Prima Pars
Lecture 31: God's Infinity and Its Distinctions

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In the name of the Father, and the Son, and the Holy Spirit, Amen. God, our light commit, 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. Help us to understand all that you have written. In the name of the Father, and the Son, and the Holy Spirit, Amen. Missed prayer, you know. You can say another, if not, if not, if not, if not, if not, if not, if not, if not, if not, if not, if not, if not, if not, if not, if not, if not, if not, if not, if not, if not, if not, if not, if not, if not, if not, if not, if not, if not, if not, if not, if not, if not, if not, if not, if not, if not, if not, if not, if not, if not, if not, if not, if not, if not, if not, if not, if not, if not, if not, if not, if not, if not, if not, if not, if not, if not, if not, if not, if not, if not, if not, if not, if not, if not, if not, if not, if not, if not, if not, if not, if not, if not, if not infinite, continuous quantity, or what, discrete quantity, okay? I think I mentioned how Thomas and the Summa Contra Gentiles are using the famous phrase of Aristotle, coerced by the truth, right? Without having a reason, Aristotle speaks in the first book of Nebuchadnezzar hearing that all the Greeks who thought about change tried to explain change by contraries, without giving a reason why one should explain change by contraries. He says, they all spoke as if coerced by the truth, right? Even without giving a reason. And Thomas says, you know, they all thought of the beginning as being infinite, as if coerced by the truth. But then when they finally realized that there couldn't be an infinite quantity, right? Then they realized that beginning has to be infinite in some other way, right? And eventually they come to the infinity of God himself. To the second one proceeds thus, it seems that something other than God is able to be infinite to its essence or nature, substance, right? For the power of a thing, the ability of a thing, is proportionate to its, what, nature, its essence. If, therefore, its essence or nature of God is infinite, it is necessary that his power be infinite. Therefore, he is able to produce an infinite effect. That's kind of a subtle way. Since the quantity of a power is known through its, what, effect, huh? Virtus in Latin, okay? Virtus in Latin, and Thomas, I mean, sometimes it has a sense not of virtue, but in the sense of, what, power and the, what, excellence of power, right? Moreover, whatever has an infinite power has an infinite, what, nature or substance. But the created understanding has an infinite power, for it grasps the universal, which extends itself to an infinity of, what, singulars. Like, I know what an odd number is, and that covers, what, infinite of things, huh? A potential. And when I say that no odd number is, is even, I'm talking about infinity of numbers, in a way. And so the first thing that, and Xavier says about the mind, is that it's unlimited or infinite. And Heraclitus had kind of anticipated that, right? You could never come to the end of the soul, he says. No matter what direction you travel, then, so deep is its, what, reason, huh? Therefore, every intellectual substance created is infinite, huh? And Thomas will admit that it's infinite in some way, right? You get into the Blessed Virgin, right? Is the grace of Mary infinite, and Thomas, I mean, Thomas, but the Pope's will in some way say that the grace of Mary is infinite, but not maybe in the fullest sense the way that Christ is infinite, but there's something unlimited. The only article that, what, the only article that you have on there in the Volta Logique is, the grace of Mary is of the hypostatic order. You know, it was talking about the universeality of the grace of Mary, huh, and the mediatrix of all grace. Moreover, the first matter, which some people call prime matter, what I call first matter, is other than God, huh? It has been shown. But the first matter is, what, infinite, huh? Therefore, something other besides God is able to be infinite, huh? But against this is that the infinite is not able to be from some beginning, as is said in the third book of the Physics. But everything that is apart from God is from God is from the first beginning. Therefore, nothing that is besides God can be, what, infinite, huh? So, I answer you, it should be said, that something apart from God is able to be infinite, what? And that's the pitch there. That same kind of distinction, it shows up again, right? We were saying it earlier when he was comparing being and good, for example, right? And that what is being simply is only good, secundum quid, and what is good, secundum quid, and what is good, secundum quid, simply without qualification, is only what? Being secundum quid. Yeah, yeah, yeah. And that kind of distinction, as I say, corresponds to the second kind of mistake outside of words, huh? So, understanding that kind of distinction helps you understand the kind of mistake, and seeing that kind of mistake being made shows you the necessity of understanding that kind of distinction. But it shows up a lot, right? And sometimes when I teach logic, I used to wonder, when should one distinguish these kinds of distinction, you know? It's kind of hard, you know, when you're in the logic of the first act, and you're first being exposed to logic, so. I usually leave it until you're talking about the four kinds of mistakes, you know, and then it's a little more, you get a little better handle on it. So, if, for if we speak of the infinite according as it belongs to matter, it is manifest that everything existing actually, or in act, has some form, right? And thus, its matter is limited by what? Form, huh? So the wood is able to be a chair, a table, a door, and maybe an infinity of other things, but it's what? By its form, it's limited to this table here, or this chair. Actually, one of those things. Yeah. But because matter, according as it is under one substantial form, remains in potency to many accidental forms, what is limited, simply speaking, to that one thing it has by the one substantial form it has, is able to be infinite, what? In some way, yeah. Well, it's always a little bit hard, you know, how to translate succulentum quid, right? We often say it in some way, but in some qualified way, in some imperfect way. As the wood is limited according to its form, but nevertheless is infant in some way, insofar as it is an ability for an infinity of different shapes or figures. If, however, we speak of the infinite according as it belongs to form, this is the distinction, right? He first spoke of infinite as pertaining to matter, right? And he said, well, matter doesn't actually exist except through form, and through form it's already limited, although it might still be infinite in accidental forms, right? Yes, in some way. Now he comes to the way in which a form is said to be infinite. If, however, we speak of the infinite according as it belongs to the form as opposed to the matter, thus is manifest that those things whose forms are in matter are simply what? Private. Private. Private. Private. Private. Private. Private. Private. Private. Private. Private. Private. Private. Private. Private. Private. Private. Private. Private. Private. Private. Private. Private. Private. Yeah. It's aggressive getting away from sleeping and giving a talk. Because if you have a form that's in matter, that exists in matter, it's contracted by the matter, right? If, however, there are some created forms not perceived in matter, but subsisting by themselves, and this would be the angels, right? As some think about the angels, right? And Thomas himself thinks that, of course. They will be, what, infinite, secundum quid, he says, insofar as these forms are not limited nor contracted by some matter. So in some way they are infinite. But because the created form, thus subsisting, has existence, but is not its own existence, right? It is necessary that its very existence be received and contracted to a determinate, what, nature. Whence is not able to be infinite, what, simply like God is, where his existence is not, what, limited to some nature that it's the existence of. Because it's not, because it's not, he is his existence, huh? Okay? I am, who am. Whence is not able to be infinite simply, huh? So it's hard to understand that kind of distinction, right? But you will see that kind of distinction over and over again, and gradually start to understand that kind of distinction a little bit better, and see that distinction being used in this particular, what, matter, right? Okay? But it comes up in the first divisions of being, right? The two main divisions of being are being into substance and accident, and being into act and ability, right? And substantial being is, we say, is being simply. And accidental being is being in some way, right? Okay? So when I came to be a geometer, I didn't come to be. But when I was generated, I came to be. So substantial being is being simply, and accidental being is being, we say, couldn't have quit until you select, right? In some, you know, qualified way, huh? Okay? Just like when I came in this room, I didn't come to be, that would, say, I won't cease to be, I don't think, anyway. I don't know, really, when I leave this room. But I will suddenly cease to be in this room, right? So if I have to qualify. And it's kind of interesting how, when we make a diminution sometimes, like a person's name, huh? You know, like a child tends to say, Daddy, you know? Or, you know, qualify it. You know, I had a girl, her name was Annette, you know? Annette means what? Little Ann, see? When she got older, she felt, for some reason, awkward about Annette, that she wanted to be called Ann rather than Annette, huh? You see? But notice how the addition there seems to, what? Yeah, I see. Just like you say, a goodie. Well, a goodie's good, but it's not the greatest good. Someone would call God a goodie, you know? Or wisdom a goodie, would you, you know? But maybe a little piece of candy or something that's a, a little cookie or something that's a goodie, you know? But that is kind of a, kind of a diminution of goodness, huh? And so, when I say, when I came into this room, I can't say I came to be. I have to add something, say I came to be in this room, right? So that's kind of a sign that we're seeing that it's not so simply, huh? Now, the other main division of being is being an act and being an ability, right? And so if I ask somebody, you know, are there chairs in this room? You say, yeah. Are there chairs in the trees out there? You'd say, no, right? And if you want to say there are chairs in the trees out there in some way, you'd want to qualify and say there's chairs in ability. There's something in the, you know, the chair in ability. You've got to put it that way. Something able to be a chair. But you wouldn't say there's chairs, period. You see? Because that would be saying there's simply chairs out there. Yeah, yeah. So being an act is being some fidgete there, and being in ability is being, say, clindum grid. Substantial being is being simply, you know, right? So right in the very first divisions of being, which is most universal, you have this distinction being used, right? Okay? And we saw that distinction being used in regard to the good as well, huh? In the early reading. Mm-hmm. And now we see it's being used in regard to the, what? The infinite. A little more particular, yeah? Now, the first objection of saying, well, God's got infinite power, so why can't he make an infinite thing, huh? He says, to the first, therefore, it should be said that this is against the definition of the made, that the very essence of the thing made be its own, what? Existence. Because it's existing being, you know, being by itself, that we see anything, is not created being. Once it is against the definition of the made as such, that it be simply and without qualification infinite. So just as, therefore, God, although he has an infinite power, is not able to make something, what? Made. For this would be, what? For contradictories to be at the same time. So he's not able to make something infinite simply, huh? When I was in grade school, that was always the thing they challenged the Catholic with, you know. Can God make a stone so big he could lift it, right? And if you say, yes, then there's something God can't do, lift the stone. And if you say, no, he can't make such a stone, then there's something he can't do also, right? So how can God be omnipotent? Most little minds do not handle this, you know, you see? When you talk about God's omnipotence, it doesn't extend to contradictories, right? Could God make a square circle? Well, not bad, but that's not a contraction of his power, because that's nothing. So, could God make something equal to himself? No. Could God make something infinite? Well, can I get this to be made, huh? And this is the question that comes up later on, you know. Can God make something that doesn't depend upon him for being? Well, no. If he could make something equal to him for being good. No. Now, the second objection is taken from the, what, reason having a power that seems to be, in a way, infinite. Oh, yeah, everything. Okay. The second, it should be said that this very fact that the power of the understanding extends in some way, right, to the infinite, proceeds from this that the understanding is a form, not in matter. That refers to my understanding soul. That's the anima intellectiva. But in English, it's the understanding soul. As opposed to the sensing soul, this beast you want to give me. And my wife's picking out plants. I talk about the souls, these plants here, you know, all around us. I don't know what you think of that, but anyway. I don't know what you think of it. I don't know what you think of it. I don't know what you think of it. I don't know what you think of it. I don't know what you think of it. I don't know what you think of it. You know, so the human mind is infinite. The infinite is God, right? Well, it's like you've never seen these distinctions in it all. And you make a mistake from not distinguishing between what is infinite simply and what is infinite succulent good. Moreover, the third objection, what about the first matter? Is that infinite? Well, the first matter does not exist in vera minitura. That's the Latin expression we'd say probably in English, in reality, right, or in the real world, but they use the expression in vera minitura, the nature of things. For the first matter does not exist in Rerum Natura by itself, since it is not a being in act, but in ability only. But nevertheless, even first matter, according as it is in potency, right, is not, isn't simply, but in some way, because its potency does not extend except to what? But natural forms, to an extent, to all forms, the forms that are the angels. But perhaps it's easier to see that it's not something existing by itself, but always through some form, and then it's always contracted, right? Okay? So, it's like the talk for, you know, talks about democratic man, and he thinks, I've got all these possibilities now I can do, you know? But you can't write down, you can't do law anyway, so you've got to be very limited in what you do. You need to do something very limited, and the infinity there is, well, it's a secundum quid, but it's still not very, actually. Not a big secundum quid, finally. Yeah, yeah, yeah, yeah. What the scripture says about the set not off in every direction. Hmm? Set not off in every direction. You can only walk one. Hmm. You can't walk three at the same time. Okay, now he's going to take up in the third and fourth ones, the infinity, as we first think of the infinite in terms of quantity, right? And, as you know, from the categories, Aristotle distinguishes two kinds of quantity, and they're usually called discrete and, what, continuous. And, in the categories, they're distinguished by the fact that in continuous quantity, the parts meet at a common, what, limit or boundary, huh? So, the parts of a line meet at a point, and the parts of a surface at a line, and the parts of a body at a surface, huh? But, in discrete quantity, the parts don't meet at any common, limit or body. So, the number seven, the two and the five, the three and the four, if we want to take it, they don't meet anywhere, you see? So, that's the distinction that you have in the chapter on quantity and how much in the categories. But then, in the natural philosophy, we learn that the continuous as such is divisible forever, right? We talked about that before, how we show that at least the mathematical line, right, can be divided forever. And, when you divide, you always get smaller lines, which can be divided again. And, the only way it could stop would be if you, what, cut each straight line into two nothings, and that's not really possible, is it? Because then it would be made out of nothing. Or, if you cut a line into two points, but then you would have made a line out of, what, points touching? But, if points touch, then you, what, coincide, and therefore have no more length at one point. So, there's no way to put points together without them touching, and therefore coinciding, and therefore having no length. So, you can't put together a line from points. So, when you cut a line, you don't end up with two nothings or two points, but two shorter lines, and invisible forever. Aristotle shows us for other continuous quantities, and sometimes he shows us for two together. Like, I think I mentioned how he takes the fact that some bodies are faster than others. So, the faster body covers the same distance and less time. And, in a lesser time, the slower body covers a lesser distance. But, that lesser distance would be covered by the faster body, even lesser time. So, using that, alternating, you can see that, what, time and distance are divisible infinitely. Absolutely, yeah, yeah. But, numbers are not divisible forever, huh? Okay. I'm actually mixed up modern. You think the one is continuous quantity, what they're kind of thinking of, right? But, the one is actually simpler than the point. So, you can't have half a point. And, so you can't take, you know, if you could take, you know, a half of three and get one and a half, let's say, right? Then, you could take half of three points and get one and a half points. And, you can't, huh? So, numbers are not divisible forever. And, that's why in the Eighth Book of Wisdom, right, Aristotle compares definitions to numbers, because they're not divisible forever. Not every, part of every definition can be defined, or needs to be defined, right? And, so you have two differences, right? Right. And, Thomas, you know, explains why the definition of the continuous is that which is divisible forever, is more appropriate than natural philosophy. Because, you're going towards the parts, and parts are like matter, and this is a science that talks about matter. But, the definition, what, of continuous is that whose parts made it a common boundary, is going towards, what, the whole. The, the unification of the parts that come into contact, right? And, to talk about the whole is like talking about the form. And, it's appropriate to, what, logic, huh? Because, logic is about form, not about matter. So, it's a very subtle thing, you realize how subtle Aristotle is, right? And, and, and I point it out to you, he says, only a guy from Laval would point it out, or say that, he says. I mean, we didn't say it first, Thomas said it, right? We just, we just, we just, try to read Thomas, you know, carefully, you know. He's explaining, you know, the simplicity in Aristotle, right? That he, he gives, uh, the definition of, the continuous is divisible forever, only in natural philosophy. But, in, in logic, he gives only the division, definition of the continuous is that whose parts made it a common boundary. And, he doesn't just, you know, do that, but, well, I'd do this one here, and this one there, or else, you know. I mean, he can recall the one from logic when he gets into that, into the actual philosophy. Then, he goes on to some other definition, which he doesn't give, in, in logic. But, that's, that's something we learned before, when you distinguish through natural philosophy and mathematics by the way they define. You see the difference here also in the way of defining it in logic and in natural philosophy. And, sometimes, they say, you know, that the real definition of man theology is imago dei, image of God. The definition of man as a two-footed animal, but has reason, would be more appropriate to the philosopher, to natural philosophy, right? No feathers. What? No feathers. Yeah. Yeah. But, what do you say, the enemies are playing with you, they pull the feathers off the chicken and throw it on the wall. Here's a man, here's a man for you. So, he's going to take up, first of all, whether it's infinite, according to what? Continuous quantity. To magnitude is the word for, used for continuous quantity. And then, he'll talk about what? Multitude in Article 4. When Aristotle talks about the infinite, he's usually thinking of the infinite in quantity, right? And what way it exists or it doesn't exist. To the third one proceeds thus. Thus, it seems that it's possible that there'd be something infinite in act, according to magnitude or continuous quantity. For in the mathematical sciences, there's not found the false. Because there's no lie in those abstracting, as Aristotle says in the second book of the physics, huh? Now, we remember that particular passage there, you know, where Aristotle is touching upon the central question of philosophy. And you define in geometry without matter in the ordinary sense, anyway. But outside the mind, sphere doesn't exist without some kind of matter. And Plato thought that the way we know must be the way things are, knowing truly. So, if we're truly knowing sphere and separation from clay or marble or whatever you might find in the sensible world, then it must truly exist in separation. And Aristotle says, no, no. And there's no falsity in self-stracting. So, he's kind of quoting this. But the mathematical sciences use the infinite in magnitude for the geometry says in the demonstration, let this line be what? Infinite. Therefore, it is not impossible that there be something infinite according to what? Magnitude, huh? But maybe that's just a way of talking. Let it be as long as we need it to be, right? But it's a way of saying, huh? I was reading the Summa Kanjian, too, this morning, you know. And the part of the Holy Spirit there and the... The objections, you know, the Macedonians who didn't think that the Holy Spirit was God and so on. And all kinds of, you know, scriptural texts they misunderstand, you know. But one is, don't sadden the Holy Spirit, you know. St. Paul says, well, to be sad is, you know, passion and undergoing, and God doesn't undergo anything. So, you know, but this is being understood metaphorically, right? All kinds of ways, you know, but there's other ways in scripture that couldn't be misunderstood. And you really need the Magisterium, the Church, and so on, to understand these things properly. But there are other, to a less extent, little ways of speaking that have to be understood, huh? I'm always bothered, you know, by our saying, you know, that the first cause is the cause of all things. We didn't say that, right? God isn't a thing, so. Well, he's a thing, yeah. Yeah, he is. Yeah, yeah, yeah, but they need to be a cause of himself, see, you know. And we had some kind of clumsy say, he's a cause of all things except himself, you know. You kind of mean that when you say he's a cause of all things, right? You don't mean he's a cause of himself, right? But there's a certain imperfection of speaking in some way, right? You know. In scripture, you see it even more because, you know, they'll take the passage, you know, no one knows the father except the son, and vice versa, right? You say, well, there's a father then, doesn't know himself, you see. And he just took the words, you know, you can understand those, you see. And Thomas says, well, scripture speaks this way, right? And the things that belong to them by reason of the divine nature are to be understood when you say it. It's even if you say it about just one of them, that no one knows the father except the son. But that pertains to the divine nature, so it's still the other one. But that's the kind of way of speaking that scripture has. Or sometimes God will be said to do something because he makes it known. Now I know that you love me, you know, Abraham or something like that, right? And Thomas says, well, now I've made known that you love me, right? But I knew already that you love me. But I mean, you just take the way of speaking, you can see how the heretic can argue from that, you know. And then Thomas has to go through and answer all these things and so on. Well, it's making, you know, something like that, but not. More of that which is not against the definition of something is not impossible to belong to it. But to be infinite is not against the definition of magnitude. But rather limited and unlimited, or to speak English, or finite or infinite, to speak Latin, seem to be passions or properties of what? Quantity, huh? Therefore it is not impossible for some magnitude to be what? Infinite, right? Moreover, magnitude is divisible forever, right? For thus the continuous is defined as what is divisible forever. It is clear in the third book of the physics, huh? But Aristotle, you know, really shows this in the sixth book, huh? You know, that's where he shows it, but he first mentions it maybe in the third book. But contraries are naturally apt to come about about the same thing. Since therefore to division is opposed addition and to diminution and growth, it seems that magnitude can increase forever. Therefore it is possible for there to be an infinite what? Magnitude, right? And, you know, you're talking about putting the hexagon in a circle, right? Well, in book four you have these inscribing and circumscribing theorems, right? So you can inscribe a square in a circle and circumscribe a square around a circle, and vice versa. Inscribe a circle in a square and circumscribe one around. So they keep on getting bigger and bigger and bigger, right? And smaller and smaller and smaller as you inscribe and as you circumscribe. So, it seems like you can go on in one direction and go on in the other direction, right? Moreover, motion and time have quantity and continuity from the magnitude over which the motion goes, as is said in the fourth book of physics. So actually in the sixth book when he takes up the continuous, he talks about the magnitude being continuous, the motion down the road being continuous, and the time it takes being continuous, right? Okay? He shows all three of them, huh? So motion and time have quantity and continuity from the magnitude over which the motion goes. But it is not against the definition of time and motion that they are very infinite. Since each thing, what? Each indivisible noted in time and in circular motion is both a beginning and an end. Therefore, it is not against the notion or definition of magnitude that it be, what? Infinite. Surprised I didn't get that other argument, you know. People will say, you know, they asked one of the Greek philosophers, an example of something that always is. The way he says time always is, right? Because how could there have been a time when time didn't exist? Augustine raises this problem again, you know. Heisenberg quotes Augustine, you know, and so on and so on. So it seems that there can't be a time when time wasn't, because then there still was time, right? And will there be a time when there is no more time? Maybe there wasn't time at that time. But I remember when my children were little, you know. Sometimes, you know, you have a book of religious pictures, but not necessarily by a Catholic or, it could be by a Catholic, but famous paintings, you know, different biblical scenes and so on, and you kind of use it to kind of like a storybook. Long time ago, and a time before there was any time. That's when all the books I get, you know, I, I, I... But against this is that every body has a surface. But every body having a surface is, what? Limited. Because a surface is a limit of a limited body. Therefore, every body is limited, and the same thing can be said about a surface and a line. Nothing, therefore, is infinite in magnitude, huh? Okay, and the first thing Thomas does is going to distinguish between infinite in, what, one's nature or substance and infinite in one's, what, magnitude or size, right? They don't mean the same thing. I answer it should be said that other, is it to be infinite in one's nature, right? And in one's, what, magnitude, right? For giving, let it, if it be given, that there was some body, right, infinite in magnitude, as an example, fire or air went on forever, right? Nevertheless, it would not be infinite in its, what, nature. Because its very nature would be limited to some, what, species through some form, and to some individual through matter. And therefore, it being had from what has been said before, that no creature is infinite in its essence or nature, it still remains to inquire whether something created is infinite in its, what, magnitude or size, huh? Okay? So what I am might be limited, right? But could I be unlimited in my size? Okay? So it should be known, therefore, that body, which is a complete magnitude, now why is it called complete magnitude? The length, width, and what? Depth, right? Is taken in two ways, huh? Mathematically, according as there is considered in it, only, what? Quantity, huh? And naturally, according as there is considered in it, matter and form. So the natural philosopher talks about, what, a body is thinking of something composed of the first matter in some form, right? When a mathematician talks about line, angle, and body, and so on, he's just talking about quantity, right? And about a natural body, that it is not able to be infinite in an act, is manifest, he says, huh? For every natural body has some substantial form that's determined, huh? Since, therefore, to a substantial form that follows the accidents or the properties, accidents there are not necessarily taken as opposed to properties, right? It is necessary that to a determined form there follows determined accidents, among which are quantity. 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So I'll first bring it out in the ninth reading there of the first book of physics, right? We argue this against the Anaxagrosis. If the parts of bodies like flesh and blood and bones can get smaller and smaller, then the whole animal can get smaller and smaller, right? But in nature we see that the whole animal doesn't have just any size or limits, which is found there for the parts of that, right? So it seems to be, because of the kind of animal or plant it is, it has a definite, what, limits as to how big or how small it is. So the ant is not as big as the elephant, let's say, thank God. And I dislike the ants as it is, you know. All you need is one termite at the end of your house. Yeah, one bite. But again, the elephant is not as small as the ant. Once it is impossible that some natural body be, what, infinite, huh? Okay. Now, this is also clear for motion. This is more the way that Aristotle shows it, really. Because every natural body has some, what, natural motion, right? But an infinite body is not able to have a natural motion. Neither one in a straight line, because nothing is moved naturally by a, what, straight line, straight line motion, except when it is outside its place, right? Which could not happen to an infinite, right? It's interesting that the older physics are, where the earth, the earth, the earth, the earth, the earth, the earth, the earth, the earth, the earth, the earth, the earth, the earth, the earth, the earth, the earth, the earth, the earth, the earth, the earth, the earth, the earth, the earth, the earth, the earth, the earth, the earth, the earth, the earth, the earth, the earth, the earth, the earth, the earth, the earth, the earth, the earth, the earth. The earth, the earth, the earth, the earth, the earth, the earth, the earth, the earth, the earth, the earth, the earth, the earth, the earth, the earth, the earth, the earth, the earth, the earth, the earth, the earth, the earth, the earth, the earth, the earth, the earth, the earth, the earth, the earth, the earth, the earth, the earth, the earth, the earth, the earth, the earth, the earth, the earth, the earth, the earth, the earth, the earth, the earth, the earth, the earth, the earth, the earth, the earth, the earth, the earth, the earth, the earth, the earth, the earth, the earth, the earth, the earth, the earth, the earth, the earth, the earth, the earth, the earth, the earth, the earth, the earth, the earth, the earth, the earth, the earth, the earth, the earth, the earth, the earth, the earth the earth, the earth, the earth, the earth, the earth, the earth, the earth, the earth, the earth. You never succeed, right? Unless one would never arrive at the place of another. Kind of subtle, right? So the second argument is more dependent upon the older view of the world, right? It's hard to know sometimes, you know, what's going on in modern physics, huh? Because, you know, they'll speak of a body moving in a straight line in uniform speed, right? It's not really changing, but staying the same. It seems like it would be at rest. Yeah, yeah. And so they'll say, you know, body in the absence of external forces, it means you didn't rest in uniform motion to stay in line. And therefore, you only need something else when you're going to disturb the thing, speed it up or slow it down or stop it or something like that. So when you consider it to be a motion, it depends upon a mover. When you consider it not to be a motion or a change, but remain the same, right? Then, you don't seem to need a mover, right? But you're not considering it as a motion anymore. But to consider a motion as not a motion is a fiction, right? So what you have here is a fiction, but maybe a useful fiction, right? But why is this fiction useful, right? Well, it's a little bit like, you know, they say, even Thomas talks about this, huh? When the astronomer is calculating some things in the sky, he can consider the earth to be a, what? Point. And you draw the lines down to the point, huh? Well, is the earth to point? No. This is a fiction, right? But a useful fiction, right? And for some reason, in this particular case, you can, what? Ignore the difference, right? Because it affects in no way, right? Or no noticeable way, I should say, right? Your calculation of the parallel axis, something like that, the distance between these things. And when they talk about, you know, bodies, you know, going around, so they'll reduce them to a point, right? That's kind of a fiction, right? But it seems to be a useful fiction, right? So, is it really a point of body? I don't think so. Is moving forward at a uniform speed state the same? Really, I don't think. But it seems to have been useful to do this, you know? So, you've got to, you know, it's kind of a weird thing, a weird thing. Like the North Pole and the South Pole. Yeah, yeah, yeah. I think I mentioned how the world historian there, McNeil, you know, he divides the world history and so on. Well, he speaks of the fictitious sharpness of historical dates, but the historian has to do that, right? Yeah, I would just say, all I could say is a blur, you know? It just, you know, he could say anything, you know? So, it's useful to say when the modern world began, 1492 or something, 1500 or, you know? And, but when did the automobile, you know, replace the horse and bug, you know? It was not a definite thing, but. So, you've got to be aware of these useful fictions, huh? But the first argument is not so dependent upon the, what, older physics, right? That's kind of interesting, huh, that Aristotle, in the third book of the physics, right, he argues there's not an infinite body, just assuming that there's, what, there's these bodies down here, right, that the Greeks admitted. And then when he gets into the book of the universe, he repeats the argument, because he now knows there's some other things that he's had to get into account, right? That's kind of strange, he used to do it twice, you know, like that, huh? And there, in a sense, he's determining the way things are using what's accepted by all his contemporaries, right? But he thinks there's something besides what all his contemporaries have in mind, and then he considers the question again. So, the very subtle way Aristotle proceeds, huh? Thomas Aquinas, you know, notes that Aristotle will give examples sometimes, right, that are acceptable to his predecessors, even though he thinks the example is something, what, false, right? Okay? And, but it illustrates the point, and then maybe later on he won't, because he determines the truth, huh? So, and I first remember Thomas pointing this out, to be in Nicomachean Ethics, Aristotle was talking about different arts and science at different ends, right? And so the end of the military art is victory, you know. The end of the household science is wealth, he says, right? Well, of course, later on, the first book of the politics, he shows us that's not the end of the household science, right? But that was a common opinion, right? And so he just, you know, takes it, huh? Sometimes I'll take water and it's H2O. I don't even know myself, I mean, it is. It's just, you know, I say something about the proton-electron and the students, you know, because they know that this will help to get across the idea. But I've never been trying to prove it from that example. It's just illustrated. And so it's like your style of ethics, you know, saying that the mean is not the same for all of us, right? But what you require and I require to eat may not be the same, right? Depending upon our size and our occupation in life, you know? You've got the example of my way to hoax every day, you know? I wasn't reading a by the way to hoax every day, but obviously the mean for him is not the same as for us, right? It makes it very clear, for example, you know? But he's not using my way to prove the point, but kind of to illustrate it, huh? So that's about the natural body, those first two arguments, right? Now about the mathematical body, also there's the same, what, argument. Because if we imagine a mathematical body existing in act, it's necessary that we imagine it under some form, right? Because nothing is in act except through its, what? Form. Hence, since the form of the quantified as such is figure, it is necessary that it has some figure when you imagine it, right? And thus it will be finite. For that is a figure, as Euclid says, which is what? Comprehended by limit or limits, huh? In case of a circle you have one limit, in case of a square you might have four limits, right? Mm-hmm. Okay. I think my brother Mark has pointed out about, you know, they sometimes speak of the, what, the parallel postulate in geometry, right? It's not really parallel postulate, it's parallel lines are lines which extend forever when they ever meet. Well, can you imagine lines extend forever, never meeting? No, the line you imagine will be, what, finite, huh? So what actually Euclid says is that if a straight line falls upon two lines and makes, what, angles less than two right angles, those lines extend will meet, right? Well, you can imagine two lines meeting. But you can't imagine infinite lines in their infinite extension, right, huh? Mm-hmm. Okay. So what you imagine is going to be, what? What? Something finite, right, huh? Okay. That's the way he does it. Now, the first objection was taken from, let this line be infinite, you know, extend it away. To the first, therefore, it ought to be said that the geometer does not need to take some line to be infinite in act, but he needs to accept, what, some line that's finite in act, from which he's able to subtract as much as he needs, right? Mm-hmm. And this he calls a, what? Infinite. Yeah, okay. It's the same way of speaking, you know, huh? Because I can extend this line as much as I need to, to have a sort of like meter or something, right? So it doesn't mean really infinite, right? But that's kind of the way we, you know, partly in the way of speaking there, right? Mm-hmm. Okay. Okay, the second objection says it's not against the notion of magnitude to be infinite, huh? To the second, it should be said that although infinite is not against the definition of magnitude in general, nevertheless is against the, what? The notion of, what? Any species of it, any particular one, huh? It's against the notion of, what? By cubit magnitude or a tricubit, huh? Or a circular or a triangular and similar, it's against any particular one. But it's not possible for something to be in the genus that is not in some, what? Species. Hence it is not possible for there to be some infinite magnitude since no species of magnitude is infinite. I don't know, I don't know. It's a puzzled argument a bit. Kind of inductively from the particulars to the general? Well, he's saying no particular magnitude is infinite, therefore there can't be this infinite in the genus, right? The third objection, talking about the infinite divisibility to the continuous, well, why can't it go in the other direction then, right? To the third, it should be said that the infinite that belongs to quantity holds itself on the side of matter. For through the division of the whole, one exceeds to the matter. For the parts have themselves in the notion of, what? Matter. I mentioned that in the chapter on the four kinds of causes there in the physics or in metaphysics of that matter. Aristotle will first distinguish the four kinds of causes, then give the three corollaries, then he comes back to the four kinds of causes and says, we can understand these in a very general way, so that all parts from which the thing is put together could be considered to be, what? The matter? When he first talks about matter, he's talking about the wood of the table or the silver of the cup or that sort of thing, the bronze of the statue, right? But matter is that from which something comes to be existing within it. And that seems to fit the parts that are put together to make some whole, right? It comes to be from those parts and they're inside of it. So all parts are like matter, right? And that's why this definition, as we were saying earlier today, the definition of the continuous is that which is divisible forever, is kind of looking at it in terms of its parts, right? And therefore looking at it in terms of what? Matter rather than form, right? By the definition and the categories, it's talking about how the parts come together to make a common boundary and therefore speaking more of it as a form or as a whole, right? So the parts are to the whole, like matter is to what? Form, right? And so we can even say, you know, the soldiers are the matter of the army, okay? Or the father and the mother and the children are the matter of the family or something like that, huh? Or the baptized are the matter of the church or something like that, right? Those are the parts of which this thing is put together, huh? So he says, The infinite that belongs to quantity holds itself on the side of matter. For through the division of the whole, one, what? Approaches matter, to matter. For the parts have themselves as the definition of matter, right? Or in the definition of matter. But through the addition of parts, one, what? Approaches the whole. Approaches the whole, which has itself in the notion of a form, right? That's a proportion, as I say, Aristotle gave there. Parts are to the whole as matter is to form, right? Mm-hmm. And therefore there is not found infinite in the addition of magnitude, but in the division, what? Only falls upon matter. Mm-hmm. That goes back to the distinction even of the categories, huh? Where quantity falls upon matter, and quality upon what form? Form, yeah. It's interesting. Because the understanding is, infinite, secundum quid would be in quality, right? Mm-hmm. Now, motion and time are not, as a whole, an act, but successively, right? Mm-hmm. Once they have ability mixed with act, but in magnitude as a whole is an act. Mm-hmm. And therefore the infinite that belongs to quantity, oh, she didn't have some games, she's there. Yeah, okay. Okay, therefore the infinite that belongs to quantity, and holds on the side of matter, is repugnant to the, what? Totality of magnitude, but not to the totality of time or motion, for to be in potency or in ability belongs to, what? Matter. So motion and time are like matter, huh? Divisible forever, huh? And not entirely there. Mm-hmm. My walking... The home is not entirely there, or here, or anywhere. Why do you like to see during Article 3 and 4? Well, he wants to, well, you can say maybe two things. He wants to show that nothing else is infinite in the way God is infinite, right? But also you might say he wants to show, perhaps, the sense in which God is not said to be infinite, huh? Okay. And sometimes you'll find Thomas saying, it's not so explicit here maybe, but that infinite said of a line, if you speak that way, infinite would be kind of a privation or a lack. It's not having limits that it could have. Now, maybe that's not even possible to not have the limits that you should have, but if you don't have the limits you should have, that's not simply a negation, but it's a what? A privation or lack, see? But infinite said of God, is that a privation? It's a non-being of something he's able to have and should have? That doesn't mean that. Infinite is merely a what? Negation. Okay? A negating of God, the contraction that would come from being a form in matter, and even the contraction that would come from your existence being contracted to some nature other than itself. So, you're simply negating something that God is not able to have either, that alone should have, right? So, Thomas, you know, we'll say it's pointed out. So, in a way, we have both those things in mind, right? That nothing else is infinite in the way God is, and which are also, in a sense, touching upon the ways in which God is not, what? Infinite, huh? Because we do speak of other things as infinite. Yeah. Yeah. And sometimes, like, wasn't it back here when he's talking about God not being a body, right? And you had, in the scripture here, question three, article one, yeah. Whether God is a body, and they're talking about God as being a Chelsea or Chiloist. What should you do, right? He's deeper than the hill, and, you know, he's longer than the earth, right? Okay. Well, if you understood that as not being metaphorical, but said property of God, right? Then what would it mean to say God's infinite? Yeah, yeah. And some people understand God being everywhere as if he's kind of spread out everywhere, right? Yeah. What? He sits around the house. Yeah, yeah, yeah. And, you know, it's kind of this puzzling thing in Sir Isaac Newton, huh? He calls space, which he thinks is infinite, extending, you know, on her. Sensorium, the sensorium of God, right? I don't know, like, what the heck he means by that, right? You know? The sensorium. Sensorium, yeah. Like, well, it's the sensorium of God, right? But, I mean, I don't know. He's a little confused there, but you're thinking of God somehow, right? Yeah. Everywhere in the way that space is thought to be everywhere or something, you know? Kind of extended out there, you know? So, he wants to eliminate these senses of infinite from God, as well as the sense of which he is infinite. See, in the Summa Contra Gentiles, he takes up the infinite last of everything. And so, he's shown both that God is not a body, it's altogether simple, and therefore, you've eliminated him being infinite in the sense of a body going on in space in Newton. And he's also shown that God is one before he shows the infinite. Here, the one will be the last thing, right? And therefore, he can't be an infinite multitude either. He can't be infinite in the way they speak of an infinite number or something, right? Infinite multitude, huh? So, he eliminates the two kinds of infinity that people might attribute to quantity, that a body extends in length and width and depth without end, right? And that there's an infinite multitude, right? And then he slows down to what he does here in the first article, to determine what way God is infinite, right? It's not the infinity that some people attribute to quantity, right? It's eliminated both of those possibilities. There's no multitude here, there's just one God, and there's no extension because he has the length, no width, no depth, okay? Or even position the continuous like the point has, okay? But here, it's kind of like, you know, he's already shown the way in which God is infinite, and then he's showing other things are not infinite. But I suppose you might say that kind of a secondary thing is to show that, what, God is not infinite in these other ways that things are claimed to be infinite, right? Okay. We take a little break now before we go on to the multitude here.