Introduction to Philosophy & Logic (1999)
26. True and False in the Simple Statement: Saying More or Less Than the Truth, and Contradictories
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[0:00] Edward Wright had a leap right when he made the divorceable right, and so on. When the divorceable right is thrown right, so part of us is actually going wrong with him.

[0:25] Instead of syllogism, we see something like that, huh? Always divided, huh? The composing parts we have to understand first, and then understand the subject parts, huh?

[0:41] Now, the next part we talk about a property of the statement, of the simple statement. What is the property here of the statement? Every simple statement has an opposite statement with the same subject and predicate, yeah. So instead of is, you just put is not, or vice versa, right? So man is a stone. As the opposite statement, man is not a stone, right? Man is not an animal.

[1:15] As the opposite statement, man is an animal. Okay. So it's a property you might say, something that follows upon every statement, right? That it has a what? Opposite statement. Okay. And later on we'll see these opposite statements in terms of truth and falsity, right? And what the opposition can be, huh? Okay. Now, now we're coming to the really interesting stuff. We're going to talk about what true and false means in the simple statement, and then later on we'll be talking about what means in the case of the compound statements, right?

[1:56] Okay. Now, what does true and false mean in the simple statement, right? Recall that simple statements either affirmative or negative, right? So it's either God is a copula, some form of it to be without the negative, or has the negative with it, right? So it's either saying that something is or is not, right, or was or was not, right? Okay. So what does truth and falsity mean in the case of the simple statement?

[2:30] Truth means saying of what is that it is. Yeah. And what is not that it is not. Truth in the statement, called the statement, simple statement, means simply that

[2:58] it says. What is in things, that is to say, is right. Or it says what is not. I say that what is not in things

[3:26] is not. So if you say, for example, that Burcus is standing now, you're speaking what truly? You're saying that what is, namely my standing, is right. So mind is false. I true. If you say that Burcus is what not sitting now, right? You're also speaking falsely. Truly, okay. You're saying what is not in things, namely my what sitting, is not right. So that is what true, right?

[4:09] I notice you could say what's common to these two meanings here is that the mind is in what conformity, right? It's in agreement with things, right? This is the conformity of the mind to things. The mind is saying what is is, and what is not is not right. Now

[4:35] falsity in the statement, simple statement, means it says what is. Things is not right. It or it says what is not in things is.

[5:15] Again, just take a very simple example here, right? Being that I'm standing now, right? If you say Burcus is not standing when he is standing, your mind is speaking falsely, right? You're saying that what is, namely my standing, is not.

[5:33] Likewise, Burcus not sitting now, right? If you say that Burcus is what sitting, they're also false, right? You're saying what is not in reality, namely my sitting doesn't exist now. You say that is right. So there's two ways of being what false, right? Okay.

[6:03] Now, take the courtroom, right? In the courtroom, they have you swear to tell the what truth, right? I swear to tell the truth, the whole truth,

[6:27] and nothing but the truth. Okay. Now, most people don't examine that phrase too carefully, but when you add the whole truth and nothing but the truth, it might seem at first sight that all you are doing is emphasizing the fact that you are going to tell the truth, right? But is that in fact all that those second and third phrases are doing? When I swear to tell the truth, and then I add the whole truth and nothing but the truth, I am making something explicit in the second and the third phrases, and not just reiterating I want to tell the truth.

[7:09] You did that well. You did that well. Definitely. What am I saying in regard when I say the whole truth and nothing but the truth? Why do you have those two phrases? What do you mean? You are saying that you won't say the two kinds of falsehood. Yeah, yeah. Now, to say the whole truth is opposed to which kind of falsity? To say that

[7:44] what is is not. Yeah. In other words, if I say that what is is not, I seem to be taking away and subtracting from the truth, right? And therefore, not giving you the whole truth, right? And nothing but the truth is opposed to what? What is not is added. Yeah. I seem to be adding, right? Okay.

[8:15] Now, Shakespeare has a similar phrase, but a more clear phrase, right? And let's give a couple of places where he does this. One is

[8:27] in King Lear, right, where he says, "All my reports go with the modest truth, nor more, nor clipped, but so. All my reports go with the modest truth. Huh? " Well, he calls the truth modest as if it's between two what extremes, right? One of which is more than the truth. And the other, instead of saying less. He says, "clipped, right?" But it's so right. Okay.

[9:16] Now, what am I saying more than the truth? You say that something that is not is. Yeah, when I say that what is not is, I'm saying more than the truth. When I say, "What am I saying less than the truth?"

[9:38] What is is not. Yeah. Now Falstaff was a great liar himself. Shakespeare. You have to realize he often puts statements in the mouths of people who exemplify the opposite of of what they say. You know, like like Polonius says. Brevity is a soul wit? And as Hamlet says, you know, Polonius is that tedious old fool, right?

[10:09] So you're either wise or brief, right? And so likewise Falstaff, the great liar, says if they say more or less than the truth. They are villains, right? And the sons of darkness. Well, they're using the phrase more or less than the what? Truth, right? Yes, the same triple phrase in Othello, where it says, you know, type of soldier, right? You say more or less than the truth, soldier, right?

[10:40] Okay. Now, let me exemplify that with a nice courtroom example here, which is my barman example, right? Suppose I, as a bartender, called upon to give testimony, right? Who was at the bar between nine and ten o'clock on Friday? And let's say that John and what Thomas were at the bar between nine and ten. Nobody else, right? Okay. Now,

[11:24] if I testify that John and Thomas, who are both good customers, who are in trouble, and Paul were there between nine and ten, right?

[11:41] I am what adding to the truth, right? But if I say John was at the what bar between nine and ten, that leaves off Thomas. Just John. Just Thomas. It doesn't get nothing. Now I'm what subtracting from the truth, right? Okay. I know that's more concrete than more abstracting. Here you're saying that what was, right? Because it's past, not right. You're saying here that what was or who was, right?

[12:19] Namely, Thomas was not, right? Okay. Here I'm saying that what was not or who was not was, right? Okay. So here I say this and false in this way. Or hiding what was not was, I am what But adding to the truth, saying more than the truth when I say. Just John was there, and I am saying that what was was not, in a sense, right. And I'm saying that Thomas is there.

[13:07] I am what subtracting, saying less than the truth, right? Okay. Now you go back to the court truth we see here. I swear to tell the truth. The truth is that John Thomas is there. The whole truth—that's again saying that just I say John is there, and nothing but the truth—that's opposed to this kind of false testimony, right? So you don't realize that. I've often thought, you know, they don't like to have a professor usually on the jury, right, or somebody of influence the other members of the jury.

[13:40] If I, you know, spelled out this phrase method, probably would be seated for the jury. I mean, people don't really stop and think what this means, right? This is very active phrase in a sense, right? There's two ways that I could depart from the truthful testimony when I'm called upon to give it in court, right? And one could be said to be adding to the truth, saying more than the truth, right?

[14:09] And one could be said to be subtracting the truth, right? Now sometimes you find because that word more or less, right? To speak the truth is the

[14:23] equality of the mind with things, right? That doesn't mean a democratic sense that the mind is equal to everything, right? Because the mind sometimes talks about things that are what greater than itself, like God, and sometimes about things that are less than itself, like the tree or something, right? But it means that the mind is saying neither what more nor less than what is out there, right?

[14:59] I cannot say truth is the agreement, huh, of the mind with things, huh? Is the conformity of the mind with things, huh? Equality is very concrete, just as referring to these two kinds of falsehoods—more or less than the truth—is very what concrete, right? Or saying one sense you're adding to the truth, right? Other case you're subtracting from it, right? And it's as bad in sense to add to the truth as to what subtracting from it, huh?

[15:41] But in all those phrases I gave you three ones there from Shakespeare where he speaks of more or less or more or clipped, right? One from Othello and one from give me the fourth place and then one is from.

[16:00] King Lear, yeah. Um, or this courtroom one, right? They're all signs that this is what truth and falsity is, right? Why do we have these two ways of being false, saying more or less than the truth, right? Why did two ways to unexclude, huh? Two full testimonies, saying the whole truth and nothing but the truth, right? It's a sign of the truth. that the false of the art, okay.

[16:37] Now, so Shakespeare speaks of modest truth. All my courts go with the modest truth, nor more nor clipped but salt. This is said by Kent there King Lear, the old faithful servant of King Lear, right? Kent

[17:00] Um, but yeah, something in intellectual virtue like you have in the moral virtues. The moral virtues are a mean between two extremes. Like generosity is in between stinginess and extravagance, right? Okay. Or or courage is in between a foolhardiness and cowardice, huh? Okay. In a sense, truth is in between two extremes, right? One of which is more than truth, and is less than truth. But as we define it, right?

[17:32] Okay. And you see this in the two mysteries of the Catholic faith, huh? because the two main mysteries are let's see, the Trinity, and Incarnation, And in a way they're just the reverse. In one case, you have the unity of nature and multiplicity of persons. In the other mystery, you have one person but a multiplicity of natures, right? So take take the Trinity first. There you have one nature and three persons, huh?

[18:11] Okay. And in the incarnation, you have one person and two natures, okay. Well, not only theoretically, but but actually in history, you have both mistakes being made, right? Huh? Okay. So there are those who say that there are three natures,

[18:43] as there are three what? Persons, huh? Okay. So they give the Son a different nature than the Father, right? And the Holy Spirit again a third nature, right? Okay. Then you have those.

[19:02] He said, you know, the three one in the same person, who was the father and the son. But insofar as he became man, he's called the son, and so. So, lead enough, I say to you. There's only as is one nature. There's also what one person. Okay.

[19:22] Who noticed the one is saying more than the truth, and the other is saying what less than the truth, right? Okay. And obviously, the person who says there's three natures and three persons is saying more than the truth, right? Okay. He's saying that what is not the second and third nature are. Okay. He's saying what is not, or to put it clearer, what are not, right? What is not is. right.

[19:59] Okay. The person who says as as one nature, so is also one person. He is subtracting from the truth, right? And he's saying that what is, or what are, I'm going to say, namely the three persons, is not. What is is not.

[20:23] Okay. So you have, in fact, you know, you've got Arius up here, right? And the Patripassians you call them, right? Those who say the Father suffered, right? He became man, died, and so on. Okay, you have, in fact, historically both of these, right? Now,

[20:46] over here you have. what would be the error corresponding those Who is saying what is not is two persons. No. Oh, I see. Yeah. Okay. Okay. So if you say there are two persons, as there are two natures,

[21:15] the story says this is a famous one of this, right? Okay. So he's saying that what is not, namely the second person, is the Christ, right? Okay. And the other one would be saying that as as one person, there is one, one nature.

[21:37] So he's saying that what is, namely two natures, is not, right? Huh? And then one nature is the monophysite right? So you can say more than the truth or less than the truth, right? The truth is a mean between two extremes in that sense.

[22:13] I notice a sign that the truth here is is modest. Is that if this middle position here is the truth, then both of the extreme positions have a part of truth, but neither one has the whole truth, right? So men are deceived when they see part of truth but not the whole truth, right? Empedocles, the great Greek philosopher, says, "You know, men are don't live very long; they're creatures of the day, and they see a part of life and they boast of having seen the whole, right?

[22:59] " But notice if one of these extreme positions was true. In the other extreme position, when they have no part of truth, right, and that's not very plausible, right? Because you have men thinking this, and there's no basis for it at all, right? So the one seizes upon the fact of one nature, and therefore they think there's one person. The other sees upon the fact that there are two persons, and therefore must have two natures.

[23:26] And similar one over here, right? Simply reversed, because here you have the unity of person and the multiplicity of nature, right? But sees you got one person, therefore must have one nature. The other one sees you have two natures, which is true, but therefore must have two persons. The truth is in between. those two extremes

[23:54] What is Shakespeare's quote again from there? All my reports go with the modest truth. True, no more, no more, nor clipped, but so. It's the same. Less he says clipped, right? Notice that thing I was mentioning before. Shakespeare says nor nor, right? We'd say we'd say English, neither more nor less, right, or neither more nor clipped, right? He says nor nor. You still see or or Shakespeare?

[24:22] Not just a good image, just changing language. Another example too, in the way that saying the what is not is and what is is not by something you hear theology, perhaps philosophy, but erring by excess, erring by defect. Yeah.

[24:50] Yeah. It's kind of custom of those making mistakes to go to extremes, right? Everything's necessary. Everything is contingent. Now we'll see later on when you compare this with the other kinds of truth and falsity, why this is the basic sense of truth or falsity, huh? Because you're talking about the agreement of the mind with things, right? Mind wants to know the way things are. Now towards the end of this section here, it's the last paragraph.

[25:43] It can be seen from induction and the above definitions of true and false that if an affirmative statement is true, the opposite negative statement, which in case of the other affirms, must be what false, right? And if a negative statement is true, the opposite affirmative statement. Which affirms and the form negates must be false. That, in a way, follows from the what definitions, right? If I'm saying that what is is, and that's true, right?

[26:16] Then the man who says the negative statement opposed to that, he's saying what is is not, and that fits the definition of what false, yeah. And if what is not is not is is true, and the man who says what is not is saying the opposite of that, and that's obviously what we mean by false, okay?

[26:43] And we can also see from the definitions of true and false in the above that the same statement cannot be both true and false, huh? It's saying what is is can't be saying what is is not, huh? So it can't be true and false at the same time. And saying what is not is not, it can't be saying what is not is.

[27:08] Now the contradictory statements, huh? And I can't help spell this out, right? When we speak of contradictory statements, we're talking about simple statements. We just call it statements, very contradictory statements.

[27:28] No, the first thing we said about them is they're simple statements, right? Secondly, we add that they have the same what? Yeah. Okay. And third, one is affirmative, and the other is negative, huh?

[28:15] Now the contradictory thing, right? And I like to spell out. They're opposed such that both cannot be true, right? Both cannot be false, but one must be true, and the other must be false, right? Regardless of whether you know which is the true or which is the false, right? Okay. And you can say the one just alone that one must be true, and other must be false by and spelled out, right?

[28:46] Both cannot be true. Both cannot be false, but one must be true, and the other false. Okay. This is something you can know from the logic of the second act. It doesn't tell you which one is true and which one is false, right? But you know that one is true and one is false. So if I say President Bush is sitting now, President Bush is not sitting now.

[29:39] Two simple statements, right? Same subject, President Bush, right? Same predicate, sitting now, right? One affirmative, President Bush is sitting now. One negative, President Bush is not sitting now. Can both of those statements be true? Can both of them be false? One must be true, the other must be false. Which is the true, which is the false one? Well, we don't know, right? Okay. Notice the logic of the second act, from its analysis of what a statement is, right?

[30:20] What an affirmative statement is, what a negative statement is, true, false, and so on, right? It sees that those two statements are contradictions. One must be true and one must be false, but it doesn't tell you which is the true, which is the false one. Okay.

[30:40] Now, there are three ways, mainly, for a buyer to know which is the true, which is the false one, if we do know them, right?

[30:53] And one way is by the senses, right? So Berquist is sitting, Berquist is not sitting, right? Like the statements, President Bush is sitting, President Bush is not sitting. But you're able to judge which is true, which is false. If Berquist is sitting is false, And Berquist is not sitting is true, right? By your senses, right? Okay. So you don't need logic, right, to use your senses, right?

[31:25] Okay. That's one way we know, right? But now, if I say, "No odd number is even," and some odd numbers even, these are contradictions, right? But which is true, which is false?

[31:51] No odd numbers. That's true. Now, do you know that by senses? No, not in approximately any way, right? Because you can't see all odd numbers or even numbers and compare them, right? Then, but you know it by understanding what an odd number is and what an even number is, right? The one is divisible into two parts parts, the other is not, right? They can't be the same, right?

[32:19] So you know it by understanding the parts. Okay. If I say no circle is a square, right? Do I know that by my senses? I might have started off by having to be drawing a more or less circle, a more or less square, right? But when I say that no circle is a square, I know that's to be true by understanding what a square and circle is.

[32:43] That may require a what definition, right? Okay. Notice whether I know it by sensing or by definition, it pertains to something other than the logic of the second act, because the senses are. Something other than the mind the reason, right? And the definition pertains to the logic of the first act. And there's a third way we can know which of two statements is true or false, besides sensing or defining, understanding what the parts mean.

[33:14] That's the third way. Yeah. Okay. So the logic of the second act tells us that contradictory statements cannot both be true; they cannot both be false. One must be true, the other must be false. But the logic of the second act doesn't tell us it can give you a pair of contradictory statements, which is true or false, right? You have to either know that by the senses or by understanding what the parts are, which may require a definition, or yes, by the reasoning, right?

[33:59] Notice that in a way it follows the definition of true or false, right? If a statement is saying what is is, right, in a statement saying that something is, it's either saying that what is is or what is not is, right? And then the negative statement will be saying just the opposite, right? So one of them has to be true and the other has to be false, right?

[34:34] If the affirmative statement is saying what is is, the negative statement is saying what is is not, and therefore it's false. If the affirmative statement is saying what is not is, negative statement is saying what is not is not, and therefore it must be what true, yeah.

[34:58] But is the affirmative statement saying what is is or what is not is? Well, I don't know either by my senses, right? When I'm saying President Bush is sitting now, am I saying what is is or what is not is? I don't know. See, call on the phone, get a opinion on these two. I have to believe that in the end, right? Okay. When I say this about you or me, right, that I can see, right?

[35:30] Okay. Man is an animal. Man is not an animal. I know enough about what a man is and what an animal to know that man is an animal, right? And therefore, man is not an animal is false. Or square is a quadrilateral. Square is not a quadrilateral, right? Might have to define square and quadrilateral, but by my understanding of what a square and quadrilateral, I know that it's true that square is a quadrilateral.

[36:00] But now, if someone says the interior angles of a triangle equal two right angles, I know what two right angles are. I know what a triangle is. I don't see that they have to go together. And then you have to what reason that out, right?

[36:18] So three ways, right? Okay. So don't let the logic of the second act do more than it can, but don't give it less credit than it has, right? Okay. And since it boils down to the fact that, in a way, you're saying that since every statement has its contradictory statement, right? In a way, of all possible statements you can make, half are true and half are what?

[36:47] False, right? Because every statement has only one contradictory, right? And one must be true, there must be false. So of all possible statements, that doesn't mean now that the number of statements that people make, that half of the statements people make in the world are what? Well, and half are true. Probably more than half are false, right? You see, it's because they don't, you know, say both, right?

[37:20] So if I say two plus two is four, and you say two plus two is five, and you say it's six, and he says seven, he says eight, then can be more false statements actually made than true ones, right? Two plus two is four. Two plus two is not four.

[37:38] Two plus two is five. Two plus two is not five. Two plus two is six. Two plus two is not six. You always get the contradictions, right? And we have exactly what? Half of them true, half them false, right? But as a matter of fact, you see, there's more mistakes than there are true statements that actually made So I mean, Thales will say water is the beginning of all things, and then Anaximenes will say air is the beginning of all things.

[38:12] Heraclitus will say fire is the beginning of all things, and the poets say Mother Earth is the beginning of all things, right? Well, if one of those statements is correct, the other three are what? False. Yes, there's more false statements than true, right? But if one person said Mother Earth is the beginning of all things, and someone else said Mother Earth is not the beginning of all things, one person says water is the beginning of all things, and someone says water is not the beginning of all things, then you have exactly half and half, right?

[38:48] You know, when you get a true/false exam, which I don't do, but but kids like to guess sometimes, you know, 50/50 chance. One time I got a little bit of true or false in one of my exams. But I announced before, and I said, "Now, if you

[39:08] leave it blank, you get a point off. If you get it wrong, you get two points off." So it's a good idea, right? But I said this is on purely Socratic grounds, right? One for not knowing the answer, one point off, and two, another point off, thinking you know you don't know. Kind of just petty. I think I found out that if a guy hits the ball plenty, he would get the highest bar.

[39:37] Now, a lot of people, you know, they get very confused in their thinking because we use words. and they get very You know, in various ways. Let me give an example of what I mean here.

[40:08] Three is an odd number. Three is an even number. You contradicted yourself. I did. But now, strictly speaking, three is an odd number and three is an even number. Are they contradictory statements as we define contradictory statements? No, no. Begin with they're both what? Affirmative statements. But contradictories are one affirmative, one negative. Right. But also, they don't have the same what? Predicate, right? Right. And contradictory statements have the same subject and the same predicate.

[40:59] So these are not contradictory statements. Strictly speaking, right? Now you you might say you know speaking more loosely right that when I say in one place that three is an odd number and another place that three is an even number I contradicted myself because in sense to say that three is an even number is to deny that it's a what? Odd. Yeah. And since it follows from this that three is not an odd number, right?

[41:32] You see that? But that's really contradictory, strictly speaking, of three is an odd number. Okay. So you want to learn to speak very precisely, right?

[41:57] Later on, when we talk about the word some, you know, if I say some women are beautiful. Now, when I say some women are beautiful, have I said that some women are not beautiful?

[42:22] No. Now, someone might infer from my saying this that I think some women are not beautiful, and maybe I do think that, right? But have I said that? No. If I say

[42:41] some twos are half a four, have I said that some twos are not half a four? Even if every two is half a four, aren't some twos half of four too Example I give in class sometimes, you know, when I'm teaching about third grade, you know. Okay. So suppose I give an exam one day, right? Okay. And uh the final exam or something, and they see the next day or so, and they say, "How'd we do?"

[43:17] And I say, "Some of you have passed." Have I said anything about the rest? I might only have corrected, you know, half the papers or something, right? So what am I saying? I am saying that some of you have passed, but they got to run off and tell the other guys, right? See, someone's still looking, you know. Why do you

[43:43] say that? Why do you say that? Might be a reason why, right? So the statement that some women are beautiful, does that contradict every woman is beautiful? No.

[44:06] And the statement that some students have passed—have every student passed? No. So you got to realize this here is kind of inference, right? And here it really is a contradiction, but it's because this is really a consequence of that, right? Now, I mean, we may speak. I mean, I might myself suddenly say, you know, if you say this, then this should contradict yourself. But strictly speaking, these are contradictory, and so the contradiction is a consequence of saying this, right?

[44:35] Okay. Okay. Now we're going to turn to the compound statements, and first again, their composing parts, right? And then we'll talk about truth and falsity in them.

[45:07] And again, you have to understand the composing parts before you can understand what truth or falsity means.