500 HUBEET FOSTON : All having to do, in thinking, with the conditioned activities and sequences of objects is effectively veiled when, as in Geometry, we assume everything to be still but the unnoted finger or eye, the faintly imagined object or forgotten impal- pability, which we are moving ; while everything is passive and unresistant but ourselves. Under this veiling, I suspect that Euclid's directions and reflexions may fairly be read as the study of a conditioning of voluntary movements to certain effects. Take the first proposition. Confronted with a finite straight line AB, recording an ever-retraceable movement (how determined itself I will not now attempt to decide), the object which I mean to move as directed is to be determined to find its way from one extremity A, safely back to the other B, having pursued in its course two and only two rectilinear directions, AC, CB, each for a distance equal to that between the extremities. And first I learn how to condition its action into movements from the extremities of the line, in any direction whatever in the plane of the line, of equal length with the line. (Or, constituting my circles by the revolu- tion of the line itself, I may say of the same length.) Then the movement is further and more definitely conditioned to be along the course of movements already potentially made in the fact of the presence of the revolving line in two such positions that the situation, C, of its extremity A, in the one case, was the same as that of its extremity B in the other. A path can now be retraced, conditioning for the complex object whose movement according to prescription is part of its psychical constitution, the desired significance a path itself conditioned to condition the desired significance when- ever actively retraced. The assumed homogeneity of the conditions of movement, as in pure space, rendering it possible to take a movement in one portion of space as the potential making of it in any other portion to which the line marked by the movement may be considered to be transferred, excludes the differential conditions on which thought depends, and apparently re- duces the mental action to such an identification of equal magnitudes in different situations as resembles the pure generalisation of minds in which the pondering and question- ing of thought has found no opening. This abandonment of further thoughtful inquiry as hopeless, and consequent un- questioning acceptance, is, I believe, somewhat oddly taken for a " necessity of thought." * 1 The question of the base of " necessity," from this point of view, connects with the philosophical problem of the existence of a world in which function as typical or general can be steadily effective. This opens up a profounder question in causation than any we have faced.
