ii SCIENTIFIC RECONSTRUCTION 259 



set out above under what conditions is generalisation 

 valid, and why under these conditions do we hold it valid ? 

 The reply to be satisfactory ought to exhibit the affinity 

 between the generalisations which we use as axioms in 

 mathematics and those which underlie scientific induction. 

 But it must begin with the recognition of their distinction. 



5. In fact, the generalisations assumed to be valid in 

 scientific and philosophical thought fall into two classes. 

 (a) On the one hand, as shown in Chapter VIII. , we can 

 generalise the results of analysis or synthesis. The func- 

 tion of synthesis consists in grasping distinct contents 

 together. So held they form a whole, and within that 

 whole it may be that characteristics appear, relations of 

 parts for example, which do not appear in the contents taken 

 severally. When we speak of * appearing' here we are 

 referring, be it remembered, to something which may be a 

 purely ideal process, something that is that becomes part 

 of our mental content when we bring ideas before the mind 

 unassisted, it may be, by any sensory accessories or models. 

 What is assumed by constructive thought and by analysis 

 also for the whole of this discussion applies mutatis 

 mutandis to the analytic as much as to the synthetic process 

 is that the attributes there presented by the ideal content will 

 be found in any part of the order of reality which conforms 

 to the elements of which that ideal content is composed. 

 This is to assume that similar elements always constitute 

 similar wholes, and conversely, that similar wholes are 

 always distinguishable into similar elements. The assump- 

 tion is only true if the whole is nothing but the summation 

 of the elements, and, as we have already seen, it is because 

 in the processes of thought it is so difficult to keep to this 

 condition and so easy to slip in some modification of the 

 elements, that dialectical fallacies arise. What we have 

 here principally to note, however, is that the assumption 

 when most carefully defined is of the nature of a generalisa- 

 tion. It affirms of reality in general a relation which I 

 find true within my mind, or, it may be, in models or 

 diagrams which I can construct. It is, moreover, a 

 generalisation which I assume whenever I put two thought- 



