n eternity of time must in
calculating all coexisting things, be regarded as having existed, but
this is impossible. Therefore an unending aggregate of actual things
cannot be regarded as a given whole and therefore also not as
coexistent. A world is therefore extension in space which is not
unlimited and which has therefore bounds. And this was the second
thing to be proved."

These statements are copied from a well-known book which made its
appearance in 1781 and is entitled "The Critique of Pure Reason," by
Immanuel Kant. They can be read there in Part I, Division 2, second
section, second part. "First Antinomy of Pure Reason." To Herr
Duehring alone remains the name and fame of having pasted the law of
fixed numbers on one of the published thoughts of Kant and of having
made the discovery that there was once a time when time did not exist
but only a universe. For the rest, therefore, when we come across
anything sensible in Herr Duehring's exposition "We" means Immanuel
Kant, and the "present" is only ninety-five years old. Quite simple
indeed, and unknown until now! But Kant does not establish the above
statement by his proof. On the other hand, he shows the reverse,
namely, that the universe has no beginning in time and no end in
space, and he fixes his antinomy in this, the unsolvable contradiction
that the one is just as capable of proof as the other. People of small
calibre might be inclined to think that here Kant had found an
insuperable difficulty, not so our bold author of fundamental results
"especially his own." He copies all that he can use of Kant's antinomy
and throws the rest away.

The matter solves itself very simply. Eternity in time and endlessness
in space signify from the very words that there is no end in either
direction, forwards or backwards, over or under, right or left. This
infinity is quite different from an endless progression, since the
latter always has some beginning, a first step. The inapplicability of
this progression idea to our object is evident directly we apply it to
space. Infinite progression translated in terms of space is a line
produced continuously in a given direction. Is infinity in space
expressed in this way, even remotely? On the contrary it requires six
of these lines drawn from this point in three opposite directions to
express the dimensions of space and we should have accordingly six of
these dimensions. Kant saw this so plainly that he employed his
progressi