ESSAYS 657 



generalisation that like begets like, he expects that the plants will have a 

 resemblance to those from which the seed came. If a. sufficient number of 

 trials be made, the average of the subsequent experiences will doubtless 

 correspond fairly with the forecasts ; but there is no certainty that any 

 individual seed will germinate ; various unknown conditions may prevent 

 it ; and of those plants which do grow, no one will be like another in every 

 respect, nor will it be exactly like those from which it is descended ; each 

 has its individual peculiarities, which in some instances may be so pro- 

 nounced that the plant will be regarded as a " sport." 



Forecasts from hypotheses which do not exclude unknown elements are 

 never quite free from such uncertainty, and verification is more or less 

 satisfactory according to the degree of uniformity in their approximate 

 agreement with subsequent experiences. Owing to the indeterminate nature 

 of verification in such cases, the idea of doubt has become so closely asso- 

 ciated with the word hypothesis that objection may be taken to its use in 

 reference to mental series whose recurrence is considered to be certain ; the 

 mental operations, however, are similar in all cases and it is convenient to 

 denote them by the same word. 



When a series whose principal elements are known is subject to varia- 

 tion under the influence of minor unknown elements, limits can in some 

 cases be assigned to this variation and the probability of a particular forecast 

 can be found. Thus in the tossing of a coin the known elements are sup- 

 posed to be such that either a " head " or a " tail " will be uppermost when 

 it comes to rest ; the moving forces, other than gravity, are undetermined, 

 but the variation introduced by them into the series is limited to the appear- 

 ance of one or other of two alternatives, whose probability is equal. It 

 will be seen, then, that probability both implies a basis of knowledge and 

 is in itself a modified kind of knowledge, since it lays down boundary lines 

 in regions where ignorance would simply leave a blank. 



Beside the division of mental series into abstract and concrete, another 

 distinction is to be noted. The natural and, as it were, automatic forma- 

 tion of series from experiences which follow one another closely, is common 

 to man and to many animals ; mankind has acquired, in addition, the 

 power of connecting, by mental association, sequences of experiences divided 

 by considerable intervals of time, such as the appearance of a plant where 

 seed was sown several months earlier. 



It has already been pointed out that, by mental association, a present 

 reaction may arouse the memory of some different reaction in the past ; 

 if this in its turn should revive the memory of the same sequence having 

 been in the mind previously, the idea of recurrence will be suggested. The 

 expectation that the sequence will always recur needs verification, but if 

 this be obtained by a sufficient number of repetitions, the connection of 

 experiences may be regarded as empirical knowledge. 



To make such knowledge systematic an hypothesis must be framed 

 by which the discontinuous experiences can be represented as forming parts 

 of some process already known and held to be continuous. The recurrence 

 of the series can then be verified more effectively than before, since it 

 becomes possible to forecast that — If the empirical sequence corresponds 

 with the known process, not only in the observed portions, but also through- 

 out its whole extent, then this-and-that will be experienced. The more 

 uniformly subsequent experiences bear out these forecasts the greater will 

 be the confidence in the validity of the hypothesis. 



Illustrations of this may be found in the history of astronomy. Very 

 early ages had bare records of what was, from time to time, noted concern- 

 ing such things as the successive phases of the moon, the recurrence of sun- 

 rise in particular positions, or the repetition of eclipses at regular intervals. 

 Then these discontinuous experiences were combined into a system by 



