Knowledge Is Both Rational and Empirical
Classic Philosophical Questions Part 5 - Knowledge
Immanuel Kant, from the A Critique of Pure Reason
Kem Stone - 27 October 2007
Before beginning my exposition I will acknowledge that my work on this journal has slowed dramatically over the
past few weeks. This may have something to do with my own natural tendency to lose a great deal of motivation
in the Fall and Winter months, or it may have to do with the fact that this particular section of the text, that on
epistemology, is one I find particularly dull and uninteresting. Though it is probably a combination of both, I have
now recognised that while I do feel that the Theory of Knowledge is extremely important—perhaps even the most
essential branch of philosophy—most of the writing on the subject does not interest me. If I ever begin a career in
philosophy, this will most certainly not be my area of focus.
That being said, Kant’s claim that knowledge is not solely rational nor solely empirical but a combination of both is
one I am inclined to agree with, in spite of some possible weaknesses. He begins by drawing the distinction
between these two types of knowledge, and making the assertion that “though all our knowledge begins with
experience, it does not follow that it all arises out of experience” (273). For Kant, experience is necessary to
have any knowledge in the first place because sensations are what give rise to our mental representations, but not
everything we know is grounded in experience because some things can be known without experience. Though
the expression “a priori” has been used to describe any knowledge that is not derived immediately from
experience, Kant wishes to limit the term to apply only to that knowledge that is independent of all experience.
Knowledge derived through experience falls under the term “a posteriori” which is to be distinguished from the
“synthetic a priori” which Kant describes later on.
There are two conditions for a judgment to be considered a priori: the proposition must be thought as necessary—
the predicate can not belong to the subject merely accidentally—and it must be universal—the predicate must
always belong to the subject without exception. Kant asserts that the proposition, “every alteration must have a
cause” is an a priori judgment because “the very concept of a cause so manifestly contains the concept of a
necessity of connection with an effect and of the strict universality of the rule” (275), which is a challenge to Hume’
s assertion that our knowledge of causes comes through our forming of associations between events and those
which immediately precede them.
A priori judgments must exist, Kant claims, because otherwise all knowledge would be derived from experience,
which always contains an element of uncertainty, and therefore all knowledge would be contingent and we would
have no first principles. That a priori judgments do exist can be demonstrated if we consider a concept and
remove all things about that concept that are derived through experience. “If we remove from our empirical
concept of a body, one by one, every feature in it which it is empirical, the colour, the hardness or softness, the
weight, even the impenetrability, there still remains the space which the body (now entirely vanished) occupied,
and this cannot be removed” (275). Because the concept of the space itself is not derived through experience
(which is a highly dubious claim) Kant believes this is proof that a priori knowledge exists.
To further clarify the distinction between the two types of judgments, Kant uses the terms “analytic” and
“synthetic” to distinguish between the two possible relations in a proposition of the subject to the predicate: “Either
the predicate B belongs to the subject A, as something which is (covertly) contained in this concept A; or B lies
outside the concept A, although it does indeed stand in connection with it” (275). Analytic judgments are of the
former type, and are therefore merely those which clarify existing concepts, while synthetic judgments—those of
the latter form—actually extend our knowledge of the concept in question. “All bodies are extended” is an
analytic judgment because the concept of extension is necessarily contained within the idea of a body. On the
other hand, “All bodies are heavy” is a synthetic judgment because according to Kant we must look outside the
mere concept of a body to attach to it the concept of weight.
The third type of judgment that Kant calls to our attention is the a priori synthetic judgment. It is necessary to
have this third category because many abstract principles are synthetic judgments and yet are not derived a
posteriori. For instance, in the proposition, “Everything which happens has its cause” the concept of a cause is
not implicitly contained in the concept of “something which happens” and we must therefore look beyond the
subject itself to discover that its predicate is in fact connected to it in a necessary and universal sense. We need
this third category because “analytic judgments are very important, and indeed necessary, but only for obtaining
that clearness in the concepts which is requisite for such a sure and wide synthesis as will lead to a genuinely new
addition to all previous knowledge” (277) but we can only add to our existing knowledge by making synthetic
Kant then makes the somewhat counter-intuitive claim that all mathematical judgments are synthetic. Because
they are necessary and universal, they are a priori, but because their predicates almost always lie outside the
subject, they must be considered synthetic. For instance, in the proposition 7 + 5 = 12, it may be supposed that
this is an analytic proposition because it follows from the principle of contradiction that 12 can be the only sum of
7 and 5, yet the concept of 7 + 5 contains only the union of two numbers, and no analysis of this concept alone
will identify the number 12. We must bring in representations such as 7 points and 5 points, and count them to
discover that when added together they add up to 12 points, and this makes it a synthetic proposition. It is more
apparent that all arithmetical propositions are synthetic if we consider larger numbers, where we must count in
order to arrive at the sum (or difference, product, etc.)
Geometrical propositions are also synthetic, such as the proposition that the shortest distance between two points
is a straight line. The concept of straight is a quality, which contains nothing of quantity, and “the shortest
distance” cannot be derived through an analysis of the concept of straight. Though the predicate is necessarily and
universally connected to the subject in this case, as it is in arithmetical propositions, one thought is not contained in
the other. “The question is not what we ought to join in thought to the given concept, but what we actually think
in it, even if only obscurely; and it is then manifest that, while the predicate is indeed attached necessarily to the
concept, it is so in virtue of an intuition which must be added to the concept, not as thought in the concept itself”
(278). Kant goes on to say that some fundamental propositions are indeed analytic and rest purely on the
principle of contradiction, such as a = a (the whole is equal to itself) or (a + b) > a (the whole is greater than its
part), but these are merely truths readily apparent to the intuition, they serve “only as links in the chain of method”
and do not add anything to our knowledge.
There are a priori synthetic judgments in the natural sciences as well, such as the proposition that the total amount
of matter in the universe remains constant, or that any action will always produce an equal and opposite reaction.
These are necessary and universal but we must go beyond the concepts themselves to make such determinations.
In the realm of metaphysics, where nearly all judgments are a priori because here we cannot appeal to
experience, Kant believes that a priori synthetic judgments are the only hope we ever have of advancing our
knowledge in this field. The business of metaphysics “is not merely to analyse concepts which we make for
ourselves a priori of things, and thereby to clarify them analytically, but to extend our a priori knowledge. And
for this purpose we must employ principles which add to the given concept of something that was not contained in
This text concludes with Kant’s discussion of the principle of contradiction, which he claims is the highest principle
of all analytic judgments. The principle itself is extremely basic: no predicate contradictory to the subject can
belong to it. In itself, this is a negative principle, used to dispel falsehood and error. If a proposition does not
conform to the principle of contradiction (i.e. if the predicate can not conceivably belong to the subject) then we
know the proposition is false. However, in an analytic judgment it can be a positive principle. “The reverse of
that which as concept is contained and is thought in the knowledge of the object, is always rightly denied. But
since the opposite of the concept would contradict the object, the concept itself must necessarily be affirmed of it”
(279). This makes the principle of contradiction sufficient for determining the truth of all analytic knowledge.
However, the principle holds no such authority when it comes to synthetic knowledge, which is the type of
knowledge that philosophy and the sciences are most concerned with. It is still necessary, in that our knowledge
claims must still conform to it, yet it is not sufficient because a thing can be false and yet contain no contradiction.
Kant argues against those who would claim the formula can still be put to use in synthetic claims, under the
principle: “It is impossible that something should at one and the same time both be and not be.” But it this case,
the principle is modified by the condition of time: a man who is young cannot at the same time be old, but it is
certainly the case that a man who is old at one time is at another time young. “The principle of contradiction,
however, as a merely logical principle, must not in any way limit its assertions to time-relations. The above
formula is therefore contrary to the intention of the principle” (280). In the context of the selected text, this
discussion serves merely to draw another distinction between analytic and synthetic knowledge, namely that in the
former the principle of contradiction is necessary and sufficient to determine truth or falsehood, while in the latter it
is necessary but not sufficient.
I believe that Kant is probably closest to the truth (if there is such a thing when it comes to this field) in claiming
that both a priori and a posteriori knowledge exist, and that while experience is necessary to have any
knowledge at all, not all of our knowledge is directly derived from experience. This is a far more reasonable idea
than that of the rationalists who claim that all knowledge ultimately rests on innate ideas, or the empiricists who
believe that it is only through experience that we can learn anything at all. It is quite sensible to believe that our
beliefs are a combination of both.
My only problem with Kant’s distinction between analytic and synthetic judgments is that the line seems a bit
blurrier than it would appear. For instance, he claims that the proposition “all bodies are extended” is analytic
because the concept of extension is contained within the very idea of a body, while “all bodies are heavy” is
synthetic because the concept of weight is separate from that of a body and must be joined to it. Kant claims that
“The question is not what we ought to join in thought to the given concept, but what we actually think in it” but
does this not render the distinction subjective? When I think of a body I do think of something with weight, or at
least something with mass. A body must be composed of matter and therefore must have mass, and so I would
assert that “all bodies are heavy” is just as much an analytic claim as “all bodies are extended” because extension
is no more fundamental to the concept of a body than mass.
The same goes for Kant’s claim that “a straight line is the shortest distance between two points” is synthetic. It
may be that when most people think of a straight line, they think merely of the quality of straightness and not the
quantitative idea of it being the shortest distance between two points. But many actually would think of the line in
such quantitative terms, particularly anyone who uses geometry in daily life, such as a mathematician or an
engineer. Does this mean that the proposition is synthetic for some but analytic for others? If we base such
distinctions purely on what ideas are attached to a concept in “the mind” we ignore the fact that all minds are
different and certain concepts may be firmly attached to one another in one mind while they require demonstration
to enjoin them in another. And if we allow subjectivity to play any role in these broad, universal categories of
knowledge, our entire system collapses.
In spite of this minor problem, I believe Kant’s distinctions are very helpful in terms of the broader scope of the
study of knowledge.