SECT. 13.] Modes of establishing the Groups or Series. 87 



of the subject, in other words, upon our substituted series 

 being kept in accordance with the actual series. Experience 

 abundantly proves that, between considerable limits, in the 

 example in question, there does exist such a correspondence. 

 But let no one attempt to enforce our assent to every remote 

 deduction that mathematicians can draw from their formulae. 

 When this is attempted the distinction just traced becomes 

 prominent and important, and we have to choose our side. 

 Either we go over to the mathematics, and so lose all right 

 of discussion about the things: or else we take part with the 

 things, and so defy the mathematics. We do not question 

 the formal accuracy of the latter within their own province, 

 but either we dismiss them as somewhat irrelevant, as apply 

 ing to data of whose correctness we cannot be certain, or 

 we take the liberty of remodelling them so as to bring them 

 into accordance with facts. 



13. A critic of any doctrine can hardly be considered 

 to have done much more than half his duty when he has 

 explained and justified his grounds for objecting to it. It 

 still remains for him to indicate, if only in a few words, 

 what he considers its legitimate functions and position to be, 

 for it can seldom happen that he regards it as absolutely 

 worthless or unmeaning. I should say, then, that when 

 Probability is thus divorced from direct reference to objects, 

 as it substantially is by not being founded upon experience, 

 it simply resolves itself into the common algebraical or arith 

 metical doctrine of Permutations and Combinations 1 . The 

 considerations upon which these depend are purely formal 

 and necessary, and can be fully reasoned out without any 

 appeal to experience. We there start from pure considera 

 tions of number or magnitude, and we terminate with them, 



1 The close connection between title of Mr Whitworth s treatise, 

 these subjects is well indicated in the Choice and Chance. 



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