[1] The distinction here drawn is not merely verbal. The greatest happiness of the greatest number may mean either the largest total of happiness in which the largest possible number of those concerned can participate, or a still larger total, which, if some of the possible participants were excluded, would be divisible among the remainder. The largest aggregate of happiness attainable by any or by all concerned, means the largest sum total absolutely, without reference to the number of participants. Writers on Utilitarianism seem to have sometimes the first, sometimes the second of these totals in view, but more frequently the second than the first.

[2] I do not form a separate class of pleasures of the affections, because these seem to me not to be elementary, but to be always compounded of two or more of the other five kinds.

[3] 'On Labour,' p. 135.

[4] 'Fortnightly Review,' June, 1868.

[5] See the No. for June, 1869.

[6] 'On Labour,' p. 93.

[7] 'Fortnightly Review' for June, 1869, p. 683.

[8] See 'Fortnightly Review' for June, 1869, pp. 687-8.

[9] 'Utilitarianism,' by J. S. Mill, pp. 64-8.

[10] 'Fortnightly Review' for June, 1869, pp. 684-5.

[11] 'Utilitarianism,' p. 267.

[12] 'Utilitarianism,' pp. 69, 70.

[13] 'Les lÉgistes leur fournirent au besoin l'appui du droit contre le droit mÊme.'—De Tocqueville, 'L'Ancien RÉgime,' p. 567.

[14] 'Utilitarianism,' pp. 72, 73.

[15] 'Utilitarianism,' p. 71.

[16] 'Utilitarianism,' pp. 81, 82.

[17] 'Utilitarianism,' pp. 84, 85.

[18] Ibid. p. 85.

[19] 'Utilitarianism,' pp. 86, 87.

[20] 'Utilitarianism,' p. 94.

[21] Ibid. pp. 94, 95.

[22] Mr. Buckle's first chapter, passim.

[23] 'Cornhill Magazine,' for June and July, 1861.

[24] 'Lay Sermons,' p. 158.

[25] A highly esteemed literary friend, who has done me the favour of looking over these pages in manuscript, considers that what I have proved is, not that Omnipotence involves the co-existence of Freewill and Necessity, but that Omnipotence itself, although capable of possessing all things, could not possess Freewill, and that consequently Freewill cannot possibly exist—that there cannot possibly be any such thing.

Although, for reasons stated four pages back, not myself prepared to accept this view of the matter, I should cheerfully accept it if I could. The argument in the text proceeds upon the assumption that people mean something when they talk about Freewill. If, however, they have no meaning, if the phrase be a simple sound signifying nothing, of course all controversy regarding the possible co-existence of that nothing with Necessity is settled at once and for ever, while no great amount of philosophy will be requisite to induce mankind to resign themselves very placidly to the absence of that same nothing.

[26] Mill's 'Logic.' Fifth edition. Vol. ii. p. 527.

[27] Mill's 'Logic,' vol. ii. p. 504.

[28] 'S'il se fÛt trouvÉ alors (vers 1750) sur le trÔne un prince de la taille et de l'humeur du Grand FrÉdÉric, je ne doute point qu'il n'eÛt accompli dans la sociÉtÉ et dans le gouvernement plusieurs des plus grands changements que la RÉvolution y a faits, non-seulement sans perdre sa couronne, mais en augmentant beaucoup son pouvoir.'—De Tocqueville, L'Ancien RÉgime, p. 274.

[29] Analysis of the Phenomena of the Human Mind. By James Mill. Edition of 1869, with Notes by Alexander Bain, Andrew Findlater, George Grote, and John Stuart Mill, vol. i. pp. 78 et seq.

[30] Mill's 'Logic.' 5th Edition. Vol. i. p. 377.

[31] 'There is a class of animals called Ascidians, which possess a heart and a circulation, and up to the year 1824 no one would have dreamt of questioning the propriety of the deduction, that these creatures have a circulation in one definite and invariable direction; nor would any one have thought it worth while to verify the point. But in that year M. von Hasselt, happening to examine a transparent animal of this class, found to his infinite surprise that after the heart had beat a certain number of times, it stopped, and then began beating the opposite way, so as to reverse the course of the current, which returned by-and-by to its original direction.'—Huxley's Lay Sermons, p. 95.

[32] ArchimÈde, pour tirer le globe terrestre de sa place et le transporter en un autre lieu, ne demandait rien qu'un point qui fÛt ferme et immobile: ainsi j'aurai droit de concevoir de hautes espÉrances si je suis assez heureux pour trouver seulement une chose qui soit certaine et indubitable.—Descartes, MÉditation DeuxiÈme.

[33] Lay Sermons, xiv. 'On Descartes' Discourse;' also an article by Professor Huxley, on 'Berkeley and the Metaphysics of Sensation,' in 'Macmillan's Magazine' for June, 1871.

[34] Article on 'Berkeley and the Metaphysics of Sensation,' in 'Macmillan's Magazine' for 1871, pp. 152 et seq.

[35] The quotations, of which those in the text are abridgments, will be found in 'Lay Sermons,' xiv. pp. 364-7.

[36] The story was thus told by Diderot, to Sir Samuel Romilly, when a young man:—'Je vous dirai un trait de lui, mais il vous sera un peu scandaleux peut-Être, car vous autres Anglais, vous croyez un peu en Dieu; pour nous autres, nous n'y croyons guÈres. Hume dÎna dans une grande compagnie avec le baron D'Holbach. Il Était assis À cÔtÉ du baron; on parla de la religion naturelle. "Pour les athÉes," disait Hume, "je ne crois pas qu'il en existe; je n'en ai jamais vu!" "Vous avez ÉtÉ un peu malheureux," rÉpondit l'autre, "vous voici À table avec dix-sept pour la premiÈre fois."'—Edinburgh Review for January 1847.

[37] 'Studies in Animal Life,' chap. v.

[38] The reader who, having skipped some of the earlier chapters, may find this language obscure, is requested to turn back to the essay on 'Huxleyism,' pp. 194-6.

[39] See again, pp. 194-6.

[40] 'Mr. Darwin's Hypotheses.' Part II. 'Fortnightly Review' for June 1868.

[41] 'Origin of Species,' p. 226.

[42] Of this treatise, no English or French translation has, I believe, been published. For my own very limited acquaintance with it, I am indebted to the extreme kindness of my friend, Professor Croom Robertson, who has most obligingly favoured me with a manuscript version of the portion referred to in the text.

[43] 'Lay Sermons,' p. 240.

[44] 'Beauties of the Anti-Jacobin,' 1799, pp. 214-6.

[45] 'Auguste Comte and Positivism,' passim.

[46] 'History of Philosophy,' 4th edition, vol. ii. pp. 654-735.

[47] Not that so restricted a meaning can, with any propriety, be placed on positivist definitions of law. See, for instance, that of Mr. Lewes ('History of Philosophy,' vol. ii. p. 701), who defines law to be 'the invariable relation between two distinct phenomena, according to which one depends on the other.'

[48] Some few additional random remarks, however, though not permissible in the text may, perhaps, be less inappropriate in a note.

My scientific deficiencies do not prevent my understanding or, at least, fancying I understand, that Comte's famous 'Classification of the Sciences' may be extremely serviceable as indicating in what order the sciences may most profitably be studied. That a student's general progress would be swifter and surer if, before entering on physics or chemistry, he had already made considerable progress in algebra, geometry, and mechanics, than if he commenced all five sciences simultaneously, seems probable enough. If, however, the classification be intended also to indicate historically the order in which the sciences have actually been studied, I cannot but suspect it to be misleading. Certainly, if knowledge of number was the earliest knowledge acquired by man, those savage races which have not even yet learnt how to count beyond four, must have been content with very few lessons in arithmetic when turning off to other branches of learning.

As to the measure of success that attended Comte's scheme of creating a Philosophy of General Science, I presume not to utter one syllable of my own, preferring to cite what Mr. Mill says of that 'wonderful systematization of the philosophy of all the antecedent sciences from mathematics to physiology, which, if he had done nothing else, would have stamped him on all minds competent to appreciate it as one of the principal thinkers of the age.' In all sincerity, I say that the mere conception of the enterprise, whose vastness is so luminously expounded by Mr. Lewes, in the last edition of his 'History of Philosophy,' seems to me to betoken superior genius. I feel, as it were, simply awe-struck in the presence of an intellectual ambition, that within the brief span of one human life could aspire to a mastery over all the sciences, sufficient, first for co-ordinating the fundamental truths and special methods, and so obtaining the philosophy of each, and then for co-ordinating the manifold philosophies so obtained, and—by condensing them all into one homogeneous doctrine, and blending them into one organic whole, whereof each part would be seen to depend on all that preceded, and to determine all that succeeded—transforming all science into philosophy.

One point however remains on which I shall speak with some confidence, that, namely, of the inclusion among 'Comte's titles to immortal fame' of the creation of a Science of Sociology. 'What the law of gravitation is to astronomy, what the elementary properties of tissues are to physiology,' that, says Mr. Lewes, in the opinion of Comte's disciples, 'is the law of the three stages to sociology.' But if, as I have shown, there are not really three but only two stages, the so-called third stage being simply a return to either the second or the first, the law of the three stages cannot be much of a law, nor the science of which it is the essence much of a science.

Mr. Lewes, nevertheless, maintains that M. Comte created Social Science. Mr. Mill considers that he did not create it, but only proved its creation to be possible. With all possible deference, I submit that what he really did was to prove its creation to be impossible.

In a passage of Mr. Mill's 'Positivism,' quoted with approval in Mr. Lewes's 'History of Philosophy,' and presumably, therefore, expressing the sentiments of both writers, Comte is described as pronouncing inappropriate to the Science of Society, the method universally admitted to be proper to all other sciences—that, namely, of obtaining by induction the laws of the elementary phenomena, then, from these laws thinking out deductively those of the complex phenomena, and, finally, of verifying by specific observation the laws obtained by deduction. Among social phenomena, he is described as arguing, the elementary ones are human feelings and actions, the laws of which are the laws of universal human nature. But the human beings, on the laws of whose nature social facts depend, are not abstract or universal, but historical human beings, already shaped and made what they are, not by the simple tendencies of universal human nature, but by the accumulated influence of past generations of human society. This being the case, the laws of universal human nature evidently cannot serve as materials, whence it would be possible for any powers of deduction, starting from the bare conception of the Being Man, to predict beforehand how successive generations of men would feel and act. Wherefore, in order to get at social laws, we must reverse the ordinary method, seizing upon any generalizations which the facts of history, empirically considered, will supply, and then using the universal laws of human nature for the verification of these generalizations.

I will not linger over the glaring inconsistency involved in the conclusion thus arrived at, of appealing, for the verification of empirical generalizations, to a species of deduction confessed to be impracticable for want of the requisite materials. I prefer to show that from Comte's own premises, as rendered by Mr. Mill, necessarily results a separate conclusion, absolutely fatal to his sociologically creative pretensions. According to him, as we have seen, the laws of elementary social facts, or of human actions and feelings, are the laws of universal human nature, which latter can, of course, be no other than whatever habits of invariably, in given circumstances, feeling and acting in given modes, may be common to all mankind. But it is admitted that the particular generation of human beings at any time existing must, by the accumulated influence of preceding generations, have been rendered very different from every preceding generation: and nothing is more certain than that two generations differing widely from each other in character, would, in many given circumstances, not only not feel and act in precisely the same, but would inevitably feel and act in widely different, manners. Nor is this all. The circumstances by which any generation is surrounded have been partly shaped for it by preceding generations, partly modified by itself—so that it is not possible for any two generations ever to find themselves in the same circumstances. Wherefore, as there never can be a repetition of either men or of circumstances precisely the same, it is manifestly impossible for any habits of feeling and thinking, in given modes in given circumstances, to be common to any two generations of men, still less to universal mankind. In other words, there cannot possibly be any laws of human nature: and if no laws of human nature, then no laws of elementary social facts; and if no laws of elementary social facts, then no laws of complex social facts; and if no laws of social facts, elementary or complex, then no single particle of material wherewith to build up the Science of Society or Sociology.

[49] 'Auguste Comte and Positivism,' pp. 133-4.

[50] 'Auguste Comte and Positivism,' pp. 25-8.

[51] 'Fortnightly Review' for June 1868, 'Mr. Darwin's Hypotheses.'

[52] 'Statistical Enquiries into the Efficacy of Prayer,' by Francis Galton, in Fornightly Review,' for August 1872.

[53] 'Contemporary Review,' July 1872. 'The Prayer for the Sick. Hints towards a serious attempt to estimate its value.' Communicated by Prof. Tyndall.