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.

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