'I
am now feeling something,' 'I am now aware of something.' On reflection
you find that the statement does not do justice to the experience. You
feel the need to say more precisely _what_ you are feeling or are aware
of, how it is related to what you experience on other occasions, and
what the 'I' is which is said to 'have' the experience. Until you have
done this your thought is a miserable reproduction of your experience,
and if you could ever do it completely, it would turn out that a really
adequate account of the most trivial experience would involve complete
knowledge of the structure and working of everything. Thus, if you once
begin to think about your experience at all, you are irresistibly driven
on to endless further reflection. If you try to stop short anywhere in
the process, the results of your reflection are found to contain
unexplained contradictions, just because you have not yet fitted on the
fact on which you are reflecting to everything else there is to know.
All the assumptions of every-day 'common sense' and all the more
recondite assumptions of the sciences are saturated with these
contradictions, because both 'common sense' and the sciences leave so
much of the whole 'story of everything' untouched. If the whole story
were told, all things would be found to be just one thing, which these
philosophers call the 'Absolute', and the only perfectly true statement
we can make would be a statement about this Absolute in which we
asserted of it all that it is. Since no science ever attempts to say
anything at all about this one sole thing, far less to get all there
might be to be said about it into a single statement, no scientific
proposition can be more than 'partially' true, and unhappily _we_ do not
know what alterations would be required to make our 'partial' truths
quite true. Naturally enough Kant's allegation that mathematical first
principles are so self-contradictory that you can rigidly demonstrate
mathematical propositions which contradict each other was grist to the
Hegelian mill. That our notions of space, time, the infinitely great,
the infinitely little, are all a jumble of contradictions was steadily
repeated by the Hegelian philosophers, and indeed the mathematicians
were accustomed to state their own principles so loosely and confusedly
that there was a great deal of excuse for the suspicion that the fault
lay with Mathematics and not with the mathematicians.

It is clear that such a