THE DOCTRINE OF REDUCTION 345 



tions or hypotheses as to the nature or cause of a thing, until we 

 happen to find the correct one. This gradual process of exclusion 

 is called abscissio infiniti. It may be symbolized as follows : 

 &quot; *S either is or is not A ; 

 But, Every A is X, 

 and S is not X, 

 . . S is not A. 



If S is not A it either is or is not B ; 

 But, Every B is F, 

 and S is not Y, 

 . : S is not B. 



And so on, till we are left with only one possible conclusion 

 Sis P.&quot;^ 



For example, in the diagnosis of a disease the physician may 

 proceed to reason thus : Smallpox has certain symptoms ; this 

 disease does not show these symptoms ; therefore it is not smallpox : 

 arid so on. Or the botanist may reason thus : Such an order of 

 plants manifests such and such properties ; this specimen has not 

 these properties ; therefore it does not belong to this order. 



The valid moods of this figure may be summed up in the scheme : 

 &quot; Rule . . . All P is M (or is not M), 

 Denial of Result . . . Some (or All) S is not M (or is M\ 

 Denial of Case . . . therefore, Some (or All) S is not P ; &quot; 

 which is otherwise expressed by the mixed hypothetical syllogism : 

 &quot; If anything is P if is M (or is not M\. 

 Certain subjects, S, are not M (or are M\ 

 therefore, they are not P.&quot; 



While the corresponding syllogism in the first figure above, inferred from 

 ground to consequence, the present one infers from denial of consequence to 

 denial of ground. 2 



Is this a distinct form of inference from that exemplified in the first figure ? 3 



1 WELTON, op. cit., p. 313. 2 KEYNES, ibid., pp. 336-7. 



3 No doubt, the first figure does not always demonstrate or give the causa essendi, 

 but sometimes only a sign or effect or index of the conclusion. But when the latter 

 is negative, and the inference is from the absence of certain symptoms or marks in 

 S, the argument runs more naturally in Cesare (or Festino) than in any mood of the 

 first figure : &quot; All fish breathe through the gills, and Whales do not .-. A whale is 

 not a fish &quot;. This is a natural argument (in Camestres). It is based on the absence 

 of a certain feature in the whale. And if I want to put the argument into the mood 

 which naturally corresponds to it in the first figure, I must make this &quot;absence &quot; of 

 an attribute my middle term and reduce (by contraposition) to Barbara: &quot;What 

 does not breathe through the gills is not a fish, and Whales do not .. The whale is 

 not a fish &quot; ; and not to Cesare, which gives a conclusion about fish, &quot; whereas whales 

 are really the subject of my thought &quot; (JOSEPH, op. cit., p. 292). Where the two ex 

 tremes are disparate accidents, the second figure may not, perhaps, be quite as natural 

 as the first, though indeed there is little to choose as between them : &quot; Some ger- 



