INDUCTIONS IMl'KOrERLY SO CALLED. 177 



that in ra,isina- a binomial to a jiower, the co^fficieiits must dcpciul 

 upon the laws of permutation and lombination : and as soon as this is 

 recognized, the theorem is demonstrated. Indeed, wheii once it was 

 seen that the law j)revailed in a few of the low^ powers, its identity 

 with the law of permutation would at once suggest the considerations 

 which prove it to olrtain universally. Even, therefore, such cases as 

 these, are but examples of what I have called induc-tion by parity of 

 reasoning, that is, not really induction, because iu)t involving any infer- 

 ence of a general proposition from particular instances.* 



§ 3. There remains a third improper use of the term Induction, 

 which it is of real importance to clear up, because the theory of 

 induction has been, to no ordinai-y degree, confused by it, and because 

 the confusion is exemplified in, the most recent and most elaborate 

 treatise on the inductive philosophy which exists in our language. 

 The error in question is that of confounding a mere description of a 

 set of observed phenomena, with an induction from them. 



Suppose that a phenomenon consists of parts, and that these parts 

 are only capable of being obser\"«d separately, aiul as it were piece- 

 meal. Wlien the observations have been inade, there is a convenience 

 . (amounting for many purposes to a necessity) in obtaining a represen- 

 tation of the phenomenon as a whole, by combining, or, as we may 

 say, piecing these detached fragments together. A navigator sailing 

 in the midst of the ocean discovers land : he cannot at first, or by any 

 one observation, determine whether it is a continent or an island ; but 

 he coasts along it, and after a few days, finds himself to have sailed 

 completely round it : he then pronounces it an island. Now there 

 was no particular time or place of observation at which he could per- 

 ceive that this land was entirely suiTounded by water : he ascertained 

 the fact by a succession of partial observations, and then selected a 

 general expression which summed up in two or three words the whole 

 of what he so observed. But is there anything of the nature of an 

 induction in this process ? Did he infer anything that had not been 

 observed, from something else which had I Certainly not. That the 

 land in question is an island, is not an inference fi-om the partial facts 

 which the navigator saw in the course of his circumnavigation ; it is 

 the facts themselves ; it is a summary of those facts ; the description of 

 a complex fact, to which those simpler ones are as the parts of a whole. 



Now there is no difference in kind between this simple operation, 

 and that by which Kepler ascertained the nature of the planetary 

 orbits : and Kepler's operation, all at least that was characteristic in 

 it, was not more an inductive act than that (jf our supposed navigator. 



The object of Kepler was to determine the real path described by 

 each of the planets, or let us say the planet Mars (for it was of that 

 body that he first established two of the three gi-eat astronomical 

 truths which bear his name). To do this there was no other mode 

 than that of direct obsei-v'atron : and all which observation could do 

 was to ascertain a great number of the successive places of the planet ; 

 or rather, of its apparent places. That the planet occupied success- 

 ively all these positions, or at all events, positions which produced the 



* I am happy to be able to refer, in confirmation of this view of what is called induction 

 in mathematics, to the highest English authority on the philosophy of algebra, Mr. Pea- 

 cock. See pp. 107-8 of liis profound Treatise on Algebra. 



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