If, accordingly, we say: "The world is either infinite in extension, or it is not infinite (non est infinitus)"; and if the former proposition is false, its contradictory opposite- the world is not infinite- must be true.And thus I should deny the existence of an infinite, without, however affirming the existence of a finite world.But if we construct our proposition thus: "The world is either infinite or finite (non-infinite)," both statements may be false.For, in this case, we consider the world as per se determined in regard to quantity, and while, in the one judgement, we deny its infinite and consequently, perhaps, its independent existence; in the other, we append to the world, regarded as a thing in itself, a certain determination- that of finitude; and the latter may be false as well as the former, if the world is not given as a thing in itself, and thus neither as finite nor as infinite in quantity.This kind of opposition I may be allowed to term dialectical; that of contradictories may be called analytical opposition.Thus then, of two dialectically opposed judgements both may be false, from the fact, that the one is not a mere contradictory of the other, but actually enounces more than is requisite for a full and complete contradiction.
When we regard the two propositions- "The world is infinite in quantity," and, "The world is finite in quantity," as contradictory opposites, we are assuming that the world- the complete series of phenomena- is a thing in itself.For it remains as a permanent quantity, whether I deny the infinite or the finite regress in the series of its phenomena.But if we dismiss this assumption- this transcendental illusion- and deny that it is a thing in itself, the contradictory opposition is metamorphosed into a merely dialectical one; and the world, as not existing in itself- independently of the regressive series of my representations- exists in like manner neither as a whole which is infinite nor as a whole which is finite in itself.
The universe exists for me only in the empirical regress of the series of phenomena and not per se.If, then, it is always conditioned, it is never completely or as a whole; and it is, therefore, not an unconditioned whole and does not exist as such, either with an infinite, or with a finite quantity.
What we have here said of the first cosmological idea- that of the absolute totality of quantity in phenomena- applies also to the others.The series of conditions is discoverable only in the regressive synthesis itself, and not in the phenomenon considered as a thing in itself- given prior to all regress.Hence I am compelled to say: "The aggregate of parts in a given phenomenon is in itself neither finite nor infinite; and these parts are given only in the regressive synthesis of decomposition- a synthesis which is never given in absolute completeness, either as finite, or as infinite." The same is the case with the series of subordinated causes, or of the conditioned up to the unconditioned and necessary existence, which can never be regarded as in itself, ind in its totality, either as finite or as infinite; because, as a series of subordinate representations, it subsists only in the dynamical regress and cannot be regarded as existing previously to this regress, or as a self-subsistent series of things.
Thus the antinomy of pure reason in its cosmological ideas disappears.For the above demonstration has established the fact that it is merely the product of a dialectical and illusory opposition, which arises from the application of the idea of absolute totality- admissible only as a condition of things in themselves- to phenomena, which exist only in our representations, and- when constituting a series- in a successive regress.This antinomy of reason may, however, be really profitable to our speculative interests, not in the way of contributing any dogmatical addition, but as presenting to us another material support in our critical investigations.For it furnishes us with an indirect proof of the transcendental ideality of phenomena, if our minds were not completely satisfied with the direct proof set forth in the Trancendental Aesthetic.The proof would proceed in the following dilemma.If the world is a whole existing in itself, it must be either finite or infinite.But it is neither finite nor infinite- as has been shown, on the one side, by the thesis, on the other, by the antithesis.Therefore the world- the content of all phenomena- is not a whole existing in itself.It follows that phenomena are nothing, apart from our representations.And this is what we mean by transcendental ideality.
This remark is of some importance.It enables us to see that the proofs of the fourfold antinomy are not mere sophistries- are not fallacious, but grounded on the nature of reason, and valid- under the supposition that phenomena are things in themselves.The opposition of the judgements which follow makes it evident that a fallacy lay in the initial supposition, and thus helps us to discover the true constitution of objects of sense.This transcendental dialectic does not favour scepticism, although it presents us with a triumphant demonstration of the advantages of the sceptical method, the great utility of which is apparent in the antinomy, where the arguments of reason were allowed to confront each other in undiminished force.
And although the result of these conflicts of reason is not what we expected- although we have obtained no positive dogmatical addition to metaphysical science- we have still reaped a great advantage in the correction of our judgements on these subjects of thought.
SECTION VIII.Regulative Principle of Pure Reason in relation to the Cosmological Ideas.