The Critique of Pure Reason Part 23

When we regard the two propositions--"The world is infinite in quant.i.ty," and, "The world is finite in quant.i.ty," as contradictory opposites, we are a.s.suming that the world--the complete series of phenomena--is a thing in itself. For it remains as a permanent quant.i.ty, whether I deny the infinite or the finite regress in the series of its phenomena. But if we dismiss this a.s.sumption--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 quant.i.ty.

What we have here said of the first cosmological idea--that of the absolute totality of quant.i.ty 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 const.i.tuting 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 ant.i.thesis.

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 const.i.tution 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.

The cosmological principle of totality could not give us any certain knowledge in regard to the maximum in the series of conditions in the world of sense, considered as a thing in itself. The actual regress in the series is the only means of approaching this maximum. This principle of pure reason, therefore, may still be considered as valid--not as an axiom enabling us to cogitate totality in the object as actual, but as a problem for the understanding, which requires it to inst.i.tute and to continue, in conformity with the idea of totality in the mind, the regress in the series of the conditions of a given conditioned. For in the world of sense, that is, in s.p.a.ce and time, every condition which we discover in our investigation of phenomena is itself conditioned; because sensuous objects are not things in themselves (in which case an absolutely unconditioned might be reached in the progress of cognition), but are merely empirical representations the conditions of which must always be found in intuition. The principle of reason is therefore properly a mere rule--prescribing a regress in the series of conditions for given phenomena, and prohibiting any pause or rest on an absolutely unconditioned. It is, therefore, not a principle of the possibility of experience or of the empirical cognition of sensuous objects--consequently not a principle of the understanding; for every experience is confined within certain proper limits determined by the given intuition. Still less is it a const.i.tutive principle of reason authorizing us to extend our conception of the sensuous world beyond all possible experience. It is merely a principle for the enlargement and extension of experience as far as is possible for human faculties. It forbids us to consider any empirical limits as absolute. It is, hence, a principle of reason, which, as a rule, dictates how we ought to proceed in our empirical regress, but is unable to antic.i.p.ate or indicate prior to the empirical regress what is given in the object itself. I have termed it for this reason a regulative principle of reason; while the principle of the absolute totality of the series of conditions, as existing in itself and given in the object, is a const.i.tutive cosmological principle. This distinction will at once demonstrate the falsehood of the const.i.tutive principle, and prevent us from attributing (by a transcendental subreptio) objective reality to an idea, which is valid only as a rule.

In order to understand the proper meaning of this rule of pure reason, we must notice first that it cannot tell us what the object is, but only how the empirical regress is to be proceeded with in order to attain to the complete conception of the object. If it gave us any information in respect to the former statement, it would be a const.i.tutive principle--a principle impossible from the nature of pure reason. It will not therefore enable us to establish any such conclusions as: "The series of conditions for a given conditioned is in itself finite," or, "It is infinite." For, in this case, we should be cogitating in the mere idea of absolute totality, an object which is not and cannot be given in experience; inasmuch as we should be attributing a reality objective and independent of the empirical synthesis, to a series of phenomena. This idea of reason cannot then be regarded as valid--except as a rule for the regressive synthesis in the series of conditions, according to which we must proceed from the conditioned, through all intermediate and subordinate conditions, up to the unconditioned; although this goal is unattained and unattainable. For the absolutely unconditioned cannot be discovered in the sphere of experience.

We now proceed to determine clearly our notion of a synthesis which can never be complete. There are two terms commonly employed for this purpose. These terms are regarded as expressions of different and distinguishable notions, although the ground of the distinction has never been clearly exposed. The term employed by the mathematicians is progressus in infinitum. The philosophers prefer the expression progressus in indefinitum. Without detaining the reader with an examination of the reasons for such a distinction, or with remarks on the right or wrong use of the terms, I shall endeavour clearly to determine these conceptions, so far as is necessary for the purpose in this Critique.

We may, with propriety, say of a straight line, that it may be produced to infinity. In this case the distinction between a progressus in infinitum and a progressus in indefinitum is a mere piece of subtlety.

For, although when we say, "Produce a straight line," it is more correct to say in indefinitum than in infinitum; because the former means, "Produce it as far as you please," the second, "You must not cease to produce it"; the expression in infinitum is, when we are speaking of the power to do it, perfectly correct, for we can always make it longer if we please--on to infinity. And this remark holds good in all cases, when we speak of a progressus, that is, an advancement from the condition to the conditioned; this possible advancement always proceeds to infinity.

We may proceed from a given pair in the descending line of generation from father to son, and cogitate a never-ending line of descendants from it. For in such a case reason does not demand absolute totality in the series, because it does not presuppose it as a condition and as given (datum), but merely as conditioned, and as capable of being given (dabile).

Very different is the case with the problem: "How far the regress, which ascends from the given conditioned to the conditions, must extend"; whether I can say: "It is a regress in infinitum," or only "in indefinitum"; and whether, for example, setting out from the human beings at present alive in the world, I may ascend in the series of their ancestors, in infinitum--mr whether all that can be said is, that so far as I have proceeded, I have discovered no empirical ground for considering the series limited, so that I am justified, and indeed, compelled to search for ancestors still further back, although I am not obliged by the idea of reason to presuppose them.

My answer to this question is: "If the series is given in empirical intuition as a whole, the regress in the series of its internal conditions proceeds in infinitum; but, if only one member of the series is given, from which the regress is to proceed to absolute totality, the regress is possible only in indefinitum." For example, the division of a portion of matter given within certain limits--of a body, that is--proceeds in infinitum. For, as the condition of this whole is its part, and the condition of the part a part of the part, and so on, and as in this regress of decomposition an unconditioned indivisible member of the series of conditions is not to be found; there are no reasons or grounds in experience for stopping in the division, but, on the contrary, the more remote members of the division are actually and empirically given prior to this division. That is to say, the division proceeds to infinity. On the other hand, the series of ancestors of any given human being is not given, in its absolute totality, in any experience, and yet the regress proceeds from every genealogical member of this series to one still higher, and does not meet with any empirical limit presenting an absolutely unconditioned member of the series.

But as the members of such a series are not contained in the empirical intuition of the whole, prior to the regress, this regress does not proceed to infinity, but only in indefinitum, that is, we are called upon to discover other and higher members, which are themselves always conditioned.

In neither case--the regressus in infinitum, nor the regressus in indefinitum, is the series of conditions to be considered as actually infinite in the object itself. This might be true of things in themselves, but it cannot be a.s.serted of phenomena, which, as conditions of each other, are only given in the empirical regress itself. Hence, the question no longer is, "What is the quant.i.ty of this series of conditions in itself--is it finite or infinite?" for it is nothing in itself; but, "How is the empirical regress to be commenced, and how far ought we to proceed with it?" And here a signal distinction in the application of this rule becomes apparent. If the whole is given empirically, it is possible to recede in the series of its internal conditions to infinity. But if the whole is not given, and can only be given by and through the empirical regress, I can only say: "It is possible to infinity, to proceed to still higher conditions in the series." In the first case, I am justified in a.s.serting that more members are empirically given in the object than I attain to in the regress (of decomposition). In the second case, I am justified only in saying, that I can always proceed further in the regress, because no member of the series is given as absolutely conditioned, and thus a higher member is possible, and an inquiry with regard to it is necessary. In the one case it is necessary to find other members of the series, in the other it is necessary to inquire for others, inasmuch as experience presents no absolute limitation of the regress. For, either you do not possess a perception which absolutely limits your empirical regress, and in this case the regress cannot be regarded as complete; or, you do possess such a limitative perception, in which case it is not a part of your series (for that which limits must be distinct from that which is limited by it), and it is inc.u.mbent you to continue your regress up to this condition, and so on.

These remarks will be placed in their proper light by their application in the following section.

SECTION IX. Of the Empirical Use of the Regulative Principle of Reason with regard to the Cosmological Ideas.

We have shown that no transcendental use can be made either of the conceptions of reason or of understanding. We have shown, likewise, that the demand of absolute totality in the series of conditions in the world of sense arises from a transcendental employment of reason, resting on the opinion that phenomena are to be regarded as things in themselves.

It follows that we are not required to answer the question respecting the absolute quant.i.ty of a series--whether it is in itself limited or unlimited. We are only called upon to determine how far we must proceed in the empirical regress from condition to condition, in order to discover, in conformity with the rule of reason, a full and correct answer to the questions proposed by reason itself.

This principle of reason is hence valid only as a rule for the extension of a possible experience--its invalidity as a principle const.i.tutive of phenomena in themselves having been sufficiently demonstrated. And thus, too, the antinomial conflict of reason with itself is completely put an end to; inasmuch as we have not only presented a critical solution of the fallacy lurking in the opposite statements of reason, but have shown the true meaning of the ideas which gave rise to these statements. The dialectical principle of reason has, therefore, been changed into a doctrinal principle. But in fact, if this principle, in the subjective signification which we have shown to be its only true sense, may be guaranteed as a principle of the unceasing extension of the employment of our understanding, its influence and value are just as great as if it were an axiom for the a priori determination of objects. For such an axiom could not exert a stronger influence on the extension and rectification of our knowledge, otherwise than by procuring for the principles of the understanding the most widely expanded employment in the field of experience.

I. Solution of the Cosmological Idea of the Totality of the Composition of Phenomena in the Universe.

Here, as well as in the case of the other cosmological problems, the ground of the regulative principle of reason is the proposition that in our empirical regress no experience of an absolute limit, and consequently no experience of a condition, which is itself absolutely unconditioned, is discoverable. And the truth of this proposition itself rests upon the consideration that such an experience must represent to us phenomena as limited by nothing or the mere void, on which our continued regress by means of perception must abut--which is impossible.

Now this proposition, which declares that every condition attained in the empirical regress must itself be considered empirically conditioned, contains the rule in terminis, which requires me, to whatever extent I may have proceeded in the ascending series, always to look for some higher member in the series--whether this member is to become known to me through experience, or not.

Nothing further is necessary, then, for the solution of the first cosmological problem, than to decide, whether, in the regress to the unconditioned quant.i.ty of the universe (as regards s.p.a.ce and time), this never limited ascent ought to be called a regressus in infinitum or indefinitum.

The general representation which we form in our minds of the series of all past states or conditions of the world, or of all the things which at present exist in it, is itself nothing more than a possible empirical regress, which is cogitated--although in an undetermined manner--in the mind, and which gives rise to the conception of a series of conditions for a given object.* Now I have a conception of the universe, but not an intuition--that is, not an intuition of it as a whole. Thus I cannot infer the magnitude of the regress from the quant.i.ty or magnitude of the world, and determine the former by means of the latter; on the contrary, I must first of all form a conception of the quant.i.ty or magnitude of the world from the magnitude of the empirical regress. But of this regress I know nothing more than that I ought to proceed from every given member of the series of conditions to one still higher. But the quant.i.ty of the universe is not thereby determined, and we cannot affirm that this regress proceeds in infinitum. Such an affirmation would antic.i.p.ate the members of the series which have not yet been reached, and represent the number of them as beyond the grasp of any empirical synthesis; it would consequently determine the cosmical quant.i.ty prior to the regress (although only in a negative manner)--which is impossible. For the world is not given in its totality in any intuition: consequently, its quant.i.ty cannot be given prior to the regress. It follows that we are unable to make any declaration respecting the cosmical quant.i.ty in itself--not even that the regress in it is a regress in infinitum; we must only endeavour to attain to a conception of the quant.i.ty of the universe, in conformity with the rule which determines the empirical regress in it. But this rule merely requires us never to admit an absolute limit to our series--how far soever we may have proceeded in it, but always, on the contrary, to subordinate every phenomenon to some other as its condition, and consequently to proceed to this higher phenomenon. Such a regress is, therefore, the regressus in indefinitum, which, as not determining a quant.i.ty in the object, is clearly distinguishable from the regressus in infinitum.

[*Footnote: The cosmical series can neither be greater nor smaller than the possible empirical regress, upon which its conception is based. And as this regress cannot be a determinate infinite regress, still less a determinate finite (absolutely limited), it is evident that we cannot regard the world as either finite or infinite, because the regress, which gives us the representation of the world, is neither finite nor infinite.]

It follows from what we have said that we are not justified in declaring the world to be infinite in s.p.a.ce, or as regards past time. For this conception of an infinite given quant.i.ty is empirical; but we cannot apply the conception of an infinite quant.i.ty to the world as an object of the senses. I cannot say, "The regress from a given perception to everything limited either in s.p.a.ce or time, proceeds in infinitum," for this presupposes an infinite cosmical quant.i.ty; neither can I say, "It is finite," for an absolute limit is likewise impossible in experience.

It follows that I am not ent.i.tled to make any a.s.sertion at all respecting the whole object of experience--the world of sense; I must limit my declarations to the rule according to which experience or empirical knowledge is to be attained.

To the question, therefore, respecting the cosmical quant.i.ty, the first and negative answer is: "The world has no beginning in time, and no absolute limit in s.p.a.ce."

For, in the contrary case, it would be limited by a void time on the one hand, and by a void s.p.a.ce 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 s.p.a.ce. 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.*

[*Footnote: The reader will remark that the proof presented above is very different from the dogmatical demonstration given in the ant.i.thesis 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 s.p.a.ce and time was denied to it--if it was not considered as occupying all time and all s.p.a.ce. Hence our conclusion differed from that given above; for we inferred in the ant.i.thesis 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 quant.i.ty, proceeds in indefinitum." This is equivalent to saying: "The world of sense has no absolute quant.i.ty, 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 s.p.a.ce.

But s.p.a.ce 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 quant.i.ty 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 quant.i.ty, and cannot therefore give us any determined conception of it--still less a conception of a quant.i.ty 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 quant.i.ty--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 simple 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, ent.i.tled 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 s.p.a.ce. Every limited part of s.p.a.ce presented to intuition is a whole, the parts of which are always s.p.a.ces--to whatever extent subdivided. Every limited s.p.a.ce is hence divisible to infinity.

Let us again apply the remark to an external phenomenon enclosed in limits, that is, a body. The divisibility of a body rests upon the divisibility of s.p.a.ce, which is the condition of the possibility of the body as an extended whole. A body is consequently divisible to infinity, though it does not, for that reason, consist of an infinite number of parts.

It certainly seems that, as a body must be cogitated as substance in s.p.a.ce, the law of divisibility would not be applicable to it as substance. For we may and ought to grant, in the case of s.p.a.ce, that division or decomposition, to any extent, never can utterly annihilate composition (that is to say, the smallest part of s.p.a.ce must still consist of s.p.a.ces); otherwise s.p.a.ce would entirely cease to exist--which is impossible. But, the a.s.sertion on the other band that when all composition in matter is annihilated in thought, nothing remains, does not seem to harmonize with the conception of substance, which must be properly the subject of all composition and must remain, even after the conjunction of its attributes in s.p.a.ce--which const.i.tuted a body--is annihilated in thought. But this is not the case with substance in the phenomenal world, which is not a thing in itself cogitated by the pure category. Phenomenal substance is not an absolute subject; it is merely a permanent sensuous image, and nothing more than an intuition, in which the unconditioned is not to be found.

But, although this rule of progress to infinity is legitimate and applicable to the subdivision of a phenomenon, as a mere occupation or filling of s.p.a.ce, it is not applicable to a whole consisting of a number of distinct parts and const.i.tuting a quantum discretum--that is to say, an organized body. It cannot be admitted that every part in an organized whole is itself organized, and that, in a.n.a.lysing it to infinity, we must always meet with organized parts; although we may allow that the parts of the matter which we decompose in infinitum, may be organized.

For the infinity of the division of a phenomenon in s.p.a.ce rests altogether on the fact that the divisibility of a phenomenon is given only in and through this infinity, that is, an undetermined number of parts is given, while the parts themselves are given and determined only in and through the subdivision; in a word, the infinity of the division necessarily presupposes that the whole is not already divided in se.

Hence our division determines a number of parts in the whole--a number which extends just as far as the actual regress in the division; while, on the other hand, the very notion of a body organized to infinity represents the whole as already and in itself divided. We expect, therefore, to find in it a determinate, but at the same time, infinite, number of parts--which is self-contradictory. For we should thus have a whole containing a series of members which could not be completed in any regress--which is infinite, and at the same time complete in an organized composite. Infinite divisibility is applicable only to a quantum continuum, and is based entirely on the infinite divisibility of s.p.a.ce, But in a quantum discretum the mult.i.tude of parts or units is always determined, and hence always equal to some number. To what extent a body may be organized, experience alone can inform us; and although, so far as our experience of this or that body has extended, we may not have discovered any inorganic part, such parts must exist in possible experience. But how far the transcendental division of a phenomenon must extend, we cannot know from experience--it is a question which experience cannot answer; it is answered only by the principle of reason which forbids us to consider the empirical regress, in the a.n.a.lysis of extended body, as ever absolutely complete.

Concluding Remark on the Solution of the Transcendental Mathematical Ideas--and Introductory to the Solution of the Dynamical Ideas.