CHAP. XV.] ARISTOTELIAN LOGIC. 239 



the study of its laws is co-extensive with the study of deductive 

 logic. For if it be so, some indication of the fact must be given 

 in the systems of equations upon the analysis of which we have 

 been engaged. It cannot be conceived that syllogism should be 

 the one essential process of reasoning, and yet the manifestation 

 of that process present nothing indicative of this high quali ty of 

 pre-eminence. No sign, however, appears that the discussion of 

 all systems of equations expressing propositions is involved in 

 that of the particular system examined in this chapter. And yet 

 writers on Logic have been all but unanimous in their assertion, 

 not merely of the supremacy, but of the universal sufficiency of 

 syllogistic inference in deductive reasoning. The language of 

 Archbishop Whately, always clear and definite, and on the sub- 

 ject of Logic entitled to peculiar attention, is very express on 

 this point. " For Logic," Jae says, " which is, as it were, the 

 Grammar of Reasoning, does not bring forward the regular Syl- 

 logism as a distinct mode of argumentation, designed to be substi- 

 tuted for any other mode ; but as the form to which all correct 

 reasoning may be ultimately reduced."* And Mr. Mill, in a 

 chapter of his System of Logic, entitled, " Of Ratiocination or 

 Syllogism," having enumerated the ordinary forms of syllogism, 

 observes, " All valid ratiocination, all reasoning by which from 

 general propositions previously admitted, other propositions, 

 equally or less general, are inferred, may be exhibited in some of 

 the above forms." And again : " We are therefore at liberty, 

 in conformity with the general opinion of logicians, to consider 

 the two elementary forms of the first figure as the universal types 

 of all correct ratiocination." In accordance with these views it 

 has been contended that the science of Logic enjoys an immunity 

 from those conditions of imperfection and of progress to which 

 all other sciences are subject ;f and its origin from the travail of 

 one mighty mind of old has, by a somewhat daring metaphor, 

 been compared to the mythological birth of Pallas. 



As Syllogism is a species of elimination, the question before 

 us manifestly resolves itself into the two following ones : 1st. 

 Whether all elimination is reducible to Syllogism ; 2ndly. Whe- 



* Elements of Logic, p. 13, ninth edition, 

 f Introduction to Kant's "Logik," 



