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.
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.
*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.But as this synthesis must constitute a series that cannot be completed, it is impossible for us to cogitate prior to it, and consequently not by means of it, a totality.For the conception of totality itself is in the present case the representation of a completed synthesis of the parts; and this completion, and consequently its conception, is impossible.
ON THE ANTITHESIS.