INDUCTIONS IMPROPEULY SO CALLED. 175 



whole class, or that what is true at certain times will be true under 

 similar circumstances at all times. 



This definition excludes from the meaning of the term Induction, 

 various logical operations, to which it is not unusual to apply that 

 name. 



Induction, as above defined, is a process of inference ; it px'oceeds 

 from the known to the unknown ; and any operation involving no in- 

 ference, any process in which what seems the conclusion is no wider 

 than the premisses from which it is drawn, does not fall within the 

 meaning of the term. Yet in the common books of Logic we find 

 this laid down as the most perfect, indeed the only quite perfect, form 

 of induction. In those books, every process which sets out from a 

 less general and terminates in a more general expression — which ad- 

 mits of being stated in the form, " This and that A are B, therefore 

 every A is B" — is called an induction, whether anything be really 

 concluded or not ; and the induction is asserted to be not perfect, un- 

 less every single individual of the class A is included in the antecedent, 

 or premiss : that is, unless what we affirm of the class, has already 

 been ascertained to be true of every individual in it, so that the 

 nominal conclusion is not really a conclusion, but a mere reassertion 

 of the premisses. If we were to say. All the planets shine by the 

 sun's light, from observation of each separate planet, or All the 

 Apostles were Jews, .because this is ti'ue of Peter, Paul, John, and 

 eveiy other apostle — these, and such as these, would, in the phrase- 

 ology in question, be called pez-fect, and the only perfect, Inductions. 

 This, however, is a totally different kind of induction from ours ; it is 

 no inference from facts known to facts unknown, but a mere short- 

 hand registration of facts known. The two simulated arguments, 

 wlilch we have quoted, are not generalizations ; the propositions pur- 

 porting to be conclusions from them, are not really general proposi- 

 tions. A general proposition is one in which the predicate is affirmed 

 or denied of an unlimited number of individuals ; namely, all, whether 

 few or many, existing or capable of existing, which possess the prop- 

 erties connoted by the subject of tlie proposition. "AH men are mor- 

 tal" does not mean all now living, but all men past, present, and to 

 come. ^Vhen the signification of the term is limited so as to render it 

 a name not for any and every individual falling under a certain gen- 

 eral description, but only for each of a number of individuals desig- 

 nated as such, and as it were counted off individually, the proposition, 

 though it may be general in its language, is no general proposition, 

 but merely that number of singular propositions, written in an 

 abridged character. The operation may be very useful, as most 

 forms of abridged notation are ; but it is no pait of the investigation 

 of ti-uth, though often bearing an important part in the preparation of 

 the materials for that investigation. 



§ 2. A second process which requires to be distinguished from 

 Induction, is one to which matliematicians sometimes give that name : 

 and which so far resembles Induction properly so called, that the 

 propositions it leads to are really general propositions. For example, 

 when we have proved, with respect to the circle, that a straight line 

 caimot meet it in more than two points, and when the same tiling has 

 been successively proved of the ellipse, the parabola, and the hyj>cr- 



