132 THE PRINCIPLES OF SCIENCE. 



of the Abecedarium are exactly the same in whatever 

 order the premises be treated on the logical slate or 

 machine. 



Some difference may doubtless exist as regards con- 

 venience to human memory. The mind may take in 

 the results of an argument more easily in one mode of 

 statement than another, although there is no real differ- 

 ence in the logical results. But in this point of view 

 I think that Aristotle and the old logicians were clearly 

 wrong. It is more easy to conclude that * all A's are C's ' 

 from ' all A's are B's and all B's are C's,' than from 

 the same propositions in inverted order, 'all B's are C's 

 and all A's are B's,' 



The Equivalency of Propositions. 



One great advantage which arises from the study of 

 this Indirect Method of Inference consists in the clear 

 notion which we thus gain of the Equivalency of Propo- 

 sitions. The older logicians showed how from certain 

 simple premises we might draw an inference, but they 

 failed to point out whether that inference contained the 

 whole, or only a part, of the information embodied in the 

 premises. Now any one proposition or group of propo- 

 sitions may be classed with respect to another proposition 

 or group of propositions, as 



1. Equivalent, 



2. Inferrible, 



3. Consistent, 



4. Contradictory. 



Taking the proposition 'All men are mortals' as the 

 original, ' All immortals are not men ' is its equivalent ; 

 ' Some mortals are men ' is inferrible, or capable of infe- 

 rence, but is not equivalent ; ' All not men are not 

 mortals ' cannot be inferred, but is consistent, that is, may 



