3. To conduct the examination with order, beginning by that of objects the most simple, and therefore the easiest to be known, and ascending little by little up to knowledge of the most complex.

4. To make such exact calculations, and such circumspections as to be confident that nothing essential has been omitted. Consciousness being the basis of all certitude, everything of which you are clearly and distinctly conscious must be true: everything which you clearly and distinctly conceive, exists, if the idea of it involve existence.'

In these four rules we have the essential part of one half of Des Cartes system, the other, which is equally important, is the attempt to solve metaphysical problems by mathematical aid. To mathematics he had devoted much of his time. He it was who, at the age of twenty-three, made the grand discovery of the applicability of algebra to geometry. While deeply engaged in mathematical studies and investigations, he came to the conclusion that mathematics were capable of a still further simplification, and of much more extended application. Impressed with the certainty of the conclusions arrived at by the aid of mathematical reasoning, he began to apply mathematics to metaphysics.

His ambition was to found a system which should be solid and convincing. Having searched for certitude, he had found its basis in consciousness; he next wanted a method, and hoped he had found it in mathematics. He tells us that Those long chains of reasoning, all simple and easy, by which geometers used to arrive at their most difficult demonstrations, suggested to him that all things which came within human knowledge, must follow each other in a similar chain; and that provided we abstain from admitting anything as true which is not so, and that we always preserve in them the order necessary to deduce one from the other, there can be none so remote to which we cannot finally attain, nor so obscure but that we may discover them.'

Acting out this, he dealt with metaphysics as we should with a problem from Euclid, and expected by rigorous reasoning to discover the truth. He, like Archimedes, had wished for a standing place from which to use the lever, that should overturn the world; but, having a sure standing place in the indubitable fact of his own existence, he did not possess sufficient courage to put forth the mighty power-it was left for one who came after him to fairly attempt the overthrow of the world of error so long existent.

Cartesianism was sufficiently obnoxious to the divines to provoke their wrath; and yet, from some of its peculiarities, it has found many opponents amongst the philosophical party. The Cartesian philosophy is founded on two great principles, the one metaphysical, the other physical. The metaphysical is Des Cartes' foundation-stone-the 'I think, therefore I am.' This has been warmly attacked as not being logical. Des Cartes said his existence was a fact a fact above and beyond all logic; logic could neither prove nor disprove it. The Cogito, ergo Sum, was not new itself, but it was the first stone of a new building the first step in a new road: from this fact Des Cartes tried to reach another, and from that others.

The physical principle is that nothing exists but substance, which he makes of two kinds-the one a substance that thinks, the other a substance extended. Actual thought and actual extension are the essence of substance, so that the thinking substance cannot be without some actual thought, nor can anything be retrenched from the extension of a thing, without taking away so much of its actual substance.

In his physical speculations, Des Cartes has allowed his imagination to

run very wild. His famous theory of vortices is an example of this. Assuming extension to be the essence of substance, he denied the possibility of a vacuum by that assumption; for if extension be the essence of substance, wherever extension is, there substance must be. This substance he assumes to have originally been divided into equal angular particles, each endowed with an equal degree of motion; several systems or collections of these particles he holds to have a motion about certain equi-distant points, or centres, and that the particles moving round these composed so many vortices. These angular particles, by their intestine motions, he supposes to become, as it were, ground into a spherical form; the parts rubbed off are called matter of the first element, while the spherical globules he calls matter of the second element; and since there would be a large quantity of this element, he supposes it to be driven towards the centre of each vortex by the circular motion of the globules, and that there it forms a large spherical body such as the sun. This sun being thus formed, and moving about its own axis with the common matter of the vortex, would necessarily throw out some parts of its matter, through the vacuities of the globules of the second element constituting the vortex; and this especially at such places as are farthest from its poles; receiving, at the same time in, by these poles, as much as it loses in its equatorial parts. And, by these means, it would be able to carry round with it those globules that are nearest, with the greater velocity; and the remoter, with less. And, further: those globules which are nearest the centre of the sun, must be smallest; because, were they greater, or equal, they would, by reason of their velocity, have a greater centrifugal force, and recede from the centre. If it should happen that any of these sun-like bodies, in the centres of the several vortices, should be so incrustated and weakened, as to be carried about in the vortex of the true sun: if it were of less solidity, or had less motion than the globules towards the extremity of the solar vortex, it would descend towards the sun, till it met with globules of the same solidity, and susceptible of the same degree of motion with itself; and thus, being fixed there, it would be for ever after carried about by the motion of the vortex, without either approaching any nearer to, or receding from the sun, and so become a planet. Supposing, then, all this, we are next to imagine that our system was at first divided into several vortices, in the centre of each of which was a lucid spherical body; and that some of these being gradually incrustated, were swallowed up by others which were larger, and more powerful, till at last they were all destroyed and swallowed up by the biggest solar vortex, except some few which were thrown off in right lines from one vortex to another, and so became comets. It should also be added, that in addition to the two elements mentioned above, those particles which may yet exist, and be only in the course of reduction to their globular form, and still retain their angular proportions, form a third element.

This theory has found many opponents; but in this state of our work we conceive our duty to be that of giving a simple narrative of the philosopher's ideas, rather than a history of the various criticisms upon those ideas, the more especially as our pages scarcely afford room for such a mode of treatment.

Having formed his method, Des Cartes proceeded to apply it. The basis of certitude being consciousness, he interrogated his consciousness, and found that he had an idea of a substance infinite, eternal, immutable, independent, omniscient, omnipotent. This he called an idea of God: he said, 'I exist as a miserably imperfect finite being, subject to change-ignorant, incapable of creating anything-I find by my finitude that I am not the

infinite; by my liability to change that I am not the immutable; by my ignorance that I am not the omniscient: in short, by my imperfection, that I am not the perfect. Yet an infinite, immutable, omniscient, and perfect being must exist, because infinity, immutability, omniscience, and perfection are applied as correlatives in my ideas of finitude, change, etc. God therefore exists: his existence is clearly proclaimed in my consciousness, and therefore ceases to be a matter of doubt any more than the fact of my own existence. The conception of an infinite being proved his real existence, for if there is not really such a being I must have made the conception; but if I could make it I can also unmake it, which evidently is not true; therefore there must be externally to myself, an archetype from which the conception was derived.' All that we clearly and distinctly conceive as contained in anything is true of that thing.' Now, we conceive clearly and distinctly that the existence of God is contained in the idea we have of him: ergo-God exists.'-(Lewes's Bio. Hist. Phil.)

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Des Cartes was of opinion that his demonstrations of the existence of God 'equal or even surpass in certitude the demonstrations of geometry.' In this opinion we must confess we cannot share. He has already told us that the basis of all certitude is consciousness-that whatever is clearly and distinctly conceived, must be true-that imperfect and complex conceptions are false ones. The first proposition, all must admit, is applicable to themselves. I conceive a fact clearly and distinctly, and, despite all resistance, am compelled to accept that fact; and if that fact be accepted beyond doubt, no higher degree of certainty can be attained. That two and two are four-that I exist-are facts which I never doubt. The Cogito, ergo Sum, is irresistible, because indubitable; but Cogito, ergo Deus est, is a sentence requiring much consideration, and upon the face of it is no syllogism, but, on the contrary, is illogical. If Des Cartes meant 'I' am conscious that I am not the whole of existence, he would be indisputable; but if he mean that I can be conscious of an existence entirely distinct, apart from, and external to, that very consciousness; then his whole reasoning from that point appears fallacious.

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We use the word 'I' as given by Des Cartes. Mill, in his System of Logic,' says, The ambiguity in this case is in the pronoun I, by which in one place is to be understood my will: in another the laws of my nature. If the conception, existing as it does in my mind, had no original without, the conclusion would unquestionably follow that "I" had made it—that is, that the laws of my nature had spontaneously evolved it; but that my will made it would not follow. Now, when Des Cartes afterwards adds that I cannot unmake the conception, he means that I cannot get rid of it by an act of my will, which is true: but is not the proposition required. That what some of the laws of my nature have produced, other laws, or those same laws in other circumstances, might not subsequently efface, he would have found it difficult to establish.'

Treating the existence of God as demonstrated from the à priori idea of perfection and infinity, and by the clearness of his idea of God's existence, Des Cartes then proceeds to deal with the distinction between body and soul. To prove this distinction was to him an easy matter. The fundamental and essential attribute of substance must be extension, because we can denude substance of every quality but that of extension; this we cannot touch without at the same time affecting the substance. The fundamental attribute of mind is thought; it is in the act of thinking that the consciousness of existence is revealed: to be without thought would be to be without consciousness.

Des Cartes has given us, amongst others, the axiom That two substances are really distinct when their ideas are complete, and no way imply each other. The idea of extension is complete and distinct from the idea of thought, which latter is also clear and distinct by itself. It follows, therefore, that substance and mind are distinct in essence.'

Des Cartes has, from the vagueness of some of his statements, subjected himself to the charge of asserting the existence of innate ideas, and the following quotations will speak for themselves on the subject:-'When I said that the idea of God is innate in us, I never meant more than this, that Nature has endowed us with a faculty by which we may know God; but I have never either said or thought that such ideas had an actual existence, or even that they were a species distinct from the faculty of thinking. ......Although the idea of God is so imprinted on our minds, that every person has within himself the faculty of knowing him, it does not follow that there may not have been various individuals who have passed through life without ever making this idea a distinct object of apprehension; and, in truth, they who think they have an idea of a plurality of Gods, have no idea of God whatever.' This seems explicit as negativing the charge of holding the doctrine of innate ideas; but in the Edinburgh Review several passages are given, amongst which is the following:- By the word idea I understand all that can be in our thoughts; and I distinguish three sorts of ideas-adventitious, like the common idea of the sun, framed by the mind, such as that which astronomical reasoning gives of the sun; and innate, as the idea of God, mind, body, a triangle, and generally all those which represent true, immutable, and eternal essences." With regard to these rather opposite statements, Lewes says, 'If Des Cartes, when pressed by objections, gave different explanations, we must only set it down to a want of a steady conception of the vital importance of innate ideas to his system. The fact remains that innate ideas form the necessary groundwork of the Cartesian doctrine.......The radical error of all ontological speculation lies in the assumption that we have ideas independent of experience; because experience can only tell us of ourselves or of phenomena; of noumena it can tell us nothing.......The fundamental question, then, of modern philosophy is this-Have we any ideas independent of experience?'

Des Cartes' disciples are of two classes, the mathematical cultivators of physics,' and the deductive cultivators of philosophy.' The first class of disciples are far in advance of their chief, and can only be considered as having received an impulse in a true direction. The second class unhesitatingly accepted his principles, and continued his thinking, although they developed his system in a different manner, and arrived at stronger conclusions than Des Cartes' courage would have supported. Some of the physical speculations of Des Cartes have been much ridiculed by subsequent writers; but many reasons may be urged, not only against that ridicule, but also against the more moderate censure which several able critics have dealt out against the intellectual character of Des Cartes. It should be remembered that the theories of all his predecessors were mere conjectural speculations respecting the places and paths of celestial bodies, etc. Innumerable hypotheses had been formed and found useless; and we ought rather to look to what Des Cartes did accomplish under the many difficulties of his position, in respect to the then state of scientific knowledge, than to judge harshly of those speculations, which, though attended with no beneficial result to humanity at large, were doubtless well intended by their author. He was the first man who brought optical science under the command of mathematics, by the discovery of the law of refraction of the

ordinary ray through diaphanous bodies; and probably there is scarcely a name on record, the bearer of which has given a greater impulse to mathematical and philosophical inquiry than Des Cartes. Although, as a mathematician, he published but little, yet in every subject which he has treated he has opened, not only a new field for investigation, but also a new road for the investigators to proceed by. His discovery of the simple application of the notation of indices to algebraical powers, has totally remodelled the whole science of algebra. His conception of expressing the fundamental property of curve lines and curve surfaces by equations between the co-ordinates has led to an almost total supersedence of the geometry of the ancients. Contemporary with Galileo, and with a knowledge of the persecution to which that father of physics was being subjected by the Church, we are tempted to express our surprise that Des Cartes did not extend the right hand of fellowship, help, and sympathy to his brother philosopher; but it is, nevertheless, the fact, that either jealous of the fame of Galileo (as some have alleged), or from a fear of being involved in the same persecutions, Des Cartes abstained from visiting the astronomer, although travelling for some time near his place of abode in Italy. Lewes, in his 'Life of Des Cartes,' says, Des Cartes was a great thinker; but having said this we have almost exhausted the praise we can bestow on him as a man. In disposition he was timid to servility. While promulgating the proofs of the existence of the Deity, he was in evident alarm lest the Church should see something objectionable in them. He had also written an astronomical treatise; but hearing of the fate of Galileo he refrained from publishing, and always used some chicanery in speaking of the world's movement. He was not a brave man; he was also not an affectionate one. There was in him a deficiency of all finer feelings. But he was even-tempered, and studious of not giving offence.'

We are tempted, after a careful perusal of the life and writings of Des Cartes and his contemporaries, to be of opinion that he was a man who wished to be considered the chief thinker of his day, and who shunned and rejected the offers of friendship from other philosophers, lest they, by being associated with him, should jointly wear laurels which he was cultivating solely to form a crown for himself. Despite all, his brow still bears a crown, and his fame has a freshness that we might all be justly proud of, if appertaining to ourselves.

We trust that in these few pages we have succeeded in presenting Des Cartes, to such of our readers who were unacquainted with his writings, sufficiently well to enable them to appreciate him, and to induce them to search further; and at the same time we hope that those better acquainted with him will not blame us for the omission of much which they may consider more important than the matter which appears in this little tract. We have endeavoured to picture Des Cartes as the founder of the deductive method, as having the foundation-stone of all his reasoning in his consciousness.