THE INDIRECT METHOD OF INFERENCE. 99 



logic gives the inference without the use of any geo- 

 metrical reasoning. I conceive however that logic gives 

 the inference only by an indirect process. De Morgan 

 claims 'to see identity in every A is B and every not-B 

 is not-A, by a process of thought prior to syllogism.' 

 But whether prior to syllogism or not, I claim that it 

 is not prior to the laws of thought and the process of 

 substitutive inference by which it may be undoubtedly 

 demonstrated. 



Employment of the Contrapositive Proposition. 



We can frequently employ the contrapositive form of 

 a proposition by the method of substitution ; and certain 

 moods of the ancient syllogism, which we have hitherto 

 passed over, may thus be satisfactorily comprehended 

 in our system. Take for instance the following syllogism 

 in the mood Camestres : 



' Whales are not true fish : for they do not respire 

 water, whereas true fish do respire water.' 



Let us take 



A = whales, 

 B = true fish, 

 C = respiring water. 

 The premises are of the form 



A = Ac, (i) 



B = BC. (2) 



Now, by the process of contraposition we obtain from (2) 



c be, 



and we can substitute this expression for c in (i), ob- 

 taining 



A = Abe, 



or ' Whales are not true fish, not respiring water/ 



The mood Cesare does not really differ from Camestres 

 except in the order of the premises, and it could be 

 exhibited in an exactly similar manner. 



H 2 





