AND ON LOGIC IN GENERAL. 215 



When a proposition proves of all, let it be called necessary. Logical necessity does not 

 distinguish the preceding cases from one another. When a proposition proves of some only, 

 not all, or not known to be all, it is contingent. 



Inference differs from proof in having reference only to the perception of the purely logical 

 part, the validity of the mode of junction of the propositions, or of the combination into one 

 of the relations they propound. 



XXXV, In verification of names, we must imagine what I may call registers. One 

 register answers, in every case, the question whether this or that object, species, attribute, is 

 within the universe. This register is used in ordinary logic : existence is supposed to be 

 ascertained before use of a name; and all existence is the universe of the propositions. I sub- 

 stitute existence in a given sphere of thought. Another register points out, for each name, the 

 cases in whicii that name applies, and in which its contrary. 



A proposition is universal, when inductive verification requires the examination of every 

 part of extension of the universe (the maximum of extension and minimum of intension) or of 

 every augmentation of intension which takes place within it : otherwise, the proposition is 

 particular. A proposition is universal both extensively and intensively, or both ways par- 

 ticular. The universals are )), ((, )•(, (•); the particulars are (), ) (, )•), (•( 



Keeping within the universe, by hypothesis, we cannot go beyond a certain extension, or 

 below a certain intension : we never decompose the intension of the whole universe, or treat its 

 intension as a compound ; we never add to the whole universe, or make its extension an 

 aggregant. Hence it is that extensively and intensively universal propositions are the same. 

 But terms are examined, not from a maximum downwards in one case, and a minimum 

 upwards in the other, but from a maximum downwards in both cases ; and the effect of this 

 difference is so marked that it might perhaps be desirable the words universal and parti- 

 cular should not be applied to both propositions and terms. 



A term is universal, extensively or intensively, when the verification by induction requires 

 examination of the whole extension, or of the whole intension, of the term : otherwise it is 

 particular. Thus in the particular proposition 'X and Y are coinadequate ' both terms are 

 extensively universal : for though a part of the universe may furnish verification, that part 

 must be ascertained to be out of the whole extent, both of X and Y. But both terms are 

 intensively particular : for if any component classes of X and Y be together inadequate, so 

 must be any compounds of those classes: consequently, a pair of components may settle the 

 matter. Speaking metaphysically, the proposition is ' X and Y are inalternative :' if any one 

 component attribute of X, and one of Y, be not necessary alternatives, neither are X and Y. 



The extensively universal is always intensively particular ; and the extensively particular 

 is always intensively universal ; and their converses. Both descriptions exist in both readings. 

 I shall use the phrases quantity universal and particular for mathematical reading, and force 

 complete and incomplete for the metaphysical reading : both having their extensive and in- 

 tensive. But, though all this distinction be in thought and nature, it is not all in habit or 

 second nature. The extensive is almost exclusively limited to the mathematical; the intensive 

 to the metaphysical : so that universal and particular quantity of extension, complete and in- 

 complete force of intension, will be the great working distinctions. 



