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.

To take first the point with which Mr. Russell has dealt.  There is one very important branch of inquiry, if we ought not rather to say that there are two, which appear to belong wholly to general Philosophy and not to any of the ‘sciences’.  We cannot so much as ask the simplest question without making the implication that there is an ultimate distinction between true assertions and false ones, and certain definite principles by which we can infer true conclusions from true premisses.  It is thus a very important part of the true ‘story of everything’ to state the principles upon which valid reasoning depends, and to enunciate the ultimate postulates which have to be taken for granted whenever we try to reason validly about anything.  This is the inquiry known by the name of logic.  We cannot expect men whose time is fully taken up with the task of reaching true conclusions about some special class of facts, those which concern the history of living organisms, or the production and distribution of ‘wealth’, or the stability of various forms of government, to burden themselves with this inquiry in addition to their other tasks.  They may fairly be allowed to leave the construction of logic to others.  But the man who makes it the business of his life to get back to ultimate first principles must plainly be a logician, though he need not be a specialist in biology or economics or ‘sociology’.  One great advantage which our children should have over their parents as students of Philosophy is that the last half-century has been one of unprecedented advance in the study of logic.  In the ‘logic of relations’, founded by De Morgan, carried out further in the third volume of Ernst Schroeder’s Algebra der Logik, and made still more precise in the earliest sections of the Principia Mathematica of Whitehead and Russell, we now possess the most potent weapon of intellectual analysis ever yet devised by man.