distinct impression; the powers of association bring forth the record when the like is felt again. By the higher faculties of judgment and reasoning the mind compares the new with the old, recognises essential identity, even when disguised by diverse circumstances, and expects to find again what was before experienced. It must be the ground of all reasoning and inference that what is true of one thing will be true of its equivalent, and that under carefully ascertained conditions Nature repeats herself.

Were this indeed a Chaotic Universe, the powers of mind employed in science would be useless to us. Did Chance wholly take the place of order, and did all phenomena come out, not of one same Infinite Lottery, to use Condorcet's expression, but out of lotteries ever changing in their conditions, there could be no reason to expect the like result in like circumstances. It is possible to conceive a world in which no two things should be associated more often, in the long run, than any other two things. The frequent conjunction of any two events would then be purely fortuitous, and if we expected conjunctions to recur continually we should be disappointed. In such a world we might recognise the same phenomenon as it appeared from time to time, just as we might recognise a marked ball as it was occasionally drawn from a ballot-box; but the approach of any one phenomenon would be in no way indicated by what had gone before, nor would it be at all a sign of what was to come after. In such a world knowledge would be no more than the memory of past coincidences, and the reasoning powers, if they existed at all, would give no clue to the nature of the present, and no presage of the

future.

Happily the Universe in which we dwell is not the result of chance, and where chance seems to work it is our own deficient faculties which prevent us from recog

nising the operation of Law and of Design. In the material framework of this world, substances and forces present themselves in definite and stable combinations. All things are not in perpetual flux, as ancient philosophers held. Element remains element; iron changes not into gold, nor oxygen into hydrogen. With suitable precautions we can calculate upon finding the same thing again endowed with the same properties. The constituents of the globe, indeed, appear in almost endless combinations; but each combination bears its fixed character, and when resolved is found to be the compound of definite substances. Misapprehensions must continually occur, owing to the limited extent of our experience. We can never have examined and registered possible existences so thoroughly as to be sure that no new ones will occur and frustrate our calculations. The same outward appearances may cover any amount of hidden differences which we have not yet suspected. To the variety of substances and powers diffused through nature at its creation, we must not suppose that our brief experience can assign a limit; and the necessary imperfection of our knowledge should be ever borne in mind.

Yet there is much to give us confidence in science. The wider our experience, the more minute our examination of the globe, the greater the accumulation of wellreasoned knowledge,-the fewer must become the failures of inference compared with the successes. Exceptions to the prevalence of Law are gradually reduced to Law themselves. Certain deep similarities have been detected among the objects around us, and have never yet been found wanting. As the means of examining distant parts of the universe have been acquired, those similarities have been traced there as here. Other worlds and stellar systems may be almost incomprehensively different from ours in magnitude, condition and disposition of parts, and

yet we detect there the same elements of which our own limbs are composed. The same natural laws can be detected in operation in every part of the universe within the scope of our instruments; and doubtless these laws are obeyed irrespective of distance, time and circumstance.

It is the prerogative of Intellect to discover what is uniform and unchanging in the phenomena around us. So far as object is different from object, knowledge is useless and inference impossible. But so far as object resembles object, we can pass from one to the other. In proportion as resemblance is deeper and more general, the commanding powers of knowledge become more wonderful. Identity in one or other of its phases is thus always the bridge by which we pass in inference from case to case; and it is my purpose in this treatise to trace out the various forms in which the one same process of reasoning presents itself in the ever-growing achievements of Scientific Method.

The Powers of Mind concerned in the Creation of

Science.

It is no part of the purpose of this work to investigate the nature of mind, except so far as its powers are requisite to the formation of Science. In this place I need only point out that the mental powers engaged in knowledge are probably three in number. substantially as Mr. Bain has stated thema :

1. The Power of Discrimination.

2. The Power of Detecting Identity.

3. The Power of Retention.

They are

We exert the first power in every act of perception. Hardly can we have a sensation or feeling unless we discriminate it from something else which preceded.

a

'The Senses and the Intellect,' Second Ed., pp. 5, 325, &c.

Consciousness would almost seem to consist in the break between one state of mind and the next, just as an induced current of electricity arises from the beginning or the ending of the primary current. We are always engaged in discrimination; and the rudiment of thought which exists in the lower animals probably consists in their power of feeling difference and being agitated by its occurrence.

But had we power of discrimination only, Science could not be created. To know that one feeling differs from another gives purely negative information. It cannot teach us what will happen. Each sensation would stand out distinct from any other, and there would be no tie, no bridge of affinity between them. We want a unifying power by which the present and the future may be linked to the past; and this seems to be accomplished by a different power of mind. Francis Bacon has pointed out that different men possess in very different degrees the powers of discrimination and identification. It may be said indeed that discrimination necessarily implies the opposite process of identification; and so it doubtless does in superficial points. But there is a rare property of mind which consists in penetrating the disguise of variety and seizing the common elements of sameness; and it is this property which furnishes the true measure of intellect. The very name of intellect (interligo) expresses the action, not of separating, but of uniting and binding together the particular and various into the general and like. Logic is but another name for the same process b, the peculiar work of reason; and Plato said of this unifying power, that if he met the man who could detect the one in the many, he would follow him as a god.

b Max Müller, Lectures on Language,' Second Series, vol. ii. p. 63.

Laws of Identity and Difference.

At the basis of all thought and science must lie the laws which express the very nature and conditions of the discriminating and identifying powers of mind. These are the so-called Fundamental Laws of Thought, usually stated as follows:

1. The Law of Identity. Whatever is, is.

2. The Law of Contradiction. A thing cannot both be and not be.

3. The Law of Duality. A thing must either be or not be.

The first of these statements may perhaps be regarded as a description of identity itself, if so fundamental a notion can admit of description. A thing at any moment is perfectly identical with itself, and if any person were unaware of the meaning of the word 'identity' we could not better describe it than by such an example.

The second law points out that contradictory attributes can never be joined together. The same object may vary in its different parts; here it may be black, and there white; at one time it may be hard and at another time soft but at the same time and place an attribute cannot be both present and absent. Aristotle truly

described this law as the first of all axioms--one of which we need not seek for any demonstration. All truths cannot be proved, otherwise there would be an endless chain of demonstration; and it is in self-evident truths like this that we find the fittest foundation.

The third of these laws completes the other two. It asserts that at every step there are two possible alternatives-presence or absence, affirmation or negation. Hence I propose to name this law the Law of Duality,

C c Metaphysics,' Bk. III. chap. iii. 9-12,