1907-8.] SPACE AND ITs DIMENSIONS. 329 
4. SPACE IS CONTINUOUS. 
Space and time are the forms in which consciousness arranges the 
facts given. To such an extent are they intimately related to conscious- 
ness that they partake so immediately of that most general property of 
consciousness, ‘‘continuity,’’ that it becomes exceedingly difficult to dis- 
tinguish between the continuity of consciousness and the continuity 
of space and time. Perhaps there is nothing to be distinguished. It 
might be worth while here to cast a brief glance at the problem of con- 
tinuity in its main issue. Have we a right to ask; What is continuity? 
I think not. Just as we have no right to ask; What is consciousness ? 
Consciousness is the conditio se qua non for all ‘‘asking,”’ for all defini- 
tion, description and explanation, indeed the condition sine qua non for 
all facts; consequently ‘‘consciousness”’ itself can never be defined or ex- 
plained. Almost the same could be said for “‘continuity; ”’ in fact it does 
not matter. whether we say consciousness or the continuity of conscious- 
ness. ‘Thus we cannot ask what is continuity. Wecan only ask ‘‘Where 
do we find continuity ?”’ 
ce 
Nevertheless there have been many attempts to explain continuity 
in general and the continuity of life philogenetically, (heredity) and 
ontogenetically (memory, consciousness) in particular. Poincaré (1) says 
that in all cases where we observe that two things are equal to a third 
yet not equal among themselves, we speak of a physical continuity. 
yet a is different from c. 
Wherever we have this contradiction against the law of identity, we 
have a continuation. This is really the question of the least observable 
difference or the threshold ; but in my opinion it has nothing to do with 
the deeper problem of continuity. The above argument is based on the 
assumption that there exists such a thing as an equation, an absolute 
identity, but there is no such thing in the given fact. Equations are either 
mathematical fictions or they refer to partial coincidence considered by 
abstraction. Even that standard equation usually indulged in when 
discussing the law of identity. ‘‘A=A” can be just as well read: ‘‘This 
A is not that A, it is another one.”’ ‘The tendency of the mathematician 
of the present day to press everything into the form of an equation is due 
to the present preponderance of the analytical side of mathematics, and 
(1) Der Wert Det Wissenshaft, translated by E. H. Weber, p. 51. 
