanding, as has been said above, understands by separating or abstracting the understandable form from this kind of matter. But what is separated from individual matter is universal? Whence our understanding directly does not know except the, what? Universals, huh? But indirectly and through a certain, what? Reflection meaning, like, coming back, right? Okay? Directly, it knows only the universal. But it can come back to the, what? Origin of its own act, huh? And by kind of reflection, it comes back to the singular. Indirectly and by certain reflection, those are Aristotle's words, is able to know the singular. Because as has been said above, even after it abstracts the understandable forms, is not able to understand and act by them except by, what? Turning itself towards images in which it understands the, what? Understandable forms, as is said in the third book about the soul. So even after you understand what a triangle is, when you actually want to understand what a triangle is right now, I will imagine a triangle, right? And I'll be understanding what it is of that triangle imagined, right? So I'm coming back to the origin, right? To the images which are the origin of my thought. Thus, therefore, the universal itself, the universal itself, it understands directly through the understandable form. But indirectly, the singulars of which they are, what? Of which there are images, right? And in this way, it forms this statement that Socrates is a, what? Man. Whence is clear the solution to the first. Incidentally, the word proposition, originally, it meant the premise of a syllogism. And that's where the etymology of it is. Pro position, right? It's placed for something, right? And then, due to custom, it became customary to call any statement a, what? Proposition, right? But I don't like that. But anyway, that's what happened. Okay? I'd like to call it a statement. Okay? So that's going to answer the first objection, he says. Because in some way, our understanding has to know the singular. You might recall the argument, you know, for the common sense. Remember that? We sense the difference between white and sweet. And the eye can't do that because it knows only white. And the sense of taste can't, what? Do it because it knows only sweet? And even the two together can't do it. But it's got to be one thing that knows both, right? So if we form the statement that Socrates is a man, or you are a man, right? Or this is a chair, right? This is a table. This is a glass. And we do form such statements, obviously, right? Then the one that forms a statement, which is reason that forms statements, must know the two things that are being put together in that statement. And since one of them is a singular, right? This chair, or Socrates, or Duane is a man or something, it must in some way know the singular, right? But it doesn't know it directly, right? Through its form, that it's received. But by turning back, right? To its origin, which is the, what? Imagination, huh? So it doesn't know it, it's like knowing it like this, right? This is the origin of it, right? And then what it knows directly is universal, and then by reflex motion, it comes back upon its origin. And that's the way it knows the singular, right? Indirectly, you know, okay? And that's why you say, you know, someone says to you, you know, if you ask me, what is Monsignor Dion like? Well, I can say a lot of things about him, but everything I say about him is something universal, huh? And any individual you want to describe, right? If you ask me, what is your mother like? Well, the only thing I would say about my mother would be something, what? Universal, right? Do you see that? I mean, unless I just pointed her, there she is, you know, you see? But then I'm, you know, back to my senses, huh? What can I say? What would you say about me? He's a man, okay? He's white, he's lost some weight, you know? But none of these things are, what? Peculiar to me, are they? Huh? He's a philosopher, thinks a lot, he drinks a lot. I know what you say, but the name, yeah, but tell me who this Wayne is, right? Well, he's a man, he thinks, he's white, hair is getting gray, or he's gray, isn't getting gray, right? These are all universal, aren't they? What can you say? No, there's something unique about each human being, but can you really express that, huh? You're going to be using universals to express it, huh? That's what you know directly. Thank you. Okay, now the second objection was saying that the practical intellect directs us to acting, but actions are about the singulars. To the second, it should be said that the choice of a particular thing to be done is as the conclusion of a syllogism of the practical what? Understanding, right? So the human body should be fed. This is a human body, therefore it should be fed. Okay, that's the kind of syllogism you have, right? But from a universal proposition directly, one is not able to conclude the singular except by medium of, right, some singular proposition that is taken up. Whence the universal reason of the practical understanding does not move except through a particular apprehension of the sensitive part as is said in the third book about the soul, right? Okay? So the doctor has universal, right? Gives the headache man an aspirin, right? This man has a headache. But he knows this man and his fever, or whatever it is, by his senses, right? So there's... He can't act without going back to his senses, huh? On you, right? Apply a cold washcloth to the feverish head. Ah, this is feverish, right? So we'll apply a cold thing. I have to go back to my senses, right? To complete this curing of you, huh? And that's the reason why, you know, our passions or emotions are so strong, huh? Because they're closer to our senses, huh? And so we may not apply the universal that we should, right? Adultery should be avoided, right? Or, you know, this is adultery, right? See, but you may not apply the universal to this particular case, right? Or you may apply, this is pleasant, rather than, this is adultery, right? And so, when a man chooses to do something like that, he's making a mistake, right? He's not applying what he should to the situation, huh? Yeah. But because the situation and what he does is singular, the senses have a great, what, role to play, right? Because they are the direct knowledge of the singular. Reason is not a direct knowledge of the singular. Reason is a direct knowledge of the universal. So the senses can dominate sometimes, right? But we do, huh? And because of emotion and so on, the right understanding of the universal may not be applied to this case in front of us. Now, the fourth one was saying that what the lower can do, the higher can do better. Well, to the fourth, it should be said that the higher power is able to do what the lower power does, but in a more eminent way. Whence what the senses know in a material way and concrete way, which is to know the singular directly, right? And also getting that word directe, right? This the understanding knows in an immaterial way and abstractly, which is to know the universal. That could be a little more expanded on, obviously. The senses as such don't know what even their objects are, right? Does the eye know what color is? No. Does the ear know what sound is? But reason is able to know what sound is or what color is to some extent, right? And so in knowing what something is, you're knowing the thing better in a way than the senses know it, huh? But as far as the singular such is concerned, the senses are knowing that directly, huh? And reason isn't, right? So when you drink the wine, reason knows more than the tongue or the sense of smell what wine is, right? What smell is that matter, right? But the sense of taste and the sense of smell know more the singular smell and flavor of this wine than the reason does, right? Reason knows only the universal. So we've got two three articles today. Maybe we can do the next three, you know? Next time. Two, three, and four, right? Okay. Say a little prayer. For our help. In the name of the Father, and the Son, and the Holy Spirit. Amen. God, our enlightenment. Guardian angels, strengthen the lights of our minds, order and illumine our images, and arouse us to consider more correctly. St. Thomas Aquinas, Angelic Doctor. Pray for us. And help us to understand all that you've written. So we're up to Article 2, I guess, huh? Question 86. To the second one proceeds thus. It seems that our understanding is able to know an infinity of things. For God exceeds all infinities. But our understanding is able to know God, as has been said above. Therefore, much more is it able to know all other infinities. Moreover, our understanding is naturally apt to know genre and species. But there are infinities of species of some genre. Dr. The second objection, right? Yes, yes, Dr. Yeah. For example, of numbers, right? And of proportions, huh? Ratios. And figures, huh? Three-sided, four-sided, five-sided. All those numbers, right? Therefore, understanding is able to know infinities. More, if one body does not impede another from existing in one and the same place, nothing prevents an infinity of bodies being in one place. But one understandable form does not prevent another from existing at the same time in the same understanding. For it is possible to understand many things habitually or in habit. Therefore, nothing prevents understanding from having in habit a knowledge of an infinity of things. Moreover, our understanding, since it is not a power of a material body, as has been said above, seems to be in some way an infinite, what? Power, huh? But infinite power is able over an infinity of things. It's capable over an infinity of things. Therefore, our understanding is able to know an infinity of things. It's a great fragment of Anaxagris. The first thing he says about the mind is that it's infinite. And Heraclitus had said this before him, right? And, of course, here are some signs that there's something infinite about the mind. It's always, what, learning something new, right? It doesn't seem to have any limit to what it can come to know, right? And it's always inventing something new, right? And if you look inwardly, if it knows universal, the universal is set of an infinity of things. So when I say that no odd number is even, I'm making a statement, in a way, about an infinity of things. But you have to specify in what way it's knowing that infinity. I mentioned the Vorbach there, the guy between Hegel and Karl Marx, huh? You know. He quotes some theologian saying the infinite is God. And then his minor premise, man's mind is infinite. Therefore, man's mind is what? God, right. Well, infinite is a word that has, what, many meanings, huh? And it's interesting, Aristotle, in the first book of the natural hearing of the so-called physics, he criticizes, um, beliefs, for mixing up two meanings of the word infinite, what, you know, has no beginning and no end. in time, with what has no, what, whose size has no limits, right? He's confusing those two senses. So, that's way, way back in the beginning of philosophy, way down here in the 19th century, have Feuerbach making the same kind of mistake, fallacy of equivocation, mixing up different senses, but of the same word, infinite. Now, again, this is what is said in the first book of the physics, that the infinite, insofar as it is infinite, is, what, unknown, huh? I answer, it should be said, that since a power or ability is proportional to its object, it is necessary in this way, that the understanding has itself towards the infinite, as it has itself towards its object, huh? Of course, we find out that the subject is the what it is of a material thing, huh? In material things, however, is not found the infinite in act, but only in, what, ability, according as one succeeds to another, as is said in the third book of the physics. And therefore, in the end, in our understanding, is found the infinite in ability in taking one thing after another. But never does our intellect understand so many things, but that it could understand, what, more, right? So it's like when you go through numbers, right? I can go on forever with the numbers, right? But I can never mention so many numbers, I can't mention still more, okay? And the children are very young, you know, Daddy, can you count to a hundred? Yeah. Wow. A little bit older, you know. Daddy, can you count to a thousand? Yeah. Wow. After a while, you realize you can always count to something larger. But our understanding, huh, in act or in habit, is not able to know an infinity of things. In act, it is not, because our understanding is not able, at the same time, right, to know except through the one form that it knows, huh? Okay? Remember how we're comparing the mind was like what? To the form which it understands, a little bit like the wax or the clay is to the shape it has. It can only have one shape at a time, huh? And so the clay that is in the shape of a sphere can't be in the shape of a cube at the same time. You can put it in the shape of a cube, but then it ceases to be in the shape of a what? Of a sphere. So you don't have two forms of the same kind in pure act, anyway, in complete act. In act, he says, not, however, do we that sense again, maybe, because our understanding is not able together at the same time in act to know more than, what? It knows through one species, huh? But the infinite does not have one, what? Species or one form. Otherwise, it would have the, what? Definition of a whole and what? Perfect, huh? Now this, you know, Thomas is basing himself a lot here upon Aristotle's consideration of the infinite in the physics, huh? So, for example, when we say that a straight line is divisible forever, huh? What does that mean? That you can actually divide it? Actually? As much as it can be divided? Is that what it means? No, we've gone through that before. Just be caught in here. If you have any mathematical lines, you have a theorem in geometry that you can bisect the line, right? Now, if you bisect the line and get two shorter lines, then since they have linked, they can be bisected too. Now, as you bisect the line, you're getting smaller and smaller lines. But, do you ever get a line that you don't cut and you're bisected into two shorter lines? No. Well, if you don't get two shorter lines, there's only two possibilities. You cut a line into two nothings, but something can't be made out of nothing. So, a line couldn't be composed of two nothings, right? Now, the other alternative, someone says, well, you cut a line and you get two points. And the points cannot be divided, huh? Okay? But that assumes that there could be a straight line put together from two points. and you're with the either-or syllogism we use to show that you can't make a line by putting together points, huh? Remember that? You know? One way that two things can touch is for part to touch part, right? One is for part of one to touch the whole of the other. One is for the whole to touch the whole or to coincide, right? And then you can speak of the edge touching at the edge, huh? Because the edge is not strictly speaking a part but the limit of the thing, huh? Well, the point has no parts, right? So, these two ways are impossible for points to touch, right? And is there any distance inside the point there, huh? So, you could distinguish between the point and the limit or the edge of it? No. The only way two points can touch is like when the whole of one touches the whole of the other. The only way two points could touch, therefore, would be to coincide. And if two points coincide, you have no more length than one point. There's no length at all. And if ten or a hundred or a million or infinity of points, like the mathematicians say sometimes, were to touch, the only way they could touch would be to coincide. If they coincide, they have no more length than one point. And therefore, you can't put together points to get a, what? A line, huh? Okay? So, the continuous is, what? Divisible forever, huh? But notice, in what way does that infinity exist, right? In the way that you could always go on and divide further, right? But you never complete the divisibility of the, what? Line, huh? So the divisibility of the line is never brought to, what? Complete act. It's never perfect or, what? A hole, as he says, huh? But it always consists in something, what? Further, right? Okay? Now, as Anne-Xeagrius pointed out, as you divide the line, right, you never come to a shortest line. But the number of lines keeps on increasing, huh? So every time I divide this, I get two, and now I got three, and now I got four, and so on. And, so if you can divide forever the straight line, and this is the way they define the continuous, what is divisible forever, then numbers can increase forever. But it's not like you ever, what? Completely dividing of the line. I can divide and subdivide and subdivide and so on, but it's always be more reduced to act but never completely made actual. So this is the potential? Yeah. So you never, you should never actually have an infinity of lines, do you? We define the continuous as that which is divisible forever. Okay? But you don't actually have the, what? The infinite, the infinity of lines there, right? You never complete that thing, huh? And therefore it is not able to be understood except by taking part after part, huh? As from its definition is clear in the third book of the physics. For the infinite is that of those taking its quantity, right? Okay? There's always something further, right? Extra to be taken, huh? Okay? So you could say this is always divisible further, right? And therefore, also the number is there always what? A greater number is always able, right? To be taken, huh? Okay? And therefore the infinite is not able to be known in act, right? Unless all its parts were what? Numbered, right? Which is what? Impossible, huh? Incidentally, in the Oxford translation of Aristotle, the English will read, you know, we'll be talking about an infinite number, huh? My old teacher, Kisraik, who forced me to learn some Greek, he says, Aristotle wouldn't speak of an infinite number. That's a contradiction in terms, huh? Look it up in the Greek, Dwayne, huh? And sure enough, of course, the word number is not there. The false translator, right, has put in a word. That doesn't, isn't in the Greek, huh? Okay? If something can be numbered, huh, then it's what? Not infinite. That's why Shakespeare will couple them, right? Countless and infinite, he'll say. If there's a number, there's a multitude, then that multitude is what? Limited, huh? I was thinking of an interesting objection, you know, in the tweet is on the Trinity there from, you know, St. Thomas objects these things. And whether there's only three persons in the Trinity. And the objection takes what is said in the Athanasian Creed, that God is what? Inmensus, right? Not miserable. Okay? He's infinite. And, well, here you're limited to just three persons. That's kind of interesting. Objection, huh? Because, you know, there's all kinds of things you have to understand about numbers there and what numbers mean in the Trinity, you know, huh? But I just got reminded of it here, right? Because of the fact that what can be numbered would seem to be, what? Limited, right? And how can the infinite be numbered, huh? Interesting objection, huh? And for the same reason, we are not able to, what? Understand the infinite inhabit. For in us, habitual knowledge is caused from, what? Some actual consideration. For by understanding something, we become, what? Knowing, right? So it's by understanding the, what, demonstrations of Euclid that I acquired this habitual knowledge that I now have of, what? Geometry, huh? Okay? So if I can't actually understand one of his demonstrations, I can't have an habitual knowledge of that theorem, can I? And so if I can't actually understand the infinite, I can't have an habitual knowledge of the infinite. Once we are not able to have the habit of infinite things by distinct knowledge unless we considered all the, what, infinites, by numbering them according to succession of knowledge, which is impossible. And therefore, neither in act nor in habit is our understanding able to know infinity of things. But it's so only in, what, potency, right? Okay? So if you compare our understanding to God, God's mind is, what, not limited at all to what he knows. But our mind is unlimited in the sense that it's always able to know something more. So, in a sense, the infinity of our mind corresponds to the fact that our mind is always incomplete in its, what, knowledge, right? So it's a gross confusion of two kinds of infinity that Forerbach is making, right? This is in Forerbach's little perverse work called The Essence of Christianity, where he maintains, you know, that God did not become man, but man himself is God. And that's one of the arguments he uses. But Karl Marx and Engels read Forerbach as young men and we're convinced by it, you see. It takes a little bit of pride to do that, huh? I remember in one class there when I was in college there, someone was describing the French positivists there, huh? Who were trying to substitute a religion of humanity for Christian religion. And, of course, they would have days set aside for the worship of humanity. Well, I just broke out laughing in class. Everybody else looked at it, it was a straight face, it just struck me so absurd to set aside days for the worship of humanity. I mean, the people seriously propose this sort of nonsense. But when you look at Karl Marx's in the preface to his doctoral thesis, he says explicitly that the human mind is the highest divinity. So, now let's look at the reply to the first objection, which is saying, we know that our mind is capable of knowing God, huh? Especially in the vision, huh? God is infinite, huh? Okay? Of course, God is infinite in a different sense, huh? To the first, therefore, it should be said, that has been said above, God is said to be infinite as a form which is not limited by some, what? Matter. But in material things, something is said to be infinite by the privation or lack of form of termination, huh? So, we speak of, eh, what? A line is limited by points, huh? So, if it had no end points, then the line would be, what? Infinite, right? He would lack something, right? Okay? But when you say infinite of God, it's a mere negation, right? Negating, what? The imperfection that would come to from him being in matter. Okay? When Aristotle is talking about perfect, the word perfect there in the fifth book of wisdom. And it distinguishes between the sense in which God is perfect, huh? And the sense in which Homer is perfect, right? Homer is perfect in his kind, huh? Homer is the perfect poet, huh? His plots, his characters, his diction, they're all there, right? Mozart is a perfect musician, right? But in some, what, genus, some particular kind, huh? Why God is perfect, right? Because he's lacking in nothing. Okay? It's not just that he's lacking nothing of his kind, some particular kind of thing, he's not limited to any particular kind of thing. You see that? That's the difference. So God is perfect in the sense of a form that is not, what, limited by matter, not limited by passive potency. Well, material things, to be infinite, means to be lacking in form, huh? And through form, that something is known. And because form by itself is known, matter without form is unknown, hence it is that the material infinite is in itself unknown. But the formal infinite, which is God, is in itself known. And only unknown to us on account of the defect of our, what, understanding. Which, in the present state of this life, has a natural aptitude for knowing, what, material things. And therefore, in the present, we're not able to know God except by material effects. So the first proof of existence of God is from motion of matter, right? You reason from motion to the dependence of motion upon a mover, right? And from the dependence of moved movers upon an unmover. That's the way we reason to God, huh? But in the future, this defect of our understanding will be taken away by glory.