UC-NRLF B 3 TES ETb /:'N LECTURES •PHILOSOPHY OF LAW: TOGETHER WITH Whewell m Hegel, and Hegel and Mr W. R. Smith. J. HUTCHISON' STIRLING. *■;♦;; LECTURES PHILOSOPHY OF LAW. LECTURES PHILOSOPHY OF LAW TOGETHER WITH WHEWELL AND HEGEL, AND HEGEL AND MR W. R. SMITH, A VINDICATION IN A PHYSICO-M ATHEMATICAL REGARD. BY JAMES HUTCHISON STIELING, F.RC.S., AND LLD., Edin. UNIVERSITY LONDONt LONGMANS, GREEN, & CO. 18 7 3. J^3S^J^ / M PREFACE TO THE LECTURES. n^HESE Lectm-es on tlie Philosophy of Law, pubhshed in The -*- Journal of Jurisprudence and Scottish Laio Magazine for the months of January, February, March, and April, 1872, were, in the fii-st instance, delivered to the Juridical Society of Edinburgh, on the evenings of the 9th, 13th, 16th, and 20th November 1871 respectively. The first lecture, let me say in especial, will be found an introduction pretty well to Philosophy in general at present, for philosophy in general at present is pretty well German Philosophy ; and such introduction was a necessity of the sub- ject ; for any explanation in Hegel's regard involves one in Kant's also, and these two men's ideas are German Philosophy in its " outcome." For I still believe the former with elimina- tion, on the whole, of Fichte and Schelling, to affiliate himself directly to the latter. Fichte's general conception, — self- development of the ego, and from the ego, certainly lies in Hegel, with infinite suggestion as concerns method and general details ; and the student cannot dispense with a know- ledge, at least of the Wissenschaftslehre. As for Schelling, again, whose philosophical production the intervention of Hegel breaks, as it were, into two very different deliverances, I cannot help regarding his study as even less important to an under- standing of Hegel than the study of Fichte. Of what I call the tivo deliverances, the second, Schelling's positive or religious Philosophy, I am disposed to regard as but the prodiict of arbitrary, happy-go-lucky, Vorstellung, and not of the necessity of the Begriff; which, therefore, however genial, will soon cease to be read, — the rather that it has no historical value, inasmuch as, despite the influence of Hegel which animates it, it contains no understanding, and is no continuation of philosophy as Hegel IV PREFACE. left it. Ruge's judgment, though too sweepingly negative, may, perhaps, be regarded as decisive here. It is different with the NaturphilosopMe, and the Transcen- dental Idealism; these, though they may be eUminated, are certainly historical in their influence, and if the student, in the case of Fichte, is expected to master the WtssenschaftsleJire, and even the Naturrecht and the Sittenlehre, he will be equally expected, in the case of Schelling, to master the two works just named, especially the Transcendental Idealism, which will always rank as Schelling's best and most important work historically. The work on " Freewill" deserves special mention, were it only that it is specially referred to by Hegel. It is possible too, that Hegel's attention was du-ected to Bohme by ScheUing, and, if so, this also must rank as one of ScheUing's merits. It is Hegel, then, who may be regarded as directly receiv- ing the historic pabulum from the hands of Kant ; and tJiat pabulum must be recognised as having been masterfully con- trolled by Hegel, into a form all his own, and, in a certain way, perhaps the most important yet, — in a certain way, perhaps even the final one. No man till Hegel, ever explicitly saw the notion, and no man till Hegel, ever built a direct system on it. This is certainly the most important philosophical achievement that has fallen to the lot of any man, and Hegel must be pronounced not only in form, but in matter, as original a philosopher as ever lived, and that notAvithstanding all his debts to Kant, or who- ever else. For it would be quite possible to represent and demonstrate aU philosophy to be but a series of attempts to find the notion, of which only that of Hegel at long and last succeeded. And it is very remarkable that Schelling, during the twenty- three years he survived Hegel, failed to see this, the work of Hegel, and to continue it as what was, historically, an der Zeit. The notion, that is, whether applicable or not to the details of nature, must now, I think, be allowed to be applicable to nature as a whole, and still more certainly applicable to the world of man. Man's life is in the crutch of the antithesis between universal and particular, for what lies in the hollow of* that crutch is thought itself. Thought, in truth, is nothing but the very antithesis named. But, named as it may be, it is certainly to the Spannung between particular and universal, that man owes at once his conscience and his generalisation, or, what is the same thing, his religions, and philosophies, and arts, PREFACE. V and sciences, and politics. These last (politics), indeed, may suggest that in their necessity — the necessity of aggregation, society— lies the birth of the universal; and, accordingly, those to whom such suggestion occurs, may desire to found all again, like the AufMcirung, and especially the Revulsion, on the mere voiMog, the mere agreement of mankind. (See Schwegler on the Sophists.) A little reflection, however, will reveal that even so the principle undergoes no discredit ; for even so, it must have been implicitly present, else there never had been its development. Further than that, at the heart of things generally, a divine element of universahty must be recognised to lie in interpretation of them, in constitution of them. These Lectures will, among other things, give, it is hoped, intelligence to all this, — precisely the assistance, perhaps, or even the revelation that is wanted, otherwise I shall have to confess to some disappointment. I may mention that a respected correspondent has referred me to the Institutes, m., xv. i., as the authority for Dr Heron's derivation of the word stipulatio ; but, at the same time, puts little stress upon it, — though doubtful also of the connection with stipula. (See note to last Lecture.) THE PHILOSOPHY OF LAW. LECTURE I. I. AN INTRODUCTION TO PHILOSOPHY IN GENERAL. Gentlemen, — My first -svord must be one of apology. That an individual who is not a lawyer should address a distinguished society of lawyers, and on their own science, has that in it — in direct statement at least — to suggest only audacity and presumption. This I have felt from the first; and I have, all along, experienced a genuine reluctance to accept this place. Nevertheless, you your- selves have so willed it, and I have simply obeyed. I comfort myself with the thought, too, that it is not strictly into law that I am required to go, but rather into pliilosophy, though only so far as philosophy has legal bearings. I comfort myself, moreover, with this other circumstance — that, viewing the state of your information in this connexion, whether private or public, I shall not be expected by you to handle this subject pr(yprio Marte, but by the aid of another or others. Indeed, I may say at once that the result of my examination of a goodly pile of books, supplied to me by your own courtesy, was to convince me that not only was Hegel's statement the most valuable in itself, but that all the others of any importance were so saturated with it as to be unintelligible without its intelli- gence. The production of this intelligence, besides, is one of the most important things that at the present moment requires to be effected, at the same time that it is one in which my own slight ability is as likely to be serviceable as in any other, perhaps. The philosophy of law, then, which I shall exhibit to you is that which has been presented in full detail by Hegel in the separate volume expressly published by himself, and named " Outlines of the Philo- sophy of Sight, or l!^atural Eight and Political Science in Ground Plan " — constituting, as I believe, the most valuable product of its author. Of the rest — Trendelenburg, Eoder, Hildenbrand, Heron, Austin, and all the others — I hope to be able to say a word before A 2 LECTURES ON THE PHILOSOPHY OF LAW. concluding. Let me recommend to you noiv only Hildenbrand, a work most accurate, most elegant, yet most easy, though steeped withal in the light of Hegel — a work, too, that shames our English books on the subject into impotent beggary. My situation, then, gentlemen, before you is a somewhat peculiar one ; and when I refer to it now, and all it implies, together with certain other circumstances of time, number, &c., known to some of you, as bearing on the composition of these lectures themselves, I wish to be understood as suggesting a few considerations in appeal to your indulgence, and I have no doubt that, with your well-trained minds, they will very readily be taken — ad avizandum. It is my duty now, then, so far as my ability permits, to make you acquainted with the Philosophy of Eight in the compass and character in which it presents itself, in its own place, within the system of Hegel. But that, as these very words suggest, entails some consideration of the system itself in which it is imbedded, and of which it forms a part ; for only through a sufficient conception of that, the whole, with which it is in connection, and from which it rises, can we ever hope to arrive at an adequate knowledge of this, the part. Besides, it is an affair of common knowledge as regards Hegel, that, in his expositions, no matter presents itself which is not the product of his peculiar dialectic, at the same time that that dialectic itself takes origin from a single principle. A preliminary word, then, will be necessary on the general system of Hegel, its dialectic, and principle. In short, I fear I shall be necessitated to disclose to you — the " Secret of Hegel." Now, do not for a moment fear, however, that I am going to inflict on you anything very detailed or very abstruse. Whatever I shall tell you shall be very short, and very plain, and, after all, perhaps, no such tax on your attention. The possibility of this, of course, may — and very excus- ably, perhaps — be doubted. For example, it is told of one of my best friends that, a gentleman finding him occupied with my work on Hegel, and inquiring what he thought of "the Secret" he answered, " Why, I think the author has kept it ! " I believe I saw from the papers, too, lately, that some gentleman, examined some- where as to the state of philosophy at Oxford, and asked particularly as to whether the Hegelianism supposed to be there now prevalent was in any way due to the " Secret of Hegel," had boldly answered — " No ; that book only makes the dark darker ! " I fain hope there may be mercy for this gentleman ; but, in view of the state of conscience he must yet come to, I really am tempted to believe that he will have a great fear in the end of going to — a very bad place ! But, joking apart, the " Secret " of Hegel is once for all open, and there need be no such very great difficulty in its regard — hard though Hegel may be to read after revelation of every secret. It appears to me that Mr. Lewes himself has at last found this to be the case. Not that I believe him yet truly to" judge Hegel ; but in the re-written article " Hegel," of the new edition of his " History LECTURES ON THE PHILOSOPHY OF LAW. 3 of Philosophy " just published, he will be found to quote from my work on Hegel at least one passage in which it appears to me the Secret is very fairly named. But, be all that as it may, I think I shall have no difficulty in finding, in characterization of the general procedure of Hegel, the short preliminary word we reqxiire here. If it is possible to shut up Kant in a sentence, it is equally possible, in a sentence, to shut up Hegel. But Kant has been so shut up, and, as I believe, more than once. Here, from the " Note" on Kant in the second and third editions of the translation of Schwegler, is what I consider one such sentence : " The sensations of the various special senses, received into the universal a priori forms of space and time, are reduced into perceptive objects, con- nected together in a synthesis of experience, by the categories." Those who do not understand such phrases as " universal a priori forms," " perceptive objects," " synthesis of experience," " categories," &c., will probably know just as little of Kant after this sentence as they did before it. Nevertheless, that is no impeachment of the truth of the assertion that this sentence does contain all the broad outlines of the cognitive theory of Kant ; and perhaps a word or two of explanation will demonstrate this — an explanation wdiich I hope you will presently find to be in place. We can all fancy an ego, an I — fancy it as a unit or unity, as the primal unit, the primal unity. Well, to feel, to know, this unit must be, so to speak, charged with something, an ohject. Now this object, whatever it be, has parts, it possesses a certain breadth, it is, as compared with the unit into which it is received, a complex, a manifold ; and it is by connecting the various units of this manifold to each other and to itself that the primal unit or unity, the ego or I, can come to possess, or, what is the same thing, to hnoio an object. In an act of cognition, the primal unit, the I, then, reduces into its own unity the plurality of some manifold or object given to it. But the I does not effect this its function of unity, its uniting power, only in a single way. The I is strictly judgment, or the / in act is strictly judgment; and judgment, as we know from logic, has twelve subordinate forms or functions, which functions are arranged by threes under the more general functions of quantity, quality, relation, and modality. We see now, then, the general constitution of the subjective factor in an act of knowledge, of what concerns the I as I. As regards the other factor in the same act, the object again, it is always a many or manifold of special sense in space and time. Now, as for space and time, they are (to Kant) neither notions nor sensations ; not the latter (sensations), for they are not due to any special sense, and they have not objects like other special sensations ; and not the former (notions), for, viewed in the relation of wholes and parts, they are seen to have the constitution, not of something intellectually or logically understood, but of something sensuously perceived. Time and space, then, Kant reasons, being neither notions nor sen- 4 LECTUKES ON THE PHILOSOPHY OF LAW. sations, and being at the same time universal and necessary, must be pronounced general perceptive forms, a joriori, or native to the mind, and lying in the mind from the first as necessary pre-conditions of special sense. This last — special sense — again, is, in all its forms, a mere affection of the subject exposed to the object. For, in all cases, an unknown object, or, as Kant calls it, a transcendental object, is to be supposed to act on special sense and excite the correspondent subjective affection. Here, now, then, we have a view of Kant's whole world ; so far, at least, as cognition is concerned. There are the various affections of the various special senses (colours, feels, &c.) ; these are received into the general perceptive forms of space and time ; and, finally, through the twelve different categorical modes of it, they are reduced into the unity of self-consciousness, or the ego. Should I repeat the sentence, and say now, then, " the sensations of the various special senses, received into the universal d priori forms of space and time, are reduced into perceptive objects, connected together in a synthesis of experience, by the categories," I think it will perhaps be less difficult for you to realize what is meant by Kant's cognitive theory being shut up in it. As for Hegel, we must understand him to have started from these constructions of Kant, and only to have modified them. To him Kant's great want was that of process, process deductive, pro- cess interconnective. Starting with the I, the ego, he (Hegel) would have, like Fichte, the whole foison of the universe derived from its one primal and, so to speak, constitutive act. Accordingly it is not enough for Hegel to take up, like Kant, abstract logic as it presents itself and say, there are twelve classes of logical judgment, and these represent twelve functions of unity in self- consciousness, or the ego. Hegel must see the ego develop out of its own self, according to its own law, according to its own rhythm, according to its own principle, according to its own special, original, and primitive nature — develop into the entire system of its own constituent in7ier furniture or contents. And in this we see, too, how Hegel differs from Fichte. Fichte assumes a sort of external law of thesis, antithesis, and synthesis, according to which he externally develops the ego into its own constitutive variety. Hegel will have nothing to do with such externality of procedure ; he must see the ego unfolding itself into its native variety, accord- ing to its own native principle, according to its own inner nature. Well then, having accomplished this — and you are simply to consider it done — having developed the ego, by its own law, into its own inner contents, Hegel will not, like Kant, only conceive it endowed further with two subjective percej^tive forms, two sub- jective cones of projection, and a variety of special sensational affections, which, received into and externalized by these cones, be- comes reduced by the categories, or functional unities of the ego, into the innumerable special objects, and the one system, of ex- perience. No ; that is for him still external, and still arbitrary LECTURES ON THE PHILOSOPHY OF LAW. O procedure ; it is for liim ^^l^yarrallted procedure, which he must reject ; and he conceives instead, after the internal process has reached its full sum, the same law to continue, and externalization of the whole internal sum to be the next result — externalization, that is, into this outward world of things. There is Nous to Hegel, thought, which in obedience to its own law, mvolved into its own inner constituent sum, is further, in obedience to the same law, evolved into its own outer constituent sura, and that is the formed universe as it exists around us. In relation to Kant, then, it is to shut up Hegel in a single sentence to say he conceives the ego to develop into its own categories, and these being complete, externalization to result from the same common law. Still Heoel, unlike Kant, thinks not of the particular ego — yours and mine — in this process, but of the uniA^ersal ego. So, to him, the ego com- pleted in its own inner, is Nous, thought, universal self-conscious- ness — God, " as He is in His eternal essence before the creation of nature or any finite spirit." This is fairly the amount of the pre- tension of Hegel when he so describes his logic as such " exposition" (Darstellung) of God. But this being the case, then, God's universe to Hegel is plainly but the contre-coup — the counter-stroke of (Jod's own inner nature. This universe is only to him in ex- ternality what God is in internality ; or it is in externality only what self-conscioutiness is in internality. These, then, are the leading ideas of these two men, Kant and Hegel, so far as theory, or cognition, is concerned ; and if one sees in them great similarity, one sees in them also great difference. In Kant's world there is no knowledge of any 7ioummal existence. Although he postulates things in themselves — that is, independent outer objects, to set up the affections of sense in ns : these affections (only farther manipulated from within) alone constitute for him all that can be called things. And though he postulates a logical unity for self-(;onsciousness, he hnoivs no existential unity to correspond to the word soul : what we call our afiections from within, as well as what we call our affections fi-om without, are only phenomenally known. In fact, all that Kant knows are phenomenal affections, phenomenally projected into optical spectra of externality, and then logiccdly gathered in into unities again. Whether as regards the subject or as regards the object, he is quite destitute of any nou- menal knowledge. Without is but sensation ; within is but sensa- tion ; both are but stretched on two spectral skeletons, time and space, to be construed thence into what is called experience. The logical element is the only one in Kant that seems to possess any noumenal character, and that, too, rather in reference to validily than to existence. There is room in Kant, that is, for attaching to his logical element the character of noumenal or objective validity, but scarcely that of noumenal or objective existence; for self-consciousness being only logical in his eyes, his whole logical element is left without any substantial basis of support — unless in the mere postulate of 6 LECTUllES ON THE PHILOSOPHY OF LAW. an inner thing in itself, as there is a postulate of outer things in themselves. Now Hegel, tliough starting from these ideas, and deeply influenced by the importance of the logical element, still arrives in the end at a construction very different. The ego is not phenomenal to him, hut noumenal ; then the furniture of the ego is not limited to these twelve categories, hut develops, and with rigorous necessity in every step, into a vast rich system. The spectral perceptive forms of space and time again do not exist for him in that character: they are the universals of externality, but externality to him is necessary, objective, and actual. These, then, are great improvements on the scheme of Kant, and there results a theory which, suj^plied with an actually external time and space, and an actually external world, is not repugnant to common sense. It is in his conception of externality and externalization, indeed, that we have one of the happiest characteristics of HegeL " God said, Let there be light, and there was light:" the summed in- ternality burst into its accurately correspondent externality : the flash of light was the birth of the universe. Directly we under- stand Hegel's dialectic, there is no difficulty at all in conceiving in- ternalization as internalization here, and externalization as ex- ternalization there, but both together as mutually complementary co-factors, as correspondent pieces of one whole: they are the counterparts of the single tally. And in that case, also, it is not difficult to understand that all farther characters of externality will flow from the very idea of externality as externality. There will be consequently a boundless possibility of outness, a boundless side by side of particulars, all material, but boundlessly different. It is but in obedience to the general conception, too, that externality itself is not an absolute chaos ; that the shadow of the tree of intellect falls on it, controlling it, and that it returns in circles, narrowing and narrowing, up to the thought, the internality from which it started, or from which it fell In regard to this Hegelian theory of externalization, I recollect one of our most famous citizens to have exclaimed to me " I cannot take in all that d — d nonsense — do you mean to say that thought made granite ? " But I really do not see this to be so very difficult : it lies in the fact that in ex- ternality as externality there must be boundless material diffhxnce: granite is simply one of the differences. Altogether, I must acknowledge myself to find Hegel's plan of externalization the happiest ever yet proposed — a plan necessary even when we say, as we do say, and must say, God made the world, for it answers the question of Jww — precisely that question how God, how thought, made granite, for example.^ ^ The moment the idea of externalit}' as externality is seized, the great difficulty will be found at an end. One ought to ask one's self what must the idea of externality — what must externality itself be ? Or, suppose you have internality completed — an ego, a boundless intussusception of thoughts, all in each other, and through or thoi'ough each other, but all in the same geometrical point — what must its externalization — and its ex- ternalization is accurately externalization as externalization — be ? Its externalization \ LECTURES ON THE PHILOSOPHY OF LAW. 7 From this account it will be evident, then, that Hegel is an idealist only as Aristotle is an idealist : he, like the Greek, would simply reduce all things to notions, would simply reduce all things to an ultimate generalization; and for what is ordinarily called idealism, he has not only no sympathy but an absolute contempt. Absolute or objective idealism is to him only the thinking of the universe ; but suhjective idealism is that spurious idealism which would make externality due to the internality of each loarticular subject, and then, for that simjjle act, take a big air as if it were philosophy. Hegel rejects such conception and such pretension utterly, and he is never tired of telling us so. In effect, it is a very insufficient reflection this, tliat because a knower can only know within, therefore there is no independent external universe ; but that is really the hidk of what is called subjective idealism. There is another side from which the work of Hegel may be regarded. It is that of explanation in general, explanation as such. j\Ian may go on as much as he likes in his merely animal capacity, marrying, doing business, journeying here and there, and enjoying his senses in general : he linds always in the end that that is not enough ; that he must think as well as live and enjoy ; above all, that he must think existence ; that he must inquire why, once for all, all this is here, why is it, whence is it, u-hither does it go ? All that may be summed up in the single pln^ase : he demands explanation. Now, of course, there are a great many explanations now-a-days. Since Bacon, and, above all, Newton, there is what is called science. Explanation is sought for as regards the stars, and there is astro- nomy. Explanation is sought for as regards the atmosphere, and there is electricity say. Explanation is sought for as regards the constituents of the earth, their inter-relations, their inter-combina- tions, &c., and there are the sciences of physics, chemistry, and what not. Well, now, all these sciences are explanatory, science in general is an explanation ; but these sciences, or science itself, are an explana- tion vjithin conditions (the stars and planets themselves, the air itself) — within condition of the element itself, so to speak, which consti- — it being an internalization — must plainly be the opposite of its ownself : whatever internalization is, extemalization will be not; just as darkness and cold are precisely what light and heat are not. Or, taking it from the other end, we see that externality is infinite out and outness, infinite difference, under infinite external necessity (or, what is the same thing here, contingency) ; while internality again, is, and must be, infinite in and inncss, infinite identity, under infinite internal necessity (or, what is the same thing here, reason). We c-an see here, too, the origin and meaning of Hegel's constant words, negation, and the negative. Externality is the negative of internality. But the former is the particular, while the larter is the universal: therefore the particular is always the negative of the universal. This may serve to show how deeply logic enters into existence. The same connection finds meaning for Hegel's perpetual abstract. Abstraction, in general, is to take any character in isolated self-identity ; and that is the same tiling as wresting any one moment apart from its connection with the rest into isolated self-identity — the work of understand- ing, not reason. 8 LECTURES ON THE PHILOSOPHY OF LAW. tutes their nidus. That element, that nidus, is simply taken as we find it, and, after every explanation of science in regard to the special laws of it, the questions in general, why, whence, whither ? remain unanswered. These questions in general constitute philosophy. We shall not stop to consider that these "questions in general" constitute religion. AVe shall confine ourselves to philosoph}'-. Philosophy, then, receives all the explanations of the sciences, of science in general, and, so instructed and prepared, proceeds to put the final question, the questions in general, why, whence, whither ? In a word, philosophy demands an explanation of existence as existence. It is all very well to say here, that is impossible, that is a demand that, by the very conditions of the case, never can be granted. This is the situation pretty well of general belief at present : there is now a renunciation of metaphysics, there is now a renunciation of religion. This renunciation can never quash the essential need, hovv^ever. JVIau is reason, and reason is irrepressible. Eeason knows itself the essence of this universe, the essence of existence, and would see itself as it is, in its own grounds, in its own connections, in its own system. In a word, reason demands explanation as explanation. Now, what is that ? What is explan- ation as explanation ? And here it is that Hegel steps in. He considers the general nature of the case, and sees how its conditions must be. An explanation, to be an explanation, says Hegel, must be so and so. Now, in this he is not singular : all philosophers who are philosophers have seen the same thing. The philosophers before Socrates, Plato, Aristotle, Plotinus, Proclus, Descartes, Sjjinoza, Leibnitz after him, have all, more or less consciously, been led, in their philosophizings, by the same want. It would be easy to illustrate this in the case of all of them. I shall only, with this view, refer to Diogenes the Apolloniate. The object of this philo- sopher, as represented in the first two or three fragments of his writings collected by Mullach (they occur also in Patter and Preller), is plainly explanation, explanation as a general problem. As necessary presuppositions to that end, he assumes that there must be a single first principle; that this principle must be indisputaUe ; that it must be adequate to the C7itire existent variety; and that consequently it must possess intelligence — for intelligence in actual fact is. Some of his particular expressions, literally translated, are these : " All things that are must be but alterations of one and the same thing, and therefore the same thing ; for if the things that are now — land, and water, and the rest — were different the one from the other, each in its own nature, and were not the same thing variously changed, it would be impossible that they could be mixed together or bring each other advantage or disadvantage : all things, then, are alterations of one and the same thing — at one time so and at another time thus, and they return to the same thing. But this thing must be great, and mighty, and eternal, and immortal, knowing much. Por without intelligence it could not be so disposed as to LECTUKES ON THE nilLOSOPIIY OF LAW. 9 possess measures of all things, of winter and summer, and night and day, and rains, and winds, and calms. And, in the same way, whoever considers them will find all other things disposed as beautifully as possible." There is involved here, as is evident, a sort of d jJriori reasoning ; as about the necessity to explanation of a common principle ; how coTild things combine together or act on each other unless they participated in a common principle, that is pretty well the thought throughout. The further thought, too, is that, in view of the evident measvire, proportion, rule, design according to which all things are disposed, this common principle can only be thought as intelligent : if there is rule, reilection, calculation in the effect, there must equally be rule, reflection, calculation in the cause. So it was, then, with Diogenes of Apollonia : he/o7'e explaining, he determined the neces- sities of explaining ; and so it was, also, with many of the others ; so it was, above all, and in a supreme degree, with Hegel. Hegel said to himself, or seems to have said to himself, for there is little that is direct in Hegel — he builds his system as a man might build a house, and lets us find out all his thoughts about it for ourselves — I, too, like other philosophers, would like to explain existence ; but what does that mean ? Evidently, I must find a single principle, a single fact ip. existence, that is adequate to all the phenomena of existence, to all the variety of existence ; and this principle, while adequate to all the variety of existence, while competent to reduce into its own identity all the difference that is, nmst bring with it its own reason for its own self, its own necessity, its proof that it is, and it alone is, that which could not not be. This for explanation, ultimate, radical, and all embracing explanation, is evidently the necessary presupposition. It will plainly never do to feign a principle, to fancy a principle: the principle must le, an actual denizen, an actual thing present in that which is. The Bed Indian who exclaims of all that he sees, of thunder and liohtnino:, of the gas when it is lit in a theatre possibly, Manou ! Manou ! does not explain : he only exclaims ; he only excites the imagination of his hearers into the vision of a monster, of a creature of fancy, of a mere Vorstellung, that is only assumed or said to have such and such power, to be such and such a cause. It does not explain rain to say there is a spout above the clouds, although there are minds which would find themselves quite contented with such a mere hypothetical image. Such mere hypothetical, vicarious image of phantasy, is not enough for Hegel then : he must find in that which actually is an all- fertile, an all-competent single principle. And here we see at once the reason of Hegel's dislike to the infidel god, the Gallic god, le dieu francais — that etre sujm^mc of Enlightenment, of the Illumination, that is an empty abstraction, a barren image of phantasy on which all only is to he hung. But that is no prejudice to Hegel's prostration before God, before the true God, before that which is the eternal centre and root, and everlasting substance of the world. 10 LECTURES ON THE PHILOSOPHY OF LAW. He really and truly believes in God, but not in God tliat is only a topical god, a circumscribed, limited, particular something that is fancied up there, an enormous big man in the air that it is not absurd for Lalande the astronomer to try to see with his telescope. He has thought too much for that, he has read too much for that, he knows his catechism too well for that. He knows that God is a Spirit, that we cannot by physical searching find God out, but that we must worship Him in spirit and in truth. To that, at all events, his own words fairly amount. This apart, then, Hegel, believing himself to acknowledge the true God, and averse only to the abstract god of the Aufklarung, would find an explanation of all that is in some actual constituent of all that is. And that is thought, reason ; that is self-conscious- ness. Self-consciousness he finds to be the one aim of existence : all that is, is, he finds only for self-consciousness. That is the one pur- pose of existence. Nature itself is but a gradual and graduated rise np from the dust of the field to the self-consciousness of man. This we can see for ourselves : in the inorganic scale, up and up to the organic, and, in this latter, up and up to man. All is exiJlaincd only when it is converted into thought, only when it is converted into ourselves, only when it is converted into self-consciousness. But if all only -^s for self-consciousness, — if all can be converted into self-consciousness — if self-consciousness is the substance and the ultimate of all, then self-consciousness can be regarded as that which ioistituted all, self-consciousness can be regarded as the prius of all: all is only there for it, and to be explained into it. In this way, it is seen, then, that self-consciousness is the principle of all — in other words, that self-consciousness is the principle of explana- tion sought. Hegel's work, consequently, is but one of ultimate generalization, of ultimate induction. Of aciimi facts, he finds self- consciousness the dominant one, the key to, and the raison d'etre of all the rest. What follows, then, is that Hegel should apply this key. Of course, there are many men now-a-days, as I may just stop to remark, who only scorn as futile any such attempt as this of Hegel, and to the sentiments of these men we find from Xenophon that Socrates long ago gave voice and authority " For he did not, like most of the others, debate of the nature of this all, speculating as to how what the Sophists call the world came into being, and by what necessities the various heavenly bodies were produced . . , and he wondered if it was not evident to these men that it was impossible for man to find out these things." These words occur in the very first chapter of the Memorabilia, and there are more beside them to the same effect, with general derision of these high speculative philosophers, who yet, as is further pointed out, with all their claims, have hardly an opinion in common. This the opinion of Socrates is a very decided one, then. Hegel knows it well, too, but he does not let it trouble him. Eather, in direct opposition to LECTURES ON THE PHILOSOPHY OF LAW. 11 Socrates, and to Socrates as praised by Cicero, he boldly exclaims " philosophy cannot be worth anything to the lives and homes of men, unless it come down from heaven ; and it is the one duty left us to carry it up into heaven." In this, it is certain that, apart from that of Socrates, the highest names can be placed on the side of Hegel. Indeed it is difficult to find a single name on the whole bright file which did not belong to one whose reflection was such as fell within the censure of Socrates. Plato and Aristotle directly followed him ; but the favourite speculation of both lay, we may say, in the hcavois, and this not less in the case of the real Aristotle than in that of the ideal Plato. These names shall suffice, then, for the side of Hegel, and we shall let all the others, modern or ancient, pass. In a word, as I said already, reason demands an explanation of existence as existence ; and we miist obey reason. On the part of Hegel, we shall see now, then, his application of the key of self-consciousness for this purpose. It was by induction, as we saw, that Hegel came to this key. Self-consciousness is in the world of facts, and all these other facts are only for it. It is the ultimate and essential drop of the universe, and explanation is only the reduction of all tilings into it. All things, indeed, stretch hands to it, rise in successive circles ever nearer and nearer to it. Now what is self-consciousness ? Its constitutive movement is the ideali- . zation of a particular through a universal into a singular, or, taking it from the other end, it is the realization of a universal through a particular into a singular. Now that may appear a very hard say- ing, but it is a very simple one in reality : it is only a general naming of the general act of self-consciousness. In every act of self-consciousness, that is, there is an object and a subject. The object on its side is a material externality of parts, while the sub- ject on the other side again is an intellectual unity, but a unity that has within it, or behind it, a whole world of thoughts. It is by these thoughts the subject would master the object, reduce it into itself These thoughts, then, that thus master the object, are the universals under which it is subsumed, and it, as so subsumed, is but the particular to these universals. The outward world, then, consists only of the particulars of the universals that constitute the inward world. I think this will be readily seen to be true. AVe can only think by generalizing, and generalizing is the reduction of particulars to universals. Evidently, then, in every act of self-con- sciousness, particulars meet universals in a singular. We were right, consequently, in describing the constitutive movement of self-consciousness to be the idealization of a particular (the object) through a universal (the thought) into a singular (the subject). When we consider, moreover, that self-consciousness is the original substantial principle, the veritable ^3r«is of all, we shall see also that it is not incorrect to describe the constitutive movement of self-consciousness as the realization of a universal through a par- ticular into a singular. Now, that is the Notion — that is the r 12 LECTURES ON THE nilLOSOPHy OF LAW. Secret of Hegel. The vital act of self-consciousness is the notion. The vsingle word notio involves all the three elements, a hnoivincj (universal) of something (particular) in a hioiver (singular). An act of knowing — idealization quite generally — is the reduction of a par- ticular through a universal into a singular; but e contra , creation — and that is realization quite generally — is the exemplification of a universal to a singular through a particular. This, then, is the one ground-notion which Hegel, by virtue of its own law, its own rhythm, as triple in its own form, and so triple that its units, though different from, are yet related to, and identical with each other — this, I say, is the one ground-notion which Hegel sees develop before him out of its own self into the sum of its own inner constituent system of notions. That inner system he then calls idea. The notion is the first and the ever present substance — every one of the derivative notions is but the notion — but the completed internal system of these notions, or of the notion, is the idea. The idea now, then, is the entire and complete universal, and it is only in obedience to the one ever-present law that it sunders into the particular — JSTature. Nature again, the particular, returns to the universal in the singular. Mind, which gradually rises from its primal involution in nature up through all its forms to the Absolute Spirit. Universal, particular, and singular are the three moments of the notion, and everything organic, everything true in this world is — however abstract its element — a concrete of these three moments, which can be seen to take on in the course of the development a thousand nanjes, as thesis, antithesis, synthesis, or a form which is a great favourite in my own explanations, simple apprehension, judgment, and reason. This notion may be illustrated in a variety of ways. Wliat is organization, for example — what is an organiza- tion to any purpose ? Eeflect on it as you may, you will find that it is the reduction of a many of particulars to the unity of a singu- lar through the menstruum of universals — the plan and what it implies. Every concrete is but such organization. The family, for example : there is no perfect family where there is not the fulfilled IDEA, where each of the three moments, universal, particular, and singular, has not full justice accorded it. So the state ; a state must be idea — perfect harmony of universal, particular, and singu- lar, else it is imperfect and not a state. The state is the accom- plished idea of the self- developing notion — here free-will, and in it, if perfect, each of the moments has its due place and its due scope. But is not the universe itself the best illustration ? The universe itself is but the realization of the universal through the particular in the singular ; and all that is said when we pronounce the single word — self-consciousness. Hegel's work now, then, can evidently be called simply the ulti- mate genercdization. He sees that if we would ultimately explain, we must fairly generalize explanation itself. Explanation is always the reduction of an ol)ject into self-consciousness; ultimate explana- LECTURES ON THE PHILOSOPHY OF LAW. 13 tion, then, must be a reduction of all into self-consciousness. But self-consciousness is a fact, it is something in rerum natura, a principle actually existing : Hegel's work, then, is in so many words the final and universal induction. Bat you will say, perhaps, the self-consciousness that is in nature is ours — there is no other self-consciousness in nature than ours : are we to suppose that Hegel views m.y self-consciousness, your self- consciousness, Ids self-consciousness as God ? In one way, I cannot deny this. Still Hegel's idealism, as I said already, is no subjective idealism : he does not conceive nature to be an externalization of the individucd subjects categories, notions, but of those of the universal subject, of those of the universal self-consciousness. But Hegel, we might object further, would certainly admit that every individual finite subject might die, and yet the imiverse would subsist. What in that case were G-od ? Would not Hegel seem simply to conceive then a potential God — a God as it were asleep in nature — and who had yet to be realized afresh in other finite self- consciousnesses ? There are professing adherents of Hegel — Euge and the so-called party of German critics — who seem to entertain some such conception. I, for my part, admit that such may appear to be the case, so far as Hegel's developments apart from time, apart from history, are concerned ; but I assert such an appearance no longer to obtain the moment the development has entered the domain of spirit. In the sphere of religion, especially, Hegel, as is well known, sums up his development in Christianity as the re- vealed religion, and in the midst of numerous expressions that are unmistakeably theistic. I may quote here what I said in the news- papers (Courant, Dec. 21, 1868) on this head three years ago: — "We are bound to accept Hegel's own professions. Again and again, and in the most emphatic manner, he has asserted himself, not only to be politically conservative, but religiously orthodox — a Lutheran Christian. If we accept, as we do, his first assertion without difficulty, we have no right to deny his second. Indeed, however pantheistic the construction, so to speak, in space may appear, the tables, as intimated, are wholly turned in the construc- tion in time, and Hegel ends not only by profession, but by philosophy, a theist and a Christian." I may say also, that this statement met at the time with the complete approbation of the non-Hegelian Professor Ueberweg — non-Hegelian, but, before his death, as both correspondence and actual published writings led me to believe, less and less so. Ueberweg, whose premature death — the premature death of perhaps the most indefatigable philosophical student of his time — we are now justly lamenting, wrote me that his belief was quite mine as expressed in the quotation I have read, and that it was impossible to establish a negative against such a religious claim for Hegel. Of course, it is to be allowed that Hegel j^^dlosoj^hizes Christianity, and that his understanding of much is not such as John Knox would 14 LECTURES ON THE PHILOSOPHY OF LAW. have accepted. Nevertheless, this is to be said, that Hegel would have claimed accord — suhstantially — even with John Knox. We believe the same historical fact and facts, he would have said ; only you see them in the Vorstcllung, while I see them in the Bcgriff. That at all events is really the true nature of the case ; and it is a piece of wisdom that is much needed at present. That single dis- tinction between Vorstellung and Begriff is fitted to bring about perfect reconciliation between the beliefs of the less educated and those of the more educated, and give the Church peace. I may add, too, that every objection from the religious side that may be taken to the rule assigned by Hegel to self-consciousness will dis- appear on due consideration of the text : " In His own image God created man." Eeturning again for a moment to the principle of self-conscious- ness itself, let me point out another advantage possessed by it as a principle of explanation. It contains within itself both difference and identity, and a little reflection will make it plain that there can be no possible explanation of this world without a principle that contains both elements. The origin of difference in identity is the point and focus of the whole problem ; but we have that at once in self-consciousness. Thought, reason, self-consciousness, is the one single necessity, the primal avdyKri, that that could not not be, and alone that that could not not be; but thought, reason, self- consciousness, is by nature a duplicity in unity, difference in identity, for to know is to be always two things in one ; what knows and what is known are for ever different but for ever identical. And so it is that evolution is possible ; for, after all, the work of Hegel is certainly an evolution. It must be regarded, however, as only di 'potential one, only one in idea, not one that takes place or ever took place in time. And this gives it a vast superiority over ordinary evolution doctrines. To suppose that there ever was a natural first germ that naturally grew into another, as, for example, that the oyster ever greio into a man, is to suppose an absurdity. The evolution is — there — in idea — and that is really by power of the idea — but it never took place in natural fact. All that in- genuity which would explain the peacock's tail by the loves of the female (whose comparative plainness then remains unaccountable) is but jjerverse and a waste of time — a waste of time in this, too, that science is quite unable to allow the explanation itself time enough. It would be easy to bring forward sufficient ingenuity to explain the spider's web — by a drop of accidental fluid accidentally emitted by some certain spider one fine day, that gave that acci- dental advantage which is necessary ; but would such ingenuity, such Vorstellung, such mere fancy, be scientific explanation ? The method of natural conjecture in fact, however amusing, leads nowhere. But let us now, in conclusion, just glance at Hegel's evolution that precedes and res\ilts in the notion of law, to which all that I LECTURES ON THE PHILOSOPHY OF LAW. 15 have yet said is only preliminary ; and I trust I have your excuse for spending so much time on what is only preliminary, my con- viction being that any shorter previous explanation would have been futile. Hegel's system, as is now pretty well known, is contained in three great spheres — the Science of Logic, the Philosophy of Nature, and the Philosophy of Spirit. Here we see at once that what we have before us is the Notion. Logic is the universal; Nature is the particular ; and Spirit is the singular. Logic, having developed into full Idea, passes into the particular as the particular, into externalization as externalization, in Nature ; and Nature, rising and collecting itself, through sphere after sphere, from exter- nality itself in the form of space, up to natural internality in the form of organic life, passes into Soul, which is the first form of Spirit. The instrument of the evolution all along, we are to under- stand, is the Notion in its three Moments. Omitting any closer consideration of the evolution in Logic and Nature — vast wholes of philosophy though they be — we shall pass to that of Spirit ; and here, too, we must be but perfunctory only until we reach our own subject. The three heads under which Spirit is treated are Sub- jective Spirit, Objective Spirit, and Absolute Spirit — obviously again in agreement with the three moments of the Notion. Under Sub- jective Spirit we have mind rising through its own faculties to its own higher forms — or the faeulties themselves are represented hut as successive stages of development in mind itself — and all as ever in obedience to the notion. Thus, theoretical spirit, or the spirit that knows, cognition that is, being complete, passes into practical spirit, the spirit that acts, the spirit that has will ; and will can only realize itself in the objective world of Law — in the State. And here we have reached at last our own subject. The introduction has been long, but not longer, I believe, than was absolutely neces- sary to enable us to understand the movement of Hegel — that dialectic which we shall find as active in what concerns Eight, Law, as elsewhere. Now, however, I think we may consider ourselves fiilly instruits ; and at our next meeting we shall effect the transition from the theoretical to the practical spirit, and enter on the objective domain of the latter — on the domain of will, and of law as its realization. 16 LECTUEES OX THE PIIILOSOniY OF LAW. LECTURE II. Gentlemen, — At our last meeting we saw tlie Notion of Hegel, and in its connection witli Kant ; for I still believe Hegel to aifiliate himself in the main directly to Kant. Let him owe what he may, principally by way of suggestion, whether to Fichte or Schelling, it is really Kant's substance that Hegel carries further. We saw that an excellent clue to that Notion was explanation as explanation. Explanation, namely, as explanation, is a reduction to self-conscious- ness, and it follows that we have reached the ultimate when we have reduced self-consciousness to its ultimate. Now, that is tlie Notion. Or the notion is an act of self-consciousness as such — the perfect generalization of such act. This, then, is the creative germ of all and everything ; and, as such, evidently it can be no blank self- identity : it must possess, in its own self, difference ; and it must return from this its difference into that its identity again. No act of self - consciousness -whatever but is seen to exemplify this abstract description. Self-consciousness so constitiited, then, is conceived to develop itself, in obedience to its own inner law, first into its own inner system. This, the realization of the logical notion, is, and in connection with that notion, the logical idea. The idea now, as completed inner system, sunders, in Nature, into the externalization of its own self and of all its constituents — into a chaos, then, of infinite "physical difference and infinite physical con- tingency. This chaos, however, re-collects itself, and returns in Spirit (Mind) to the Universal again. Mind now, or Spirit, appears in a succession of faculties, and rises through its subjective and ob- jective forms into its absolute form — into Absolute Spirit. Sub- jectively, more particularly, it reaches, through stages of Perception, Conception, Thought, the full fruition of theoretical intelligence, and it is at the transition of this into Practical Spirit, into Will, that we have now arrived. This transition it will not be difficult to understand, if we shall but fairly realize to ourselves what the completion of theory is. Theory when complete, that is., has converted its objects into itself. The objects of theory are indeed outer, but when it under- stands them it has fairly made them inner : all that they truly are, LECTURES ON THE PlIILOSOniY OF LAW. 17 all that they substantially are, is now within. It has abolished their alienation, their foreignness, it has made them its — it has deter- mined them its — it has determined objects as its. But intelligence that determines objects is Will. This is Hegel's transition from what we know in common parlance as the intellectual powers to what we know in the same parlance as the aetive powers, or this is Hegel's transition from theory to practice, from what he calls theoretical spirit or intelligence to practical spirit or will. AVe see at once that it is ingenious — that it is ingeniously figurative. Theory surveys an object, and enjoys its survey; but the residt of such survey is to make the outward inward ; and, if the outward is inward, it is theory's own, it is determined by theory, which is now will, and its enjoyment has become an act. Hegel, of course, does not expect us to see in this transition an actual fact in time, but only the potential connection of intelligence and will, only their connection sub specie mternitatis. And viewed so, it is perfectly credible ; for intelligence and will are not in reality different, but the same : they are but action and counter-action of the same com- mon life. Where the one is, the other is : will is but thought in act, thought is but will i7i potentia. It is, therefore, true in an absolute, or perfectly general, reference, that thought of itself de- termines itself into will, remaining, at the same time, the suhstance of it — of will. This, I think, will be seen to be true from the very nature of the case, and apart from the ingenious figurativeness of Hegel's steps, wliich are again briefly these : — To think an object is to understand it. The thinking of an object, then, is the birth of a new object out of or in the old object. But this new object be- longs to thought ; and this new object is at the same time all that is true in the old object. This new object is all that the old object really is — this new object is, in fact, the old object. But thought has thus manifested itself to determine an object, and thought that determines an object is will. Will, then, is thought determining itself out of its own seK into objects, or, as we more generally figure it, into action on objects — a difference of phrase, however, that makes no difference in the facts ; for as we have just seen, our action on objects is to determine these objects as our own. They are indeed outer to us, but in that we understand them, we enter into them, we participate in them, we establish a community between them and us — that is, we make them ours. But though there be this intimate connection between them, it is certain that will does not, in the first instance, appear as thought — appear, that is, on the stage of existence. Will, as we first find it, is, like everything else, in a state of nature. Will, as we so find it, even in man, is rather an instinct than a rational thought. The needs arid greeds of the mere animal are the matter in which it first asserts itself. Nevertheless, man is essentially reason, and even in yielding to these needs and greeds, it is reason that comes gradually B 18 LECTURES ON THE PHILOSOPHY OF LAW. to tlie front. For example, will cannot yield even to these needs and greeds without reflection, and reflection, once begun, can only end in full-fledged reason. The needs and greeds are com- pared with their objects and the means of obtaining these. They are compared with each other. They are compared, however vaguely at first, with the chief end of man, thought, reason, which in all cases, is always at leas^ imjilicitly present. The result of this com- parison on the part of reflection is a subordination and classification of the various needs and greeds, of the various desires, — a subordi- nation and classification that can only end in System. This system now is what we call happiness, and the needs and greeds, accordingly as they variously contribute in quality and quantity to happiness, are variously arranged and valued. But, after all, this arrangement never becomes perfect, never becomes satisfactory. The needs and greeds are even infinite ; subject differs from subject in regard to them ; according to times and seasons, subject differs from his own self in regard to them ; the whole quest of what is called happiness manifests itself to be indefinite, obscure, and contingent; and let it end in what criterion it may, this criterion remains always an enjoyment, something subjective and contingent, something limited. In this way, then, it becomes plain that will can never content itself with what is called happiness as a final aim, and that there must be found for it an object wider, deeper, and more essential. This object can only be its own self The only satisfactory final object to will can only be will. This is one of those expressions that is peculiarly perplexing and distressing to the English reader of the philo- sophical Germans. The difficulty, however, is only in the phrase and not in its import. As we have already seen, will is identical with thought, with reason, and when we substitute these synonyms in the phrase that will can only will will, all ambiguity vanishes. That the object of will should be will — this may appear an empty phrase, but it is not so when we say the object of reason is reason. Eeason, we know, has realized itself in the world around us, in God's world ; and it does not seem strange, with that fact before us, to say reason seeks reason. But reason has also realized itself in the world of man, in its body of laws, in its code of morals, in the general arrangements of what is called the State. Now when we know that it is Avill which has realized reason in law, morals, and state, it will no longer appear absurd to say will realizes its own self; the object of will is will, or will wills will. It will at once suggest itself to us, then, that the will so spoken of is thinking will, and thinking will is free will. Of course, as we are all now educated in Great Britain, this is considered by all of us, or all but all of us, an absurdity; the sup- position of free-will is an absurdity. Most modern English authori- ties are of this opinion, and they really have brought their public to the safm,^ opinion. Now, this state of opinion on the part whether LECTUEES ON THE PHH^OSOPIIY OF LAW. 19 of author or reader, results from making judicious play 'wiih.v^ho.t are called motives. We never act, it is said, but from a motive ; this motive presents itseK to us by necessity of the case, and it involves us in a like necessity. Some few writers seem to doubt this, and not to be sure that they cannot act without motives. Mr. Alexander, not long since, fairly posed Mr. Mill by asking him, having touched the left side of your nose, do you not feci that you could have touched the right instead ? Notwithstanding the fairness of the question, and the earnestness of the " yes or no " with which it was followed up, Mr. Alexander, it appears, so far as I have learned, did not succeed in coaxing an answer from Mr. Mill. But, of course, we all feel that it is quite free to the great bulk of us at present to touch either side of our nasal prominence we please. Not that it will be altogether possible for us to exclude, even in such a case as this, what may be called the play of motives. Whether we elect to touch the risht side or to touch the left side, it will be difficult to banish from our mind's eye what might be called a motive, — and a motive not a bit too trivial when compared with the action. We do not generally act without a motive, and, in fact, we feel ourselves in no circum- stances at a greater loss than when that is required of us. Your socks lie there for you to put on of a morning, and it is really, for the most part, quite indifferent to you which shall be made right and which left. There is no doubt you can put eithey^ on the right foot, and you are really quite willing to jmt either on it ; but you feel it a bore that such a question should have at all turned up. You sit there with your feet naked, feeling that but for the question they would have been clothed, and, motive or no motive, without diffi- culty. You are glad to compound for a motive by making right the sock nearest to the right foot, by closing your eyes and taking the first you catch, or even by tossing up to settle first choice. All this shows, however, how habitually man acts by motives, how im- possible it is for him to act without motives, even in circumstances the most trivial and indijfferent. Eather than act without a motive, we shut our eyes, or ive toss up. Now the true light on the matter is just a reversal of what is usually believed in England on this question. To act hy motive is to act freely, to act without motive is to act under necessity. Possibly some of you may object here — We know that distinction already, but we remain unconvinced, for though moral necessity is not physical necessity, it is still a necessity, and compels obedience. But my answer is briefly. Physical necessity (and I beg you to observe that physical means natural — what is of mere nature) — physical necessity is the only necessity, and moral necessity is freedom. Tliat only is free which is amenable solely to its own self; but in obeying moral motive it is my own self — my own inmost, deepest, truest self I obey ; and, therefore, it is that in the very obeying of it I am free, and all the more free the more thoroughly moral it is — the more thoroughly it is my own 20 LECTURES ON THE PHILOSOPHY OF LAW, self. In the case of the socks no motive was present, and I was not free ; to free myself I had to shut my eyes, I had to toss up, or I had arbitrarily to invent a motive and take the sock nearest. Now, what I call being bound in regard to the socks, is what would be generally stated in England as a proof of freedom ; whereas, what would appear very generally a proof of necessity in England would possibly, according to the views which I adopt, be used as a proof of freedom. Thus, as regards the socks, I should be held free in England so long as I was ivitliout motive, and bound only when in obedience to a motive, I put the one rather than the other on the right foot. Now my way is to reverse this. Should I discover, for example, that the one sock had been worn on the right foot the day before, and decide, for economical motives, to give it the benefit of a change and wear it on the left foot to-day, I should really be acting in freedom, for I should be acting according to reason, — I should have a reason for my action, I should have a motive for my action. Eeally Kant and Hegel have completely determined this qiiestion. Kant is nowhere more convincing than precisely here, and it is precisely here that he is ever eloquent. What fine pictures he gives us in this connexion of how a man acquires the esteem of others, acquires his own esteem, just in proportion to the complete- ness with which he tramples on cominoditij, on self-interest, and yields to the universal — to moral motive — and that without hope, without chance of reward ! Accordingly, it is quite clear to Kant that, besides empirical motives — that is sensuous motives, or, as he otherwise calls them, material motives, patliological motives — there are motives of ideas, motives from within and not from without, actual preserijots of reason ttnto its own self. If motives were only empirical, he argues, action would be only hypothctically conditioned, that is, the action would be viewed only as a means to an end. Eeason in such circumstances could only assist in the discovery of the advisable : it could not command the obligatory. There would result only prudential rules, not laws of duty — directions, prescripts technical merely, suggestive of an art to be acquired rather than a course of conduct to be categorically required. Where motive is empirical, will can only receive a maxim, not an imperative command ; for an emp)irical object must act on appetition, on desire, must presuppose a craving subject under the influence of pathological feelings — inclination or aversion, &c. Maxims, then, are only subjective ; and the most general expression for a subjective maxim is self-love, the general object of which again is felicity, happiness, one's own satisfaction. But felicity, as already said, though naming a lohole of satisfaction, and though, in such generality, an ascension over the random contingency of particular desire, cannot furnish a law ; it is but a general title over infinite diversity : no two, as we saw, are agreed on happiness : but even were there agreement among, us as to the object of happiness, the foundation would still be pathological and contingent, devoid of the necessity of a law. LECTURES ON THE PHILOSOPHY OF LAW. 21 In fact, it is plain that Kant sees happiness, though a general name, to be still — as its aim is enjoyment — a particular desire. There is, theu, a will that takes no note of happiness, that respects itself, and is respected just as it tramples down happiness, just as it tramj^les down self-love. This will, independent of all sensuous motive, obedient only to its own self in its own reason, to its own law, to its own categorical imperative, is free will. And how such pure rational form, free from all sensuous matter, should be adequate to objective commands, a priori binding, and universally necessary — to categorical injunctions good for all rational beings, it is not difficult to understand. Were it not so — were there not a practical voice of reason, unmistakeable, irresistible, clear, intelligible even to the commonest, it is plain to Kant that morality would be destroyed. I may mention here one or two of Kant's illustrations in his general support — " Labour when young not to starve when old : " here plainly there is a condition offered you, and the j)rescript is only hypothetical. This is not so, however, in the case of such a propo- sition as " you must not promise falsely : " there the command is categorical and direct. Kant asks, too, " under penalty of death, would you, at command of the King, give false witness for the destruction of an innocent man ? " and points out that your own state of mind will prove that you can die rather than so act, as it is clear there tliat you at all events ought to. In this way, Kant shows the eye of duty to be bent forward to work only, and never thrown backward to consequences. That active duty is attended by a sense of doing what is right, which may be called satisfaction, cannot be doubted ; but it is not for this satisfaction — it is not for the satisfaction expected — it is only for the command given that duty acts. Many a one has died for duty, at the stake or on the wheel, with scarcely a feeling but that of the physical suffering, knowing only that it was necessary for him so to do. It is absurd, then, to convert moral satisfaction into pleasure (eudremonism), and assert the same to be the sole rule of action. That man must have a disinterested nature — that man must be thankful for small mercies, who can see in such cases (as death on the wheel or at the stake) a satisfaction for the enjoyment of which he would readily die ! It is thus, then, that Kant, contrasting subjective, empirical, con- tingent, hypothetical maxims, dependent on pathological, material desire, with objective, pure, apodictic, categorical imperatives, dependent on absolute form of reason — it is thus, I say, that Kant in the existence of the latter makes good the fact of free-will. In this matter Hegel only follows Kant, bringing ultimate abstraction to all, ultimate completion, ultimate system, ultimate support. He, too, accentuates free-will — that to Hegel also is the whole ground and basis of the practical world. " The object of the science of Eight," he tells us, " is the human will, with special re- ference to the relation of the particular to the universal will ; " and free-will, accordingly, is that will which hears the universal only — 22 LECTURES ON THE PHILOSOPHY OF LAW. which implicitly obeys the universal — let the interest of the par- ticular be what it may. He contrasts the phenomena of will with those of physical nature, and insists on the inapplicability of the law of causality to the former. In this law he observes the cause, but repeats itself in the effect — the motion in the ball is the same motion that was in the bat, the water on the street, is the same water that was in the rain-cloud — but we see no such identity be- tween the motive and the act of will. The motive does not repeat itself in the act : the act is the expression not of the nature of the motive, but of the nature of the agent who is simply roused to put himself into operation. Here it is no mere effect that we see passively repeating the necessity that lay in the cause, but a wholly new power in act, a power that meets actively what comes to it as motive, that changes its direction, that modifies it, and can even negate it. " Circumstances and motives," exclaims Hegel, " master a man only so far as he yields to them. . . . He who appeals for excuse to such influences only degrades himself into a thing of nature : his act is his own, not that of somebody else, not the effect of something external to him." But Hegel goes systematically to work here, and displays at large the nature of the will, and accord- ing to every movement of the notion. The will, in fact, is an excellent illustration of the notion, for the will is concrete, the will just is the notion. The will is the Begriff, that that ideally be- grips or be-grasps all, that that ideally involves or implies all ; or it is that in whose pure negativity, in whose pure self to self ideality, the whole foison of the universe potentially lies. So, it is specially in its own form proper ; so, it is specially universal. Will can re- tire into its own self, will can abstract from all and everything, will is the possibility of pure universality. It is this possibility that is the condition of volition itself: without this power of reflection, without this power of abstraction, it would be in vain to talk of volition at all, which only is, if it can keep itself indefinite. This then is the moment of universality in will in which it abstracts from every determinate state of its own self, and, under every de- termination, remains indeterminate and equal to itself. Man can abstract, in suicide, from his very life : the beast cannot, whatever anecdotes to the contrary may be told to amuse us. But the will cannot remain abstract, it must realize itself ; uni- versal will must pass into particular will, and the question now is. What shall be willed ? If only the gratification of our sensuous needs and greeds, then evidently what is willed is something foreign to will itself, sometliing limited, something contingent. Will, even there, knows itself not the particular greed, and capable of denying suck This is freedom, but it is only freedom in form, only formal freedom ; it is not material freedom, not freedom in matter : and without freedom in matter, there can be no true freedom, no free- will. To that it is necessary that will should will its own self. And this is the singular, this is tha moment of singularity ; here LECTURES ON THE PHILOSOPHY OF LAW. 23 will is present only with its own self, and so free. But how shall will will its own self ? How otherwise than by willing its own thought. Will is but thought, thought is hut will. Free- agency is the realization of one's own self, but that is thought, and the realization of thought as thought can only take place in ethical institutions — in Law, Morality, and the State. In exposition and illustration of these three moments of will much can be alleged, and, by Hegel, has been alleged. A word or two in regard to this must now suffice however — As regards universality, for example, that is really just one aspect of man as capable of generalization, as the powder that generalizes. The focus, the imndum vitale in man, is simply generalization, which is only another word for thought. But to generalize thought is the same thing as to universalize will. The least is driven ever by an individual conception, by an individual motive ; but man in both respects will be controlled — ultimately — only by the uni- versal. And what a difference this makes one can see without difficulty. To have a habit — as a beast may have — is one thing, but to hioiv I have a habit is quite another thing. In this latter case reflection has set in ; the habit is not only known, but what is other to it, its opposite is known, and a judgment that may negate the habit becomes at once possible. The particular, in short, is now received into the imiversal, and may disappear there. There are times when such disappearance becomes the one historical fact. During the French Eevolution, it w'as the universal of will alone functioned. Every jxcr^fci^/ar, accordingly, was nought — even the particulars, particular after particular, then and there suggested — and madness ruled the hour, destruction w^as the lord of all. ISTot a single particular, not one difference could be tolerated, whether rank, or birth, or fortune, or talent, or virtue, or even beauty. That will can withdraw itself into the abstract universal, and become actively the universal void, is here evident, just as it is evident that it can be- come also, in the worship of Brahma for example, the passive void. As concerns will in 'particularity again, that form is familiar to all of us, for it is will, as each of us, for the most part, uses it. This is the form that is commonly either opposed or defended as free-will, and, as we have seen, both opposers and defenders are equally beside the point. Sufiice it to say here that man certainly receives from nature a variety of desires, and that, as a natural being, he obeys these. That he should so obey, however, is not for him a necessity ; man is also a rational being, and can receive every particular at the bar of the universal. It is his, then, to raise the desires of nature into motives of reason — to convert them into the rational system of social life, and when he obeys them then, he but obeys his own self However limited, contingent, subjective, our desires may be, it is certain that they can be freed, articulated, and objectified into an organic whole — Law, Morals, and the State. This is the " liberty of a wise restraint" this is " the necessity in duty 24 LECTURES ON THE PHILOSOPHY OF LAW. that will make wsfrcc" and the man who knows not so to restrict and restrain himself, will never come to anything. Only he who can accept the limit will ever reach the true illimitahle. This limitation, in fact, is the true concrete will, the particularized universal, will in the moment of singularity (and singularity here has not the meaning of individuality). This, in a word, is the true free-will. For what is tliis but thinking will — will, then, that wills its own implement, its own self. And it is certain that to be a free being it is only necessary to be a thinking being: the right of freedom is but the privilege of reason. What Hegel calls objective spirit is but the recdizaiion of free-will — of will, rational will, think- ing will, substantiating itself in actual outward fact. That actual outward fact is the world of Eight, the rational system of obser- vances, legal, moral, and political, into which a community of reasoning beings, by very nature, and that is hj very nature of the notion, sunders. So, however, will only works itself free from its own individuality — its state of nature — emancipates itself from nature into reason — realizes itself into the substantial freedom of organized universality. What we have here, in fact, is the great distinction — in a moral reference — between subjectivity and objec- tivity. When I think what is mine only, when I do what is mine only, I think a mere subjectivity, I do a mere subjectivity, which in rei'um natura, which in the universe of things, is simply nothing and nowhere and of no account ; but when I think and do what all in thinking and doing can appropriate and call theirs, then I think and do an objectivity, a concrete and a permanent that actually functions in fact. To such a word as mine, subjectivity and objec- tivity give a double accent. What is mine subjectively, as of this special particular passing individual who now speaks, I must italicize; but what is mine objectively, I must write in small capitals ; for that mine is MINE as belonging to my essence, which is humanity as humanity, reason as reason. The italicized mine is what sunders and separates and isolates us, each from the other, as so many uncommunicating and incommunicable individual distinct atoms ; whilst the mine with a double accent, the mine in small capitals, is what brings us all togetlier into a concrete unity, into a living universal. And it is here that we can discern our only duty which is to raise subjectivity into objectivity, the contingent indi- vidual into the necessary universal. Almost, we might say, our only duty is twice to italicize " mine," or our only duty is in tliis way to negate the negation. To italicize "mine" once is to*set subjectivity, to destroy " mine," really to negate it ; but to italicize " mine " twice, is to set objectivity, and negate the negation. Now this is the one object of education — or this is Mdiat ought to be that one object; for education is not a mere chattering of vocables. Nature is a system of mechanical necessity ; every one member of it is in blind interdexiendence with and on all the rest, and none is for itself. Tliis, too, is the case with man, so far as what is called LECTUEES ON THE PHILOSOPHY OF LAW. 25 nature in hiiu is concerned. Nature in man, in that sense, is his needs and greeds, and in these man is bound and not free ; but there is in him the possibility of freedom : he can reflect, he can retire into his universal and negate nature — nature in the sense that it is the individual particular. Reflection does not remain by the particular that is presented to it, but opposes to it another — opposes to it its own contrary. Now, precisely this is the business proper of education — to rouse reflection, to convert instinctive action into reflective action, and reflective action into free action — into the free action of the emancvpated universal. So it is that our needs and greeds, our vanities and vainglories, and all that holds of mere nature in us, are controlled — our own essential will, our free-will realized. " Education," says Hegel, " has for object to raise man into a self-dependent being, that is, into a being of free-will. With this intention many restrictions are imposed on the inclinations of children. They must learn to obey, so that their individual or special will in its dependence on sensuous needs and greeds may be sublated, and their true will freed." In man, then, evidently, there is a possibility that lies not in the lower animals : his will may be raised from a will of nature, a will of the particular into a will of reason, a will of the universal ; but there exists in tlds world no power that could raise their wills so. The lower animal is adequate to a imrticular only : its motives are individual incitement after individual incitement, each of which it only blindly obeys ; universal it has none. On the other hand, it is the single antithesis of universal and particidar that makes the whole world of man : that cross is the foundation of his science ; that cross is the foundation of his law, morals, politics, art ; tliat cross is the foundation of his religion. The antagonism that lies in tliis cross is the pulse of history, each beat of which is but the con- version of the lower into the higher. This antithesis or cross has hardly yet been looked at by any man in full consciousness, as it were, with his eyes open, perfectly aware of the importance of what he looked at. Nevertheless, it is the ultimate and absolute secret : it is the Notion, the concrete notion. No highest philosopher for centuries will have anything to do, but to make this notion explicit, bring it into full consciousness. Free-will, as we have seen, is but another name for it, and free-will is but a will according to con- scious motives. Those, then, as we have seen already, who have hitherto discussed this question have simply mistaken the hinge on which it turned, whether they supposed themselves to attack, or whether they supposed themselves to defend. It is as erroneous to say on the one side man must act by motive and is bound, as to say, on the other side, man can act without motive and is free. Man miist act by motive, and it is the very necessity of that must that frees him. If man coidd act without motive, he were not free, but bound. It is the eifistence of conscious motive that proves the 26 LECTUEES ON THE PHILOSOPHY OF LAW. existence of the universal, and in the subordination of the particular motive to the universal motive lies freedom. As Hegel points out, then, that man is free because he can do what he likes, is a concep- tion very wide of the mark. In short, man is free because he can not do what he likes : man is free because he must obey motive — man, that is, in reference to the universal in him. Similar blunders are not rare in philosophy. There is subjective idealism, for example. Well, because in the relation of a subject and an object, there is no possible way of the former knoioing the latter but within, it is argued that the latter also must he within. That is, the very reasons I allege for knowing an object tvithout are used by sub- jective idealism for not knowing an object without. That that alone renders a knowledge of externality possible — the very con- dition in which that knowledge roots — is used for the annihilation of all possibility of its own progeny ! "We see the same thing again in regard to a substance and its qualities ; a substance can only make itself known by its qualities. Such is the temper of the day, that because that is the case, it is supposed to be philosophy to say, though it is only in consequence of its qualities that a substance is known, it is also only in consequence of its qualities that a substance is not known, and just because it is only in consequence of its qualities that it is known ! Here again we see the very condition of knowledge is made the very reason of ignorance — the reasoner looking very grave at the result, pulling his collar up, and calling himself a philosopher. As it is in these cases, then, so it is in that of free-will. It is only in consequence of sensation that we can know an external world, and therefore, it is only in consequence of sensation that we cannot know an external world. It is only through qualities that a substance is known, and therefore it is only through qualities that a substance is not known. It is only through motives that a free-will is possible, and therefore it is only through motives that a free-will is impossible. It is really marvellous how long very respectable men, how long the whole world, will allow itself to be stultified by such transparent hocus-pocus. It is not moral necessity but moral freedom that we should say of will then; for in truth the necessity of will is the only freedom. All outward things, all things of nature, have their very essence in mechanical necessity; but all inward things again, all things of reason, have their very essence in freedom, and so it is that the two worlds are opposed. Will is universal; there is no object its that it does not make its ; it can abstract from everything. Will, then, wills its own self, and, therefore, is it free. The will that wills its own self must not be conceived as self-will however. The will that must indulge itself in every motive it wills, is a vain, weak, spoiled, sensuous will, and is generally named self-wiU, or caprice. That is a will given up to mere nature, and is not free but bound. There is a will again which we name wilfulness ; a will, that is, that will LECTURES ON THE PHILOSOPHY OF LAW. 27 not give up what it wills, and for no other reason than that it is it wills. Such wilfulness is sometimes regarded as constituting strength of character ; but without the universal, it is as weak as the will that I have called spoiled will, and certainly, for the most part, far more dangerous. It is neither the indulgence of spoiled will, tiien, nor the stubbornness of wilfulness that makes freedom ; it is only the universal, and in the universal lies the community of mankind. All take part in an action, aZZ approve or disapprove, for each in will feels himself universal, and through that universality reflected in the other. This subject of free-will — which, as has more than once tran- spired, is the root of law, and which I have been obliged somewhat to lean on as the very principle and centre of the philosophy of law, — this subject cannot be better closed than by a sentence or two direct from Hegel : — ' " Of no idea is it so generally known that it is indefinite, am- biguous, liable to the greatest misconstructions, and, in reality, consequently, subjected to them, than of the idea of free-will, and none is in current use with so little intelligence. But, as we may express ourselves, the free spirit being the actual existent spirit, or the spirit that actually prevails in human affairs being the spirit of free-will, misconstructions in regard to it are of the most enormous consequence ; for when persons and peoples are once for all pos- sessed by the abstract notion of freedom as such, freedom on its own account, no other has such iiTesistible power, and just because it is the very inmost being of spirit, — its very actuality and self Entire quarters of the globe, Africa, and the East, have never had, and have not yet this idea. The Greeks and Eomans, Plato and Aris- totle and the Stoics, had it not. On the contrary, they conceived only that a man by his birth (as Athenian or Spartan citizen, &c.), or by strength of character, by education, by philosophy (the wise man is free even when a slave or in chains), only so did they conceive a man to be free. This idea came into the world through Christianity, in which it is that the individual, as such, has an infinite worth, as being aim and object of the love of God, and destined, consequently, to liave his absolute relation to God as spirit, to have this spirit dwell- ing in him. Christianity it was, namely, that revealed man in him- self to be destined to supreme freedom .... This idea, then, is the very actuality of man, and not that he has it, but that he is it. Christianity has made it the very actuality of its adherents, — the very actuality of its adherents, not to be a slave for example. If reduced to slavery, if the control over their property is to depend on caprice and not on laws and courts of justice, then they find the very substance of their being violated. This volition of freedom is no longer an impulse, an instinct that demands its gratification ; it is now character, — a spiritual consciousness that is above impulse, that is above instinct. But this freedom, this free-will, and free- agency, that possesses such implement, such filling, such aims and 28 LECTUKES ON THE PHILOSOPHY OF LAW. ends, cannot remain as notion only, as mere principle of the mind or the heart ; it must unclose itself into objectivity, — into an organic actuality, lecjal, moral, political, and religious." This, then, is the position we have now reached : that man, as free-will, is the objective spirit, and must realize himself in the institutions, legal and other, by which society lives. In one word, then, the matter of law is our own free-will, and its existence in the state is but its realization. It is the course which this realiza- tion, in obedience to its very principle, takes that we have now to see. Free-will, then, is the root of all, and freedom, liberty, itself must constitute the contents ofliight or of Law. But free-will, at first, taken just so, is abstract, is without this development of its contents into its own concrete system — is, as yet, but notion ; it is not yet idea. So it is, as yet, but direct or immediate to itself and us ; it is, as yet, but one and single. Thus immediate, direct, single, one, it is a Per- son. But free-will is essentially an action, and that action is essen- tially a movement from within outwards. Now, the nearest outer to its own self is another — another person. The first prescript of Eight, then, is. Be a person, and respect others as persons. It is plain also, that in this abstraction there are no other interests present — no variety of concrete interests as under morality. There is no concrete with its various composing members or interests to disturb beside it. There is no interest in question but the single interest of free-will, no command but that will is to be free. But, as between persons, that amounts only to a prohibitio7i — obstruct not the free-will of the person. This prohibition is also categorical ; it gives no reasons for itself ; it interposes no conditions ; it is cate- gorical, and not hypothetical. It does not require, as is required in morals, the other person to follow it with intelligence, assent, con- viction ; it never asks for any motive or design, or intention on the part of the other person. It simply says, categorically. Infringe not the free-will of the person, or violate not personality. These con- sequences really flow directly from the nature of the case. So it is, then, that this division of Right — the first — is but formal, ab- stract, without any concrete filling, implement of humanity as such. Or personality gives the capacity for legal rights ; it is the founda- tion from which all abstract, formal right arises ; but even as such, it is only abstractly universal. There is no particularity in it, as in morals, no special interest that concerns me as an individual, say. It has no thought of my individual advantage or welfare ; and is whoUy indifferent to my agreement with it, to my convictions in its regard, or to my designs and intentions in the realization of it. The very abstractness of the universality here has its own limita- tions, then. To be a person is, in one sense, to be what is highest ; but to be a person is to let all our other concrete humanity fall, and be also what is lowest, or, at all events, least. So it is that we find LECTURES ON THE PHILOSOPHY OF LAW. 29 the individual wlio is only a person, the individual who only fixes himself in his right, for the most part so thin and naiTow. We see, also, that it is generally the rude and unformed man who so stubborns himself in his abstract right, while the richer, fuller nature has an eye for every side of the interest at stake, and has no difficulty in complete resignation of his abstract right. An exalted sense for formal right may prove in the end but mere wil- fulness, indeed — a formal will, that in its own intensely pure for- mality, can only remain blind to every concrete consideration beside it. I recollect of a case, indeed, where a poor man nearly ruined himself by the consistency of his faith in formal or abstract right. He was the landlord of a workshop ; and the tenant, with- out consent asked or given, took it upon him to enlarge the old win- dows in this workshop, and open new ones. The workshop is mine said the landlord, and you have infringed my rights. But what I have done, said the tenant, I have done at my own expense, and what I have done is an improvement to the property. I admit that, said the landlord, but you had no right to make alterations in 7iiy property without my consent, and I will take you to law there- for. Accordingly, this landlord did take this tenant to law ; he lost his case before judge after judge, and he was just on the point of taking it to the House of Lords, when death kindly stepped in, and by its abstraction did justice to his. Here was a true instance of exalted devotion to abstract right, but the concrete injury did not stop there ; for the tenant, disgusted with the doings of the landlord, neglected his business, neglected the property, allowed a valuable boiler to burst, became in the end bankrupt, and left a workshop that was worth a great deal to the landlord worth next to nothing to his heirs. So much for the worship of formality. The higher nature, then, may, in view of other and more concrete interests, let its formal right fall. And it is very subtle on the part of Hegel to point out, accordingly, that formal right is only a possibility, for a possibility, as he expressly defines it here, " is a Seyn, a being, an existent something, that has the import also not to be," and we can see that in the interest before us. My abstract right is, but how often is it also not ? as I think it not worth while to assert it. That is, abstract right, beside concreter interests, has only the significance of a possibility, and it has its own felicity when Hegel remarks further, that accordingly, the legal assignment here is only an Erlauhniss or a Befugniss, which, I suppose, I may translate by "permission and title — the meaning being that such rights may remain empty, and be nothing but a permission to, a title to. Nevertheless, though such be the dangers of formal or abstract right, the importance of the position must not be lost sight of. Neither individuals nor nations are even concretely advanced until they have reached a knowledge of the stage of abstract personality. Such advance must be allowed to have 30 LECTURES ON THE PHILOSOPHY OF LAW. been largely an achievement of the Eomans, of whom it may be said, in reference to their legal assignments, that their greatest feat even in the very acme of their development was to perfect this consciousness — to perfect the inviolability of the person as person ; for the particular individual, if richer, more concrete, is so mostly on the natural side, and it is consideration of the universal individual, the person, that brings freedom. " In personality, indeed, it lies that I, as, on all sides of me, in inward desire, need, greed, and appetition, and in direct outward existence, this perfectly limited and finite indi- vidual, am yet — as person that is — pure self-reference, and know myself, even in my finitude, as what is infinite, universal, and free." In abstract Eight, then, it is the mere universal will that is con- sidered, without respect of the individual in his further concrete interests, or in his (moral) convictions and intentions : it has no object but the human free agent as such. In short, free-will respects only its own self. Even in the other it respects only its own self. So it is that each is a person, and so it is also that all the edicts of law here are interdicts — all its positive commands are in ultimate instance inhibitions. This by reason specially of the very abstract- ness of the person. I may add here that, if in respecting other persons we respect also ourselves, it is "very important to see that in respecting ourselves we respect also them ; and this is a profound lesson to that morbid self-contempt that, in these days of loudness and superficiality, is so common in the quieter and the deeper. But the Person cannot remain abstract : he must realize his freedom, obtain objective existence for it; the notion must become idea. So abstractly immediate, so abstractly direct to its own self as will on this stage is — and at the same time so abstractly inner to its own self — for plurality, the consideration of persons, makes no difference here, each is but a person, and as empty and abstract as the other — so abstractly immediate, though inner, then, what different thing will can here realize itself in, will be itself imme- diately and externally abstract — a thing, an external thing. But for will to realize itself in an external thing is to take possession of it — is to enter into its Property. Of course. Gentlemen, you see what all this amounts to. In this mode of statement, when one part of a subject is completed, and it is now necessary to go to a new part, this new part must introduce itself, and not be just turned to. Thus we saw how, the intellectual powers having been discussed, and the turn of the active powers being now arrived, these latter were not just tacked on to the former, but the former actually became the latter. Theory, by a turn of the hand, became practice ; intelligence, will. Now will, thus come upon, is as yet undeveloped, and so it can be figured as still some- thing single, one, internal to its oivn self, abstract, &c. But will that can be so described corresponds to the definition of a Person, and is LECTURES ON THE PHILOSOPHY OF LAW. 31 therefore a Person. Again, this abstract personality must realize itself, but, being so abstract and internal itself, the other, in which only it can realize itself, must, on its side, be externally abstract, &c. — that is, an outward material tiling — Property. I am not sure that you will yet altogether relish this new mode of proof; but I think you will now see something of its nature. We have now once for all arrived at Property; and Property, Contract, and Penalty shall be the themes of our two remaining lectures. 32 LECTURES ON THE PHILOSOPHY OF LAW, LECTURE III. Gentlemen, — In our last lecture, we saw the realization of freewill into a person on the one hand, and property on the other. Tree- will itself was the terminal result into which all that held of theory had collapsed, — a result which, simply as that and no more, was necessarily undeveloped. But this undevelopedness gives freewill, as we so have it, a character of singleness and oneness — or this undevelopedness and firstness, so to speak, give it a character of abstractness ; for that is abstract — as sweetness, whiteness — that is in isolated self-identity only. And we can see that if whiteness is abstract in consequence of its isolatedness to self, for the same reason the broken-off hand of a watcli, or a separated main-spring, is also abstract. In short, any one member of a concrete is, being isolated, abstract : so any one moment of the notion or of a notion — the universal, the particular, or the singular — being isolated, is abstract. Freewill, then, as it lirst emerges, has, being undeveloped, the character of singleness, oneness, and abstractness. But a will, a freewill, single, one, and abstract — that is a person. This personality now must realize itself, for if overtly, explicitly abstract, it is also latently, implicitly concrete, and that for no other reason than that it is will — thinking will. But realization takes place always through something else or other ; now, to such an abstract inner, what can be other but a similarly abstract outer ? and that is an external thing, property. These considerations are hard, for they are wholly peculiar and wholly new — in this peculiarity and strangeness they may not carry conviction either — stiU they will be allowed to possess their own subtlety and felicity. Again, it must not escape notice that the machine engaged in the manipulation and working up of aU this is the notion : we have but a single substance, a single material, all through, passing from roUer to roller of the various moments. Will, coming to us as bare result, is the undeveloped universal that, in itself, or implicitly concrete, must strive forward into its correspondent particular, and thence further into its coiTespondent singular. This is the march everywhere, and, so far at least, w^e may acknowledge in the person a moment of universality as in property a moment of particularity. LECTUEES ON THE nilLOSOrHY OF LAW. 33 The most common sense passage I can find in Hegel bearing on these points is this : — " All things are capable of being made man's property, because man is freewill, and, as such, in and for himself" (that is, responsible, amenable only to his own self) ; " but what is opposed to him has not this quality. Every man has the right, then, to set his will in the things of existence, to sublate them, and make them his ; for they, as external, have no self-end ; they are not the infinite reference of self to self" (which every subject is) ; " they are even to themselves externalities. The lower animals, even, are such externalities, and, so far, things. Only will is infinite, absolute to all else, whilst all else is only relative. To make them mine is at bottom, consequently, only to manifest the dignity of my will as compared with external things, and demonstrate that they are not in and for themselves, or have no self-end. The mani- festation itself takes place in this way that I set in the particular thing another end than that which it immediately had. I give to the lower animal another soul than what it had. I give it my soul." It is in this way that Hegel places us in presence of freewill and of an outer world in which it is to realize itself ; and he really believes that he never makes a single step in advance without its own de- duction. "We are once for all arrived, then, at the notions of person and property : the one the abstract, self-mternal immediate, the other the abstract, self-^jcternal immediate. This word imme- diate I have used before, and it always gives a certain difficulty ; but what is separated, isolated, secluded to its own self, what is abstracted (or abstracted from) is something taken out of all its he- mediating connections and relations, and so therefore something immediate and direct. Hegel treats the subject of a philosopliy of right vmder the three great divisions of Abstract Eight, Morality, and what he calls Sitt- lichJceit ; and the principle that guides him in this is, as always and every wliere, the notion. The first division, that is, is but right in its universality ; the second, right in its particularity ; and the third, light in its singularity. But though such is the succession in Hegel, we are not to suppose that the latter members depend upon the former as earlier in time or superior in dignity. That they are members is what we must not allow to escape us, and that the truth conseqiiently is the one concrete whole. Still, for all that, Hegel is not quite without an historical consideration here — say, in the transition from abstract law to subjective molality. Law, as treated elsewhere, is very often referred to a moral basis, while here in Hegel, morals, on the contrary, would appear to be referred to a legal basis. Now that is not without a certain historical support. It cannot be denied that what Hegel means by morality was repre- sented — fairly represented — nay, very perfectly represented, in the person of Socrates ; while what he means by abstract right did not reach full historical development till under tlie Eoman Empire. Still it is not in Socrates, but in Christianity, that Hegel acknowledges c 34 LECTURES ON THE PHILOSOPHY OF LAW. the veritable historical first of subjective morality, or the law of conscience, inner righteousness, on the one hand, and of the law of love on the other. And surely these are correct ideas — surely it was only after Christianity that tlie individual, and not isolatedly, but in connection with the whole community, came to know the full im- port of what is named moral experience. Christianity it was that wrought as a purifying ferment in the souls of men, abasing all the greeds of sense, shaming the lusts and prides and vanities of self, awakening repentance, chastening the heart, and leading the soul generally into candour and simplicity and humility and love. Now that is precisely the position of subjective morality, and as opposed to abstract right. Under the latter the requisite is only to do the right, no matter whether you agree with it or not, and no matter what your motives, intentions, or general spirit may be. But morality is plainly an internalization of such a standpoint, of such a material. While the standard under law was without, it is now under morality within — it has become conscience. And really the one step may be regarded as having led to the other : only after men had long mechanically and unreflectingly obeyed law did they come to make its prescripts their own principles, did they come to see that these prescripts were but what their own nature, and no mere external authority, commanded. But the moment the faintest edge of such an experience as that was received into the heart, morality had begun. Morality, then, is but a particularization of law, or it is but law in the moment of particularity. Law, namely, as we have seen, is wholly universal. Its prescripts are directed only to the abstract person, only to freewill as freewill. But there is an advance in concretion now : the person has become a subject, or better, a neighbour. And the very word neighbour opens a vista into a sphere of concrete interests infinitely^icher and more compli- cated than that connected with the abstract rights of a person. What Hegel means by Sittlichheit, again, is a still higher advance in concretion. This word really means simply morality. The Sitte is but the Greek ry^os, the Latin Mos, our own Cus- tom. What Hegel sees in it, however, is the substantial custom that has sprung from objective reason, and is fixed, established, stereotyped in the conscience and practice of a people. So it is that I translate it observance, sometimes instinetive, sometimes sub- stantial observance. And these words, I think, will pretty well con- vey the meaning, though it must be confessed that the task of a translator here is excessively puzzling. One wrong translation I will refer to. I have seen the word SittlicKkeit translated conven- tionality. But that is a mistake. Early in one's studies, no doubt, such a translation has its own temptations ; but it is entirely to miss the matter in hand to yield to them. What we mean by conven- tionalities are temporary customs, mere arbitrary agreements. Thus it is a convention when leaving home and desirous that your friends should call on you when you return, that you pay them a visit to LECTURES ON THE PHILOSOPHY OF LAW. 35 say goodbye, or, in their absence, leave a card for them with P.P.C. — pour prendre covgd — written on it. That is a convention. Again, it used to be a custom that when the representatives of a family made their periodical and ceremonious call on another family, the gentle- man in handing in the card for himself and wife, bent in a corner of it with his thumb. JSTow that is something purely and simply con- ventional. But such conveutionality is very remote indeed from the Hegelian Sitte. By it we are to understand something not sub- jective but objective, not contingent but necessary, not arbitrary but rational — something fixed, permanent, established — something looked upon as sacred and springing from a sacred source. I have tried all manner of English words for it, and once thought I had got over the difficulty by translating Sittlich, Sittlichkeit, and Sitte, re- spectively by the terms ritual, rituality, and rite, but had to give them up too, what they suggested being either too ecclesiastical or too externally ceremonial. Were we to reserve the Latin morality for Hegel's Moralitcit, and the Greek ethicality for Hegel's Sittlich- keit, the end so far would be pretty well attained, but we should still want a word for Sitte. It is this word Sitte that I propose to ren- der by observance, and I really have been qiiite unable to find any single English term that would suit better. Could we use custom — the commonest term of all — that indeed woxild be preferable, but 1 think your ears will tell you that that is impossible, at all events at first. If we consider it well, there is an abstractness, a one-sidedness observable in will, whether as manifested in right, or as manifested in morality ; whereas in observance will is concrete, and any such defect disappears. In right, for example, will is realized in some- thing merely external, while in morality again it is realized only internally in the contingent individual subject. This is not so, how- ever, in regard to the Sittlich, the observational, Avhere what is inner is also outer, and what is outer is also inner. Take filial obedience, for example, there is a Sitte, a sacred usage, a civil custom, a sub- stantial observance, and we can see it to be no less real as an outward act than as an inward sentiment, and no less real as an inward sen- timent than as an outward act. Societary usage that is as well socie- tary sentiment, or societary sentiment that is as well societary usage, — that, then, is SittlichJceit, that then, is observance. In such usage we see society to be in enjoyment of what we may call the second or higher nature ; such usage, or the system of such usages, we can see also to be capable of being named the substance of freewill, a sub- stance which each individual freewill, each member of the society knows to be that individual member's own proper substance. He then possesses virtue, ethical personality, whose whole nature is per- meated and pervaded by this substantial life, who regards accordingly his particular place in the system as not negative to him, but peace- fully accepts it, trusting implicitly in the whole, and ready to sac- rifice himself to it ; and this is so, not as regards the State only, but as regards every one of its subordinate particular institutions. 36 LECTURES ON THE PHILOSOPHY OF LAW. We see, then, the nature of Hegel's threefold division of the science of right, and we see more particularly that this division has been prescribed by the notion. The first division, abstract right, or what we may call legality, is will in the universality of the person ; the second, morality, is will in the particularity of the neighbour ; and the third, Sittlichlccit, ethicality, or we may even say politi- cality, is will in the singularity of the citizen or political subject. Of course the series, legality, morality, politicality, as well as the series, person, neighbour, citizen, can only correspond to the series universality, particularity, singularity, when the words of each are precisely understood as Hegel understands them. Understood as we understand them, person, neighbour, for example, are perhaps each less universal than citizen. Both words, indeed, neighbour and citizen, are, as used here, my own, and there must be seen in them only Hegel's notions. The same principle that conditions the general classifications conditions also tlie subordinate ones, and when legality or abstract right is divided into Property, Contract, and Penalty, it is still the march of the notion through its moments that Hegel sees and would have us see. What respects form, how- ever, will perhaps be still more intelligible when we draw into preciser consideration the matter discussed. The essence of property, as w^e have seen, then, is that a physical object — an object without will — is transformed from its own brute externality and meaningiessness into an embodiment of free will. In property, accordingly, there is a union of two factors ; of free will on the one hand, and of an external object on the other, and this union is as necessary to the one as to the other. If the object acquires meaning and function only when it is taken up into the life of the person, this person, for his part can become manifestible only through the object. Singly and in disunion either element is abstract, only in union, only together are they both concrete. From this, then, we see at once the tautology of the prescript that what I can take as property must be res nullius; that va sans dire; for what already expresses free will is already my will, and no longer an alien object that only waits embodiment. Again the will, as we have it in the person, is, as has already been discussed, very evidently single ; what it takes into possession must be single also. It cannot take possession, then, of genera, or of the elements. The person, in his singleness, cannot take possession of the genus vegetable or of the element air. Being single, he cannot make private property of what is universal. Even to make good his right of community in what is universal, this universal itself must be converted into singles, as into breaths of air and draughts of water. We are to perceive here then, that it is the nature of the person rather than that of the object that is the dictating element ; just as it is this person's will, and not the fact merely of his being first, that enables him to make anything his. It would be idle for freewill to make its what were already its; and to make mine LECTURES ON THE PHILOSOPHY OF LAW. 37 what is his is to negate freewill, is to negate my own will. For property is an absolute assignment, and no mere result of mutual agreement. This is not mine simply because of my acknowledg- ment that that is yours. This is mine, that is yours, because free- will as freewill has set itself into either. Freewill is embodied in property, and tlirough property is the intercourse of freeM'ill with freewill mediated. But as this is so, or as it is the possession of property that gives objective reality to my freewill, it is my duty to possess property — property, I say, and not such and such pro- perty. What and how much property I may possess are not con- siderations that belong to our present sphere, where we are confined to the abstract right of the person. Of that person, however, it is cer- tainly not only the right, but also the duty, to bea possessor of property. And here I may point out the importance of the lesson indicated. It used to be very much the fashion to run down riches and cry up poverty — especially wherever and w'henever it was supposed that the young w^ere in hearing. The bliss of poverty and the bale of riches — this was set us in every copy line. ISTo page of any primer but was sonorous with it, and it was rounded into our ears in every new tongue we came to — Latin, or Greek, or French, or German. We heard it in Church too, just as we heard it at home, or as we heard it in school. And when we came to the University we were assured by the Professor of Morals that that was philo- sophy — that that was wisdom. Then we read it in the ancients and we read it in the moderns: Cicero and Horace and the seven wise men, Simonides and Phocylides and the rest, were for ever talking of it, and even in these very days our last great man asserted, as by an authority de par le roi, that if he had a true man to bring up, with the heart of a man in him, he would say rather let him be poor ! It may seem very bold then, should I at all hint disagreement here w4th an opinion that has been so long, so variously, and so authoritatively sanctioned. Nevertheless, it does seem to me that the effects of this opinion have not been always good. I fear that too many a bright young literary soul has been led away by it, despising money as money, and undervaluing the honest industry that was to bring it, marrying improvideutly, living au jour lejour, believing that every mouth brought its own bite with it, and trusting quite unmis- givingly to the future, till having piped his best all his summer of youth like the grasshopper, he w^as refused food by the ants and told only to dance his best in the winter of his old ag^ Of course, I would not for a moment have it supposed that I take^he opposite extreme, and counsel the pursuit of riches as man's sole business. These very days of ours are not less full of the futility of that vul- garity than of the disappointment and regret that are the end of the former delusion. What I have only to point out here is that it is the duty of man as man to possess property. In truth no man is a man till he is also a proprietor. Then it is only that he has entered into the concrete life of the state, and is of any true 38 LECTURES ON THE PHILOSOPHY OF LAW. value — then it is only that he has attained life — a concrete life for himself. He is a person now, a citizen, a neighbour ; no nerve or artery of the whole but meets in him ; he lives the whole and enjoys the whole, and feels in short that only now properly can he say that he lives at all. How different the young literary enthusiasts who will not make money, but will only pipe ! These, after all, live only an abstract life, and they feel themselves in the end, not as their fellows, but isolated and apart, lonely, useless, miserable. This, then, is the lesson here, that it is about the first duty of man- hood to respect property, knowing that only through property does a man enter into the state and become one with the concrete. So it will be advisable that all those j^oung literary enthusiasts who threaten to live only abstract lives should undergo apprenticeship in a lawyer's ofiice. There probably sooner than anywhere else will they be brought to sanity as regards property. It is the duty, then, of every freewill, of every person, to possess property; and so far all freewills, all persons, are equal. And here it is we get the true light on that equality that is so current among certain political parties now-a-days. All human beings, that is, in so far as they are persons, are not only free but equal. Equality and freedom are by no means convertible terms however ; they are not even in direct, but rather in inverse proportion. Hegel's own expressions in this reference are amoug his happiest and most exoteric, and I think you will not ask me to beg pardon for follow- ing them here pretty closely. Hegel commences by admitting that it is not incorrect to regard the main interests of a constitution as centring in what the words Freedom and Equality imply ; but he complains that, as generally used, they are abstract and can only lead to the destruction of the concrete that the state is. This concrete itself, the state, is precisely what on one side introduces inequality and must introduce in- equality ; for the distinctions of rulers and subjects, of ranks and classes, of authorities and of those amenable to these, are insepar- able from it. To carry equality rigorously out then would be to put an end to these and the state itself. Then it is said all men are equal by nature; but it is quite plain that when physical nature is meant all men are rather unequal by nature ; while, by natvire the notion being meant, all men are indeed so far equal, but not to the exclusion of infinite inequality otherwise. That we should be pAnounced equal as persons, as men — and not as in Greece and Eome because we happen to be certain men, and not certain other men — this is not the product of nature but of the conscious- ness of the deepest principle in our spiritual structure, and of the long and laborious evolution of this consciousness into its present universality. Again, as said, equality as persons does not exclude infinite inequality otherwise. That all citizens are equal before the law has no extension beyond that legal equality of the person. Otherwise, or the person apart, we are not more equal before the LECTUKES ON THE PHILOSOPHY OF LAW. 39 1^"^ than away from the law. It is precisely according to that inequality away from the law that the law itself indeed taxes us. In regard to taxes plainly, it would be monstrous injustice in the law to regard us all as equal, though, at the same time, it must and can be led only by what it sees equal in us in regard to property, age, ability, sex, &c. As regards freedom again it ought not to be taken abstractly as the freedom of subjective self-will. Legal restriction ought to be seen to be the true freedom ; and formerly, precisely such restric- tions used to be called the freedoms, the liberties. In effect, every veritable law is a freedom, a liberty, for it is a result of objective reason. In the best sense, it is not true, then, that the state is but the mutual limitation of each other's liberties ; in the best sense, on the contrary, the state is a realization of liberty ; for in reality to restrain particular or formal will is to emancipate universal and substantial will. We see but a similar mistake when it is said too, that modern nations are more susceptible of equality than liberty ; what is in question here is but abstract equality and abstract liberty, and it is only right that abstract presuppositions in regard to liberty, as these are, should be found to Ireak on the realm of reality and fact as more rational and powerful in its concretion than they in their abstraction. It is more correct in this reference to say, on the contrary, that the high development of the modern state introduces the greatest concrete individual inequality; while, on the other hand, the deeper rationality and the firmer stability of the laws lead to a proportionally greater liberty, which also they can more readily concede and endure. The very word liberty more- over implies a certain antithesis to equality, and the more firmly established liberty is as the security of person and property, as opportunity to develop and make available talent and other advan- tages, the less there is of equality, and the more of liberty itself even in a subjective sense, as that of the will of the individual. These are excellent reflections, Gentlemen, and they readily sug- gest important applications. It is that cry of equality that is the dominant phenomenon of the day now, and we may understand it in its true light by the assistance of these observations of Hegel. The workmen find themselves as good as their masters, the servants as their mistresses, our wives as their husbands, and they all cry equality, meaning only an abstract identity that is utterly impos- sible. So much does the cry continue extending, neveMiheless, that we may presently expect to meet a demand for the equality of children with parents, or to hear the tailor complain that it is very unjust he should be a tailor, the dancing-master similarly rebel against his vocation, and grocers and haberdashers and linen- drapers, and even perhaps lawyers and lecturers — all complain that they are very ill-used individuals, and insist on the original iden- tity which is their birthright. That word identity, indeed, mirrors the whole matter, and we simply see that the differences are tired 40 LECTUllES ON THE THILOSOPHY OF LAW. of being differences, and would fain sink to rest together in the negation of the blank identity which were the only equality. In short, it is the old story of the revolt of the members, the state being substituted for the belly as that that is to be destroyed. It seems indeed to be the creed of the highest enlightment now-a-days that what is called a state is but an expensive superfluity ; that society, civilization, is nothing but, the raising of commodities and the exchange of them, and that no control is required there but that of the policeman to keep the workman quiet. Accord- ingly, with this end in view, we are exhorted to doctor and parson ourselves, and I suppose I may add, lawyer ourselves and lecture ourselves. If we would cure the evil, we must cure it in the root, however, that is we must quash the raising of commodities itself ; for it is quite certain that from that root the whole ramified and overshadowing calamity springs. To raise a single commodity, taking the commodity as a commodity, and not as a single cabbage or a single potato, supposes the whole iniquitous system, supposes workmen and food and clothes and ships and railroads and steam- engines — supposes science, and all the rest in short ; and all the rest, as the concrete differences, can only be kept together in the single concrete identity, in the single concrete life that is the state. Common sense would seem to suggest, then, that we should be far better employed in telling the story of Menenius now-a-days, than in exhorting the hands not to carry and the teeth not to chew. In further connection with the subject of equality, Hegel refers to the proposal of an equal division of property, and convicts its " emptiness and superficiality" from the very nature of the case. " Not only external nature in its contingency but the entire round of spirit in its infinite individual developments, though under a rational organic whole, falls into particularity ;" and in saying as much, Hegel intimates that existence, whether physical or meta- physical, must obey the law that lies in the moment of the notion named the particular, and inequality is inevitable — not only so, that is, but we must thankfully see it to be so, and that it is only "an empty superficial understanding'' which, in its abstractions, can blind itself to it. It is but the same blind understanding, too, that complains of the injustice of nature in the inequality of her distributions ; for nature, as without freedom, is neither just nor unjust. As for its being the right of every man to have a suffi- ciency, He^l remarks, that this, so vaguely spoken, " is only a well- meant, but, 'as what is well-meant generally is, non-objective moral wish, the question at all of sufficiency besides not falling to be dis- cussed under property, but under civil society." It is but in har- mony with such views that we find Hegel referring to the Agrarian laws and pointing to the triumph — though at some cost to right otherwise — of the more rational moment in the struggle that took place in their regard between public and private property in land. Family Pacts and Fidd commissa in the same connection, Hegel also LECTUKES ON THE PHILOSOPHY OF LAW. 41 mentions here as opposed to the right of personality and conse- quently to that of property. In regard to Plato's republic, he remarks that it fails in the moment of particularity, and is unjust to the person in making him incapable of private property ; and as for pious benevolent brotherhoods for a community of goods, we are told that such an idea may present itself without difficulty to a moral imagination that misunderstands the nature of right, free- will, of spirit, in its moments, and reminds us that Epicurus objected to some friends of his who had made such proposals that, in the moral and religious reference, they are bad, for they manifest mis- trust, and those who mistrust each other are not friends. Further, observes Hegel, " the equality which might be introduced as to distribution of goods, would, depending as these do on industry, speedily dissolve itself again. But what is not to be done, neither shall it be tried to be done. For men are indeed equal, but only as persons, only as regards the principle of possession. By virtue of that principle it is the duty of every one to possess property. If we will speak of equality, this, then, we must regard as the only one. But the question of particularity, what and how much I may possess, that belongs elsewhere; and the allegation is false that right demands equality of property for all of us, for right demands only that each of us shall have property. Bather it expressly is in particularity that inequality has its place, and equality there were unright." In short, private property is a necessity of reason. Free- will must realize itself; that is, necessarily in an outer as outer. Will as will is also singular or individual. Property, therefore, is personal, is tliis particular property, is mine — is this particular property of this particular me. " Seizure is the enunciation of the judgment that a thing is mine. My will has subsumed it — given it that predicate of mine. It is the right of will so to subsume in itself all external things whatever, for it is in itself the universal, while they, not referent of themselves to themselves, are only under necessity and not free. It is in right of this relation that man takes to himself all outer things, and makes of them other things than they are. He treats them so only in accordance with their veritable nature." Hegel considers this to be the case even as regards the body and life itself: those, "like all other things," he says, " I possess only in so far as it is my will," and he adds " the brute cannot mutilate or put an end to itself; only man can ; the brute has itself indeed in possession ; its soul possesses its body ; but it has no right to its own life, because it does not will it." Of course, if it is as will-less that external things are capable of being taken into possession, the same reason applies to the lower animals, and we may reconcile ourselves to the whole position, it being premised as necessary and indispensable condition that there shall be no cruelty, that they shall be with us happier even than they would have been with nature. As for the putting of them to death, that, so far as it is only that, is not cruelty. An animal 42 LECTUEES ON THE PHILOSOPHY OF LAW. reflects not, it knows nothing of death, thinks nothing of death : its life is as it were infinite, an infinite affirmation, for of the two negatives, birth and death, between which this affirmation hangs, it knows nothing ; its life, consequently, is fairly infinite, and death is no diminution to it. How different with us ! " We look before and after, : And pine for what is not : Our sincerest laughter With some grief is fraught : Our sweetest songs are those that tell of saddest thought." Man's life alone of all below is to its own self a life of limitation, a life of finitude: all other lives, even those of what is inorganic, if we may figure its existence so, are to their own selves infinite; for to their own selves they begin not, and neither do they end. Strange too, it is the very finitude of them that makes their infinitude ; it is man's very infinitude — the infinitude of his thought — that makes the finitude of his life. And this may be regarded as, in its way, an argument for the immortality of the individual soul ; only such immortality were justice to man; for the privilege of reason is but a privilege of pain. To Hegel, then, even the body, nay, the mind itself, requires to be taken possession of to become in actuality ours. Culture, edu- cation, is required for both. The body, in the immediacy of its existence, is inadequate to the soul, and must be made its ready organ and its animated tool. The mind, too, is at first, as it were, immersed in nature, and requires enfranchisement. " This enfran- chisement is in each subject the hard lahour against mere subjec- tivity of action, and against the immediacy of appetite, as against the subjective vanity of feeling and the arl3itrariness, or caprice, of self-will. But through this labour it is that subjective will attains to objectivity and becomes capable and worthy of being the actuality of the idea. For so particularity is wrought into universality, and through universality becomes the concrete singular." My body, as mine, must be to another sacred, then, for violence is done my will when violence is done my body. My freedom is my body's freedom, and I cannot be degraded into a beast of burden. It is this immediacy of body to mind that makes the difference between an offence to the person and an offence to one's more external property. As regards monstration of possession, the human shape divine is for personality alone ample credentials and authenticity enough ; but it is otherwise in regard to external things generally ; for the possession of wliich monstration is indis- pensable. It is only children, as Hegel points out, who allege bare will as proof of property and as against monstration ; and it is certainly not uncommon to find one child trying to prevent another from seizing something by calling out, " It's mine." Mere will will not suffice men, however ; for them monstration of some kind is imperatively necessary and rationally so, for an outward objec- LECTURES ON THE PHILOSOPHY OF LAW. 43 tivity can alone guarantee the inward subjectivity. The setting of will in an object is certainly the notion of property, but there is required also a realization of this. Seizin, seizure, occupation, possession, or the taking into posses- sion, appropriation, &c. — the mode of this varies and must vary according to infinite conditions bearing on the nature of the object and the power of the individual. As a general rule, it may be said that the more I introduce formation into anything, the more I make it mine. It does not follow, however, that so to speak only mine in it is mine, that is, that the form alone is mine. If the form is mine so also is the matter, and it is a mere idle subtlety on the part of Fichte to suggest that the gold cup which I have made a cup is only my cup, and that it is another's to take the gold if he can. Truly, if he can ! A substance without qualities is an empty abstraction, and for the rest it is in the substance that I have set my will, and the formation is only a sign thereof In such cases there is really nothing, then, that, as masterless, another may take. Hegel treats the whole subject o^possession under the three heads of Seizure, Use, and Alienation, I and affects still to see in this the y^ moments ofthe notion. We may say, for example, that the affir- mation of will in an object corresponds to the moment of simple apprehension, while will that only uses an object only negates it — a process, as it were, of judgment, and will that alienates an object returns out of externality into its own self, which may be regarded so far as a moment of reason. For I may remark here, as I have remarked already, in the manipulation of the moments, it is often a convenience to substitute the concreter moments of simple appre- hension, judgment, and reason, for the more abstract ones of univer- sality, particularity, and singularity — a substitution for the rest, that throws its own light on the nature of the general ideas involved, which, however, I hope my first lecture demonstrated at fuU. To correlate seizure, use, and alienation with the moments of the notion, is, nevertheless, I fear, somewhat forced — a remark that must be extended perhaps to Hegel's immediate division here of Appropriation into Bodily Seizure, Formation, and Designation. In that triplet Hegel also affects to see an adumbration of the mo- ments of the notion, and points out that they are — which indeed they are — a rise in generalization, a rise from individuality to uni- versality. I know not that it is worth while for me to enter at length into all that may be said on these three forms of appropriation. Know- ing that I have to say so much in these lectures that is hard to understand, there is a certain temptation to expatiate on what at length will prove universally intelligible, and so get credit, as it were, for having said something at last ; but it appears to me to belong far more nearly to my duty to occupy myself rather with what is difficult, and so do at least some actual work in the way of explanation. Of the natural limitations of bodily seizure, of its 44 LECTURES ON THE PHILOSOPHY OF LAW. extension by inference to what is in connection with the amount seized, or of its extension in actual fact through artificial means — of all that I think I need say nothing, for a little reflection will suggest it to every one. As regards what is referred to as connec- tions, for example, there are conterminous rivers, seas, lakes, pas- tures, and hunting-grounds — there are rocks and minerals — there are alluvial deposits, strandings, and wreckings, waifs and strays, flotsam,jetsam,game, &c. As concerns such things, it is the under- standing that decides with its grounds and counter-grounds, and not the notion with its moments of reason. What concerns formation is as exoteric as Avhat concerns bodily seizure, and may be perfunctorily passed with quite as little scruple. It is evidently a more perfect form of monstration as a more per- manent and complete one. The cultivation of the soil, the planting of trees, the raising of cattle must all be regarded as instances of it. The protection of game may also be regarded as a species of forma- tion, and so also may the pasturing, hunting, and fishing of nomads, or other people that come and go, though, so far as monstration is concerned, they are less perfect. I add also that no formation can make a slave, can make property of a human being ; and the reason lies not in any expediency of the understanding, but in reason itself, in the notion : man is free-will, and must be respected as such. It is to be allowed, however, that in certain past times, slavery was not so wholly u.njustifiable, so far, that is, as many men then had not yet taken possession of themselves, had not yet formed themselves into free-will, but were, so to speak, in mere undeveloped externality and naturality, creatures simply of instinct and brute nature. Now, however, that the seat of industry is the ethical state, slavery is no longer possible, for the ethical state is but the realized idea of liberty. As for the remaining mode of occupancy, designation, or the em- ployment of signs, it is pleasant to see that such a man as Hegel, even with such an infallible touchstone and test in hand as the notion, must have had considerable difficulty in deciding as to what lie was to say of it, whether he was to say that it was more perfect or less perfect than the others. Understanding — and with all the mooning madness that his unintelligible dialect and dialectic have attached to him, Hegel's understanding is really about the toughest and soundest going — understanding seems to have led him to say, in the first instance, as to his pupils at Niirnberg, that " occupancy by mere designation of the object is imperfect." And really the attachment of a mere sign — some mere badge, some mere ticket, to an article, appears at first sight about the most partial, perishable, and feeble way of seizing that one can well imagine. So it is we find Hegel remarking in those Nlirnberg days : — " The sign, token, or ticket, that does not constitute, as formation does, at the same time the thing itself, is an object that has a signification which lies not in its own nature, but is foreign to it, while, on the other hand, LECTUKES ON THE PHILOSOPHY OF LAW. 45 that which is signified again has a nature alien to its nature. De- signation is therefore arbitrary. What a thing shall be the sign of, is more or less a matter of convenience." Even in the text of the Rechtsphilosophie, something of hesitation as to the relative ranks of the three modes of seizure still unmistakably betrays itself. There bodily seizure is spoken of as " on the sensuous side the completest mode, though otherwise only subjective, temporary, and restricted." "Formation" is called "the seizure the most adequate to the idea, as bringing to unity in itself both the subjective and the objective element." Nay, in the Rechtsphilosophie, it is directly said of designation itself, that it is " very indefinite." It is in what are called the Zusdtze, the additions after his death from public lectures, as supplied by students or his own manuscripts, that we find Hegel at last doing designation the justice of acknowledgment which he had all along done it of position : it was always third. There he points out the rise in generalization represented by the three modes in their relative places, which I have already alluded to ; characterizes designation as essentially intellectual, and there- fore easily applicable to an entire whole; and finally concludes thus : — " Occupancy by means of designation is the most perfect of all, for the other kinds of it are also more or less of the nature of a sign. When I seize a thing, or form a thing, the ultimate import is always a sign that, to the exclusion of others, I have set my will in the thing. The notion of a sign is namely this, that a thing does not stand for what it is, but for what it signifies. A cockade signifies, for example, the nationality of a man, though the colour has no connection whatever with the nation, and exhibits not itself but the nation. By this, that he can give a sign, and by its means acquire, man shows his sovereignty over things." Here, then, we see that Hegel is led to the truth at last, even by his own notion ; for there is no doubt but that designation, as in- tellectual, is the preferable mode of seizure. Thus it is that the mark, the token, the ticket, however msignificant, becomes signifi- cant. It is a great help and a welcome, encouragement to us poor mortals, however, to see our own weaknesses and hesitations reflected in a Hegel, and to know thus that we possess a common nature even with him. The transition from seizure to use is very characteristic of Hegel, and, of course, accomplished through the notion. It is im- possible to express this better than Hegel does ; but unfortunately it is also impossible to find direct equivalents in English for Hegel's German terms. I must content myself with some faint adumbra- tion of it. In seizure, will has made a thing its. The will is thus as it were positive in the relation, and the thing negative. But the will thus particularly determined by the thing is will in a particular volition, or particular will in a desire, and the negative thing further is at the same instant determined as only /or it and serving it, ministering to it. We have thus a particular will using a parti- 46 LECTURES ON THE PHILOSOPHY OF LAW. cular thing. If any one will take the trouble to analyze this, he will find that our last result has simply been put into the power of the Notion as so much material to grind — which it accomplishes through its successive rollers of the universal, the particular, and the singular moments. The illustration of Hegel's general pro- cedure, and the source and true nature of its figurativeness contained here, is, as it appears to me, exceedingly telling. The definition of use that is evidently the consequent result is this : — " Use is the realization of my desire through the alteration, destruction, consumption of the thing, the selflessness of whose nature is thus manifested, and which accordingly accomplishes thus its destiny." Hegel is said to have exclaimed once at table when the dishes were long of coming, " Only let them come — we will soon achieve on them their own destiny." He must, plainly, have had then in mind this sentence of his own composition. Hegel remarks of use that it is the real side of property, and that the perception of this lies at the bottom of the pretext put forth often in cases of wrongful occupation, that what is so occupied was unused. Nevertheless he decides that property is the universal, use the particular, and that, in the first instance, it is the former must be deferred to. Still he observes further, that formation, designation, &c., are in themselves external, unless will, actually present, give them meaning and value. Property, then, become masterless, as devoid of actual will, may be lost or acquired, in lapse of time, through prescription — which has thus a philosophical basis, and not one of mere expediency. For will to have, it is necessary for will to manifest itself. National monuments are national property, so long as the national honour and memory live in them : when these cease, they become the prey of him who likes. The extinction of copyright depends on the same principle, though in an inverse manner: literary productions become in lapse of time a universal property, and pass into contingent private posses- sion. Mere land, as burying ground, or otherwise privileged to non-use, involves a simply arbitrary unactual will, by infringement of which no veritably real interest is injured, and respect for which, therefore, cannot be guaranteed. Hegel has several very fine obser- vations here on attempted distinctions between property and use, on partial and temporary use, value, &c. ; but at present I can only refer you to them. It is in this connection that he remarks, " It is more than fifteen hundred years since the liberty of the person through Christianity began to flourish, and became a universal principle for a part — a small one indeed — of the human race. The liberty of property, however, has only since yesterday, we may say, been here and there recognized as a principle. An example from universal history of the length of time required by Spirit for its advance in self-consciousness — and a rebuke to the impatience of foolish opinion." LECTURES OX THE PHILOSOPHY OF LAW. 47 LECTURE IV. Gentlemen, — The last subject of consideration with us was the alienation of property through long omission of the manifestation of will in it. There the omission was indirect, and the step from indirect to direct omission constitutes the transition from the subject of the use of property to that of its alienation proper. A thing is mine when it is willed mine, and not mine, consequently, when it is willed not mine ; or, from that into which I have set my will, I can also withdraw it again. This is alienation which may be an act direct, explicit, and declared, as well as one indirect, im- plicit, and undeclared. What is alienable, however, must be by very nature external; whereas, what is by very nature internal, is also by the very terms inalienable. I cannot outer what is wholly and solely inner. Now, such is my personality as personality ; such my freewill, my moral sense, my religious conviction. These I cannot commit to the disposal of another ; for they are my very inmost being, my very principle of existence, my very self; and the nature of one's absolute seK is freewill, and that is freedom, liberty. I can neither he a slave then, nor have a slave. All compulsion is unlawful, hut that of laiv itself, which, properly considered, is no compulsion ; for it is the restoration of right, of freewill, not only to him who has been compelled, but to him who has been the compeller. Or, to put it otherwise, no man can be compelled, but to undo his compulsion, which evidently is the restoration of his own right. He who gives into the possession of another his capability of rights, his moral and religious principles, gives away what he does not possess. Let him once possess them, let him once take his own freewill into possession, and such alienation is impossible. Eetrocession from an immoral covenant, then, is no wrong, for the right that might be said to be wronged, as regards either contract- ing party, no matter which, never could have been his. The inviolable inner of my being is no externality, and once I have taken it into my possession as such, every externality is powerless against it. Nevertheless, a part is, as in relation to the whole, external; and I may alienate to another the temporary and par- tial use of my inner abilities. Were such alienation not partial, but complete, then I were again a slave. This question of partial 48 LECTUEES ON THE PHILOSOPHY OF LAW. alienation of what is in its nature inward leads Hegel to speak of right in reference to the various products of mind, and one remark here is this : " The merely negative, but indispensably /7^si!, further- ance of the arts and sciences is to secure those who work in them from theft, and allow them the protection of their property, just as it was the indispensably first, and the most important, furtherance of trade and industry to procure them safety from robbery on the roads." Hegel, naturally also, considers here the question of self- alienation, of the alienation of one's life, of suicide. The complete totality of our external activity, life, is not to the j)ersonality which it naturally constitutes an outer thing ; it is not my right to seek death, then, unless at call of the ethical universal in which 1 am held, and which is my substance. " Suicide," says Hegel, " may be possibly thought bravery, but it is the false bravery of tailors and girls." Still he seems a little soft to the suicides of the heroes. " When Hercules burns himself," he says, " when Brutus falls on his sword, that is the bearing of the hero to his own personality ; but when the question is of the simple right of suicide, it must be denied to the heroes as well as to the rest." The prohibition here, however, hardly seems a strong one, seeing that it appears to be admitted that there is an heroic bearing to which personal life is an externality. Property, as external, is in connection with other things external, which are also properties ; but the principle of property is will, and j)roperty to property is consequently will to will. This relation of will to will is the true and proper element in which freewill has existence ; and property, no longer through subjective will and an external object, but property through a common will, through the will of another — this is the sphere of Contract. And, perhaps, there is that in this transition which will reveal to you at last how the triplet Property, Contract, and Penalty, is conditioned by the moments of the Notion. In property, for example, the relation is that of a single will, in contract that of several wills, and in penalty that of the common or universal will. Very plainly then, there is here but the ordinary succession of the moments, singular, par- ticular, and universal ; and I may remark in this connection, that Hegel does not tie himself down to the universal being always first, but allows it freely to exchange places with the singular. The main moments with Hegel in his treatment of contract are the act of will which constitutes it — from the very notion, and that the realization is a simple consequence of this act, and necessarily contained or implied in it. " My promise in the case of a contract," he says, " implies that I, with my own will, have excluded something from the sj)here of what is mine, and at the same time, that I have acknowledged that the other person has received it into the sphere of what is his. The thing, then, by virtue of the contract, is already the property of the other, inas- much as, that a thing is mine, so far as it depends on me has its LECTUKES ON THE PHILOSOPHY OF LAW. 49 ground in my will. In so far, then, as I should not render to the other the matter of the contract, or fail to put him in possession of it, I should be infringing his property. The contract itself binds me to its realization." There is that in the relation of the mutual wills present in con- tract which is peculiarly interesting to Hegel. He sees in it all the features of the notion, and so, as he is fain to believe, its sanction also. He finds property an affair of wills now, and no longer to depend for manifestation on an external object. Contract, he says, is " the process in which there is exhibited and resolved the contra- diction that I am and remain independent proprietor, excludent of the other will, so far as, in a will identical with the otlier will, I cease to be a proprietor." I not only can, but must alienate property; for it lies in its very notion, that will should be made objective, external. But if it is external it is another — that is another will, as it were ; and so we have the unity of different wills — a unity in which this difference is at once negated and affirmed. This, how- ever, is the very movement of the notion, — the identification of differences, the differentiating of identity — and signifies the produc- tion of an identical will in the absolute difference of independent proprietors, in which each, with his own will and with the will of the other, ceases to be a proprietor, remains a proprietor, and heeomes a proprietor. It follows, then, that each issues from con- tract the same proprietor that he entered into it, or that there is virtu- ally between them an identical property, this is the value in which the articles of the contract are, with all their specific external differ- ences, equal to each other. So it is, says Hegel, that a Icesio enormis cancels the obligation of a contract. It is in this neighbourhood also that Hegel censures the unilateral and bilateral and other divi- sions of contract in Eoman law — accusing them of superficiality and confusion. Possession stands to Property as in a relation of substantiality to externality. Property, namely, is an assertion of will, of which possession is the internal reality. This same relation but repeats itself in contract in its two terms of agreement and fulfilment {prcestatio, solutio). The agreement is wholly substantial, it is in the element of ideality ; and the utterance of ideality — expression — is the sign. So the agreement brings itself through the stipulation, in the symbolical formalities of gestures or of speech (which last is the fittest expression of ideality) into a sign. The stipulation, there- fore, gives an outer body to the ideality of the agreement. Formali- ties, doubtless, get simpler and simpler ; still, for the conversion of subjectivity into objectivity, an externality is necessary, and formalities of some kind will remain as necessary for the expression of will, as speech generally for the expression of thought — it lying in these very words that the expression of will will reduce itself more and more to the expression of thought as such. The formalities of contract, then, are not there only to bring a fee to officials, but 50 LECTURES ON THE PHILOSOPHY OF LAW. that the mobile inwardness of will may be stereotyped in an out- ward and undeniable form. It is impossible to gainsay the value, in all cases, of the external 'proof : a thousand witnesses to the con- tents of a letter are really impotent beside production of the letter itself Where agreement and prestation are not simultaneous, then, the stipulation must be regarded as a real essential. What is implicitly meant must be explicitly set. The derivation of the word stipulation, as an outer expression to an inward will, does not seem quite certain. Kant derives it irom. stipula: the contracting parties broke a straw between them. Dr. D. C. Heron, again, has it that "whatever was firm was termed a stipulum by the ancients: probably from stipes, the trunk of a tree."^ The stipulation is the guarantee, then, that something does not lie only in the will, but actually is willed, and so lies out of will — a fact. The stipulation further, then, must be regarded as what in contract is legally substantial, or in the stipulation the transfer of property must be regarded as virtually accomplished. This is the declaration of the notion; but, of course, between the stipulation and the prestation there is allowed the usual latitude of understanding : understanding has always the fact of the equal value — in regard to what is given and what is taken — as basis and standard. Stipulation, moreover, as substantial, only applies to what is substantial — value. A contract is not a mere promise ; and the stipulation gives shape and fixture to the differ- ence. Fichte and others are quite wrong, then, in assuming the obligation in contract only to begin with the beginning of the pres- tation. Contract is an affair of legal, not of moral right, and has nothing to do with the secret intentions, the state of mind morally, of either side. Duplicity of moral meaning is not allowable in con- tract, and the stipulation is the embodied and undeniable guarantee of that. Prestation is but the inevitable result of stipulation, and that there are contracts — loans, deposits, &c. — in which agreement and prestation are simultaneous is no proof to the contrary. As regards the classification of contracts Hegel differs but little from Kant, and as it may be readily found by reference I shall not spend time in its exposition. Hegel points out that in contract will is not will as such, not absolute will, but, as limited to, included in, an outer object — so to speak transformed to it — is only formal will, individual will, self- will. That is, in contract the will is but natural will, the object but a natural object, and there is no necessity of reason between them : the will may express itself in the object, but it may also withdraw itself again. In contract, then, the wills are self-wills, natural, individual wills ; the one will that results is only one of community, and not of substantial universality; and the object, as at 1 Nevertheless, in tlie libris "Originum sen Etymologiarum" of Isiclorus Hispalen- sis, we find it said (iv. 24) : " Stipulatio a stipula, — veteres enim quando sibi aliqnid promittebant, stipulam tenentes frangehant," which would seem to be dead against Dr. Heron, who, for the rest, supports his own statement by no authority. LECTUKES ON THE PHILOSOPHY OF LAW. 51 all alienable by self-will, is only an individual external object. Neither the State nor marriage, therefore, are matters of contract. The State, for its part, is very evidently our natural absolute : we can neither enter it nor leave it by wlQ of our own : it is no result consequently of any artificial reciprocal agreement ; it is a natural growth, but a growth from reason ; it is a realization in time of objective reason, of the rational will. The State is a single national spirit, and it is that spirit which is the substantial contents of every individual subject. These subjects are indebted to it, then, and not it, in the first place, to them. The preservation of the State conse- quently is infinitely more than the preservation of the individual, and it is the latter's duty to perceive and acknowledge this. As regards marriage, there is a wonderful superiority in the teaching of Hegel to that of Kant. In fact, the sort of good old-maiden Kant is almost even disgusting here, and Hegel has a perfect right to speak of him as having exhibited the subsumption of marriage under the notion of contract " in its SchdncUichkeit ;" that is in its shame- fulness, or scandalously. Marriage to Kant, namely, is in so many words, a contracted interchange of the use of the sexual organs, and his whole exposition in connection with it teems with offensive expressions. It is only that old-maid enness of Kant, perhaps, that can supply any excuse for him. He has lived all his life, namely, at such a distance from the kindly mysteries of Hymen, that when he gets a chance in philosophy to approach them he cannot help extending a half- weak, half- wicked hand to the drapery. Hegel exhibits here an admirable contrast to Kant. To him the origin of marriage is ethical. The individual does indeed seek for him- self the substantial existence of his own naiurcd universal, the genus, the family, but the relation of sex in it takes on intellectual quality in a union of love and the spirit of trust. Sentiment, then, — feeling — is stiU the element in which the family lives, and its rights and duties are moral or ethical rather than legal, for the individual con- stituents of the family are members of its one unity, of its one per- sonality, rather than themselves persons, and the legal side is consequently subordinate to the moral. In this way Hegel deduces the necessity of monogamy, and presents the bodily union as rather a result of the ethical one. It is very true that we have all been much interested in certain views in regard to capture in marriage and other facts in its reference of an historical character, but the evolution in time neither dictates the evolution of the notion, nor renders it untrue. So far as time is concerned, religion may have begun in plant-worship, or brute -worship, or star- worship, or what- ever worship you please ; but, for all that, religion is a principle of reason, and has its own evolution of reason. The evolution in time generally is but — if we are to believe Hegel — the evolution of the notion in representation, as it were. As such external representa- tion, history, then, is but necessarily a scene of contingency, which contingency gives to the evolution a scattered, partial, miscellaneous 52 LECTUKES ON THE PHILOSOPHY OF LAW. look — even a look of caricature ; still, nevertheless, the evolution of the notion is but the evolution in time, stripped of its contingency. To arrange law, morals, and politics, according to the notion, there- fore, is not really to fall into contradiction with the phenomena of history how motely soever. Contract, as we have seen, then, is an agreement on the part of two wills — an agreement to a certain performance on the part of each, Now there are certain possibilities in this relation. The one term may have mistaken the other; or expression may not have corresponded to inner intention on the part of either; or per- formance in the case of the one or the other may fail. Suppose, then, in the first place, a mistake. In this case there is a differ- ence, but neither denies the right of the other : neither denies right as right ; each on his own side only insists on his right. Never- theless, there is wrong here somewhere, though both are by supposition innocent in its regard. This, then, is the position of unintentional wrong, unintentional injustice, and the result is simply the civil suit, the action at law. The position is different, however, if we suppose expression in the case of either not to have corresponded with the state of his mind. Here the wrong, then, is no longer unintentional, but intentional ; and the result is decep- tion, fraud. But so the wrong is criminal : it amounts to a denial of right as right, at the same time that it acknowledges it in form. But let us suppose, lastly, that there is intentional and express non-performance of the contract. In that case, the right of the other person is not only denied, but right as right is denied, and we have criminality in terms. Logically, as Hegel points out, in the unintentional wrong that gives rise to the civil suit, we have only a simple negative judgment ; it is only denied in it that such and such particular is capable of subsumption under the genus, under the general rule ; whereas in the case of crime, it is the genus itself, the general rule itself that is denied ; and the judgment is of the kind that is called infinite. To say this rose is not red, is to deny a particular, but implicitly to admit a general ; whereas to deny that fraud is crime, is to deny the genus itself, is to deny the per- son to be a person. This, then, is the sort of external statement of the various positions, but how are they internally ? how do they relate them- selves to the notion ? The notion here is that of will, particular personal will contracting with particular personal will under sanction and prescription of the universal will, of universal right. Now, the fact that it is particular will that is concerned, and in regard as well to a particular externality, some one article of pro- perty, introduces contingency, the possibility of accident. Neither will may deny the universal will, and each may insist on its right as particular ; but, in its own contingency, one or other may err. Again, in the second instance, or in the case of fraud, universal will is formally maintained by both, but it is secretly denied by LECTUKES ON THE PHILOSOPHY OF LAW. 53 one of them. In the third case, lastly, universal right as right is denied, and the individual sets up his own will in its place. Now, it is from this last that the notion of punishment, penalty, evolves itself ; and, believing the rest by implication intelligible, it is to this now that we shall confine our attention. The criminal, then, has done two things: he has negated the universal will, and he has affirmed in place of it his own particular will How is this disturbance of the true balance to be restored ? To negate the universal will is to do something that is in itself null ; and this null thing, to restore the affirmative, must be itself nullified. The criminal has resorted to force — a- negation, and this negation can only be converted into the affirmative by being itself negated. The negation of the negation, like a double nega- tive, effects position again, affirmation; and punishment is the true remedy. But again, the criminal has set up his own particular will in place of the universal will ; and as a free being, he has, in so willing, willed what ought to be, or what ought to be supposed to be, universal. It is but justice, then, that the criminal be sub- sumed under his own law — force. Nay, as a free being, it is universal will he must acknowledge to be his own true will; therefore, it is but the affirmation of his own true wiU that he must recognize in the negation of his own false particular will. The first result, in mere natural circumstances, of the assertion of a mere 2yccrtieular will as law, is the counter-assertion, and with equal positiveness, so to speak even, with equal right, of the opposite particular — this is revenge. But this counter-assertion, as itself proceeding only from what is private and particular, is itseK a new offence, and so there is initiated a progress, or better, a regress ad infinitum, as we see in the vendette of the Corsicans or of the Arabians. This continuity of an endless repetition is in- terrupted now by the judge, who, as disinterested representative of Eight qua Eight, rounds the action back into itself through retri- bution, and restores the universal will — the true will, that is, of the criminal himself. And we can readily see that the judge is the only proper administrator of any such function. His private feel- ings are not concerned — he is there for the universal only; whereas even the righteous man that would only revenge, that by re- taliation would only restore the disturbed balance, acts, and can act, only under private feelings — and probably under the private feeling that his wrong is wrong as wrong, and can only be atoned for by an utter negation — a negation that infinitely transcends the ori- ginal negation of the criminal himself. The only legal compulsion, then, is the legal retaliation of the illegal compulsion. He who has forced or deforced the law, must be in turn forced or deforced, and that can be realized only where he is seizable, only in his person or property. Of course the word force must be understood to have acquired a width of meaning here beyond its usual physical appli- cation : whatever is even passively illegal, as a negligence or even S4 LECTURES ON THE PHILOSOPHY OF LAW. a mere omission, is, as infringement of the universal, capable of being regarded as force. In the same way it is allowable to view the sensuousness and mere nature of children as so much force which can be redressed only — raised into the universal of reason — by so much counter-force of training and restraint, discipline and education. The natural will is to the rational will really in the relation of the particular to the universal, and the former must be negated into the latter. To the family as by law established, to the community as by law established, all untutored rude individualism of will or manner may be allowably said to stand as in a relation of force. Even suppose an entire society in a state of nature, that whole society may be convicted of force — force to its own uni- versal, and the resultant helium omnium contra omnes is but the necessary process for the discovery of the heroic will, which, in- stinctively universal, subjects the rest to itself. Mr. Grote would fain see this war of all against all brought back again ; for he would have no standard for the individual but the individual. He is so much surprised, indeed, that any one should think otherwise that he cannot help referring him to what he calls " notorious facts ; " and is thus absolutely blind to his own suicidal self-contradiction. Not only are the " notorious facts " he affirms the universal stan- dard he denies ; but that he, an individual, and claiming to be amenable only to the individual, should express surprise at an indi- vidual, simply for making good his own claim: this is the very ndiveU of self-deception, the very ncdveU of self-conviction, and the very ndiveU of self-confutation. Only in the possibility of such confutation, indeed, is it that there is room for the very existence of the State. Were there no universal, were individualism all, then there were no State. It is the same possibility then, the same fact, that constitutes the very foundation and the origin and the reason of penalty. Many have found much difficulty in this. The Stoics, for example, in assuming only one virtue, necessarily implied also only one punishment, as realized in the laws of Draco, which made death the penalty of offences and crimes alike. Freewill is realized in a necessarily varied externality, however, and the infringements of it are subjected to a correspondent variety both as regards quality and quantity. Analogous variety of punishment, then, is but jus- tice. It is gratifying to observe, however, that there is a decided tendency throughout all civilized communities to mitigate punish- ments, and all the more gratifying that this does not result from a laxer but from an exacter estimation of law and justice. It is be- cause the many so correctly regard the law that we can afford to punish less the few who err. In this way, we see that the character and amount of penalty does not depend altogether on the notion, but on the actual historical condition of the particular people. That is the circumstance that explains the apparent para- dox : the more a people abhors crime, the less it punishes it. Such a people is secure in itself, and stands not in need of extraordinary LECTUKES ON THE PHILOSOPHY OF LAW. 55 examples. It is probably this circumstance that has led some to oppose the punishment of death, and others all punishments whatever. Beccaria, for example, even denies the State any- right of capital punishment, and he assigns for reason that it is not to be presumed that the social contract contains the consent of in- dividuals to their own death. But the state is not a contract ; and, as the established universal, it possesses a right to claim the sacri- fice of the individual for its interests. To others, again, it appears absurd because of one evil to will another. Accordingly they either reject punishment altogether, or admit it only because of its ten- dency to intimidate, deter, prevent, &c. Such views, as Hegel points out, however, resemble the lifting of a stick to a dog : they do not really respect man, they do not really respect him as a free being, but treat him as a dangerous animal, that must be kept under. But punish- ment is an idea on its own account, and has its foundation in the very nature of the will, in the very nature of reason. The true, even to realize itself, must destroy the false : so the false will of the criminal must realize the true universal will, and it lies in the very notion of the relation that the false will should contradict itself, negate itself, and how can that be done but by submitting it to its own law ? This is to be borne in mind as against all that moral sublime which encounters us but too frequently in medical books now-a-days. In these we find generally a thousand physiological reasons pleaded in proof that the criminal but obeyed his own necessity, but did what he could not do otherwise ; and that the true punishment of the criminal is the rewarding of him by making him, through the infinite cares and privileges of public protection, a mere pampered pet, a sort of humanely and scientifically crammed animal ! This is to pervert the very notion of will ; this is to pervert the very notion of reason ; this is to pervert the very notion of nature her- self; for nature, when it is man that approaches her, is herself reason. No ; let us to return to health, let us abandon all these pillows and bolsters — all these feather beds of sentimentality on which vice is to fall soft, and let us tell men that they must be men, and that when they declare their self-will the universal will, they must be subsumed under it and abide the consequences. For this there is provided the universal law — for this there is provided the judge, who dispassionately and disinterestedly knows the uni- versal, and dispassionately and disinterestedly can subsume the wrong and the false under it. In the very criminal there lies the universal that is to do him justice. This universal, then, is his own, and in the very fact that it is his own, he has given his consent to its essential and necessary action even against himself The universal will has a right to negate what would negate if, and that very universal will is the criminal's own. The kind of punishment, then, depends on the particular crime, and on the particular condition of society, and that is an affair of under- standing ; but punishment itself depends on the notion, depends 56, LECTUKES ON THE PHILOSOPHY OF LAW. on reason, and is an inevitable and rational result. " An act of justice cannot be degraded into any mere means : justice is not exercised in order that anything but itself be attained and realized. The fulfilment and self-manifestation of justice is an absolute end, an end unto its own self" It is precisely in punish- ment that the criminal himself is honoured; and it is precisely by this that such punishment lies in his own act, that he is specially honoured. The particular will that is only the particular will, is an offence to the universal ; and must be sublated through its own very self into the universal again, with restoration of the pristine, rational, and absolute unity. Now, in the relation of crime and penalty, the edge of internality appears. The observance of law, namely, may, in many respects, be observance only- — an external and mechanical mode of conduct in certain references, without a thought further than the required externality; but this externality becomes deepened, becomes re- flected inwards, becomes internalized into inner ideal principles of right and wrong, in the relation of crime and its consequences. This is the more apparent when we contrast physical necessity with moral freedom. Only because the sun, the planet, the rock, the river, the sea, the clod, the plant, the animal cannot depart from the prescripts of its universal, is it bound, is it under necessity, and in- capable of imputation ; whereas it is only because the human being can contradict and oppose, and set himself against his universal, that he is free and within reach of imputation. It is in the relation of crime and its consequences then, that the majesty of the universal will, which is one's true will, and the nullity of the particular will, which is only one's false will, appear and mani- fest themselves: and in this way Bight passes into — Morality. The rights which we have just considered are often named natural rights. There is involved here an essential and fundamental mistake, however. In a state of nature, that is, there are no rights — in a state of nature there are only the unrights of cunning and of strength. Only in the civil community is it that there are really rights, and these are such as we have just seen sketched in refer- ence to the relations of Property, Contract, and Penalty. The sketch has been slight, but I trust it has not been altogether with- out true traits. I trust that you understand also, that it has been limited to Eight as Eight, and that the Moral and Political sections of the book we have had always in view have only been inciden- tally alluded to. I have said that for these lectures I had the advantage of the ex- amination of a considerable number of authorities kindly lent me for the purpose ; and that the result was to establish my confidence in the exposition of Hegel as regards depth and truth of insight. The consideration now of an objection or two will enable me, by the addition of a word on these authorities, to bring these lectures fittingly to a close. LECTUKES OX THE PHILOSOPHY OF LAW. 57 Eoder accuses the Hegelian exposition of " formalism," and of all nations praises the Italian for this that it has " fortunately let the Hegelian goblet pass by." As regards "formalism," there is a certain outside show of reason, for the Notion may be considered something merely artificial ; but as regards the Italians it is Roder who is " unfortunate," for in no part of the world at this moment is Hegelianism more in the ascendant than precisely in Italy : whether at Florence, or at Naples, or even at Eome, under Spaventa, and Mariano, aud Vera, it isHegelianism that, as philosophy, is taught. When Eoder further, then, accuses Hegel and his discij^les of " obscuring," " degrading," " distorting," " disfiguring," " caricatur- ing," " the simplest truths of Eights and Politics," " on the rack of an equally clumsy and unintelligible method," by the "trickery" of a new " scholasticism," &c., we have good grounds to suspect him of incorrectness, at the same time that we see internal ignorance to be the condition of the show of truth that applies to the outside. Eoder, for the rest, though writing clearly and with much detail, is all too plainly wholly under the power of the biassed and subjective Pan- entheism of his master Krause. Trendelenburg's is a good book, and by a very able man ; but, though, there is latently to be under- stood disagreement with Hegel, it is the spirit of Hegel that is the valuable element in it. This spirit, too, is what informs the work of IMichelet, at the same time that he must be pronounced largely original and valuably so, especially in historical references. What Hilden- brand gives us is a history of the notions of Eight, and not — at least as yet — a system. As a history, it is most excellent. In all German historical writers on philosophical matters now, there is a single common story, especially in reference to the ancients, but it must be acknowledged that Hildenbrand, for his part, tells this story with perfect elegance and ease, and with the most careful accuracy. I come now to Lassalle, who is a writer at once of original power and great importance. In recent philosophy there are few works of greater mark than his work on Heraclitus the Dark. His work on the Erbrecht also gains more attention daily. But Lassalle is an Hegelian, and he glories in the name. Nevertheless, he has an objection to the Bcchtsphilosophie of Hegel. This objection I believe to be a mistake, but as it concerns the one pressing question of the day, I shaU state it. It concerns, namely, the question of acquired rights, of property, and Lassalle looks upon the ideas of liberalism, of the bourgeoisie, of what we know as the passive political economy of the middle-classes, represented by Mr. Mill, say, as at once nar- row and erroneous in regard to it. He surely is not wrong in believing this qu3stion to contain the " politico-social thought that underlies our epoch," what " forms the inmost ground of our political and social struggles " now. This it is, he says, that " thrills the world's heart at present;" and "the mere necessity just to refer to this only shows in what soulless platitude and superficiality political prin- 58 LECTUEES ON THE PHILOSOPHY OF LAW, ciples are imdcvstood by the spokesmen of the liberal l)ourgeoisie." "The isolatedness," he continues, " in which the liberal bourgeoisie places politics — it is that which characterizes its standpoint and its mental horizon, and conditions its performances. It is this isolated- ness which gives at the same time to its political diatribes their astonishingly philistine colour," ..." a dead isolatedness in which the soul has resigned its life and its vision, to lose itself in mere words, and with words, on words, for words, to battle." He would oppose to this word-cultus substantial thought, and he points out the necessity of reconsideration scientifically of many particulars in the science of Pdght, in order to attain to a scientific theory of acquired rights. He says, " It is now more than forty years since Hegel published his first edition of his Philosophy of Ptight," and remarks that this work, from its historical conditions, could only be a first attempt to exhibit right as a rational organism, and censures his disciples for not having regarded it as a mere logical foundation on which it was theirs to build farther. He regards with Hegel the scientific evolution of will as alone capable of yielding a philosophy of Eioht ; Hegelianism is to him the " quintessence of all Wissen- schaftlichkeit," and Hegel's ground-principles, and method w-ill, he believes, always remain. But the principles of Eight are, as he also believes, no stereotyped logiccd category : they are substantial ideas that historically change and historically progress. Hegel himself did not, he thinks, sufficiently see this, otherwise he would have treated Law as he treated Pteligion, and would have demonstrated it in evolution through various historical stages. It is but Hegel himself then that must be used here to correct Hegel. Indeed " Hegel himself and his philosophy bear none of the blame here," is his slightly self-contradictory further avowal; "on every page of his w^orks Hegel is never tired of making it prominent that philosophy is identical with the totality of empiricism, that philosophy stands in greater need of nothing than of penetration into the em- pirical sciences ; reconciliation of natural andjjositive right, that was Hegel's object," but his disciples have neglected to carry it out into actual realization in the empirical or historical matter of law. In short, Lassalle would have Positive Law regarded as consisting of but siiccessive historical transformations of natural law, and he proceeds with great eloquence and fulness to illustrate this idea, with special reference to property. The progress of law, he remarks, is towards limitation of the indi- vidual's right to private property — towards the liberation of objects from individual dominion. We see this in the abrogation of Fidei Commissa even, though so much is this mistaken, that it is generally regarded as an increase of the liberty of property — a removal of its restrictions. This abrogation, namely, lessens the power of a pro- prietor over his own property. The same is the case with the " free competition" of the present day. That, too, is vaunted as a giving LECTUKES ON THE rillLOSOPIIY OF LAW. 59 freedom to the right of property, whereas it is rather a restricting of the power of the private proprietor ; for the thought in it is, there shall be no more monopoly, no longer any privileged individuals. The private property, then, that was once possible, is now impossible. Man, Lassalle substantially continues, at^ first, like the infant, stretches out his hands to everything — would make all his — recog- nizes no limits to his self-will. The fetish-worshipper breaks his idol when his desires are crossed, and thus treats his very gods as his pro- perty. Long after the rescue of these from such position, man him- self continues to constitute to man an article of property. The con- queror regarded the life of the conquered as his ; and slavery, at first unconditioned, then conditioned, has only in our own day been abrogated. Formerly one's wife was property, and could be bought and sold. Formerly one's children and one's debtors were so com- pletely in the same category that the former might be put to death by us and the latter taken as slaves. In like manner, the power of disinheritance was but a fuller right of private property, while sub- sequent legislation has been all in restriction of it. So the slave rises into the serf, tlie serf from privilege to privilege, into full eman- cipation. Here even the Jus 2^Timce noctis is a restriction of property ; the seigneur compounds for his right to the very life of the slave by accepting her virginity. The middle ages, though freed from slavery proper, are the very time when the human will ca,n, in all its three moments, be set as private property. Public will is then an object of such property on many grades, and this he illustrates by the privilege of sovereigns and other feudal superiors to arrogate a property in everj^thiug, air, and water, and tilings public, things religious, &c. ■ As for particular will being in similar relations, monopolies, and guilds, &c., are referred to, and as regards indivi- dual will in the middle ages, lastly, we are reminded of villenage, and of such rights even over the personally free as the choice by the feudal lord of a husband for his female vassal. The French. Eevolution Lassalle conceives to have been the sublation of said pri- vate property, and in all its three moments. As regards the present, it is incorrect, he says, to call this the age of individualism, and individualism the character of liberalism. Liberalism is particular- ism (as we may say, classism) : it Avants freedom, that is, not for the individual, but for the tax-paying, capital-holding particular, and that is a class. This is but a remnant of the middle ages, Lassalle believes, and must disappear. The social question now, he inti- mates in conclusion, is : whether, in these days, when there is no longer property immediately/ in another human being, such may exist mediately ; and he proceeds to describe the relative positions of capital and labour as we must daily witness them. It cannot be denied, then, that Lassalle regards the historical progress as e mancipio — emancipation, that is, a release from private property; and that such release is equivalent to the positive realization of 60 LECTURES ON THE THILOSOPllY OF LAW. human liberty. Neitlier can we well doubt that there is much in what he says highly worthy of our very closest attention (it is curious that we should have here in Edinburgh so recent and striking an example of portion of his doctrine in the changes we have seen effected on the Merchant Schools) ; still, what concerns us here is mainly the alleged correction of a defect in Hegel. ' And so far as adhesion to the right of private property is a defect, Hegel must be pronounced guilty of that defect. Hegel undoubtedly signalizes the advantages — the necessity of the institution of private property. Still, it is to be borne in mind, that it is the State that is to Hegel paramount — that to him the State is there with power to sist any contingent unreason of the lower spheres — that the State has a Machtspmch over all, and a perfect right of negation. This is manifest in almost every page he writes. Evidently, then, if Hegel is averse to the one extreme, the individualism of such men as Lassalle and Fichte, he is equally averse to the other extreme, the superficial pedantry of those spurious, passive, political economists, who believe their laws to be laws of nature, not reason, that need only be allowed to work on like gravitation or a waterfall; and who look forward to that day of light at length, when we shall parson, and doctor, and lawyer ourselves; and when the whole earth will be inhabited only by a single rational community of exchanging animals, with nothing but the buttons of the policeman to clear up, and shine away any foggy nodus of misunderstanding that may arise. That I take to be Hegel's position — a position, then, as it seems to me, that corrects the very correction Lassalle would offer it. It is not correct either to accuse Hegel's Rcclitsphilosophie of being independent of history, or of dealing only in stereotyped categories, like those of Logic and Nature. The Rcclitsphilosophie itself contains many references to history, and the wliole " Philosophy of History" may be regarded SiS just such reference by itself and at full. Eight, besides, is not Eeligion, as little as Religion is Art: the Bcc1itspMlosop)hie, and the Rcligionsphilos- ajyli ie, Siud the Acsthetik must he allowed to prescribe tbemselves each its own specific character. Neither can it be said, that in Hegel's philosophy of law, Hegel would have all regarded as fixed and stereotyped, a Seyn, and not a Werden, a Being, and not a Becoming. Hegel, on the contrary, is so convinced of the truth of an historical becoming, that he does not regard Zogic itself as fixed — in the sense, that is, of the impossibility of new categories. He will be found saying, that all revolutions in science, no less than in history, depend on this, that man has changed his categories, and preciser proofs to the same effect might be readily adduced. It is in place now to refer to Austin, and the remarkable contrast his opinions exhibit to those of Lassalle and Hegel. Of the public good this writer speaks thus : — LECTURES ON THE PHILOSOPHY OF LAW. 61 " "When I speak of tlic public good, or of the general good, I mean the aggregate enjoyments of the single or individual persons who compose that public or general to which my attention is directed. The good of mankind is the aggregate of the 2^i€:asures which are respectively enjoyed by the individuals who constitute the human race. The good of England is the aggregate of the pleasures which fall to the lot of Englishmen, considered individually or singly.'* This, you will observe, is the very voice of the modern English spurious enlightenment. According to it, what is, is but the various motely individuals, and no universal exists, but only a motely aggregate ; while good, again, is only enjoyment — 'pleasure. These are doctrines that know nothing of morals, nothing of the State, and nothing of the law : these are doctrines that, carried into effect, would, almost in an instant, scatter the race into an incoherent atomism of un- connected and irresponsible single savages. This really is the only word they deserve ; yet in his peculiar Wahn, so sure is their author of the truth of them, that he says, " AVlien it is stated strictly and nakedly, this truth is so plain and palpable, that the statement is almost laughable." He ought to have said, not almost, but quite laughable, though for a very different reason. This he does not say, however, but continues, this " truism is unknown in that notion of the public good which was current in the ancient republics." " Agree- ably to that notion of the public good, the happiness of the individual citizens is sacrificed without scruple, in order that the common weal may wax and prosper ; the only substantial interests are the victims of a barren abstraction, of a sounding but empty phrase." The state of Mr. Austin's knowledge, as regards all that constitutes the philosophy of history, is so plain here, that it is useless to point out more than the depenclenee of the individual on that universal — on that common stock which is his suhstanee, and apart from which he is little better than the gorilla our so enlightened modern science would make of him. As regards the labouring classes, Mr. Austin speaks thus : — " It is certainly to be wished, that their reward were greater, and that they were relieved from the incessant drudgery to which they are now condemned. But the condition of the working-people (whether their wages shall be high or low, their labour moderate or extreme), depends upon their own will, and not upon the will of the rich. In the true principle of population, detected by the sagacity of Mr. Malthus, they must look for the cause and the remedy of their penury and excessive toil. There they may find the means which would give them comparative affluence ; which would give them the degree of leisure necessary to knowledge and refinement; which would raise them to personal dignity and political influence, from grovelling and sordid subjection to the arbitrary rule of the few." The rule of the few is arbitrary and bad, then, to Mr. Austin ; but, if only the working-classes would 62 LECTURES ON THE PHILOSOrHY OF LAW. refrain from making children, we should have a heaven on earth ! This, with education, is Mr. Austin's panacea. Mr. Austin is, in many respects, a very worthy gentleman ; but it is his own wife (an admirable and amiable lady) who tells us, that " the experience of the thirty years which have elapsed since the foregoing lecture was written, does not seem to justify the author's sanguine anticipa- tions." I should like to read you several other extracts here which naively confute the doctrines involved by the wholly innocent but unthinking propos of a disciple who has got by heart only ; but.I must refitiin from want of space. I was prepared also to give some consideration of Mr. Austin's views of Utility, as well as to discuss, at some length, his ideas of the principles of law ; but I must now ■deny myself in these references also. If any gentleman, however, will consider that a command as such is to Mr. Austin the essence of law and morals, as well as in ivhat he places this command to give it meaning, source, reason, and authority, he will be able to form some conception of what I might finally say of him. Mr. Austin, in short, is one of those finical, over-refined, almost female minds, that, without power in themselves, attach themselves blindly to the guidance of 'another or others ; and his book is a work of infinite external verbal distinction, but it has not a vestige of internal thinking rationale. Heron's book is, to my mind, a book much more useful to the student, though it is very much of a fete mele, undigested compilation. Here, too, I have to suppress much. I have now to conclude these lectures by sincerely thanking you for the very kind and generous attention with which you have assisted me in a very dubious and difficult undertaking. MUIB AND PATERSON, PEINTEKS, EDINBURGH. s WHEWELL AND HEGEL, AND HEGEL AND MR W. R. SMITH: A i.V INDICATION IN A PH YSI CO-MATHEMATICAL REGARD. PREFATORY LETTER C. MANSFIELD INGLEBY, Esq., M.A., LL.U., Etc., Etc. My dear Dr Ingleby, — You may remember that I mentioned to you the first 'part oi ^^^SL^iudication, as designed to connect itself with the centenary^^ Kegel, now two years ago ; and that I requested to be allowed to dedicate it to you. Circum- stances interfered with the design of publication at the time ; and now that it is accomplished, but in association as you see it, I dare not fonnally dedicate to you what is allowed, as here, only the second place. Nevertheless, though precluded in this way from the directer action, it is still with this vindication that I specially desire to conjoin your name, and I presume, accord- ingly, to write its preface in a letter to you. Nor will the reason of this special desire of mine be any difficulty to you, for it was you who gently hinted to me the propriety of freeing Hegel, if possible, from the strong prejudice of scientific ignorance to which, since Whewell, he had very generally been submitted in England. I have the hope, then, that you will take kindly my prefatory letter, so far as the paper on Whewell is concerned. I have the same hope, also, as regards the other, its companion, in the mathematical reference ; for the occasion of that, too, you know, having done me the honour, I think, to follow its every aspect. I mean, of course, tlie little newspaper controversy into which I had been already led by the mentioned prejudice against Hegel, even before I had had an opportunity of examining what may be called its root in AVhewell. I need say no more to you, then, in introduction, or in indication of the motive of these two papers. As for the general reader, while I should like him to take 66 PREFATORY LETTER. witli him the newspaper controversy in allusion {Edinburgh Courant, Dec. 21-29, 1868; Dec. 28-30, 1869; Jan. 20-24, 1870), I should also like him to know in what manner that controversy originated. Sometime after the publication of the Secret of Hegel, the newspapers printed an extract, in depreciation of Hegel, fi'om a lecture by a distinguished university professor, on the part of whom, as I both heard and saw, other similar deliverances fol- lowed. One of these I at length noticed (Courant, Dec. 21, 1868). Hereupon Mr W. R. Smith, then a young gentleman of promise in science, assistant to the distinguished professor in allusion, was induced to communicate with the Royal Society of Edin- burgh ; and the further newspaper controversy ensued. Mr Smith, in his communications, however, travelled beyond what I considered the original issues, and was, accordingly, not followed by me further than these. But now that completeness in the general reference seems desirable, I attempt to answer his observations in full. If I am right in this answer, Mr Smith will be found to have fallen only into a mistake, and a series of mistakes, against which I know not that he can claim any set-off, unless on the plea of his youth at the time, the peculiarity, perhaps, of his position then, and the difficulty of Hegel. We might, indeed, be good-natured enough to excuse on these grounds his hasty examination and his unavoidable misintelligence ; but justice compels us to think of Hegel, and of the enormous injury that, with the most gratuitous cruelty, has been done his name and his fame in consequence. Thus, very much to Mr Smith is it to be attributed that, in so strictly scientific an organ as Nature, and on the part of one of the most distinguished of professors, there appeared (in the number for Nov. 30, 1871) so monstrous a misrepresentation as this, — Hegel " proved that Newton did not understand fluxions, nor even the law of gravitation!" Nay, may it not, in part at least, be attributable to Mr Smith that, with respect to Leibnitz, the same distinguished authority — but no ! I respect genius, I respect manliness, I respect Smel- fungus, even when he falls foul of the Venus de Medicis, and treats her no better than a cinder-wench I The occasions of these papers, being now, I think, intelligible, I hasten to conclude what I have to premise here. And, perhaps, I had better remark at once that I do not say, as will presently appear, that Hegel has any pretensions to be regarded PREFATORY LETTER. 07 as a pliysico-mathematical expert ; but I do say that for his position, and on the whole, he made himself very sufficiently acquainted with whatever he was minded to talk on, and his blunders are surprisingly few and venial. His principle of the notion demanded realisation everywhere indeed. Physics, mathematics, science in general, therefore, could be no excep- tion. Accordingly, even in these respects, the faithful labour he demonstrates is simply enormous ; and, far from exciting our ridicule, in consequence of the strange look of the new principle in the old matter, it ought to command our feincerest admiration. In physiology, for example, where, from speciality of education, I may be allowed something of the ability to judge, it would be a blunder to attribute to ignorance many queer things that are due only to the Notion ; and as it is in physiology, so it is in physics and mathematics. For myself, again, let me take here the opportunity to say that, as regards these latter, whatever I may claim for Hegel, I disclaim for myself all pretensions to the position even of a student now ; and I beg indeed humbly to apologise for my interference with them. This all the more, too, that I have felt it my duty to stand alone on the present occasion, unsupported by any aid fi'om without. I hope for excuse, however, if not in the compul- sion that seems put upon me, then in this, that Hegel, even in the physical and mathematical reference, is only metaphysically, or philosophically, employed. I have hope, too, that, be the result mathematically or physically what it may, perhaps no student of pliilosophy at this time will regret to have read these papers. It is proper to add, perhaps, that the paper on Whewell was written before the " Lectures" Avere thought of. And now let me close this prefatory letter by assuring you, my dear Dr Ingleby, that your ideal presence has been a great support to me in the course of it ; and that I am. Yours very truly, J. HUTCHISON STIRLING. Edinburgh, October 7, 1872. WHEWELL AND HEGEL, OR THE VINDICATION OF THE LATTER IN THE PHYSICAL REFERENCE, The writings of Dr Wliewell, alluded to in the prefatory letter, consist of those remarks and translations which, constituting Appendix H in the volume entitled by him, " On the Philosophy of Discovery," were communicated to the Cambridge Philo- sophical (Society, so long ago, for the most part, as May 21, 1849. Into the matter of these writings, it will be necessary to enter with some minuteness, and I begin with the translations as constituting the foundation on which the 7'emarks rest. From § 269 of Hegel's Encyclopcedia (2d Ed. 1827), Dr Whewell's first translation is as follows : — "Gravitation is the true and determinate conception of material Corporeity, which (Concejjtion) is realised to the Idea (zur Idee). General Corporeity is separable essentially into particular Bodies, and connects itself with the Element of Individimlity or subjectivity, as apparent (phenomenal) presence in the Motion, which by this means is immediately a system of several Bodies. Universal gravitation must, as to itself, be recognised as a profound thought, although it was principally as apprehended in the sphere of Reflexion that it eminently attracted notice and confidence on account of the quantitative determinations there- with connected, and was supposed to find its confirmation in Experiments (Erfahrung) pursued from the Solar System down to the phenomena of Capillary Tubes. — But Gravitation contradicts immediately the Law of Inertia, for in virtue of it (Gravitation^, matter tends out of itself to the other (matter). — In the Conception of Wciyht, there are, as has been shown, involved the two elements — Self-existence, and Continuity, which takes away self-existence. These elements of the Conception, however, experience a fate, as particular forces, corresponding to Attractive and Repulsive Force, and are thereby apprehended in nearer determination, as Centnpetal and Centrifugal Force, which (Forces) like weight, act up>on Bodies, independent of each other, and are supposed to come in contact accidentally m a third thmg, Body. By this means, what there is of profound in the thought of universal weight, is again reduced to nothing ; and Conception and Reason cannot make their way into the doctrine of absolute motion, so long as the so highly-prized discoveries of Forces are dominant there. In the conclusion which contams the Idea of Weight, namely, [contains this Idea] as the Conception which, in the case of motion, enters into external Reality through the particularity of the Bodies, and at the same time into this [Reality], and into their Ideality and self-regarding Reflexion (Keflexion-in-sich), the rational identity and inseparability of the elements is mvolved, which at other times are represented as independent. Motion itself, as such, has only its meaning and existence in a system of several bodies, and those, such as stand in relation to each other, according to different determinations." Now, I am a stranger, and I come to this prepared with all that is usually taught and mathematically formulised as regards the phenomena of centripetal and centrifugal forces, of gravita- tion generally in this universe — what am I to think of it ? 70 WIIEWELL AND I-IE(JEL, OR THE VIXDICATIOX OF What but this? I have before me not an active, sensible, intelligent man, with his wits about him, looking at the thing in a business-like manner, and treating- it so on the common stage of education and intelligence as it is now, but an out-of-the-way sort of body, a mooning creature with a craze, who, in pure ignorance, non-knowledge, non-education, non-intelligence, simply impregnates a mist of his own ^\dth confused figm-es of his own, that have no earthly application to the business in hand — as a Jacob Bohm or other mere stupid dreamer might do. That any reputable persons of the usual education and position, should be caught Avith such self-evident, gratuitous, muddle-headed nonsense, fills me with the ordinary surprise, regret, sorrow, which other such spectacles of human aberra- tion, — and they are matters of every day, — are knoAvn to bring to everybody. I have no difiiculty in the matter. In society I simply avoid, as much as possible, the bitten. This may be allowed fairly to represent the attitude of the unprepared, intelhgent, well-educated stranger who first reads the above passage ; and it is an attitude, surely, in the first instance, thoroughly well justified. " Which (Conception) is realised to the Idea." How can said stranger possibly realise such a phrase as that to his idea? "Connects itself with the Element of Individuality or subjectivity," " presence in the Motion, which, by this means, is immediately a system of several Bodies ? " What is all that ? he exclaims to himself, — " Were such things here, as we do speak about, Or have we eaten of the insane root That takes the reason prisoner ' " Then " gravitaiion, as to itself, a profound thought," but " in the sphere of Reflexion," etc. Surely it is but some infatuated wiseacre who can permit himself to canvas for credit by mouth- ing in that way ! " Matter tends otit of itself to the other." " Self-existence, and Continuity, which takes away self-exist- ence." " Conception, which, in the case of motion, enters into external Reality through the particularity of the Bodies, and, at the same time, into this Reality and into their Ideality and self- regarding Reflexion." What can all that, to the stranger figured, or indeed to any one, seem, but the purest midsummer madness *? " It may be sense," will be the thought only of the kindliest reader, " but, meantime, I am simply maddened by trying to think what instantly eludes every attempt to think it." It cannot be wondered at, then, that the conclusion of the stranger is, that he has before him only the pretentious verbiage of an ignorant charlatan. Let this stranger know now, however, that the wi-iter of the passage translated (or, as w^e may see, mistranslated), Avas really a man thoroughly awake — so far as activity, education, intelligence, thought were concerned, — a man so awake that THE LATTER IN THE PHYSICAL REFERENCE. 71 beside even the greatest of his fellows, he would show singu- larly manifestly, as the man who knew, saw, and could do. Further, let the stranger know the passage he has read is couched (even when Avell translated) in a language of its own, a language belonging to a peculiar general theory of the uni- verse which, however opposed it may appear to received doctrines of science, really is not so, but is in itself — once seen — perfectly simple, perfectly articulate, and perfectly in ac- cordance with general reason. So prepared, I say, this stranger will probably be ready, and even anxious, to listen further. Now, it is very difficult to give in any curt formula an intel- ligible conception of the Hegelian theory. Much depends on an understanding of its genesis, and that is a long matter. Kant and Fichte must be understood for that. Nay, the main ideas of every philosophical thinker, from Thales to Schelling, must be understood for that. Then, prepared as we all are at this moment, so much requires to be explained — for adequacy — that less than a volume would not suffice. Having, once for all, •undertaken to discuss the matter as here with reference to Dr Whewell, however, at least the attempt to explain is neces- sary, let it be as difficult as it may. I shall leave out a thousand needful considerations then, and endeavour to find such few as will suffice all present purposes. Hegel regards a thinking being as the ultimate essential drop of the vast crass universe. The universe is there for nothing but the production (to say so) of this drop. In the remotest crassitude there is a nisus to this drop. Properly looked at, this crassitude will be seen to rise in circles, ever less and less crass, toioards this drop. This drop, then, is the purpose of the uni- verse, and this drop is the purport of the universe. It is the principle of the universe, the soul of the universe, the self of the universe. That is — all else being merely ancillary and for it — it is the universe. As it is for it that the universe is, its idea is the potential first, or it itself is really the prius of the universe. The universe but represents it, the universe is but the realisa- tion, the materialisation of it. It, as an internality, has its own constituent internal forms ; of these forms — internal to it — the universe is but the externalisation. (^ Now the very idea of externalisation as externalisation, involves a boundless extension of difference — a boundless out and out of atoms infinite and in- finitely different, presided over by material contingency and mate- rial necessity. This, then, is the circumferential crassitude — involved in the very idea of externality as externality ; and we may illustrate it by its corre spon dent idea of internality as inter- nality. Internality as internality, an Ego, is boundless intussus- ception. It has myriads of thoughts, but it itself is a point, and these thoughts are all there in this point, and they are all through one another ; they mutually penetrate and per- 72 WIIEWELL AND HEGEL, OR THE VINDICATION OF , vade each other in the single point, which is pregnant with ' them all. If externality, then, as externality, is an infinite out and out of infinite difference under M-rational necessity (physi- cal contingency, etc.), internality as internality is an infinite in and in of infinite identity under rational necessity (Freedom, true Free-'will). The counterparts are perfectly laid off", the one against the other, and what is, the single thing that is, the roc's egg, is their antithesis. Antithesis must be if there is to be any definiteness, or just anything. Infinite affirmation were nothing; it is something only by retui-ning on itself, only through negation. The universe, then, is, in its na^ura/ aspect, externalisation. and, as externalisa- tion, the negation by which the thinking being makes itself definite, by which it realises itself, for what is externalised can only be its (the thinking being's) own internal spiritual forms. But that being so, it will be possible to trace the spiritual in the material. Explanation of Nature will be the reduction of this to that ; as said, it will be the gradual reconduction of external crassitude into the inner reasonable life. To explain, then, is to reduce into the unity of thought. The farthest crassest nebulas and hugest volcanic suns must, to be explained, be all resolved into the single essential c/rop. But the drop itself must have a principle. Now, the drop of the drop is the notion, the act of judgment, the ultimate nerve, the single throb of thought, — the pulse, the rhythm of self- consciousness, — the primeval and eternal syllogism. What is ^/^ that ? It is the schema of universal, particular, and singular. ^ ^Every concrete is a universal, through a particular, into a / singular. ( This schema is seen perfectly only at last in self- consciousness as self-consciousness ; but still, wherever we go, we shall find all but less or more correspondent adumj^rations of it. ) In the very passage before us, this is what Hegel is attempting to show us. In the solar system, gravitation appears as the universal ; the various planets, etc., as the parti- cular ; and, as a sort of approach to subjectivity, motion as the singular. Dr Whewell did not see that, and he is hardly to be blamed : — how many have ? Aristotle's conception of an Entelechy it is, then, that domi- nates Hegel. An entelechy is a something that is there on its OAvn account, and realises itself into a whole through assimila- tion of something other than, different from, itself. Every living thing is an entelechy : it is a principle of life, of something on its own account that realises itself into a whole, a completed system (the particular living being), through assimilation of another, something diff"erent from itself. The acorn realises itself into the oak through assimilation of another. The soul realises itself through the body and whatever is offered to the body. An end realises ITSELF, — a purpose makes itself end, — J THE LATTER IN THE PHYSICAL REFERENCE. 73 through appropriation of the means. These are entelechies. And -wherever a principle reahses itself into a co-articulated system of members, Hegel sees an entelechy. In his language an entelechy is Idea, and the principle that realises itself is Begriff (notion). This is the schema of a living, thinking subject. The living, thinking subject has its other (matter, externahty as externality, the external material universe) opposite it, and it realises itself by appropriation of its other. This is the general principle ; and Hegel sees it everywhere in the miiverse, — sees the imiverse as nothing but this, as every- where in entelechies. Ideas, less and less crass, more and more perfect, ascending to this. This, then, is what Hegel has before him in the passage translated by Dr Whewell, as, I think, wall be quite evident when it is re-rendered as follows : — " Gravitation is the true and proper Notion {Begnff) of material corporeity, realised into Idea {Idee.) Universal Corporeity dis-cerns {urtheili) itseK, as their underlying general nature and principle, into particular bodies, and closes (si/Uoyises) itself into the moment of sinr/idarit>/ or suhjectivity, as existent manifestation in motion, which (motion) is hereby directly (unmittelbar — immediately as to sense) a system of several iodies." As intimated, Hegel's meaning, absolutely di'iven off by the translation of Dr WheweU, will, perhaps, be seen here. This meaning will be comj^letely seen, however, only when the equi- valents used for the technical words, Allgemein, Besonder, Ein- zeln, Begriff, Idee, realisirt, urtheilen, scliliessen, loesentlich, Moment, Siibjectivitdt, erscheinend, Daseyn, and unmittelbar, are perfectly understood in the Hegehan sense, for Hegel's dialect is absolutely his own: — " Universal Gravitation must be recognised as a deep thought in itself, though it is especially by reason of the quantitative applications connected with it, that it has attracted attention and credit, and though its verification has only been placed in Exjierience — ay, from the solar system dowTi to the manifestation of the capillary tube ; so that, regarded in the sphere of Reflexion, it has only the import of a result of abstraction generally, and, more concretely, only that of (jrarity in the quantitative consideration of Fall (a falling body), not the import, as given above, of the Idea expli- cated in its reality. Gravitation directly contradicts the law of Inertia ; for, by virtue of the former, matter tends out of itself away into another than itself." This, as a remark on the section (§), is, on the whole, exoteric ; but the teclmical word Reflexion would require much too long an explanation to be in place at present. I may point out only that Comte's Metajyhi/sical refers, but in its way certainly, to the same sphere. Still, the translation T\all, it may be, prove intelligible on the whole, which that of Dr "Whewell hardly is. As a certain support to Hegel's allegation ui reference to Gravity and Inertia, it may be mentioned that Professor Bain (Inductive Logic, p. 13) remarks of inertia, that "it is totally distinct from gravity," and that " it cannot be maintained that these properties are mutually implicated : we can easily suppose matter (considered as inert) without the property of distant 74 WHEWELL AND HEGEL, OR THE VINDICATION OF mutual attraction, or gravitation; this last property may be fairly viewed as added to or superinduced upon mere inertia ; nor can we call the two either cause and effect, or effects of a common cause : our knowledge does not entitle us to make either supposition." Still, I apprehend that inertia and gravita- tion are but two aspects of the same fact, and that Hegel him- self, contradictory as it may seem, would have so declared himself. " In the Notion of gravitation, as has been shown, there are included the two mo- ments of Individuality, and of the Continuitij that sublates individuality. It has been the fate of these moments of the notion to be regarded as different Forces, correspond- ing to attracting and repelling force, more precisely as centripetal and centrifugal force, which are supposed, like gravity, to act on bodies, and — independently of each other and casually — to tumble together in a third something (a body). In this way, what- ever of a deeper meaning lay in the thought of universal gravity, gets extinguished again ; and thought and reason will be unable to penetrate into the theory of absolute motion, so long as the so much vaunted discoveries of Forces obtain there. In the syllogism which constitutes the Idea of gravitation — where gravitation itself namely appears as the Notion which, through the i^articularity of the various bodies, explicates itself mto external reality, and at the same time, in their ideality and reflexion into self, in motion, shows itself shut together with itself (syllogised), — are contained the rational identity and inseparabiUty of the moments, which in the other way of it are conceived as independent. Motion as such gets sense and existence only in a system of several bodies that stand in relation to one another, but in different determination. This nearer specification as regards the syllogism of totality, which syllogism is itself a system of three syllogisms, has been given in the notion of objectivity (sect. 198)." Hegel's sentences are all, as his very individual terms are, ^syllogisms. He is true to his one single principle everywhere, --y and his very syntax is the reflecting of a Particular, through a '' Unwersal,viiio a Singular. Each sentence is like a hving organism, into which its constituent members are duly folded. Translators of Hegel, then, have a peculiar claim to be only considerately judged ; and it would be very unfair to make Dr Whewell an exception. But, leaving Hegelian German as Hegehan German — a dark to Dr Whewell absolutely without a gleam — entirely out of account, must it not be said, that Dr Whewell in the above appears to great disadvantage even as a translator of Ger- man simply as German % In the first sentence all meaning is effaced by the words used. In the second sentence again, to leave the words alone, the atrocities that have been perpetrated on the syntax, will be self-evident to every tyro. It is not different with the other sentences, which are all so much " clotted nonsense," whether as representative of the words or syntax of their original. I wiU only refer to the gratuitous confusion introduced by translating soiist " at other times " instead of " in the other way of it," for it applies plainly to the counter explanation by means of mere o^eflected abstractions, dwhheA forces. Observe " different determinations " in the last sentence too. The question now is, what has Hegel said in all that ? For one thing, he must not be understood to deny gravitation, nor even centripetal and centrifugal forces I Gravitation is to Hegel the very principle and notion of body ; and of the legiti- THE LATTER IN THE PHYSICAL REFEREXCE. 75 macy and convenience of attractive and repnlsive forces as expedients in calculation, he is well assured. All that he wants to do is to convert all these various materials into the moments, and render them into the rhythm, of the Notion. He would make Idea of them, Entelechy — an Idea and Entelechy wdiich, however crass and rudimentary, should still show as an analogue of that of Self- Consciousness. That is his simple object; to do that is, as Hegel beheves, to explaui. Throw all into successive entelechies (Ideas), from the ijifinitely extense circumference to the infinitely intense centre, and to him the universe is explained. It is not difficult to convince ourselves of the truth of this in the case before us. The section itself is nothing but this Idea ; and the comments only remark as much. There is Gravitation as the Begynff, the unqualified potential universal of Corporeity ; ' this appears par^icw/an'secZ in the Urtheil oi t\ie various bodies; and these are, as it were, idealised, reflected into themselves in the ]\Iotion which is their one expressed actual Singular — the Schluss. The whole is an Idea — a Amotion with its realisation — a realisation into system through moments. Compared with the Idea of Self-consciousness, Gravitation occupies the place of the Logos, Thought; the Bodies that of Nature, Matter; and Motion that of Spirit, the thinking subject. In regard to an italicised determination which occurs above, I may remark that this word (Bestimmung) always refers (when strictly used) to specification according to the notional moments ; and it is so that Hegel strikes out the thought of Motion as Motion. Dr Whewell's translation of § 270 runs now as follows : — " As to what concerns bodies in which the conception of gravity (weight) is realised free by itself, we say that they have for the determinations of their different nature the elements (momente) of their conception. One [conception of this kind] is the universal centre of the abstract reference [of a body] to itself. Opposite to this [conception] stands the immediate, extrinsic, centreless Tndiriduality appearing as CorjMi-eiiy similarly inde- pendent. Those [Bodies], however, which are particular, which stand in the determina- tion of extrinsic, and at the same time, of intrmsic relation, are centres for themselves, and [also] have a reference to the first as to their essential unity." One can see from what we may know now, the general drift of Hegelian meaning in this translation, but still too vaguely, too indefinitely, for satisfaction. As more precise, the follow- ing will perhaps be also plainer : — " As regards the bodies in which the notion of gravitation is freely and inde- pendently realised, they are determined in their diverse natures by the moments of their notion. One, then, is the universal centre of abstract reference to Self [the Sun] Over against this extreme, there is that of centreless mmjularity, immediate, and absolutely external to its own self, also apparent as independent corporeity [Comets, etc.] The paiticidar bodies, lastly, are those which, characterised as well by externality as by internality to their own selves, are centres for themselves, and yet refer themselves to the first-mentioned body, as to their essential unity" [the Planets]. Notwithstanding the general di"ift of meaning seen in it b}' light from elsewhere, Dr Whewell's translation, compared F 7G WHEWELL AND HEGEL, OR THE VINDICATION OF with this one, will again appear, perhaps, a mere muddle generally, so far as the exact sense is concerned. In reference, too, to this sense, 1 remark that the business here (with us, that is) is rather to signalise its true nature than to justify it in itself. In application to Nature, the Hegelian schema often succeeds, hut, probably, not always, and perhaps, in general principle, it will never prove wholly satisfactory. Those -who already understand what has been said about Notion and Idea will not require any further comment here. For the remainder of Dr Whewell's Hegelian translations, I must now refer to Dr Whewell's own work ; but, before pro- ceeding to examine his remarks, I think it right to continue my own translation to the extent of his, intercalating such . explanatory comments as may appear necessary. " The planetary ho&ies !i,ve, as the directly concrete ones, the most perfect in their existence. People usually regard the sun as what is most excellent, inasmuch as understanding prefers the abstract to the concrete, an example of which is that the fixed stars are in loftier account than the bodies of the solar system. The centreless corporeity, as in its nature mere externality as such, particularises itself in itself into the antithesis of the lunar and the cometary body." This passage, as rather of an exoteric nature, though still rendered in darkness, is not so badly translated by Dr AV hew ell. It will probably appear to every one that the association of comets with the moon is an unfortunate concep- tion on the part of Hegel. Still, it must be borne in mind that it is the general position of satellites that, in its relation to the moments of the Notion, dominates the thought of Hegel ; and that even while he is so dominated, he has clearly before him all the usaal knowledge on the subject as in reference to physical science, I do not seek, at the same time, to induce any one to make credible to himself any such notional copart- nership of moons and comets. " The Laivs of absolutely free Motion were discovered, as is well known, by Kepler — a discovery of immortal fame. Kepler proved them, too, in the sense that he found for the empu-ical data their general expression (§ 227). It has suice become a current d plu-ase that Newton first found the ptroofs of those laws. Seldom has credit more unjustly passed from a first discoverer to another person. I remark here as foUows : — 7^ " 1. It is admitted by mathematicians themselves that the Newtonian formulas may ^ be deduced from Kepler's laws. The quite direct derivation, however, is simply this : A^ A. A^ C In Kepler's third law, the constant quantity is 7=^. This being stated as — ^ — ' and A =2 being called with Newton universal gravitation, we get at once Newton's expres- sion for the action of this so-named gravitation m the inverse ratio of the square of the distances. d 2. Newton's proof of th^proposition that a body in subjection to the law of gravita- tion moves round the central body in an ellipse, gives a conic section in general, while what is to be proved is precisely this, that the path of such a body is not a circle or any other conic section, but the edipse alone. To said proof in itself ^Prino. Math. 1. 1, sect. ii. prop. 1), objections otherwise may be taken ; and analysis has ceased to use it, though g basis of the Newtonian theory. The conditions which render the path of the body a certom conic section are in the analytical formula constant quantities ; and their deter- ujlnation is referred to an empirical circumstance, namely, to a certain position of THE LATTER IN THE PHYSICAL REFERENCE. 77 the body at a certain time, and the fortuitous strength of an impulse which it is sup- J posed ro have at first received; so that the circumstance which determines the curve to be an ellipse falls outside of the formula that is supposed to be proved, and of any proof of this circumstance there has never been even a thought. "3. Newton's so-called law of the Force of gravitation has likewise only been inductively demonstrated from experience. " The only difference to be seen is that what Kelper, in a simple and sublime manner, ff enunciated as Laws of celestial motion, Newton converted into the reflexvinal form of force of gravitation, and of this force as the law of its magnitude is found in Fall. If Newton's form has not only its convenience, but also its necessity for the method of analysis, this is a mere difference of mathematical formula ; analysis has long under h stood the derivation from the form of Kepler's laws of Newton's expression and the : propositions connected with it (I refer here to the elegant exposition in Francoiurs Traite elem. de Micanique, Liv. ii. ch. 11. n. iv.). In general, the older manner of the so-called proof exhibits a tangled tissue of lines of merely geometrical construction, to which a physical sense of independent forces is given, and of empty reflexional forms, aa the already named accelerating force, and the /orce of inertia, hut especially the relation of so-called gravitation itself to a centripetal and a centrifugal force," etc. The numbered paragraphs in the above (as Dr Whewell has it) commencing with "that," reminds that Dr Whewell had, on the whole, before him an edition of the Encyclojycedia earlier than the last (he names the 2d Ed., 1827, but also "additions" from the " new edition "). My own translations, I may mention, depend on a comparison of Rosenkranz's edition of the Encydo- pcedia with the second edition of Michelet's redaction of the Philosophy of Nature. Still, in every edition referred to, the text is essentially the same, and the remarks which I permit myself to make may be held to be unaffected, on the whole, by difference of edition. It is curious to observe how, as a horse pricks up his ears and mends his pace, when he recognises his road as previously known to him, Dr Whewell here makes very good running in his own physical element. Neglecting singu- lars for plurals and plurals for singulars, the slip of the pen, " fall " for path, sundry unimportant and sundry not so unim- portant omissions, his translation of the passage in hand may, on the whole, be named correct. " The observations made here stand in need of a more detailed discussion than is in place in a compendium. Propositions which do not accord with what is received appear as assertions, and, in contradicting such high authorities, as something still worse, namely as pretensions. I shall not appeal to the fact that, for the rest, an interest in these subjects has occupied me 25 j'ears long. What has been adduced, nevertheless, is not so much propositions as naked facts ; and the due reflection is only this, that the distinctions and determination.s brought forward by mathematical analysis, and the course it has to follow according to its method, are to be wholly distinguished from those which a physical reality naturally has. The pre-suppositions, the course, and the results, which analysis requires and prescribes, remain quite on the outside of the objections which concern the physical value and the 'physical import of said considerations and said course. To this it is, that attention should be directed; what is wanted is a conscious- ness of the inundation of physical mechanics with an unspeakable metaphysic which — contrary to experience and the (philosophical) notion — has alone said mathematical assignments as its source." The above passage differs little from what corresponds to it in the translation of Dr Whewell. The latter omits, however, the words, " What has been adduced, nevertheless, is not so much propositions as naked facts, and the requisite reflection is 78 WIIEWELL AND HEGEL, OR THE VINDICATION OF only this;" and substitutes for tliera, "but it is more precisely to the purpose to remark." Vaguer words are sometimes used also than the meaning of the original demands, as " that which is assumed" for "what is received." Jc " It is acknowledged that, — besides the basis of analytical treatment, the progress of which has, for the rest, rendered superfluous, nay, rejected much that belonged to Newton's essential principles and fame, — what material moment Newton added to the scope of Kepler's laws is the principle of Perturbation; — a prmciple, the importance of which is to be mentioned here, inasmuch as it rests upon the proposition that Attraction (so called) is an effect of all the mdividual portions of bodies as material. There is implied m that, that matter gives itself its own centre. The mass of the particular body is by consequence to be considered as a moment in the determination of its place, and the collective bodies of the system determuie their own sun. Even the particular bodies, however, according to the relative positinn which they assume mutually in their general movement, form a momentary relation of gravity with each other, and do not merely hold themselves mutually in the mere abstract relation of space, distance, but give themselves, one with the other, ». particular centre, which, however, in the general system, partly sublates itself again, partly, too, at least when such relation is permanent (in the mutual disturbances of Jupiter and Saturn), remains in subjection thereto." Dr Whewell's translation here must be pronounced very bad. He seems seldom to see the general idea. Thus the concluding sentence is not only strangely clipped and curtailed, but it is otherwise darkened out of all articulate meaning. The evasion of the difficult " Inludtsvolle Moment " (matter-full, result-full, translated simply " material moment "), is a small matter ; but to render " anzufuhren " by " accept," instead of " mention," " Masse " by " figure," " sich setzen " by " recognise a reference " instead of " give themselves," — to use the awkward " as being- material," — to say " their gravity " for " gravity " alone, — and to omit the important word " distance ; " these are not small' matters. It is important to see here, what Whewell does not, Hegel's striving to find the Notion, Reason, active on these out- skirts of existence. " If now in this way some main features are assigned as to how the leading char- acteristics of Free Motion cohere icith the Notion, this cannot be cariied out mto any fuller details of rational foundation, and must therefore, at present, be left to its fate. The principle concerned is, that the proof of reason in regard to the quantitative charac- ters of free motion can rest alone upon the notional elements of space and time, the moments [space and time] whose relation (but not an external one) is Motion. When will science get to acquire a consciousness of the metaphysical categories used by it, and lay the notion of the thing itself, instead of this metaphysic, at the bottom of its reasoning ?" Dr Whewell's respective translation is here again wretched. The important last sentence is wholly omitted, and the first sentence is completely bungled, — in syntax, and every-way. How he could possibly translate " Grundziige " ("main features") by " features of the path," must remain a psychological enigma. Hegel's honesty too, in regard to the difficulties in the way of his notional assignments, as well as that it is the metaphysic of physics alone that he finds finilt with, comes well to the surface. m "That, j)i the Urst place, Motion in general is a sf//»-rf«r«/n^ o«f, lies in the peculiar de- THE LATTER IN THE PHYSICAL REFERENCE. 79 termination of the bodies of Particularity and Singularity generally (§ 269), to have partly a centre in themselves, and independent existence, and pai-tly, at the same time, to have their centre in another than themselves. These are the notional moments which underlie the conceptions of centripetal, and ccnti-lfur/al forces, hut -peTVertud into that j^ form, as if each of them existed and acted independenthj by itself, apart from the other, and encountered the other in its actions only externally, and consequently contingently. They are, as alreadj' pointed out, the Unes which must be drawn for the mathema.tical mode of demonstration, converted into physical realities." In the greater part of his translation of this passage, Dr Whewell is as unhappy as elseAvhere. Omissions as usual occur, and any perception of the original is for the most part absent. " As if they only came in contact in their operations, and con- sequently externally,'' for example, is a translation quite false and misleading. Hei-e I must point out an error in the text of the usual collective addition, that is corrected by reference to that of the original one (as edited by Rosenkranz.) In the middle sen- tence, the collective edition prints " zum Grunde liegen, aber darin verkehrt werden ; " while in that of Rosenkranz, the same phrase runs, — " zum Grunde liegen aber darein verkehrt werden." There is but a difference of a comma, and of the accusative form " darein," instead of the dative or ablative form "darin;" but the difference is all important. In the one form, the first, we might have felt it natural to translate the last four words simply " but inverse-wise," which would have been wholly to misrepresent, and to miss Hegel's meaning of the moments of the notion having been perverted into the centripetal and centrifugal forces. " Further, this motion is uniformly accelerated, (and, as retvu-ning into itself, in turn uniformly retarded.) In motion as free motion, space and time come, as what they are, as differcnts, to express themselves in the quantitative determmation of motion (§ 267 Aiim.), and not to relate themselves as in the abstract, or pure uniform velocity, q In the so-called explanation of the uniformly accelerated and retarded motion by means of the alternate decrease and increase of the centripetal and centrifugal forces, the confusion introduced by the assumption of such independent forces, appears at its 1> worst. According to this exjilanation, in the passing of a planet from the aphelion to the perihelion, the centrifugal force is less than the centripetal one, whilst in the perihelion itself, the centrifugal force is to be supposed to become immediately again greater than the centripetal force ; and for the transition from perihelion to aphelion, the forces are in a like manner represented as passing into the opposite relation. It is manifest that such a sudden turn round of the attained preponderance of the one force into a succumbing under the other one, is not anything drawn from the natm'e of the forces. On the contrary, the conclusion ought to be that a preponderance obtained by the one force over the other should not only maintain itself, but proceed to the complete destruction of the other force ; and that the motion should pass, either through the preponderance of the centripetal force into rest (by the fall, namely, of the planet into the central body), or through the preponderance of the centrifugal force into a straight line. The only conclusion made, however, is : because, onwards from its /T perihelion, the body moves farther from the sun, the centrifugal force becomes again*"'^ greater ; and because, in the aphelion, it is farthest from the sun, it is there at its maximum. This metaphysical monster of an independent force, centrifugal or centri- petal, is a pre-supposition ; upon these fictions of the understanding, however, there is no further understanding to be applied — it is not to be asked how either of these forces, being independent, is, out of its own self, to make itself, or be made, now less, now greater than the other, and then, again, to destroy, or allow to be destroyed, its own preponderance. Should this, in itself, groundless alternate increase and decrease, be looked at closer, there will be found in the mean distance from the 80 WHEWELL AND HEGEL, OR THE VINDICATION OF apsides points in which the forces are in equilibrio. Their ensuing transition from this equilibrium is as unmotived as the suddenness of then- reversal. It wiU Le easy to discover that, with such a mode of explanation, the mending of a false position by- further discussion leads to new and worse difficulties. An analogous confusion occurs in the explanation of the phenomenon that, under the equator, the oscillations of the pendulum are slower. This is ascribed to the greater centrifugal force which is to be supposed to obtain there ; it might quite as well be ascribed to the increased gravity drawing the pendulum more strongly to the perpendicular line of rest." The above passage is so completely exoteric, that Dr Whewell in his corresponding translation, is in several sentences quite successful. He has found the second sentence about time and space as moments of motion so hopeless, however, that, discovering himself to be sinking in the beginning of it, he has fairly jumped the rest. Then in the middle, after the sentence that ends with " a straight line," the long sentence that occm-s in Whewell, we must believe to relate to a different text from either of those before us. The sentence that directly follows is also unhappy. "Just as little without any sufficient reason" (translated above " as unmotived") ought evidently to be just as much, etc. r "As concerns the form of the path, the circle is only regardable as the path of an out and out uniform motion. Conceivable (as the word goes) it certainly also is that a miiformly increasing or decreasing motion should take place in a circle. But this con- ceivability or probability is only an abstract imaginableness [not ^/tiwi-ableness], which leaves out of sight the rational quality or qualifiedness [the rationally deter- mined specific nature] alone in question, and is therefore not only superficial but false. The circle is the self-returning line, in which all radii are eriual; that is to say, it is completely qualified by the radius [to the nature of the radius it owes its o^vn specific nature as a whole] ; there is only one specificity [qualifying element] and that the [pervading or] ichole one. In free motion, on the other hand, where space-quality and time-quality combine into diversity, into a mutual qualitative relation, this relation necessarily emerges in the spnce-element itseK as a difference of it, which ^accordingly exacts tico characters. For this reason the form of the path that returns into itself [of bodies, thatis, in/rce or absolute motion] is naturally an ellipse ; the first of Kepler's laws. The abstract distinctive quality that constitutes the cu-cle, manifests itself also in this S way, that the arc or angle contamed between any two radii, is independent of them, in their regard a quite empirical quantity. But in motion which the notion has deter- mined [motion as motion, the free, absolute motion in space could only be determined by the notion — reason] it was necessary that the distance from the centre, and the arc described in a certain unit of time, should be comprehended m one determmateness, should constitute one whole (moments of the notion are not contingently related) ; and thus there is present a space-determination of two dimensions — the Sector. The arc is in this way by very nature a function of the Radius Vector, and as in equal times unequal involves the inequality of the radii. That the determination of space by time appears as a determination of two dimensions, as plane, connects itself with what has been said above (§ 267) in the case of Fall in reference to the same element, now aa t time in the root, and again as space in the square. Here, however, the quadratic ity\ of space is through the return of the line of motion into itseK confined to tne kiecforn These, plamly, are the general principles on which rests Kepler's second law of eciual Sectors in equal times." Dr Whewell unaccountably, as it seems, heads this section, § 240. As usual, the translation is infested generally by utter darkness to the Hegelian meaning. Whewell's second last paragraph, perhaps, shows this at plainest. There is mucli confusion towards the middle of the last paragraph also. THE LATTER IN THE PHYSICAL REFERENCE. 81 " This law concerns only the relation of the arc to the Radius Vector ; and the time is here abstract xinity, in which the various sectors are compared, because it is the determin- ing factor as unity [arithmetically as it were]. But the further relation is that of the time, not as unity [or unit], but as quantum generally, as period of revolution, — to the magnitude of the path, or what is the same thing, to that of the distance from the centre. As root and square, we saw time and space related together in Fall, the half- free motion which on one side indeed is determined by the notion, but on the other externally. But in absolute motion, the realm of free Measure [Proportion], each element attains its totality. Time as root, is a merely empirical magnitude, and as qualitative only abstract unity. A s moment of the explicated totality, however, 'time ^ is, at the same time, in its own form definite unity, totality per se; it produces itself and therein refers itself to its own self : as in itself the dimensionless element, it attains in its production only formal identity with itself — the square. Space, on the other hand, as the positive Asunder (out-of-one-another) attains the dimensions of the Notion ,, ■ — the Cube. Their realisation, therefore, retains at the same time the original . distinction of them. This is Kepler's third\a,w, the relation of the Cubes of the Distances to the Squares of the Times ; — a law that is on this account so very great, because it so simply and directly demonstrates the reason of the thing. The formula of Newton, on the contrary, whereby it is transformed into a law for the force of gravitation, exhibits the perversion and inversion of Reflexion stopped half way." Dr Whewell's translation here, not so unfortunate on the whole, retains still some of the usual blots. I will only point out that in translating the phrase, " Reich der freien Maasze," he has treated it as equivalent to Reich der freien Massen (" domain of free Measure or Proportion " converted into " domain of free masses"). I have written Maasze, though I prefer in general to write Maasse, simply to make prominent the dijBference of the sibilant letters, as respectively in the short contracted and long open form, in the two German words concerned. Maasze, too, while evidently in the singular, is printed with a double a, which, I should think, Masse never is. Dr Whewell now closes with what he heads — " Additions to New Edition, § 269," — a passage which I translate as follows : — " The centre has no sense without the circumference, nor the circumference without the centre. This puts to the rout the physical hypotheses which start now with the centre, and now with the pai-ticular bodies, sometimes constituting the former and sometimes the latter the original element The centrifugal force, as the tendency to fly off in the du-ection of the tangent, is to be wealdy supposed communi- cated to the heavenly bodies by a fling to one side, a swing, a shove, which they shall have received in the beginning. Such contingency of externally produced motion, as when in a string whirled obliquely a stone tends to fly from the string, has place only in inert matter. We should not speak of forces, then. If we viill say force, then that %(] force is only One, the moments of which do not as two forces pull away at diff'erent sides. The motion of the heavenly bodies is not any such pull this way or that way : it is the free (absolute) Motion, and they proceed, as the ancients said, like blessed Gods. Corporeity, as in free space, is not such as can possibly have the principle of motion or rest outside of it. Because a stone is inert, and- the entire earth consists of stones, that therefore the other heavenly bodies are the same, is a conclusion which sets the qualities of the whole equal to those of the parts. Push, Pressure, Resistance, Friction, Pulling, and the like, apply to another kind of existence on the part of matter than corporeity in free space. Both are matter, indeed, as a good thought and a bad one are both thoughts ; but the bad one is not therefore good, because the good x one is a thought." In an exceedingly ordinary passage such as this, Dr Whewell is still unable to achieve perfect success. What he translates are arbitrary fragments too. " Sometimes assign this, some- 82 WHEWELL AND HEGEL, OR THE VINDICATION OF 1 iines that as the original [cause of motion]." Tliese words in the first sentence do not enable ns to be perfectly assured that Dr \Miewell understood that by the various theorists, sometimes the sun and sometimes the planets were regarded as the primi- tive element. Again he sayg, " If we will speak of Force, there is one Force whose elements do not di*aw bodies to different sides as if they were two Forces!" It would be difficult to make a more irrelevant meaning of an easier sentence, even if we were specially to try. Probably the whole design in quot- ing this passage was to bring before the eyes of the reader what appeared the self-evident absurdity about the "blessed gods," — but that leads to consideration now of Dr Whewell's own special observations on the passages translated, to which I have affixed his own references (a, b, c, etc). Dr Whewell begins his remarks by apologising for taking any notice of those who, though "the Newtonian doctrine of universal gravitation, as the cause of the motions which take place in the solar system, is so entu-ely established in our minds, and the fallacy of all the ordinary arguments against it is so clearly understood among us," " yet reject the Newtonian opinions, and deny the validity of the proofs commonly given of them." Now, I can hardly believe that any reader, however much he may be inclined to shake his head at the views of Hegel, will regard Dr Whewell's way of putting it as a fair statement of the attitude, so to speak, of the Hegelian to the Newtonian doctrine. Hegel, though no expert, and not always quite true to the facts, will appear to him, probably, as a man who not only knows but accepts the general arrange- ments of Newton, and has no desire further but to insinuate into them a theory of his OAvn, which rather absorbs and assimilates than rejects the theory of Newton. There is reason to believe that he will probably think that Hegel is not — certainly not as professedly a non-expert — ignorant, but that he is generally well-informed on the Newtonian theory, both as a whole and in its principal details. There can be no doubt indeed that Hegel has taken very considerable pains with the subject, and that though discontented with the Metaphysics of Newton, he is not discontented with either his Physics or Mathematics, in themselves and as such. This, I think, very fairly states the general nature of the case. In disposition of his Physics and his Mathematics, Newton has involuntarily recourse to a certain Metaphysic. Hegel, meddling neither with his Matheihatics nor his Physics as such, would simply replace the Metaphysic of Newton by his own. What this Metaphysic of Hegel is, we must now pretty satisfactorily possess in general idea. It is the Notion. Every act of " /perception, every act of judgment, every act of reason, is the V Singularisation of a Particular through a Universal. Every THE LATTER IN THE PHYSICAL REFERENCE. 83 concrete in existence is a realisation of this, and, as such rcaH- sation, an Idea. Every Idea, then, is an expHcated Notion, or a Notion and its reaHsation. The Notion itself, even in its own ultimate form, appears as Idea ; it is, in that form, the reflexion of a Particular, .through a Universal, into a Singular.'^ This is the ultimate pulse of Thought; this is Thought itself; this is Reason ; this is the Logos of the Universe. This is the single throb that is the principle of all life, and of all that is. We see this rhythm in its concretest form when we simply say God created the ivorld. If God created the world, he did not do so out of the arbitrary self-wiU of Caliban's Setebos, but out of Reason, out of the necessity of reason, out of his own Freewill. For Will out of the necessity of Reason is Freewill, while Will out of the Self-will (the Caprice) of a Caliban's Setebos is enslaved will, bondage. *' God created the locrld" then, amounts to this : — God reflects the realised universe (a Particular) through his own Logos (a Universal) into Himself (a Singular). Evidently, then, in its own first form, where it is called Notion par excellence, the Notion is very fairly Idea. ([ The reciprocal relation of Univer- sal, Particular, and Singular, constitutes a Concrete, an Idea ; for even in it there is a Principle which passes into realisation through its Moments. "; The Singular (take God as such) realises itself through its Moments, the Universal and the Particular. If even this first form, then, which is strictly the Notion, be more than Notion, be Idea, we are driven for an ultimate ultimate to what we have called the Principle of this form, and that was — the Singular. But so-placed, the Singular is'^Subject, and we cannot think of a subject but as involving a Particular and a Universal ; so in the very ultimate ultimate that we would have as bare Principle, bare Notion, we have at once imjilication of its moments, we have at once Idea. The very ultimate principle of the very ultimate form is the Singular, the Subject, God. In its abstractest form, then, the Notion, and in its concretest, the Absolute Spirit, God, the principle of Hegel coalesces with its own self. To assert, accordingly, that the Notion is the principle of Hegel, is not more true than to assert that it is God — Geist. Nevertheless, those who have cried Geist, Geist, have in general been blind to what was concerned : KnoAving the general schema of Geist, and carrying- it vaguely out, they knew not the Notion — 7iot in itself — and still less in its derivation from Kant, if to some extent throur/h Fichte. — ' This principle is the Hegelian Metaphysic now, that, not denying, but accepting Newtonian Physics and Mathematics, would simply replace 'Neyvtonian Metajjhysic. The principle may be all wrong, but if Hegel believed in it, he is not to be blamed for his action ; and not he, but they only are ignorant — relatively that is — ivho accuse Hegel of ignorance. G u 84 WHE^VELL AND HEGEL, OR THE VINDICATION OF I Before passing on, I Avoiild jiist say one word on the advan- ' tages that HegeFs principle, at all events at first sight, seems to possess. It is at once an abstract and a concrete — the last abstraction, the last concretion. It is an ultimate, and, as present, a prime. It is also a recognised principle, a principle in rerum natura, and it is a living principle — it is, in fact, the highest principle that all mankind, by necessity of conscious- ness, have named but never exhibited. It is a unity too, biit a unity that in its very nature involves plurality — an absolute identity, but with its own absolute native differences. Universal and Particular are but each the other, and both are the Singular. These are three flexions of the one fact, and each is the other/) The reader must see that we occupy now such a height as will leave little trouble for the demonstration of just one grand mistake on the part of Dr Whewell as regards Hegel ; and he will probably also have little hesitation in accepting the distinction between Physics and Mathematics on the one hand, and Meta- physics on the other. Neither will he be unable to forgive Hegel, if, in the desire to introduce this so splendid-seeming new metaphysic of his, he should be betrayed into a little straining of the situation now and then. Nay, he will probably find positive oversights in the facts not altogether unvenial in a professed and confessed non-expert, who yet knows so much, and has taken so much trouble to be correct. One thing, however, he will not think excusable even in a Hegel : this latter's unsparing bitterness of tone to him — Newton — Avhom as a productive thinker mankind have so much reason sincerely to thank and supremely to honour. Even on this head, we can say that this teas HegeVs way : he saw keenly and he spoke keenly — and he made none an exception, not — nay less than Newton — the good old Kant, whose riches it is that enable Hegel to challenge a place that may yet be the fu*st. It may strike some here that the " Secret of Hegel," as now explained, being so very simple a matter, it is strange that Hegel himself should have been so silent, or, worse, so very enigmatic about it. How much might have been spared had he been franker, they may think. The thought is not only a natural, but a very just one : Hegel might have made every- thing easy by a turn of his pen. Why did he not do so ? It is to be said at once that the longer he lived, Hegel actually was more and more open in his communications, and that it was probably only, his sudden death that prevented a clear, precise, and complete revelation. Human nature is but, at its best, Aveak ; Hegel's halo in G ennany before his death was perhaps more truly nameable divine than that of any mortal that ever lived: how can I tell them it! he might have thought. That I have simply taken all the ordinary matter of Metaphysic, Logic, the Philosophy of Nature, Anthropology, Psychology, TUE LATTER IX THE PIIYkSICAL EEFEREXCE. 85 Morals, Politics, History, Aesthetics, aud Religion — that I have" simply taken all this matter and re-arranged it in Eiitelechies, in Ideas, in Notional Reciprocities of Universal, Particular, and Singular, all mutually inter-connected, all sj)ringing from the one single principle that is the principle of this arrangement, and all rounding into the same — how am I to tell them this?' Will they see these pictorial inter-dependent reciprocities to be explanation — they who are accustomed to, who expect grounds, reasons ? This is what is meant when I have alluded to artifice at any time in regard to Hegel, — when I have spoken of " the forcible construction of an artificial system on a merely external receipt." It is evident that Hegel, — after all his claims (claims made probably in the first heat of believed discovery) — ^must have recoiled before literal avowal. Nay, we may be more charitable still, — we may conceive Hegel to have nourished belief in his principle to the last, to have ever fondly dreamed that the " Secret of Hegel " was the secret of the universe, the secret of God, and that it Avould be found so. If that were so, why should he be at pains to give a psychological history of how he had to come upon it (this secret), of all his experiences, of all his efforts, of all his shifts, in actually setting it to work 1- After all, too, is it so certain that Hegel's principle will not prove the principle, — the principle of the universe? What is explanation but reduction into thought ? And to say things are explained by bemg re-duced to thought, is not that tantamount to saying things are pro-duced by thought ? What is explana- tion ? Is it not to bring the Particular (all natural existence) through the Universal (all intellectual generalisations) into the Singular (the subject — youiind me)? Or may not this process be reversed? May not th(\JJniversal (the intellectual subject's own constituent intellectual units) be only reahsed to the Singular (said subject) throiigh the Particular (actually existent particula?'^) ?^The Singular, then, is the Universal, — the latter is the former's necessary constituent Logos — the first is the second, the second is the first — and realisation of the one to the other is only possible through the Particular of actual existence. And what have we been naming all this while — what but the process and rhythm of God ? He eternally goes out into Plis other. Nature, and eternally retin-ns into Himself. God, that is, is Self-Consciousness ; for self-consciousness is that w^hich to realise itself goes out into its other, and returns into itself. That is my self-consciousness — that is your self-consciousness. Our life is as Singular to go out into the other. Nature (the Particular), and return thence as Universal (conscious thought) into ourselves. This, then, is the final name for the principle, the " secret," of Hegel — self-consciousness. Self-consciousness, the subject as subject, is to Hegel the Absolute — the one sole, 8(3 WHEWELL AND HEGEL, Oil THE VIXDICATION OP siui^'lc all-producing root ; and the pulso, tlie throb, the rhythm, the life of self-consciousness is the Notion — the reciprocity of Universal, Particular, and Singular that realises the Idea — that realises the Absolute Spirit. For tlie truth of these views, consider the Universe itself — how it is constituted. Would it be a Universe, were it but blank Space and Time? Would it be a Universe, were these filled only with the chaos of a nebula — were these filled only with sidereal bodies, mutually related, wheeling, wheeling ever on mere mathematical reason '? Would it be a Universe, even were such sidereal systems inhabited by creatures that went blindly to and fro on mere animal reason — instinct I Can it be a universe till it rushes into meaning, into one, in the thought, the focus, of a Spirit ? It is there, then, only for this Spirit — it truly is only this Spirit. Thought is the Prius of the Universe, — thought is all that is. All that is, is but a pulse of thought. What is, is God; and God is Self-consciousness. All is His; but as Self-consciousness alone, is it that He trult/ is. Man is the finite Self-consciousness, and he is in the infinite Self- consciousi:ess — in God. It gives quite another turn to all this, then, to say, that Hegel saw that in actual fact. Self-consciousness was the highest thing in existence, that accordingly he made it the principle of his philosoj^hy, and explained the world to be a continuous chain of attempts to realise the form and rhythm of Self-consciousness up from the most distant circumferential crassitude into the central life of the Absolute Spirit — God. This is to do for the principle of Hegel, Avhat present physical philosophy precisely requires — demonstrate it to exist, to be in reriim natura, to be a vera causa. No one can doubt, that, if we look at wliat nature everywhere brings it to — nature alone, that is, being regarded as the agent — now to a nebula in blank space, now to inorganic masses in inter-connected whirl, now to minerals of various kinds, now to land, water, and air, now to the dead geological skeleton, now to the plant (from the toad-stool to the oak), and now t(j the animal (from the tadpole to the elephant), it is self-consciousness that is her highest product. No one can doubt, indeed, that it is only as having produced self-consciousness that nature can be said to have succeeded. It is only in selt-consciousness that nature first fairly reaches and meets her own self. There at last the chaos of multiplicity is summed, the whole huge many articulated into a shape, Avhich shape is, in its own glance, seized, con- sumed, burned into a spirit, — the sole true one. Well, then, is there not some reason for making this one the principle % It is there an actual fact, — the highest actual fact, — and it is evidently the one object to which the many-layered activities of nature in tlie end tended. THE LATTER IX THE PHYSICAL REFERENCE. 87" If Aristotle held the man who said Kous, to be the only sober man among all the babblers who were bawling out Water, Air, Fire, Earth, &c., I think we are quite jnstilied in holding Hegel, — the man who says Self-consciousness to be sanity itself, beside the representatives of most modern cries. If nature is to be honoured (and explained thereby) for protoplasm and monkeys, much more ought she to be held as honoured and explained m her own highest feat, — self-consciousness. Why, what do all men do when they seek to explam nature ? Do they not seek to find notions and a notion in her 1 What ciDi, then, ultimate explana- tion be but the reduction of Nature to the notion itself, — to self- consciousness '? That surely is the inmost hving principle, and that surely is the single quest of nature, — a quest that, in all her myriad stages, sought on each, fails and falls on all, till it " arrives at last the blessed goal," and leaps up one, the all- intussuscepted one — Spuit — in humanity. We must not allow ourselves to be blind, then, to this inter- nality, to this empirical truth of the principle of Hegel, even when, for the sake of explanation, we talk of externality and artifice on the part of it and hun. So far as that is concerned, we may regard the principle as (ffom Kant and Fichte) won externally, and as then with reference to the ordinary matter of philosophy introduced externally. The formal rhythm of self- consciousness in fact is what beats everj'^vhere in the system. As Zeno's stoicism was conveyed by a gesture, so may Hegelianism; for here, too, pugnus, and palma, and pugnus again — that, as symbol, is the whole. In sign, that is the universal, the parti- cular, and the singular. That is identity, difference, and con- crete unity. That is notion, judgment, syllogism. That is Logic, Natiu-e, Spirit. That is ponation, sublation, and repona- tion. That is the myriad-named triplicity in unity that is the systole-diastole, the rhythm of self-consciousness. This rhythm is the origin of the whole, the principle of the whole, the form and matter of the whole. Of this rhythm, as in self-con- sciousness, the notion is the name and its reahsation is idea. Or call this reahsation entelechy — the one single realised self- end, self-object, that is — then notion is the subjective side of this entelechy, idea the objective one. The rhythm, as self- realising, is notion ; as self-realised, idea. The ultimate nerve of self-consciousness is universal, particular, and singular ; that, too, is the ultimate expression of the notion; and that finally, as implying realisation of the particular through the universal in the singular, is the ultimate form of the idea. I tliink I may take it for granted now, then, that the reader has it quite plainly before him how much Dr ^^'hewell was speaking beside the point when he referred to Hegel as reject- ing the Newtonian hypothesis, and den^nng the validity of its proofs. Hegel accepts Newton's physical fact of universal 88 WHEWELL AND HEGEL, OR THE VINDICATION OF gravitation, and mathematically denies not liis proofs : meta- physically only he would name and explain otherwise. In the same way when he praises the physical theories of Aris- totle, as compared with certain modern empirical theories, we are not to acQiise him of ignorance in regard to the latter, because he finds the metaphysic they bring with them poor. In tills connection, he says, for example, " the conception that the heavenly bodies would continue to move in a straight line, MnlesB fortuitoicsb/ attrsicted by the sun is an empty thought ; " but this by no means argues ignorance of physics, though he certainly prefers to consider the solar sj^stem eternal and necessary, in virtue of his metaphysics. " This is nothing else than that Epicurus judged according to analogy, or made what is called exj^kination the principle of the analysis of nature ; and this is the principle that still obtains in the usual natural science. We make experiments, observations, which concern sensations easily surveyed. We come thus to general ideas, laws, forces, etc., as Electricity, Magnetism ; and we then apply these to such objects and actions as we cannot ourselves directly experience . . . Thus the nerves are pictured to consist of quite minute spheres, invisible even under the most poAverful lenses, the last of wbich spheres it is, however, that, on occasion of a touch, leaps off and hits the soul." This, again, if a mockery of m.etaphysic is not by any means to be understood as ignor- ance of what relates to electricity, magnetism, and physiology. These remarks, I take it, exhaust Dr Whewell's whole case against Hegel, but it may be desirable to see as much in the details as Avell. ■ To assist the particular application now in place, I make the following extracts from Dr Whewell's own statements in his History of the Inductive Sciences, Chapters iv. (Book v.), to ii. (Book vii) : — "The leading thought which suggested and animated all Kepler's attempts was true, and, we may add, sagacious and phUosophical ; namely, that there must be some numerical or geometx-ical relations among the times, distances, and velocities of the revolving bodies of the solar system. " Many of Kepler's guesses . . . have been confirmed by succeeding discoveries ui a manner which makes them appear marvellously sagacious ; as, for instance, his assertion of the rotation of the sun on his axis, before the invention of the telescope, and his opinion that the obliquity of the ecliptic was decreasing, but would, after a long- continued diminution, stop, and then increase again. " Kepler's talents were a kindly and fertile soil, which he cultivated with abundant toil and vigour ; but with great scantiness of agricultural skill and implements. Weeds and the gram throve and flourished side by side almost undistinguished ; and he gave a peculiar appearance to his harvest, by gathering and preserving the one class of plants with as much care and diligence as the other. "This rule" (Kepler's third law) "is expressed in mathematical terms by saying that the squares of the periodic times are in the same proportion as the cubes of the distances ; and was of great importance to Newton in leading him to the law of the sun's attractive force. " Kepler always sought his formal laws by means of physical reasonings. " Kepler replunges himself in the relations of music to the motions, the distance, and THE LATTER IN THE PHYSICAL REFERENCE. 89 the eccentricities of the planets. . . . But . . . recollect that Newton has sought for analogies between the spaces occupied by the prismatic colours and the notes of the gamut. " The law, as &foiinal rule, was complete in itself. "The physical theories of Kepler, and the reasonings of other defenders of tlie Copernican theory, led inevitably, after some vagueness and perplexity, to a sound science of mechanics. " We make a transition from the formal to the physical sciences, — from time and space to force and matter, — hora phenomena to causes. "Natural motion is stronger towards the end, as the motion of a falling body. " Kepler's doctrine is that a certain force or virtue resides in the sun, by which all bodies within his influence are carried round him . . . comparing it ... to the Mag- netic Power, which it resembles in the circumstances of operating at a distance, and also in exercising a feebler influence as the distance becomes greater. * What if the sun Be centre to the world ; and other stars. By his attractive virtue, and their own Incited, dance about him various rounds ? ' — Par, Lost, B. viii. " It was undoubtedly a great advance towards the true theory of the universe to consider the motion of the planets round the sun as a mechanical question, to be solved by a reference to the laws of motion, and by the use of mathematics. So far the English philosophers appear to have gone before the time of Newton. Hooke, indeed, when the doctrine of gravitation was published, asserted that he had discovered it previously to Newton. ... In 1674 ... he (Hooke) distinctly states that the planets would move in straight lines, if they were not deflected by central forces. "The proposition that the attractive force of the sun varies inversely as the square of the distance from the centre, had already been divined, if not fully established. . . These inferences were all comiected with Kepler's law. "Newton had so far been anticipated, that several persons had discovered it to be true, or nearly true ; that is, they had discovered that if the orbits of the planets were circles, the proportions of the central force to the inverse square of the distance would follow from Kepler's third law. " The two steps requisite for the discovery [of the sun's force on the different planets] were to propose the motions of the planets as simply a mechanical problem, and to apply mathematical reasoning so as to solve this problem, with reference to Kepler's third law considered as a fact. "The inference of the law of the force from Kepler's two laws concerning the ellipti- cal motion was a problem quite different from the precedmg, and much more difficult. " He [Newton] has traced its consequences [those of the proposition relating to force in different points of an orbit], and solved various problems flowing from it with his usual fertility and beauty of mathematical resource ; and has there shown the neces- sary connection of Kepler's third law with his first and second. "We have already seen that, by calculating from Kepler's laws, and supposing the orbits to be circles, the ride of the force appears to be the inverse duplicate proportion of the distance ; and this, which had been current as a conjecture among the pre- vious generation of mathematicians, Newton had already proved by indisputable reasonings. " Kepler's laws were merely formal rules governing the celestial motions according to the relations of space, time, and number ; Newton's was a causal law. "As Newton's laws assumed Kepler's, Kepler's laws assumed as facts the results of the planetary theory of Ptolemy. " Those which he [Newton] had more peculiarly to take hold of, were the facts of the planetary motions as given by Kepler, and those of the moon's motions as given by Tycho Brahe and Jeremy Horrox." From these extracts it will appear tliat Newton's merit was to complete, chiefly through unrivalled mathematical powers, the theory of gravitation — out of various materials already in great part provided to his hands, and that among these mate- rials by far the most important Avere those which bore to be discoveries of Kepler. Nay, it will even appear that the main 90 WIIEWELL ANT) HEGEL, OR THE VINDICATION OF j)roposition, at all connected witli gravitation, was not only deducible, but actually had been deduced, from Kepler's laws, especially the third. Now, Hegel says no more than this, and lie only objects to the vulgar transference of the glory of dis- covery to the allegation oi proof . Apply these laws, as you may, says Hegel, no mathematical process can supersede the discovery of them ; and the allegation of their proof, which just means their farther application and connection, ought not to be allowed to interfere with the merit of the discoverer. That Hegel pre- ferred Kepler to Newton (if he really did so), I should consider almost a solitary instance of departure on his part from his own admirably self-consistent sound sense. Newton was un- doubtedly by much the greatest physico-mathematical thinker that ever lived, and, compared with even the genial Kepler, probably an incommensurably deeper nature.* Still it is difficult to understand the wrath of Whewellf and others, at this simple statement of Hegel: — " Kepler discovered the laws of free motion ; a discovery of immortal glory. It has since been the fashion to say tliat Newton first found out the proof of these rules. It has seldom happened that the glory of the first discoverer has been more unjustly transferred to another person." It is in a perfect white rage that Whewell remarks here : — " It may appear strange that any one in the present day should hold such language." But I for one would beg to be allowed to ask why ? I do not take one jot or tittle from the fame of Newton, who worked up Kepler's laws and other materials into wonderful connection — into the connection of the single theory Avhich is the glory of the human intellect ; but why should I not be allowed to point out that no mathematical operation is adequate to discovery of a wholly new qualitative fact, which merit, in the case of his laws, belongs to Kepler *? To say that the proo/ was not alleged as in supersession of the discovery, is not to convict Hegel of ignorance. For the transference of the glory from the discoverer to the prover was a wide-spread vulgar prejudice, to which it was perfectly in place for Hegel to object. I think we may say as much as this even though the merit of the application on the part of Newton were infinitely greater than that of discovery on the part of Kepler. It is m vain to * It is thus eloquently that Whewell himself speaks of Newton : — " The ponderous instrument of synthesis, so effective in his hands, has never since been grasped by one who could use it for such purposes ; and we gaze at it with admiring curiosity as on some gigantic implement of war, which stands idle among the memorials of ancient days, and makes us wonder what manner of man he was who could wield as a weapon what we can hardly lift as a biu'den." It is this enormous mathematical power that is Newton ; the ideas it wrought up were, according to Whewell, for the most part already to hand. Kepler himself shall have known " that gravity was the common quahty of bodies, that the attraction of the moon was the cause of the tides, and that the irregularities of the lunar motion were due to the conjunct action of sun and earth." t gee History of the Inductive Scienceg, vol. ii., p. 188. THE LATTER IN THE PHYSICAL REFEREXCE. 1)1 point to Newton's independent labours as regards the moon in objection here. It must be admitted at last that the theory of gravitation is more indebted to Kepler's laws than Kep- ler's laws to the theory of gravitation. The latter certainly gave connection, meaning, completion to the former; but the important fact is that Kepler's laws were first, and that the theory of gra\dtation lay in them. It is really difficult to under- stand the offence taken at Hegel's vindication of the glory of Kepler's laws for the discoverer from the jyrove}\ or the assump- tion of that ^dndication as a denial of gravitation, and a direct attack on Newton. Hegel's facts are precisely Whewell's facts. It is Whewell who asserts Kepler's thu'd law to have been "of great im- portance to Newton in leading him to the law of the sun's attractive force"; and Hegel asserts no more. Again, it is Whewell points out the distinction between formal and physical, phenomena and causes, formal relations of sjxice and time, and a causal law ; and Hegel means precisely the same thing when he grumbles about the '■^reflexion' of Kepler's rationahsed phenomena into Newton's abstraction of causal force. " Kepler's laws," says Dr Whewell, " were merely formal rules governing the celestial motions according to the relations of space, time, and number ; Newton's w^as a causal law :" and this is accurately what Hegel said. But let us pass now to Dr Whewell's particular remarks, for the discussion of which we are at last, perhaps, fully prepared. Not pretending " to offer here any opinion upon the value and character of Hegel's philosophy," Dr Whewell still intimates that examination of the other parts of the Hegelian system would confirm the very unfavourable judgment he finds himself compelled to pronounce ; but it is not difficult to pardon a sohd man even when he blunders by precipitation, and this I pass. Expressing sm-prise, though only -with the most Jovine twitch of the eyebrow, that Hegel should offer his proof (he only offers his metaphysic) of Kepler's laws, Dr Whewell proceeds to what, marked (a), concerns these laws in Newton's refer- ence. He states Hegel's averment (b) to be, "it is allowed by mathematicians that the Newtonian formula may be derived from the Keplerian laws." Dr Whewell evidently takes great offence at the word formula ; " but let us see," he says, " what he" (Hegel) "says further of this derivation of the New- tonian ' formula' from the Keplerian law. It is evident that by caUing it a formula, he means to imply, what he also asserts, that it is no new law, but only a new form (and a bad one) of a previously known truth." Now, I think we may say at once, that Hegel never meant to imply any such thing, and, conse- quently, that he does not assert it. Hegel pays, in his own way, his tribute of admiration to the thought of gravitation, and H 92 WHEWELL AND HEGEL, OR THE VINDICATION OF — adopts it. He only points out that, for the phenomena, it is what he calls a form of reflexion. Dr Whewell admits " I am not able to assign any precise meaning to the reflexion, which is here used as a term of condemnation, applicable especially to the New- tonian doctrine ;" he accordingly entirely puts himself out of court as regards the application of this term ; and we can say at once that, springing from a certain point of view, it certainly does not carry with it the special condemnation of Newton which Whewell attributes to it. To understand the meaning of the term reflexion (certainly a prerequisite for a judge that would say anything to the purpose) would demand an under- standing of a whole volume — of that volume of the Logic, namely, which Hegel superscribes " Wesen." That volume concerns what Hegel calls " previous metaphysic," and endeavours to show, so far as reflexion is concerned, that there was a tendency at a certam historical epoch to reflect phenomena into what were called general principles, but which remained, nevertheless, mere general names. Certain phenomena are called manifesta- tions, for example, and are reflected into a supposed imit that is to stand for them, named force. Hegel acknowledges this to be historically a necessaiy stage of generahsation, but he denies it to be the final one. These abstract forces he would replace in all cases by the notion. Gravitation, then, however true on that stage, is but a form of reflexion. Hegel, however, would never assert that his supposed metaphysical improvement was meant to show that Newton's theory of gravitation, with all its mathe- matical consequences, was technically incorrect. Far from it. He has no eye whatever in that duection. He is merely busied on metapJiT/sical explanation, and accepts physical facts and mathe- matical demonstrations towards it. Dr Whewell misses all this, and only sees in Hegel's statements — what does not exist there, andneverwasintendedto exist there—charges of ^ec/mz'ca^MWorrecif- ness agamst Newton. It may appear small, then, but it really has some bearing here to point out that Hegel does not throw this ugly reproach of formula, as Whewell thinks it, at Newton's head. Hegel does not speak of Newton's formula, but of Newton's formulas, and he means no reproach by the term. Dr W^hewell ought to have known this : there are present not only a plural noun, adjective, and article, but even a plural verb. There is no reason whatever for asserting, as Dr Whewell does, that Hegel infers the Newtonian law not to be " an addi- tional truth." It cannot be said even that Hegel denies to Newton " the discovery of the cause which produces a certain phenomenal law." So far as the operation of reflexion is con- cerned, Hegel admits that. He only grumbles that the inter- vention of the reflexion was not in the case of Kepler's laws an assistance to the notion. THE LATTER IN THE PHYSICAL REFERENCE. 93 Dr W he well proceeds : — "' The Newtonian formula may be derived from the Keplerian law.' It was pro- fessedly so derived; but derived by introducing the Idea of Force, which Idea and its consequences were not introduced and developed tiU after Kepler's time." Precisely what I say, says Hegel, only that I remark of the reflexion — foixe, things that you do not understand. " ' The Newtonian formula may be derived from the Keplerian law.' And the Keplerian law may be derived, and was derived, from the observations of the Greek astronomers and their successors ; but was not the less a new and great discovery on that account." Hegel here would have his o^m. reflections about what the thought of Kepler j9Mi into the observations of the Greek astrono- mers, and into those of others after them ; but he would be disposed to remark, well, in a certain way, agreed, but what is that to anything I have said ? Kepler gave the law, Newton the force of gravitation as the cause, and I grumble that the latter did not proceed to what I call the notion of reason ! A? Under (c) Hegel remarks that the -=^ of Kepler's law being A A^ A . stated as ' , and -=^ being named with Newton universal gravitation, we get at once Newton's expression for the law concerned. Dr Whewell's correspondent remark, representing A . Hegel to say, Newton "calls" y^ universal gravitation, and A that he " defines " gravitation to be -=^, whereas Newton only "proves that in circles the central force (not the universal gravi- A . . tation) is as =^," is incorrect to the import of Hegel's words, and in every way small. DrWhewell next takes up Hegel's statement (*), which is this: — " Analysis has long understood the derivation from the form of Kepler's laws of Newton's expression and the propositions connected with it (I refer to the elegant ex- position in Francceur, &c.). In general, the older manner of the so-called proof exhibits a tangled tissue of lines of merely geometrical construction to which a physical sense of independent forces is given, and of empty reflexional forms as the already-named accelerating force, and the force of inertia, but especially the relation of so-called gravity itself to a centripetal and a centrifugal force, etc." Now, really, Hegel has nothing at heart but his metaphysic here : he has not the slightest idea of calling the physics or the mathematics as such bad, but only the metaphysic they involve. He admits that "Newton's form has not only its convenience, but also its necessity for the method of analysis ; " but he ob- serves, " this is a mere difference of mathematical formula," meaning thereby that the reason which he sees in the celestial motions is untouched by the mathematical processes, let them 94 WHEWELL AND IIEGEL, OR THE VINDICATION OF be what tliey may. It is only in reference to tlie single rational notion present in the phenomena that he demm'S to the splitting up of that unity for mere mathematical purposes into lines this way for centripetal forces, and lines that way for centrifugal forces. Such fictions lie not in the notion, he intimates, and are mere conveniences for the mathematical operations which, in their own way, are certainly correct. It is hardly worth while following Dr Whewell more closely on this point ; he wholly misapprehends the import of Hegel's relative speech, and says a variety of things quite beside the question. He holds, for instance, that Hegel wants " to show that the 'lines' of the Mewtonian construction are superfluous." That is simply absurd; Hegel expressly grants the necessity of such construction according to a certain method mathematically, and would only point out the interference of these lines with his own notion metaphysically. What follows on Whewell's part, about analysis and geometry, is, in ignorance of Hegel's object, similarly speech in the air; and when he says, " so much for Newton's comparison of the forces in difierent circular orbits, and for Hegel's power of understanding and criticising it," we would only remark, so much for Dr Whewell's power of under- standing and criticising Hegel. We have much the same thing to see in Dr Whewell's remarks under (o). Here he objects to Hegel talking of "the velocity in an elliptical orbit alternately increasing and diminish- ing" in connection with centrifugal and centripetal forces. He asserts Newton nowhere to employ " centrifugal force " in his explanations, but ackjiowledges that reference to that force "is introduced in some treatises, and may, undoubtedly, be used with perfect truth and propriety." That is quite enough to justify Hegel in demonstrating the metaphysical incongruities in all such explanations ; and Dr Whewell's remarks here are not only uncalled for, but vexatious. He cavils at Hegel's use of the words uniform motion, — words understood in all their senses quite as weU by Hegel as by Whewell ; and he misplaces in his quotation (p) centrifugal and centripetal, which, however, are not securely placed by Hegel himself. His own statement is a complete proof of the confusion which the hypothesis of centri- petal and centrifugal forces introduces into the inetaphhysical notion, let them end in what mathematical correctness they may. Hegel, then, is really imtouched when Whewell concludes here thus : — " This reasoning is so elementary, that when a person who cannot see this, writes on the subject with an air of authority, 1 do not see what can be done but to point out the oversight, and leave it." Dr Whewell goes on to animadvert {q) on Hegel's reference to another mode of explanation in this matter, and triumphantly THE LATTER IN THE PHYSICAL REFERENCE. 95 exclaims tliat tliis other mode is the same as the former one. I can see no justification for this in Hegel's text : so far as I see, Hegel refers there to no more than one mode of explanation. 1 know not, then, that Hegel can be confuted of any technical error here ; even when he ignores the mechanical explanation of acceleration and retardation which Ur Whewell himself details to us very clearly. Hegel, in that, has still only the one object : the metaphysical confusion introduced by the only convenient reflexional forms of two opposed forces. And Dr Whewell, thougli he there certainly says something to the point, does not altogether remove this metaphysical confusion when he remarks that, though there is supposition of two forces, — one intrinsic, and one extrinsic, — there is no supposition of " two distinct forces both extrinsic to the motion." Dr Whewell's reference (ii) falls into this remark, in regard to the subject of which we may allowably say in general that, while Hegel plays his metaphysics too close upon physics quite to come off scatheless, his opponent, even on his own side, is too fastidious to be quite secure. We have aU heard too much of centrifugal and centripetal forces to be as fierce against Hegel in this matter as Whewell is. In the Ninth Edition (1844) of " Conversations-Lexicon," under the heading Gravitation, we can still read a doctruie of the two forces not dissimilar from that on which Hegel comments. There we learn that if no other force than gravitation acted on the planets, they would tend in a straight line towards the sun ; and that, therefore, we must assume another force, which shall have bestowed in the beginning of its movement a push sidewards on each planet. It is to the two forces that the curve of movement is due, which curve Newton proved to be necessarily a conic section, whether parabola, hyperbola, or ellipse, depending upon the magnitude of the tangential or centrifugal force. Nor are our own English encyclopaedias and elementary works discrepant.* The next point that Dr Whewell notices is (d) Hegel's objec- tion that for the path of the planets Newton's proof gives a conic section in general, and not an ellipse in particular. And here Dr Whewell intimates that an elhpse is no necessity of the * Professor Bain of Aberdeen {The Senses and the Intellect, 2d ed., p. 521), has the following : — " Newton had for years been studying the celestial motions : by the application of the doctrines of the composition and the resolution of forces to the planetary move- ments, he had found that there were two actions at work in the case of each planet ; that one of these actions was in the direction of the sun, and the other in the direction of the planet's movement at each instant — that the effect of the first, acting alone, would be to draw the body to the sun, and the effect of the second, acting alone, would be to make it fly ofi" at a tangent, or in a straiifht line through space." Whewell abuses Hegel for saying this in 1830, and here Professor Bain, who, helanntlkh, might fill any physical chair in the kingdom, says the same thing in 1864 ! 96 WHEWELL AND HEGEL, OR THE VINDICATION OF nature of the case : planets might move in circles, and some planets actually do move " in orbits hardly distinguishable from circles." Hegel's idea certainly is that the ellipse is a neces- sary outcome of the notion on this the stage of free motion according to the relations of time and space as moments. If planets do move in circles, or even if planets might move in circles, Hegel would have here to confess a failure. It would be his' metaphysic that in that event would suffer, however, rather than his knowledge of physics. In the meantime, the fact is that the cm-ve of movement still remains an ellipse, and Hegel so far is not in error. Dr Whewell now objects (e) to Hegel's critique of the "push sidewards," which has been mentioned as the necessary assump- tion in explanation of the check to gravitation that results in the curve of movement. But here Hegel, his own point of view being considered, is perfectly unassailable. What Hegel seeks is the necessary demonstration of reason. If, then, to the theory of the particular ellipse, it is necessary only to suppose that the planet was in such and such an empirical position, and that then such and such a push or kick was administered to it to launch it on its way, such a man as Hegel has no alternative but to say, You tell me stories for children; I want proof; even in your alleged proof the most important condition is unproved and remains a mere assumption : what is all this you prattle — about times infinitely far back, and accidental positions then, followed by pushes we know not from what or how ? Ur Whewell, then, is here seen to be again speaking quite into the air. We know nothing about " why " he keeps on saying angrily and loudly. Pooh ! says Hegel, that is all I'm talking about : you don't suppose I am criticising your theories from your own grounds, mathematical and physical, do you? In short, Hegel's whole stand-point, quite unknown to Whewell and others, will be clear from this extract from the Logik (vol. i., p. 416) : — " It is a great service to enable us to know the empirical numbers of nature, as the distances of the planets from each other ; but it is an infinitely greater service, causing the empirical quanta to disappear, to raise them into the universal form of quantitative relations, so that they become moments of a law ; immortal services which Galilei for the principle of Fall, and Kepler for the movement of the heavenly bodies, have achieved. Tlae laws thus found they have 2^roved in this sense, that they have shown the whole compass of the particulars of observation to correspond to them. But yet a still hio'her 2^roof is required for these laws ; nothing else, that is, than that their quantitative relations be known from the qualities or special notions, as time and space, that are correlated." 'J'his will enable us to see something of the wants of Hegel, and to understand why he took so much offence at the " current phrase" about Newton having found the proofs for Kepler's laws. According to Hegel's meaning of the words, Kepler had proved his laws, so far as they could be proved without inter- THE LATTER IN THE PHYSICy^ REFERENCE. 97 vention of philosophy proper, and it was unjust to say that for proof these laws had to wait for Newton, whose merit it was only mathematically to clear and connect them — them and the principle of gravitation that lay in them. Proof means to Hegel reduction to the notion of reason ; and that is what ought always to be borne in mind in his regard, or that what Hegel means by proof is Hegel's OAvn metaphysic. l)r Whewell now remarks that " Hegel himself has offered proof of Kepler's laws," and to this he turns himself with some curiosity, but with what result it is easy to surmise. Dr Whe- well, that is, merely finds himself in a region unintelligible to him, and to him also necessarily imreasonable and absurd. The point he first signalises here is (?') what concerns the elHpse as the necessary curve of motion. All that Hegel says in that reference amounts to this : — The circle being determined by the radius has but one quality, perfect uniformity ; but the rela- tions .of space and time involve difference, and that difference asserts itself in the free motion that results from these relations : its curve of movement is the double-centred ellipse. I do not ask any uninitiated reader not to laugh here ; but I will ask him to consider that Hegel is engaged rationalising the origin of thmgs. Why there is such a thing as space, and such a thing as time, and according to Hegel's meaning of ichy — really, so far, Hegel succeeds very well. From these he proceeds, as we see, to find motion and matter implied in the very relations of time and space — nay, implied in the same relations, the very nature of the path of motion. In this I do not say he succeeds, but I certainly say the enterprise is a thoroughly legitimate one, and that the outcome of it, even so far, is at least neither despicable nor ridiculous. At all events, it is not as Whewell and others suppose it, — the mere conceited ravings of ignorant and wholly incompetent bias. There is still here at work the most alert, the most thoroughly-prepared, the most practical, the most irresistible intellect that I, for my part, know. What Whewell makes of it is simply nonsense ; liis translation con- tains not a dream of what is meant by the diff'erence (he says differences) that is held to emerge naturally from the very relations of space and time. Whewell, too, evidently looks at it all as a physico-mathematician, in which aspect it can have no meaning ; for it can have no reference to physico-mathe- matical science as such, but simply to metaphysic. That those who are physicists, then, and nothing more, should express dis- gust at such utterances of Hegel, and should pronounce it a loss of time to hear more of them, cannot prove surprising to any one who will simply look at the state of the case. Dr Whewell here objects also {m) that the " line returning into itself," which Hegel supposes liimself to prove for free motion does not, in consequence of " movable apses," always 98 WHEWELL AND HEGEL, OR THE VINDICATION OP in point of fact exist. The objection is a small one, however, and can hardly be acknowledged to apply, especially in view of the admission of Perturbations on the part of Hegel. At the same time, it is to be pointed out, that Dr Whewell owns himself nnable to find "precise meaning " in Hegel's respective deliverance. Under (s), which concerns Kepler's second law (" that the elliptical sectors swept by the radius vector are proportional to the time"), we may allow Dr Whewell's objection simply to stand in its own shape : " If we could regard this as reasoning, it would not prove the conclusion, but only, that the arc is so^ne function or other of the radii." By the word " prove,^' Dr Whewell has in his eye not the notion, but some mathematical process. Dr AVhewell next only mentions (t) what he calls " a reason why there must be an arc involved," and in the same ignorance as always of what Hegel is at, remarks, " Probably my readers have had a sufficient specimen of Hegel's mode of dealing with these matters." He then proceeds to Hegel's "proof ^^ of Kepler's third law (w). The defect of Whewell's translation in this reference may stand for the defect of his intelligence. The references under (v) and (g) concern "reflexion,''^ and only illustrate what in that connection has been already said. The remarks under (k) and (/) which follow concern " Pertur- bations." They point out that Hegel here admits the law of gravitation, and manifest the consequent perplexity of Dr Whewell, who has always supposed him — sans ^:)/i?Y(se — to deny it. The last thing Dr Whewell notices is (x), that Hegel com- pares universal gravity to a good thought, and particular gravity to a bad one, and opines that though both are (as gvdiYities or as thoughts) the same, yet still the diflference is. It is quite intelligible how to Hegel universal gravity, as being infinite, should be nameable good, while particular gravity as being in the finite sphere, should be nameable bad; it is pre- cisely so with thoughts. Dr Whewell closes with (ic) Hegel's allusion to "the blessed gods." To the Jovine serenity of Dr Whewell this is too clearly ludicrous, and a thing only to be named. Others, in these days, share Dr Whewell's conviction, and think they have only to point to these " blessed gods " to ensure the instant disappear- ance of all benighted wretches whatever who would see anything in Hegel. Is this really the case, however? Has Hegel really reason to feel shame of his allusion, or any man after him? The reader can consider the passage (tv) for himself. Reader and writer, doubtless, know the law of gravitation to be true, as others do ; so did Hegel. That is no reason, how- ever, why Hegel should not develop free motion from the THE LATTER IX THE PHYSICAL REFERENCE. ;>i> notion, and represent it as it is — as something absolute. There is no man who may not be perfect master of the Principia and the Mecanique Celeste, and yet who may not, in view of Hegel's con- ceptions of absolute motion, talk of the stars and planets, "■going along, as the ancients said, like blessed gods^ Such talk on the part of Hegel is not of yesterday ; it all occurs as early as 1801 in his Dissertatio jyro licentia docendi. Of this dissertation the first sentences are as follows : — " Quum prffiter corpora coelestia, omnia alia quEe natura gignit, quamvis in suo genere perfecta sjjeciem universi exprimant, in prima naturas vi, quas est gravitas, sibi non sufficiant, et vi totius oppressa pereant, corpora autera ccElestia glebse non adscripta et centrum gi-avitatis perfectius in se gerentia, Deorum more per levem aera incedant : animali Uli, quod systema solis appellamus, non alia est sublimior puriorque rationis expressio, neque quse philosophica contemplatione dignior sit. Et laus Ula, quse a Cicerone Socrati tribuitur, quod philosophiam de coelo detraxerit, et in vitam domosque hominum introduxerit, vel par-\i habenda, vel ita interpretanda erit, ut philosophiam de vita et domibus hominum bene mereri non posse dicamns, nisi a ccelo descendat, omnemque operam in eo ponendam esse, ut in ccelum evehatur." As usual in such cases, this Latin is somewhat lahoriose, but it is not hard to translate. The only difficulty, possibly, arises from the phrase " animali illi," which, treated as a dative, would lead to a comparison unsatisfactory through imphcation of tauto- logical terms, and which, therefore, perhaps, ought to be regarded as a shp of the pen or as a misprint for animali illo. But this apart, surely that incession of the celestial bodies like gods through the thin air does not bring Tvdth it any suggestion of absurdity. The figure^, is perfectly in place, and it is here pre- cisely as in the other j^assage of Hegel which has been so much mocked. Besides this gloss on the important matter of the ''blessed gods," this dissertation will be found to contain almost all those physico-metaphysical pecuharities of doctrine at which the physicists special have taken so much offence. Indeed, it is remarkable that these gentlemen should have neglected a Latin statement which they could read and might understand, and should have preferred a German one, for which they were con- fessedly incompetent in both respects. In the case of this dissertation they would have enjoyed the pecuhar advantage, too, of an opportunity of turning their knives in the wound in- flicted on the philosophical demonstrator of a necessary astrono- mical chasm, by the discovery of the smashed planet that so meanly came forward in the very instant to fill it up. For, of the thi-ee designs of the essay, the last is to " demonstrate, by a remarkable example drawn from ancient philosophy, what philosophy can do even in assignment of the mathematical ratios of quantities," — an example that applies the Platonic Timseus to prove the non-necessity of the very Ceres that, non- existent to the philosophical Hegel, was actually then existent to the astronomical Piazzi ! Hegel could speak afterwards of this I 100 WHE^^^2LL and kegel, or the vindication of mishap with perfect good-himionr. For my part, however, I confess to sorrow that the Dissertatio was ever VTitten. The reasoning in it has a crude Schelhngian look, and, not to men- tion the lamentably weak collation of the apple of Newton with those of Adam and Paris, the blunder about the pendulum is very glaringly put. We see in it his general object, neverthe- less, to replace mechanical chance by philosophical necessity, while admission at the same time of the principle of gravitation is unreserved. And at last this is plain, that it was no idle appeal of Hegel's, that namely, to his "interest of twenty-five years long in these objects," and in consequence of such facts, we may reasonably allow ourselves a certain confidence in Hegel, especially when we see in the end that it is not physics he proposes to supersede, but only metaphysics. In fact, it may now be said at last, that, so far as Kepler and Newton are concerned (and it is here we are to seek the very head and front of Hegel's offending in the eyes of the mathema- ticians), both Whewell and Hegel tell precisely the same story. Kepler endeavoured to detect " numerical and geometrical rela- tions among the parts of the solar system," Dr Whewell says {Op. cit. i. 429-431), and "after extraordinary labotu', persever- ance, and ingenuity, he was eminently successful in discovering such relations ; but the glory and merit of interpreting them according to their physical meaning, ^was reserved for his greater successor, Newton." And Hegel, in effect, claiming no more for Kepler, allows Newton no less ; for the interpretation of Kepler's laws, " according to their physical meaning," is pre- cisely the "glory and merit" he attributes to Newton. Only, it belonged to the philosophy of Hegel to see, in the reflexion of phenomena into an abstract force, not what the philosophy of Whewell could see in it ; and it is only Hegel's exclusive atten- tion to the peculiar metaphysic referred to, wliich misled him occasionally into an appearance of direct injustice towards Newton, at the same time that, indirectly, Hegel cannot hide his sense of Newton's transcendent greatness. It was only natural, too, that Hegel should have a soft side for Kepler. "Kepler," says Dr Whewell, "always sought his /orma/ laws by means oi physi- cal reasonings." And .Kepler says himself: — " The motion of the earth, which Copernicus had proved by mathematical resi^oViS, I wanted to prove by physical, or, if you prefer it, METAPHY- SICAL." In a word, Kepler looked at the world precisely as Hegel did ; both sought to see in it a whole, a system, a one of reason. To attempt to explain the world by mere outside mechanical arrangement, was not to Hegel the great thing that the conversion of this Avorld into the internality of reason — into the substance of this me — was. But Newton represented the former position, Kepler the latter, and Hegel had not an instant's hesitation in preferring the spirit of him whose THE LATTER IN THE PHYSICAL REFERENCE. lOT *' highest wish was to find within the God whom he found every- where without." It does not follow from all that, however, but that Hegel might have thought Newton the greater man ; and it must never be forgotten that — without intending it — Hegel was infinitely more unjust to Kant (to whom also he acknow- ledged his greatest debts) than ever he was to Newton. The true nature of Hegel's feelings towards Newton, and his reasons for them may be easily inferred from the following extracts : — "Newton {Hist, of Phil. iii. 401), famous for his matliematical discovei-ies and physical reasonings, indisputably contributed the most to the extension of Locke's philo- sophy, or of the English manner of philosophising in general, and in particular, of its application to all the physical sciences. 'Physics, take care of metaphysics,' —this was his motto ; and so, then, science take care of thought. And he himself, certainly, as well as all the physical sciences, to this very day, have faithfully kept to this, refus- ing all uivestigation of their ideas, the thinking of their thoughts. Physics, neverthe- less, cannot do anything without thinking ; they get their categories, their laws, only from thought, and without thought there is nothing to be done. Newton has espe- cially contributed to the introduction into them of the reflexional forms of forces ; he has placed science on the position of reflexion, set up laws of forces instead of the laws of the phenomena. . . . This is still so. In the beginning of treatises on physical science we read, for example, of the force of inertia, of accelerating force, molecules, centrifugal and centripetal forces, as of stable entities that are just /oimc?; what are the last results of reflexion are set up as the first pruiciples. ... It is certainly Newton's merit, that his form possesses great advantages for the mathematical treatment. It is often envy that is at work when the fame of great men is detracted from ; but, on the other hand, it is superstition to regard their fame as something ultimate and final." {Encyc. § 270, Zusatz). Of Kepler, Hegel can still speak with correct knowledge. " Kepler ( ibid.) found his laws empirically, through induction, in connection with the observations of Tycho Brahe ; for separated details to find the universal law, is the work of geni-us in this field." I think, then, in view of Dr Whewell's incompetency whether to translate or understand Hegel, we may simply pronounce his relative .criticism, a material for the fire only. At the same time, I would not blame Dr Whewell for this incompetency, and only very mildly, indeed, for his precipitation and Kechheit in spite of it. I do not say, either, that Dr Whewell has detected no Hegelian bare bits ; but I am certainly inclined to say that what he has found is altogether insignificant in comparison with what he supposed himself to find. He has also proved himself unnecessarily fastidious in reference to the apparent ascription, on the part of Hegel, of the idea of centrifugal force to Newton. It would not be difficult to prove, I think, that that idea was entertained by Newton. I may remark, also, here that Dr Whewell had directly before him certain pleasant proofs of Hegel's honesty which it might have been fair to have signalised. The first of the following quotations is given, in his own way, by Dr Whewell, and the others are in the same neighbourhood. " If now, in this way, some main features are assigned as to how the leading char acteristics of Free Motion cohere with the Notion, this cannot be carried out into and fuller details of rational foundation, and mu-st, therefore, at present, be left to its fate. 102 WIIEWELL AND IIEGEL, 01^ THE VINDICATION OF "... The laws of this motion concern two tilings — the form of the path and the velocity of the movement. The thing to be clone i.s to develop these from the JS'otion. That would give rise to a science of many details ; because of the difficulty of execution, this has not yet been fully realised. . . . The exposition of the solar system is not com- pleted ill what has been said. ... To develop these particular features, that is the harder matter, and we have not got that length yet. ... I have given here the mere elements of the rational (notional) consideration." I tliink, too, it will be evident to the reader, that if Hegel very certainly makes no dishonest claim for himself, as little are we dishonest in om- claim for him. Various admissions have been already made, and the deliverance about the pendu- lum, which Dr AVhewell seems only to have contemptuously translated, and left so, ^vithout a word of remark, may be now referred to. We have seen that what was said, in this respect, was, that the slow pendulum at the equator, instead of being explained by the greater centrifugal force which is to be supposed to obtain there, might quite as well be ascrib'ed to the increased gravity drawing it (the pendulum) more strongly to the perpen- dicular line of rest. A spring balance, if there were nothing else — and there is much else — relatively in place, would, if he had thought of it, have convinced Hegel, to his shame, that he had made " a shockingly bad shot" here. This, then, is a gross blunder, and a blunder of the most elementary kind ; but what then ? Shall Hegel be consigned to everlasting obli^don there- for? Do we treat our other great men for their accidental blunders so ? On the second page of Carlyle's French Revolution, it was once read, and, I am led to believe, still is : — " Look to it, D'Aiguillon, sharply as thou didst, from the Mill of St Cast, on Quiberon and the invading English." Chronologically, the St Cast affah took place in 1758 ; the Quiberon one, again, in 1795. Geographi- cally, when D'Aiguillon, at St Cast, looked to the sea, Quiberon was exactly at his back, away across the country, some hundred miles off. To have done what Mr Carlyle says, then, D'Aiguillon must have literally followed Mr Carlyle's injunction, and looked very " sharply" indeed — through space and through time. I am sure I read once in a work of Emerson's, too, that Chaucer had horroioed from Lyclgate through Caxton! As a third example, Kant, speaking of two astronomers who were in dispute, tells us : — " The one reasoned thus, namely : the moon turns on its axis, because it keeps always the same side to the earth ; the other : the moon turns not on its axis, just because it keeps always the same side to the earth." Kant adds : " Both reasoned rightly, according to the position each chose from which to observe the moon's motion." Now this, though Kant says it, is quite absurd. The moon either turns on its axis, or it does not. But if a body, revolving round another, keeps always the same side to the latter, the former THE LATTER IN THE PHYSICAL REFERENCE. 108 necessarily turns on its axis. This, however, is the case with the moon, relatively to the earth ; therefore the moon turns once on its own axis in accomplishing a terrestrial revolution.* Here are three blunders, then, each as absurd as the other, and all of them as absurd as Hegel's. Yet the most of us call Carlyle the greatest of literary men in the world now ; I, for my part, think Emerson, and surely with a very large consent, morally and intellectually," perhaps the most perfect human being at present alive ; and as for Kant, universal mankind proclaims him the greatest of the great since Aristotle. We may let Hegel off about the pendulum, then ! Blunders, indeed, are a matter of everyday, and, small or big, no mortal is excepted from them. It were idle to multiply words, then ; Hegel has been simply misunderstood. Not one received physical principle did he deny ; his sole object was to replace, not physics by physics, but metaphysics by metaphysics. That he was wrong in pre- ferring Kepler to Newton — and that is not a certainty — is pro- bably beyond a doubt. 1, for one, cannot conceive the eager, restless Kepler as a greater man than the deep, quiet, true Newton. But we ought to remember that there have been countrymen of our own who did conceive this, and to reflect that, if Hegel did prefer, to physics and an Englishman, meta- physics and a German, a German of his native Wiirtemberg, too, this would have been only very natural on his part. Further, Hegel was not wrong in the substance of what he said for Kepler ; and it is only his manner that is objectionable as against Newton, That manner, moreover, was but a personal peculiarity, a twitch of the lip, a trick of the voice, and it accompanied him even in his references to those he revered. That being borne in mind, indeed, as well as that metaphysic, and what metaphysic, was alone his object, his excuse will be well nigh complete. While astronomers of old rejoiced in a process of bowhng, and, at convenient seasons, used to give their huge balls a cast of the hand, a kick of the foot, or a shove of the shoulder, Hegel would have the heavenly bodies dance to the Notion. For in his eyes to dance to the Notion is to obey reason. So it was that Kepler's "Laws" pleased him better than Newton's " Force." To Whewell, on the contrary, Force is a higher character than Law ; and Newton's transition " from time and space to force and matter, from phenomena to causes," was to him an advance. Kepler's " relations of space, * If any one doubts this, let him put a penny-piece on this page, and carry his finger twice round the rim of it, once with the top of his nail always turned to the to[) of the page, and again with the same spot on one side of his finger always applied to the rim of the coin. The ease in the one case, and the j^ain in the other, will prove UTesistible. Or let him take an iron pillar in his hand, and turn round it with his nose against it — if he does so, he wiU soon find he turns on himself, and will see that the results are not changed, should the pillar be a million miles round and a million miles off, if, while he turns round it, he keeps but his nose to it. 104 WHEWELL AND HEGEL. time, and number," however, could be construed into tlie Notion, whereas Newton's "causal force" was but a category of the understanding. To bring phenomena to "law" was much more " proof" than to reduce them to a mere " reflexion." So Hegel thought, and we, too, ought to see, perhaps, that when we talk of force, we have but reflected a phenomenal many into the mere one of a word. " Descartes said, that he should think it little to show how the world is constructed, if he could not also show that it must of necessity have been so con- structed." This, though censured by Whewell, who cites it, is the true philosophical instinct ; and it was, very conspicuously, the guiding principle of Hegel. It is man's business to explain this spectacle, and he wiU never cease attempting to do so. But to explain is to reduce an is to a must. To know the former, however, is as absolutely indispensable as to accomplish the latter. This Hegel acknowledged, and though his aim is the philosophical must, it is our misfortune to be blind to the enormous importance, in his eyes, of an intimate acquaintance with the empirical is. n. HEGEL AND MR W. R. SMITH, OR THE VINDICATION OF THE FORMER IN THE MATHEMATICAL REFERENCE. Mr Smith's paper — already, as regards its occasion, etc., sufficiently introduced in the Prefatory Letter — has the follow- ing title : — " Hegel and the Metaphysics of the Fluxional Calculus by W. Robertson Smith, M.A., Assistant to the Professor of Natural Philosophy in the University of Edinburgh. From the Transactions of the Royal Society of Edinburgh, vol. xxv. Edinburgh : Printed for the Society by Neill & Company." Further notifications are — " Communicated by Professor Tait," and " Read 17th May 1869." These, indicated, are important interests, then, which support Mr Smith, and I can only lament the compromise he has brought upon them. In Mr Smith's own words, it is his belief, namely, that what he has to refute in Hegel is " an attempt to establish the calculus on a new and very inadequate basis," and there is no such thing in all Hegel ! Hegel never made a mathematical sug'gestion in his life. Mr Smith has simply deluded himself. The best way to prove this, perhaps, will be just to produce the actual contents of the notes which Mr Smith asserts to contain this " attempt." This I shall do. But it will be well, first, to hear Mr Smith further in expression of his own views. It is from page 505 of Mr Smith's paper that I quote as above, and it is from that page onwards that, as he says, he " now proceeds to " the consideration of this " attempt to estabhsh the calculus on a new and very inadequate basis." Naturally, then, we shall expect the chief interest to lie in what follows, but still, when we find that, while only some six pages are allowed this, there are fourteen or fifteen that precede, we shall see it to be impossible for us altogether to neglect these. These, too, bear their own testimony to Mr Smith's belief in lOO HEGEL AND MR SMITH, OR THE VINDICATION OF this " attempt " at a new calculus on the part of Hegel. It is in this reference that we have the expression (p. 499), "If Hegel, however, shut his eyes to Newton's notion, he has got one of his own ;" and Mr Smith does not " intend to attempt to take up anything but the concrete applications of this notion." On page 497, he promises us that " we shall see " "a Hegelian calculus ; " and (p. 493), lastly, we have the words : — " To this subject Hegel devotes his second note, professing to point out a purely analytical method, whereby, without any application of the doctrine of limits, everything necessary for practice can be deduced." These words, I must add, too, are followed by the intimation that said new "analytical method" will be demonstrated to " produce results mathematically false," and to be, in brief, " radically unsound." ]\Ir Smith does not let his belief suffer for any want of manifestation, then, and I can only wonder again at the delusion that underlies it ; for there is no such thing as "the attempt" described either in the note named, or in any of these notes, — no, not (as has been already declared) in all Hegel ! Hegel never dreamed for himself any " analytical method ; " Hegel never dreamed for himself an " Hegelian Calculus." But there must be more than this in these fourteen or fifteen pages, and we may as well see it. I shall just quote, in the first place, however, what on the part of a distinguished mathe- matician will place us in a better position, perhaps, to do justice to the veritable action of Hegel in this connection. In the appendix to the first edition of Professor James Thomson's Calcuhis, namely, there will be found certain remarks on the various modes of opening and conducting the different methods of th(3 higher analysis. Of the Infiuitesmal Calculus, for example, we learn that it finds the differential of the product by " rejecting" the ''last term" as "infinitely small" "com- pared " with " either " of the others. " It has been justly objected to the method of Fluxions ;" we are told again, " that it involves the ideas of motion and time, which are foreign to the nature of the magnitudes that are the subject of investi- gation in Pm-e Mathematics." We hear also that "the method of limits, which is due to D'Alembert, is free from some of the objections to which the methods of Newton and Leibnitz are liable, . . . but the principle on which it depends ... is still, in a considerable degree obscm-e." Lastly, we have the fijllowing : — "The method of Lagrange, which has been followed, in its general principle, in the present work, is not liable to any of the objections that have been advanced agauist the others. It does not, like that of Leibnitz, involve the consideration of quantities that are infimtely small, or of quantities that are infinitely smaller than these. It is free from the obscurity attendant on the consideration of the ratio of evanescent quantities, as in the principles of D'Alembert and Maclaurin ; and except in its application in mechanical philosophy, it excludes the idea of motion which is involved in the theory of Fluxions." THE FORMER IN THE MATHEMATICAL REFERENCE. 107 Now these remarks of Thomson, and the spirit in which they are made, form a complete key to Hegel's remarks, and the spu'it of Hegel's remarks, against which Mr Smith directs him- self. Thus, the method of Lagrange, as it is preferred by Thomson, so it is preferred by Hegel ; and the latter regards quite as the former what concerns " evanescent quantities," " infinitely small quantities," " the ideas of motion and time," etc. Infinitesimal Calculus, Methods of Fluxions, Methods of Limits, all are approached by Hegel as burthened simply by the difiicul- ties that Thomson mentions ; and almost, we may say, that the objectionable principle of omission for the reason of " relative smallness" is the former's sole thought, Mr Smith speaks of Hegel (p. 492) as proposing principles of his own on which " he would base the calculus." That is not so. Hegel has no such principles to offer — never dreams of any such. He knows that the ]3rinciples of the mathematicians are the only true ones ; that they are all thoroughly correct ;-that "limits," " fluxions," " infinitesimals," all work rightly, all work " splendidly," all involve the most important of principles. But he understands withal that every method has its own dissatisfaction with itself, and mainly because of the mode in which it accomplishes, or in which it rationalises, its rejection of the single term, dxdy. Really, that is all. Mathematically, Hegel has not the semblance of a proposition to offer. Only, he thinks that, meta- physically, he sees better than the mathematicians into the abstract principle of the calculus, and into the interest that determines its characteristic movement. It is in that reference alone he has any remarks to make, and solely at call of the mathematicians themselves. He no more thinks of denying the " splendid" work of the calculus — its matter — than Thomson did ; and no more than this latter, or any other mathematician, does he think of attributing unsatisfactoriness to its form. He believes himself, as said, to answer only a public call ; and it must be allowed that Professor Thomson fairly substantiates this call. Indeed, to my own knowledge, as late as 1839, this most amiable of men, this most excellent of teachers, this most accomplished of mathematicians, propounded in his class pre- cisely the same views in regard to the various " methods" that were published by Hegel in 1812, or twenty-seven years earlier. We are now prepared, then, before proceeding to our main work, to consider what Mr Smith advances in his first fourteen or fifteen pages. And the opening paragraph in these runs as follows : — " It is now many years since Dr WheweU drew the attention of the Cambridge Philosophical Society to the courageous, if somewhat Quixotic, attempts of Hegel to cast discredit on Newton's law of gravitation, and on the mathematical demonstration of Kepler's laws given in the 'Principia.' At the time when WheweU wrote, it would probably have been difficult to find in Britain any one ready to maintain the cause of Hegel in this matter, or even to hint that the astounding arguments of the Naturphilosophie flowed from any deeper source than self-complacent ignorance." K 108 HEGEL AND MR SMITH, OR THE VINDICATION OF Setting out with tliese misappveliensions wliicli have now, I hope, been thoroughly disposed of, we can readily conjecture what we have to expect from Mr Smith. Accordingly, it is quite in keeping, that he talks in his next paragraph of Dr Stirling not venturing " to say that Hegel's proof of Kepler's laws is j'lght" " Proof" — " right ! " Is recognition of Kepler's laws as in harmony with the Notion a mathematical " proof," then '? And is that "proof" technically/ "right?" Really, one must sym- pathise with the self-complacency of Mr Smith in his own mercy: when Dr Stirling "feels sure that it" (said proof) "would repay the attention of the mathematicians," "it would not, perhaps, be impossible," Mr Smith intimates, " to rob Dr Stirling of even that sorry consolation ! " We may take the next three paragraphs together and say that, according to them, the " views of Hegel " are to Mr Smith these — The mathematicians have " never been able to put the higher calculus on a basis thoroughly free from confusion or even error ; " Newton, sjoecially, has not been " so far master of his own thought as to be able fairly to deduce the practical rules of his method ; " Newton has fallen into " real errors ; " Newton has determined the fluxion of a product " in a manner analytically unsound ! " Dr Stu-ling, too, " has no hesitation in pronouncing Newton guilty of an obvious mathematical blunder ! " It is difficult to believe that any one could so utterly overlay and squelch the small mouse of truth here, and by such a very mountain of — misapprehension. The mathematicians have "never been able to put the higher calculus on a basis thoroughly free from confusion or even error !" Hegel is pre- cisely as Thomson in that regard, and I fancy even Mr Smith would not misinterpret what I have quoted from the latter into a charge of mathematical confusion and technical error against the mathematicians. In point of fact, Hegel charges these gentlemen with no " error ; " and even the word " con- fusion" can become pertinent only by being translated into logical unsatisfactoriness — precisely the same unsatisfactoriness that is both meant and mentioned by Thomson. Newton not " master of his own thought ! " And it is Hegel who shall have said so — Hegel, whose delight in Newton's mastery of thought is utter and express! Then "errors?" Hegel has to allude to one error on the part of Newton, as referred to by Lagrange, which error Mr Smith allows to have been recognised and corrected in the second edition of NcAvton's own work. Again Hegel has to alhide to an astronomer, Schubert, who shall have " admitted that, in the point which is the nerve of the proof, it is not exactly so situated as Newton assumes." Mr Smith's manner of stating this is as follows — " admitted that ... in the point, which is the nerve of the proof, the truth is not as THE FORMER IN THE MATHEMATICAL REFERENCE. 109 Newton assumes it." That, one sees, is categorical, and to accomplish this categorical effect, Mr Smith made a break in his quotation and omitted the italicised " not exacthj I " Yet one might not be very wide of the truth, if one said, that very italicising of " exactly " is precisely the " nerve " of the quota- tion. Why, then, did Mr Smith omit it ? Lastly, in regard to the fluxion of the product, Hegel simply put side by side with one arithmetical result another — objecting thus not to the former result itself, which was right, as he knew, and as every- body knew, but to the formal expedient in justification of it. This last sentence contains the amount of " Dr Stirling's" sin also, and the conclusion of the whole must be that Hegel, alluding to one admitted error and one admitted " not exactly " on the part of Newton, never, as of himself, or from himself, accused this latter of any one " error " whatever. A draT\Ting near the mathematicians in the spuit of Thomson, then, a delighted acknowledgment of Newton's " mastery," an allusion to two remarks on the part of others, each remark situated as we said, and a mere sly side hi/ side on his own part, — that, in regard to Hegel, shall be material enough for those enormous misrepre- sentations of Mr Smith ! All. or most, of this matter, however, we shall, directly or indirectly, see again. Meantime, let it be understood that there is not a single statement in it which is not " schief," tcrong, to caricature. This one example, in fact, is perfectly appHcable to the entu'e procedure of Mr Smith. Throughout, he has done but one thing only — confounded l ogical unsatisfactor iness with mathematical maccuracy. Mr Smith now explains what lie is going to do. ^I do not profess," he says, " to be able to treat this question from the stand-point of Hegel's own philosophy ; " but the above " assei- tions " (conceived as Hegel's, that is) are such, he maintains, as "can fairly be examined by one who does not profess to have mastered Hegel's system." Now that, as we see, is decisive, and capable of bemg used in bar of all ftuther discussion. Mr Smith does not know Hegel, and attributes to him "assertions " which he (Hegel) never even dreamed. Mr Smith's relative industry, then, must be simply a speaking into the ah*. I shall not pretermit further discussion, for all that, if only for the hope of some not unfruitful results in the end. Mr Smith, then, proceeds to say that he will independently state the case of Newton, and apply the consequences in test of these alleged Hegelian "assertions." "It is possible, however," he adds, " to go further than this ; " and then he tells us of the proposed new " Hegelian calculus," and of his ability, as he de- clares, to demonstrate it to produce "results mathematically false," and to be in general " radically unsoimd." Mr Smith's Avhole "plan" consequently is double: there iB,Jirst, what concerns New- ton; and, second, the "Hegelian calculus." We Bee now, then, the 110 HEGEL AND MR SxMITH. OR THE VINDICATION OF business of Mr Smith's first fourteen or fifteen pages, and as re- gards their general interest, Newton, we shall have an opportunity for a more advantageous discussion later, when we examine, as intimated, Hegel's oAvn matter. Nevertheless, a word or two may not unprofitably be placed now. Mr Smith's account of Newton's general proceedings runs as follows : — " Newton saw that there were two ways in which quantities might be conceived as generated. The first of these is that which the usual processes of arithmetic have made familiar to everybody, viz., the addition of discrete units. . . . Newton saw, how- ever, that arithmetic in its most perfect form could give full mastery over quantity, only on the supposition that quantity, as it comes before us in the universe, is always produced by the synthesis of ultimate units, or, in other words, of indivisibles. Instead therefore of endeavouring to eke out this view of quantity by arbitrary assump- tions, Newton resolved to return to Nature herseK, and inquire how quantity is really generated in the objective viniverse. ' Linete,' he writes, ' describuntur ac describendo generantur non per appositiimes partium sed per motum continuum punctorum ; super- ficies per motum linearum ; solida per motum superficierum ; anguli per rotationem laterum.' . . . In a word, Newton's fundamental position is, that the arithmetical conception of quantity is not that with which nature herself presents us, and is not, therefore, universally applicable. On the other hand, ever}^ quantity that has objective reality [i.e., is an object of real intuition] is generated by continuous motion. By means of these profound, yet simple considerations, Newton is at once able to revolutionise the whole theory of quantity, and to substitute for the relation of unit, and sum that of velocity and quantity generated, or, in Newton's own language, of fluxion and fluent." Hegel would have said all this in a single line. Quantity has two moments, discretion and continuity : you may calculate according to either. Consider what contradictory commixture of the dross and slag of the Vorstellung with the metal of the Begriff that would have spared ! The appeal to external nature for example, and the decision that what she presents us with, on the one hand, is " lines" flowing into " planes," *' planes" flowing into "solids," "sides rotating into angles;" and what she does not present us with, on the other hand, is " the arithmetical conception of quantity !" " The arithmetical conception of quantity is not that with which nature herself presents us." Had Mr Smith been even superficially acquainted with the Logic of Quantity he Avould have knoAvn that the moment of discretion was, even with reference to Nature, quite as authentic as the moment of continuity. Nay, we may say more than that ; if nature, which is only the external picture or representation of the Begriff, is to be the standard, then the moment of continuity — at least as above expressed — is even less authentic than the moment of discretion. Who ever saio lines flowing into planes, planes into solids, or sides rotating into angles. And yet who has not seen sand and salt and sawdust, berries on the bush, apples on the tree, coals in a sack, peas and beans, and small shot, and a pocketful of marbles % It is in continuation of the same pollution of the Begriff with the externality of the Vorstellung that Mr Smith proceeds. " This conception of time, as the one absolute and independent vari- able, is undoubtedly one of the most splendid and fruitful in the THE for:mer in the mathematical reference. hi liistoiy of Inunan thought, and well deserves the attention of metaphysicians." If Mr Smith would only see for himself, he would hud that metaphysicians, especially of the type of Hegel, have rather a partiality for such a fine metaphysical reality as time. Still we may conceive them to say here — Time is certainly an excellent type of quantity, but rigour and purity will dispense with it — rigour and purity will confine you to the notion quantity and its own moments, when you would make a science of quantity : so, you will be even better led. Professor Thomson had reason, then, when he objected to Newton time, and also motion. In fact, such want of due abstraction is the whole objection of Hegel, in a mathematical reference, every- where. This we see at once in the single look with which he regards the one interest — the omission of dxdy. If, he says, you find dxdy useless, and would fain, accordingly, get quit of it, you ought to consider that it must be useless hy the nature of the case. Show that, then, and get rid of it so ; but, for the sake of logic, for the sake of common sense, do not perform arithmetical operations ^diere arithmetical operations have no place, and do not say you reject from a sum — a sum that is still, for all that, to be absolutely full — an actual quantity — and actually belonging to that sum — " because it is so small." Really, that is what Hegel says ; and it is that Mr Smith has converted into all those monstrous charges of error and incapacity against the mathematicians in general and Newton in particular, just as Dr Whewell converted " Reflexion" and the " Notion" into a denial of gravitation and a new " proof" for Kepler's laws ! In very truth, there is not one of these things that is not the chimera of a misjudging brain. It is also in consequence of this imperfect Huldigung of abstraction on the part of Mr Smith that (pp. 496, 497) he begins his attack on Hegel with a little bit of business. Unable to see the real gist of what is discussed, and believing simply in a necessarily unfounded assault on Newton, Mr Smith lumps together a few incoherent expressions from disjmict pages, and summarily pronounces upon them — " Hegel cooUy ignores the whole foundation of the doctrine of fluxions" — [motion and time, namely, as Professor Thomson did] — " Hegel comments in the most edifying manner ;" " Hegel triumphantly refers ; and so, upheld bj^ the dictum of this forgotten astronomer, Hegel goes on to inveigh against the mere jugglery by which Newton, already knowing Kepler's results, avails himself of the ' mist of the infinitely little ' to bring out apparent mathematical proofs of these resiUts ; one does not know whether the singular perversity of this accusation against Newton's moral character, or the incredible ignorance of the argument by which it is supported, is most to be wondered at. ... A Hegelian calculus, as we shall see, would certainly have been of little service to physics." Such tossing to and fro, with execration, oi disjecta membra/^Q as meaningless as such disjecta must be ; and we cannot wonder that he who finds in Hegel a neio " analytical calculus," can find in him also " an accusation against Newton's moral character I" 112 HEGEL AND MR SMITH, OR THE VINDICATION OP What Hegel means about Kepler's laws and Newton's " proofs," Mr Smith simply fails to understand. Hegel, as we saw already, has been told — /don't say by Newton, but certainly by others — that these " proofs" amount to a supersession of the " dis- covery ;" and he simply remarks the " discovery" must stand on its own legs — no mathematical process, purely as such, is adequate to the discovery of any new fact in experience. It is just possible, all the same, that the "incredible ignorance" must change sides. It is in this neighbimrhood that a note refers to Dr Stirling as havingj " read" a nur for a nun ; and there is no doubt but that Mr Smith is correct so far. The 7Lur was seen ; but, as memoranda remind me, it was deliberately changed, as atopical, into ■ a topical particle of transition nun. This, possibly, too, had better remain so, notwithstanding the air of correctness to the contrary due to — Mr Smith's judicious collocation of passages. This note is appended to the following quotation from the Secret of Hegel :— " Newton only explained what he means by his terms, without showing that such a notion has internal truth." Mr Smith rejects this criticism of Hegel's, but seems to allow it some weight, if we are " to pay no regard to consider- ations of velocity and motion." That, however, is to Mr Smith not so : we must pay such regard ; we must have recourse to " actual intuition," and, in that respect, " Newton's definitions enjoy fully the advantage which Kant ascribes to mathematical definitions in general." Such definitions Mr Smith intimates, " cannot err, because they simply unfold a construction by means of which the notion is actually pro- duced." Now this to Hegel is simply the reversal of philosophy. To him it is not the " construction " (the Vorstellung) produces the " notion " (the Begriff) ; but, on the contrary, the latter the former. So it is that Hegel is not likely to quake before any "intuition," even Kant's. Leaving aside discussion of the role of intuition at present, let me illustrate something of Hegel's meaning in this connection by a reference to one of Mr Smith's utterances in this place. " That quantity which, varying according to a definite rule, always represents at any given time the ratio of the increments, may still be constructed when the time is made zero, and is now equal to unity, or is equal to the ratio at which the incre- ments startr Now that, said as against Hegel, is what Hegel himself is always saying. It is about the main thing, in fact, that he has to say. O^ily, Mr Smith says it in the language of the Vorstellung ; Hegel, on the other hand, in the language of the Begriff. What is concerned, says Hegel, is a qualitative ratio. It is capable of appearing in various empirical quantities, and under various empirical conditions, according to the nature of the empirical case ; but to obtain it — it itself — it in its purity THE FOR:kIER IN THE MATHEMATICAL REFERENCE. 113 — it as it only qualitatively is — all these must be abstracted from. You only muddle and puddle the notion — the qualify — that that Newton himself declares independent of quantity — by all these mixed expressions, through wliich the due abstraction only shoios, but to an eye that is educated. One wonders, indeed, to find Mr Smith so obstinately persist- ing in the sort of mere rough and ready of the Vorstellung, at the very moment that he quotes, and with the import of the Begriff, as clear '^^Titing of Hegel's own as is well conceivable. For example, on the sentence — " The limit of a qualitative relation is that in which it both is and is not, or, more accur- ately, that in which the quantum has disappeared, and there remains the relation only as qualitative relation of quantity," he can only comment thus : — by y "This sentence must mean that in the equation Lt — =-^ the left hand side 8x X vanishes as quantum in the same sense in which b x and by vanish, or, as Hegel often puts it, — ^ is 'infinite,' just as truly as §y and ^x. Now, we are told again and dx again that the ' infinity ' of the b x and b y does not lie in their being infinitely small, but in their having ceased to be any determinate Taagnitude, and only representing the qualitative principle of a magnitude. To this statement Newton woiild probably not have objected . . . But certainly he would never have dreamed of admitting that —is also indeterminate ; for both numerator and denominator of this fraction are in X their nature definite quantities. That the fraction can be expressed as — is to Newton by no means the essential point. On the contrary, he argues distinctly that - must have a definite value ... To Hegel, however, the fascinating element is just this -, which for his ends would be quite spoiled by being evaluated. That wotild reduce it to a mere quantum ; but, in the meantime, it is 'a qualitative relation of quantity,' which is a far finer thing. Not unnatiu-ally, however, Hegel has now to ask himself, b y what is to be the practical use of this Lt -— , which certainly ' expresses a certain value which lies in the function of variable magnitude.' In asking this question, he stm supposes himself to be criticising Newton and the mathematicians, and accord- dy ingly proceeds, with much severity of manner, to knock down the indeterminate — — which he has just set up." Now, I can hardly find a single relevant word in all that. It is probably quite as pertinent to Confiitsi as it is to Hegel. I have translated or " conveyed" the entire note, and considered it a score of times; but I really do not know in it anything that Mr Smith is talking of. It can only seem to me as if Mr Smith, desperate at being unable to make a continuous reading of Hegel, had just wildly grasped up handfuls here and there, that he might once for all seem to say something. In the sen- tence Mr Smith quotes, for example, Hegel appears to me to be talking perfectly generally, and to have no symbol whatever 114 HEGEL AND MR SMITH, OR THE VINDICATION OF before liim, wlietlier to vanisli left or to vanish right. That much is correct : that what is called infinitely little is only qualita- tive, and is neither little nor great, nor quantitative at all. Still it is utterly incorrect, for all that, to suppose that Hegel denies it a quantitative role. Something incapable of being " evaluated," that Hegel should desire that, it is impossible to conceive any- thing more absurd. It is not certain, either, though what it represents may prove fascinating to him, that the symbol itself —has any charms for Hegel. On the contrary, he seems to argue, as in reference to Euler, as well as in tliis neighbourhood itself, that Zeros are not happy counters in such a service. In fact, I should say that, to Hegel's mind, all these symbols, meaningless in themselves, only represent a certain qualitative relation, and may be regarded as definite so ; but quantitatively they are only possibilities and indefinite till applied in some particular problem. I, for my part, do not know any meaning x has in and of itself, and yet I do know it to be extremely useful in algebra. When Mr Smith, then, calls any of these symbols " definite quantities," simply as they appear, I must admit him to differ from Hegel, but then I must avow also that I do not understand him. Nay, I must avow that I cannot believe, though Mr Smith says so, that Newton himself regarded such mere symbols as possessing " definite values," All this seems to me wide only, and still more what follows : — " In asking this question," Mr Smith observes, " Hegel still supposes himself to be criticising Newton and the mathematicians, and accordingly proceeds, with much severity of manner, to knock down the indeterminate ^ which he has just set up." The question ax Hegel is supposed to ask himself is referred to what in his note, concerns the Method of Limits; but there Hegel has quite ceased to have any thought of Newton; Newton's corres- pondent place in the general critique is even some dozen pages earher. Yet Mr Smith holds that Hegel, " in asking this ques- tion, still supposes himself to be criticising Newton!" This I may call wide, then ; but as for the felling of -— ^, that I must pronounce fairly out of sight. Hegel, " with much severity of manner," shall have knocked down what he had just set up ! Though Hegel cannot be said to have set this symbol up, he certainly seems to have accepted it from the mathematicians with complete satisfaction. To hear that he shall have knocked it down, then, fills me with surprise, and I exclaim where? how? why? But we have now entered on Mr Smith's critique in regard to particulars, and I shall defer its further considera- tion till we draw into sight Hegel's own work. THE FORMER IN THE MATHEMATICAL REFERENCE. 1 1 5 This work is containedin the thi-eelongmathematical notes with which the second cliapter of Quantity, in the first volume of the Logic, terminates. These notes fill nearly one hundred octavo pages, and it is evident that any detailed treatment of them is im- possible for us here. Mr Smith confines his attention to the first two of these notes; but I, for my part, shall extend consider- ation to the whole three of them, and even begin with the last. The centre of this note is Cavalleri's method of indivisibles : all else that is said in it is either suggested by, or receives meaning fi-om, this method. According to Cavalleri, " all mag- nitudes," says Thomson, " are regarded as resolvable into in- divisible elements, or elements so small as not to admit of farther division, . . . thus, a parallelogram is supposed to be made up of straight lines parallel to one of its sides." Now, what Hegel wishes us to see here is that the essential consideration is of quality, and not of quantity. It is a mistake to lay any weight on the number, the empirical amount, the quantity that may be concerned. In the parallelogram, the idea of Cavalleri being purely applied, we are to see the essential consideration to be quality. There is present in it a single regula, a single propor- tion, which is determinative of it. That regula, that proportion is wholly qualitative ; it is no actual fixed empii-ical amount. It is the spiritual soul, as it were, of the actual parallelogram ; while to this soul the parallelogram itself is but as representative body. The parallelogram is but Daseyn — as it were, so much representative 'proexumbration, Vorstellung, — to a certain Begriff, which in itself and as such is quahtative, — independent of any assignable quantity whatever. Nor, indeed, is it different with the other "methods;" in these, too, what is essential is qualita- tive, and the whole confusion arises from the necessary quanti- tative expression — representative body — being alone, or one- sidedly, regarded. And this may be illustrated thus : — To multiply the numerical expression of one line into the numerical expression of another fine is to obtain — externally — only so much more line, only so much more magnitude of the same sort. It is not considered — the numerical expression being alone before us — that a change of quality has taken place, that a line multi- plied by a line has passed into a square, etc. All the same, the incommensurability — the difierence of quality — that is present, will make itself sensible — in the interminable or infinite series. Continua are not discreta, right lines are not curves, the diameter differs in quality from the circle ; and the incommen- surability that arises when these respective pairs are treated as homogeneous is the sign of the difference. In this, then, w^e see that what is active and operative in Hegel is still — even in this sphere — the Notion. He would inform mathematics, too, with the speculative regard. Under that regard the " infinitely little " is but the qualitative regula or principle in quanta ; and L 11(3 HEGEL AND MR SMITH, OR THE VINDICATION OF in effect, it is actually present to the instinct of mathematicians, so, though confusion of expression arises from still viewing it as infinitely little, that is, as quantitative. The expedient to remove the difficulty, the state of the case not being- thoroughly seen into, has really been introductive of the dijfficulty. What alone is concerned is to give adequate quantitative body, Avhen actual concrete cases occur in demand, to a certain quahtative species that is always self-identical. The true infinite is the regula itself, not its repetition into mass, its proexumbration into a body. But to return to the method of Cavalleri — he distinguishes in a continuum its external existence — its natural magnitude as it is there — and its principle, that relation of elements which pre- scribes its precise qualitative (geometrical) nature, whatever be its quantitative (arithmetical) size or amount. The principle may be called the determinant, the infinitely little (i.e., non- quantitative) unit, the common figure of relations, the shape, the species, the regula, the proportion, but a qualitative pro- portion that is neither small nor great, all question of actual quantity being eliminated from it, etc. In fact, it is not any quantitative infinite that we are to see here, but a certain fashion of limitatedness. Cavalleri distinguishes, then, between external existence and the specific or essential constitutive character — between the body and the soul. There is a Dasei/n, an outward bulk ; but the secret of it is an inward invisible form, which withdrawn, the whole bulk vanishes. This is the sort of attendant vision with Avhich Ave are to see Hegel approach everything. Always he universalises a particular into a singular. That, as said, is the speculative regard ; it is the Notion itself ; and Hegel attributes it here, more or less, to Cavalleri. There is a single qualitative shape — prototype. We are to see this intellectually, and, as it were, through ihe outside Anschauung. When we have ihe jylan, we need not carry about with us so much stone and lime. The outside Anschauung being viewed as the continuum, the regula may be regarded as the discretum ; but it were a false concep- tion, that of the continuum as tnade up of an infinite number of discreta (regulae) infinitely small. Such continuum is but exemplification, proexumhration, externalisation of the regula, and is there — (cannot but be there, natiu'e and I'oSs being thought of!) — from the mere proportion, the mere la"w of the regula ; it is not composed, made up of regulae at all.' (The regula, in fact, is the true continuum.) The arithmetical expression, operated upon or with, may be an infinite series ; but still the regula is alone the arffirmative element present, while the infinite of expression is what is negative: negative in this way, that it is only the particular to the universal — the application of the regula ; or in this way, that it is quantity to quality ; or in this THE FORMER IN THE MATHEMATICAL REFERENCE. 117 way, that it expresses the quaUtative difference, the inexhaus- tible incommensurability of kinds. We have but here in fact, as always, what we have on the great scale in reference to the universe. Nature is to mind simply in the same relations. It is but a quantification of quality, a particularisation of the universal (the regula) ; and the one can be reduced — arithmetically, so to speak — to the other only by the method of infinite series, which only names the existent incommensur- ability, and never annuls it. Nature's infinite out-and-out, its infinite difference, is but as these infinite series, when compared with the qualitative universal (vovg) from which it flows. What has just been said constitutes (though, of course, there are additions) not much less than the main gist of this whole paper (No. 3.) What is ancillary I may mention now. In case of any mistake, let me say, in the first place, that what refers to s^ : f bears on Hegel's attempt to rationalise (into the Notion) free mechanics, the mechanics of the heavens. He would like that, with this view, the s^ could be used as the space-factor, the geometrical one, and the'^^ as the time-factor, or arithmetical one. Perhaps his very best hit here concerns the expedient of superposition in geometry. He shows that certain pieces being given, in which the determinating peculiarity is exhausted, the question is only of a single figure (triangle — say), and that the resort to superposition is but a childish help to mere exter- nal perception. What occurs in reference to trapezoid and rectangle, the comparative areas of circle and ellipse, etc., but meets possible objections. He makes good use of Tacquet's blunder in reference to Barrow and the cone, by showing that the difficulty arose wholly from the quantitative consideration, and would not have existed had the quaUtative one been thought of. Here, too, as regards the " characteristic triangle," the thing is asserted to lie in the relation of the elements, and that it hides this to direct attention only to what is curvilinear being viewed as rectilinear. I may refer now to what Hegel says in this note of his general object as regards the principle of the calculus. In the beginning of it he states hi« result to be that tlie quaUtative element is the main one as regards the calculus — the affirmative bearing that at once arises on application, and that it is connected with power-forms and the relation of the derived function to the original power. In the end of it he speaks thus : — " The intention of these remarks has been to signalise the affinnative meanings which, in the various applications of the infinitely little, have been, so to speak, left in the back ground, and to wrest them free from the nebulosity in which that category, merely negatively held, has hitherto concealed them." 118 HEGEL AND MR SMITH, OR THE VINDICATION OF In Cavallcrl's method of indivisibles, for example — we may, paraphrastically, go on thus — the ajjirmative side is the elementary principle as a whole of relations of the magnitudes concerned, independent of the actual how much (quantity) of these magnitudes themselves. They are magnitudes, and so, necessarily, quantities, and quantitative ; still as geometrical magnitudes thf y involve relations ; these relations constitute their quality ; it is this quality which prescribes the magnitudes, each its own special nature, independent of the actual empirical amounts in which they may be present. The analytic expan- sion, in general, has the simply arithmetical form of a number of terms arithmetically homogeneous, and without manifesta- tion, in their relations so, of the quahtative reference that is really present and alone the interest. We have nothing before us, in the first instance, but what is of an ordinary quantitative or arithmetical nature, and suggests no other treatment. But the instant there is application of the analytic relations — to actual objects, namely,^ — the qualitative implication appears, in the form, that is, of the transposition of what is linear into what is planar, of what is discrete into what is continuous, etc. In a word, in the arithmetical transition, the geometrical (or qualitative) one is lost sight of. It has been usual, indeed, only to signalise the negative (quantitative) and not the affirmative (qualitative) element. Or the latter (qualitative) element has still been regarded as quantitative, but in an infinitely small degree, or as an infinitely Httle. The very fiction of an infinitely little has been resorted to for no other purpose than to meet the qualitative requirement, and it is just this that has been lost sight of in the, so to speak, arithmetical or quantitative treatment. The geometrical continuity of the construction in space, which may be concerned, for example, has been figured as composed, made up of an infinite number of these infinitely littles. Now this never-ending number is a negative assignment : it never comes to an affirmative. The infinitely little is itself negative, for it names quantitatively what — unless in mere vehicle, so to speak — is not quantitative at all (the phrase infinitely little, all the same, involves in itself both characters) ; and quantity is the negative of quality, the parti- cular to its universal. In general the practice of directing exclusive attention to the infiniteness of the elements is in every way negative ; for it conceals the true interest. It is negative also in this way, that there is present an original difference of elements which is the true source of the unending series between the two. Or the infinite, the irreducibleness, ■ the constant non-success depends on the negative that, though latent, is always actually present in this, that what is treated as discrete is really continuous, what as straight really curved, etc. The fiction of the infinitely little cannot extinguish the THE FORMER IN THE MATHEMATICAL REFERENCE. 119 difference, which is ever, in the end, cast up, like the sandal ot Empedocles. You cannot treat this quality of quantity as that one "without introduction of the infinite series, which is the practical rift between the pieces. For difference is always negative — a presence of two, a non-coalescence, a not meeting, a disagreement, an over-lapping, etc. And such is the result always where, though quality is present, quantity is alone attended to. The arithmetical expression of a square, taken only arithmetically, is transition to a lower dimension. What, arithmetically, is a simple multiplication, is, geometrically, the production of a plane — a change of quality; and that intro- duces the inevitable watershed of which the infinite series is only the sign. Insight into the thing itself, then, is all that is required for intelligence of the mathematical mfinite, whether as in series or as in the fiction of infinitesimals. This is the gist of what Hegel says in his Remark 3, and pretty Avell the gist, at the same time, of all that he has to say in the mathematical reference generally, — not without errors, be it remarked, however, either of press, or pen, or both. I turn now to Remark 1. Its theme concerns wholly and solely the metaphysical notion that underlies the introduction of the calculus, and the special peculiarities of the various proposals in migitation of the diffi- culties involved in the usual mathematical explanations and expressions of this notion. That is, there is no matter in it that is not metaphysical, though in mathematical reference, and there is not a single mathematical suggestion. Accordingly, it is-attempted to be proved that, while all the proposals to re- move the starting difficulties are philosophically defective, the mathematical infinite — what is concerned in the calculus — is a relation, a law, of quantities, not as they are quantitatively, but as they are qualitatively, in each other's regard. And it is con- tended that this idea is imjjlicit in every usual explanation of the beginning principle, but not, nevertheless, expressed pm-ely or abstractly enough by any of them. With Newton's explana- tions, however, Hegel's satisfaction and delight cannot be sup- pressed. He quotes, with positive enjoyment, many phrases here that, in the delicate incisiveness of their metaphysic, won- derfully resemble those peculiarly his own ; and his objections to unnecessary concrete accessaries are more gentle in the case of Newton than is usual with Hegel. In sh(jrt, in this note Hegel's whole business is to see the interest concerned in its own exact specific quality, and then to name it with intellectual consistency and logical accuracy ; and the result of the whole is this, that the mathematicians are substantially right, and let them gam the most they may from Hegel, that most, whatever it may be theoretically, would have no essential effect whatever on their work. 1 20 HEGEL AND MR SMITH, OR THE VINDICATION OF We may say, in a word, that the paper has no object — mathematical imperfection of explanation and expression apart — but to show that the principle concerned in the calculus is simply quantity in the simple notion that constitutes it ; and that notion may be said again to be simply quantity reflected into its oion self. The phrase may appear without meaning, but it will not be difficult to find it one. A reference of Hegel's to Newton (Logik, i., p. 305), I trans- late (Secret of Hegel, ii., p. 357), — with slight modification now — thus : — " These, Newton's generative magnitudes or princixiles, are not more interesting than the generated magnitudes. A generated magnitude (genita) is a product or quotient, rectangles, squares, or sides of these, — in general a finite magnitude. Such magnitude being considered as variable, as in continual movement and flux, increasing and decreasing, he understands by the name of moments its momentary increments or decrements. These, however, are not to be taken as particles of a definite magnitude (particulaB finitse) Such were not themselves moments, but magnitudes generated out of moments ; what is to be understood is rather the principles or beginnmgs of finite magnitudes in process of becommg." Now this that we have here from Newton is quantity reflected into itself — quantity not in its externality as an actual em- pirical so much, but quantity in its internality as first principle, as notion. That is, as we saw suggested already in Mr Smith's meta- physic of these matters, there are two modes of viewing quantity — the mechanical and the dynamical ; the oiie giving rise to the arithmetic of discretion, and the other to the arith- metic of continuity. Now, it is the latter, opposed as concrete to the former as abstract, that is by much the more important. So, quantity is as intensive magnitude, as infinite moment, as element ; it has collapsed into the simple intensity, into the specificity, of its own quality, of its own distinctive qualitative nature, of its own notion. For what is quantity ? It is never a dry independent unit and something, no matter what all else may be. It is a boundless relativity ; it is the indifferent limit. To have a quantity, you must have always quanti^^es. Draw a line between any two things as quantities — either is as it is, not in itself, but relatively to the other ; either depends on and is as infinitely variable as the other. This absolute relativity, this absolutely indifferent limit, this flight ever into the Beyond (the other side) that must ever re-collect itself again, cannot escape intelligence if it be steadily looked at. Quantity, then, has no meaning, so to speak, by itself. If no quantity were but that of a pea, a pear, a solar system, the one were as good as the other. Absolutely, a pea is not small ; absolutely, a solar system is not great. It is absurd, then, to lose one's self in the external immeasurableness that a one-sided use of the moments of quantity leads to. It is futile to " pile these millions upon millions up," they all lie in the one notion, — and that is THE FORMER IN THE MATHEMATICAL REFERENCE. 121 the reflection of quantity into itself. This notion attained, it is self-stultification to go on repeating its moments as in exter- nality. Quantity has no meaning but 8S in relation, — that is, as reflected into itself from the relation. Now, this describes what Newton sees in his dynamical quantity — in those principles of becoming, those moments, those non-quantitative beginnings into which he would conceive all actual quantities reduced, and so acquire new power over them. A square is a quantum; but it may be conceived as increasing or decreasing, and if it be so conceived, there can be conceived also to lie in it a principle that, whether there be increase or decrease, is always the same — infinite, then, non- quantitative, qualitative only ; and, reflected into it, the square is reflected into itself. But the calculus is simply an application of this notion. In it we have to determine in regard to concrete quantities mutually inter-dependent. These are reflected into themselves, or made non-quantitative, and the relation between them is similarly reflected into itself or made non-quantitative. So we have -j-^. Hegel is quite correct, then, in pointing out that to refer to motion, to increments, etc., is to disturb the abstrac- tion we om'selves have reached. Ever, however, there are the two sides. There is no such thing as dynamical quantity alone, or mechanical quantity alone. The arithmetic of discretion is the necessary body (the Fiir- Eines) to the necessary soul (the Fih-Sich). And this names the mystery of the world : this names the notion. The misfor- tune is that the world can see only one side of this notion at a time. Most men, indeed, take either one side or the other, and thus remain hopelessly abstract. Nature, the Senses, that is the mechanical side — the side of the arithmetic of discretion ; and it can yield no infinite but the spurious one, — the boundless out and out, — the Progressus ad infinitum. The true concrete man is he who preserves his humanity, and who insists on the return — the retm-n of quantity into itself, of the Fiu--Eines into the Fih-Sich, of the abstract discretes into the continuity in which alone they have meaning. For the notion, and for the notion here concerned, we must always figure an abiding relation — the return — the return from an expressing body into an expressed soul. That is the typus of the imiverse. Hegel calls it " the infinite difference," as it were the infinite disjunction, the infinite dif-ference of the two brought into the one — into the one of the single specificity. Two go to the bent bow, but the result is one. This is quality. And let us persist in the absoluteness of the one side, the quan- titative side, we lose ourselves only in the spurious progi'essus, 122 HEGEL VXD MR SMITH, OR THE VINDICATION OP which, synthesise it as we may, is always inexliaustible — has always a Beyond in it that may not be overtaken. All this is implicit in Newton's conception of genita and then* generating principles. The mathematical infinite is the true infinite, the notion of quantity as quantity, and not the spurious one of infinite external progression. To that, repeat it endlessly as you may, no meaning can be found but in relation ; and it can be found as well at first as at last. For the quantitative relation, both sides must be sublated. In this way the infinite relativity returns into itself, and is held fast so. The externality is, so to speak, the material of the single virtue, but, as infinitely variable, or only relative, it is negated. That is, there is question of quanta — externality — as a Fur-Eines, but what is vital is only the Fiu'-Sich — the quality to which that is reduced. We have no question longer, then, of any apparently fixed finite empirical quantity — but of the quality, be the apparently fixed finites what they may. It is that qualitativity that is the infinitude. It is the relation that is the thing ; the precise quantity, whatever it be, is only a moment taking meaning from the other in relation with it. Consequently, the quanti- tativity, as such, disappears. Spinosa's expression for the state of the case is, " That the nature of the thing itself exceeds every determinateness" — every quantitative determinateness by which stand might be made. I pass to a description of the general course of Remark 1 itself. We are emphatically told at once that it is the theory of the calculus Hegel alone considers. It is that that is as yet imper- fectly justified ; but the practice of the calculus, on the other hand, is said to have fully justified itself— and splendidly so. What, in fact, then, is alone considered in this Remark is the starting act of the calculus — on the whole, the arbitrary omis- sion of the tei'ms after the second — and the various attempts which have been made to justify it. What is first signalised is, that the principle in question, though involving quantitative application, is itself non-quantitative. Mathematicians have erred, in the first place, in not steadily seeing and firmly naming this. The reference to Kant that follows would make good only that Kant's infinite is but the spmious progressus. This is accomplished in the usual admirably searching and infinitely significant terms. What presents itself next as regards the notion of the infinite as well as the Fth-Eines, etc., may be now passed as already exhausted. To illustrate this notion of the infinite, however, Hegel proceeds to take up the various stages of the mathematical expression of quantity as a moment of relation, and he intimates his own view to be implicitly illus- trated by all of them. The first stage is the fi-action. Take f, for example ; that THE FORMER IN THE MATHEMATICAL REFERENCE. 123 may be as well ^, ^, etc. There is here, then, already a certain quantitative indifference, as well as a certain qualitative unity. The numbers themselves, 2, 7, etc., are no longer seen to count as such ; what alone counts is the relation — or to take it generally, in a mere fraction there is a one qualitative regula, species, soul, etc., and there is also a quantitative externality which is indifferent to a certain extent, but which maybe regarded as the sort of natural manifold or plurality of a body. Implicitly, there is a single quality ; explicitly, there is infinite quantity, quite indifferent so long as the quality is preserved. Thus, even the fraction is but a type, — like the universe itself, — of the notion. In it, too, the Particular (quantity) is Universalised (or thought) into the Singular (the quality, the single speci- ficity). Self-reflection is What-is is. That is the qualitative antithesis that is present everywhere ; for there can be no quality without antithesis, and that has the single type — reflec- tion of the many (the particular) through the universal into the one (the singular). But, if everything — if every manifestation be necessarily an antithesis, then, for manifestation, it is neces- sary that there should be in everything a negative, or its own negative. Only so is affirmation possible. Now, the element of the particular is the element also that can be called the negative. This will enable us to understand what Hegel pro- ceeds to as regards the ordinary infinite or interminable series, which, he says, have not their negative within them, and so never reach an end. Perhaps it were better to say that, as they are themselves the bare negative and never reach self-reflection, it is so that they are interminable. The return is the ultimate secret, — almost we might say the return is the turning-point of the universe. Otherwise named, it is the negation of the negation. An excellent glimpse is got into it in what Hegel, after examination of such an expression as -, (as well as series), goes on to adduce in regard to Spinosa, and the true as opposed to the false infinite. It is here he talks of the true (the mathe- matical) infinite being only apparently burthened with inexacti- tude, while it is the false (or metaphysical) infinite that is really so burthened. Hegel advances now to higher forms, to further mathemati- cal expressions of quantitative relation, but I may state at once the general result here to be nearly this, — While, firstly, non- quantitative, variability is, in the second place, erroneously applied as distinctive of such higher forms. Thirdly, again, what is distinctive in the variability itself is the presence of power- forms higher than the first. This last reference, we can under- stand now, from what we saw in the third note, that transition of power, though arithmetically homogeneous and quantitative, is geometrically and existentially heterogeneous and qualitative. M 124 HEGEL AND MR SMITH, OR THE VINDICATION OF Hegel thus accurately stamps out the metaphysical nature of the principle concerned, and vindicates it from some general objections as in regard to comparison, middle-states, etc. In his remarks that respect all this matter, Mr Smith is peculiarly unfortunate. He simply finds himself lost, and talks incoherently. Read, for instance, what he says about Hegel's assertion that the princij^le is non-quantitative : he actually pillories Hegel for denial of the very quantitative application he is engaged affirming, — '* Hegel does not seem to have seen that - has a real quantitative value !" This occurs passim in Mr Smith, but it is only an ineptitude. It is not only idle, that is, but inept, with such things before us, to talk of Hegel as denying a quantitative rule to, the necessity of evaluation for, the various symbols. But very far from seeing that, Mr Smith expressly follows (p. 506) the above up by, " And further tliere was in Hegel a rigid determination not to see the real qualita- tive difference between the continuous quantity of the higher analysis and of actual nature, and the discrete quantity of arith- metical abstraction !" We have seen already that the allusion to nature, always at least equally relevant to the arithmetical side, were better suppressed here; but can one well believe one's eyes in the reference otherwise % Hegel, in these notes, shall have manifested " a rigid determination not to see the real qualitative difference" which, as between the continuity of the higher analysis and the discretion of arithmetic, is — absolutely — the only thing he does see and endeavours to get others to see ! Why, we have just learned that said difference is pre- cisely the Notion — the Hegelian Notion — the secret of Hegel ! Hegel shall have manifested " a rigid determination not to se(j" his own Notion ! But Mr Smith has, in his own siipport, a note here : — " Hegel absolutely identifies analysis with arithmetical process — 'Auf analytische d. i. ganz arithmetische Weise.'" Now, that is quite true, but that analysis is 7iot the higher one. The word analytic as used in the above phrase is used merely etymologically. It is convenient to oppose, as occurs more than once in this very paper, to "arithmetical" "analytical," meaning by the latter what concerns the higher calculus. But an arithmetical amount is very certainly an analytical amount — analytical signifymg ana-lytical, clis-soluble, decomposable into discretes. Now, when Hegel correlates the two words, it is in that sense only. He tells us, for example (Logik, i. 237), " number, because of its prmciple (the unit), is a something externally put together as such, a purely analytic figure which implies no inner connection," or (239) it is " a Synthesiren that is still wholly of analytic nature, seeing that the connection is entirely factitious, that there is nothing in it, or comes into it, that is not quite externally to hand." That reference to what THE FORSIER IN THE MATHEMATICAL REFERENCE. 125 is of the nature of a sundering aggregate, or possibly sundering aggregate of possible discretes, is what Mr Smith ought to have seen in what he has converted into its own opposite. But, as said, this incoherence, this Verloren-seijn, on the part of Mr Smith, is, in reality, but the biu'then of every separate sentence. In what folloAvs, for example, when Hegel, in allusion to what is so capital with him — the changed quality in the geometrical object introduced by squaring, etc., says the relation now is not of X to y, but of X to ip, Mr Smith, " with much severity of manner," must, rising on his virtuous toes, convict tliis same Hegel of the ignorant denial of x having still a relation to y! Hegel remarks that, in f, the 2 and 7 are, each by itself, definite quanta, and that no necessary connection is involved between them, that further this fraction is a fixed quantum, a certain quotient. Even alter the numerator, he says, as into 4, 6, 8, and the denominator, as into 14, 21, 28 ; nevertheless, the ratio or relation remains the same. But all tliis, he points out, is essentially changed when we have to do with such an expres- sion as '—=p, for example: " x and y," he says, "have here the sense of being able to be definite quanta ;" but the question before us now is not of the quotient between x and i/, but between x and y^. Not only the sides of the ratio are not cer- tain fixed empirical amounts, but the ratio itself is not that — the very quotient is as quantum completely variable. It is the introduction of the square does this. " The relation of a magni- tude to a power is not a quantum, but essentially a quahtative relation." What Mr Smith sees in all this is that Hegel, assert- ing the ratio in question to be now of x to y', has denied any ratio longer to exist between x and y ! Accordingly, it is ^dth perfect moral pathos that he cries — " It is needless to say that the man who could make ' no constant ratio' identical with ' no ratio.' . . is hardly Jit to construct a neiv theory of the calculus /" He who finds, when Hegel points to the effect of squaring, that all relation is denied for the root, may well find " a new- theory of the calculus" in Hegel, and he who finds the latter may weU fin d the former. In fact everything is possible to him who sees Heerel " set up" ^, and stiU more to him who ° d X sees Hegel " knock it down." But returning to our description of the contents of Hegel's first note, we have now the pleasm'e of hearing this very Hegel tell us " the thought " that underlies the origin of the calculus " cannot be more correctly expressed than it has been expressed by Newton." Only, as Prof. James Thomson disapproved of " the ideas of motion and time, which are foreign to the nature of the magnitudes that are the subject of investigation in pure 126 HEGEL AND MR SMITH, OR THE VINDICATION OF mathematics," so Hegel would eliminate wliat concerns " con- ception of motion and velocity," because tlie thought expressed so, is not " expressed in the due abstraction, but concretely mixed up with inessential forms." This " due abstraction," as we have seen and see, is sufficiently innocent and well in- tended; it is common to Hegel with the greatest mathematicians themselves, too ; nevertheless, it is here that Mr Smith. actually feels himself, perhaps, securest, and he belabours Hegel with such violence because of motion, Lagrange, and the rest, as might make a Thomson starts fnomhis grave. " It was Hegel's misfortune to live at a^^tiine when, among other fruits of the Aufkliirung, Lagrans^s formal and superficial method of treat- ing physics wasin^eat repute; and surely it was a cruel fate that the great enemy of the Aufklarung should, through a defective matheniatical education, be made a willing captive to a mathematical ^ufkliirung which has, from its intrinsic weak- ness, fallen as fa'st as it rose." Mr Smith might be quoted to a like lesson as regards Newton, motion, time, etc., and had he reflected that Hegel entertained the same ideas in these refer- ences that had been expressed by the mathematicians them- selves, being without object, indeed, but to offer help in the spirit of these ideas, it is not likely that he (Hegel) would have been accused of an ignorance he had only received from the mathematicians, or that his propositions would have been met by a wrath so blindly, so contradictorily, in error, as to take for a no what was precisely a yes. That is really the character of Mr Smith's criticism ; and surely to demand the same abstrac- tion that the mathematicians themselves demanded, was not, on Hegel's part, sufficient provocation to have his work de- nounced as simply its* own reverse. Nay, this due abstrac- tion itself is probably only enhanced correctness. Fluxions may be to Mr Smith a sort of mathematical philosophy of time and motion ; but, perhaps, they ought to be regarded, for all that, as the dynamics of Quantity. This seems Hegel's view, and he is certainly supported in it by the greatest mathematical thinkers of all time, and, specially, by Newton; for Newton's references by way of illustration to time and motion cannot hide the pure abstraction of dynamical quan- tity that lies in their midst. That is seen in what he says of rectangles, squares, etc., constantly increasing or diminishing. To increase or diminish certainly seems to imply time and motion. Nevertheless, said transition ought to be held as inde- pendent of both, and as only resulting in the qualitative law or regula, which is the timeless and motionless principle of these quanta. That, at least, is Hegel's quest, — this principle ; and tliat, implicitly, we shall hold to be also Newton's quest. It was, after all, really only enhanced correctness on Hegel's part, THE FORMER IN THE IVIATHEMATIOAL REFERENCE. 127 then, to demand this due abstraction, and Thomson, as we saw, demanded the same. What Hegel says of Carnot in this place, too, surely does justice to Carnot, though duly signahsing certain impurities in the general conception. The next reference is to Infinitesimals. These he affirms to be already implied in, but very much behind, Newton's pro- cedes, — so far as purity and consistency of conception are con- cerned. It is here that what is mainly in Hegel's thought, — the omission of d ,v d y, comes to the surface, and Hegel now proceeds to consider the various expedients • in mitigation or justification of this. Euler, for example, in reference to the disappearance of quantitativity, introduces the conception of zero; but (besides other weak points) to express the relation as between zeros is objectionable, — in exi^ression, and rather darkens down the essential point, which is the relation as between non-quantitative but qualitative sides (though in quantitative matter). The quanta are assuredly zeros (in a certain way), as quanta, but zero to zero is not adapted to express the quahtativity that still remains. Though this is what is imphcit in the whole action, it is precisely this that the action itself tends to render inexplicit. Format, Barrow, and others make the process easy by re- ference to relative insignificancy, but understanding remains unenlightened — despite the magnanimous attempt of Wolf. We come now to the capital point that concerns Newton's expedient for the omission of the dxdy term. This is the fons et origo of all these evils, and demands our most serious inquest. But, in the first place, I will say what Hegel does not do here. He does not wish the drndy term retained. He knows that the correct result cannot be obtained unless with its omission. This presupposition in regard to dxdy accom panics him, as a condition necessarily understood, everywhere indeed ; and it is sufficiently singular that Mr Smith should be unaware of any such constantly concomitant ground-under- standing. Mr Smith asserts Hegel to accuse Newton of deter- mining the fluxion of a product in a manner "analytically unsound." Now that not only is not so, but, the "ground- understanding" considered, cannot be so. Hegel knows the result to be analytically sound; he only objects to an apparent arithmetical stratagem in deduction of it. Mr Smith's mistake is so complete, however, that he actually tells us, p. 503, — " Instead, therefore, of Newton rejecting a quantity on the ground of relative smallness, we find that Hegel has gratuitously introduced such a quantity," — dx d y, namely! Now, this mistake of Mr Smith is bad enough in itself, but it is Tvorse in its consequences. It misled, namely, two of our most distinguished men of science into illustrations from steam- 128 HEGEL AND MR SMITH, OR THE VINDICATION OF boats and railway carriages that were quite beside the point. Misled, indeed, into proceedings so superfluous, it was no wonder that they talked of " the incapacity of metaphysicians to understand even the most elementary mathematical demon- strations." That fortunately is not so ; the best metaphysi- cians have always been the best mathematicians ; and one is almost disposed to augur badly for the future of mathematics and mathematicians, if it is true that they contemplate dissolu- tion of the ancient marriage. But be that as it may, no meta- physician can feel at all aggrieved at the remark in question, seeing that, in this very paper, there has been such striking and abundant demonstration of at least a mathematician's incapacity to understand the metaphysician, or even the logic of his own processes. What Hegel, in the second place, does do is this, — but, first, let me quote from Professor James Thomson. In the Infini- tesimal Calculus, this mathematician tells us, the difi'erence of the function increased by the infinitesimal increment, from the original function is foimd thus, u being assumed as = « ?/ : — " Here by increasing xhj dx and y by d y, denoting by id what the function then becomes, and subtracting, we obtain u' — u= xdy + ydx + dxdyT That, then, is the difference re- quired. Of course. Professor Thomson goes on to tell us that dxdy is rejected as "infinitely small compared with," etc. What Ave have to see, however, is that, under supposition of an arithmetical process, the whole arithmetically " correct " result is xdy + y dx + d X dy. Analytically, we know that that is not so ; analytically, we know that dxdy must — for "correctness " — be got rid of. Leibnitz proposes to reject dydxaa relatively insignificant, intimating by that phrase, that even so, the arith- metical process may be regarded as " correct," quite as well as the analytical one. Newton, too, for analytical correctness, has to reject dxdy; but he would effect reconciliation of analysis with arithmetic, he would preserve " correctness " to both, by the following stratagem : When the product of x and y, each being lessened by subtraction of a half of its infinite difference, is taken from the product of x and y, each being increased by addition of a half of its infinite difference, there remains x dy + ydx, and this is the differential of the product xy. The in- voluntary answer is obvious : I see what comes out arithmeti- cally by tlie turn of your hand ; but what came out also arithmetically by turn of the correct arithmetical hand was different ; and it is vain to say your result is a correct arithmetical result arithmetically deduced from the same premises from which the other correct arithmetical result was also arithmetically deduced; for, in that case, xdy + ydx would be equal to xdy + ydx + dxdy, which is absurd. Hegel, then, does not quarrel with the rejection of dxdy, but only with the various excuses for it. THE FORMER IN THE MATHEMATICAL REFERENCE. 129 The above, to be sure, is not Newton's language, and Mr Smith almost objects as much; but it is a perfectly fair transla- tion of Newton's language into infinitesimal terms. The language may seem indifierent, then, the problem being the same in either ? It is easy to fall into such a supposition as this ; but I, for my part, must confess to have been misled by the mere change of language, correct though it be ; and it is also my sincere belief that Hegel has been similarly misled. I do not believe that he, for his part, would ever have thought it free to him to change Newton's language, and, accordingly, I take it for granted that he must have been directly under guidance of some mathematical authority other than Newton. Had Hegel studied Newton's own language, he would have seen that Newton was not only perfectly correct in the analytical result, but perfectly unassailable also in the formal process thereto. This process, under change of language, cannot but appear arithmetical. In Newton's hands, however, not only the result, but the process is analytical, and the rejection of dxdy is conditioned precisely as Hegel wished it to be — by tlie nature of the case itself. The expedient, in short, of considering one half on this side, and one half on that, of the point to be determined is really unimpeachable, and, in its simplicity and efficiency, does the usual honour to Newton's extraordinary penetration and unrivalled resource. The change of language, pre-occupied as I was by its legiti- macy, prevented me from seeing this for long ; otherwise the truth would have been told — without mention, I think, of Hegel's " harpoon ; " and now only that I can tell it, and do tell it^— now only is that I am truly "jubilant ! " Acknowledg- ment of so much misleading, however, is evidently wholly un- available m excuse of Mr Smith, who has utterly failed to see what Hegel meant, whether arithmetically or analytically. What follows, again, concerns Newton, but is not much. It has no object but to show the dangerousness of considering, not the nature of the case, but the tempting (though illogical) idea of relative smallness, and resorting, consequently, to rejection of what is so characterised. It is to that is to be attributed a certain error of Newton's discussed by Lagrange, and cor- rected, as Mr Smith reminds us, in Newton's own second edition. Qualitative considerations, on the part of Newton, might or might not have prevented the momentary oversight ; still Hegel has, very possibly, perfect reason for asserting that the whole general difficulty in question would disappear, were the operation made to depend not on the quantity, but on the quality concerned. Certain terms shall have validity, only as containing the qualitative character requh-ed, and the rest none, simply as non-qualitative, and not merely as quantita- tively insignificant. What is to be looked to is not a sum, but 130 HEGEL AND MR SMITH, OR THE VINDICATION OF a relation. All this appears pretty full in the Secret of Hegel. As Mr Smith says himself, Hegel leans on Lagrange here so far as concerns the mathematical facts ; it is Lagrange, there- fore, and not Hegel, whom he should abuse in that reference ; the latter only insisting on that peculiar qualitative idea of his as in connection with the material he simply receives. It is in this place Mr Smith asks, " Would not these relations be violated, and all mathematics rendered absurd, if the term that is qualitatively important could be quantitatively negligible?" That is pretty well HegeVs single question : ought mathemati- cians to allow themselves so unmeaning and dangerous an ex- pedient as rejection on account of quantitative insignificancy, seeing that, in point of fact, they reject only because of quali- tative insignificancy '? Paragraphs on Carnot and Lagrange have precisely the same burthen, and I pass at once to Hegel's remarks on the Method of Limits. These are to this effect. Though the true idea is present, he says, the category limit just as little expresses it as the category infinitely little: neither the one nor the other suggests the relation that is the interest at stake. No light comes from the loord limit, and neither does the character limit enter as such, and with relief of intelligence, into the treatment. Limit here, in fact, is very peculiarly limit : it requires an ex- planation of its own, and brings its own difficulties. Neither is the mode in which it is mathematically /ou/ic?, logically without inconsequences. And Hegel, in regard to this mode, proceeds to point to the contradictory aspects — in mere general, not analytic reference — which the setting h = o, and the introduc- tion generally of such a sign as o, or -, lead to. It is such con- tradictory aspect to him, for example, that what has become = -, should still remain a relation : and it seems to him that o ' there is no gain in -r^ being represented as = - for there is not the slightest hint in any such expression of the single thing that is wanted — the peculiar qualitativity. Mr Smith meets this objection — as we have seen already — with the incredibly inapposite words, "Accordingly Hegel proceeds, with much d y severity of manner, to knock down the indeterminate t-^ which he has just set up !" To say that- gives no clue to the the quahtativity of -7-^ is to knock the latter expression down ! The concluding observation of Hegel here is, that when you press for an explanation of the result, p, in the middle of all I THE FORMER IN THE MATHEMATICAL REFERENCE. 131 these contradictory expressions, introduced by the expedient of h = 0, you can only force the arbitrary assertion : ' Well, then, if you must know, it is just such and such a co-efficient, and so and so derived.' Accordingly Hegel intimates that that is really just what it is, and that it might have been far better said at once. All that is wanted is a certain term; for that term contains the qualitative law that alone functions, and all the rest falls to the ground, not because of this expedient, and that expedient, specially not because of its quantitative insignificance, but be- cause of its qualitative insignificance. It is, then, simply the expedient of setting h = o that Hegel chiefly objects to in this place. The whole result shall be sup- posed to depend on making something nothing at last, which something, if it had been similarly .regarded as nothing at the beginning, would have stifled all result in the birth ! That a quantity be conceived to vanish is certainly a very common device in mathematics, and quite legitimately so — in expres- sions that bear to be correct, let the quantity conceived to vanish assume what value it may. For Hegel, then, it is cer- tainly to be said here that what is before us cannot be held to carry this character on its face. But be that as it may, once again we see that Hegel has not in view any internal, material, analytical objections, but only external, formal, arithmetical, or rather logical objections; and once again we are called upon to see also how fearfully Mr Smith mistakes all this. We have had already before us (p. 113) the first half of what Mr Smith says as in reference to Hegel and the method of limits, and need now consider only the remainder. In this part of Mr Smith's work the first reference is to Taylor's theorem, and the mode in which the limit is determined ; and here, according to Mr Smith, Hegel shall be completely ehalii to find p turn up in that capacity, and "not, as it should have been,-/" It is really almost incredible that Mr Smith should have even dreamed himself to see the thmgs he believes himself to see awake here. The good Hegel never either thought or said that the result should be -, and not p. He has not a single refer- ence to the result as correct or incorrect mathematical outcome — he has not a single reference in an analytic or material direc- tion. He only points to certain formal logical appearances of inconsistency which certain mathematical expedients bring with them. Under the hallucination, however, that Hegel is disputing the analytic results, Mr Smith proceeds thus : — " This, of course, is sadly inconsistent ; for instead of our fine qualitative determina- tion, here is a stubborn quantum turning up. Now, says Hegel, the mathematicians try to get over this by saying that p is not really = - but is only a definite value, tu 132 HEGEL AND MR SMITH, OR THE VINDICATION OF which - comes as near as you please. Of course, if this is so, it is as evident as any o thing can be that the difference between p and - is not a quantitative one. But, adds the philosopher, naively enough, that does not help one over — li :=— . Suppose now a X o ■ . that we were to say — really = p (a, definite quantity), as, in fact, mathematicians dx do say, then it is obvious that 5 x couldn't have been = o. Or, if, finally, it is con- ceded that ^ = (which Hegel seems to think most likely, since § y and 5 x d X vanish together), then what can p be ? Now, can any one say that the man who devised this argument knew what he was doing?" That, perhaps, is the most exquisite piece of fooling ever Avitnessed — Mr Smith gravely representing Hegel as coming to reason witli the mathem"aticians 7nathematically, and all so regularly from stage to stage ; whereas Hegel has only logically in his eye that expedient of h = o ! The wonder is how or where Mr Smith got these things. Fancy this, for example : " If Hegel allows that there is no quantitative difference be- tween p and — why does he assume a qualitative one 1" Ah, me I o, why indeed % " Or, above all, why try to explain Newton's doctrine without ever deigning more than a contemptuous glance at the one central point of the whole % " Well now, Mr Smith might have seen that — this, namely, that Hegel has not a thought of Newton in the locus cited, but only of what is peculiar to the method of limits as the method of limits. " Can any one say that the man who devised this argument knew what he was doing 1 " Will it be permitted me to point out here that the " man " spoken of — the only man who " devised " the "argument" in question — is Mr Smith himself? And, in that case, will it be uncharitable to agree with him, that " he knew not what he was doing ? " Mr Smith follows up, how- ever : — " Hegel boasts that half-an-hour would suffice to learn the calculus ; certainly he might have employed a good many hours in unlearning his false conceptions of it." I have else- where shown that the " half-hour " in allusion is again a " boast" only in Mr Smith's own Hegelian incompetency; and as for his opinion that Hegel " might have employed a good many hours in unlearning," etc., we now know what value to attribute to it. It is Mr^ Smith's " half-hour " — the half-hour he was induced to bestow on his hasty enterprise — that will appear in the end, perhaps, the worst spent half-hour in his whole lifetime. Hegel proceeds now to the category of approximation, to the conversion of quantities, to the physical senses assigned to analytical terms, etc., but in this matter there seems nothing to occur that calls for special mention on my part. We can now THE FORMER IN THE MATHEMATICAL REFERENCE. 133 pass also the opposition between "discovery" and "proof" as in reference to Kepler for the one and Newton for the other ; nor need we spend a single moment on the mere hint of Hegel's Golhesque optical perversity. All that is to be found at full elsewhere. Indeed I may now say that I have allowed myself a certain perfunctoriness all through the consideration of Re- mark 1, inasmuch as the whole of it is conveyed in the Secret of Hegel — and not badly on the whole, perhaps, despite the small number of corrections I have already collected for future use. I pass in the last place to Remark 2. Hegel has already told us that the object of this note is to be the meaning of the differential expression, derived from the ex- pansion of the binomial, or how it may. He will show in what concrete need the calculus originated, and what is the sense of its characteristic movement when referred to the facts of nature it is supposed to manipulate. On the whole, the fulcrum of all this seems to lie for Hegel in what we have already seen, when engaged with the method of Cavalleri : the qualitative conver- sion, namely, that lurks in the arithmetical ascent to powers. Such qualitative conversions occur in regard of the dimensions of space, for example. So motion, as uniform and as uniformly accelerated. Such considerations, then, are essentially quali- tative, and it is with considerations essentially qualitative that the differential calcuhis deals. Now, it is just possible, there- fore, that this qualitative conversion in concrete objects may be precisely that Avhich requhes to be connected with the evolu- tion of the calculus. The calculus always concerns equations that contain powers higher than the first, and its movement is a lowering of these by development in quest of a certain rela- tion. It is in this reference that Hegel talks of the power as capable of being considered a system of relations within itself — the original magnitude being so considered, and, consequently^ as essentially a binomial — and that so regarded and expanded, there result functions in determinate relation to the quantity itself. This relation of the derivative to the primitive is the relation sought in regard to concrete applications. It is obvious, consequently, how it explains nothing to say, the differential is just such and such a term, and the others are simply thrown out. We must see that it is the original immanent relation, and correspondent to relations in the concrete — a qualitative rela- tion which is called infinite only as independent of any particular quantitative assignment, not but that particular problems will always involve such. In view of these determinations we may neglect what Hegel says about Inde^ erminates. Series, the in- appositeness of various other expressions, etc., and confine our- selves to his illustrations. Hegel's nearest specification here is, that the operation of reducing to a lower dimension an equation which is at the same 134 IIKGEL AND MR SMITH, OR THE VINDICATION OF time considered with reference to the derivative functions of the variables it contains, yields a result which is veritably no longer an equation but a relation, and this relation is the special object of the differential calculus. He announces that it is the method of Lagrange supports his references, but he would bring all into its due abstraction. So only will the fortuitous look be banished from the calculus, and all the apparent contradictions of its opening be reconciled to general principles otherwise. The calculus cannot have arisen from or of itself; it must be the result of some concrete need. But in it, as is usual else- where, the first attempts would be instinctive rather than fully conscious, and practice would precede theory. In a word, says Hegel, it is in the various Tangential methods that we must find the thing itself in its successive steps from the first on- wards. Again, he says, — "Let us take the simplest example from curves determined by an equation containing a power of the second degree. The relation of the co-ordinates is given by the equa- tion at once in a power-form {poxver meaning any power above the first). Consequences of the fundamental determination are the determinations of the other straight lines , tangent, subtangent, normal, etc., which are in connection with the co-ordinates. But the equations between these lines and the co-ordinates are lintar equations; the wholes, in regard to which these lines are determined as parts, are right-angled triangles formed by straight lines. The transition frqm the original equation, which contains the power- fonn, to said linear equations involves now the mentioned transition from flie original function (which is an equation) to the derived one (which is a relation, a relation between certam lines that belong to the curve). The connection between the relation, of these luies and the equation of the curve — it is the finding of that that is in question. " It is not without interest, as regards the history of the general question, to remark that the first discoverers were confined to a mere empirical statement of what they had fomid, without being able to give any account of their operation, which remained, for its part, wholly external. It is enough here to refer to Barrow, Newton's teacher. In his Lect. Opt. et Ueom., in which he treats problems of the higher geometry on the method of indivisibles — a method distinct, properly, from what is peculiar to the differ- ential calculus, he communicates. (Lect. x.) his process in determination of tangents — " because his friends have urged him." One must read in the book itself, all about this communication, in order to realise a competent conception of how the process is delivered merely as an external rule, — in the same style as school books give the rule of three or the proof by nmes. He draws the lines, afterwards known as the incre- ments in the characteristic triangle of a curve, and gives the direction, in the manner of a mere rule, to reject as sujierfluous the terms which, en suite of the development, come in as powers of said increments or products (etenun isti termini nihUum valebunt) ; in the same way, the terms constituted by the magnitudes contained in the original equation are to be rejected ( — the subsequent subtraction of the original equation from that formed with the increments); and at last for the increments of ordinate and absciss, the ordinate itself and the subtangent are to be substituted. The operation, if we may so, cannot be given in a manner more schoolmaster-like. The said substitution is, in the ordinary differential method, the assumption, made fundamental, of the pro- portionality of the increments of the ordinate and the absciss to the ordinate and the subtangent. In Barrow, we see this assumption in its naive nakedness. A simple mode of determmmg the subtangent was found. The methods of Eoberval and Permat have a similar scope. The method of the latter to find the least and greatest values, points to the same basis and the same process. It was a mathematical craze of the time to try to find such methods, properly rules, and make a secret of them — which was not only easy to do, but for the same reason, in a certain respect, unavoidable, — because, namely, the discoverer had discovered only an empirical external iixle, no method, that is, or not what had been deduced from established principles. Leibnitz and Newton, both from the time, the latter from his teacher, had to receive such so-caUed methods. Through generalisation of their form and application, these masters have paved new ways for THE FORMER IN THE MATHEMATICAL REFERENCE 135 the sciences. But they had, at the same time, to wrest free the process from the mere manner of external rules, and have both sought to procure for it the necessary legiti- mation. " If we more particularly analyse the method, the actual procedure will be seen to be this, — firstly, the power-forms (of the variables, of course), contamed in the equation, are reduced to theu- first functions. But so the value of the terms of the equation is altered. There remains not any longer an equation, but there has arisen a relation — between the first function of the one variable and the first function of the other. Instead oi p x ^ y"^ we have p •" 2 y; or, instead of 2 a a; — so" =y- we have a — x -.y, which comes after- wards to be designated as the relation —J. The equation is equation of the curve ; — a X this relation that, quite dependent on it, is derived (above by a mere rule) from it, is, on the contrary, in quality, a linear determination, with which certain lines are in pro- portion p:2y,0T a — x: y — these are themselves relations of straight lines of the curve, the co-ordinates and the parameters. But with all that uothing is yet J^nown. The interest is to know, of other lines iii regard to the ciirve, that this relation attaches also to them; or the interest is to find the equality of two relations. Secondly, therefore, the question is to discover what are the lines determined by the nature of the curve which stand in such relation 1 But this is just what was already hnown, — namely, that such so found relation is the relation of the ordinate to the subtangent. This, ingeni- ously, the ancients had discovered geometrically ; what the moderns have come upon is the empirical process so to prepare the equation of the curve that said first relation is yielded, of which it was already known that it is equal to a relation belonging to the line, here the subtangent, whose determination was sought. Partly, now, said prepara- tion of the equation --the differentiation — has been methodically conceived and executed. Partly, again, the imagmary increments of the co-ordinates, and the imaginary charac- teristic triangle, formed thereby and a similar increment of the tangent, have been invented, in order that the proportionality of the relation, found by depressing (lowering a degree) the equation, to the relation of the ordinate and the subtangent, may be ex- hibited, not as something only empirically assumed from what was known of old, but as something demonstrated. The knowledge from of old, however, manifests itself gener- ally, and most uumistakeably in the said form of rules, as the only occasion and respective legitimation of the assumption of the characteristic trianr/le and said proport ionality. ' ' Lagrange now, Hegel proceeds to tell us, " rejected this simulation, and struck into the scientific path proper." That means that, in the same connection, Lagrange made no assump- tion, but attempted to reach the same point by a mode of procedure regular and rigorous. We have to thank his method, Hegel continues, for signalisation of the point that is vitally concerned. It separates, and handles apart, the two processes on which the solution of the problem depends, — that is, first, the theoretical consideration in regard to the finding of the first fimction from the given equation ; and, second, in regard to the finding of the concrete elements which stand in the relation expressed by said first function. This latter need, he says, is directly accomplished ; and then he proceeds to describe more particularly how, and always so, that the inherent agreement with Hegel's metaphysical ideas is made manifest. But the great point of Hegelian interest here, so to speak, is this, that Lagrange, even when resorting to the assistance of " the objectionable increment," is held to do so geometrically, and, consequently, ?mobjectionably, or so that the consideration mainly concerned is qualitative and not quantitative. I have not consulted the original either, but I see no reason for assuming Hegel not to have correctly described what he had simply 136 HEGEL AND MR SMITH, OR THE VINDICATION OF before him. When I say " correctly," I mean essentially correctly ; for it is not necessary for me to laud the description as well done, or even to assert it free from such errors of press or pen as I have, not unfrequently, found in the last two of the three Remarks. I can say, notwithstanding, that it is precisely here that Mr Smith's main delusion in regard to an Hegelian calculus comes to the front. He actually regards a mere description in Lagrange's reference as " simply an excessively clumsy adaptation of the method of Lagrange !" Adaptation ! Hegel has no mathematical object whatever : he only thinks, and would show, that Lagrange's mathematics agree more or less 'with his metaphysics. Mr Smith here also, as in what concerned limits, has simply misapprehended what it was all about. He has merely fooled himself into a formal wrangling against a mathematical ratiocination that nowhere exists. Quotation would make this even ludicrously apparent, were one not inclined to spare the printer sundry compound mathematical expressions. Hegel now seeks further illustration of what he has in mind in a reference to Descartes, on which there is no call to enter, whether as respects Mr Smith or the general subject. What Hegel has specially in view is well seen in his eulogium of Descartes, when he pronounces his procedure "the genial Griff of an dcM analytical head, in comparison with which " the quite assertorically assumed proportionality of the subtangent and the ordinate with the suppositious so-called infinitely-small increments of the absciss and the ordinate stands quite in the back-ground." Remarks follow in the general spirit of what we have already seen — that mathematicians fail to signalise the precise thing concerned, and resort, in consequence, to objectionable expe- dients. That numerical operation may be qualitative transi- d u tion, is again alluded to. " The equation -j^ = P," it is said, " expresses nothing more than that P is a relation, and there is cl V otherwise no real sense to be ascribed to -j^ . Of this relation = P, however, it is still undecided what other relation it is equal to ; such equality, the proportioyiality, only first of all gives it a value and a signification." Altogether what occurs here seems consistent and to the point. But for the length to which this paper already extends, I would translate it, every word. What follows next, on Hegel's part, is a certain reference to mechanics, of which Mr Smith makes game thus : — " That t and s in Kepler's law are not variables, but constants determined for each planet ; that the equation has no analogy whatsoever with the equation of motion ; that its differentiation would be THE FORaiER IN THE MATHEMATICAL REFERENCE. 137 meaningless unless space were filled witli planets ; and that then it would have nothing to do with ' the determinations of that absolute motion,' are considerations that never entered Hegel's head." What Hegel says is this (and wliat part Lagrange has in it must be determined by others — Hegel cer- tainly begins by quoting Lagrange) : — " The law of foiling bodies, says Lagrange, is expressed iii the equation s = at- ; the simplest next motion after that one would have the equa- tion s = ct^ ; no such motion is seen in nature ; but then there is a motion expressed in Kepler's law, s^ = at" ; what the first 2 at derivative function, o"^, etc., may mean there, etc., .... must appear an interesting problem, in which analysis would show itself in its most appropriate splendom-." So far as ]\Ir Smith is right in this reference, by all means let there be assumed another blunder for Hegel. Mr Smith's comments on Hemark 2 cease here, I think, and I shall pass to a conclusion on its remaining contents. The follo-udng sentence in the neighbourhood immediately before us, is very significant as to Hegel's general purpose : — "The preceding has had for object to make prominent and precise the simple specific procede of the differential calculus, and to demonstrate its presence in a few of the usual elementary examples. Said proccdi has been found to consist in this, that from an equation of power-functions, the co- efficient of the term of development, the so- called first function, is obtained, and the relation, which this function represents, is demonstrated in moments of the concrete object ; by means of which so-got corre- spoftdence between the two relations these moments are themselves determined." The phrases do not run well, perhaps, but the meaning will be clear. One more quotation, and the last : — " Because, in a certain process of Archimedes, as weU as, later, in Kepler's treatment of stereometric objects, the conception of the infinitely little presents itself, this has been often used as an authority for the employment which is made of such conception in the differential calculus — without what was distinctive and peculiar in it having been duly signalised. The infinitely little signifies, in strictness, the negation of quantum as quantum, that is, of a so-called finite expression, of the completed deter- minateness which quantum as quantum is. In like mamier, in the celebrated methods of Valerius, Cavalleri, and others, which are founded on the consideration of the 7-cla- tions of geometrical objects, the ground- character is, that the quantum as quantum of the object of investigation, which is properly examined only in its constituent relation, is to be put out of view, or rather taken as a iton-quantum. Partly, however, so, the affirmative which lurks behind the merely negative consideration, has not been recog- nised and signalised — the affirmative which was exhibited above, abstractly, as the qualitative determinateness of magnitude, and as more precisely lying in the power- relation. Partly, at the same time, this relation including in itself a number of more particular relations, as that of a power and its function of development, these latter more particular relations have been again supposed to be grounded on the general and negative character of the same infinitely little, and derived from it. In the exposition of Lagrange just seen, the precise affirmative that lies in Archimedes' treatment of the problem comes to light, and accordingly there is given to the operation, burthened with the unUmited progressus, its own due limit. The magnitude of the modern invention per se, and its ability to solve problems previously intractable, as well as to treat the previously soluble in a simple manner, is solely to be placed in the discovery of the relation of the original to the so-called derived functions, and of the parts which in the 138 HEGEL AND MR SMITH, OR THE VINDICATION OF case of a mathematical whole stand in such relation. The statements made may suffice to manifest the peculiarity of -the relation of magnitudes which is the object of the special calculus in question. These statements it was fortunately possible to confine to simple problems and their modes of resolution ; it would have neither been expedient as regards the determination of the notion, which determination is here alone concerned, nor would it have lain in the author s power to have reviewed the entire compass of the so-called application of the calculus, and, — through reference of aU the respective pro- blems and their resolutions to the principle which has been here demonstrated, — to have completely carried out the induction of this principle being its (the calculus') foundation." AVitli these words before us, it is impossible to deny eitber Hegel's conceptions of bis own problem, or the preteiisions with which he approached it. The former are, after all, not less simple than the latter are modest. Hegel, in fact, has nothing new, — nothing whatever to propose mathematically; he would only demonstrate his own metaphysics in the existent actual (i.e., of the calculus), without a dream of subverting it, — without a dream even of correcting it, unless in the interest of mere logical simplicity and consistency. With what radical misconception, and in what lamentable spirit of gratuitous abuse, Mr Smith has treated all this, we have already seen, and I shall now quote from his paper, a few final passages : — " Since we are told that in the equation, s == ct there is no scope for dififerentiation, s - not bemg qualitative [Hegel, of course, does not say that], we may at least conclude that Hegel does not regard miiform motion as continuous. . . . I do not, there- fore, think it needful to go into details on this part, of Hegel's method. . . . His method has the same fundamental fallacy as that of Lagrange. . . . An obvious analytical absurdity. ... I shall, in passing from the subject of geometry, merely enunciate a simple deduction from Hegel's result in an intelligible form. ' At any point of a curve there are an infinite number of tangents, which may be got by nniting that point with any other point on the curve whose abscissa is not different by a quantity greater than unity.' I present this proiaosition, which is entirely due to Hegel, and m the development of which my share has been ' jjurely mechanical,' for the admiration of all Hegelians whatsoever. . . . These notes show [i.e. on Hegel's part] quite clearly, — fy'sf, substantial ignorance of the subject in hand, bolstered up by some hasty glances at the ' literature of the subject;" secondly, great disingenuousness m criticising Newton, without having ever given his views a careful study ; tJurdly, almost incredible coirfusion of mind, in so far as he seems to have thought that he knew his own meaning when he really had no meaning at aU; and lastly, to add nothing more, such a degree of self-complacent arrogance as led him to fancy the results of his ' half hour ' more valuable than the fruit of the whole life of men like Newton." The reader will have perceived that, in describing the con- tents of Hegel's Remarks, I have inserted from time to time the counter observations of Mr Smith. In this way, indeed, I suppose myself now to have done pretty well all that is necessary. That Hegel neither proposed, nor dreamed of proposing any analytical method of his own must by this time be as obvious to the reader as Mr Smith's amusing resolution to wrangle such actual proposition of a new method mathematically out with him. Mr Smith's mistake must prove altogether sm-pris- ing, indeed, in presence of Hegel's own express declaration of THE FORMER IN THE MATHEMATICAL REFERENCE. 139 insufficient mathematical proficiency even to cany out the illustration of his metaphysical explanations in the entire compass of the mathematical details. Still, for all that, it is not exactly mathematical ignorance that we shall feel impelled to remark in Hegel, — on the contrary, we shall probably see good reason for entertaining even mathematical gratitude towards him, and just because of those "explanations" of his in a mathematical reference. The mistake of the mathema- ticians (of the Royal Society) in this connection has been, indeed, utter ; to them Hegel, whose every word assumed that d X d y was of course to be thrown out, and of course correctly, — to them this same Hegel shall have held Newton guilty of "analy- tical imsoundness," because he threw it out ! How much they have mistaken, too, the spirit of his apparent criticism ! I shall have shown, in allusion to the fourth proposition of the first book of the elements of Euclid, that, certain pieces being given, the question is only of a single figure, and that superposition conse- quently is no more than a superfluity in illustration — I shall have shown this, and because I shall have shown this, I shall be supposed to have accused Euclid of incompetency, and to have impeached the principles of geometry in general ! Or, to Mr Smith specially, Hegel, when demonstrating the presence of his own notion in the mathematical proceedings of Lagrange, and others, shall be only fighting mathematically for his own hand, hke the Gow Chrom, and actually proposing a rival calculus ! To Mr Smith — at that time not much more than a youthful student — Hegel, certainly at least one of the two greatest metaphysicians since Aristotle, shall have shown " quite clearly " " almost incredible confusion of mind, in so far as he seems to have thought that he knew his own meaning when he really had no meaning at all ! " One finds ample revenge for Hegel, however, when one thinks of all the rabid nonsense, not only in English, but even in French, that oiu- mathematicians have written against him, — above all, when one thinks of the twenty-one pages, from p. 491 top. 511, in the twenty-fifth volume of the Transactions of the Royal Society of Edinburgh. Finally, it may be suggested that it will be only fair to try Hegel's " explanations " by reference to what precedes, and not to what succeeds, the year 1812. /^^'"I'lf,"^^ UNIVERSITY Works by James Hutchison Stirling. /?^ 2 Vols. Svo,])]}. 1164, ^mce 28s., THE SECRET OF HEGEL; BEING THE HEGELIAN SYSTEM IN ORIGIN, PRINCIPLE, FORM, AND MATTER. In 8vo, price 5s., SIR WILLIAM HAMILTON; BEING THE PHILOSOPHY OF PERCEPTION. AN ANALYSIS. Price 2s., AS REGARDS PROTOPLASM. NEW AND IMPROVED EDITION, COMPLETED BY ADDITION OF PART IL, IN REFERENCE TO MR HUXLEY'S SECOND ISSUE, AND OF PREFACE, IN REPLY TO MR HUXLEY IN " YEAST." London : LONGMANS & Co., Paternosteb Row. OUT OF PRINT. MATERIALISM IN RELATION TO THE STUDY OF MEDICINE. AN ADDRESS. Edinburgh : WILLIAM BLACKWOOD & SONS. Fourth Edition, price 6s., H ANDBO OK of the HISTORY OF PHILOSOPHY. By DR albert SCHWEGLER. TRANSLATED AND ANNOTATED. Edinburgh : EDMONSTON & DOUGLAS. 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