HAMILTON, SIR WILLIAM, BART. (1788-1856), one of the most eminent of Scottish metaphysicians, was born in Glasgow, on the 8th March 1788. His father, Dr William Hamilton, had in 1781, on the strong recommendation of the celebrated William Hunter, been appointed to succeed his father, Dr Thomas Hamilton, as professor of anatomy in the university of Glasgow ; and when he died in 1790, in his thirty-second year, he had already gained a reputation that caused his early death to be widely and deeply regretted. William Hamilton and a younger brother (afterwards Captain Thomas Hamilton, noticed above) were thus brought up under the sole care of their mother, - a woman, fortunately, of considerable ability and force of character. William received his early education in Scotland, except during two years which lie spent in a private school near London, and went in 1807, as a Snell exhibitioner, to Balliol College, Oxford. There he pursued his studies zealously, though for the most part independently, - devoting himself chiefly to Aristotle, but in other directions also laying the foundations of that wide and profound scholarship with which his name is associated. In November 1810 he took the degree of B.A. with first-class honours, utter an examination so much above the usual standard in the number and difficulty of the works which it embraced that the memory of it was long preserved at Oxford. He had been intended for the medical profession, but, soon after leaving Oxford, gave up this idea, and in 1813 became a member of the Scottish bar. Henceforward Edinburgh was his place of residence, and, except on occasion of two short visits to Germany in 1817 and 1821, he never again quitted Scotland. Neither his ambition nor his success was such as to absorb his time in professional pursuits. His life was mainly that of a student ; and the following years, marked by little of outward incident, were filled by researches of all kinds, through which he daily added to his stores of learning, while at the same time he was gradually forming his philosophic system. The outward and visible traces of these researches remain in his common-place books, especially in one which, having been in constant use, is a valuable record of his studies from this time onwards to the close of his life. He did not withdraw himself from society, but his favourite companions were the books of his own and of every library within his reach. Among these he lived in a sort of seclusion, from which only now and then, when stirred by some event of the world around, did he come forth, in vigorous pamphlets, to denounce, or protest, or remonstrate, as the case might be.

His own investigations enabled him to make good his claim to represent the ancient family of Hamilton of Preston, and in 1816 he took up the baronetcy, which had lain dormant since the death (in 1701) of Sir Robert Hamilton, well known in his day as a Covenanting leader.

In 1820 he was an unsuccessful candidate for the chair of moral philosophy in the university of Edinburgh. Soon afterwards lie was appointed professor of civil history, and as such delivered several courses of lectures on the history of modern Europe and the history of literature. In 1829 his career of authorship began with the appearance of the well-known essay on the Philosophy of the Unconditioned, - the first of a series of articles contributed by him to the Edinburgh Review. He was elected in 1836 to the Edinburgh chair of logic and metaphysics, and from this time dates the influence which, during the next twenty years, he exerted over the thought of the younger generation in Scotland. Much about the same time he began the preparation of an annotated edition of Reid's works, intending to annex to it a number of dissertations. Before, however, this design had been carried out, he was struck with paralysis of the right side, which seriously crippled his bodily powers, though it left his mind wholly unimpaired. The edition of Reid appeared in 1846, but with only seven of the intended dissertations, - the last, too, unfinished. It was Sir William's distinct purpose to complete the work, but this purpose remained at his death unfulfilled, and all that could be done afterwards was to print such materials for the remainder, or such notes on the subjects to be discussed, as were found among his MSS. Considerably before this time he had formed his theory of logic, the leading principles of which were indicated in the prospectus of " an essay on a new analytic of logical forms" prefixed to his edition of Reid. But the elaboration of the scheme in its details and applications continued during the next few years to occupy much of his leisure. Out of this arose in 1847 a sharp controversy with the late Professor De Morgan of University College, London. The essay did not appear, but the results of the labour gone through are contained in the valuable appendices to his Lectures on Logic. Another occupation of these years was the preparation of extensive materials for a publication which lie designed on the personal history, influence, and opinions of Luther. Here be advanced so far as to have planned and partly carried out the arrangement of the work; but it did not go farther, and still remains in MS. In 1852-53 appeared the first and second editions of his Discussions in Philosophy, Literature, and Education, a reprint, with large additions, of his contributions to the Edinburgh Bailey. Soon after, his general health began to fail. Still, however, aided now as ever by his courageous and devoted wife - (he had married in 1829) - he persevered in literary labour; and during 1851-55 he brought out nine volumes of a new edition of Stewart's works. The only remaining volume was to have contained a memoir of Mr Stewart from his pen ; but this lie did not live to write. lie taught his class for the last time in the winter of 1855-56. Shortly after the close of the session he was taken ill, and•on the 6th May 1856 ho died at his house in Edinburgh.

Sir W. H Imilton's philosophy is presented in writings either more or less fragmentary in form and occasional in purpose, or else, in whole or in part, prepared for publication by others, not by himself. Helms, not only do sonic points receive what seems almost a superfluity of attention, while others of equal importance are treated with barely enough of detail, but there is no complete statement of the latest results of his thinking in their mutual relations. It may be that this imperfection of the outward form has tended to obscure the real harmony of his system, and in part led to its being pronounced - as it has too often been - an assemblage of contradictory doctrines. How far this is from being the case, and how closely the various parts are connected, becomes apparent when it is seen how they are all developed from the central conception of consciousness. In the following sketch that conception will be used as a point from which briefly to view the system as a whole, and to trace the bearing on one another of its leading doctrines.

Consciousness is regarded by Hamilton under three chief aspects : - (1) as it is in itself ; (2) as realized under actual conditions; (3) as a source of truth.

Consciousness in itself is to Hamilton but another name for immediate or intuitive knowledge. For such knowledge is a relation between a subject (knowing) and an object (known), which, as it is viewed from the side of the one or the other term, is properly celled consciousness or knowledge : there are two aspects, but the thing itself is one. Immediate knowledge or consciousness involves the existence of bath subject and object, - it is the affirmation by the subject implicitly of its own existence, explicitly of that of the object. In this relation as realized in the primary judgment, that which knows is conceived as the ego or self, - that which is known, either as a mole of the ega or self, or as a mode of the non-ego or not-self. Thus we have, in the terms of the relation, a division of co.:is/en:6 into the noumenon self and the contrasted phenomena of mind an I of matter ; while the relation itself yields a division of Inzefeielje into philosophy, corresponding to its subjective, and science, corresponding to its objective, phase, - the latter being further subdivided. into the sciences of mental and those of material Oen om ens.' Hamilton adopted the division of mental phenomena (not as states but as elements) into the three groups or classes of cognition., fecliny, and coast ion. Cognitions he classified according to the different relations between subject and object, calling these relations, - as subjective, powers or faculties, - as objective, forms or stages, of knowle lge. Under these, cognition is either immediate or mediate, i.e., either consciousness itself or the datum of consciousness. The first of the faculties, therefore, is of immediate knowledge, - the acquisitive or presentative power, which yields perception (external an L internal). The second is of that form of mediate knowledge which is representative of an individual object. Here Hamilton distinguished three moments or phases, which lie termed the retentive, the reproductive, and the representative po•ers, - distinguished them perhaps to widely, but at the same time indicated their essential unity. The third is of that form of mediate knowledge in which a number of objects receive a factitious unity from being thought under a common relation. This he named the elaborative or discursive faculty.' Here, where he had to deal with conscious- ness in the form of experience, realized under actual conditions and comprehending every variety of mental life, Hamilton showed, in the first place, how the mutual action and reaction of the several clam Tits produces the complexity which the phenomena present. Renumseenee, imagination, and judgment are all, as acts of which we are conscious, awl which imply a prior immediate knowledge, contained in self-perception. But, on the other hand, our knowledge or perception even of self could not be what it is, did pro cesses of reminiscence, imagination, and judgment not enter into its composition. Consciousness includes all the particular forms of knowledge ; yet its development into a whole is the effect of the agencies which make up its content." In the next place, he showed the laws of mental action in the conditions under which consciousness is exercised. From the variety and the limitation of consciousness, under the relation of time, arises the successive variation of its units, - in other words, the train of thought. By the limitation of consciousness is meant the limited number of objects to which it can at one time be directed, but this issues in a farther limitation, consisting in the disproportion between consciousness and the whole sum of mental modifications. Sir W. Hamilton held that consciousness is the mental modes or "movements, rising above a certain degree of intensity," and that " the movements beyond the conscious range arc still properties - and effective properties - of the mental ego." This doctrine he used to explain not only the phenomena of ordinarily latent knowledge and of forgetfulness but also those of the abnormal recovery of apparently lost knowledge and of the formation of habits and dexterities.4 The units (or rather groups of units) of the train - partly former thoughts again present, partly thoughts for the first time present to the mind--follow one another according to what Hamilton called the law of integration, i.e., "only as they stand. together as relative parts of the same common whole." Of this supreme law subordinate phases determine more special conseeutions of thought. The reappearance of former thoughts (reminiscence voluntary or involuntary) is governed by the laws of (1) redintegration and (2) repetition. " Thoughts tend to suggest one another which are co-identical (1) iu time or (2) in mode." New wholes of thought are framed by successive analyses and syntheses. Under the law of integration these analyses are effected by means of attention and abstraction, i.e., by consciousness being continuously and repeatedly concentrated. on certain parts or aspects of objects and withdrawn from others. The syntheses of thought are infinitely diverse in character, yet possess in common an invariable form. This process of forming new wholes, by discrimination and comparison, out of the materials supplied by perception and reeolleetiom is the one kind of mental activity recognized by Hamilton in the various products of thought, from the simplest to the most complex. In other words, he regards judgment as the fundamental act of mind, the proposition, or expressed judgment, as its primary product.' Hamilton's theory of consciousness in its third aspect, i.e., as a source of principles, is embodied iu his doctrines of the conditioned and of common sense. The former is so called because it professes to be a demonstration that "the conditionally limited (what we may briefly call the conditioned) is the only possible object of knowledge and of positive thought." The name of the latter was adopted by Hamilton, not as in itself a good one, but as sanctioned by the usage of philosophers in general and of Scottish philosophers in particular. The doctrine itself is that the primary data of consciousness are, as such, i.e., as facts, and solely on the authority of consciousness, to be accepted as trims. The two doctrines are complements of each other, as severally explications of the principle of the relativity of human knowledge, which, common to both, is manifested in the one through that which we cannot know, - in the other through 'the inexplicable character of our fundamental cognitions.

The primary data of consciousness Hamilton held to he of two orders, otherwise diverse, but in this the same, that they are known merely as facts. These are - (1) truths of perception - the conviction of the reality as modes of self of our own thoughts and feelings, and the allied conviction that in sense-perception we conic into contact with a reality external to the mind:; and (2) truths of reason - the fundamental laws of logic, the necessary forms of thought or relations of existence (i.e., quality, and quantity in its threefold aspect as time, space, degree), the causal judgment, the principle of substance and phenomenon, Ree.6 Now here it was Hamilton's peculiar contribution to philosophy that he placed.the data of perception along with the data of thought, and affirmed that both classes alike are inexplicable, yet as facts clear ; that both rest on the same authority ; and that, if the one be accepted as true, so also should be the other. He was a realist, because he held realism to be the dictate of consciousness. Evidently here the ground of the view is of even more importance than the view itself, and so to Hamilton the question of realism versus idealism was momentous chiefly from its connexion with that of the authority of consciousness. He was fully aware that, since he claimed so high an authority for the primary data of consciousness, it was necessary to supply the means of deciding whether any given cognition is or is not entitled to be placed among such ; and to this end he laid down certain criteria of alleged primary facts of consciousness. These criteria are (1) simplicity, (2) universality and (subjective) necessity, (3) comparative evidence and certainty, (9) incomprehensibility. In other words, no cognition is an original datum of consciousness which is not simple (i.e., incapable of being resolved into another), not held by all men as a self-evident and necessary truth, and not in itself inexplicable. Now the doctrine of the immediate knowledge of the non-ego will, Hamilton affirmed, stand all these tests. It is the simple residuum of truth in the crude and erroneous beliefs of men as to what they perceive through their senses ; it is the spontaneous conviction of all (as to this he cited as witnesses philosophers who regarded the belief as a mistake and a delusion); and it does not admit of being made comprehensible.' That this is so can hardly be denied. Practically, indeed, all acknowledge that consciousness dues intuitively affirm what he alleges it to affirm ; and, the question being one of fact, a practical acknowledgment is quite as good as a theoretical one.

Here let it be remarked in passing that Hamilton's doctrine of common sense is wholly misrepresented when held up as an appeal to the belief of the unthinking multitude versus the judgment of philosophers. Rather it carries the appeal into a sphere where the philosophic and the vulgar have ceased to be distinguished ; it shows that not the mind of the philosopher, and not the mind of the vulgar, but the mind of man, is what philosophy has to deal with, and that its office is to resolve current beliefs into their elements, not satisfied till it has reached the final and absolutely pure deliverance of consciousness.

But it may be said, as it often has been said, that consciousness is not competent to affirm immediate knowledge of the non-ego, because to discriminate the non-ego from the ego is beyond its power. Hamilton's answer is that., if knowledge be, as he holds, essentially relative, self cannot be known except with and through not-self, and that natural realism is but a corollary of the general principle of the relativity of knowledge. On that principle lie hell that " we think one thing only as we think two things mutually and together," and that, self being inherently a relative notion, we should never interpret by it facts of our experience, if experience did not come before us under a relation that needs both terms (self and not-self) for its expression. Hamilton certainly implies, if he does not expressly say, that, had we no knowledge of a not-self, we could never objectify self so as to know it as such at all. To him a knowledge of the ego alone would be absolute, not relative - such a knowledge, that is, as he held to be impossible. But, viewing knowledge as a relation between an existing subject and an existing object, he saw no reason why the object should not be what it is known as - sometimes a mode of self, sometimes a mode of notself, - and why consciousness of the ego should not include also that which stands in relation with it.° But that there has been so amazing an amount of misconception- on the point, it might seem hardly needful to say that Hamilton did not hold that in perception we know the thing-in-itself. His doctrine of relativity included phenomenalism, though it was more than phenomenalism ; and not only his oft-repeated assertions that there can be no such object of knowledge, but the whole tenor of his philosophy, are directly against this interpretation. In passages where he speaks of "the thing" as directly known, the word is obviously used, not for noumenon or the thing in itself, but for the real as opposed to the ideal in phenomena. There can be no doubt that he held the object in sense-perception to be a phenomenon of the non-ego ; and arguments that proceed upon a different supposition are of no effect against his theory.

The relativity of perception on that theory is, indeed, not open to doubt. According to him, we perceive phenomena alone, - such alone as we have faculties to apprehend, - such alone as stand in relation to our organs of sense ; and we perceive only under the contrast of self and not-self. There is thus in every act of perception a twofold relation - (l) between the thing and the organ, manifested in sensation being a condition of perception, and (2) between self and not-self, manifested in consciousness and perception being different names for the same thing. This of itself should show that he cannot be expected to state definitely what is the object in perception, - as it has often been said that he does not do, or does differently in different places. The object of intuition or perception does not admit of being definitely stated. For individual objects cannot as such be conceived, still less named, till knowledge has risen above the intuitive or perceptive stage. On this, as on all points relating to perception, Hamilton's mature and carefully expressed view is to be found in his dissertations appended to ileid's works. There he divides the qualities of body into three classes, - primary, secondary, and secundo-primary. Ile shows that sensation and perception proper, though up to a certain point inseparable, are not only distinct, but above that point actually in the inverse ratio of one another ; that sensations proper (identical with the secondary qualities) are merely subjective affections of the animated organism, and afford no knowledge of external reality ; that in perception proper the material organism, which is to be regarded as an external reality, is presented under those relations which constitute its extension, i.e., we know its primary qualities ; and that in sensation and perception together we know the secnndo-primary qualities, i.e., objects external to the body become known, as directly related, through various modes of resistance, to the organism in motion. The object in perception is, then, according to him, a primary quality of the organism, or the quasi-primary phase of a secundoprimary quality. It is a fundamental point of Hamilton's doctrine that the organism is differently related to the ego in perception proper and in sensation proper. In his own words - " the organism is the field of apprehension to both, but with this difference, that the former views it as of the ego, the latter as of the non-ego, - that the one draws it within, the other shuts it out from, the sphere of self." On this distinction is partly founded his doctrine of the twofold character of space, as at once an a priori conception and an a posteriori perception. He held with Kant that space is a necessary condition of thought, and as such not derived from experience ; but lie at the same time held that through sense we have a perception of something extended, i.e., of extension. low the cognition of extension is a cognition of relations, - properly therefore realized by a simple energy of thought ; but the facts that sensation. is an essential condition of this cognition, and that what is known as extended is the organism, 101101 is its much external to the ego as any other part of the material world, seemed to him to justify these relations being regarded not as subjective but as objective.

Hamilton's doctrine of the conditioned relates to the second group of primary truths or original data of consciousness. Relativity, as a general condition of the thinkable, he asserts, is brought to bear under three principal and necessary relations : - the first (subjective) the contrast of self and not-self, the second (objective) quality, and the third (objective) quantity. Quality is realized under the twofold aspect of substance and phenomenon. Quantity has three phases is - time (proteusive), space (extensive), degree (intensive). Now the doctrine of the conditioned is (1) that under these relations - specially those of quality and time - we must think everything ; (2) that the unconditioned as such is either the unconditionally limited - the absolute, or the unconditionally unlimited--the infinite ; (3) that, under the necessary relations of thought, we are unable positively to conceive either unconditional limitation or unconditional illimitation ; e.g., an absolute whole or part of existence in time or in space or in degree is inconceivable, so is infinite increase or division ; absolute quality is inconceivable, quality infinitely undetermined is so equally.' Thus this doctrine Claims to demonstrate the limited range of positive thought, by showing that the mind is tossed from the one to the other of two contradictory extremes, unable to conceive either, yet compelled to believe that one or other is actual. The kind of inconceivability of the two extremes is indeed different, and it may be regretted that, in his expositions of this part of his philosophy, Hamilton did not more explicitly recognize that fact. It seems true that to combine the absolute with existence regarded quantitatively, i.e., in time or in space or in degree, or the infinite with existence regarded qualitatively, is impossible, not only as beyond but as against thought, i.e., as involving a contradiction ; and therefore that, in respect of one of the two extremes, the mind is not simply impotent, seeing it rejects it as that to which there can be nothing answering in actual existence. But then it does so only to find itself face to face with an alternative which, while it must he inferred to be actual, can by no effort be realized in thought. So that, even if this objection be allowed, the doctrine still remains intact as a demonstration how limited is the sphere of human thought as compared with that of existence, and how little human powers of conception are to be made the measure of truth.

Its significance becomes still more apparent in the original and ingenious application made of it by Hamilton to the solution of such philosophic problems as the origin of the principles of cause and effect, substance and phenomenon, &e. That the sum of existence of one set of modes has passed into another mode is, according to him, what we mean by saying that an event bad causes. Consciousness is a knowledge of existence only as conditioned in time, and we are impotent - (it matters not how) - to conceive the forms of existence within our experience as having bad an absolute commencement ; therefore we conceive them as having existed in oilier forms, in other words, as caused. Thus it is in order to escape from the necessity of thinking an absolute beginning for existence in time that we view all things as a series of causes and effects. In like manner, it is because we can think neither that which exists in and for itself nor that which exists merely in and through something else that we recognize all objects under the double aspect of substance and phenomenon, - knowing nothing but the latter, yet always supposing the former.° Having showed that the original data of consciousness, however different in other respects, are alike in this, that they are as facts - but only as facts - clear and certain, and as cognitions relative, more properly indeed, beliefs than cognitions, - Hamilton claims for all that, on the sole authority of consciousness, they be accepted as truths. This is the point to which the irhole of his philosophy leads np ; hence he offers no arguments in its support. He only asks - lf the authority of consciousness be disallowed, what other warrant of truth remains ? Where else will a source of certainty be found ? He saw no alternative between absolute scepticism and implicit reliance on consciousness. But his reliance was no absolute and blind belief. Ile claimed implicit credence for consciousness only after having investigated and laid down the conditions of its credibility. The inexplicability that is to him a mark of truth must be proved to be that which springs from the fundamental character of the cognition. While the establishment of principles on which belief may be sure, rational, and consistent is the ultimate aim of his philosophy, groundless or inconsistent belief he sweeps away wherever he meets with it. Thus he will not allow the validity of belief in an external reality which, ex hypothesi, is not known.' Be it noted too, that it is conscious-MSS, i. reason, for which he claims stain eme authority.' His position is best understood through the mutual relation (already referred to) of his doctrines of the conditioned and of common lens?. The former extends the bounds of existence as much as it narrows those of thought, and so makes room for belief ; while the latter shows belief to be the condition on which alone even primary and fundamental truths can be apprehended. Thus, for example, on the ground of both, he held that freedom of will and necessity are alike inconceivable, but that we are not entitled to reject the testimony of consciousness to the fact that as moral agents we are free, on account of the speculative difficulties with which it is surrounded.' These two doctrines Sir W. Hamilton did not himself apply to theology, and in themselves they have no direct theological bearing, since the one is concerned with the infinite and the absolute merely as notions, and the other with simple forms of thought long prior to those of theology. But his references to this subject indicate clearly what lie considered to be the true relation of theology to philosophy, and show that, in the one as in the other, he held wisdom to lie in such a conviction of human ignorance as disposes the mind to accept harmony with the facts of consciousness as evidence of truth.4 Of the three classes into which, as we have seen, Hamilton divided mental phenomena, the third - the phenomena of collation - is not treated of in his _Lectures, and his other works contain only fragmentary discussions of particular ethical points. Several lectures, however, are devoted to the consideration of the phenomena of feeling and the development of a theory of pleasure, founded chiefly on that of Aristotle, which is. in substance that pleasure is the reflex in consciousness of the spontaneous and unimpeded exercise of power or energy, - pain being, on the other hand, the consciousness of overstrained or repressed exertion.' The logic with which Sir W. Hamilton's name is associated is a purely formal science. Nothing else indeed did he consider properly to be called logic. For it seemed to hint an unscientific mixing together of heterogeneous elements to treat as parts of the same science the formal and the material conditions of knowledge. He was quite ready to allow that on this view logic cannot be used as a means of discovering or guaranteeing facts, even the most general, and expressly asserted that it has to do, not with the objective validity, but only with the mutual relations, of judgments. He further held that induction and deduction are correlative processes of formal logic, each resting on the necessities of thought, and deriving thence its several laws. In establishing the distinction between logical and scientific induction, he showed that deduction no more than induction is self-sufficient, since it also must have a prior process to start from before it can be applied to nature. He also held that no other than formal logic can be distinguished from the body of the sciences. Perhaps he may have too much overlooked the fact that the search for causes (a problem common to all the sciences) and the presumable uniformity of nature (a principle capable of guaranteeing general inferences) yield the conditions of a logic entitled to the name of a science of science, and possessing all the importance of the knowledge whose organon it is. Yet it is well to be reminded by a difference of name that a science such as this, consisting of inferences from the actual order of things, is quite distinct from the body of truths developed from the conditions of thought as such.

The only logical laws recognized by Hamilton were the three axioms of identity, non-contradiction, and excluded middle, which he regarded as severally phases of one general condition of the possibility of existence and, therefore, of thought. The law of reason and consequent he considered not as different, but merely as expressing metaphysically what these express logically. He added as a postulate - which in his theory was of importance - " that logic be allowed to state explicitly what is thought implicitly."

The changes by which he to a great extent remodelled formal logic were the result (1) of applying to propositions and syllogisms• the two aspects of notions as wholes, - exicnsiom, answering to the. objects denoted, and idtension, answering to the attributes connoted, - and (2) of assigning quantity to the predicate as well as to the subject in judgments of extension. These judgments receive. the form of an equation. Only simple conversion is allowed, but; all propositions being shown to be capable of simple conversion, the. class of immediate inferences is greatly increased. Categorical syllogisms (inductive and deductive) may be either unfigured or figured, according as the distinction of subject and predicate and the. distinctions included in that are or are not recognized. Unfigured syllogism has but one form ; figured syllogisms are of three forms, according to the position of the middle term in the premises. Of these the first conesponds to the first and fourth figures of ordinary logic, - the moods of the latter being shown to be merely indirect intensive moods of the first. The laws of categorical syllogism are,re&aced to one. On the other hand, one of the results of the quantification of the predicate being to increase the number of propositional forms, a number of new moods are added, and each figure contains twelve. Hypothetical and disjunctive inferences, whether regarded as inediate,or as immediate, - (as to this Hamilton varied in opinion, cf., Lats., iv. 369, 371, 373, 374), - foini a separate class. of syllogisms, - the conditional, properly subdivided into conjunctive and disjunctive ; for, according to Hamilton, as all inference is hypothetical, this term ought not to be used as the name of one particular group. The quantities allowed by him in logic were-hut two - the definite, including the univergal and singular, and -the indefinite. The latter also lie considered to be twofold, - partiality as such, from which the universal, both affirmative and negative; is excluded, and partiality which excludes only one universal extreme, while possibly admitting the other. All these improvements were embodied in a notation that clearly and compendiously presents to the eye the whole logical scheme.' Even from this imperfect outline of Hamilton's system of psychology, metaphysics, and logic it appears how. extensive and original were his labours in the various departments of philosophy, how powerful an impetus he. gave to speculation, and how much he himself contributed to, the elucidation of the ultimate problems of thought. By.his thorough-going analysis of consciousness and of the relation of consciousness to mind he did much to promote the scientific study of psychology in his own country and in America, - in particular to give it at once a sound method and:a well-defined sphere. He did not himself trace the growth of consciousness ; but, by showing that it is both simple and complex, both involving and evolved, he implied that it had grown, and suggested the problem of the conditions of: its development. On the other hand, to him there was a wide gulf between mental and material phenomena, and the acceptance of innate ideas was attended with no difficulty ; thus his point of view is so far removed from that of most of the psychologists of the present day that probably his influence now is much less either than it was in his own lifetime or than it may be hereafter.

In metaphysics fns place is plainly marked. Taking his stand at once on the exclusive authority and on the limited sphere of human consciousness, lie comes into direct , antagonism with all schools of philosophy that find in the Unconditioned a field for speculation. At the same tine he is divided from scepticism by his assertion that, as the realm of existence transcends that of thought, so belief is wider than knowledge, and from empiricism by his admission of a priori and inexplicable cognitions. He ranked himself among the Scottish school of philosophers ; yet there he stands by himself, since even those doctrines which he held in common with his predecessors he held after a fashion widely different as to both grounds and results. The doctrine of common sense, in particular, he set, in a new light, rescued from misapprehension, and showed, on the testimony of every school of thought, to be one of the most widely recognized of philosophic tenets. In Reid he. found a philosopher to whom by many ties of intellectual affinity he was bound, and who seemed to him to have so unskilfully used the right clue to a solution of the problems with which he dealt as to justify the doubt whether he really had it. Hence he made Reid's writings, as it were, his own, corrected his errors, and gave a solid basis to the theory which he had himself failed even to make plain.

The philosopher to whom above all others he professed allegiance was Aristotle. His works were the object of his profound and constant study, and supplied in fact the mould in which his whole philosophy was cast. With the commentators on the Aristotelian writings, ancient, mediaeval, and modern, he was also familiar ; and the scholastic philosophy he studied with care and appreciation at a time when it had hardly yet begun to attract attention in his country. His wide reading enabled him to trace many a doctrine to the writings of forgotten thinkers ; and nothing gave him greater pleasure than to draw forth such from their obscurity, and to give due acknowledgment, even if it chanced to be of the prior possession of a view or argument that he had thought out for himself. Of modern German philosophy ha was a diligent, if not always a sympathetic, student, How profoundly his thinking was modified by that of Kant is evident from the tenor of his speculations ; nor was this less the case because, on fundamental points, he came to widely different conclusions. There is a closer likeness as to results between his system and that of Jacobi, - from which, however, his is distinguished by its more scientific character, especially by intuition being more clearly identified with the voice of reason, and more rigidly required to prove its authority as such.

His labours in logic coincided in time with a general movement by which formal logic was effectually advanced and improved. Bat as to the originality of his contributions, especially in mud to the quantification of the predicate, there is no room for doubt. No evidence has ever >>een adduced that in the smallest degree weakens the force of the abundant evidence brought forward in its support.

Any account of Hamilton would be incomplete which regarded him only as a philosopher, for his knowledge and his interests embraced all subjects related to that of the human mind. Physical and mathematical science had, indeed, no attraction for him; but his study of anatomy and physiology was minute and experimental. In literature alike ancient and modern he was widely and deeply read ; and, from his unusual powers of memory, the stores which lie had acquired were always at command, every topic sug- gesting to him apt quotations or pertinent examples. If there was one period with the literature of which he was more particularly familiar, it was the 16th and 17th centuries. Here in every department he was at home. He had gathered a vast amount of its theological lore, had a critical knowledge especially of its Latin poetry, and was minutely acquainted with the history of the actors in its varied scenes, not only as narrated in professed records, but as revealed in the letters, table-talk, and casual effusions of themselves er their contemporaries. His article on the Epistolce Obscurorum Virorum, and his pamphlet on the Disruption of the Church of Scotland in 1S43, may be cited in confirmation and illustration of what has now been said. Among his literary projects were editions of the works of George Buchanan and Julius Cesar Scaliger. His general scholarship found expression in his library, which, though mainly, was far from being exclusively, a philosophical collection. It now forms a distinct portion of the library of the university of Glasgow.

His chief practical interest was in education, - an interest which he manifested alike as a teacher and as a writer, and which had led hint long before he was either to a study of the subject both theoretical and historical. He thence adopted views as to the ends and methods of education that, when afterwards carried out or advocated by him, met with general recognition ; but he also expressed in one of his articles an unfavourable view of the study of mathematics as a mental gymnastic which excited much opposition, but which he never saw reason to alter. As himself a teacher, he was zealous and successful. He did not indeed deem it necessary to give to his lectures the elaboration and precision that he bestowed on his published writings. But he made them sufficient for the cud which they had to accomplish, he supplemented them at times by other instruction, and he strove, not only by all academic means, but also by his personal influence, to develop the speculative energy and interest of his pupils. His writings on university organization and reform had, at the time of their appearance, a decisive practical effect, and contain much that is of permanent value.

Many of his moral as well as intellectual characteristics are expressed in his writings, - the intensity and force of his nature, his tendency to be carried away by polemical ardour, his freedom from anything like pettiness, his perfect sincerity and candour. Such a reflex is at best very imperfect, but here could hardly be bettered by description, which, therefore, is not attempted.

His posthumous works are his Lectures on Metaphysics and Logic•, 4 vols., edited by the Rev. II. L. Manse], Oxford, and Professor Veatch (Ilietaphysies, 1858 ; Lode, 18G0); and Additional Notes to Reid's Works, from Sir W. Hamilton's MSS., under the editorship of the Rev. H. L. Manse], D.D., 1862. A Memoir of Sir 1J'. Hamilton, by Professor Witch, appeared in 1869. (E. IL) Winckelmann, and Piaggi. Recalled in 1800, he died April 6, 1803.

Sir William Hamilton's second wife, Emma Lyon or Harte, whose name is so notoriously associated with that among others the painter Romney, who depicted her in no fewer than twenty-three of his works. Sir William Hamilton married her in 1791 ; • and, going with him the same year to Naples, she speedily acquired an ascendency over the mind of the queen, which at the instigation of Nelson she used for the advantage of the British fleet.. On the death of Sir William she lived in a house at Merton Place, provided for her by Nelson, but on his death in 1805 she soon squandered the modest fortune left her by her husband, and after being imprisoned for debt, retired with Nelson's daughter Horatia to Calais, where she died, January 16, 1815. Her Memoirs appeared in the year of her death.