THE OPPOSITE OF COMTE 5 S LAW. 181 



possible to present, with great plausibility, just the opposite 

 generalization to that which he enunciates. While he as 

 serts that the rational order of the sciences, like the order 

 of their historic development, &quot; is determined by the de 

 gree of simplicity, or, what comes to the same thing, of 

 generality of their phenomena;&quot; it might contrariwise bo 

 asserted, that, commencing with the complex and the spe 

 cial, mankind have progressed step by step to a knowledge 

 of greater simplicity and wider generality. So much evi 

 dence is there of this as to have drawn from Whewell, in 

 his History of the Inductive Sciences, the general remark 

 that &quot; the reader has already seen repeatedly in the course 

 of this history, complex and derivative principles present 

 ing themselves to men s minds before simple and elemen 

 tary ones.&quot; 



Even from M. Comte s own work, numerous facts, ad 

 missions, and arguments, might be picked out, tending to 

 show this. We have already quoted his words in proof 

 that both abstract and concrete mathematics have pro 

 gressed towards a higher degree of generality, and that ho 

 looks forward to a higher generality still. Just to strength 

 en this adverse hypothesis, let us take a further instance. 

 From the particular case of the scales, the law of equilibri 

 um of which was familiar to the earliest nations known, Ar 

 chimedes advanced to the more general case of the unequal 

 lever with unequal weights; the law of equilibrium of 

 which includes that of the scales. By the help of Galileo s 

 discovery concerning the composition of forces, D Alembert 

 &quot; established, for the first time, the equations of equilibrium 

 of any system of forces applied to the different points of a 

 solid body &quot; equations which include all cases of levers 

 and an infinity of cases besides. Clearly this is progress 

 towards a higher generality towards a knowledge more 

 independent of special circumstances towards a study of 

 phenomena &quot; the most disengaged from the incidents of 



