656 SCIENCE PROGRESS 



it remains to enquire how they are utilised for the benefit of the organism. 

 This is effected by means of the farther hypothesis that they will recur, so that, 

 if the earlier parts of a series should subsequently be repeated, the rest of 

 the associated reactions will follow in their original order. This expectation 

 of recurrence is the only basis on which forecasts of the future can be drawn 

 from the experience of the past. 



Now each of us includes in many of his mental series elements which 

 he must regard as being his own actions, and is aware, moreover, that the 

 subsequent experiences in some of these series are desirable, in others un- 

 desirable. An expectation of the recurrence of these series would be mani- 

 fested by repeating actions which had been followed by desirable experiences 

 and refraining from the others. This is characteristic of the conduct of all 

 the more highly organised animals, and is to be noticed in the actions of 

 human infants even while very young. Its appearance at an early age in 

 a great variety of organisms gives the idea that the aptitude for developing 

 the expectation of recurrence is inherited and might be classified under 

 the rather ill-defined heading of instincts. 



Actions, then, can be guided by forecasts of future experience, drawn 

 from the experience of the past in virtue of the hypothesis of the recurrence 

 of series ; but we find that this is often applied too indiscriminately, every 

 sequence of reactions mentally arranged in a series being expected to recur. 

 Man's experience, as it widens, teaches that there are many exceptions, and 

 it becomes evident that before knowledge can be a trustworthy guide 

 it must distinguish between the series which are, and those which are 

 not, recurrent. 



The method by which hypotheses are tested is called verification ; it 

 consists in framing forecasts on the basis of the hypotheses and then com- 

 paring them with actual experience ; the more uniform the correspondence 

 between forecast and experience, the more complete is the verification, and 

 the greater will be the confidence that the hypotheses are valid. Those 

 propounded at the beginning of this article lead to forecasts of the way in 

 which ideas will be found to originate ; their validity must be tested by 

 experience of what actually takes place. 



There is one fundamental recurrence-hypothesis which, when it can be 

 submitted to verification, has never been known to fail, and which is there- 

 fore regarded as absolutely beyond question — namely, that if aU the elements 

 essential to a series be repeated, the series will recur. Hence, if all the 

 elements of a series be abstractions by whose nature every extraneous 

 element is excluded, one single experience may be sufficient for a verification, 

 giving certain assurance of its recurrence. 



For instance, three parallel rows of four dots each can be arranged in 

 a parallelogram, and it is seen that the same dots may be regarded as four 

 rows of three. It is at once felt as a certainty that a forecast of repetition 

 will hold good, and that multiplier and multiplicand will always be inter- 

 changeable provided that they represent the same abstractions (integral 

 units) which are exemplified by the dots. This is no guarantee of recur- 

 rence when the elements of the series are other than unit quantities ; in 

 quaternions abstract factors are used which have a different relation. 



In the case of concrete sequences verification is more difficult, because 

 the mental associations of the series cannot include more than a finite 

 number of the noticeable elements of the sequence, and it is never certain 

 that these will be the only ones affecting the recurrence of the series. When 

 a gardener, taking seeds from plants of a particular species, sows and tends 

 them according to a certain plan, he forecasts approximately what will 

 be the outcome of his work ; he expects that some of the seeds will develop 

 into plants because he knows that seeds of that species have often done 

 so under conditions not obviously different, and relying on the hypothetical 



