614 • . LOGIC OF THE MORAL SCIENCES. 



CHAPTER VIII. 



OF THE GEOMETRICAL, OR ABSTRACT, METHOD. 



§ 1. The misconception discussed in the preceding chapter is, as we 

 said, chiefly committed by persons not much accustomed to scientific in- 

 vestigation : practitioners in politics, who rather employ the commonplaces 

 of philosophy to justify their practice than seek to guide their practice by 

 philosophic principles ; or imperfectly educated persons, who, in ignorance 

 of the careful selection and elaborate comparison of instances required for 

 the formation of a sound theory, attempt to found one upon a few coinci- 

 dences which they have casually noticed. 



The erroneous method of which we are now to treat is, on the contrary, 

 peculiar to thinking and studious minds. It never could have suggested 

 itself but to persons of some familiarity with the nature of scientific re- 

 search ; who, being aware of the impossibility of establishing, by casual 

 observation or direct experimentation, a true theory of sequences so com- 

 plex 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 concern- 

 ed. These thinkers perceive (what the partisans of the chemical or exper- 

 imental theory do not) that the science of society must necessarily be de- 

 ductive. But, from an insufficient consideration of the specific nature of 

 the subject-matter — and often because (their own scientific education hav- 

 ing 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 as- 

 tronomy and natural philosophy, that they unconsciously 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 Causation which have been rendered deductive, 

 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 simul- 

 taneously, as if they had acted one after another, or by turns ; and it is 

 in this that the difference between mechanical and chemical laws consists. 

 But still the effects, whether produced by successive or by simultaneous 

 action, do, wholly or in part, cancel one another : 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, Avhat would be true if no 

 other geometrical principles existed, can not be altered and made no longer 

 true by reason of some other geometrical principle. What is once proved 

 true is true in all cases, whatever supposition may be made in regard to 

 any other matter. 



