36 



to the combiiiation of attributes, and have no interpretation 

 relating to the extent of classes; in other words, they can 

 be interpreted only in comprehension ; while addition and 

 subtraction, on the contrary, can be interpreted only in 

 extension. 



The subject of the mutual relation of classes as to 

 inclusion and exclusion, total and partial, is of such vast 

 importance that it appears to be often believed to cover the 

 whole ground of logical science ; but this is by no means 

 the fact, even if we confine our view to elementary logic, 

 and exclude the logic of relative terms. There are proposi- 

 tions of the form 



x = y-p 



which can be interpreted in extension only, and have no 



interpretation in comprehension; — such as "Lothian is part 



of Scotland ; " or " hydrogen is a constituent of water." 



These have all the most generally recognized properties of 



propositions, and may enter into syllogisms, thus : — " Lothian 



is part of Scotland; Scotland is part of Great Britain; 



therefore Lothian is part of Great Britain." And there are 



also propositions of the form 



x = xy 



which admit of interpretation in comprehension only, and 

 not in extension. To this class belong hypothetical pro- 

 positions, with the syllogisms formed from them, such as : — 

 " If he can discredit this witness, he will obtain a verdict ; 

 if he obtains a verdict, his position will be established; 

 therefore if he can discredit this witness, his position will 

 be established." 



* Mr. Harley added the following remarks : — 



Mr. Venn, in his Symbolic Logic, sets forth his view 



