Page:On an Evolutionist Theory of Axioms.djvu/14

7 entire series of individuals of which he forms the last term.'

I will read a passage which describes how all this happens:—

'Little more need be said to make it clear how certain primary space-relations are presented to consciousness under the form of necessary relations. If a segment of a circle be looked at, the image of it cast on the retina is necessarily such that the arc covers a greater number of retinal elements than the chord; and since each of these retinal elements yields its separate impression to consciousness, the series of impressions produced by the arc is felt as larger than the series produced by the chord. This continues to hold however much the arc is flattened: so long as it has any perceptible curvature at all, it is felt to be longer than the chord uniting its extremes. Parallel experiences are derived from the ocular muscles. Carrying the eye along the line of the curve, yields to consciousness a greater quantity of sensation than carrying the eye along the chord does. As the curve is flattened this difference diminishes; but some of it continues as long as the curve continues appreciable. Thus the truth that a straight line is the shortest line between two points, lies latent in the structures of the eyes and the nervous centres which receive and co-ordinate visual impressions. We cannot think otherwise because, during that adjustment between the organism and the environment which evolution has established, the inner relations have been so moulded upon the outer relations that they cannot by any effort be made not to fit them. Just in the same way that an infant's hand, constructed so as to grasp by bending the fingers inwards, implies ancestral hands which have thus grasped, and implies objects in the environment to be thus grasped by this infantine hand when it is developed; so the various structures fitting the infant for apprehensions of space-relations, imply