To the question, therefore, respecting the cosmical quantity, the first and negative answer is: "The world has no beginning in time, and no absolute limit in space."For, in the contrary case, it would be limited by a void time on the one hand, and by a void space on the other.Now, since the world, as a phenomenon, cannot be thus limited in itself for a phenomenon is not a thing in itself; it must be possible for us to have a perception of this limitation by a void time and a void space.But such a perception- such an experience is impossible; because it has no content.Consequently, an absolute cosmical limit is empirically, and therefore absolutely, impossible.**The reader will remark that the proof presented above is very different from the dogmatical demonstration given in the antithesis of the first antinomy.In that demonstration, it was taken for granted that the world is a thing in itself- given in its totality prior to all regress, and a determined position in space and time was denied to it- if it was not considered as occupying all time and all space.
Hence our conclusion differed from that given above; for we inferred in the antithesis the actual infinity of the world.
From this follows the affirmative answer: "The regress in the series of phenomena- as a determination of the cosmical quantity, proceeds in indefinitum." This is equivalent to saying: "The world of sense has no absolute quantity, but the empirical regress (through which alone the world of sense is presented to us on the side of its conditions)rests upon a rule, which requires it to proceed from every member of the series, as conditioned, to one still more remote (whether through personal experience, or by means of history, or the chain of cause and effect), and not to cease at any point in this extension of the possible empirical employment of the understanding." And this is the proper and only use which reason can make of its principles.
The above rule does not prescribe an unceasing regress in one kind of phenomena.It does not, for example, forbid us, in our ascent from an individual human being through the line of his ancestors, to expect that we shall discover at some point of the regress a primeval pair, or to admit, in the series of heavenly bodies, a sun at the farthest possible distance from some centre.All that it demands is a perpetual progress from phenomena to phenomena, even although an actual perception is not presented by them (as in the case of our perceptions being so weak as that we are unable to become conscious of them), since they, nevertheless, belong to possible experience.
Every beginning is in time, and all limits to extension are in space.But space and time are in the world of sense.Consequently phenomena in the world are conditionally limited, but the world itself is not limited, either conditionally or unconditionally.
For this reason, and because neither the world nor the cosmical series of conditions to a given conditioned can be completely given, our conception of the cosmical quantity is given only in and through the regress and not prior to it- in a collective intuition.But the regress itself is really nothing more than the determining of the cosmical quantity, and cannot therefore give us any determined conception of it- still less a conception of a quantity which is, in relation to a certain standard, infinite.The regress does not, therefore, proceed to infinity (an infinity given), but only to an indefinite extent, for or the of presenting to us a quantity- realized only in and through the regress itself.
II.Solution of the Cosmological Idea of the Totality of the Division of a Whole given in Intuition.
When I divide a whole which is given in intuition, I proceed from a conditioned to its conditions.The division of the parts of the whole (subdivisio or decompositio) is a regress in the series of these conditions.The absolute totality of this series would be actually attained and given to the mind, if the regress could arrive at ****** parts.But if all the parts in a continuous decomposition are themselves divisible, the division, that is to say, the regress, proceeds from the conditioned to its conditions in infinitum;because the conditions (the parts) are themselves contained in the conditioned, and, as the latter is given in a limited intuition, the former are all given along with it.This regress cannot, therefore, be called a regressus in indefinitum, as happened in the case of the preceding cosmological idea, the regress in which proceeded from the conditioned to the conditions not given contemporaneously and along with it, but discoverable only through the empirical regress.We are not, however, entitled to affirm of a whole of this kind, which is divisible in infinitum, that it consists of an infinite number of parts.For, although all the parts are contained in the intuition of the whole, the whole division is not contained therein.The division is contained only in the progressing decomposition- in the regress itself, which is the condition of the possibility and actuality of the series.Now, as this regress is infinite, all the members (parts) to which it attains must be contained in the given whole as an aggregate.
But the complete series of division is not contained therein.For this series, being infinite in succession and always incomplete, cannot represent an infinite number of members, and still less a composition of these members into a whole.
To apply this remark to space.Every limited part of space presented to intuition is a whole, the parts of which are always spaces- to whatever extent subdivided.Every limited space is hence divisible to infinity.