God Is Great

I have a fantasy that I participate in a debate against Christopher Hitchens, the best-selling author of God is Not Great: How Religion Poisons Everything. The debate topic is identical to the one Hitchens took up with Reverend Al Sharpton on May 9, 2007, at the New York Public Library: “Is God Great?” And I take the affirmative position!

Here is my argument, which world-class debater Hitchens would have to concede is valid:

If I say that everyone in this room is a billionaire, you can easily disprove this claim by pointing out that you are not a billionaire. But you can’t disprove my claim that everyone in this room who is ten feet tall is a billionaire. To falsify this claim, you would have to provide someone who is both ten feet tall and not a billionaire. Similarly, if I say all gods are great, there is only one way to falsify this claim. You would have to produce a god who is not great. Since we agree that no such god exists, the debate is over. I win!

The validity of my argument relies solely on the rudiments of logic, which covers all forms of mathematical proof. An argument is said to be valid if and only if its conclusion follows from its premises. For example, suppose an argument has three premises (A, B, C) and a conclusion (D). The argument is valid if the conclusion D is true under all circumstances in which its premises A, B, and C are true. An argument is invalid only if we can give an instance where A, B, and C are true, but D is false.

More simply, we can combine all the premises into one called P, with a conclusion called Q. Then any argument may be reduced to P implies Q, which is true except when P is true and Q is false.

To illustrate this argument for those who are resistant to symbols, I’ll give a couple of examples with words. Here is one I used to hear as a child. I didn’t then recognize it was meant to make fun of what creationists thought evolutionists believed.
If the moon is made of green cheese (or some equally preposterous statement, P), then I’m a monkey’s uncle (Q). This is a true statement, because P and Q are both false. On the other hand, this next statement is demonstrably false: If the moon contains iron and silicon (it does), then I’m a monkey’s uncle.

While we’re talking about the moon, here is a popular story that sounds too good to be true, so it probably is, but it illustrates an important point. When Neil Armstrong walked on the moon, his first words were, “That’s one small step for man, one giant leap for mankind.” As he was leaving the moon, he also uttered words into an open microphone that few people heard. “Good luck, Mr. Gorsky.” When Armstrong returned to earth, the press asked him who Mr. Gorsky was. Armstrong just smiled and said it was a personal moment. Finally, a few years ago a reporter asked him again. This time, Armstrong agreed to explain, saying that everyone involved had died and there was no chance of anyone’s being embarrassed.

As a child, Armstrong’s next-door neighbors were named Gorsky. One afternoon when he and his brother were playing baseball, his brother hit a ball over the fence into the Gorskys’ yard. When Neil went to retrieve the ball, he discovered it had landed under their open bedroom window. As he picked up the ball, he heard Mrs. Gorsky say, “Sex! You want sex? I’ll give you sex when the kid next door walks on the moon!”

However apocryphal the story, Mrs. Gorsky constructed what she thought would be a valid argument to avoid sex (at least with her husband) for the rest of her life. On July 20, 1969, the day her unlikely premise (and promise) came true, Mrs. Gorsky was obligated to fulfill her husband’s request. It would have been more prudent for Mrs. Gorsky to have promised sexual favors to her husband only when the Messiah finally makes an appearance.

Before returning to my fantasy debate with Christopher Hitchens, I need to say something about the concept of sets. A set is simply a collection of objects, called elements. A set that contains no elements is called the empty set. The set
of existing tooth fairies or gods can be described as the empty set. The empty set does have properties that are not immediately intuitive, which we can see when we describe subsets.

Set A is said to be a subset of a set B if every element of A is an element of B. For example, if A = {1, 3, 4} and B = {1, 2, 3, 4}, clearly A is a subset of B. On the other hand, B is not a subset of A because we can find an element in B, namely 2, that is not in the set A. Is the empty set a subset of A? Surprisingly, yes. If it weren’t a subset of A, then we could produce an element of the empty set that isn’t an element of A. But all its elements (all none of them) are elements of A. In other words, the empty set is a subset of every set. In fact, every element of the empty set is 17, Christopher Hitchens, or any other property you would like it to have. Otherwise, we could find an element of the empty set that doesn’t have the property in question.

Confused? So are many of my math students, initially, at least. The confusion lies in the difference between truth and validity. A conclusion may be true (which makes the argument valid) despite inane reasoning. For instance: “All men are mortal. Socrates is a man. Therefore, I am an atheist.” My conclusion happens to be true, but my reasoning is not.

A valid argument, as we have seen, may have a false conclusion. This occurs if the conclusion is false whenever the premise is false. “If it is cold and not cold, then blah blah blah” is a valid argument regardless of the blahs, because the premise is logically false.

My fantasy “God Is Great” victory over Christopher Hitchens comes from his inability to produce a god who is not great. But all is not lost for him. The title of his book, God Is Not Great is equally valid, since nobody can produce a god who is great. Every god that exists is great, and every god that exists is not great. That last statement is true only because no gods have been proven to exist.

Such is the power of the empty set, the set with no elements. And, to quote Gershwin, “I Got Plenty O’ Nuthin.”