13 
The old dictum de omni et nullo may be thus expressed: — 
That which is true of any individual of a class, as denoted 
by any particular quality, is true of the entire class.” This 
is necessarily true — indeed it is a merely identical propo- 
sition — but it is not true in every sense. That which is 
true of one is true of any one and of every one, but it is not 
true of all. Any man, or every man, has two hands and no 
more, but all men, added together, have about two thousand 
millions of hands. A proposition relating to a class may or 
may not give information relating to the members of the 
class. To say that the British army is brave ” asserts that 
it consists of brave soldiers, but to say that “ the British 
army is comparatively small ” says nothing about the men 
who compose it. Boole has not seen this; he reads his 
symbol of totality, 1, as if it meant all, to the exclusion of 
every, or any. Now, as we have seen 
x= \x. 
If X or lx is taken to mean all x, then the expression 
cc -f- sc is obviously uninterpretable ; an entire class cannot 
be added to itself. But if x is taken to mean any or every 
specimen of the class x, then the equation 
x + x = x 
asserts that if we add any substance to itself we have still 
the same substance. Add water to water, for instance, and 
we still have water. Perhaps the very simplicity of this 
interpretation has prevented its being seen. 
But totality in the sense of cdl is equally legitimate in 
logic with totality in the sense of every ; and it may be 
desirable to have distinct symbolic expressions for them. 
I would propose to use x in the usual sense of every x, and 
lx in the special sense of the entire class of x, I have not 
found occasion for this, but in my paper communicated to 
the Manchester Philosophical Society on “ The Transforma- 
tions of a Logical Proposition containing a single Belative 
