OF ARTS AND SCIENCES : APRIL 9, 1867. 277 



We have already seen that the former of these is of the form of 

 the second figure, and the latter of the form of the third figure of 

 syllogism. 



Hence it appears that no syllogism of an indirect figure can be re- 

 duced to the first figure without a substitution which has the form of 

 the very figure from which the syllogism is reduced. In other words, 

 the indirect syllogisms are of an essentially different form from that 

 of the first figure, although in a more general sense they come under 

 that form. 



§ 6. The Theophrastean Moods. 



It is now necessary to consider the five moods of Theophrastus, viz. 

 Baralipton, Celantes, Dabitis, Fapesmo, Frisesomorum. Baralipton is 

 included in Dabitis, and Fapesmo in Frisesomorum, in the same way 

 in which Darapti is included in Disamis and Datisi, and Felapton in 

 Bocadro and Ferison. The Theophrastean moods are thus reduced to 

 three, viz. : — 



No X is Y, No X is Y, Some Y is Z, 



All Z is X; Some Y is Z; All Z is X; 



.-. Any Y is not Z. .'. Some Z is not X. .'. Some X is Y. 



Suppose we have, 1st, a Rule ; 2d, a Case under that rule, which is 

 itself a Rule ; and, 3d, a Case under this second rule, which conflicts 

 with the first rule. Then it would be easy to prove that these three 

 propositions must be of the form, 



1. No X is r: 



2. All Z is X. 



3. Some Y is Z. 



These three propositions cannot all be true at once ; if, then, any two 

 are asserted, the third must be denied, which is what is done in the 

 three Theophrastean moods. 



These moods are resolved into one another by the contraposition of 

 propositions, and therefore should be considered as belonging to differ- 

 ent figures. 



They can be ostensively reduced to the first Aristotelian figure in 

 two ways ; thus, 



