the stump of an old tree, the cry of an owl, or the flight of a magpie.

Such is the opposition between science and sentiment, between the steam-engine and poetry. Thus, as we gradually unlearn the marvellous and mysterious powers with which we at first had invested all nature, we learn, pari passu, to analyse the powers of our own souls. When we come to attribute to animals animal and not human life, we arrive at the knowledge that our own life may be represented as animal life plus that character of reason and intellect which constitutes humanity: so in the next step we come to understand that animal life may be supposed to consist of vegetative life plus consciousness and spontaneity; and next that vegetable life may consist of existence plus powers of growth. But all these it is clear are but notions derived from our self-consciousness; they are but the results of the analysis of our projected selves. Therefore, with regard to the substance, essence, or existence of things, we know no more of them than what we put into them ourselves, not by individual caprice, but by a law of our

nature.

It is generally objected to these psychological metaphysics, that they do not in any way account for the possibility of general, much less of universal and necessary propositions. Let us see whether this objection holds good.

We have assumed what we have termed, for the sake of convenience, two poles of the soul: one the rational, which has to do with space and time, and all that can be perceived only in relations of space and time; the other, the intellectual, or understanding, the subject-matter of which is spirit, life, substance, existence, and all such qualities as cannot be defined by straight lines and curves, by colours, sounds, or savours. Their operations may be exemplified in the two possible meanings of the copula in the propositions "A is A" and "A is." The former affirms the identity of one idea with another, or with itself, without any implication of the reality of its existence; the other affirms this reality of existence. The one is logical, the other intellectual; one is a function of the reason, the other of the understanding; the one is true or false simply according to its form, the other according to its contents.

When the proposition is not general, most philosophers will allow that it may be given by intuition or consciousness. By consciousness I know that I am a thinking being; but when we generalise a proposition, e. g. " that which thinks exists," they generally give another term to the function of thought which asserts it; Balmez, for instance, calls it evi

The sole

dence. Consciousness, he says, cannot give necessary results, cannot pronounce an apodictical judgment. It is not necessary that I, the particular individual, should exist; but evidence does result in universal and necessary propositions. It is necessary that that which thinks should exist. criterion of evidence, he says in another place, is the necessity and universality of its conclusions; and this can only result from the identity of the subject with the predicate, either as whole or as part: therefore we conclude that evidence may result from the intuition of this identity, and therefore there is no real distinction in kind between evidence and intuition.

The function of the understanding is not logical thought; this belongs to the reason, and it is only in the reason that propositions can be generalised, or perceived as universally and necessarily true. Behind this sensitive and rational pole of the mind there is the formal idea of space, hung up like a great white sheet, to receive the colours projected upon it by the magic-lantern of the sensitive or intuitive faculties. These are the senses, the memory, and the intuition; the senses present us with a mass of individual phenomena, and the consciousness of the similarity or dissimilarity of these particular sensations gives rise to particular judgments. The memory is a faculty by which we can reproduce a sensation more or less perfectly, and multiply it at will: if I have once seen an orange, I can remember and fancy as many as I please; if I have tasted it, I have a general consciousness that oranges are good. The intuition is a faculty by which we can build up shapes and produce lines and divisions in the formal idea of space, and this faculty alone gives us universal and necessary conclusions. The representations in my memory and fancy are only reproductions and multiplications of sensations, and therefore can never be necessary and universal; for a contrary sensation may turn up any day. But the representations in our intuition come only from ourselves; what we create we know perfectly; and when we have once produced the equilateral triangle, we know that it is perfectly impossible that an other equilateral triangle should be produced with different properties: we may not know all its properties, our intuition of it may not yet be perfect; but so far as we know it, we know that it cannot be different. This is the doctrine of Vico: "The intellect knows what it creates, and only what it creates, and because it creates it." To this Balmez objects, that" in the intellectual order, before you can create, you must understand; hence it is not the creative act, but the intuition of the object, which should be placed as the origin of all knowledge.' Balmez says that we cannot form any

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thing till we have conceived it; we say that, in fact, we cannot conceive a triangle, or any other figure, till we have formed it. But in order that we may know it as a universal truth, we must form it on a rule or definition; and this we suppose is the meaning of Aristotle, Dugald Stewart, and others, who make mathematical necessity depend on definitions. The opponents of this theory answer, that it is derived from the leading property expressed in the definition; for if the definition did not express a real property, nothing would follow; we might impose a name on an impossible figure, but we could draw no inference from it. Quite true; but such a mere verbal definition would not be a true mathematical one: the true mathematical definition is genetic, teaching how to make the figure, and being the law of its production. Thus we produce a straight line by tracing the most uniform direction between two points, and a circle by tracing a series of points in two directions from a given one, all equidistant from another point called the centre. The definition is a mere problem, too simple to need more proof than the mere statement. The problem, on the other hand, is a definition which cannot be intuitively perceived without a very careful production of it in the intuition. Such is mathematical truth.

gical truth is of the same kind. The rules of logic supply empty forms or measures, which are compared in the intuition, and which must be filled up with matter by the rea

soner.

Thus reasoning, so far as relates to the form, is a mere arithmetic: it is, as Hobbes says, the addition and subtraction of parcels. "In whatever matter there is room for addition and subtraction, there is room for reason; and where these have no place, there reason has nothing to do." This proposition is illustrated by Hallam as follows: "When we assert that all A is B, we mean, that B=A+x, or that B-x=A; now since we do not compare A with x, we only mean that A=A, or that a certain part of B is the same as itself;" and so on, carrying the same idea through all judgments. All necessary and universal judgments are thus reduced either to the analysis of that which we produce in the intuition or to identical propositions. Thus Kant's "universal problem of pure reason," viz. "how are synthetical judgments à priori possible?" is all moonshine; it does not appear that there are such. There is a synthesis in the intuition (by drawing figures) and a synthesis in the conception (the idea of these figures) which take place à priori, but no distinct à priori synthetical judgment. As empirical judgments come after sensation, so do à priori judgments come after intuition.

The quality of the judgment follows the quality of the sensation, or intuition, on which it rests. A particular sensation gives a particular judgment: reproduce and multiply this sensation in the memory or fancy, and you have a general judgment; produce mere empty divisions in the white tablet of the idea of space, and the intuition of these will give you necessary and universal judgments. Thus all generalisation comes from a certain productive and quasi-creative power in the mind; the power, namely, of reproducing and recombining in the memory what it has perceived, and of dividing and partitioning out its own intuitive idea of space. In fact, we may say that all human perception is judgment: we attribute to beasts, for convenience sake, sensation, like our own, without judgment; but because the act is thus divisible in idea, it does not follow that it should be so in nature. The human perception is judgment; the perception of the individual in the sensation is particular judgment; that of the general quality in the memory is a general judgment; that of the necessary in the intuition is a universal and necessary judgment.

But up to this time we have only dealt with phenomena, and with the bare empty spaces in which they are contained. With these alone can the reason deal; a man would not be rational who denied that A is A, that phenomena are appearances, that 2+2=4. But when we come to the understanding faculty, there is no such absolute necessity. A man may refuse to attribute essential reality to phenomena, or he may insist on attributing even life and soul to earth and sea, yet not lose his claim to rationality. In these cases it is, as Schlegel says, "the will that decides;" a man becomes spiritualist or materialist, infidel or believer, by no mere logical process, but by a voluntary act of the understanding faculty, projecting more or less of the spiritual nature of which he is conscious into the conceptions and judgments which the rational faculty supplies. He may be immoral, infidel, heretical, absurd, in affirming or denying that A is, or has a real existence, but no such proposition can make him irrational.

The use of the attributive faculty cannot therefore be strictly defined by any logical necessity; and yet it is this faculty which must determine all the really interesting questions of humanity; by this alone can we come to comprehend, or even form, any theory of the existence of things. What is matter. Determine the question only by the rational part of the mind, and you can only say that it is phenomenon extended in space. Phenomenon is only subjective, so this term must be withdrawn. Extension in space is infinitely subdivisible, and the last term of the division is a point, which is

nothing; therefore extended phenomenon, or matter, consists of an infinity of nothings, that is, it is nothing. Determine the question by the understanding, and we answer with Faraday, it is a system of forces: but what is force? It is something akin to the spiritual power we are conscious of in the soul, which we feel to consist of knowledge, power, and will. Or again, in the conception of the old magical mythologists, matter was the pronunciation, the expression of the Creator; but expression and pronunciation are simply projected knowledge; thus we can only understand matter, not as it is in itself, but as it can be represented by one or other of the powers or forms of our understanding faculty, power, knowledge, or will.

Further, those things to which we cannot attribute any of the forms of the understanding are for that reason unintelligible to us as essences. We have shown that simple existence is the last step in the analysis of our spiritual consciousness, the feeblest idea of actuality that we can attribute to objects of perception. There are objects to which we cannot attribute this idea, and whose objective existence is unintelligible to us; they lie further back, nearer to nothing than our intelligence can reach. But we must beware how we decide that they are therefore nothing; they may be nonexistent in any sense in which our understanding can comprehend existence; but our soul need not be the measure of possible existence, any more than our senses are of possible phenomena; there are numberless vibrations of æther and air on both sides of those which are to us visible and audible; these may be seen and heard by other beings with organs of the same kind as ours; so it may be with the understanding. There may be possible existences which lie beyond the limits of its forms, power, knowledge, will, and substance. If we ever come to an idea to which we cannot attribute substance, we have no other understanding-conception to attribute to it; substance is the last idea in our analysis of actual being, and we cannot halve it, nor attribute to conceptions an actuality that is not yet substance. Thus we are tempted to deny to such conceptions any actuality whatever, and to reduce them to nonentities, though we have no reason for refusing them a certain unintelligible kind of existence. Time and space are examples of this kind of conception; we cannot pronounce true space and time to be objectively real, without, as Kant says, laying down the existence of two infinite and eternal nonentities. Not that we should allow as much as this; we affirm that our intelligence of entity need not reach so far back as possible existence; there may be an almost infinite distance between the simplest mode of existence that we can under