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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.2 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.-Mill on Hamilton, ubi supra.

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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,1 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

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1 'Meta autem scientiarum vera et legitima non alia est quam ut dotetur vita humana novis inventis et copiis.'—Nov. Org., lib. i. aph. 81. 2 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."

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;1 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,'' 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.

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

1 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.

▲ 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,1 armed with proper instruments, and disciplined by appropriate culture, was sufficient in itself to enable man to arrive at an adequate knowledge of them.2 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,'')—in confining research to the invariable relations which constitute Natural Laws, and in limiting the range of their philosophical theories by the axioms, that

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'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.

2 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.

observed facts are the only basis of sound speculation, and that no proposition that is not finally reducible to the enunciation of a fact, particular or general, can offer any real and intelligible meaning.1

It remains to be remarked of these illustrious men, that they were proficients in Philosophy, rather than in Science, and, more eminently, Philosophy of human than of general nature; and, if it be the case, as an eminent professor has lately sought to show, that Comte possessed but slight actual acquaintance with scientific processes, it must be admitted that Bacon probably had less. Harvey, who was the Huxley of Lord Bacon's day, said of Bacon sneeringly, that he wrote of Science ' like a Lord Chancellor.' But, though their Science be sneered at, or their Philosophy sought to be refuted, they cannot be deprived of their splendour of genius, their elevation of view, and their devotion to the highest moral law of Science-love of the Spirit of

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I Comte, vol. ii. p. 511. It has been suggested that this feature of the Inductive Philosophy is at present exercising a decidedly prejudicial influence on the English intellect, by producing an excessive distaste for the higher generalisations, and for all speculations that do not lead directly to practical results.-Lecky's Rationalism, vol. i. p. 443. But Mr. Mill has justly remarked, that such tendency is the effect of an exclusive following of what is imagined to be the teaching of Bacon, being in reality the result of a slovenly conception of him, leaving on one side the whole spirit and scope of his speculations.-Mill on Hamilton, p. 541, note.

2 Huxley, Lay Sermons, &c., 'Scientific Aspects of Positivism.' Macmillan & Co., 1870.

3 Nothing more is meant by this juxtaposition of the names of Harvey and Huxley than that they are alike in the relation in which they stand towards the objects of their censure-viz., men of special science criticising philosophers. Harvey was a great discoverer as well as a profound physiologist.

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