CAUSE AND EFFECT— PROBABILITY 149 



routine, although r, or the number of times it has been 

 tested, be very small.^ 



Our discussion of the probability basis for routine in 

 the sequences of perceptions has perforce been brief, and 

 only touched the fringe of a vast and difficult subject. 

 Yet it may perhaps suffice to indicate that the odds 

 in favour of that routine being preserved in the immediate 

 future, or, indeed, for any finite interval, both with regard 

 to old and to new groups of perceptions, are overwhelming." 

 We may be absolutely unable to demonstrate any inherent 

 necessity for routine from our perceptions themselves, but 

 our complete ignorance of such necessity, combined with 

 our past experience, enables us by aid of the theory of 

 probability to gauge roughly how unlikely it is that the 

 possibility of knowledge and the power of thinking will 

 be destroyed in our generation by those breaches of 

 routine which, in popular language, we term miracles. 



So much science can tell us at present ; more we can 

 only hope to knozu, if we admit that routine flows from 

 the nature of our perceptive faculty and not from the 

 sphere beyond sense-impression. If science must at the 

 present stage perforce be content with a belief in the im- 

 mediate permanency of the universe (based on a probability 



^ We must be cautious in applying this formula to take a sufficiently com- 

 prehensive sequence of perceptions. We must see that the causes are really 

 the same, before we predict on the basis of past experience of routine in per- 

 ceptions a repetition of sequence in any particular case. That I have twice 

 seen a certain river overflowing its banks, and never seen that river without a 

 flood, will not enable me to predict that the flood will always occur when I 

 see the river. I must add to these perceptions, those of the season of the 

 year, of the amount of sun which has acted on the snow-fields and glaciers at 

 its source, of the condition of its banks, etc., etc., before I have a sufficiently 

 wide range of causes to enable me to predict from two repetitions the occurrence 

 of a third. I must indeed show that in my supposed identical sequences there 

 are really the same components. The reader who wishes to study this point 

 more thoroughly must be referred to Mill's "Canons of Induction" {Systein 

 of Logic, book iii.), an elementary discussion of which will be found in the 

 "Lessons on Induction," pp. 210-64 of Stanley Jevons' Elementary Lessons 

 in Logic. 



^ The odds in favour of a sequence repeating itself s times when the past 

 shows / repetitions and no failure are / + i to s. The number of repeated 

 sequences in the universe, or p, is practically infinite, so that the odds are 

 overwhelming so long as s is finite. We cannot, however, argue from this 

 result for an injijiite future of repetition. 



