236 ARISTOTELIAN LOGIC. [CHAP. XV. 



SECOND CONDITION OF INFERENCE. Two universal middle 

 terms. 



RULE OF INFERENCE. Change the quantity and quality of 

 either extreme, and equate the result to the other extreme un- 

 changed. 



There are in the case of unlike middle terms no other condi- 

 tions or rules of syllogistic inference than the above. Thus the 

 equation (IV.), though reducible to the form of a syllogistic con- 

 clusion, when w = 1 and v = 1, does not thereby establish a new 

 condition of inference ; since, by what has preceded, the single 

 condition v = 1, or w = 1, would suffice. 



8. The following examples will sufficiently illustrate the ge- 

 neral rules of syllogism above given : 



1. All Fs area's. 

 All Z's are Fs. 



This belongs to Case 1 . All Y's is the universal middle term. 

 The extremes equated give as the conclusion 

 Ally's are JTs; 



the universal term, All Z's, becoming the subject ; the particular 

 term (some) X's, the predicate. 



2. AU X's are Y's. 

 No Z's are Y's. 



The proper expression of these premises is 



AU X's are Fs. 



All Z's are not- Fs. 



They belong to Case 2, and satisfy the first condition of inference. 

 The middle term, Fs, in the first premiss, is particular-affirma- 

 tive ; that in the second premiss, not- Fs, particular-negative. 

 If we take All Z's as the universal extreme, and change its 

 quantity and quality according to the rule, we obtain the term 

 Some not-^'s, and this equated with the other extreme, All X's, 

 gives, 



All X's are not-Z's, i. e., No ^s are Z's. 



If we commence with the other universal extreme, and proceed 

 similarly, we obtain the equivalent result, 

 No Z's are X's. 



