APPROXIMATE GENERALISATIONS. 



387 



not confine our notice to such genera- 

 lisations from experience as profess to 

 be universally true. There is a class 

 of inductive truths avowedly not uni- 

 versal, in which it is not pretended 

 that the predicate is always true of 

 the subject, but the value of which, 

 as generalisations, is nevertheless ex- 

 tremely great. An important portion 

 of the field of inductive knowledge 

 does not consist of universal truths, 

 but of approximations to such truths ; 

 and when a conclusion is said to rest 

 on probable evidence, the premises it 

 is drawn from are usually generalisa- 

 tions of this sort. 



As every certain inference respect- 

 ing a particular case implies that 

 there is ground for a general proposi- 

 tion, of the form, Every A is B ; so 

 does every probable inference suppose 

 that there is ground for a proposition 

 of the form, Most A are B ; and the 

 degree of probability of the inference 

 in an average case will depend on the 

 proportion between the number of 

 instances existing in nature which 

 accord with the generalisation, and 

 the number of those which conflict 

 with it. 



§ 2. Propositions in the form, Most 

 A are B, are of a very difiFerent degree 

 of importance in science, and in the 

 practice of life. To the scientific 

 inquirer they are valuable chiefly as 

 materials for, and steps towards, uni- 

 versal truths. The discovery of these 

 is the proper end of science : its work 

 is not done if it stops at the proposi- 

 tion that a majority of A are B, with- 

 out circumscribing that majority by 

 some common character, fitted to dis- 

 tinguish them from the minority. 

 Independently of the inferior pre- 

 cision of such imperfect generaUsa- 

 tions, and the inferior assurance with 

 which they can be applied to indivi- 

 dual cases, it is plain that, compared 

 with exact generalisations, they are 

 almost useless as means of discovering 

 ulterior truths by way of deduction. 

 We may, it is true, by combining the 

 proposition Most A are B, with an 



universal proposition, Every B is C, 

 arrive at the conclusion that Most A 

 are C. But when a second proposi- 

 tion of the approximate kind is intro- 

 duced, — or even when there is but 

 one, if that one be the major premise, 

 — nothing can in general be positively 

 concluded. When the major is Most 

 B are D, then, even if the minor be 

 Every A is B, we cannot infer that 

 most A are D, or with any certainty 

 that even some A are D. Though 

 the majority of the class B have the 

 attribute signified by D, the whole of 

 the sub-class A may belong to the 

 minority.* 



Though so little use can be made, 

 in science, of approximate generalisa- 

 tions, except as a stage on the road to 

 something better, for practical guid- 

 ance they are often all we have to 

 rely on. Even when science has 

 really determined the universal laws 

 of any phenomenon, not only are 

 those laws generally too much en- 

 cumbered with conditions to be 

 adapted for everyday use, but the 

 cases which present themselves in life 

 are too complicated, and our decisions 

 require to be taken too rapidly, to 

 admit of waiting till the existence of 

 a phenomenon can be proved by what 

 have been scientifically ascertained to 

 be universal marks of it. To be in- 

 decisive and reluctant to act, because 

 we have not evidence of a perfectly 

 conclusive character to act on, is a 

 defect sometimes incident to scientific 

 minds, but which, wherever it exists, 

 renders them unfit for practical emer- 

 gencies. If we would succeed in ac- 

 tion, we must judge by indications 

 which, though they do not generally 

 mislead us, sometimes do ; and must 

 make up, as far as possible, for the 



* Mr. De Morgan, in his Formal Logic, 

 makes the just remark, that from two 

 such premises as Most A are B, and Most 

 A are C, we may infer with certainty that 

 some B are C. But this is the utmost 

 limit of the conchisions which can be 

 drawn from two approximate generalisa- 

 tions, when tlie precise degree of their 

 approximation to universality is unknQWi» 

 or undefined. 



