The Critique of Pure Reason Part 19

The ideas which we are at present engaged in discussing I have called cosmological ideas; partly because by the term world is understood the entire content of all phenomena, and our ideas are directed solely to the unconditioned among phenomena; partly also, because world, in the transcendental sense, signifies the absolute totality of the content of existing things, and we are directing our attention only to the completeness of the synthesis--although, properly, only in regression.

In regard to the fact that these ideas are all transcendent, and, although they do not transcend phenomena as regards their mode, but are concerned solely with the world of sense (and not with noumena), nevertheless carry their synthesis to a degree far above all possible experience--it still seems to me that we can, with perfect propriety, designate them cosmical conceptions. As regards the distinction between the mathematically and the dynamically unconditioned which is the aim of the regression of the synthesis, I should call the two former, in a more limited signification, cosmical conceptions, the remaining two transcendent physical conceptions. This distinction does not at present seem to be of particular importance, but we shall afterwards find it to be of some value.

SECTION II. Ant.i.thetic of Pure Reason.

Thetic is the term applied to every collection of dogmatical propositions. By ant.i.thetic I do not understand dogmatical a.s.sertions of the opposite, but the self-contradiction of seemingly dogmatical cognitions (thesis c.u.m ant.i.thesis), in none of which we can discover any decided superiority. Ant.i.thetic is not, therefore, occupied with one-sided statements, but is engaged in considering the contradictory nature of the general cognitions of reason and its causes.

Transcendental ant.i.thetic is an investigation into the antinomy of pure reason, its causes and result. If we employ our reason not merely in the application of the principles of the understanding to objects of experience, but venture with it beyond these boundaries, there arise certain sophistical propositions or theorems. These a.s.sertions have the following peculiarities: They can find neither confirmation nor confutation in experience; and each is in itself not only self-consistent, but possesses conditions of its necessity in the very nature of reason--only that, unluckily, there exist just as valid and necessary grounds for maintaining the contrary proposition.

The questions which naturally arise in the consideration of this dialectic of pure reason, are therefore: 1st. In what propositions is pure reason unavoidably subject to an antinomy? 2nd. What are the causes of this antinomy? 3rd. Whether and in what way can reason free itself from this self-contradiction?

A dialectical proposition or theorem of pure reason must, according to what has been said, be distinguishable from all sophistical propositions, by the fact that it is not an answer to an arbitrary question, which may be raised at the mere pleasure of any person, but to one which human reason must necessarily encounter in its progress. In the second place, a dialectical proposition, with its opposite, does not carry the appearance of a merely artificial illusion, which disappears as soon as it is investigated, but a natural and unavoidable illusion, which, even when we are no longer deceived by it, continues to mock us and, although rendered harmless, can never be completely removed.

This dialectical doctrine will not relate to the unity of understanding in empirical conceptions, but to the unity of reason in pure ideas. The conditions of this doctrine are--inasmuch as it must, as a synthesis according to rules, be conformable to the understanding, and at the same time as the absolute unity of the synthesis, to the reason--that, if it is adequate to the unity of reason, it is too great for the understanding, if according with the understanding, it is too small for the reason. Hence arises a mutual opposition, which cannot be avoided, do what we will.

These sophistical a.s.sertions of dialectic open, as it were, a battle-field, where that side obtains the victory which has been permitted to make the attack, and he is compelled to yield who has been unfortunately obliged to stand on the defensive. And hence, champions of ability, whether on the right or on the wrong side, are certain to carry away the crown of victory, if they only take care to have the right to make the last attack, and are not obliged to sustain another onset from their opponent. We can easily believe that this arena has been often trampled by the feet of combatants, that many victories have been obtained on both sides, but that the last victory, decisive of the affair between the contending parties, was won by him who fought for the right, only if his adversary was forbidden to continue the tourney. As impartial umpires, we must lay aside entirely the consideration whether the combatants are fighting for the right or for the wrong side, for the true or for the false, and allow the combat to be first decided.

Perhaps, after they have wearied more than injured each other, they will discover the nothingness of their cause of quarrel and part good friends.

This method of watching, or rather of originating, a conflict of a.s.sertions, not for the purpose of finally deciding in favour of either side, but to discover whether the object of the struggle is not a mere illusion, which each strives in vain to reach, but which would be no gain even when reached--this procedure, I say, may be termed the sceptical method. It is thoroughly distinct from scepticism--the principle of a technical and scientific ignorance, which undermines the foundations of all knowledge, in order, if possible, to destroy our belief and confidence therein. For the sceptical method aims at certainty, by endeavouring to discover in a conflict of this kind, conducted honestly and intelligently on both sides, the point of misunderstanding; just as wise legislators derive, from the embarra.s.sment of judges in lawsuits, information in regard to the defective and ill-defined parts of their statutes. The antinomy which reveals itself in the application of laws, is for our limited wisdom the best criterion of legislation. For the attention of reason, which in abstract speculation does not easily become conscious of its errors, is thus roused to the momenta in the determination of its principles.

But this sceptical method is essentially peculiar to transcendental philosophy, and can perhaps be dispensed with in every other field of investigation. In mathematics its use would be absurd; because in it no false a.s.sertions can long remain hidden, inasmuch as its demonstrations must always proceed under the guidance of pure intuition, and by means of an always evident synthesis. In experimental philosophy, doubt and delay may be very useful; but no misunderstanding is possible, which cannot be easily removed; and in experience means of solving the difficulty and putting an end to the dissension must at last be found, whether sooner or later. Moral philosophy can always exhibit its principles, with their practical consequences, in concreto--at least in possible experiences, and thus escape the mistakes and ambiguities of abstraction. But transcendental propositions, which lay claim to insight beyond the region of possible experience, cannot, on the one hand, exhibit their abstract synthesis in any a priori intuition, nor, on the other, expose a lurking error by the help of experience. Transcendental reason, therefore, presents us with no other criterion than that of an attempt to reconcile such a.s.sertions, and for this purpose to permit a free and unrestrained conflict between them. And this we now proceed to arrange.*

[*Footnote: The antinomies stand in the order of the four transcendental ideas above detailed.]

FIRST CONFLICT OF THE TRANSCENDENTAL IDEAS.

THESIS.

The world has a beginning in time, and is also limited in regard to s.p.a.ce.

PROOF.

Granted that the world has no beginning in time; up to every given moment of time, an eternity must have elapsed, and therewith pa.s.sed away an infinite series of successive conditions or states of things in the world. Now the infinity of a series consists in the fact that it never can be completed by means of a successive synthesis. It follows that an infinite series already elapsed is impossible and that, consequently, a beginning of the world is a necessary condition of its existence. And this was the first thing to be proved.

As regards the second, let us take the opposite for granted. In this case, the world must be an infinite given total of coexistent things.

Now we cannot cogitate the dimensions of a quant.i.ty, which is not given within certain limits of an intuition,* in any other way than by means of the synthesis of its parts, and the total of such a quant.i.ty only by means of a completed synthesis, or the repeated addition of unity to itself. Accordingly, to cogitate the world, which fills all s.p.a.ces, 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 s.p.a.ce, not infinite, but enclosed in limits. And this was the second thing to be proved.

[*Footnote: We may consider an undetermined quant.i.ty 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.]

ANt.i.tHESIS.

The world has no beginning, and no limits in s.p.a.ce, but is, in relation both to time and s.p.a.ce, 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 s.p.a.ce; it follows that it must exist in a void s.p.a.ce, which is not limited. We should therefore meet not only with a relation of things in s.p.a.ce, but also a relation of things to s.p.a.ce. 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 s.p.a.ce is merely a relation to no object. But such a relation, and consequently the limitation of the world by void s.p.a.ce, is nothing. Consequently, the world, as regards s.p.a.ce, is not limited, that is, it is infinite in regard to extension.*

[*Footnote: s.p.a.ce is merely the form of external intuition (formal intuition), and not a real object which can be externally perceived.

s.p.a.ce, prior to all things which determine it (fill or limit it), or, rather, which present an empirical intuition conformable to it, is, under the t.i.tle of absolute s.p.a.ce, 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 s.p.a.ce (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--s.p.a.ce 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 s.p.a.ce, or a determination of the mutual relation of both, cannot possibly be perceived, and is therefore merely the predicate of a notional ent.i.ty.]

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 quant.i.ty. A quant.i.ty is infinite, if a greater than itself cannot possibly exist. The quant.i.ty 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 quant.i.ty, 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 quant.i.ty, 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 a.s.sumed 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 quant.i.ty 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 const.i.tuting 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 quant.i.ty 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 const.i.tute 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 ANt.i.tHESIS.

The proof in favour of the infinity of the cosmical succession and the cosmical content is based upon the consideration that, in the opposite case, a void time and a void s.p.a.ce must const.i.tute the limits of the world. Now I am not unaware, that there are some ways of escaping this conclusion. It may, for example, be alleged, that a limit to the world, as regards both s.p.a.ce and time, is quite possible, without at the same time holding the existence of an absolute time before the beginning of the world, or an absolute s.p.a.ce extending beyond the actual world--which is impossible. I am quite well satisfied with the latter part of this opinion of the philosophers of the Leibnitzian school. s.p.a.ce is merely the form of external intuition, but not a real object which can itself be externally intuited; it is not a correlate of phenomena, it is the form of phenomena itself. s.p.a.ce, therefore, cannot be regarded as absolutely and in itself something determinative of the existence of things, because it is not itself an object, but only the form of possible objects. Consequently, things, as phenomena, determine s.p.a.ce; that is to say, they render it possible that, of all the possible predicates of s.p.a.ce (size and relation), certain may belong to reality. But we cannot affirm the converse, that s.p.a.ce, as something self-subsistent, can determine real things in regard to size or shape, for it is in itself not a real thing. s.p.a.ce (filled or void)* may therefore be limited by phenomena, but phenomena cannot be limited by an empty s.p.a.ce without them. This is true of time also. All this being granted, it is nevertheless indisputable, that we must a.s.sume these two nonent.i.ties, void s.p.a.ce without and void time before the world, if we a.s.sume the existence of cosmical limits, relatively to s.p.a.ce or time.

[*Footnote: It is evident that what is meant here is, that empty s.p.a.ce, in so far as it is limited by phenomena--s.p.a.ce, that is, within the world--does not at least contradict transcendental principles, and may therefore, as regards them, be admitted, although its possibility cannot on that account be affirmed.]

For, as regards the subterfuge adopted by those who endeavour to evade the consequence--that, if the world is limited as to s.p.a.ce and time, the infinite void must determine the existence of actual things in regard to their dimensions--it arises solely from the fact that instead of a sensuous world, an intelligible world--of which nothing is known--is cogitated; instead of a real beginning (an existence, which is preceded by a period in which nothing exists), an existence which presupposes no other condition than that of time; and, instead of limits of extension, boundaries of the universe. But the question relates to the mundus phaenomenon, and its quant.i.ty; and in this case we cannot make abstraction of the conditions of sensibility, without doing away with the essential reality of this world itself. The world of sense, if it is limited, must necessarily lie in the infinite void. If this, and with it s.p.a.ce as the a priori condition of the possibility of phenomena, is left out of view, the whole world of sense disappears. In our problem is this alone considered as given. The mundus intelligibilis is nothing but the general conception of a world, in which abstraction has been made of all conditions of intuition, and in relation to which no synthetical proposition--either affirmative or negative--is possible.

SECOND CONFLICT OF TRANSCENDENTAL IDEAS.

THESIS.