APPROXIMATE GENERALISATIONS. 



389 



fit : We are forced, therefore, to draw 

 our conclusions from coarser and more 

 fallible indications. 



§ 4. Proceeding now to consider 

 what is to be regarded as sufficient 

 evidence of an approximate generalisa- 

 tion, we can have no difficulty in at 

 once recognising that when admissible 

 at all, it is admissible only as an em- 

 pirical law. Propositions of the form, 

 Every A is B, are not necessarily 

 laws of causation, or ultimate uni- 

 formities of co-existence ; propositions 

 like Most A are B, cannot be so. 

 Propositions hitherto found true in 

 every observed instance may yet be 

 no necessary consequence of laws of 

 causation or of ultimate imiformities, 

 and unless they are so, may, for aught 

 we know, be false beyond the limits 

 of actual observation : still more evi- 

 dently nmst this be the case w^ith pro- 

 positions which are only true in a mere 

 majority of the observed instances. 



There is some difference, however, 

 in the degree of certainty of the pro- 

 position, Most A are B, according as 

 that approximate generalisation com- 

 prises the whole of our knowledge of 

 the subject or not. Suppose, first, 

 that the former is the case. We 

 know only that most A are B, not 

 why they are so, nor in what respect 

 those which are, differ from those 

 which are not. How then did we 

 learn that most A are B ? Precisely 

 in the manner in which we should 

 have learnt, had such happened to be 

 the fact, that all A are B. We col- 

 lected a number of instances sufficient 

 to eliminate chance, and having done 

 so, compared the number of instances 

 in the affirmative 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 proposi- 

 tion true, we cannot 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 

 Englishmen, Frenchmen, Germans, 

 North Americans, and so forth ; but 

 if on this evidence alone we extended 

 the assertion to Orientals, we should 

 step beyond 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 approxi- 

 mate generalisation. 



In the case where the approximate 

 proposition is not the ultimatum of 

 our scientific knowledge, but only the 

 most available form of it for practical 

 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 distin- 

 guished from the portion wnich has 

 it not ; we are rather more favourably 

 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 

 examining whether the proposition 

 admits of being deduced from the 

 known cause, or from any known 

 criterion, of B. Let the question, for 

 example, be whether most Scotchmen 

 can read? We may not have ob- 

 served or received the testimony of 

 others respecting a sufficient number 

 a!id 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 determining the question presents 

 itself, namely, by inquiring whether 

 most Scotchmen have been sent to 

 schools where reading is effectually 

 taught. Of these two modes, some- 

 times one and sometimes the other is 

 the more available. In some cases, the 

 frequency of the effect is the more 

 accessible to that extensive and varied 

 observation which is indispensable 

 to the establishment of an empirical 



