ourse, from space as
represented by our familiar Euclidian geometry. Then comes the question
of fusing these different sorts of experience into a single experience
of which geometry may be an intelligible transcription. Enriques finds a
parallel between the historical development and the psycho-genetic
development of the postulates of geometry (_loc. cit._, p. 214 _seq._).
"The three groups of ideas that are connected with the concepts that
serve as the basis for the theory of continuum (_Analysis situs_), of
metrical, and of projective geometry, may be connected, as to their
psychological origin, with three groups of sensations: with the general
tactile-muscular sensations, with those of special touch, and of sight,
respectively." Poincare even evokes ancestral experience to make good
his case (_Sci. and Hyp._, Ch. V, end). "It has often been said that if
individual experience could not create geometry, the same is not true of
ancestral experience. But what does that mean? Is it meant that we could
not experimentally demonstrate Euclid's postulate, but that our
ancestors have been able to do it? Not in the least. It is meant that by
natural selection our mind has _adapted_ itself to the conditions of the
external world, that it has adopted the geometry _most advantageous_ to
the species: or in other words, the _most convenient_."

Now undoubtedly there may be a certain modicum of truth in these
statements. As implied by the last quotation from Poincare, the modern
scientist can hardly doubt that the fact of the adaptation of our
thinking to the world we live in is due to the fact that it is in that
world that we evolved. As is implied by both writers, if one could limit
human contact with the world to a particular form of sense response,
thought about that world would take place in different terms from what
it now does and would presumably be less efficient. But these admissions
do not imply that any light is thrown upon the nature of mathematical
entities by such abstractions. Russell (_Scientific Method in
Philosophy_) is in the curious position of raising arithmetic to a
purely logical status, but playing with geometry and sensation after the
manner of Poincare, to whom he gives somewhat grudging praise on this
account.

The psychological methods upon which all such investigations are based
are open to all sorts of criticisms. Chiefly, the conceptions on which
they are based, even if correct, are only abstractions.