CLASS fFTCA TIOX. 393 



the fact that mathematical or other certain laws may en 

 tirely forbid the existence of some combinations. The 

 circle may be defined as a plane curve of equal curvature, 

 and it is a property of it that it contains the greatest area 

 within the least possible perimeter. May we then con 

 template mentally a circle not a figure of greatest possible 

 area I Or, to take a still simpler example, a parallelogram 

 possesses the property of having the opposite angles equal. 

 May we then mentally divide parallelograms into two 

 classes according as they do or do not have their opposite 

 angles equal 1 It might seem absurd to do so, because we 

 know that one of the two species of parallelogram would 

 be non-existent. But, then, what is the meaning of the 

 thirty-fourth proposition of Euclid s first book, unless the 

 student had previously contemplated the existence of 

 both species as possible. We cannot even deny or dis 

 prove the existence of a certain combination without 

 thereby in a certain way recognising that combination as 

 an object of thought. 



The general conclusion, then, at which I arrive, is in 

 opposition to that of Mr. Herbert Spencer. I think that 

 whenever we abstract a quality or circumstance we do 

 generalize or widen the notion from which we abstract. 

 Whatever the terms A, B, and C may be, I hold that in 

 strict logic AB is mentally a wider term than ABC, 

 because AB includes the two species ABC and ABc. The 

 term A is wider still, for it includes the four species ABC, 

 ABc, A6C, Abe. The Logical Abecedarium, in short, is the 

 only limit of the classes of objects which we must contem 

 plate in a purely logical point of view. Whatever notions 

 be brought before us, we must mentally combine them in 

 all the ways sanctioned by the laws of thought and ex 

 hibited in the Abecedarium, and it is a matter for after 

 consideration to determine how many of these combina 

 tions exist in outward nature, or how many are actually 



