Introduction to Philosophy & Logic (1999)
24. The Art of Division: Integral and Universal Wholes, Distinction, and the Rule of Two or Three
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[0:00] Now let's look a little bit at division here, right? We can get to the rule two or three, right? Who knows? Okay. Now, using now division here to refer to the not the definition itself, but to divisions that are not a definition, right? And division in the strict sense is the distinction of the parts of some whole, right?

[0:50] Division is the distinction of the parts of some whole. So in logic, we want to distinguish at least two kinds of division, according to there being two kinds of wholes.

[1:15] Now the one kind of whole, which is the original meaning of the word whole, they sometimes call it the integral whole. I like to call it the composed whole, right? Just see both words. You have, the integral or composed whole,

[1:35] and then a second sense of whole, the universal whole. Now, in distinguishing and in a way defining these two kinds of whole, I use an affirmative and a negative, part of a definition, and the two definitions are just reverse. So the integral or composed whole is, as the word composed means, is put together from its parts,

[2:17] but it's not said of its parts. So the chair you're sitting on, right? Huh? Is put together from the seat and the legs and the back and so on, but chair is not said of the seat and the legs. The leg is not a chair, right? The seat is not a chair, right? The back is not a chair, but put together these make a chair, right? Okay.

[3:00] The word cat is put together from the letters C, A, and T, right? But the letter C is not the word cat. The letter A is not the word cat, right? And so, on. But you have to put these together. A definition is a what? Integral composed whole, right? The genus is put together. The definition is put together from the genus and the differences, right? But the genus is not a definition.

[3:31] The difference is not a definition, right? But put together in a certain way, they are forming a definition, right? Now the universal whole is just the reverse. It's said of its parts, meaning said of each one individually, right? But not composed of, not put together from them, huh?

[4:02] Okay. So quadrilateral is the universal whole. It's set of what? Square, oblong, rhombus, rhomboi, trapezium, but it's not composed of them, right? Okay. The animal is the universal whole set of man, dog, cat, and horse. But it's not put together from them, right? Otherwise, when you say man is a animal, you say man is something composed of cat, dog, or elephant, and so on. It's absurd, right?

[4:34] Okay. You say square is a quadrilateral. It's not something composed of square, oblong, parallelogram, But you know, trapezium okay, okay. So if you understand one of these definitions, the other one is just the what? Reverse, right? Okay. But the integral composed whole is the first meaning of the word whole. And the Greek word for for genus or for the general comes the Greek word for whole, right?

[5:01] And what comes under the whole we sometimes call the particular, but it's like a part, right? So you have these two kinds of holes in every what? reasoned out knowledge, right? What I do when I explain this to students sometimes in college, there I'll go through all the sciences inductively, right? And you see that every one of them divides in both of these ways. Take for example grammar, right?

[5:30] Which is the first science you learn in the way. Grammar is about the sentence. English grammar is about making sentences in English. In Greek, grammar is about making sentences in Greek. Sentence is the subject of grammar, really. Now, what does he divide sentence into? Sometimes what they call the parts of speech: noun, verb, adjective, adverb, right? That's a division of an integral or composed whole into its parts, right?

[6:03] So, is the noun a sentence? No, is the verb a sentence? No, but man walks, right? Composed of a noun and verb is a sentence, right? But then he divides sentence into what? Affirm, or declarative sentence, maybe, right? Question, command, prayer, right? And each one of those is a sentence by itself, right? Okay, but it's not composed of these, is it? Sentence.

[6:35] Sentence is not composed of command, prayer, question, declaration, is it? No, but it's said of each one of these, right? Okay. So the grammarian divides in both ways, right? Okay. Does the geometry divide in both ways?

[6:54] When Euclid divides the circle into two semicircles, is a semicircle a circle? No. He divides a, a parallelogram into two triangles, right? The triangle parallelogram. No, that's a division of a whole into its parts, right? When you divide parallelogram into let's say square and oblong and rhombus and rhomboid, then you divide into the universal whole. So he divides in both ways, and sometimes the same thing in both ways, right?

[7:30] If you go to chemistry and they talk about the atom, they might divide the atom into what? Proton, electron, neutron, and that's what kind of division?

[7:44] Proton is not an atom. Electron is not an atom, right? Maybe an atom is composed of these, right? When I divide atom, like you do in the periodic table, into the hydrogen atom and the nitrogen atom and oxygen atom and so on, then you have a universal whole, right? Okay. So the chemist divides in both ways, right? Okay. Does the biologist divide in both ways, son? How does he divide tree?

[8:11] Well, leaves and roots, and you know, what's in between the roots and the branches. Trunk. Trunk. yeah. See. What kind of division is that of tree? Composed of. Yeah. I think divides tree into the broad leaf tree and the needle tree, right? That's this kind, right? Okay. Yeah, a noun is not a statement, right? But an affirmation is a statement, and negation is a statement, right? But a statement is not composed of affirmation, negation.

[8:54] And since you know Locke is mixing up these two kinds of division when he's saying the triangle in general, is what all or none of these, right? It's species, huh? Like it's kind of we run them all together, right? It's like you know I get the idea of animal by taking a dog and a cat and a horse and so on, and run them? All together, and they're all mixed up, and that's animal.

[9:15] No, no, it's not that, right? You separate out what they have in common, and you left aside their their differences, huh? Now, let me clarify one more thing here about the three words here we've used. the letter D here. You take the word distinction, which I use in the definition of division, division, and division, and then the definition.

[10:01] Since a definition has parts, in a way you break up something into parts, right? You could say a definition in a way is a division, right? Okay, but not every division is a what definition. So division is more universal than what definition, right? Okay. So in the first chapter of the Physics, Aristotle speaks of the definition as diairesis that divides into parts, right? Okay. Now sometimes division and distinction, you know, are used loosely to mean the same thing, right?

[10:36] But in the strict sense, only some divisions are the strict use of the word division are distinctions. I mean, only some distinctions are divisions, but not vice versa. The division in the strict sense is like I defined it there: the distinction of the parts of some whole. So you need a whole already, right? In order to have division, right? Okay. But distinction is is the most universal, right?

[11:04] So every division is a distinction, but not every distinction is a what division, right? And sometimes I have talked to you in Logic, the first act, about those distinctions are not division, but usually I, you know, or contemporaries I leave it to the consideration of famous fallacies, right? Because they are based upon the most fundamental ones, upon overlooking certain distinctions, huh? Okay. And you'll see Thomas Aquinas say, sometimes he uses division, you know, distinction kind interchangeably, but sometimes he's very careful about it, right?

[11:43] One place he's very careful about is when he talks about the Trinity, right? You distinguish between the Father and the Son, the Holy Spirit. You distinguish between the three of them, right? But is that a division?

[12:01] Well, he'll deny that this is a division, right? God is not divided into the Father, the Son, the Holy Spirit, right? But nevertheless, no, that would imply that the Father and the Son, the Holy Spirit, are somehow like a what? Part, right? Which case you're thinking of? God as a composed whole, composed of the Father, the Son, the Holy Spirit, and that would be a very serious mistake about the Trinity, right?

[12:28] Okay. But there is a real distinction between the Father and the Son and the Holy Spirit, right? There's a real distinction between the Father and the Son, and then a real distinction between the Father and the Son and the Holy Spirit that proceeds from them, right? So distinction is really broader in meaning than division, right? Every division is a distinction, but not every distinction is a division.

[12:56] And so when you distinguish the senses of a word, like we did the word before a long ago, right? As we did distinguish the senses of the word "whole," is that really a division, or should be called a distinction, but not a division? Distinction. make up a whole.

[13:16] Or when you distinguish between the the per se and the accidental, such and the accidental and so on. Or you distinguish between the simply and in some respect, right? There are certain distinctions that are very important in thinking, but they're not really divisions in the strict sense. We have a part there in the strict, I mean, whole part in the strict sense.

[13:41] So the word "wise." As they say, a lot of times you use the word "division" and "distinction" kind of interchangeably, you know. It's not some of the same thing, you know. Can you say what is a distinction between them? No, a distinction. What is it? Define a distinction. A division. is a distinction Well, yeah, well, basically, distinction. The basis of distinction really is opposition, right? You have to have some kind of opposition, so you have to go into a study of the four kinds of opposites, right?

[14:18] To explain distinction. Yeah, yeah, yeah. But in the case of division, you add something to that, right? The idea of why we're being distinguished are really parts of some whole, right? Okay.

[14:33] So these are. Descending from the more universal to the less universal. You notice that how we mentioned before how distinction comes before order, right? And when Aristotle in the categories and in the fifth book of wisdom, before he takes up before he talks about opposition, right? That's the basis of distinction.

[15:11] But there are four kinds of opposites, and that would be able to study it in itself. In the commentary on the sentences of Peter Lombard, where we have the distinctions. Yeah. Would they be used in that sense or in a different sense? Meaning for the training, you knew it. More for the arts and the commentary.

[15:35] Yeah, that's a little different sense there. You know, I mean, involves making distinctions, right? You see, but it's like the word, you know, speech and rhetoric. It's a little different sense than what you had in mind. Yeah, they would. They wouldn't involve it. You know, distinctions in there. Yeah, yeah, yeah. So it's thinking more of the idea you're investigating the question, coming to a more distinct knowledge or whatever the question is about, right?

[16:03] Okay. Now, one more thing that we point out there towards the end of that part on division there is that division should exhaust, right, all the parts, right. And some people want to say that the word division comes from the word or the word divide, and divide comes from empty, right? So the way you divide something, you're emptying it out, right? Nothing left there, right? There should be nothing left in there, right?

[16:43] If I divide triangles into equilateral say and isosceles, there's all something in the basket still, right? Scalene, right? you know, you didn't dump a lot, right?

[17:05] Now we come to my invention here, the rule of two or three, right? Okay. And I begin with the question, you know, whether there's any number into which you should divide, right?

[17:25] And can you give any rule about this, right? I don't think you can give a rule that is true universally for any number to divide into. I think you can give a rule that is true for the most part, right? Okay. But the way you approach this is kind of dialectically, and if you go down to the history of philosophy, you see that there are two famous thinkers who are known for always dividing into a particular number, right?

[17:59] In the dialogues of Plato, when you get into division, there in the dialogue called the Sophist and so on, Socrates is always dividing into what? Two, right? Okay, Socrates or Plato, right? You don't know who's original there, okay? But Socrates or Plato in the dialogues is always dividing into two. In Aristotle, the pupil of Plato, in the biological works there, he criticizes the Platonists for always dividing into two, right?

[18:32] Okay. But notice Plato is one of the chief philosophers. And you can give a reason why you should divide into two, and that is that the basis of distinction is what. Yeah, and opposites are two, right? Okay. So you can syllogize there, right? We should divide by opposites, but opposites are two, therefore you should divide into what? Two, right? So it makes a lot of sense what he's doing there, right?

[19:02] And so you have all these divisions, like you know, the arithmetician. he divides numbers into what? Odd and even, right? Well, those are opposites, right? Divisible into two equal parts, not into two parts. Okay. You divide the numbers into prime and composite. Measured by another number, not measured by another number. Okay. I pin the biologists down; they have to admit that the division really makes sense. It's an animal into vertebrate and invertebrate into two, right?

[19:36] Okay. Now, if you don't divide by opposites, it doesn't seem to be a good division, right? If I divide human beings into male and good into male and good,

[19:54] well, some of them could be both a male and good, right? Okay. So it makes some sense to divide human beings into male and female, right? Because their opposites are good and bad, right? Okay. But male and white. Female and white, right? You've got to have opposites, right? You can't belong to the same thing. And opposites are two, so there's a lot of truth in saying you should divide into two, right?

[20:25] Okay. But sometimes it seems more natural to divide into three, like when you divide a triangle, right? Into equilateral, isosceles, and scalene, right? So the force to divide into two, and then you know, you're good. I mean, you know, really, it seems more natural to divide it into three, right? Or the Greeks divided government into three, you know, monarchy, oligarchy, democracy, ruled by one, by a few, or by a many, right?

[20:56] Seems to make sense, right? Um. Nevertheless, as I say, there's a very good reason to divide into two, right? There's a lot of truth in what's been the saying, and there are all kinds of divisions into two, right? As I say, Aristotle criticizes them for always trying to divide into two, right? Now, the only other philosopher who's known for always dividing into certain numbers is Hegel, right?

[21:25] In modern times, 1770, 1831, right? In Hegel's system, he's always dividing into what? Three, right? Now it's more difficult to give a reason for always dividing into three, right? But there's a sign which Aristotle himself gives, right, in the book of the Heavens, that three is the first number about which we say what all, right? Okay. As we were saying before, when you divide, you want to have what all the parts, right?

[22:01] And if three is the first number about which we say all, with two we just say both, right? You got to have all the parts. Well, then three would seem to be that's a sign, right? You divide into three, and some people see it too in connection with beginning, middle, and end. That seems to be all there is, right? Reflection of the Trinity in sense. And Karl Marx says that as a young man, under the influence of Hegel down in the general universities, you're always dividing into three, right?

[22:31] And then after a while, he begins to suspect that there's something kind of artificial in force. It's kind of forcing even in the three other time. Maybe

[22:42] he wasn't always adapting to himself to that, right? Okay. Now, to my knowledge, there's no famous thinker other than these two who's ever tried to always divide into some definite number. Okay. But there's something probable about both, right? So if you combine the two and say don't always divide into two, don't say that like Plato says, don't always divide into three, right? But divide into two or three, right?

[23:14] That has more probability than either what Plato's saying or Hegel's saying, right? Still, I wouldn't say one should always divide into two or three. It seems to me that for the most part, one should divide into either two or three, and that if you divide into more than three, right, you are probably right. Either crisscrossing two divisions, right, or you're dividing and then subdividing into multiple things, right?

[23:51] And so inductively, I see, you know, that most divisions that are into more than three are result, right, of one of those two things, right? And so when you analyze it, you have to divide. See how it's based on divisions into two or three, and sometimes they'll say Aristotle divides government into six kinds of government: monarchy, tyranny, oligarchy, aristocracy, democracy, republic. Right. At six kinds of government, but really he's combining two divisions, right?

[24:29] Division of government into good and bad. that's the name of the good of the whole is good of the part. That's the one division. And then ruled by the one, the few, or the many, and he crisscrosses those two divisions, and you end up with what six. Yeah, we saw Thomas dividing order into four. Remember that, okay? Which he examines more closely, and he distinguishes the order not made by reason, and then three orders made by reason.

[24:59] That's really a division into two, isn't it? Order not made by reason, made by reason. Perhaps that's right, and then he divides the second of those, not by the maker, but by that in which they make, the act of reason itself, which logic will consider right, and the act of the will or an exterior act. So he really has a division into two, and one of them subdivided into three, and that's he gets four, right?

[25:31] Now, take a theological example here, right? You might say that there are seven sacraments. You might divide sacrament into seven, right? Okay, but that's not the way Thomas would divide them in theology. How would you do? How many divisions or how many distinctions

[25:53] does Thomas use to arrive at there being seven sacraments, or to arrive at the seven sacraments and see the distinction one from the other? How many divisions do you use? Three, no, six. You use five distinctions, right?

[26:09] You divide what? You know the sacraments. You know are something sensible, right? And they have some likeness to the natural life, right? Okay. And the first distinction Thomas points out is that

[26:31] there are those who have to be fed and directed, right? To the life, like my grandchildren, they have to be fed and directed, and so on, right? Then there are those who what propagate and direct these little ones, right? Okay. That's the fundamental distinction, right? And so he divides five of them against two of them, right? Okay. And the sacrament of matrimony and the sacrament of orders are analogous to what the ones who propagate and direct others, right?

[27:02] And then the other five to those in themselves, right? Okay. So that's a division into two, right? You distinguish matrimony and orders against the five. The other five of them ordered to the good of the individual, might say, in himself, and the other two what ordered to what directing others, right? So that's a division into two, right? Okay. And then you can distinguish between matrimony and orders, right?

[27:30] That's the second distinction, right? In that group, right? Then, in the first group of five, he divides, but baptism, confirmation, Eucharist against, but confession or what? do you want to call it And the last anointing not even oil, right? Okay. Yeah, that's the third distinction, right? And then he divides his first three according to analogy of bodily life. You have to be generated, you grow, you nourish, right?

[28:05] And he compares it to the three parts of the soul: plant soul, right? Reproductive power, and then, the power to grow, the power to feed itself, and then the ones where we run into trouble, right? You know, become sick or something, right? And then he distinguishes between the way penance is ordered to that and the way anointing is first divide the first division is the one whereby you divide matrimony and orders against. the other what five right?

[28:39] That's one distinction right? In a sense, matrimony and order is a little bit like distinction in philosophy between the family and the city, right?

[28:57] Then he subdivides those, right? And then these five, he divides the three things necessary for the you know spiritual life, according to analogy, of what's necessary for the body life. And then when the defect takes place, right? So he divides the three against the two, right? And then he subdivides um pennants against uh the last anointing, anointing of the oil, and then he divides these three, right?

[29:26] Okay. So you've got one division, two divisions, three divisions, four divisions, five divisions, right? So in order to you know see distinctly the distinction of seven sacraments, you need five divisions, right?

[29:42] But notice, huh? Every division is into either two, or what? three? Now, if you wanted to, I mean, you can you know you can bypass that and say we've got seven sacraments, right? But you don't understand the seven sacraments and their distinction and relations, so on, like you do when you go through these divisions, right?

[30:11] So how do you get from sacrament to these seven? So you have to make five separate divisions or distinctions, right? Then you see exactly each one in respect.

[30:26] Just like we went, you know, from names etymologically as many things, right? You go to the 5, there are 5 of them, right? If you really try to understand why there are 5, you have to divide the 3 against the two, right? And then proper and accident are distinguished, right? And then

[30:46] So you have three divisions there. We get to five, right? And even with the categories, you know, Thomas when he divides it, it's always into two or three, right? That's how he gets the name something said of individual substances by reason of what they are, by reason of something existing in them or something outside of them, right? Then he subdivides the second and the third. It's always into either two or what three, right?

[31:18] So I think there's a lot of truth. There's some lot of truth in in both what Hegel does and what Plato does. And in fact, no other famous philosopher has tried any other number, right? But, if you combine the two, right, you know. For the most part, again, I don't say always. I mean, we know Aristotle dividing quality, Aristotle divides it into four, right?

[31:42] And as I mentioned there, you know, I worked for years on dividing Shakespeare's plays. You know, setting aside the ten history plays, which has some special problems of classification, and divide the the twenty seven plays into four kinds. So I don't always divide it two or three. I am not a fanatic, right? There is an awful lot of truth in there, right? And for the most part, I think it fits.

[32:09] You know what you are dividing, but also I think it fits our mind for the most part too. Our mind has a very hard time understanding division into more than three. It ends up being what we call an enumeration and not a division, right? You see, I can enumerate more than three.

[32:26] Do do you have a sense of Hegel's reasoning for his views? Well, it's there is a perverse imitation of the Trinity there. There is a perverse imitation of the Trinity. Oh, really? Yeah, yeah, yeah.

[32:47] And then there is later on a perverse imitation of the incarnation. In the Hegel system, yeah, yeah, yeah. You see, the Trinity, in the Trinity, the the uh the son proceeds from the Father, right? And then, from the Father Son proceeds the Holy Spirit, see, well, Hegel has a perverse imitation of that, right? Where he has the you know the thesis and the antithesis, yeah, you know, something there, negation, negation, and you have this thing, and you have the same thing reiterated.

[33:21] That's kind of a bizarre imitation of the Trinity, and very genius, but very imaginative, right? But it doesn't really uh fit things very well. And then he, you know, he does this for a while, and this is all mental, and then he suddenly jumps to matter. This is kind of a perverse imitation of the word was made flesh, right? But understood in in uh in the sense in which those heretics, you know, say the word was made flesh, that the word itself became flesh, right?

[33:49] You know, you know, thought becomes matter. Then you have union of thought and matter rising up in the spirit. You know, you get the Hegel system, which is the culmination of all history, right? So I mean, there's more theology there than philosophy, right? But perverse imitation. Yeah. After him comes comes. Feuerbach right? And Feuerbach was a bridge between Hegel and Marx. And Feuerbach's famous work is the Essence of Christianity, right?

[34:21] Where he says the real meaning of Christianity is that that that man is God. So, I mean, you know, it's really perverse what goes on in the modern philosophers, you know, they could go on.

[34:39] But he was very theological, right? You know, not Catholic, circles, in circles and so on. But I think part of the problem with the modern philosophers is is they've given up the faith, and they've given up, therefore, theology, right? And therefore, they can't distinguish between theology and philosophy. Because I think I mentioned the principle before. I think it's a universal principle, but I I- I show it usually inductively first that it always belongs to the higher knowledge, right?

[35:13] And the knowledge that has more the character of wisdom to distinguish between itself and the lower knowledge, and to show the order between them. Mm. And I can, you know, show this inductively the first distinction we make is between the reason and the senses, right? And it's belong to reason or the senses to see that distinction. Well, the senses can't distinguish between reason and senses. But reason is the is the higher knowledge, and it's more has the character of wisdom, right?

[35:43] Okay. And does belong to uh uh if you take even the inward senses like the imagination. does the It's a distinction between imagination and reason belong to the imagination or reason to make that distinction. Yeah, and therefore the order of the senses to reason or the imagination to reason belongs to only what? Reason. okay. Then, um, uh,

[36:17] the distinction, say between mathematics and natural philosophy, where is that made? is it reason or what science? Yeah, it's made in mathematics and natural philosophy. Natural philosophy, yeah, yeah, and that is more the character of wisdom. In fact, it was thought to be wisdom, right? But the distinction between wisdom and natural philosophy, mathematics, is made in wisdom, right? Okay. So if you compare theology and philosophy, theology is wisdom in a higher sense, than philosophy, as Aristotle himself would agree, if he knew about, it right?

[36:54] Because the great great Greek philosophers all say that God either alone is wise or God most of all, right? Mm. So a theology um, that's based on revelation, right? Based on the word of God, is a sharing of God's wisdom. It's more the character wisdom. So Thomas says in the first question, of Summa, right, the theology, revealed theology, has more the character of wisdom than the philosophical wisdom.

[37:17] So therefore, the distinction between philosophy and theology doesn't belong to philosophy, but to theology. And to show, therefore, the order of the one to the other. So now the Greeks aren't in the need to distinguish between philosophy and revealed theology because they don't have any revealed theology, right? See, they don't mix them up, right? But the modern philosophers are in a civilization, that was originally Christian, right, and where there are still believers around and where they're exposed to theology and so on.

[37:46] But in having given up revealed theology, the faith, revealed theology, they've given up the very knowledge whereby they could distinguish between the two, and so they start to mix up the two, right? And they start to use philosophy also as a substitute for theology, and they seek in philosophy things that they've given up in theology. They can't get it, you see.

[38:12] And it's a tendency, you know. Sometimes, sometimes people, you know, they get uh they have a uh they're a philomythos as, Aristotle said, right? They have a love of the myth and the stories and so on, and they're something like a philosopher, right? But then philosophy is too high for them or too abstract or whatever, right? And they kind of seek in literature a substitute for philosophy, right? And that's kind of understandable, right?

[38:38] So the modern philosophers seek, in a sense, a substitute for theology in philosophy, right? And that's why you find the demands of modern philosophers—you know—they're always criticizing the senses because the senses are an imperfect way of knowing, right? And the Greeks knew the senses were an imperfect way of knowing, but but it becomes a chronic complaint of the modern philosophers, right? And they're demanding a certitude that doesn't in any way depend upon the senses.

[39:09] And as a human being, just naturally, you can't you can't you can't get in like that. And so they end up all in despair or you know skepticism like that. They're demanding a certitude that's more than human. They're demanding you know the certitude of theology in philosophy. They can't get it there, right? Theology is more certain, being based on the word of God than philosophy. And so in a sense, they're seeking a substitute, right?

[39:37] In philosophy, for the pseudo they gave up, they gave up the faith in theology. They can't get it there, right? So I mean, I hope the stage. stage.

[39:56] Plato in the dialogues he's always distinguishing between between rhetoric and what in political philosophy, right? And to whom does it belong to distinguish between those two?

[40:12] Political philosophy. Yeah, that has more the character of wisdom, right? But the rhetoricians can't make that distinction, right? And Aristotle says in the book on rhetoric that some rhetoricians, you know, who are good at persuading people, they think they're politically wise, right? Partly because of boastfulness, partly from ignorance of how these kinds of knowledge perceived, right? Not that you have weaknesses, he says.

[40:40] But the rhetoricians can't do this, right? You know, when he was distinguishing before between speaking properly and speaking metaphorically, right, or figuratively, right. To whom does it belong to make that distinction?

[40:58] Yeah, yeah. You know, you can't define what a metaphor is using metaphors. You can exemplify, you know, metaphors, but you can't define what it is to speak metaphorically using metaphors. It doesn't know itself, right? So it doesn't have the character, much the character of wisdom. But in speaking properly, I can say what it is to speak properly. I can define definition. and so on, huh? Or you distinguish between knowledge in words and statements, and knowledge and mathematical symbols and equations.

[41:34] To whom does it belong to distinguish between those two knowledges? Has knowledge in words, Yeah, yeah. I can say in words what it is what a word is, right? We've been saying what a name is here and so on. But you can't write an equation that says what an equation is.

[41:57] So the knowledge in mathematical symbols and equations doesn't know itself, right? That's the first thing for a wise man to know himself, right? So the knowledge in words and statements is has more the character of wisdom than the knowledge in mathematical symbols and equations, huh? Because Heisenberg recognizes that, huh? He's talking about trying to put into words what the scientist has gotten in symbols and equations, right?

[42:26] He often speaks of how the mathematics is wiser than we are. We don't know what it means, you know? And they try to state in words, you know. He says, "Well, we have to go and talk to other people, but even for the scientists, he says that's a criterion of how much he understands: his ability to express it

[42:42] in words. " So, and it's a kind of a universal principle that it always belongs to the higher knowledge. The knowledge has more the character of wisdom to distinguish between itself and the what lower knowledge, right? And, there, consequently, since distinctions before order, right, it always belongs to the higher knowledge to say what the order is, right? So, it belongs to the natural philosopher, the natural scientist, to say to what extent mathematics is useful in natural science, right, and how it can be used, right.

[43:18] And the limitations of math was seen by the modern scientists, huh? Aristotle. too. So that kind of covers this kind of way. Now, let me give you the. I'm going to be away for a little while. You know, I've got a grandfatherly concerns, right?

[43:47] I'm going away this Thursday, Thursday this week, and then coming back on the thirty first, right? So, yeah, I don't. I'm going to probably get in late that day, so