APPROXIMATE GENERALIZATIONS. 41V 



truths by way of deduction. We may, it is true, by combining the prop- 

 osition Most A are B, with a universal proposition, Every B is C, arrive 

 at the conclusion that Most A are C. But when a second proposition of 

 the approximate kind is introduced — 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 can not 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 generaliza- 

 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 encumbered with conditions to be adapted for every- 

 day 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 scientific- 

 ally ascertained to be universal marks of it. To be indecisive and reluc- 

 tant 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 emergencies. If we 

 would succeed in action, 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 incomplete conclusiveness of any one indication, by ob- 

 taining others to corroborate it. The principles of induction applicable to 

 approximate generalization are thei*efore a not less important subject of in- 

 quiry than the rules for the investigation of universal truths ; and might 

 reasonably be expected to detain us almost as long, were it not that these 

 principles are mere corollaries from those which have been already treat- 

 ed of. 



§ 3. There are two sorts of cases in which we are forced to guide our- 

 selves by generalizations of the imperfect form. Most A are B. The first 

 is, when we have no others ; when we have not been able to carry our in- 

 vestigation of the laws of the phenomena any further ; as in the following 

 propositions — Most dark-eyed persons have dark hair; Most springs con- 

 tain mineral substances; Most stratified formations contain fossils. The 

 importance of this class of generalizations is not very great ; for, though it 

 frequently happens that we see no reason why that which is true of most 

 individuals of a class is not true of the remainder, nor are able to bring the 

 former under any general description which can distinguish them from the 

 latter, yet if we are willing to be satisfied with propositions of a less de- 

 gree of generality, and to break down the class A into sub-classes, we may 

 generally obtain a~collection of propositions exactly true. We do not know 

 why most wood is lighter than water, nor can we point out any general 

 property which discriminates wood that is lighter than water from that 

 which is heavier. But we know exactly what species are the one and 

 what the other. And if we meet with a specimen not conformable to any 



* Mr. De Morgan, in his Formal Logic, makes the just remark, that from two such prem- 

 ises 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 conclusions which can be drawn from two approximate 

 generalizations, when the precise degree of their approximation to universality is unknown or 

 undefined. 



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