§ 1. Of the Sources of Metaphysics.
If it becomes desirable to formulate any cognition as science, it will
be necessary first to determine accurately those peculiar features
which no other science has in common with it, constituting its
characteristics; otherwise the boundaries of all sciences become
confused, and none of them can be treated thoroughly according to its
nature.
The characteristics of a science may consist of a simple difference of
object, or of the sources of cognition, or of the kind of cognition,
or perhaps of all three conjointly. On this, therefore, depends the
idea of a possible science and its territory.
First, as concerns the sources of metaphysical cognition, its very
concept implies that they cannot be empirical. Its principles
(including not only its maxims but its basic notions) must never be
derived from experience. It must not be physical but metaphysical
knowledge, viz., knowledge lying beyond experience. It can therefore
have for its basis neither external experience, which is the source of
physics proper, nor internal, which is the basis of empirical
psychology. It is therefore a priori knowledge, coming from pure
Understanding and pure Reason.
But so far Metaphysics would not be distinguish able from pure
Mathematics; it must therefore be called pure philosophical cognition;
and for the meaning of this term I refer to the Critique of the Pure
Reason (II. "Method of Transcendentalism," Chap. I., Sec. i), where
the distinction between these two employments of the reason is
sufficiently explained. So far concerning the sources of metaphysical
cognition.
§ 2. Concerning the Kind of Cognition which can alone be called
Metaphysical.
a. Of the Distinction between Analytical and Synthetical Judgments in
general.—The peculiarity of its sources demands that metaphysical
cognition must consist of nothing but a priori judgments. But whatever
be their origin, or their logical form, there is a distinction in
judgments, as to their content, according to which they are either
merely explicative, adding nothing to the content of the cognition, or
expansive, increasing the given cognition: the former may be called
analytical, the latter synthetical, judgments.
Analytical judgments express nothing in the predicate but what has
been already actually thought in the concept of the subject, though
not so distinctly or with the same (full) consciousness. When I say:
All bodies are extended, I have not amplified in the least my concept
of body, but have only analysed it, as extension was really thought to
belong to that concept before the judgment was made, though it was not
expressed; this judgment is therefore analytical. On the contrary,
this judgment, All bodies have weight, contains in its predicate
something not actually thought in the general concept of the body; it
amplifies my knowledge by adding something to my concept, and must
therefore be called synthetical.
b. The Common Principle of all Analytical Judgments is the Law of
Contradiction.—All analytical judgments depend wholly on the law of
Contradiction, and are in their nature a priori cognitions, whether
the concepts that supply them with matter be empirical or not. For the
predicate of an affirmative analytical judgment is already contained
in the concept of the subject, of which it cannot be denied without
contradiction. In the same way its opposite is necessarily denied of
the subject in an analytical, but negative, judgment, by the same law
of contradiction. Such is the nature of the judgments: all bodies are
extended, and no bodies are unextended (i.e., simple).
For this very reason all analytical judgments are a priori even when
the concepts are empirical, as, for example, Gold is a yellow metal;
for to know this I require no experience beyond my concept of gold as
a yellow metal: it is, in fact, the very concept, and I need only
analyse it, without looking beyond it elsewhere.
c. Synthetical Judgments require a different Principle from the Law of
Contradiction.—There are synthetical a posteriori judgments of
empirical origin; but there are also others which are proved to be
certain a priori, and which spring from pure Understanding and Reason.
Yet they both agree in this, that they cannot possibly spring from the
principle of analysis, viz., the law of contradiction, alone; they
require a quite different principle, though, from whatever they may be
deduced, they must be subject to the law of contradiction, which must
never be violated, even though everything cannot be deduced from it. I
shall first classify synthetical judgments.
1. Empirical Judgments are always synthetical. For it would be absurd
to base an analytical judgment on experience, as our concept suffices
for the purpose without requiring any testimony from experience. That
body is extended, is a judgment established a priori, and not an
empirical judgment. For before appealing to experience, we already
have all the conditions of the judgment in the concept, from which we
have but to elicit the predicate according to the law of
contradiction, and thereby to become conscious of the necessity of the
judgment, which experience could not even teach us.
2. Mathematical Judgments are all synthetical. This fact seems
hitherto to have altogether escaped the observation of those who have
analysed human reason; it even seems directly opposed to all their
conjectures, though incontestably certain, and most important in its
consequences. For as it was found that the conclusions of
mathematicians all proceed according to the law of contradiction (as
is demanded by all apodeictic certainty), men persuaded themselves
that the fundamental principles were known from the same law. This was
a great mistake, for a synthetical proposition can indeed be
comprehended according to the law of contradiction, but only by
presupposing another synthetical proposition from which it follows,
but never in itself.
First of all, we must observe that all proper mathematical judgments
are a priori, and not empirical, because they carry with them
necessity, which cannot be obtained from experience. But if this be
not conceded to me, very good; I shall confine my assertion to pure
Mathematics, the very notion of which implies that it contains pure a
priori and not empirical cognitions.
It might at first be thought that the proposition 7 + 5 = 12 is a mere
analytical judgment, following from the concept of the sum of seven
and five, according to the law of contradiction. But on closer
examination it appears that the concept of the sum of 7 + 5 contains
merely their union in a single number, without its being at all
thought what the particular number is that unites them. The concept of
twelve is by no means thought by merely thinking of the combination of
seven and five; and analyse this possible sum as we may, we shall not
discover twelve in the concept. We must go beyond these concepts, by
calling to our aid some concrete image (Anschauung), i.e., either our
five fingers, or five points (as Segner has it in his Arithmetic), and
we must add successively the units of the five, given in some concrete
image (Anschauung), to the concept of seven. Hence our concept is
really amplified by the proposition 7 + 5 = 12, and we add to the
first a second, not thought in it. Arithmetical judgments are
therefore synthetical, and the more plainly according as we take
larger numbers; for in such cases it is clear that, however closely we
analyse our concepts without calling visual images (Anschauung) to our
aid, we can never find the sum by such mere dissection.
All principles of geometry are no less analytical. That a straight
line is the shortest path between two points, is a synthetical
proposition. For my concept of straight contains nothing of quantity,
but only a quality. The attribute of shortness is therefore altogether
additional, and cannot be obtained by any analysis of the concept.
Here, too, visualisation (Anschauung) must come to aid us. It alone
makes the synthesis possible.
Some other principles, assumed by geometers, are indeed actually
analytical, and depend on the law of contradiction; but they only
serve, as identical propositions, as a method of concatenation, and
not as principles, e.g., a = a, the whole is equal to itself, or a + b
> a, the whole is greater than its part. And yet even these, though
they are recognised as valid from mere concepts, are only admitted in
mathematics, because they can be represented in some visual form
(Anschauung). What usually makes us believe that the predicate of such
apodeictic{8} judgments is already contained in our concept, and that
the judgment is therefore analytical, is the duplicity of the
expression, requesting us to think a certain predicate as of necessity
implied in the thought of a given concept, which necessity attaches to
the concept. But the question is not what we are requested to join in
thought to the given concept, but what we actually think together with
and in it, though obscurely; and so it appears that the predicate
belongs to these concepts necessarily indeed, yet not directly but
indirectly by an added visualisation (Anschauung).
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{8} The term apodeictic is borrowed by Kant from Aristotle who uses it
in the sense of "certain beyond dispute." The word is derived from
ἀποδείκνυμι (= I show) and is contrasted to dialectic
propositions, i.e., such statements as admit of controversy.—Ed.
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§ 3. A Remark on the General Division of Judgments into Analytical
and Synthetical.
This division is indispensable, as concerns the Critique of human
understanding, and therefore deserves to be called classical, though
otherwise it is of little use, but this is the reason why dogmatic
philosophers, who always seek the sources of metaphysical judgments in
Metaphysics itself, and not apart from it, in the pure laws of reason
generally, altogether neglected this apparently obvious distinction.
Thus the celebrated Wolf, and his acute follower Baumgarten, came to
seek the proof of the principle of Sufficient Reason, which is clearly
synthetical, in the principle of Contradiction. In Locke's Essay,
however, I find an indication of my division. For in the fourth book
(chap. iii. § 9, seq.), having discussed the various connexions of
representations in judgments, and their sources, one of which he makes
"identity and contradiction" (analytical judgments), and another the
coexistence of representations in a subject, he confesses (§ 10) that
our a priori knowledge of the latter is very narrow, and almost
nothing. But in his remarks on this species of cognition, there is so
little of what is definite, and reduced to rules, that we cannot
wonder if no one, not even Hume, was led to make investigations
concerning this sort of judgments. For such general and yet definite
principles are not easily learned from other men, who have had them
obscurely in their minds. We must hit on them first by our own
reflexion, then we find them elsewhere, where we could not possibly
have found them at first, because the authors themselves did not know
that such an idea lay at the basis of their observations. Men who
never think independently have nevertheless the acuteness to discover
everything, after it has been once shown them, in what was said long
since, though no one ever saw it there before.
§ 4. The General Question of the Prolegomena.—Is Metaphysics at all
Possible?
Were a metaphysics, which could maintain its place as a science,
really in existence; could we say, here is metaphysics, learn it, and
it will convince you irresistibly and irrevocably of its truth: this
question would be useless, and there would only remain that other
question (which would rather be a test of our acuteness, than a proof
of the existence of the thing itself), "How is the science possible,
and how does reason come to attain it?" But human reason has not been
so fortunate in this case. There is no single book to which you can
point as you do to Euclid, and say: This is Metaphysics; here you may
find the noblest objects of this science, the knowledge of a highest
Being, and of a future existence, proved from principles of pure
reason. We can be shown indeed many judgments, demonstrably certain,
and never questioned; but these are all analytical, and rather concern
the materials and the scaffolding for Metaphysics, than the extension
of knowledge, which is our proper object in studying it (§ 2). Even
supposing you produce synthetical judgments (such as the law of
Sufficient Reason, which you have never proved, as you ought to, from
pure reason a priori, though we gladly concede its truth), you lapse
when they come to be employed for your principal object, into such
doubtful assertions, that in all ages one Metaphysics has contradicted
another, either in its assertions, or their proofs, and thus has
itself destroyed its own claim to lasting assent. Nay, the very
attempts to set up such a science are the main cause of the early
appearance of scepticism, a mental attitude in which reason treats
itself with such violence that it could never have arisen save from
complete despair of ever satisfying our most important aspirations.
For long before men began to inquire into nature methodically, they
consulted abstract reason, which had to some extent been exercised by
means of ordinary experience; for reason is ever present, while laws
of nature must usually be discovered with labor. So Metaphysics
floated to the surface, like foam, which dissolved the moment it was
scooped off. But immediately there appeared a new supply on the
surface, to be ever eagerly gathered up by some, while others, instead
of seeking in the depths the cause of the phenomenon, thought they
showed their wisdom by ridiculing the idle labor of their neighbors.
The essential and distinguishing feature of pure mathematical
cognition among all other a priori cognitions is, that it cannot at
all proceed from concepts, but only by means of the construction of
concepts (see Critique II., Method of Transcendentalism, chap. I.,
sect. 1). As therefore in its judgments it must proceed beyond the
concept to that which its corresponding visualisation (Anschauung)
contains, these judgments neither can, nor ought to, arise
analytically, by dissecting the concept, but are all synthetical.
I cannot refrain from pointing out the disadvantage resulting to
philosophy from the neglect of this easy and apparently insignificant
observation. Hume being prompted (a task worthy of a philosopher) to
cast his eye over the whole field of a priori cognitions in which
human understanding claims such mighty possessions, heedlessly severed
from it a whole, and indeed its most valuable, province, viz., pure
mathematics; for he thought its nature, or, so to speak, the
state-constitution of this empire, depended on totally different
principles, namely, on the law of contradiction alone; and although he
did not divide Judgments in this manner formally and universally as I
have done here, what he said was equivalent to this: that mathematics
contains only analytical, but metaphysics synthetical, a priori
judgments. In this, however, he was greatly mistaken, and the mistake
had a decidedly injurious effect upon his whole conception. But for
this, he would have extended his question concerning the origin of our
synthetical judgments far beyond the metaphysical concept of
Causality, and included in it the possibility of mathematics a priori
also, for this latter he must have assumed to be equally synthetical.
And then he could not have based his metaphysical judgments on mere
experience without subjecting the axioms of mathematics equally to
experience, a thing which he was far too acute to do. The good company
into which metaphysics would thus have been brought, would have saved
it from the danger of a contemptuous ill-treatment, for the thrust
intended for it must have reached mathematics, which was not and could
not have been Hume's intention. Thus that acute man would have been
led into considerations which must needs be similar to those that now
occupy us, but which would have gained inestimably by his inimitably
elegant style.
Metaphysical judgments, properly so called, are all synthetical. We
must distinguish judgments pertaining to metaphysics from metaphysical
judgments properly so called. Many of the former are analytical, but
they only afford the means for metaphysical judgments, which are the
whole end of the science, and which are always synthetical. For if
there be concepts pertaining to metaphysics (as, for example, that of
substance), the judgments springing from simple analysis of them also
pertain to metaphysics, as, for example, substance is that which only
exists as subject; and by means of several such analytical judgments,
we seek to approach the definition of the concept. But as the analysis
of a pure concept of the understanding pertaining to metaphysics, does
not proceed in any different manner from the dissection of any other,
even empirical, concepts, not pertaining to metaphysics (such as: air
is an elastic fluid, the elasticity of which is not destroyed by any
known degree of cold), it follows that the concept indeed, but not the
analytical judgment, is properly metaphysical. This science has
something peculiar in the production of its a priori cognitions, which
must therefore be distinguished from the features it has in common
with other rational knowledge. Thus the judgment, that all the
substance in things is permanent, is a synthetical and properly
metaphysical judgment.
If the a priori principles, which constitute the materials of
metaphysics, have first been collected according to fixed principles,
then their analysis will be of great value; it might be taught as a
particular part (as a philosophia definitiva), containing nothing but
analytical judgments pertaining to metaphysics, and could be treated
separately from the synthetical which constitute metaphysics proper.
For indeed these analyses are not elsewhere of much value, except in
metaphysics, i.e., as regards the synthetical judgments, which are to
be generated by these previously analysed concepts.
The conclusion drawn in this section then is, that metaphysics is
properly concerned with synethetical propositions a priori, and these
alone constitute its end, for which it indeed requires various
dissections of its concepts, viz., of its analytical judgments, but
wherein the procedure is not different from that in every other kind
of knowledge, in which we merely seek to render our concepts distinct
by analysis. But the generation of a priori cognition by concrete
images as well as by concepts, in fine of synthetical propositions a
priori in philosophical cognition, constitutes the essential subject
of Metaphysics.
Weary therefore as well of dogmatism, which teaches us nothing, as of
scepticism, which does not even promise us anything, not even the
quiet state of a contented ignorance; disquieted by the importance of
knowledge so much needed; and lastly, rendered suspicious by long
experience of all knowledge which we believe we possess, or which
offers itself, under the title of pure reason: there remains but one
critical question on the answer to which our future procedure depends,
viz., Is Metaphysics at all possible? But this question must be
answered not by sceptical objections to the asseverations of some
actual system of metaphysics (for we do not as yet admit such a thing
to exist), but from the conception, as yet only problematical, of a
science of this sort.
In the Critique of Pure Reason I have treated this question
synthetically, by making inquiries into pure reason itself, and
endeavoring in this source to determine the elements as well as the
laws of its pure use according to principles. The task is difficult,
and requires a resolute reader to penetrate by degrees into a system,
based on no data except reason itself, and which therefore seeks,
without resting upon any fact, to unfold knowledge from its original
germs. Prolegomena, however, are designed for preparatory exercises;
they are intended rather to point out what we have to do in order if
possible to actualise a science, than to propound it. They must
therefore rest upon something already known as trustworthy, from which
we can set out with confidence, and ascend to sources as yet unknown,
the discovery of which will not only explain to us what we knew, but
exhibit a sphere of many cognitions which all spring from the same
sources. The method of Prolegomena, especially of those designed as a
preparation for future metaphysics, is consequently analytical.
But it happens fortunately, that though we cannot assume metaphysics
to be an actual science, we can say with confidence that certain pure
a priori synthetical cognitions, pure Mathematics and pure Physics are
actual and given; for both contain propositions, which are thoroughly
recognised as apodeictically certain, partly by mere reason, partly by
general consent arising from experience, and yet as independent of
experience. We have therefore some at least uncontested synthetical
knowledge a priori, and need not ask whether it be possible, for it is
actual, but how it is possible, in order that we may deduce from the
principle which makes the given cognitions possible the possibility of
all the rest.
The General Problem: How is Cognition from Pure Reason Possible?
§ 5. We have above learned the significant distinction between
analytical and synthetical judgments. The possibility of analytical
propositions was easily comprehended, being entirely founded on the
law of Contradiction. The possibility of synthetical a posteriori
judgments, of those which are gathered from experience, also requires
no particular explanation; for experience is nothing but a continual
synthesis of perceptions. There remain therefore only synthetical
propositions a priori, of which the possibility must be sought or
investigated, because they must depend upon other principles than the
law of contradiction.
But here we need not first establish the possibility of such
propositions so as to ask whether they are possible. For there are
enough of them which indeed are of undoubted certainty, and as our
present method is analytical, we shall start from the fact, that such
synthetical but purely rational cognition actually exists; but we must
now inquire into the reason of this possibility, and ask, how such
cognition is possible, in order that we may from the principles of its
possibility be enabled to determine the conditions of its use, its
sphere and its limits. The proper problem upon which all depends, when
expressed with scholastic precision, is therefore:
How are Synthetic Propositions a priori possible?
For the sake of popularity I have above expressed this problem
somewhat differently, as an inquiry into purely rational cognition,
which I could do for once without detriment to the desired
comprehension, because, as we have only to do here with metaphysics
and its sources, the reader will, I hope, after the fore going
remarks, keep in mind that when we speak of purely rational cognition,
we do not mean analytical, but synthetical cognition.{9}
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{9} It is unavoidable that as knowledge advances, certain expressions
which have become classical, after having been used since the infancy
of science, will be found inadequate and unsuitable, and a newer and
more appropriate application of the terms will give rise to confusion.
[This is the case with the term "analytical."] The analytical method,
so far as it is opposed to the synthetical, is very different from
that which constitutes the essence of analytical propositions: it
signifies only that we start from what is sought, as if it were given,
and ascend to the only conditions under which it is possible. In this
method we often use nothing but synthetical propositions, as in
mathematical analysis, and it were better to term it the regressive
method, in contradistinction to the synthetic or progressive. A
principal part of Logic too is distinguished by the name of Analytics,
which here signifies the logic of truth in contrast to Dialectics,
without considering whether the cognitions belonging to it are
analytical or synthetical.
===================================
Metaphysics stands or falls with the solution of this problem: its
very existence depends upon it. Let any one make metaphysical
assertions with ever so much plausibility, let him overwhelm us with
conclusions, if he has not previously proved able to answer this
question satisfactorily, I have a right to say: this is all vain
baseless philosophy and false wisdom. You speak through pure reason,
and claim, as it were to create cognitions a priori by not only
dissecting given concepts, but also by asserting connexions which do
not rest upon the law of contradiction, and which you believe you
conceive quite independently of all experience; how do you arrive at
this, and how will you justify your pretensions? An appeal to the
consent of the common sense of mankind cannot be allowed; for that is
a witness whose authority depends merely upon rumor. Says Horace:
"Quodcunque ostendis mihi sic, incredulus odi."
"To all that which thou provest me thus, I refuse to give credence."
The answer to this question, though indispensable, is difficult; and
though the principal reason that it was not made long ago is, that the
possibility of the question never occurred to anybody, there is yet
another reason, which is this that a satisfactory answer to this one
question requires a much more persistent, profound, and painstaking
reflexion, than the most diffuse work on Metaphysics, which on its
first appearance promised immortality to its author. And every
intelligent reader, when he carefully reflects what this problem
requires, must at first be struck with its difficulty, and would
regard it as insoluble and even impossible, did there not actually
exist pure synthetical cognitions a priori. This actually happened to
David Hume, though he did not conceive the question in its entire
universality as is done here, and as must be done, should the answer
be decisive for all Metaphysics. For how is it possible, says that
acute man, that when a concept is given me, I can go beyond it and
connect with it another, which is not contained in it, in such a
manner as if the latter necessarily belonged to the former? Nothing
but experience can furnish us with such connexions (thus he concluded
from the difficulty which he took to be an impossibility), and all
that vaunted necessity, or, what is the same thing, all cognition
assumed to be a priori, is nothing but a long habit of accepting
something as true, and hence of mistaking subjective necessity for
objective.
Should my reader complain of the difficulty and the trouble which I
occasion him in the solution of this problem, he is at liberty to
solve it himself in an easier way. Perhaps he will then feel under
obligation to the person who has undertaken for him a labor of so
profound research, and will rather be surprised at the facility with
which, considering the nature of the subject, the solution has been
attained. Yet it has cost years of work to solve the problem in its
whole universality (using the term in the mathematical sense, viz.,
for that which is sufficient for all cases), and finally to exhibit it
in the analytical form, as the reader finds it here.
All metaphysicians are therefore solemnly and legally suspended from
their occupations till they shall have answered in a satisfactory
manner the question, "How are synthetic cognitions a priori possible?"
For the answer contains which they must show when they have anything
to offer in the name of pure reason. But if they do not possess these
credentials, they can expect nothing else of reasonable people, who
have been deceived so often, than to be dismissed without further ado.
If they on the other hand desire to carry on their business, not as a
science, but as an art of wholesome oratory suited to the common sense
of man, they cannot in justice be prevented. They will then speak the
modest language of a rational belief, they will grant that they are
not allowed even to conjecture, far less to know, anything which lies
beyond the bounds of all possible experience, but only to assume (not
for speculative use, which they must abandon, but for practical
purposes only) the existence of something that is possible and even
indispensable for the guidance of the understanding and of the will in
life. In this manner alone can they be called useful and wise men, and
the more so as they renounce the title of metaphysicians; for the
latter profess to be speculative philosophers, and since, when
judgments a priori are under discussion, poor probabilities cannot be
admitted (for what is declared to be known a priori is thereby
announced as necessary), such men cannot be permitted to play with
conjectures, but their assertions must be either science, or are worth
nothing at all.
It may be said, that the entire transcendental philosophy, which
necessarily precedes all metaphysics, is nothing but the complete
solution of the problem here propounded, in systematical order and
completeness, and hitherto we have never had any transcendental
philosophy; for what goes by its name is properly a part of
metaphysics, whereas the former science is intended first to
constitute the possibility of the latter, and must therefore precede
all metaphysics. And it is not surprising that when a whole science,
deprived of all help from other sciences, and consequently in itself
quite new, is required to answer a single question satisfactorily, we
should find the answer troublesome and difficult, nay even shrouded in
obscurity.
As we now proceed to this solution according to the analytical method,
in which we assume that such cognitions from pure reasons actually
exist, we can only appeal to two sciences of theoretical cognition
(which alone is under consideration here), pure mathematics and pure
natural science (physics). For these alone can exhibit to us objects
in a definite and actualisable form (in der Anschauung), and
consequently (if there should occur in them a cognition a priori) can
show the truth or conformity of the cognition to the object in
concreto, that is, its actuality, from which we could proceed to the
reason of its possibility by the analytic method. This facilitates our
work greatly for here universal considerations are not only applied to
facts, but even start from them, while in a synthetic procedure they
must strictly be derived in abstracto from concepts.
But, in order to rise from these actual and at the same time
well-grounded pure cognitions a priori to such a possible cognition of
the same as we are seeking, viz., to metaphysics as a science, we must
comprehend that which occasions it, I mean the mere natural, though in
spite of its truth not unsuspected, cognition a priori which lies at
the bottom of that science, the elaboration of which without any
critical investigation of its possibility is commonly called
metaphysics. In a word, we must comprehend the natural conditions of
such a science as a part of our inquiry, and thus the transcendental
problem will be gradually answered by a division into four questions:
1. How is pure mathematics possible?
2. How is pure natural science possible?
3. How is metaphysics in general possible?
4. How is metaphysics as a science possible?
It may be seen that the solution of these problems, though chiefly
designed to exhibit the essential matter of the Critique, has yet
something peculiar, which for itself alone deserves attention. This is
the search for the sources of given sciences in reason itself, so that
its faculty of knowing something a priori may by its own deeds be
investigated and measured. By this procedure these sciences gain, if
not with regard to their contents, yet as to their proper use, and
while they throw light on the higher question concerning their common
origin, they give, at the same time, an occasion better to explain
their own nature.