We are not to look on the illusion, a nonentity, or as

from body occupying space. extension thus reached as an nothing. If we know, as I maintain we do, body in space, the space must have an existence (I do not say what sort of existence), just as much as the body has. When we separately contemplate the extension, we are contemplating a reality just as verily as when we perceive the body. It will not do to dismiss space summarily by describing it as a mere abstraction: in order to our apprehension of it there is need of abstraction, but it is an abstraction of a real part from a real whole.

To this cognition of space, and to every apprehension of it, there is attached a number of intuitive beliefs. It is the business of the metaphysician to unfold these in an inductive manner, and point out and determine their nature and laws as precisely as possible. This requires to be done in another Book of this Treatise, to which therefore I adjourn the further discussion of space, as it embraces a larger faith than it does of a cognitive element in our apprehension of it.

Prof. Bain maintains (The Senses and Intellect, 2d ed. p. 397), that the localization of our bodily feelings is the result of experience. I admit that it is by the muscular sense and the eye that we know the external configuration of our frame, and that it is by a gathered experience we connect this with the internal feelings. But I hold that we give an externality and a direction to our bodily sensations. Mr. Bain acknowledges that the body is to us an external object (p. 397). If so, it must be known in space. But it has never yet been shown how we can know an object as external to us and in space except intuitively. "I do not see," says Mr. Bain, in criticising Hamilton (p. 376), "how one sensation can be felt out of another without already supposing that we have a feeling of space." What we suppose is that in thus regarding the body as external and localizing the sensations we get the idea of space. It is a law of this localizing that the sensation is felt at the part of the body to which the nerve reaches. And when different parts of

the thickness of the same nerves are severally subjected to irritation, the same sensations are produced as if the different terminal branches of these parts of the nerves had been irritated. If the ulnar nerve be irritated mechanically, particularly by pressing it from side to side with the finger, the sensation of pins and needles is produced in the palm and back of the hand, and in the fourth and fifth fingers. But according as the pressure is varied the pricking sensation is felt by turns in the fourth finger, in the fifth, in the palm of the hand, on the back of the hand, and both in the palm and on the back of the hand the situation of the pricking sensation is different according as the pressure on the nerves is varied, that is to say, according as different fibres or fasciculi of fibres are more pressed upon than others (Müller's Physiology, pp. 745-747). Surely all this is instinctive, not acquired. So deep is the disposition to localize that it cannot be eradicated. "When a limb has been removed by amputation, the remaining portion of the nerve which ramified in it may still be the seat of sensations which are referred to the lost part." "These sensations are not of an undefined character; the pains and tingling are distinctly referred to single toes, to the sole of the feet, to the dorsum," etc. A case is quoted of a person whose arm had been amputated, and who declared twenty years after that "the sense of the integrity of the limb is never lost." There is appended a note by Baly: "Professor Valentin has observed, that individuals who are the subjects of congenital imperfection or absence of the extremities have nevertheless the internal sensations of such limbs in their perfect state. A girl aged nineteen years, in whom the metacarpal bones of the left hand were very short, and all the bones of the phalanges absent, a row of imperfectly organized wartlike projections representing the fingers, assured M. Valentin that she had constantly the internal sensation of the palm of the hand on the left side as perfect as in the right."

CHAPTER XI.

NUMBER.

WE seem to derive our knowledge of number from our cognition of being, and especially from our cognition of self as a person. We know self as one object; we also know other and external objects as singulars. Already then have we number in the concrete, involved in this our primary knowledge. Every object known, and especially self, is known as one. Every other object known is known as another one. If we know self as one, then the external object which is known as different from self is known as a second one. The mind can now think of one object, and of one object another object, or of two, and of one object + another object + another object, or of three. It can then, by a process of abstraction, separate the numbers from the objects, in order to their separate consideration. Not that it supposes for one instant that numbers can exist apart from objects, but it can separately contemplate them. One cannot exist apart from one object, or two from two objects, but the mind can think about the one or the two apart from the peculiarity of the objects. Its judgments and its conclusions in all such cases, if conducted according to the laws of thought, will apply to objects; that is, all its judgments regarding one, two, or a thousand, will apply to a corresponding number of objects. Having obtained in this way a knowledge of numbers in the concrete, and numbers in the abstract, the mind is prepared to discover relations among numbers in a man

ner to be afterwards specified in the book on Primitive Judgments.

But before leaving our present topic, it may be proper to state that the mind has no such conviction of the existence of numbers separate from the objects numbered, as it has of space, distinct from the objects in space, or as it has of time, distinct from the events which happen in time; nor has it any intuitive belief as to the necessary infinity of objects or of numbers. True, it can set no limit to the number of objects, but it is not compelled to believe that there can be no limits, as it is constrained to believe that there can be no bounds to space or to time.

Aristotle places number among the sensibles perceived by the common sense (De Anima, 11. 6; III. 1). He says each sense perceives unity: ékáσtn yàp év aiolávetaι atolnois (III. 1, 5, ed. Trend.). Descartes makes number perceived by us in all perceptions of body (Prin. Part 1. 69). Locke says of Unity or One: “ Every object our senses are employed about, every idea in our understandings, every thought of our minds, brings this idea along with it" (Essay, II. xvi. 1). Buffier says that the knowledge that I exist, I am, 1 think, is in a sense the same as, or at least includes this, I am one (Prem. Vér. Part II. 10).

CHAPTER XII.

MOTION.

OUR perception of motion is, as it appears to me, intuitive. But it supposes more than sense, or senseperception, in the narrow sense of the term. It is probable that we have an apprehension of change of place, from the movement of our intuitively localized organs,

Be

say from a member of the body being moved by the locomotive energy, as when I lift my arm; this perception will be especially apt to arise when we move the hand along organs to which a place has been given. Or we may apprehend an extra-organic body by the touch or muscular sense, and by the same sense feel our hand or some other extra-organic body passing over it. We may also get the perception by the sense of sight. The child touching a part of the body by its hand, will see the image of its hand moving to perform the act. sides, the "image of our own body occupies, in nearly all pictures on our retina, regularly some determinate space in the upper, middle, or lower part of the field of vision;" it remains constant while the other images are seen moving. There is more here, however, than immediate cognition. There is a brief exercise of memory; we must, at the same time that we perceive the body as now in one place, remember that it was formerly in another place. There is an exercise, too, of comparison in noticing the relation between the object in respect of the place in which it has been, and the place in which it now is. And upon our discovering change of any kind