viii CONCEPTUAL RECONSTRUCTION 133 



to constitute a precisely similar whole, and conversely, if a 

 whole can be resolved into elements of a certain character 

 a precisely similar whole can be resolved into precisely 

 similar elements. If this is true it will follow that if there 

 is any real combination of elements corresponding to a 

 synthesis which we effect in our minds, the whole which 

 those elements form will correspond, and its characters will 

 correspond, 1 to those of our resulting concept. This will 

 hold good subject to a condition to be noted lower down. 

 But this correspondence depends entirely on the assump- 

 tion that the mode of combination is the same in both 

 cases. If there is any possible ambiguity on this point 

 there is opening for error. Accordingly sound and 

 unambiguous mental construction is dependent on one 

 or other of two conditions, (a) The combination may 

 be so simple as to admit of no ambiguity. The clearest 

 case is that in which the combination involves no specific 

 relation of the parts, the bare fact of combination 

 irrespective of order or mutual position being the only 

 presupposition. Such a combination in the case of two 

 quantities is sufficient for the purpose of addition, and 

 addition like more complicated syntheses yields a whole 

 with a character of its own, of which further things are 

 found to be true, and which is not arrived at till the 

 components are added. Subtraction is at bottom the con- 

 verse operation by which a whole is divided into parts 

 standing side by side. But furthermore, (b) certain rules 

 of synthesis with their results may be verified once for all 

 and applied in any number of cases. Thus higher rules of 

 computation can be educed from simple addition and sub- 

 traction. Further, certain axioms result from the general 

 principles already laid down, and serve as principles in 

 computation. We have assumed that when a certain 

 result is arrived at by a process combining given elements 

 in a given way, that result can be generalised. It follows, 

 e.g. that if we start from similar concept-elements and con- 



1 In a more ultimate sense the principle depends on the axiom 

 that relations which hold between certain terms as such hold between 

 them universally. This, it will be argued later (Part II. Ch. II.), is one 

 form of the final principle involved in the reasoning process. 



