SECTION III. Systematic Representation of all Synthetical
Principles of the Pure Understanding.
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 according
to which everything 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 characteristic of necessity, and we
may therefore at least expect them 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
understanding, 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 principles
for principles of the pure understanding, or conversely; for the
character of necessity, according to conceptions which distinguish the
latter, and the absence of this in every empirical proposition, how
extensively valid soever it may be, is a perfect safeguard against
confounding them. There are, however, 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 experience,
consequently their objective validity, nay the possibility of such a
priori synthetical cognitions (the deduction thereof) rests entirely
upon the pure understanding.
On this account, I shall not reckon among my principles those 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 conceptions to intuition, and not
from intuition to conceptions.
In the application of the pure conceptions of the understanding to
possible experience, the employment of their synthesis is either
mathematical or dynamical, for it is directed partly on the
intuition alone, partly on the existence of a phenomenon. But the a
priori conditions of intuition are in relation to a possible
experience absolutely necessary, those of the existence of objects
of a possible empirical intuition are in themselves contingent.
Hence the principles of the mathematical use of the categories will
possess a character of absolute necessity, that is, will be
apodeictic; those, on the other hand, of the dynamical use, the
character of an a priori necessity indeed, but only under the
condition of empirical thought in an experience, therefore only
mediately and indirectly. Consequently they will not possess that
immediate evidence which is 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 is naturally our guide to the table of
principles, because these are nothing else than rules for the
objective employment of the former. Accordingly, all principles of the
pure understanding are:
1
Axioms
of Intuition
2 3
Anticipations Analogies
of Perception of Experience
4
Postulates of
Empirical Thought
in general
These appellations I have chosen advisedly, in order that we might
not lose sight of the distinctions in respect of the evidence and
the employment of these principles. It will, however, soon appear
that- a fact which concerns both 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 principles of these categories are distinguishable from those of
the two others, in as much as the former are possessed of an
intuitive, 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.* 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. Accordingly, I have named these principles rather
with reference to their application than their content; and I shall
now proceed to consider them in the order in which they stand in the
table.
*All combination (conjunctio) is either composition (compositio)
or connection (nexus). The former is the synthesis of a manifold,
the parts of which do not necessarily belong to each other. For
example, the two triangles into which a square is divided by a
diagonal, do not necessarily belong to each other, and of this kind is
the synthesis of the homogeneous in everything that can be
mathematically considered. This synthesis can be divided into those of
aggregation and coalition, the former of which is applied to
extensive, the latter to intensive quantities. The second sort of
combination (nexus) is the synthesis of a manifold, in so far as its
parts do belong necessarily to each other; for example, the accident
to a substance, or the effect to the cause. Consequently it is a
synthesis of that which though heterogeneous, is represented as
connected a priori. This combination- not an arbitrary one- I
entitle dynamical because it concerns the connection of the
existence of the manifold. This, again, may be divided into the
physical synthesis, of the phenomena divided among each other, and the
metaphysical synthesis, or the connection of phenomena a priori in the
faculty of cognition.
1. AXIOMS OF INTUITION.
The principle of these is: All Intuitions are Extensive
Quantities.
PROOF.
All phenomena contain, as regards their form, an intuition in
space and time, which lies a priori at the foundation of all without
exception. Phenomena, therefore, cannot be apprehended, that is,
received into empirical consciousness otherwise than through the
synthesis of a manifold, through which the representations of a
determinate space or time are generated; that is to say, through the
composition of the homogeneous and the consciousness of the
synthetical unity of this manifold (homogeneous). Now the
consciousness of a homogeneous manifold in intuition, in so far as
thereby the representation of an object is rendered possible, is the
conception of a quantity (quanti). Consequently, even the perception
of an object as phenomenon is 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 manifold
in the conception of a quantity is cogitated; that is to say, all
phenomena are quantities, and extensive quantities, because as
intuitions in space or time they must be represented by means of the
same synthesis through which space and time themselves are determined.
An extensive quantity I call that wherein the representation of
the parts renders possible (and therefore necessarily antecedes) the
representation of the whole. I cannot represent to myself any line,
however small, without drawing it in thought, that is, without
generating from a point all its parts one after another, and in this
way alone producing this intuition. Precisely the same is the case
with every, even the smallest, portion of time. I cogitate therein
only the successive progress from one moment to another, and hence, by
means of the different portions of time and the addition of them, a
determinate quantity of time is produced. As the pure intuition in all
phenomena is either time or space, so is every phenomenon in its
character of intuition an extensive quantity, inasmuch as it can
only be cognized in our apprehension by successive synthesis (from
part to part). All phenomena are, accordingly, to be considered as
aggregates, that is, as a collection of previously given parts;
which is not the case with every sort of quantities, but only with
those which are represented and apprehended by us as extensive.
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, "be tween two
points only one straight line is possible," "two straight lines cannot
enclose a space," etc. 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 various propositions
synthetical and immediately certain (indemonstrabilia); 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 production of the one quantity with the production of the other;
whereas axioms must be a priori synthetical propositions. On the other
hand, the self-evident propositions as to the relation of numbers, are
certainly synthetical but not universal, like those of geometry, and
for this reason cannot be called axioms, but numerical formulae.
That 7 + 5 = 12 is not an analytical proposition. For neither in the
representation 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 question;
for in the case of an analytical proposition, the only point is
whether I really cogitate the predicate in the representation of the
subject.) But although the proposition is synthetical, it is
nevertheless only a singular proposition. In so far as regard is
here had merely to the synthesis of the homogeneous (the units), it
cannot take place except in one manner, although our use of these
numbers is afterwards general. If I say: "A triangle can be
constructed with three lines, any two of which taken together are
greater than the third," I 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 is possible only in one manner, and so is likewise 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 formulae.
This transcendental principle of the mathematics of phenomena
greatly enlarges our a priori cognition. For it is by this principle
alone that pure mathematics is rendered applicable 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 can
be applied to phenomena. The synthesis of spaces and times as the
essential form of all intuition, is that which renders possible the
apprehension of a phenomenon, and therefore every external experience,
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 erroneously 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 understanding. But in
this case, no a priori synthetical 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.
2. ANTICIPATIONS OF PERCEPTION.
The principle of these is: In all phenomena the Real, that
which is an object of sensation, has Intensive Quantity,
that is, has a Degree.
PROOF.
Perception is empirical consciousness, that is to say, a
consciousness which contains an element of sensation. Phenomena as
objects of perception are not pure, that is, merely formal intuitions,
like space and time, for they cannot be perceived in themselves.
They contain, then, over and above the intuition, the materials for an
object (through which is represented something existing in space or
time), that is to say, they contain the real of sensation, as a
representation merely subjective, which gives us merely the
consciousness that the subject is affected, and which we refer to some
external object. Now, a gradual transition from empirical
consciousness to pure consciousness is possible, inasmuch as the
real in this consciousness entirely vanishes, and there remains a
merely formal consciousness (a priori) of the manifold in time and
space; consequently there is possible a synthesis also of the
production of the quantity of a sensation from its commencement,
that is, from the pure intuition = 0 onwards up to a certain
quantity of the sensation. Now as sensation in itself is not an
objective representation, and in it is to be found neither the
intuition of space nor of time, it cannot possess any extensive
quantity, and yet there does belong to it a quantity (and that by
means of its apprehension, in which empirical consciousness can within
a certain time rise from nothing = 0 up to its given amount),
consequently an intensive quantity. And thus we must ascribe intensive
quantity, that is, a degree of influence on sense to all objects of
perception, in so far as this perception contains sensation.
All cognition, by means of which I am enabled to cognize and
determine a priori what belongs to empirical cognition, may be
called an anticipation; and without doubt this is the sense in which
Epicurus employed his expression prholepsis. But as there is in
phenomena something which is never cognized a priori, which on this
account constitutes the proper difference between pure and empirical
cognition, that is to say, sensation (as the matter of perception), it
follows, that sensation is just that element in cognition which cannot
be at all 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 posteriori 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 is, if I do not take into consideration a succession of many
sensations. As that in the phenomenon, the apprehension of which is
not a successive synthesis advancing from parts to an entire
representation, sensation has therefore no extensive quantity; the
want of sensation in a moment of time would represent it as empty,
consequently = O. That which in the empirical intuition corresponds to
sensation is reality (realitas phaenomenon); that which corresponds to
the absence of it, negation = O. Now every sensation is capable of a
diminution, so that it can decrease, and thus gradually disappear.
Therefore, between reality in a phenomenon and negation, there
exists a continuous concatenation of many possible intermediate
sensations, the difference of which from each other is always
smaller than that between the given sensation and zero, or complete
negation. That is to say, the real in a phenomenon has always a
quantity, which however is not discoverable in apprehension,
inasmuch as apprehension take place by means of mere sensation in
one instant, and not by the successive synthesis of many sensations,
and therefore does not progress from parts to the whole. Consequently,
it has a quantity, but not an extensive quantity.
Now that quantity which is apprehended only as unity, and in which
plurality can be represented only by approximation to negation = O,
I term intensive quantity. Consequently, reality in a phenomenon has
intensive quantity, that is, a degree. if we consider this 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 momentum, for example, the momentum of
weight; and for this reason, that the degree only indicates that
quantity the apprehension 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 quantity, 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,
etc.
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 boundaries (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 is, the mere places or positions
of their limitation. 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 synthesis
(of the productive imagination) in the production of these
quantities is a progression in time, the continuity of which we are
accustomed to indicate by the expression flowing.
All phenomena, then, are continuous quantities, in respect both to
intuition and mere perception (sensation, and with it reality). In the
former case they are extensive quantities; in the latter, intensive.
When the synthesis of the manifold of a phenomenon is interrupted,
there results merely an aggregate of several phenomena, and not
properly a phenomenon as a quantity, which is not produced by the mere
continuation of the productive synthesis of a certain kind, but by the
repetition of a synthesis always ceasing. For example, if I call
thirteen dollars a sum or quantity of money, I employ the term quite
correctly, inasmuch as I understand by thirteen dollars the value of a
mark in standard silver, which is, to be sure, a continuous
quantity, in which no part is the smallest, but every part might
constitute a piece of money, which would contain material for still
smaller pieces. If, however, by the words thirteen dollars I
understand so many coins (be their value in silver what it may), it
would be quite erroneous to use the expression a quantity of
dollars; on the contrary, I must call them aggregate, that is, a
number of coins. And as in every number we must have unity as the
foundation, so a phenomenon taken as unity is a quantity, and as
such always a continuous quantity (quantum continuum).
Now, seeing all phenomena, whether considered as extensive or
intensive, are continuous quantities, the proposition: "All change
(transition of a thing from one state into another) is continuous,"
might be proved here easily, and with mathematical evidence, were it
not that the causality of a change lies, entirely beyond the bounds of
a transcendental philosophy, and presupposes empirical principles. For
of the possibility of a cause which changes the condition of things,
that is, which determines them to the contrary to a certain given
state, the understanding gives us a priori no knowledge; not merely
because it has no insight into the possibility of it (for such insight
is absent in several a 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 fundamental 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 is built upon certain fundamental
experiences.
Nevertheless, we are in no want of proofs of the great influence
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.
If all reality in perception has a degree, between which and
negation there is an endless sequence of ever smaller degrees, 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
is, if no part thereof is empty, yet because every reality has its
degree, which, with the extensive quantity of the phenomenon
unchanged, can diminish through endless gradations down to nothing
(the void), there must be infinitely graduated degrees, with which
space or time is filled, and the intensive quantity in different
phenomena may be smaller or greater, although the extensive quantity
of the intuition remains equal and unaltered.
We shall give an example of this. Almost all natural philosophers,
remarking a 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 suspect that
these for the most part mathematical and mechanical inquirers into
nature should ground this conclusion solely on a metaphysical
hypothesis- a sort of hypothesis which they profess to disparage and
avoid? Yet this they do, in assuming that the real in space (I must
not here call it impenetrability or weight, because these are
empirical conceptions) is always identical, and can only be
distinguished according to its extensive quantity, that is,
multiplicity. Now to this presupposition, for which they can have no
ground in experience, and which consequently is merely metaphysical, I
oppose a transcendental demonstration, 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 presupposition 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 phenomenal 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 to their specific gravity; I wish only to prove,
from a principle of the pure understanding, that the nature of our
perceptions makes such a mode of explanation possible, and that it
is erroneous to regard the real in a phenomenon 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 inquirer whom initiation into
transcendental philosophy has rendered cautious. We must naturally
entertain some doubt whether or not the understanding can enounce
any such synthetical proposition as that respecting the degree of
all reality in phenomena, and consequently the possibility of the
internal difference of sensation itself- abstraction being made of its
empirical quality. Thus it is a question not unworthy of solution:
"How the understanding can pronounce synthetically and a priori
respecting phenomena, and thus anticipate these, even in that which is
peculiarly and merely empirical, that, namely, which concerns
sensation itself?"
The quality of sensation is in all cases merely empirical, and
cannot be represented a priori (for example, colours, taste, etc.).
But the real- that which corresponds to sensation- in opposition to
negation = O, only represents something the conception of which in
itself contains a being (ein seyn), and signifies nothing but the
synthesis in an empirical consciousness. 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
sensation as an aggregate of many other surfaces less illuminated.
We can therefore make complete abstraction of the extensive quantity
of a phenomenon, and represent to ourselves in the mere sensation in a
certain momentum, a synthesis of homogeneous ascension from 0 up to
the given empirical consciousness, All sensations therefore as such
are given only a 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 a priori anything more than
the intensive quantity thereof, namely, that they have a degree. All
else is left to experience.
3. ANALOGIES OF EXPERIENCE.
The principle of these is: Experience is possible only
through the representation of a necessary connection
of Perceptions.
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 consciousness; and this unity
constitutes the essential of our cognition of objects of the senses,
that is, of experience (not merely of intuition or sensation). Now
in experience our perceptions come together contingently, so that no
character of necessity in their connection appears, or can appear from
the perceptions themselves, because apprehension is only a placing
together of the manifold of empirical intuition, and no representation
of a necessity in the connected existence of the phenomena which
apprehension brings together, is to be discovered therein. But as
experience is a cognition of objects by means of perceptions, it
follows that the relation of the existence of the existence of the
manifold must be represented in experience not as it is put together
in time, but as it is objectively in time. And as time itself cannot
be perceived, the determination of the existence of objects in time
can only take place by means of their connection in time in general,
consequently only by means of a priori connecting conceptions. Now
as these conceptions always possess the character of necessity,
experience is possible only by means of a representation of the
necessary connection of perception.
The three modi of time are permanence, succession, and
coexistence. Accordingly, there are three rules of all relations of
time in phenomena, according to which the existence of every
phenomenon is determined in respect of the unity of all time, and
these antecede all experience and render it 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, consequently, as
this unity lies a 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 complex of all representations),
and indeed relates a priori to its form, that is 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- a necessity imposed by the a priori
transcendental unity of apperception, to which is subjected all that
can belong to my (i.e., my own) cognition, and therefore all that
can become an object for me. This synthetical and a priori
determined unity in relation 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, and the synthesis of the empirical intuition 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
phenomena 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 determinately, 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 mathematical,
in consideration of the fact of their authorizing the application of
mathematic 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 quantities, 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 construct, the degree
of our sensations of the sunlight. We may therefore entitle these
two principles constitutive.
The case is very different with those principles whose province it
is to subject the existence of phenomena to rules a priori. For as
existence does not admit of being constructed, 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 perception is given us,
in a certain relation of time to other (although undetermined)
perceptions, we cannot then say a priori, what and how great (in
quantity) the other perception necessarily connected with the former
is, but only how it is connected, quoad its existence, in this given
modus of time. Analogies in philosophy mean something very different
from that which they represent in mathematics. In the latter they
are formulae, which enounce the equality of two relations of quantity,
and are always constitutive, so that if two terms of the proportion
are given, the third is also given, that is, can be constructed by the
aid of these formulae. But in philosophy, analogy is not the
equality of two quantitative but of two qualitative relations. In this
case, from three given terms, I can give a priori and cognize the
relation to a fourth member, but not this fourth term itself, although
I certainly possess a rule to guide me in the search for this fourth
term in experience, and a mark to assist me in discovering it. An
analogy of experience is therefore only a rule according to which
unity of experience must arise out of perceptions in respect to
objects (phenomena) not as a constitutive, but merely as a
regulative principle. The same holds good also of the postulates of
empirical thought in general, which relate to the synthesis of mere
intuition (which concerns the form of phenomena), the synthesis of
perception (which concerns the matter of phenomena), and the synthesis
of experience (which concerns the relation of these perceptions).
For they are only regulative principles, and clearly distinguishable
from the mathematical, which are constitutive, not indeed in regard to
the certainty which both possess a priori, but in the mode of evidence
thereof, consequently 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 concerning
them synthetically a priori. But they are nothing but phenomena; a
complete knowledge of which- a knowledge 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 empirical cognition in the unity of synthesis of
phenomena. 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
unrestricted by any sensuous condition. These principles will
therefore authorize us to connect phenomena according to an analogy,
with the logical and universal unity of conceptions, and
consequently to employ the categories in the principles themselves;
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 "formulae" of the former.
A. FIRST ANALOGY.
Principle of the Permanence of Substance.
In all changes of phenomena, substance is permanent, and the
quantum thereof in nature is neither increased nor diminished.
PROOF.
All phenomena exist in time, wherein alone as substratum, that is,
as the permanent form of the internal intuition, coexistence and
succession can be represented. Consequently time, in which all changes
of phenomena must be cogitated, remains and changes not, because it is
that in which succession and coexistence can be represented only as
determinations thereof. Now, time in itself cannot be an object of
perception. It follows that in objects of perception, that is, in
phenomena, there must be found a substratum which represents time in
general, and in which all change or coexistence can be perceived by
means of the relation of phenomena to it. But the substratum of all
reality, that is, of all that pertains to the existence of things,
is substance; all that pertains to existence can be cogitated only
as a determination of substance. Consequently, the permanent, in
relation to which alone can all relations of time in phenomena be
determined, is substance in the world of phenomena, that is, the
real in phenomena, that which, as the substratum of all change,
remains ever the same. Accordingly, as this cannot change in
existence, its quantity in nature can neither be increased nor
diminished.
Our apprehension of the manifold in a phenomenon is always
successive, is Consequently always changing. By it alone we could,
therefore, never determine whether this manifold, as an object of
experience, is coexistent or successive, unless it had for a
foundation something fixed and permanent, of the existence of which
all succession and coexistence are nothing but so many modes (modi
of time). Only in the permanent, then, are relations of time
possible (for simultaneity and succession are the only relations in
time); that is to say, the permanent is the substratum of our
empirical representation of time itself, in which alone all
determination of time is possible. Permanence is, in fact, just
another expression for time, as the abiding correlate of all existence
of phenomena, and of all change, and of all coexistence. For change
does not affect time itself, but only the phenomena in time (just as
coexistence cannot be regarded as a modus of time itself, seeing
that in time no parts are coexistent, but all successive). If we
were to attribute succession to time itself, we should be obliged to
cogitate another time, in which this succession would be possible.
It is only by means of the permanent that existence in different parts
of the successive series of time receives a quantity, which we entitle
duration. For in mere succession, existence is perpetually vanishing
and recommencing, and therefore never has even the least quantity.
Without the permanent, then, no relation in time is possible. Now,
time in itself is not an object of perception; consequently the
permanent in phenomena must be regarded as the substratum of all
determination of time, and consequently also as the condition of the
possibility of all synthetical unity of perceptions, that is, of
experience; and all existence and all change in time can only be
regarded as a mode in the existence of that which abides unchangeably.
Therefore, in all phenomena, the permanent is the object in itself,
that is, the substance (phenomenon); but all that changes or can
change belongs only to the mode of the existence of this substance
or substances, consequently to its determinations.
I find that in all ages not only the philosopher, but even the
common understanding, has preposited this permanence as a substratum
of all change in phenomena; indeed, I am compelled to believe that
they will always accept this as an indubitable fact. Only the
philosopher expresses himself in a more precise and definite manner,
when he says: "In all changes in the world, the substance remains, and
the accidents alone are changeable." But of this decidedly synthetical
proposition, I nowhere meet with even an attempt at proof; nay, it
very rarely has the good fortune to stand, as it deserves to do, at
the head of the pure and entirely a priori laws of nature. In truth,
the statement that substance is permanent, is tautological. For this
very permanence is the ground on which we apply the category of
substance to the phenomenon; and we should have been obliged to
prove that in all phenomena there is something permanent, of the
existence of which the changeable is nothing but a determination.
But because a proof of this nature cannot be dogmatical, that is,
cannot be drawn from conceptions, inasmuch as it concerns a
synthetical proposition a priori, and as philosophers never
reflected that such propositions are valid only in relation to
possible experience, and therefore cannot be proved except by means of
a deduction of the possibility of experience, it is no wonder that
while it has served as the foundation of all experience (for we feel
the need of it in empirical cognition), it has never been supported by
proof.
A philosopher was asked: "What is the weight of smoke?" He answered:
"Subtract from the weight of the burnt wood the weight of the
remaining ashes, and you will have the weight of the smoke." Thus he
presumed it to be incontrovertible that even in fire the matter
(substance) does not perish, but that only the form of it undergoes
a change. In like manner was the saying: "From nothing comes nothing,"
only another inference from the principle or permanence, or rather
of the ever-abiding existence of the true subject in phenomena. For if
that in the phenomenon which we call substance is to be the proper
substratum of all determination of time, it follows that all existence
in past as well as in future time, must be determinable by means of it
alone. Hence we are entitled to apply the term substance to a
phenomenon, only because we suppose its existence in all time, a
notion which the word permanence does not fully express, as it seems
rather to be referable to future time. However, the internal necessity
perpetually to be, is inseparably connected with the necessity
always to have been, and so the expression may stand as it is.
"Gigni de nihilo nihil; in nihilum nil posse reverti,"* are two
propositions which the ancients never parted, and which people
nowadays sometimes mistakenly disjoin, because they imagine that the
propositions apply to objects as things in themselves, and that the
former might be inimical to the dependence (even in respect of its
substance also) of the world upon a supreme cause. But this
apprehension is entirely needless, for the question in this case is
only of phenomena in the sphere of experience, the unity of which
never could be possible, if we admitted the possibility that new
things (in respect of their substance) should arise. For in that case,
we should lose altogether that which alone can represent the unity
of time, to wit, the identity of the substratum, as that through which
alone all change possesses complete and thorough unity. This
permanence is, however, nothing but the manner in which we represent
to ourselves the existence of things in the phenomenal world.
*[Persius, Satirae, iii.83-84. "Nothing can be produced from
nothing; nothing can be returned into nothing."]
The determinations of a substance, which are only particular modes
of its existence, are called accidents. They are always real,
because they concern the existence of substance (negations are only
determinations, which express the non-existence of something in the
substance). Now, if to this real in the substance we ascribe a
particular existence (for example, to motion as an accident of
matter), this existence is called inherence, in contradistinction to
the existence of substance, which we call subsistence. But hence arise
many misconceptions, and it would be a more accurate and just mode
of expression to designate the accident only as the mode in which
the existence of a substance is positively determined. Meanwhile, by
reason of the conditions of the logical exercise of our understanding,
it is impossible to avoid separating, as it were, that which in the
existence of a substance is subject to change, whilst the substance
remains, and regarding it in relation to that which is properly
permanent and radical. On this account, this category of substance
stands under the title of relation, rather because it is the condition
thereof than because it contains in itself any relation.
Now, upon this notion of permanence rests the proper notion of the
conception change. Origin and extinction are not changes of that which
originates or becomes extinct. Change is but a mode of existence,
which follows on another mode of existence of the same object; hence
all that changes is permanent, and only the condition thereof changes.
Now since this mutation affects only determinations, which can have
a beginning or an end, we may say, employing an expression which seems
somewhat paradoxical: "Only the permanent (substance) is subject to
change; the mutable suffers no change, but rather alternation, that
is, when certain determinations cease, others begin."
Change, when, cannot be perceived by us except in substances, and
origin or extinction in an absolute sense, that does not concern
merely a determination of the permanent, cannot be a possible
perception, for it is this very notion of the permanent which
renders possible the representation of a transition from one state
into another, and from non-being to being, which, consequently, can be
empirically cognized only as alternating determinations of that
which is permanent. Grant that a thing absolutely begins to be; we
must then have a point of time in which it was not. But how and by
what can we fix and determine this point of time, unless by that which
already exists? For a void time- preceding- is not an object of
perception; but if we connect this beginning with objects which
existed previously, and which continue to exist till the object in
question in question begins to be, then the latter can only be a
determination of the former as the permanent. The same holds good of
the notion of extinction, for this presupposes the empirical
representation of a time, in which a phenomenon no longer exists.
Substances (in the world of phenomena) are the substratum of all
determinations of time. The beginning of some, and the ceasing to be
of other substances, would utterly do away with the only condition
of the empirical unity of time; and in that case phenomena would
relate to two different times, in which, side by side, existence would
pass; which is absurd. For there is only one time in which all
different times must be placed, not as coexistent, but as successive.
Accordingly, permanence is a necessary condition under which alone
phenomena, as things or objects, are determinable in a possible
experience. But as regards the empirical criterion of this necessary
permanence, and with it of the substantiality of phenomena, we shall
find sufficient opportunity to speak in the sequel.
B. SECOND ANALOGY.
Principle of the Succession of Time According
to the Law of Causality.
All changes take place according to the law of the
connection of Cause and Effect.
PROOF.
(That all phenomena in the succession of time are only changes, that
is, a successive being and non-being of the determinations of
substance, which is permanent; consequently that a being of
substance itself which follows on the non-being thereof, or a
non-being of substance which follows on the being thereof, in other
words, that the origin or extinction of substance itself, is
impossible- all this has been fully established in treating of the
foregoing principle. This principle might have been expressed as
follows: "All alteration (succession) of phenomena is merely
change"; for the changes of substance are not origin or extinction,
because the conception of change presupposes the same subject as
existing with two opposite determinations, and consequently as
permanent. After this premonition, we shall proceed to the proof.)
I perceive that phenomena succeed one another, that is to say, a
state of things exists at one time, the opposite of which existed in a
former state. In this case, then, I really connect together two
perceptions in time. Now connection is not an operation of mere
sense and intuition, but is the product of a synthetical faculty of
imagination, which determines the internal sense in respect of a
relation of time. But imagination can connect these two states in
two ways, so that either the one or the other may antecede in time;
for time in itself cannot be an object of perception, and what in an
object precedes and what follows cannot be empirically determined in
relation to it. I am only conscious, then, that my imagination
places one state before and the other after; not that the one state
antecedes the other in the object. In other words, the objective
relation of the successive phenomena remains quite undetermined by
means of mere perception. Now in order that this relation may be
cognized as determined, the relation between the two states must be so
cogitated that it is thereby determined as necessary, which of them
must be placed before and which after, and not conversely. But the
conception which carries with it a necessity of synthetical unity, can
be none other than a pure conception of the understanding which does
not lie in mere perception; and in this case it is the conception of
"the relation of cause and effect," the former of which determines the
latter in time, as its necessary consequence, and not as something
which might possibly antecede (or which might in some cases not be
perceived to follow). It follows that it is only because we subject
the sequence of phenomena, and consequently all change, to the law
of causality, that experience itself, that is, empirical cognition
of phenomena, becomes possible; and consequently, that phenomena
themselves, as objects of experience, are possible only by virtue of
this law.
Our apprehension of the manifold of phenomena is always
successive. The representations of parts succeed one another.
Whether they succeed one another in the object also, is a second point
for reflection, which was not contained in the former. Now we may
certainly give the name of object to everything, even to every
representation, so far as we are conscious thereof; but what this word
may mean in the case of phenomena, not merely in so far as they (as
representations) are objects, but only in so far as they indicate an
object, is a question requiring deeper consideration. In so far as
they, regarded merely as representations, are at the same time objects
of consciousness, they are not to be distinguished from
apprehension, that is, reception into the synthesis of imagination,
and we must therefore say: "The manifold of phenomena is always
produced successively in the mind." If phenomena were things in
themselves, no man would be able to conjecture from the succession
of our representations how this manifold is connected in the object;
for we have to do only with our representations. How things may be
in themselves, without regard to the representations through which
they affect us, is utterly beyond the sphere of our cognition. Now
although phenomena are not things in themselves, and are
nevertheless the only thing given to us to be cognized, it is my
duty to show what sort of connection in time belongs to the manifold
in phenomena themselves, while the representation of this manifold
in apprehension is always successive. For example, the apprehension of
the manifold in the phenomenon of a house which stands before me, is
successive. Now comes the question whether the manifold of this
house is in itself successive- which no one will be at all willing
to grant. But, so soon as I raise my conception of an object to the
transcendental signification thereof, I find that the house is not a
thing in itself, but only a phenomenon, that is, a representation, the
transcendental object of which remains utterly unknown. What then am I
to understand by the question: "How can the manifold be connected in
the phenomenon itself- not considered as a thing in itself, but merely
as a phenomenon?" Here that which lies in my successive apprehension
is regarded as representation, whilst the phenomenon which is given
me, notwithstanding that it is nothing more than a complex of these
representations, is regarded as the object thereof, with which my
conception, drawn from the representations of apprehension, must
harmonize. It is very soon seen that, as accordance of the cognition
with its object constitutes truth, the question now before us can only
relate to the formal conditions of empirical truth; and that the
phenomenon, in opposition to the representations of apprehension,
can only be distinguished therefrom as the object of them, if it is
subject to a rule which distinguishes it from every other
apprehension, and which renders necessary a mode of connection of
the manifold. That in the phenomenon which contains the condition of
this necessary rule of apprehension, is the object.
Let us now proceed to our task. That something happens, that is to
say, that something or some state exists which before was not,
cannot be empirically perceived, unless a phenomenon precedes, which
does not contain in itself this state. For a reality which should
follow upon a void time, in other words, a beginning, which no state
of things precedes, can just as little be apprehended as the void time
itself. Every apprehension of an event is therefore a perception which
follows upon another perception. But as this is the case with all
synthesis of apprehension, as I have shown above in the example of a
house, my apprehension of an event is not yet sufficiently
distinguished from other apprehensions. But I remark also that if in a
phenomenon which contains an occurrence, I call the antecedent state
of my perception, A, and the following state, B, the perception B
can only follow A in apprehension, and the perception A cannot
follow B, but only precede it. For example, I see a ship float down
the stream of a river. My perception of its place lower down follows
upon my perception of its place higher up the course of the river, and
it is impossible that, in the apprehension of this phenomenon, the
vessel should be perceived first below and afterwards higher up the
stream. Here, therefore, the order in the sequence of perceptions in
apprehension is determined; and by this order apprehension is
regulated. In the former example, my perceptions in the apprehension
of a house might begin at the roof and end at the foundation, or
vice versa; or I might apprehend the manifold in this empirical
intuition, by going from left to right, and from right to left.
Accordingly, in the series of these perceptions, there was no
determined order, which necessitated my beginning at a certain
point, in order empirically to connect the manifold. But this rule
is always to be met with in the perception of that which happens,
and it makes the order of the successive perceptions in the
apprehension of such a phenomenon necessary.
I must, therefore, in the present case, deduce the subjective
sequence of apprehension from the objective sequence of phenomena, for
otherwise the former is quite undetermined, and one phenomenon is
not distinguishable from another. The former alone proves nothing as
to the connection of the manifold in an object, for it is quite
arbitrary. The latter must consist in the order of the manifold in a
phenomenon, according to which order the apprehension of one thing
(that which happens) follows that of another thing (which precedes),
in conformity with a rule. In this way alone can I be authorized to
say of the phenomenon itself, and not merely of my own apprehension,
that a certain order or sequence is to be found therein. That is, in
other words, I cannot arrange my apprehension otherwise than in this
order.
In conformity with this rule, then, it is necessary that in that
which antecedes an event there be found the condition of a rule,
according to which in this event follows always and necessarily; but I
cannot reverse this and go back from the event, and determine (by
apprehension) that which antecedes it. For no phenomenon goes back
from the succeeding point of time to the preceding point, although
it does certainly relate to a preceding point of time; from a given
time, on the other hand, there is always a necessary progression to
the determined succeeding time. Therefore, because there certainly
is something that follows, I must of necessity connect it with
something else, which antecedes, and upon which it follows, in
conformity with a rule, that is necessarily, so that the event, as
conditioned, affords certain indication of a condition, and this
condition determines the event.
Let us suppose that nothing precedes an event, upon which this event
must follow in conformity with a rule. All sequence of perception
would then exist only in apprehension, that is to say, would be merely
subjective, and it could not thereby be objectively determined what
thing ought to precede, and what ought to follow in perception. In
such a case, we should have nothing but a play of representations,
which would possess no application to any object. That is to say, it
would not be possible through perception to distinguish one phenomenon
from another, as regards relations of time; because the succession
in the act of apprehension would always be of the same sort, and
therefore there would be nothing in the phenomenon to determine the
succession, and to render a certain sequence objectively necessary.
And, in this case, I cannot say that two states in a phenomenon follow
one upon the other, but only that one apprehension follows upon
another. But this is merely subjective, and does not determine an
object, and consequently cannot be held to be cognition of an
object- not even in the phenomenal world.
Accordingly, when we know in experience that something happens, we
always presuppose that something precedes, whereupon it follows in
conformity with a rule. For otherwise I could not say of the object
that it follows; because the mere succession in my apprehension, if it
be not determined by a rule in relation to something preceding, does
not authorize succession in the object. Only, therefore, in
reference to a rule, according to which phenomena are determined in
their sequence, that is, as they happen, by the preceding state, can I
make my subjective synthesis (of apprehension) objective, and it is
only under this presupposition that even the experience of an event is
possible.
No doubt it appears as if this were in thorough contradiction to all
the notions which people have hitherto entertained in regard to the
procedure of the human understanding. According to these opinions,
it is by means of the perception and comparison of similar
consequences following upon certain antecedent phenomena that the
understanding is led to the discovery of a rule, according to which
certain events always follow certain phenomena, and it is only by this
process that we attain to the conception of cause. Upon such a
basis, it is clear that this conception must be merely empirical,
and the rule which it furnishes us with- "Everything that happens must
have a cause"- would be just as contingent as experience itself. The
universality and necessity of the rule or law would be perfectly
spurious attributes of it. Indeed, it could not possess universal
validity, inasmuch as it would not in this case be a priori, but
founded on deduction. But the same is the case with this law as with
other pure a priori representations (e.g., space and time), which we
can draw in perfect clearness and completeness from experience, only
because we had already placed them therein, and by that means, and
by that alone, had rendered experience possible. Indeed, the logical
clearness of this representation of a rule, determining the series
of events, is possible only when we have made use thereof in
experience. Nevertheless, the recognition of this rule, as a condition
of the synthetical unity of phenomena in time, was the ground of
experience itself and consequently preceded it a priori.
It is now our duty to show by an example that we never, even in
experience, attribute to an object the notion of succession or
effect (of an event- that is, the happening of something that did
not exist before), and distinguish it from the subjective succession
of apprehension, unless when a rule lies at the foundation, which
compels us to observe this order of perception in preference to any
other, and that, indeed, it is this necessity which first renders
possible the representation of a succession in the object.
We have representations within us, of which also we can be
conscious. But, however widely extended, however accurate and
thoroughgoing this consciousness may be, these representations are
still nothing more than representations, that is, internal
determinations of the mind in this or that relation of time. Now how
happens it that to these representations we should set an object, or
that, in addition to their subjective reality, as modifications, we
should still further attribute to them a certain unknown objective
reality? It is clear that objective significancy cannot consist in a
relation to another representation (of that which we desire to term
object), for in that case the question again arises: "How does this
other representation go out of itself, and obtain objective
significancy over and above the subjective, which is proper to it,
as a determination of a state of mind?" If we try to discover what
sort of new property the relation to an object gives to our subjective
representations, and what new importance they thereby receive, we
shall find that this relation has no other effect than that of
rendering necessary the connection of our representations in a certain
manner, and of subjecting them to a rule; and that conversely, it is
only because a certain order is necessary in the relations of time
of our representations, that objective significancy is ascribed to
them.
In the synthesis of phenomena, the manifold of our representations
is always successive. Now hereby is not represented an object, for
by means of this succession, which is common to all apprehension, no
one thing is distinguished from another. But so soon as I perceive
or assume that in this succession there is a relation to a state
antecedent, from which the representation follows in accordance with a
rule, so soon do I represent something as an event, or as a thing that
happens; in other words, I cognize an object to which I must assign
a certain determinate position in time, which cannot be altered,
because of the preceding state in the object. When, therefore, I
perceive that something happens, there is contained in this
representation, in the first place, the fact, that something
antecedes; because, it. is only in relation to this that the
phenomenon obtains its proper relation of time, in other words, exists
after an antecedent time, in which it did not exist. But it can
receive its determined place in time only by the presupposition that
something existed in the foregoing state, upon which it follows
inevitably and always, that is, in conformity with a rule. From all
this it is evident that, in the first place, I cannot reverse the
order of succession, and make that which happens precede that upon
which it follows; and that, in the second place, if the antecedent
state be posited, a certain determinate event inevitably and
necessarily follows. Hence it follows that there exists a certain
order in our representations, whereby the present gives a sure
indication of some previously existing state, as a correlate, though
still undetermined, of the existing event which is given- a
correlate which itself relates to the event as its consequence,
conditions it, and connects it necessarily with itself in the series
of time.
If then it be admitted as a necessary law of sensibility, and
consequently a formal condition of all perception, that the
preceding necessarily determines the succeeding time (inasmuch as I
cannot arrive at the succeeding except through the preceding), it must
likewise be an indispensable law of empirical representation of the
series of time that the phenomena of the past determine all
phenomena in the succeeding time, and that the latter, as events,
cannot take place, except in so far as the former determine their
existence in time, that is to say, establish it according to a rule.
For it is of course only in phenomena that we can empirically
cognize this continuity in the connection of times.
For all experience and for the possibility of experience,
understanding is indispensable, and the first step which it takes in
this sphere is not to render the representation of objects clear,
but to render the representation of an object in general, possible. It
does this by applying the order of time to phenomena, and their
existence. In other words, it assigns to each phenomenon, as a
consequence, a place in relation to preceding phenomena, determined
a priori in time, without which it could not harmonize with time
itself, which determines a place a priori to all its parts. This
determination of place cannot be derived from the relation of
phenomena to absolute time (for it is not an object of perception);
but, on the contrary, phenomena must reciprocally determine the places
in time of one another, and render these necessary in the order of
time. In other words, whatever follows or happens, must follow in
conformity with a universal rule upon that which was contained in
the foregoing state. Hence arises a series of phenomena, which, by
means of the understanding, produces and renders necessary exactly the
same order and continuous connection in the series of our possible
perceptions, as is found a priori in the form of internal intuition
(time), in which all our perceptions must have place.
That something happens, then, is a perception which belongs to a
possible experience, which becomes real only because I look upon the
phenomenon as determined in regard to its place in time,
consequently as an object, which can always be found by means of a
rule in the connected series of my perceptions. But this rule of the
determination of a thing according to succession in time is as
follows: "In what precedes may be found the condition, under which
an event always (that is, necessarily) follows." From all this it is
obvious that the principle of cause and effect is the principle of
possible experience, that is, of objective cognition of phenomena,
in regard to their relations in the succession of time.
The proof of this fundamental proposition rests entirely on the
following momenta of argument. To all empirical cognition belongs
the synthesis of the manifold by the imagination, a synthesis which is
always successive, that is, in which the representations therein
always follow one another. But the order of succession in
imagination is not determined, and the series of successive
representations may be taken retrogressively as well as progressively.
But if this synthesis is a synthesis of apprehension (of the
manifold of a given phenomenon),then the order is determined in the
object, or to speak more accurately, there is therein an order of
successive synthesis which determines an object, and according to
which something necessarily precedes, and when this is posited,
something else necessarily follows. If, then, my perception is to
contain the cognition of an event, that is, of something which
really happens, it must be an empirical judgement, wherein we think
that the succession is determined; that is, it presupposes another
phenomenon, upon which this event follows necessarily, or in
conformity with a rule. If, on the contrary, when I posited the
antecedent, the event did not necessarily follow, I should be
obliged to consider it merely as a subjective play of my
imagination, and if in this I represented to myself anything as
objective, I must look upon it as a mere dream. Thus, the relation
of phenomena (as possible perceptions), according to which that
which happens is, as to its existence, necessarily determined in
time by something which antecedes, in conformity with a rule- in other
words, the relation of cause and effect- is the condition of the
objective validity of our empirical judgements in regard to the
sequence of perceptions, consequently of their empirical truth, and
therefore of experience. The principle of the relation of causality in
the succession of phenomena is therefore valid for all objects of
experience, because it is itself the ground of the possibility of
experience.
Here, however, a difficulty arises, which must be resolved. The
principle of the connection of causality among phenomena is limited in
our formula to the succession thereof, although in practice we find
that the principle applies also when the phenomena exist together in
the same time, and that cause and effect may be simultaneous. For
example, there is heat in a room, which does not exist in the open
air. I look about for the cause, and find it to be the fire, Now the
fire as the cause is simultaneous with its effect, the heat of the
room. In this case, then, there is no succession as regards time,
between cause and effect, but they are simultaneous; and still the law
holds good. The greater part of operating causes in nature are
simultaneous with their effects, and the succession in time of the
latter is produced only because the cause cannot achieve the total
of its effect in one moment. But at the moment when the effect first
arises, it is always simultaneous with the causality of its cause,
because, if the cause had but a moment before ceased to be, the effect
could not have arisen. Here it must be specially remembered that we
must consider the order of time and not the lapse thereof. The
relation remains, even though no time has elapsed. The time between
the causality of the cause and its immediate effect may entirely
vanish, and the cause and effect be thus simultaneous, but the
relation of the one to the other remains always determinable according
to time. If, for example, I consider a leaden ball, which lies upon
a cushion and makes a hollow in it, as a cause, then it is
simultaneous with the effect. But I distinguish the two through the
relation of time of the dynamical connection of both. For if I lay the
ball upon the cushion, then the hollow follows upon the before
smooth surface; but supposing the cushion has, from some cause or
another, a hollow, there does not thereupon follow a leaden ball.
Thus, the law of succession of time is in all instances the only
empirical criterion of effect in relation to the causality of the
antecedent cause. The glass is the cause of the rising of the water
above its horizontal surface, although the two phenomena are
contemporaneous. For, as soon as I draw some water with the glass from
a larger vessel, an effect follows thereupon, namely, the change of
the horizontal state which the water had in the large vessel into a
concave, which it assumes in the glass.
This conception of causality leads us to the conception of action;
that of action, to the conception of force; and through it, to the
conception of substance. As I do not wish this critical essay, the
sole purpose of which is to treat of the sources of our synthetical
cognition a priori, to be crowded with analyses which merely
explain, but do not enlarge the sphere of our conceptions, I reserve
the detailed explanation of the above conceptions for a future
system of pure reason. Such an analysis, indeed, executed with great
particularity, may already be found in well-known works on this
subject. But I cannot at present refrain from making a few remarks
on the empirical criterion of a substance, in so far as it seems to be
more evident and more easily recognized through the conception of
action than through that of the permanence of a phenomenon.
Where action (consequently activity and force) exists, substance
also must exist, and in it alone must be sought the seat of that
fruitful source of phenomena. Very well. But if we are called upon
to explain what we mean by substance, and wish to avoid the vice of
reasoning in a circle, the answer is by no means so easy. How shall we
conclude immediately from the action to the permanence of that which
acts, this being nevertheless an essential and peculiar criterion of
substance (phenomenon)? But after what has been said above, the
solution of this question becomes easy enough, although by the
common mode of procedure- merely analysing our conceptions- it would
be quite impossible. The conception of action indicates the relation
of the subject of causality to the effect. Now because all effect
consists in that which happens, therefore in the changeable, the
last subject thereof is the permanent, as the substratum of all that
changes, that is, substance. For according to the principle of
causality, actions are always the first ground of all change in
phenomena and, consequently, cannot be a property of a subject which
itself changes, because if this were the case, other actions and
another subject would be necessary to determine this change. From
all this it results that action alone, as an empirical criterion, is a
sufficient proof of the presence of substantiality, without any
necessity on my part of endeavouring to discover the permanence of
substance by a comparison. Besides, by this mode of induction we could
not attain to the completeness which the magnitude and strict
universality of the conception requires. For that the primary
subject of the causality of all arising and passing away, all origin
and extinction, cannot itself (in the sphere of phenomena) arise and
pass away, is a sound and safe conclusion, a conclusion which leads us
to the conception of empirical necessity and permanence in
existence, and consequently to the conception of a substance as
phenomenon.
When something happens, the mere fact of the occurrence, without
regard to that which occurs, is an object requiring investigation. The
transition from the non-being of a state into the existence of it,
supposing that this state contains no quality which previously existed
in the phenomenon, is a fact of itself demanding inquiry. Such an
event, as has been shown in No. A, does not concern substance (for
substance does not thus originate), but its condition or state. It
is therefore only change, and not origin from nothing. If this
origin be regarded as the effect of a foreign cause, it is termed
creation, which cannot be admitted as an event among phenomena,
because the very possibility of it would annihilate the unity of
experience. If, however, I regard all things not as phenomena, but
as things in themselves and objects of understanding alone, they,
although substances, may be considered as dependent, in respect of
their existence, on a foreign cause. But this would require a very
different meaning in the words, a meaning which could not apply to
phenomena as objects of possible experience.
How a thing can be changed, how it is possible that upon one state
existing in one point of time, an opposite state should follow in
another point of time- of this we have not the smallest conception a
priori. There is requisite for this the knowledge of real powers,
which can only be given empirically; for example, knowledge of
moving forces, or, in other words, of certain successive phenomena (as
movements) which indicate the presence of such forces. But the form of
every change, the condition under which alone it can take place as the
coming into existence of another state (be the content of the
change, that is, the state which is changed, what it may), and
consequently the succession of the states themselves can very well
be considered a priori, in relation to the law of causality and the
conditions of time.*
*It must be remarked that I do not speak of the change of certain
relations, but of the change of the state. Thus, when a body moves
in a uniform manner, it does not change its state (of motion); but
only when all motion increases or decreases.
When a substance passes from one state, a, into another state, b,
the point of time in which the latter exists is different from, and
subsequent to that in which the former existed. In like manner, the
second state, as reality (in the phenomenon), differs from the
first, in which the reality of the second did not exist, as b from
zero. That is to say, if the state, b, differs from the state, a, only
in respect to quantity, the change is a coming into existence of b -
a, which in the former state did not exist, and in relation to which
that state is = O.
Now the question arises how a thing passes from one state = a,
into another state = b. Between two moments there is always a
certain time, and between two states existing in these moments there
is always a difference having a certain quantity (for all parts of
phenomena are in their turn quantities). Consequently, every
transition from one state into another is always effected in a time
contained between two moments, of which the first determines the state
which leaves, and the second determines the state into the thing
passes. the thing leaves, and the second determines the state into
which the thing Both moments, then, are limitations of the time of a
change, consequently of the intermediate state between both, and as
such they belong to the total of the change. Now every change has a
cause, which evidences its causality in the whole time during which
the charge takes place. The cause, therefore, does not produce the
change all at once or in one moment, but in a time, so that, as the
time gradually increases from the commencing instant, a, to its
completion at b, in like manner also, the quantity of the reality
(b - a) is generated through the lesser degrees which are contained
between the first and last. All change is therefore possible only
through a continuous action of the causality, which, in so far as it
is uniform, we call a momentum. The change does not consist of these
momenta, but is generated or produced by them as their effect.
Such is the law of the continuity of all change, the ground of which
is that neither time itself nor any phenomenon in time consists of
parts which are the smallest possible, but that, notwithstanding,
the state of a thing passes in the process of a change through all
these parts, as elements, to its second state. There is no smallest
degree of reality in a phenomenon, just as there is no smallest degree
in the quantity of time; and so the new state of reality grows up
out of the former state, through all the infinite degrees thereof, the
differences of which one from another, taken all together, are less
than the difference between o and a.
It is not our business to inquire here into the utility of this
principle in the investigation of nature. But how such a
proposition, which appears so greatly to extend our knowledge of
nature, is possible completely a priori, is indeed a question which
deserves investigation, although the first view seems to demonstrate
the truth and reality of the principle, and the question, how it is
possible, may be considered superfluous. For there are so many
groundless pretensions to the enlargement of our knowledge by pure
reason that we must take it as a general rule to be mistrustful of all
such, and without a thoroughgoing and radical deduction, to believe
nothing of the sort even on the clearest dogmatical evidence.
Every addition to our empirical knowledge, and every advance made in
the exercise of our perception, is nothing more than an extension of
the determination of the internal sense, that is to say, a progression
in time, be objects themselves what they may, phenomena, or pure
intuitions. This progression in time determines everything, and is
itself determined by nothing else. That is to say, the parts of the
progression exist only in time, and by means of the synthesis thereof,
and are not given antecedently to it. For this reason, every
transition in perception to anything which follows upon another in
time, is a determination of time by means of the production of this
perception. And as this determination of time is, always and in all
its parts, a quantity, the perception produced is to be considered
as a quantity which proceeds through all its degrees- no one of
which is the smallest possible- from zero up to its determined degree.
From this we perceive the possibility of cognizing a priori a law of
changes- a law, however, which concerns their form merely. We merely
anticipate our own apprehension, the formal condition of which,
inasmuch as it is itself to be found in the mind antecedently to all
given phenomena, must certainly be capable of being cognized a priori.
Thus, as time contains the sensuous condition a priori of the
possibility of a continuous progression of that which exists to that
which follows it, the understanding, by virtue of the unity of
apperception, contains the condition a priori of the possibility of
a continuous determination of the position in time of all phenomena,
and this by means of the series of causes and effects, the former of
which necessitate the sequence of the latter, and thereby render
universally and for all time, and by consequence, objectively, valid
the empirical cognition of the relations of time.
C. THIRD ANALOGY.
Principle of Coexistence, According to the Law
of Reciprocity or Community.
All substances, in so far as they can be perceived in space
at the same time, exist in a state of complete reciprocity
of action.
PROOF.
Things are coexistent, when in empirical intuition the perception of
the one can follow upon the perception of the other, and vice versa-
which cannot occur in the succession of phenomena, as we have shown in
the explanation of the second principle. Thus I can perceive the
moon and then the earth, or conversely, first the earth and then the
moon; and for the reason that my perceptions of these objects can
reciprocally follow each other, I say, they exist contemporaneously.
Now coexistence is the existence of the manifold in the same time. But
time itself is not an object of perception; and therefore we cannot
conclude from the fact that things are placed in the same time, the
other fact, that the perception of these things can follow each
other reciprocally. The synthesis of the imagination in apprehension
would only present to us each of these perceptions as present in the
subject when the other is not present, and contrariwise; but would not
show that the objects are coexistent, that is to say, that, if the one
exists, the other also exists in the same time, and that this is
necessarily so, in order that the perceptions may be capable of
following each other reciprocally. It follows that a conception of the
understanding or category of the reciprocal sequence of the
determinations of phenomena (existing, as they do, apart from each
other, and yet contemporaneously), is requisite to justify us in
saying that the reciprocal succession of perceptions has its
foundation in the object, and to enable us to represent coexistence as
objective. But that relation of substances in which the one contains
determinations the ground of which is in the other substance, is the
relation of influence. And, when this influence is reciprocal, it is
the relation of community or reciprocity. Consequently the coexistence
of substances in space cannot be cognized in experience otherwise than
under the precondition of their reciprocal action. This is therefore
the condition of the possibility of things themselves as objects of
experience.
Things are coexistent, in so far as they exist in one and the same
time. But how can we know that they exist in one and the same time?
Only by observing that the order in the synthesis of apprehension of
the manifold is arbitrary and a matter of indifference, that is to
say, that it can proceed from A, through B, C, D, to E, or
contrariwise from E to A. For if they were successive in time (and
in the order, let us suppose, which begins with A), it is quite
impossible for the apprehension in perception to begin with E and go
backwards to A, inasmuch as A belongs to past time and, therefore,
cannot be an object of apprehension.
Let us assume that in a number of substances considered as phenomena
each is completely isolated, that is, that no one acts upon another.
Then I say that the coexistence of these cannot be an object of
possible perception and that the existence of one cannot, by any
mode of empirical synthesis, lead us to the existence of another.
For we imagine them in this case to be separated by a completely
void space, and thus perception, which proceeds from the one to the
other in time, would indeed determine their existence by means of a
following perception, but would be quite unable to distinguish whether
the one phenomenon follows objectively upon the first, or is
coexistent with it.
Besides the mere fact of existence, then, there must be something by
means of which A determines the position of B in time and, conversely,
B the position of A; because only under this condition can
substances be empirically represented as existing contemporaneously.
Now that alone determines the position of another thing in time
which is the cause of it or of its determinations. Consequently
every substance (inasmuch as it can have succession predicated of it
only in respect of its determinations) must contain the causality of
certain determinations in another substance, and at the same time
the effects of the causality of the other in itself. That is to say,
substances must stand (mediately or immediately) in dynamical
community with each other, if coexistence is to be cognized in any
possible experience. But, in regard to objects of experience, that
is absolutely necessary without which the experience of these
objects would itself be impossible. Consequently it is absolutely
necessary that all substances in the world of phenomena, in so far
as they are coexistent, stand in a relation of complete community of
reciprocal action to each other.
The word community has in our language* two meanings, and contains
the two notions conveyed in the Latin communio and commercium. We
employ it in this place in the latter sense- that of a dynamical
community, without which even the community of place (communio spatii)
could not be empirically cognized. In our experiences it is easy to
observe that it is only the continuous influences in all parts of
space that can conduct our senses from one object to another; that the
light which plays between our eyes and the heavenly bodies produces
a mediating community between them and us, and thereby evidences their
coexistence with us; that we cannot empirically change our position
(perceive this change), unless the existence of matter throughout
the whole of space rendered possible the perception of the positions
we occupy; and that this perception can prove the contemporaneous
existence of these places only through their reciprocal influence, and
thereby also the coexistence of even the most remote objects- although
in this case the proof is only mediate. Without community, every
perception (of a phenomenon in space) is separated from every other
and isolated, and the chain of empirical representations, that is,
of experience, must, with the appearance of a new object, begin
entirely de novo, without the least connection with preceding
representations, and without standing towards these even in the
relation of time. My intention here is by no means to combat the
notion of empty space; for it may exist where our perceptions cannot
exist, inasmuch as they cannot reach thereto, and where, therefore, no
empirical perception of coexistence takes place. But in this case it
is not an object of possible experience.
*German.
The following remarks may be useful in the way of explanation. In
the mind, all phenomena, as contents of a possible experience, must
exist in community (communio) of apperception or consciousness, and in
so far as it is requisite that objects be represented as coexistent
and connected, in so far must they reciprocally determine the position
in time of each other and thereby constitute a whole. If this
subjective community is to rest upon an objective basis, or to be
applied to substances as phenomena, the perception of one substance
must render possible the perception of another, and conversely. For
otherwise succession, which is always found in perceptions as
apprehensions, would be predicated of external objects, and their
representation of their coexistence be thus impossible. But this is
a reciprocal influence, that is to say, a real community
(commercium) of substances, without which therefore the empirical
relation of coexistence would be a notion beyond the reach of our
minds. By virtue of this commercium, phenomena, in so far as they
are apart from, and nevertheless in connection with each other,
constitute a compositum reale. Such composita are possible in many
different ways. The three dynamical relations then, from which all
others spring, are those of inherence, consequence, and composition.
These, then, are the three analogies of experience. They are nothing
more than principles of the determination of the existence of
phenomena in time, according to the three modi of this
determination; to wit, the relation to time itself as a quantity
(the quantity of existence, that is, duration), the relation in time
as a series or succession, finally, the relation in time as the
complex of all existence (simultaneity). This unity of determination
in regard to time is thoroughly dynamical; that is to say, time is not
considered as that in which experience determines immediately to every
existence its position; for this is impossible, inasmuch as absolute
time is not an object of perception, by means of which phenomena can
be connected with each other. On the contrary, the rule of the
understanding, through which alone the existence of phenomena can
receive synthetical unity as regards relations of time, determines for
every phenomenon its position in time, and consequently a priori,
and with validity for all and every time.
By nature, in the empirical sense of the word, we understand the
totality of phenomena connected, in respect of their existence,
according to necessary rules, that is, laws. There are therefore
certain laws (which are moreover a priori) which make nature possible;
and all empirical laws can exist only by means of experience, and by
virtue of those primitive laws through which experience itself becomes
possible. The purpose of the analogies is therefore to represent to us
the unity of nature in the connection of all phenomena under certain
exponents, the only business of which is to express the relation of
time (in so far as it contains all existence in itself) to the unity
of apperception, which can exist in synthesis only according to rules.
The combined expression of all is this: "All phenomena exist in one
nature, and must so exist, inasmuch as without this a priori unity, no
unity of experience, and consequently no determination of objects in
experience, is possible."
As regards the mode of proof which we have employed in treating of
these transcendental laws of nature, and the peculiar character of
we must make one remark, which will at the same time be important as a
guide in every other attempt to demonstrate the truth of
intellectual and likewise synthetical propositions a priori. Had we
endeavoured to prove these analogies dogmatically, that is, from
conceptions; that is to say, had we employed this method in attempting
to show that everything which exists, exists only in that which is
permanent- that every thing or event presupposes the existence of
something in a preceding state, upon which it follows in conformity
with a rule- lastly, that in the manifold, which is coexistent, the
states coexist in connection with each other according to a rule-
all our labour would have been utterly in vain. For more conceptions
of things, analyse them as we may, cannot enable us to conclude from
the existence of one object to the existence of another. What other
course was left for us to pursue? This only, to demonstrate the
possibility of experience as a cognition in which at last all
objects must be capable of being presented to us, if the
representation of them is to possess any objective reality. Now in
this third, this mediating term, the essential form of which
consists in the synthetical unity of the apperception of all
phenomena, we found a priori conditions of the universal and necessary
determination as to time of all existences in the world of
phenomena, without which the empirical determination thereof as to
time would itself be impossible, and we also discovered rules of
synthetical unity a priori, by means of which we could anticipate
experience. For want of this method, and from the fancy that it was
possible to discover a dogmatical proof of the synthetical
propositions which are requisite in the empirical employment of the
understanding, has it happened that a proof of the principle of
sufficient reason has been so often attempted, and always in vain. The
other two analogies nobody has ever thought of, although they have
always been silently employed by the mind,* because the guiding thread
furnished by the categories was wanting, the guide which alone can
enable us to discover every hiatus, both in the system of
conceptions and of principles.
*The unity of the universe, in which all phenomena to be
connected, is evidently a mere consequence of the admitted principle
of the community of all substances which are coexistent. For were
substances isolated, they could not as parts constitute a whole, and
were their connection (reciprocal action of the manifold) not
necessary from the very fact of coexistence, we could not conclude
from the fact of the latter as a merely ideal relation to the former
as a real one. We have, however, shown in its place that community
is the proper ground of the possibility of an empirical cognition of
coexistence, and that we may therefore properly reason from the latter
to the former as its condition.
4. THE POSTULATES OF EMPIRICAL THOUGHT.
1. That which agrees with the formal conditions (intuition and
conception) of experience, is possible.
2. That which coheres with the material conditions of experience
(sensation), is real.
3. That whose coherence with the real is determined according to
universal conditions of experience is (exists) necessary.
Explanation.
The categories of modality possess this peculiarity, that they do
not in the least determine the object, or enlarge the conception to
which they are annexed as predicates, but only express its relation to
the faculty of cognition. Though my conception of a thing is in itself
complete, I am still entitled to ask whether the object of it is
merely possible, or whether it is also real, or, if the latter,
whether it is also necessary. But hereby the object itself is not more
definitely determined in thought, but the question is only in what
relation it, including all its determinations, stands to the
understanding and its employment in experience, to the empirical
faculty of judgement, and to the reason of its application to
experience.
For this very reason, too, the categories of modality are nothing
more than explanations of the conceptions of possibility, reality, and
necessity, as employed in experience, and at the same time,
restrictions of all the categories to empirical use alone, not
authorizing the transcendental employment of them. For if they are
to have something more than a merely logical significance, and to be
something more than a mere analytical expression of the form of
thought, and to have a relation to things and their possibility,
reality, or necessity, they must concern possible experience and its
synthetical unity, in which alone objects of cognition can be given.
The postulate of the possibility of things requires also, that the
conception of the things agree with the formal conditions of our
experience in general. But this, that is to say, the objective form of
experience, contains all the kinds of synthesis which are requisite
for the cognition of objects. A conception which contains a
synthesis must be regarded as empty and, without reference to an
object, if its synthesis does not belong to experience- either as
borrowed from it, and in this case it is called an empirical
conception, or such as is the ground and a priori condition of
experience (its form), and in this case it is a pure conception, a
conception which nevertheless belongs to experience, inasmuch as its
object can be found in this alone. For where shall we find the
criterion or character of the possibility of an object which is
cogitated by means of an a priori synthetical conception, if not in
the synthesis which constitutes the form of empirical cognition of
objects? That in such a conception no contradiction exists is indeed a
necessary logical condition, but very far from being sufficient to
establish the objective reality of the conception, that is, the
possibility of such an object as is thought in the conception. Thus,
in the conception of a figure which is contained within two straight
lines, there is no contradiction, for the conceptions of two
straight lines and of their junction contain no negation of a
figure. The impossibility in such a case does not rest upon the
conception in itself, but upon the construction of it in space, that
is to say, upon the conditions of space and its determinations. But
these have themselves objective reality, that is, they apply to
possible things, because they contain a priori the form of
experience in general.
And now we shall proceed to point out the extensive utility and
influence of this postulate of possibility. When I represent to myself
a thing that is permanent, so that everything in it which changes
belongs merely to its state or condition, from such a conception alone
I never can cognize that such a thing is possible. Or, if I
represent to myself something which is so constituted that, when it is
posited, something else follows always and infallibly, my thought
contains no self-contradiction; but whether such a property as
causality is to be found in any possible thing, my thought alone
affords no means of judging. Finally, I can represent to myself
different things (substances) which are so constituted that the
state or condition of one causes a change in the state of the other,
and reciprocally; but whether such a relation is a property of
things cannot be perceived from these conceptions, which contain a
merely arbitrary synthesis. Only from the fact, therefore, that
these conceptions express a priori the relations of perceptions in
every experience, do we know that they possess objective reality, that
is, transcendental truth; and that independent of experience, though
not independent of all relation to form of an experience in general
and its synthetical unity, in which alone objects can be empirically
cognized.
But when we fashion to ourselves new conceptions of substances,
forces, action, and reaction, from the material presented to us by
perception, without following the example of experience in their
connection, we create mere chimeras, of the possibility of which we
cannot discover any criterion, because we have not taken experience
for our instructress, though we have borrowed the conceptions from
her. Such fictitious conceptions derive their character of possibility
not, like the categories, a priori, as conceptions on which all
experience depends, but only, a posteriori, as conceptions given by
means of experience itself, and their possibility must either be
cognized a posteriori and empirically, or it cannot be cognized at
all. A substance which is permanently present in space, yet without
filling it (like that tertium quid between matter and the thinking
subject which some have tried to introduce into metaphysics), or a
peculiar fundamental power of the mind of intuiting the future by
anticipation (instead of merely inferring from past and present
events), or, finally, a power of the mind to place itself in community
of thought with other men, however distant they may be- these are
conceptions the possibility of which has no ground to rest upon. For
they are not based upon experience and its known laws; and, without
experience, they are a merely arbitrary conjunction of thoughts,
which, though containing no internal contradiction, has no claim to
objective reality, neither, consequently, to the possibility of such
an object as is thought in these conceptions. As far as concerns
reality, it is self-evident that we cannot cogitate such a possibility
in concreto without the aid of experience; because reality is
concerned only with sensation, as the matter of experience, and not
with the form of thought, with which we can no doubt indulge in
shaping fancies.
But I pass by everything which derives its possibility from
reality in experience, and I purpose treating here merely of the
possibility of things by means of a priori conceptions. I maintain,
then, that the possibility of things is not derived from such
conceptions per se, but only when considered as formal and objective
conditions of an experience in general.
It seems, indeed, as if the possibility of a triangle could be
cognized from the conception of it alone (which is certainly
independent of experience); for we can certainly give to the
conception a corresponding object completely a priori, that is to say,
we can construct it. But as a triangle is only the form of an
object, it must remain a mere product of the imagination, and the
possibility of the existence of an object corresponding to it must
remain doubtful, unless we can discover some other ground, unless we
know that the figure can be cogitated under the conditions upon
which all objects of experience rest. Now, the facts that space is a
formal condition a priori of external experience, that the formative
synthesis, by which we construct a triangle in imagination, is the
very same as that we employ in the apprehension of a phenomenon for
the purpose of making an empirical conception of it, are what alone
connect the notion of the possibility of such a thing, with the
conception of it. In the same manner, the possibility of continuous
quantities, indeed of quantities in general, for the conceptions of
them are without exception synthetical, is never evident from the
conceptions in themselves, but only when they are considered as the
formal conditions of the determination of objects in experience. And
where, indeed, should we look for objects to correspond to our
conceptions, if not in experience, by which alone objects are
presented to us? It is, however, true that without antecedent
experience we can cognize and characterize the possibility of
things, relatively to the formal conditions, under which something
is determined in experience as an object, consequently, completely a
priori. But still this is possible only in relation to experience
and within its limits.
The postulate concerning the cognition of the reality of things
requires perception, consequently conscious sensation, not indeed
immediately, that is, of the object itself, whose existence is to be
cognized, but still that the object have some connection with a real
perception, in accordance with the analogies of experience, which
exhibit all kinds of real connection in experience.
From the mere conception of a thing it is impossible to conclude its
existence. For, let the conception be ever so complete, and containing
a statement of all the determinations of the thing, the existence of
it has nothing to do with all this, but only with thew question
whether such a thing is given, so that the perception of it can in
every case precede the conception. For the fact that the conception of
it precedes the perception, merely indicates the possibility of its
existence; it is perception which presents matter to the conception,
that is the sole criterion of reality. Prior to the perception of
the thing, however, and therefore comparatively a priori, we are
able to cognize its existence, provided it stands in connection with
some perceptions according to the principles of the empirical
conjunction of these, that is, in conformity with the analogies of
perception. For, in this case, the existence of the supposed thing
is connected with our perception in a possible experience, and we
are able, with the guidance of these analogies, to reason in the
series of possible perceptions from a thing which we do really
perceive to the thing we do not perceive. Thus, we cognize the
existence of a magnetic matter penetrating all bodies from the
perception of the attraction of the steel-filings by the magnet,
although the constitution of our organs renders an immediate
perception of this matter impossible for us. For, according to the
laws of sensibility and the connected context of our perceptions, we
should in an experience come also on an immediate empirical
intuition of this matter, if our senses were more acute- but this
obtuseness has no influence upon and cannot alter the form of possible
experience in general. Our knowledge of the existence of things
reaches as far as our perceptions, and what may be inferred from
them according to empirical laws, extend. If we do not set out from
experience, or do not proceed according to the laws of the empirical
connection of phenomena, our pretensions to discover the existence
of a thing which we do not immediately perceive are vain. Idealism,
however, brings forward powerful objections to these rules for proving
existence mediately. This is, therefore, the proper place for its
refutation.
REFUTATION OF IDEALISM.
Idealism- I mean material idealism- is the theory which declares the
existence of objects in space without us to be either () doubtful
and indemonstrable, or (2) false and impossible. The first is the
problematical idealism of Descartes, who admits the undoubted
certainty of only one empirical assertion (assertio), to wit, "I
am." The second is the dogmatical idealism of Berkeley, who
maintains that space, together with all the objects of which it is the
inseparable condition, is a thing which is in itself impossible, and
that consequently the objects in space are mere products of the
imagination. The dogmatical theory of idealism is unavoidable, if we
regard space as a property of things in themselves; for in that case
it is, with all to which it serves as condition, a nonentity. But
the foundation for this kind of idealism we have already destroyed
in the transcendental aesthetic. Problematical idealism, which makes
no such assertion, but only alleges our incapacity to prove the
existence of anything besides ourselves by means of immediate
experience, is a theory rational and evidencing a thorough and
philosophical mode of thinking, for it observes the rule not to form a
decisive judgement before sufficient proof be shown. The desired proof
must therefore demonstrate that we have experience of external things,
and not mere fancies. For this purpose, we must prove, that our
internal and, to Descartes, indubitable experience is itself
possible only under the previous assumption of external experience.
THEOREM.
The simple but empirically determined consciousness of
my own existence proves the existence of external
objects in space.
PROOF
I am conscious of my own existence as determined in time. All
determination in regard to time presupposes the existence of something
permanent in perception. But this permanent something cannot be
something in me, for the very reason that my existence in time is
itself determined by this permanent something. It follows that the
perception of this permanent existence is possible only through a
thing without me and not through the mere representation of a thing
without me. Consequently, the determination of my existence in time is
possible only through the existence of real things external to me.
Now, consciousness in time is necessarily connected with the
consciousness of the possibility of this determination in time.
Hence it follows that consciousness in time is necessarily connected
also with the existence of things without me, inasmuch as the
existence of these things is the condition of determination in time.
That is to say, the consciousness of my own existence is at the same
time an immediate consciousness of the existence of other things
without me.
Remark I. The reader will observe, that in the foregoing proof the
game which idealism plays is retorted upon itself, and with more
justice. It assumed that the only immediate experience is internal and
that from this we can only infer the existence of external things.
But, as always happens, when we reason from given effects to
determined causes, idealism bas reasoned with too much haste and
uncertainty, for it is quite possible that the cause of our
representations may lie in ourselves, and that we ascribe it falsely
to external things. But our proof shows that external experience is
properly immediate,* that only by virtue of it- not, indeed, the
consciousness of our own existence, but certainly the determination of
our existence in time, that is, internal experience- is possible. It
is true, that the representation "I am," which is the expression of
the consciousness which can accompany all my thoughts, is that which
immediately includes the existence of a subject. But in this
representation we cannot find any knowledge of the subject, and
therefore also no empirical knowledge, that is, experience. For
experience contains, in addition to the thought of something existing,
intuition, and in this case it must be internal intuition, that is,
time, in relation to which the subject must be determined. But the
existence of external things is absolutely requisite for this purpose,
so that it follows that internal experience is itself possible only
mediately and through external experience.
*The immediate consciousness of the existence of external things is,
in the preceding theorem, not presupposed, but proved, by the
possibility of this consciousness understood by us or not. The
question as to the possibility of it would stand thus: "Have we an
internal sense, but no external sense, and is our belief in external
perception a mere delusion?" But it is evident that, in order merely
to fancy to ourselves anything as external, that is, to present it
to the sense in intuition we must already possess an external sense,
and must thereby distinguish immediately the mere receptivity of an
external intuition from the spontaneity which characterizes every
act of imagination. For merely to imagine also an external sense,
would annihilate the faculty of intuition itself which is to be
determined by the imagination.
Remark II. Now with this view all empirical use of our faculty of
cognition in the determination of time is in perfect accordance. Its
truth is supported by the fact that it is possible to perceive a
determination of time only by means of a change in external
relations (motion) to the permanent in space (for example, we become
aware of the sun's motion by observing the changes of his relation
to the objects of this earth). But this is not all. We find that we
possess nothing permanent that can correspond and be submitted to
the conception of a substance as intuition, except matter. This idea
of permanence is not itself derived from external experience, but is
an a priori necessary condition of all determination of time,
consequently also of the internal sense in reference to our own
existence, and that through the existence of external things. In the
representation "I," the consciousness of myself is not an intuition,
but a merely intellectual representation produced by the spontaneous
activity of a thinking subject. It follows, that this "I" has not
any predicate of intuition, which, in its character of permanence,
could serve as correlate to the determination of time in the
internal sense- in the same way as impenetrability is the correlate of
matter as an empirical intuition.
Remark III. From the fact that the existence of external things is a
necessary condition of the possibility of a determined consciousness
of ourselves, it does not follow that every intuitive representation
of external things involves the existence of these things, for their
representations may very well be the mere products of the
imagination (in dreams as well as in madness); though, indeed, these
are themselves created by the reproduction of previous external
perceptions, which, as has been shown, are possible only through the
reality of external objects. The sole aim of our remarks has, however,
been to prove that internal experience in general is possible only
through external experience in general. Whether this or that
supposed experience be purely imaginary must be discovered from its
particular determinations and by comparing these with the criteria
of all real experience.
Finally, as regards the third postulate, it applies to material
necessity in existence, and not to merely formal and logical necessity
in the connection of conceptions. Now as we cannot cognize
completely a priori the existence of any object of sense, though we
can do so comparatively a priori, that is, relatively to some other
previously given existence- a cognition, however, which can only be of
such an existence as must be contained in the complex of experience,
of which the previously given perception is a part- the necessity of
existence can never be cognized from conceptions, but always, on the
contrary, from its connection with that which is an object of
perception. But the only existence cognized, under the condition of
other given phenomena, as necessary, is the existence of effects
from given causes in conformity with the laws of causality. It is
consequently not the necessity of the existence of things (as
substances), but the necessity of the state of things that we cognize,
and that not immediately, but by means of the existence of other
states given in perception, according to empirical laws of
causality. Hence it follows that the criterion of necessity is to be
found only in the law of possible experience- that everything which
happens is determined a priori in the phenomenon by its cause. Thus we
cognize only the necessity of effects in nature, the causes of which
are given us. Moreover, the criterion of necessity in existence
possesses no application beyond the field of possible experience,
and even in this it is not valid of the existence of things as
substances, because these can never be considered as empirical
effects, or as something that happens and has a beginning.
Necessity, therefore, regards only the relations of phenomena
according to the dynamical law of causality, and the possibility
grounded thereon, of reasoning from some given existence (of a
cause) a priori to another existence (of an effect). "Everything
that happens is hypothetically necessary," is a principle which
subjects the changes that take place in the world to a law, that is,
to a rule of necessary existence, without which nature herself could
not possibly exist. Hence the proposition, "Nothing happens by blind
chance (in mundo non datur casus)," is an a priori law of nature.
The case is the same with the proposition, "Necessity in nature is not
blind," that is, it is conditioned, consequently intelligible
necessity (non datur fatum). Both laws subject the play of change to
"a nature of things (as phenomena)," or, which is the same thing, to
the unity of the understanding, and through the understanding alone
can changes belong to an experience, as the synthetical unity of
phenomena. Both belong to the class of dynamical principles. The
former is properly a consequence of the principle of causality- one of
the analogies of experience. The latter belongs to the principles of
modality, which to the determination of causality adds the
conception of necessity, which is itself, however, subject to a rule
of the understanding. The principle of continuity forbids any leap
in the series of phenomena regarded as changes (in mundo non datur
saltus); and likewise, in the complex of all empirical intuitions in
space, any break or hiatus between two phenomena (non datur hiatus)-
for we can so express the principle, that experience can admit nothing
which proves the existence of a vacuum, or which even admits it as a
part of an empirical synthesis. For, as regards a vacuum or void,
which we may cogitate as out and beyond the field of possible
experience (the world), such a question cannot come before the
tribunal of mere understanding, which decides only upon questions that
concern the employment of given phenomena for the construction of
empirical cognition. It is rather a problem for ideal reason, which
passes beyond the sphere of a possible experience and aims at
forming a judgement of that which surrounds and circumscribes it,
and the proper place for the consideration of it is the transcendental
dialectic. These four propositions, "In mundo non datur hiatus, non
datur saltus, non datur casus, non datur fatum," as well as all
principles of transcendental origin, we could very easily exhibit in
their proper order, that is, in conformity with the order of the
categories, and assign to each its proper place. But the already
practised reader will do this for himself, or discover the clue to
such an arrangement. But the combined result of all is simply this, to
admit into the empirical synthesis nothing which might cause a break
in or be foreign to the understanding and the continuous connection of
all phenomena, that is, the unity of the conceptions of the
understanding. For in the understanding alone is the unity of
experience, in which all perceptions must have their assigned place,
possible.
Whether the field of possibility be greater than that of reality,
and whether the field of the latter be itself greater than that of
necessity, are interesting enough questions, and quite capable of
synthetic solution, questions, however, which come under the
jurisdiction of reason alone. For they are tantamount to asking
whether all things as phenomena do without exception belong to the
complex and connected whole of a single experience, of which every
given perception is a part which therefore cannot be conjoined with
any other phenomena- or, whether my perceptions can belong to more
than one possible experience? The understanding gives to experience,
according to the subjective and formal conditions, of sensibility as
well as of apperception, the rules which alone make this experience
possible. Other forms of intuition besides those of space and time,
other forms of understanding besides the discursive forms of
thought, or of cognition by means of conceptions, we can neither
imagine nor make intelligible to ourselves; and even if we could, they
would still not belong to experience, which is the only mode of
cognition by which objects are presented to us. Whether other
perceptions besides those which belong to the total of our possible
experience, and consequently whether some other sphere of matter
exists, the understanding has no power to decide, its proper
occupation being with the synthesis of that which is given.
Moreover, the poverty of the usual arguments which go to prove the
existence of a vast sphere of possibility, of which all that is real
(every object of experience) is but a small part, is very
remarkable. "All real is possible"; from this follows naturally,
according to the logical laws of conversion, the particular
proposition: "Some possible is real." Now this seems to be
equivalent to: "Much is possible that is not real." No doubt it does
seem as if we ought to consider the sum of the possible to be
greater than that of the real, from the fact that something must be
added to the former to constitute the latter. But this notion of
adding to the possible is absurd. For that which is not in the sum
of the possible, and consequently requires to be added to it, is
manifestly impossible. In addition to accordance with the formal
conditions of experience, the understanding requires a connection with
some perception; but that which is connected with this perception is
real, even although it is not immediately perceived. But that
another series of phenomena, in complete coherence with that which
is given in perception, consequently more than one all-embracing
experience is possible, is an inference which cannot be concluded from
the data given us by experience, and still less without any data at
all. That which is possible only under conditions which are themselves
merely possible, is not possible in any respect. And yet we can find
no more certain ground on which to base the discussion of the question
whether the sphere of possibility is wider than that of experience.
I have merely mentioned these questions, that in treating of the
conception of the understanding, there might be no omission of
anything that, in the common opinion, belongs to them. In reality,
however, the notion of absolute possibility (possibility which is
valid in every respect) is not a mere conception of the understanding,
which can be employed empirically, but belongs to reason alone,
which passes the bounds of all empirical use of the understanding.
We have, therefore, contented ourselves with a merely critical remark,
leaving the subject to be explained in the sequel.
Before concluding this fourth section, and at the same time the
system of all principles of the pure understanding, it seems proper to
mention the reasons which induced me to term the principles of
modality postulates. This expression I do not here use in the sense
which some more recent philosophers, contrary to its meaning with
mathematicians, to whom the word properly belongs, attach to it-
that of a proposition, namely, immediately certain, requiring
neither deduction nor proof. For if, in the case of synthetical
propositions, however evident they may be, we accord to them without
deduction, and merely on the strength of their own pretensions,
unqualified belief, all critique of the understanding is entirely
lost; and, as there is no want of bold pretensions, which the common
belief (though for the philosopher this is no credential) does not
reject, the understanding lies exposed to every delusion and
conceit, without the power of refusing its assent to those assertions,
which, though illegitimate, demand acceptance as veritable axioms.
When, therefore, to the conception of a thing an a priori
determination is synthetically added, such a proposition must
obtain, if not a proof, at least a deduction of the legitimacy of
its assertion.
The principles of modality are, however, not objectively
synthetical, for the predicates of possibility, reality, and necessity
do not in the least augment the conception of that of which they are
affirmed, inasmuch as they contribute nothing to the representation of
the object. But as they are, nevertheless, always synthetical, they
are so merely subjectively. That is to say, they have a reflective
power, and apply to the conception of a thing, of which, in other
respects, they affirm nothing, the faculty of cognition in which the
conception originates and has its seat. So that if the conception
merely agree with the formal conditions of experience, its object is
called possible; if it is in connection with perception, and
determined thereby, the object is real; if it is determined
according to conceptions by means of the connection of perceptions,
the object is called necessary. The principles of modality therefore
predicate of a conception nothing more than the procedure of the
faculty of cognition which generated it. Now a postulate in
mathematics is a practical proposition which contains nothing but
the synthesis by which we present an object to ourselves, and
produce the conception of it, for example- "With a given line, to
describe a circle upon a plane, from a given point"; and such a
proposition does not admit of proof, because the procedure, which it
requires, is exactly that by which alone it is possible to generate
the conception of such a figure. With the same right, accordingly, can
we postulate the principles of modality, because they do not
augment* the conception of a thing but merely indicate the manner in
which it is connected with the faculty of cognition.
*When I think the reality of a thing, I do really think more than
the possibility, but not in the thing; for that can never contain more
in reality than was contained in its complete possibility. But while
the notion of possibility is merely the notion of a position of
thing in relation to the understanding (its empirical use), reality is
the conjunction of the thing with perception.
GENERAL REMARK ON THE SYSTEM OF PRINCIPLES.
It is very remarkable that we cannot perceive the possibility of a
thing from the category alone, but must always have an intuition, by
which to make evident the objective reality of the pure conception
of the understanding. Take, for example, the categories of relation.
How (1) a thing can exist only as a subject, and not as a mere
determination of other things, that is, can be substance; or how
(2), because something exists, some other thing must exist,
consequently how a thing can be a cause; or how (3), when several
things exist, from the fact that one of these things exists, some
consequence to the others follows, and reciprocally, and in this way a
community of substances can be possible- are questions whose
solution cannot be obtained from mere conceptions. The very same is
the case with the other categories; for example, how a thing can be of
the same sort with many others, that is, can be a quantity, and so on.
So long as we have not intuition we cannot know whether we do really
think an object by the categories, and where an object can anywhere be
found to cohere with them, and thus the truth is established, that the
categories are not in themselves cognitions, but mere forms of thought
for the construction of cognitions from given intuitions. For the same
reason is it true that from categories alone no synthetical
proposition can be made. For example: "In every existence there is
substance," that is, something that can exist only as a subject and
not as mere predicate; or, "Everything is a quantity"- to construct
propositions such as these, we require something to enable us to go
out beyond the given conception and connect another with it. For the
same reason the attempt to prove a synthetical proposition by means of
mere conceptions, for example: "Everything that exists contingently
has a cause," has never succeeded. We could never get further than
proving that, without this relation to conceptions, we could not
conceive the existence of the contingent, that is, could not a
priori through the understanding cognize the existence of such a
thing; but it does not hence follow that this is also the condition of
the possibility of the thing itself that is said to be contingent. If,
accordingly; we look back to our proof of the principle of
causality, we shall find that we were able to prove it as valid only
of objects of possible experience, and, indeed, only as itself the
principle of the possibility of experience, Consequently of the
cognition of an object given in empirical intuition, and not from mere
conceptions. That, however, the proposition: "Everything that is
contingent must have a cause," is evident to every one merely from
conceptions, is not to be denied. But in this case the conception of
the contingent is cogitated as involving not the category of
modality (as that the non-existence of which can be conceive but
that of relation (as that which can exist only as the consequence of
something else), and so it is really an identical proposition: "That
which can exist only as a consequence, has a cause." In fact, when
we have to give examples of contingent existence, we always refer to
changes, and not merely to the possibility of conceiving the
opposite.* But change is an event, which, as such, is possible only
through a cause, and considered per se its non-existence is
therefore possible, and we become cognizant of its contingency from
the fact that it can exist only as the effect of a cause. Hence, if
a thing is assumed to be contingent, it is an analytical proposition
to say, it has a cause.
*We can easily conceive the non-existence of matter; but the
ancients did not thence infer its contingency. But even the
alternation of the existence and non-existence of a given state in a
thing, in which all change consists, by no means proves the
contingency of that state- the ground of proof being the reality of
its opposite. For example, a body is in a state of rest after
motion, but we cannot infer the contingency of the motion from the
fact that the former is the opposite of the latter. For this
opposite is merely a logical and not a real opposite to the other.
If we wish to demonstrate the contingency of the motion, what we ought
to prove is that, instead of the motion which took place in the
preceding point of time, it was possible for the body to have been
then in rest, not, that it is afterwards in rest; for in this case,
both opposites are perfectly consistent with each other.
But it is still more remarkable that, to understand the
possibility of things according to the categories and thus to
demonstrate the objective reality of the latter, we require not merely
intuitions, but external intuitions. If, for example, we take the pure
conceptions of relation, we find that (1) for the purpose of
presenting to the conception of substance something permanent in
intuition corresponding thereto and thus of demonstrating the
objective reality of this conception, we require an intuition (of
matter) in space, because space alone is permanent and determines
things as such, while time, and with it all that is in the internal
sense, is in a state of continual flow; (2) in order to represent
change as the intuition corresponding to the conception of
causality, we require the representation of motion as change in space;
in fact, it is through it alone that changes, the possibility of which
no pure understanding can perceive, are capable of being intuited.
Change is the connection of determinations contradictorily opposed
to each other in the existence of one and the same thing. Now, how
it is possible that out of a given state one quite opposite to it in
the same thing should follow, reason without an example can not only
not conceive, but cannot even make intelligible without intuition; and
this intuition is the motion of a point in space; the existence of
which in different spaces (as a consequence of opposite
determinations) alone makes the intuition of change possible. For,
in order to make even internal change cognitable, we require to
represent time, as the form of the internal sense, figuratively by a
line, and the internal change by the drawing of that line (motion),
and consequently are obliged to employ external intuition to be able
to represent the successive existence of ourselves in different
states. The proper ground of this fact is that all change to be
perceived as change presupposes something permanent in intuition,
while in the internal sense no permanent intuition is to be found.
Lastly, the objective possibility of the category of community
cannot be conceived by mere reason, and consequently its objective
reality cannot be demonstrated without an intuition, and that external
in space. For how can we conceive the possibility of community, that
is, when several substances exist, that some effect on the existence
of the one follows from the existence of the other, and
reciprocally, and therefore that, because something exists in the
latter, something else must exist in the former, which could not be
understood from its own existence alone? For this is the very
essence of community- which is inconceivable as a property of things
which are perfectly isolated. Hence, Leibnitz, in attributing to the
substances of the world- as cogitated by the understanding alone- a
community, required the mediating aid of a divinity; for, from their
existence, such a property seemed to him with justice inconceivable.
But we can very easily conceive the possibility of community (of
substances as phenomena) if we represent them to ourselves as in
space, consequently in external intuition. For external intuition
contains in itself a priori formal external relations, as the
conditions of the possibility of the real relations of action and
reaction, and therefore of the possibility of community. With the same
ease can it be demonstrated, that the possibility of things as
quantities, and consequently the objective reality of the category
of quantity, can be grounded only in external intuition, and that by
its means alone is the notion of quantity appropriated by the internal
sense. But I must avoid prolixity, and leave the task of
illustrating this by examples to the reader's own reflection.
The above remarks are of the greatest importance, not only for the
confirmation of our previous confutation of idealism, but still more
when the subject of self-cognition by mere internal consciousness
and the determination of our own nature without the aid of external
empirical intuitions is under discussion, for the indication of the
grounds of the possibility of such a cognition.
The result of the whole of this part of the analytic of principles
is, therefore: "All principles of the pure understanding are nothing
more than a priori principles of the possibility of experience, and to
experience alone do all a priori synthetical propositions apply and
relate"; indeed, their possibility itself rests entirely on this
relation.
