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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.

SECT. VII.-ON 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, in volved 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 manner 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 1 Aristotle places number among the sensibles perceived by the common sense (De Anima п. 6; I. 1). He says each sense perceives unity: ¿uάóτη yàp ëv albarer aïó0n615 (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, п. xvi. 1). Buffier says that the knowledge that I exist, I am, I think, is in a sense the same as, or at least includes this, I am one (Prem. Vér. Part I. 10).

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.

SECT. VIII.-ON MOTION.

Our perception of motion is, as it appears to me, intuitive. But it supposes more than sense, or sense-perception, 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, 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. Besides, 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 18

1 (Müller's Physiology, trans. by Baly, p. 1083.) Aristotle places motion, like number, among the common sensibles, Descartes among the properties perceived in every perception of body (see places in last note), and Locke among the primary qualities of bodies, which are always in them (п. viii. 22). The young man operated upon by Dr. Franz for cataract, three days after the operation, saw "an extensive field of light, in which every thing appeared dull, confused, and in motion." In a case reported by Dr. Wardrop, the woman returning home after the operation, saw a hackney coach pass, and asked, 'What is that large thing that passed us ?" (See Abbot, Sight and Touch, p. 153.)

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spect of the place in which it has been, and the place in which it now is. And upon our discovering change of any kind in the motion, the intuition of cause comes in to declare that there must have been active power at work. This is one of those cases which will come before us more and more frequently as we advance, in which cognitions, beliefs, and judgments mingle together; and yet the act can scarcely be described as complex, except in this sense, that on other occasions some of the parts can exist separately or in other combinations. The circumstance that these other elements conjoin in our conviction as to motion, will bring the subject before us in other parts of the Treatise.

SECT. IX.-ON POWER.

I have been labouring to show, in the last chapter and in this, that power is involved in our knowledge of substance. We can never know either self, or bodies beyond self, except as exercising influence or potency. Not that we are to suppose that we have thus by intuition an abstract or a general idea of power; all that we have is a knowledge of a given substance acting. This seems the only doctrine in accordance with the revelations of consciousness. It is involved in the common statement that we cannot know substance except by its properties; for what are properties but powers acting when the needful conditions are supplied? I reckon it as an oversight in a great body of metaphysicians that they have been afraid to ascribe our apprehension of power to intuition. In consequence of this neglect, some never get the idea of power, but merely of succession, within the bare limits of experience, which can never entitle us to argue that the world must have proceeded from Divine Power; others have been obliged to find cause, not in any perception of the mind as it looks on things, but in some form imposed by the mind on subjects; while a considerable number hesitate and vacillate in their account, representing it now as an original conviction, and now as an acquisition of experience.

Wherever there is power in act, there is an effect. But the discovery of the relation between cause and effect cannot be discovered, except by an exercise of judgment. The discussion of

the nature of our conviction of Power will be resumed under the head of Primitive Judgments.

SECT. X.-(SUPPLEMENTARY.)—THE VARIOUS KINDS OF POWER KNOWN BY EXPERIENCE.

We are led by the cognitive nature of the mind to look on the substance as necessarily possessing potency, but it is after all by experience that we have to determine the nature of the power exercised by any particular substance. Experience shows us that all potency is not of the same description. The precise nature of the power residing in any one substance is to be ascertained by a generalization of its individual operations. Though it does not fall within our precise province, yet it may help to clear up some important metaphysical questions, if we particularize some of the kinds of potency made known by experience.

I. FORCE IN INANIMATE OBJECTS.-In order to the exercise of this potency there is need of two or more bodies in a particular relation to each other. A simple body existing alone in the universe, and in a state of isolation, that is, in no relation to any other body, could exercise no active power whatever. Indeed, the power of a body seems to be a power to influence some other body or some other substance. It seems also to be a law of the action of bodies that when any one body acts on another, that other acts on it. In all material causation there is thus mutual action; and experience seems to show that the action of each of the bodies is equal to that of the other. It is the aim of the physical sciences to determine the nature and measure of this reciprocal operation.

According to this account there is need, in order to material action, of two or more bodies. When these bodies are in such a relation as suits their several properties, action takes place, and an effect is produced. It follows that causemeaning by cause the invariable and unconditional cause, that which of itself will produce the effect, and ever produce the effect-must always be more or less complex; it always implies two or more bodies in a particular relation to each other. The effect will always be found to be of the same complex character, will always be found to consist of the bodies which acted as a cause, being in some way changed. To illustrate what I mean:-Let us suppose that we have two material substances to experiment with, salt and water. Place the two out of relation to each other, and no effect will be produced. Bring them into contact, and action will commence. The salt acts on the water, and the water on the salt. The cause, properly speaking, of this action is not the salt alone, or the water alone, but the salt and water in a particular relation. This is the true cause, productive and necessary; the cause which, wherever it exists, will tend to produce the same effect, and in fact produce it, except when counteracted by other forces. The effect is also dual, and it is to be found in the very substances which acted as the cause; it is not to be found in the salt, or in the water, or in a third substance, but in the salt and water in a new and different state. This is the invariable effect which will be for ever produced by the

same cause.

Such seems to be the nature of material causation and effectuation. In all cases the cause is dual, or plural, as is also the effect; and the bodies which acted as the cause are the bodies acted on in the effect. I am persuaded that

the well-known law of action and reaction proceeds on this circumstance, which is also intimately connected with the polar action of substances. In the common statements as to cause and effect there is only one of the elements of the complex cause or complex effect mentioned, the other being omitted because it does not seem needful to express it. Thus we speak of the salt as the cause, making the water of a particular taste as the effect. But there is an omission in all such statements, which requires to be completed by calling in the missing part, when we profess to give a thoroughly accurate and philosophic account of the process. There are cases in which the complexity of the cause or of the effect is not so evident as in the example I have given. Thus, if a picture were to fall upon a table and break it, we would say in loose language that the fall of the picture was the cause of the breaking of the table. But when the full cause is spread out, it is seen to be the picture falling with a particular force, and striking the table in a particular direction, while the effect consists not in the breaking of the table merely, but also in the picture losing a portion of its momentum. We have but to reflect for a very little to see and be prepared to acknowledge that in all gravitating action, in all chemical, in all magnetic and electric, there is the co-operation of two or more bodies, and that the cause consists of the bodies in one state and the effects of the same bodies in a different state.1

The grand doctrine established in our day of the Conservation of the Physical Forces seems to follow from the principles here enunciated. As the powers or properties of bodies are fixed it follows that the sum of force in the whole is always one and the same, and cannot be increased or diminished by creature action.

IL VITAL POWER.-The attempts which have been made to determine wherein life consists cannot be said to have as yet been crowned with anything like success. There is every reason to think that there is a vital power so far different from the mechanical or chemical, but science has not yet ascertained its nature and its laws. So far as we have glimpses of its mode of operation, it seems to involve a complexity of agents. One part of the cell acts on another, or one cell acts on another, or it acts on external matter, and whatever acts is being acted on.

A curious question is here started, What is the nature of the power involved in vegetable and animal reproduction? This is a subject still involved in great mystery, but there are obvious and well-ascertained facts which go to establish a general doctrine.

First, There is a duality in all vital reproduction. In certain portions of the vegetable kingdom, the reproductive powers are in different organs, in others they are on different plants. In the animal creation the reproductive organs are commonly in different individuals, which must therefore pair in order to the production of young. This is an example in a higher scale, and in a more patent form, of that duality in causation which wo traced already in inanimate creation, and which makes all physical creation so dependent on arrangements which have been made by the Creator of all things.

Secondly, There is a positive and adequate power in the dual parentage to produce the offspring as an effect. No living creature can proceed except from a parent of its own kind; no vegetable or animal can spring from a vegetable or animal inferior to itself in the order of beings. This is one of the best established generalizations of natural history; and it has not been shaken by any of the attempts which have been made to find exceptions to it, certainly not by the analogies which have been urged against it, derived from objects totally 1 This subject is illustrated, Method of Divine Government, Book II. Chap. i.

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