APPENDIX. 583 



idea utterly alien. The mathematician, too, and the mathe- 

 matical physicist, occupied exclusively with the phenomena 

 of number, space, and time, or, in dealing with forces, deal- 

 ing with them in the abstract, carry on their researches in 

 such ways as may, and often do, leave them quite unconscious 

 of the traits exhibited by the general transformations which 

 things, individually and in their totality, undergo. In a chap- 

 ter on " Discipline " in the Study of Sociology, I have com- 

 mented upon the uses of the several groups of Sciences — 

 Abstract, Abstract-Concrete, and Concrete — in cultivating 

 different powers of mind; and have argued that while for 

 complete preparation, the discipline of each group of sciences 

 is indispensable, the discipline of any one group alone, or 

 any two groups, leave certain defects of judgment. Especially 

 have I contrasted the analytical habit of thought which study 

 of the Abstract and Abstract-Concrete Sciences produces, with 

 the synthetical habit of thought, produced by study of the 

 Concrete Sciences. And I have exemplified the defects of 

 judgment to which the analytical habit unqualified by the 

 synthetical habit, leads. Here we meet with a striking illus- 

 tration. Scientific culture of the analytical kind, almost as 

 much as absence of scientific culture, leaves the mind bare 

 of those ideas with which the Concrete Sciences deal. Exclu- 

 sive familiarity with the forms and factors of phenomena, no 

 more fits men for dealing with the products in their totalities, 

 than does mere literary study. 



An objection made to the formula of evolution by a sympa- 

 thetic critic, Mr. T. E. Cliffe Leslie, calls for notice. It is 

 urged in a spirit widely different from that displayed by Mr. 

 Kirkman and his applauder Professor Tait; and it has an 

 apparent justification. Indeed many readers who before ac- 

 cepted the formula of Evolution in full, will, after reading 

 Mr. Cliffe Leslie's comments, agree with him in thinking that 

 it is to be taken with the qualifications he points out. We 

 shall find, however, that a clearer apprehension of the mean- 

 ings of the words used, and a clearer apprehension of the 

 formula in its totality, excludes the criticisms Mr. Leslie 

 makes. 



In the first place he dissociates from one another those 

 traits of Evolution which I have associated, and which I have 

 alleged to be true only when associated. He quotes me as 

 saying that a change from the homogeneous to the hetero- 



