28 LECTURES AND ESSAYS [1869- 



Q=p + q8x + etc., 



and then letting Sx and 8y vanish Lt~ = # ; not as it 



O^ 



should have been = -. This, of course, is sadly incon 

 sistent ; for instead of our fine qualitative determination, 

 here is a stubborn quantum turning up. Now, says 

 Hegel, the mathematicians try to get over this by saying 



that p is not really = --, but is only a definite value, to 



which - comes as near as you please. Of course, if this 

 is so, it is as evident as anything can be that the difference 

 between p and - is not a quantitative one. But, adds the 

 philosopher, naively enough, that doesn t help one over 

 j~ = -. Suppose now that we were to say J- really = p (a 



definite quantity), as, in fact, mathematicians do say, then 

 it is obvious that Sx couldn t have been = 0. Or if, 



finally, it is conceded that ~ = (which Hegel seems to 



oX 



think most likely, since 8y and &x vanish together), then 

 what can p be ? 



Now, can any one say that the man who devised this 

 argument knew what he was doing ? When did any 



mathematician suppose that after evaluation - is in 

 determinate ? Or had Hegel never read Newton s first 

 lemma, with its &quot; fiunt ultimo aequales &quot; ? Or, again, 

 if Hegel allows that there is no quantitative difference 



between p and -, why does he assume a qualitative one ? 



Or, above all, why try to explain Newton s doctrine 

 without ever deigning more than a contemptuous glance 

 at the one central point of the whole ? Hegel boasts that 



