274 PROCEEDINGS OF THE AMERICAN ACADEMY 



Now, these are properly not premises, for they express no facts ; 

 they are merely forms of words without meaning. Hence, as no com- 

 plete argument has less than two premises, the conversions and contra- 

 positions are not inferences. The only other substitutions which have 

 been made have been of not-P and some-*S for their definitions. 

 These also can be put into syllogistic form ; but a mere modification 

 of language is not an inference. Hence no inferences have been em- 

 ployed in reducing the arguments of the second and third figures to 

 such forms that they are readily perceived to come under the general 

 form of syllogism. 



There is, however, an intention in which these substitutions are in- 

 ferential. For, although the passage from holding for true a fact 

 expressed in the form " No A is B," to holding its converse, is not an 

 inference, because, these facts being identical, the relation between 

 them is not a fact ; yet the passage from one of these forms taken 

 merely as having some meaning, but not this or that meaning, to 

 another, since these forms are not identical and their logical relation 

 is a fact, is an inference. This distinction may be expressed by 

 saying that they are not inferences, but substitutions having the form of 

 inferences. 



Thus the reduction of the second and third figures, considered as 

 mere forms, is inferential ; but when we consider only what is meant 

 by any particular argument in an indirect figure, the reduction is a 

 mere change of wording. 



The substitutions made use of in the ostensive reductions ai*e shown 

 in the following table. Where 



e, denotes simple conversion of ^; 



i, denotes simple conversion of /; 



a2, contraposition of A into £ ; 



tts, contraposition A into /; 



0-2, the substitution of " Some S is not M" for " Any J/is not some-*S"' ; 



O3, the substitution of "Some iJ/is not F" for "Some not-P is M"; 



e", introduction of not-P by definition ; 



i", introduction of some-S by definition. 



