hese relations.

Poincare's position is a strong one. He in effect challenges anyone to
point out any factor in nature which gives a preeminent status to the
congruence relation which mankind has actually adopted. But undeniably
the position is very paradoxical. Bertrand Russell had a controversy
with him on this question, and pointed out that on Poincare's principles
there was nothing in nature to determine whether the earth is larger or
smaller than some assigned billiard ball. Poincare replied that the
attempt to find reasons in nature for the selection of a definite
congruence relation in space is like trying to determine the position of
a ship in the ocean by counting the crew and observing the colour of
the captain's eyes.

In my opinion both disputants were right, assuming the grounds on which
the discussion was based. Russell in effect pointed out that apart from
minor inexactitudes a determinate congruence relation is among the
factors in nature which our sense-awareness posits for us. Poincare asks
for information as to the factor in nature which might lead any
particular congruence relation to play a preeminent _role_ among the
factors posited in sense-awareness. I cannot see the answer to either of
these contentions provided that you admit the materialistic theory of
nature. With this theory nature at an instant in space is an independent
fact. Thus we have to look for our preeminent congruence relation amid
nature in instantaneous space; and Poincare is undoubtedly right in
saying that nature on this hypothesis gives us no help in finding it.

On the other hand Russell is in an equally strong position when he
asserts that, as a fact of observation, we do find it, and what is more
agree in finding the same congruence relation. On this basis it is one
of the most extraordinary facts of human experience that all mankind
without any assignable reason should agree in fixing attention on just
one congruence relation amid the indefinite number of indistinguishable
competitors for notice. One would have expected disagreement on this
fundamental choice to have divided nations and to have rent families.
But the difficulty was not even discovered till the close of the
nineteenth century by a few mathematical philosophers and philosophic
mathematicians. The case is not like that of our agreement on some
fundamental fact of nature such as the three dimensions of space. If
space has only three dimensions we should expe