January 31, 1887. J 



SCIEJSC'Ji]. 



65 



ments of others, though we do not apprehend or 

 reahze the meaning of what is asserted, and are 

 somewhat hazy as to what the assertion concerns. 

 We teachers are very liable to produce vagueness 

 and confusion in this way. We impose our judg- 

 ments on our pupils ; we are contented with their 

 ready assurance that ' they see ; ' we rush on from 

 step to step, and then are astonished to find how- 

 hazy and muddled the children's views are. 

 Teachers have even been known to grow quite 

 impatient with the children on this account, re- 

 senting delay, and setting all the confusion down 

 to a wilful perversity on the child's own part. 

 The other qualities which characterize sound 

 and serviceable judgments need no particular re- 

 mark here. 



Many of our judgments are arrived at immedi- 

 ately or intuitively, such as, ' This fire is warm,' 

 ' I saw my friend last week.' These are called 

 * intuitive ' judgments. But, on the other hand, 

 it is plain that many of our assertions are reached 

 by a process of reasoning or inference. Just as 

 we connect two concepts or representations to 

 form a judgment, so we may connect two or more 

 judgments to form another judgment in advance 

 of these. Thus, from the assertions that ' all 

 metals are elements ' and ' iron is a metal,' we 

 may derive the judgment that ' iron is an ele- 

 ment ; ' or we may infer that ' all material bodies 

 have weight,' because we have found that this 

 and many other material bodies have weight. 

 The resulting judgment we term a ' conclusion,' 

 and the judgments from which it is derived 

 'premises.' To reason, then, is to pass from 

 a certain judgment or judgments to a new 

 one. This implies that we recognize the relation 

 between the new and the old judgments ; that we 

 apprehend the connecting link or similarity be- 

 tween them. Reasoning is, in fact, as Mr. Sully 

 observes, '• only a higher and more complex pro- 

 cess of assimilation, identification, or classing." 

 From mere difference we can infer nothing. If 

 X and y are both equal to z, we can infer that 

 X = y ; but if x and y are both greater or less than 

 z, we cannot from these facts infer any thing as 

 to the relation between x and y. Again : in our 

 reasoning the premises and the conclusion may 

 both be particular. A boy may have noticed 

 that on several occasions when the wind V7as in 

 the east his master was cross, and he may infer, 

 that, the wind being in the east to-day, his master 

 will be cross. Or the premises may both, or one 

 of them, be general, and the conclusion be either 

 general or particular ; as when we reason, that 

 oxygen being a material body, and all material 

 bodies having weight, therefore oxygen must 

 have weight ; or that all gases have weight, 



because all gases are material bodies. The 

 former is called implicit, the latter explicit, 

 reasoning. But the distinction is not of great value 

 to the logician, because we do, as a matter of fact, 

 in implicit reasoning, tacitly assume a general 

 premise : the boy in our example, consciously or 

 unconsciously, assumes that all east winds make 

 his master cross. There is another distinction, how- 

 ever, which applies to reasoning, and which will 

 be of great use to us. We may either argue up to a 

 general truth from premises which are particular, 

 or at least less general ; or we may apply this gen- 

 eral truth to cases which are less general or particu- 

 lar. Thus, having found that gold and silver and 

 copper, etc., are all elements, we may arrive at 

 the conclusion that all metals are elements ; or, 

 seeing that all birds die, and all fishes die, etc., 

 we may infer that all animals die. On the other 

 hand, from the general truth that all the radii of 

 a i;ircle are equal, we may infer that two particu- 

 lar straight lines, AB and AC, being the radii of 

 the same circle, are equal to one another. In the 

 former case, our reasoning is said to be inductive ; 

 in the latter, deductive. 



The chief point to notice in induction is, that in 

 general our conclusion goes beyond what our 

 premises give us the right of asserting as actually 

 true. We can never, therefore, be certain, in such 

 cases, of arriving at absolute truth, but only at a 

 greater or less degree of probability. When we 

 assert that all planets move round the sun in the 

 same direction, the ' all ' includes more cases than 

 are mentioned in the premises, — more cases than 

 we have observed. Further experience may prove 

 that some of our general conclusions are wrong. 

 This has been the cas& with the emission theory of 

 light, which has now been abandoned for the 

 wave theory. Or, to quote a simpler case, Mr. 

 Jevons mentions that Format maintained that 

 1 + 2^ always represents a prime number for all 

 values of x ; and so it does, till the product 

 reaches the large number 4,294,967,297, which is 

 divisible by 641. This danger should be a warn- 

 ing to us in our use of inductive reasoning with 

 children at school. We are all of us, young and 

 old, far too much given to generalizing* from too 

 few particulars, and to asserting that what has 

 happened in a certain number of particular cases 



1 It will toe well to note, in order to avoid confusion, how 

 inductive reasoning, whicli is a kind of generalization, 

 diif ers from the generalization of judgment. In each case 

 we trace out a similarity among a numtoer of different 

 things. In judgment, we do so in things viewed as single 

 and apart, in order to connect with one or all of^them a gen- 

 eral notion applicatole to them all: in induction, it is the 

 relations of things to one another to which we attend, and 

 we seek to establish some connection between these rela- 

 tions, and thus to arrive at some wider relations between 

 the things themselves. 



