:v.] DEDUCTIVE REASONING. 



PQ-PQB, (I) 



B = BU; (2) 



hence, by substitutioii, as before, 



PQ = rQRC. (3) 



Except that the formula look a little more complicated 

 there is no difference whatever. 



The mood Perio is of exactly the same character as 

 Darii or Barbara, except that it involves the use of a 

 negative term. Take the example, 



Bodies which are equally elastic in all directions do 



not doubly refract light; 

 Some crystals are bodies equally elastic in all direc- 

 tions; therefore, some crystals do not doubly 

 refract light. 

 Assigning the letters as follows :— 

 A = some crystals, 



P> = bodies equally elastic in all directions, 

 C = doubly I'efracting light, 

 c = not doubly reiracting light. 

 Our argument is of the same form as before, and njay 

 be concisely stated in one line, 



A = AH = AL(.. 

 If it is preferred to put PQ for the indefinite sojne crystals, 

 we have 



PQ ■-= PQP = PQBc. 

 The only difference is that the negative term c takes the 

 place of C iu the mood Darii. 



Ellipsis of Terms in Partial Identities. 



The reader will pi-obably have noticed that the conclu- 

 sion which we obtain from premises is often moi'e full thiiii 

 that drawn by the old Ari-stotelian processes. Thus from 

 "Sodium is a metal," and " Metals conduct electricity," we 

 inferred (p. 55) that " Sodium = sodium, metal, conduct- 

 ing elrclricity," whereas the old logic simply concludes 

 that "Sodium conducts electricity." Symbolically, from 

 A = AJ'., and ]'> = J5C, w^e get A = AI5C, whereas "the old 

 logic gets at the most A = AC. It is therefore well to 

 show that without emjjloyiug any other principles of 

 inference tlian those already described, we may infer 

 A = AC from A = ABC, though we cannot infer the latter 



