THE STUDY OF SOCIOLOGY. 421 



That this may be better seen, let me briefly indicate the indispen- 

 sable discipline which each class of sciences gives to the intellect, and 

 also the wrong intellectual habits produced if that class of sciences is 

 studied exclusively. 



Entire absence of training in the Abstract Sciences leaves the 

 mind without due sense of necessity of relation. Watch the mental 

 movements of the wholly ignorant, before whom not even the exact 

 and certain results of Arithmetic have been frequently brought, and 

 it will be seen that there exists nothing like irresistible conviction 

 that from given data there is an inevitable inference. That which to 

 you has the aspect of a necessity, seems to them not free from doubt. 

 Even men whose educations have made numerical processes and re- 

 sults tolerably familiar, will show, in a case where the implication is 

 logical only, that they have not absolute confidence in the dependence 

 of conclusion on premisses. 



Unshakable beliefs in necessities of relation, are to be gained 

 only by studying the Abstract Sciences, Logic and Mathematics. 

 Dealing with necessities of relation of the simplest class, Logic is of 

 some service to this end ; though often of less service than it might 

 be, for the reason that the symbols it uses are not translated into 

 thought, and the connections stated not really represented. Only 

 when, for a logical implication expressed in the abstract, there is sub- 

 stituted an example so far concrete that the interdependencies can be 

 contemplated, is there an exercise of the mental power by which logi- 

 cal necessity is grasped. Of the discipline given by Mathematics, 

 also, it is to be remarked that the habit of dealing with the necessities 

 of numerical relation, though in a degree useful for cultivating the 

 consciousness of necessity, is not in a high degree useful ; because, in 

 the immense majority of cases, the mind, occupied with the symbols 

 used, and not passing beyond them to the groups of units they stand 

 for, does not really figure to itself the relations expressed does not 

 really discern their necessities, and has not therefore the conception 

 of necessity perpetually repeated. It is the more special division of 

 Mathematics, dealing with Space-relations, which, above all other 

 studies, yields necessary ideas, and so makes strong and definite the 

 consciousness of necessity in general. A geometrical demonstration 

 time after time presents premisses and conclusion in such wise that 

 the relation alleged is seen in thought cannot be passed over by 

 mere symbolization. Each step exhibits some connection of positions 

 or quantities as one that could not be otherwise ; and hence the habit 

 of taking such steps makes the consciousness of such connections 

 familiar and vivid. 



But, while mathematical discipline, and especially discipline in 

 Geometry, is extremely useful, if not indispensable, as a means of 

 preparing the mind to recognize throughout Nature the absoluteness 



