INDUCTIONS IMPROPERLY SO CALLED. 321 



must be made. If in concluding that all animals have a 

 nervous system, we mean the same thing and no more as if 

 we had said " all known animals," the proposition is not 

 general, and the process by which it is arrived at is not in- 

 duction. But if our meaning is that the observations made 

 of the various species of animals have discovered to us a law 

 of animal nature, and that we are in a condition to say that a 

 nervous system will be found even in animals yet undiscovered, 

 this indeed is an induction ; but in this case the general pro- 

 position contains more than the sum of the special proposi- 

 tions from which it is inferred. The distinction is still more 

 forcibly brought out when we consider, that if this real gene- 

 ralization be legitimate at all, its legitimacy probably does not 

 require that we should have examined without exception every 

 known species. It is the number and nature of the instances, 

 and not their being the whole of those which happen to be 

 known, that makes them sufficient evidence to prove a general 

 law: while the more limited assertion, which stops at all 

 known animals, cannot be made unless we have rigorously 

 verified it in every species. In like manner to (return to a 

 former example) we might have inferred, not that all the 

 planets, but that all planets, shine by reflected light: the 

 former is no induction ; the latter is an induction, and a bad 

 one, being disproved by the case of double stars self-luminous 

 bodies which are properly planets, since they revolve round a 

 centre. 



2. There are several processes used in mathematics 

 which require to be distinguished from Induction, being not 

 unfrequently called by that name, and being so far similar to 

 Induction properly so called, that the propositions they lead 

 to are really general propositions. For example, when we 

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

 cannot meet it in more than two points, and when the same 

 thing has been successively proved of the ellipse, the parabola, 

 and the hyperbola, it may be laid down as an universal pro- 

 perty of the sections of the cone. The distinction drawn in 

 the two previous examples can have no place here, there being 

 VOL. i. 21 



