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History of Philosophy and Christian Thought - Lesson 17

Law of Non-Contradiction

Discussion of the strengths and weaknesses of the law of non-contradiction.

Ronald Nash
History of Philosophy and Christian Thought
Lesson 17
Watching Now
Law of Non-Contradiction

Aristotelian Philosophy

Part 6
 

X. The Law of Noncontradiction

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

B. The Distinction between B and Non-B

C. Relationship to Language

D. There are no logical contradictions in Christianity.

E. Opposition to the Law of Noncontradiction

1. W. T. Stace

2. Kierkegaard, Brunner, Barth, and Torrance

3. Herman Dooyeweerd

4. Cornelius Van Til

5. Donald Bloesch

F. Necessary Truth: 2 + 2 = 4


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  • Thales and Anaximander were two philosophers in the sixth century BC that lived in Miletus.

  • Heraclitus and Pythagoras lived into the 5th century BC.

  • Any worldview addresses the subjects of God, ultimate reality, human knowledge, ethics and human persons.

  • Fundamental beliefs of a naturalistic worldview is that nothing exists outside the physical universe and that all things evolved.

  • Plato was a student of Socrates and lived into the fourth century BC. He opposed hedonism, empiricism, relativism, materialism, atheism and naturalism.

  • Plato described the universe as having three levels: the world of particulars, the world of forms, and the form of the good.

  • Plato's view of the universe was dualistic.

  • One of Plato's fundamental arguments is that the human soul is immortal.

  • Evaluation of Plato's arguments and comparison of Plato's philosophy with biblical theology.

  • Empiricism teaches that all human knowledge arises from sense experience. Rationalism teaches that some human knowledge does not arise from sense. experience

  • Aristotle was a student of Plato and lived in the fourth century BC.

  • Aristotle rejected Plato's doctrine of two worlds.

  • Discussion of Aristotelian philosophy as it relates to the incarnation.

  • Aristotle's philosophy as it relates to attributes of God and fundamental assumptions about psychology.

  • Aristotle made a distinction between passive intellect and active intellect.

  • Discussion of the strengths and weaknesses of the law of non-contradiction.

  • Discussion of the nature and substance of matter.

  • Hellenistic philosophy was an approach that was popular from the fourth century BC to the fifth century AD.

  • Stoics were determinists who believed in living according to nature.

  • Hedonism emphasized pleasure as the greatest good. "Eat, drink and be merry for tomorrow we might be dead."

  • Philo's philosophy was based on a synthesis of Stoicism and Platonism.

  • Implicit "Logos" Christianity is an underlying theme in the book of Hebrews.

  • Plotinus lived in the third century AD and is considered the founder of Neoplatonism.

  • Augustine is a Latin church father, is considered by many to be one of the most important figures in the development of Western Christianity.

  • Augustine wrote Confessions as an autobiographical work to record his experience as a sinful youth and his experience becoming a follower of Christ.

  • Augustine wrote to refute some heresies of the day by focusing on the concepts of faith and reason.

  • Augustine writes about the problem of evil and describes evil as the absence of good.

  • Augustine writes to refute Pelagianism by focusing on the biblical teaching about sin.

  • Augustine writes to refute Donatism.

  • The fundamental idea of skepticism is that no one can know anything. Augustine this statement contradicts itself because the skeptic is claiming that you can know that you can't know anything.

  • When Augustine wrote "The City of God," he had a linear view of history.

  • In Augustine's theory of knowledge, he says that eternal reason and human reason are two different levels of reason.

  • Augustine was personally convinced of the importance of divine illumination.

  • The intellectual background of Thomas Aquinas was influenced by the discovery of ancient manuscripts, the rise of universities, the rise of religious brotherhoods and the rise of Muslim philosophy.

  • Aquinas describes faith as whatever a human can know through special revelation, and reason as whatever a human can know outside of special revelation.

  • Aquinas attempts to prove God's existence.

  • Aquinas describes four kinds of law as eternal, divine, natural and positive.

  • The rationalists and empiricists set the stage for Kant and other philosophers of the modern era.

  • Kant argued that moral requirements are based on a standard of rationality he dubbed the “Categorical Imperative."

  • Kants two worlds are the phenomenal world and the noumenal world.

  • Discussion of criticisms and questions about Kant's ideas.

  • Similarities between Kant's ideas and postmodernism.

  • The dialectic is a central idea in Hegel's philosophy.

  • Ideally, Marxism begins with class struggle, then revolution, dictatorship of the proletariat, withering away of the state, and a utopian classless society.

  • Discussion of four faces of Marxism.

  • Nietzsche proclaimed that, "God is dead." His cure was to live life knowing there is no ultimate meaning. Kierkegaard emphasized a worldview based on true faith.

In this class, you will explore the rich history of philosophy and its relationship with Christian thought. The course begins with an introduction to the definition and importance of philosophy in Christian theology. You will then delve into the evolution of philosophical thought from the Pre-Socratic era, through the Classical Greek philosophers, and into the Hellenistic period. As you progress, you will discover how early Christian thought emerged and developed during the Patristic period, with a special focus on Augustine. The class continues with an examination of medieval Christian thinkers, such as Anselm and Thomas Aquinas, and concludes with an analysis of modern philosophers like Descartes, Kant, and Kierkegaard, and their influence on contemporary Christian thought.

Two other books that are recommended reading for this class are Confessions by Augustine and Phaedo by Plato.

 

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    Law of Non-Contradiction

    Lesson Transcript

     

    I now want to talk about the law of non contradiction in Aristotle. This is so important, friends, because there are there are sincere Christians these days who have nasty things to say about the law of non contradiction or critical things to say about the law of non contradiction. And you know, I'm seldom dogmatic, seldom because I want to I don't want to deprive you of your intellectual liberty. But one of the areas of life in which I am dogmatic is the inescapable ability of the law of non contradiction. If you play games with the law of non contradiction, then every time you open your mouth and say anything, you're cheating. Every time you make a choice in life, you're cheating. A person who denies the law of non contradiction. Watch me here. A person who denies the law of non contradiction is like a person who does this. Oh, there is no air. Now for the people listening by tape, I just took a deep breath of air before I said there is no air. I mean, it's foolish. How did you ever get out of high school? By denying the law of non conviction. Now, this is chapter eight in the intro book. Here is Aristotle's definition of the law of non contradiction. A cannot be both B and non be at the same time in the same sense. Now in this formulation A and B function like variables. Now we're used to variables because we encountered them in high school geometry. Only the variables in geometry were numbers or letters. Yeah, letters X, Y and z usually, you know, so that we learn that X squared plus Y squared equals Z squared or something like that.

     

    [00:02:36] And then you try to figure out what number is represented by X and Y and Z and so on. Only in this case, the law of known contradiction. The variables are letters again, but we focus primarily upon A and B, and on B. Here are two common examples of the law of non contradiction of that in action, an object cannot be both round and square at the same time and in the same sense. An object cannot be both round and square at the same time and in the same sense. I remember once teaching this to a bunch of high school students in Colorado Springs and what I had said or what I said as a part of this was not even God can create a square circle. Well, a little nice little high school girl got very upset at me and she said, When did you stop being a Christian? Actually, not even God can create a square circle. Suddenly this means I'm a heretic. She said, Isn't your name Clark Pennock? I said, No, my name is Ron Nash. Okay. Well, she says, Anybody who says there is anything that God can't do is a heretic. To which I replied, In this way, Did you know that the Bible tells us that there are things that God can't do? She said, Well, yeah, yeah, yeah, yeah. I said, Well, for starters, why don't we look at the Book of Hebrews? The Book of Hebrews was written by a friend of mine. I'm one of the few people who knows who wrote the book of Hebrew. All right. I have Simon kiss Tomoko the other day, who wrote the book of Hebrews. He said, God only knows. I said, Well, I do too. Okay, well, I'm going to tell you who he is next week.

     

    [00:04:39] But Hebrews Chapter six, Gus says, God cannot lie. Oh. The little girl said, There are things that God can't do. And you know what? The statement, the Biblical statement from Hebrews Chapter six God cannot lie, is simply an exemplification of the law of non contradiction. If God cannot lie, there is an inseparable distinction between a true proposition and a false proposition. If God can't lie, there's an inseparable distinction between truth and error. Truth on the line. Hebrews Chapter six says another thing God cannot do. God cannot swear by a being greater than himself. Do you know why God can't swear by a being greater than himself? Because there ain't one. Okay, There isn't one. That's why. But can you not also see how that's the Hebrew statement? In Hebrew six is another exemplification of the law of non contradiction. If the law, if the law of non contradiction doesn't obtain, if the law of non contradiction is not presupposed in every on every page of the Bible, then God can do all kinds of contradictory things, including swearing by a being greater than himself. If the law of non contradiction is not part and parcel of the Word of God. The Bible. Then at the final judgment. God cannot utter these words. I know that I once said that I would promise eternal life. I know that I once promised eternal life to those human beings who placed their faith and trust in my son. But you see, this is God speaking hypothetically at the law, at the final judgment. If the law of non contradiction doesn't obtain, then there's no difference between giving eternal life to those who have trusted my son for their salvation and those who have blasphemed my son. So because there's no difference, I'm going to send all of you Christians to hell and I'm going to give eternal life to these Muslim terrorists.

     

    [00:07:06] You don't like that? Well, then stop playing games with the law of non contradiction. Okay. Now, furthermore, if there's no difference between the law of non contradiction, if the law of non contradiction is not essential to the Christian faith that is absolutely inseparable from it. Then there's no difference between heaven and hell. There isn't. If there is even one fixed distinction in the Christian faith and there are many, of course there are many, then the law of non contradiction obtains. If there's no if the law of non contradiction is not essential to the Christian faith, then there's no difference between God and the devil. These are serious theological implications. Okay. Now, I then go on in my chapter to draw a little chart, and if you can find it, it's in chapter eight. I draw in your book a rectangle, and inside the rectangle is a smaller square. Understanding what I symbolize with this little diagram is crucial to understanding the truth of the law of non contradiction. The indispensability of the law of non contradiction. The absolute necessity of the law of non contradiction. This isn't just something you can take or leave. This is. This is. This is ground zero. Now, what we have here in inside this rectangle is a smaller square that we will call B and B represents any class of things that you would like it to be. B could represent the class of all trees, the class of all human beings, the class of all mountains and so on. Now what we're going to call the rest of the larger figure, the big rectangle, we're going to call that the class of non B people who do not understand the message I'm communicating here. People who do not understand the true nature of the true difference between B and non B will never understand what this law of non contradiction is all about.

     

    [00:09:31] And that's why you'll be so easy to fool on irrelevant matters. Now here's the sentence that you must remember. The class of Non B is the complement of B. What this means is this the class of non B isn't just some phony little opposites or difference from B, the class of non B is everything else in the universe that is not a B. So if you're talking here about the class of all dogs, non is not just the class of all cats. Non B is the class of everything else in the universe that is not a dog. Now let me illustrate this with a sentence. Socrates is a man by what you mean in a human being. Socrates is a man. Socrates is a human being. When we do, when we see that we're taking a particular class, the class of B, let us say, and we're saying that Socrates is a member of that class. If B is the class of all human beings and Socrates is a human being, then he is a member of B. Now, however, if you or anybody else denies the law of non contradiction, then your position entails that Socrates is yes a man. But Socrates is also at the same time in in the same sense, everything else in the universe. Socrates is a man, he's a dog, he's a cow, he's a river, he's a mountain, he's a star. He is everything else in the universe. Do you know what that entails, then? Entails pantheism. Because among all of these other things that represent Nonbeing, you're also saying that Socrates is God. Can you begin to see the theological. Consequences of denying the law of non contradiction. If there's no difference between being non B, then there's no difference between drinking milk and drinking arsenic.

     

    [00:11:58] If there's no difference between B and non B, then there's no difference between driving on the right side of Interstate four and driving on the left side of a four. Can you imagine somebody inviting you on on a date saying, you know, I'm tired of driving on the right side of the median of I-4. You see the same stuff. Let's drive on the other side of the median and it'll be a whole new world. Well, it won't last long, but it'll be a whole new world. Okay. Now, one last point. This also applies to language. Every word either means B or non B, every word of every sentence you ever utter, including the sentence. The law of non contradiction is optional. You can take it or leave it. The word optional either means B or non B, and what is non B? It means everything else in the universe. Okay. Now, here's the point. Unless words have some significant meaning. Human language becomes impossible. Now we all know words that are ambiguous. That is, they have a number of different meanings. Take the word dog. I suppose it's possible that there are ten different meanings of the word dog. We can distinguish them. We can just say dog sense. One dog sense two. Dog sense ten. But you see, if you deny the law of non contradiction, then every word you use has not just ten possible meanings, it has an infinite number of meanings. And if every word has an infinite number of meanings, communication becomes. If every word has an infinite number of meanings, then every person who denies or ridicules or disparages the law of non contradiction is cheating. Every time he speaks a sentence or writes a sentence, he is cheating.

     

    [00:14:24] Because he's assuming the very law that he is ridiculing. Why don't more people recognize this? Well, I don't know. I don't know. The law of Don contradiction is ground zero in any kind of serious thinking or communication about anything whatsoever. If you ever run up against anybody who insists that the law of non contradiction is not a necessary principle of human action thinking communication. If you if you hope to to reason carefully with them about the Christian faith, listen to me very carefully when I say this. If anybody could ever prove that there is a logical contradiction at the center of Christian theology, I would be the first to abandon it. Oh. Yeah, because listen, God doesn't. God expects us to use our minds, all right? Our God is not an irrational God. I don't know if I've mentioned this before, but when I gave my first lecture in the Soviet Union in June of 1991, in Moscow, there was a professor of philosophy in the audience. And afterwards she came up and she told me, and, you know, I'm not swayed by phony baloney stuff. She said, My that was a wonderful lecture, Dr. Nash. And I thought, Aha. But she said, I have one complaint. And I said, Oh, what is that complaint? And she said, You are too much of a rationalist. Now, she thought that she was criticizing me when people accused me of being a rationalist. I thank them. I said, Bless you, bless you. Because do you know what the opposite of being a rationalist is? It's being a near rationalist. All right. Now, I should have said, Well, I guess that means that you're too much of an ear rationalist. But I didn't do that. Okay, I didn't do that.

     

    [00:16:57] If if the if the incarnation really is a logical contradiction, if the doctrine of the Trinity really is a logical contradiction, if there's something if the problem of evil points to a logical contradiction in the Christian faith, it's time to give it up, friends, because a system of belief that is logically incoherent is not just false. It is necessarily false. It is false in every possible world. There's a difference between being all problematically false or, you know, but to be necessarily false means only an idiot would believe this. Now I am here to comfort you by saying that there are no logical contradictions in the Christian faith. And if you want me to defend the Christian faith against alleged contradictions, I'll be glad to do it, probably in the apologetics course, because I do have a lot of a lot of fish to fry today. Now, after last week's class, a number of people walked across the hall and met with me there because, you know, we have to empty this room and time for the next class. And one of you asked me to identify some thinkers who actually do deny the law of non contradiction. And I forgot when I talked to you, I forgot to tell you about which chapter is it in this book? I think it's chapter ten. In the book, the Word of God on the mind of man. Or is it? Yeah, it's chapter. I'm sorry. Here it is. Chapter nine. It's a it's a chapter titled A Religious Revolt Against Logic. So let me share with you some of these other names. I'm, you know, once in a while, at my age, my mind goes blank. Actually, it happens about every 5 minutes. But beyond that, let me just go through chapter nine and give you the names of some people who have been foolish enough to separate religion from logic.

     

    [00:19:13] The first one I mention is a philosopher named W.T. Stace. You can read all about him, and I quote from I tell you where to find one of his writings in which he actually says that okay, w t states he was not a Christian. But then I talk about some other people. I deny that. Kirkuk. Some of you may be may know a little bit about Soren Kirkuk. He is often accused of being an enemy of logic, but he was not. Soren Kierkegaard never argued that there are logical contradictions in the Christian faith. He did argue that there are things in the Christian faith that our puny little reason, our puny little minds cannot understand. But just because you can't or I can't understand something doesn't mean it's a logical contradiction. You cannot turn Kirk Igor into an enemy of the law of non contradiction. Okay. But there are some other so-called theologians. There's Emil Bruner, there's Carl Bart, and there's T.F. Torrance, Tom Torrance, who seems to be highly admired on some of the campuses of Reformed Seminary. I don't know why Tom Torrance, in my judgment, was a real enemy of the Christian church. He was at one time the head of the Church of Scotland. I think he's a serious enemy of the Christian faith. And I don't have I don't I have much respect for his books or his opinions. Anyway, I tell you a little bit about Tom Torrance in here. And then I talk about a man named Hermann de Vere. Now, probably none of you have ever heard the name David. You probably wouldn't pronounce it right now. I happen to know quite a bit about De Vere because I wrote my first book on him. Now, here's what David believed.

     

    [00:21:10] He believed that God created the laws of logic, the laws of geometry and the laws of arithmetic, so that the only reason why two plus two equals four is because of the chance event that God happened to create that law. But God could have created that law. So the two plus two would equal five or three or zero. Now that's just now let me be let me be empathetic here. Instead of saying something unkind, let me just say that's just nonsense, okay? That's just nonsense. The laws of arithmetic, the laws of logic are necessary truths. They are true in every possible world. So there's David. Now, the next guy I mention is one of the most spiritual people I've ever met. And I know this may offend some of you. And as we know, if I do offend anybody today, this would be the first time this semester that I've offended anybody. Okay. But this next person's name is Cornelius Van. Till now, I know that this is subject to some interpretation. Okay. I once took Van Taylor out to lunch. Van Taylor was a famous professor at Westminster Theological Seminary in Philadelphia and all of our faculty member. Bers who went to Westminster before a certain time took courses from vamp till I regard you know, I met him on a number of occasions. What a lot of people around here don't know is that his pastor, near the end of his life, was a former student of mine who he took as his name was Bob Drake. Robert Drake. He's now living somewhere near Asheville, North Carolina, but he was pastor of the Orthodox Presbyterian Church, to which many of the Westminster faculty went and attended and so on. Well, anyway, I took the until out to lunch and I said, Dr.

     

    [00:23:25] King And I listen, He was, as I said, one of the most godly men I've ever met. On another occasion, when I was at Westminster for a graduation, after the graduation ceremony was over, I was standing with my former student, Bob Drake, and we were just sort of talking and Dr. Van Hill came up and said to Bob Drake, Pastor, if you're going to do any hospital visitation this afternoon, I'd like to go with you. Now, I'll tell you, frankly, that is the only theologian I have ever heard tell a pastor that he'd be glad to go to the hospital and do some visitation with the pastor. Most Christian philosophers are too busy to do that. Anyway, Mantill and I are at lunch and I said, Dr. Van Till, may I ask you three questions? And he said, Sure, go ahead. Well, I said, the first question is this Do you know that two plus two equals four? You're probably thinking, what's going on here? Okay. Now, Dr. Van Till answered my question properly. He said, Yes, I know that two plus two equals four. What's your second question? I said, Well, if you know, I'll. Here's my second question. Does God know that two plus two equals four? And this was Van Tils answer. He held out both of his hands, palms up, and he shrugged his shoulders and basically said, I don't know. Now I ask you, what should we make of a great theologian and and been to was. But what can we make of a great theologian who says in effect, I don't know if God knows that two plus two equals four. I hadn't expected quite that blunt reply. I wasn't really surprised with the answer, but it was, you know, that made my third question totally irrelevant, because my third question was going to be this If God knows that two plus two equals four and you and I know that two plus two equals four is what we know, identical with what God knows.

     

    [00:25:56] See Now, I'll tell you my answer. My answer is yes. If God knows something and I know something different, I hope you're getting this in your notes. If God knows something and what I know differs from what God knows, then I don't have knowledge. Did you hear me? If God knows that P where P is any proposition whatsoever. And what I know differs from what God knows, then I don't have knowledge. And you're only kidding yourself if you think you do. Now, actually, what I was getting at in my famous luncheon meeting with the until is the heart of a debate that he had with one of my mentors, Gordon H. Clarke, during the 1940s after the end of World War Two. Gordon Clarke and Cornelius Van Till got into a heresy trial within the Orthodox Presbyterian Church until it finally ground down. But this was one of the most unfortunate events in the history of evangelicalism, I think in the 20th century, that these two fine old gentlemen, actually they were probably in their fifties when this debate got started, dared to go to the church courts and and file heresy charges and well, actually, it was Van Till and his group filing heresy charges against Gordon Clarke. And what was the charge about that? When God knows something, I can know why God now I don't know what God knows. That was what the heresy charge was about. Now, here's how I interpret what Van Hill said to me. I interpret that to mean that Van Tille and I can't understand it in any other way, that the late van, til the van til that I talked to in the late seventies had surrendered to the Deutsche Viridian position, that the only thing that makes sense to Van til saying, I don't know whether God knows that two plus two equals four is that he had surrendered to Van to die of AIDS, claim that God created the laws of arithmetic and therefore two plus two could equal something different than four for God.

     

    [00:28:32] Okay. I think that's there's some serious bad thinking going on there. But maybe there are other ways to interpret them till I don't know. Well, are there any other religious thinkers who deny the law of non contradiction? Yeah. And I talk about them, I think in the last later on in the book. There's a fellow that I regard as a friend of mine. His name is Donald. Blush blow e. S c. H. Blush authored a two or three volume theology book. But boy, his real contempt for logic shows throughout that book. And he's he's kicking around Gordon Clarke and Karl Henry and somebody named Nash. I think maybe he's a relative of mine blush and I carried on some conversations about his view and then he more recently has started to publish single volumes and a series of theology books published by again, the InterVarsity Press, which only recently has well, no, InterVarsity Press is still publishing stuff that is very suspect theologically. The whole open theism stuff is right there in the middle of the InterVarsity press catalog. Okay. But anyway, in Blessures volume on holy Scripture, once again, he really denies the doctrine of propositional revelation that God can actually reveal truth to the mind of man. So those are some of the guys that you need to look at If you're looking for people that I am critiquing here in my defense of the law of non contradiction. Why is two plus two equal to four a necessary truth? And here's the answer. It is a necessary truth because God has been thinking that truth for eternity. That truth and and including all other all other true propositions, not just logically true propositions, but every other true proposition is a part of God's noetic structure from eternity.

     

    [00:30:56] Okay. And the reason why two plus two equals four is is is completely grounded in the fact that that's the way God has been thinking now. Could God think about those thoughts in any other way? No, not if it's his nature to think those that truth. Okay. So I don't I don't want to use the word bound. I just. Let's just say that what unnecessary truth is necessarily true? Because God has been thinking it. And if you want to push if you want to push the envelope a little further and ask, could God have thought about that proposition in any other way? The answer is no, he couldn't.