The
principle
of these is, "In all phamomena the Real, thai tvnich is an object of sensation, has Intensive Quantity, that has
Degree.
Degree.
Kant - Critique of Pure Reason
The possibility of these principles, however, will necessarily be considered here, inasmuch as they are synthetical judgments h priori, not indeed for the purpose of proving their accuracy and apodeictic certainty, which is unnecessary, but merely to render conceivable and deduce the possibility of such evident << priori cognitions.
But we shall have also to speak of the principle of analy tical judgments, in opposition to synthetical judgments, which is the proper subject of our enquiries, because this very oppo
? ? ? ? SYSTEM O1 PRINCIPLES. 113
<<ition will free the theory of the latter from nll ambiguity, ami place it clearly before our eyes in its true nature.
Ststem of the Principled or the Pure Under standing.
SECTION FIRST.
Of the Supreme Principle of all Analytical Judgments.
Whatever may be the content of our cognition, and in whatever manner our cognition may be related to its object, the universal, although only negative condition of all our judgments is that they do not contradict themselves ; other wise these judgments are in themselves (even without respect to the object) nothing. But although there may exist no contradiction in our judgment, it may nevertheless connect conceptions in such a manner, that they do not correspond to the object, or without any grounds either a priori or a pos teriori for arriving at such a judgment, and thus, without being self-contradictory, a judgment may nevertheless be either false or groundless. "
Now, the proposition, No subject can have a predicate that contradicts it," is called the principle of contradiction, and is an universal but purely negative criterion of all truth. But it belongs to logic alone, because it is valid of cognitions, merely as cognitions, and without respect to their content, and declares that the contradiction entirely nullifies them. We can also, however, make a positive use of this princi ple, that not merely to banish falsehood and error (in bo far as rests upon contradiction), but also for the cog nition of truth. For the judgment analytical, be affirmative or negative, its truth must always be recognizable
means of the principle of contradiction. For the contrary of that which lies and cogitated as conception in the cogni tion of the object will be always properly negatived, but the conception itself must always be affirmed of the object, inas much as the contrary thereof would be in contradiction to the object.
We must therefore hold the principle contradiction to be the universal and fully sufficient principle all analytical tocnitiox. But as sufficient criterion of truth, has no further
? ? ? a
it is, is
of I it of
is
2
by
if
it
? 116 ANALYTIC Of 1'BINCIPLES.
utility or authority. For the fact that no cognition can be at variance with this principle without nullifying itself, consti tutes this principle the sine qua non, but not the determining ground of the truth of our cognition. As our business at present is properly with the synthetical part of our knowledge only, we shall always be on our guard not to transgress this inviolable principle ; but at the same time not to expect from it any direct assistance in the establishment of the truth of any synthetical proposition.
There exists, however, a formula of this celebrated principle --a principle merely formal and entirely without content -- which contains a synthesis that has been inadvertently and quite unnecessarily mixed up with it. It is this : -- " It is impossible for a thing to be and not to be at the same time. " Not to mention the superfluousness of the addition of the word impossible to indicate the apodeictic certainty, which ought to be self-evident from the proposition itself, the propo sition is affected by the condition of time, and as it were says :
? " A thing-- A, which is something=J? , cannot at the same time be non-B. " But both, B as well as non-B, may quite well exist in succession. For example, a man who is young cannot at the same time be old ; but the same man can very well be at one time young, and at another not young, that old. Now the principle of contradiction as merely logical propo sition must not any means limit its application merely to relations of time, and consequently formula like the pre ceding quite foreign to its true purpose. The misunder standing arises in this way. We first of all separate predicate of thing from the conception of the tiling, and afterwards connect with this predicate its opposite, and hence do not establish any contradiction with the subject, but
only wit'. i its predicate, which 1ms been conjoined with the
? ubject synthetically, --
contradiction, moreover, which ob tains only when the first and second predicate are affirmed in the same time. If say " man who ignorant not
learned," the condition "at the same time" must be added, for he who at one time ignorant, may at another be learned. But say "No ignorant man learned man," the pro position analytical, because the characteristic ignorance now constituent part of the conception of the subject and in this case the negative proposition evident immediately
? ? a if I
is
is
: is
a
by
is
I : A
a
aa
is a
is
; is is, is a
? BTSTEM OT PBnCCIFLES.
117
from the proposition of contradiction, without the necessity of adding the condition " at the same time. " --This is the reason why I have altered the formula of this principle, --an alteration which shows very clearly the nature of an analytical proposition.
TnE System of the Pbincifi-es O1 the Pubs Uhdeb- STAlTDING.
SECTION SECOND.
Of the Supreme Principle of all Synthetical Judgments.
The explanation of the possibility of synthetical judgments is a task with which general Logic has nothing to do ; indeed she needs not even be acquainted with its name. But in trans cendental Logic it is the most important matter to be dealt with, -- indeed the only one, if the question is of the possibility of synthetical judgments a priori, the conditions and extent of their validity. For when this question is fully decided, it can reach its aim with perfect ease, the determination, to wit, of the extent and limits of the pure understanding.
In an analytical judgment I do not go beyond the given conception, in order to arrive at some decision respecting it.
If the judgment is affirmative, I predicate of the conception only that which was already cogitated in it ; if negative, I merely exclude from the conception its contrary. But in syn thetical judgments, I must go beyond the given conception, in order to cogitate, in relation with something quite dif ferent from that which was cogitated in relation which consequently never one either of identity or contradiction, and
means of which the truth or error of the judgment cannot be discerned merely from the judgment itself.
Granted then, that we must go out beyond given concep tion, in order to compare synthetically with another, third thing necessary, in which alone the synthesis of two con ceptions can originate. Now what this tertium quid, that
to be the medium of all synthetical judgments It only complex,* in which all our representations are contained,
? the internal sense to wit, and its form priori, Time*
The synthesis of our representations rests upon the imagi nation their synthetical unity (which requisite to judg
ment), upon the unity of apperception. In this, therefore, u lnbcgriff
? ? a is ;
by is
* it
is
it, a
a
is
a
is
h
is
it,
a t
? AJCALTTIC OF PKIKCIPLKB.
to be sought the possibility of synthetical judgments, and at all three contain the sources of a priori representations, the
possibility of pure synthetical judgments also ; nay, they are necessary upon these grounds, if we are to possess a know ledge of objects, which rests solely upon the synthesis of re presentations.
If a cognition is to have objective reality, that to relate to an object, and possess sense and meaning in respect to
necessary that the object be given in some way or ano ther. Without this, our conceptions are empty, and we may indeed have thought bymeans of them, but such thinking, we have not, in fact, cognized anything, we have merely played with representation. To give an object, this expression be understood in the sense of to present the object, not mediately but immediately in intuition, means nothing else than to apply the representation of to experience, be that experience real or only possible. Space and time themselves, pure as these conceptions are from all that empirical, and certain as
that they are represented fully priori in the mind, would be completely without objective validity, and without sense and significance, their necessary use in the objects of experi ence were not shewn. Nay, the representation of them
mere schema, that always relates to the reproductive imagina tion, which calls up the objects of experience, without which they have no meaning. And so with all conceptions without distinction.
The possibility 'experience then, that which gives objective reality to all our priori cognitions. Now experience depends upon the synthetical unity of phsenomena, that upon synthesis according to conceptions of the object of pheno mena in general, synthesis without which experience never could become knowledge, but would be merely rhapsody of perceptions, never fitting together into any connected text, according to rules of thoroughly united (possible) conscious ness, and therefore never subjected to the transcendental and necessary unity of apperception. Experience has therefore for foundation, priori principles of its form, that to say, general rules of unity in the synthesis of phenomena, the objective reality of which rules, as necessary conditions -- even of the possibility of experience --can always shewn experience. But apart from this relation, prion synthetical
? ? ? 1
if
by
J>e
is,
is,
a
it is
&
a a
if A of
a
is,
it & is
is it
is
in a a is it,
is
it
? AYETEM OF P&INCil'LES. 119
propositions are absolutely impossible, because they have no third term, that no pure object, in which the synthetical
unity can exhibit the objective reality of its conceptions. Although, then, respecting space, or the forms which pro
ductive imagination describes therein, we do cognize much priori in synthetical judgments, and are really in no need
of experience for this purpose, such knowledge would never theless amount to nothing but a busy trifling with mere chimera, were not space to be considered as the condition of the phsenomena which constitute the material of ex ternal experience. Hence those pure synthetical judgments do relate, though but mediately, to possible experience, or rather to the possibility of experience, and upon that alone
founded the objective validity of their synthesis.
While then, on the one hand, experience, as empirical syn thesis, the only possible mode of cognition which gives reality to all other synthesis on the other hand, this latter synthesis, as cognition priori, possesses truth, that ac cordance with its object, only in so far as contains nothing more than what necessary to the synthetical unity of ex perience.
Accordingly, the supreme principle of all synthetical judg ments Every object subject to the necessary conditions of the synthetical unity of the manifold of intuition in possible experience.
A priori synthetical judgments are possible, when we ap ply the formal conditions of the priori intuition, the synthe sis of the imagination, and the necessary unity of that syn thesis in transcendental apperception, to possible cognition of experience, and say The conditions of the possibility of ex perience in general, are at the same time conditions of the pos sibility of the objects of experience, and have, for that reason, objective validity in an priori synthetical judgment.
Mental synthesis. --Jr.
? ? ? a
is :
?
4 is&
:
a
it
d
a
is
is,
is,
a
;*
is is
a
? 120 ASATiTTIC Or PMWCIPLER.
STSTEM O1 THE PRINCIPLES OF THE PrjBB UhDIR- ST>>Nnrso,
SECTION THIRD.
Systematic Representation of all Synthetical Principles thereof.
That principles exist at all is to be ascribed solely to the pure understanding, which is not only the faculty of rules in regard to that which happens, but is even the source of principles ac cording to which every thing that can be presented to us as an object is necessarily subject to rules, because without such rules we never could attain to cognition of an object. Even the laws of nature, if they are contemplated as principles of the empirical use of the understanding, possess also a charac teristic of necessity, and we may therefore at least expect thera to be determined upon grounds which are valid a priori and antecedent to all experience. But all laws of nature, without distinction, are subject to higher principles of the under standing, inasmuch as the former are merely applications of the latter to particular cases of experience. These higher principles alone therefore give the conception, which contains the necessary condition, and, as it were, the exponent of a rule ; experience, on the other hand, gives the case which comes under the rule.
There is no danger of our mistaking merely empirical prin ciples for principles of the pure understanding, or conversely ; for the character of necessity, according to conceptions which distinguishes the latter, and the absence of this in every em pirical proposition, how extensively valid soever it may be, is a perfect safeguard against confounding them. There are, how ever, pure principles a priori, which nevertheless I should not ascribe to the pure understanding -- for this reason, that they are not derived from pure conceptions, but (although by the mediation of the understanding) from pure intuitions. But understanding is the faculty of conceptions. Such principles mathematical science possesses, but their application to ex
? their objective validity, nay the possi bility of such a priori synthetical cognitions (the deduction
thereof) rests entirely upon the pure understanding.
On this uccoint, I shall not reckon among my principl. ?
perience, consequently
? ? ? PRINCIPLES OF PUItE UNDERSTANDING. 121
? . hose of mathematics ; though I shall include those upon the possibility and objective validity a priori, of principles of the mathematical science, which, consequently, are to be looked upon as the principle of these, and which proceed from con ceptions to intuition, and not from intuition to conceptions.
In the application of the pure conceptions of the under standing to possible experience, the employment of their syn thesis is either mathematical or dynamical, for it is directed partly on the intuition alone, partly on the existence of a pheno menon. But the d priori conditions of intuition are in relation
to a possible experience absolutely necessary, those of the ex istence of objects of a possible empirical intuition are in them selves contingent. Hence the principles of the mathematical use of the categories will possess a character of absolute necessity, that will be apodeictic those, on the other hand, of the dynamical use, the character of an priori necessity indeed, but only under the condition of empirical thought in nn experience, therefore only mediately and indirectly. Con sequently they will not possess that immediate evidence which peculiar to the former, although their application to experience does not, for that reason, lose its truth and certitude. But of this point we shall be better able to judge at the conclusion of this system of principles.
The table of the categories naturally our guide to the table of principles, because these are nothing else than rules
? for the objective employment of the former. all principles of the pure understanding are--
Axioms of Intuition.
Accordingly,
3. Analogies
of Experience.
have chosen advisedly, in order that we might not lose sight of the distinctions in respect of tht
2. Anticipations
of Perception.
These appellations
4. Postulates of Empirical Thought in general.
? ? I
1.
is
is
a
is,
;
? 122 TRANSCENDENTAL DOCTRINE.
evidence and the employment of these principles. It will, however, soon nppear that --a fact which concerns bcth the evidence of these principles, and the a priori determination of phenomena -- according to the categories of Quantity and Quality (if we attend merely to the form of these), the prin ciples of these categories are distinguishable from those of the two others, inasmuch as the former are possessed of an intui tive, but the latter of a merely discursive, though in both instances a complete certitude. I shall therefore call the former mathematical,* and the latter dynamical principles. f It must be observed, however, that by these terms I mean,
just as little in the one case the principles of mathematics, as those of general (physical) dynamics, in the other. I have
here in view merely the principles of the pure understanding, in their application to the internal sense, (without distinction of the representations given therein), by means of which the sciences of mathematics and dynamics become possible. Ac cordingly, I have named these principles rather with reference to their application, than their content ; and I shall now pro ceed to consider them in the order in which they stand in the table.
I.
Axioms of Intuition.
The principle of these "All Intuitions are Extensive Quantities. "
Mathematically, in the Kantian sense. -- 7V.
All combination (conjunctio) either composition {composilio) or connection (nexus). The former the synthesis of manifold, the parts of which do not necessarily belong to each other. For example, the two triangles into which square divided by diagonal, do not necessarily belong to each other, and of this kind the synthesis of the homogeneous in every thing that can be mathematically considered. This synthesis can be divided into those of aggregation and coalition, the former of which
applied to extensive, the latter to intensive quantities. The second sort of combination {nexus) the synthesis of manifold, in so far as its parti do belong necessarily to each other for example, the accident to sub stance, or the effect to the causa. Consequently synthesis of that which, though heterogineous, represented as connected, priori. This combination -- not an arbitrary one -- entitle dynamical, because con cerns the connection of the existence of the manifold. This, again, may be divided into the physical synthesis of the phenomena among each other, and the mitaphysical synthesis, or the connection of phenomena a priori in the faculty of cognition.
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;
is
I
a
is is
a
it a
is
is
t*
it
is a a
a
a
is
is,
? AXIOMS Of INTUITIOIC. 123
Pboof.
All phenomena contain, as regards their form, an intuition in space and time, which lies a priori at the foundation of all with out exception. Phenomena, therefore, cannot be apprehended, that received into empirical consciousness otherwise than through the synthesis of manifold, through which the repre sentations of determinate space or time are generated that
to say, through the composition
the consciousness of the synthetical unity of this manifold
(homogeneous). Now the consciousness of homogeneous manifold in intuition, so far as thereby the representation of an object rendered possible, the conception of quan tity (quanti). Consequently, even the perception of an object as phsenomenon possible only through the same synthetical unity of the manifold of the given sensuous intuition, through which the unity of the composition of the homogeneous mani fold the conception of quantity cogitated that to
say, all phenomena are quantities, and extensive quantities, because as intuitions in space or time, they must be repre sented by means of the same synthesis, through which space and time themselves are determined.
An extensive quantity call that wherein the representa tion of the parts renders possible (and therefore necessarily antecedes) the representation of the whole. cannot repre sent to myself any line, however small, without drawing in thought, that is, without generating from point all its parts one after another, and in this way alone producing this intui tion. Precisely the same the case with every, even the smallest portion of time. cogitate therein only the succes sive progress from one moment to another, and hence, by means of the different portions of time and the addition of them, determinate quantity of time produced. As the pure intuition in all phenomena either time or space, so every phenomenon in its character of intuition an extensive
? inasmuch as can only be cognized in our appre hension by successive synthesis (from part to part). All phenomena are, accordingly, to be considered as aggregates, that as collection of previously given parts which not the case with every sort of quantities, but only with those
which are represented and apprehended by us as extensive.
quantity,
? ? is,a in a
is
is,
;
a
I
a
is
is
it
is
it
I is is
I
in
a
is
is is
a
;
is a is
a
;
? 124 TRAXSCEWDKJTTAL DOCTBITTE.
On this successive synthesis of the productive imagination, in the generation of figures, is founded the mathematics of extension, or geometry, with its axioms, which express the conditions of sensuous intuition a priori, under which alone the schema of a pure conception of external intuition can exist ; for example, " between two points only one straight line is possible," " two straight lines cannot enclose a space," &c. These are the axioms which properly relate only to quantities (quanta) as such.
But, as regards the quantity of a thing (quantitas), that is to say, the answer to the question, How large is this or that object ? although, in respect to this question, we have vari ous propositions synthetical and immediately certain (inde- monstrabilia) ; we have, in the proper sense of the term, no axioms. For example, the propositions, " If equals be added to equals, the wholes are equal ;" " If equals be taken from equals, the remainders are equal ;" are analytical, because I am immediately conscious of the identity of the produc tion of the one quantity with the production of the other ; whereas axioms must be h priori synthetical propositions. On the other hand, the self-evident propositions as to the relation of numbers, are certainly synthetical, but not uni versal, like those of geometry, and for this reason cannot be called axioms, but numerical formula? . That 7+5 = 12, is not an analytical proposition. For neither in the represen tation of seven, nor of five, nor of the composition of the two numbers, do I cogitate the number twelve. (Whether I cogitate the number in the addition of both, is not at present the ques tion ; for in the case of an analytical proposition, the only point whether really cogitate the predicate in the repre sentation of the subject. ) But although the proposition synthetical, nevertheless only singular proposition. In so far as regard here had merely to the synthesis of the homogeneous (the units), cannot take place except in onn manner, although our use of these numbers afterwards ge neral. If say, " triangle can be constructed with three lines, any two of which taken together are greater than the third," exercise merely the pure function of the productive imagination, which may draw the lines longer or shorter, and construct the angles at its pleasure. On the contrary, the number seven possible only in one manner, and so like
? ? ? is
it is
is
I
I
is,
I A
is
is it
a
is
? ANTICIPATIONS OF PERCEPTION. 123
wise the number twelve, which results from the synthesis of seven and five. Such propositions, then, cannot be termed axioms (for in that case we should have an infinity of these), but numerical formule.
This transcendental principle of the mathematics of phe nomena greatly enlarges our & priori cognition. For it is by this principle alone that pure mathematics is rendered appli cable in all its precision to objects of experience, and without it the validity of this application would not be so self-evident ; on the contrary, contradictions and confusions have often arisen on this very point. Phenomena are not things in themselves. Empirical intuition is possible only through pure intuition
(of space and time) ; consequently, what geometry affirms of the latter, is indisputably valid of the former. All evasions, such as the statement that objects of sense do not conform to the rules of construction in space (for example, to the rule of the infinite divisibility of lines or angles), must fall to the ground.
For, if these objections hold good, we deny to space, and with it to all mathematics, objective validity, and no longer know wherefore, and how far, mathematics cnn be applied to phe nomena. The synthesis of spaces and times as the essential form of all intuition, is that which renders possible the appre hension of a phenomenon, and therefore every external expe rience, consequently all cognition of the objects of experience ; and whatever mathematics in its pure use proves of the former, must necessarily hold good of the latter. All objections are but the chicaneries of an ill-instructed reason, which errone ously thinks to liberate the objects of sense from the formal
conditions of our sensibility, and represents these, although mere phenomena, as things in themselves, presented as such to our understandings. But in this case, no a prion syn thetical cognition of them could be possible, consequently not through pure conceptions of space, and the science which
determines these conceptions, that is to say, geometry, would
itself be impossible.
II. Anticipations of Perception.
The principle of these is, "In all phamomena the Real, thai tvnich is an object of sensation, has Intensive Quantity, that has
Degree. "
? ? ? a
is,
? TKANSCEWBENTAL DOCTMKE.
Proof.
Perception is empirical consciousness, that is to say, u con
sciousness, which contains an element of sensation. Phsenomena
as objects of perception are not pure, that merely formal in tuitions, like space and time, for they cannot be perceived in themselves. * They contain, then, over and above the intui tion, the materials for an object (through which represented something existing in space or time), that to say, they con tain the real of sensation, as representation merely subjec tive, which gives us merely the consciousness that the subject
affected, and which we refer to some external object. Now, gradual transition from empirical consciousness to pure con
sciousness possible, inasmuch as the real in this conscious ness entirely evanishes, and there remains merely formal consciousness priori) of the manifold in time and space consequently there possible synthesis also of the production of the quantity of sensation from its commencement, that from the pure intuition = onwards, up to certain quantity of the sensation. Now as sensation in itself not an objective
? and in to be found neither the intuition of space nor of time, cannot possess any extensive quantity, and yet there does belong to quantity (and that means of its
apprehension, in which empirical consciousne*is can within certain time rise from nothing = up to its given amount), consequently an intensive quantity. And thus we must ascribe intensive quantity, that degree of influence on sense to all objects of perception, in so far as this perception contains sensation.
All cognition, by means of which am enabled to cognize and determine a priori what belongs to empirical cognition, may be called an Anticipation and without doubt this the sense in which Epicurus employed his expression vpoy. ^i;. But as there in phsenomena something which never cog nized priori, which on this account constitutes the proper difference between pure and empirical cognition, that to say, sensation (as the matter of perception), follows, that
sensation just that element in cognition which cannot be at
They can be perceived only as phsenomena, and some part of them
must always belong to the non-ego whereas pure intuitions are entirely the orodncts of the mind itself, and as such arc cognized in thenuehn. -- Tr
representation,
? ? ;
;
a
*
h
is
is
is (a
it
is
by
is
is
I
0
is, a
it a
it is
0
a
a
is,
;
it
a is
is a
a
is is, is
a is
? disappear.
ANTICIPATIONS OP PKBCEPTIOJT.
127
? 11 anticipated. On the other hand, we might very well term the pure determinations in space and time, as well in regard to figure as to Quantity, anticipations of phenomena, because they represent a priori that which may always be given a pos teriori in experience. But suppose that in every sensation, as sensation in general, without any particular sensation being thought of, there existed something which could be cognized a priori, this would deserve to be called anticipation in a special sense --special, because it may seem surprising to forestall experience, in that which concerns the matter of experience, and which we can only derive from itself. Yet such really is the case here.
Apprehension,* by means of sensation alone, fills only one moment, that do not take into consideration succes sion of many sensations. As that in the phenomenon, the apprehension of which not successive synthesis advancing from parts to an entire representation, sensation has therefore no extensive quantity the want of sensation in moment of time would represent as empty, consequently = 0. That which in the empirical intuition corresponds to sensation rea
? lity (real as phenomenon) absence of negation = 0. of diminution, so that
that which corresponds to the
Now every sensation capable can decrease, and thus gradually
Therefore, between reality phenomenon and negation, there exists continuous concatenation of many pos sible intermediate sensations, the difference of which from each other always smaller than that between the given sen sation and zero, or complete negation. ' That to say, the realiia phenomenon has always quantity, which however not discoverable in Apprehension, inasmuch as Apprehension takes place means of mere sensation in one instant, and not the successive synthesis of many sensations, and there fore does not progress from parts to the whole.
has quantity, but not an extensive quantity.
Now that quantity which apprehended only as unity, and in which plurality can be represented only by approximation
to negation = term intensive quantity. Consequently, rea lity in phenomenon has intensive quantity, that degree,
Apprehension tbs Kantian word for perception, in the largest ? cast in which we employ that term. the genus which includes under
M species, perception proper and sensation proper. -- Tr.
Consequently,
? ? It is
is
it
;
is a
ii
is
*
a
it a
a
is
0, I
is,
is, a
is
a
is a
by by
is
it it,
a
a
it ;
in a
is
if 1
? 128 TRANSCENDENTAL iJOCTltlNX.
If we consider tins reality as cause (be it of sensation or of another reality in the phenomenon, for example, a change) ;
we call the degree of reality in its character of cause a momen tum, for example, the momentum of weight; and for this reason, that the degree only indicates that quantity the appre hension of which is not successive, but instantaneous. This, however, I touch upon only in passing, for with Causality I have at present nothing to do.
Accordingly, every sensation, consequently every reality in phenomena, however small it may be, has a degree, that is, an intensive quautity, which may always be lessened, and between reality and negation there exists a continuous connection of possible realities, and possible smaller perceptions. Every colour -- for example, red -- has a degree, which, be it ever so small, is never the smallest, and so is it always with heat, the momentum of weight, &c.
This property of quantities, according to which no part of them is the smallest possible (no part simple*), is called their continuity. Space and time are quanta continua, because no part of them can be given, without enclosing it within bound aries (points and moments), consequently, this given part is itself a space or a time. Space, therefore, consists only of spaces, and time of times. Points and moments are only boundaries, that the mere places or positions of their limi tation. But places always presuppose intuitions which are to limit or determine them and we cannot conceive either space or time composed of constituent parts which are given
before space or time. Such quantities may also be called flowing, because the synthesis (of the productive imagination) in the production of these Quantities progression in time, the continuity of which we are accustomed to indicate the
expression flowing.
All phenomena, then, are continuous quantities, in respect
both to intuition and mere perception (sensation, and with
In the former case they are extensive quanti ties in the latter, intensive. When the synthesis of the manifold of phenomenon interrupted, there results merely an aggregate of several phenomena, and not properly phe- nomenon as quantity, which not produced by the mere continuation of the productive synthesis of certain kind, bul
Simplex. -- 7V.
? reality).
? ? a
a
a
*
is
;
is
a
by
it ;
is a
is,
? AjrTicii'vrioxs or fekception. 129
by the repetition of a synthesis always ceasing. For example, if I call thirteen dollars a sum or quantity of money, 1 employ the term quite correctly, inasmuch as I understand by thirteen dollars the value of a mark in standard silver, which to be sure, continuous quantity, in which no part the smallest, but every part might constitute piece of money, which would contain material for still smaller pieces. If, however, the words thirteen dollars understand so many coins (be their value in silver what may), would be quite erroneous to use the expression quantity of dollars on the contrary, must call them aggregate, that number of coins. And as in every number we must have unity as the foundation, so phenomenon taken as unity quantity, and as such always
continuous quantity (quantum continuum).
Now, seeing all phsenomena, whether considered as extensive
or intensive, are continuous quantities, the proposition, "All change (transition of thing from one >>tate into another) con tinuous," might be proved here easily, and with mathematical evidence, were not that the causality of change lies entirely beyond the bounds of transcendental philosophy, and presup
poses empirical principles. For of the possibility of cause which changes the condition of things, that which de termines them to the contrary of certain given state, the under standing gives us priori no knowledge; not merely because has no insight into the possibility of (for such insight ab sent in several priori cognitions), but because the notion of change concerns only certain determinations of phenomena, which experience alone can acquaint us with, while their cause lies in the unchangeable. But seeing that we have
nothing which we could here employ but the pure funda mental conceptions of all possible experience, among which of course nothing empirical can be admitted, we dare not, without injuring the unity of our system, anticipate general physical science, which built upon certain fundamental
experiences.
Nevertheless, we are in no want of proofs of the great in
fluence which the principle above developed exercises in the anticipation of perceptions, and even in supplying the want of them, so far as to shield us against the false conclusions which otherwise we might rashly draw.
all reality in perception has degree, between which ai. d x
? ? ? If
a
is
& it &
a
aa it
a
a
it I
it
a ais,a
is,
is
a
;
a
is
is, by
is
it aI
a
is
? 130 THANSCENDENTAi DOCTIlUiE.
negation there is an endless sequence of ever . smaller degree*, and if nevertheless every sense must have a determinate degree of receptivity for sensations ; no perception, and consequently no experience is possible, which can prove, either immediately
or mediately, an entire absence of all reality in a phenomenon ; in other words, it is impossible ever to draw from experience a proof of the existence of empty space or of empty time. For in the first place, an entire absence of reality in a sensuous intuition cannot of course be an object of perception ; secondly, such absence cannot be deduced from the contemplation of any single . phenomenon, and the difference of the degrees in its reality ; nor ought it ever to be admitted in explanation of any phenomenon. For if even the complete intuition of a determinate space or time is thoroughly real, that no part thereof empty, yet because every reality has its degree, which, with the extensive quantity of the phenomenon un changed, can diminish through endless gradations down to nothing (the void), there must be infinitely graduated degrees, with which space or time filled, and the intensive quantity in different phenomena may be smaller or greater, although the ex tensive quantity of the intuition remains equal and unaltered.
We shall give an example of this. Almost all natural philo
sophers, remarking great difference in the quantity of the matter of different kinds in bodies with the same volume (partly on account of the momentum of gravity or weight, partly on account of the momentum of resistance to other bodies in motion), conclude unanimously, that this volume (extensive quantity of the phenomenon) must be void in all bodies, although in different proportion. But who would sus pect that these for the most part mathematical and mechanical inquirers into nature should ground this conclusion solely on metaphysical hypothesis -- sort of hypothesis which they profess to disparage and avoid Yet this they do, in assuming that the real in space must not here call impenetrability or weight, because these are empirical conceptions) always iden tical, and can only be distinguished according to its extensivo quantity, that is, multiplicity. Now to this presupposition, Air which they can have no ground in experience, and which conse
? quently merely metaphysical, oppose
transcendental de-
* It should be remembered that Kant means by matter, that which in the object corresponds to sensation the subject--the real in pheno menon. -- V.
? ? 2
a
is * is
in
I
a
a
is, if
a
is
it
(I
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a
is
? ANTICIPATIONS OF PERCEPTION. 1. 31
monstration, which it is true will not explain the difference in the filling up of spaces, but which nevertheless completely does away with the supposed necessity of the above-mentioned pre supposition that we cannot explain the said difference otherwise than by the hypothesis of empty spaces. This demonstration, moreover, has the merit of setting the understanding at liberty to conceive this distinction in a different manner, if the explanation of the fact requires any such hypothesis. For we perceive that although two equal spaces may be completely filled by matters altogether different, so that in neither of them is there left a single point wherein matter is not present, nevertheless, every reality has its degree (of resistance or of weight), which, without diminution of the extensive quantity, can become less and less ad infinitum, before it passes into nothingness and disappears. Thus an expansion which fills a space -- for example, caloric, or any other reality in the phsenomenal world -- can decrease in its degrees to infinity, yet without leaving the smallest part of the space empty ; on the contrary, filling it with those lesser degrees, as completely as another phenomenon could with greater. My intention here is by no means to maintain that this is really the case with the difference of matters, in regard
I wish
ciple of the pure understanding, that the nature of our per
ceptions makes such a mode of explanation possible, and that it is erroneous to regard the real in a phsenomenon as equal quoad its degree, and different only quoad its aggregation and extensive quantity, and this, too, on the pretended authority of an a priori principle of the understanding.
Nevertheless, this principle of the anticipation of perception must somewhat startle an enquirer whom initiation into tran scendental philosophy has rendered cautious. We may natu rally entertain some doubt whether or not the understanding can enounce any such synthetical proposition as that respecting the degree of all reality in phsenomena, and consequently--the possibility of the internal difference of sensation itself ab straction being made of its empirical quality. Thus it is a question not unworthy of solution : How the understanding can pronounce synthetically and & priori respecting pheno-
mena, and thus anticipate these, even in that which is pecu liarly and merely empirical, that, namely, which concerns sen
? to their specific gravity ;
only
to
prove,
from a
prin
sation itself?
x2
? ? ? 132 TRANSCENDENTAL TOl. TltlNE.
The quality of sensation is in all cases n. erely empirical, and cannot be represented a priori (for example, colours, taste, &c). But the real -- that which corresponds to sensation -- iu opposition to negation=0, only represents something the conception of which in itself contains a being (ein seyn), and signifies nothing but the synthesis in an empirical con sciousness. That is to say, the empirical consciousness in the internal sense can be raised from 0 to every higher degree, so that the very same extensive quantity of intuition, an illuminated surface, for example, excites as great a sen sation as an aggregate of many other surfaces less illumi nated. We can therefore make complete abstraction of the extensive quantity of a phenomenon, and represent to our selves in the mere sensation in a certain momentum,* a syn thesis of homogeneous ascension from 0 up to the given empirical consciousness. All sensations therefore as such are given only d posteriori, but this property thereof, namely,
that they have a degree, can be known a priori. It is worthy of remark, that in respect to quantities in general, we can cognize a priori only a single quality, namely, continuity ; but in respect to all quality (the real in phenomena), we cannot cognize d priori any thing more than the intensive quantity thereof, namely, that they have a degree. All else is left to experience.
III.
ANALOGIES OF EXPERLENCB.
The principle of these is : Experience is possible only through the representation of a necessary connection of per
? ceptions.
Proof.
Experience is an empirical cognition ; that is to say, a cognition which determines an object by means of perceptions. It is therefore a synthesis of perceptions, a synthesis which is not itself contained in perception, but which contains the synthetical unity of the manifold of perception in a consci-
? The particular degree of " reality," that is, the particular power oi nlensive quantity in the cauie of a sensation, for example, redness, weight, Ac, is called in the Kantian terminology, Us moment. The term momentum which we employ, must not he confounded with the word com "conly employed ic :atural science. -- Ti.
? ? ? AXALOGIES OP EXPEllIEKCJt. 133
ousness ; and this unity constitutes the essential of our cog
nition of objects of the senses, that of experience merely of intuition or sensation). Now in experience our perceptions come together contingently, so that no character of necessity in their connexion appears, or can appear from the perceptions themselves, because apprehension only placing together of the manifold of empirical intuition, and no representation of necessity the connected existence of the phenomena which apprehension brings together, to be discovered therein. But as experience cognition of objects means of perceptions, follows that the relation of the existence of the manifold must be represented in expe rience not as put together time, but as objectively
time. And as time itself cannot be perceived, the determina tion of the existence of objects in time can only take place ny means of their connexion in time in general, consequently ouly means of priori connecting conceptions. Now as these conceptions always possess the character of necessity, experience possible only by means of representation of the necessary connexion of perception.
The three modi of time are permanence, succession, and co existence. Accordingly, there are three rules of all relations of time in phenomena, according to which the existence of every phenomenon determined in re-pect of the unity of all time, and these antecede all experience, and render possible.
The general principle of all three analogies rests on the necessary unity of apperception in relation to all possible empirical consciousness (perception) at every time, conse quently, as this unity lies priori at the foundation of all mental operations, the principle rests on the synthetical unity of all phenomena according to their relation in time. For the original apperception relates to our internal sense (the com plex of all representations), and indeed relates priori to its form, that to say, the relation of the manifold empirical consciousness in time. Now this manifold must be combined in original apperception according to relations of time, --
the a priori transcendental unity of ap perception, to which subjected all that can belong to my
e. my own) cognition, and therefore all that can become *n object for me. This synthetical and priori determine*?
necessity imposed
(not
? ? ? ii
a
is
(i.
in
by is
is a
a
is
it
il
it
&
by is
by
is a
is it a
in
it
in
a is
is
is,
? 134
7BAKS0IKDETITA1 DOOTBIJ'E.
unity in relntion of perceptions in time is therefore the rule : " All empirical determinations of time must be subject to rules of the general determination of time ;" and the analogies of experience, of which we are now about to treat, must be rules of this nature.
These principles have this peculiarity, that they do not concern phenomena, aid the synthesis of the empirical in tuition thereof, but merely the existence of phenomena and their relation to each other in regard to this existence. Now the
mode in which we apprehend a thing in a phenomenon can be determined a priori in such a manner, that the rule of its
? synthesis can give, that is to say, can produce this a priori intuition in every empirical example. But the existence of phe nomena cannot be known a priori, and although we could arrive by this path at a conclusion of the fact of some existence, we could not cognize that existence determiuately, that is to say, we should be incapable of anticipating in what respect the empirical intuition of it would be distinguishable from that of others.
The two principles above mentioned, which I called mathe matical, in consideration of the fact of their authorizing the application of mathematic to phenomena, relate to these phenomena only in regard to their possibility, and instruct us how phenomena, as far as regards their intuition or the real in their perception, can be generated according to the rules of a mathematical synthesis. Consequently, numerical quan tities, and with them the determination of a phenomenon as a quantity, can be employed in the one case as well as in the other. Thus, for example, out of 200,000 illuminations by the moon, I might compose, and give a priori, that is con struct, the degree of our sensations of the "in-light. * We may therefore entitle these two principles constitutive.
The case is very different with those principles whose pro vince it is to subject the existence of phenomena to rules a priori. For as existence does not admit of being con-
? Kant's meaning is : The two principles enunciated under the heads of " Aiioms of Intuition," and " Anticipations of Perception," authorize the application to phamacnena of determinations of size and number, that is, of mathematic. For example, I may compute the light of the sun, and say, that its quantity is a certain number of times greater than that of the moon. In the same way, heat is measured by the comparison of its dif
ferent effects on water, *c, and on mercury in a thermometer. -- 7V.
? ? ? ANALOGIES OF EXPEBIENCE. 13. 1
st. ucted, it is clear that they must only concern the relations of existence, and be merely regulative principles. In this case, therefore, neither axioms nor anticipations are to be thought of. Thus, if a perceptkin is given us, in a certain relation 01 time to other (although undetermined) perceptions, we can not then say a priori, what and how great (in quantity) the other perception necessarily connected with the for mer but only how connected, quoad its existence, in
Analogies in philosophy mean something very different from that which they represent in mathematics. In the latter they are formule, which enounce
the equality of two relations of quantity,* and are always constitutive, so that two terms of the proportion are given, the third also given, that can be constructed the aid of these formule. But in philosophy, analogy not the equality of two quantitative but of two qualitative relations. In this case, from three given terms, can give a priori and cognize the relation to fourth member, but not this fourth term itself, although certainly possess rule to guide me in the search for this fourth term in experience, and mark to assist me in discovering it. An analogy of experience therefore only rule according to which unity of experience must arise out of perceptions in respect to objects (pheno mena) not as constitutive, but merely as regulative principle. The same holds good also of the postulates of empirical thought
general, which relate to the synthesis of mere intuition (which concerns the form of phsenomena), the synthesis of per ception (which concerns the matter of phsenomena), and the synthesis of experience (which concerns the relation of these
? For they are only regulative principles, and clearly distinguishable from the mathematical, which are con
perceptions).
stitutive, not indeed in regard to the certainty which both
Known the two terms and and the relation of to not only the relation of to some other number given, but that number itself, 12, given, that constructed. Therefore 3:6=6: 12. -- TV.
Given known effect, known cause, and another known effect, we reason, by analogy, to an unknown cause, which we do not cognize, but ? hose relation to the known effect we know from the comparison of the
Thus, our own known actions our own known motives -= the known actions of others x, that the inotivrs of others
three given terms.
which we cannot immediately cognize. -- TV.
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? lIUNsCKItDKNTAL TWICTRrRK.
possess & priori, but in the mode of evidence thereof, conse quently also in the manner of demonstration.
But what has been observed of all synthetical propositions, and must be particularly remarked in this place, is this, that these analogies possess significance and validity, not as principles of the transcendental, but only as principles of the empirical use of the understanding, and their truth can therefore be proved only as such, and that consequently
the phenomena must not be subjoined directly under the categories, but only under their schemata. For if the objects to which those principles must be applied were things in themselves, it would be quite impossible to cognize aught con cerning them synthetically h priori. But they are nothing but phcenomena ; a complete knowledge of which -- a know ledge to which all principles a priori must at last relate --is the only possible experience. It follows that these principles can have nothing else for their aim, than the conditions of the unity of empirical cognition in the synthesis of plienomena. But this synthesis is cogitated only in the schema of the pure conception of the understanding, of whose unity, as that of a synthesis in general, the category contains the function unre stricted by any sensuous condition. These principles will therefore authorize us to connect phsenomena according to an analogy, with the logical and universal unity of conceptions, and consequently to employ the categories in the principles them selves ; but in the application of them to experience, we shall use only their schemata, as the key to their proper application, instead of the categories, or rather the latter as restricting conditions, under the title of formulce of the former.
A.
FIRST ANALOOY.
PBIKCIFLX OF THE PEBMAKEXCE OF STTBSTAWCE.
In all changes of phcenomena, substance is permanent, and the quantum thereof in nature is neither increased nor dimi nished.
Pboof.
But we shall have also to speak of the principle of analy tical judgments, in opposition to synthetical judgments, which is the proper subject of our enquiries, because this very oppo
? ? ? ? SYSTEM O1 PRINCIPLES. 113
<<ition will free the theory of the latter from nll ambiguity, ami place it clearly before our eyes in its true nature.
Ststem of the Principled or the Pure Under standing.
SECTION FIRST.
Of the Supreme Principle of all Analytical Judgments.
Whatever may be the content of our cognition, and in whatever manner our cognition may be related to its object, the universal, although only negative condition of all our judgments is that they do not contradict themselves ; other wise these judgments are in themselves (even without respect to the object) nothing. But although there may exist no contradiction in our judgment, it may nevertheless connect conceptions in such a manner, that they do not correspond to the object, or without any grounds either a priori or a pos teriori for arriving at such a judgment, and thus, without being self-contradictory, a judgment may nevertheless be either false or groundless. "
Now, the proposition, No subject can have a predicate that contradicts it," is called the principle of contradiction, and is an universal but purely negative criterion of all truth. But it belongs to logic alone, because it is valid of cognitions, merely as cognitions, and without respect to their content, and declares that the contradiction entirely nullifies them. We can also, however, make a positive use of this princi ple, that not merely to banish falsehood and error (in bo far as rests upon contradiction), but also for the cog nition of truth. For the judgment analytical, be affirmative or negative, its truth must always be recognizable
means of the principle of contradiction. For the contrary of that which lies and cogitated as conception in the cogni tion of the object will be always properly negatived, but the conception itself must always be affirmed of the object, inas much as the contrary thereof would be in contradiction to the object.
We must therefore hold the principle contradiction to be the universal and fully sufficient principle all analytical tocnitiox. But as sufficient criterion of truth, has no further
? ? ? a
it is, is
of I it of
is
2
by
if
it
? 116 ANALYTIC Of 1'BINCIPLES.
utility or authority. For the fact that no cognition can be at variance with this principle without nullifying itself, consti tutes this principle the sine qua non, but not the determining ground of the truth of our cognition. As our business at present is properly with the synthetical part of our knowledge only, we shall always be on our guard not to transgress this inviolable principle ; but at the same time not to expect from it any direct assistance in the establishment of the truth of any synthetical proposition.
There exists, however, a formula of this celebrated principle --a principle merely formal and entirely without content -- which contains a synthesis that has been inadvertently and quite unnecessarily mixed up with it. It is this : -- " It is impossible for a thing to be and not to be at the same time. " Not to mention the superfluousness of the addition of the word impossible to indicate the apodeictic certainty, which ought to be self-evident from the proposition itself, the propo sition is affected by the condition of time, and as it were says :
? " A thing-- A, which is something=J? , cannot at the same time be non-B. " But both, B as well as non-B, may quite well exist in succession. For example, a man who is young cannot at the same time be old ; but the same man can very well be at one time young, and at another not young, that old. Now the principle of contradiction as merely logical propo sition must not any means limit its application merely to relations of time, and consequently formula like the pre ceding quite foreign to its true purpose. The misunder standing arises in this way. We first of all separate predicate of thing from the conception of the tiling, and afterwards connect with this predicate its opposite, and hence do not establish any contradiction with the subject, but
only wit'. i its predicate, which 1ms been conjoined with the
? ubject synthetically, --
contradiction, moreover, which ob tains only when the first and second predicate are affirmed in the same time. If say " man who ignorant not
learned," the condition "at the same time" must be added, for he who at one time ignorant, may at another be learned. But say "No ignorant man learned man," the pro position analytical, because the characteristic ignorance now constituent part of the conception of the subject and in this case the negative proposition evident immediately
? ? a if I
is
is
: is
a
by
is
I : A
a
aa
is a
is
; is is, is a
? BTSTEM OT PBnCCIFLES.
117
from the proposition of contradiction, without the necessity of adding the condition " at the same time. " --This is the reason why I have altered the formula of this principle, --an alteration which shows very clearly the nature of an analytical proposition.
TnE System of the Pbincifi-es O1 the Pubs Uhdeb- STAlTDING.
SECTION SECOND.
Of the Supreme Principle of all Synthetical Judgments.
The explanation of the possibility of synthetical judgments is a task with which general Logic has nothing to do ; indeed she needs not even be acquainted with its name. But in trans cendental Logic it is the most important matter to be dealt with, -- indeed the only one, if the question is of the possibility of synthetical judgments a priori, the conditions and extent of their validity. For when this question is fully decided, it can reach its aim with perfect ease, the determination, to wit, of the extent and limits of the pure understanding.
In an analytical judgment I do not go beyond the given conception, in order to arrive at some decision respecting it.
If the judgment is affirmative, I predicate of the conception only that which was already cogitated in it ; if negative, I merely exclude from the conception its contrary. But in syn thetical judgments, I must go beyond the given conception, in order to cogitate, in relation with something quite dif ferent from that which was cogitated in relation which consequently never one either of identity or contradiction, and
means of which the truth or error of the judgment cannot be discerned merely from the judgment itself.
Granted then, that we must go out beyond given concep tion, in order to compare synthetically with another, third thing necessary, in which alone the synthesis of two con ceptions can originate. Now what this tertium quid, that
to be the medium of all synthetical judgments It only complex,* in which all our representations are contained,
? the internal sense to wit, and its form priori, Time*
The synthesis of our representations rests upon the imagi nation their synthetical unity (which requisite to judg
ment), upon the unity of apperception. In this, therefore, u lnbcgriff
? ? a is ;
by is
* it
is
it, a
a
is
a
is
h
is
it,
a t
? AJCALTTIC OF PKIKCIPLKB.
to be sought the possibility of synthetical judgments, and at all three contain the sources of a priori representations, the
possibility of pure synthetical judgments also ; nay, they are necessary upon these grounds, if we are to possess a know ledge of objects, which rests solely upon the synthesis of re presentations.
If a cognition is to have objective reality, that to relate to an object, and possess sense and meaning in respect to
necessary that the object be given in some way or ano ther. Without this, our conceptions are empty, and we may indeed have thought bymeans of them, but such thinking, we have not, in fact, cognized anything, we have merely played with representation. To give an object, this expression be understood in the sense of to present the object, not mediately but immediately in intuition, means nothing else than to apply the representation of to experience, be that experience real or only possible. Space and time themselves, pure as these conceptions are from all that empirical, and certain as
that they are represented fully priori in the mind, would be completely without objective validity, and without sense and significance, their necessary use in the objects of experi ence were not shewn. Nay, the representation of them
mere schema, that always relates to the reproductive imagina tion, which calls up the objects of experience, without which they have no meaning. And so with all conceptions without distinction.
The possibility 'experience then, that which gives objective reality to all our priori cognitions. Now experience depends upon the synthetical unity of phsenomena, that upon synthesis according to conceptions of the object of pheno mena in general, synthesis without which experience never could become knowledge, but would be merely rhapsody of perceptions, never fitting together into any connected text, according to rules of thoroughly united (possible) conscious ness, and therefore never subjected to the transcendental and necessary unity of apperception. Experience has therefore for foundation, priori principles of its form, that to say, general rules of unity in the synthesis of phenomena, the objective reality of which rules, as necessary conditions -- even of the possibility of experience --can always shewn experience. But apart from this relation, prion synthetical
? ? ? 1
if
by
J>e
is,
is,
a
it is
&
a a
if A of
a
is,
it & is
is it
is
in a a is it,
is
it
? AYETEM OF P&INCil'LES. 119
propositions are absolutely impossible, because they have no third term, that no pure object, in which the synthetical
unity can exhibit the objective reality of its conceptions. Although, then, respecting space, or the forms which pro
ductive imagination describes therein, we do cognize much priori in synthetical judgments, and are really in no need
of experience for this purpose, such knowledge would never theless amount to nothing but a busy trifling with mere chimera, were not space to be considered as the condition of the phsenomena which constitute the material of ex ternal experience. Hence those pure synthetical judgments do relate, though but mediately, to possible experience, or rather to the possibility of experience, and upon that alone
founded the objective validity of their synthesis.
While then, on the one hand, experience, as empirical syn thesis, the only possible mode of cognition which gives reality to all other synthesis on the other hand, this latter synthesis, as cognition priori, possesses truth, that ac cordance with its object, only in so far as contains nothing more than what necessary to the synthetical unity of ex perience.
Accordingly, the supreme principle of all synthetical judg ments Every object subject to the necessary conditions of the synthetical unity of the manifold of intuition in possible experience.
A priori synthetical judgments are possible, when we ap ply the formal conditions of the priori intuition, the synthe sis of the imagination, and the necessary unity of that syn thesis in transcendental apperception, to possible cognition of experience, and say The conditions of the possibility of ex perience in general, are at the same time conditions of the pos sibility of the objects of experience, and have, for that reason, objective validity in an priori synthetical judgment.
Mental synthesis. --Jr.
? ? ? a
is :
?
4 is&
:
a
it
d
a
is
is,
is,
a
;*
is is
a
? 120 ASATiTTIC Or PMWCIPLER.
STSTEM O1 THE PRINCIPLES OF THE PrjBB UhDIR- ST>>Nnrso,
SECTION THIRD.
Systematic Representation of all Synthetical Principles thereof.
That principles exist at all is to be ascribed solely to the pure understanding, which is not only the faculty of rules in regard to that which happens, but is even the source of principles ac cording to which every thing that can be presented to us as an object is necessarily subject to rules, because without such rules we never could attain to cognition of an object. Even the laws of nature, if they are contemplated as principles of the empirical use of the understanding, possess also a charac teristic of necessity, and we may therefore at least expect thera to be determined upon grounds which are valid a priori and antecedent to all experience. But all laws of nature, without distinction, are subject to higher principles of the under standing, inasmuch as the former are merely applications of the latter to particular cases of experience. These higher principles alone therefore give the conception, which contains the necessary condition, and, as it were, the exponent of a rule ; experience, on the other hand, gives the case which comes under the rule.
There is no danger of our mistaking merely empirical prin ciples for principles of the pure understanding, or conversely ; for the character of necessity, according to conceptions which distinguishes the latter, and the absence of this in every em pirical proposition, how extensively valid soever it may be, is a perfect safeguard against confounding them. There are, how ever, pure principles a priori, which nevertheless I should not ascribe to the pure understanding -- for this reason, that they are not derived from pure conceptions, but (although by the mediation of the understanding) from pure intuitions. But understanding is the faculty of conceptions. Such principles mathematical science possesses, but their application to ex
? their objective validity, nay the possi bility of such a priori synthetical cognitions (the deduction
thereof) rests entirely upon the pure understanding.
On this uccoint, I shall not reckon among my principl. ?
perience, consequently
? ? ? PRINCIPLES OF PUItE UNDERSTANDING. 121
? . hose of mathematics ; though I shall include those upon the possibility and objective validity a priori, of principles of the mathematical science, which, consequently, are to be looked upon as the principle of these, and which proceed from con ceptions to intuition, and not from intuition to conceptions.
In the application of the pure conceptions of the under standing to possible experience, the employment of their syn thesis is either mathematical or dynamical, for it is directed partly on the intuition alone, partly on the existence of a pheno menon. But the d priori conditions of intuition are in relation
to a possible experience absolutely necessary, those of the ex istence of objects of a possible empirical intuition are in them selves contingent. Hence the principles of the mathematical use of the categories will possess a character of absolute necessity, that will be apodeictic those, on the other hand, of the dynamical use, the character of an priori necessity indeed, but only under the condition of empirical thought in nn experience, therefore only mediately and indirectly. Con sequently they will not possess that immediate evidence which peculiar to the former, although their application to experience does not, for that reason, lose its truth and certitude. But of this point we shall be better able to judge at the conclusion of this system of principles.
The table of the categories naturally our guide to the table of principles, because these are nothing else than rules
? for the objective employment of the former. all principles of the pure understanding are--
Axioms of Intuition.
Accordingly,
3. Analogies
of Experience.
have chosen advisedly, in order that we might not lose sight of the distinctions in respect of tht
2. Anticipations
of Perception.
These appellations
4. Postulates of Empirical Thought in general.
? ? I
1.
is
is
a
is,
;
? 122 TRANSCENDENTAL DOCTRINE.
evidence and the employment of these principles. It will, however, soon nppear that --a fact which concerns bcth the evidence of these principles, and the a priori determination of phenomena -- according to the categories of Quantity and Quality (if we attend merely to the form of these), the prin ciples of these categories are distinguishable from those of the two others, inasmuch as the former are possessed of an intui tive, but the latter of a merely discursive, though in both instances a complete certitude. I shall therefore call the former mathematical,* and the latter dynamical principles. f It must be observed, however, that by these terms I mean,
just as little in the one case the principles of mathematics, as those of general (physical) dynamics, in the other. I have
here in view merely the principles of the pure understanding, in their application to the internal sense, (without distinction of the representations given therein), by means of which the sciences of mathematics and dynamics become possible. Ac cordingly, I have named these principles rather with reference to their application, than their content ; and I shall now pro ceed to consider them in the order in which they stand in the table.
I.
Axioms of Intuition.
The principle of these "All Intuitions are Extensive Quantities. "
Mathematically, in the Kantian sense. -- 7V.
All combination (conjunctio) either composition {composilio) or connection (nexus). The former the synthesis of manifold, the parts of which do not necessarily belong to each other. For example, the two triangles into which square divided by diagonal, do not necessarily belong to each other, and of this kind the synthesis of the homogeneous in every thing that can be mathematically considered. This synthesis can be divided into those of aggregation and coalition, the former of which
applied to extensive, the latter to intensive quantities. The second sort of combination {nexus) the synthesis of manifold, in so far as its parti do belong necessarily to each other for example, the accident to sub stance, or the effect to the causa. Consequently synthesis of that which, though heterogineous, represented as connected, priori. This combination -- not an arbitrary one -- entitle dynamical, because con cerns the connection of the existence of the manifold. This, again, may be divided into the physical synthesis of the phenomena among each other, and the mitaphysical synthesis, or the connection of phenomena a priori in the faculty of cognition.
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? AXIOMS Of INTUITIOIC. 123
Pboof.
All phenomena contain, as regards their form, an intuition in space and time, which lies a priori at the foundation of all with out exception. Phenomena, therefore, cannot be apprehended, that received into empirical consciousness otherwise than through the synthesis of manifold, through which the repre sentations of determinate space or time are generated that
to say, through the composition
the consciousness of the synthetical unity of this manifold
(homogeneous). Now the consciousness of homogeneous manifold in intuition, so far as thereby the representation of an object rendered possible, the conception of quan tity (quanti). Consequently, even the perception of an object as phsenomenon possible only through the same synthetical unity of the manifold of the given sensuous intuition, through which the unity of the composition of the homogeneous mani fold the conception of quantity cogitated that to
say, all phenomena are quantities, and extensive quantities, because as intuitions in space or time, they must be repre sented by means of the same synthesis, through which space and time themselves are determined.
An extensive quantity call that wherein the representa tion of the parts renders possible (and therefore necessarily antecedes) the representation of the whole. cannot repre sent to myself any line, however small, without drawing in thought, that is, without generating from point all its parts one after another, and in this way alone producing this intui tion. Precisely the same the case with every, even the smallest portion of time. cogitate therein only the succes sive progress from one moment to another, and hence, by means of the different portions of time and the addition of them, determinate quantity of time produced. As the pure intuition in all phenomena either time or space, so every phenomenon in its character of intuition an extensive
? inasmuch as can only be cognized in our appre hension by successive synthesis (from part to part). All phenomena are, accordingly, to be considered as aggregates, that as collection of previously given parts which not the case with every sort of quantities, but only with those
which are represented and apprehended by us as extensive.
quantity,
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? 124 TRAXSCEWDKJTTAL DOCTBITTE.
On this successive synthesis of the productive imagination, in the generation of figures, is founded the mathematics of extension, or geometry, with its axioms, which express the conditions of sensuous intuition a priori, under which alone the schema of a pure conception of external intuition can exist ; for example, " between two points only one straight line is possible," " two straight lines cannot enclose a space," &c. These are the axioms which properly relate only to quantities (quanta) as such.
But, as regards the quantity of a thing (quantitas), that is to say, the answer to the question, How large is this or that object ? although, in respect to this question, we have vari ous propositions synthetical and immediately certain (inde- monstrabilia) ; we have, in the proper sense of the term, no axioms. For example, the propositions, " If equals be added to equals, the wholes are equal ;" " If equals be taken from equals, the remainders are equal ;" are analytical, because I am immediately conscious of the identity of the produc tion of the one quantity with the production of the other ; whereas axioms must be h priori synthetical propositions. On the other hand, the self-evident propositions as to the relation of numbers, are certainly synthetical, but not uni versal, like those of geometry, and for this reason cannot be called axioms, but numerical formula? . That 7+5 = 12, is not an analytical proposition. For neither in the represen tation of seven, nor of five, nor of the composition of the two numbers, do I cogitate the number twelve. (Whether I cogitate the number in the addition of both, is not at present the ques tion ; for in the case of an analytical proposition, the only point whether really cogitate the predicate in the repre sentation of the subject. ) But although the proposition synthetical, nevertheless only singular proposition. In so far as regard here had merely to the synthesis of the homogeneous (the units), cannot take place except in onn manner, although our use of these numbers afterwards ge neral. If say, " triangle can be constructed with three lines, any two of which taken together are greater than the third," exercise merely the pure function of the productive imagination, which may draw the lines longer or shorter, and construct the angles at its pleasure. On the contrary, the number seven possible only in one manner, and so like
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? ANTICIPATIONS OF PERCEPTION. 123
wise the number twelve, which results from the synthesis of seven and five. Such propositions, then, cannot be termed axioms (for in that case we should have an infinity of these), but numerical formule.
This transcendental principle of the mathematics of phe nomena greatly enlarges our & priori cognition. For it is by this principle alone that pure mathematics is rendered appli cable in all its precision to objects of experience, and without it the validity of this application would not be so self-evident ; on the contrary, contradictions and confusions have often arisen on this very point. Phenomena are not things in themselves. Empirical intuition is possible only through pure intuition
(of space and time) ; consequently, what geometry affirms of the latter, is indisputably valid of the former. All evasions, such as the statement that objects of sense do not conform to the rules of construction in space (for example, to the rule of the infinite divisibility of lines or angles), must fall to the ground.
For, if these objections hold good, we deny to space, and with it to all mathematics, objective validity, and no longer know wherefore, and how far, mathematics cnn be applied to phe nomena. The synthesis of spaces and times as the essential form of all intuition, is that which renders possible the appre hension of a phenomenon, and therefore every external expe rience, consequently all cognition of the objects of experience ; and whatever mathematics in its pure use proves of the former, must necessarily hold good of the latter. All objections are but the chicaneries of an ill-instructed reason, which errone ously thinks to liberate the objects of sense from the formal
conditions of our sensibility, and represents these, although mere phenomena, as things in themselves, presented as such to our understandings. But in this case, no a prion syn thetical cognition of them could be possible, consequently not through pure conceptions of space, and the science which
determines these conceptions, that is to say, geometry, would
itself be impossible.
II. Anticipations of Perception.
The principle of these is, "In all phamomena the Real, thai tvnich is an object of sensation, has Intensive Quantity, that has
Degree. "
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? TKANSCEWBENTAL DOCTMKE.
Proof.
Perception is empirical consciousness, that is to say, u con
sciousness, which contains an element of sensation. Phsenomena
as objects of perception are not pure, that merely formal in tuitions, like space and time, for they cannot be perceived in themselves. * They contain, then, over and above the intui tion, the materials for an object (through which represented something existing in space or time), that to say, they con tain the real of sensation, as representation merely subjec tive, which gives us merely the consciousness that the subject
affected, and which we refer to some external object. Now, gradual transition from empirical consciousness to pure con
sciousness possible, inasmuch as the real in this conscious ness entirely evanishes, and there remains merely formal consciousness priori) of the manifold in time and space consequently there possible synthesis also of the production of the quantity of sensation from its commencement, that from the pure intuition = onwards, up to certain quantity of the sensation. Now as sensation in itself not an objective
? and in to be found neither the intuition of space nor of time, cannot possess any extensive quantity, and yet there does belong to quantity (and that means of its
apprehension, in which empirical consciousne*is can within certain time rise from nothing = up to its given amount), consequently an intensive quantity. And thus we must ascribe intensive quantity, that degree of influence on sense to all objects of perception, in so far as this perception contains sensation.
All cognition, by means of which am enabled to cognize and determine a priori what belongs to empirical cognition, may be called an Anticipation and without doubt this the sense in which Epicurus employed his expression vpoy. ^i;. But as there in phsenomena something which never cog nized priori, which on this account constitutes the proper difference between pure and empirical cognition, that to say, sensation (as the matter of perception), follows, that
sensation just that element in cognition which cannot be at
They can be perceived only as phsenomena, and some part of them
must always belong to the non-ego whereas pure intuitions are entirely the orodncts of the mind itself, and as such arc cognized in thenuehn. -- Tr
representation,
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ANTICIPATIONS OP PKBCEPTIOJT.
127
? 11 anticipated. On the other hand, we might very well term the pure determinations in space and time, as well in regard to figure as to Quantity, anticipations of phenomena, because they represent a priori that which may always be given a pos teriori in experience. But suppose that in every sensation, as sensation in general, without any particular sensation being thought of, there existed something which could be cognized a priori, this would deserve to be called anticipation in a special sense --special, because it may seem surprising to forestall experience, in that which concerns the matter of experience, and which we can only derive from itself. Yet such really is the case here.
Apprehension,* by means of sensation alone, fills only one moment, that do not take into consideration succes sion of many sensations. As that in the phenomenon, the apprehension of which not successive synthesis advancing from parts to an entire representation, sensation has therefore no extensive quantity the want of sensation in moment of time would represent as empty, consequently = 0. That which in the empirical intuition corresponds to sensation rea
? lity (real as phenomenon) absence of negation = 0. of diminution, so that
that which corresponds to the
Now every sensation capable can decrease, and thus gradually
Therefore, between reality phenomenon and negation, there exists continuous concatenation of many pos sible intermediate sensations, the difference of which from each other always smaller than that between the given sen sation and zero, or complete negation. ' That to say, the realiia phenomenon has always quantity, which however not discoverable in Apprehension, inasmuch as Apprehension takes place means of mere sensation in one instant, and not the successive synthesis of many sensations, and there fore does not progress from parts to the whole.
has quantity, but not an extensive quantity.
Now that quantity which apprehended only as unity, and in which plurality can be represented only by approximation
to negation = term intensive quantity. Consequently, rea lity in phenomenon has intensive quantity, that degree,
Apprehension tbs Kantian word for perception, in the largest ? cast in which we employ that term. the genus which includes under
M species, perception proper and sensation proper. -- Tr.
Consequently,
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? 128 TRANSCENDENTAL iJOCTltlNX.
If we consider tins reality as cause (be it of sensation or of another reality in the phenomenon, for example, a change) ;
we call the degree of reality in its character of cause a momen tum, for example, the momentum of weight; and for this reason, that the degree only indicates that quantity the appre hension of which is not successive, but instantaneous. This, however, I touch upon only in passing, for with Causality I have at present nothing to do.
Accordingly, every sensation, consequently every reality in phenomena, however small it may be, has a degree, that is, an intensive quautity, which may always be lessened, and between reality and negation there exists a continuous connection of possible realities, and possible smaller perceptions. Every colour -- for example, red -- has a degree, which, be it ever so small, is never the smallest, and so is it always with heat, the momentum of weight, &c.
This property of quantities, according to which no part of them is the smallest possible (no part simple*), is called their continuity. Space and time are quanta continua, because no part of them can be given, without enclosing it within bound aries (points and moments), consequently, this given part is itself a space or a time. Space, therefore, consists only of spaces, and time of times. Points and moments are only boundaries, that the mere places or positions of their limi tation. But places always presuppose intuitions which are to limit or determine them and we cannot conceive either space or time composed of constituent parts which are given
before space or time. Such quantities may also be called flowing, because the synthesis (of the productive imagination) in the production of these Quantities progression in time, the continuity of which we are accustomed to indicate the
expression flowing.
All phenomena, then, are continuous quantities, in respect
both to intuition and mere perception (sensation, and with
In the former case they are extensive quanti ties in the latter, intensive. When the synthesis of the manifold of phenomenon interrupted, there results merely an aggregate of several phenomena, and not properly phe- nomenon as quantity, which not produced by the mere continuation of the productive synthesis of certain kind, bul
Simplex. -- 7V.
? reality).
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? AjrTicii'vrioxs or fekception. 129
by the repetition of a synthesis always ceasing. For example, if I call thirteen dollars a sum or quantity of money, 1 employ the term quite correctly, inasmuch as I understand by thirteen dollars the value of a mark in standard silver, which to be sure, continuous quantity, in which no part the smallest, but every part might constitute piece of money, which would contain material for still smaller pieces. If, however, the words thirteen dollars understand so many coins (be their value in silver what may), would be quite erroneous to use the expression quantity of dollars on the contrary, must call them aggregate, that number of coins. And as in every number we must have unity as the foundation, so phenomenon taken as unity quantity, and as such always
continuous quantity (quantum continuum).
Now, seeing all phsenomena, whether considered as extensive
or intensive, are continuous quantities, the proposition, "All change (transition of thing from one >>tate into another) con tinuous," might be proved here easily, and with mathematical evidence, were not that the causality of change lies entirely beyond the bounds of transcendental philosophy, and presup
poses empirical principles. For of the possibility of cause which changes the condition of things, that which de termines them to the contrary of certain given state, the under standing gives us priori no knowledge; not merely because has no insight into the possibility of (for such insight ab sent in several priori cognitions), but because the notion of change concerns only certain determinations of phenomena, which experience alone can acquaint us with, while their cause lies in the unchangeable. But seeing that we have
nothing which we could here employ but the pure funda mental conceptions of all possible experience, among which of course nothing empirical can be admitted, we dare not, without injuring the unity of our system, anticipate general physical science, which built upon certain fundamental
experiences.
Nevertheless, we are in no want of proofs of the great in
fluence which the principle above developed exercises in the anticipation of perceptions, and even in supplying the want of them, so far as to shield us against the false conclusions which otherwise we might rashly draw.
all reality in perception has degree, between which ai. d x
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? 130 THANSCENDENTAi DOCTIlUiE.
negation there is an endless sequence of ever . smaller degree*, and if nevertheless every sense must have a determinate degree of receptivity for sensations ; no perception, and consequently no experience is possible, which can prove, either immediately
or mediately, an entire absence of all reality in a phenomenon ; in other words, it is impossible ever to draw from experience a proof of the existence of empty space or of empty time. For in the first place, an entire absence of reality in a sensuous intuition cannot of course be an object of perception ; secondly, such absence cannot be deduced from the contemplation of any single . phenomenon, and the difference of the degrees in its reality ; nor ought it ever to be admitted in explanation of any phenomenon. For if even the complete intuition of a determinate space or time is thoroughly real, that no part thereof empty, yet because every reality has its degree, which, with the extensive quantity of the phenomenon un changed, can diminish through endless gradations down to nothing (the void), there must be infinitely graduated degrees, with which space or time filled, and the intensive quantity in different phenomena may be smaller or greater, although the ex tensive quantity of the intuition remains equal and unaltered.
We shall give an example of this. Almost all natural philo
sophers, remarking great difference in the quantity of the matter of different kinds in bodies with the same volume (partly on account of the momentum of gravity or weight, partly on account of the momentum of resistance to other bodies in motion), conclude unanimously, that this volume (extensive quantity of the phenomenon) must be void in all bodies, although in different proportion. But who would sus pect that these for the most part mathematical and mechanical inquirers into nature should ground this conclusion solely on metaphysical hypothesis -- sort of hypothesis which they profess to disparage and avoid Yet this they do, in assuming that the real in space must not here call impenetrability or weight, because these are empirical conceptions) always iden tical, and can only be distinguished according to its extensivo quantity, that is, multiplicity. Now to this presupposition, Air which they can have no ground in experience, and which conse
? quently merely metaphysical, oppose
transcendental de-
* It should be remembered that Kant means by matter, that which in the object corresponds to sensation the subject--the real in pheno menon. -- V.
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? ANTICIPATIONS OF PERCEPTION. 1. 31
monstration, which it is true will not explain the difference in the filling up of spaces, but which nevertheless completely does away with the supposed necessity of the above-mentioned pre supposition that we cannot explain the said difference otherwise than by the hypothesis of empty spaces. This demonstration, moreover, has the merit of setting the understanding at liberty to conceive this distinction in a different manner, if the explanation of the fact requires any such hypothesis. For we perceive that although two equal spaces may be completely filled by matters altogether different, so that in neither of them is there left a single point wherein matter is not present, nevertheless, every reality has its degree (of resistance or of weight), which, without diminution of the extensive quantity, can become less and less ad infinitum, before it passes into nothingness and disappears. Thus an expansion which fills a space -- for example, caloric, or any other reality in the phsenomenal world -- can decrease in its degrees to infinity, yet without leaving the smallest part of the space empty ; on the contrary, filling it with those lesser degrees, as completely as another phenomenon could with greater. My intention here is by no means to maintain that this is really the case with the difference of matters, in regard
I wish
ciple of the pure understanding, that the nature of our per
ceptions makes such a mode of explanation possible, and that it is erroneous to regard the real in a phsenomenon as equal quoad its degree, and different only quoad its aggregation and extensive quantity, and this, too, on the pretended authority of an a priori principle of the understanding.
Nevertheless, this principle of the anticipation of perception must somewhat startle an enquirer whom initiation into tran scendental philosophy has rendered cautious. We may natu rally entertain some doubt whether or not the understanding can enounce any such synthetical proposition as that respecting the degree of all reality in phsenomena, and consequently--the possibility of the internal difference of sensation itself ab straction being made of its empirical quality. Thus it is a question not unworthy of solution : How the understanding can pronounce synthetically and & priori respecting pheno-
mena, and thus anticipate these, even in that which is pecu liarly and merely empirical, that, namely, which concerns sen
? to their specific gravity ;
only
to
prove,
from a
prin
sation itself?
x2
? ? ? 132 TRANSCENDENTAL TOl. TltlNE.
The quality of sensation is in all cases n. erely empirical, and cannot be represented a priori (for example, colours, taste, &c). But the real -- that which corresponds to sensation -- iu opposition to negation=0, only represents something the conception of which in itself contains a being (ein seyn), and signifies nothing but the synthesis in an empirical con sciousness. That is to say, the empirical consciousness in the internal sense can be raised from 0 to every higher degree, so that the very same extensive quantity of intuition, an illuminated surface, for example, excites as great a sen sation as an aggregate of many other surfaces less illumi nated. We can therefore make complete abstraction of the extensive quantity of a phenomenon, and represent to our selves in the mere sensation in a certain momentum,* a syn thesis of homogeneous ascension from 0 up to the given empirical consciousness. All sensations therefore as such are given only d posteriori, but this property thereof, namely,
that they have a degree, can be known a priori. It is worthy of remark, that in respect to quantities in general, we can cognize a priori only a single quality, namely, continuity ; but in respect to all quality (the real in phenomena), we cannot cognize d priori any thing more than the intensive quantity thereof, namely, that they have a degree. All else is left to experience.
III.
ANALOGIES OF EXPERLENCB.
The principle of these is : Experience is possible only through the representation of a necessary connection of per
? ceptions.
Proof.
Experience is an empirical cognition ; that is to say, a cognition which determines an object by means of perceptions. It is therefore a synthesis of perceptions, a synthesis which is not itself contained in perception, but which contains the synthetical unity of the manifold of perception in a consci-
? The particular degree of " reality," that is, the particular power oi nlensive quantity in the cauie of a sensation, for example, redness, weight, Ac, is called in the Kantian terminology, Us moment. The term momentum which we employ, must not he confounded with the word com "conly employed ic :atural science. -- Ti.
? ? ? AXALOGIES OP EXPEllIEKCJt. 133
ousness ; and this unity constitutes the essential of our cog
nition of objects of the senses, that of experience merely of intuition or sensation). Now in experience our perceptions come together contingently, so that no character of necessity in their connexion appears, or can appear from the perceptions themselves, because apprehension only placing together of the manifold of empirical intuition, and no representation of necessity the connected existence of the phenomena which apprehension brings together, to be discovered therein. But as experience cognition of objects means of perceptions, follows that the relation of the existence of the manifold must be represented in expe rience not as put together time, but as objectively
time. And as time itself cannot be perceived, the determina tion of the existence of objects in time can only take place ny means of their connexion in time in general, consequently ouly means of priori connecting conceptions. Now as these conceptions always possess the character of necessity, experience possible only by means of representation of the necessary connexion of perception.
The three modi of time are permanence, succession, and co existence. Accordingly, there are three rules of all relations of time in phenomena, according to which the existence of every phenomenon determined in re-pect of the unity of all time, and these antecede all experience, and render possible.
The general principle of all three analogies rests on the necessary unity of apperception in relation to all possible empirical consciousness (perception) at every time, conse quently, as this unity lies priori at the foundation of all mental operations, the principle rests on the synthetical unity of all phenomena according to their relation in time. For the original apperception relates to our internal sense (the com plex of all representations), and indeed relates priori to its form, that to say, the relation of the manifold empirical consciousness in time. Now this manifold must be combined in original apperception according to relations of time, --
the a priori transcendental unity of ap perception, to which subjected all that can belong to my
e. my own) cognition, and therefore all that can become *n object for me. This synthetical and priori determine*?
necessity imposed
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? 134
7BAKS0IKDETITA1 DOOTBIJ'E.
unity in relntion of perceptions in time is therefore the rule : " All empirical determinations of time must be subject to rules of the general determination of time ;" and the analogies of experience, of which we are now about to treat, must be rules of this nature.
These principles have this peculiarity, that they do not concern phenomena, aid the synthesis of the empirical in tuition thereof, but merely the existence of phenomena and their relation to each other in regard to this existence. Now the
mode in which we apprehend a thing in a phenomenon can be determined a priori in such a manner, that the rule of its
? synthesis can give, that is to say, can produce this a priori intuition in every empirical example. But the existence of phe nomena cannot be known a priori, and although we could arrive by this path at a conclusion of the fact of some existence, we could not cognize that existence determiuately, that is to say, we should be incapable of anticipating in what respect the empirical intuition of it would be distinguishable from that of others.
The two principles above mentioned, which I called mathe matical, in consideration of the fact of their authorizing the application of mathematic to phenomena, relate to these phenomena only in regard to their possibility, and instruct us how phenomena, as far as regards their intuition or the real in their perception, can be generated according to the rules of a mathematical synthesis. Consequently, numerical quan tities, and with them the determination of a phenomenon as a quantity, can be employed in the one case as well as in the other. Thus, for example, out of 200,000 illuminations by the moon, I might compose, and give a priori, that is con struct, the degree of our sensations of the "in-light. * We may therefore entitle these two principles constitutive.
The case is very different with those principles whose pro vince it is to subject the existence of phenomena to rules a priori. For as existence does not admit of being con-
? Kant's meaning is : The two principles enunciated under the heads of " Aiioms of Intuition," and " Anticipations of Perception," authorize the application to phamacnena of determinations of size and number, that is, of mathematic. For example, I may compute the light of the sun, and say, that its quantity is a certain number of times greater than that of the moon. In the same way, heat is measured by the comparison of its dif
ferent effects on water, *c, and on mercury in a thermometer. -- 7V.
? ? ? ANALOGIES OF EXPEBIENCE. 13. 1
st. ucted, it is clear that they must only concern the relations of existence, and be merely regulative principles. In this case, therefore, neither axioms nor anticipations are to be thought of. Thus, if a perceptkin is given us, in a certain relation 01 time to other (although undetermined) perceptions, we can not then say a priori, what and how great (in quantity) the other perception necessarily connected with the for mer but only how connected, quoad its existence, in
Analogies in philosophy mean something very different from that which they represent in mathematics. In the latter they are formule, which enounce
the equality of two relations of quantity,* and are always constitutive, so that two terms of the proportion are given, the third also given, that can be constructed the aid of these formule. But in philosophy, analogy not the equality of two quantitative but of two qualitative relations. In this case, from three given terms, can give a priori and cognize the relation to fourth member, but not this fourth term itself, although certainly possess rule to guide me in the search for this fourth term in experience, and mark to assist me in discovering it. An analogy of experience therefore only rule according to which unity of experience must arise out of perceptions in respect to objects (pheno mena) not as constitutive, but merely as regulative principle. The same holds good also of the postulates of empirical thought
general, which relate to the synthesis of mere intuition (which concerns the form of phsenomena), the synthesis of per ception (which concerns the matter of phsenomena), and the synthesis of experience (which concerns the relation of these
? For they are only regulative principles, and clearly distinguishable from the mathematical, which are con
perceptions).
stitutive, not indeed in regard to the certainty which both
Known the two terms and and the relation of to not only the relation of to some other number given, but that number itself, 12, given, that constructed. Therefore 3:6=6: 12. -- TV.
Given known effect, known cause, and another known effect, we reason, by analogy, to an unknown cause, which we do not cognize, but ? hose relation to the known effect we know from the comparison of the
Thus, our own known actions our own known motives -= the known actions of others x, that the inotivrs of others
three given terms.
which we cannot immediately cognize. -- TV.
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possess & priori, but in the mode of evidence thereof, conse quently also in the manner of demonstration.
But what has been observed of all synthetical propositions, and must be particularly remarked in this place, is this, that these analogies possess significance and validity, not as principles of the transcendental, but only as principles of the empirical use of the understanding, and their truth can therefore be proved only as such, and that consequently
the phenomena must not be subjoined directly under the categories, but only under their schemata. For if the objects to which those principles must be applied were things in themselves, it would be quite impossible to cognize aught con cerning them synthetically h priori. But they are nothing but phcenomena ; a complete knowledge of which -- a know ledge to which all principles a priori must at last relate --is the only possible experience. It follows that these principles can have nothing else for their aim, than the conditions of the unity of empirical cognition in the synthesis of plienomena. But this synthesis is cogitated only in the schema of the pure conception of the understanding, of whose unity, as that of a synthesis in general, the category contains the function unre stricted by any sensuous condition. These principles will therefore authorize us to connect phsenomena according to an analogy, with the logical and universal unity of conceptions, and consequently to employ the categories in the principles them selves ; but in the application of them to experience, we shall use only their schemata, as the key to their proper application, instead of the categories, or rather the latter as restricting conditions, under the title of formulce of the former.
A.
FIRST ANALOOY.
PBIKCIFLX OF THE PEBMAKEXCE OF STTBSTAWCE.
In all changes of phcenomena, substance is permanent, and the quantum thereof in nature is neither increased nor dimi nished.
Pboof.
