Yi.] THE INDIRECT METHOD OF INFERENCE. 85 



" Whales are not true fish ; for they do not respire water, 

 wliereas true fish do resj^ire water." 

 Let us take 



A = whale 

 B = true fish 

 C = respiring water 

 The premises are of the forms 



A = Ac (i) 



B = BC (2) 



Now, by the process of contraposition we obtain from 

 the second premise 



c ^hc 

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

 taining 



A = Ahc 

 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 ex- 

 hibited in an exactly similar manner. 



The mood Baroko gave much trouble to the old logicians, 

 who could not reduce it to the first figure in the same 

 manner as the other moods, and were obliged to invent, 

 specially for it and for Bokardo, a method of Indirect 

 Reduction closely analogous to the indirect proof of Euclid. 

 Now these moods require no exceptional treatment in this 

 system. Let us take as an instance of Baroko, the argu 

 meut 



All heated solids give continuous spectra (i) 



Some nebulfe do not give continuous spectra (2) 

 Tlierefore, some nebulae are not heated solids (3) 

 Treating the little word some, as an indeterminate adjec- 

 tive of selection, to which we assign a symbol like any 

 other adjective, let 



A = some 

 B = nebulae 



C = giving continuous spectra 

 1) = heated solids 

 The premises then become 



D = DC (I) 



AB = ABc (2) 



Now from (i) we obtain by the indirect method the cou- 

 trapositive proposition 



