ch. xi.] THE QUESTION STATED. 269 



looking for. Obviously mathematics, dealing only with 

 relations of number, form, and magnitude, cannot supply the 

 ultimate principle from which may be deduced such pheno- 

 mena as the condensation of a nebula, the segmentation of 

 an ovum, or the development of a tribal community. To 

 build a system of philosophy upon any possible theorem of 

 mathematics, would only be to repeat, after twenty-four 

 centuries, the errors of Pythagoras. And the helplessness of 

 abstract logic, for our purposes, is too manifest to need 

 illustration. 



Let us then turn to the abstract- concrete sciences ; for in 

 the widest generalizations at which these sciences have jointly 

 arrived we must find, if anywhere, the theorem which we 

 desire. I say "jointly," for in the deepest sense the subject- 

 matter is the same, in molar physics, in molecular physics, 

 and in chemistry. All three sciences deal, in one way or 

 another, with the most general laws of those redistributions 

 of matter and motion which are continually going on 

 throughout the knowable universe. The first deals with the 

 movements of masses ; the second deals with movements of 

 molecules, and with the laws of aggregation of molecules 

 that are homogeneous ; the third deals with the laws of 

 aggregation of molecules that are heterogeneous. In either 

 case the phenomena dealt with are movements of matter, 

 whether movements of translation through space, or move- 

 ments of undulation among molecules, or movements whose 

 conspicuous symptom is change of physical state or of 

 chemical constitution. The widest theorems, therefore, 

 which the three abstract-concrete sciences can unite in 

 affirming, must be universal propositions concerning Matter 

 and Motion. 



Obviously it is in this region of science that we must look 

 for our primordial theorem. But little reflection is needed 

 to convince us that all the truths attainable by the concrete 

 sciences must ultimately rest upon truths relating to the 



