64 Dr. WHEWELL'S CRITICISM OF ARISTOTLE'S ACCOUNT OF INDUCTION. 



$11 " But such a syllogism is an inference of a first truth and immediate proposition. 

 $ 12 " For when there is a mean term, there is demonstrative syllogism through the 

 mean ; but when there is not a mean, there is proof by Induction. 



$ 13 " And in a certain way, Induction is contrary to Syllogism ; for Syllogism proves, 

 by the middle term, that the extreme is true of the third thing : but Induction proves, by 

 means of the third thing, that the extreme is true of the mean. 



^ 14 " And Syllogism concluding by means of a middle term is prior by nature and 

 more usual to us ; but the proof by Induction is more luminous." 



I think that the chapter, thus interpreted, is quite coherent and intelligible ; although at 

 first there seems to be some confusion, from the author sometimes saying that Induction is a 

 kind of Syllogism, and at other times that it is not. The amount of the doctrine is this. 



When we collect a general proposition by Induction from particular cases, as for instance, 

 that all animals destitute of gall-bladder, (acholous) are long-lived, (if this proposition were 

 true, of which hereafter) we may express the process in the form of a Syllogism, if we will 

 agree to make a collection of particular cases our middle term, and assume that the proposition 

 in which the second extreme term occurs is convertible. Thus the known propositions are 

 Elephant, horse, mule, &c, are long-lived. 

 Elephant, horse, mule, &c, are acholous. 

 But if we suppose that the latter proposition is convertible, we shall have these propo- 

 sitions, 



Elephant, horse, mule, &c, are long-lived. 

 All acholous animals are elephant, horse, mule, &c, 

 from whence we infer, quite rigorously as to form, 

 All acholous animals are long-lived. 

 This mode of putting the Inductive inference shews both the strong and the weak point 

 of the illustration of Induction by means of Syllogism. The strong point is this, that we 

 make the inference perfect as to form, by including an indefinite collection of particular cases, 

 elephant, horse, mule, &c, in a single term, C. The Syllogism then is 

 All C are long-lived. 

 All acholous animals are C. 

 Therefore all acholous animals are long-lived. 

 The weak point of this illustration is, that, at least in some instances, when the number 

 of actual cases is necessarily indefinite, the representation of them as a single thing involves 

 an unauthorized step. In order to give the reasoning which really passes in the mind, we 

 must say 



Elephant, horse, &c, are long-lived. 

 All acholous animals are as elephant, horse, &c, 

 Therefore all acholous animals are long-lived. 

 This "as" must be introduced in order that the "all C" of the first proposition may be 

 justified by the " C" of the second. 



This step is, I say, necessarily unauthorized, where the number of particular cases is 

 indefinite ; as in the instance before us, the species of acholous animals. We do not know 



