Quartz Hill School of Theology

Logic and the Laws of Thought

There are three:

1. Law of identity
2. Law of noncontradiction
3. Law of the excluded middle

These laws cannot be proved or disproved. In order to demonstrate them, they must be assumed. To deny them is self-contradictory. They are presupposed in all rational -- that is, consistent -- thought and discourse.

Do the laws of thought apply to all of reality?

Are they the basic rules of reality, or of thought only?

Rationalism holds that the laws of thought apply to everything whatever because they are the most general truths of reality. They apply not only to what we think and say but also to what we think and talk about.

Empiricism holds that the laws of thought are useful verbal conventions applying only to the way we think or talk, not necessarily to what we think and talk about or even necessarily how we must think or talk.

    a) The Principle of Identity

Simply stated, the first of the fundamental laws is a tautology. If any statement is true, then it is true. Some have criticized this first principle on the basis that things change. For instance, in 1790 one could make the statement: "The United States of America is made up of 13 states." But obviously such a statement is not true today. However, the fact of change in human affairs does not negate this principle of logic. Statements which change over time are said to be elliptical, or incomplete statements. Thus, the statement "The United States of America is made up of 13 states" is a partial formulation of the statement, "The United States of America was made up of 13 states in 1790." Such a statement is as true today as it was in 1790. Thus, as Copi said, "When we confine our attention to complete or non elliptical formulations, the Principle of Identity is perfectly true and unobjectionable."

    b) The Principle of Noncontradiction

Simply proposed, this asserts that "no statement can be both true and false." Or to take it a step further, "a given thing cannot be and not be in the same way and to the same extent at the same time." This is a vital principle, without which reasoned thinking is not possible. While it may seem obvious that a given object cannot be both an apple and a peach, this principle is often ignored or twisted out of shape by both secularists and theologians.

The word "paradox" is used sometimes to describe contradictions -- contradictions that, some would say, must be accepted. For instance, the famous experiments with light, which indicate that under certain experimental conditions, light can be demonstrated absolutely to be made of particles, while under other experimental conditions, light can be demonstrated absolutely to be made of waves. A contradiction! In some circles it has been concluded that light is both and neither and we must live with the contradiction.

Occam would shout "poppycock" to that conclusion. The simpler explanation, by making use of Occam's razor, is to say that the experiments have settled nothing, and that further study is needed. We can't just throw up our hands and say, "oh well, it's both; lets say light is made of 'wavicles'." What the heck is a 'wavicle'?

The same thing arises in theology in attempts to explain the Trinity, the relationship of free will to divine sovereignty, or how a good, all powerful God could permit sin. Too often, theologians are satisfied with the paradox -- "the apparent contradiction" -- and leave it at that. Again, Occam's razor would simply slice through the gobbledygook and tell the theologians that they have more work to do. Frank Wilczek and Betsy Devine, writing about nature (the general revelation of God), made a very perceptive point, which has definite implications for understanding the Bible (the special revelation of God):

Nature poses many riddles but contains no contradictions. By solving one of her puzzles, therefore, we are guaranteed to learn something -- and the weirder, the more impossible the paradox seems at first, the more mind-expanding will be its ultimate resolution. [F. Wilczek and B. Devine. Longing for the Harmonies: Themes and Variations From Modern Physics, New York: W.W. Norton, 1988, p. 218]

What all this means then, is that contradictions cannot be real. Such a conclusion is a very hopeful and useful tool, and has been of immense impetus to scientific research, because this principle of non contradiction assures the researcher, in whatever field, that there is, indeed, an answer to any conundrum. And if there is an answer, then it is possible to find it.
On a personal level, this principle of non contradiction has some serious implications. Every day, we discover people who, within their lives, are not living up to the principle. George Orwell described the problem as "doublethink". An older word for this sort of person is simply "hypocrite". The Bible calls such a person a "double-minded man":

If any of you lacks wisdom, he should ask God, who gives generously to all without finding fault, and it will be given to him. But when he asks, he must believe and not doubt, because he who doubts is like a wave of the sea, blown and tossed by the wind. That man should not think he will receive anything from the Lord; he is a double-minded man, unstable in all he does. [James 1:5-8]
Come near to God and he will come near to you. Wash your hands, you sinners, and purify your hearts, you double-minded. [James 4:8]

Notice the sheer idiocy and irrationality of the hypocrisy: a person goes to God to request something that He has promised to give, but then doesn't believe God will give it. Such an attitude irrationally contradicts the truthfulness and goodness of God, not to mention explicit biblical statements that God does not lie.

The second passage in James 4:8 goes even further, equating hypocrisy with sin, or better yet, portrays the sinner as being a hypocrite by definition. After all, a Christian claims to be filled with the Holy Spirit, cleansed by the sacrifice of Christ, a new creature, and yet he sins. Contradiction.

Of all things a nonbeliever delights in most, it is to point out the inconsistency of believers. I give two examples:

Catholic theology teaches that the Pope and Church are infallible. The doctrines and traditions handed down from the fathers are as much the words of God as the Bible. Yet, thousands who claim to be Catholic, feel perfectly justified ignoring the Catholic Church's teaching on birth control, abortion, or women in the Church. How can this be?

Doublethink; hypocrisy; inconsistency. To be a consistent Catholic, to obey the concept of non contradiction, the follower of Rome must accept what the Catholic Church says in all things. Otherwise, that one becomes by definition, no longer Catholic -- but Protestant.

By contrast, Baptists claim (in the Protestant tradition) that the Bible alone is authoritative, that the individual Christian is free to interpret the Bible for himself, and that all believers are priests, equal before God. Yet in practice, the standard, traditional interpretation of the Bible is the true authority, and to dissent from that interpretation (particularly if you act upon it) will often result in church discipline, censure, and possible expulsion, as the pastor alone is really in charge of things. Where then is biblical authority? Where then is soul liberty? Where then is the priesthood of all believers? They are swallowed in doublethink.

What is in our heads rarely matches our practice, and often contradicts other ideas in our heads. Humans are strange that way. Listen to George Orwell:

    The Party said that Oceania had never been in alliance with Eurasia. He, Winston Smith, knew that Oceania had been in alliance with Eurasia as short a time as four years ago. But where did that knowledge exist? Only in his own consciousness, which in any case must soon be annihilated. And if all others accepted the lie which the Party imposed -- if all records told the same tale -- then the lie passed into history and became truth. "Who controls the past," ran the Party slogan, "controls the future: who controls the present controls the past." And yet the past, though of its nature alterable, never had been altered. Whatever was true now was true from everlasting to everlasting. It was quite simple. All that was needed was an unending series of victories over your own memory. "Reality control," they called it; in Newspeak, "doublethink."
"Stand easy!" barked the instructress, a little more genially.
    Winston sank his arms to his sides and slowly refilled his lungs with air. His mind slid away into the labyrinthine world of doublethink. To know and not to know, to be conscious of complete truthfulness while telling carefully constructed lies, to hold simultaneously two opinions which canceled out, knowing them to be contradictory and believing in both of them, to use logic against logic, to repudiate morality while laying claim to it, to believe that democracy was impossible and that the Party was the guardian of democracy, to forget whatever it was necessary to forget, then to draw it back into memory again at the moment when it was needed, and then promptly to forget it again, and above all, to apply the same process to the process itself -- that was the ultimate subtlety: consciously to induce unconsciousness, and then, once again, to become unconscious of the act of hypnosis you had just performed. Even to understand the word "doublethink" involved the use of doublethink. [George Orwell, 1984, pp. 35-36]

    c) The Principle of the Excluded Middle

The principle of the excluded middle asserts that "any statement is either true or false". Some have objected that if this principle is accepted one is forced into a "two-valued orientation" which implies that everything is "either-or", with no middle ground possible. Such an objection results from a misunderstanding of the principle. If you have something that is gray, for instance, the statements "this is black" or "this is white" are both false. When faced with a situation where one is given such statements, "this is white" or "this is black", while both statements cannot be true, they very easily might both be false. When one restricts oneself to statements that are unambiguous and precise, then the principle of excluded middle is perfectly valid.

In other words, what this principle asserts is that REAL paradox is not possible, only APPARENT paradox, the result of limited language or data. By the principle of excluded middle, when faced with the question of whether light is made of waves or particles, since the experiments contradict each other, it is best to assume that light is neither wave nor particle, but something else: GRAY.

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Quartz Hill School of Theology
43543 51st Street West
Quartz Hill, CA 93536

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