OF ARTS AND SCIENCES : NOVEMBER 13, 1867. 425 



long as Kant's law holds, and as long as logical quantities can only be 

 compared as being more or less and not directly measured, and as long 

 as the different hinds of quantity cannot be compared at all, a third 

 quantity must be directly proportional to one or other of the known 

 quantities, and therefore must measure the same thing, or else must be 

 independent of the other two, and be quite unconnected with them. 



§ 4. Three Principal Senses in which Comprehension and Extension 



will be taken in this Paper. 



I shall adopt Hamilton's terms, breadth and depth, for extension and 

 comprehension respectively, and shall employ them in different senses, 

 which I shall distinguish by different adjectives. 



By the informed breadth of a term, I shall mean all the real things 

 of which it is predicable, with logical truth on the whole in a supposed 

 state of information. By the phrase " on the whole" I mean to indicate 

 that all the information at hand must be taken into account, and that 

 those things of which there is not on the whole reason to believe that a 

 term is truly predicable are not to be reckoned as part of its breadth. 



If T be a term which is predicable only of S', S", and S"', then the 

 S"s, the S'"s, and the S""s, will constitute the informed breadth of T. 

 If at the same time, S' and S" are the subjects of which alone another 

 term T' can be predicated, and if it is not known that all S'" 's are 

 either S' or S", then T is said to have a greater informed breadth than 

 T'. If the S"' 's are known not to be all among the S' 's and S" 's, this 

 excess of breadth may be termed certain, and, if this is not known, it 

 may be termed doubtful. If there are known to be S'" 's, not known 

 to be S' 's or S" 's, T is said to have a greater actual breadth than T' ; 

 but if no S"i's are known except such are known to be S''s, and S"'s 

 (though there may be others), T is to have a greater potential breadth 

 than T'. If T and T' are conceptions in different minds, or in different 

 states of the same mind, and it is known to the mind which conceives 

 T that every S'" is either S" or S', then T is said to be more exten- 

 sively distinct than T'.* 



By the informed depth of a term, I mean all the real characters (in 

 contradistinction to mere names) which can be predicated of it t (with 



* For the distinction of extensive and comprehensive distinctness, see Scotus, i. 

 dist. 2.qu.3. 



t That is, of whatever things it is applicable to. 



vol. vii. 54 



