LOGIC 293 



Subalterns may both be false and both true, or one may 

 be false and the other true in either case. 



A term is said to be distributed, when it includes every 

 individual of the class to which it refers. Thus, when we 

 say " fixed stars twinkle " and " no man can fly, "we mean 

 to include the whole of the fixed stars in one case, and all 

 men in the other. 



In all universal propositions, the subject is distributed 

 as in the instances just given. In all negative proposi- 

 tions, the predicate is distributed as " Men are not 

 immortal "and "some whales are not toothed." "Im- 

 mortal " is distributed because it refers to all men, and 

 "not toothed" is distributed because it refers to all those 

 whales which are referred to and included in the above 

 proposition. 



Therefore in universal negative propositions, both 

 terms are distributed, while in particular affirmative 

 propositions, neither term is distributed. 



Propositions can be inverted ; that is, the two terms of 

 a proposition can be transposed, and this process is 

 termed conversion. In order that this may be carried out 

 validly, no term must be distributed in the converted 

 proposition, which was not distributed before its con- 

 version. 



Since in universal negatives (E) both terms are 

 distributed, e.g., " No horses are winged creatures," 

 and in particular affirmatives (I) neither term is 

 distributed, e.g.-, "Some horses are lame," therefore 

 in both these cases the terms can be simply trans- 

 posed and yet the propositions must remain true as 

 "winged creatures are not horses" and " lame are some 

 horses." 



A universal affirmative (A) may be converted by 

 changing it into a particular affirmative (I), as, " All men 



