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CHAPTER XXIII. 



OF APPROXIMATE GENERALIZATIONS, AND 

 PROBABLE EVIDENCE. 



1 . IN our inquiries into the nature of the induc- 

 tive process, we have hitherto confined our notice to 

 such generalizations from experience as profess to be 

 universally true. We indeed recognised a distinction 

 between generalizations which are certain and those 

 which are only probable : but the propositions them- 

 selves, though they differed in being more or less doubt- 

 ful in the one case, and not at all doubtful in the other, 

 were always of the form, Every A is B ; they claimed 

 nothing less than universality, whatever might be the 

 completeness or the incompleteness of our assurance 

 of their truth. There remain, however, a class of 

 propositions avowedly not universal ; in which it is 

 not pretended that the predicate is always true of the 

 subject; but the value of which, as generalizations, is 

 nevertheless extremely 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 upon probable 

 evidence, the premisses it is drawn from are usually 

 generalizations of this sort. 



As every certain inference respecting a particular 

 case, implies that there is ground for a general propo- 

 sition, of the form, Every A is B ; so does every probable 

 inference suppose that there is ground for a propo- 

 sition of the form. Most A are B : and the degree of 

 probability of the inference in an average case, will 

 depend upon the proportion between the number of 



