228 ARISTOTELIAN LOGIC. [CHAP. XV. 



consciously or unconsciously, to the particular models of the pro- 

 cesses which have been classified in the writings of logicians. 



3. The course which I design to pursue is to show how 

 these processes of Syllogism and Conversion may be conducted 

 in the most general manner upon the principles of the present 

 treatise, and, viewing them thus in relation to a system of Logic, 

 the foundations of which, it is conceived, have been laid in the 

 ultimate laws of thought, to seek to determine their true place 

 and essential character. 



The expressions of the eight fundamental types of proposi- 

 tion in the language of symbols are as follows : 



1. All Y's area's, y = vx. 



2. No Y's are X's, y = v(l-x). 



3. Some Y's are X 's, vy = vx. 



4. Some Y's are not-X's, vy v (1 - x). 



5. All not- Y's are X's, 1 - y = vx. (1) 



6. No not- Y's are X's, I - y = v (1 - x). 



7. Some not- Y's are X'a, v (1 -y) = vx. 



8. Some not- Y's are not-X's, v (1 -y) = v (1 - x). 



In referring to these forms, it will be convenient to apply, in 

 a sense shortly to be explained, the epithets of logical quantity, 

 "universal" and "particular," and of quality, "affirmative" and 

 " negative," to the terms of propositions, and not to the propo- 

 sitions themselves. We shall thus consider the term " All Y's," 

 as universal-affirmative ; the term ** Y's," or " Some Y's," as 

 particular-affirmative ; the term " All not- Y's," as universal-ne- 

 gative ; the term " Some not- Y's," as particular-negative. The 

 expression " No Y's," is not properly a term of a proposition, for 

 the true meaning of the proposition, " No Y's are X's," is "All 

 Y's are not-X's." The subject of that proposition is, therefore, 

 universal-affirmative, the predicate particular-negative. That 

 there is a real distinction between the conceptions of " men" and 

 "not men" is manifest. This distinction is all that I contem- 

 plate when applying as above the designations of affirmative and 

 negative, without, however, insisting upon the etymological pro- 

 priety of the application to the terms of propositions. The 

 designations positive and privative would have been more ap- 



