The Problems of Philosophy Bertrand Russell (chrome ebook reader .TXT) 📖

confirm nor confute, yet which, at least in its more concrete applications, appears to be as firmly rooted in us as many of the facts of experience. The existence and justification of such beliefs⁠—for the inductive principle, as we shall see, is not the only example⁠—raises some of the most difficult and most debated problems of philosophy. We will, in the next chapter, consider briefly what may be said to account for such knowledge, and what is its scope and its degree of certainty. VII On Our Knowledge of General Principles

We saw in the preceding chapter that the principle of induction, while necessary to the validity of all arguments based on experience, is itself not capable of being proved by experience, and yet is unhesitatingly believed by everyone, at least in all its concrete applications. In these characteristics the principle of induction does not stand alone. There are a number of other principles which cannot be proved or disproved by experience, but are used in arguments which start from what is experienced.

Some of these principles have even greater evidence than the principle of induction, and the knowledge of them has the same degree of certainty as the knowledge of the existence of sense-data. They constitute the means of drawing inferences from what is given in sensation; and if what we infer is to be true, it is just as necessary that our principles of inference should be true as it is that our data should be true. The principles of inference are apt to be overlooked because of their very obviousness⁠—the assumption involved is assented to without our realizing that it is an assumption. But it is very important to realize the use of principles of inference, if a correct theory of knowledge is to be obtained; for our knowledge of them raises interesting and difficult questions.

In all our knowledge of general principles, what actually happens is that first of all we realize some particular application of the principle, and then we realize that the particularity is irrelevant, and that there is a generality which may equally truly be affirmed. This is of course familiar in such matters as teaching arithmetic: “two and two are four” is first learnt in the case of some particular pair of couples, and then in some other particular case, and so on, until at last it becomes possible to see that it is true of any pair of couples. The same thing happens with logical principles. Suppose two men are discussing what day of the month it is. One of them says, “At least you will admit that if yesterday was the 15th today must be the 16th.” “Yes,” says the other, “I admit that.” “And you know,” the first continues, “that yesterday was the 15th, because you dined with Jones, and your diary will tell you that was on the 15th.” “Yes,” says the second; “therefore today is the 16th.”

Now such an argument is not hard to follow; and if it is granted that its premises are true in fact, no one will deny that the conclusion must also be true. But it depends for its truth upon an instance of a general logical principle. The logical principle is as follows: “Suppose it known that if this is true, then that is true. Suppose it also known that this is true, then it follows that that is true.” When it is the case that if this is true, that is true, we shall say that this “implies” that, and that that “follows from” this. Thus our principle states that if this implies that, and this is true, then that is true. In other words, “anything implied by a true proposition is true,” or “whatever follows from a true proposition is true.”

This principle is really involved⁠—at least, concrete instances of it are involved⁠—in all demonstrations. Whenever one thing which we believe is used to prove something else, which we consequently believe, this principle is relevant. If anyone asks: “Why should I accept the results of valid arguments based on true premises?” we can only answer by appealing to our principle. In fact, the truth of the principle is impossible to doubt, and its obviousness is so great that at first sight it seems almost trivial. Such principles, however, are not trivial to the philosopher, for they show that we may have indubitable knowledge which is in no way derived from objects of sense.

The above principle is merely one of a certain number of self-evident logical principles. Some at least of these principles must be granted before any argument or proof becomes possible. When some of them have been granted, others can be proved, though these others, so long as they are simple, are just as obvious as the principles taken for granted. For no very good reason, three of these principles have been singled out by tradition under the name of “Laws of Thought.”

They are as follows:

The law of identity: “Whatever is, is.”

The law of contradiction: “Nothing can both be and not be.”

The law of excluded middle: “Everything must either be or not be.”

These three laws are samples of self-evident logical principles, but are not really more fundamental or more self-evident than various other similar principles: for instance, the one we considered just now, which states that what follows from a true premise is true. The name “laws of thought” is also misleading, for what is important is not the fact that we think in accordance with these laws, but the fact that things behave in accordance with them; in other words, the fact that when we think in accordance with them we think truly. But this is a large question, to which we must return at a later stage.

In addition to the logical principles which enable us to prove from a given premise that something is certainly true, there are other logical principles which enable us to prove, from a given premise, that there is a greater or