RATIOCINATION,, OR SYLLOGISM. 241 



If we generalize this process, and look out for the 

 principle or law involved in every such inference, and 

 presupposed in every syllogism the propositions of 

 which are anything more than merely verbal; we 

 find, not the unmeaning dictum de omni et nullo, but 

 a fundamental principle, or rather two principles, 

 strikingly resembling the axioms of mathematics. 

 The first, which is the principle of affirmative syllo- 

 gisms, is, that things which coexist with the same 

 thing, coexist with one another. The second is the 

 principle of negative syllogisms, and is to this effect : 

 that a thing which coexists with another thing, with 

 which other a third thing does not coexist, is not coex- 

 istent with that third thing. These axioms mani- 

 festly relate to facts, and not to conventions : and one 

 or other of them is the ground of the legitimacy of 

 every argument in which facts and not conventions 

 are the matter treated of. 



4. It only remains to translate this exposition of 

 the syllogism from the one into the other of the two 

 languages in which we formerly remarked* that all 

 propositions, and of course therefore all combinations 

 of propositions, might be expressed. We observed 

 that a proposition might be considered in two different 

 lights ; as a portion of our knowledge of nature, or as 

 a memorandum for our guidance. Under the former, 

 or speculative aspect, an affirmative general proposi- 

 tion is an assertion of a speculative truth, viz., that 

 whatever has a certain attribute has a certain other 

 attribute. Under the other aspect, it is to be re- 

 garded not as a part of our knowledge, but as an aid 

 for our practical exigencies, by enabling us when we 



* Supra, p. 157- 

 VOL, I. 



