say to itself, when it comes across them, ‘You great duffer, aren’t you going to ask Why?’ Suppose that, by way of experiment, I assume that the fourth angle of my quadrilateral will be acute, or again obtuse, will the body of conclusions I can now deduce from my set of postulates be free from contradictions or not?  If I really give my mind to the task, cannot I define a continuous function which is not differentiable?  The raising of the first question led in fact to the discovery of what is called ‘non-Euclidean’ geometry, the raising of the second has banished from the text-books of the Calculus the masses of bad reasoning which long made that branch of mathematics a scandal to logic and led distinguished philosophers—­Kant among them—­to suspect that there are hopeless contradictions in the very foundations of mathematical science.

Now, the effect of such careful scrutiny of first principles is not, of course, to upset any conclusions which have been correctly drawn from a set of premisses.  All that happens is that the conclusion is no longer asserted by itself as a truth; what is asserted is that the conclusion is true if the premisses are true.  Thus we no longer assert the ‘theorem of Pythagoras’ as a categorical proposition; what we assert is that the theorem follows as a consequence from the assertion of some half-dozen ultimate postulates which will be found on analysis to be the premisses of Euclid’s proof of his forty-seventh proposition.

To come back to the point I wish to illustrate.  The peculiarity of the philosopher is simply that he still goes on to ‘wonder’ and ask Why when other persons are ready to leave off.  He is less contented than other men to take things for granted.  Of course, he knows that, in the end, you cannot get away from the necessity of taking something for granted, but he is anxious to take for granted as few things as possible, and when he has to take something for granted, he is exceptionally anxious to know exactly what that something is.  De Morgan tells a story of a very pertinacious controversialist who, being asked whether he would not at least admit that ’the whole is greater than the part’, retorted, ’Not I, until I see what use you mean to make of the admission.’  I am not sure whether De Morgan quotes this as an ensample for our following or as a warning for our avoidance, but to my own mind it is an excellent specimen of the philosophic temper.  Until you know what use is going to be made of your admission, you do not really know what it is you have admitted.  It is this superior thoroughness of Philosophy which Plato has in mind when he says of his supreme science ‘Dialectic’ that its business is to examine and even to ‘destroy’ ([Greek:  anairein]) the assumptions of all the other sciences.  It does not let propositions which they have been content to take for granted pass without challenge, and it may actually ‘destroy’ them by showing that there is no justification for