132 DEVELOPMENT AND PURPOSE CHAP. 



straight lines, but three straight lines do not necessarily 

 form a triangle. They form a triangle only when brought 

 into certain mutual relations, and these relations as well as 

 the straight lines themselves are necessary elements in the 

 combination that yields the triangle. Now on the one 

 hand, it is very easy to overlook a condition of this sort, 

 that is to say, to omit some of the conditions required to 

 give to a combination a particular character, and this is one 

 great root of fallacy in deductive argument. On the other 

 hand, if the only synthesis that we can legitimately form 

 is one in which all the elements are given, and if the c ele- 

 ments ' are to include all the parts and the relations in which 

 they are combined, it is not easy to see how we make any 

 advance at all. Do not the parts in their relation constitute 

 the whole, and if so is not the whole already given when 

 the 'elements' (which include that relation) are fully 

 enumerated? How then do we make any advance in 

 thinking ? The reply is that the whole is not given when 

 the parts are enumerated and the relation between them 

 stated, but when they are actually combined. It is then 

 recognised as something with a character of its own con- 

 stituted by distinguishable and assignable elements. I 

 may think of two straight lines diverging from a point 

 and then of a third cutting them both at some distance 

 from the point. When the process is complete I have my 

 triangle, a figure with a recognisable character of its own 

 constituted by the elements specified, which remain recog- 

 nisably distinct within it. This figure moreover may 

 possess some distinct qualities and present some distinct 

 relation of its parts which belongs to it only as a whole 

 e.g. the three angles of the triangle. But if this charac- 

 teristic is a true character of the whole itself, and does not 

 contain any element that is not part of the whole, it will 

 be found in any other whole constituted in a precisely 

 similar way, that is to say, it will follow from the synthesis 

 of the elements as such. 



We have now, accordingly, reached one of the general 

 principles governing the valid synthesis and analysis of 

 concepts. If two or more elements constitute a whole of 

 a certain character precisely similar elements will be found 



