33 



Ordinary Meeting, December 11th, 1883. 

 Balfour Stewart, LL.D., F.II.S., in the Chair. 



"On the Quantification of the Predicate, and on the 

 Interpretation of Boole's Logical Symbols," by Joseph John 

 Murphy. Communicated by the Rev. Robert Harley, 

 M.A., F.R.S. 



If a student, after hearing his first lecture on crystal- 

 lography and the geometry of polyhedra, were to say to his 

 teacher, "You have not made it clear to me whether the 

 cube is derived from the octohedron or the octohedron from 

 the cube"; this would not be a stupid question, but it 

 would show a puzzled state of the understa,nding ; and of 

 course the reply would be, " Whichever you please ; either 

 form may be equally well regarded as the fundamental 

 and the other derived from it." 



The question of the "quantification of the predicate," 

 which was raised by Sir William Hamilton of Edinburgh, 

 seems to admit of a somewhat similar reply. 



That question may thus be stated :— Whether is the 

 fundamental form of proposition the equation, " x and y are 

 identical :" or the predication, " x is y" without implying 

 that 2/ is a; ? The former is the reply given by Sir William 

 Hamilton; the latter, by Aristotle and logicians generally. 



When we use notation instead of language, we write the 



equation 



x = y 

 and the predication 



x<y 



Procebdtnss— Lit. & Phil. Soc— Vol. XXIII.— No. 4.— Session 1883-4; 



