136 THE GENESIS OF SCIENCE. 



longs to the more complex science, dynamics ; and tbat this 

 " single principle " underlying all rational mechanics — this 

 most general form which includes alike the relations of stat- 

 ical, hydrostatical, and dynamical forces — was reached so 

 late as the time of Lagrange. 



Thus it is not true that the historical succession of the 

 divisions of mathematics has corresponded with the order 

 of decreasing generality. It is not true that abstract math- 

 ematics was evolved antecedently to, and independently 

 of concrete mathematics. It is not true that of the sub- 

 divisions of abstract mathematics, the more general came 

 before the more special. And it is not true that concrete 

 mathematics, in either of its two sections, began with the 

 most abstract and advanced to the less abstract truths. 



It may be well to mention, parenthetically, that in de- 

 fending his alleged law of progression from the general to 

 the special, M. Comte somewhere comments upon the two 

 meanings of the word general^ and the resulting liability to 

 confusion. Without now discussing whether the asserted 

 distinction can be maintained in other cases, it is manifest 

 that it does not exist here. In sundry of the instances 

 above quoted, the endeavors made by M. Comte himself to 

 disguise, or to explain away, the precedence of the special 

 over the general, clearly indicate that the generality spoken 

 of, is of the kind meant by his formula. And it needs but 

 a brief consideration of the matter to show that, even did 

 he attempt it, he could not distinguish this generaUty, which, 

 as above proved, frequently comes last, from the generality 

 which he says always comes first. For what is the nature 

 of that mental process by which objects, dimensions, 

 weights, times, and the rest, are found capable of having 

 their relations expressed numerically ? It is the formation 

 of certain abstract conceptions of unity, duality and multi- 

 plicity, which are applicable to all things alike. It is the 

 invention of general symbols serving to express thenumer- 



