FIRST CONFLICT OF THE TRANSCENDENTAL IDEAS.
Thesis.
The world has a beginning in time, and is also limited in
regard to space.
PROOF.
Granted that the world has no beginning in time; up to every given
moment of time, an eternity must have elapsed, and therewith passed
away an infinite series of successive conditions or states of things
in the world. Now the infinity of a series consists in the fact that
it never can be completed by means of a successive
synthesis. It
follows that an infinite series already elapsed is impossible and
that, consequently, a beginning of the world is a necessary
condition of its existence. And this was the first thing to be proved.
As regards the second, let us take the opposite for granted. In this
case, the world must be an infinite given total of coexistent
things. Now we cannot cogitate the dimensions of a quantity, which
is not given within certain limits of an intuition,* in any other
way than by means of the synthesis* of its parts, and the total of such
a quantity only by means of a completed synthesis, or the repeated
addition of unity to itself. Accordingly, to cogitate the world, which
fills
all spaces, as a whole, the successive synthesis of the parts of
an infinite world must be looked upon as completed, that is to say, an
infinite time must be regarded as having elapsed in the enumeration of
all co—existing things; which is impossible. For this reason an
infinite aggregate of actual things cannot be considered as a given
whole, consequently, not as a contemporaneously given whole. The world
is consequently, as regards extension in space,
not infinite, but
enclosed in limits. And this was the second thing to be proved.
[*]
What is meant by successive synthesis must be tolerably plain. If I am
required to form some notion of a piece of land, I may assume an arbitrary standard, — a
mile, or an acre, — and by the successive addition of mile to mile or acre to acre till the
proper number is reached, construct for myself a notion of the size of the land. — Tr.
[*]
We may consider an undetermined quantity as a whole, when it is
enclosed within limits, although we cannot construct or ascertain
its totality by measurement, that is, by the successive synthesis of
its parts. For its limits of themselves determine its completeness
as a whole.
Antithesis.
The world has no beginning, and no limits in space, but is, in
relation both to time and space, infinite.
PROOF.
For let it be granted that it has a beginning. A beginning is an
existence which is preceded by a time in which the thing does not
exist. On the above supposition, it follows that there must have
been a time in which the world did not exist, that is, a void time.
But in a void time the origination of a thing is impossible;
because
no part of any such time contains a distinctive condition of being, in
preference to that of non—being (whether the supposed thing
originate of itself, or by means of some other cause). Consequently,
many series of things may have a beginning in the world, but the world
itself cannot have a beginning, and is, therefore, in relation to past
time, infinite.
As regards the second statement, let us first take the opposite
for granted— that the world is finite and limited in space; it follows
that it must exist in a void space, which is not limited. We should
therefore meet not only with a relation of things in space, but also a
relation of things to space. Now, as the world is an absolute whole,
out of and beyond which no object of intuition, and consequently no
correlate to which can be discovered, this relation of the world to
a void space is merely a relation to no object. But such a relation,
and consequently the limitation of the world by void space, is
nothing. Consequently, the world, as regards space, is not limited,
that is, it is infinite in regard to extension.*
[*]
Space is merely the form of external intuition (formal
intuition), and not a real object which can be externally perceived.
Space, prior to all things which determine it (fill or limit it),
or, rather, which present an empirical intuition conformable to it,
is, under the title of absolute space, nothing but the mere
possibility of external phenomena, in so far as they either exist in
themselves, or can annex themselves to given intuitions. Empirical
intuition is therefore not a composition of phenomena and space (of
perception and empty intuition). The one is not the correlate of the
other in a synthesis, but they are vitally connected in the same
empirical intuition, as matter and form. If we wish to set one of
these two apart from the other— space from phenomena— there arise
all sorts of empty determinations of external intuition, which are
very far from being possible perceptions. For example, motion or
rest of the world in an infinite empty space, or a determination of
the mutual relation of both, cannot possibly be perceived, and is
therefore merely the predicate of a notional entity.
