touch, of which we have optical signs of various sorts, such as the image's apparent magnitude, its 'faintness' or 'confusion,' and the 'strain' of accommodation and convergence. By distance being an object of 'touch,' Berkeley meant that our notion of it consists in ideas of the amount of muscular movement of arm or legs which would be required to place our hand upon the object. Most authors have agreed with Berkeley that creatures unable to move either their eyes or limbs would have no notion whatever of distance or the third dimension.

This opinion seems to me unjustifiable. I cannot get over the fact that all our sensations are of volume, and that the primitive field of view (however imperfectly distance may be discriminated or measured in it) cannot be of something flat, as these authors unanimously maintain. Nor can I get over the fact that distance, when I see it, is a genuinely optical feeling, even though I be at a loss to assign any one physiological process in the organ of vision to the varying degrees of which the variations of the feeling uniformly correspond. It is awakened by all the optical signs which Berkeley mentioned, and by more besides, such as Wheatstone's binocular disparity, and by the parallax which follows on slightly moving the head. When awakened, however, it seems optical, and not heterogeneous with the other two dimensions of the visual field.

The mutual equivalencies of the distance-dimension with the up-and-down and right-to-left dimensions of the field of view can easily be settled without resorting to experiences of touch. A being reduced to a single eyeball would perceive the same tridimensional world which we do, if he had our intellectual powers. For the same moving things, by alternately covering different parts of his retina, would determine the mutual equivalencies of the first two dimensions of the field of view; and by exciting the physiological cause of his perception of depth in various degrees, they would establish a scale of equivalency between the first two and the third.

First of all, one of the sensations given by the object would be chosen to represent its 'real' size and shape, in accordance with the principles so lately laid down. One sensation would measure the 'thing' present, and the 'thing' would measure the other sensations—the peripheral parts of the retina would be equated with the central by receiving the image of the same object. This needs no elucidation in case the object does not change its distance or its front. But suppose, to take a more complicated case, that the object is a stick, seen first in its whole length, and then rotated round one of its ends; let this fixed end be the one near the eye. In this movement the stick's image will grow progressively shorter; its farther end will appear less and less separated laterally from its fixed near end; soon it will be screened by the latter, and then reappear on the opposite side, the image there finally resuming its original length. Suppose this movement to become a familiar experience; the mind will presumably react upon it after its usual fashion (which is that of unifying all data which it is in any way possible to unify), and consider it the movement of a constant object rather than the transformation of a fluctuating one. Now, the sensation of depth which it receives during the experience is awakened more by the far than by the near end of the object. But how much depth? What shall measure its amount? Why, at the moment the far end is about to be eclipsed, the difference of its distance from the near end's distance must be judged equal to the stick's whole length; but that length has already been seen and measured by a certain visual sensation of breadth. So we find that given amounts of the visual depth-feeling become signs of given amounts of the visual breadth-feeling, depth becoming equated with breadth. The measurement of distance is, as Berkeley truly said, a result of suggestion and experience. But visual experience alone is adequate to produce it, and this he erroneously denied.

The Part played by the Intellect in Space-perception.But although Berkeley was wrong in his assertion that out of optical experience alone no perception of distance can be evolved, he gave a great impetus to psychology by showing how originally incoherent and incommensurable in respect of their extensiveness our different sensations are, and how our actually so rapid space-perceptions are almost altogether acquired by education. Touch-space is one world; sight-space is another world. The two worlds have no essential or intrinsic congruence, and only through the association of ideas' do we know what a seen object signifies in terms of touch. Persons with congenital cataracts relieved by surgical aid, whose world until the operation has been a world of tangibles exclusively, are ludicrously unable at first to name any of the objects which newly fall upon their eye. "It might very well be a horse," said the latest patient of this sort of whom we have an account, when a 10-litre bottle was held up a foot from his face. Neither do such patients have any accurate notion in motor terms of the relative distances of things from their eyes. All such confusions very quickly disappear with practice, and the novel optical sensations translate themselves into the familiar language of touch. The facts do not prove in the least that the optical sensations are not spatial, but only that it needs a subtler sense for analogy than most people have, to discern the same spatial aspects and relations in them which previouslyknown tactile and motor experiences have yielded.

Conclusion. To sum up, the whole history of space-perception is explicable if we admit on the one hand sensations with certain amounts of extensity native to them, and on the other the ordinary powers of discrimination, selection, and association in the mind's dealings with them. The fluctuating import of many of our optical

*Cf. Kaehlmann in Zeitschrift für Psychol. und Physiol. der Sinnesorgane, II. 79.

sensations, the same sensation being so ambiguous as regards size, shape, locality, and the like, has led many to believe that such attributes as these could not possibly be the result of sensation at all, but must come from some higher power of intuition, synthesis, or whatever it might be called. But the fact that a present sensation can at any time become the sign of a represented one judged to be more real, sufficiently accounts for all the phenomena without the need of supposing that the quality of extensity is created out of non-extensive experiences by a super-sensational faculty of the mind.

CHAPTER XXII.

REASONING.

What Reasoning is. We talk of man being the rational animal; and the traditional intellectualist philosophy has always made a great point of treating the brutes as wholly irrational creatures. Nevertheless, it is by no means easy to decide just what is meant by reason, or how the peculiar thinking process called reasoning differs from other thought-sequences which may lead to similar results.

Much of our thinking consists of trains of images suggested one by another, of a sort of spontaneous revery of which it seems likely enough that the higher brutes should be capable. This sort of thinking leads nevertheless to rational conclusions, both practical and theoretical. The links between the terms are either contiguity' or 'similarity,' and with a mixture of both these things we can hardly be very incoherent. As a rule, in this sort of irresponsible thinking, the terms which fall to be coupled together are empirical concretes, not abstractions. A sunset may call up the vessel's deck from which I saw one last summer, the companions of my voyage, my arrival into port, etc.; or it may make me think of solar myths, of Hercules' and Hector's funeral pyres, of Homer and whether he could write, of the Greek alphabet, etc. If habitual contiguities predominate, we have a prosaic mind; if rare contiguities, or similarities, have free play, we call the person fanciful, poetic, or witty. But the thought as a rule is of matters taken in their entirety. Having been thinking of one, we find later that we are thinking of another, to which we have been lifted along, we hardly know how. If an abstract