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.