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XIII.—Hegel and the Metaphysics of the Fluxional Calculus

Published online by Cambridge University Press:  17 January 2013

W. Robertson Smith
W. Robertson Smith
Affiliation:
Assistant to the Professor of Natural Philosophy in theUniversity of Edinburgh.
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Extract

It is now many years since Dr Whewell 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 demonstrations of Kepler's laws given in the “Principia.” At the time when Whewell 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.

The present state of matters is different. The philosophy of Hegel is now for the first time beginning to have a direct and powerful influence on British speculation. Men are beginning to study Hegel; and an author whose works confessedly demand the labour of years, if they are to be fully understood, can hardly be studied at all except by devoted disciples. A man whose determination to master Hegel's philosophy survives the repelling impression which the obscurity and arrogance of the philosopher are sure to produce at first, is very likely to be carried away by the calm assumption of omniscience which runs through Hegel's writings. It is not, therefore, surprising that Dr Stirling extends his admiration to Hegel's physical positions; and if he does not venture to say that Hegel's proof of Kepler's laws is right, at least feels sure that it would repay the attention of mathematicians.

Type
Research Article
Information
Earth and Environmental Science Transactions of The Royal Society of Edinburgh , Volume 25 , Issue 2 , 1869 , pp. 491 - 511
Copyright
Copyright © Royal Society of Edinburgh 1869

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References

page 492 note * Here and elsewhere I adopt, as far as possible, the language of Dr Stirling's own translations from Hegel, which may be viewed as authoritative.

page 499 note * Dr Stirling (ii. 355) seems to have read “Nach dem damaligen Stande der wissenschaftlichen Methode wurde nun erklärt.” In the collected edition of the “Werke,” iii. 303, I read “wurde nur erklärt,” which seems to give a more intelligible sense.

page 506 note * Hegel absolutely identifies analysis with arithmetical process—“Auf analytische d. i. ganz arithmetische Weise” (iii. 328). Had Hegel ever studied the treatment of incommensurables in ordinary algebra? If algebra is “ganz arithmetisch,” the whole doctrine of indices is false.

page 508 note * Hegel uses p = aq + b, but I keep Lagrange's own letters throughout.