THE GEOMETRICAL METHOD. 



579 



with the nature of scientific research ; 

 who, — being aware of the impossi- 

 bility of establishing, by casual obser- 

 vation or direct experimentation, a 

 true theory of sequences so complex 

 as are those of the social phenomena, 

 — have recourse to the simpler laws 

 which are immediately operative in 

 those phenomena, and which are no 

 other than the laws of the nature of 

 the human beings therein concerned. 

 These thinkers perceive (what the 

 partisans of the chemical or experi- 

 mental theory do not) that the science 

 of society must necessarily be deduc- 

 tive. But, from an insufficient con- 

 sideration of the specific nature of the 

 subject-matter, — and often because 

 (their own scientific education having 

 stopped short in too early a stage) 

 geometry stands in their minds as the 

 type of all deductive science, — it is to 

 geometry, rather than to astronomy 

 and natural philosophy, that they un- 

 consciously assimilate the deductive 

 science of society. 



Among the differences between 

 geometry (a science of co-existent 

 facts, altogether independent of the 

 laws of the succession of phenomena) 

 and those physical Sciences of Causa- 

 tion which have been rendered deduc- 

 tive, the following is one of the most 

 conspicuous : That geometry affords 

 no room for what so constantly occurs 

 in mechanics and its applications, the 

 case of conflicting forces ; of causes 

 which counteract or modify one an- 

 other. In mechanics we continually 

 find two or more moving forces pro- 

 ducing, not motion, but rest ; or 

 motion in a different direction from 

 that which would have been produced 

 by either of the generating forces. It 

 is true that the effect of the joint 

 forces is the same when they act 

 simultaneously, as if they had acted 

 one after another, or by turns ; and 

 it is in this that the difference between 

 mechanical and chemical law consists. 

 But still the effects, whether produced 

 by successive or by simultaneous ac- 

 tion, do, wholly or in part, cancel one 

 pother ; what the one force does the 



other, partly or altogether, undoes. 

 There is no similar state of things in 

 geometry. The result which follows 

 from one geometrical principle has 

 nothing that conflicts with the result 

 which follows from another. What 

 is proved true from one geometrical 

 theorem, what would be true if no 

 other geometrical principles existed, 

 cannot be altered and made no longer 

 true by reason of some other geomet- 

 rical principle. What is once proved 

 true is true in all cases, whatever sup- 

 position may be made in regard to any 

 other matter. 



Now a conception, similar to this 

 last, would appear to have been 

 formed of the social science, in the 

 minds of the earlier of those who have 

 attempted to cultivate it by a deduc- 

 tive method. Mechanics would be a 

 science very similar to geometry if 

 every motion resulted from one force 

 alone, and not from a conflict of forces. 

 In the geometrical theory of society, 

 it seems to be supposed that this is 

 really the case with the social pheno- 

 mena ; that each of them results al- 

 ways from only one force, one single 

 property of human nature. 



At the point which we have now 

 reached, it cannot be necessary to say 

 anything either in proof or in illustra- 

 tion of the assertion that such is not 

 the true character of the social pheno- 

 mena. There is not, among these 

 most complex and (for that reason) 

 most modifiable of all phenomena, any 

 one over which innumerable forces do 

 not exercise influence ; which does 

 not depend on a conjunction of very 

 many causes. We have not, there- 

 fore, to prove the notion in question 

 to be an error, but to prove that the 

 error has been committed ; that so 

 mistaken a conception of the mode in 

 which the phenomena of society are 

 produced has actually been ascer- 

 tained. 



§ 2. One numerous division of the 

 reasoners who have treated social facts 

 according to geometrical methods, not 

 admitting any modification of one law 



