Logic (2016)
15. Quantity, Time and Reason: Individuation, the Properties of Quantity, and Number as Abstraction
Class of 2017-01-05
https://berquistcourse.com/course/philosophy/2-logic-2016/015-quantity-time-and-reason-individuation-the-properties-of/

[0:00] We have seen two divisions by contradictories in the second chapter give rise to what? Four parts. What was that division? No, not in here. No, I mean in the categories, the book itself. You had the universal substance and the particular substance, and universal accident, particular accident. So you got four, right? But when we crisscross two divisions by contradictories, we do not always get four parts, right?

[0:48] When Aristotle, for example, divides the parts of a plot by the contradictories before and not before, and after not after, does he get four parts? No.

[1:00] There cannot be a part of the plot which is neither before anything nor after anything, It, wouldn't fit in at all, right? Likewise, when we divide quantity by two contradictories, we do not get four parts.

[1:16] A quantity either does have parts that have a common limit or not, right? And it has parts that either have a position toward each other or not. Line, surface, body, and place have parts that have a common limit, and also that have a position toward each other, right? Number and speech have parts that have neither a common limit nor position toward each other. What is time? Time has parts that have a common limit, but not position toward each other, right?

[1:48] But is there a quantity whose parts have a position toward each other but no common limit? This does not seem to be a real possibility, right? Okay. So it's like the example before and after, right? In the definition of.

[2:10] If Aristotle had divided quantity a second time by the natural differences, I call the natural differences because they're done in natural philosophy. But what's the reason why it's more appropriate for the natural philosopher to speak of continuous quantity as a quantity who's just divisible forever? Why it's more appropriate for the logician to say, no, it's one whose parts meet at a common boundary. Why?

[2:40] Natural philosophy, matter. Yeah, yeah. And parts are like matter, right? Most divisible forever, going down. You know. And but the whole is like the form, right? It's appropriate to the logician. I used to talk about the forms of things, right? Species, our English word for species, is form, right? Okay. I used to love to talk about the forms of fiction, right?

[3:20] Why does Aristotle divide quantity twice and quality only once? Perhaps there is a special reason for emphasizing quantity having parts and position. We generally say that accidents are individualized by their subject or substance in which they exist, but quantities that have position are individualized by themselves. Now, what sacrament does that illuminate?

[4:07] See, are the dimensions of the bread right in the eucharist right? Are they individual? Not that's not a universal thing, is it? It's individual, right? But are the individualized? Substance? No. No. You see. See. And why is that? Because quantity is a little bit like what substance, right? Then it can be individualized in a sense from its own, by its own very nature, right? If it's that kind of quantity that is what has position, right?

[4:44] Yeah. So it's good for Aristotle. Hopefully, yes. God is knowing it. Yeah, yeah, yeah. It shows you how how quantity, and again, it's another example of how quantity is close to substance in some way, right? See. And so the the the color of the bread, right, or the taste of the bread, right, now. That's individualized by being in the what quantity of the bread, right? It's kind of amazing, right?

[5:19] Quantity is actually a bit like a a substance, right? I mentioned before how people confuse, you know, my friend Descartes, there, you know, body, which is a species of quantity, with the body, which is a species of what substance, right?

[5:39] In Plato and the Pythagoreans, thought that numbers are the substance of things, right? But there's affinity there between quantity, right? Aristotle gives that right after, after quantity, right? Right after substance, I mean, huh? What what's the cause? What's the cause of the individual individuation of material substances, right? How is it possible we can have five men in this room here? Yeah, because we've got enough flesh and blood and bones to go around.

[6:13] I don't need your flesh, and you don't need my flesh. It's enough flesh and see. But why can we have all these chairs that are more or less the same kind, right? The simplest answer is you have enough wood. See, Hard that a grandma can make you know a couple dozens of these cookies at Christmas time. My grandmother, great cookie maker. Because you get enough dough, right?

[6:40] Yeah, yeah, yeah, yeah, yeah. So it's matter as subject to what quantity. That is the beginning of individuation in material things. Not in the angels, right? But the difference between one angel and another angel is is wholly what formal, right? That's why Thomas says that no two angels are really the same in what species and kind.

[7:13] Interesting, right? Now we can find out something about you know distinctions of the angels, right? They don't have that composition we have, right? So why are there many chairs of the same kind in this room? We have enough wood for it, you know. As a carpenter, right?

[7:53] Now look from this great book here, Summa Contra Gentiles. I recommend this book to you. Okay. Thomas says habet autem hoc proprium, proper to quantity among accidents. I think he means right.

[8:13] Quantitas dimensiva—that's what his name of sense means for what continuous quantity, right? But not maybe what all continuous quantity, right? Doesn't fit time, right? Inter accidentia radical among the other accidents, quod ipsa secundum se, in itself or by itself, is what? Yeah.

[8:40] And that is because positio, which is the order of parts in a whole, right, is in its what? Yeah, put it in its definition, right? Okay, a quantity having what position, right? Okay. I want you to distinguish this positio from positio, which is a category, right? Okay, that's.

[9:11] I'm laying down. I'm sitting down now, right now. That's a different kind of position, right now. This again brings out the closeness of quantity to substance, and this also perhaps explains why the order of the species is reversed in the second division, because according to this difference, continuous quantities having parts in position toward each other have a special connection with their likeness to what substance.

[9:40] And in another passage here, Thomas touches upon this closeness of quantity to what substance. He distinguishes the modes of quantity, and about this, there's a C missing there. This does three things, right? First, he distinguishes quantity into that which is what quantum per se, right? To wit, a line, and that which is quantum praeter quantum per se, ut musicum right? And secondly, he, distinguishes quantum per se, which is twofold, huh?

[10:21] For some signify per modum substantiae et subjecti, right? There's some likeness to that, right? Just as line or surface or what number, right? So I talk about numbers as if they're something existing by themselves, don't I? You know, I'm all crazy about these numbers, right?

[10:47] Each of these substantially is quantity, quantified, because the definition of each of them is place quantity, right? For a line is a quantity that's continuous according to length, and it's divisible, right? Finite and so on, and similarly about other ones, right? As infinite, you couldn't measure it, right?

[11:12] But some things per se pertain to the genus of quantity, and are signified by way of what habitus, huh? Or the passion of such as substance.

[11:25] It should be known, Thomas says, that quantity, among other accidents, propinquius, right? It's nearer to substance, whence some, like Descartes, and you know, some of the Pythagoreans and so on, think quantities to be what substances, right? Terrible mistake, right? But understandable, as line and even number, right? And surface and what body, right?

[11:59] For only quantity has division in its own parts, right? After substance, huh? For whiteness is not able to be divided, and consequently neither is it understood to be individuated, except through its what, subject, right?

[12:20] And therefore is only in quantity, in the genus of quantity. Some things are signified as subject, and others as what, passions, huh? Moreover, that the divisions include the same species, with the exception of time, show a special place for time. This is something I was talking about before, there, right? Although time is a continuous quantity, it is also very much the number of something, right? How old are you?

[12:52] How old are you? And like number, it's parts of order, but not position. But not what, position, okay? It's interesting, huh? Let me anticipate something here. But as I was thinking about it the other day, I was thinking about how am I going to torture these guys, you know, with a study of statement, right?

[13:22] And well, one division you make of statement is into its parts, right? And sometimes you divide it into nominal and verbal, right? Noun and verb, right? Onoma and rhema rhema in Greek, right?

[13:46] Now, can you have a statement without having a noun and a verb? Something like that. Those kind of the basic ones to get at one. So you say, man thinks, right? Man plays, huh? Man eats, okay? One is a noun, one is a verb, right? Now, noun and verb have in common that they both are names, right? In sense that they are vocal sounds, right? that signify by human agreement, no part of which signifies something by itself, right?

[14:22] But what's the difference between a noun and a verb, huh? Yeah. The time, the verb signifies with time, and the noun signifies what, without time, right? Now,

[14:40] kind of interesting, huh? In in I think in Latin and in Greek, huh? They had the same name for noun and name. But in English we have the two words, name and noun, right?

[14:56] But if you look in the Greek and the Latin, it's like you have name, instead of both, and then name, instead of one in distinction from the other, right?

[15:09] Well, we talked about this way of naming things, right? The name is now of Nomen, or the name of Onoma, has become what? Equivocal by reason, right? Has been kept by one of the two things it's said of as its own name, and the other gets a what? A new name. A new name, I'm sorry. Yeah. Now, why does one of them, in this case, get a a its own name, right?

[15:39] And the other keeps the common name? Yeah, something that kind of stands out in some way, right? Now, I was very struck by this the other day, I was thinking about. it.

[15:59] You know, we sometimes in philosophy distinguish between doing and making. And other times we say when you're making something you're doing something. So doing can be said of doing and making, right? And then is a different meaning when you're juxtaposing, or you know. Now the distinction between doing and making lies behind the distinction of two virtues of reason. Art and foresight So, art is right reason about making.

[16:43] My grandma had right reason about making cookies. All she did. I never tasted as good cookies as my, my, my grandmother. Grandmother. His model life was I aim to please. That's her motto. She's a, great woman. Great woman. Achieve. Achieve her goal. Oh yeah, I said great woman, great woman, great woman.

[17:15] So this is a very important distinction. But why does making get the new name, right? Yeah, stands out, right? And what do you got to show for it, right?

[17:34] I used to say to the kids, I said sex without children is exciting, it's fun, and so on, pleasurable, right? But what do you got to show for it?

[17:46] So you have a, you know, a cookie or a child or a, you know, chair or whatever it is you made stands out, right? So it gets the new name, right? It doesn't mean that making is necessarily better than doing, right? Okay, in this case, but there's something in addition to it, right? So why does verb get the new name and nomen keep it in Latin and in green?

[18:13] Yeah, yeah. it signifies with time and it doesn't, right? Well, time is is is the measure of what motion, right? And things in motion, sooner catch the eye than what not stirs, right? Okay. That's very striking, isn't it? That shows, you know, what was struck by us on thinking about the first sense of of looking before and after is in time, right? And uh was Aristotle right in putting that first.

[18:43] Well, it's so much so that you can't make a statement without using the verb, right? And the verb signifies the time. It's like, you know, the question is can we get beyond that? Not only is it the first sense, but how can we say anything, right? How can we talk about God who's not in time, right? You know, you know, If Abraham was. I am, huh? Is that good grammar?

[19:09] But you're you're stretching the language, right, huh? To express something, right, that's not in time, right? That's not in motion, not subject to motion, right? Our mind is so much tied to to motion, right? Okay. Not only doesn't it move, it can't catch your eye. Yeah, yeah, yeah, yeah, yeah. So I was thinking, you know, now when we start talking about statement, you know, we'll talk about that again.

[19:35] But it's kind of a confirmation of I think of what we're saying right now, that the first sense of reason, looking before and after, is in time, huh? We're always saying, "well, what can we do in time? We're going to do this if I do that." You know, you know, no big deal, but but we're living that way all the time, right? When Shakespeare says, "You know, what is a man if his chief good and market of his time be but to sleep and feed a beast no more?"

[20:02] But what does he say? "Market of his time." What does time mean? It means his life, doesn't it, right? But why should use the word time for our life in place of the word for life there? Because our time is so measured by time, right now. It's so known by time, right now.

[20:24] Divide up your day, don't you, in some way? You have to, right? When you have to go, you have to be at the. Bell rings. Yeah, yeah, got a bit to think. Yeah, yeah, yeah.

[20:36] Now teaching is always an art. I look at no head of time. Thanks. Yeah, you want your students to see? You look at the time, you know, but you know, you realize you got to get through this, or you got to go on to their class or something, you know. But try to get class on time, you know. There we go. Students get the impression that you're in all the time of the world of torture.

[20:57] Yeah. Moreover, that the divisions include the same species, right? The two divisions, right? They kind of conspire, don't they, right? Just like if you were to divide the quantity into quantity that is divisible forever and quantity that is not divisible forever, that would give you the same division as discrete and what Continuous, right? Right. Okay, but now has parts that have position in respect to each other and does not, right?

[21:43] That almost seems to be the same again, but with this oddball thing called what And some people wanted to say, "well, you should really say time is a number. " We'll be careful about that, no? Well, I'm going to sit right there for you know about eight days. That's a number, isn't it? Eight days. It's not it's not the abstract number, but it's it's it's the numbered number, right?

[22:19] Huh? One of the first things because Sirius is in his doctoral list I guess. But the distinction between numbering number and numbered number, right? Yeah. Well, time is a is is numbered number, right? Huh? You know, that's like ten grandchildren, right? That's a numbered number, right? But the abstract number is the numbering number ten.

[22:42] So this is that's been beautiful Aristotle does it right now. He brings out time right now. What does Richard II say? There he's in prison there, right?

[22:57] He's counting his his tears, you know. And he says, now it's time made me her. What numbering clock, right? Yeah, numbering clock. Moreover, that, that the divisions include the same species, the exception of time, shows a special place for time, right?

[23:16] Although time is a continuous quantity, it is also very much the number of something, huh? And like number, its parts have order, but not position.

[23:31] That the parts of time have order is important in the categories, because as we have seen in Thomas, this is the reason why in the last six highest genera there are two genera connected with place, where and position, right? And only one with time. Why? See, when the idea of time already is the idea of before and after, right? It's the number of time, the before and after in time, right?

[24:01] So you already have the idea of order there in the idea of time. Why place is where you are, right? But where you are, your body might be in what, sitting or laying down or standing or something, right? And so you need this other category, which is the order of parts in place, right? But you don't have to have that in time, right? It's already in the idea of time.

[24:26] Okay. So notice how that how that helps you to understand the last six, right? Why are there two ones for place, right? You know that'll be on your final exam, right? Well, why are there two ones for place, but only one for time, right? Huh? See how wonderful this is. Okay.

[24:57] But even more important is that before and after have their first meaning in time. Aristotle exemplifies the second meaning with like, Number. Remember how the second sense of before and after was what I'd say in being, right? But Aristotle's example, one is before two. Why does it take number, right? One can be without two, but two cannot be without what? One.

[25:33] Five be without one? Yeah. There's one man here, right? One man here. One man. One man. One man here. And each one of us could be without the five of us.

[25:46] But the five of us couldn't be here without each one of us being here. So each one of us is before all five of us. Aristotle's even simpler than that. One is before two. Okay.

[26:04] There are very important connections between time and reason. And Aristotle points out, time would not be fully without reason. See, I mean, how can I count three days because yesterday is gone? So I can't, you know. I can count my folders here, you know, because they're all here, but not all my folders, but folders in my my thing there. But

[26:35] I don't have the three days here: yesterday and today and tomorrow, right? So how can I count them? Yeah, I can remember yesterday, right? Anticipate tomorrow. I can remind you of that, you know. Aristotle raises after he takes up time: would time be without the mind? Not fully. See, how can there be a number of days without?

[27:03] You know, reality time hardly exists, right? You know, I just love to tell people, you know, that that God never changes; He's always the same. Sounds awfully boring, His life, doesn't it? Absolutely. yeah. No, right, right, variety is the spice of life. I grew up with that proverb, you know, being said by adults and so on. You know, you know the same thing for dinner every night.

[27:40] It's driving my wife crazy, you know. Come out, you know, use a bookshop another edition of Shakespeare. Another edition. Doing the same thing over and over again. Yeah.

[28:00] When I retire from assumption, I say I'm going to get all these books. I don't throw away these books of modern philosophy. You know, I'm not going to read those in my retirement. But here I'm reading the Summa Contra Gentiles and then the prima pars and so on. I have to read the De Potentia next. You know, most powerful disputed questions ever written. Boy, those are marvelous things.

[28:26] Very important for the Trinity too. So there are very important connections between time and reason. Time would not be fully without reason, right? That's a very important connection, right?

[28:43] And we've seen before the definition of reason as reason is through before and after, right? As Shakespeare has taught us, reason is the ability to look before and after, right? In the first sense, the before and after is in time, right?

[29:07] So when Christ said before Abraham was I am, right? He's using the word before in the later sense, right? And it strikes us kind of strange at first, right? But he expressed himself as well as our language allows him to express himself, right? Before Abraham was, I am. Doesn't say I was. I was thinking of this the other day, and I didn't have a chance to look it up.

[29:32] When John the Baptist says, "He who comes after me is before me," at least that's one translation. I don't know exactly the words that were used in Greek. Yeah. I was thinking of that. Yeah. But he's thinking probably of being before in excellence, you know. But it is coming after me in time. But it's kind of interesting. You have to know the sense of before to really expound what he's probably saying there, right?

[29:55] Now, further, the categories is ordered to the Peri Hermeneias, the logic of the first act to the Peri Hermeneias, and Thomas explains that right. That's the book on statements, right? Peri Hermeneias, and the truth of statements whose formal part is the verb that signifies with time. Well, you know, another thing we'll do when we think out a statement we'll say it's speech signifying the true or the false, right?

[30:31] Okay. That's very important for reason, right? But you can't express this without the verb. And verb signifies the time, right? So I mean, you see all these connections between time and reason, you know. Say, hey, this is this is really interesting.

[30:54] After Aristotle has distinguished the species of quantity, he distinguishes quantities through happening as opposed to per se, right? Huh? From quantities through themselves, the above species are quantities through themselves, and other things are quantified through them and not through themselves right? Huh?

[31:16] So white is the white wall there when it's big bother you in the summer? You know. Because it's it's it's size, right? But its size is it belong to whiteness as such, or is it because whiteness is in the the wall, right?

[31:34] Thus, as Aristotle says, there is much white when the surface which is white is large, or a trip is long when the time it takes is what long.

[31:47] Why does he distinguish per se and per accidens quantities, but not substances or qualities? That's well. Part of the reason is that quantity is the subject of certain qualities, right? And therefore, they are what

[32:04] quantified per accidens, right? Huh? Because their subject is spread out, right? If color is in the surface of a body, right, and surface is a what continuous quantity, right? Then the color is what spread out, right? No, that's because of what the surface. Okay. And this again brings out the order of these two highest genera. Okay. Now the properties of quantity does not have a contrary. That's what you'll find with some of these qualities, right?

[32:36] Is not said more or less. Okay. Is one three more three than another three? See, one sweet thing is sweeter maybe than another sweet thing, right? But is one

[32:54] three more three? It's not said more or less. That doesn't have does have a contrary. Equal or unequal, right? That's a very nice property. Okay. You know, say we're all equal. You know, we hold these truths to be self-evident that all men are created equal, right? Well, I mean, some men are taller. Some the basketball players are taller than me. And some guys are shorter than me, you know, huh?

[33:28] You know. For some reason, I guess you know, a man doesn't like to marry a woman taller than himself. The woman doesn't like to marry a man shorter than herself, right? And once in a while, we're in a couple where there is this, you know, and it's kind of interesting, you know. I don't don't dare ask them how they resolve this, you know, you know. But

[33:58] yeah, I remember in in grade school there was Roy Lepak and Margot. Roy was a tall guy, the tallest guy in the class, and Margo was a tall girl, right? So she had to you know get go with.

[34:12] Poor Roy is getting in charge, being pursued by Margo all the time because of his height the poor man. I think he became a priest by then. He drove into the priesthood. I don't know. He pursued by Margot. I kind of

[34:26] felt sorry for Margot, but I felt sorry for for Roy too, you know. But yeah, basically, we're not all equal, are we? You know, in quantity, right? We're equally healthy, equally strong, equally beautiful, equally virtuous, equally vicious.

[34:54] The first property of quantity given by Aristotle is that it does not have a contrary. Aristotle spends the most time on this property, which quantity shares with what substance, huh?

[35:09] Some confuse relations that follow upon quantity with quantity, and Aristotle speaks at some length to refute this mistake. Large and small, for example, might seem to be contrary what? Yeah. But they belong to the genus what? Relation, or towards something, right? Remember later on now. Okay, Aristotle says here a little bit here, but Aristotle will take up relation or towards something, right? After quantity, before what? Yeah.

[35:43] But when he enumerates the ten genera, right now, he gives quality before or towards something, right? What happened to the guy? You know, get mixed up in the order of these things.

[35:55] See. Well, no, you're going to find out, right? And that Plato and the you know people had defined relation as something that's said to be of Another right, or towards another in some way, right? Well, knowledge is said to be knowledge of something, right? Whether it is knowledge, a relation, you see. Aristotle's got to distinguish between what is said relatively in a way, right? Like knowledge needs to be knowledge of something, and what is essentially a relation, right?

[36:36] So he's got to clear that first, you know. Okay, but here he's already in the sense pointing out that you don't want to confuse quantity with relation either, right? Large and small, you might say. Well, these are what quantities, yeah, yeah. Are they quantities or are they relations? Huh? You see. When I learned, you know, these quantities are divisible forever, you can get something that's very large compared to anything,

[37:05] and and something that's very small, right? Because you can get small, small, small, right? Then, you know, so you take any line, right? You can divide it forever, and you can get, you know, all the way down. One is larger, and one is smaller. It's just small compared to the whole line, but it's you know larger than this other part of the line, and so on.

[37:27] Thank you. Some confuse relations that follow upon quantity with quantity, and Aristotle speaks of some length to refute this mistake, huh? Large and small, right? For example, might seem to be contrary qualities, but they belong to the genus relation, or to speak in the teaching of Suritome towards something, right? The same quantity can be called large and small, but toward other things, right? If they were contraries, contraries would belong to the same thing at the same time, and something would be contrary to itself, right?

[38:14] Aristotle seems to exclude place from this property. Indeed, the definition of contrary seems to get its words from place, because we say that contraries are the species furthest apart in any genus, right? So in the genus of color, black and white are furthest apart, right? Huh? And in the genus of habit, it's virtue and vice, right? So continence and incontinence are not as far apart as virtue and vice, right?

[38:44] Huh? Because incontinent man, he eats too much or drinks too much, but he's kind of ashamed of himself or something, right? Why the the drunkard? Right? That's the way to that's the way to live.

[39:03] Yes. He's an Irish man. His name is probably James. I always call him Seamus. And I always tell him there's no shame in Seamus.

[39:20] The second property of quantity is all shared with substance, huh? It's not said more or less. This again would show that quantity is closer to substance than quality, right? And follows upon the first property. One quantity is not more or less another. One three is not more or less three than another. One three foot line is not more or less three feet long than another. The third property of quantity is to be equal or unequal.

[39:50] This is a property in a more strict sense of the word than the first two properties, because they're common to many things, right? Okay. I have a lot of appendix here, right? All this stuff is, you know, it's gathered.

[40:26] I wasn't writing this as a book. This is for my notes, you know, in my computer there, so you can say, what are you throwing all these things at us?

[40:42] There's connection between number and the continuous, huh? According to Avicenna, right, in his Metaphysics, unity and number, which the arithmetician considers, right, are not that unity and multitude which are found in all what beings, huh?

[41:04] But only according as they are found in material things, according as plurality is caused from the division of the what continuous, huh? And from this we are able, okay, we'll stop for a minute.

[41:22] Why is it that numbers can what increase forever, right? Well, it's because the continuous is divisible forever, right? So if a line is divisible forever into lines, right, then the number of lines can grow beyond any what number. Okay. And

[41:50] is that possible for the species of quantity to grow beyond any number? Well, if you get down to numbers, the species of numbers are, but if you take the more general division, Aristotle makes a discrete and continuous, right? That's it. There's two. There's two of them, right? Yeah, two or three, right?

[42:25] What kind of multitude is that, right? Or you see there are ten categories, right? Does that ten categories arise from division of the continuous? But what did you divide up and you got into ten?

[42:46] If it arose from the division of the continuous, it would go on forever, right? It'd be infinity of highest genera, right? And it is. It turns out there's only ten of them. This is kinda like with the trendy in a while to five persons or two hundred persons or.

[43:06] When Thomas says, you know, why there's not more than three, right? Huh? He goes back to the fact that there's only really two, but kinds of intrinsic operations of God, right? Understanding and loving, right? Huh? One proceeds by way of God understanding Himself, and the other by way of loving Himself, right? But that's a much different multitude than that of what you have in number, right? The multitude in number arises from the division of the continuous.

[43:37] Can go on forever. From this, one can find all those passions and numbers which mathematicians demonstrate there's multiplication and bringing together and things of this sort, which are founded upon the infinite division of continuous, right? Once there is infinity in numbers, according to the philosopher in the third book of the physics, and therefore such a unity is in potency every number.

[44:18] Is a number which is a species of quantity, numbering number or a numbered number. Well, if numbering number is the same as numerus absolutus in the following text, and absolute number is not what?

[44:39] It's not absolute for a number of things, except in the understanding, right? And the categories are a division of being outside the soul, reason. Then the number which is a species of quantity would be a numerous, which is in numbered time. yeah, time is also a numbered number, right? Huh?

[45:00] Let's see. This text is from the Summa. Further, wherever there is number, there is a whole and what parts, huh? If therefore in God there is a number of persons, there will be in God a whole and part. Which is repugnant to the divine simplicity.

[45:22] To the fourth, it should be said that number is twofold. To wit, simple number or absolute number has two or three or four. Right, a number which is in things numbered has two men and two what horses.

[45:45] If therefore in divine things one takes number absolutely or abstractly, nothing prevents their being in him whole and part. Right, but thus it is not except in the way our mind what takes it. Right,

[46:03] for absolute number is not what for number is not. Separate from numbered things, except in the understanding, right? If, however, we take number in so far as it's in numbered things, then in things created, one is part of two, and two of three, as one man of two and two men of three, right? But it's not thus in God, because as much as is the Father, so much is the what?

[46:38] Trinity, as will become clear, below you know, right? On the other hand, a number like two men or two horses seems to involve more than one highest genus, right? Just like white man involves more than what? One genus, right? What's a white man? What genus do you put a white man in? Well, man belongs in substance, and white belongs in quality, right? So, where do you put two men?

[47:12] Yeah, yeah. I don't wonder if that's right, they'll say. Moreover, logic considers things in so far as they are in reason. An abstract number is in reason only.

[47:26] Another text, Thomas compares the foundation in things, which that should be probably with with what is known by mathematical abstraction. It has logical intentions It's a little bit confusing Yeah, by probably My text. right Okay.

[47:59] Now I get this. this is a very important text, but it's you know, so you have to go to the sentences sometimes, right? Huh? Well, I've seen it of course, you know.

[48:11] Passage, you know, forgotten about, you know, in sentences, you know. Wait for me to read this text. yeah, yeah, yeah, yeah. But but sometimes something is taken up a little bit, you know, just said about a little different way, you know. This is one of these texts. This is not the text he was talking about. I find texts like this. I got to put it in here because I might.

[48:33] This is this is a most subtle text, though. You know, the conception of the understanding in three ways has itself towards the thing which is outside the soul, right? Did you know that three ways? Three. A distinction of three, yeah. So compared to Thomas' mind, you have a mind of.

[49:03] For sometimes, what the understanding conceives is a likeness of a thing existing outside the soul. Just as one conceives about this name, man, right? And such a conception of the mind, of the mind, has a foundation in the thing immediately, right? In so far as the thing itself, right, from its conformity to the understanding, makes what is understood to be true, right? And that such a name signifying that thing understood,

[49:40] yeah. Sometimes what the name signifies is not a likeness of the thing existing outside the soul, but something that follows upon the way of understanding the thing which is outside the soul. And this are the intentions which our understanding introduces as the signification of this name genus, right?

[50:07] We met genus there in our proem right, but it was taken from Aristotle's fifth book of wisdom. Genus is not a likeness of something outside the soul existing, right? But from the fact that the understanding understands animal as something common to many species, right? It attributes to that thing understood as common to them the intention of being a genus, right?

[50:35] And of this kind of intention, although the proximate foundation is not in the thing, right, but in understanding understanding what's common to them, right? Unless you're a Platonist right, and you think there's a man himself man himself, right? Nevertheless, there is a remote foundation in the thing itself, right? Once the understanding is not false, which introduces these intentions, these thoughts.

[51:07] And this is the interesting text, and it's similar about all other things which follow upon the way of understanding, as is the abstraction of what.

[51:18] Yeah. It's a very subtle thing, right? See, and that's why there's a controversy now about that text in the premium to the Nicomachean Ethics. Remember that text we talked about before. Thomas says order is compared to reason in four ways. He's going to distinguish the knowledge of reason by the order that it's a knowledge of, right? So he wants to distinguish order in comparison to reason, right?

[51:54] Now, you know, distinction of four is not understandable, of course. But you look at what Thomas does there. He says there's one order which is not made by reason but can be known by reason, right? And then there's the order made by reason, right? And the order made by reason, he divides into three, right? That's how he gets his four, right? There's the order which reason makes in its own acts, in its own thoughts.

[52:23] There's order which reason makes in the acts of the will, and therefore in our actions, right? There's the order which reason makes in exterior matter, in a chair or something, right? In wood. And then he says, okay, now the order which reason makes in its own acts belongs to logic to consider, right? The order which reason makes in the acts of the will belongs to practical philosophy, and the order which reason makes in exterior matter belongs to the mechanical arts, he calls them, right?

[52:59] That's the technical term. But the art of carpentry, the art of cooking, and so on, right? Art of making cookies. now the art which reason considers the order which reason does not make, right? This is what natural philosophy is about, this order, right? And he says wisdom also belongs there, right? He doesn't say mathematics.

[53:25] I see. Some people want to say, well, yeah, but does he divide, you know, looking sciences into these three, you know, and mathematics be understood in there, you know? He just mentions, you know, you know, we got to be careful. Maybe, maybe there's some kind of what?

[53:42] Some kind of abstraction that's peculiar to mathematics, right? I keep on thinking I'm worried about that one that is the beginning of number, right? One what?

[53:54] It's something abstract to me, right? Does Does that one really exist outside my mind? Yeah, yeah, yeah, yeah. I've always wondered about that I find number very difficult to understand. Yeah, yeah. It seems continuous quantity is easier to understand. than number. Yeah, yeah. And this two or three exists outside I think continuous quantity exists out, you know. I mean, if you eat the whole pie, I'll be complaining about it.

[54:22] But but does two and three really exist outside my mind? I mean, two or three men do, or two or three chairs do. Best I ever. Go get me a three. Yeah, yeah, yeah. Yeah. You know, there's some kind of. So Warren Murray and myself, we both, you know, there's something about this text, you know, that makes you got to read that other text carefully. Maybe maybe it's significant that he doesn't, you know, it's such a mess.

[54:49] It's funny, but but it doesn't give this example, right? He gives natural philosophy is about an order, right? And then wisdom is also about that, right? Okay. But the fact that the interior angle of a triangle is two angles is not something that exists. It's closer to geometry, in that sense it seems closer. Yeah, yeah, yeah.

[55:12] Yeah. Even there, there's kind of a separation, there's a kind of abstraction there because it's not sensible matter anymore, right? You see? Yeah. Yeah.

[55:29] But notice he says there in that second paragraph, and simile est de omnibus aliis quae consequuntur ex modo intelligendi, sicut abstractio mathematicorum et huiusmodi. You see a certain likeness between what logic, right, and what mathematics, right, that it's dealing with something that has a remote foundation in things, right, but the proximate foundation maybe is in the what the mind, you know. And these are two kinds of abstraction, right?

[56:00] The abstraction that you have in mathematics, which is from sensible matter, right? So I always say to students, I used to take the example of a geometrical. sphere Right now. Now, if you throw a glass ball against the wall, it'll probably what shatter, right? If you throw a rubber ball against the wall, it'll bounce back. If you throw a steel ball against it, probably get stuck or go through the wall, right?

[56:22] What about geometrical sphere? Now, you throw it against the wall, but bounce off, or it gets stuck, you know? Yeah, yeah, yeah, yeah. It doesn't seem to be, you know, seems to be something abstract, right? Now, not maybe as abstract as two and three, but still, you know, abstract, right? So, now the third thing now. Sometimes that which is signified by the name does not have a foundation in the thing, neither a proximate one, like the word man above, right?

[56:56] Or the word cat, or the word dog, right? Huh? You know, there's a dog out here that, you know, he came a friend to me when I came out. You know, like I'm an old, old, old friend. Yeah, I don't know if they She knows me enough. If he knew you were a friend of cats, he wouldn't like. Yeah.

[57:18] At the conception of a chimera, right? It's kind of the word for the imaginative thing, right? See, right? So like a unicorn or something like that, right? Huh? You know, you know, yeah. Which is neither a likeness of something outside the soul, right? Huh? Nor does it follow from the way of understanding truly something, right? Huh? And therefore, this conception is falsa right? Okay.

[57:52] Okay. Once it is clear that ratio is said to be in the thing, in so far as the signifying signified by the name, is in the thing, and this happens when the conception of the understanding is the likeness of the thing. Now, yeah, stop at four thirty, right? Yeah. Yeah. The unity of number is difficult to understand. We'll come back to this next weekend. Wow.