§ 14.
Nature is the existence of things, so far as it is determined
according to universal laws. Should nature signify the existence of
things in themselves, we could never cognise it either a priori or a
posteriori. Not a priori, for how can we know what belongs to things
in themselves, since this never can be done by the dissection of our
concepts (in analytical judgments)? We do not want to know what is
contained in our concept of a thing (for the [concept describes what]
belongs to its logical being), but what is in the actuality of the
thing superadded to our concept, and by what the thing itself is
determined in its existence outside the concept. Our understanding,
and the conditions on which alone it can connect the determinations of
things in their existence, do not prescribe any rule to things
themselves; these do not conform to our understanding, but it must
conform itself to them; they must therefore be first given us in order
to gather these determinations from them, wherefore they would not be
cognised a priori.
A cognition of the nature of things in themselves a posteriori would
be equally impossible. For, if experience is to teach us laws, to
which the existence of things is subject, these laws, if they regard
things in themselves, must belong to them of necessity even outside
our experience. But experience teaches us what exists and how it
exists, but never that it must necessarily exist so and not otherwise.
Experience therefore can never teach us the nature of things in
themselves.
§ 15. We nevertheless actually possess a pure science of nature in
which are propounded, a priori and with all the necessity requisite to
apodeictical propositions, laws to which nature is subject. I need
only call to witness that propaedeutic of natural science which, under
the title of the universal Science of Nature, precedes all Physics
(which is founded upon empirical principles). In it we have
Mathematics applied to appearance, and also merely discursive
principles (or those derived from concepts), which constitute the
philosophical part of the pure cognition of nature. But there are
several things in it, which are not quite pure and independent of
empirical sources: such as the concept of motion, that of
impenetrability (upon which the empirical concept of matter rests),
that of inertia, and many others, which prevent its being called a
perfectly pure science of nature. Besides, it only refers to objects
of the external sense, and therefore does not give an example of a
universal science of nature, in the strict sense, for such a science
must reduce nature in general, whether it regards the object of the
external or that of the internal sense (the object of Physics as well
as Psychology), to universal laws. But among the principles of this
universal physics there are a few which actually have the required
universality; for instance, the propositions that "substance is
permanent," and that "every event is determined by a cause according
to constant laws," etc. These are actually universal laws of nature,
which subsist completely a priori. There is then in fact a pure
science of nature, and the question arises, How is it possible?
§ 16. The word "nature" assumes yet another meaning, which determines
the object, whereas in the former sense it only denotes the conformity
to law [Gesetzmässigkeit] of the determinations of the existence of
things generally. If we consider it materialiter (i.e., in the matter
that forms its objects) "nature is the complex of all the objects of
experience." And with this only are we now concerned, for besides,
things which can never be objects of experience, if they must be
cognised as to their nature, would oblige us to have recourse to
concepts whose meaning could never be given in concreto (by any
example of possible experience). Consequently we must form for
ourselves a list of concepts of their nature, the reality whereof
(i.e., whether they actually refer to objects, or are mere creations
of thought) could never be determined. The cognition of what cannot be
an object of experience would be hyperphysical, and with things
hyperphysical we are here not concerned, but only with the cognition
of nature, the actuality of which can be confirmed by experience,
though it [the cognition of nature] is possible a priori and precedes
all experience.
§ 17. The formal [aspect] of nature in this narrower sense is
therefore the conformity to law of all the objects of experience, and
so far as it is cognised a priori, their necessary conformity. But it
has just been shown that the laws of nature can never be cognised a
priori in objects so far as they are considered not in reference to
possible experience, but as things in themselves. And our inquiry here
extends not to things in themselves (the properties of which we pass
by), but to things as objects of possible experience, and the complex
of these is what we properly designate as nature. And now I ask, when
the possibility of a cognition of nature a priori is in question,
whether it is better to arrange the problem thus: How can we cognise a
priori that things as objects of experience necessarily conform to
law? or thus: How is it possible to cognise a priori the necessary
conformity to law of experience itself as regards all its objects
generally?
Closely considered, the solution of the problem, represented in either
way, amounts, with regard to the pure cognition of nature (which is
the point of the question at issue), entirely to the same thing. For
the subjective laws, under which alone an empirical cognition of
things is possible, hold good of these things, as Objects of possible
experience (not as things in themselves, which are not considered
here). Either of the following statements means quite the same:
A judgment of observation can never rank as experience, without the
law, that "whenever an event is observed, it is always referred to
some antecedent, which it follows according to a universal rule."
"Everything, of which experience teaches that it happens, must have a
cause."
It is, however, more commendable to choose the first formula. For we
can a priori and previous to all given objects have a cognition of
those conditions, on which alone experience is possible, but never of
the laws to which things may in themselves be subject, without
reference to possible experience. We cannot therefore study the nature
of things a priori otherwise than by investigating the conditions and
the universal (though subjective) laws, under which alone such a
cognition as experience (as to mere form) is possible, and we
determine accordingly the possibility of things, as objects of
experience. For if I should choose the second formula, and seek the
conditions a priori, on which nature as an object of experience is
possible, I might easily fall into error, and fancy that I was
speaking of nature as a thing in itself, and then move round in
endless circles, in a vain search for laws concerning things of which
nothing is given me.
Accordingly we shall here be concerned with experience only, and the
universal conditions of its possibility which are given a priori.
Thence we shall determine nature as the whole object of all possible
experience. I think it will be understood that I here do not mean the
rules of the observation of a nature that is already given, for these
already presuppose experience. I do not mean how (through experience)
we can study the laws of nature; for these would not then be laws a
priori, and would yield us no pure science of nature; but [I mean to
ask] how the conditions a priori of the possibility of experience are
at the same time the sources from which all the universal laws of
nature must be derived.
§ 18. In the first place we must state that, while all judgments of
experience (Erfahrungsurtheile) are empirical (i.e., have their ground
in immediate sense perception), vice versa, all empirical judgments
(empirische Urtheile) are not judgments of experience, but, besides
the empirical, and in general besides what is given to the sensuous
intuition, particular concepts must yet be superadded—concepts which
have their origin quite a priori in the pure understanding, and under
which every perception must be first of all subsumed and then by their
means changed into experience.{11}
===================================
{11} Empirical judgments (empirische Urtheile) are either mere
statements of fact, viz., records of a perception, or statements of a
natural law, implying a causal connexion between two facts. The former
Kant calls "judgments of perception" (Wahrnehmungsurtheile) the latter
"judgments of experience" (Erhfahrungsurtheile).—Ed.
===================================
Empirical judgments, so far as they have objective validity, are
judgments of experience; but those which are only subjectively valid,
I name mere judgments of perception. The latter require no pure
concept of the understanding, but only the logical connexion of
perception in a thinking subject. But the former always require,
besides the representation of the sensuous intuition, particular
concepts originally begotten in the understanding, which produce the
objective validity of the judgment of experience.
All our judgments are at first merely judgments of perception; they
hold good only for us (i.e., for our subject), and we do not till
afterwards give them a new reference (to an object), and desire that
they shall always hold good for us and in the same way for everybody
else; for when a judgment agrees with an object, all judgments
concerning the same object must likewise agree among themselves, and
thus the objective validity of the judgment of experience signifies
nothing else than its necessary universality of application. And
conversely when we have reason to consider a judgment necessarily
universal (which never depends upon perception, but upon the pure
concept of the understanding, under which the perception is subsumed),
we must consider it objective also, that is, that it expresses not
merely a reference of our perception to a subject, but a quality of
the object. For there would be no reason for the judgments of other
men necessarily agreeing with mine, if it were not the unity of the
object to which they all refer, and with which they accord; hence they
must all agree with one another.
§ 19. Therefore objective validity and necessary universality (for
everybody) are equivalent terms, and though we do not know the object
in itself, yet when we consider a judgment as universal, and also
necessary, we understand it to have objective validity. By this
judgment we cognise the object (though it remains unknown as it is in
itself) by the universal and necessary connexion of the given
perceptions. As this is the case with all objects of sense, judgments
of experience take their objective validity not from the immediate
cognition of the object (which is impossible), but from the condition
of universal validity in empirical judgments, which, as already said,
never rests upon empirical, or, in short, sensuous conditions, but
upon a pure concept of the understanding. The object always remains
unknown in itself; but when by the concept of the understanding the
connexion of the representations of the object, which are given to our
sensibility, is determined as universally valid, the object is
determined by this relation, and it is the judgment that is objective.
To illustrate the matter: When we say, "the room is warm, sugar sweet,
and wormwood bitter"{12}—we have only subjectively valid judgments. I
do not at all expect that I or any other person shall always find it
as I now do; each of these sentences only expresses a relation of two
sensations to the same subject, to myself, and that only in my present
state of perception; consequently they are not valid of the object.
Such are judgments of perception. Judgments of experience are of quite
a different nature. What experience teaches me under certain
circumstances, it must always teach me and everybody; and its validity
is not limited to the subject nor to its state at a particular time.
Hence I pronounce all such judgments as being objectively valid. For
instance, when I say the air is elastic, this judgment is as yet a
judgment of perception only—I do nothing but refer two of my
sensations to one another. But, if I would have it called a judgment
of experience, I require this connexion to stand under a condition,
which makes it universally valid. I desire therefore that I and
everybody else should always connect necessarily the same perceptions
under the same circumstances.
===================================
{12} I freely grant that these examples do not represent such judgments
of perception as ever could become judgments of experience, even
though a concept of the understanding were superadded, because they
refer merely to feeling, which everybody knows to be merely
subjective, and which of course can never be attributed to the object,
and consequently never become objective. I only wished to give here an
example of a judgment that is merely subjectively valid, containing no
ground for universal validity, and thereby for a relation to the
object. An example of the judgments of perception, which become
judgments of experience by superadded concepts of the understanding,
will be given in the next note.
===================================
§ 20. We must consequently analyse experience in order to see what is
contained in this product of the senses and of the understanding, and
how the judgment of experience itself is possible. The foundation is
the intuition of which I become conscious, i.e., perception
(perceptio), which pertains merely to the senses. But in the next
place, there are acts of judging (which belong only to the
understanding). But this judging may be twofold—first, I may merely
compare perceptions and connect them in a particular state of my
consciousness; or, secondly, I may connect them in consciousness
generally. The former judgment is merely a judgment of perception, and
of subjective validity only: it is merely a connexion of perceptions
in my mental state, without reference to the object. Hence it is not,
as is commonly imagined, enough for experience to compare perceptions
and to connect them in consciousness through judgment; there arises no
universality and necessity, for which alone judgments can become
objectively valid and be called experience.
Quite another judgment therefore is required before perception can
become experience. The given intuition must be subsumed under a
concept, which determines the form of judging in general relatively to
the intuition, connects its empirical consciousness in consciousness
generally, and thereby procures universal validity for empirical
judgments. A concept of this nature is a pure a priori concept of the
Understanding, which does nothing but determine for an intuition the
general way in which it can be used for judgments. Let the concept be
that of cause, then it determines the intuition which is subsumed
under it, e.g., that of air, relative to judgments in general, viz.,
the concept of air serves with regard to its expansion in the relation
of antecedent to consequent in a hypothetical judgment. The concept of
cause accordingly is a pure concept of the understanding, which is
totally disparate from all possible perception, and only serves to
determine the representation subsumed under it, relatively to
judgments in general, and so to make a universally valid judgment
possible.
Before, therefore, a judgment of perception can become a judgment of
experience, it is requisite that the perception should be subsumed
under some such a concept of the understanding; for instance, air
ranks under the concept of causes, which determines our judgment about
it in regard to its expansion as hypothetical.{13} Thereby the expansion
of the air is represented not as merely belonging to the perception of
the air in my present state or in several states of mine, or in the
state of perception of others, but as belonging to it necessarily. The
judgment, "the air is elastic," becomes universally valid, and a
judgment of experience, only by certain judgments preceding it, which
subsume the intuition of air under the concept of cause and effect:
and they thereby determine the perceptions not merely as regards one
another in me, but relatively to the form of judging in general, which
is here hypothetical, and in this way they render the empirical
judgment universally valid.
===================================
{13} As an easier example, we may take the following: "When the sun
shines on the stone, it grows warm." This judgment, however often I
and others may have perceived it, is a mere judgment of perception,
and contains no necessity; perceptions are only usually conjoined in
this manner. But if I say, "The sun warms the stone," I add to the
perception a concept of the understanding, viz., that of cause, which
connects with the concept of sunshine that of heat as a necessary
consequence, and the synthetical judgment becomes of necessity
universally valid, viz., objective, and is converted from a perception
into experience.
===================================
If all our synthetical judgments are analysed so far as they are
objectively valid, it will be found that they never consist of mere
intuitions connected only (as is commonly believed) by comparison into
a judgment; but that they would be impossible were not a pure concept
of the understanding superadded to the concepts abstracted from
intuition, under which concept these latter are subsumed, and in this
manner only combined into an objectively valid judgment. Even the
judgments of pure mathematics in their simplest axioms are not exempt
from this condition. The principle, "a straight line is the shortest
between two points," presupposes that the line is subsumed under the
concept of quantity, which certainly is no mere intuition, but has its
seat in the understanding alone, and serves to determine the intuition
(of the line) with regard to the judgments which may be made about it,
relatively to their quantity, that is, to plurality (as judicia
plurativa).{14} For under them it is understood that in a given
intuition there is contained a plurality of homogenous parts.
===================================
{14} This name seems preferable to the term particularia, which is used
for these judgments in logic. For the latter implies the idea that
they are not universal. But when I start from unity (in single
judgments) and so proceed to universality, I must not [even indirectly
and negatively] imply any reference to universality. I think plurality
merely without universality, and not the exception from universality.
This is necessary, if logical considerations shall form the basis of
the pure concepts of the understanding. However, there is no need of
making changes in logic.
===================================
§ 21. To prove, then, the possibility of experience so far as it
rests upon pure concepts of the understanding a priori, we must first
represent what belongs to judgments in general and the various
functions of the understanding, in a complete table. For the pure
concepts of the understanding must run parallel to these functions, as
such concepts are nothing more than concepts of intuitions in general,
so far as these are determined by one or other of these functions of
judging, in themselves, that is, necessarily and universally. Hereby
also the a priori principles of the possibility of all experience, as
of an objectively valid empirical cognition, will be precisely
determined. For they are nothing but propositions by which all
perception is (under certain universal conditions of intuition)
subsumed under those pure concepts of the understanding.
Logical Table of Judgments.
1. 2.
As to Quantity. As to Quality.
Universal. Affirmative.
Particular. Negative.
Singular. Infinite.
3. 4.
As to Relation. As to Modality.
Categorical. Problematical.
Hypothetical. Assertorial.
Disjunctive. Apodeictical.
Transcendental Table of the Pure Concepts of the Understanding.
1. 2.
As to Quantity. As to Quality.
Unity (the Measure). Reality.
Plurality (the Quantity). Negation.
Totality (the Whole). Limitation.
3. 4.
As to Relation. As to Modality.
Substance. Possibility.
Cause. Existence.
Community. Necessity.
Pure Physiological Table of the Universal Principles of the Science of Nature.
1. 2.
Axioms of Intuition. Anticipations of Perception.
3. 4.
Analogies of Experience. Postulates of Empirical Thinking
generally.
§ 21a. In order to comprise the whole matter in one idea, it is first
necessary to remind the reader that we are discussing not the origin
of experience, but of that which lies in experience. The former
pertains to empirical psychology, and would even then never be
adequately explained without the latter, which belongs to the Critique
of cognition, and particularly of the understanding.
Experience consists of intuitions, which belong to the sensibility,
and of judgments, which are entirely a work of the understanding. But
the judgments, which the understanding forms alone from sensuous
intuitions, are far from being judgments of experience. For in the one
case the judgment connects only the perceptions as they are given in
the sensuous intuition, while in the other the judgments must express
what experience in general, and not what the mere perception (which
possesses only subjective validity) contains. The judgment of
experience must therefore add to the sensuous intuition and its
logical connexion in a judgment (after it has been rendered universal
by comparison) something that determines the synthetical judgment as
necessary and therefore as universally valid. This can be nothing else
than that concept which represents the intuition as determined in
itself with regard to one form of judgment rather than another, viz.,
a concept of that synthetical unity of intuitions which can only be
represented by a given logical function of judgments.
§ 22. The sum of the matter is this: the business of the senses is to
intuite—that of the understanding is to think. But thinking is
uniting representations in one consciousness. This union originates
either merely relative to the subject, and is accidental and
subjective, or is absolute, and is necessary or objective. The union
of representations in one consciousness is judgment. Thinking
therefore is the same as judging, or referring representations to
judgments in general. Hence judgments are either merely subjective,
when representations are referred to a consciousness in one subject
only, and united in it, or objective, when they are united in a
consciousness generally, that is, necessarily. The logical functions
of all judgments are but various modes of uniting representations in
consciousness. But if they serve for concepts, they are concepts of
their necessary union in a consciousness, and so principles of
objectively valid judgments. This union in a consciousness is either
analytical, by identity, or synthetical, by the combination and
addition of various representations one to another. Experience
consists in the synthetical connexion of phenomena (perceptions) in
consciousness, so far as this connexion is necessary. Hence the pure
concepts of the understanding are those under which all perceptions
must be subsumed ere they can serve for judgments of experience, in
which the synthetical unity of the perceptions is represented as
necessary and universally valid.{15}
===================================
{15} But how does this proposition, "that judgments of experience
contain necessity in the synthesis of perceptions," agree with my
statement so often before inculcated, that "experience as cognition a
posteriori can afford contingent judgments only?" When I say that
experience teaches me something, I mean only the perception that lies
in experience,—for example, that heat always follows the shining of
the sun on a stone; consequently the proposition of experience is
always so far accidental. That this heat necessarily follows the
shining of the sun is contained indeed in the judgment of experience
(by means of the concept of cause), yet is a fact not learned by
experience; for conversely, experience is first of all generated by
this addition of the concept of the understanding (of cause) to
perception. How perception attains this addition may be seen by
referring in the Critique itself to the section on the Transcendental
faculty of Judgment [viz., in the first edition, Von dem Schematismus
der reinen Verstandsbegriffe].
===================================
§ 23. Judgments, when considered merely as the condition of the
union of given representations in a consciousness, are rules. These
rules, so far as they represent the union as necessary, are rules a
priori, and so far as they cannot be deduced from higher rules, are
fundamental principles. But in regard to the possibility of all
experience, merely in relation to the form of thinking in it, no
conditions of judgments of experience are higher than those which
bring the phenomena, according to the various form of their intuition,
under pure concepts of the understanding, and render the empirical
judgment objectively valid. These concepts are therefore the a priori
principles of possible experience.
The principles of possible experience are then at the same time
universal laws of nature, which can be cognised a priori. And thus the
problem in our second question, "How is the pure Science of Nature
possible?" is solved. For the system which is required for the form of
a science is to be met with in perfection here, because, beyond the
above-mentioned formal conditions of all judgments in general offered
in logic, no others are possible, and these constitute a logical
system. The concepts grounded thereupon, which contain the a priori
conditions of all synthetical and necessary judgments, accordingly
constitute a transcendental system. Finally the principles, by means
of which all phenomena are subsumed under these concepts, constitute a
physical{16} system, that is, a system of nature, which precedes all
empirical cognition of nature, makes it even possible, and hence may
in strictness be denominated the universal and pure science of nature.
===================================
{16} [Kant uses the term physiological in its etymological meaning as
"pertaining to the science of physics," i.e., nature in general, not
as we use the term now as "pertaining to the functions of the living
body." Accordingly it has been translated "physical."—Ed.]
===================================
§ 24. The first one{17} of the physiological principles subsumes all
phenomena, as intuitions in space and time, under the concept of
Quantity, and is so far a principle of the application of Mathematics
to experience. The second one subsumes the empirical element, viz.,
sensation which denotes the real in intuitions, not indeed directly
under the concept of quantity, because sensation is not an intuition
that contains either space or time, though it places the respective
object into both. But still there is between reality
(sense-representation) and the zero, or total void of intuition in
time, a difference which has a quantity. For between every given
degree of light and of darkness, between every degree of heat and of
absolute cold, between every degree of weight and of absolute
lightness, between every degree of occupied space and of totally void
space, diminishing degrees can be conceived, in the same manner as
between consciousness and total unconsciousness (the darkness of a
psychological blank) ever diminishing degrees obtain. Hence there is
no perception that can prove an absolute absence of it; for instance,
no psychological darkness that cannot be considered as a kind of
consciousness. This occurs in all cases of sensation, and so the
understanding can anticipate even sensations, which constitute the
peculiar quality of empirical representations (appearances), by means
of the principle: "that they all have (consequently that what is real
in all phenomena has) a degree." Here is the second application of
mathematics (mathesis intensorum) to the science of nature.
===================================
{17} The three following paragraphs will hardly be understood unless
reference be made to what the Critique itself says on the subject of
the Principles; they will, however, be of service in giving a general
view of the Principles, and in fixing the attention on the main
points.
===================================
§ 25. Anent the relation of appearances merely with a view to their
existence, the determination is not mathematical but dynamical, and
can never be objectively valid, consequently never fit for experience,
if it does not come under a priori principles by which the cognition
of experience relative to appearances becomes even possible. Hence
appearances must be subsumed under the concept of Substance, which is
the foundation of all determination of existence, as a concept of the
thing itself; or secondly—so far as, a succession is found among
phenomena, that is, an event—under the concept of an Effect with
reference to Cause; or lastly—so far as coexistence is to be known
objectively, that is, by a judgment of experience—under the concept
of Community (action and reaction).{18} Thus a priori principles form
the basis of objectively valid, though empirical judgments, that is,
of the possibility of experience so far as it must connect objects as
existing in nature. These principles are the proper laws of nature,
which may be termed dynamical.
===================================
{18} [Kant uses here the equivocal term Wechselwirkung.—Ed.]
===================================
Finally the cognition of the agreement and connexion not only of
appearances among themselves in experience, but of their relation to
experience in general, belongs to the judgments of experience. This
relation contains either their agreement with the formal conditions,
which the understanding cognises, or their coherence with the
materials of the senses and of perception, or combines both into one
concept. Consequently it contains Possibility, Actuality, and
Necessity according to universal laws of nature; and this constitutes
the physical doctrine of method, or the distinction of truth and of
hypotheses, and the bounds of the certainty of the latter.
§ 26. The third table of Principles drawn from the nature of the
understanding itself after the critical method, shows an inherent
perfection, which raises it far above every other table which has
hitherto though in vain been tried or may yet be tried by analysing
the objects themselves dogmatically. It exhibits all synthetical a
priori principles completely and according to one principle, viz., the
faculty of judging in general, constituting the essence of experience
as regards the understanding, so that we can be certain that there are
no more such principles, a satisfaction such as can never be attained
by the dogmatical method. Yet is this not all: there is a still
greater merit in it.
We must carefully bear in mind the proof which shows the possibility
of this cognition a priori, and at the same time limits all such
principles to a condition which must never be lost sight of, if we
desire it not to be misunderstood, and extended in use beyond the
original sense which the understanding attaches to it. This limit is
that they contain nothing but the conditions of possible experience in
general so far as it is subjected to laws a priori. Consequently I do
not say, that things in themselves possess a quantity, that their
actuality possesses a degree, their existence a connexion of accidents
in a substance, etc. This nobody can prove, because such a synthetical
connexion from mere concepts, without any reference to sensuous
intuition on the one side, or connexion of it in a possible experience
on the other, is absolutely impossible. The essential limitation of
the concepts in these principles then is: That all things stand
necessarily a priori under the afore-mentioned conditions, as objects
of experience only.
Hence there follows secondly a specifically peculiar mode of proof of
these principles: they are not directly referred to appearances and to
their relations, but to the possibility of experience, of which
appearances constitute the matter only, not the form. Thus they are
referred to objectively and universally valid synthetical
propositions, in which we distinguish judgments of experience from
those of perception. This takes place because appearances, as mere
intuitions, occupying a part of space and time, come under the concept
of Quantity, which unites their multiplicity a priori according to
rules synthetically. Again, so far as the perception contains, besides
intuition, sensibility, and between the latter and nothing (i.e., the
total disappearance of sensibility), there is an ever decreasing
transition, it is apparent that that which is in appearances must have
a degree, so far as it (viz., the perception) does not itself occupy
any part of space or of time.{19} Still the transition to actuality from
empty time or empty space is only possible in time; consequently
though sensibility, as the quality of empirical intuition, can never
be cognised a priori, by its specific difference from other
sensibilities, yet it can, in a possible experience in general, as a
quantity of perception be intensely distinguished from every other
similar perception. Hence the application of mathematics to nature, as
regards the sensuous intuition by which nature is given to us, becomes
possible and is thus determined.
===================================
{19} Heat and light are in a small space just as large as to degree as
in a large one; in like manner the internal representations, pain,
consciousness in general, whether they last a short or a long time,
need not vary as to the degree. Hence the quantity is here in a point
and in a moment just as great as in any space or time however great.
Degrees are therefore capable of increase, but not in intuition,
rather in mere sensation (or the quantity of the degree of an
intuition). Hence they can only be estimated quantitatively by the
relation of 1 to 0, viz., by their capability of decreasing by
infinite intermediate degrees to disappearance, or of increasing from
naught through infinite gradations to a determinate sensation in a
certain time. Quantitas qualitatis est gradus [i.e., the degrees of
quality must be measured by equality].
===================================
Above all, the reader must pay attention to the mode of proof of the
principles which occur under the title of Analogies of experience. For
these do not refer to the genesis of intuitions, as do the principles
of applied mathematics, but to the connexion of their existence in
experience; and this can be nothing but the determination of their
existence in time according to necessary laws, under which alone the
connexion is objectively valid, and thus becomes experience. The proof
therefore does not turn on the synthetical unity in the connexion of
things in themselves, but merely of perceptions, and of these not in
regard to their matter, but to the determination of time and of the
relation of their existence in it, according to universal laws. If the
empirical determination in relative time is indeed objectively valid
(i.e., experience), these universal laws contain the necessary
determination of existence in time generally (viz., according to a
rule of the understanding a priori).
In these Prolegomena I cannot further descant on the subject, but my
reader (who has probably been long accustomed to consider experience a
mere empirical synthesis of perceptions, and hence not considered that
it goes much beyond them, as it imparts to empirical judgments
universal validity, and for that purpose requires a pure and a priori
unity of the understanding) is recommended to pay special attention to
this distinction of experience from a mere aggregate of perceptions,
and to judge the mode of proof from this point of view.
§ 27. Now we are prepared to remove Hume's doubt. He justly
maintains, that we cannot comprehend by reason the possibility of
Causality, that is, of the reference of the existence of one thing to
the existence of another, which is necessitated by the former. I add,
that we comprehend just as little the concept of Subsistence, that is,
the necessity that at the foundation of the existence of things there
lies a subject which cannot itself be a predicate of any other thing;
nay, we cannot even form a notion of the possibility of such a thing
(though we can point out examples of its use in experience). The very
same in comprehensibility affects the Community of things, as we
cannot comprehend how from the state of one thing an inference to the
state of quite another thing beyond it, and vice versa, can be drawn,
and how substances which have each their own separate existence should
depend upon one another necessarily. But I am very far from holding
these concepts to be derived merely from experience, and the necessity
represented in them, to be imaginary and a mere illusion produced in
us by long habit. On the contrary, I have amply shown, that they and
the theorems derived from them are firmly established a priori, or
before all experience, and have their undoubted objective value,
though only with regard to experience.
§ 28. Though I have no notion of such a connexion of things in
themselves, that they can either exist as substances, or act as
causes, or stand in community with others (as parts of a real whole),
and I can just as little conceive such properties in appearances as
such (because those concepts contain nothing that lies in the
appearances, but only what the understanding alone must think): we
have yet a notion of such a connexion of representations in our
understanding, and in judgments generally; consisting in this that
representations appear in one sort of judgments as subject in relation
to predicates, in another as reason in relation to consequences, and
in a third as parts, which constitute together a total possible
cognition. Besides we cognise a priori that without considering the
representation of an object as determined in some of these respects,
we can have no valid cognition of the object, and, if we should occupy
ourselves about the object in itself, there is no possible attribute,
by which I could know that it is determined under any of these
aspects, that is, under the concept either of substance, or of cause,
or (in relation to other substances) of community, for I have no
notion of the possibility of such a connexion of existence. But the
question is not how things in themselves, but how the empirical
cognition of things is determined, as regards the above aspects of
judgments in general, that is, how things, as objects of experience,
can and shall be subsumed under these concepts of the understanding.
And then it is clear, that I completely comprehend not only the
possibility, but also the necessity of subsuming all phenomena under
these concepts, that is, of using them for principles of the
possibility of experience.
§ 29. When making an experiment with Hume's problematical concept
(his crux metaphysicorum), the concept of cause, we have, in the first
place, given a priori, by means of logic, the form of a conditional
judgment in general, i.e., we have one given cognition as antecedent
and another as consequence. But it is possible, that in perception we
may meet with a rule of relation, which runs thus: that a certain
phenomenon is constantly followed by another (though not conversely),
and this is a case for me to use the hypothetical judgment, and, for
instance, to say, it the sun shines long enough upon a body, it grows
warm. Here there is indeed as yet no necessity of connexion, or
concept of cause. But I proceed and say, that if this proposition,
which is merely a subjective connexion of perceptions, is to be a
judgment of experience, it must be considered as necessary and
universally valid. Such a proposition would be, "the sun is by its
light the cause of heat." The empirical rule is now considered as a
law, and as valid not merely of appearances but valid of them for the
purposes of a possible experience which requires universal and
therefore necessarily valid rules. I therefore easily comprehend the
concept of cause, as a concept necessarily belonging to the mere form
of experience, and its possibility as a synthetical union of
perceptions in consciousness generally; but I do not at all comprehend
the possibility of a thing generally as a cause, because the concept
of cause denotes a condition not at all belonging to things, but to
experience. It is nothing in fact but an objectively valid cognition
of appearances and of their succession, so far as the antecedent can
be conjoined with the consequent according to the rule of hypothetical
judgments.
§ 30. Hence if the pure concepts of the understanding do not refer to
objects of experience but to things in themselves (noumena), they have
no signification whatever. They serve, as it were, only to decipher
appearances, that we may be able to read them as experience. The
principles which arise from their reference to the sensible world,
only serve our understanding for empirical use. Beyond this they are
arbitrary combinations, without objective reality, and we can neither
cognise their possibility a priori, nor verify their reference to
objects, let alone make it intelligible by any example; because
examples can only be borrowed from some possible experience,
consequently the objects of these concepts can be found nowhere but in
a possible experience.
This complete (though to its originator unexpected) solution of Hume's
problem rescues for the pure concepts of the understanding their a
priori origin, and for the universal laws of nature their validity, as
laws of the understanding, yet in such a way as to limit their use to
experience, because their possibility depends solely on the reference
of the understanding to experience, but with a completely reversed
mode of connexion which never occurred to Hume, not by deriving them
from experience, but by deriving experience from them.
This is therefore the result of all our foregoing inquiries: "All
synthetical principles a priori are nothing more than principles of
possible experience, and can never be referred to things in
themselves, but to appearances as objects of experience. And hence
pure mathematics as well as a pure science of nature can never be
referred to anything more than mere appearances, and can only
represent either that which makes experience generally possible, or
else that which, as it is derived from these principles, must always
be capable of being represented in some possible experience.
§ 31. And thus we have at last something definite, upon which to
depend in all metaphysical enterprises, which have hitherto, boldly
enough but always at random, attempted everything without
discrimination. That the aim of their exertions should be so near,
struck neither the dogmatical thinkers nor those who, confident in
their supposed sound common sense, started with concepts and
principles of pure reason (which were legitimate and natural, but
destined for mere empirical use) in quest of fields of knowledge, to
which they neither knew nor could know any determinate bounds, because
they had never reflected nor were able to reflect on the nature or
even on the possibility of such a pure understanding.
Many a naturalist of pure reason (by which I mean the man who believes
he can decide in matters of metaphysics without any science) may
pretend, that he long ago by the prophetic spirit of his sound sense,
not only suspected, but knew and comprehended, what is here propounded
with so much ado, or, if he likes, with prolix and pedantic pomp:
"that with all our reason we can never reach beyond the field of
experience." But when he is questioned about his rational principles
individually, he must grant, that there are many of them which he has
not taken from experience, and which are therefore independent of it
and valid a priori. How then and on what grounds will he restrain both
himself and the dogmatist, who makes use of these concepts and
principles beyond all possible experience, because they are recognised
to be independent of it? And even he, this adept in sound sense, in
spite of all his assumed and cheaply acquired wisdom, is not exempt
from wandering inadvertently beyond objects of experience into the
field of chimeras. He is often deeply enough involved in them, though
in announcing everything as mere probability, rational conjecture, or
analogy, he gives by his popular language a color to his groundless
pretensions.
§ 32. Since the oldest days of philosophy inquirers into pure reason
have conceived, besides the things of sense, or appearances
(phenomena), which make up the sensible world, certain creations of
the understanding (Verstandeswesen), called noumena, which should
constitute an intelligible world. And as appearance and illusion were
by those men identified (a thing which we may well excuse in an
undeveloped epoch), actuality was only conceded to the creations of
thought.
And we indeed, rightly considering objects of sense as mere
appearances, confess thereby that they are based upon a thing in
itself, though we know not this thing in its internal constitution,
but only know its appearances, viz., the way in which our senses are
affected by this unknown something. The understanding therefore, by
assuming appearances, grants the existence of things in themselves
also, and so far we may say, that the representation of such things as
form the basis of phenomena, consequently of mere creations of the
understanding, is not only admissible, but unavoidable.
Our critical deduction by no means excludes things of that sort
(noumena), but rather limits the principles of the Aesthetic (the
science of the sensibility) to this, that they shall not extend to all
things, as everything would then be turned into mere appearance, but
that they shall only hold good of objects of possible experience.
Hereby then objects of the understanding are granted, but with the
inculcation of this rule which admits of no exception: "that we
neither know nor can know anything at all definite of these pure
objects of the understanding, because our pure concepts of the
understanding as well as our pure intuitions extend to nothing but
objects of possible experience, consequently to mere things of sense,
and as soon as we leave this sphere these concepts retain no meaning
whatever."
§ 33. There is indeed something seductive in our pure concepts of the
understanding, which tempts us to a transcendent use, —a use which
transcends all possible experience. Not only are our concepts of
substance, of power, of action, of reality, and others, quite
independent of experience, containing nothing of sense appearance, and
so apparently applicable to things in themselves (noumena), but, what
strengthens this conjecture, they contain a necessity of determination
in themselves, which experience never attains. The concept of cause
implies a rule, according to which one state follows another
necessarily; but experience can only show us, that one state of things
often, or at most, commonly, follows another, and therefore affords
neither strict universality, nor necessity.
Hence the Categories seem to have a deeper meaning and import than can
be exhausted by their empirical use, and so the understanding
inadvertently adds for itself to the house of experience a much more
extensive wing, which it fills with nothing but creatures of thought,
without ever observing that it has transgressed with its otherwise
lawful concepts the bounds of their use.
§ 34. Two important, and even indispensable, though very dry,
investigations had therefore become indispensable in the Critique of
Pure Reason,—viz., the two chapters "Vom Schematismus der reinen
Verstandsbegriffe," and "Vom Grunde der Unterscheidung aller
Verstandesbegriffe überhaupt in Phänomena und Noumena." In the
former it is shown, that the senses furnish not the pure concepts of
the understanding in concreto, but only the schedule for their use,
and that the object conformable to it occurs only in experience (as
the product of the understanding from materials of the sensibility).
In the latter it is shown, that, although our pure concepts of the
understanding and our principles are independent of experience, and
despite of the apparently greater sphere of their use, still nothing
whatever can be thought by them beyond the field of experience,
because they can do nothing but merely determine the logical form of
the judgment relatively to given intuitions. But as there is no
intuition at all beyond the field of the sensibility, these pure
concepts, as they cannot possibly be exhibited in concreto, are void
of all meaning; consequently all these noumena, together with their
complex, the intelligible world,{20} are nothing but representation of a
problem, of which the object in itself is possible, but the solution,
from the nature of our understanding, totally impossible. For our
understanding is not a faculty of intuition, but of the connexion of
given intuitions in experience. Experience must therefore contain all
the objects for our concepts; but beyond it no concepts have any
significance, as there is no intuition that might offer them a
foundation.
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{20} We speak of the "intelligible world," not (as the usual expression
is) "intellectual world." For cognitions are intellectual through the
understanding, and refer to our world of sense also; but objects, so
far as they can be represented merely by the understanding, and to
which none of our sensible intuitions can refer, are termed
"intelligible." But as some possible intuition must correspond to
every object, we would have to assume an understanding that intuites
things immediately; but of such we have not the least notion, nor have
we of the things of the understanding [Verstandeswesen], to which it
should be applied.
===================================
§ 35. The imagination may perhaps be forgiven for occasional
vagaries, and for not keeping carefully within the limits of
experience, since it gains life and vigor by such flights, and since
it is always easier to moderate its boldness, than to stimulate its
languor. But the understanding which ought to think can never be
forgiven for indulging in vagaries; for we depend upon it alone for
assistance to set bounds, when necessary, to the vagaries of the
imagination.
But the understanding begins its aberrations very innocently and
modestly. It first elucidates the elementary cognitions, which inhere
in it prior to all experience, but yet must always have their
application in experience. It gradually drops these limits, and what
is there to prevent it, as it has quite freely derived its principles
from itself? And then it proceeds first to newly-imagined powers in
nature, then to beings, outside nature; in short to a world, for whose
construction the materials cannot be wanting, because fertile fiction
furnishes them abundantly, and though not confirmed, is never refuted,
by experience. This is the reason that young thinkers are so partial
to metaphysics of the truly dogmatical kind, and often sacrifice to it
their time and their talents, which might be otherwise better
employed.
But there is no use in trying to moderate these fruitless endeavors of
pure reason by all manner of cautions as to the difficulties of
solving questions so occult, by complaints of the limits of our
reason, and by degrading our assertions into mere conjectures. For if
their impossibility is not distinctly shown, and reason's cognition of
its own essence does not become a true science, in which the field of
its right use is distinguished, so to say, with mathematical certainty
from that of its worthless and idle use, these fruitless efforts will
never be abandoned for good.
§ 36. How is Nature itself possible?
This question—the highest point that transcendental philosophy can
ever reach, and to which, as its boundary and completion, it must
proceed—properly contains two questions.
First: How is nature at all possible in the material sense, by
intuition, considered as the totality of appearances; how are space,
time, and that which fills both—the object of sensation, in general
possible? The answer is: By means of the constitution of our
Sensibility, according to which it is specifically affected by
objects, which are in themselves unknown to it, and totally distinct
from those phenomena. This answer is given in the Critique itself in
the transcendental Aesthetic, and in these Prolegomena by the solution
of the first general problem.
Secondly: How is nature possible in the formal sense, as the totality
of the rules, under which all phenomena must come, in order to be
thought as connected in experience? The answer must be this: It is
only possible by means of the constitution of our Understanding,
according to which all the above representations of the sensibility
are necessarily referred to a consciousness, and by which the peculiar
way in which we think (viz., by rules), and hence experience also, are
possible, but must be clearly distinguished from an insight into the
objects in themselves. This answer is given in the Critique itself in
the transcendental Logic, and in these Prolegomena, in the course of
the solution of the second main problem.
But how this peculiar property of our sensibility itself is possible,
or that of our understanding and of the apperception which is
necessarily its basis and that of all thinking, cannot be further
analysed or answered, because it is of them that we are in need for
all our answers and for all our thinking about objects.
There are many laws of nature, which we can only know by means of
experience; but conformity to law in the connexion of appearances,
i.e., in nature in general, we cannot discover by any experience,
because experience itself requires laws which are a priori at the
basis of its possibility.
The possibility of experience in general is therefore at the same time
the universal law of nature, and the principles of the experience are
the very laws of nature. For we do not know nature but as the totality
of appearances, i.e., of representations in us, and hence we can only
derive the laws of its connexion from the principles of their
connexion in us, that is, from the conditions of their necessary union
in consciousness, which constitutes the possibility of experience.
Even the main proposition expounded throughout this section—that
universal laws of nature can be distinctly cognised a priori—leads
naturally to the proposition: that the highest legislation of nature
must lie in ourselves, i.e., in our understanding, and that we must
not seek the universal laws of nature in nature by means of
experience, but conversely must seek nature, as to its universal
conformity to law, in the conditions of the possibility of experience,
which lie in our sensibility and in our understanding. For how were it
otherwise possible to know a priori these laws, as they are not rules
of analytical cognition, but truly synthetical extensions of it?
Such a necessary agreement of the principles of possible experience
with the laws of the possibility of nature, can only proceed from one
of two reasons: either these laws are drawn from nature by means of
experience, or conversely nature is derived from the laws of the
possibility of experience in general, and is quite the same as the
mere universal conformity to law of the latter. The former is
self-contradictory, for the universal laws of nature can and must be
cognised a priori (that is, independent of all experience), and be the
foundation of all empirical use of the understanding; the latter
alternative therefore alone remains.{21}
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{21} Crusius alone thought of a compromise: that a Spirit, who can
neither err nor deceive, implanted these laws in us originally. But
since false principles often intrude themselves, as indeed the very
system of this man shows in not a few examples, we are involved in
difficulties as to the use of such a principle in the absence of sure
criteria to distinguish the genuine origin from the spurious, as we
never can know certainly what the Spirit of truth or the father of
lies may have instilled into us.
===================================
But we must distinguish the empirical laws of nature, which always
presuppose particular perceptions, from the pure or universal laws of
nature, which, without being based on particular perceptions, contain
merely the conditions of their necessary union in experience. In
relation to the latter, nature and possible experience are quite the
same, and as the conformity to law here depends upon the necessary
connexion of appearances in experience (without which we cannot
cognise any object whatever in the sensible world), consequently upon
the original laws of the understanding, it seems at first strange, but
is not the less certain, to say:
The understanding does not derive its laws (a priori) from, but
prescribes them to, nature.
§ 37. We shall illustrate this seemingly bold proposition by an
example, which will show, that laws, which we discover in objects of
sensuous intuition (especially when these laws are cognised as
necessary), are commonly held by us to be such as have been placed
there by the understanding, in spite of their being similar in all
points to the laws of nature, which we ascribe to experience.
§ 38. If we consider the properties of the circle, by which this
figure combines so many arbitrary determinations of space in itself,
at once in a universal rule, we cannot avoid attributing a
constitution (eine Natur) to this geometrical thing. Two right lines,
for example, which intersect one another and the circle, howsoever
they may be drawn, are always divided so that the rectangle
constructed with the segments of the one is equal to that constructed
with the segments of the other. The question now is: Does this law lie
in the circle or in the understanding, that is, Does this figure,
independently of the understanding, contain in itself the ground of
the law, or does the understanding, having constructed according to
its concepts (according to the quality of the radii) the figure
itself, introduce into it this law of the chords cutting one another
in geometrical proportion? When we follow the proofs of this law, we
soon perceive, that it can only be derived from the condition on which
the understanding founds the construction of this figure, and which is
that of the equality of the radii. But, if we enlarge this concept, to
pursue further the unity of various properties of geometrical figures
under common laws, and consider the circle as a conic section, which
of course is subject to the same fundamental conditions of
construction as other conic sections, we shall find that all the
chords which intersect within the ellipse, parabola, and hyperbola,
always intersect so that the rectangles of their segments are not
indeed equal, but always bear a constant ratio to one another. If we
proceed still farther, to the fundamental laws of physical astronomy,
we find a physical law of reciprocal attraction diffused over all
material nature, the rule of which is: "that it decreases inversely as
the square of the distance from each attracting point, i.e., as the
spherical surfaces increase, over which this force spreads," which law
seems to be necessarily inherent in the very nature of things, and
hence is usually propounded as cognisable a priori. Simple as the
sources of this law are, merely resting upon the relation of spherical
surfaces of different radii, its consequences are so valuable with
regard to the variety of their agreement and its regularity, that not
only are all possible orbits of the celestial bodies conic sections,
but such a relation of these orbits to each other results, that no
other law of attraction, than that of the inverse square of the
distance, can be imagined as fit for a cosmical system.
Here accordingly is a nature that rests upon laws which the
understanding cognises a priori, and chiefly from the universal
principles of the determination of space. Now I ask:
Do the laws of nature lie in space, and does the understanding learn
them by merely endeavoring to find out the enormous wealth of meaning
that lies in space; or do they inhere in the understanding and in the
way in which it determines space according to the conditions of the
synthetical unity in which its concepts are all centred?
Space is something so uniform and as to all particular properties so
indeterminate, that we should certainly not seek a store of laws of
nature in it. Whereas that which determines space to assume the form
of a circle or the figures of a cone and a sphere, is the
understanding, so far as it contains the ground of the unity of their
constructions.
The mere universal form of intuition, called space, must therefore be
the substratum of all intuitions determinable to particular objects,
and in it of course the condition of the possibility and of the
variety of these intuitions lies. But the unity of the objects is
entirely determined by the understanding, and on conditions which lie
in its own nature; and thus the understanding is the origin of the
universal order of nature, in that it comprehends all appearances
under its own laws, and thereby first constructs, a priori, experience
(as to its form), by means of which whatever is to be cognised only by
experience, is necessarily subjected to its laws. For we are not now
concerned with the nature of things in themselves, which is
independent of the conditions both of our sensibility and our
understanding, but with nature, as an object of possible experience,
and in this case the understanding, whilst it makes experience
possible, thereby insists that the sensuous world is either not an
object of experience at all, or must be nature [viz., an existence of
things, determined according to universal laws{22}].
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{22} The definition of nature is given in the beginning of the Second
Part of the "Transcendental Problem," in § 14.
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