He did it again!

What are the odds that someone contributes to change your life not only once, or twice, but three times? Jim Choury did it again! He has just changed my life again.

He has been doing it through books. The first time it happened, he introduced me to Discipling Nations, by Darrow Miller. I had quit being a leftist, or Marxist, if you prefer. I had been a Christian for some years then, but still could not replace the old ideas of my youth in my mind. I mean, I knew they were wrong and vaguely incompatible with my new faith, but I did not know what to put in their place.

Reading Miller's book, I astonishingly found I had everything I needed to bury the Marxist in me. The Christian faith had everything I needed to fundament my worldview. That was liberating! It had not been the first step into that, though. Years before, I had learned with Jim that to be Christian one has to be rational, or a non-dogmatic person. That was quite a surprise for me, who always kept my faith and my rational beliefs in separate compartments.

I have been struggling, ever since, to purify my worldview and influence others with the truth. The problem is even if you possess the truth and you know it, it does not make it automatically easier to transmit it to others. People are too complex for that. And so are their ideas.

This is where Jim came in to change my life again. He sent me an e-mail and told me about his adventures in Denver, Colorado, talking to people about Jesus. I am not sure how exactly, the Lord touched him to send me the books that were helping him in that task. And he was generous enough to just do it!

I have just finished reading the first one, Tactics, by Gregory Koukl and I can tell it changed my life profoundly! The author taught me to be prepared to defend my beliefs like never before! Not only that, his arguments are so powerfully built, that it enables one to oppose virtually anybody's wrong ideas.

May the Lord keep blessing Jim and his wife Barb for all they have been doing to touch others lives like he did with me. I could never express my full gratitude, Jim.

Chance and Intelligent Design (Part 4)

James A. Choury
WorldVenture missionary to North Brazil

[Leia este artigo em português]

One common misconception regarding probability is that enough time makes even highly improbable events almost certain. This misconception may be a result of confusing two different types of circumstances. These circumstances are known as independent and dependent events. To illustrate this difference we can use coins and cards since this makes possible fairly simple mathematical calculations.

Two events are independent when the result of one has absolutely no effect on the other. Tossing one coin twice or tossing two coins at the same time are independent events. Drawing one card from a deck and replacing and shuffling the deck and then drawing the second card are two independent events. The odds remain unchanged when dealing with independent events. For example, the odds of tossing a head on any given toss of a coin are 50%. If I have tossed the coin three times and never have gotten a head the odds on the fourth toss of getting a head are still just 50%. This is a simple example of how our natural tendency is to think that the odds get better when, in fact, they do not.

However, drawing one card from a deck and not replacing it definitely affects the odds on the next draw of a card. The deck has been modified! This is an example of dependent events.

The odds of drawing a spade from a deck of cards on the first draw are 13/52 or .25000 or 25%. If the first card was not a spade, and the card is not replaced, the odds of drawing a spade on the second draw are 13/51 or .25490 or 25.4%. Note that the odds improved. After drawing 8 cards and never getting a spade and not replacing the cards the odds of getting a spade on the ninth draw would be 13/44 or .29545 or 29.5%. If no spade is drawn in 39 draws and the cards were not replaced then the odds of drawing a spade just before the 40th draw would be 13/13 or 1.000 or 100% because at that point there would only be spades in the deck and drawing a spade would be a certainty.

In discussions concerning the origins of the universe and of life, we can begin talking of independent events where the odds remain the same with each new “trial” (i.e. they never improve) and slip into treating the independent events as though they were dependent. From there it is easy to conclude that the desired event must eventually occur because the odds continually improve until becoming a certainty.

One example might be the thought that life originated when lightning struck a pool with slime in it. (Seldom is the question of where the slime came from addressed). Lightning strikes the pool. The odds of life being formed in this way are highly unlikely and in this case nothing happens. (By the way, it is much more probable that any “incipient” life be extinguished in this way than produced). But some time later another pool of slime is struck by lightning. Again nothing happens but sometime later another pool of slime is struck by lightning, etc. Clearly these are independent events and the odds never improve. Yet we are tempted to think that given billions of years it has got to happen eventually. Given enough time it becomes a certainty. Actually the probability never gets any better. (Perhaps it would improve the odds if lightning were to strike the same pool of slime many times but that only brings in more highly unlikely events).

When discussing issues dealing with probability we must remember that if the events are independent the odds do not improve with time.

Here is a less controversial example to illustrate the point. Let’s imagine a large tray with 50 coins in it. The odds of all the coins being “heads” by chance are 1/250 or 8.88 to the negative 16th power. There is only one way all the coins can come up heads. There are 1,125,899,907,000,000 ways for the coins to come up not all heads. If the tray were “bumped” every second allowing the coins to fly into the air and land again in the tray they would never “by chance” come up all heads because the odds never improve. The odds at each trail would still be 8.88 to the negative 16th power against it. It is ever more probable that at least one coin will be “rebellious” to our wishes and insist on coming up tails.

In discussions of the origin of the universe and of life we are often encouraged to think that given enough time it would have to happen simply by chance. Understanding the difference between independent and dependent events helps us see the error of this way of thinking. The point is the odds never get any better no matter how much time is allowed.

In this brief, four part, study of logic and probability we have seen that the debate concerning the origin of life and of the universe quite naturally and of necessity falls into two camps, i.e., chance or intelligent design. The Law of the Excluded Middle forces the debate into those two, mutually exclusive, options. We have also seen though our rapid lesson on probability that joint, complex, interrelated and highly improbable events are extremely unlikely so as to border on the impossible. These logical and mathematical realities should lead the unbiased inquirer to conclude that the universe and life itself came into being by means of intelligent design.

Why then do so many cling so tenaciously to the “by chance” explanation of the origin of the universe and of life? One reason may be the Law of the Excluded Middle combined with rejection of the concept of a designer. Remember, if it wasn’t by chance then it must have been by “not chance”. But “not chance” is equivalent to saying design and that means intelligent design. One must either accept intelligent design or insist that everything that exists and life itself happened by chance. Those with a philosophical commitment which excludes design are left with chance as the only logical choice available to them. The problem lies in that often this philosophical presupposition is believed to be science and is proclaimed as science. The actual scientific evidence and logic lie on the side of intelligent design.

Christian Discernment

Kerby Anderson

[Leia este artigo em português]

Introduction

Turn on a television or open a newspaper. You are immediately presented with a myriad of ethical issues. Daily we are confronted with ethical choices and moral complexity. Society is awash in controversial issues: abortion, euthanasia, cloning, race, drug abuse, homosexuality, gambling, pornography, and capital punishment. Life may have been simpler in a previous age, but now the rise of technology and the fall of ethical consensus have brought us to a society full of moral dilemmas.

Never has society needed biblical perspectives more to evaluate contemporary moral issues. And yet Christians seem less equipped to address these topics from a biblical perspective. The Barna Research Group conducted a national survey of adults and concluded that only four percent of adults have a biblical worldview as the basis of their decision-making. The survey also discovered that nine percent of born again Christians have such a perspective on life.{1}
It is worth noting that what George Barna defines as a biblical worldview would be considered by most people to be basic Christian doctrine. It doesn’t even include aspects of a biblical perspective on social and political issues.

Of even greater concern is the fact that most Christians do not base their beliefs on an absolute moral foundation. Biblical ethics rests on the belief in absolute truth. Yet surveys show that a minority of born again adults (forty-four percent) and an even smaller proportion of born again teenagers (nine percent) are certain of the existence of absolute moral truth.{2} By a three-to-one margin adults say truth is always relative to the person and their situation. This perspective is even more lopsided among teenagers who overwhelmingly believe moral truth depends on the circumstances.{3}

Social scientists as well as pollsters have been warning that American society is becoming more and more dominated by moral anarchy. Writing in the early 1990s, James Patterson and Peter Kim said in The Day America Told the Truth that there was no moral authority in America. “We choose which laws of God we believe in. There is absolutely no moral consensus in this country as there was in the 1950s, when all our institutions commanded more respect.”{4} Essentially we live in a world of moral anarchy.

So how do we begin to apply a Christian worldview to the complex social and political issues of the day? And how do we avoid falling for the latest fad or cultural trend that blows in the wind? The following are some key principles to apply and some dangerous pitfalls to avoid.
Biblical Principles

A key biblical principle that applies to the area of bioethics is the sanctity of human life. Such verses as Psalm 139:13-16 show that God’s care and concern extend to the womb. Other verses such as Jeremiah 1:5, Judges 13:7-8, Psalm 51:5 and Exodus 21:22–25 give additional perspective and framework to this principle. These principles can be applied to issues ranging from abortion to stem cell research to infanticide.

A related biblical principle involves the equality of human beings. The Bible teaches that God has made “of one blood all nations of men” (Acts 17:26). The Bible also teaches that it is wrong for a Christian to have feelings of superiority (Philippians 2). Believers are told not to make class distinctions between various people (James 2). Paul teaches the spiritual equality of all people in Christ (Galatians 3:28; Colossians 3:11). These principles apply to racial relations and our view of government.

A third principle is a biblical perspective on marriage. Marriage is God’s plan and provides intimate companionship for life (Genesis 2:18). Marriage provides a context for the procreation and nurture of children (Ephesians 6:1-2). And finally, marriage provides a godly outlet for sexual desire (1 Corinthians 7:2). These principles can be applied to such diverse issues as artificial reproduction (which often introduces a third party into the pregnancy) and cohabitation (living together).

Another biblical principle involves sexual ethics. The Bible teaches that sex is to be within the bounds of marriage, as a man and the woman become one flesh (Ephesians 5:31). Paul teaches that we should “avoid sexual immorality” and learn to control our own body in a way that is “holy and honorable” (1 Thessalonians 4:3-5). He admonishes us to flee sexual immorality (1 Corinthians 6:18). These principles apply to such issues as premarital sex, adultery, and homosexuality.

A final principle concerns government and our obedience to civil authority. Government is ordained by God (Rom.13:1-7). We are to render service and obedience to the government (Matt. 22:21) and submit to civil authority (1 Pet. 2:13-17). Even though we are to obey government, there may be certain times when we might be forced to obey God rather than men (Acts 5:29). These principles apply to issues such as war, civil disobedience, politics, and government.

Biblical Discernment

So how do we sort out what is true and what is false? This is a difficult proposition in a world awash in data. It underscores the need for Christians to develop discernment. This is a word that appears fairly often in the Bible (1 Samuel 25:32-33; 1 Kings 3:10-11; 4:29; Psalm 119:66; Proverbs 2:3; Daniel 2:14; Philippians 1:9 [NASB]). And with so many facts, claims, and opinions being tossed about, we all need to be able to sort through what is true and what is false.
Colossians 2:8 says, “See to it that no one takes you captive through philosophy and empty deception, according to the tradition of men, according to the elementary principles of the world, rather than according to Christ.” We need to develop discernment so that we are not taken captive by false ideas. Here are some things to watch for:

1. Equivocation — the use of vague terms. Someone can start off using language we think we understand and then veer off into a new meaning. Most of us are well aware of the fact that religious cults are often guilty of this. A cult member might say that he believes in salvation by grace. But what he really means is that you have to join his cult and work your way toward salvation. Make people define the vague terms they use.

This tactic is used frequently in bioethics. Proponents of embryonic stem cell research often will not acknowledge the distinction between adult stem cells and embryonic stem cells. Those trying to legalize cloning will refer to it as “somatic cell nuclear transfer.” Unless you have a scientific background, you will not know that it is essentially the same thing.
2. Card stacking — the selective use of evidence. Don’t jump on the latest bandwagon and intellectual fad without checking the evidence. Many advocates are guilty of listing all the points in their favor while ignoring the serious points against it.

The major biology textbooks used in high school and college never provide students with evidence against evolution. Jonathan Wells, in his book Icons of Evolution, shows that the examples that are used in most textbooks are either wrong or misleading.{5} Some of the examples are known frauds (such as the Haeckel embryos) and continue to show up in textbooks decades after they were shown to be fraudulent.

Another example would be the Y2K fears. Anyone who was concerned about the potential catastrophe in 2000 need only read any of the technical computer journals in the 1990s to see that no computer expert was predicting what the Y2K fear mongers were predicting at the time.

3. Appeal to authority — relying on authority to the exclusion of logic and evidence. Just because an expert says it, that doesn’t necessarily make it true. We live in a culture that worships experts, but not all experts are right. Hiram’s Law says: “If you consult enough experts, you can confirm any opinion.”

Those who argue that global warming is caused by human activity often say that “the debate in the scientific community is over.” But an Internet search of critics of the theories behind global warming will show that there are many scientists with credentials in climatology or meteorology who have questions about the theory. It is not accurate to say that the debate is over when the debate still seems to be taking place.

4. Ad hominem — Latin for “against the man.” People using this tactic attack the person instead of dealing with the validity of their argument. Often the soundness of an argument is inversely proportional to the amount of ad hominem rhetoric. If there is evidence for the position, proponents usually argue the merits of the position. When evidence is lacking, they attack the critics.

Christians who want public libraries to filter pornography from minors are accused of censorship. Citizens who want to define marriage as between one man and one woman are called bigots. Scientists who criticize evolution are subjected to withering attacks on their character and scientific credentials. Scientists who question global warming are compared to holocaust deniers.

5. Straw man argument — making your opponent’s argument seem so ridiculous that it is easy to attack and knock down. Liberal commentators say that evangelical Christians want to implement a religious theocracy in America. That’s not true. But the hyperbole works to marginalize Christian activists who believe they have a responsibility to speak to social and political issues within society.

Those who stand for moral principles in the area of bioethics often see this tactic used against them. They hear from proponents of physician assisted suicide that pro-life advocates don’t care about the suffering of the terminally ill. Proponents of embryonic stem cell research level the same charge by saying that pro-life people don’t care that these new medical technologies could alleviate the suffering of many with intractable diseases. Nothing could be further from the truth.

6. Sidestepping — dodging the issue by changing the subject. Politicians do this in press conferences by not answering the question asked by the reporter, but instead answering a question they wish someone had asked. Professors sometimes do that when a student points out an inconsistency or a leap in logic.

Ask a proponent of abortion whether the fetus is human and you are likely to see this tactic in action. He or she might start talking about a woman’s right to choose or the right of women to control their own bodies. Perhaps you will hear a discourse on the need to tolerate various viewpoints in a pluralistic society. But you probably won’t get a straight answer to an important question.

7. Red herring — going off on a tangent (from the practice of luring hunting dogs off the trail with the scent of a herring fish). Proponents of embryonic stem cell research rarely will talk about the morality of destroying human embryos. Instead they will go off on a tangent and talk about the various diseases that could be treated and the thousands of people who could be helped with the research.

Be on the alert when someone in a debate changes the subject. They may want to argue their points on more familiar ground, or they may know they cannot win their argument on the relevant issue at hand.

In conclusion, we have discussed some of the key biblical principles we should apply to our consideration and debate about social and political issues. We have talked about the sanctity of human life and the equality of human beings. We have discussed a biblical perspective on marriage and on sexual ethics. And we have also talked about a biblical perspective on government and civil authority.

We have also spent some time talking about the importance of developing biblical discernment and looked at many of the logical fallacies that are frequently used in arguing against a biblical perspective on many of the social and political issues of our day.

Every day, it seems, we are confronted with ethical choices and moral complexity. As Christians it is important to consider these biblical principles and consistently apply them to these issues. It is also important that we develop discernment and learn to recognize these tactics. We are called to develop discernment as we tear down false arguments raised up against the knowledge of God. By doing this we will learn to take every thought captive to the obedience to Christ (2 Corinthians 10:4-5).

Notes

1. "A Biblical Worldview Has a Radical Effect on a Person's Life," The Barna Update (Ventura, CA), 1 Dec. 2003.
2. "The Year's Most Intriguing Findings, From Barna Research Studies," The Barna Update (Ventura, CA), 12 Dec. 2000.
3. "Americans Are Most Likely to Base Truth on Feelings," The Barna Update (Ventura, CA), 12 Feb. 2002.
4. James Patterson and Peter Kim, The Day America Told the Truth (New York: Prentice Hall Press, 1991).
5. Jonathan Wells, Icons of Evolution: Science or Myth? (Washington: Regnery Publishing, 2000).

© 2006 Probe Ministries

________________________________________

About the Author

Kerby Anderson is National Director of Probe Ministries International. He received his B.S. from Oregon State University, M.F.S. from Yale University, and M.A. from Georgetown University. He is the author of several books, including Genetic Engineering, Origin Science, Living Ethically in the 90s, Signs of Warning, Signs of Hope, Moral Dilemmas, and Christian Ethics in Plain Language. He also served as general editor for the Kregel Publications books Marriage, Family and Sexuality and Technology, Spirituality, & Social Trends. He is a nationally syndicated columnist whose editorials have appeared in the Dallas Morning News, the Miami Herald, the San Jose Mercury, and the Houston Post. He is the host of the "Probe" radio program, and frequently serves as host on "Point of View" (USA Radio Network).

What is Probe?

Probe Ministries is a non-profit ministry whose mission is to assist the church in renewing the minds of believers with a Christian worldview and to equip the church to engage the world for Christ. Probe fulfills this mission through our Mind Games conferences for youth and adults, our 3 1/2 minute daily radio program, and our extensive Web site at www.probe.org.

Further information about Probe's materials and ministry may be obtained by contacting us at:
Probe Ministries
1900 Firman Drive, Suite 100
Richardson, TX 75081
(972) 480-0240 FAX (972) 644-9664
info@probe.org
www.probe.org

Chance and Intelligent Design 3

By James A. Choury, serving with WorldVenture in North Brazil

[leia este artigo em Português]

To answer the query concerning the probability of the universe and life coming into being by chance we need to understand how probability is defined and calculated.

Probability: The number of possible ways of attaining a result divided by the total number of possible outcomes. Probability is always a fraction between 0 and 1.

Examples: The chances of getting a head on any toss of a coin is ½ because there is only one way of getting a head and there are two possible outcomes of tossing a single coin; heads or tails. Therefore the probability is ½ or .50 or 50%.
The chances of rolling a die and getting a one is 1/6 because there is only one way to get a one on top and there are six different ways a die can land. So the probability is 1/6 or .16666666…. or 16.66 %.
The chance of getting a four in rolling two dice is 3/36 because you can get a 1-3 or a 3-1 or a 2-2 and the total number of possible outcomes is 36. So the probability is 3/36 or 1/12 or .0833333…. or 8.33333%.

We should notice that a greater number of possible outcomes results in a smaller probability of any one of them occurring. Any outcome of tossing a single coin (only two possible outcomes) has a greater probability than any possible outcome of tossing a die (six possible outcomes). We also note that tossing two dice creates many more possible outcomes (36) and hence the probability of any particular outcome is considerably reduced. In Mathematics, this last phenomenon is termed “joint occurrence”. Joint occurrence calculations give us the probability of event A and event B both occurring by chance.

We say two or more events are independent when the outcome of any particular one has nothing to do with the outcome of the others. Tossing one coin twice or tossing two coins at the same time are examples of independent events. To calculate the probability of joint, independent events we simply multiply the probability of one by the probability of the other or others. Since probability is always a fraction between 0 and 1 we always come up with smaller and smaller probabilities as the number of joint events increases (unless we are dealing with certainties). That means that getting all heads when tossing 5 coins is much less likely than getting all heads when only tossing one coin (3.125% as opposed to 50%).

What does this have to do with evidence of God’s existence? Let’s look at some examples:

Example #1. You walk into a room. There is a table in the room and among the normal clutter there are five coins on the table. All the coins are heads up. What do you conclude? The odds of five coins being all heads up on the table is 1/32. By chance there is only one way all the coins could end up all heads. There are 31 ways that they can end up not all heads up. (They must be either all heads up or not all heads up by the law of the excluded middle). What would a reasonable, unbiased, rational person conclude when finding himself in a room with a table with five coins on it all heads up? It is possible that it just happened by chance but it is much more probable and reasonable that someone was arranging things that way. It is 31 times more probable that someone was arranging things. Suppose there are fifteen coins on the table all heads up? In that case the odds of all fifteen coins being heads up is 1/32,768. There is still only one way you can get all heads. There are 32,767 ways of getting “not all heads”. From this example we see that the odds of fall drastically as the number of joint occurrences increases.

Example #2. Four students go out of town for the college football game knowing that on Monday they have a math exam. None of them prepare for the test and do not show for the exam. On Tuesday they all come wanting to take the test saying that they went to the game, had a flat tire, and didn’t get back in time to take the test on Monday. The professor agrees to give them the test immediately and has each student sit in one of the far corners of the room. He announces that there will be only one question on the test. Each student receives a blank sheet of paper and a pencil. The professor writes the following question on the board: “Which tire?” What are the odds that, without prior planning or collusion, they will all give the same answer? There are four ways they can all agree out of 256 possible outcomes. What if the number of students had been eight going to the game in a van? In that case the odds of all eight students agreeing which tire blew out, without planning or collusion would be 4 out of 65,536 or .00006103515625.

The odds drop off very quickly when we are looking at “joint occurrences”. Joint occurrences are cases where all four students must agree, for example. These examples use very simple circumstances (heads or tails, four students and four tires on the car, etc.) The real world is much more complex. When talking of the origins of the universe or of life it is universally acknowledged that many highly unlikely circumstances would have had to have occurred jointly for the universe and life to have come into being by chance. This joint occurrence makes the odds astronomical against such a thing happening. The probability of life and the universe coming into existence by chance is not easy to calculate but it is generally agreed that the odds are extremely small.* If it was not by chance then it must have been designed or arranged.

Observation: Some believe that even highly unlikely events will eventually take place given enough time. Is this true? For more on this see the study entitled “Chance and Intelligent Design Part 4 dealing with the difference between independent and dependent events and probability.

* Richard Dawkins, staunch evolutionist and popular writer calculates that the odds of the DNA code developing twice by chance is one in a million, million, million, million, million. A River Out of Eden: A Darwinian View of Life by Richard Dawkins, p. 12.

Exercises:

Explain why the probability of joint occurrences drops off as the number of possible outcomes increases.

Come up with an example of your own showing the unlikelihood of joint occurrences.

If the probability of the DNA code developing independently twice is one in 1030, what would be the odds for it developing just once? Would you consider this a good probability?

Chance and Intelligent Design (part 2)

By James A. Choury, serving with WorldVenture in North Brazil

[Leia este artigo em português]

What do Logic and the laws of probability have to do with evidence of God’s existence? The first verse of the Bible states that in the beginning God created the heavens and the earth. Psalm 19.1-4 and Romans 1.20 tell us that the creation proclaims God’s existence and His invisible attributes and that that proclamation is intelligible to mankind to such an extent that not heeding it leads to man’s condemnation.

How does the creation proclaim God’s existence and invisible attributes to such an extent as to leave any one who does not recognize Him without excuse?

At least a part of the answer is to be found in the probability calculus. In the study of probability we learn that complex and interrelated phenomenon very seldom happen simply by chance. When we find something complex and interrelated the rational inclination is to assume that it was designed or prearranged. So the proclamation of God’s existence, power and divine nature are revealed by creation’s order and complexity because experience and an understanding of mathematics tell us that complex and interrelated things come about through design. Discussions about God’s existence naturally (and, as we shall see later, necessarily) revolve around the issue of chance or design.←

Let’s return to the Law of the Excluded Middle described in Part I. Logically we can affirm that life and the universe came about by chance or they came about by “not chance”. It was either chance or not chance and it must have been one or the other. If it was chance then we are automatically driven into the area of Mathematics and the Probability Calculus. If it was chance it is logical to ask “what are the odds?” “Are they good odds?”* Is chance a reasonable explanation for the existence of the universe and of life?

If we consider the only other logical alternative, “not chance”, what are we driven to there? When we say something resulted from “not chance” we are talking about design or some kind of intelligent intervention.

We are caught between two options by the law of the excluded middle. Chance or not chance. Can we agree that “not chance” is just another way of saying “design”? If so, we are talking about chance or design. Can there be design without intelligence? If not, we are talking about chance or intelligent design. No other options. That’s the Law! The Law of the Excluded Middle.

Now, some astute thinker may propose a third alternative: “It may have been partly by chance and partly by design”. Good thinking! But this option only leads us back to the former genuine dilemma. If part was by chance we need to know which part? If some part was by chance we need to ask what are the odds? If part was by design we need to ask who or what was the designer? No, there is no escape along that avenue. The Law of the Excluded Middle is only strengthened by that third, proposed alternative.

We have demonstrated that the Law of the Excluded Middle, when applied to the existence of life and the universe, leaves us with only two rational options: “chance” or “not chance”. If we chose “chance” we are faced with some hard questions about the probability of such chance. If we chose “not chance” we fall logically into affirming that life and the universe are a result of design and are faced with the question of the designer’s existence and identity.

Exercises:

1. Write a short essay on the thoughts found in Genesis 1.1, Psalm 19.1-4 and Romans 1.20.
2. Try to come up with a third possibility for the existence of life and the universe not included in the above options of “chance” or “not chance”.

Chance or Intelligent Design ? (part 1)

By James Andrew Choury, serving with WorldVenture in North Brazil September, 2005

[Leia este artigo em português]

Logic and Mathematics. What have these disciplines to do with evidence of God’s existence?

The Law of the Non Contradiction is a fundamental law of logic. The law states that a proposition and its contradictory can never both be true. In symbols we write [ ~ (A & -A)] where the & symbol means that both A and ~A are true and the tilde (~) means “not”. This phrase is logically equivalent to (A v ~ A) which tells us that one or the other (A or ~A) must be true without exceptions (this by the way is called the Law of the Excluded Middle). In short, the Law of Non Contradiction tells us that a proposition and its contradictory are never both true and the Law of the Excluded Middle tells us that one of them must be true. A more classical way of describing contradictories is that one is the negation of the other and they cannot both be true and they cannot both be false. Logical conversation about any subject must observe these basic laws of deduction.

Examples of the Law of Non Contradiction/Law of the Excluded Middle: *

This table is rectangular or this table is not rectangular.
Two plus two is four or two plus two is not four.
The Bible was inspired by God or the Bible was not inspired by God.
Christ rose from the dead or Christ did not rise from the dead.
My name is James or my name is not James.

In order to more fully understand this important concept let’s imagine a typical closet. We will very likely find shoes, shirts, trousers, umbrellas, coats, hats, baseball bats, gloves, table games on the shelves and many other odds and ends. Let’s have the closet represent any given collection of things. We can go through the closet and sort out everything in it. We can divide everything into two categories, say shoes and not shoes. In another sorting we can do trousers and not trousers. Stuff to throw out and stuff not to throw out. In any given sorting everything in the closet will fall into one of two categories. In every case we will end up with two piles (one pile may not have anything in it and that, in mathematics, is called the empty set). That is what the Law of the Excluded Middle tells us. Nothing will be both a shoe and not a shoe. Every item will be either a shoe or not a shoe.

Of course we must first define our terms and eliminate any ambiguities. But, when all has been clarified, any rational conversation must recognize and respect the Laws of the Excluded Middle and Non Contradiction. Let’s always remember that it is impossible for a proposition and its contradictory to both be true. It is logically necessary that either a proposition or its contradictory be true, i.e., one of them must be true!

Still unconvinced? Try to disprove the Law. Think of any collection of things (in mathematics called a set) and try to come up with something within the set that is both X and not X where X is some unambiguous quality or quantity. Don’t forget that X must be defined unambiguously.

More examples:

The set of all animals can be sorted into mammals and non-mammals.
The set of all vehicles can be sorted into front wheel drive and not front wheel drive vehicles.
The set of all athletes can be sorted into Olympic Gold Medal winners and not Olympic Gold Medal winners.
The set called “furniture” can be sorted into chairs and non chairs.
The set of all beings can be sorted into the categories of divine and not divine.

Remember that a very important part of logical debate and conversation is clear definition. When things are clearly defined we will never find a case where a proposition and its contradictory are both true. We will always find that one of them must be true.

* Aristotle correctly codified these basic laws of deduction together with the Law of Identity and for well over a thousand years they were believed to be the fundamental “laws of thought”. With the development of modern symbolic logic one plainly sees that these three statements are logically equivalent and express the same truth in three different ways. Although they may not deserve the elevated position attributed to them by the ancients they are very definitely inescapable and true.

Note: Some objections have been raised asserting that the Law of the Excluded Middle makes everything either black or white. This is a misunderstanding of the Law. The Law of the Excluded middle actually makes everything either black or not black, round or not round, tall or not tall, etc. when, of course, these terms are well defined.

Exercises:

1. See if you can formulate the Law of Identity for yourself or do some research and find it formulated.
2. Come up with five more examples of the Law of the Excluded Middle.
3. Define the following items or concepts leaving as little ambiguity as possible:
A. a tree
B. a book
C. a box
D. imperialism
E. rectangular
4. Check your definition against that of a good dictionary. How did you do? How did the dictionary do?