Logic (2016)
Lecture 45: Syllogistic Form, Matter, and Demonstration versus Dialectic

Transcript
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No A is B to no B is A. Now, I'm not sure about the prerequisite. I don't accept that. I'm from Missouri. How do you know you can turn that around, huh? I just put an assumption in the part of the prerequisite. Well, you worked at Assumpton College, so that works. That's appropriate. I want you to prove to me that if no A is B, then no B is A. Well, that's quite a demanding thing, right? Because, I mean, there's an infinity of the statements that could be in the form of no A is B, right? Why don't you show me in every one of those examples where no A is B? I mean, no dog is a cat, no cat is a dog, right? One circle is a square, and one square is a circle. Yeah, but, you know, there's an infinity of the universal negative statements, right? I can't go through them all, right? You make that thing, you take that or stop, right? I maintain that if no A is B, then no B is A. Now, if you say that ain't necessarily so, that it's possible, when no A is B, that sum B, at least one B, is like A, right? Well, let it happen. You see, it could happen, right? It ain't necessarily this case. Now, sum B is A, let's give a name to the B that is an A, even with just one single B, right? We'll call the sum B that is an A, X, right? Then X is both a B and an what? A A. Okay? Could you say that, could you say there could be, sum B, at least one B that is an A, right? And so, if you call that B that is an A, X, since it's a B that is an A, it's both a B and an A, isn't it? Therefore, there's sum A that is what? B. Which, if X is both A and B or B and A, then there's sum A that is a B. But that contradicts this, right? Can sum A be a B when no A is a B? That goes back to the axiom, you know, of contradiction, right? No A is a B and sum A is a B. Contradictive. Can't stand, right? So you would contradict this unless you admit this, right? If you deny this, you have to admit this by contradiction and then you end up with something being both a B and an A. And then you end up contradicting that. So you're forced by the truth itself, right? Thomas is, you know, I was reading the 22nd question there of the, uh, the Egritate, Bonitate I call it, you know, because it starts with the, you know, later on. He's talking about, you know, can you coerce the will, right? He's arguing you can't, right? But you can in a way coerce the mind, right? Because sometimes the mind doesn't want to admit something, you know, and then you're forced by the truth itself, right? To admit that it's true, huh? So this guy didn't want to admit it. He turned this around. He thought that was wild deep, right? But now he showed that he must admit that, forcing him against it. He had the student out of California, you know, he always committed almost every class with an objection, you know. I've been all the same. You know, it wasn't a real difficulty to solve it yet. But one time we had a conversation and something after the course was completed, you know, and so on, he said, I was shot today, you know. But he's a student though, right? And when I started to be planning, he'd be planning for it. And as I gradually, you know, he saw all these objections, you know, it seemed kind of relaxing. We didn't, you know, have a story that I teach on your toes. So, if you can turn this around, then you've got no V as A, and just keep every C as V. And lo and behold, by magic, by conversion, at least, if not by magic, you are in what figure now? Well, it's obvious now that no C is what? No C is A, right? So, it follows necessarily that no C is A, but it's not quite as clear as the first figure. And you have to convert in order to make it clear that the set of all or the set of none in this case applies, right? And you get back to the first figure. So, the first figure, right, is called first, right? Now, can I turn this around? And get a conclusion that no C is A? Well, I can't work this out with a set of all, obviously. I can't use a set of none here because nothing is said to be a C, right? But I could turn this over into what? No B is C, and every A is a B. Now, if no B is a C, but every A is a B, then what? B is C. Yeah. I want something with C as a subject, right? A as a predicate. Oh, I can take two steps. I have to convert twice, right? So, it does follow that no C is A, but I got, oh my God, twice, right? But I get something like the first figure in both cases, right? So, I can get a universal negative from, perhaps, just in this form and one in this form, right? I remember when I was a young philosopher and learning logic a little bit, and actually, you know, when Richard started teaching me logic, I was in high school there, you know? So, I found an exam. I did it, right? I used to give you credit for the course that I was taking, right? But, when I got thinking, you know, about, you know, the God and so on, right? Well, God is not a universal, right? Every God is pure act. This individual God, right? Is pure act, right? But, can you convert, you know, a singular like that? If you say that God is not composed, can you turn it around and say, if that's true, that God is not composed, that nothing composed is God? Because if something composed was, what, God, then God would be, in that case we'll call X the thing composing that it's God, and it's both God and composed, and then God is, what, composed. So, you can convert that, right? Take a simple example here. Socrates is not a, what, woman. Can you turn it around and say no woman is Socrates? Because, if you don't admit that no woman is Socrates, then some woman could be Socrates, right? Now, some woman is Socrates, let's give her a name, call her X, right? Well, X is both a woman and Socrates. Therefore, Socrates, who's X, is a woman. And you said Socrates is not a woman, right? Okay? Okay? So you can turn around, you know? Well, I thought it was important for me to say that we still try to be like God, right? That you can, what, treat God, not composed, and turn around and say nothing composed is God, right? God is infinite. Let me define it as God, right? Right? Right? Right. Right. Right. Right. Right. Right. Right. Right. Right. Can't do anything with them, right? Because even for the sin of none, you've got to have an affirmative statement, right? So, I expect you can find examples for A, B, and C to prove that this is nothing, right? Nothing down here, right? Nothing follows, necessarily. Okay, this is kind of simple stuff, right? You can take animal, right? Now, to avoid stupid mistakes, you always check your material. No A is B. No animal is a stone. That's true. No C is B. No cat is a stone. That's true. No tree is a stone. That's true. So, with these examples, the premises are true, but matter is perfect, right? So, if there's any defect, it can't be the matter. My matter is perfect. If you have an argument that an animal is a stone and no cat is a stone, you might say, can you prove from that that every cat is an animal? Well, it might be that no C is an A, right? So, you have one example where every C is an A, and that means that no negative statement is always the case. No tree is a what? Every is an animal, therefore no affirmative statement is always the case, right? So, no affirmative and no negative statement is always the case, and therefore none of them can be what? Necessarily following, right? So, nothing necessarily. It ain't the syllogism, right? It isn't the syllogism. the son holy spirit amen god our enlightenment move us god to know and love you help us god to know and love you pride in angels strengthen the lights of our minds or to illumin our images and arouse us to consider more correctly saint thomas aquinas angelic doctor pray for us help us to understand what you are written in the father son holy spirit amen so what's the difference between a demonstration and a dialectical syllogism do they have different forms this is the distinction between the form and the matter of the syllogism is that distinction well you know i'm making kind of a monoduxio right you say what's the difference between um adding subtracting multiplying or dividing correctly right and then having the right numbers to add subtract multiply or divide right and to get the right number from adding subtracting multiplying or dividing right you must do two things right you must add or subtract or multiply or divide correctly but you can do with even the wrong numbers right which must also have the what right right numbers right huh so i took the example there from being on the beach there with uh 19 grandchildren and after swimming and so on there was an ice cream place there right right on the beach so it was generally agreed that grandpa should buy ice cream cones yeah for the 19 grandchildren plus the adults that were present right and so um i had to multiply the number of people who were going to get ice cream cones with the cost of the ice cream cone right so it's one thing to multiply correctly those numbers right it's another thing to have the what yeah yeah now there's something like that with the soldiers given these uh premises right and does something follow necessarily from them what is that like in the what's that proportional to in the calculation yeah yeah and then are these propositions themselves you know true or false or the necessary or probable or something like that uh that's analogous to what yeah are you sure these are the numbers right this is really what ice cream cone cost you know they really have the right number of grandchildren or it's only probable this is what it's going to cost right last time about ice cream cone cost this or something you know but it might be different on the beach or more or less or something right huh you know so the difference between demonstration and dialectic right is in the form or in the matter yeah yeah now it's given the premises right that the demonstrator uses right and given the premises that the dialectician uses you can ask does something fall necessarily from these what premises right and that's what we do when you talk about a b and c which drives my wife crazy right i thought i can't follow cbc stuff she says men are understand better than women but women are more capable of loving than men i get to accept that okay but when you use letters you kind of abstract from what what the matter is right so you don't mix up the two things right and uh but then the premises from which the uh demonstrator reasons are seen by him as being necessarily true right either because they're obvious like the axioms and the postulates of geometry all right angles are equal and so on right the whole is more than the part and quantities but yeah i'll take the simple example there of the theory geometry there where it says that straight lines intersect these opposite angles will be what yeah and then these two will be equal right okay now how do you know that right well you have to realize that if this is a straight line meeting a straight line right these two angles must be equal to two right angles right okay because you know what a right angle is when a straight line meets a straight line it makes equal angles we call them right angles right when i use it meets it at an angle it's going to be equal to what you divide into their parts it's going to be equal to two right angles right so i'm giving these letters here now you can say x plus b must be equal to two right angles right and what a plus x must be equal to right angles so x plus b must be equal to a plus x right and if equal subtracts from equals results are equal to therefore so i demonstrated that right that's pretty smart right okay but i demonstrated it from statements that are what either obvious or that are what either obvious or that are what shown to things are obvious right okay so the demonstration the demonstrator sees his premises as necessarily true right either because they are evident in themselves known to themselves or because they have been arrived at through what real syllogisms right from statements that are obvious right okay you're wondering you know what we call science that all respect to science in the modern world because all these things that come from science right like telephones and you know because she had funny and so on but um is science and if you actually what is euclid's elements i'd say it's reasoned out knowledge when i say reasoned out that's the ultimate thinking out right so there's thinking out distinctions divisions definitions picking out statements right and finally picking out conclusions right so i include everything that comes before conclusions right but i say it's a reasoned out knowledge of things right is that what science is in modern things is reasoned out knowledge using reasoned out knowledge too many it depends that because that's the general perspective of culture but there is cutting edge experimentation you know see einstein the manual 1905 right presented a published i guess three what papers right all of which were worthy of the billbell prize they say but they're believed that is as fruitful as einstein right huh seems on terms of those things but einstein says that a hypothesis in science right is freely imagined is that reasoned out yeah and people notice the fact that the great discoveries in science you know are made by young men maybe in their 20s or 30s or at least right as they get older in their 40s or 50s something like that they don't have because they're not their imagination that's free and rigorous and so on see and i read heisenberg's you know things that he's talking about his own theories right he did as a young man right in his 20s and so on right he keeps on explaining the pattern very better you know but he's not you know discovering making very disgusting kind of amazing ones that he did right now because you wonder is that really reasoned out of knowledge right sure it is and you know the way you you say what do you do with the sector if the hypothesis is freely imagined it doesn't it's not self-evident knowledge right uh how do you test a hypothesis or you tend to test it by itself your predictions right but is that a syllogism if a is so then b is so my hypothesis is correct would be at the tips of the sun at 10 o'clock at 10 o'clock exactly at the tips of the sun does that prove that my hypothesis is correct You know, this is a big dispute between Fugins and Newton, right, huh? Newton was explaining light as a shower of little particles, and Fugins was what? It was a wave effect. And so they experimented fine, right? And the light behaved like what? It was waves. Therefore, they said it was waves. But then the photoelectric effect in 1905, Einstein showed that what? The photoelectric effect, you know, follows if you say that it's made of little particles, but not its waves. I'm really puzzled, right, huh? Is it waves or is it what? Little particles, which they eventually call photons, right, huh? So I guess what happens is when light strikes a thing and what? Knocks out electrons, right? If you increase the intensity of the light, you don't find any things coming out, what? Faster, right? Which would be if it was just a wave-like phenomena. But you find that more electrons are coming out at the same speed. So it's like this individual collision between what? Little particles, which they did around and called photons, eventually, right? And individual. So it had been proven, right, that Newton was mistaken as to what light was, and Hugh James was correct when there was an experiment where it acted like a wave, right? Then there's another experiment where it acts like what? A shower of particles, right? Well, how could it be both? As Heisenberg said, Einstein just knew there was a contradiction here, appearance at least, right? But it could explain the photoelectric effect except by assuming that, what? This hypothesis. So you wonder whether it's using that knowledge, right? Maybe it isn't. Interface between reason and reason-out knowledge that one has, and also flashes of inspiration, intuition, or does that question even make any sense? Yeah. People live in kind of a familiar era to these things, and they kind of get an insight into what they are like, probably, you know? It was Niels Bohr, right? He took the quantum and applied it to the atom, right? Kind of amazing. But he wouldn't like that much into that right now, right? Okay? So, when Aristotle wrote the prior analytics, right? That's about the form of syllogism, right? So it's done in terms of what? Letters, right? I'll use examples to show that some form is not a syllogism, right? But Aristotle says that, you know, to demonstrate the dialectician, they syllogize in the same way, right? The conclusion follows what, necessarily, right? The same way, you see, you know, you work with the correct numbers, and I work with the incorrect numbers, we multiply, or... The same way you and I, right? So as far as our multiplication, right? My multiplication is as good as yours. But you have the right numbers to multiply. And I've got maybe only one of them right, or one of them wrong, or something, right? That's, that's like the map, right? Okay? Your conclusion follows from your premises, just as much as my conclusion follows from your premises, right? But one of his premises is certain. Oh, great, man. I'll start with Thomas today, you know, because I've been reading it in 23 there, yeah, on the, uh, Libra and Pipitreum, right? And Thomas is asking, now, is this a, a, um, a power-up that we have, right? Well, of course, what the word, um, Iuditium Libra means, what? Well, the objection says, that's an act. It's not a power. Judgment is an act. So then, Libra or Pipitreum is not, what? A power. It's an act. So how does Thomas answer that, do you think? To me, he's got to conclude, it's the will, but, you know, or the reason, it's going to be a power, right? He says, well, he says, the vis, the vocabulary, right? It would seem to indicate that it's an act, right? But, uh, from the custom of speaking, right, yeah? It's understood to be the source of this act, right? Now, I was doing something like that the last time. Remember the word philosopher? And I said, is God a philosopher? What would you say? He said, if you look at the word philosopher, it means a lover of what? Is God a lover of wisdom? But I don't know if it's a good idea to go around saying that God is a philosopher. It's my favorite philosopher. Yeah, yeah. Even though he's a lover of wisdom, he loves wisdom more than we do. He's wisdom itself, right? He loves himself. He's the only one that loves himself adequately. So he's the most, of all, a lover of wisdom. But according to the, what, the origin of the word, right, huh? What is the intention of, of, uh, Pythagoras when they said, you know, you're wise. I mean, the wonderful things you're discovering, you know, right? The Pythagorean theorem and things of this sort, right? And, uh, he said, don't call me wise. God alone is wise, right? Well, what shall we call you? I call you something. Don't call me a lover of wisdom. It's, uh, the name of a man who, what? Knows himself not to be wise as God is wise, right? With the person that God is not wise, in fact, right? But he loves wisdom. Well, then you see, it's not. The word itself, it seemed to indicate it could be applied to God as much as to, what? Pythagoras. And more to God than to Pythagoras, right? Because he loves wisdom more than Pythagoras does. But he had to respect, you know, the custom, right? Because these things signify by custom, right? And he said it didn't mean he was equally a lover of wisdom with God. He meant that he didn't really have wisdom, right? You know? But he was trying to pursue it as far as he could, right? So the prior amlytics, which is about the form, they call it, of the syllogism, right? And it has all those letters in it and so on. Uh, that's looking to see whether, given these statements, something else follows necessarily from the right. That doesn't say anything about whether the statements themselves are necessary or probable, And in the demonstration, the premises will be seen to be, what? Necessarily true, huh? But in the case of the dialectic, they'll be seen merely as, what? Probable, right? Okay. Now, um, you can see a dialectical syllogism is a syllogism from probable, what? Opinions, right? Now, did we talk last time about how we define probable opinions or how Aristotle does, right? Okay. Let's speak here of a dialectical syllogism. So, syllogism, probable, opinions. Opinion, Aristotle says, is probable because of the quantity, or the quality of men, what? Thinking it, right? So, it's the opinion, probable opinion, is the opinion of all or most men, right? That's probable because of the, what? Quantity, the number of men holding it, right? If all or most men think, right? The sugar is sweet. That's probable because all or most men think that, right? Or the opinion of all or most or the... Okay. most famous of men in a given art or science, or the opinion of all or most men, or the most famous, when speaking about what pertains to that art or science, when speaking of what pertains to that art or science. So if most doctors say that smoking is bad for your health, if all doctors or most doctors say that smoking is bad for your health, that's a probable opinion, right? Because there are men in a particular art or science, and it's speaking about a matter that pertains to their what? Art or science, right? What is helpful for health and bad for health, right? Or you take the most famous men, right, huh? Okay. So I was quoting Einstein, right? Einstein is the most famous scientist, right, huh? And he says the hypothesis in science is free of the imagination. Well, that's probable because what? Einstein said, right? I was quoting that statement of Einstein. Why is Einstein's opinion based? You know, you're a philosopher, right? But you've got to consider that seriously, right? Okay. So you'll see any disputed questions of Thomas, you know, often they'll have a quote from Gustin or a quote from Anselm or a quote from Damascene or somebody, right, who's famous in the art or the science of theology, right? And if he says this, well, then you've got to take that seriously, right? Think about it, right? Think about it, right? Not to say it's necessarily true, but, you know, okay? Which is more important than opera? The words of the music. Mozart is famous for his operas, right, huh? They perform Mozart's operas all over the world, right? Every year, right, huh? My son's at West Point there was the bicentennial Mozart's birth, and they had Mozart opera in the fall, right? And they had Mozart opera in the spring, right? The Eisenhower, that part of the Eisenhower opera, right? And they're bringing those, you know, good groups to the city opera in New York and so on, right? So Mozart's famous, you know, for writing operas, right? And he says, in music, in opera, he says, the words must be all together to obedience. The words have a masculine element, right? He's a female, okay? But, you know, so in fact, even the famous, you know, the father is famous for his operas too, right? That wasn't my mind, isn't it? So, you could say, opinion is said to be probable because of the number of men holding it, right? The quantity of men, and that's if all men say this or most men say this, right? Or because of the quality of the men. If all or most men, or the most famous in some art of science, say something that pertains to that art of science, right? What's the most famous book of geometry in the book? Yeah, Euclid's Ellen, right? And for thousands of years, right, it was, you know, the text, right? And so, if Euclid says, you know, that the interior angles are triangle to right angles, that's probable, right? Or if the figure says that in a right angle, triangle, the square and the side opposite the right angle, right, is exactly equal, always to the squares and the sides, and take right angles, that's probable, right? I mean, men who have a theorem meaning after them, right? Euclid's Ellen is about the only theorem I know, reading, you know, geometry, right? That's being after somebody, right? He's famous, he's famous, right? We're philosophers, too. We've got to be stepped in that, right? What does the word mathematician mean, by the way? Well, it means one fond of, like, learning. It's a synonym for philomathes, a lover of learning, right? So, Plato says that philosopher must be philomathes. So, there's a similarity between the word philosopher and the word philomathes, right? Philosopher is more precise as to what the ultimate goal of all learning is, which is wisdom, right? Sophia says his analogy back, right, huh? But in general, that'd be a philomathes, a lover of learning, right? To be a, what, philosophus, right? So, there's a similarity to realize that, huh? To go back to the Greek, huh? So, now in the case of the demonstration, the premises are, what, seen to be necessary, right? The big difference between them, they differ in their matter, right? And therefore, if you perceive for opinions that are probable, then the conclusion is necessarily probable, right? Because it follows necessarily from, but it ain't necessarily so, right? But in demonstration, if it follows necessarily, right? If it has the form of syllogism, right? The conclusion follows necessarily from the premises, and the premises themselves are necessarily true, right? I mean, all of them, right? Then the conclusion is, what, necessarily true, right? The conclusion is, what, necessarily true, right? The conclusion is, what, necessarily true, right? The conclusion is, what, necessarily true, right? The conclusion is, what, necessarily true, right? The conclusion is, what, necessarily true, right? The conclusion is, what, necessarily true, right? The conclusion is, what, necessarily true, right? The conclusion is, what, necessarily true, right? The conclusion is, what, necessarily true, right? The conclusion is, what, necessarily true, right? The conclusion is, what, necessarily true, right? It must be so, right? So, going back to the theorem that I gave you before. Simple enough. Straight lines intersecting is the cause of what? The equality of these angles, right? When you go through the demonstration, you see why those angles must be what? Equal, right? And you know the cause of it. The lines intersecting are straight. And you know that it can't be otherwise now, right? So, you have these three elements in the, what, definition, the demonstration, what, or quit. You're going from cause to what? The effect, right? You know these intersecting lines before you know that these angles must be equal, right, huh? But you reason from the fact that there are straight lines and they intersect, right, huh? That those angles will be equal, right? So, you're reasoning with the same. You're reasoning with the same. You're reasoning with the same. You're reasoning with the same.