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The Critique of Pure Reason by Immanuel Kant

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experience. Examples are always contagious; and they exert an especial
influence on the same faculty, which naturally flatters itself that
it will have the same good fortune in other case as fell to its lot
in one fortunate instance. Hence pure reason hopes to be able to extend
its empire in the transcendental sphere with equal success and
security, especially when it applies the same method which was
attended with such brilliant results in the science of mathematics.
It is, therefore, of the highest importance for us to know whether
the method of arriving at demonstrative certainty, which is termed
mathematical, be identical with that by which we endeavour to attain
the same degree of certainty in philosophy, and which is termed in
that science dogmatical.

Philosophical cognition is the cognition of reason by means of
conceptions; mathematical cognition is cognition by means of the
construction of conceptions. The construction of a conception is the
presentation a priori of the intuition which corresponds to the
conception. For this purpose a non-empirical intuition is requisite,
which, as an intuition, is an individual object; while, as the
construction of a conception (a general representation), it must be
seen to be universally valid for all the possible intuitions which
rank under that conception. Thus I construct a triangle, by the
presentation of the object which corresponds to this conception,
either by mere imagination, in pure intuition, or upon paper, in
empirical intuition, in both cases completely a priori, without
borrowing the type of that figure from any experience. The
individual figure drawn upon paper is empirical; but it serves,
notwithstanding, to indicate the conception, even in its universality,
because in this empirical intuition we keep our eye merely on the
act of the construction of the conception, and pay no attention to
the various modes of determining it, for example, its size, the length
of its sides, the size of its angles, these not in the least affecting
the essential character of the conception.

Philosophical cognition, accordingly, regards the particular only in
the general; mathematical the general in the particular, nay, in the
individual. This is done, however, entirely a priori and by means of
pure reason, so that, as this individual figure is determined under
certain universal conditions of construction, the object of the
conception, to which this individual figure corresponds as its schema,
must be cogitated as universally determined.

The essential difference of these two modes of cognition consists,
therefore, in this formal quality; it does not regard the difference
of the matter or objects of both. Those thinkers who aim at
distinguishing philosophy from mathematics by asserting that the
former has to do with quality merely, and the latter with quantity,
have mistaken the effect for the cause. The reason why mathematical
cognition can relate only to quantity is to be found in its form
alone. For it is the conception of quantities only that is capable
of being constructed, that is, presented a priori in intuition;
while qualities cannot be given in any other than an empirical
intuition. Hence the cognition of qualities by reason is possible only
through conceptions. No one can find an intuition which shall
correspond to the conception of reality, except in experience; it
cannot be presented to the mind a priori and antecedently to the
empirical consciousness of a reality. We can form an intuition, by
means of the mere conception of it, of a cone, without the aid of
experience; but the colour of the cone we cannot know except from
experience. I cannot present an intuition of a cause, except in an
example which experience offers to me. Besides, philosophy, as well
as mathematics, treats of quantities; as, for example, of totality,
infinity, and so on. Mathematics, too, treats of the difference of
lines and surfaces--as spaces of different quality, of the
continuity of extension--as a quality thereof. But, although in such
cases they have a common object, the mode in which reason considers
that object is very different in philosophy from what it is in
mathematics. The former confines itself to the general conceptions;
the latter can do nothing with a mere conception, it hastens to
intuition. In this intuition it regards the conception in concreto,
not empirically, but in an a priori intuition, which it has
constructed; and in which, all the results which follow from the
general conditions of the construction of the conception are in all
cases valid for the object of the constructed conception.

Suppose that the conception of a triangle is given to a
philosopher and that he is required to discover, by the
philosophical method, what relation the sum of its angles bears to
a right angle. He has nothing before him but the conception of a
figure enclosed within three right lines, and, consequently, with
the same number of angles. He may analyse the conception of a right
line, of an angle, or of the number three as long as he pleases, but
he will not discover any properties not contained in these
conceptions. But, if this question is proposed to a geometrician, he
at once begins by constructing a triangle. He knows that two right
angles are equal to the sum of all the contiguous angles which proceed
from one point in a straight line; and he goes on to produce one
side of his triangle, thus forming two adjacent angles which are
together equal to two right angles. He then divides the exterior of
these angles, by drawing a line parallel with the opposite side of
the triangle, and immediately perceives that he has thus got an exterior
adjacent angle which is equal to the interior. Proceeding in this way,
through a chain of inferences, and always on the ground of
intuition, he arrives at a clear and universally valid solution of
the question.

But mathematics does not confine itself to the construction of
quantities (quanta), as in the case of geometry; it occupies itself
with pure quantity also (quantitas), as in the case of algebra,
where complete abstraction is made of the properties of the object
indicated by the conception of quantity. In algebra, a certain
method of notation by signs is adopted, and these indicate the
different possible constructions of quantities, the extraction of
roots, and so on. After having thus denoted the general conception
of quantities, according to their different relations, the different
operations by which quantity or number is increased or diminished
are presented in intuition in accordance with general rules. Thus,
when one quantity is to be divided by another, the signs which
denote both are placed in the form peculiar to the operation of
division; and thus algebra, by means of a symbolical construction of
quantity, just as geometry, with its ostensive or geometrical
construction (a construction of the objects themselves), arrives at
results which discursive cognition cannot hope to reach by the aid
of mere conceptions.

Now, what is the cause of this difference in the fortune of the
philosopher and the mathematician, the former of whom follows the path
of conceptions, while the latter pursues that of intuitions, which
he represents, a priori, in correspondence with his conceptions? The
cause is evident from what has been already demonstrated in the
introduction to this Critique. We do not, in the present case, want
to discover analytical propositions, which may be produced merely by
analysing our conceptions--for in this the philosopher would have
the advantage over his rival; we aim at the discovery of synthetical
propositions--such synthetical propositions, moreover, as can be
cognized a priori. I must not confine myself to that which I
actually cogitate in my conception of a triangle, for this is
nothing more than the mere definition; I must try to go beyond that,
and to arrive at properties which are not contained in, although
they belong to, the conception. Now, this is impossible, unless I
determine the object present to my mind according to the conditions,
either of empirical, or of pure, intuition. In the former case, I
should have an empirical proposition (arrived at by actual measurement
of the angles of the triangle), which would possess neither
universality nor necessity; but that would be of no value. In the
latter, I proceed by geometrical construction, by means of which I
collect, in a pure intuition, just as I would in an empirical
intuition, all the various properties which belong to the schema of
a triangle in general, and consequently to its conception, and thus
construct synthetical propositions which possess the attribute of

It would be vain to philosophize upon the triangle, that is, to
reflect on it discursively; I should get no further than the
definition with which I had been obliged to set out. There are
certainly transcendental synthetical propositions which are framed
by means of pure conceptions, and which form the peculiar
distinction of philosophy; but these do not relate to any particular
thing, but to a thing in general, and enounce the conditions under
which the perception of it may become a part of possible experience.
But the science of mathematics has nothing to do with such
questions, nor with the question of existence in any fashion; it is
concerned merely with the properties of objects in themselves, only
in so far as these are connected with the conception of the objects.

In the above example, we merely attempted to show the great
difference which exists between the discursive employment of reason
in the sphere of conceptions, and its intuitive exercise by means of
the construction of conceptions. The question naturally arises: What
is the cause which necessitates this twofold exercise of reason, and
how are we to discover whether it is the philosophical or the
mathematical method which reason is pursuing in an argument?

All our knowledge relates, finally, to possible intuitions, for it
is these alone that present objects to the mind. An a priori or
non-empirical conception contains either a pure intuition--and in this
case it can be constructed; or it contains nothing but the synthesis
of possible intuitions, which are not given a priori. In this latter
case, it may help us to form synthetical a priori judgements, but only
in the discursive method, by conceptions, not in the intuitive, by
means of the construction of conceptions.

The only a priori intuition is that of the pure form of phenomena-
space and time. A conception of space and time as quanta may be
presented a priori in intuition, that is, constructed, either alone
with their quality (figure), or as pure quantity (the mere synthesis
of the homogeneous), by means of number. But the matter of
phenomena, by which things are given in space and time, can be
presented only in perception, a posteriori. The only conception
which represents a priori this empirical content of phenomena is the
conception of a thing in general; and the a priori synthetical
cognition of this conception can give us nothing more than the rule
for the synthesis of that which may be contained in the
corresponding a posteriori perception; it is utterly inadequate to
present an a priori intuition of the real object, which must
necessarily be empirical.

Synthetical propositions, which relate to things in general, an a
priori intuition of which is impossible, are transcendental. For
this reason transcendental propositions cannot be framed by means of
the construction of conceptions; they are a priori, and based entirely
on conceptions themselves. They contain merely the rule, by which we
are to seek in the world of perception or experience the synthetical
unity of that which cannot be intuited a priori. But they are
incompetent to present any of the conceptions which appear in them
in an a priori intuition; these can be given only a posteriori, in
experience, which, however, is itself possible only through these
synthetical principles.

If we are to form a synthetical judgement regarding a conception, we
must go beyond it, to the intuition in which it is given. If we keep
to what is contained in the conception, the judgement is merely
analytical--it is merely an explanation of what we have cogitated in
the conception. But I can pass from the conception to the pure or
empirical intuition which corresponds to it. I can proceed to
examine my conception in concreto, and to cognize, either a priori
or a posterio, what I find in the object of the conception. The
former--a priori cognition--is rational-mathematical cognition by
means of the construction of the conception; the latter--a
posteriori cognition--is purely empirical cognition, which does not
possess the attributes of necessity and universality. Thus I may
analyse the conception I have of gold; but I gain no new information
from this analysis, I merely enumerate the different properties
which I had connected with the notion indicated by the word. My
knowledge has gained in logical clearness and arrangement, but no
addition has been made to it. But if I take the matter which is
indicated by this name, and submit it to the examination of my senses,
I am enabled to form several synthetical--although still empirical-
propositions. The mathematical conception of a triangle I should
construct, that is, present a priori in intuition, and in this way
attain to rational-synthetical cognition. But when the
transcendental conception of reality, or substance, or power is
presented to my mind, I find that it does not relate to or indicate
either an empirical or pure intuition, but that it indicates merely
the synthesis of empirical intuitions, which cannot of course be given
a priori. The synthesis in such a conception cannot proceed a
priori--without the aid of experience--to the intuition which
corresponds to the conception; and, for this reason, none of these
conceptions can produce a determinative synthetical proposition,
they can never present more than a principle of the synthesis* of
possible empirical intuitions. A transcendental proposition is,
therefore, a synthetical cognition of reason by means of pure
conceptions and the discursive method, and it renders possible all
synthetical unity in empirical cognition, though it cannot present
us with any intuition a priori.

[*Footnote: In the case of the conception of cause, I do really go
beyond the empirical conception of an event--but not to the intuition
which presents this conception in concreto, but only to the
time-conditions, which may be found in experience to correspond to
the conception. My procedure is, therefore, strictly according to
conceptions; I cannot in a case of this kind employ the construction
of conceptions, because the conception is merely a rule for the synthesis
of perceptions, which are not pure intuitions, and which, therefore,
cannot be given a priori.]

There is thus a twofold exercise of reason. Both modes have the
properties of universality and an a priori origin in common, but
are, in their procedure, of widely different character. The reason
of this is that in the world of phenomena, in which alone objects
are presented to our minds, there are two main elements--the form of
intuition (space and time), which can be cognized and determined
completely a priori, and the matter or content--that which is
presented in space and time, and which, consequently, contains a
something--an existence corresponding to our powers of sensation. As
regards the latter, which can never be given in a determinate mode
except by experience, there are no a priori notions which relate to
it, except the undetermined conceptions of the synthesis of possible
sensations, in so far as these belong (in a possible experience) to
the unity of consciousness. As regards the former, we can determine
our conceptions a priori in intuition, inasmuch as we are ourselves
the creators of the objects of the conceptions in space and time-
these objects being regarded simply as quanta. In the one case, reason
proceeds according to conceptions and can do nothing more than subject
phenomena to these--which can only be determined empirically, that
is, a posteriori--in conformity, however, with those conceptions as
the rules of all empirical synthesis. In the other case, reason proceeds
by the construction of conceptions; and, as these conceptions relate
to an a priori intuition, they may be given and determined in pure
intuition a priori, and without the aid of empirical data. The
examination and consideration of everything that exists in space or
time--whether it is a quantum or not, in how far the particular
something (which fills space or time) is a primary substratum, or a
mere determination of some other existence, whether it relates to
anything else--either as cause or effect, whether its existence is
isolated or in reciprocal connection with and dependence upon
others, the possibility of this existence, its reality and necessity
or opposites--all these form part of the cognition of reason on the
ground of conceptions, and this cognition is termed philosophical.
But to determine a priori an intuition in space (its figure), to divide
time into periods, or merely to cognize the quantity of an intuition
in space and time, and to determine it by number--all this is an
operation of reason by means of the construction of conceptions, and
is called mathematical.

The success which attends the efforts of reason in the sphere of
mathematics naturally fosters the expectation that the same good
fortune will be its lot, if it applies the mathematical method in
other regions of mental endeavour besides that of quantities. Its
success is thus great, because it can support all its conceptions by
a priori intuitions and, in this way, make itself a master, as it
were, over nature; while pure philosophy, with its a priori discursive
conceptions, bungles about in the world of nature, and cannot accredit
or show any a priori evidence of the reality of these conceptions.
Masters in the science of mathematics are confident of the success
of this method; indeed, it is a common persuasion that it is capable
of being applied to any subject of human thought. They have hardly
ever reflected or philosophized on their favourite science--a task
of great difficulty; and the specific difference between the two modes
of employing the faculty of reason has never entered their thoughts.
Rules current in the field of common experience, and which common
sense stamps everywhere with its approval, are regarded by them as
axiomatic. From what source the conceptions of space and time, with
which (as the only primitive quanta) they have to deal, enter their
minds, is a question which they do not trouble themselves to answer;
and they think it just as unnecessary to examine into the origin of
the pure conceptions of the understanding and the extent of their
validity. All they have to do with them is to employ them. In all this
they are perfectly right, if they do not overstep the limits of the
sphere of nature. But they pass, unconsciously, from the world of
sense to the insecure ground of pure transcendental conceptions
(instabilis tellus, innabilis unda), where they can neither stand
nor swim, and where the tracks of their footsteps are obliterated by
time; while the march of mathematics is pursued on a broad and
magnificent highway, which the latest posterity shall frequent without
fear of danger or impediment.

As we have taken upon us the task of determining, clearly and
certainly, the limits of pure reason in the sphere of
transcendentalism, and as the efforts of reason in this direction
are persisted in, even after the plainest and most expressive
warnings, hope still beckoning us past the limits of experience into
the splendours of the intellectual world--it becomes necessary to
cut away the last anchor of this fallacious and fantastic hope. We
shall, accordingly, show that the mathematical method is unattended
in the sphere of philosophy by the least advantage--except, perhaps,
that it more plainly exhibits its own inadequacy--that geometry and
philosophy are two quite different things, although they go band in
hand in hand in the field of natural science, and, consequently,
that the procedure of the one can never be imitated by the other.

The evidence of mathematics rests upon definitions, axioms, and
demonstrations. I shall be satisfied with showing that none of these
forms can be employed or imitated in philosophy in the sense in
which they are understood by mathematicians; and that the
geometrician, if he employs his method in philosophy, will succeed
only in building card-castles, while the employment of the
philosophical method in mathematics can result in nothing but mere
verbiage. The essential business of philosophy, indeed, is to mark
out the limits of the science; and even the mathematician, unless his
talent is naturally circumscribed and limited to this particular
department of knowledge, cannot turn a deaf ear to the warnings of
philosophy, or set himself above its direction.

I. Of Definitions. A definition is, as the term itself indicates,
the representation, upon primary grounds, of the complete conception
of a thing within its own limits.* Accordingly, an empirical
conception cannot be defined, it can only be explained. For, as
there are in such a conception only a certain number of marks or
signs, which denote a certain class of sensuous objects, we can
never be sure that we do not cogitate under the word which indicates
the same object, at one time a greater, at another a smaller number
of signs. Thus, one person may cogitate in his conception of gold,
in addition to its properties of weight, colour, malleability, that
of resisting rust, while another person may be ignorant of this
quality. We employ certain signs only so long as we require them for
the sake of distinction; new observations abstract some and add new
ones, so that an empirical conception never remains within permanent
limits. It is, in fact, useless to define a conception of this kind.
If, for example, we are speaking of water and its properties, we do
not stop at what we actually think by the word water, but proceed to
observation and experiment; and the word, with the few signs
attached to it, is more properly a designation than a conception of
the thing. A definition in this case would evidently be nothing more
than a determination of the word. In the second place, no a priori
conception, such as those of substance, cause, right, fitness, and
so on, can be defined. For I can never be sure, that the clear
representation of a given conception (which is given in a confused
state) has been fully developed, until I know that the
representation is adequate with its object. But, inasmuch as the
conception, as it is presented to the mind, may contain a number of
obscure representations, which we do not observe in our analysis,
although we employ them in our application of the conception, I can
never be sure that my analysis is complete, while examples may make
this probable, although they can never demonstrate the fact. Instead
of the word definition, I should rather employ the term exposition--
a more modest expression, which the critic may accept without
surrendering his doubts as to the completeness of the analysis of
any such conception. As, therefore, neither empirical nor a priori
conceptions are capable of definition, we have to see whether the only
other kind of conceptions--arbitrary conceptions--can be subjected
to this mental operation. Such a conception can always be defined;
for I must know thoroughly what I wished to cogitate in it, as it was
I who created it, and it was not given to my mind either by the nature
of my understanding or by experience. At the same time, I cannot say
that, by such a definition, I have defined a real object. If the
conception is based upon empirical conditions, if, for example, I have
a conception of a clock for a ship, this arbitrary conception does
not assure me of the existence or even of the possibility of the object.
My definition of such a conception would with more propriety be termed
a declaration of a project than a definition of an object. There
are no other conceptions which can bear definition, except those which
contain an arbitrary synthesis, which can be constructed a priori.
Consequently, the science of mathematics alone possesses
definitions. For the object here thought is presented a priori in
intuition; and thus it can never contain more or less than the
conception, because the conception of the object has been given by
the definition--and primarily, that is, without deriving the definition
from any other source. Philosophical definitions are, therefore,
merely expositions of given conceptions, while mathematical
definitions are constructions of conceptions originally formed by
the mind itself; the former are produced by analysis, the completeness
of which is never demonstratively certain, the latter by a
synthesis. In a mathematical definition the conception is formed, in
a philosophical definition it is only explained. From this it follows:

[*Footnote: The definition must describe the conception completely
that is, omit none of the marks or signs of which it composed; within
its own limits, that is, it must be precise, and enumerate no more
signs than belong to the conception; and on primary grounds, that is
to say, the limitations of the bounds of the conception must not be
deduced from other conceptions, as in this case a proof would be necessary,
and the so-called definition would be incapable of taking its place
at the bead of all the judgements we have to form regarding an object.]

(a) That we must not imitate, in philosophy, the mathematical
usage of commencing with definitions--except by way of hypothesis or
experiment. For, as all so-called philosophical definitions are merely
analyses of given conceptions, these conceptions, although only in
a confused form, must precede the analysis; and the incomplete
exposition must precede the complete, so that we may be able to draw
certain inferences from the characteristics which an incomplete
analysis has enabled us to discover, before we attain to the
complete exposition or definition of the conception. In one word, a
full and clear definition ought, in philosophy, rather to form the
conclusion than the commencement of our labours.* In mathematics, on
the contrary, we cannot have a conception prior to the definition;
it is the definition which gives us the conception, and it must for
this reason form the commencement of every chain of mathematical

[*Footnote: Philosophy abounds in faulty definitions, especially such
as contain some of the elements requisite to form a complete
definition. If a conception could not be employed in reasoning
before it had been defined, it would fare ill with all philosophical
thought. But, as incompletely defined conceptions may always be
employed without detriment to truth, so far as our analysis of the
elements contained in them proceeds, imperfect definitions, that is,
propositions which are properly not definitions, but merely
approximations thereto, may be used with great advantage. In
mathematics, definition belongs ad esse, in philosophy ad melius esse.
It is a difficult task to construct a proper definition. Jurists are
still without a complete definition of the idea of right.]

(b) Mathematical definitions cannot be erroneous. For the conception
is given only in and through the definition, and thus it contains only
what has been cogitated in the definition. But although a definition
cannot be incorrect, as regards its content, an error may sometimes,
although seldom, creep into the form. This error consists in a want
of precision. Thus the common definition of a circle--that it is a
curved line, every point in which is equally distant from another point
called the centre--is faulty, from the fact that the determination
indicated by the word curved is superfluous. For there ought to be
a particular theorem, which may be easily proved from the definition,
to the effect that every line, which has all its points at equal
distances from another point, must be a curved line--that is, that
not even the smallest part of it can be straight. Analytical
definitions, on the other hand, may be erroneous in many respects,
either by the introduction of signs which do not actually exist in
the conception, or by wanting in that completeness which forms the
essential of a definition. In the latter case, the definition is
necessarily defective, because we can never be fully certain of the
completeness of our analysis. For these reasons, the method of
definition employed in mathematics cannot be imitated in philosophy.

2. Of Axioms. These, in so far as they are immediately certain,
are a priori synthetical principles. Now, one conception cannot be
connected synthetically and yet immediately with another; because,
if we wish to proceed out of and beyond a conception, a third
mediating cognition is necessary. And, as philosophy is a cognition
of reason by the aid of conceptions alone, there is to be found in
it no principle which deserves to be called an axiom. Mathematics,
on the other hand, may possess axioms, because it can always connect
the predicates of an object a priori, and without any mediating term,
by means of the construction of conceptions in intuition. Such is the
case with the proposition: Three points can always lie in a plane.
On the other hand, no synthetical principle which is based upon
conceptions, can ever be immediately certain (for example, the
proposition: Everything that happens has a cause), because I require
a mediating term to connect the two conceptions of event and cause-
namely, the condition of time-determination in an experience, and I
cannot cognize any such principle immediately and from conceptions
alone. Discursive principles are, accordingly, very different from
intuitive principles or axioms. The former always require deduction,
which in the case of the latter may be altogether dispensed with.
Axioms are, for this reason, always self-evident, while
philosophical principles, whatever may be the degree of certainty they
possess, cannot lay any claim to such a distinction. No synthetical
proposition of pure transcendental reason can be so evident, as is
often rashly enough declared, as the statement, twice two are four.
It is true that in the Analytic I introduced into the list of
principles of the pure understanding, certain axioms of intuition;
but the principle there discussed was not itself an axiom, but served
merely to present the principle of the possibility of axioms in
general, while it was really nothing more than a principle based
upon conceptions. For it is one part of the duty of transcendental
philosophy to establish the possibility of mathematics itself.
Philosophy possesses, then, no axioms, and has no right to impose
its a priori principles upon thought, until it has established their
authority and validity by a thoroughgoing deduction.

3. Of Demonstrations. Only an apodeictic proof, based upon
intuition, can be termed a demonstration. Experience teaches us what
is, but it cannot convince us that it might not have been otherwise.
Hence a proof upon empirical grounds cannot be apodeictic. A priori
conceptions, in discursive cognition, can never produce intuitive
certainty or evidence, however certain the judgement they present
may be. Mathematics alone, therefore, contains demonstrations, because
it does not deduce its cognition from conceptions, but from the
construction of conceptions, that is, from intuition, which can be
given a priori in accordance with conceptions. The method of
algebra, in equations, from which the correct answer is deduced by
reduction, is a kind of construction--not geometrical, but by symbols-
in which all conceptions, especially those of the relations of
quantities, are represented in intuition by signs; and thus the
conclusions in that science are secured from errors by the fact that
every proof is submitted to ocular evidence. Philosophical cognition
does not possess this advantage, it being required to consider the
general always in abstracto (by means of conceptions), while
mathematics can always consider it in concreto (in an individual
intuition), and at the same time by means of a priori
representation, whereby all errors are rendered manifest to the
senses. The former--discursive proofs--ought to be termed acroamatic
proofs, rather than demonstrations, as only words are employed in
them, while demonstrations proper, as the term itself indicates,
always require a reference to the intuition of the object.

It follows from all these considerations that it is not consonant
with the nature of philosophy, especially in the sphere of pure
reason, to employ the dogmatical method, and to adorn itself with
the titles and insignia of mathematical science. It does not belong
to that order, and can only hope for a fraternal union with that science.
Its attempts at mathematical evidence are vain pretensions, which
can only keep it back from its true aim, which is to detect the
illusory procedure of reason when transgressing its proper limits,
and by fully explaining and analysing our conceptions, to conduct us
from the dim regions of speculation to the clear region of modest
self-knowledge. Reason must not, therefore, in its transcendental
endeavours, look forward with such confidence, as if the path it is
pursuing led straight to its aim, nor reckon with such security upon
its premisses, as to consider it unnecessary to take a step back, or
to keep a strict watch for errors, which, overlooked in the
principles, may be detected in the arguments themselves--in which case
it may be requisite either to determine these principles with
greater strictness, or to change them entirely.

I divide all apodeictic propositions, whether demonstrable or
immediately certain, into dogmata and mathemata. A direct
synthetical proposition, based on conceptions, is a dogma; a
proposition of the same kind, based on the construction of
conceptions, is a mathema. Analytical judgements do not teach us any
more about an object than what was contained in the conception we
had of it; because they do not extend our cognition beyond our
conception of an object, they merely elucidate the conception. They
cannot therefore be with propriety termed dogmas. Of the two kinds
of a priori synthetical propositions above mentioned, only those which
are employed in philosophy can, according to the general mode of
speech, bear this name; those of arithmetic or geometry would not be
rightly so denominated. Thus the customary mode of speaking confirms
the explanation given above, and the conclusion arrived at, that
only those judgements which are based upon conceptions, not on the
construction of conceptions, can be termed dogmatical.

Thus, pure reason, in the sphere of speculation, does not contain
a single direct synthetical judgement based upon conceptions. By means
of ideas, it is, as we have shown, incapable of producing
synthetical judgements, which are objectively valid; by means of the
conceptions of the understanding, it establishes certain indubitable
principles, not, however, directly on the basis of conceptions, but
only indirectly by means of the relation of these conceptions to
something of a purely contingent nature, namely, possible
experience. When experience is presupposed, these principles are
apodeictically certain, but in themselves, and directly, they cannot
even be cognized a priori. Thus the given conceptions of cause and
event will not be sufficient for the demonstration of the proposition:
Every event has a cause. For this reason, it is not a dogma;
although from another point of view, that of experience, it is capable
of being proved to demonstration. The proper term for such a
proposition is principle, and not theorem (although it does require
to be proved), because it possesses the remarkable peculiarity of being
the condition of the possibility of its own ground of proof, that
is, experience, and of forming a necessary presupposition in all
empirical observation.

If then, in the speculative sphere of pure reason, no dogmata are to
be found; all dogmatical methods, whether borrowed from mathematics,
or invented by philosophical thinkers, are alike inappropriate and
inefficient. They only serve to conceal errors and fallacies, and to
deceive philosophy, whose duty it is to see that reason pursues a safe
and straight path. A philosophical method may, however, be
systematical. For our reason is, subjectively considered, itself a
system, and, in the sphere of mere conceptions, a system of
investigation according to principles of unity, the material being
supplied by experience alone. But this is not the proper place for
discussing the peculiar method of transcendental philosophy, as our
present task is simply to examine whether our faculties are capable
of erecting an edifice on the basis of pure reason, and how far they
may proceed with the materials at their command.

SECTION II. The Discipline of Pure Reason in Polemics.

Reason must be subject, in all its operations, to criticism, which
must always be permitted to exercise its functions without
restraint; otherwise its interests are imperilled and its influence
obnoxious to suspicion. There is nothing, however useful, however
sacred it may be, that can claim exemption from the searching
examination of this supreme tribunal, which has no respect of persons.
The very existence of reason depends upon this freedom; for the
voice of reason is not that of a dictatorial and despotic power, it
is rather like the vote of the citizens of a free state, every member
of which must have the privilege of giving free expression to his
doubts, and possess even the right of veto.

But while reason can never decline to submit itself to the
tribunal of criticism, it has not always cause to dread the
judgement of this court. Pure reason, however, when engaged in the
sphere of dogmatism, is not so thoroughly conscious of a strict
observance of its highest laws, as to appear before a higher
judicial reason with perfect confidence. On the contrary, it must
renounce its magnificent dogmatical pretensions in philosophy.

Very different is the case when it has to defend itself, not
before a judge, but against an equal. If dogmatical assertions are
advanced on the negative side, in opposition to those made by reason
on the positive side, its justification kat authrhopon is complete,
although the proof of its propositions is kat aletheian

By the polemic of pure reason I mean the defence of its propositions
made by reason, in opposition to the dogmatical counter-propositions
advanced by other parties. The question here is not whether its own
statements may not also be false; it merely regards the fact that
reason proves that the opposite cannot be established with
demonstrative certainty, nor even asserted with a higher degree of
probability. Reason does not hold her possessions upon sufferance;
for, although she cannot show a perfectly satisfactory title to
them, no one can prove that she is not the rightful possessor.

It is a melancholy reflection that reason, in its highest
exercise, falls into an antithetic; and that the supreme tribunal
for the settlement of differences should not be at union with
itself. It is true that we had to discuss the question of an
apparent antithetic, but we found that it was based upon a
misconception. In conformity with the common prejudice, phenomena were
regarded as things in themselves, and thus an absolute completeness
in their synthesis was required in the one mode or in the other (it
was shown to be impossible in both); a demand entirely out of place
in regard to phenomena. There was, then, no real self-contradiction
of reason in the propositions: The series of phenomena given in
themselves has an absolutely first beginning; and: This series is
absolutely and in itself without beginning. The two propositions are
perfectly consistent with each other, because phenomena as phenomena
are in themselves nothing, and consequently the hypothesis that they
are things in themselves must lead to self-contradictory inferences.

But there are cases in which a similar misunderstanding cannot be
provided against, and the dispute must remain unsettled. Take, for
example, the theistic proposition: There is a Supreme Being; and on
the other hand, the atheistic counter-statement: There exists no
Supreme Being; or, in psychology: Everything that thinks possesses
the attribute of absolute and permanent unity, which is utterly
different from the transitory unity of material phenomena; and the
counter-proposition: The soul is not an immaterial unity, and its
nature is transitory, like that of phenomena. The objects of these
questions contain no heterogeneous or contradictory elements, for they
relate to things in themselves, and not to phenomena. There would
arise, indeed, a real contradiction, if reason came forward with a
statement on the negative side of these questions alone. As regards
the criticism to which the grounds of proof on the affirmative side
must be subjected, it may be freely admitted, without necessitating
the surrender of the affirmative propositions, which have, at least,
the interest of reason in their favour--an advantage which the
opposite party cannot lay claim to.

I cannot agree with the opinion of several admirable thinkers--Sulzer
among the rest--that, in spite of the weakness of the arguments
hitherto in use, we may hope, one day, to see sufficient demonstrations
of the two cardinal propositions of pure reason--the existence of a
Supreme Being, and the immortality of the soul. I am certain, on the
contrary, that this will never be the case. For on what ground can
reason base such synthetical propositions, which do not relate to the
objects of experience and their internal possibility? But it is also
demonstratively certain that no one will ever be able to maintain the
contrary with the least show of probability. For, as he can attempt
such a proof solely upon the basis of pure reason, he is bound to prove
that a Supreme Being, and a thinking subject in the character of a pure
intelligence, are impossible. But where will he find the knowledge
which can enable him to enounce synthetical judgements in regard to
things which transcend the region of experience? We may, therefore,
rest assured that the opposite never will be demonstrated. We need not,
then, have recourse to scholastic arguments; we may always admit the
truth of those propositions which are consistent with the speculative
interests of reason in the sphere of experience, and form, moreover,
the only means of uniting the speculative with the practical interest.
Our opponent, who must not be considered here as a critic solely, we
can be ready to meet with a non liquet which cannot fail to disconcert
him; while we cannot deny his right to a similar retort, as we have on
our side the advantage of the support of the subjective maxim of
reason, and can therefore look upon all his sophistical arguments with
calm indifference.

From this point of view, there is properly no antithetic of pure
reason. For the only arena for such a struggle would be upon the field
of pure theology and psychology; but on this ground there can appear
no combatant whom we need to fear. Ridicule and boasting can be his
only weapons; and these may be laughed at, as mere child's play.
This consideration restores to Reason her courage; for what source
of confidence could be found, if she, whose vocation it is to
destroy error, were at variance with herself and without any
reasonable hope of ever reaching a state of permanent repose?

Everything in nature is good for some purpose. Even poisons are
serviceable; they destroy the evil effects of other poisons generated
in our system, and must always find a place in every complete
pharmacopoeia. The objections raised against the fallacies and
sophistries of speculative reason, are objections given by the nature
of this reason itself, and must therefore have a destination and
purpose which can only be for the good of humanity. For what purpose
has Providence raised many objects, in which we have the deepest
interest, so far above us, that we vainly try to cognize them with
certainty, and our powers of mental vision are rather excited than
satisfied by the glimpses we may chance to seize? It is very doubtful
whether it is for our benefit to advance bold affirmations regarding
subjects involved in such obscurity; perhaps it would even be
detrimental to our best interests. But it is undoubtedly always
beneficial to leave the investigating, as well as the critical reason,
in perfect freedom, and permit it to take charge of its own interests,
which are advanced as much by its limitation, as by its extension of
its views, and which always suffer by the interference of foreign
powers forcing it, against its natural tendencies, to bend to certain
preconceived designs.

Allow your opponent to say what he thinks reasonable, and combat him
only with the weapons of reason. Have no anxiety for the practical
interests of humanity--these are never imperilled in a purely
speculative dispute. Such a dispute serves merely to disclose the
antinomy of reason, which, as it has its source in the nature of
reason, ought to be thoroughly investigated. Reason is benefited by
the examination of a subject on both sides, and its judgements are
corrected by being limited. It is not the matter that may give
occasion to dispute, but the manner. For it is perfectly permissible
to employ, in the presence of reason, the language of a firmly
rooted faith, even after we have been obliged to renounce all
pretensions to knowledge.

If we were to ask the dispassionate David Hume--a philosopher
endowed, in a degree that few are, with a well-balanced judgement:
What motive induced you to spend so much labour and thought in
undermining the consoling and beneficial persuasion that reason is
capable of assuring us of the existence, and presenting us with a
determinate conception of a Supreme Being?--his answer would be:
Nothing but the desire of teaching reason to know its own powers
better, and, at the same time, a dislike of the procedure by which
that faculty was compelled to support foregone conclusions, and
prevented from confessing the internal weaknesses which it cannot
but feel when it enters upon a rigid self-examination. If, on the
other hand, we were to ask Priestley--a philosopher who had no taste
for transcendental speculation, but was entirely devoted to the
principles of empiricism--what his motives were for overturning
those two main pillars of religion--the doctrines of the freedom of
the will and the immortality of the soul (in his view the hope of a
future life is but the expectation of the miracle of resurrection)-
this philosopher, himself a zealous and pious teacher of religion,
could give no other answer than this: I acted in the interest of
reason, which always suffers, when certain objects are explained and
judged by a reference to other supposed laws than those of material
nature--the only laws which we know in a determinate manner. It
would be unfair to decry the latter philosopher, who endeavoured to
harmonize his paradoxical opinions with the interests of religion,
and to undervalue an honest and reflecting man, because he finds himself
at a loss the moment he has left the field of natural science. The
same grace must be accorded to Hume, a man not less well-disposed,
and quite as blameless in his moral character, and who pushed his abstract
speculations to an extreme length, because, as he rightly believed,
the object of them lies entirely beyond the bounds of natural science,
and within the sphere of pure ideas.

What is to be done to provide against the danger which seems in
the present case to menace the best interests of humanity? The
course to be pursued in reference to this subject is a perfectly plain
and natural one. Let each thinker pursue his own path; if he shows
talent, if he gives evidence of profound thought, in one word, if he
shows that he possesses the power of reasoning--reason is always the
gainer. If you have recourse to other means, if you attempt to
coerce reason, if you raise the cry of treason to humanity, if you
excite the feelings of the crowd, which can neither understand nor
sympathize with such subtle speculations--you will only make
yourselves ridiculous. For the question does not concern the advantage
or disadvantage which we are expected to reap from such inquiries;
the question is merely how far reason can advance in the field of
speculation, apart from all kinds of interest, and whether we may
depend upon the exertions of speculative reason, or must renounce
all reliance on it. Instead of joining the combatants, it is your part
to be a tranquil spectator of the struggle--a laborious struggle for
the parties engaged, but attended, in its progress as well as in its
result, with the most advantageous consequences for the interests of
thought and knowledge. It is absurd to expect to be enlightened by
Reason, and at the same time to prescribe to her what side of the
question she must adopt. Moreover, reason is sufficiently held in
check by its own power, the limits imposed on it by its own nature
are sufficient; it is unnecessary for you to place over it additional
guards, as if its power were dangerous to the constitution of the
intellectual state. In the dialectic of reason there is no victory
gained which need in the least disturb your tranquility.

The strife of dialectic is a necessity of reason, and we cannot
but wish that it had been conducted long ere this with that perfect
freedom which ought to be its essential condition. In this case, we
should have had at an earlier period a matured and profound criticism,
which must have put an end to all dialectical disputes, by exposing
the illusions and prejudices in which they originated.

There is in human nature an unworthy propensity--a propensity which,
like everything that springs from nature, must in its final purpose
be conducive to the good of humanity--to conceal our real sentiments,
and to give expression only to certain received opinions, which are
regarded as at once safe and promotive of the common good. It is true,
this tendency, not only to conceal our real sentiments, but to profess
those which may gain us favour in the eyes of society, has not only
civilized, but, in a certain measure, moralized us; as no one can
break through the outward covering of respectability, honour, and
morality, and thus the seemingly-good examples which we which we see
around us form an excellent school for moral improvement, so long as
our belief in their genuineness remains unshaken. But this disposition
to represent ourselves as better than we are, and to utter opinions
which are not our own, can be nothing more than a kind of provisionary
arrangement of nature to lead us from the rudeness of an uncivilized
state, and to teach us how to assume at least the appearance and
manner of the good we see. But when true principles have been
developed, and have obtained a sure foundation in our habit of
thought, this conventionalism must be attacked with earnest vigour,
otherwise it corrupts the heart, and checks the growth of good
dispositions with the mischievous weed of air appearances.

I am sorry to remark the same tendency to misrepresentation and
hypocrisy in the sphere of speculative discussion, where there is less
temptation to restrain the free expression of thought. For what can
be more prejudicial to the interests of intelligence than to falsify
our real sentiments, to conceal the doubts which we feel in regard
to our statements, or to maintain the validity of grounds of proof
which we well know to be insufficient? So long as mere personal vanity
is the source of these unworthy artifices--and this is generally the
case in speculative discussions, which are mostly destitute of
practical interest, and are incapable of complete demonstration--the
vanity of the opposite party exaggerates as much on the other side;
and thus the result is the same, although it is not brought about so
soon as if the dispute had been conducted in a sincere and upright
spirit. But where the mass entertains the notion that the aim of
certain subtle speculators is nothing less than to shake the very
foundations of public welfare and morality--it seems not only prudent,
but even praise worthy, to maintain the good cause by illusory
arguments, rather than to give to our supposed opponents the advantage
of lowering our declarations to the moderate tone of a merely
practical conviction, and of compelling us to confess our inability
to attain to apodeictic certainty in speculative subjects. But we ought
to reflect that there is nothing, in the world more fatal to the
maintenance of a good cause than deceit, misrepresentation, and
falsehood. That the strictest laws of honesty should be observed in
the discussion of a purely speculative subject is the least
requirement that can be made. If we could reckon with security even
upon so little, the conflict of speculative reason regarding the
important questions of God, immortality, and freedom, would have
been either decided long ago, or would very soon be brought to a
conclusion. But, in general, the uprightness of the defence stands
in an inverse ratio to the goodness of the cause; and perhaps more
honesty and fairness are shown by those who deny than by those who
uphold these doctrines.

I shall persuade myself, then, that I have readers who do not wish
to see a righteous cause defended by unfair arguments. Such will now
recognize the fact that, according to the principles of this Critique,
if we consider not what is, but what ought to be the case, there can
be really no polemic of pure reason. For how can two persons dispute
about a thing, the reality of which neither can present in actual or
even in possible experience? Each adopts the plan of meditating on
his idea for the purpose of drawing from the idea, if he can, what
is more than the idea, that is, the reality of the object which it
indicates. How shall they settle the dispute, since neither is able
to make his assertions directly comprehensible and certain, but must
restrict himself to attacking and confuting those of his opponent?
All statements enounced by pure reason transcend the conditions of
possible experience, beyond the sphere of which we can discover no
criterion of truth, while they are at the same time framed in
accordance with the laws of the understanding, which are applicable
only to experience; and thus it is the fate of all such speculative
discussions that while the one party attacks the weaker side of his
opponent, he infallibly lays open his own weaknesses.

The critique of pure reason may be regarded as the highest
tribunal for all speculative disputes; for it is not involved in these
disputes, which have an immediate relation to certain objects and
not to the laws of the mind, but is instituted for the purpose of
determining the rights and limits of reason.

Without the control of criticism, reason is, as it were, in a
state of nature, and can only establish its claims and assertions by
war. Criticism, on the contrary, deciding all questions according to
the fundamental laws of its own institution, secures to us the peace
of law and order, and enables us to discuss all differences in the
more tranquil manner of a legal process. In the former case,
disputes are ended by victory, which both sides may claim and which
is followed by a hollow armistice; in the latter, by a sentence, which,
as it strikes at the root of all speculative differences, ensures to
all concerned a lasting peace. The endless disputes of a dogmatizing
reason compel us to look for some mode of arriving at a settled
decision by a critical investigation of reason itself; just as
Hobbes maintains that the state of nature is a state of injustice
and violence, and that we must leave it and submit ourselves to the
constraint of law, which indeed limits individual freedom, but only
that it may consist with the freedom of others and with the common
good of all.

This freedom will, among other things, permit of our openly
stating the difficulties and doubts which we are ourselves unable to
solve, without being decried on that account as turbulent and
dangerous citizens. This privilege forms part of the native rights
of human reason, which recognizes no other judge than the universal
reason of humanity; and as this reason is the source of all progress
and improvement, such a privilege is to be held sacred and inviolable.
It is unwise, moreover, to denounce as dangerous any bold assertions
against, or rash attacks upon, an opinion which is held by the largest
and most moral class of the community; for that would be giving them
an importance which they do not deserve. When I hear that the
freedom of the will, the hope of a future life, and the existence of
God have been overthrown by the arguments of some able writer, I
feel a strong desire to read his book; for I expect that he will add
to my knowledge and impart greater clearness and distinctness to my
views by the argumentative power shown in his writings. But I am
perfectly certain, even before I have opened the book, that he has
not succeeded in a single point, not because I believe I am in
possession of irrefutable demonstrations of these important
propositions, but because this transcendental critique, which has
disclosed to me the power and the limits of pure reason, has fully
convinced me that, as it is insufficient to establish the affirmative,
it is as powerless, and even more so, to assure us of the truth of
the negative answer to these questions. From what source does this
free-thinker derive his knowledge that there is, for example, no
Supreme Being? This proposition lies out of the field of possible
experience, and, therefore, beyond the limits of human cognition.
But I would not read at, all the answer which the dogmatical
maintainer of the good cause makes to his opponent, because I know
well beforehand, that he will merely attack the fallacious grounds
of his adversary, without being able to establish his own
assertions. Besides, a new illusory argument, in the construction of
which talent and acuteness are shown, is suggestive of new ideas and
new trains of reasoning, and in this respect the old and everyday
sophistries are quite useless. Again, the dogmatical opponent of
religion gives employment to criticism, and enables us to test and
correct its principles, while there is no occasion for anxiety in
regard to the influence and results of his reasoning.

But, it will be said, must we not warn the youth entrusted to
academical care against such writings, must we not preserve them
from the knowledge of these dangerous assertions, until their
judgement is ripened, or rather until the doctrines which we wish to
inculcate are so firmly rooted in their minds as to withstand all
attempts at instilling the contrary dogmas, from whatever quarter they
may come?

If we are to confine ourselves to the dogmatical procedure in the
sphere of pure reason, and find ourselves unable to settle such
disputes otherwise than by becoming a party in them, and setting
counter-assertions against the statements advanced by our opponents,
there is certainly no plan more advisable for the moment, but, at
the same time, none more absurd and inefficient for the future, than
this retaining of the youthful mind under guardianship for a time,
and thus preserving it--for so long at least--from seduction into error.
But when, at a later period, either curiosity, or the prevalent
fashion of thought places such writings in their hands, will the
so-called convictions of their youth stand firm? The young thinker,
who has in his armoury none but dogmatical weapons with which to
resist the attacks of his opponent, and who cannot detect the latent
dialectic which lies in his own opinions as well as in those of the
opposite party, sees the advance of illusory arguments and grounds
of proof which have the advantage of novelty, against as illusory
grounds of proof destitute of this advantage, and which, perhaps,
excite the suspicion that the natural credulity of his youth has
been abused by his instructors. He thinks he can find no better
means of showing that he has out grown the discipline of his
minority than by despising those well-meant warnings, and, knowing
no system of thought but that of dogmatism, he drinks deep draughts
of the poison that is to sap the principles in which his early years
were trained.

Exactly the opposite of the system here recommended ought to be
pursued in academical instruction. This can only be effected, however,
by a thorough training in the critical investigation of pure reason.
For, in order to bring the principles of this critique into exercise
as soon as possible, and to demonstrate their perfect even in the
presence of the highest degree of dialectical illusion, the student
ought to examine the assertions made on both sides of speculative
questions step by step, and to test them by these principles. It
cannot be a difficult task for him to show the fallacies inherent in
these propositions, and thus he begins early to feel his own power
of securing himself against the influence of such sophistical
arguments, which must finally lose, for him, all their illusory power.
And, although the same blows which overturn the edifice of his
opponent are as fatal to his own speculative structures, if such he
has wished to rear; he need not feel any sorrow in regard to this
seeming misfortune, as he has now before him a fair prospect into
the practical region in which he may reasonably hope to find a more
secure foundation for a rational system.

There is, accordingly, no proper polemic in the sphere of pure
reason. Both parties beat the air and fight with their own shadows,
as they pass beyond the limits of nature, and can find no tangible
point of attack--no firm footing for their dogmatical conflict.
Fight as vigorously as they may, the shadows which they hew down,
immediately start up again, like the heroes in Walhalla, and renew
the bloodless and unceasing contest.

But neither can we admit that there is any proper sceptical
employment of pure reason, such as might be based upon the principle
of neutrality in all speculative disputes. To excite reason against
itself, to place weapons in the hands of the party on the one side
as well as in those of the other, and to remain an undisturbed and
sarcastic spectator of the fierce struggle that ensues, seems, from
the dogmatical point of view, to be a part fitting only a malevolent
disposition. But, when the sophist evidences an invincible obstinacy
and blindness, and a pride which no criticism can moderate, there is
no other practicable course than to oppose to this pride and obstinacy
similar feelings and pretensions on the other side, equally well or
ill founded, so that reason, staggered by the reflections thus
forced upon it, finds it necessary to moderate its confidence in
such pretensions and to listen to the advice of criticism. But we
cannot stop at these doubts, much less regard the conviction of our
ignorance, not only as a cure for the conceit natural to dogmatism,
but as the settlement of the disputes in which reason is involved with
itself. On the contrary, scepticism is merely a means of awakening
reason from its dogmatic dreams and exciting it to a more careful
investigation into its own powers and pretensions. But, as
scepticism appears to be the shortest road to a permanent peace in
the domain of philosophy, and as it is the track pursued by the many
who aim at giving a philosophical colouring to their contemptuous
dislike of all inquiries of this kind, I think it necessary to present
to my readers this mode of thought in its true light.

Scepticism not a Permanent State for Human Reason.

The consciousness of ignorance--unless this ignorance is
recognized to be absolutely necessary ought, instead of forming the
conclusion of my inquiries, to be the strongest motive to the
pursuit of them. All ignorance is either ignorance of things or of
the limits of knowledge. If my ignorance is accidental and not
necessary, it must incite me, in the first case, to a dogmatical
inquiry regarding the objects of which I am ignorant; in the second,
to a critical investigation into the bounds of all possible knowledge.
But that my ignorance is absolutely necessary and unavoidable, and
that it consequently absolves from the duty of all further
investigation, is a fact which cannot be made out upon empirical
grounds--from observation--but upon critical grounds alone, that is,
by a thoroughgoing investigation into the primary sources of
cognition. It follows that the determination of the bounds of reason
can be made only on a priori grounds; while the empirical limitation
of reason, which is merely an indeterminate cognition of an
ignorance that can never be completely removed, can take place only
a posteriori. In other words, our empirical knowledge is limited by
that which yet remains for us to know. The former cognition of our
ignorance, which is possible only on a rational basis, is a science;
the latter is merely a perception, and we cannot say how far the
inferences drawn from it may extend. If I regard the earth, as it
really appears to my senses, as a flat surface, I am ignorant how
far this surface extends. But experience teaches me that, how far
soever I go, I always see before me a space in which I can proceed
farther; and thus I know the limits--merely visual--of my actual
knowledge of the earth, although I am ignorant of the limits of the
earth itself. But if I have got so far as to know that the earth is
a sphere, and that its surface is spherical, I can cognize a priori
and determine upon principles, from my knowledge of a small part of
this surface--say to the extent of a degree--the diameter and
circumference of the earth; and although I am ignorant of the
objects which this surface contains, I have a perfect knowledge of
its limits and extent.

The sum of all the possible objects of our cognition seems to us
to be a level surface, with an apparent horizon--that which forms
the limit of its extent, and which has been termed by us the idea of
unconditioned totality. To reach this limit by empirical means is
impossible, and all attempts to determine it a priori according to
a principle, are alike in vain. But all the questions raised by pure
reason relate to that which lies beyond this horizon, or, at least,
in its boundary line.

The celebrated David Hume was one of those geographers of human
reason who believe that they have given a sufficient answer to all
such questions by declaring them to lie beyond the horizon of our
knowledge--a horizon which, however, Hume was unable to determine.
His attention especially was directed to the principle of causality;
and he remarked with perfect justice that the truth of this principle,
and even the objective validity of the conception of a cause, was not
commonly based upon clear insight, that is, upon a priori cognition.
Hence he concluded that this law does not derive its authority from
its universality and necessity, but merely from its general
applicability in the course of experience, and a kind of subjective
necessity thence arising, which he termed habit. From the inability
of reason to establish this principle as a necessary law for the
acquisition of all experience, he inferred the nullity of all the
attempts of reason to pass the region of the empirical.

This procedure of subjecting the facta of reason to examination,
and, if necessary, to disapproval, may be termed the censura of
reason. This censura must inevitably lead us to doubts regarding all
transcendent employment of principles. But this is only the second
step in our inquiry. The first step in regard to the subjects of
pure reason, and which marks the infancy of that faculty, is that of
dogmatism. The second, which we have just mentioned, is that of
scepticism, and it gives evidence that our judgement has been improved
by experience. But a third step is necessary--indicative of the
maturity and manhood of the judgement, which now lays a firm
foundation upon universal and necessary principles. This is the period
of criticism, in which we do not examine the facta of reason, but
reason itself, in the whole extent of its powers, and in regard to
its capability of a priori cognition; and thus we determine not merely
the empirical and ever-shifting bounds of our knowledge, but its necessary
and eternal limits. We demonstrate from indubitable principles, not
merely our ignorance in respect to this or that subject, but in regard
to all possible questions of a certain class. Thus scepticism is a
resting place for reason, in which it may reflect on its dogmatical
wanderings and gain some knowledge of the region in which it happens
to be, that it may pursue its way with greater certainty; but it
cannot be its permanent dwelling-place. It must take up its abode only
in the region of complete certitude, whether this relates to the
cognition of objects themselves, or to the limits which bound all
our cognition.

Reason is not to be considered as an indefinitely extended plane, of
the bounds of which we have only a general knowledge; it ought
rather to be compared to a sphere, the radius of which may be found
from the curvature of its surface--that is, the nature of a priori
synthetical propositions--and, consequently, its circumference and
extent. Beyond the sphere of experience there are no objects which
it can cognize; nay, even questions regarding such supposititious
objects relate only to the subjective principles of a complete
determination of the relations which exist between the
understanding-conceptions which lie within this sphere.

We are actually in possession of a priori synthetical cognitions, as
is proved by the existence of the principles of the understanding,
which anticipate experience. If any one cannot comprehend the
possibility of these principles, he may have some reason to doubt
whether they are really a priori; but he cannot on this account
declare them to be impossible, and affirm the nullity of the steps
which reason may have taken under their guidance. He can only say:
If we perceived their origin and their authenticity, we should be able
to determine the extent and limits of reason; but, till we can do
this, all propositions regarding the latter are mere random
assertions. In this view, the doubt respecting all dogmatical
philosophy, which proceeds without the guidance of criticism, is
well grounded; but we cannot therefore deny to reason the ability to
construct a sound philosophy, when the way has been prepared by a
thorough critical investigation. All the conceptions produced, and
all the questions raised, by pure reason, do not lie in the sphere
of experience, but in that of reason itself, and hence they must be
solved, and shown to be either valid or inadmissible, by that faculty.
We have no right to decline the solution of such problems, on the
ground that the solution can be discovered only from the nature of
things, and under pretence of the limitation of human faculties, for
reason is the sole creator of all these ideas, and is therefore
bound either to establish their validity or to expose their illusory

The polemic of scepticism is properly directed against the
dogmatist, who erects a system of philosophy without having examined
the fundamental objective principles on which it is based, for the
purpose of evidencing the futility of his designs, and thus bringing
him to a knowledge of his own powers. But, in itself, scepticism
does not give us any certain information in regard to the bounds of
our knowledge. All unsuccessful dogmatical attempts of reason are
facia, which it is always useful to submit to the censure of the
sceptic. But this cannot help us to any decision regarding the
expectations which reason cherishes of better success in future
endeavours; the investigations of scepticism cannot, therefore, settle
the dispute regarding the rights and powers of human reason.

Hume is perhaps the ablest and most ingenious of all sceptical
philosophers, and his writings have, undoubtedly, exerted the most
powerful influence in awakening reason to a thorough investigation
into its own powers. It will, therefore, well repay our labours to
consider for a little the course of reasoning which he followed and
the errors into which he strayed, although setting out on the path
of truth and certitude.

Hume was probably aware, although he never clearly developed the
notion, that we proceed in judgements of a certain class beyond our
conception if the object. I have termed this kind of judgement
synthetical. As regard the manner in which I pass beyond my conception
by the aid of experience, no doubts can be entertained. Experience
is itself a synthesis of perceptions; and it employs perceptions to
increment the conception, which I obtain by means of another
perception. But we feel persuaded that we are able to proceed beyond
a conception, and to extend our cognition a priori. We attempt this
in two ways--either, through the pure understanding, in relation to
that which may become an object of experience, or, through pure
reason, in relation to such properties of things, or of the
existence of things, as can never be presented in any experience. This
sceptical philosopher did not distinguish these two kinds of
judgements, as he ought to have done, but regarded this augmentation
of conceptions, and, if we may so express ourselves, the spontaneous
generation of understanding and reason, independently of the
impregnation of experience, as altogether impossible. The so-called
a priori principles of these faculties he consequently held to be
invalid and imaginary, and regarded them as nothing but subjective
habits of thought originating in experience, and therefore purely
empirical and contingent rules, to which we attribute a spurious
necessity and universality. In support of this strange assertion, he
referred us to the generally acknowledged principle of the relation
between cause and effect. No faculty of the mind can conduct us from
the conception of a thing to the existence of something else; and
hence he believed he could infer that, without experience, we
possess no source from which we can augment a conception, and no
ground sufficient to justify us in framing a judgement that is to
extend our cognition a priori. That the light of the sun, which shines
upon a piece of wax, at the same time melts it, while it hardens clay,
no power of the understanding could infer from the conceptions which
we previously possessed of these substances; much less is there any
a priori law that could conduct us to such a conclusion, which
experience alone can certify. On the other hand, we have seen in our
discussion of transcendental logic, that, although we can never
proceed immediately beyond the content of the conception which is
given us, we can always cognize completely a priori--in relation,
however, to a third term, namely, possible experience--the law of
its connection with other things. For example, if I observe that a
piece of wax melts, I can cognize a priori that there must have been
something (the sun's heat) preceding, which this law; although,
without the aid of experience, I could not cognize a priori and in
a determinate manner either the cause from the effect, or the effect
from the cause. Hume was, therefore, wrong in inferring, from the
contingency of the determination according to law, the contingency
of the law itself; and the passing beyond the conception of a thing
to possible experience (which is an a priori proceeding, constituting
the objective reality of the conception), he confounded with our synthesis
of objects in actual experience, which is always, of course,
empirical. Thus, too, he regarded the principle of affinity, which
has its seat in the understanding and indicates a necessary connection,
as a mere rule of association, lying in the imitative faculty of
imagination, which can present only contingent, and not objective

The sceptical errors of this remarkably acute thinker arose
principally from a defect, which was common to him with the
dogmatists, namely, that he had never made a systematic review of
all the different kinds of a priori synthesis performed by the
understanding. Had he done so, he would have found, to take one
example among many, that the principle of permanence was of this
character, and that it, as well as the principle of causality,
anticipates experience. In this way he might have been able to
describe the determinate limits of the a priori operations of
understanding and reason. But he merely declared the understanding
to be limited, instead of showing what its limits were; he created
a general mistrust in the power of our faculties, without giving us
any determinate knowledge of the bounds of our necessary and
unavoidable ignorance; he examined and condemned some of the
principles of the understanding, without investigating all its
powers with the completeness necessary to criticism. He denies, with
truth, certain powers to the understanding, but he goes further, and
declares it to be utterly inadequate to the a priori extension of
knowledge, although he has not fully examined all the powers which
reside in the faculty; and thus the fate which always overtakes
scepticism meets him too. That is to say, his own declarations are
doubted, for his objections were based upon facta, which are
contingent, and not upon principles, which can alone demonstrate the
necessary invalidity of all dogmatical assertions.

As Hume makes no distinction between the well-grounded claims of the
understanding and the dialectical pretensions of reason, against
which, however, his attacks are mainly directed, reason does not
feel itself shut out from all attempts at the extension of a priori
cognition, and hence it refuses, in spite of a few checks in this or
that quarter, to relinquish such efforts. For one naturally arms
oneself to resist an attack, and becomes more obstinate in the resolve
to establish the claims he has advanced. But a complete review of
the powers of reason, and the conviction thence arising that we are
in possession of a limited field of action, while we must admit the
vanity of higher claims, puts an end to all doubt and dispute, and
induces reason to rest satisfied with the undisturbed possession of
its limited domain.

To the uncritical dogmatist, who has not surveyed the sphere of
his understanding, nor determined, in accordance with principles,
the limits of possible cognition, who, consequently, is ignorant of
his own powers, and believes he will discover them by the attempts
he makes in the field of cognition, these attacks of scepticism are
not only dangerous, but destructive. For if there is one proposition
in his chain of reasoning which be he cannot prove, or the fallacy
in which he cannot evolve in accordance with a principle, suspicion
falls on all his statements, however plausible they may appear.

And thus scepticism, the bane of dogmatical philosophy, conducts
us to a sound investigation into the understanding and the reason.
When we are thus far advanced, we need fear no further
attacks; for the limits of our domain are clearly marked out, and we
can make no claims nor become involved in any disputes regarding the
region that lies beyond these limits. Thus the sceptical procedure
in philosophy does not present any solution of the problems of reason,
but it forms an excellent exercise for its powers, awakening its
circumspection, and indicating the means whereby it may most fully
establish its claims to its legitimate possessions.

SECTION III. The Discipline of Pure Reason in Hypothesis.

This critique of reason has now taught us that all its efforts to
extend the bounds of knowledge, by means of pure speculation, are
utterly fruitless. So much the wider field, it may appear, lies open
to hypothesis; as, where we cannot know with certainty, we are at
liberty to make guesses and to form suppositions.

Imagination may be allowed, under the strict surveillance of reason,
to invent suppositions; but, these must be based on something that
is perfectly certain--and that is the possibility of the object. If
we are well assured upon this point, it is allowable to have recourse
to supposition in regard to the reality of the object; but this
supposition must, unless it is utterly groundless, be connected, as
its ground of explanation, with that which is really given and
absolutely certain. Such a supposition is termed a hypothesis.

It is beyond our power to form the least conception a priori of
the possibility of dynamical connection in phenomena; and the category
of the pure understanding will not enable us to excogitate any
such connection, but merely helps us to understand it, when we meet
with it in experience. For this reason we cannot, in accordance with
the categories, imagine or invent any object or any property of an
object not given, or that may not be given in experience, and employ
it in a hypothesis; otherwise, we should be basing our chain of
reasoning upon mere chimerical fancies, and not upon conceptions of
things. Thus, we have no right to assume the existence of new
powers, not existing in nature--for example, an understanding with
a non-sensuous intuition, a force of attraction without contact, or
some new kind of substances occupying space, and yet without the property
of impenetrability--and, consequently, we cannot assume that there
is any other kind of community among substances than that observable
in experience, any kind of presence than that in space, or any kind
of duration than that in time. In one word, the conditions of possible
experience are for reason the only conditions of the possibility of
things; reason cannot venture to form, independently of these
conditions, any conceptions of things, because such conceptions,
although not self-contradictory, are without object and without

The conceptions of reason are, as we have already shown, mere ideas,
and do not relate to any object in any kind of experience. At the same
time, they do not indicate imaginary or possible objects. They are
purely problematical in their nature and, as aids to the heuristic
exercise of the faculties, form the basis of the regulative principles
for the systematic employment of the understanding in the field of
experience. If we leave this ground of experience, they become mere
fictions of thought, the possibility of which is quite indemonstrable;
and they cannot, consequently, be employed as hypotheses in the
explanation of real phenomena. It is quite admissible to cogitate
the soul as simple, for the purpose of enabling ourselves to employ
the idea of a perfect and necessary unity of all the faculties of
the mind as the principle of all our inquiries into its internal
phenomena, although we cannot cognize this unity in concreto. But to
assume that the soul is a simple substance (a transcendental
conception) would be enouncing a proposition which is not only
indemonstrable--as many physical hypotheses are--but a proposition
which is purely arbitrary, and in the highest degree rash. The
simple is never presented in experience; and, if by substance is
here meant the permanent object of sensuous intuition, the possibility
of a simple phenomenon is perfectly inconceivable. Reason affords no
good grounds for admitting the existence of intelligible beings, or
of intelligible properties of sensuous things, although--as we have
no conception either of their possibility or of their impossibility--it
will always be out of our power to affirm dogmatically that they do
not exist. In the explanation of given phenomena, no other things
and no other grounds of explanation can be employed than those which
stand in connection with the given phenomena according to the known
laws of experience. A transcendental hypothesis, in which a mere
idea of reason is employed to explain the phenomena of nature, would
not give us any better insight into a phenomenon, as we should be
trying to explain what we do not sufficiently understand from known
empirical principles, by what we do not understand at all. The
principles of such a hypothesis might conduce to the satisfaction of
reason, but it would not assist the understanding in its application
to objects. Order and conformity to aims in the sphere of nature
must be themselves explained upon natural grounds and according to
natural laws; and the wildest hypotheses, if they are only physical,
are here more admissible than a hyperphysical hypothesis, such as that
of a divine author. For such a hypothesis would introduce the
principle of ignava ratio, which requires us to give up the search
for causes that might be discovered in the course of experience and
to rest satisfied with a mere idea. As regards the absolute totality
of the grounds of explanation in the series of these causes, this can
be no hindrance to the understanding in the case of phenomena;
because, as they are to us nothing more than phenomena, we have no
right to look for anything like completeness in the synthesis of the
series of their conditions.

Transcendental hypotheses are therefore inadmissible; and we
cannot use the liberty of employing, in the absence of physical,
hyperphysical grounds of explanation. And this for two reasons; first,
because such hypothesis do not advance reason, but rather stop it in
its progress; secondly, because this licence would render fruitless
all its exertions in its own proper sphere, which is that of
experience. For, when the explanation of natural phenomena happens
to be difficult, we have constantly at hand a transcendental ground
of explanation, which lifts us above the necessity of investigating
nature; and our inquiries are brought to a close, not because we
have obtained all the requisite knowledge, but because we abut upon
a principle which is incomprehensible and which, indeed, is so far
back in the track of thought as to contain the conception of the
absolutely primal being.

The next requisite for the admissibility of a hypothesis is its
sufficiency. That is, it must determine a priori the consequences
which are given in experience and which are supposed to follow from
the hypothesis itself. If we require to employ auxiliary hypotheses,
the suspicion naturally arises that they are mere fictions; because
the necessity for each of them requires the same justification as in
the case of the original hypothesis, and thus their testimony is
invalid. If we suppose the existence of an infinitely perfect cause,
we possess sufficient grounds for the explanation of the conformity
to aims, the order and the greatness which we observe in the universe;
but we find ourselves obliged, when we observe the evil in the world
and the exceptions to these laws, to employ new hypothesis in
support of the original one. We employ the idea of the simple nature
of the human soul as the foundation of all the theories we may form
of its phenomena; but when we meet with difficulties in our way, when
we observe in the soul phenomena similar to the changes which take
place in matter, we require to call in new auxiliary hypotheses. These
may, indeed, not be false, but we do not know them to be true, because
the only witness to their certitude is the hypothesis which they
themselves have been called in to explain.

We are not discussing the above-mentioned assertions regarding the
immaterial unity of the soul and the existence of a Supreme Being as
dogmata, which certain philosophers profess to demonstrate a priori,
but purely as hypotheses. In the former case, the dogmatist must
take care that his arguments possess the apodeictic certainty of a
demonstration. For the assertion that the reality of such ideas is
probable is as absurd as a proof of the probability of a proposition
in geometry. Pure abstract reason, apart from all experience, can
either cognize nothing at all; and hence the judgements it enounces
are never mere opinions, they are either apodeictic certainties, or
declarations that nothing can be known on the subject. Opinions and
probable judgements on the nature of things can only be employed to
explain given phenomena, or they may relate to the effect, in
accordance with empirical laws, of an actually existing cause. In
other words, we must restrict the sphere of opinion to the world of
experience and nature. Beyond this region opinion is mere invention;
unless we are groping about for the truth on a path not yet fully
known, and have some hopes of stumbling upon it by chance.

But, although hypotheses are inadmissible in answers to the
questions of pure speculative reason, they may be employed in the
defence of these answers. That is to say, hypotheses are admissible
in polemic, but not in the sphere of dogmatism. By the defence of
statements of this character, I do not mean an attempt at
discovering new grounds for their support, but merely the refutation
of the arguments of opponents. All a priori synthetical propositions
possess the peculiarity that, although the philosopher who maintains
the reality of the ideas contained in the proposition is not in
possession of sufficient knowledge to establish the certainty of his
statements, his opponent is as little able to prove the truth of the
opposite. This equality of fortune does not allow the one party to
be superior to the other in the sphere of speculative cognition; and
it is this sphere, accordingly, that is the proper arena of these
endless speculative conflicts. But we shall afterwards show that, in
relation to its practical exercise, Reason has the right of
admitting what, in the field of pure speculation, she would not be
justified in supposing, except upon perfectly sufficient grounds;
because all such suppositions destroy the necessary completeness of
speculation--a condition which the practical reason, however, does
not consider to be requisite. In this sphere, therefore, Reason is
mistress of a possession, her title to which she does not require to
prove--which, in fact, she could not do. The burden of proof
accordingly rests upon the opponent. But as he has just as little
knowledge regarding the subject discussed, and is as little able to
prove the non-existence of the object of an idea, as the philosopher
on the other side is to demonstrate its reality, it is evident that
there is an advantage on the side of the philosopher who maintains
his proposition as a practically necessary supposition (melior est
conditio possidentis). For he is at liberty to employ, in
self-defence, the same weapons as his opponent makes use of in
attacking him; that is, he has a right to use hypotheses not for the
purpose of supporting the arguments in favour of his own propositions,
but to show that his opponent knows no more than himself regarding
the subject under 'discussion and cannot boast of any speculative

Hypotheses are, therefore, admissible in the sphere of pure reason
only as weapons for self-defence, and not as supports to dogmatical
assertions. But the opposing party we must always seek for in
ourselves. For speculative reason is, in the sphere of
transcendentalism, dialectical in its own nature. The difficulties
and objections we have to fear lie in ourselves. They are like old
but never superannuated claims; and we must seek them out, and settle
them once and for ever, if we are to expect a permanent peace. External
tranquility is hollow and unreal. The root of these contradictions,
which lies in the nature of human reason, must be destroyed; and
this can only be done by giving it, in the first instance, freedom
to grow, nay, by nourishing it, that it may send out shoots, and
thus betray its own existence. It is our duty, therefore, to try to
discover new objections, to put weapons in the bands of our
opponent, and to grant him the most favourable position in the arena
that he can wish. We have nothing to fear from these concessions; on
the contrary, we may rather hope that we shall thus make ourselves
master of a possession which no one will ever venture to dispute.

The thinker requires, to be fully equipped, the hypotheses of pure
reason, which, although but leaden weapons (for they have not been
steeled in the armoury of experience), are as useful as any that can
be employed by his opponents. If, accordingly, we have assumed, from
a non-speculative point of view, the immaterial nature of the soul,
and are met by the objection that experience seems to prove that the
growth and decay of our mental faculties are mere modifications of
the sensuous organism--we can weaken the force of this objection by
the assumption that the body is nothing but the fundamental phenomenon,
to which, as a necessary condition, all sensibility, and consequently
all thought, relates in the present state of our existence; and that
the separation of soul and body forms the conclusion of the sensuous
exercise of our power of cognition and the beginning of the
intellectual. The body would, in this view of the question, be
regarded, not as the cause of thought, but merely as its restrictive
condition, as promotive of the sensuous and animal, but as a hindrance
to the pure and spiritual life; and the dependence of the animal
life on the constitution of the body, would not prove that the whole
life of man was also dependent on the state of the organism. We
might go still farther, and discover new objections, or carry out to
their extreme consequences those which have already been adduced.

Generation, in the human race as well as among the irrational
animals, depends on so many accidents--of occasion, of proper
sustenance, of the laws enacted by the government of a country of vice
even, that it is difficult to believe in the eternal existence of a
being whose life has begun under circumstances so mean and trivial,
and so entirely dependent upon our own control. As regards the
continuance of the existence of the whole race, we need have no
difficulties, for accident in single cases is subject to general laws;
but, in the case of each individual, it would seem as if we could
hardly expect so wonderful an effect from causes so insignificant.
But, in answer to these objections, we may adduce the transcendental
hypothesis that all life is properly intelligible, and not subject
to changes of time, and that it neither began in birth, nor will end
in death. We may assume that this life is nothing more than a sensuous
representation of pure spiritual life; that the whole world of sense
is but an image, hovering before the faculty of cognition which we
exercise in this sphere, and with no more objective reality than a
dream; and that if we could intuite ourselves and other things as they
really are, we should see ourselves in a world of spiritual natures,
our connection with which did not begin at our birth and will not
cease with the destruction of the body. And so on.

We cannot be said to know what has been above asserted, nor do we
seriously maintain the truth of these assertions; and the notions
therein indicated are not even ideas of reason, they are purely
fictitious conceptions. But this hypothetical procedure is in
perfect conformity with the laws of reason. Our opponent mistakes
the absence of empirical conditions for a proof of the complete
impossibility of all that we have asserted; and we have to show him
that he has not exhausted the whole sphere of possibility and that
he can as little compass that sphere by the laws of experience and
nature, as we can lay a secure foundation for the operations of reason
beyond the region of experience. Such hypothetical defences against
the pretensions of an opponent must not be regarded as declarations
of opinion. The philosopher abandons them, so soon as the opposite
party renounces its dogmatical conceit. To maintain a simply
negative position in relation to propositions which rest on an
insecure foundation, well befits the moderation of a true philosopher;
but to uphold the objections urged against an opponent as proofs of
the opposite statement is a proceeding just as unwarrantable and
arrogant as it is to attack the position of a philosopher who advances
affirmative propositions regarding such a subject.

It is evident, therefore, that hypotheses, in the speculative
sphere, are valid, not as independent propositions, but only
relatively to opposite transcendent assumptions. For, to make the
principles of possible experience conditions of the possibility of
things in general is just as transcendent a procedure as to maintain
the objective reality of ideas which can be applied to no objects
except such as lie without the limits of possible experience. The
judgements enounced by pure reason must be necessary, or they must
not be enounced at all. Reason cannot trouble herself with opinions.
But the hypotheses we have been discussing are merely problematical
judgements, which can neither be confuted nor proved; while,
therefore, they are not personal opinions, they are indispensable as
answers to objections which are liable to be raised. But we must
take care to confine them to this function, and guard against any
assumption on their part of absolute validity, a proceeding which
would involve reason in inextricable difficulties and contradictions.

SECTION IV. The Discipline of Pure Reason in Relation to Proofs.

It is a peculiarity, which distinguishes the proofs of transcendental
synthetical propositions from those of all other a priori synthetical
cognitions, that reason, in the case of the former, does not apply its
conceptions directly to an object, but is first obliged to prove, a
priori, the objective validity of these conceptions and the possibility
of their syntheses. This is not merely a prudential rule, it is
essential to the very possibility of the proof of a transcendental
proposition. If I am required to pass, a priori, beyond the conception
of an object, I find that it is utterly impossible without the guidance
of something which is not contained in the conception. In mathematics,
it is a priori intuition that guides my synthesis; and, in this case,
all our conclusions may be drawn immediately from pure intuition. In
transcendental cognition, so long as we are dealing only with
conceptions of the understanding, we are guided by possible experience.
That is to say, a proof in the sphere of transcendental cognition does
not show that the given conception (that of an event, for example)
leads directly to another conception (that of a cause)--for this would
be a saltus which nothing can justify; but it shows that experience
itself, and consequently the object of experience, is impossible
without the connection indicated by these conceptions. It follows that
such a proof must demonstrate the possibility of arriving,
synthetically and a priori, at a certain knowledge of things, which was
not contained in our conceptions of these things. Unless we pay
particular attention to this requirement, our proofs, instead of
pursuing the straight path indicated by reason, follow the tortuous
road of mere subjective association. The illusory conviction, which
rests upon subjective causes of association, and which is considered as
resulting from the perception of a real and objective natural affinity,
is always open to doubt and suspicion. For this reason, all the
attempts which have been made to prove the principle of sufficient
reason, have, according to the universal admission of philosophers,
been quite unsuccessful; and, before the appearance of transcendental
criticism, it was considered better, as this principle could not be
abandoned, to appeal boldly to the common sense of mankind (a
proceeding which always proves that the problem, which reason ought to
solve, is one in which philosophers find great difficulties), rather
than attempt to discover new dogmatical proofs.

But, if the proposition to be proved is a proposition of pure
reason, and if I aim at passing beyond my empirical conceptions by
the aid of mere ideas, it is necessary that the proof should first
show that such a step in synthesis is possible (which it is not), before
it proceeds to prove the truth of the proposition itself. The so-called
proof of the simple nature of the soul from the unity of apperception,
is a very plausible one. But it contains no answer to the objection,
that, as the notion of absolute simplicity is not a conception which
is directly applicable to a perception, but is an idea which must be
inferred--if at all--from observation, it is by no means evident how
the mere fact of consciousness, which is contained in all thought,
although in so far a simple representation, can conduct me to the
consciousness and cognition of a thing which is purely a thinking
substance. When I represent to my mind the power of my body as in
motion, my body in this thought is so far absolute unity, and my
representation of it is a simple one; and hence I can indicate this
representation by the motion of a point, because I have made
abstraction of the size or volume of the body. But I cannot hence
infer that, given merely the moving power of a body, the body may be
cogitated as simple substance, merely because the representation in
my mind takes no account of its content in space, and is consequently
simple. The simple, in abstraction, is very different from the
objectively simple; and hence the Ego, which is simple in the first
sense, may, in the second sense, as indicating the soul itself, be
a very complex conception, with a very various content. Thus it is
evident that in all such arguments there lurks a paralogism. We
guess (for without some such surmise our suspicion would not be
excited in reference to a proof of this character) at the presence
of the paralogism, by keeping ever before us a criterion of the
possibility of those synthetical propositions which aim at proving
more than experience can teach us. This criterion is obtained from
the observation that such proofs do not lead us directly from the
subject of the proposition to be proved to the required predicate,
but find it necessary to presuppose the possibility of extending our
cognition a priori by means of ideas. We must, accordingly, always
use the greatest caution; we require, before attempting any proof,
to consider how it is possible to extend the sphere of cognition by
the operations of pure reason, and from what source we are to derive
knowledge, which is not obtained from the analysis of conceptions,
nor relates, by anticipation, to possible experience. We shall thus
spare ourselves much severe and fruitless labour, by not expecting
from reason what is beyond its power, or rather by subjecting it to
discipline, and teaching it to moderate its vehement desires for the
extension of the sphere of cognition.

The first rule for our guidance is, therefore, not to attempt a
transcendental proof, before we have considered from what source we
are to derive the principles upon which the proof is to be based,
and what right we have to expect that our conclusions from these
principles will be veracious. If they are principles of the
understanding, it is vain to expect that we should attain by their
means to ideas of pure reason; for these principles are valid only
in regard to objects of possible experience. If they are principles
of pure reason, our labour is alike in vain. For the principles of
reason, if employed as objective, are without exception dialectical
and possess no validity or truth, except as regulative principles of
the systematic employment of reason in experience. But when such
delusive proof are presented to us, it is our duty to meet them with
the non liquet of a matured judgement; and, although we are unable
to expose the particular sophism upon which the proof is based, we
have a right to demand a deduction of the principles employed in it;
and, if these principles have their origin in pure reason alone,
such a deduction is absolutely impossible. And thus it is
unnecessary that we should trouble ourselves with the exposure and
confutation of every sophistical illusion; we may, at once, bring
all dialectic, which is inexhaustible in the production of
fallacies, before the bar of critical reason, which tests the
principles upon which all dialectical procedure is based. The second
peculiarity of transcendental proof is that a transcendental
proposition cannot rest upon more than a single proof. If I am drawing
conclusions, not from conceptions, but from intuition corresponding
to a conception, be it pure intuition, as in mathematics, or empirical,
as in natural science, the intuition which forms the basis of my
inferences presents me with materials for many synthetical
propositions, which I can connect in various modes, while, as it is
allowable to proceed from different points in the intention, I can
arrive by different paths at the same proposition.

But every transcendental proposition sets out from a conception, and
posits the synthetical condition of the possibility of an object
according to this conception. There must, therefore, be but one ground
of proof, because it is the conception alone which determines the
object; and thus the proof cannot contain anything more than the
determination of the object according to the conception. In our
Transcendental Analytic, for example, we inferred the principle: Every
event has a cause, from the only condition of the objective
possibility of our conception of an event. This is that an event
cannot be determined in time, and consequently cannot form a part of
experience, unless it stands under this dynamical law. This is the
only possible ground of proof; for our conception of an event
possesses objective validity, that is, is a true conception, only
because the law of causality determines an object to which it can
refer. Other arguments in support of this principle have been
attempted--such as that from the contingent nature of a phenomenon;
but when this argument is considered, we can discover no criterion
of contingency, except the fact of an event--of something happening,
that is to say, the existence which is preceded by the non-existence
of an object, and thus we fall back on the very thing to be proved.
If the proposition: "Every thinking being is simple," is to be proved,
we keep to the conception of the ego, which is simple, and to which
all thought has a relation. The same is the case with the transcendental
proof of the existence of a Deity, which is based solely upon the
harmony and reciprocal fitness of the conceptions of an ens
realissimum and a necessary being, and cannot be attempted in any
other manner.

This caution serves to simplify very much the criticism of all
propositions of reason. When reason employs conceptions alone, only
one proof of its thesis is possible, if any. When, therefore, the
dogmatist advances with ten arguments in favour of a proposition, we
may be sure that not one of them is conclusive. For if he possessed
one which proved the proposition he brings forward to demonstration-
as must always be the case with the propositions of pure reason-
what need is there for any more? His intention can only be similar
to that of the advocate who had different arguments for different
judges; this availing himself of the weakness of those who examine
his arguments, who, without going into any profound investigation,
adopt the view of the case which seems most probable at first sight
and decide according to it.

The third rule for the guidance of pure reason in the conduct of a
proof is that all transcendental proofs must never be apagogic or
indirect, but always ostensive or direct. The direct or ostensive
proof not only establishes the truth of the proposition to be
proved, but exposes the grounds of its truth; the apagogic, on the
other hand, may assure us of the truth of the proposition, but it
cannot enable us to comprehend the grounds of its possibility. The
latter is, accordingly, rather an auxiliary to an argument, than a
strictly philosophical and rational mode of procedure. In one respect,
however, they have an advantage over direct proofs, from the fact that
the mode of arguing by contradiction, which they employ, renders our
understanding of the question more clear, and approximates the proof
to the certainty of an intuitional demonstration.

The true reason why indirect proofs are employed in different
sciences is this. When the grounds upon which we seek to base a
cognition are too various or too profound, we try whether or not we
may not discover the truth of our cognition from its consequences.
The modus ponens of reasoning from the truth of its inferences to the
truth of a proposition would be admissible if all the inferences
that can be drawn from it are known to be true; for in this case there
can be only one possible ground for these inferences, and that is
the true one. But this is a quite impracticable procedure, as it
surpasses all our powers to discover all the possible inferences
that can be drawn from a proposition. But this mode of reasoning is
employed, under favour, when we wish to prove the truth of an
hypothesis; in which case we admit the truth of the conclusion-
which is supported by analogy--that, if all the inferences we have
drawn and examined agree with the proposition assumed, all other
possible inferences will also agree with it. But, in this way, an
hypothesis can never be established as a demonstrated truth. The modus
tollens of reasoning from known inferences to the unknown proposition,
is not only a rigorous, but a very easy mode of proof. For, if it
can be shown that but one inference from a proposition is false,
then the proposition must itself be false. Instead, then, of
examining, in an ostensive argument, the whole series of the grounds
on which the truth of a proposition rests, we need only take the
opposite of this proposition, and if one inference from it be false,
then must the opposite be itself false; and, consequently, the
proposition which we wished to prove must be true.

The apagogic method of proof is admissible only in those sciences
where it is impossible to mistake a subjective representation for an
objective cognition. Where this is possible, it is plain that the
opposite of a given proposition may contradict merely the subjective
conditions of thought, and not the objective cognition; or it may
happen that both propositions contradict each other only under a
subjective condition, which is incorrectly considered to be objective,
and, as the condition is itself false, both propositions may be false,
and it will, consequently, be impossible to conclude the truth of
the one from the falseness of the other.

In mathematics such subreptions are impossible; and it is in this
science, accordingly, that the indirect mode of proof has its true
place. In the science of nature, where all assertion is based upon
empirical intuition, such subreptions may be guarded against by the
repeated comparison of observations; but this mode of proof is of
little value in this sphere of knowledge. But the transcendental
efforts of pure reason are all made in the sphere of the subjective,
which is the real medium of all dialectical illusion; and thus
reason endeavours, in its premisses, to impose upon us subjective
representations for objective cognitions. In the transcendental sphere
of pure reason, then, and in the case of synthetical propositions,
it is inadmissible to support a statement by disproving the
counter-statement. For only two cases are possible; either, the
counter-statement is nothing but the enouncement of the
inconsistency of the opposite opinion with the subjective conditions
of reason, which does not affect the real case (for example, we cannot
comprehend the unconditioned necessity of the existence of a being,
and hence every speculative proof of the existence of such a being
must be opposed on subjective grounds, while the possibility of this
being in itself cannot with justice be denied); or, both propositions,
being dialectical in their nature, are based upon an impossible
conception. In this latter case the rule applies: non entis nulla sunt
predicata; that is to say, what we affirm and what we deny, respecting
such an object, are equally untrue, and the apagogic mode of
arriving at the truth is in this case impossible. If, for example,
we presuppose that the world of sense is given in itself in its
totality, it is false, either that it is infinite, or that it is
finite and limited in space. Both are false, because the hypothesis
is false. For the notion of phenomena (as mere representations) which
are given in themselves (as objects) is self-contradictory; and the
infinitude of this imaginary whole would, indeed, be unconditioned,
but would be inconsistent (as everything in the phenomenal world is
conditioned) with the unconditioned determination and finitude of
quantities which is presupposed in our conception.

The apagogic mode of proof is the true source of those illusions
which have always had so strong an attraction for the admirers of
dogmatical philosophy. It may be compared to a champion who
maintains the honour and claims of the party he has adopted by
offering battle to all who doubt the validity of these claims and
the purity of that honour; while nothing can be proved in this way,
except the respective strength of the combatants, and the advantage,
in this respect, is always on the side of the attacking party.
Spectators, observing that each party is alternately conqueror and
conquered, are led to regard the subject of dispute as beyond the
power of man to decide upon. But such an opinion cannot be
justified; and it is sufficient to apply to these reasoners the

Non defensoribus istis
Tempus eget.

Each must try to establish his assertions by a transcendental
deduction of the grounds of proof employed in his argument, and thus
enable us to see in what way the claims of reason may be supported.
If an opponent bases his assertions upon subjective grounds, he may
be refuted with ease; not, however to the advantage of the dogmatist,
who likewise depends upon subjective sources of cognition and is in
like manner driven into a corner by his opponent. But, if parties employ
the direct method of procedure, they will soon discover the
difficulty, nay, the impossibility of proving their assertions, and
will be forced to appeal to prescription and precedence; or they will,
by the help of criticism, discover with ease the dogmatical
illusions by which they had been mocked, and compel reason to renounce
its exaggerated pretensions to speculative insight and to confine
itself within the limits of its proper sphere--that of practical

CHAPTER II. The Canon of Pure Reason.

It is a humiliating consideration for human reason that it is
incompetent to discover truth by means of pure speculation, but, on
the contrary, stands in need of discipline to check its deviations
from the straight path and to expose the illusions which it
originates. But, on the other hand, this consideration ought to
elevate and to give it confidence, for this discipline is exercised
by itself alone, and it is subject to the censure of no other power.
The bounds, moreover, which it is forced to set to its speculative
exercise, form likewise a check upon the fallacious pretensions of
opponents; and thus what remains of its possessions, after these
exaggerated claims have been disallowed, is secure from attack or
usurpation. The greatest, and perhaps the only, use of all
philosophy of pure reason is, accordingly, of a purely negative
character. It is not an organon for the extension, but a discipline
for the determination, of the limits of its exercise; and without
laying claim to the discovery of new truth, it has the modest merit
of guarding against error.

At the same time, there must be some source of positive cognitions
which belong to the domain of pure reason and which become the
causes of error only from our mistaking their true character, while
they form the goal towards which reason continually strives. How
else can we account for the inextinguishable desire in the human
mind to find a firm footing in some region beyond the limits of the
world of experience? It hopes to attain to the possession of a
knowledge in which it has the deepest interest. It enters upon the
path of pure speculation; but in vain. We have some reason, however,
to expect that, in the only other way that lies open to it--the path
of practical reason--it may meet with better success.

I understand by a canon a list of the a priori principles of the
proper employment of certain faculties of cognition. Thus general
logic, in its analytical department, is a formal canon for the
faculties of understanding and reason. In the same way, Transcendental
Analytic was seen to be a canon of the pure understanding; for it
alone is competent to enounce true a priori synthetical cognitions.
But, when no proper employment of a faculty of cognition is
possible, no canon can exist. But the synthetical cognition of pure
speculative reason is, as has been shown, completely impossible. There
cannot, therefore, exist any canon for the speculative exercise of
this faculty--for its speculative exercise is entirely dialectical;
and, consequently, transcendental logic, in this respect, is merely
a discipline, and not a canon. If, then, there is any proper mode of
employing the faculty of pure reason--in which case there must be a
canon for this faculty--this canon will relate, not to the
speculative, but to the practical use of reason. This canon we now
proceed to investigate.

SECTION I. Of the Ultimate End of the Pure Use of Reason.

There exists in the faculty of reason a natural desire to venture
beyond the field of experience, to attempt to reach the utmost
bounds of all cognition by the help of ideas alone, and not to rest
satisfied until it has fulfilled its course and raised the sum of
its cognitions into a self-subsistent systematic whole. Is the
motive for this endeavour to be found in its speculative, or in its
practical interests alone?

Setting aside, at present, the results of the labours of pure reason
in its speculative exercise, I shall merely inquire regarding the
problems the solution of which forms its ultimate aim, whether reached
or not, and in relation to which all other aims are but partial and
intermediate. These highest aims must, from the nature of reason,
possess complete unity; otherwise the highest interest of humanity
could not be successfully promoted.

The transcendental speculation of reason relates to three things:
the freedom of the will, the immortality of the soul, and the
existence of God. The speculative interest which reason has in those
questions is very small; and, for its sake alone, we should not
undertake the labour of transcendental investigation--a labour full
of toil and ceaseless struggle. We should be loth to undertake this
labour, because the discoveries we might make would not be of the
smallest use in the sphere of concrete or physical investigation. We
may find out that the will is free, but this knowledge only relates
to the intelligible cause of our volition. As regards the phenomena
or expressions of this will, that is, our actions, we are bound, in
obedience to an inviolable maxim, without which reason cannot be
employed in the sphere of experience, to explain these in the same
way as we explain all the other phenomena of nature, that is to say,
according to its unchangeable laws. We may have discovered the
spirituality and immortality of the soul, but we cannot employ this
knowledge to explain the phenomena of this life, nor the peculiar
nature of the future, because our conception of an incorporeal
nature is purely negative and does not add anything to our
knowledge, and the only inferences to be drawn from it are purely
fictitious. If, again, we prove the existence of a supreme
intelligence, we should be able from it to make the conformity to aims
existing in the arrangement of the world comprehensible; but we should
not be justified in deducing from it any particular arrangement or
disposition, or inferring any where it is not perceived. For it is
a necessary rule of the speculative use of reason that we must not
overlook natural causes, or refuse to listen to the teaching of
experience, for the sake of deducing what we know and perceive from
something that transcends all our knowledge. In one word, these
three propositions are, for the speculative reason, always
transcendent, and cannot be employed as immanent principles in
relation to the objects of experience; they are, consequently, of no
use to us in this sphere, being but the valueless results of the
severe but unprofitable efforts of reason.

If, then, the actual cognition of these three cardinal propositions is
perfectly useless, while Reason uses her utmost endeavours to induce us
to admit them, it is plain that their real value and importance relate
to our practical, and not to our speculative interest.

I term all that is possible through free will, practical. But if the
conditions of the exercise of free volition are empirical, reason
can have only a regulative, and not a constitutive, influence upon
it, and is serviceable merely for the introduction of unity into its
empirical laws. In the moral philosophy of prudence, for example,
the sole business of reason is to bring about a union of all the ends,
which are aimed at by our inclinations, into one ultimate end--that
of happiness--and to show the agreement which should exist among the
means of attaining that end. In this sphere, accordingly, reason
cannot present to us any other than pragmatical laws of free action,
for our guidance towards the aims set up by the senses, and is
incompetent to give us laws which are pure and determined completely
a priori. On the other hand, pure practical laws, the ends of which
have been given by reason entirely a priori, and which are not
empirically conditioned, but are, on the contrary, absolutely
imperative in their nature, would be products of pure reason. Such
are the moral laws; and these alone belong to the sphere of the
practical exercise of reason, and admit of a canon.

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