| 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. |
| [*Footnote; 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.* |
| [*Footnote; 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. |