CHAP. XV.] ARISTOTELIAN LOGIC. 241 



induction may probably receive some attention in another part of 

 this work. 



10. It has been remarked in this chapter that the ordinary 

 treatment of hypothetical, is much more defective than that of 

 categorical, propositions. What is commonly termed the hypo- 

 thetical syllogism appears, indeed, to be no syllogism at all. 

 Let the argument 



If^L is B, CisD, 

 But A is B 9 

 Therefore C is D 9 

 be put in the form 



If the proposition X is true, Y is true, 

 But X is true, 

 Therefore Y is true ; 



f 



wherein by X is meant the proposition A is B, and by Y, the 

 proposition C is D. It is then seen that the premises contain 

 only two terms or elements, while a syllogism essentially involves 

 three. The following would be a genuine hypothetical syllogism : 



If X is true, Y is true ; 

 If Y is true, Z is true ; 

 ,'. If X is true, Z is true. 



After the discussion of secondary propositions in a former 

 part of this work, it is evident that the forms of hypothetical 

 syllogism must present, in every respect, an exact counterpart to 

 those of categorical syllogism. Particular Propositions, such as, 

 " Sometimes if X is true, Y is true," may be introduced, and the 

 conditions and rules of inference deduced in this chapter for ca- 

 tegorical syllogisms may, without abatement, be interpreted to 

 meet the corresponding cases in hypotheticals. 



1 1 . To what final conclusions are we then led respecting the 

 nature and extent of the scholastic logic? I think to the following : 

 that it is not a science, but a collection of scientific truths, too 

 incomplete to form a system of themselves, and not sufficiently 

 fundamental to serve as the foundation upon which a perfect 

 system may rest. It does not, however, follow, that because the 

 logic of the schools has been invested with attributes to which it 



