ABSTRACT

But it is not difficult to see that in certain cases at least deduction gives us new knowledge.1 If we already know that two and two always make four, and that Asquith and Lloyd George are two and so are the German Emperor and the Crown Prince, we can deduce that Asquith and Lloyd George and the German Emperor and the Crown Prince are four. This is new knowledge, not contained in our premisses, because the general proposition, " two and two are four/' never told us there were such people as Asquith and Lloyd George and the German Emperor and the Crown Prince, and the particular premisses did not tell us that there were four of them, whereas the particular proposition deduced does tell us both these things. But the newness of the knowledge is much less certain if we take the stock instance of deduction that is always given in books on logic, namely " All men are mortal; Socrates is a man, therefore Socrates is mortal." In this case what we really know beyond reasonable doubt is that certain men, A, B, C, were mortal, since, in fact, they have died. If Socrates is one of these men, it is foolish to go the roundabout was through " all men are mortal " to arrive at the conclusion that probably Socrates is mortal. If Socrates is not one of the men on whom our

induction is based, we shall still do better to argue straight. from our A, B, C, to Socrates, than to go round by the general proposition, "all men are mortal." For the probability that Socrates is mortal is greater, on our data, than the probability that all men are mortal. This is obvious, because if all men are mortal, so is Socrates; but if Socrates is mortal, it does not follow that all men are mortal. Hence we shall reach the conclusion that Socrates is mortal, with a greater approach to certainty if we make our argument purely inductive than if we go by way of " all men are mortal " and then use deduction.