Piershill, Edinburgh
Decr. 23, 1869
Dear Sir,
I beg to thank you for your attention in sending me your paper on Hegel & Newton.[3] I fear I cannot give it time just at present, but I shall be happy to do so as leisure serves. I saw the newspaper report of the meeting in connection with the reading of your paper. I could not be sure from it that you rightly apprehended Hegel’s object, & I certainly thought that Professor Tait & Sir Wm. Thomson had given way to strange misconceptions in regard to it. Hegel has no quarrel with internalities in the question concerned — only with externalities. Dissatisfaction with these he believed to obtain among mathematicians themselves & such, since my discipline under Prof. James Thomson[4] , has been, I confess, my own belief. Hegel, then, would attempt to put these externalities on the way to remedy, by endeavouring thoroughly to expiscate the underlying notion. To estimate that attempt all his three long notes must be taken into account, for they all concern this notion. (His text, indeed, ought to be taken along with these notes).
Apart from this notion, there is a negative critique in Hegel’s first note (translated by myself) of the various ways in which mathematicians have handled these externalities. The critique is thus necessarily external; still I believe it to be inexpugnable so far as it goes!! Take the animadversion on the conversion of h into nothing, for example. Surely no one is simple enough to believe that Hegel objected to this as a correct mathematical expedient that led to a correct mathematical result. He only makes the sly external objection — suppose we make this conversion earlier — apply it everywhere?
Now that external objection is perfectly sound so far as it
goes. Then, as regards the point that started the discussion, I am sure Hegel
is perfectly correct under his presupposition. I have not referred to Newton,
but Hegel’s statement is evidently not fluxional, & I suppose him to have
taken it from some one else who had been inspired by Berkeley perhaps. The
presupposition may itself be wrong, then, but if it is correct, then
Hegel is in the right. If the whole matter is to be understood, that is,
as an ingenious expedient of Newton’s for throwing out the importunate tail,
Hegel has with equal ingenuity thrown this tail back again. Of course this he
does quite externally as in the case of the h. If du is usually got by proposition A, & by Newton by proposition
B, the A & B may be set equal, which develops the whole old
contradiction.
These objections are only justifiable so far as they can be taken to point to legitimate defects of form. Can the form be cleared of such objections, or are the objections themselves of no importance? Internally they are certainly of no importance whatever. I endeavoured to explain as much as this to Prof. Tait, but he would not listen to me.
Yours faithfully,
J H Stirling
W. R. Smith, Esq.
[1] CUL ADD 7449 D698 MS
[2] Stirling, James Hutchison (1820–1909): was the acknowledged British expert on Hegel at this time, and author of The Secret of Hegel (1st edn. 1865). His letter to WRS was, as indicated, a brief response to the latter’s paper, “Hegel and the Metaphysics of the Fluxional Calculus” There is no doubt that the paper was written at Tait’s instigation since it develops an attack (see L&E, pp.10f.) on Stirling, Berkeley and Hegel, initiated at an earlier meeting of the Society, when Smith’s previous paper criticising J. S. Mill’s geometrical reasoning had been presented.
[3] In L&E, pp.13–43.
[4] Thomson, James (1786–1849): father of both William (later Lord Kelvin) and James J. Thomson, was appointed to the chair of Mathematics at Glasgow University in 1832 where Stirling was a student for nine successive sessions, from 1833–42. [DNB]. In 1831 Thomson had published a textbook, The Differential and Integral Calculus.