Immanuel Kant's Critique of Pure Reason — trans. F. Max Müller

For let us assume that it has a beginning. Then, as beginning is an existence which is preceded by a time in which the thing is not, it would follow that antecedently there was a time in which the world was not, that is, an empty time. In an empty time, however, it is impossible that anything should take its beginning, because of such a time no part possesses any condition as to existence rather than non-existence, which condition could distinguish that part from any other (whether produced by itself or through another cause). Hence, though many a series of things may take its beginning in the world, the world itself can have no beginning, and in reference to time past is infinite.

With regard to the second, let us assume again the opposite, namely, that the world is finite and limited in space. In that case the world would exist in an empty space without limits. We should therefore have not only a relation of things in space^ but also of things to space. As however the world is an absolute whole, outside of [p. 429] which no object of intuition, and therefore no correlate of the world can be found, the relation of the world to empty

346 Transcendental Dialectic

Thesis a completed synthesis, or by the repeated addition of unity to itself.^ In order therefore to conceive the world, which fills all space, as a whole, the successive synthesis of the parts of an infinite world would have to be looked upon as completed ; that is, an infinite time would have to be looked upon as elapsed, during the enumeration of all co-existing things. This is impossible. Hence an infinite aggregate of real things cannot be regarded as a given whole, nor, therefore, as given at the same time. Hence it follows that the world is not infinite, as regards extension in space, but enclosed in limits. This was the second that had to be proved.

[p. 430] OBSERVATIONS ON THE

On the Thesis

In exhibiting these conflicting arguments I have not tried to avail myself of mere sophisms for the sake of what is called special pleading, which takes advantage of the want of caution of the opponent, and gladly allows his appeal to a misunderstood law, in order to establish his own illegitimate claims on its refutation. Every one of our proofs has been deduced from the nature of the case, and no advantage has been taken of the wrong conclusions of dogmatists on either side.

1 The concept of totality is in this case nothing but the representation of the completed synthesis of its parts, because, as we cannot deduce the concept from the intuition of the whole (this being in this case impossible) , we can conceive it only through the synthesis of its parts, up to the completion of the infinite, at least in the idea.

Transcendental Dialectic 347

Antithesis space would be a relation to 7io object. Such a relation, and with it the limitation of the world by empty space, is nothing, and therefore the world is not limited with regard to space, that is, it is infinite in extension. ^

FIRST ANTINOMY [p- 43i]

II

On the Antithesis

The proof of the infinity of the given series of world, and of the totality of the world, rests on this, that in the

1 Space is merely the form of external intuition (formal intuition) and not a real object that can be perceived by external intuition. Space, as prior' to all things which determine it (fill or limit it), or rather which give an empirical intuition determined by its form, is, under the name of absolute space, nothing but a mere possibility of external phenomena, so far as they either exist already, or can be added to given phenomena. Empirical intuition, therefore, is not a compound of phenomena and of space (perception and empty intuition). The one is not a correlate of the other in a synthesis, but the two are only connected as matter and form in one and the same empirical intuition. If we try to separate one from the other, and to place space outside all phenomena, we arrive at a number of empty determinations of external intuition, which, however, can never be possible perceptions; for instance, motion or rest of the world in an infinite empty space, i.e. determination of the mutual relation of the two, which can never be perceived, and is therefore nothing but the predicate of a mere idea.

348 Transcendental Dialectic

Thesis