Logic (2016)
34. Truth and Falsity in Statements: Either/Or and If-Then Statements and Syllogisms
Class of 2017-03-09
https://berquistcourse.com/course/philosophy/2-logic-2016/034-truth-and-falsity-in-statements-either-or-and-if-then-statements/

[0:00] Let's talk a little about the statement and say why that is important, right? Well, Aristotle himself points out where do you find truth and falsity? You find it in things. You find it in the mind, but in the second act, right, not in the first act, right. So if I say, if I say,

[0:37] dog, right, true or false? You've got to say something other than dog, right? To make a statement. Say a dog is a cat. Well, that's false. A dog is an animal. That's true, right? Okay.

[0:52] Dogs are ferocious, Thomas says. There are exceptions. But? We have an exception. So sometimes I distinguish between a statement or a simple statement, you'd call it, right, and a compound statement, right. Okay. Let's take a simple statement first. You say, well, what does truth and falsity mean, right? Okay. So if I say that a take an easy example, a square is a quadrilateral. A square is a what?

[1:50] Circle. A square is not a quadrilateral. And the square is a what? Quadrilateral. Oh, you had that before, a square is not a circle. Yeah, this is not a circle. So then, the square is a circle, right? Okay. Well, we see these first two statements are true, right? And the second two statements are false. So when you say that what is is, you're being what true. And when you say what is not is not, you're being what true.

[2:37] And you're being false when you say that what is not is, or what is is not rather, or when you say what is not is, right? It's fairly easy to see, right, what it means, right? Okay. But maybe you don't understand a little bit better. You have to think out the division of a statement, right? A simple statement, right?

[3:12] Now, let's go. Okay. Now let's go back to the rule two or three, right? Now I usually say it's the rule two or three, but sometimes I'm more distinct and I say two or three or both, right? Necessary. And my favorite example, which Aristotle divides the plot into two or three and two, right? Now you can divide a statement, and it seems natural in some cases to divide it into two, right?

[3:48] Then you divide the statement into mainly a noun and a verb, right? Okay. Now this is thinking out the division of a statement into its composing parts, right? Statement is a speech, right? It's composed at least of a noun and a verb, right? Okay. So we can say Socrates sits, Socrates eats, Socrates thinks, Socrates walks, and so on, right? Now both the noun and the verb are a name or a speech.

[4:38] Well, they're both a what? Name, right? Okay. But what's the difference between a noun and a verb? Signifies with time. About that, yeah. Now I notice in Latin and in Greek, I guess they tend to use the same word for noun and for name, Like onoma or something like that, right? Greek, yeah. Or nomen, right? Well, I didn't actually have a different word for a name and noun, right?

[5:17] Okay. So it's interesting, though, right? That if you call both noun and verb a name in Greek or in Latin, then the noun would keep that name as its own, and the verb gets a what? A new name, right? Why? Because it adds something noteworthy that it signifies with time, right? They both signify something, like the name does, but one has something in addition that it signifies with time, right?

[5:53] That's very striking, right? Grammatically, you can't make a statement without something that can now into a verb, and a verb signifies the time. So it's very hard to talk about God if it's not in time, right? Okay.

[6:11] No, a verb. And I remind them of the great, you know, inability to go beyond imagination, right? When the Greeks said, you know, whatever is must be somewhere. If it isn't somewhere, it doesn't exist. And they think naturally, whatever is must be in what time, right? So it's very hard for us to escape from time and place, right?

[6:38] No, our knowledge and our knowing starts from the continuous, right? Place and time, which are species of the continuous, as you know from the categories, huh? Okay. It also strikes me, you know, the fact that as we learned in our study of the word before, right, what's the first meaning of before? Yeah. No, I said, yeah, that's where we begin. We can't get beyond this use, right?

[7:09] Christ tells you there is no memory. He says, "Before Abraham was, I am." It's just that I was, right? But he's trying to express that God, in His divine nature, He's not in what. He's not before Abraham in time. It's in duration, since eternity is before, but that's eternal now, right? It's very strange. It's eternal now, right? Okay. Remember how Thomas talks about the eight senses Aristotle distinguishes in, right?

[7:48] He said, "Hey, you left out one, right? " And in time, right? Thomas said, "Why that stayed alongside in place because they're both similar, right? An external measure. " You dummy! Did you see that, right? No. And that's where Thomas began to teach me, you know, that that you don't put all the senses of a word, equivocal, for a reason, together in one line, right? But you put the central chief senses right in a straight line, and then you attach other ones if there's an affinity for one of these.

[8:22] So to be in time is not one of the central senses, but it's attached to be in place, right? But there's a real similarity between these two. It's very hard for us to transcend that, right? So someone said, well, where is God. you know? Is he up way up in the heavens there? Okay. You know, astronauts there, and up there, you know. Well, no God up there.

[8:45] Hey, we're good. Talking about that there, right? The God is not in place, right? And you know, a lot of times, you know, when you believe or you know. That your soul is immortal, right? You say, where will my soul be? You know, I die, right? Will my soul be in place?

[9:10] Is heaven really a place, right? There's no sense in the word place, right? Very hard for us to kind of seme these, right? But you see that first sense of of of end is one to which time is attached, right? Now you see time getting involved in the verb, right? Okay.

[9:32] Time is our master, Shakespeare says in the comedy of errors, right? So this is thinking out the parts of a composed whole. Statement can be divided into noun and verb, or we think out the definition of what it means for this to be true or false, right? Okay.

[10:01] Now, sometimes though you can divide something into what both two and three, right? Now, give you an example Aristotle divides the five into both two and three, right? You could divide a family into the parents and children. Makes sense, I think. I think it makes sense to divide the family to father and mother and children, right? Huh? Okay. You can divide a name said of many things into two.

[10:37] Another short quote, just two ways: either one meaning or more than one. That's it. It's division of two, right? But then later on you divide equivalent to equivocal by chance and equivocal by what? Okay, so you divide into two and subdivide one into two and two. Two, two. But then sometimes Kant comes along and says sometimes a one name said of many things instead of entirely the same meaning instead of each of them or entirely different meanings instead of each of them, or partly the same, partly different.

[11:16] Right? Now he's dividing the same three, right? Entirely the same equivocal, entirely different equivocal by chance, partly the same, partly different, right? There's some connection between the meanings, not just arbitrary or by chance, right? It's by reason there's an order. Reason looks before and after there's order. That's equivocal. Sometimes they give the name called analogy. I'm kind of want to be careful with the name analogy because it seems to signify one particular kind of name is equivocal by reason, one that is what analogy means proportional.

[11:56] Of course, Townsley sometimes uses proportion for ratio, and Euclid, you know, again he speaks of it as the length of a circle. So we can divide the statement also into three, and that's when you divide the statement into facing. You know that the square is a quadrilateral, right? Well, square is the one part, and quadrilateral is another part, and is joins the two together, right? Or the square is not a circle, right?

[12:36] It seems more natural to divide it into three, doesn't it? Now, see, and we call the what square in that example the subject, and what's being said of it or not said of it, we call that the predicate,

[12:54] and then the sign that is or is not, they call that the what. Copula, which is you know more more fits the third in the negative. They do right. And you tend to divide them into those three, right? And that second division is important. to get to reasoning, right? Because you get the famous principles of the said of all and the said of none, right? If A is said of all B, then A is said of whatever B is said of.

[13:20] It's said of none, A is said of none of these, it's said of none of the things, that B is said of right. So it's kind of natural to divide it into these three: the subject and the predicate, and then either say they is the same or it is not. You know. So this is a good example, I think, of so I divide to two or three, but sometimes you do into both, right?

[13:46] Okay. You divide the plot into two or 3 parts. The beginning, middle, and end is very important, right? Aristotle says that Homer taught all the other poets how to make a good plot. It's not about what happened, you know. everything that happened to some man that had no connection. It's got to be a course of action. that has a beginning, and middle, and end. You're studying the great Homer, right?

[14:15] Yeah. There's also you could make sense and say that you tie knots and then what? Untie them, right? Okay. Again, philosophy, you can see that it's got a beginning, middle, and end, but it's also tying knots and untying them. It's more untying. Yeah.

[14:42] An article in the Summa is divided into how many parts? Three and four. Yeah. So the objections, right, Then what they call the corpus of the body of the article, and then the reply, right? And naturally divided into three. Okay. So you have this. You can divide a statement though into both of these, right?

[15:09] You're talking about what we could call a simple statement because there's going to be another kind of statement, right? The compound statement, right? Okay. Now

[15:32] there's three compound statements that are fairly common, right? and one we call the disjunctive, right? I don't like that name. I call it the either or statement, right?

[16:01] Now you can state this fully, or you can state it um, contracted a bit. You could say, let's say, a number. Either a number is odd, or a number is even. I find it to be a little more brevity of soul, so you'd say a number is either odd. or even But it's really kind of put together two statements, right? A number is odd, or a number is even.

[16:29] Right? It's one or the other, right? Okay. What's important is that you exhaust the possibilities, right? It's not hard to see with odd and even, but, You know, Aristotle says that the virtues in looking reason are either natural understanding or episteme, reasoned out knowledge or wisdom. Hmm? Is it all? You know, it's a little hard to see, right? Okay. So, you can say the either-or statement depends upon sufficiency of your what division, right?

[17:08] Okay. I used to think you'd say human beings are either a man or a woman, but now you go. Well, you were only considering nature. You haven't considered choice. Yeah. You're stuck with. I'm a woman? a woman by nature, by choice a man, or vice versa.

[17:29] No, you're by choice insane. that's what it is. Yeah, Yeah. I want to make a object to making that distinction, though, right? You know, you are a woman by choice, I'll say, to her, and but you're a man. By I mean, you're a woman by nature, right? But you're you're a man. Got it. It says I'm a madman. It says they should not. Okay, so there's the either-or statement, right?

[17:57] Huh? It might have two. It might have three. It might have more, right? Huh? Okay. You know, I'm kind of the same. You know, In what sense of before? does one sense of before? come before? another sense of before? Well it's either this. this. this. or this. You know, when Thomas argues, you know, that God, the Father, is not before God the Son, he says either he is before Him in duration, or he's before Him in nature, right?

[18:32] Or he's before Him in knowledge, right? Or he's before him in what? He's better than him Or listen And uh so he can eliminate all that, right? Okay. But now, when he's arguing, you know, how are the Father and the Son distinguished, right? Well, he's either distinguished by a material distinction or a formal distinction. Does that exhaust the basis? Yeah. And he's not by material distinction because he's not a what?

[19:07] A negative quantity of matter. Therefore, it must be by formal distinction. Formal distinction is either by contradiction, or by lacking and having, or by contraries, or by relations. And then he eliminates three of those, right, and concludes to the fourth, right. So this is done in very, what, proper, probable things, right? In in

[19:37] in the case of the father being before the son, he says no way, right? He eliminates every sense right? And then, but with the distinction of the father and the son, they really are distinct, right? And then he eliminates all but one, concludes to that, right? And sometimes Euclid does that, right? Sometimes argues from an either or statement, right? Okay. Now, we say statement is speech signifying the true or the false.

[20:11] But does this true or false in the case of the either or statement mean what? What it means exactly in the simple statement? When I say that a number is either odd or even, well, which is it? When I say that something is,

[20:36] something is it is, or something is not it is not. Or am I saying, you know, it's it's a little different meaning, right? But is there some connection with the meaning of truth and falsity in the primary sense, which is that of the simple statement? Are you is it true that you're listing all the possibilities? Yeah, yeah. And you say either it's true that this number is even, or it's true that this number is what?

[21:05] odd. Ah, yeah. So one of those two simple statements is true, and the other is like false, false, yeah. So you refer back to the truth and false the meaning of simple statement, but it's not the same thing as a simple statement. is it? See? Okay.

[21:28] So this human being is either man or woman. Which one is it? You know, you want to know that, right? You know, this act is either good or bad. Okay, I'm not going with that. But you want to know which it is, right? Good or bad, right? So the either or statement is a we call these compound statements, right? Compound statement.

[21:55] This is a very important either or, right? We saw Thomas using it, right, in the highest matter of the Trinity, right? Okay. Now, the other if then, the other one that is very important, I think, is the if I call it the if then statement, right? Now, a lot of people call it the hypothetical statement, hypothesis has a meaning that is, you know, in experimental science especially, something that is not, stable, right?

[22:34] You know, but if then statement would be very stable, right? This figure is a square. Then this figure is Is it quite reliable That's really, reasonably true, right? Right

[22:50] Um a number. If is a perfect number, then it is what Prime or composite number? It's got to be a composite number, right? That's very rigorous. Right.

[23:16] Okay. Now I like the if-then statement because right in the if-then statement there is a what kind of an order there, right? Okay. Now what's the odd thing about if-then statements? Could an if-then statement be true and yet be made out of two false simple statements? Yeah.

[23:44] If I am a mother, then I am a woman. True or false? But it's false that I am a mother. It's false that I am a what woman, right? Okay.

[24:01] That shows you it doesn't mean truth doesn't mean the same thing, does it? See, but you're saying with the if-then that if this simple statement in the if part is true, right, and the way this simple statement is true, then this other one that's in the then part will also be true, right? You're not saying in fact either one is true; in fact, they could both be false, right?

[24:24] So. Now later on you'll meet in the logic of the third act the I call it the if-then syllogism, right? Okay. And sometimes they talk about if-then syllogism in terms of using letters to show the form of it, right? And you say if

[24:52] okay that's your first statement, right? Then these. A is so. then B is so. if A is so. Okay. Now sometimes you look at what

[25:30] A, right? And you might find out that A is in fact so, right? Okay. Now in the if-then statement you're not saying that A is so. is in fact so or that B is in fact so? You're merely saying if A is so, then B is so, right? Okay. If I am a mother, then I am a woman, right? Okay. Now if you find out that in fact A is so.

[25:58] will something follow necessarily about B. Yeah. Then B is so, right? Okay. Um, this is kind of obvious when you stop and think about it, right? In the first sentence here, you're not saying that A is in fact so. You're not saying that in fact B is so. But you are saying that if A is so, then B will be so, right? And since in the second statement you admit that A is in fact so, then you must admit that B is so, right?

[26:36] Now suppose you find out that A is not so. Does anything follow then necessarily about B, given that form? Hmm? What? B must not be so. I got you. I got you. You think it follows, but it doesn't follow the form, right? So

[27:15] if I am a mother, then I am a woman, right? Huh? Okay. I'm not a mother. Can I still be a woman without being a mother?

[27:27] A woman, right? Not you. Yeah, yeah, yeah, yeah. You see? So, um, uh, that's what Shakespeare's arguing, right? Huh? What is a man if his chief good and market of his time, but to sleep and be a beast no more, right? Huh? Okay. Now you may say, you know, that uh, what is two of it be? What? Half of four, or half of five, I'd say, right?

[28:03] Or half of six, right? Excuse me. What if three is half of four? Then three is what? Yeah. Yeah. There's there are many cases where B might be something more, what? Universal, right? See, like if I am a dog, then I am an animal. Okay. I'm not a dog. Therefore, I'm not an animal. See? Wouldn't follow those cases, would it? Okay.

[28:44] Um, or if you have a what? Um, an effect that could follow from many causes, right? Okay If Berquist dropped dead last night, then he will be absent from class today. But he did not drop dead last night. Therefore, he will not be absent. Could have been some emergency or something, right? Could have been lazy. Could happen, you know. Okay. So when you have A being one possible cause of B, right?

[29:27] Okay. If it's not so, the effect could still be, right? Okay. If I drink this amount of beer, then I will be drunk, right? I didn't. I still get drunk if I drink that much wine or whiskey. You see what I mean? So, well, in the logic of the third act, we'll say nothing follows necessarily in this form, right? Nothing follows. Okay. Now, what about this down here?

[30:07] If A is so, then B is so. Suppose you find out that B is so. Do you think you can say necessarily about A? What do you think? Depends on maybe there are other causes why B is so than A. Yeah. Yeah.

[30:39] I think you're right. I think it follows that A is so or something, you know. But notice, taking the same example there, right now.

[30:48] If Berquist dropped dead last night, then Berquist will be absent from class. Berquist is absent from class. Therefore, he must have dropped dead last night. No. See. If Berquist is a dog, then Berquist is an animal. Berquist is an animal. If Berquist is a dog. So if you give me that I'll find you guilty every time.

[31:19] If you are the man who robbed the bank last night, then you are a man. But you are a man. Therefore, you're the man who robbed the bank last night. you're all in prison, you know? Which would be a big pleasure, you know. but... You know what I mean? See? Okay. Um.

[31:37] So Berquist dropped dead last night and B is so, then he's absent from class. He's absent from class. Did he drop dead last night? No. So that's that's wishful thinking, sir. But not logical thinking. It's always the example of class. Okay. So nothing follows.

[32:00] Necessarily, right? And notice the weakness there in experimental science, a bit, right? Huh? I've got a hypothesis, huh? And if my hypothesis is correct, there will be an eclipse of the sun tomorrow at ten o' six.

[32:16] We wait for tomorrow at ten o' six, and sure enough, eclipse of the sun. Wow! Confirmation of your hypothesis, Does it follow necessarily? I'm arguing in the form, right? If my hypothesis is so, right, then

[32:42] B will be so, right? B is so. Does it follow necessarily that my hypothesis is correct? No. Because your hypothesis is not the cause of the eclipse. Yeah, yeah.

[32:54] But at least with the form there itself, right? It doesn't follow, right? And you can say though, nevertheless, if I predict something very accurate, right, like 10: 06 in the star, right, no, there's more probability to my hypothesis, right? No, that's why it would work better in physics than in sociology, right? But the predictions would be very sloppy and not be very precise, right? You see, how do you get, you know, he could predict it would be a 10: 06 and exactly what it was.

[33:29] That's really amazing, you know. So the more things that follow from my hypothesis, right, that turn out to be so, the more probability to my hypothesis, right? But but the form of the argument never has necessity, right? But it has great probability, right? It's a bit like induction, right? Where you never see all the singulars, right? But the more you see that it's so, makes it more probable, right?

[33:59] But Aristotle would make induction be more a dialectical argument, right, than a demonstrative argument, right? Okay. So in terms of being a syllogism, a argument which some statements laid down, another follows necessarily. It doesn't follow necessarily that A is so, right? Okay. So these two are not a syllogism, right? This one is in the sense of the if then syllogism, right? Okay. How if A is so, then B is so, and you find out that what B is not so, does anything follow about A necessarily?

[34:43] You're shaking your head, right? Now before you thought something followed and it didn't follow, now you're thinking something doesn't follow and it does follow. But this case is not as obvious as the first case, right? See? See? if B is not so, then how could A be so? Because if A was so, then B would have been so, but it's not so.

[35:07] So A must not be so, right? So it follows necessarily that A is not so, right? And so notice, I said sometimes I'm paraphrasing from a scientist, right? He says if my hypothesis is correct, there will be a eclipse at 10: 06 tomorrow morning. There's an eclipse at 10: 06 doesn't prove my hypothesis. But there's no eclipse at 10: 06. So there's more rigor in rejecting the hypothesis, right?

[35:39] And as consequence, turns out to be so, right, Then your hypothesis, your conclusion, or your prediction becomes true, right? Okay. Seems unfair. Logic is not fair? in that it's negative. Yeah, yeah, yeah. So you have these two ways of reasoning, right?

[36:17] But sometimes you can bring something else in, right? Yes, in the convertible, right? You know, if you say if this number is what two, then this number is half of 4. But this number, what two, is half of 4, Therefore, it's true, right? There it's because the things are convertible, right? But it's not from the form here as it's stated here, right? This is can be so.

[36:48] Okay. So Shakespeare is arguing in a way with necessity, right? He's arguing, explaining to students, you know, you are saying that what if three is half of four, then three is no more than one, two, right? What's false? Both that three is half of four, and that it's no more than two. But if it were half of 4, it would be no more than two. So if man's chief good is the chief good of the beast, then man is more than the beast,

[37:37] man is more than the beast, right? Therefore, his chief good is not the chief good of the beast. But notice in these forms, I'll erase the two patterns here for the time being.

[37:55] Uh, Some man I read, you know, he said that reason looks before and after, right? Now, in these two syllogisms here, right? How many befores do you see?

[38:13] What was the question? In these two syllogisms, in each of these two syllogisms, how many befores do you see? I was saying last night, to my minister on Monday night. um, uh, if knowledge of the soul, right?

[38:36] knowledge of a better thing, right? is better, right? How many befores and afters are you seeing here, right? Well, one you are seeing is that knowledge of the soul is better than knowledge of the body, right? But you are also seeing why it's better, right? Because the knowledge of better things. You are seeing two befores and afters, right? Okay. Well, how many befores and afters are there in these in this syllogism and in this?

[39:14] I guess two, maybe two. Two is two is the first number of both you say all. Yeah. So it must be. Dangerous ground. See? Well, I would say first of all that the premises.

[39:38] Yeah, yeah. Syllogism is speech in which some statements lay down, another follows necessarily, right? So it's a before and after there, right? Premises are before the conclusion, right? And premise probably comes from what the great Latin scholar, right? Sent before or something I don't know. Pre. Pre-mitre. What? Pre mitre. Yes, Thomas often calls them principia, right? But principia come before, right? What's that before? Okay, so the premises are before the what conclusion, right?

[40:13] That's one before, right? And the other before. Knowledge. Being. Well, let me just talk about the form here. Um, once you see that the if then statement is before this statement here, this is the fundamental statement, right? And then you can look either at the antecedent or the consequent, right? And either affirm or deny them, right? So here the statement comes first, right? And then you what?

[40:41] Take the statement second, right? Okay. So the if then statement is before the simple statement. Well, just you know, in the discourse of reason, right? Okay. And then what's the third before?

[41:06] This is the antecedent. This is the consequent, right? This. is, in the if then statement itself there's a before and after, right? So in the if then syllogism, you have three what? Before and after, right? The if the if then statement itself is a before and after, right? And so they call the the if part the antecedent and the what? Then part the consequent, right? And then that is the chief the first statement, right?

[41:39] And then you either look at the antecedent and affirm or deny it, or you look at the consequent and affirm or deny it, and you draw your conclusion, right? So the premises are before the conclusion. The if then one is before the simple statement, and the if then one is another before. Very very before and afterish sort of thing, isn't it? I mean, that's to be to think out.

[42:07] The order, right? That's one of the senses of thinking out, right? To think out the order in there, right? Now, in the regular syllogism, we use just simple statements, right? Just give an example of the form of a regular syllogism.

[42:31] A very simple one, where it's no difficulty, right? Now, B and A just, you know, are, terms now rather than, you know, statements, right? Every B is A.

[42:48] Every C is what B, right? What follows necessarily? C is A. Yeah, kind of obvious, right now. Okay, it's based upon this principle, subset of all, which I sometimes state in our order. You know, if every B is an A, whatever is a B is going to have to be an A, right? It's kind of obvious, right? So, conclusion is every C is A, right now. What they call this one the major premise, and this the what minor premise, right?

[43:24] So this premise comes naturally first, right? So the major premise, so we call, is before the minor premise, huh? Okay, that's one before and after, right? But the main before and after is that the premises are before the conclusion, right? That's where we draw a line that they help us, you know. Distinguish, right? What's before? What's after, right now? Okay. But in the if in syllogism, you've got three, you know.

[43:57] So we people who love to look before and after, we really like that because in so just right, it's you know what? What kind

[44:09] of time? Come at the boss, like all this.