INDUCTION IN ITS VARIOUS SENSES 43 



A truth cannot be said to be discovered in the full and complete 

 sense of the word until it is thoroughly verified, or proved to be 

 a truth. It may be formulated and held as true with more or 

 less probability as the result of an enumerative induction or of an 

 analogical argument, as an hypothesis or as an &quot;empirical general 

 ization,&quot; but it cannot be fairly said to be fully &quot;discovered&quot; 

 until we have both &quot; verified &quot; it, or proved that it is true, and 

 &quot;explained&quot; it, or shown why and wherefore it is true, by 

 connecting it necessarily with already known and established 

 truths. In any case, Mill de facto regarded his &quot; inductive 

 methods &quot; as methods of discovery as well as of proof, and de 

 scribed induction itself as &quot; the operation of discovering and 

 proving general propositions&quot;. 1 



Finally, we may mention Jevons, 2 as an author who takes a thoroughly 

 enumerative view of induction, making the whole process consist in a succes 

 sive enumeration and determination of all the mathematically possible hypo 

 theses that might account for a given result or phenomenon. Obviously, in 

 this view certitude about our inductive conclusions is practically never attainable, 

 for the ideal of a perfect enumeration of instances is beyond our reach. 3 The 

 method is open to the same objections as Bacon s method, which Jevons him 

 self criticizes. In the &quot; infinite ballot-box &quot; of nature, the determination of the 

 chances of an invariable sequence of any two &quot; balls &quot; is a problem in the 

 mathematical theory of probability, the solution of which cannot of its nature 

 give us certitude (267). Nor can the result of this &quot; inverse problem &quot; be made 

 any more certain or definite by arbitrarily limiting the elements in the ante 

 cedent to those contained in the consequent, nor, indeed, by arbitrarily limiting 

 them in any way. &quot; If, for instance, we ... say : Given that certain com 

 binations of A, B, and C, are the existent ones, find a solution in terms of A, 

 B, C, and nothing else, from which this result shall follow, no complaint can 

 be made. The problem is a very limited one, but it may be useful. . . . But 

 to make the same restriction when the problem is, Given that dew is copious 

 on a cold, clear night, or given that a magnetic needle is deflected by an electric 

 current, find a solution which shall introduce no fresh terms into the statement 

 of the phenomena, would be a mere parody of physical investigation.&quot; 4 In 

 deed, the only way of reaching certitude is that precluded by Jevons s view of 

 induction ; namely, by abandoning the enumerative ideal and addressing our 

 selves to an analysis of the nature of the phenomena in question, on the rational 

 assumption that constant coexistences or sequences of phenomena have their 

 explanation in the existence of fixed natures, of stable tendencies and lines of 

 action, in the phenomena themselves, and with the conviction that these fixed 



1 Logic, iii., I., 2. 



2 Flourished 1835-1882 ; Logical writings : Principles of Science (2 \ols. 1874; 

 2nd edit, i vol. 1877) ; Elementary Lessons in Logic (1870) ; Primer of Logic (1876) 

 Studies in Deductive Logic (1880). 



*Cf. JOSEPH, Logic, p. 487. &amp;lt;VENN, Empirical Logic, pp. 360, 361. 



