330 TRANSACTIONS OF THE CANADIAN INSTITUTE. [Vou. VIII. 
this is based on the false idea that Geometry is only a special case of a 
more general theory of pure quantity. Not ‘‘equality”’ but ‘‘dependence”’ 
is the most general relation, and consequently the most fundamental 
formula is not A= B, but A isdependent upon B or A=f (B), where ‘‘is” 
has no other significance than that of a grammatical copula. The mathe- 
matical proposition that if two things are equal to a third, they must be 
equal to one another is of course only valid under the assumption that 
the three things or quantities do not change but remain the same. But 
if I say e. g., a certain region (a) of the spectrum is in quality equal to a 
neighboring region (b), and this region (b) cannot be distinguished from 
another region (c), though if I compare (a) and (c) I immediately see a 
difference, we have here in no way an application of the above mathe- 
matical axiom. For a colour quality is what it is only in relation to others, 
and if I compare a with 0 it is not really the same a as that which I com- 
pare withc. Here is where the mistake is made. We have, strictly speak- 
ing, no right to say a quality is the same because it is attached in some 
way to what we call the same ‘‘thing’”’ That ‘‘same thing” is like the 
“‘thing”’ itself, a rather complicated abstraction to which nothing in reality 
corresponds. We have through thousands of years of training become 
so accustomed to speak in terms of ‘‘things”’ instead of in terms of ele- 
mentary given facts (states of consciousness), that we are prone to attri- 
bute to these ‘‘things’”’ a higher type of reality than to those directly 
given facts. A striking example of this is* given in the discussion of 
contrast where frantic efforts are made to show why the ‘‘same”’ piece of 
grey paper looks once reddish and another time greenish according to the 
background on which it is seen, while the real problem should read: How 
do we, starting with that difference in the given facts, 2. e., in the sen- 
sations of colour, intensity, etc., arrive at the idea that we have to do 
with the ‘‘same” piece of ‘‘grey”’ paper. 
oe 
Furthermore, if Poincaré believes he can reduce the continuum to 
something which refers to quality and inequality, he is very much mis- 
taken, for in order to make that statement or to have that idea of equality 
he must have continuity first. .How can he compare a with 6 if he has 
not space or time continuity or what includes both, the continuity of 
consciousness. He has first @ in his consciousness, and then 0 enters 
while a must continue in some way or else he could never compare them. 
No matter how far they are separated in time and space he must bring 
them (7. e., the one and the memory image of the other) together at the 
same time or at the same space and this he can only do by making use 
of the continuity of space and time or the continuity of consciousness as 
he finds it at the very outset. 
