Introduction to Philosophy & Logic (1999)
41. Demonstration versus Dialectic: Necessity, Per Se Properties, and Opinion in the Posterior Analytics and Topics
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[0:07] From statements or premises we call them necessarily true. In fact, you could add "and seen" by the reason is necessarily true. And seen as necessarily true.

[0:37] Okay. Now I was just going to give you a very strong argument because being a syllogism, the conclusion will follow necessarily from the premises, and because the premises themselves are necessarily true, then the conclusion must be what necessarily true, right? Okay.

[1:01] And this word "demonstration" is a Latin word which they translate the Greek word, right? Greek word is apodeixis Get the word apodeictic. The horrible word nameless. But apodeixis and demonstration come from the respective words in Greek and in Latin to show something, right? Right. I'm going to show you this is true, right? And sometimes even English that word to show means what something that's going to be very clear, right?

[1:39] That is so, right? And was it Missouri has that license plate? I'm from Missouri. You got to show me, right? As if you've got somebody like Cebes in the dialogue, right? Who's insisting upon you know a necessary argument, right? You've got to show me before I can accept it, right? So that that Greek word comes from that same word, showing. Okay. And that's why in maybe editions, you know, of Euclid and so on, at the beginning of each demonstration, he'll propose what he's going to prove.

[2:18] In English, they translate it proposition, but really propose those more the sense of it, right? What he proposes to to demonstrate, right? And then at the end, he indicates kind of an epilogue that he has demonstrated what he proposed to demonstrate, right? And so you see sometimes Q E D. You see that in the text there of Euclid, which I guess you know is the letters for the Latin.

[2:50] What was to be demonstrated, right? Now we've now demonstrated what was to be demonstrated in this particular proposal, right? Okay. So sometimes you find people using the word Q. E. D. right. I remember William F. Buckley one time um using it in an ironic sense, right? You know, he was kind of recounting the the bad reasoning of his opponents, right? Q. E. D. says.

[3:19] That's kind of plural. But in Euclid, of course, it's supposed to mean? what? Something that is truly a demonstration, right? Okay. Um. And the clearest examples of demonstration are in geometry or in the science of numbers, right? And so, if you read Aristotle's book on demonstration, which is called in English the Posterior Analytics, there are these two books that go together: the Prior and the Posterior Analytics.

[3:52] But in the Prior Analytics, he teaches you how to take apart a argument to see if the conclusion follows necessary from the premises, like we were doing when we went through the forty-eight cases and the three figures there. But in the Posterior Analytics, he teaches you how to examine the premises from which the syllogism proceeds to see if they are necessarily true or not. Okay. But in that book, the Posterior Analytics, he often takes his examples from geometry or from the science of numbers, not only but mainly, right?

[4:32] Because it's more clear that you have a demonstration there. Einstein has had a biographical sketch. You know, if you look at these two volumes there that are out on Harper, there it says Einstein, scientist, philosopher, something like that. And it's actually a collection of essays by different writers, many of them scientists, some philosophers, about the work of Einstein. And there is a number of volumes in this series now, but there is one or two volumes actually voted to Einstein.

[5:11] And then at the end of that, usually the man who's being written up has a chance to what write a reply, you know, comment on these papers, you know, if he finds something he wants to criticize or reinforce, and what they say. And in the Einstein volumes, there is also an autobiographical sketch of Einstein, use of his life, but kind of more of his scientific inclinations. And he says in there that if Euclid did not arouse your youthful enthusiasm, you were not born to be a scientist.

[5:47] But you know, it speaks of the effect that Euclid had on him as a child, and but in terms of the rigor, which one thing was shown from another thing, right? Okay. So I mean, even you know, in our own century, there we see. Most clearly there, right? This rigor of reasoning. And Plato, you know, has these dialogues which we call the Socratic conversations. Sometimes, dialogue is a Greek word for conversation, and they're called Socratic conversations because Socrates is in almost all of them kind of dominates the conversation.

[6:25] But often the conversation is named from the other person with whom Socrates talks. Otherwise, you have to call all Socrates, Socrates, Socrates, Socrates. But the other person that he talks with is a person with whom there'd be some reason to have a conversation about whatever the topic of that dialogue is. So it's something significant, then, about the man with whom he speaks, huh? So he might talk to a Hippias He might talk to Protagoras, or you might talk to Gorgias, or some sophist who teaches the art of rhetoric.

[7:07] He might talk to them about the nature of rhetoric, huh? Because here's a man who should, you know, has some acquaintance with it. He talks with Euthyphro about piety with a man who's charged his own father for being impious, right? And some man you shouldn't talk about piety if you're doing something fairly impious, like charging your own father for being impious. And or he talks in the in the Laches Laches Laches, about courage, that virtue, right?

[7:38] But with whom does he talk? Who's Laches, huh? Well, he's an old general, presumably an old soldier with some experience of courage and and the opposite of courage, right? He's a soldier all these years, right? So here's a man you would talk to about courage, right? Well, what dialogue is about demonstration or about episteme, which is that reason of knowledge, that's an effective demonstration. Well, the dialogue is called the Theaetetus, huh?

[8:10] And Socrates talks with Theaetetus, who's a young man at the time. He's an historical person, it was Theaetetus, who made important contributions to Euclid's Elements, you know, to the mathematics of Euclid's Elements, huh? And so why would Socrates talk with a mathematician about demonstration and reason out knowledge, right? Because such a man might have some experience of this kind of thing, right? Okay. But it's not only in mathematics that you have demonstrations, right?

[8:46] There are some demonstrations in natural philosophy in the beginning, huh? There are demonstrations on logic itself, right? There are demonstrations of wisdom and so on. But the more obvious examples. and easier to get a hold of than geometry or the science of numbers, huh? Okay.

[9:09] Now, that's why you know the customers use that there, right? Not elsewhere, but that's kind of a sign of this, right? And that's why mathematics is named from learning, huh? Because the student, in a sense, most of all, can learn, not simply believe the teacher, right? Because of the rigorous demonstrations and the comparative ease with which those demonstrations can be grasped if you go through them. Interesting.

[9:50] Mathematics and Sacra Doctrina, the one is named from the student, Mathetes the learner, and the other is named from the teacher, doctrina. Doctor, teacher, right? Because in in Sacra Doctrina, most of all, you depend upon the teacher, right? Who's ultimately God Himself, right? When the what our teacher Christ, right? And you most of all the belief there, right? But in geometry, you need belief the least of all.

[10:23] Just an initial stage there, but you know, once you see the demonstration, you no longer believe Euclid, You now know yourself, right? No matter what Euclid says, and then on, you know that this is to be so, right? Okay.

[10:39] Sometimes these teachers lose their mind, you know. Cases of that, right? They start saying very strange things. So, what did they say? Seems to have lost his mind, but but if you understand the demonstration yourself, then you say no matter what he says, right? I'm going to hold on to this, right? I don't need dependent on him.

[11:05] Now, the other main kind of syllogism is the dialectical syllogism. Not one word to name dialectical syllogism. And this is just as much a syllogism as a demonstration, but the premises are not. Either they're not necessarily true, or they're not seen as necessarily true anyway. They're seen only as what probable, right? Okay. So this is a syllogism

[11:44] from probable statements, probable premises. Let's say premises are what statements lead to syllogize. So, syllogism from probable statements, huh? Now, in the book on this, which the kind of translate there in English as they usually do, the English title will be Topics, right? Okay, Topica. That's not for your translation, right? That's kind of I call it what transliteration, right? Just simply referring to apology of Socrates, right?

[12:32] The Greek word is apologia, so apology is what. And letter for letter put into English, right? But apology in English doesn't mean what apologia means in Greek. Apologia in Greek means what a legal defense in the courtroom, right? And so Cardinal Newman, you know, in his kind of autobiographical defense of himself, right, you know, that gives a Latin title, the Apologia. Pro Vita Sua, right? Kind of justifying his leaving Anglicans and becoming a Catholic, and all to the great scandal of Anglicans, right?

[13:08] And maybe enmity of them in some cases, you know. But it's kind of like a legal—I mean, not legal in the strict sense, but it's it's such an apology for it. It's a real what attempt to defend the reasonableness of what he did, right? Leaving Anglicans and becoming a Roman Catholic.

[13:26] So, when it comes to apology, it's not really a translation, but a more like a transiteration. Because translation means what you you keep the meaning, not necessarily the the word or even the form of the word, right? Okay. So, in English, you know they translate this the title. Aristotle's word topics, right? But the root of that word in Greek "topos" is place, okay. And in sense, the Greek title is there about places, right?

[14:03] And a place, you know, without saying it to say so, it is a place is where you look to find a dialectical argument, right? So topics. Let's do that at all, right? Okay. But in the so-called topics, this book about places,

[14:29] Aristotle defines the probable, or actually, more precisely, you might say probable opinions, which is another way of saying it. Say, proceeds from probable opinions.

[14:51] He defines probable there as the opinions of all men, right, or most men, right, or the opinions of all or most men in a given what art or science when they're speaking about the matter of that art or science, right? Or the most famous, illustrious of men in that art or science, right?

[15:17] I notice those five things he says you could divide into two at first, huh? You say an opinion is probable because of the number, the quantity of men thinking, that right, or because of the quality of these men, right? Okay. So it's the opinions of all or most men,

[15:44] and there is simply the number of men that hold this gives a certain probability to the opinion, right? Okay. Or all or most men. Or the most famous

[16:06] in a given art, but when they're speaking, obviously about something that contains that art, right? Okay. So, if all or most geometries say that a square on the side opposite the right angle is equal to the squares on the sides containing the right angle, then that's probably right because all or most geometries are saying this, right? Okay. Or if Einstein says that a scientific hypothesis is freely imagined, that statement is now probable, right?

[16:48] Because this most famous scientist, who in one year had three papers with the Nobel Prize, right? He says that these scientific hypotheses are not reasoned out, but they are freely imagined. Oh, okay. Okay. Um. Shakespeare, right? Says, or stiff, not the modesty of nature. Anything so overdone is from the purpose of playing. Who then, both in the beginning and now, is as poor to hold the mirror up to nature, to show virtue on face or on image, in the very age and body that time is forming pressure.

[17:26] Well, Shakespeare says that the purpose of what happens to hold the mirror up to nature, right? And that's probable because Shakespeare is such an illustrious what dramatist, right?

[17:40] Mozart in his letter to his father there on the representation of anger, right? Huh. In the aria of Osmin there in the touching from the Serail right? He says how the music has to imitate the anger of Osmin, and as soon as he kind of controls himself, right? But not, he says, in a way that is displeasing to the ear, or in other words, ceasing to be music?

[18:03] So Mozart, the most illustrious and famous of the composers, if he says that music must be pleasing to the ear, or not music, that's it. That's certainly a very probable opinion, right? Okay. And especially men are apt to follow the advice of all or most men in given art or science, or the most famous of them.

[18:25] Especially, it's not contrary to what all most men are thinking, right? Huh. Okay. But sometimes the most famous men in an art or science are saying something different from from most men in that art or science. And sometimes you know the most illustrious men are ahead of the other men, right? Or they see more, right? And I've seen examples of this, right? Okay. So it's possible that the opinions of most men and the opinions of.

[18:59] Even all or most men in a given area of science, or most men still, they might not be the same, right? They might hold opposite opinions. So most men, for example, might think that sense pleasure is the greatest thing in life, right?

[19:16] But maybe, but maybe most moral philosophers would not think so, right? Or the most famous ones, like Aristotle and so on, would not think this is the best thing in life, right? So there is some probability in saying sense pleasure is the best thing in life, and some probability in saying it isn't, right?

[19:43] But if a statement is necessarily true, then its contradictory is necessarily what? False. Yeah. If you go back to our logic of the second act, there, when we talked about contradictory statements, right? Statements with the same subject and predicate, right? One affirmative, one negative. And opposed such that both cannot be true, both cannot be false. One must be true and the other must be false, regardless of whether you know which is the true or which is the false one, right?

[20:19] So if you see one half of a contradiction necessarily true, you must at the same time, as it were, see the opposite side as necessarily what false. But if you see one side of a what contradiction as probable, right?

[20:39] Well, then the opposite side need not be what manifestly false, because if the contradictory was manifestly clearly false or necessarily false in any sense and then the side you work would be more than just probable. You see? So there is that

[21:01] ambiguity, right, in the mind there in probable things, right? There can be probability to some extent on both what sides, right? Okay. It might be, you know, that we might be probable for what is more probable, right? Especially if it's very probable, and it's not very probable at all, right? But there's some fear that the other side might have something in it too, right? Okay.

[21:31] Now sometimes Aristotle will speak of dialectical reasoning then as reasoning from probable opinions to contradictory conclusions. Since you can have even opposite sides of the contradiction have some probability, it's possible from probable opinions to reason to contradictory conclusions. Not necessarily as strong on one side as the other, right? But it is to some extent on both, right? But in the case of demonstration, one never reasons to contradictory conclusions, Conclusion that follows necessarily

[22:15] from such premises that are seen to be necessarily true. is seen to be necessarily true itself, right? And therefore its opposite is necessarily false. So you never demonstrate truly demonstrate contradictory statements, huh? But you can reason dialectically, right? To contradictory statements, huh? And have you people read some of the the Meno right? Yeah. Well the third part of the Mino, Mino still wants to know whether virtue can be taught, although he does not know too well what virtue is.

[22:54] And Socrates says, "Well, we should really find what virtue is first before we try to, you know, show that it's one or the other. But if you want to, I'll try to think about it, right? And so he looks and says, "Is any reason to think that virtue can be taught, right? " And he works out an argument, right, that virtue can be taught. And then he he reasons on the contradictory side, right, that virtue can not be taught, right?

[23:21] Okay. Of course, the mind can't accept a contradiction, right? And so after Socrates has reasoned that virtue can be taught, virtue can be taught, and he reasoned that virtue cannot be taught, and in both cases there's some probability in what he's saying, right?

[23:43] He argues that virtue is knowledge and it can be taught, which seems reasonable, right? And then he gives an argument to say that virtue is in fact knowledge, right? And it goes something like, you know, virtue directs us to the good, and that sounds probable, right? What directs us to the good would seem to be some what knowledge, right? Therefore, virtue is knowledge, right? So that sounds reasonable, right?

[24:11] But then he argues on the other side and says that virtue is is can be taught. There will be teachers of it, right? Given the immense what importance of virtue for civic life and living together, right? But then Meno himself admits there seem to be many teachers of it, right? Except those sophists whom you know one would trust, right? His son what? I mean, he's got a very little opinion of the sophists, right?

[24:40] And they're charlatans and they're quacks, you know. So maybe people had their opinion about the sophists. huh? Maybe they were Quacks. So it seems then that it's not the sort of thing that can be taught, right? But then Socrates, when Socrates comes back and he says, "Well, is one of these sides stronger than the other, right? " See, another way of looking at it is there are weaknesses on one of these sides rather than the other, right?

[25:12] And then he goes back and he says, "Well, his thought that virtue is knowledge, and let's go back to that, the back of it for that, you know. " And he says,

[25:28] "Virtue directs us to the good. What directs us to the good is knowledge. " Where's that major premise? What directs us to the good is knowledge? Is that necessarily true? Aren't people directed to the good also by having the right opinion, the true opinion, right? Even a correct hunch, right? And so, so you know, my simple example that I give: the man going down the road, he comes to the fork in the road, right?

[25:57] He wants to go to Boston. Which one goes to Boston? The one goes to Providence, right? Okay. And if he knows that the right fork is the road to Boston, he would take that and get to Boston like he wants to, right? But he doesn't know that's the way to Boston, but he thinks it is the way to Boston. Even though he doesn't know, he's thinking correctly, right?

[26:24] He doesn't know. He's going to take that. He thinks that's the road to take, right? Okay. So he can get there by right opinion, as well as by knowledge, right?

[26:40] So maybe the the great men of Athens did not direct Athens to the to the good. What was good for Athens? Because they knew what was good for Athens, but because they had the right opinion about what was what good for Athens, right? Huh? Is it right? Huh? Is it? And that's so clear in these human affairs, you know, whether the man really knew what was good for the country, or he had the right opinion, right?

[27:09] See, could MacArthur, you know, my famous example there, could MacArthur really have known that the Inchon landing would succeed? He had contingent plans in case it didn't, right? He couldn't really maybe know with all the factors involved, and and that's why the the Navy and the you know Navy and the you know chief of staff were opposed to it, right? You know, as a matter of fact, MacArthur had the right opinion at least, right?

[27:35] You see, but whether he knew, I don't know how great his mind was or not. Whether he knew or merely the right opinion, you know, it led us to something good, right?

[27:48] You see the idea? Okay. Now in another dialogue, I guess I think it's in the Protagoras. You see a weakness on the other side, right? You know that there are no teachers of virtue, right? And I think Protagoras says, well, you know, it's like saying there's no teachers of Greek, right? See. I can name the man who first taught me French, let's say, right. You know. But who was my teacher of English?

[28:23] Well, my mother to some extent, my father, my older my father, my older brothers, my uncles, my aunts, right? You see, they all taught me how to speak English, right? You know, so it's kind of diffused there, right?

[28:40] But I can't, you know, point to a, you know, whom did I hire to teach my children to speak English? I didn't hire anybody. It must be that nobody teaches English to my children, right? See, I I hired somebody to teach them piano, right? And I can point to that person, right? I can point to that person, right? But I didn't hire anybody to teach them English.

[29:02] Must not be teachable, right? See, you see. So Socrates, you know, or Plato, at least, in another dialogue, this comes back, right? And there you see a weakness on the other side, right? So this is dialectical reasoning, huh? Reasoning from probable opinions to what? Contradictory conclusions, even sometimes, huh?

[29:29] But you know, if one side is really true and the other is false, maybe you can find more probability on one side than the other, right? But as Thomas says, in the major proemium to Wisdom there, but with formidine you know, with fear of the opposite, right? There might be something, right? You see? Just like MacArthur was convinced, huh, that we should do the Inchon landing, but there was still some fear in his mind, right?

[29:56] And I mentioned how when he was going there, he called his subordinate officer up, and he went over the whole thing, you know. That's the thing to do, then he said, you know. And he can, you know, thinking about it again, you know. And then he went read his Bible, you know, wait to see if it worked out. You see, So there's that, you know, certain fear that this could fail, right?

[30:14] All kinds of things that happen, right? Now, this is the way Aristotle speaks in the in the beginning of the the Topics, and and so-called book about places. But there he also speaks of the sophistical syllogism, which is opposed to dialectical syllogism. And then he talks about what the name from geometry, but the falsigraphical, the falsely drawn, right? A syllogism that would have a defect as opposed to what's requiring demonstration, okay?

[30:57] But sometimes you just distinguish these two because these are two that are what good, right? Okay. But sophistical syllogism would appear to be a good dialectical syllogism, but it is not, right? Okay. We'll talk about those later on a little bit. And there are some things that would appear to be a what a demonstration that are not, right? Okay. But anyway, these are the two forms that are good.

[31:28] And sometimes Aristotle will, like in the beginning of the Prior Analytics, here he'll go back to what we saw in the logic of the second act, of what contradictory statements are, right?

[31:46] And he'll point out that the demonstrator, right, he takes one half of the contradiction and lays it down as necessarily true, right? And excludes the other half, right? Discards the other half as manifestly false, right? The dialectician, in the concrete, in his conversation with another man, he gives you what a choice, right? Do you think this is or is not so, right? And you say yes or no, right?

[32:19] Huh? According to which one seems probable to you, right? So the real difference there, right? Because the demonstrator sees one half of the contradiction necessarily true, right? The dialectician doesn't see this side as necessarily true, and therefore he gives you what choice as to what seems more probable to you, right? Okay.

[32:48] Now, I must talk a little bit more about necessarily true here now. One thing that comes out in the Posterior Analytics about the necessary

[33:03] is the connection between the necessary and what Greek is called the kath' hauto right? Called per se in Latin, right? The through itself. Or the as such, right? Okay. Connection between these,

[33:25] the through itself, or the as such. Okay. That phrase, "through itself as such," is very abstract, as we just stated here, right? But when you take an example, then you kind of begin to see what you mean by this.

[34:01] Suppose I say that two is a number. Is that necessarily true that two is a number? Yes. Yeah. Okay. Or that two is half of four. Is that necessarily true too? Okay. Now you see a connection between

[34:42] these here and through itself or as such. Is two through itself a number? Yes. Is two through being two a number? What do you say?

[35:10] Okay. And of course, number pertains to what two is, right? Okay. And so, what something has through being itself, through being what it is, right? Obviously, belongs to it through itself or as such, right? Now, half of four

[35:35] is not a part of the definition of two, right? Two, right? Half of four is really a property of two, right? But a property in strict sense, something that belongs only to two, to every two, and always, right? It's something that follows necessarily upon being two, right? Okay. So that, although in another sense, right, belongs to two through itself. Two through being two is half of four, right?

[36:13] Two as such. Is what half of four, right? Okay. Do you see that? Now take another example. If I say the triangle, the triangle is a plane figure. Or I

[36:41] say a triangle is a rectilineal plane figure, right? Does that belong to triangle as such, to itself, to be a plane figure? Yeah. If you're going to define a triangle, you'd say it's a rectilineal plane figure, right? Contained by three straight lines.

[37:04] So to be a plane figure, as opposed to a solid figure like a sphere or a cube like that, that belongs to triangle because of what it is, right? Okay. Anything pertains to definition of a thing belongs to it what as such and to itself, right? Has belonged to triangle as such to be a three sided. triangle as such? Yeah. So the genus or difference, right? Anything that is within the definition of a thing belongs to it through being what it is.

[37:51] It belongs to it as such, right? Okay. And sometimes Aristotle says if something's necessary, it's through itself or as such, right? And sometimes he says the reverse. If it's through itself or as such, it must be what necessary, right? Okay.

[38:12] Now, what if I say that a triangle has its interior angles equal to two right angles? Well, this is not part of the definition, is it, of triangle, right? But does belong to triangle as such in some other ways? It's something that follows upon the nature of triangle, right? Okay. And so the geometer, when he demonstrates this of the triangle, right, he shows it belongs to triangle to what it is, right?

[39:01] So, you know, it presupposes another theorem, but let's take a little simpler than Euclid. Euclid does too, still the same thing, right? But because what triangle is, you can always draw a straight line through one vertex that's parallel to the opposite side, right? And if you know the parallel theorems, you know these alternate angles are equal, and these alternate angles are equal. And then it's obvious that these two add to those two, and the third one will make what?

[39:30] Two right angles, right? So you're seeing something now that belongs to the triangle as such, right? Through being a triangle, right? Something necessarily follows upon the triangle, right? That if a triangle is made, you've made angles equal to right angles. Okay? You go as a definition of what you're doing, right? When you're making a triangle, right? But something that follows necessarily.

[39:59] Now you can see the importance of this for the necessary, and the importance from this for definition, right? Okay? Because the definition gives you things that belong to a thing as such, to itself. And the definition also is involved in seeing what follows upon the what nature of the thing or what it is, because the definition is speech making known what a thing is, right? Making known the nature of the thing, right?

[40:38] And once that nature is made known clearly through the definition, then you can see what belongs to the thing through its nature, right? Okay. Well, if the nature is not understood clearly enough, you might not see what follows from it, huh? Do you see that? Okay.

[40:59] Of course, it was Plato, the great Plato, who first brought out the importance of the through itself, kath' hauto in Greek, right? Okay. For

[41:14] episteme, for necessary knowledge, right? But now, if I say that a triangle is green, a triangle is green. Well, a triangle might be green, right? But is it through being a triangle is green? Does it belong to the triangle as such to be green? Okay.

[41:49] And could you know by thinking about what a triangle is? Could you discover that a triangle is green? No, it doesn't pertain to the definition of triangle. And does it follow necessarily upon what a triangle is?

[42:12] So I could never demonstrate that a triangle is green. Reason, huh? Now I could go back to my senses, right? And I might see a green triangle, right? Okay, that would be a matter of sensing, but not a matter of what demonstrating in reason, huh? Okay.

[42:37] Now snow is white. Does it belong to snow as such to be white? Now maybe it does, but I don't see that it belongs to snow as such to be white, huh? In other words, I don't know well enough the nature of snow to see that it must be white, huh? Maybe somebody else does, but I certainly don't see it well enough. I say snow is white, or even that all snow is white, because of the induction, right?

[43:18] The snow that I see, right, is all been white, huh? But if someone went to Mars or some other place and said, "You know, there is green snow there," I'd be surprised, right? Would I say it's impossible?

[43:35] See, if a man lived in darkest Africa, he was black, and every man he saw was black, right? He'd say all men are black, just like he'd say all snow is what white. All men are black, like all snow is white. Because he'd never seen anything other than a black man, right? But would his mind see that a man must be black?

[44:02] Because when one tries to define man, one defines man as an animal with reason, right? One doesn't put black there in the definition of man. So that all snow is white would be for me a statement that I see as probable, right? And we see it as being necessarily true, but snow as such has got to be white, okay?

[44:28] But if someone said that a triangle, I know if a triangle or I met a triangle that didn't have its interior angles, you could have two right angles. Um I say you are crazy, or you are using the word triangle in a different sense, right? Now, sometimes you know people will talk about a triangle drawn from the North Pole down to the Equator, right? Okay, you draw a line from the North Pole down to the Equator, and then you go over while in the Equator, and then you up again, right?

[44:58] So you got two right angles down here, and then you got something up here, you know, an angle up here. So you got more than two right angles, right? But that's being what sophistical in the first way we'll talk about. it. You're equivocating on the word what triangle, right? Okay, so

[45:19] that's not a plain figure, right? It's not a plain surface. right? So if you're taking a triangle, right equivocally, then you see it has to have its interior angles and right angles, huh?

[45:39] What's interesting, Parmenides, sometimes Aristotle reasons from being necessary to being about the through itself and sometimes reverse itself, and sometimes reverse, right? And Thomas says, "Well, isn't he violating his own rule that we don't argue in a what circle, right? " And Thomas says, "Well, the real demonstration is from necessary to what to itself, right? " But you might take as a probable opinion, and certainly one of Plato's, right?

[46:07] It's a common opinion that science or necessary knowledge is about the what if we state this real knowledge is about the as such, right? And if we make reason from that back to this, right? Okay, but as far as as the demonstration is concerned, the reasons for it to be necessary to its being about the through itself or the what, as such, right? Okay.

[46:35] So is that because is is the first thing is that the demonstration has to be certain? Yeah, yeah. But anyway, apart from that, right? In fact, there are stock reasons in both ways. It very much shows the connection of these two, right? Okay. And as myself, you know, I've talked to you about the the first road and the natural road in our knowledge, right? And sometimes I reason that the first road must be the what natural road, right?

[47:07] And sometimes I reason that the natural road must be the first road. But because they're kind of convertible, right? The nature of the thing or what it is is what's first in that thing, right? It must be what you are before you can be anything else. So because the first road it must be the natural road, and it's the natural road it must be the first. They're very closely tied, natural first, right?

[47:32] That's why in the definition of nature in the second book of the physics, there first is in the definition of nature. Very essential to see that it's first, huh?

[47:49] So here you see that connection between necessary and as such, right? You know my my name for if I mistake me, right? The right translated term reasoned out knowledge, right? I think that helps you to see one could never reason out that a triangle must be green, right?

[48:11] One could reason out that a triangle has its interior angles equal to two right angle because that is a necessary connection of what a triangle is, right? And if I know what a triangle is, I might be able to reason out that it's green. but never that it's green. That would be at best a matter of sensing, right? See that? Not a matter of reasoning out something.

[48:35] Okay. When I define man, I define man as an animal with reason, right? Okay. Now the old you know stock example used to be of a property of man that he's risible, right? Capable of laughter.

[48:53] Any kind of a good good example is taken the medieval thinkers there, huh? But do you see a connection between being an animal with reason and being capable of laughter, right? See, because the incongruity that provokes laughter is something that reason will see, huh? And but the animal aspect, you know, the exterior movements of the body parts, right, when you laugh, huh? But I can see a connection, therefore, between the ability to laugh and what man is—an animal with reason, right?

[49:31] But do I see a connection between being an animal with reason and being white like I am? Do you? No. But because you're an animal, you have to be white. Well, you know, I tell you to watch out for black cats, right? Across your path, huh? So because you're an animal, you don't have to be white, do you? No. And because you have reason, that's any connection there, right?

[50:02] So maybe an animal with reason is white, but it'd be a matter of a sensation looking at myself in the mirror. Oh yeah, or seeing you or something, right? You know. You see that?

[50:16] So sometimes I would distinguish more than one sense of as. Such, right? And we're talking here about two senses, two most basic senses. One is where part of the definition or part of the definition belongs to that which is being defined as such, right? And the other, the property, right, belongs to its species as such, right? But the property is more defined by the species, and and the others just reverse, right?

[50:55] The predicate will be defining the the subject of the statement. This is part of the way we recognize the as such, right? Now, take a little different example of this, here.

[51:29] Must a philosopher love reason? Must a philosopher love reason? Must a philosopher love popcorn? Okay. What do you say about those two questions? Yes, to the first one. Okay. No, to the second. Okay.

[52:20] Now, there must be some as such there, right? If it's necessary that the philosopher love reason, right? But now I might begin with the very definition of philosopher, and say, well, a philosopher, as the Greek word means, is a lover of wisdom.

[52:58] This is the very definition of philosopher, right? He's a lover of wisdom, right? Now Shakespeare says, "Love and reason keep little company nowadays." Okay.

[53:15] But what about he's going to be thinking romantically, right? Okay. But now, is there connection between the other part of that definition, wisdom? Because wisdom would seem to name what the highest or the greatest perfection of what reason, right? Okay. Even the way the modern biologists name man, the Homo sapiens, right? They're using the word Homo there, which means man and human being in Latin. They're using it though in a broader sense for a manlike thing.

[54:05] So popular, you might say, ape. Okay. I used to say to students, used to be a book you see in the bookstores, the one that was very popular, you see it in the window. The Naked Ape, right? It's about man, the Naked Ape. I said, is that the scientific name of man? The Naked Ape. Man has less, you know, fur we'll call it hair than the ape has, right?

[54:29] So compared to other apes he's not naked, right? But that's not the scientific name of man, is it? It's Homo sapiens, the wise, ape, right? Right. Of course, obviously, man is wise compared to the other apes because he has what reason, okay, or excellence of reason, right? So wisdom seems to name that excellence of reason, huh? So could I love wisdom, which is the chief good or the greatest good of reason, without loving reason?

[55:05] So if it belongs to the philosopher as such to be a lover of wisdom, and wisdom as such is the what highest or greatest perfection of reason.

[55:26] Well, could one love wisdom then without loving reason? No, could one love health without loving one's own body? Because health is a good of the body, right? In fact,

[55:47] you could say going both ways, right? Do you love your body? You don't love health. Or do you love health without loving your body?

[56:03] If I want your good, I must love you, right? You see, if I love you, I must want your good, right? So if I want the good of the body, which is health, I must love the body, right? And I love the body, I must want the good of the body, which is health, right?

[56:23] So if I love wisdom, then I have to love reason. And maybe even the reverse is true. If I love reason, I have to love what? Wisdom, right? And then I tell the students, but man is an animal with reason, so if you don't love reason, you don't love yourself. So if you don't love wisdom, you don't love yourself.

[56:44] But it seems to belong as such, right? If man is an animal with reason, how does man love himself if he doesn't love reason, right? And if he loves reason, doesn't he have to love the perfection of reason, the good of reason, right? So what about in the angelic? order? Must an angel love reason? Well, yeah, I mean he's got something better than reason, you know. He's got understanding, right?

[57:09] I think I mentioned how sometimes we call reason understanding. You know, understanding can name the act, it can name the faculty, right? But it's sometimes they will what? Divide understanding

[57:30] into what? Understanding and reason, okay? And it's because man has in a very weak way the ability to understand, right? This is what understanding means here, right? If he's an angel, he understands everything. He naturally understands at once. My son Marcus when he was a little boy said, Why can't we be born knowing everything we need to know?" I said, You want to be an angel? That's what an angel is, baby.

[58:03] Knowing everything he naturally knows, right? Yeah, it's pretty good, you know. Did you like that, huh? So when Shakespeare defines reason, he defines it as ability for large discourse, right? Looking before and after, right? But looking means what? Trying to see, trying to understand, right? You know, man is more trying to understand than actually understanding, but he does understand some things, right? But you know, like Augustine says, there are more things in the Bible I don't understand than that I do understand, right?

[58:37] Even though he devoted his life to understanding the Bible, my son. So since man has imperfectly what is meant by understanding, the ability to understand, he gets a new name, right? Just like the

[58:57] other examples we gave there, right? Just like the kitten gets a new name, right? And the adult cat keeps the name cat because he is fully what a cat is. You can see the angel, right?

[59:15] If he loves the ability to understand, he obviously loves truth and wisdom, right? Yeah. Okay. That's why, in a sense, the fallen angels are going to be tormented, right? Huh? Because they naturally want to see God face to face, right? But they won't. That's very frustrating. That's very frustrating.

[59:43] That's the frustrating frustration you've had in this life. And the souls in purgatory are extremely anxious to see God as He is, right? Huh? So I think it matters to to get to see Him face to face, right? And they have to be purified, huh? Purged, huh? Some more.

[1:00:11] So what's his name? Saint John of the Cross said to his friend, "You know, pray that I have my purgatory on Earth." Unusual request, right? From a friend, right? But you know, it's a very wise request,