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