214 Mr- J- J- Murphy on 



that every term has its negative). In the second column^ 

 the partial is substituted for the total in the second premise,, 

 and the premises become " All not-B is A ; — Some not-B 

 is C " : — with the same conclusion as before, that " some 

 things are both A and C." In the third column, the 

 partial is substituted for the total in the first premise, and 

 the syllogism becomes " Some B is not A : — all not B 

 is C ; " which premises yield no conclusion. Every syllogism 

 in the following statement may be reduced to one of these 

 six typical forms. 



Same sign — same phase. 

 Ev.E = E Ey.n= nxE = n 



JVxJV='n7 Nxe^Ti' exN= 



Same sign — opposite phases. 



Ex E^ = 717 E xn"' — m^ nx E^ = 



E7 xE = n Ey xn = n 71^ y. E = 



NxN^ = E JVxe^= exN^ = n 



N^x N'=E^ N'^xe^ e" x N= v7 



Opposite signs — same phase. 



ExJSr=N Exe= nxN^e 



E''xN'' = N^ E^xe^= n^xN^ = e' 



NxE = e JVxn=e^ 

 N^xE^^e N^x'n:' = e 



exE = 



e^ xE^ = 



Opposite signs — opposite phases. 



ExN^ = e^ Exe' = e nxN^^ 

 E^xN=e E^xe-=e n^ x N= 



NxE^ = J\ NxrC' = 



e + E^ = e 

 <rxE = e^ 



