ERROR AND FALLACIES 321 



mental training, proceeded to argue that the branches he had 

 shown to have the first value must have the second value like 

 wise : on the ground that it &quot; would be utterly contrary to the 

 beautiful economy of nature, if one kind of culture were needed 

 for the gaining of information and another kind were needed 

 as a mental gymnastic &quot;. l This is simply assuming as universally 

 true what he wanted to prove of the cases he examined. Here 

 are a few briefer instances : &quot; The imposition of legacy duties is 

 justifiable, because all property passing by will ought to be 

 taxed&quot; ; &quot; His cruelty may be inferred from his cowardice, for 

 all cowards are cruel &quot; ; &quot;A table of logarithms must be entertain 

 ing, for all books are so &quot;. 



If our assent to the principle of the Uniformity of Nature were based 

 upon simple enumerative induction, and if at the same time all induction de 

 pended for its validity on a prior belief in the Uniformity of Nature, we 

 should never be able rationally to justify this belief, or, consequently, to put 

 our trust in any single inductive generalization (apart altogether from this other 

 damaging fact, that enumerative induction can never beget scientific certitude). 

 Yet Mill contends that the petitio principii, apparently involved in this attitude, 

 is only apparent, not real. Unfortunately, it is real. And when Mill attempts 

 to show that the position is free from the fallacy, so far from succeeding, the 

 attempt only involves him in the fallacy afresh. His line of argument has 

 been examined already (224), but the matter is of such importance that a 

 reference to it in the present context will not be superfluous. 



According to Mill, the principle of the Uniformity of Nature is the 

 &quot; ultimate major premise of all induction &quot; ; communicating its reliability to 

 all inductions ; without which none would be valid ; which, therefore, we 

 must hold for certain, antecedently to all inductions that are scientific, that give 

 certitude. How, then, do we come to give a certain assent to this principle ? 

 on what grounds ? by what process ? We reach it, Mill answers, through a 

 vast induction per enumerationem simplicem, by which we accumulate and 

 generalize &quot;many laws of inferior generality,&quot; each of which was reached by 

 a like process of generalizing from enumerated instances 2 . But how can we 

 make an induction per enumerationem simplicem, before we are sure of the 

 principle, if all induction presupposes certitude about the principle ? And, 

 anyhow, is not enumerative induction so admittedly weak that of itself it can 

 never carry us beyond an empirical generalization, to the certitude we need 

 for the principle of uniformity as a .basis for scientifically certain physical laws ? 

 Mill replies that most enumerative inductions do presuppose the principle 

 established ; that, therefore, this process does not and cannot in ordinary 

 cases establish a law ; but he attempts to show that the enumerative induction 

 by whic^ we reach the principle in question is different from all other lesser 

 enumerative inductions, and does give us certitude about the principle. And 

 here is how he proceeds : The wider the field of experience over which we 

 generalize by enumerative induction, the safer this process becomes ( a state- 



1 apud WELTON, op. cit., ii., p. 284. 2 Cf. WELTON, op. cit., ii., pp. 42, 43. 



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