Faulty Logic and Sense Perception

Today on Renewing Your Mind. We as human beings, as well trained as we may be in the science of logic, are still capable of making incorrect inferences and errors in deduction. And that's one of the reasons why great minds will come to differing conclusions about significant issues because somewhere along the way somebody's made a logical leap and so they come to a different conclusion.

That happens all the time, doesn't it? Politics is just one example. People can come to very different conclusions about the issues of the day. But what about religion? Why do some people believe wholeheartedly in God while others are indifferent, even disdainful of God? Here's Dr. R.C.

Sproul. We continue our study of the psychology of atheism, and in our last session we talked briefly about why it is that people of great and indeed impeccable academic and scientific credentials will disagree on very important issues, none more important, of course, than the question of the existence of God. And I listed four main reasons why people of equal brilliance may come to differing conclusions on the same question. And I mentioned those four are, first of all, differing epistemologies or systems or theories of knowledge, the second one, formal errors, the third one, factual errors, and the fourth one, psychological prejudice.

Now, we've already looked in some detail at the first one, the idea of differing epistemologies, and today I want to try to cover the other three if I can squeeze it in within the timeframe. The second, the first one we're going to look at today, is the second of these four, what we call formal errors. Now, what is meant here by formal errors is not that the errors are dressed in a tuxedo and wearing a white tie. Formal errors or errors in form have to do with logical mistakes. These are mistakes that are made in our reasoning process where we are capable, for example, of violating principles of logic, of drawing incorrect inferences from the data that we examine, or in other ways committing all kinds of fallacies of rational thought in our thinking processes themselves. I remember when I was a student of philosophy in college, I was required to take a course in logic, as all philosophy majors were, and in the standard textbook, Cope's Introduction to Logic, which is a classic in the field, we had the occasion to examine the various fallacies that are committed in the reasoning process. And what struck me about this particular textbook was that when the author gave examples of fallacious reasoning, he would lift passages to use as illustrations in his textbook, not from the tabloid magazines or from cartoons or from uneducated people, but he took passages from the works of the most brilliant thinkers in history. There would be a passage from John Stuart Mill that violated one of the rules of logic, and there would be a passage from Immanuel Kant that violated another rule of logic. And the point that the author was trying to show is that even the most brilliant scholars are capable of making some serious blunders in their thinking. Aristotle once remarked that in the corner of every genius's mind lies the portion of the fool.

So even Homer nods from time to time, and we can make formal errors. One of my favorite illustrations of this is the way in which logic can be used deceptively. I do this for fun sometimes in my classroom with my seminary students. I try to prove to them that cats have nine tails. And I'll start by asking, how many of you believe that cats have nine tails and nobody raised their hand? And I say, well, I believe that cats have nine tails, and I'm going to prove it to you. And I prove it by starting this way.

My first premise is a universal negative assertion. No cat has eight tails. I ask them, have you ever seen a cat with eight tails? No. I say, do you believe that cats don't have eight tails in general?

Yes, they believe that. If there was one found with eight tails, it would be a freak of nature. Generally, normal cats do not have eight tails.

It's okay. Now we can agree, because you say that cats don't have eight tails, and I say they have more than eight tails. They have nine tails, but they don't have eight tails. So our first premise is no cat has eight tails.

Then I asked this question. I said, suppose I had two boxes up here in front of the classroom, and one box contained a cat, and the other box was empty. Now here's a simple question, elementary mathematics. We have two boxes. How many more cats are in the box that has the cat than in the box that is empty?

It's pretty simple. The answer is what? One. There's one more cat in the box with the cat than there is in the empty box. So okay, now the real question is how many cats' tails are in the box with the cat compared to the empty box?

How many more tails? Now these people are all convinced that cats only have one tail, so they say, what? One more cat's tail in this box than there is in the other box.

That's okay. Now it gets me to my second thesis here, my second premise. One cat has one more tail than no cats. So if you have one cat here, no cat over here, how many more cats do you have here than you have over here? One. How many more cats' tails do you have over here than you have over here? One. They all agree.

It's okay. The premise is one cat has one more tail than no cats. Now it's just a simple matter of logical deduction, elementary mathematics. If no cat has eight tails and one cat has one more tail than no cat, then how many tails does one cat have? One cat has nine tails, right?

Because, let me show it to you again. No cat has eight tails, and one cat has one more tail than no cat. And if no cat has eight tails, eight and one make nine. So one cat has to have nine tails.

What's wrong with this picture? Now there's a formal technical name for the game that I just played here and the fallacy that's been committed, but I'm going to give you the simple word for it. It's called the fallacy of equivocation, by which the term no cat changes its meaning in the middle of the argument. And by slipping in a different meaning to the term no cat, I used my premises to come to a false conclusion. Now I don't think that most errors in logic that are made are this blatant or this silly, but I want you to see that that's the kind of problem you find.

You find equivocation taking place all the time in reasoning, where in the middle of the discussion the terms that are being discussed change their meaning, and now you have problems. One of the most brilliant philosophers that I admire the most, I won't mention him on the air, argues that the whole is greater than the sum of its parts. And then he proves his point by describing Rembrandt's Night Watch. He said if you look at the Night Watch, that masterful painting that hangs in the Rijksmuseum in Amsterdam is made up of hundreds and hundreds and hundreds of individual brushstrokes.

But when you add all of those individual brushstrokes together and get the whole painting, what you have is not just a glob of undifferentiated brushstrokes, you have a masterpiece of great art. So the whole is greater than the sum of its parts. What's wrong with that argument? Think about that for a second. What's wrong with that argument? What's wrong with this picture?

What has happened here? The axiom, the whole, cannot be greater than the sum of its parts. In what sense is the word greater being used here? In a qualitative sense or a quantitative sense? In a quantitative sense. That is, if you have a hundred individual brushstrokes, the total brushstrokes cannot exceed what number?

A hundred. Because a hundred times one is a hundred. But what has slipped into this man's argument is now, in the first premise, greater is defined quantitatively.

But when he says the Night Watch is greater than the sum of its parts, he's speaking of greatness in a qualitative sense. So in the middle of the argument, the word greater changes significantly. That's a logical error. That's a formal error that leads to a false conclusion.

And that's just one example. We could go on all day giving examples that we as human beings, as well trained as we may be in the science of logic, are still capable of making incorrect inferences and errors in deduction. And that's one of the reasons why great minds will come to differing conclusions about significant issues, because somewhere along the way, somebody's made a logical leap, somebody's made an error in their thinking, and so they come to a different conclusion. Now, the third reason for coming to different conclusions is factual errors. And what I mean here are simply empirical errors, as we talked about Descartes and Descartes' skepticism about basing knowledge on what we can see and hear and taste and touch. And I told about the policeman that was in our audience whose head was smaller than the size of my thumbnail, because when I put my thumbnail in front of my eye, as I looked at him from a distance, I could cover up his head with my thumbnail.

That's an error in perception, isn't it? One of the most interesting illustrations of this I've ever seen took place back in the 60s in the middle of the whole craze over artificial drugs, with Timothy Leary being the high priest of LSD. And you recall that when Leary was at the University of Harvard teaching in the psychology department, that he got in trouble with the law for using LSD in some of his experiments, because it was illegal. And when his case went to trial, he was accused of using hallucinogenic drugs unlawfully in his experimentation.

And the defense that he came up with was fascinating. His attorney and Leary tried to argue that LSD was not a hallucinogen, that it was not hallucinogenic, but it was psychedelic. Before that, I'd never heard the term psychedelic in my life, and all of a sudden, a word entered into the currency of our language and became a pop term overnight, the word psychedelic. And as the attorneys argued, the term psychedelic means mind expanding. Now what's the difference between a hallucinogenic drug and a psychedelic drug? What Leary was trying to prove was this, that a hallucinogenic drug causes a distorted view of reality, whereas a psychedelic drug does not distort reality but gives you a heightened perception of reality.

And in order to defend his case, he brought in people to testify from various areas of the world. He had musicians come in who said that under the use of LSD, that these musicians were able to hear tonal relationships, harmonic relationships that they couldn't hear with the naked ear, as it were. He had artists come in who testified that under the use of LSD, they had such a heightened perception of shades and nuances of the hues of the colors on their palette that they had now an expanded opportunity of sophistication in the coloring of their paintings. Then they had people come in, this was in Time Magazine, who talked about the sexual intensification of LSD, that the sensory organs of the human body are so heightened by this use that they were testifying to having orgasms in their elbows.

That was too much for Time Magazine and made the whole country want to go out and buy LSD. But the problem is this. How can you know?

Who's telling the truth here? How do we know? This is the oldest problem of philosophy there is. How do we know that the external world is as we perceive it to be exactly?

We know that the power of our sensory organs is limited. When I was a kid, my mom got me a puppy, and I went to the store to buy a whistle, a doggy whistle, to call my dog. I bought the whistle, walked back home, and I blew on the whistle, and there was no sound. So, I figured it was broken. I took it back to the store, and I said to the store man, I said, I want to get a new whistle.

This one doesn't work. He said, what's the matter? I said, well, I blew on it.

It didn't make any sound. He said, wait, let me ask you something. I said, what? He said, did your dog come?

And I said, yes, but I don't know why. And he said, because this thing is pitched at a higher register than is perceivable by the human ear, but the dog can hear sounds at a higher level than we can. So, we don't want to bother everybody in the neighborhood when you want to whistle for your dog, you just use this whistle, you won't hear it, your neighbor won't hear it, but your dog will hear it. If anybody's ever been involved in hunting deer, they know how important it is to know which way the wind is blowing because the olfactory sense of the deer is so much more advanced than the human beings. And we know all kinds of animals whose power of perception is greater, either greater hearing or seeing or smelling or whatever, than what we have. What Leary was saying is our senses are so weak that they can distort reality.

That's why scientists use telescopes and microscopes to improve the ability of human perception to scan the external world. So, all of this is simply to show that we can make mistakes in what we observe. It's interesting how important eyewitness testimony is in trials in the courtroom. I remember many years ago when F. Lee Bailey had a regular program on television, he conducted an experiment where in the middle of his speech, he was standing on the stage of a large theater, and he was giving a speech, and in the middle of his speech, he was interrupted when this guy ran out on the stage behind him yelling, and this other guy came from the other side yelling back, and the two of them came right up to each other, and they're waving their arms at each other and having this furious argument, and then they run away. And Bailey said, what happened? And they polled the studio audience, and I don't remember the exact number or percentage, but an overwhelming number of the people in the audience testified that they saw the hostile man strike the other man.

And Bailey said, are you sure? And they said, yes, we saw it. Then they ran the videotape back. And the amazing thing was the man was gesticulating with his arms and waving them all around in a hostile manner, but his hands never ever touched the other person. Now, of course, Bailey staged that to show how the people fill in the gaps with their eyes. They anticipated that the man was going to hit the other man when he was flailing his arms, and so they actually believed they saw him hit him. I remember once lecturing in Pennsylvania.

We had a regular weekly Bible study with this one group, and there were about 50 people in the group. And we had questions and answers at the end of the thing, and this one lady raised her hand and asked me a question about something that I had said. And I said to her, I didn't say that. She said, yes, you did. I said, I'm sure I didn't say that. I said, such and such. She said, no, I know you said that.

And now I'm starting to doubt. I said, really? Did I say that?

And did anybody else hear that? Every person in the room raised their hand and said, yes, you said that, R.C. I said, I can't believe it. And we had taped it. So we turned a tape recorder on, and we ran it back, and I hadn't said it. Fifty people in that room heard me say something I didn't say. It was astonishing, because by that point I believed I had said it with all that testimony. But all of those things illustrate that as reliable as our senses may be for common ordinary usage, they're not perfect.

And we can make mistakes with our senses. We all know cases where this has happened to us, and we think that we heard something that we didn't hear or that we saw something, or we jumped to conclusions that we shouldn't jump to. I remember I've told this story before when I was in Holland, and I had to do some work in the yard, and my two-year-old daughter wanted to go outside with me. And there was this little stoop there that I told her to stay on, this little front porch, because the road was only about 20 feet away, and I didn't want her wandering off and getting hit by a car. So I said, honey, you can come out here, but you have to stay on the stoop. She said, okay, Daddy. And I started my work, and I turned around, and I see her wandering around the yard. I go over and pick her up, put her back up on the stoop. I said, honey, I told you to stay on the stoop. She said, okay, Daddy. Two minutes later, she's wandering around the room.

I put her back on there. I told her this time, I said, honey, if you get off the stoop again, I'm afraid Daddy's going to have to spank you. She said, okay, Daddy. Fifteen seconds later, she's off the stoop. And I walked over, and I said, I told you I was going to have to spank you, and I spanked her.

She looks up at me sobbing and tears coming down her face. I said, I told you to stay on the stoop. And she said, Daddy. And I said, what?

She said, what's a stoop? I said, you're looking at one. See, I had made the assumption that she knew what I meant. And we do that with all kinds of things, and it leads us to erroneous conclusions. Well, that is a clear explanation, isn't it, of why we come to such diverse conclusions? We're glad you joined us today for Renewing Your Mind and another lesson from Dr. R.C. Sproul's series, The Psychology of Atheism. It's based on R.C.

's book, If There's a God, Why Are There Atheists? We'd like to send you the paperback edition of this book, 200 pages, and when you contact us today with your donation of any amount, we'll add Dr. Sproul's teaching series to your online learning library, allowing you to stream all 15 lessons right away. Find us online at renewingyourmind.org or call us with your gift. Our number is 800-435-4343. We are grateful for your financial support. Together, we're reaching around the world to evangelize and disciple the nations. Our gifts provide sound biblical teaching and theologically rich resources to believers around the world, so thank you.

Before we go, I'd like for you to hear a portion of a message that Dr. Stephen Lawson, one of our teaching fellows, delivered at one of our Ligonier conferences. He's referring to Romans chapter 1, where the Apostle Paul says that atheists suppress the truth in unrighteousness. Why would anyone suppress the truth in order to cling to their unrighteousness? He says in verse 19, because that which is known about God is evident within them. There is a knowledge of God within every person.

It is within them. There is a God consciousness, and God has placed that God consciousness within every man. Solomon will say in Ecclesiastes that the Lord has set eternity within every heart, for God made it evident to them. God is the revealer of Himself to every man on the planet. There is general revelation, and there is special revelation. And general revelation is made known to every man, every woman, every boy, every girl on the planet, and it is a general revelation of the fact of God, of the existence of God, of the being of God, of the person of God. Now, general revelation is not enough to know that God. There must be special revelation, which is found in the gospel of our Lord and Savior Jesus Christ. And not everyone receives special revelation.

There are people on this planet who are born, live their lives, and die without ever hearing the name of Jesus Christ. But they nevertheless have general revelation. It is not enough to save them, but it is enough to condemn them. And it is enough to hold them accountable to God.

And He will say in verse 20 that no one is without excuse before God. So at the end of verse 19, God made it evident to them. It is clear. It is obvious. And verse 20 explains how God has made it evident to every man and every woman on planet earth.

The word for introduces an explanation. And verse 20, for since the creation of the world, that means from the very beginning of time, from the dawn of human history, since the creation of the world, His invisible attributes, His eternal power, His divine nature, please note this, have been clearly seen. It is obvious. It is glaring. A blind man can see it, have been clearly seen.

How? He says later in verse 20, being understood through what has been made. It's a very simple philosophical point that every effect must have an adequate cause. And the mere fact that there is creation around us necessitates an adequate cause. And there is only one reasonable, rational explanation for the universe and for creation, and it is that there is a Creator, capital C. There is no corporation who could have created everything out of nothing.

There is no individual. There is no religion. There is no philosophy that could have made everything out of nothing.

And as R.C. Sproul has said, if there was ever a time when there was nothing, then there could never be anything. Because before creation, there had to be a Creator. There had to be God. Such a helpful perspective on the futility of atheism.

That's Dr. Stephen Lawson. And I hope you'll join us again tomorrow as we continue Dr. Sproul's discussion on why people come to different conclusions about very serious matters. We'll take a look at how our personal bias influences our thinking. So I hope you'll join us tomorrow for Renewing Your Mind. Copyright © 2020, New Thinking Allowed Foundation