INDUCTION IN ITS VARIOUS SENSES 29 



symbolized by M as being greater in point of possible extension 

 than the individuals enumerated (S\ though actually equal to 

 them, and naturally less than the genus characterized by the 

 attribute P. 



What is to be said about the value of this process ? 



Firstly, it will not be valid unless the enumeration is com 

 plete. The enumeration must be Bia Trdvrwv, as Aristotle 

 expresses it ; else the argument will be fallacious : there will be 

 an illicit process of the subject of the conclusion. St. Thomas 

 likewise insists that as long as we base our conclusion on enumera 

 tion the latter must be complete. 1 So long then as we concentrate 

 our attention on the mere enumeration of instances, and disregard 

 their nature, we can never be certain of our conclusion until we are 

 certain that our enumeration is actually complete : &quot; opportet sup- 

 ponere quod accepta sint omnia &quot;. Now we can practically never 

 be certain, in regard to the occurrence of natural phenomena, that 

 our enumeration of instances is complete : and this is the first 

 obvious limitation of the process as a means of reaching certain 

 knowledge. Mere &quot; enumerative &quot; induction, then, has only a pro 

 visional value. It enables us to say that so far as our actual 

 knowledge goes, such or such an enumeration may be regarded as 

 complete ; that it is complete we usually have no warrant to affirm 

 categorically. There are, of course, cases in which an incomplete 

 enumeration of instances may yield a very high degree of proba 

 bility for a universal conclusion, viz. when we are dealing with 

 phenomena such that if an instance contrary to those examined 

 existed we should in all probability have encountered it. The 

 truth of such a generalization cannot reasonably be doubted so 

 long as no negative instance turns up. 2 



Secondly, even where the enumeration of instances is complete, 

 the process does not lead to scientific knowledge, i.e. the knowledge 

 of a strictly universal conclusion embodying what can be called a 

 law. And the reason is manifest. The conclusion expresses a 

 simple addition of instances, and is, therefore, simply a collective 

 proposition whose subject is an actual whole ; whereas the strict 



1 &quot; Opportet supponere quod accepta sint omnia quae continentur sub aliquo 

 communi ; alioquin inducens non poterit ex singularibus acceptis concludere uni- 

 versale. . . . Patet quod inducens facta inductione quod Socrates currat et Plato et 

 Cicero, non potest ex necessitate concludere, quod omnis homo currit, nisi detur sibi 

 a respondente, quod nihil aliud contineatur sub homine, quam ista quae inducta 

 sunt &quot; (In II. Anal. Post., lect. 4). 



2 Cf. JOSEPH, Logic, p. 491 ; MELLONE, op. cit., p. 251, referring to Aristotle, 

 Top., viii., 8. 



