Christian Apologetics - Lesson 4

The Law of Non-Contradiction

The law of non-contradiction states that A cannot be B and non-B at the same time and in the same sense.

Ronald Nash
Christian Apologetics
Lesson 4
Watching Now
The Law of Non-Contradiction

Postmodern Irrationalism and the Christian Worldview

Part 1

I.  The Law of Non-contradiction

A.  A cannot be B and non-B at the same time and in the same sense.

B.  Examples of the Law of Non-contradiction

C.  Logic is an essential property of God.

D.  Logic is subordinate to God.

E.  Effects of Ignoring the Law of Non-contradiction

  • Introduction to Apologetics.

  • Apologetics involves finding evidence and presenting arguments to defend the Christian faith.

  • Two prominent worldviews are Christian theism and naturalism.

  • The law of non-contradiction states that A cannot be B and non-B at the same time and in the same sense.

  • Explanations and responses to different worldviews.

  • If God is good and all powerful, then why does evil exist?

  • Discussion about how the existence of evil is consistent with God's character.

  • Your noetic structure, presuppositions and view of epistemology are important elements in the formation of your worldview.

  • Discussion of deductive presuppositionalism vs. inductive presuppositionalism.

  • Objections to inductive presuppositionalism.

  • Arguments for and against evidentialism.

  • Arguments for and against foundationalism.

  • Discussion of natural theology.

  • There are valid, sound and cogent arguments for the existence of God, but no coercive proofs.

  • Discussion of different arguments for God's existence.

  • One version of the cosmological argument for God's existence emphasizes God as first in time, another emphasizes God as first in importance.

  • A possible world is a way the real world could have been. Modal logic, propositions, state of affairs and eternal entities are some of the considerations when discussing a possible world.

  • Something is logically possible if its description does not include a logical contradiction. The existence of the laws of knowledge refute the system of naturalism.

  • Middle knowledge is a form of knowledge attributed to God by Molina.

  • Miracles are a dividing line and central to Christianity.

  • David Hume's rational arguments against miracles and responses to those arguments.

  • Two miracles central to Christianity are the incarnation and resurrection.

  • The question of whether or not Jesus is the only savior touches on pluralism, inclusivism and exclusivism.

  • Pluralism is the view that all religions have salvific value.

  • Inclusivism is the view that even though the work of Christ is the only means of salvation, it does not follow that explicit knowledge of Christ is necessary in order for a person to be saved.

  • Salvation is totally the work of God and all children who die in infancy are elect of God.

  • Discussion from a biblical perspective of God's character and attributes.

  • Open theists believe that God does not have a perfect knowledge of the future.

  • Divine omnipotence and divine omniscience are two attributes of God.

  • When contemplating life after death, remember, Jesus has been there and come back. Will you commit your life to him or reject him?

These lectures were given at Reformed Theological Seminary in Orlando, Florida during the fall of 2001.


Dr. Ronald Nash
Christian Apologetics
The Law of Non-Contradiction
Lesson Transcript


As I've told you, most of the content of today makes up a message that I give frequently in various parts of the world. When I do, it's often identified in the program or the Bulletin of the Church or whatever. Under this heading it's called. Will the real Air rationalists please stand up? Now, that title comes from a very old television program. I understand there's a pale imitation of that program on cable television these days. In fact, I don't even know if if the program has the same name in the old days was called to tell the truth. That may be the name it has today for my listeners who may be old enough to remember when that program started. The guest host was a man named Bud Collyer in the early days of radio. When I was just a youngster during the 1940s, Bud Collyer was the voice of Superman. Maybe someday you can. You can find old tapes of the old Superman program and hear that dynamic voice of Bud Collyer, a much more dynamic voice than the fellow who played Superman in the movies ever had. Then Bud Collyer, bless his heart, got cancer and died, and he was replaced by a not too funny comedian named Gary Moore. But the purpose of the tell the truth was to bring together three fairly unimportant people from Hollywood or Broadway or whatever else. And then three guests, all of whom claim to be something. And, of course, two of those guests were lying. They'd been properly coached. How to lie and answer to questions from the the panel. But only one of the persons was telling the truth. The one episode of that show that I remember concerned a man who claimed to have climbed the highest mountain in all 50 states. And that interested me because at that time I had already climbed the highest mountain in Ohio and Florida. So I was kind of thinking, what? I want to do that as a as a hobby. And anyway, after a period of questions and answers, Gary Moore, the host, would say, Will the real mountain climber please stand up? And in my living room I stood up to say I stood up. Well, in the academic world, huge numbers of people. They may be students, they may be professors. They believe that when people become Christians, they lose. They they give up their intellect. They become your rationalists. For most people who are non-Christians in the academic world and maybe in the regular world as well, to become a Christian means you sacrifice your intellect on the altar of faith. Every day you get up and take blind leaps of faith in the dark and there's nothing you really say carries any weight with these people because they, of course, are the intellectuals. And you, of course, and I are the irrationalism. But after 45 years of doing this stuff, I can tell you truthfully that the real fear rationalists in the world are the non-Christians. Now, I'm not saying there aren't any irrational Christians in the world. There are some. Most of them, in fact, have programs on cable television. Excuse me for laughing. If any of them are listening, may these poor souls look into their hearts and see if they are? You know, there are Christians who behave like a rationalist. But there's no reason for that to be the case. Philosophy is not an enemy of the Christian faith. God is a rational God. He has created us in his image to be rational beings. So we don't have to be afraid of philosophy or logic. These things can be very helpful to us. In fact, they are really quite essential to us in the performance of our Christian duties. So what I'm going to do today as the time permits, So what we're going to do is give you reasons to recognize how an understanding of the fundamentals of logic of philosophy can help you defend the Christian faith against a number of beliefs, a number of worldview, beliefs that are very prominent in colleges and universities around the world. But those worldviews are actually irrational. Those worldviews are actually logically self defeating. Now, let's begin by putting on the screen a definition of the law of non contradiction. And I think this is an almost identical quote from Aristotle, the man who discovered the law of non contradiction. Never for one moment. Accept any suggestion that Aristotle invented or created the law of non contradiction. The laws of logic were not created any more than the multiplication tables were created, any more than the laws of arithmetic were created. So here is a quote directly from Aristotle. This is a little parenthesis for our tape audience here. A lot of people think that Aristotle once played football for the Cleveland Browns. Something like that. Okay, people, today, you know, we have a lot of culturally illiterate people in America. They don't The names Plato and Aristotle are on there on the tips of their tongues. If they do know anything about Plato and Aristotle, all they know is that they're dead white European males and thus we can ignore them. Aristotle, of course, was Plato's great pupil. He lived. He was born about 386 B.C. He died 322 B.C.. Of course, those of you who've taken the history of philosophy course for me, you know that Aristotle had as one of his pupils, the great General Alexander the Great. When Alexander the Great was just a teenager back in Macedonia. Okay, here's the definition of the law of non contradiction. A cannot be both B and non B at the same time and in the same sense. First, a comment about the letters A and B. In this proposition. The letters function as variables. That is, you substitute for them. Obviously, there's little point in just going around for the rest of your life saying how you cannot be both be a non B at the same time. That that gets kind of boring after a while. So you substitute for A and B much the way in which we substitute for the letters X, Y and Z and algebra and algebra. We substitute numbers here, we substitute words. Let's give you a couple of examples of A, B and non B. Take this example. A that is a proposition cannot be both true and false at the same time and in the same sense. Now, it used to be that nobody challenged that. It used to be that if anybody challenged that proposition, they were probably residents of banana insane asylum. Okay. Of course, today a large number of the people who challenged the truth of the Proposition A cannot proposition cannot be both true and false at the same time. Most of those people are now university professors, and usually they get the Professor of the Year award from their basically culturally illiterate students. A a proposition is not be both true and false at the same time and in the same sense. Here's another example. An object cannot be both round and square at the same time and in the same sense. Now I'm going to utter a proposition that I've had some high school students object to. Not even God can create a square circle. Not even God. Can communicate a proposition that is both true and false at the same time and in the same sense. I once uttered that statement to students of a youth ministry in Colorado a few years ago, and some of the students said, Dr. Nash, when did you stop being a Christian? How dare you suggest that there is anything that God cannot do? Well, I'm sorry, and I'll try and indicate here how I answered some of those students. The Bible tells us that there are things that God cannot do. Where does the Bible do that? Well, try Hebrews. Chapter six, written by my good friend, a Polish, as many of you know. If people are listening to me for the first time in one of my other courses, I prove the identity of the man who wrote the episode of the Hebrews. His name was a Polish. His name is in the Bible. Read the Book of Acts, Chapter 18. But we can't go into that right now. Hebrews Chapter six tells us two things that God cannot do. First of all, God cannot lie. Hebrews Chapter six says that. Now think, if you will, about a necessary presupposition for that sentence. What does that verse presuppose? In addition to telling us that God can't lie, it it implies it presupposes that there is an essential, unbreakable difference between a true proposition and a false proposition. If a proposition can be true, true and false at the same time and in the same sense, then God can lie. But God can't according to Scripture, and thank God he can't. What else does Hebrews six tell us? It says that God cannot swear by any being greater than himself. Now, you all know, coming on to people on the tape, I'm talking here to the one one of the most brightest, intelligent, good looking group of students I have ever had in my entire life. So they know why God cannot swear by any being greater than himself. Because there is no being greater than God. When you are the omnipotent, omniscient, omnipresent deity. You mean there's no contest? No one comes close. So God cannot swear by any being greater than himself. That claim also presupposes the law of non contradiction. As I'll try to explain more clearly later on. Finally, notice that they cannot be both be a non B at the same time and in the same sense. Obviously, there was a time in human history when Ron Nash had hair. Okay. There was a time when the statement Ron Nash has hair was true. But over the passage of time, things change. So it cannot be both be a non B at the same time and in the same sense. So don't let anybody play games as is sometimes done in the case of logic textbooks for purposes of humor. Aristotle recognized the unchallengeable exceptions that must exist here. Now I'm switching to another overhead. Let me describe it for the people listening by tape. Here I have, first of all, an oblong occupying o a big chunk of the screen. A rectangle. My right here. Thank you. The to the audience. I told you what a bright group of people I am here. It's a rectangle. And inside the rectangle, which is colored gray, there is a smaller white square. And inside the white square, the small square. I've written the letter B, and then outside the letter B, I have written the term non B. Now, this larger rectangle represents the entire universe. Let me give you a little parenthesis here. What The point I am making here is essential to understanding the law of non contradiction. If you ever run across anybody who does not understand the law of non contradiction and why the law of non contradiction is an absolutely essential, unavoidable principle of human thought and being its because that purpose that person doesn't understand this chart right here. Now important to this chart is the difference between the area the the large gray area called non B and the little white square that's called B. Notice the comments that I have on the screen here. First of all, non B is the complement of B. Notice the spelling c o employee M.A. the complementary class. A B Now what does that mean? The next sentence on the screen will tell you the class of non B is the complement of B because it contains everything else in the universe that does not belong to be. So here you have this little white square that is the class of B, and then everything else in the universe is non B. Let me unpack that. Let me unpack that. Let's allow the class A, B to be any class of things whatsoever. The this could be the class of all dogs, the class of all horses, the class of all trees. And we could go on for a very long time, non b everything else in the universe that is not a cat or a dog or a horse is non b. Now, let me begin to show you the nonsense that follows when you deny the law of non contradiction. Let's take a simple proposition. Socrates is a man. Okay. What we're saying when we utter that is this. Socrates belongs to the white square. Socrates belongs to the class of B, which for us is the class of all men. When somebody denies the law of non contradiction or says the law of non contradiction could be optional. Maybe it works sometimes. Maybe it doesn't. What that person is really telling you is that at the same time that Socrates is a man, Socrates is also everything else in the universe that is not a man. This is nonsense. The person who denies the law of non contradiction must believe that even though Socrates is a man, he is also a horse, a cow, a tree, a river, a mountain. A black hole. A planet. A moon. A piece of hair. Okay, he's. Now, wait a minute. If there is no distinction between. Socrates being a man and Socrates being everything else in the universe at the same time and in the same sense. Then do you understand? We have no distinctions at all. No distinctions at all. And you know what that reduces to That reduces to pantheism. Because among all of the other things that Socrates is, he is also God. And as a result of everything else, God is everything else at the same time and in the same sense, that is heresy. Pantheism is not an option in the Christian worldview. Now, if some of you have been taking the law of non contradiction casually before you go to bed tonight, I want you to utter this sentence. I am a heretic. And do you know where heretics go? All right. When they die. Regulations. Chapter one If anyone come under you bearing any other gospel than that which I have preached on to you, let him be coerced. Listen to me. If you deny the law of non contradiction, then there is no difference between a born again believer and a non born again reprobate. If the law of non contradiction doesn't obtain to God, then listen to these options. There's no difference between heaven and hell. Another little parentheses. If there is even one time in the life of any crazy person, consider someone who is New Age where that person makes an unbreakable distinction. That person is assenting to the law of non contradiction. If there's no difference between being non B, then there's no difference between heaven and hell. If there's no difference between B, anon B, there is no difference between God and the devil. Okay. Let me paraphrase C.S. Lewis. From their Christianity. Don't come to me with any of this patronizing nonsense. That the law of non contradiction is a nice thing to have around now and that or that the law of non contradiction is handy because it works. The question is, why does it work? And the answer is because it can't be any other way. And it can't be any other way for you. And it can't be any other way for God. Now, some of you may be thinking, Boy, this guy's dogmatic. No. I'm just not an idiot, that's all. All right. This is. This is fundamental. This is ground zero. You play games with law, non contradiction, or you propagate a religion that plays games with the law of non contradiction. And you're doing a disservice to God. And you're also cheating because you're going to be all through your ministry. You're going to be making distinctions that you have no right to make unless the law of non contradiction obtains for God and universally for everybody else who exists. Now, sometimes people think that John Frame and I disagree about these issues. The first day I met John Frame when he came here o over a year ago to interview, I said, John, what's the relationship between the law of non contradiction and God? And John Frame said, Logic is a property of God. Write that down. Logic is a property of God. That's a quote from John Frame. That's a true quote. Okay. I then said to John Frame, Is logic an essential property of God? Or a non essential property of God. Now let me explain the differences there. If logic is a non-essential property of God, then logic can be different than it is. The law of non contradiction can be different than it is. John Frame gave me the right answer. He said Logic is an essential property of God. That is, if God is not a logical God, if he is not a rational God, he isn't God. Okay. That's what the term essential property of God means. So frame, and I agree on that stuff. There is a book out there. I won't give you the title. Should I name the author? Well, he's gone on to glory. His name is Rufus Rushdoony is the father of Gary North. And some Theon almost some of you may know that group. And if you know them too well, some of us are praying for you. All right. Even though they may be listening to these tapes someday in that book, which was written 40 years ago, what was it called? I think it's called by what standard? Bruce Rushdoony I believe, you know, I'm getting old and my memory may fail me. I believe that Bruce's Rushdoony portrayed my position, which has not changed in more decades than most of you who have been alive. Bruce Rushdoony portrayed my position as one in which I dared to place logic above God, which means that he thought I subordinated God to the laws of logic. Listen, if I did that, I would be a heretic. Okay. I don't do that. Ruthless Rushdoony, I think I may be wrong. Set in that same book that Ron Nash has an altar in his backyard to the law of non contradiction. And when the moon is full, he goes out and prostrate himself before the law of non contradiction. Let me put the lie to that. I do not pray to the law of non contradiction. I do not place logic above God. I agree rather with John Frame that logic is an essential property of God. Some people have even even pointed out that the close relationship between logic and God may be one of the points John is making in the Prolog to the fourth gospel. Let me you know, fourth gospel says in the beginning was the word. The word was with God, the word was God, and all things were made by him. But the Greek word there, translated word is the word Lagos, from which we get the word logic. Now, I'm not saying that we all know who and what the Divine Lagos was. That was the second person of the Trinity. I'm not saying God is logic, but I am saying there's an intrinsic relationship here between God and logic, and we better be very careful before we start separating them. Okay. Let me give you a couple of a couple of examples of the nonsense that follows when people ignore the difference between be a non B. For example, I once heard about a graduate of a theological seminary somewhere in the mid-Atlantic states who got called into the IRS for an audit, and the tax auditor said to this young student, this seminary student, he said, You haven't filed a tax return in the last four years since you started going to that seminary, as a matter of fact. Why haven't you done that? And he said, Well, ma'am, you don't understand. One of the things I learned in seminary is there's no difference between B and non B. And the tax auditor said, Young man, I don't have a clue what you're talking about. Well, he said, I know you're a little slow, so let me draw you a picture here. Anybody who talks to a tax auditor like that is obviously out of his mind. Okay. He said, You see, if there's no difference between B, anon B, then there's no difference between filing a tax return and not filing a tax return. So the tax auditor said, Oh, I got the picture, now I've got the picture. Then you must also believe that there's no difference between being in jail and not being in jail. You're supposed to laugh, but laugh loudly so they can hear you on the tape. All right. I do have an audience here. If there's no difference between being on B, then there's no difference between driving on the right side of eye for the median and driving on the left side of the median on I-4. To those who don't know, I-4 is otherwise known as the highway from hell. Okay. In Florida, you have to have a special insurance policy just to drive on I-4. I mean, that's how dangerous it is. So if there's no difference, look, if you deny the law of non contradiction, why not drive on the left side of the highway? You might then you might also want to believe. Then there's no difference between being dead and being alive. Okay. If there's no difference between B, anon B, then it makes no difference which house you drive up to. Which house is the front door you knock on and which woman who opens the door you kiss. All right. Now, if I were teaching this course at a secular university not far from here, I could probably, you know, students would leave saying, well, all I can do, all I have to do is say there's no difference between being a non B.