Being Logical: A Guide to Good Thinking

by D.Q. McInerny

To my mind, logic is the missing piece of the American educational system, the subject that informs every other subject from English to history to science and math.

Preparing the Mind for Logic

A subjective fact is one that is limited to the subject experiencing it. A headache would be an example of a subjective fact. If I am the one experiencing the headache, then I have direct evidence of its factualness. But if it is you experiencing the headache, I can establish its factualness only indirectly. I must take your word that you have a headache. Establishing the reality of subjective facts depends entirely on the trustworthiness of those who claim to be experiencing them.

Because the establishment of the factualness of a subjective fact pertaining to another person depends entirely on the trustworthiness of that person, you must first, insofar as it is possible, establish the trustworthiness of the person in question.

An idea is the subjective evocation of an objective fact. Clear ideas, then, are ideas that faithfully reflect the objective order from which they derive. Unclear ideas, conversely, are those that give us a distorted representation of the objective world.

The more we focus on our ideas in a way that systematically ignores their objective origins, the more unreliable those ideas become.

Instead of seeing the world as it is, we see a projected world, one that is not presented to our minds but which is the product of our minds.

There are three basic components to human knowledge: first, an objective fact (e.g., a cat); second, the idea of a cat; third, the word we apply to the idea, allowing us to communicate it to others (e.g., in English, “cat”). It all starts with the cat. If there were no real cats, there would be no idea about them, and there would be no word for the idea.

How are we to explain bad (that is, unclear or unsound) ideas? An idea is unclear or unsound to the degree that it is distanced from and unmindful of its originating source in the objective world.

Bad ideas do not just happen. We are responsible for them. They result from carelessness on our part, when we cease to pay sufficient attention to the relational quality of ideas, or, worse, are a product of the willful rejection of objective facts.

In order to guarantee accuracy in your use of words, go back to the objective facts that are the foundational explanations for words.

In the effort to come up with words that accurately convey ideas, our ultimate purpose should always be this: to so shape our language that it communicates to others the way things actually are—objective reality.

Matching words to ideas is the first and most basic step in communication.

Words have been called the building blocks of language, but it is the statement that logic starts with, for it is only at the level of the statement that the question of truth or falsity is introduced, and logic is all about establishing what is true and distinguishing it from what is false.

Here are some basic guidelines for effective communication:

Don’t assume your audience understands your meaning if you don’t make it explicit.

When in doubt, spell out the background information. It is always better to err on the side of saying too much than on the side of saying too little.

Speak in complete sentences.

Don’t treat evaluative statements as if they were statements of objective fact.

“The Pearce Building is on the corner of Main and Adams” is a statement of objective fact, and as such it is either true or false. “The Pearce Building is ugly” is an evaluative statement, and as such it combines both subjective and objective elements.

True statements of objective fact are not open to argument; evaluative statements are. If I want an evaluative statement to be accepted, I must argue for it.

Avoid double negatives.

In Spanish, double negatives have the effect of intensifying the negative import of a sentence. In English, double negatives cancel each othe...

To avoid that confusion, and for greater clarity of expression, avoid double negatives. Instead of saying, “It is not unlikely that she would be welcome,” say “She would be welcome.

Gear your language to your audience.

As a rule, the more general the word, the vaguer it is. A sure preventative against vagueness, then, is to make your words as precise and sharply focused as possible.

Terms like “love,” “democracy,” “fairness,” “equality,” “good,” and “evil” can be vague, not because they have no meaning but because they are especially rich in meaning.

The only way to avoid ambiguity is to spell things out as explicitly as possible: “Keep left. Do not use trail to the right. Grizzly bears in the area.

There is a place for euphemism in language. But we have to be careful that euphemistic usage doesn’t become a way of evading what really is at issue.

If we consistently use language that serves to distort reality, we can eventually come to believe our own twisted rhetoric.

It is juvenile to use language simply to shock. But shocking language is preferable to evasive language, if it can disabuse people of hazy ideas and acquaint them with the truth.

The whole purpose of reasoning, of logic, is to arrive at the truth of things. This is often an arduous task, as truth can sometimes be painfully elusive.

Truth has two basic forms. There is “ontological” truth and “logical” truth. Of these two, ontological truth is the more basic. By ontological truth we refer to the truth of being or existence. Something is said to be ontologically true, then, if it actually exists; it has real being. The lamp sitting on my desk is ontologically true because it is really there. It is not an illusion. The opposite of ontological truth is nonexistence.

Logical truth, as you might suspect, is the form of truth we are most directly concerned with as logicians.

Logical truth is simply the truth of statements. More broadly, we could say that it is truth as it manifests itse...

Establishing the truth in any particular situation is a matter of determining whether what one believes to be true, or suspects might be true, has a basis in fact.

Logical truth, in other words, is founded upon ontological truth.

A word in passing about lies. Lying is more a psychological problem than a logical one. When I lie, I have no doubts about an actually existing situation in the real world, but in my statement about that situation I consciously and deliberately contradict my own knowledge. I know the situation to be properly expressible in the form “A is B,” but my statement says “A is not B.

The coherence theory of truth maintains that any given statement is true if it harmoniously fits into (is coherent with) an already established theory or system of thought.

We should be aware, though, that the coherence theory of truth can be seriously abused, which would be the case if a statement is judged to be true merely by virtue of the fact that it fits into an established theory or system of thought that itself does not correspond with reality, or does so only questionably.

For example, if Marxist economic theory can be shown to be dubious, then the claim that a certain statement about economic matters is true because it is consonant with that theory is likewise dubious.

Whether logic is regarded as a science, an art, or a skill—and it can properly be regarded as all three—there must be principles, seminal regulating ideas, that shape the enterprise and guide its activities.

A science is any organized body of knowledge that is possessed of first principles. The first principles of any science are those fundamental truths upon which the science is founded and by which all its activities are informed.

Logic, as a science, has its first principles, but logic stands in a unique relationship to all other sciences because the first principles of logic apply not just to logic but to all the sciences.

This being so, the terms “the first principles of logic” and “the first principles of human reason” can be said to refer to the same thing.

There are four first principles of logic (or of human reason); the one we are most concerned with here is the principle of contradiction. To put it in its proper context, however, let us first review the three other first principles of logic.

THE PRINCIPLE OF IDENTITY Stated: A thing is what it is. Explanation: The whole of existing reality is not a homogenous mass. It is a composition of individuals, and the individuals are distinguishable from one another. If a thing is what it is, obviously it is not something other than what it is. An apple is an apple. It is not an orange, a banana, or a pear.

THE PRINCIPLE OF THE EXCLUDED MIDDLE Stated: Between being and nonbeing there is no middle state. Explanation: Something either exists or it does not exist; there is no halfway point between the two. The lamp sitting on my desk is either really there or it is not. There is no other possibility. We might ask: How about becoming? Isn’t the state of becoming between those of being and nonbeing? The answer is no. There is no such thing as just becoming; there are only things that become. The state of becoming is already within the realm of existence. A lamp in the process of being made is not yet a lamp; however, the parts that will go to compose it actually exist, and the lamp’s “becoming” depends entirely on their existence. There is, then, no becoming in the absolute sense, no passage from nonbeing to being. Elaine, who is becoming every day a more accomplished musician because of assiduous practice, could not be becoming a musician if she were not already Elaine. There is no becoming with respect to the very existence of a human person. Elaine is “becoming” relatively, not absolutely: She is not becoming Elaine; she is becoming Elaine the more accomplished musician. Again, the basic idea behind the principle of excluded middle is that there are no gaps in being. What we call “becoming” is not a passage from nonbeing to being, but an alteration in a thing or in things already in existence.

THE PRINCIPLE OF SUFFICIENT REASON Stated: There is a sufficient reason for everything. Explanation: The principle could also be called “the principle of causality.” It states that everything that actually exists in the physical universe has an explanation for its existence. What is implied in the principle is that nothing in the physical universe is self-explanatory or the cause of itself. (For a thing to be a cause of itself, it would somehow have to precede itself, which is absurd.) One thing is said to be the cause of another thing because (a) it explains the very existence of that thing, or (b) it explains why the thing exists in this or that particular way, the “mode” of its existence. Larry’s mother and father are the cause of his very existence; if it were not for them, he would not be. Larry’s tennis coach in high school is a cause of his being a good tennis player. The coach is the cause of Larry’s being in a particular way—in this case, a good tennis player. The coach did not, as did Larry’s parents, bring him into being, but he caused a modification in his being. (Of course, there could have been other causes contributing to Larry’s being a good tennis player, so the coach may be only one among several causes.)

THE PRINCIPLE OF CONTRADICTION Stated: It is impossible for something both to be and not be at the same time and in the same respect.