It is to be confessed,
however, that our accounts on this point are somewhat conflicting. One
authority actually says that he formulated motion as eternal also. So far as
he attempted to grasp the idea of difference in relation to that of unity,
he seems to have regarded the principle of change or difference as inhering
in the infinite itself. Aristotle in this
connection contrasts his doctrine with that of
Anaxagoras, who formulated two principles of existence—Matter and
Mind. Anaximander, he points out, found all he wanted in the one.
As a mathematician
Anaximander must have been familiar in various aspects with the functions of
the Infinite or Indefinable in the organisation of thought. To the student
of Euclid, for example, the impossibility of adequately defining any of the
fundamental elements of the science of geometry—the point, the line, the
surface—is a familiar fact. In so far as a science of geometry is possible
at all, the exactness, which is its essential characteristic, is only
attainable by starting from data which are in themselves impossible, as of a
point which has no magnitude, of a line which has no breadth, of a surface
which has no thickness. So in the science of abstract number the fundamental
assumptions, as that 1=1, x=x, etc., are contradicted by every fact
of experience, for in the world as we know it, absolute equality is simply
impossible to discover; and yet these fundamental conceptions are in their
development most powerful instruments for the extension of man’s command
over his own experiences.
A History of Greek Philosophy /
THE SCHOOL OF MILETUS /
ANAXIMANDER
