Prima Pars
29. Summa I, Q7, Articles 2–3: Can anything besides God be infinite, in essence or in size? (Simply vs. in some way, first matter, and useful fictions in physics)
Class of 2006-04-06
https://berquistcourse.com/course/theology/10-prima-pars/029-summa-i-q7-articles-2-3-can-anything-besides-god-be-infinite/

[0:00] Shall we pray? 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. Saint Thomas Aquinas, angelic doctor. Pray for us. Help us to understand all that you've written. In the Name of the Father, Son, Holy Spirit. Amen. Here he comes. Mister Pray, Missed prayer you know, you can say another.

[0:37] It's not a sin, honest. Deo gratias Okay, you're up to the second article in question seven, if I believe right. And the first article was whether God was infinite, right? Now, whether something other than God is able to be infinite in its essence or its nature, right? And then you have the two articles about quantity there, whether infinite, continuous quantity, or what discrete quantity, huh? Okay.

[1:14] 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 Natural 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 the all spoke as if coerced by the truth, right?

[1:42] Even without giving a reason, and Thomas says, you know, the all thought at the beginning as being infinite, huh? As if quasi a veritate 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.

[2:09] The second one proceeds thus: It seems that something other than God is able to be infinite through its essence or nature, or substance, right? For the power of a thing, the ability of the thing, is proportionate to its what nature, its essence. If, therefore, the essence or nature of God is infinite, it is necessary that His power be infinite. Therefore, He's able to produce an infinite effect.

[2:42] That's kind of a subtle way. Since the quantity of a power is known through its what effect, huh? Okay. Virtus in Latin and Thomas means sometimes it has a sense not of virtue but in the sense of what power and the what excellence of power, right?

[3:04] 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? Potential. And when I say that no odd number is is even, I'm talking about infinity of numbers in a way.

[3:37] And so the first thing that Anaxagoras 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 in, so deep is its what reason, huh?

[4:00] Therefore, every intellectual substance created is infinite, huh? 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, that Thomas, but the popes 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 one article, but the only article beyond there in the Voltaire logic is the grace of Mary is of the hypostatic order.

[4:32] You know, was talking about the universality of the grace of Mary, huh? The mediatrix of all grace. Moreover, the first matter, which some people call prime matter, what I call first matter, is other from than God. Huh? Has been shown. But the first matter is what infinite, huh? Therefore, something other besides God is able to be infinite, huh?

[5:02] 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 a first beginning. Therefore, nothing that is besides God can be what infinite, huh?

[5:25] So I answer: It should be said that something apart from God is able to be infinite. What? Secundum quid. And not simpliciter That same kind of distinction shows up again, right? We saw it earlier when he was comparing being and good, for example, right? And 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.

[5:54] Being secundum quid. Yeah, yeah, yeah. And that that kind of distinction, as I say, corresponds to the second. Kind of mistake outside of words,

[6:09] so understanding that kind of distinction helps you understand that 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?

[6:26] 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, in the logic of the first act, and the first being exposed to logic. So I usually leave it until you're talking about the four kinds of mistakes, you know, and it's a little more you would get a little better handle.

[6:52] 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, right?

[7:23] This chair. 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. It's always a little bit hard, you know, how to translate secundum quid, right? We often say in some way, but in some qualified way, in some imperfect way.

[8:03] As the wood is limited according to its form, but nevertheless it's infinite in some way, insofar as it is an ability for an infinity of different shapes or figures.

[8:17] If, however, we speak of the infinite according as it belongs to form, this is a distinction, right? He first spoke of infinite as pertaining to matter, right? I mean, so when matter doesn't actually exist except through form, through form it's already limited, although it might still be infinite in accidental forms, right? Yes, in kind, infinite in some way. Now he comes to the way in which a a form is said to be infinite.

[8:44] If, however, we speak of the infinite according as it belongs to the form. form as opposed to matter, thus it is manifest that those things whose forms are in matter are simply what infinite. Yeah. yeah. That's what Kierkegaard says, right? You know, positive relationship with a woman will make you very limited.

[9:14] (He broke off his engagement. I think you know. he was too confiding, you know. My mother used to joke, you know, because they come back, and my mother and father may go to bed, and my mother would be telling my father the little things that happen around the neighborhood, you know, and my father.

[9:35] Well, she realized it helped him to get to sleep, you know. So she didn't really mind when he fell asleep when he's telling me the little things that happened but it kind of attracts to the here and now. I'm sure maybe if you maybe if you or Mark tried telling her a few a few things that happen in philosophy, she'd end up doing the same thing. That's true that's true yeah yeah. Yeah, it's interesting getting away from sleep when you give a talk

[10:10] Because the if you have a form that's in matter, it exists in matter, it's contracted by the matter, right? Okay. If, however, there are some created forms not received in matter, but subsisting by themselves, this would be the angels, right? As some think about the angels, right? Okay, and Thomas himself thinks that first. They will be what infinite secundum quid he says, huh?

[10:42] In so far 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? 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, who his existence is not what limited to some nature that's existence of.

[11:21] 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? And

[11:38] but you will see that kind of distinction over and over again, and gradually start to understand that that kind of distinction a little bit better, and see that distinction being used in this particular what matter, right? Okay. But it comes it comes up in the 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?

[12:04] 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 secundum quid, he is a Latin, right? In some, you know, qualified way, okay. Just like when I came in this room, I didn't come to be.

[12:34] That would saying I won't cease to be. I don't think anyway. Don't know really when I leave this room, but I will suddenly cease to be in this room, right? So I have to qualify. And it's kind of interesting how when we make a diminution sometimes, that can a person's name, huh? Like a child sometimes

[12:59] to say daddy, you know, you know, qualified. You know, I knew a girl. Her name was Annette. You know, Annette means what? Little Anne. See, when she got older, she felt, for some reason, awkward about Annette, and she wanted to call Anne rather than Annette. You see, but but does how how the dictionary seems to what? Yeah, I see. Just like you say, a goody. Well, goody's good, but it's not the greatest good.

[13:34] 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 little cookie or something that's a goody, you know. But that's kind of a kind of a diminution of goodness.

[13:48] 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 it's kind of a sign they'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?

[14:09] You say, yeah. Are there chairs in the trees out there? You'd say no, right? And if you wanted to say there are chairs in the trees out there in some way, you'd want to qualify and say there's chairs and ability. There's something in the, you know, the chair and ability. You have to put that way. Something able to be a chair, but you wouldn't say there's chairs.

[14:28] Period. You see, because that would be saying there's there's simply chairs out there. Yeah, yeah. So being an act is being simpliciter and being an ability is being secundum quid. Substantial being is being simply, and the other, right? So, so right in the very first divisions of being, which is most universal, you have this distinction being used, right? Okay.

[14:55] And we saw the distinction being used in regard to the good as well, huh? In the earlier reading. Now we see it's being used in regard to the what? The infinite, a little more particular than.

[15:11] Now, first objection of saying, "Well, God's got infinite power, so why can't He make an infinite thing?" Huh? He says, "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 existing

[15:41] 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 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?

[16:12] When I was in grade school, that was always the thing they challenged a Catholic with, you know? Can God make a stone so big He can 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.

[16:36] You see. Well, you talk about God's omnipotence. It doesn't extend to contradictories, right? Could God make a square circle? No, but that's not a contraction of His power because that's nothing.

[16:56] So could God make something equal to Himself? No. Could not God make something infinite? Contradictories being made. And to make the question that comes up later on, 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?

[17:34] 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. And even our universal reason is not in what the body, huh? But it's either wholly separated, as are the substances of the angels, or at least the power of understanding is separated from the body, because it is not the act of some organ, as Aristotle shows on the third book on the soul.

[18:13] This is the case in the what understanding soul joined to the what body, huh? Shakespeare, one play refers, some character 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 wanted to give me. Yeah. And my wife's picking out plants. I talk about the souls of these plants here, you know, all around us.

[18:44] I don't know what you think of that, but anyway, I love it. I suppose if he had a dog named Fido and he died, they'd talk about the soul of the faithful departed.

[19:09] When he says "quodammodo I suppose it's way referring to the idea of "quidam quid," right? Okay. If I mention how, how, Feuerbach says 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

[19:36] between what is infinite simply and what is infinite "secundum quid." Moreover the, third objection. What about first? The first matter is that infinite. Well, the first matter does not exist in rerum natura. 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 rerum natura, the nature of things. So the first matter, does not exist in Rerum natura by itself, since it is not a being in act, but in ability only.

[20:14] But nevertheless, even first matter, according as it is in potency, right, is not infinite simply, but in some way, because its potency does not extend except to what natural forms, doesn't extend 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,

[20:51] like the talk for you know talks about democratic man, he thinks I got all these possibilities and I can do you know, but you can't write down you can't do a lot anyway. So you got to be very limited what you do, and end up doing something very limited, and and the the infinity there is well, it's secundum quid, but it's not very actually. Not a big secundum quid.

[21:15] Yeah, yeah, yeah, yeah. The scripture says about setting off in every direction. Set setting out off in every direction. You can only walk one direction; you can't walk three the same time.

[21:34] 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 point, limit, or boundary.

[22:10] 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. 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, whatever you 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.

[22:39] 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 a straight line into two nothings. And that's not really possible, is it?

[23:13] Because then it'd be made out of nothing. Or if you cut a line into two points, but then you would have made a line out of like points touching. Points touch, they would 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.

[23:37] So when you cut a line, you don't end up with two nothings or two points, but two shorter lines that are divisible forever. Aristotle shows us further continuous quantities, and sometimes he shows it 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 in less time. And in that lesser time, the slower body covers a lesser distance.

[24:06] 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, yeah. But numbers are not divisible forever. Okay. I'm sure mixed up modern. You think the the one is continuous quantity, but they're kind of thinking that, right? But the one is actually simpler than the point. So you can't have half a point.

[24:35] 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. You can't. 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?

[25:09] And so you have two differences, right? And Thomas, you know, explains why the definition of the continuous as that which is divisible forever is more appropriate than natural philosophy because you're going towards the parts, and parts are like matter. This is a science that talks about matter. But the definition what of continuous as that whose parts meet at a common boundary is going towards what the whole, the unification of the parts by coming into contact, right?

[25:42] And to talk about the whole is like talking about the form. And that's appropriate to what logic, because logic is about about form and not about matter. So it's very subtle things. 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 that out." Or say that he says. I mean, we didn't say it first.

[26:08] Thomas said, "Right." We just tried 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 logic, he gives only the division definition of the continuous as having parts meeting at a common boundary. And he doesn't just you know do that way. I do this one here and this one there, right?

[26:40] I mean, he can recall the one from logic when he gets into natural philosophy, and then he goes on to other definitions he doesn't give in in logic. But that's that's something we learned before when you distinguish two natural philosophy and mathematics by the way they define. You see the difference here also in the way of defining in logic and in natural philosophy. And sometimes they'll say, you know, that the real definition of man theology is imago dei, image of God.

[27:14] The definition of man as a two-footed animal that has reason would be more appropriate to the philosopher to natural philosophy, right? No feathers. What? No feathers. Yeah.

[27:29] Yeah. But what do you say? the enemies are playing with you, They pull the feathers off the chicken. and throw it over the wall It's a man. It's a man for you. Yeah. Okay. So it's going to take up first of all whether it's infinite according to what continuous quantity. The magnitude is the word for used for continuous quantity. And then we'll talk about what multitude in Article Four.

[28:03] When Aristotle talks about the infinite, he's usually thinking infinite in quantity, right? And what way it exists or it doesn't exist. To the third one proceeds thus. It seems that it is possible that there be something infinite in act, according to magnitude or continuous quantity. From the mathematical sciences, there is not found the false, because there is no lie in those abstracting, as Aristotle says in the second book of the Physics.

[28:32] I remember that particular passage there. You know, Aristotle is touching upon the central question of philosophy, and you define in geometry without matter in the ordinary sense, anyway.

[28:50] 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. We're knowing truly. So, if we're truly knowing sphere and separation from clay or marble or whatever we might find in the sensible world, then it must truly exist in separation. Aristotle says, "No, no." And there's no falsity in self-tractics. So, he's kind of quoting this.

[29:22] But the mathematical sciences use the infinite in magnitude for the geometrical demonstration. Let this line be what infinite. Therefore, it is not impossible that there be some something infinite, according to what magnitude. But maybe that's just just a way of talking. Let it be as long as we need it to be, right? That's the way of saying it.

[29:52] I was reading the Summa Contra Gentiles this morning. You know, and the part on 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 text misunderstand, you know. But when it's don't don't sadden the Holy Spirit, you know, Saint Paul says, well, to be sad is you know passion and undergoing, and God doesn't undergo anything, so you know.

[30:20] So, but this is being understood metaphorically, right? All kinds of ways, you know. But there's certain ways of scripture that can be misunderstood, and you really need the magisterium of the Church and so on to to understand these things properly. But there are other, to less extent, little ways of speaking that have to be understood. I'm always bothered, you know, by our saying, you know, that the first cause is the cause of all things.

[30:47] We'll say that right. All God is of the things. Well, he's a thing, yeah. Yeah, he is. Yeah, yeah, yeah. But then the cause of himself, see, you know. And we had some kind of clumsy say he's the cause of all things except himself, you know. But you can't mean that when you say he's the cause of all things, right? You don't mean he's the cause of himself, right?

[31:05] 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 they'll take the passage. You know, no one knows the Father except the Son, and and vice versa, right? You say, well, is the Father then doesn't know himself? You see, and we just took the words, you know, you can misunderstand those, you see. And Thomas says, well, Scripture speaks this way, right?

[31:40] And the things that that belong to them by reason of the divine nature are to be understood when you say it, even if you say it about just one of them. But no one knows the Father except the Son. But but that pertains to divine nature, so it's understood the other. But that's a kind of way of speaking that scripture has, or or sometimes God will be said to do something because He makes it known.

[32:07] Now I know that you love me, you know Abraham, or something like that, right? And Thomas said, "Well, now I've made known that you love me, right? But I knew already you love me. " I mean, you just take the way of speaking, you can see how the heretic can can can argue from that, you know, and and then Thomas has to go through and answer all these things.

[32:26] Well, this might be something like that, but not, but not there. 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, 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?

[33:05] 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 us in the sixth book, you know, where he shows it. But if it's mentioned, it may be in the third book. But contraries are naturally apt to come about about the same thing, since therefore to divisions opposed addition and to diminution growth.

[33:37] It seems that magnitude can increase forever. Therefore, it is possible for there to be an infinite what magnitude, right? And you know, you talk about the hexagon and the circle, right? 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 the circle, and vice versa. Inscribe a circle in a square and circumscribe one around.

[34:05] 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 go on in one direction while on the other direction.

[34:21] Moreover, motion and time have quantity and continuity from the magnitude over which the motion goes. This is in the fourth book of physics. So actually, in the sixth book, he takes up the continuous. He 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 a few of them.

[34:50] So motion and time have quantity and continuity from the magnitude over which the motion goes. But is not against the definition of time and motion that they are infinite,

[35:07] since each thing what each indivisible noted in time and 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.

[35:30] Yeah, surprise doesn't get that other argument. You know, people will say, you know, that's when the Greek philosophers, an example of something that always is. Who he says time always is, right? How could there have been a time when time didn't exist? You know, and Augustine, you know, raises this problem again. You know, and Heisenberg quotes Augustine, you know, and so on. So, so it seems that it can't be time when time wasn't, because then you're.

[35:58] There still was time, right? Will there be a time when there is no more time? Maybe there wasn't time at that time. But everyone, like some of us were little, you know. Sometimes you know you have a book of religious pictures, but not necessarily by a Catholic or could be a Catholic, but famous paintings, you know, different biblical scenes and so on, and you kind of use it kind of like a storyboard.

[36:22] Long time ago, in a time before there was any time. That's one of the books again, y'all. Once upon a time, yeah. But against this is that every body has a surface, but every body having a surface is what limited, because the surface is a limit of a limited body. Therefore, every body is limited, and the same thing can be said about a surface, any line. Nothing, therefore, is infinite in magnitude.

[37:08] 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, if it be given that there was some body, right, infinite in magnitude, as example, fire or air went on forever, right.

[37:45] 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?

[38:19] But could I be unlimited by size? Okay. So it should be known, therefore, that body, which is a complete magnitude. Now, why is he called complete magnitude? The length, width, and what depth, right,

[38:42] 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 something composed of the first matter in some form, right? When mathematician talks about line, angle, and body, and so on, he's just talking about what quantity, right?

[39:20] And about a natural body that it is not able to be infinite in act is manifest, he says. For every natural body has some substance. substantial form that's determined. Since, therefore, to a substantial form that follows the accidents or the properties, accidents—they are not necessarily taken as opposed to properties, right?

[39:47] Is necessary that to a determined form there follows determined accidents, among which are quantity. Once every natural body has a determined quantity. Both in the direction of the large and in the direction of the small. So I'll first, bring it out in the ninth reading, there, of the first book of physics, right? He argues against Anaxagoras that 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?

[40:22] But in nature, we see that the whole animal doesn't have just any size; there are limits to which it's found. Therefore, the parts of that, right? So it seems to be because of the kind of animal or plant it is that 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.

[40:42] I dislike ants as it is, you know. All you need is one termite at the end of your house. Yeah, yeah. What bite? And but again, the adult elephant is not as small as the ant. Hence, it is impossible that some natural body be what infinite, huh? Okay.

[41:08] 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? Okay, isn't that the order of physics?

[41:43] Exactly. Right, they're far and wide; each have their own place, right? And they go in a straight line to their own place, but only when they are what outside their place, right? They get to their place, they they rest, right? Okay.

[42:01] So he says nothing is naturally moved by a what rectilinear motion, a straight line, except when it is outside its own place, right? Which could not happen to an infinite body because it would occupy all places, and thus indifferently each place would be its what place, huh?

[42:28] Okay. And likewise, neither in a circular motion, which seems to be the sun and the moon and the stars, right? Okay. Because in circular motion, is necessary that one part of the body be transferred or carried over to the place in which was the other part, which was in the circular body. Okay, but in the circular body, if we lay down, it's infinite. This is not able to be, because two lines drawn from the center, as they are what, drawn longer, further from the center, so they are more distant, right?

[43:11] If therefore the body is infinite, an infinite, the lines would be distant from each other, and then you'd have to cover what infinite distance to to evolve. You never succeed, right? Unless one would never arrive at the place of another. Kind of subtle, right? Okay.

[43:37] So the second argument is more dependent upon the older view of the world, right? Huh? It's hard to know sometimes, you know, what's going on in in modern physics, huh?

[43:58] Because you know they'll they'll speak of a body moving in a straight line in uniform speed, right? As not really changing, but staying the same. So it's like it's at rest It seems like it would be right. Yeah, yeah.

[44:24] And so they'll say, you know, body in the absence of external forces, it means it is rest or uniform motion in a straight line, and therefore you only need something else when you're going to disturb this 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?

[44:54] Then you don't see the need to move it, 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?

[45:26] Well, it's open like you know they say, even Thomas talks about this, huh? When the astronomer is calculating some things in the sky, he can

[45:40] consider the Earth to be a what Point point? And you draw the lines down to the point, huh? What 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's it's it's affects

[46:08] in no way, right? Or no noticeable way, that is to say, right? Your calculation of the parallax, something like that, the distance, between these things. Um, and when they talk about you know bodies, you know going around, so they'll 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?

[46:34] I don't think so. Is moving forward at a uniform speed state the same? Really, I don't think. But it seems to been useful to do this, you know.

[47:02] So you 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 how the world historian there, McNeill, you know, he divides world history in time.

[47:18] He speaks of the fictitious sharpness of historical dates, but the historian has to do that, right? To make it tolerable. so it's useful to say when the modern world began, fourteen ninety two or something, fifteen hundred. You know, and and.

[47:52] But when did the automobile, you know, replace the horse and buggy? You know, it was not a definite thing, but. So, gotta be aware of these useful fictions, huh?

[48:15] But the first argument is not so dependent upon the what older physics, right? That's kind of interesting that Aristotle in the third book of the Physics, right? He argues there's not an infinite body, just assuming that there is what these 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 is some other things that he's got to take into account, right?

[48:46] That's kind of strange since he did it twice, you know, like that, huh? And 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?

[49:24] 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?

[49:42] So if you remember Thomas pointing this out, to be in Nicomachean Ethics. Aristotle was talking about different arts and sciences, 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 that's not the end of the household science, right? But that was a common opinion, right?

[50:03] 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'm not trying to prove it from that example; we just illustrate it, and so. Take

[50:30] your style of ethics, you know, saying that the the mean is not the same for all of us, right? But 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 got the example of Milo. we had to walk every day, you know. It wasn't really a mile away to walk every day, but obviously the mean for him is not the same as for us, right?

[50:53] The picture is very clear. Example, you know, but he's not using Milo to prove the point, but kind to illustrate it, huh? Okay. So that's about the natural body. Those first two arguments, right?

[51:22] Now about the mathematical body, also there's the same what argument? Because if we imagine a mathematical body existing in act, is necessary that we imagine it under some form, right? Because nothing is an act except through its what form.

[51:44] Hence, since the form of the quantified, as such, is figure, 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. In the case of circle, you have one limit, and in the case of a square, you might have four limits, right? Okay.

[52:12] Um, I think my brother Marcus pointed out about you know they sometimes speak of the what the parallel postulate in geometry, right? But it's not really the parallel postulate. It's parallel lines are lines which extend forever, will never meet. Well, can you imagine lines extending forever, never meeting? No, any 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 right angles, those lines extend will meet, right?

[52:51] Well, you can imagine two lines meeting, but you can't imagine infinite lines in their infinite extension, right? Huh? Okay. So what you imagine is going to be what? Something finite, right? Huh? Okay. That's the way he does it.

[53:13] Now, the first objection was taken from let this line be infinite, you know, extend away. To the first, therefore, ought to be said that the geometer does not need to take some line to be infinite in act, but he needs to to accept what some line that's finite in act, from which he is able to subtract as much as he needs, right? And this he calls a what?

[53:39] Infinite. Yeah. Okay. Some 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 this kind of way we partly in the way of speaking there, right? Okay. Okay.

[53:59] 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,

[54:17] nevertheless, is against the what? The notion of what? Some. Any species of any particular one, huh? It's against the notion of what? a bicubit magnitude or a tricubit, huh? Or a circular or a triangular, and so on. 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,

[54:51] it is not possible for there to be some infinite magnitude, since no species of magnitude is infinite. I don't know. I know. He's trying to argue, kind of inductively from the particulars to the general. Well, yeah, he's saying no particular particular magnitude is infinite.

[55:25] Therefore, they can't be this infinite in the genus, right? Oh. The third objection, talking about the infinite divisibility of the continuous. Well, why can't it go the other direction then, right?

[55:54] 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 had themselves in the notion of what Matter. matter. Now I mentioned that in 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, and 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.

[56:40] 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?

[57:02] And that's why this definition, as we were saying earlier today, the definition of the continuous as that which is divisible forever, is kind of looking at it in terms of its parts, right? And therefore, looking at in terms of what matter rather than form, why the definition in the categories is 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?

[57:27] So the parts are to the whole like matter is to what form, right? And so you 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? They're the parts of which this thing is put put together, huh?

[57:51] So he says the infinite that belongs to quantity holds itself from the on the side of matter, for through the division of the whole one what approaches matter to matter, for parts had themselves in the as the definition of matter, right, or in the definition of matter, but through the addition of parts one what approaches the whole, which has itself in the notion of a form, right?

[58:20] Well, that's the proportion as the Aristotle gave there. Parts are to the whole as matter is to form, right? And therefore, there is not found infinite in the addition of magnitude, but in the division what only falls upon matter.

[58:40] That goes back to the distinction even of the categories, huh? Where quantity falls upon matter and quality upon what form, yeah. Interesting, because the understanding is infinite secundum quid would be in quality, right? Um,

[59:06] now motion and time are not. As a whole, an act, but successively, right? Hence, they have ability mixed with act, but a magnitude as a whole is an act, and therefore the infinite that belongs to quantity—oh, shoot, I'm getting confused here. 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.

[59:45] For to be in potency or in ability belongs to what? Matter. So, motion and time are like matter, divisible forever, and not entirely there.

[1:00:00] My walking. Home is not entirely there or here or anywhere. Why is he doing Article Three and Four? Kind of like a confused man Well, he wants to.

[1:00:24] Well, you could say really two things. He wants to show that nothing else is infinite in the way God is infinite, right? But also, you might say he he wants to show perhaps the sense in which God is not said to be infinite. Okay. Okay. And

[1:00:48] sometimes you find Thomas saying, "You know, 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 lack. "

[1:01:06] It's not having limits that it could have. Maybe that's not even possible. It's not having 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? Privation or lack. See, but infinite said of God is that a a privation? It's a non-being, something it's able to have and should have. That doesn't mean that. Infinite is merely a what?

[1:01:37] Negation. Okay, you're 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, Let alone should have, right? So Thomas, you know, was first pointed out. So in a way, you have both those things in mind, right?

[1:02:10] 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.

[1:02:26] Because we don't speak of other things as infinite. Yeah, and sometimes, like like like, wasn't it back here when he's talking about God not being a body, right? And you had in Scripture here,

[1:02:44] yeah, Question Three, Article One here, where God is a body, and talking about God as being a Chelsea or Chiloist What should you do, right? He's deeper than the hill, and when you know, he's longer than the earth, right? Okay. Well, if you took, 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?

[1:03:23] Yeah. Around the what? He sits around the house. Yeah, yeah, yeah, and you know it's kind of this puzzling thing. And Sir Isaac Newton, he calls space, which he thinks is infinite, extending, you know, upon her sensorium, the sensorium of God, right? What the heck he means by that? You know, the sensorium. Sensorium, not like, well, it's the sensorium of God, right? But I mean, I don't know.

[1:03:51] He's a little confused there, but but you think of God somehow, right? Yeah, he seems to be everywhere. Everywhere in the way that space is 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 which is infinite. Um. See in the Summa Contra Gentiles, he takes up the infinite last of everything,

[1:04:23] and so he's shown both that God is not a body, these altogether simple, and therefore you've eliminated him being infinite in the sense of of a body going on forever, like the space in in Newton. And he's also shown that God is one before he shows 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?

[1:04:51] Infinite multitude, huh? So he eliminates the two kinds of infinity that people might attribute to quantity, that a body extends in length and within depth without end, right? And that there's a infinite multitude, right? Ah, and then he slows himself down to 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?

[1:05:22] Which eliminated both of those possibilities. There's no multitude here, There's just one God, and there's no extension because he doesn't have length, no width, no depth, okay, or even position in the continuous like the point has, okay.

[1:05:39] Um. But here it's kind of like you know he's already shown the way in which God is infinite, and then he's he's showing other things are not infinite and.

[1:05:58] But I suppose you might say that kind of a secondary thing is is to show that what God is not infinite in these other ways that things are claimed to be infinite, right?

[1:06:20] We take a little break now before we go on to the multitude here.