APPROXIMATE GENERALIZATIONS. 147 



taken in conjunction, the propositions may co-operate 

 towards the result in two different ways. In the one, 

 each proposition is separately applicable to the case in 

 hand, and our object in combining them is to give to 

 the conclusion in that particular case the double pro- 

 bability arising from the two propositions separately. 

 This may be called joining two probabilities byway of 

 Addition ; and the result is a probability greater than 

 either. The other mode is, when only one of the pro 

 positions is directly applicable to the case, the second 

 being only applicable to it by virtue of the application 

 of the first. This is joining two probabilities by way 

 of Deduction ; the result of which is a less probability 

 than either. The type of the first argument is, Most 

 A are B ; most C are B ; this thing is both an A and 

 a C ; therefore it is probably a B. The type of the 

 second is, Most A are B ; most C are A ; this is a C ; 

 therefore it is probably an A, therefore it is probably a 

 B. The first is exemplified when we prove a fact by 

 the testimony of two unconnected witnesses ; the 

 second, when we adduce only the testimony of one 

 witness that he has heard the thing asserted by 

 another. Or again, in the first mode it may be argued 

 that the accused committed the crime, because he con- 

 cealed himself, and because his clothes were stained 

 with blood ; in the second, that he committed it because 

 he washed or burnt his clothes, which is supposed to 

 render it probable that they were stained with blood. 

 Instead only of two links, as in these instances, we may 

 suppose chains of any length. A chain of the former 

 kind was termed by Mr. Bentham* a self-corroborative 

 chain of evidence ; the second, a self-infirmative chain. 

 When approximate generalizations are joined by 



* Rationale of Judicial Evidence. Book v. Circumstantial, 



L 2 



