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 asserting them. Thus Euclid's assumption about parallels ceased to be included among the indispensable premisses of geometry, and was 'destroyed' in Plato's sense when Lobatchevsky, Bolyai, and Riemann showed that complete bodies of self-consistent geometrical theory can be deduced from sets of postulates in which Euclid's assumption is explicitly denied. There are two further points I should like to put before you in this connexion. One of them has been forcibly argued by Mr. Bertrand Russell in his admirable little work _The Problems of Philosophy_; the other has not. Indeed, it is just in his unwillingness to allow the second of these points to be raised at all that Mr. Russell seems to me to fall conspicuously and unaccountably short of being what, by his own showing, a great philosopher ought to be.