Negatives

In the movie Kelly's Heroes, there's a completely anachronistic character called Odd-ball, played brilliantly by Donald Sutherland (Mr. Bennet in the Keira Knightley Pride and Prejudice). He's famous for delivering, during World War II, such sixties hippy phrases as, "What's with the negatives waves?"

While such a thing is certainly hilarious, I wonder if there is not something philosophically deeper going on in today's culture. To illustrate what I'm talking about, I'm going to dive into some technical material which I hope I explain clearly. I would STRONGLY encourage you to try to follow my train of thought.

In symbolic logic, there is a concept called "adequacy of a set of connectives." The idea goes like this: in certain kinds of logic, you have what are called Boolean variables; they're just like an on/off switch or a bit in computers. The Boolean variable can hold the value "true" or it can hold "false". So there are two options for one Boolean variable. Suppose you have two Boolean variables that you can distinguish one from the other. How many different ways can those variables be set? Well, you could have (true, true) or (true, false), or (false, true) or (false, false). So that makes four possibilities. If you look at three variables, you'll see that you can have eight possibilities. So in general, if you have n Boolean variables, there are 2 to the n possible ways of setting those variables.

Now introduce the concept of a function of Boolean variables. What is that? Well, we'll build up from scratch again. Suppose you have one Boolean variable, call it x. There are, as we already discussed, two possible ways to set that variable. Now a function f of the Boolean variable x, which we will write as f(x), is another variable whose value depends on the value of x. How many functions of one Boolean variable are there? Well, you could have the function that is always true no matter what x is (the true function), or also the function that is always false (the false function), or you could have just x right back at you (the identity function), or you could have the function that changes true to false and false to true (the negation function). So that's four possible functions of one Boolean variable. It turns out that if you have n Boolean variables, there are 2 to the 2 to the n possible functions on those variables.

Let us examine quietly one possible function, call it q, on two Boolean variables, call them x, y. So we'll say that q is true only when both x and y are true. So it looks like this:

q(true, true) = true
q(true, false) = false
q(false, true) = false
q(false, false) = false.

We have a notation for this function: ^. So we write q(x,y) = x ^ y. This is called the "and" connective, because it connects x and y in a functional way.

There are many such connectives, including "or", "exclusive or", "nand", "nor", "Sheffer stroke", and others. One question that logicians have concerned themselves with in the past is the following: given an arbitrary function on n Boolean variables, can I write that function using only one or possibly two known connectives? This is the question of adequate connectives.

It turns out that there are only two adequate connectives (of the possible sixteen functions on two variables). Both of them have the word "not" in their description.

My patient readers may be wondering why I dragged them through so much symbolic logic. The reason is this: the conclusion many have come to is that in order to be complete, or adequate to express things, you must be able to say "no" in some manner or other. No language is going to be adequate to express everything worth expressing if it cannot do negation.

This grates against the sensibilities of the post-mods, and the politically correct, who want to employ a "both-and" kind of logic. "You can embrace both this and that," regardless of the fact that they're contradictions. They can't do this consistently. As Ravi Zacharias said once (I paraphrase), "Either you use the both-and logic, or you don't, isn't that right?" And the person he was speaking to, a professor of Eastern religions, said, "The either-or logic does seem to emerge, doesn't it?" Whereupon Zacharias replied, "Yes, and I've got some shocking news for you. Even in India, we look both ways before crossing the street. EITHER the bus, OR me, not both of us." You can listen to the whole broadcast by going here, and clicking on the link for 2006-01-30. This acceptance of contradiction is nonsense, and leads to intellectual suicide. You must be able to distinguish between things. If you read the Bible at all, this should become very clear; just read Leviticus. In Leviticus, one central theme is the holiness of God. God was to be approached only by what was "clean," and NOT by anything that was "unclean." Clean and unclean was defined in excruciating detail by divine fiat. God gave priests a great many rules about how to decide if a thing or a person was clean or unclean.

R. C. Sproul once said, "If it's the prerogative of the woman to change her mind, it's the prerogative of the theologian to make distinctions." Distinctions are absolutely necessary in order to talk intelligently about just about anything.

So my little analogy from symbolic logic is that you have to be able to negate things in order to fully realize the expressive capabilities of your system. But this carries over into language, philosophy, and theology. I would claim that this concept comes from the Bible, and not from logic. I only started with the logic point for rhetorical effect: to argue from the lesser to the greater.

If someone comes to you, claiming that you are "intolerant of their views," first ask them what they mean by that. What they most likely want you to do is to accept all these views as equally true. It's just relativism thinly disguised, or not disguised at all. Christianity, though, makes absolute claims. "Jesus said to him, 'I am the way, and the truth, and the Life. No one comes to the Father except through me.'" - John 14:6 (ESV). That is an exclusive statement; if it is true, no other claims can also be true. Your detractor might say, "Well, that's true for you, but not for me." This is nonsense! They are claiming there is no absolute truth. In which case you just ask them whether the statement, "There is no absolute truth" is true for everyone, or not. The fact is, they've just uttered an absolute truth.

Philosophically, we are "trapped" into believing in absolutes. We cannot consistently do otherwise. But let us remember that the truth will set us free. But falsehood, the negation of truth, will do no such thing.