Henri Poincare (_Science and Hypothesis_, Ch. IV, _The Value of Science_, Ch. IV) and Enriques (_Problems of Science_, Ch. IV, esp. B--_The Psychological Acquisition of Geometrical Concepts_) furnish two of the most familiar examples of this sort of philosophizing. Each isolates special senses, sight, touch, or motion, and tries to show how a being merely equipped with one or the other of these senses might arrive at geometrical conceptions which differ, of course, 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.