[This subject is also treated in Modes of the Finite, Part 1, Section 1, Chapters 7 and 8, and also in Part 1, Section 2.]

3.1. The Principle of Contradiction

One of the presuppositions in knowing anything at all for certain is the basic law of all thought: that there are no real contradictions.

This can be formulated in various ways, and is known as the Principle of Contradiction. (Actually, as everyone who has ever taught epistemology has said, it should be known as the Principle of Non-Contradiction; but it's always been known the other way, so we might as well keep the tradition.)

DEFINITION: The PRINCIPLE OF CONTRADICTION states that the same thing cannot be both true and false at the same time in the same respect. [Logical formulation] The same thing cannot be what it is not while it is what it is. [Ontological formulation]

The "logical" formulation of the principle states it in terms of truth and falseness (which exist in the mind or in statements, and so deal with thinking--logos in Greek. The "ontological" formulation deals with reality, because "ontology" is the study of being or reality.

DEFINITION: A CONTRADICTION is a statement that asserts and denies the same thing. Or it claims that what it says is true is false.

Thus the relativist position, for instance, is a contradiction, when it asserts as absolutely true that nothing is absolutely true. The skeptical position as a position is a contradiction insofar as it asserts as known for certain that nothing can be known for certain.

The reason I say that contradictions are statements is that you can't think a contradiction, because your thought is self-evident. You can't think that you're not thinking what you're thinking. Nor can you think that what you think is true is false; if you think it's true, then you know that you think it's true--and so you can't think that it's false. You can say things like this, but you can't think them.

In fact, you can say all sorts of interesting things that make certain types of philosophers write books. For instance:

"This statement is false." If by "this statement" you mean the statement "this statement is false," then, of course, that statement would be true if it were false, and false if it were true. It contradicts itself in a rather interesting way.

Or you can talk about the barber in Seville, who shaved all and only those in Seville who did not shave themselves, and then ask, "Who shaved the barber?" Obviously, if he shaved himself, he didn't shave himself, and if he didn't, he did. Just as obviously, there never was any such barber in Seville.

Statements like this are possible because they use words according to the rules of grammar; but they correspond to no thought, because the only way they can be made is by not realizing that they are nonsense until after you have made them; and thought knows what it is doing while it does it.

The philosophers (like Bertrand Russell) who write books about such statements try to rule them out on linguistic grounds, such as by making a "law" that no statement is to refer to itself. But that would make "This statement is in English" meaningless, when in fact it is not only meaningful but true. Unfortunately, the "laws" of linguistics describe language as we use it, and don't prescribe it; which means that that "law" is not a real law of language.

3.1.1. Its self-evidence

Now why is the Principle of Contradiction presupposed in any knowledge?

Because if you know something, you know that it is true and not false.

If it were possible for something to be simultaneously true and false, then what is known to be true could be false insofar as it is true, and then it could not be known to be true and not false.

Thus, if the Principle were not true, then it couldn't be absolutely certain that there is something, because it would be possible that it might be false that there is something because it is true that there is something. (Forgive me for talking nonsense; but that's what denying the Principle of Contradiction gets you into.)

So if the Principle weren't known to be true, it would not be possible to be absolutely certain that there is something--and we are absolutely certain.

This should not be taken as a proof of the Principle; it simply shows that it is presupposed in anything we know. The only way you could "prove" it would be by means of something that you knew to be true and not false, which would of course presuppose that what is true cannot be false in the respect in which it is true--and so you have to admit the truth of the Principle before you could hope to prove it--which means that proof of it is not possible.

Similarly, the Principle needs no proof; since it merely is an expression in words of the basic way we think, and the operation of our mind is aware of itself while it is going on, then the Principle is immediately evident.

3.1.2. The Principle of Identity

There are some things that you could call corollaries or reformulations of the Principle of Contradiction.

These are statements that are different ways, really of looking at the same truth that is stated in the Principle.

DEFINITION: The PRINCIPLE OF IDENTITY states that what is is what it is.

DEFINITION: A TAUTOLOGY is a statement of an identity.

The Principle of Identity can also be called the Principle of Tautology, and it is sometimes formulated "A is A," where "A" stands for anything you want to put in its place: "A horse is a horse," "The Principle of Identity is the Principle of Identity," and so on.

Obviously, if this Principle weren't true, then the Principle of Contradiction wouldn't be true; because then something would be what it wasn't, and the same thing would be true and false at the same time.

Again, this does not prove the Principle of Identity, but merely shows that it, like the Principle of Contradiction, is presupposed in anything we think. It would be impossible to think of anything as true if it weren't what it was.

Some tautologies, by the way, are partial tautologies; for instance, "A hummingbird is a bird," where the "bird" is contained within the meaning of the subject of the sentence, though the subject means something in addition to what is said in the predicate. Immanuel Kant called statements like this, where the predicate is contained within the meaning of the subject analytic statements.

DEFINITION: An ANALYTIC statement is either a total or partial tautology.

Tautologies, of course, are useless sorts of statements, because they don't say anything about the subject, but only repeat it. They crop up every now and then, however, because people sometimes don't know the meaning of the words they use, and think their statements utter a fact about the subject when in fact they don't say anything. There was a friend of our family who used to talk about "sugar diabetes" as if this was one type of diabetes; and I once heard someone refer to "the urban areas of our cities," without realizing that "urban" means "of a city." And so on. Definitions

Definitions are special kinds of tautologies.

They use combinations of words to express the same meaning that the word defined has. The idea in a definition, of course, is that the predicate (the combination of words) is a group of words the hearer knows, and whose combination he can grasp; while the subject (the word to be defined) is an unfamiliar term).

DEFINITION: A DEFINITION is a statement whose predicate shows the meaning of the subject.

DEFINITION: NOMINAL DEFINITIONS use synonyms or derivations to reveal the meaning of the word.

These are the "dictionary definitions." It is assumed or hoped that the reader knows the meanings of the synonyms or of the original words from which the word to be defined is derived.

Thus, "sincere" can be defined as "without wax," explaining that unscrupulous sellers of marble in Italy used to fill cracks in defective pieces with wax, which would make the block look intact.

Alternatively, "sincere" might be defined as "frank, candid, truthful, honest," with the idea that the list of synonyms would convey what the word means.

DEFINITION: OSTENSIVE DEFINITIONS name or point to objects which exemplify the subject.

For example, to define a "planet" you could say that Jupiter is a planet, Saturn is a planet, Mars is a planet, but stars are not planets, the sun is not a planet and neither is the moon.

DEFINITION: CAUSAL DEFINITIONS (also called OPERATIONAL DEFINITIONS) define something as the cause of some effect which the predicate describes.

For example, you could define "existence" as "whatever can make a mind react."

DEFINITION: The ARISTOTELIAN DEFINITION defines by "genus and specific difference"; that is, it gives a larger class to which the object to be defined belongs, and then gives the characteristic which separates all members of the defined class from other members of the larger class.

"Man is a rational animal" is the Aristotelian definition of a human being.

Some philosophers consider the Aristotelian definition to be the only "true" definition; and therefore, words like "being" (which obviously has no larger class) cannot be defined. But it seems to me that this is to take too narrow a definition of "definition"; and the assumption that, because something like "being" cannot be defined in the Aristotelian sense, therefore everyone knows what the word means, has caused a great deal of confusion in philosophy--because in fact different philosophers use the word in different senses.

3.1.3. The Principle of the Excluded Middle

There is another reformulation of the Principle of Contradiction.

This one stresses the fact that what is true is not false and what is false is not true; it is called the Principle of the Excluded Middle.

DEFINITION: The PRINCIPLE OF THE EXCLUDED MIDDLE states that there is no middle ground between truth and falsity, or being and non-being.

Basically, this says that you are either talking about something or you aren't talking about anything; if it doesn't exist, then there's nothing there to talk about, and if it does exist, then it exists. You can't get (in this sense) halfway into existence, so that you neither exist nor not exist.

Similarly, a statement (one that is meaningful, now) is either true or false. You may not know which it is, but it's one or the other. The Principle of Contradiction says that it can't be both true and false; this Principle says that it can't be neither true nor false.

Well, what about half-developed things, or even half-truths?

Half-developed beings exist; and so they are real. They haven't got all the characteristics they will eventually have (and that is why we call them "half-developed"); but they aren't half-real.

Similarly, half-truths are statements that are true in one respect and not true in another respect. "Human beings can make mistakes" is, as I've tried to show, a half-truth. It is true that human beings can make mistakes if they aren't dealing with what is immediately evident; but they can't make mistakes if they are dealing with what is immediately evident.

Half-truths, then, are statements that can be taken in several senses, only some of which are true. But each of the senses is either true or false, and is not "halfway" true.

You mustn't be fooled into thinking that there's something deep or profound in these principles; they're simply statements of what might be called the "absolutely obvious"; they are so obvious that they sound either "terribly deep" or as if they have some hidden meaning--because otherwise, why would anybody bother to say them? But it is sometimes useful to bring into the open what is painfully obvious, that's all.

3.2. The Principle of Causality

Another self-evident First Principle of knowledge is one that has been denied lately.

Those who do so are (among others) called "Logical Positivists," such as Philipp Frank; but it was first denied, shortly before the American Revolution, by David Hume. I think the denial is based on a misunderstanding of it. But first let me state it and give what I think is the true interpretation of it.

DEFINITION: The PRINCIPLE OF CAUSALITY states that every effect has a cause.

DEFINITION: An EFFECT is a set of facts which, taken by themselves, contradict each other.

DEFINITION: The CAUSE is the fact which, when added to the effect, makes the whole set of facts not a contradiction.

The Principle itself is, nominally speaking, a tautology, if you define "effect" nominally; because an "effect" is "something that has a cause"; and so the Principle, taken that way, merely says, "Everything that has a cause has a cause." Therefore, some philosophers have stated the Principle as "Every event has a cause," and have, I think, both watered down the Principle and muddied the water. First of all, one could grant, perhaps, that every event is an effect (but this would need showing--which would be why this Principle would not be a tautology--but it doesn't follow that every effect is an event.

The way I defined "effect," however, shows that the Principle is not a tautology, nor is it exactly a reformulation of the Principle of Contradiction, but an application of it to certain situations.

The Principle supposes that we can get into situations in which the evidence available to us is contradictory. When this happens, the Principle of Contradiction takes over in our minds, and we refuse to accept the evidence as a complete description of the situation, and so search for some other fact which will establish that there wasn't actually a real contradiction "out there."

Thus, if you put coins into your pocket and later reach into your pocket and find none, you have an effect, based on your knowledge of the behavior of coins. The effect could be stated this way. "I put those coins in my pocket, and if nothing took them out, then they're still there; but they aren't still there."

The conclusion of this syllogism is "Therefore, something took them out"; but you will notice that you have no direct evidence of anything taking them out of your pocket; so as far as the evidence you now have, the coins are both there and not there. But, because of the Principle of Contradiction, you cannot accept this as true.

Actually, there are several possibilities other than the conclusion which might be true: (a) you didn't actually put the coins in your pocket; (b) the coins are actually there, but you missed them when you felt in your pocket; or (c) these coins are peculiar in that they could self-destruct without your noticing it. Notice that each of these possibilities simply denies one or the other statements that you took for evidence.

All of these, the conclusion included, are called explanations of the effect.

DEFINITION: An EXPLANATION is a statement by which an effect can be shown not to be a contradiction.

The difference between an explanation and a cause is that the cause is a fact, and the explanation is simply a statement of what could be a cause. If you will, you could define the cause of a given effect as the explanation which is the true one.

There are, usually, an enormous number of explanations for any given effect, some involving very far-fetched assumptions (such as the self-destructive nature of the coins above). Of course, no explanation can itself be a contradiction, because then it simply compounds the contradictoriness of the effect and does not explain it. The problem, then, in using the Principle of Causality is to find which of the explanations is the true one.

For instance, if you call home, and find out that the coins are still on your dresser, then the cause of the effect in question is your faulty memory of putting them into your pocket. If you can prove that you actually did put them into your pocket, but then you discover that there's a hole in your pocket, and indeed you find coins on your driveway when you get back home, then the cause was undoubtedly that they fell through the hole. And so on. There are ways of eliminating various explanations, or of assuring oneself that one has found the cause.

It isn't all that simple, of course; and finding which of many explanations is the cause is actually what science is about--but this would involve a book on philosophy of science, which is not our purpose here.

At any rate, what the Principle of Causality states is that any effect has a cause; and this is absolutely certain, because otherwise, there would be a real contradiction. But what the cause is is another story.

3.2.1. History of the Principle

Well, if everything is so obvious, why have people denied the Principle?

Let me give the briefest of histories of how the Principle was understood, to show the cause of why something self-evident has been denied.

I will begin with Aristotle, around 350 B.C. He developed a theory of "cause" as "the reason" for something, in the sense of "the answer to the question 'Why?'." Now of course, in fact we ask "why" when we don't understand something; and if we are confronted with an effect, it is a contradiction and doesn't make sense--and therefore, effects in my sense are the kinds of situations that make us ask the question "why." But all Aristotle did was note that in fact sometimes we ask this question, and the "cause" is the answer. Well, of course, this means that every effect ("why-question") has a cause ("answer").

He developed a theory that there were four classes of causes, based on four situations in which the question "why" was in order; but they don't need to concern us here.

As this theory developed in the Middle Ages, "cause" became defined as "that which influences the existence of something else." Instead of starting with perplexing situations and looking to the explanation of them, the attention had centered on causes which were discovered, and noted that the cause produced the effect. Thus, the force of gravity produced the effect of making the coins fall through the hole in your pocket.

In general, when causes "explain" real events, they do it by making a difference in the reality in question, either by producing something or making some change in something. Real causes actually do things in the world.

So the tendency then began to be to argue from the cause to the effect; knowing what the cause is, you can predict what it will do, and how it will "influence" the world.

But this is a dangerous procedure, for at least two reasons. First of all, it takes the "cause" as a thing or object instead of an abstract fact about some thing or object (or maybe even about a set of things or objects); and the "cause" as an "object" has all kinds of properties that have nothing to do with its being the cause.

For instance, we say that the cue ball "caused" the 7-ball to move down the pool table when it hit it. And so we call the cue ball the "cause" of the motion. But the fact that the cue ball is white or round has nothing to do with the motion of the 7-ball; it was merely the momentum of the cue ball that did it. A locomotive, touching the 7-ball in the same place with the same momentum, would have produced exactly the same movement.

Secondly, the notion of "influence" (from the Latin in-fluere, "to flow into") was gradually interpreted to mean that the cause "gave" some of its "reality" to the effect, or "poured" something into it. And this implied that the cause had to have the same type of reality that the effect had, and in fact more of it than the effect had (or, it was assumed, it would vanish when it produced the effect; but in any case, it couldn't give the effect more than it actually had itself).

In many cases, these supposedly "self-evident" truths (self-evident if "effect" and "caused" are defined in this way and you still take the Principle as self-evident) actually occur; and so they "stand to reason."

But silly things follow when you try applying them. This interpretation would mean, for instance, that the beaver which causes a dam "has" more of "damness" in him than the dam itself--because he has to "give" the reality of the dam to the dam, because he is the "cause" of the dam. And there were philosophers who actually said such things.

Then around the time of the American Revolution, David Hume took this notion of causality and showed how it didn't make sense. We don't see the cue ball "pouring" anything into the 7-ball; all we see is that the cue ball was moving, it came into contact with the 7-ball, and the 7-ball began to move. We assume, Hume said, that, because all the times we have seen a moving ball collide with a stationary one, the stationary one begins to move, there "must have been" some "influence" of the first on the second. But we didn't actually see the influence; it's just a habit we got into by seeing the sequence repeated all the time. So the "self-evident Principle of Causality" isn't true at all; it's just a delusion we got into because of habit.

This brought about the demise of "causality" from modern thought; because, although Immanuel Kant tried to show how we would necessarily have to think this way when we considered an "event" as beginning to happen, it still said that causality was "all in our minds" and there were no real causes "out there"--which, of course, the Principle proclaims.

Unfortunately, Hume's "destruction" of the Principle only "destroys" the silly interpretation of it; but it itself is a cure that is as silly as the disease, and in fact relies on the Principle to "prove" that it is false.

First, why is the cure as bad as the disease? Because it means that whatever we are in the habit of seeing as coming before something else, we think of as "the cause" of that other thing. Thus, we would think of night as "the cause" of day, the dawn or the light sky in the morning as "the cause" of the sunrise (rather than the other way round, because the sky gets light before the sun rises), robins as the "cause" of Spring, roads as the "cause" of the automobiles that later appear on them, and so on.

In case you think this laughable and wonder how anyone could take Hume's explanation of "causality" seriously, I pointed this out once at a meeting of the Kentucky Philosophical Association, when a lecturer had been using a Humean sense of "cause," and one of the members of the audience raised his hand and said, "But the passing of the night does cause the day." It just goes to show that philosophers too can be wedded to their theories so closely that sanity goes out the window.

DEFINITION: POST HOC ERGO PROPTER HOC ("it came after, therefore it was caused by") is the fallacy of saying that what happens after something else was caused by what it follows.

Hume actually made this fallacy into what he thought was the Principle of Causality itself.

Secondly, Hume used the Principle in its true and fundamental sense, because (a) he was curious as to why we thought that effects had to have causes when in fact we don't see the cause "pouring" anything into the effect, and (b) he explained this curious situation by resorting to "habitual sequence."

His explanation is a bad explanation, however, because it is supposed to explain why we think in terms of cause; but if it were true, then we would think that night causes day and so on.

Hence, the cause of why we think in terms of "cause and effect" is not that we see causes doing things to effects, but that effects, taken by themselves, are contradictions, and there are no contradictions. Whether the "resolution of the contradiction" involves having something done to the affected object or not is something that may be true in some cases and not in others; but that the effect cannot stand on its own is absolutely certain, if on its own it is a contradiction.

Thus, the Principle of Causality stands as one of the basic laws of thought, and is therefore absolutely certain.

3.2.2. Causality and evidence

It can now be seen a little more clearly what the definition of "evidence" in chapter 1 (p.27) means.

We said there that evidence is the cause of our knowledge that something is a fact.

If we take what we now know about cause and effect and apply it to evidence and our knowledge of facts, we can say the following things:

Our knowledge of self-evident facts is not an effect. That is, when the fact is self-evident, then there is no contradiction involved in our knowing that it is true just by knowing what it is; it needs nothing to "explain" why we know that it is true. The only "explanation" in this case is to explain what the words of the statement mean.

In all other cases, our knowledge of what a statement means does not include a knowledge of its truth; therefore, some other fact must give us a knowledge of its truth. This other fact is our evidence for the statement's truth.

This involves a little subtlety in thinking, so see if you can follow it. Take your knowledge of the existence of Moscow (assuming you've never been there). If there were no Moscow, then all the people who have ever mentioned it to you are lying, and in a conspiracy to deceive you that there actually is such a city. Now while it is conceivable that this is the case, it is so fantastic as to be for practical purposes a contradiction.

Hence, the independent testimony of many people talking about Moscow is an effect whose cause is Moscow's existence. It is this effect which is the cause of your knowing that Moscow exists.

Hence, evidence (the effect whose cause is the truth of what it is evidence for) is the cause of our knowledge of that truth. An effect is a cause? Sure. It's the effect of the fact we know and the cause of the knowledge of the fact. Think about this a little.

But now it is time to investigate certainty a bit more closely.

Summary of Chapter 3

The basic law of thought is that there are no real contradictions. A contradiction asserts and denies the same thing (says the same thing is both true and false). The Principle of Contradiction holds that the same thing cannot be both true and false (or cannot be what it is not while it is what it is).

This is self-evident, because whenever we know something we know that it is true and not false, which would not be possible if something could be false because it is not false. It is an unprovable principle, because any attempt to prove it would presuppose it by beginning with something accepted as true (and not false).

A second way of stating this law is the Principle of Identity: What is is what it is. Tautologies are statements of identity, where the predicate says no more than what the subject says. Analytic statements are total or partial tautologies.

A definition is a tautologial sentence in which the predicate restates the subject in terms which are more known to the hearer. Nominal definitions use derivations or synonyms; ostensive definitions point to instances of the term to be defined; causal definitions define the term as "the cause of [some observable effect]." The Aristotelian definition gives "genus" (larger class) and "specific difference" the property that separates the defined class from other members of the larger one.

A third formulation of the Principle of Contradiction is the Principle of the Excluded Middle: There is no middle ground between truth and falsity or being and non-being. Any meaningful statement, then, must be either true or false, not both [Principle of Contradiction] and not neither [Principle of Excluded Middle].

The Principle of Causality states that every effect has a cause. It is an application of the Principle of Contradiction because an effect is a set of facts which, taken by themselves, contradict each other, and the cause is the fact which, when added to the effect, makes the total set of facts not a contradiction. Sometimes, because our knowledge is incomplete, the facts we know can contradict each other; in which case, we immediately (because of the Principle of Contradiction) know that we do not know all the facts--and we look for a cause to "make sense" out of the facts we know. An explanation is a possible cause for a given effect; the cause is the explanation which in fact is true.

Aristotle formulated the notion of "cause" as the answer to the question "why"; later, since causes in the real world "explain" by doing something to effects, it became understood as that which "gives some of its reality" to the effect--which had many absurd consequences. David Hume debunked this view of cause, but was nonetheless explaining why we think in terms of causes; but his explanation was faulty, in that he thought that habitual sequences of events led us to think of the first as causing the second, which falls into the fallacy of "post hoc ergo propter hoc" which has its own absurd consequences. Hence, the definition above is more accurate.

Our knowledge of self-evident facts is not an effect, because our knowledge of them needs no explanation (it is self-explanatory, since we know our knowledge). Our knowledge of any other fact is due to the fact that some self-evident fact is an effect of this fact for which it is evidence. (That is, if the fact indirectly known were not true, the immediately evident fact could not be true either.) The fact that the immediately evident fact is an effect of the other fact causes us to know the truth of the other fact.