262 PROCEEDINGS OF THE AMERICAN ACADEMY 



The leading principle can contain nothing irrelevant or superfluous. 



No fact, not superfluous, can be omitted from the premises without 

 being thereby added to the leading principle, and nothing can be 

 eliminated from the leading principle except by being expressed in 

 the premises. Matter may thus be transferred from the premises to 

 the leading principle, and vice versa. 



There is no argument without premises, nor is there any without a 

 leading principle. 



It can be shown that there are arguments no part of whose leading 

 principle can be transferred to the premises, and that every argument 

 can be reduced to such an argument by addition to its premises. For, 

 let the premises of any argument be denoted by P, the conclusion by 

 C, and the leading principle by L. Then, if the whole of the leading 

 principle be expressed as a premise, the argument will become 



ZandP 



.-. a 



But this new argument must also have its leading principle, which 

 may be denoted by L'. Now, as L and P (supposing them to be 

 true) contain all that is requisite to determine the probable or necessary 

 truth of C, they contain L'. Thus L' must be contained in the lead- 

 ing principle, whether expressed in the premise or not. Hence every 

 argument has, as portion of its leading principle, a certain principle 

 which cannot be eliminated from its leading principle. Such a princi- 

 ple may be termed a logical principle. 



An argument whose leading principle contains nothing which can 

 be eliminated is termed a complete., in opposition to an incomplete, 

 rhetorical, or enthymematie argument.* 



* Neither of these terms is quite satisfactory. Enthymeme is usually defined as 

 a syllogism with a premise suppressed. This seems to determine the same sphere 

 as the definition I have given ; but the doctrine of a suppressed premise is objec- 

 tionable. The sense of a premise which is said to be suppressed is either conveyed 

 in some way, or it is not. If it is, the premise is not suppressed in any sense which 

 concerns the logician ; if it is not, it ceases to be a premise altogether. What I 

 mean by the distinction is this. He who is convinced that Sortes is mortal because 

 he is a man (the latter belief not only being the cause of tlie former, but also being 

 felt to be so) necessarily says to himself that all sncJi arguments are valid. This 

 genus of argument is either clearly or obscurely recognized. In the former case, 

 the judgment amounts to another premise, because the proposition (for example), 

 " All reasoning from humanity to mortality is certain," only says in other words 



