APPROXIMATE GENERALIZATIONS. 419 



in the aiRrmative with the number in the negative. The result, like other 

 unresolved derivative laws, can be relied on solely within the limits not 

 only of place and time, but also of circumstance, under which its truth has 

 been actually observed; for, as we are supposed to be ignorant of the 

 causes which make the proposition true, we can not tell in what manner 

 any new circumstance might perhaps affect it. The proposition, Most 

 judges are inaccessible to bribes, would probably be found true of English- 

 men, Frenchmen, Germans, North Americans, and so forth ; but if on this 

 evidence alone we extended the assertion to Orientals, we should step be- 

 yond the limits, not only of place but of circumstance, within which the 

 fact had been observed, and should let in possibilities of the absence of the 

 determining causes, or the presence of counteracting ones, which might be 

 fatal to the approximate generalization. 



In the case where the approximate proposition is not the ultiuiatum of 

 our scientific knowledge, but only the most available form of it for practi- 

 cal guidance; where we know, not only that most A have the attribute B, 

 but also the causes of B, or some properties by which the portion of A 

 which has that attribute is distinguished from the portion which has it 

 not, we are rather more favorably situated than in the preceding case. 

 For we have now a double mode of ascertaining whether it be true that 

 most A are B; the direct mode, as before, and an indirect one, that of ex- 

 amining whether the proposition admits of being deduced from the known 

 cause, or from any known criterion, of B. Let the question, for example, 

 be wliether most Scotchmen can read? We may not have observed, or 

 received the testimony of others respecting, a sufficient number and variety 

 of Scotchmen to ascertain this fact; but when we consider that the cause 

 of being' able to read is the having been taught it, another mode of deter- 

 mining the question presents itself, namely, by inquiring whether most 

 Scotchmen have been sent to schools where reading is effectually taught. 

 Of these two modes, sometimes one and sometimes the other is the more 

 available. In some cases, the frequency of the effect is the more accessi- 

 ble to that extensive and varied observation which is indispensable to the 

 establishment of an empirical law ; at other times, the frequency of the 

 causes, or of some collateral indications. It commonly happens that nei- 

 ther is susceptible of so satisfactory an induction as could be desired, and 

 that the grounds on which the conclusion is received are compounded of 

 both. Thus a person may believe that most Scotchmen can read, because, 

 so far as his information extends, most Scotchmen have been sent to school, 

 and most Scotch schools teach reading effectually ; and also because most 

 of the Scotchmen whom he has known or heard of could read ; though nei- 

 ther of these two sets of observations may by itself fulfill the necessary 

 conditions of extent and variety. 



Although the approximate generalization may in most cases be indis- 

 pensable for our guidance, even when we know the cause, or some certain 

 mark, of the attribute predicated, it needs hardly be observed that we may 

 always replace the uncertain indication by a certain one, in any case in 

 which we can actually recognize the existence of the cause or mark. For 

 example, an assertion is made by a witness, and the question is whether to 

 believe it. If we do not look to any of the individual circumstances of the 

 case, we have nothing to direct us but the approximate generalization, 

 that truth is more common than falsehood, or, in other words, that most 

 persons, on most occasions, speak truth. But if we consider in what cir- 

 tnimstances the cases where truth is spoken differ from those in which it is 



