SECTION VII. Critical Solution of the Cosmological Problem
The antinomy of pure reason is based upon the following dialectical
Argument: "If that which is conditioned is given, the whole series
Of its conditions is also given; but sensuous objects are given as
Conditioned; consequently..." This syllogism, the major of which seems
So natural and evident, introduces as many cosmological ideas as there
Are different kinds of conditions in the synthesis of phenomena, in
So far as these conditions constitute a series. These ideas require
Absolute totality in the series, and thus place reason in inextricable
Embarra**ment. Before proceeding to expose the fallacy in this
Dialectical argument, it will be necessary to have a correct
Understanding of certain conceptions that appear in it
In the first place, the following proposition is evident, and
Indubitably certain: "If the conditioned is given, a regress in the
Series of all its conditions is thereby imperatively required." For the
Very conception of a conditioned is a conception of something related
To a condition, and, if this condition is itself conditioned, to
Another condition--and so on through all the members of the series
This proposition is, therefore, an*lytical and has nothing to fear
From transcendental criticism. It is a logical postulate of reason:
To pursue, as far as possible, the connection of a conception with its
Conditions
If, in the second place, both the conditioned and the condition are
Things in themselves, and if the former is given, not only is the
Regress to the latter requisite, but the latter is really given with
The former. Now, as this is true of all the members of the series, the
Entire series of conditions, and with them the unconditioned, is at the
Same time given in the very fact of the conditioned, the existence of
Which is possible only in and through that series, being given. In
This case, the synthesis of the conditioned with its condition, is a
Synthesis of the understanding merely, which represents things as they
Are, without regarding whether and how we can cognize them. But if
I have to do with phenomena, which, in their character of mere
Representations, are not given, if I do not attain to a cognition of
Them (in other words, to themselves, for they are nothing more than
Empirical cognitions), I am not entitled to say: "If the conditioned
Is given, all its conditions (as phenomena) are also given." I cannot
Therefore, from the fact of a conditioned being given, infer the
Absolute totality of the series of its conditions. For phenomena are
Nothing but an empirical synthesis in apprehension or perception, and
Are therefore given only in it. Now, in speaking of phenomena it does
Not follow that, if the conditioned is given, the synthesis which
Constitutes its empirical condition is also thereby given and
Presupposed; such a synthesis can be established only by an actual
Regress in the series of conditions. But we are entitled to say in this
Case that a regress to the conditions of a conditioned, in other
Words, that a continuous empirical synthesis is enjoined; that, if the
Conditions are not given, they are at least required; and that we are
Certain to discover the conditions in this regress
We can now see that the major, in the above cosmological syllogism
Takes the conditioned in the transcendental signification which it has
In the pure category, while the minor speaks of it in the empirical
Signification which it has in the category as applied to phenomena
There is, therefore, a dialectical fallacy in the syllogism--a sophisma
Figurae dictionis. But this fallacy is not a consciously devised one
But a perfectly natural illusion of the common reason of man. For
When a thing is given as conditioned, we presuppose in the major its
Conditions and their series, unperceived, as it were, and unseen;
Because this is nothing more than the logical requirement of complete
And satisfactory premisses for a given conclusion. In this case, time
Is altogether left out in the connection of the conditioned with
The condition; they are supposed to be given in themselves, and
Contemporaneously. It is, moreover, just as natural to regard phenomena
(in the minor) as things in themselves and as objects presented to the
Pure understanding, as in the major, in which complete abstraction was
Made of all conditions of intuition. But it is under these conditions
Alone that objects are given. Now we overlooked a remarkable distinction
Between the conceptions. The synthesis of the conditioned with its
Condition, and the complete series of the latter (in the major) are not
Limited by time, and do not contain the conception of succession. On the
Contrary, the empirical synthesis and the series of conditions in the
Phenomenal world--subsumed in the minor--are necessarily successive and
Given in time alone. It follows that I cannot presuppose in the minor
As I did in the major, the absolute totality of the synthesis and of
The series therein represented; for in the major all the members of the
Series are given as things in themselves--without any limitations or
Conditions of time, while in the minor they are possible only in and
Through a successive regress, which cannot exist, except it be actually
Carried into execution in the world of phenomena
After this proof of the viciousness of the argument commonly employed
In maintaining cosmological a**ertions, both parties may now be justly
Dismissed, as advancing claims without grounds or title. But the process
Has not been ended by convincing them that one or both were in the
Wrong and had maintained an a**ertion which was without valid grounds
Of proof. Nothing seems to be clearer than that, if one maintains: "The
World has a beginning," and another: "The world has no beginning," one
Of the two must be right. But it is likewise clear that, if the evidence
On both sides is equal, it is impossible to discover on what side the
Truth lies; and the controversy continues, although the parties have
Been recommended to peace before the tribunal of reason. There remains
Then, no other means of settling the question than to convince the
Parties, who refute each other with such conclusiveness and ability
That they are disputing about nothing, and that a transcendental
Illusion has been mocking them with visions of reality where there is
None. The mode of adjusting a dispute which cannot be decided upon its
Own merits, we shall now proceed to lay before our readers
Zeno of Elea, a subtle dialectician, was severely reprimanded by Plato
As a sophist, who, merely from the base motive of exhibiting his
Sk** in discussion, maintained and subverted the same proposition by
Arguments as powerful and convincing on the one side as on the other. He
Maintained, for example, that God (who was probably nothing more, in his
View, than the world) is neither finite nor infinite, neither in motion
Nor in rest, neither similar nor dissimilar to any other thing. It
Seemed to those philosophers who criticized his mode of discussion
That his purpose was to deny completely both of two self-contradictory
Propositions--which is absurd. But I cannot believe that there is any
Justice in this accusation. The first of these propositions I shall
Presently consider in a more detailed manner. With regard to the others
If by the word of God he understood merely the Universe, his meaning
Must have been--that it cannot be permanently present in one place--that
Is, at rest--nor be capable of changing its place--that is, of
Moving--because all places are in the universe, and the universe itself
Is, therefore, in no place. Again, if the universe contains in itself
Everything that exists, it cannot be similar or dissimilar to any other
Thing, because there is, in fact, no other thing with which it can be
Compared. If two opposite judgements presuppose a contingent impossible
Or arbitrary condition, both--in spite of their opposition (which is
However, not properly or really a contradiction)--fall away; because the
Condition, which ensured the validity of both, has itself disappeared
If we say: "Everybody has either a good or a bad smell," we have omitted
A third possible judgement--it has no smell at all; and thus both
Conflicting statements may be false. If we say: "It is either
Good-smelling or not good-smelling (vel suaveolens vel non-suaveolens),"
Both judgements are contradictorily opposed; and the contradictory
Opposite of the former judgement--some bodies are not
Good-smelling--embraces also those bodies which have no smell at all. In
The preceding pair of opposed judgements (per disparata), the contingent
Condition of the conception of body (smell) attached to both conflicting
Statements, instead of having been omitted in the latter, which is
Consequently not the contradictory opposite of the former
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 an*lytical
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 a**uming 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 a**umption--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
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 institute 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 space 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 constitutive 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 anticipate 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 constitutive
Cosmological principle. This distinction will at once demonstrate the
Falsehood of the constitutive 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 constitutive 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**erted 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 quantity 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**erting 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 incumbent 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 quantity 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 constitutive 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 quantity of the universe (as regards space 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 quantity 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 quantity 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
Quantity of the universe is not thereby determined, and we cannot affirm
That this regress proceeds in infinitum. Such an affirmation would
Anticipate 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 quantity
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 quantity cannot be given prior to the regress. It
Follows that we are unable to make any declaration respecting the
Cosmical quantity 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 quantity 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 quantity in the object, is
Clearly distinguishable from the regressus in infinitum
It follows from what we have said that we are not justified in declaring
The world to be infinite in space, or as regards past time. For this
Conception of an infinite given quantity is empirical; but we cannot
Apply the conception of an infinite quantity to the world as an object
Of the senses. I cannot say, "The regress from a given perception to
Everything limited either in space or time, proceeds in infinitum," for
This presupposes an infinite cosmical quantity; neither can I say, "It
Is finite," for an absolute limit is likewise impossible in experience
It follows that I am not entitled to make any a**ertion 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 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
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 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, 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
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 space, 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 space, the law of divisibility would not be applicable to it as
Substance. For we may and ought to grant, in the case of space, that
Division or decomposition, to any extent, never can utterly annihilate
Composition (that is to say, the smallest part of space must still
Consist of spaces); otherwise space would entirely cease to
Exist--which is impossible. But, the a**ertion 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 space--which constituted
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 space, it is not applicable to a whole consisting of a number
Of distinct parts and constituting 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 an*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 space 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 space, But in a quantum discretum the multitude 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 an*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
We presented the antinomy of pure reason in a tabular form, and we
Endeavoured to show the ground of this self-contradiction on the part
Of reason, and the only means of bringing it to a conclusion--namely, by
Declaring both contradictory statements to be false. We represented
In these antinomies the conditions of phenomena as belonging to the
Conditioned according to relations of space and time--which is the
Usual supposition of the common understanding. In this respect, all
Dialectical representations of totality, in the series of conditions
To a given conditioned, were perfectly h*mogeneous. The condition was
Always a member of the series along with the conditioned, and thus the
h*mogeneity of the whole series was a**ured. In this case the regress
Could never be cogitated as complete; or, if this was the case, a member
Really conditioned was falsely regarded as a primal member, consequently
As unconditioned. In such an antinomy, therefore, we did not consider
The object, that is, the conditioned, but the series of conditions
Belonging to the object, and the magnitude of that series. And thus
Arose the difficulty--a difficulty not to be settled by any decision
Regarding the claims of the two parties, but simply by cutting the
Knot--by declaring the series proposed by reason to be either too long
Or too short for the understanding, which could in neither case make its
Conceptions adequate with the ideas
But we have overlooked, up to this point, an essential difference
Existing between the conceptions of the understanding which reason
Endeavours to raise to the rank of ideas--two of these indicating a
Mathematical, and two a dynamical synthesis of phenomena. Hitherto, it
Was necessary to signalize this distinction; for, just as in our general
Representation of all transcendental ideas, we considered them under
Phenomenal conditions, so, in the two mathematical ideas, our discussion
Is concerned solely with an object in the world of phenomena. But as
We are now about to proceed to the consideration of the dynamical
Conceptions of the understanding, and their adequateness with ideas, we
Must not lose sight of this distinction. We shall find that it opens up
To us an entirely new view of the conflict in which reason is involved
For, while in the first two antinomies, both parties were dismissed, on
The ground of having advanced statements based upon false hypothesis; in
The present case the hope appears of discovering a hypothesis which may
Be consistent with the demands of reason, and, the judge completing the
Statement of the grounds of claim, which both parties had left in an
Unsatisfactory state, the question may be settled on its own merits
Not by dismissing the claimants, but by a comparison of the arguments on
Both sides. If we consider merely their extension, and whether they are
Adequate with ideas, the series of conditions may be regarded as all
h*mogeneous. But the conception of the understanding which lies at the
Basis of these ideas, contains either a synthesis of the h*mogeneous
(presupposed in every quantity--in its composition as well as in its
Division) or of the heterogeneous, which is the case in the dynamical
Synthesis of cause and effect, as well as of the necessary and the
Contingent
Thus it happens that in the mathematical series of phenomena no other
Than a sensuous condition is admissible--a condition which is itself a
Member of the series; while the dynamical series of sensuous conditions
Admits a heterogeneous condition, which is not a member of the series
But, as purely intelligible, lies out of and beyond it. And thus reason
Is satisfied, and an unconditioned placed at the head of the series
Of phenomena, without introducing confusion into or discontinuing it
Contrary to the principles of the understanding
Now, from the fact that the dynamical ideas admit a condition of
Phenomena which does not form a part of the series of phenomena, arises
A result which we should not have expected from an antinomy. In former
Cases, the result was that both contradictory dialectical statements
Were declared to be false. In the present case, we find the conditioned
In the dynamical series connected with an empirically unconditioned
But non-sensuous condition; and thus satisfaction is done to the
Understanding on the one hand and to the reason on the other.* While
Moreover, the dialectical arguments for unconditioned totality in mere
Phenomena fall to the ground, both propositions of reason may be shown
To be true in their proper signification. This could not happen in
The case of the cosmological ideas which demanded a mathematically
Unconditioned unity; for no condition could be placed at the head of
The series of phenomena, except one which was itself a phenomenon and
Consequently a member of the series