| 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.] |
| OBSERVATIONS ON THE FIRST ANTINOMY. |
| ON THE THESIS. |
| In bringing forward these conflicting arguments, I have not been on the search for sophisms, for the purpose of availing myself of special pleading, which takes advantage of the carelessness of the opposite party, appeals to a misunderstood statute, and erects its unrighteous claims upon an unfair interpretation. |
| Both proofs originate fairly from the nature of the case, and the advantage presented by the mistakes of the dogmatists of both parties has been completely set aside. |
| The thesis might also have been unfairly demonstrated, by the introduction of an erroneous conception of the infinity of a given quantity. |
| A quantity is infinite, if a greater than itself cannot possibly exist. |
| The quantity is measured by the number of given units- which are taken as a standard--contained in it. |
| Now no number can be the greatest, because one or more units can always be added. |
| It follows that an infinite given quantity, consequently an infinite world (both as regards time and extension) is impossible. |
| It is, therefore, limited in both respects. |
| In this manner I might have conducted my proof; but the conception given in it does not agree with the true conception of an infinite whole. |
| In this there is no representation of its quantity, it is not said how large it is; consequently its conception is not the conception of a maximum. |
| We cogitate in it merely its relation to an arbitrarily assumed unit, in relation to which it is greater than any number. |
| Now, just as the unit which is taken is greater or smaller, the infinite will be greater or smaller; but the infinity, which consists merely in the relation to this given unit, must remain always the same, although the absolute quantity of the whole is not thereby cognized. |
| The true (transcendental) conception of infinity is; that the successive synthesis of unity in the measurement of a given quantum can never be completed.* Hence it follows, without possibility of mistake, that an eternity of actual successive states up to a given (the present) moment cannot have elapsed, and that the world must therefore have a beginning. |
| [*Footnote; The quantum in this sense contains a congeries of given units, which is greater than any number--and this is the mathematical conception of the infinite.] |
| In regard to the second part of the thesis, the difficulty as to an infinite and yet elapsed series disappears; for the manifold of a world infinite in extension is contemporaneously given. |
| But, in order to cogitate the total of this manifold, as we cannot have the aid of limits constituting by themselves this total in intuition, we are obliged to give some account of our conception, which in this case cannot proceed from the whole to the determined quantity of the parts, but must demonstrate the possibility of a whole by means of a successive synthesis of the parts. |