Today I'd like to, in this first hour, give you just a brief introduction to, first, the necessity of logic, and second, the necessity of studying logic. And it's best that we begin with some definitions. After all, if you don't define your terms, you don't know what you're talking about. The definition that Dr. Clark offers of logic in his textbook is the science of necessary inference. Logic is the science of necessary inference. Let me put that on the overhead here. I hope you can read my writing. The science of necessary inference. Well, what do we mean by necessary inference or necessary implication? Sometimes that phrase is used, necessary implication. It's the same thing as necessary inference. And I have two examples that I'll give you at this point. One of which is a standard example you'll find in all logic textbooks. Another is an example from the Bible. Here are two examples of necessary inference or necessary implication. The first is, if all men are mortal, if Socrates is a man, then Socrates is mortal. It's a necessary implication or a necessary inference. You cannot avoid the conclusion given the two premises. And we'll explain what a conclusion and a premise is in a moment. Or, if you prefer a biblical example, if David was king of Israel, if Absalom was the son of David, then Absalom was the son of a king of Israel. You can't avoid that conclusion. Even though at no point in the Bible may we be told, I haven't checked it, this may or may not be true, you can check it as part of your homework. See if you find the sentence anywhere, Absalom was the son of the king of Israel. Let's assume for the moment that we don't. Are we justified in concluding that Absalom was the son of the king of Israel even though it's not explicitly stated in the Bible? Of course we are. It's required that we do so. Given the two statements that are in the Bible, David was king of Israel and Absalom was the son of David, we must conclude that Absalom was the son of the king of Israel, even though it may not be found in so many words in the Bible. Well, that's a brief definition of logic, and over the next few days we're going to be studying the rules by which we decide what inferences or what implications are necessary, what necessary means, and how to tell a necessary inference from an inference that is not necessary. I should emphasize at this point that logic is not psychology. Don't confuse the two. When we talk about logic, we're talking about rules of correct thinking. We're not talking about how people actually think, what their moods are. We'll talk about moods, but logical moods are quite different from psychological moods. Logical figures are quite different from any other type of figure. So don't confuse logic with psychology, please. They're quite different things. Logic is in history. When we talk about logic, we are not giving you the history of logic. In the textbook, Dr. Clark has a chapter, I think it's chapter 8, along there, in which he discusses a little bit of the history of logic. But logic itself is not history, and we're not going to get into the history of the study of logic at all. Logic is not math. Don't confuse those two. Logic is not mathematics. It's quite different. Arithmetic is perhaps a very simplified form of reasoning, syllogistic reasoning. But the two are quite different things. Perhaps arithmetic can be reduced to logic, but you cannot reduce logic to arithmetic or math. So don't confuse logic with any of those things. Logic applies to all thinking, and this is fundamental. The place of logic in the curriculum is very important. We teach young children reading and writing and arithmetic, because they're basic to all further studies. If the child is going to learn geography at a later time, or history, He has to know how to read. If he's going to pursue his studies diligently, he certainly has to know how to write. And if he's going to pursue any higher math, he has to know arithmetic. Those things are fundamental. They're basic. But there's something even more basic than those things, and that subject is logic. We don't teach it first in the curriculum because it's not the easiest. It's much easier to teach a child how to form letters, and how to decipher written symbols on a page into sounds, than it is to teach him the rules of logic. But logic is fundamental. It's basic. It's basic to all thinking and all thought. It cannot be avoided, and that's why it's necessary to study it. I should also mention that there is only one logic. Karl Marx, the great socialist thinker of the 19th century said that there were more than one form of logic. In fact, he thought that each economic class, whether it's the proletariat or the bourgeoisie or the aristocracy, had its own form of logic by which it thought. He developed a doctrine that became known as polylogism. polylogism, many logics. It was part of his attack on what he saw as bourgeois culture, bourgeois power structure. The proletariat simply thought different. The unemployed workers, the proletariat simply thought different from the capitalists. They had a different logic. Their logic was the logic of the future. They would triumph And they didn't need to listen to any arguments from the capitalists, because the capitalists were using a different logic that was the logic of the past. Their time had come and gone. The future belonged to the proletariat. Today, we hear the same doctrine, polylogism, perhaps not in strict Marxist terms, but in terms of multiculturalism. That's the fayade. in academia, one of the fads in academia today. Multiculturalism. Each culture, we're told, has its own peculiar logic, its own peculiar way of thinking. There are many different ways of thinking, many different logics. There is no one logic. And if we go to teach in another culture, if a Christian missionary leaves the United States, goes into a third-world culture and teaches He is engaging in cultural imperialism. He is imposing American culture, American ways of thinking, Western ways of thinking, Greek ways of thinking on cultures that know none of that and have gotten along quite well without them. That's the typical attitude in much of academia. even in so-called Christian colleges. I had the experience just a couple of months ago of speaking at a so-called Christian college in California in which I met with that attitude in a quite adamant form. The academic dean and his wife very much were in favor of multiculturalism. They thought it was horrible what Christian missionaries were doing if they expected the natives in whatever culture to believe the Bible and understand it as we understand it. They might get something completely different from the Bible. Well, what does the Bible have to say about multiculturalism and polylogism? Well, there's a pertinent chapter in the Bible, and I'll put it up there, and I hope you will read it at your leisure. This is the first chapter of the Gospel of John. In nearly every translation it says, in the beginning was the Word. The Greek word is Logos. It's the word from which we get the word logic. Logos. In the beginning was the Logos. And the Logos was with God and the Logos was God. He was in the beginning with God. All things were made through him. And without him nothing was made that was made. In him was life, and the life was the light of men. And the light shines in the darkness, and the darkness did not comprehend it. That was the true light which gives light to every man who comes into the world." Notice that every. This is what logicians call a universal quantifier, or it's simply a universal. There are no exceptions to it. Every man is lit by Christ, the logic, the logos of God. We're told in Genesis 1 and 2 that man was created in the image of God, and this is the image. This is the true light that gives light to every man who comes into the world. Notice it doesn't say Christ gives light only to members of the bourgeoisie, or only to members of the proletariat. or only to members of Western culture, or Eastern culture, or African culture, or anything of that sort. There's one image of God. Man is the image, and that image is logic, or rationality, the ability to use reason. There's only one logic. Having said that, let me give you briefly an introduction to the The fundamental laws of logic, there are three. Later on we'll get into some more rules for detecting validity or invalidity, but these are the three laws of logic. Contradiction, sometimes it's called non-contradiction, but people mean the same thing by it. The proper name is contradiction. The second law is excluded middle. The law of the excluded middle. And the third is identity. The law of identity. These are the three fundamental laws of logic. In his book, Dr. Clark argues that contradiction is the most fundamental, and in fact the other two can be deduced. from the law of contradiction, but we'll treat them all as our starting points. Here are the three laws of logic. Contradiction, not both A and not A. Excluded middle, either A or not A. Identity, A is A. Now, what does A mean? A means anything you wish it to mean. It's like algebra. It's like the X in algebra. It's simply a letter standing for whatever item you're talking about. Another way of looking at contradiction is this, that a term in order to mean something, a word in order to mean something, must also mean not something. Let me repeat that. A word in order to mean something and this is where the word, the term contradiction comes from, must also mean not something. Now that may sound confusing, but it's really not. For the term D.O.G. to refer to a domestic pet that barks, it cannot refer at the same time to mountains, to trees, to cats, to roosters, to husbands and wives. It means those It means those, not those things. It means dog, D-O-G, refers to domestic canines, but it also does not mean these other things. Well, let's assume that it did. Let's assume the term dog meant all those things. And when I said dog, what message would you get? When I thought dog, what message would I get? It's absolutely necessary, and I'll give you the biblical roots for this later in the week. I think it's in tomorrow night's lecture when we talk about Christ's use of logic, and Wednesday night's lecture when we talk about Paul's use of logic, you'll see the biblical roots for this. But in those cases, if we use dog and it does not not mean something, the word is absolutely meaningless. It has no meaning whatsoever. Does everybody see that? It has to not mean something as well as mean something in order for it to have meaning. And unless we understand that, we're not going to get very far in logic. In the Bible, we can read and understand the Bible because each word is an illustration or an example of the law of contradiction. It has a definite meaning. in the first verse of the Bible does not mean a thousand years after the beginning. It doesn't mean five seconds after the beginning. It has a definite meaning. If it meant any number of things, the Bible would be a nonsense book. But what do we mean by the law of excluded middle? What does this mean? Well, it means a thing either is or is not. There is no middle ground. No shades of gray, as it were. There's nothing in between a thing and not-thing. Nothing in between it at all. There's no fuzzy area where something may or may not be. Now, some philosophers have attacked the law of excluded middle as well as the law of contradiction. If you read William James and John Dewey, for example, you'll see their attack on both, but particularly the law of excluded middle. You see it reappearing, of all places, in some professed Calvinist theologians, this attack on the law of excluded middle. One of them, for example, argues that it's very difficult, perhaps impossible, to describe what snow is like when it's somewhere between rain and actual snow. They say, here's a physical example of something that violates the law of excluded middle. It's not really rain, and it's not really snow. It's something in between. Well, they simply fail to understand what the law of excluded middle is. They also fail to understand that Eskimos, I'm told, have 26 names for different types of snow, different types of precipitation. Eskimos have not operated on that principle, and they have learned to distinguish twenty-six different types of precipitation. We may do with two, or three, if we include sleep, but Eskimos don't do that. And they know quite well, even though they may not have studied logic, that there is a law of excluded middle. A thing is itself, or nothing else. The final law here is identity, and if I'm going over these too fast, please be reassured we'll get back to them later on in these lectures. But I want to introduce you to some of the basics in this first hour. The final law is A is A. A thing is itself. Another way that some philosophers and theologians attack this is, oh, this is the truism. It's obviously true. Why do we bother with such trivialities? Well, we bother with them because they're absolutely fundamental. There's no way of thinking correctly without dealing with these truisms, these trivialities, so-called. They're of fundamental importance. A thing is itself. Those are the three most fundamental rules or laws of logic, first formulated by Aristotle. Aristotle was a Greek philosopher. lived about the fourth century B.C., and in his analytics, a book called, actually two books on analytics, he developed these laws and stated them for the first time in so many words. That leads me to observe that some people have said, well, we can't trust Aristotle. He was a pagan Greek philosopher. And in so saying, they have committed one of the blunders of logic, and that is the so-called abusive ad hominem argument. We'll get into that tomorrow. And you'll see that the abusive ad hominem, Aristotle was a pagan Greek philosopher, therefore we don't need to use logic, is simply one of the more common fallacies that people use. are reluctant perhaps to agree with that, recall that God can make jackasses speak the truth when he wishes to do so, and therefore we shouldn't be surprised if sometimes a pagan philosopher gets things right as well. So, those are the three laws of logic. Logic is necessary because it is fundamental to making all distinctions. Let me emphasize that. Every distinction that can be made, whether it's in thought, whether it's in communication, whether it's in ethics, the distinction between right and wrong, our understanding of the Ten Commandments, of our Shelton of Steele, depends on the law of contradiction. That sentence does not mean thou shalt steal. That sentence does not mean thou shalt steal. Our understanding of the laws of God, our understanding of all the commands in Scripture, our understanding of all these scriptural narratives, depends on these laws. There's no way of getting around it, and these laws are not something found outside of Scripture and imported into Scripture, they're found in Scripture itself. All distinctions depend on the law, particularly the law of contradiction, in ethics and every other field. Paul gives, to use an example off the top of my head, Paul uses an example from music. He says, if an instrument gives an uncertain sound. He says, who's going to respond to it? It has to have a clear sound. It has to have a univocal sound. He says, and I would rather speak five words in the church in an intelligible tongue than ten thousand in an unintelligible language. Meaning and understanding require the use of logic and logical categories. In ethics, we're told today that there are no blacks and whites, there are only shades of gray. The idea is you can't make these clear distinctions between right and wrong, between good and evil, between justice and injustice. If, well, the last time I checked, gray was a mixture of black and white. If there are no blacks and whites, there are no shades of gray. And I think it's important to see that all of the arguments of ethical relativists, as well as other kinds of relativists, depend upon using logic while denying it. Relativism, the idea that something may be true for you, but it's not true for me, or it might be true in some other culture, but it's not true in American culture, is all false. The Bible knows nothing of relic of truth. It knows only of truth, objective truth, which is true for everyone without exception. It's impossible to do without logic. It's the image of God in man. Logic, in fact, we can say, is God thinking. It's the way God thinks. If we do not understand the rules of necessary implication, we will tend to misunderstand the scriptures. Have any of you read Martin Luther's The Bondage of the Will? Well, you should go home now, forget the rest of this class, and read it. The Bondage of the Will was, in many ways, the manifesto of the Protestant Reformation of the 16th century. Luther, of course, was the leader of the Reformation of the 16th century. And in that book, he deals with many logical blunders that people make in interpreting and understanding Scripture. One of the things he deals with is this, and this will become clearer as we go on, that you cannot make any inference, you cannot draw an inference from a command. You can draw an inference only from a proposition. You cannot draw an inference from a sentence in the imperative mood. I presume you've all had some good English grammar, and you know what the distinction is between the imperative mood and the declarative mood. The imperative mood is something like the Ten Commandments. Thou shalt not do something. It's a command. A declarative mood sentence is something else. It's a statement about something. David was king of Israel. It's not a command. It's simply a sentence in the declarative mood. One of Luther's arguments in the Bondage of the Real is that people are drawing inferences from commands. They think, for example, that because God tells them to be perfect, they can be perfect. And Luther says this is an elementary blunder, a blunder worthy of schoolchildren. He says, it's a logical mistake. He says, God tells you to be perfect to show you that you can't do it. And that's why you need a Savior. If you could do it on your own power, there's no point in having Christ die on the cross. But many people in that day and in our day think that because there's a command in Scripture, that implies we can do it. And Luther gives a little lesson in logic. right there in the bondage of the will about drawing inferences from commands rather than from declarative sentences. One of the reasons for studying logic is that people tend to overestimate their abilities. They tend to think, well, they tend to confuse logic and common sense, and everybody thinks he's well-endowed with common sense. So what's the point of studying logic? And to illustrate how people overestimate their abilities, let me give you this example. Or overestimate common sense, perhaps, is a better way to put it. Let's assume you finish high school, go on to college, get a college degree. You're offered a job. Actually, you're offered two jobs. You go out and you interview. You're offered two jobs. One job, well, they both offer you the same amount each year, $20,000 a year. Job A offers you $20,000 a year. Job B offers you $20,000 a year. But there's this difference. The company that offers you job A, A company, says, we'll give you a $500 raise every six months. The other company that offers you the other job, Company B, says, we'll give you a $2,000 raise every year. Which job would you take? Who would take job A, $500 every six months? A few people. Who would take job B, $2,000 every year, annual raise? But it seems to be the obvious choice. It seems to be the common sense choice. But let's look at the math here a little bit. Let's use some hard thought in analyzing this. Let me put down the terms of this first. Job A and job B, they both started the same salary, $20,000 a year. Job A gives you $500 a year raise. I'm sorry, $500 every six months. Job B gives you $2,000 a year. I hope you can read this scribbling. Perhaps you can't, but this is just to keep it in front of us. Let's break it down into six-month increments. How much do you make in Job A in the first six months? You make $10,000. Everybody see that? How much do you make in job B? $10,000. Okay. How about the second six months? How much do you make in job A? $50,000? $10,500. How much do you make in job B? At the end of the first year, which job has paid you more? How much money do you make in your third six months in job A? How about your third six months in job B? 11,000. Half of 22, you got your $2,000 raise. Half of 22. How about the fourth? Job A. The fourth in job B, which job has paid you more the second year? Job A. This continues. You make $500 a year more in job A than you do in job B. The common sense answer is, of course you take job B. You get $2,000 a year raise. You'd be an idiot to take job A. But if you do the analysis and figure out how much each job pays every six months, then you can see that the job to take is job A. And common sense can't be trusted. That's my point. You cannot trust your common sense, even in matters as simple as this. You have to have first true premises, revealed information to go on, and then you've got to use some rules, some procedure for distinguishing truth from falsehood. In five years, you're going to be making $2,500 more, or you will have made $2,500 more in job A than you made in job B. But job B sounds so good. There were a lot more people that held up their hands who would take job B than those who held up their hands in job A. The final point I want to make is that not only is logic necessary for all thought, it's necessary to study logic. It's necessary to study the rules for correct thinking. It's necessary to study the science of necessary inference. We all tend to think more highly of ourselves and our native ability than we should. And this is simply one illustration of how easy it is to go astray relying on one's common sense. If you were to take all the things that have been regarded as common sense through the centuries, you would have quite a list. It's common sense to believe that the world is flat. Anyone who believes the world is round is silly. From culture to culture, you see differences in what's regarded as common sense. Now, some of these statements may be true. Some common sense opinions may or may not be true. The difficulty is, how do you tell which are which? And you can't tell unless you do some rigorous thought and some analysis. And that's what we hope to do here over the course of this week. in this course on logic. Are there any questions? We have a few minutes before we need to adjourn, I think. And then we'll come back in about 15 minutes after that. Yes, right here in front. would make that $6,000 or $6,000 that year. That would be $2,000 a year. It would be $12,000. It's $2,000 a year so the second year you're going to make $22,000 and half of that is $11,000. That's what you make in each six month period. You see that? You start out at $20,000. On your first anniversary you get a $2,000 raise. That brings you up to $22,000. So during the next six months, you're going to be making $11,000, half of that money. Any other questions? I hear lots of buzzing, but I don't see any hands. Yes, sir? If you had asked the question a hundred years ago, the answer would have been yes, but I'm afraid logic and the study of formal logic has disappeared. from academy. What has replaced it to a great extent is something called critical thinking, which is a somewhat different animal. Well, if there are no further questions, let's take a break. Yes, sir? I did have a question. I was wondering if you could give an example of the identity and importance of a foundational principle. I am that I am, in the name of God. God is who he is, and it's absolutely foundational to theology, to any correct thinking, the law of identity. If God is not who he says he is, if God is not who he is, then we might as well go home and shoot ourselves. That's the alternative, folks. If there's no logic, if there's no rhyme or reason to it all, you would be better off doing that. Yes, sir? In the text, it talks about the other approaches to logic have to use logic in order to describe them. Can you give an example of that? Well, yes. I guess I could give you the example of Marx himself. Marx wrote voluminously, and every word in his book assumes the law of contradiction. He may have attacked logic and Aristotelian thinking in his books, but every word assumes those three laws. There's no way you can do it. If a person wrote a book and he used the word dog a hundred thousand times in the book because he doesn't believe in the law of contradiction, the book would be absolutely meaningless. He would write, perhaps, the word dog six times and put a period, and then to him that might have meant, you know, the proletariat needs to overthrow the bourgeoisie, but who's going to get that meaning out of it without the law of contradiction? They must depend on these laws in order to attack the laws.