374 INDUCTION. 



There is, however, no such test. A coincidence may occur again and 

 again, and yet be only casual. Nay, it would be inconsistent with what we 

 know of the order of nature to doubt that every casual coincidence M'ill 

 sooner or later be repeated, as long as the phenomena between which it oc- 

 curred do not cease to exist, or to be reproduced. The recurrence, there- 

 fore, of the same coincidence more than once, or even its frequent recur- 

 rence, does not prove that it is an instance of any law ; does not prove that 

 it is not casual, or, in common language, the effect of chance. 



And yet, when a coincidence can not be deduced from known laws, nor 

 proved by experiment to be itself a case of causation, the frequency of its 

 occurrence is the only evidence from which we can infer that it is the re- 

 sult of a law, Not, however, its absolute frequency. The question is not 

 whether the coincidence occurs often or seldom, in the ordinary sense of 

 those terms; but whether it occurs more often than chance will account 

 for ; more often than might rationally be expected if the coincidence were 

 casual. "We have to decide, therefore, what degree of frequency in a coin- 

 cidence chance will account for ; and to this there can be no general an- 

 swer. We can only state the principle by which the answer must be de- 

 termined ; the answer itself will be different in every different case. 



Suppose that one of the phenomena. A, exists always, and the other phe- 

 nomenon, B, only occasionally ; it follows that every instance of B will be 

 an instance of its coincidence with A, and yet the coincidence will be mere- 

 ly casual, not the result of any connection between them. The fixed stars 

 have been constantly in existence since the beginning of human experience, 

 and all phenomena that have come under human observation have, in every 

 single instance, co-existed with them ; yet this coincidence, though equally 

 invariable with that which exists between any of those phenomena and its 

 own cause, does not prove that the stars are its cause, nor that they are in 

 anywise connected with it. As strong a case of coincidence, therefore, as 

 can possibly exist, and a much stronger one in point of mere frequency 

 than most of those which prove laws, does not here prove a law ; why ? be- 

 cause, since the stars exist always, they must co-exist with every other phe- 

 nomenon, whether connected with them by causation or not. The uniform- 

 ity, great though it be, is no greater than would occur on the supposition 

 that no such connection exists. 



On the other hand, suppose that we were inquiring whether there be any 

 connection between rain and any particular wind. Rain, we know, occa- 

 sionally occurs with every wind ; therefore, the connection, if it exists, can 

 not be an actual law ; but still rain may be connected with some particular 

 wind through causation ; that is, though they can not be always effects of 

 the same cause (for if so they would regularly co-exist), there may be some 

 causes common to the two, so that in so far as either is produced by those 

 common causes, they will, from the laws of the causes, be found to co-exist. 

 How, then, shall we ascertain this? The obvious answer is, by observing 

 whether rain occurs with one wind more frequently than with any other. 

 That, however, is not enough ; for perhaps that one wind blows more fre- 

 quently than any other; so that its blowing more frequently in rainy 

 weather is no more than would happen, although it had no connection with 

 the causes of rain, provided it were not connected with causes adverse to 

 rain. In England, westerly winds blow during about twice as great a por- 

 tion of the year as easterly. If, therefore, it rains only twice as often with 

 a westerly as with an easterly wind, we have no reason to infer that any 

 law of nature is concerned in the coincidence. If it rains more than twice 



