198 Mr DE morgan, ON THE SYLLOGISM, No. Ill, 



universal, because we speak of its aggregants separately ; each aggregant is animal. Throw 

 out any class of man, and the proposition is only crippled, not falsified. But animal is par- 

 ticular, extensively : we cannot throw out any arbitrary formation of class we please, savage 

 animal for instance, because men may be among them, and it need not be true that All man 

 is (in what is left of) animal. Now pass to intensive quantity (which we shall call force when 

 we speak of attributes) mathematically considered. The quantities change names ; and this 

 always happens: the extensive universal is always the intensive particular, &c. Man is in- 

 tensively particular, and animal is intensively universal, in the proposition above. We may 

 reject any component of animal: man is in the class indicated by the remaining compound. 

 But we may not at pleasure reject any component of m.an : for in so doing we may reject a 

 restricting class which takes the common part of the remaining compounded classes out of 

 animal in some part of its extension. Speaking metaphysically, animal is a component of man : 

 animal enters in its complete force, but not man : all the attributes of animal compound into 

 a component of man. 



As another instance, suppose 'I deny the co-exclusion of X and Y,' When a relation is 

 convertible, it is convenient that the word should denote it : so, instead of saying that X is an 

 external of Y, I say that X and Y are co-externals. Here X and Y are both extensively 

 particular : we cannot make the denial of any aggregant of either, necessarily. For this 

 reason they are both intensively universal: I deny that any component of X is excluded from 

 any component of Y. In the metaphysical reading, it will be ' I deny the repugnance of the 

 notions X and Y'; and both have complete force. Speak thus of metallic and fluid, to both 

 of which belongs mercury: in thus speaking, I deny that brilliancy is repugnant to equality 

 of pressure ; I deny that high specific gravity is repugnant to mobility : either of these 

 repugnances would create repugnance between metallic and Jluid. 



XV. The following symbols will be used : — 



Mathematical Reading. 



X) or (X X Extensively universal or inten- 

 sively particular 



X( or X) X Extensively particular or in- 

 tensively universal 



Metaplijaical Beading. 



]X or Xr X of complete force 

 [X or X] X of incomplete force. 



1 call this notation spicular, a name first given in derision, but not the worse for that : it 

 is better than parenthetic, which has a derived meaning. 



XVI. In the old use of the word intension, it referred to intensity of degree, a kind of 

 extension, since there was more or less of the same; but continuous, not increasing by indivi- 

 duals. We may distinguish, when needful, between intensity of degree and intensity of com- 

 position : the two kinds are of the same logical power. We may dissect class until we come 

 down to the individual, either by successive intensifications of composition, or of degree : some 

 do one thing, some the other, and dispute arises on the result. Thus one man arrives at his 

 highest member of any class, poet, artist, general, &c. by the greatest intension of degree of 

 the attribute on which he most admires the merit of the class ; another by greatest intension 

 of composition of constitutive attributes ; a third balances the two. 



