icians and
mathematicians actually observe in the terms they use are a small
selection from all those that really obtain, even in their chosen
field; so that, for instance, as Mr. Russell was telling us, it was
only the other day that Cantor and Dedekind observed that although
time continually eats up the days and years, the possible future
always remains as long as it was before. This happens to be a fact
interesting to mankind. Apart from the mathematical puzzles it may
help to solve, it opens before existence a vista of perpetual youth,
and the vital stress in us leaps up in recognition of its inmost
ambition. Many other things are doubtless implied in infinity which,
if we noticed them, would leave us quite cold; and still others, no
doubt, are inapprehensible with our sort and degree of intellect.
There is of course nothing in essence which an intellect postulated
_ad hoc_ would not be able to apprehend; but the kind of intellect we
know of and possess is an expression of vital adjustments, and is
tethered to nature.

That a few eternal essences, then, with a few of their necessary
relations to one another, do actually appear to us, and do fascinate
our attention and excite our wonder, is nothing paradoxical. This is
merely what was bound to happen, if we became aware of anything at
all; for the essence embodied in anything is eternal and has necessary
relations to some other essences. The air of presumption which there
might seem to be in proclaiming that mathematics reveals what has to
be true always and everywhere, vanishes when we remember that
everything that is true of any essence is true of it always and
everywhere. The most trivial truths of logic are as necessary and
eternal as the most important; so that it is less of an achievement
than it sounds when we say we have grasped a truth that is eternal and
necessary.

This fact will be more clearly recognised, perhaps, if we remember
that the cogency of our ideal knowledge follows upon our intent in
fixing its object. It hangs on a virtual definition, and explicates
it. We cannot oblige anybody or anything to reproduce the idea which
we have chosen; but that idea will remain the idea it is whether
forgotten or remembered, exemplified or not exemplified in things. To
penetrate to the foundation of being is possible for us only because
the foundation of being is distinguishable quality; were there no set
of differing characteristics, one or more of which an