CH. xii.] THE INDUCTIVE OR INVERSE METHOD. 241 



so ; for there are but two suppositions which we can make 

 as to the reason of the cards being in that particular 

 order : 



1. They may have been intentionally arranged by some 

 one who would probably prefer the numerical order. 



2. They may have fallen into that order by chance, that 

 is, by some series of conditions which, being unknown to 

 us, cannot be known to lead by preference to the particular 

 order in question. 



The latter supposition is by no means absurd, for any 

 one order is as likely as any other when there is no prepon- 

 derating tendency. But we can readily calculate by the 

 doctrine of permutations the probability that fifty-two 

 objects would fall by chance into any one particular order. 

 Fifty-two objects can be arranged in 52 x 51 x . . X3 

 x 2 x I or about 8066 x (io) 64 possible orders, the 

 number obtained requiring 68 places of figures for its 

 full expression. Hence it is excessively unlikely that 

 anyone should ever meet with a pack of cards arranged 

 in perfect order by accident. If we do meet with a 

 pack so arranged, we inevitably adopt the other supposi- 

 tion, that some person, having reasons for preferring that 

 special order, has thus put them together. 



We know that of the immense number of possible 

 orders the numerical order is the most remarkable ; it is 

 useful as proving the perfect constitution of the pack, and 

 it is the intentional result of certain games. At any rate, 

 the probability that intention should produce that order is 

 incomparably greater than the probability that chance 

 should produce it ; and as a certain pack exists in that 

 order, we rightly prefer the supposition which most pro- 

 bably leads to the observed result. 



By a similar mode of reasoning we every day arrive, 

 and validly arrive, at conclusions approximating to cer- 

 tainty. Whenever we observe a perfect resemblance 

 between two objects, as, for instance, two printed pages, 

 two engravings, two coins, two foot-prints, we are war- 

 ranted in asserting that they proceed from the same type, 

 the same plate, the same pair of dies, or the same boot. 

 And why ? Because it is almost impossible that with 

 different types, plates, dies, or boots some apparent dis- 

 tinction of form should not be produced. It is impossible 



B 



