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The Critique of Pure Reason 

 Introduction: B



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Immanuel Kant (1724-1804)



Editor’s prefatory comment:

The following constitutes the entire text -- color highlighted (the Paul Guyer translation) -- of the Introduction to The Critique of Pure Reason, Second Edition (B), plus commentary; alternate translations in plain text.

Note: in the Kant literature, the first edition is known as the "A" version, with the second edition as the "B".



auxiliary sources for 'The Critique'

VG: Prof. Victor Gijsbers, Netherlands, youtube lectures

DR: Prof. Daniel Robinson, Oxford, youtube lectures

RPW: Prof. Robert Paul Wolff, youtube lectures

MJT: translation, Mieklejohn

PGT: translation, Paul Guyer

MMT: translation, Max Muller: "[His] main merit, as he has very justly claimed, is his greater accuracy in rendering passages in which a specially exact appreciation of the niceties of German idiom happens to be important for the sense." NST

NST: translation, N.K. Smith

PRTC: translation-commentary, P.M. Rudisill

NSC: commentary, N.K. Smith

SGC: commentary, Sebastian Gardner

SP: glossary, Stephen Palmquist

LT: glossary, Lucas Thorpe




Introduction <B>

I. On the difference between pure and empirical cognition.

There is no doubt whatever that all our cognition begins with experi
ence; for how else should the cognitive faculty be awakened into exer
cise if not through objects that stimulate our senses and in part
themselves produce representations, in part bring the activity of our un
derstanding into motion to compare these, to connect or separate them,
and thus to work up the raw material of sensible impressions into a
cognition of objects that is called experience? As far as time is con
cerned, then, no cognition in us precedes experience, and with experi
ence every cognition begins.

MJT: "That all our knowledge begins with experience there can be no doubt.
For how is it possible that the faculty of cognition should be awakened
into exercise otherwise than by means of objects which affect our senses,
and partly of themselves produce representations, partly rouse our powers
of understanding into activity, to compare to connect, or to separate these,
and so to convert the raw material of our sensuous impressions into a
knowledge of objects, which is called experience? In respect of time,
therefore, no knowledge of ours is antecedent to experience, but begins with it."

VG: The empiricists had said that all our knowledge comes from experience, but Kant is going to say that this is not true, however there is a sense in which all our knowledge begins with experience. Because without experience our minds would never get started doing anything.

But, even more importantly than correcting the empiricists is Kant’s description of how human cognition actually works, what experience actually is. It consists of two things: (1) in part, there are these objects which stimulate our senses, producing representations, and, (2) in part, the activity of our understanding which works on the raw objects producing what we call experience.

What we see here is that experience is not just a sense impression which comes from the object, but then we’re going to do something with that impression. Our mind, the cognitive power, is going to work on it, to compare, separate, connect, and this is going to generate a cognition of objects which is worthy of being termed experience.

In contrast, Kant would say that the following is not experience: under the influence of psychedelic drugs we might see colors and visions, but unless these are linked to objects, and become objective, Kant would say this is not experience, as he defines it.

Experience requires (1) the spontaneity of the understanding and (2) the receptivity of what Kant calls the intuition which is our direct connection to the objects.

But although all our cognition commences with experience, yet it
does not on that account all arise from experience.

VG: Kant begins to explain how not all our cognitions arise from experience, and he makes the first of two important distinctions here, the distinction between cognitions a priori and cognitions a posteriori, or as he likes to say “empirical,” which means the same thing as a posteriori.

An a priori cognition is one that can be justified without any appeal to experience. An a posterior or empirical judgment can be justified only by an appeal to experience. For example, if I say there are 17 cars on my street, this can be affirmed only by a posterior or empirical method, I can’t get it from pure reason alone.

The terms a priori and a posteriori were not invented by Kant but part of the philosophy of his time.

For it could well be that even our experiential cognition is a composite of that which we receive through impressions and that which our own cognitive faculty (merely prompted by sensible impressions) provides out of itself, which addition we cannot distinguish from that fundamental material until long practice has made us attentive to it and skilled in separating it out.

MJT: "For, on the contrary, it is quite possible that our empirical knowledge is a compound of that which we receive through impressions, and that which the faculty of cognition supplies from itself (sensuous impressions giving merely the occasion), an addition which we cannot distinguish from the original element given by sense,

It is therefore at least a question requiring closer investigation, and
one not to be dismissed at first glance, whether there is any such cog
nition independent of all experience and even of all impressions of the
senses. One calls such cognitions a priori, and distinguishes them
from empirical ones, which have their sources a posteriori, namely in

The former expression is nevertheless not yet sufficiently determi
nate to designate the whole sense of the question before us. For it is customary to say of many a cognition derived from experiential sources that we are capable of it or partake in it a priori, because we do not derive it

immediately from experience, but rather from a general rule that we
have nevertheless itself borrowed from experience. So one says of someone who undermined the foundation of his house that he could have known a priori that it would collapse, i.e., he need not have waited for the experience of it actually collapsing. Yet he could not have known this entirely a priori.

For that bodies are heavy and hence fall if their support
is taken away must first have become known to him through experience. In the sequel therefore we will understand by a priori cognitions not those that occur independently of this or that experience, but rather those that occur absolutely independently of all experience.

VG: Kant distinguishes between pure and impure cognitions. Impure cognitions are those which we could not have without some reference to experience. The pure cognition involves concepts which come only from reason itself.

absolutely: see the glossary: Absolute is the past participle of absolvere, 'to absolve, to acquit, to free from debt'… it either qualifies something as free from any relation, condition or limitation, or designates that which is thus free.”

Opposed to them are empirical cognitions, or those that are possible only a posteriori, i.e., through experience. Among a priori cognitions, however, those are called pure with which nothing empirical is intermixed. Thus, e.g., the proposition "Every alteration has its cause" is an a priori proposition, only not pure, since alteration is a concept that can be drawn only from experience.

II. We are in possession of certain a priori cognitions, and
even the common understanding is never without them.

At issue here is a mark by means of which we can securely distinguish a pure cognition from an empirical one. Experience teaches us, to be
sure, that something is constituted thus and so, but not that it could not
be otherwise.

Editor’s note: How can we know, asks Kant, whether a cognition is pure or empirical? Necessity means “must” not “may” be such and such. The necessary couldn’t be any other way. We don’t get this sense of “must” from experience. There, we see contingency, “It could have been this way or that way.” And so, says Kant, when we find the necessary, “it is absolutely a priori.”

VG: Experience can tell us what is but not what must be. Experience can tell me there are 17 cars on my street but not that there must be 17 cars.

First, then, if a proposition is thought along with its necessity, it is an a priori judgment; if it is, moreover, also not derived from any proposition except one that in turn is valid as a necessary proposition, then it is absolutely a priori.

Second: Experience never
gives its judgments true or strict but only assumed and comparative
universality (through induction), so properly it must be said: as far as
we have yet perceived, there is no exception to this or that rule. Thus if a judgment is thought in strict universality, i.e., in such a way that no
exception at all is allowed to be possible, then it is not derived from ex
perience, but is rather valid absolutely a priori.

Empirical universality is
therefore only an arbitrary increase in validity from that which holds in
most cases to that which holds in all, as in, e.g., the proposition "All
bodies are heavy," whereas strict universality belongs to a judgment es
sentially; this points to a special source of cognition for it, namely a fac-
ulty of a priori cognition. Necessity and strict universality are therefore
secure indications of an a priori cognition, and also belong together in-

Editor’s note: When something enjoys “strict universality,” then, says Kant, “no exception at all is allowed to be possible.” This makes both of them, strict universality and necessity, “secure indications of an a priori cognition.” Strict universality impinges extremely closely upon necessity, entering close kinship, and “belong together inseparably.”

But since, in their use, it is sometimes easier to show the em-
pirical limitation in judgments than the contingency in them, or is often
more plausible to show the unrestricted universality that we ascribe to
a judgment than its necessity, it is advisable to employ separately these
two criteria, each of which is in itself infallible.

Editor’s note: The root of “universality” is “uni”, that is, one, or unity. A universal statement concerns “all” as opposed to the “particular” which focuses on “part” or some. Closely aligned with strict universality and necessity is “absolute” which speaks to no contingency or limitation.

Now it is easy to show that in human cognition there actually are
such necessary and, in the strictest sense, universal, thus pure a priori
judgments. If one wants an example from the sciences, one need only
look at all the propositions of mathematics; if one would have one
from the commonest use of the understanding, the proposition that
every alteration must have a cause will do; indeed in the latter the very
concept of a cause so obviously contains the concept of a necessity of
connection with an effect and a strict universality of rule that it would
be entirely lost if one sought, as Hume did, to derive it from a frequent
association of that which happens with that which precedes and a habit
(thus a merely subjective necessity) of connecting representations aris-
ing from that association.

Even without requiring such examples for
the proof of the reality of pure a priori principles in our cognition, one
could establish their indispensability for the possibility of experience
itself, thus establish it a priori.

For where would experience itself get
its certainty if all rules in accordance with which it proceeds were
themselves in turn always empirical, thus contingent?; hence one
could hardly allow these to count as first principles. Yet here we can
content ourselves with having displayed the pure use of our cognitive
faculty as a fact together with its indication.

VG: Here Kant is suggesting that the very activity of cognition that generates experience requires a priori rules, which tell us how to proceed, and these rules cannot come from experience because they are presupposed by all experience. He gives us two examples, space and substance (see below).

VG: We begin to understand what Kant is talking about here with “rules” relating to “experience” when we understand the debate about “what is objective knowledge?” A popular answer was, we have objective knowledge when, in a sense, we have a copy of that object in the mind; when the mind is the mirror of nature. But how can we know that the mind is actually a good mirror? Kant is going to say that to know is not to mirror. When the senses give us images, these do not become "knowledge" unless they are fitted into a larger whole; for example, we may think we see something, like a cow in the room, but we need to compare that perception with everything else we know about the world, and we'll likely find that we were mistaken. This is an easy example, but [allowing for and bearing in mind that, in the odd case, there could be a cow in the room, and sometimes we chance upon brand new but anomalous information] we engage in this process all the time with higher level purported aspects of knowledge.

Not merely in judgments,
however, but even in concepts is an origin of some of them revealed a
priori. Gradually remove from your experiential concept of a body
everything that is empirical in it - the color, the hardness or softness,
the weight, even the impenetrability - there still remains the space
that was occupied by the body (which has now entirely disappeared), and you cannot leave that out.

Likewise, if you remove from your empirical concept of every object, whether corporeal or incorporeal, all those properties of which experience teaches you, you could still not
take from it that by means of which you think of it as a substance or
as dependent on a substance (even though this concept contains more
determination than that of an object! in general). Thus, convinced by
the necessity with which this concept presses itself on you, you must
concede that it has its seat in your faculty of cognition a priori.

MJT: “Not only in judgements, however, but even in conceptions, is an a priori origin manifest. For example, if we take away by degrees from our conceptions of a body all that can be referred to mere sensuous experience —colour, hardness or softness, weight, even impenetrability—the body will then vanish; but the space which it occupied still remains, and this it is utterly impossible to annihilate in thought. Again, if we take away, in like manner, from our empirical conception of any object, corporeal or incorporeal, all properties which mere experience has taught us to connect with it, still we cannot think away those through which we cogitate it as substance, or adhering to substance, although our conception of substance is more determined than that of an object. Compelled, therefore, by that necessity with which the conception of substance forces itself upon us, we must confess that it has its seat in our faculty of cognition a priori.”

VG: If you try to think away everything in your experience for your judgments, space is still going to remain, and substance is going to remain.

III. Philosophy needs a science that determines the possibility,
the principles, and the domain of all cognitions a priori.

Editor’s note: Here in section III Kant asserts that what philosophy needs is to become a science, intimating his desire for rules and standards, as these could then pass judgment on cognitions in an a priori manner. We detect a wistful hope as he delineates current trends that do the opposite. See the further Editor’s note below.

But what says still more than all the foregoing is this, that certain cognitions even abandon the field of all possible experiences, and seem to expand the domain of our judgments beyond all bounds of experience through concepts to which no corresponding object at all can be given in experience.

And precisely in these latter cognitions, which go beyond the world
of the senses, where experience can give neither guidance nor correc-
tion, lie the investigations of our reason that we hold to be far more
preeminent in their importance and sublime in their final aim than everything that the understanding can learn in the field of appearances,
in which we would rather venture everything, even at the risk of erring,
than give up such important investigations because of any sort of reser
vation or from contempt and indifference. These unavoidable prob-
lems of pure reason itself are God, freedom and immortality. But the
science whose final aim in all its preparations is directed properly only
to the solution of these problems is called metaphysics, whose proce-
dure is in the beginning dogmatic, i.e., it confidently takes on the exe-
cution of this task without an antecedent examination of the capacity or
incapacity of reason for such a great undertaking.

Now it may seem natural that as soon as one has abandoned the ter-
rain of experience one would not immediately erect an edifice with cog
nitions that one possesses without knowing whence, and on the credit
of principles whose origin one does not know, without having first as
sured oneself of its foundation through careful investigations, thus that
one would all the more have long since raised the question how the un
derstanding could come to all these cognitions a priori and what do
main, validity, and value they might have. And in fact nothing is more
natural, if one understands by the word natural that which properly
and reasonably ought to happen; but if one understands by it that which usually happens, then conversely nothing is more natural and compre-
hensible than that this investigation should long have been neglected.


For one part of these cognitions, the mathematical, has long been reli-
able, and thereby gives rise to a favorable expectation about others as
well, although these may be of an entirely different nature. Further
more, if one is beyond the circle of experience, then one is sure of not
being refuted through experience. The charm in expanding one's cog-
nitions is so great that one can be stopped in one's progress only by
bumping into a clear contradiction. This, however, one can avoid if one
makes his inventions carefully, even though they are not thereby inven
tions any the less. Mathematics gives us a splendid example of how far
we can go with a priori cognition independently of experience. Now it
is occupied, to be sure, with objects and cognitions only so far as these
can be exhibited in intuitions. This circumstance, however, is easily
overlooked, since the intuition in question can itself be given a priori,
and thus can hardly be distinguished from a mere pure concept.


Captivated by such a proof of the power of reason, the drive for ex-
pansion sees no bounds. The light dove, in free flight cutting through
the air the resistance of which it feels, could get the idea that it could
do even better in airless space. Likewise, Plato abandoned the world of
the senses because it set such narrow limits for the understanding, and
dared to go beyond it on the wings of the ideas, in the empty space of
pure understanding. He did not notice that he made no headway by his
efforts, for he had no resistance, no support, as it were, by which he
could stiffen himself, and to which he could apply his powers in order
to put his understanding into motion. It is, however, a customary fate
of human reason in speculation to finish its edifice as early as possible
and only then to investigate whether the ground has been adequately
prepared for it.

But at that point all sorts of excuses will be sought to as
sure us of its sturdiness or also, even better! to refuse such a late and
dangerous examination. What keeps us free of all worry and suspicion
during the construction, however, and flatters us with apparent thor
oughness, is this. A great part, perhaps the greatest part, of the business
of our reason consists in analyses of the concepts that we already have of objects.

This affords us a multitude of cognitions that, although they
are nothing more than illuminations or clarifications of that which is al-
ready thought in our concepts (though still in a confused way), are, at
least as far as their form is concerned, treasured as if they were new in-

sights, though they do not extend the concepts that we have in either
matter or content, but only set them apart from each other. Now since this procedure does yield a real a priori cognition, which makes secure
and useful progress, reason, without itself noticing it, under these pre-
tenses, surreptitiously makes assertions of quite another sort, in which
reason adds something entirely alien to given concepts and indeed does so a priori, without one knowing how it was able to do this and without such a question even being allowed to come to mind.

I will therefore deal with the distinction between these two sorts of cognition right at the outset.

Editor’s note: The following comments include observations from VG’s lecture, other writers, plus a few items of my own.

Why is philosophy in such chaos? Why is there so much error, sloppy thinking, and mere opinion posing as knowledge? – worse, universal “laws”. (See Rupert Sheldrake's "The Science Delusion.")

People love to say “all” when, at best, they should be saying “some”. They make grand pronouncements on how things work in all of life, or the universe, or about God, and they make these sweeping statements without a foundation of fact, experience, or thorough investigation. They want to “expand the domain of our judgments beyond all bounds of experience through concepts to which no corresponding object at all can be given in experience.”

Kant wants us to know that some hidden things of the world can be known a priori, that is, without experience, but there’s a right and wrong way of going about this.

Think of the typical church, or political party, and even much of what is called science. The concepts promoted, very often, are nothing more than a cluster of unsubstantiated opinions, just private agenda. In the article on “metaparadigm,” we discussed how these unfounded propositions give direction, set the course, trim the sails, of one’s entire life.

These foundational assumptions “whose procedure is in the beginning dogmatic, i.e., it confidently takes on the execution of this task without an antecedent examination of the capacity or incapacity of reason for such a great undertaking.” Yes, they are very bold, take to themselves a degree of knowledge which, if verified, would require godlike perspicacities, but this lack of capacity to attain to such heights does not slow them down at all.

Now, a reasonable person, one would think, should be more cautious in rendering these universal judgments; for, if one has “abandoned the terrain of [confirming] experience [then] one would not immediately erect an edifice with cognitions that one possesses without knowing whence, and, on the credit of principles whose origin one does not know, without having first assured oneself of its foundation through careful investigations, thus that one would all the more have long since raised the question how the understanding could come to all these cognitions a priori and what domain, validity, and value they might have.”

But where is this cautious view? the sense that, “I might be wrong in this blanket statement”. We don’t see much of this sort of tempered assertion.

I think Kant is suggesting that, when properly crafted and executed, the a priori statement is meant to be a natural part of one’s life. We are hard-wired to use this as a tool when experience cannot answer our questions. But, instead, we are plagued by a distorted version of what should be an ordinary part of how we live.

Kant uses an analogy to draw attention to the farcical, mad-hatter way of thinking. He speaks of a dove in flight, enjoying itself with its soaring and gliding. And now we imagine it saying, “I'm really doing well with this flying thing, really good at it, but I notice there’s this air-resistance creating drag for me. I’m betting I could fly even better in a vacuum where there’s no air at all” – meaning, of course, the dove doesn’t realize that the air is necessary to the entire process. And the dogmatists who fancy themselves making such great progress in solving the big questions of life, but without recourse to facts and experience, are unaware that experience and knowledge are vital to the whole dynamic.

But, what is driving this seeming need and craving to make wild, unsupported, unverified pontifications? We were made to seek for the a priori way - because the really important questions can never be answered without it. Kant gives us clues concerning our nature: he says there is a “charm”, a good feeling, in doing this; that, these teachers are “captivated” by what they deem to be “a proof of the power of [their own] reason” - they really want to get into this; they see themselves as doing so very well with this “drive for expansion see[ing] no bounds”. But their success is “illusory” as they’ve set up a checkered system to “flatter” their dubious achievements; for, “if one is beyond the circle of experience, then one is sure of not being refuted through experience.” Well, that's very convenient to those who rig the election of their own judgments.

And if anyone should dare question their brilliance, then “all sorts of excuses will be sought to assure us of its sturdiness or also, even better, to refuse such a late and dangerous examination.”

Sounds like the cultish politicians today who censor and attack anyone who disagrees with their sainted precepts, which they call a “dangerous examination,” and misinformation.

This is the philosophical backdrop, Kant wants us to know, to what he will put forward as a better way of thinking.

IV. On the difference between analytic and synthetic judgments.

VG: This distinction is original to Kant.

Editor's note: See the writing which explains the difference.

In all judgments in which the relation of a subject to the predicate is
thought (if I consider only affirmative judgments, since the application
to negative ones is easy) this relation is possible in two different ways.
Either the predicate B belongs to the subject A as something that is
(covertly) contained in this concept A; or B lies entirely outside the con
cept A, though to be sure it stands in connection with it. In the first case
I call the judgment analytic, in the second synthetic. Analytic judgments (affirmative ones) are thus those in which the connection of the
predicate is thought through identity, but those in which this connec-
tion is thought without identity are to be called synthetic judgments.

Identity = the subject is also found in the predicate

One could also call the former judgments of clarification, and the latter judgments of amplification, since through the predicate the for-
mer do not add anything to the concept of the subject, but only break
it up by means of analysis into its component concepts, which were al-
ready thought in it (though confusedly); while the latter, on the con-
trary, add to the concept of the subject a predicate that was not thought
in it at all, and could not have been extracted from it through any analy-
sis; e.g., if I say: "All bodies are extended," then this is an analytic judg-
ment. For I do not need to go beyond the concept that I combine with
the body in order to find that extension is connected with it, but rather
I need only to analyze that concept, i.e., become conscious of the man-
ifold that I always think in it, in order to encounter this predicate
therein; it is therefore an analytic judgment.

On the contrary, if I say, "All bodies are heavy," then the predicate is something entirely different from that which I think in the mere concept of a body in general.

The addition of such a predicate thus yields a synthetic judgment.
Judgments of experience, as such, are all synthetic. For it would
be absurd to ground an analytic judgment on experience, since I do not
need to go beyond my concept at all in order to formulate the judg-
ment, and therefore need no testimony from experience for that. That
a body is extended is a proposition that is established a priori, and is not a judgment of experience.

For before I go to experience, I already have
all the conditions for my judgment in the concept, from which I merely
draw out the predicate in accordance with the principle of contradiction, and can thereby at the same time become conscious of the neces
sity of the judgment, which experience could never teach me. On the contrary, although I do not at all include the predicate of weight in the
concept of a body in general, the concept nevertheless designates an object of experience through a part of it, to which I can therefore add stilI other parts of the same experience as belonging with the former. I can first cognize the concept of body analytically through the marks of extension, of impenetrability, of shape, etc., which are all thought in this
concept. But now I amplify my cognition and, looking back to the ex-
perience from which I had extracted this concept of body, I find that
weight is also always connected with the previous marks, and I there-
fore add this synthetically as predicate to that concept.

It is thus experience on which the possibility of the synthesis of the predicate of weight with the concept of body is grounded, since both concepts, though the one is not contained in the other, nevertheless belong together, though only contingently, as parts of a whole, namely experience, which is itself a synthetic combination of intuitions.

But in synthetic a priori judgments this means of help is entirely lacking. If I am to go beyond the concept A in order to cognize another B as combined with it, what is it on which I depend and by means
of which the synthesis becomes possible, since I here do not have the
advantage of looking around for it in the field of experience?

Take the proposition: "Everything that happens has its cause." In the concept of something that happens, I think, to be sure, of an existence that was preceded by a time, etc., and from that analytic judgments can be drawn. But the concept of a cause lies entirely outside that concept,
and indicates something different than the concept of what happens in
general, and is therefore not contained in the latter representation at
all. How then do I come to say something quite different about that
which happens in general, and to cognize the concept of cause as be
longing to it, indeed necessarily, even though not contained in it?

Editor’s note: Earlier, Kant said that anytime we encounter "necessity," we can know that an a priori judgment is in play. This is so because necessity means “must” not “may” be such and such. The "necessary" couldn’t be any other way. We don’t get this sense of “must” from experience. There, we see contingency. But in the case of "everything that happens has its cause" there is no identity in the predicate, that is, necessity is not contained in "everything that happens." We believe that all things have a cause but we cannot gain this necessity from experience because experience cannot give us "must."

What is the unknown =X here on which the understanding depends
when it believes itself to discover beyond the concept of A a predicate
that is foreign to it yet which it nevertheless believes to be connected
with it? It cannot be experience, for the principle that has been adduced
adds the latter representations to the former not only with greater gen-
erality than experience can provide, but also with the expression of
necessity, hence entirely a priori and from mere concepts. Now the entire final aim of our speculative a priori cognition rests on such synthetic, i.e., ampliative principles; for the analytic ones are, to be sure, most important and necessary, but only for attaining that distinctness of concepts which is requisite for a secure and extended synthesis as a really new acquisition.

“What is the unknown = X here”: What is the hidden connection here? With analytic judgments, subject and predicate are brought together through clarification as the latter is contained in the former; such as, “all dogs are animals.” Synthetic judgments rely on experience to connect subject and predicate: “this cup is hot.” But what is the hidden “X factor” here, the connecting link between “all things that happen” and “have a cause”?

“final aim of our speculative a priori cognition”: Analytic cognitions are good as they clarify and hone what we know, but what we’re really after is to amplify and add to our knowledge. We want answers to the big questions of metaphysics – all the big a priori questions dealing with necessity and universality – but we can’t get to this higher knowledge with analytic thinking. What we need is to extend our knowledge (more than clarify) but without recourse to experience.

V. Synthetic a priori judgments are contained as principles in all theoretical sciences of reason.

"theoretical sciences of reason": VG: the sciences of reason are not empirical sciences as these would lead us to a posteriori knowledge not a priori. The sciences of reason deal with the theoretical, the speculative, the domain of reason itself. The aim of these sciences of reason is to extend our knowledge but without aid of experience.

Kant now offers three examples of the sciences of reason.

1. Mathematical judgments are all synthetic.

VG: This is not precisely correct because in mathematics we can have “3 = 3” or “all triangles are triangles” but these are not the propositions in focus.

This proposition seems to have escaped the notice of the analysts of human reason until now, indeed to be diametrically opposed to all of their conjectures, although it is incontrovertibly certain and is very important in the sequel.

For since one found that the inferences of the mathematicians all pro
ceed in accordance with the principle of contradiction (which is re-
quired by the nature of any apodictic certainty), one was persuaded that
the principles could also be cognized from the principle of contradic-
tion, in which, however, they erred; for a synthetic proposition can of
course be comprehended in accordance with the principle of contradic-
tion, but only insofar as another synthetic proposition is presupposed
from which it can be deduced, never in itself.

It must first be remarked that properly mathematical propositions are
always a priori judgments and are never empirical, because they carry
necessity with them, which cannot be derived from experience.

VG: Always a priori because we don’t have to do empirical research to know the 2+2=4, no experiments, and “we got 4 this time, who knows what the next experiments will show.” Everyone believes that math is a priori, but Kant wants to claim that it is synthetic a priori, and this is the controversial thesis.

But if one does not want to concede this, well then, I will restrict my proposition to pure mathematics, the concept of which already implies that it does not contain empirical but merely pure a priori cognition.

To be sure, one might initially think that the proposition "7 + 5 = I2"
is a merely analytic proposition that follows from the concept of a sum
of seven and five in accordance with the principle of contradiction. Yet
if one considers it more closely, one finds that the concept of the sum
of 7 and 5 contains nothing more than the unification of both numbers
in a single one, through which it is not at all thought what this single
number is which comprehends the two of them. The concept of twelve
is by no means already thought merely by my thinking of that unifica-
tion of seven and five, and no matter how long I analyze my concept of
such a possible sum I will still not find twelve in it.

VG: Kant is saying that when I claim that 5 + 7 = 12, this can’t be an analytic judgment because the concept of 12, in no way, is contained in the concepts of 5, plus, 7 or equals. With 5 + 7, I can think of the number 5, I can think of the number 7, I can think of the +, and I know I should add one to the other, that’s what the + tells me, but simply by looking at the meaning of these individual concepts, Kant says, I am never going to discover the concept of 12, as 12 is not in those concepts, per se, and therefore there is no analytic judgment.

One must go beyond these concepts, seeking assistance in the intuition that corresponds to one of the two, one's five fingers, say, or (as in Segner's arithmetic) five points, and one after another add the units of the five given in the intuition to the concept of seven.

For I take first the number 7, and, as I
take the fingers of my hand as an intuition for assistance with the con-
cept of 5, to that image of mine I now add the units that I have previously taken together in order to constitute the number 5 one after
another to the number 7, and thus see the number I2 arise. That 7
should be added to 5 I have, to be sure, thought in the concept of a sum = 7 + 5, but not that this sum is equal to the number I2 .

VG: We can see that we "should" put together 5 and 7, but this does not reveal 12.

VG: What is Kant doing? In order to get from 5 and 7 to 12, Kant says we have to use, what he calls, my “intuition.” We are going to learn that “intuition”, for human beings, means “sensation” or “that which makes sensation possible” maybe. In mathematics, Kant is going to tell us, we use pure intuition, which is the “form of our sensation” – which is going to turn out to be space and time.

VG: So, when I do 5+7, maybe I am sort of semi-visualizing 5 and 7 spatial regions, and sort of visualizing them together and getting to the number 12. Or maybe it is my conception of counting in time, like “one, two, three…”, counting out 5 and 7 and this process in time allows me to move from the concept of 5 and the concept of 7 to the further concept of 12.

The arithmetical proposition is therefore always synthetic; one becomes all the more distinctly aware of that if one takes somewhat larger numbers, for it is then clear that, twist and turn our concepts as we will, without getting help from intuition we could never find the sum by means of the mere analysis of our concepts.

VG: What I say here, asserts Kant, is all the more obvious if we deal with the addition of larger numbers, as this will readily expose that the sum is not seen in the addends.

Just as little is any principle of pure geometry analytic. That the straight line between two points is the shortest is a synthetic proposition.

For my concept of the straight contains nothing of quantity, but only a quality. The concept of the shortest is therefore entirely addi tional to it, and cannot be extracted out of the concept of the straight line by any analysis. Help must here be gotten from intuition, by means of which alone the synthesis is possible.

VG: The straight line is the shortest line. Could this be an analytic statement? Can I see this from the meaning of the concepts alone? Kant says, no. The concept of the “straight” is nothing of quantity but only of quality. It is not about more or less but a qualitative concept of no curves. Whereas “shortest” is about quantity, you have to measure and count to know this. Short and straight seem to be very different concepts, and so it’s hard to see how “the straight line is the shortest” could be analytic, in that, the definitions themselves do not reveal the new understanding, and yet we seem to have new knowledge in the conclusion. And so, Kant is saying, the concepts of arithmetic and geometry are synthetic statements, moving beyond the first part of the statement when the second part is stated. We are adding new knowledge, it’s more than a relation of definitions of concepts, and I do this through my grasp of my intuition of space and time.

To be sure, a few principles that the geometers presuppose are actu-
ally analytic and rest on the principle of contradiction; but they also
only serve, as identical propositions, for the chain of method and not as
principles, e.g., a = a, the whole is equal to itself, or (a + b) > a, i.e., the whole is greater than its part. And yet even these, although they are
valid in accordance with mere concepts, are admitted in mathematics
only because they can be exhibited in intuition.

What usually makes
us believe here that the predicate of such apodictic judgments already
lies in our concept, and that the judgment is therefore analytic, is
merely the ambiguity of the expression. We should, namely, add a cer-
tain predicate to a given concept in thought, and this necessity already
attaches to the concepts. But the question is not what we should think
in addition to the given concept, but what we actually think in it,
though only obscurely, and there it is manifest that the predicate cer-
tainly adheres to those concepts necessarily, though not as thought in
the concept itself, but by means of an intuition that must be added to
the concept.

VG: Current philosophers in the main do not agree with Kant that mathematical statements are synthetic, but, they say, are analytic. To briefly summarize the “modern” view, mathematical systems are “not supposed to be true.” There is no one set of axioms, according to this view, of geometry which must be learned or discovered and from these we can determine what is “true.” Instead, there are conceived to be many different axiomatic systems; we can have Euclidean geometry but also non-Euclidean geometries. And the same is true for the numbers, which can be axiomatized in different ways. With this view, it’s not about finding “the truth” but “given these axioms, what can I derive?” Therefore, these systems of axioms are very “formalizable,” a logical and purely analytic procedure. [This is merely truth by definition.] However, the question then becomes, if math is just a system of axioms that we can dream up to suit the fancy, how can this apply to the real world? Out there, most contemporary thinkers would say that this is an empirical question, that is, we must find the best system to conform to the real world. Under this view, there is no room for the Kantian synthetic a priori in mathematics.

What now? How does this affect students of Kant? What Kant says about the example of mathematics is not a fundamental pillar in his argument for the synthetic a priori. Even if Kant is wrong about mathematics – and it’s not clear that he is wrong – this will not impact the main thesis of The Critique. Concerning Kant’s math statements, these may not be totally hopeless. The new systems are not without their own problems and are no panacea in terms of accessing all correctness.

2. Natural science (Physica) contains within itself synthetic a priori judgments as principles.

I will adduce only a couple of propositions as examples, such as the proposition that in all alterations of the
corporeal world the quantity of matter remains unaltered, or that in all
communication of motion, effect and counter-effect must always be
equal. In both of these not only the necessity, thus their a priori origin,
but also that they are synthetic propositions is clear. For in the concept of matter I do not think persistence, but only its presence in space
through the filling of space.

VG: Kant offers some very general principles from science which seem to be true at all times and places; therefore, an element of necessity is attached to them. As such, they would be classified, Kant is saying, as a priori concepts.

Thus I actually go beyond the concept of
matter in order to add something to it a priori that I did not think in it.
The proposition is thus not analytic, but synthetic, and nevertheless
thought a priori, and likewise with the other propositions of the pure
part of natural science.

VG: Why does Kant think these are a priori? Aren’t these things we find out empirically by doing science? Kant will say that very general concepts of science can be gained via metaphysics, and these general concepts will serve as foundation of metaphysics as a science, but these are not detailed here. It will turn out to be that these fundamental truths of metaphysics will be applied to physical science, to matter. These are suggestive, not conclusive, toward confirming the synthetic a priori.

3. In metaphysics, even if one regards it as a science that has thus far merely been sought but is nevertheless indispensable because of the nature of human reason, synthetic a priori cognitions are supposed to be contained, and it is not concerned merely with analyzing concepts
that we make of things a priori and thereby clarifying them analytically,
but we want to amplify our cognition a priori; to this end we must make
use of such principles that add something to the given concepts that was not contained in them, and through synthetic a priori judgments go so far beyond that experience itself cannot follow us that far, e.g., in the
proposition "The world must have a first beginning," and others be
sides, and thus metaphysics, at least as far as its end is concerned, consists of purely synthetic a priori propositions.

So many of the “laws” of science, along with the major tenets of common belief systems, cannot be investigated directly. How can one empirically determine that “the world must have had a beginning” as we cannot go back in time to check. Experience will not be available. We need a priori concepts to solve this problem, but can we get them as foundation for our thinking?

VI. The general problem of pure reason. 

One has already gained a great deal if one can bring a multitude of in
vestigations under the formula of a single problem. For one thereby not
only lightens one's own task, by determining it precisely, but also the
judgment of anyone else who wants to examine whether we have satis
fied our plan or not. The real problem of pure reason is now contained
in the question: How are synthetic judgments a priori possible?
That metaphysics has until now remained in such a vacillating state
of uncertainty and contradictions is to be ascribed solely to the cause
that no one has previously thought of this problem and perhaps even of
the distinction between analytic and synthetic judgments.

VG: Kant wants to establish that it’s possible to secure metaphysics as a science, and this will be done by showing how metaphysical synthetic a priori truths are possible.

On the solution of this problem, or on a satisfactory proof that the possibility that it demands to have explained does not in fact exist at all, metaphysics now stands or falls. David Hume, who among all philosophers came closest to this problem, still did not conceive of it anywhere near determinately enough and in its universality, but rather stopped with the synthetic proposition of the connection of the effect with its cause (Principium causalitatis), believing himself to have brought out that such an a priori proposition is entirely impossible, and according to his inferences everything that we call metaphysics would come down to a mere delusion of an alleged insight of reason into that which has in fact merely been borrowed from experience and from habit has taken on the appearance of necessity; an assertion, destructive of all pure philosophy, on which he would never have fallen if he had had our problem in its generality before his eyes, since then he would have comprehended that according to his argument there could also be no pure mathematics, since this certainly contains synthetic a priori propositions, an assertion from which his sound understanding would surely have protected him.

In the solution of the above problem there is at the same time con
tained the possibility of the pure use of reason in the grounding and ex
ecution of all sciences that contain a theoretical a priori cognition of
objects, i.e., the answer to the questions:
How is pure mathematics possible?
How is pure natural science possible?

About these sciences, since they are actually given, it can appropri-
ately be asked how they are possible; for that they must be possible is
proved through their actuality. *

* Some may still doubt this last point in the case of pure natural science. Yet one need merely consider the various propositions that come forth at the outset of proper (empirical) physics, such as those of the persistence of the same quantity of matter, of inertia, of the equality of effect and counter-effect, etc., and one will quickly be convinced that they constitute a physica pura (or rationalis), which well deserves to be separately established, as a science of its own, in its whole domain, whether narrow or wide.

As far as metaphysics is concerned,
however, its poor progress up to now, and the fact that of no meta-
physics thus far expounded can it even be said that, as far as its essential end is concerned, it even really exists, leaves everyone with ground to doubt its possibility.

But now this kind of cognition is in a certain sense also to be re
garded as given, and metaphysics is actual, if not as a science yet as a
natural predisposition (metaphysica naturalis). For human reason, with
out being moved by the mere vanity of knowing it all, inexorably pushes
on, driven by its own need to such questions that cannot be answered
by any experiential use of reason and of principlesa borrowed from such
a use; and thus a certain sort of metaphysics has actually been present
in all human beings as soon as reason has extended itself to speculation
in them, and it will also always remain there. And now about this too
the question is:

How is metaphysics as a natural predisposition possible? i.e., how do the questions that pure reason raises, and which it is
driven by its own need to answer as well as it can, arise from the nature
of universal human reason?

But since unavoidable contradictions have always been found in all
previous attempts to answer these natural questions, e.g., whether the
world has a beginning or exists from eternity, etc., one cannot leave it
up to the mere natural predisposition to metaphysics, i.e., to the pure
faculty of reason itself, from which, to be sure, some sort of metaphysics (whatever it might be) always grows, but it must be possible to bring it
to certainty regarding either the knowledge or ignorance of objects, i.e., to come to a decision either about the objects of its questions or about the capacity and incapacity of reason for judging something about them, thus either reliably to extend our pure reason or else to set de terminate and secure limits for it. This last question, which flows from the general problem above, would rightly be this:

How is metaphysics possible as science?
The critique of reason thus finally leads necessarily to science; the
dogmatic use of it without critique, on the contrary, leads to groundless assertions, to which one can oppose equally plausible ones, thus to

Further, this science cannot be terribly extensive, for it does not deal
with objectsb of reason, whose multiplicity;c is infinite, but merely with
itself, with problems that spring entirely from its own womb, and that
are not set before it by the nature of things that are distinct from it but
through its own nature; so that, once it has become completely familiar
with its own capacity" in regard to the objects that may come before it
in experience, then it must become easy to determine, completely and
securely, the domain and the bounds of its attempted use beyond all
bounds of experience.

Thus one can and must regard as undone all attempts made until now
to bring about a metaphysics dogmatically; for what is analytic in one
or the other of them, namely the mere analysis of the concepts that in
habit our reason a priori, is not the end at all, but only a preparation for
metaphysics proper, namely extending its a priori cognition syntheti-
cally, and it is useless for this end, because it merely shows what is con
tained in these concepts, but not how we attain such concepts a priori in
order thereafter to be able to determine their valid use in regard to the objects of all cognition in general. It also requires only a little self
denial in order to give up all these claims, since the contradictions of
reason, which cannot be denied and which are also unavoidable in dog
matic procedure, have long since destroyed the authority of every pre-
vious metaphysics.

More resolution will be necessary in order not to he
deterred by internal difficulty and external resistance from using an
other approach, entirely opposed to the previous one, in order to pro
mote the productive and fruitful growth of a science that is indis
pensable for human reason, and from which one can chop down every
stem that has shot up without ever being able to eradicate its root.


VII. The idea and division of a special science under the name of a critique of pure reason.

Now from all of this there results the idea of a special science, which can be called the critique of pure reason. For reason is the faculty
that provides the principles of cognition a priori. Hence pure reason is
that which contains the principlese for cognizing something absolutely
a priori. An organon of pure reason would be a sum total of all those
principles! in accordance with which all pure a priori cognitions can be acquired and actually brought about. The exhaustive application of
such an organon would create a system of pure reason.

But since that requires a lot, and it is still an open question whether such an amplification of our knowledge is possible at all and in what cases it would be possible, we can regard a science of me mere estimation of pure reason, of its sources and boundaries, as the propaedeutic to the system of pure reason. Such a thing would not be a doctrine, but must be called only a critique of pure reason, and its utility in regard to speculation would really be only negative, serving not for the amplification but only for the purification of our reason, and for keeping it free of errors, by which a great deal is already won.

I call all cognition transcendental that is occupied not so much with objects but rather with our mode of cognition of objects insofar as this is to be possible a priori. A system of such concepts would be called transcendental philosophy.

VG: Kant here defines “transcendental.” It refers not to objects, there is no transcendental object, but when we do transcendental philosophy we are thinking about how we can have knowledge of objects a priori, it’s about how we think, it’s a reflection on our relation to the world, and to knowledge. The word “transcendent” for Kant is much different and means “beyond the bounds of knowledge” or beyond the bounds of experience.” So, transcendent knowledge would be, maybe, knowledge of God, for example. “Transcendent philosophy” would go beyond the bounds of experience. Kant thinks transcendent philosophy is impossible, and that we should not strive for it.

But this is
again too much for the beginning. For since such a science would have
to contain completely both the analytic as well as the synthetic a priori
cognition, it is, so far as our aim is concerned, too broad in scope, since
we need to take the analysis only as far as is indispensably necessary in
order to provide insight into the principles of a priori synthesis in their
entire scope, which is our only concern. This investigation, which we
can properly call not doctrine but only transcendental critique, since it
does not aim at the amplification of cognitions themselves but only at
their correction, and is to supply the touchstone of the worth or worth
lessness of all cognitions a priori, is that with which we are now con-

Such a critique is accordingly a preparation, if possible, for an
organon, and, if this cannot be accomplished, then at least for a canon,
in accordance with which the complete system of the philosophy of
pure reason, whether it is to consist in the amplification or mere limi-
tationa of its cognition, can in any case at least some day be exhibited
both analytically and synthetically. For that this should be possible, in
deed that such a system should not be too great in scope for us to hope
to be able entirely to complete it, can be assessed in advance from the
fact that our object is not the nature of things, which is inexhaustible,
but the understanding, which judges about the nature of things, and this
in turn only in regard to its a priori cognition, the supply of which, since
we do not need to search for it externally, cannot remain hidden from
us, and in all likelihood is small enough to be completely recorded, its
worth or worthlessness assessed, and subjected to a correct appraisal.


Even less can one expect here a critique of the books and systems of
pure reason, but rather that of the pure faculty of reason itself. Only if
this is one's ground does one have a secure touchstone for appraising
the philosophical content of old and new works in this specialty; other
wise the unqualified historian and judge assesses the groundless asser
tions of others through his own, which are equally groundless.


Transcendental philosophy is here the idea of a science for which
the critique of pure reason is to outline the entire plan architectonically,
i.e., from principles, with a full guarantee for the completeness and cer-
tainty of all the components that comprise this edifice.

It is the system of all principles of pure reason. That this critique is not itself already called transcendental philosophy rests solely on the fact that in order to be a complete system it would also have to contain an exhaustive analy sis of all of human cognition a priori. Now our critique must, to be sure, lay before us a complete enumeration of all of the ancestral conceptsh that comprise the pure cognition in question.

Only it properly refrains from the exhaustive analysis of these concepts themselves as well as from the complete review of all of those derived from them, partly because this analysis would not be purposeful,a since it does not contain the difficulty encountered in the synthesis on account of which the whole critique is actually undertaken, partly because it would be con trary to the unity of the plan to take on responsibility for the com
pleteness of such an analysis and derivation, from which one could yet
be relieved given its aim. This completeness of the analysis as well as
the derivation from the a priori concepts that are to be provided in the
future will nevertheless be easy to complete as long as they are present
as exhaustive principlesb of synthesis, and if nothing is lacking in them
in regard to this essential aim.

To the critique of pure reason there accordingly belongs everything
that constitutes transcendental philosophy, and it is the complete idea
of transcendental philosophy, but is not yet this science itself, since it
goes only so far in the analysis as is requisite for the complete estima
tion of synthetic a priori cognition.


The chief target in the division of such a science is that absolutely no
concept must enter into it that contains anything empirical, or that the
a priori cognition be entirely pure. Hence, although the supreme prin-
ciples of morality and the fundamental concepts of it are a priori cogni-
tions, they still do not belong in transcendental philosophy,' for, while
they do not, to be sure, take the concepts of pleasure and displeasure,
of desires and inclinations, etc., which are all of empirical origin, as the
ground of their precepts, they still must necessarily include them in the
composition of the system of pure morality in the concept of duty, as
the hindrance that must be overcome or the attraction that ought not
to be made into a motive. Hence transcendental philosophy is a philos
ophy of pure, merely speculative reason. For everything practical, in
sofar as it contains incentives, is related to feelings, which belong
among empirical sources of cognition.

VG: What Kant is telling us is that in The Critique he’s not going to say very much about ethics, or action in the world, but we’re thinking about theoretical knowledge here.

Now if one wants to set up the division of this science from the gen
eral viewpoint of a system in general, then what we will now present
must contain first a Doctrine of Elements and second a Doctrine of
Method of pure reason. Each of these main parts will have its subdivi
sion, the grounds for which cannot yet be expounded.

All that seems
necessary for an introduction or preliminary is that there are two stems
of human cognition, which may perhaps arise from a common but to us
unknown root, namely sensibility and understanding, through the first
of which objects are given to us, but through the second of which they
are thought. Now if sensibility were to contain a priori representations,
which constitute the condition under which objects are given to us, it will belong to transcendental philosophy.

The transcendental doctrine of the senses will have to belong to the first part of the science of elements, since the conditions under which alone the objects of human cognition are given precede those under which those objects are thought.

VG: What Kant is doing here is to briefly introduce his incredibly important claim that we must make a distinction between sensibility and understanding, as the two stems of human cognition. He’s going to tell us that they always have to work together if any knowledge is to be possible. He’ll talk about sensibility first, that through which objects are given to us, which he’ll do this in the Transcendental Aesthetic. 

RPW: “There are two sources of human knowledge, two cognitive powers of the human mind. One of them is our power to be affected by objects – sensibility; this is the Transcendental Aesthetic. And the other is our capacity for formulating concepts and reasoning about our experience, and this is the Transcendental Logic. And this distinction is a fundamental distinction, it’s the groundwork of Kant’s theory of knowledge.”







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