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the style of Comte; whose conscientious care to clothe his thoughts in the clearest language has impressed his pages with the appearance of painstaking precision, whilst depriving them of the power of reflecting any other image than the fidelity of the philosopher and the integrity of his truth. We miss also from Comte's pages that incessant play of wit, luxuriance of fancy, and brilliancy of illustration, with which the genius of Bacon has succeeded in adorning the rugged ascent of scientific research, and which are to the striving student as is the glittering profusion of many-coloured flowers, that so continually greet the gaze and refresh the toiling traveller as he climbs the Alpine heights. Bacon had received no special mathematical training, although, like his in this respect more accomplished successor, he clearly saw and expressly asserted that

" Comte's work is in the form of lectures, the delivery of which was spread over many years, 1830-1842, and this extension necessitated an amount of recapitulation very injurious to its philosophical aspect. "M. Comte's style is singular. It is at the same time rich and diffuse. Every sentence is full fraught with meaning; yet it is overloaded with words. His scrupulous honesty leads him to guard his enunciation with epithets so constantly repeated that, though to his own mind they are necessary in each individual instance, they become wearisome, especially towards the end of his work, and lose their effect by constant repetition.'—Miss Martineau's Preface to Comte's Work.

? Comte was a consummate mathematician, and had the highest possible opinion of the utility of mathematics in their applied relations (this immense and admirable science, as he terms them); applauding highly the title of Newton's great work, · Philosophiæ Naturalis Principia Mathematica,' as indicating with energetic conciseness that the general laws of astronomical phenomena are the basis of all our real knowledge.-Comte, vol. i. p. 142.

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Mathematics was the true handmaid of Natural Philosophy, “the mother of the Sciences.? Comte had also the advantage of living long subsequently, being thereby so much the nearer to Truth, according to Bacon's quaint adage, that • Truth was the daughter of Time, and not of authority,'' and when the accumulated amount of then existing scientific knowledge, systematised as it was by Comte's own powerful mind, lent an aid to his speculations that Bacon had to do without. Both these eminent men were endowed with the faculty of imagination in superlative measure, enabling them, with apparent ease, by means of true hypotheses and real analogies, to grasp after and attain a reach of knowledge that to ordinary minds seems truly marvellous. Both insisted that the great end of Philosophy was to furnish a practical rule and guidance to man


Applied mathematics is not simply the measurement of extension and number. It is the measurement, by means of extension and number, of other quantities, which extension and number are marks of, and the ascertainment, by means of quantities of all sorts, of those qualities of things which quantities are marks of. The application of Algebra to Geometry (discovered by Descartes) made the first step in applied mathematics; the second was their application to Mechanics, that is, to the general laws and theory of force in the abstract. As the laws of number underlie the laws of extension (both underlying the laws of force), so do the laws of force underlie all the other laws of the material universe.--Millon Hamilton, ubi supra.

1 Recte enim Veritas Temporis filia dicitur, non auctoritatis.' — Nov. Org. lib. i. aph. 84.

2 Yet in each the imagination was duly subordinated to the understanding or reasoning faculty. “Bounded and conditioned by cooperant Reason, imagination becomes the mightiest instrument of the physical discoverer.'- Professor Tyndall On the Scientific Use of the Imagination. Longmans, 1870.

in his career on earth, and both were alike imbued with that over-mastering desire to be of service to their fellow-creatures which the inborn benevolence of true genius has almost invariably displayed? They were also alike conspicuous for the extraordinary range and compass of their intellectual vision, and each, in his own way, took a profound and masterly survey of the entire field of knowledge, and noted its deficiencies. Both conceived that the miseries of life chiefly resulted from human ignorance, or, as we might, in the fashion of the hour, now perhaps call it, • Intellectual Destitution,' and both set themselves to the arduous task of pointing out in what such ignorance mainly consisted, and how it might be effectually removed ; they believing, that in making men wiser, you are making them better. They did not separate the enlargement of reason from the growth of virtue. Knowledge,' observes Bacon, is not only Power, it is Truth. Nor is there in the whole universe of nature so intimate a sympathy as that between Truth and Goodness, which only differ, as the seal differs from its impression.’4 . !'Meta autem scientiarum vera et legitima non alia est quam ut dotetur vita humana novis inventis et copiis.'-Nov. Org., lib. i. aph. 81.

? De Dig. et Aug. lib. vii. cap. i.

* The remarkable view given by Bacon in the Advancement of Learning and De Dig. et Aug. Scient., is well known. Comte's survey of the sciences, occupying the first three volumes of his great work, is yet more astonishing for extent of knowledge and grasp of mind. Every division of knowledge and classification of science can be objected to. Bacon's has not escaped censure, and Comte's analysis has been acutely criticised by Herbert Spencer. See his Classification of the Sciences, 2nd edition, Williams and Norgate, 1869.

De Dig. et Aug., lib. i. cap. i.; and Advancement of Learning, book i. “For truth prints goodness.'

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Both considered Science, or the knowledge and explanation of Nature, to be the grand organon or machinery by which ignorance was to be dispelled; Bacon, with prophetic foresight, exhorting our universities, instead of imagining that by the labours of the ancients everything had been attained, to set their whole might towards the advancement of the sciences, and to leave off attacking each other, in order to unite their forces against the strongholds of nature; and both arrived at the belief that the theological theory of life (as regards God's secular providence, or the method of the Divine Government on Earth) was not the true theory : Bacon warning his disciples · Fidei dentur tantum quæ fidei sunt,'2 that they should give to Faith the things only that are Faith's; and Comte declaring that the rational progress of theological conceptions consists in the perpetual diminution of their intensity, and that the development of the Inductive Philosophy must eventually emancipate the human mind altogether from theological guardianship. Both,

• Goodness is seen with the eye of the understanding, and the light of that eye is reason.'- Hooker, Eccles. Pol., book i. chap. vü. sec. 2.

* Knowledge must precede Virtue, for no chance act can be a moral one. Vice is always the companion of ignorance, rarely of knowledge, never of wisdom.'—Mackay's Progress of the Intellect, vol. i. p. 70.

See the remarkable letters of Lord Bacon to the Universities of Oxford and Cambridge.--Bacon's Works, 2 vols. 1837, Ball. Vol. ii. Epistolæ, p. 751.

2 . Itaque salutare admodum est, si mente sobria fidei tantum dentur quæ fidei sunt.'— Nov. Org., lib. i. aph. 65.

3 Comte, vol i. p. 310. 4 Ibid., vol. ii. p. 315.

too, considered it a part at least of man's highest duty, to find out and study the laws of Nature, and to endeavour to regulate his life in accordance with their dictates; for they were alike animated with the same heroic confidence in Nature, and intense love of reality, and both had the firm unalterable conviction that human happiness, and not suffering, was the great object of Nature's arrangements, and that the Intellect, that noblest of God's gifts to man, armed with proper instruments, and disciplined by appropriate culture, was sufficient in itself to enable man to arrive at an adequate knowledge of them. Lastly, it is noticeable that these profound and comprehensive thinkers agreed in rejecting the study or investigation of causes first and final, (regarding it as a theological invasion of scientific rights; for, in Bacon's witty conceit, like a virgin consecrated to God, it bears nothing,'3)-in confining research to the invariable relations which constitute Natural Laws, and in limiting the range of their philosophical theories by the axioms, that.

I'Do what we will, the highest efforts of human thought can conceive nothing higher than the supremacy of Intellect.'—Mackay, Progress of the Intellect, &c., p. 113. “We have learned at last to recognise that the intellect is a divine gift.'-Miss Cobbe's Preface to the Works of Theodore Parker. Trübner, 1863.

9 Nov. Org., lib. i.; and Instauratio Magna, Distributio Operis, passim. Those prodigious resources of the human understanding, which are often despised by men who are ignorant of them; but which in reality are so great that no one has yet arisen able to scan them in the whole of their gigantic dimensions.'-Buckle, Hist. of Civil., vol. i. p. 729.

3. Nam causarum finalium inquisitio sterilis est, et, tanquam virgo Deo consecrata, nihil parit.'-De Dig. et Aug., lib. iii. cap. v.; Comte, vol. ii. pp. 351, 511.

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