Examining Kant’s most famous project — What are the conditions that make experience possible?

Immanuel Kant (1724–1804) was a German philosopher and professor who introduced a revolution in Western philosophy. It is no exaggeration to say that Kant remains one of the most influential thinkers of all time. Because of his notoriously complex writing style and the difficulty of his ideas, this blog post will first offer a clear introduction to his theory of transcendentalism before moving on to a more systematic reading of the Critique of Pure Reason.

The Critique of Pure Reason was first published in 1781, known as the A edition. Six years later, Kant released a revised B edition (1787), which clarified several arguments in response to misinterpretations and criticisms of the first edition. The Cambridge Edition, edited by Paul Guyer and Allen W. Wood, includes both versions, and it will serve as the basis for analysis and citation in this post. I will focus on the B edition.

This post aims to provide an introductory understanding of Kant’s transcendental philosophy by examining the Preface and Introduction of the Critique. For readers who want a more well-rounded understanding of Kant’s project, I also recommend reading the Transcendental Aesthetic (the first part of Part I) and the Metaphysical Deduction (Division One of the Transcendental Analytic, Book I).

Kant’s Transcendental Turn

Prior to examining the specific sections, let us examine Kant’s general project. Kant is particularly known for his attempt to “solve” the long-standing debate between rationalism and empiricism — a debate about the origins of human knowledge:

• Rationalists argued that knowledge derives from reason; the mind conforms to objects through rational concepts, which must correspond to reality as it is in itself. The three great rationalists are René Descartes, Baruch Spinoza, and Gottfried Wilhelm Leibniz.
• Empiricists argued that knowledge derives from sensory experience; the mind conforms to objects through the senses. The three great empiricists are John Locke, George Berkeley, and David Hume.

Before Kant, philosophers focused on how the mind conforms to objects — that is, they believed the mind’s task was to mirror reality as it truly is. In this view, objects exist “out there,” fully formed and independent of the subject, while the subject’s thoughts must adjust to match them. Both rationalists and empiricists shared this basic assumption — that the mind must conform to objects — even though they disagreed about how this conformity occurs. The general mapping is as follows:

• Rationalists: reason → knowledge of objects → mind
• Empiricists: objects → senses → mind

Kant proposed a radical reversal: instead of assuming that the mind conforms to objects, he asked — what if objects conform to the mind? This idea, which he called his “Copernican Revolution,” became the foundation of his Critique of Pure Reason, and is how he developed his “transcendentalism.” Unlike the rationalists and empiricists, Kant’s framework is as follows:

• Kant: mind (and the conditions of the mind) → objects

Preface

Kant outlines the central philosophical problem of his time and reflects on the state of philosophy that preceded him. He writes:

Up to now it has been assumed that all our cognition must conform to the objects; but all attempts to find out something about them a priori through concepts that would extend our cognition have, on this presupposition, come to nothing.

As explained earlier, Kant challenges the traditional philosophical assumption that the mind must conform to objects. In both rationalism and empiricism, the dominant view was that cognition depends on the mind adapting itself to external objects. The object was thought to exist “out there,” independent of the mind, and the task of human knowledge was to grasp it accurately. For the rationalists, this occurred through reason — by aligning the mind’s concepts with the true reality of things. For the empiricists, it occurred through the senses — by allowing sensory experience to shape the mind’s understanding of objects.

Kant explains his pivotal shift:

Hence let us once try whether we do not get farther with the problems of metaphysics by assuming that the objects must conform to our cognition, which would agree better with the requested possibility of an a priori cognition of them, which is to establish something about objects before they are given to us.

This move by Kant is revolutionary. Instead of framing the question in terms of how the mind conforms to objects, he reverses it, asking how objects conform to the mind. In other words, Kant highlights that the mind does not passively receive reality but actively structures it. He considers this reversal a necessary approach for explaining a priori knowledge — knowledge that is independent of experience, such as mathematics or causality.

For Kant, the question is no longer what we know, but how we are able to know at all. The Kantian project is to uncover the conditions under which objects can appear to the mind — in short, the conditions that make experience possible.

He himself says that this is akin to the Copernican Revolution:

This would be just like the first thoughts of Copernicus, who, when he did not make good progress in the explanation of the celestial motions if he assumed that the entire celestial host revolves around the observer, tried to see if he might not have greater success if he made the observer revolve and left the stars at rest.

Nicolaus Copernicus was a 15th-century astronomer and philosopher who made a groundbreaking discovery: the Earth is not at the center of the universe. He overturned the geocentric model — in which everything revolves around the Earth — and replaced it with a heliocentric model, where the planets revolve around the sun. This shift laid the groundwork for the broader Scientific Revolution.

Kant claims that he is doing something equally transformative — but for metaphysics. Akin to Copernicus reversing the relationship between the Earth and the sun, Kant reverses the relationship between the mind and the object. This marks the necessary beginning of a metaphysical revolution.

Introduction

I. On the difference between pure and empirical cognition.

Kant begins by explaining that cognition does not exist independently of experience — all knowledge begins with experience in time:

As far as time is concerned, then, no cognition in us precedes experience, and with experience every cognition begins.

Yet, he quickly clarifies that not all knowledge arises from experience:

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

This may appear contradictory at first glance, but Kant is making a deliberate distinction between two kinds of cognition. The mind does not passively receive objects as if knowledge were a one-way street from the world to us. Yet neither is the mind detached from objects altogether. Instead, Kant argues that the mind is an active agent in the formation of experience — the mind contributes the necessary structures through which objects can appear to us in the first place.

The two kinds of cognitions are as follows:

One calls such cognitions a priori, and distinguishes them from empirical ones, which have their sources a posteriori, namely in experience. (Emphasis mine)

To clarify between the two kinds of cognition, Kant offers an example:

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 example of the weak foundation of a house, Kant explains that a person could foresee the collapse of their home without needing to witness it actually fall. This foresight is a priori knowledge — it is known through reason, not through experience. The person does not need to see the event to recognize that a house built on a weak foundation will inevitably collapse. However, this reasoning still depends on certain a posteriori concepts — such as the empirical understanding of gravity, weight, and the materials that make up a house — all of which are learned through experience.

From here, Kant distinguishes between two kinds of a priori knowledge. In the case of the collapsing house, the recognition that it would eventually fall still relies on experience. Yet there are other forms of a priori knowledge that do not depend on any empirical content:

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.

The two kinds of a priori knowledge are pure and impure. Pure a priori knowledge refers to concepts that hold true independently of all experience and contain no empirical content. An example of this is mathematical knowledge, which is grounded entirely in the operations of reason. Impure a priori knowledge, by contrast, refers to concepts that are necessary and universal in form but still drawn from experience — for instance, the idea of causality, which presupposes our empirical awareness of change and succession.

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

Kant continues to explain how we possess various a priori cognitions:

Experience teaches us, to be sure, that something is constituted thus and so, but not that it could not be otherwise.

Experience allows us to conclude that an object is constituted in a particular way. However, empirical observation alone cannot demonstrate that the object must be that way, or that it could not have been otherwise. Yet we still treat objects as operating according to universal and necessary laws. This implies that there must be faculties of the mind that structure and condition our experience of objects in the first place.

There are two particular a priori cognitions that Kant describes:

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.

The first is necessity. No amount of sensory experience can ever lead us to conclude that an object must necessarily be the way it is. So, it must be a structure in the mind. Furthermore:

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.

The second is universality. In this case, Kant distinguishes between two kinds. We often generalize from experience — for example, we might claim that “all swans are white.” This statement is universal, but it is only based on repeated observation; we have not seen all swans. Kant calls this empirical universality, a generalization that holds as far as we have observed. By contrast, strict universality belongs to judgments that are not predicated from empirics — for instance, mathematical propositions or the claim that “every alteration has a cause.” These are not derived from experience but arise necessarily from the mind’s own faculty of understanding.

Kant’s Subtle Shift — Beginning

Something noticeable here is that in Section I of the Introduction, Kant distinguishes between pure and impure a priori cognitions. He claims that mathematical propositions are examples of pure a priori cognition, whereas concepts such as causality are impure a priori cognitions because they presuppose empirical content (for instance, the idea of one ball causing another to move).

However, Kant quietly shifts his definition of pure as the Introduction progresses. In Section II, pure a priori cognition comes to mean a priori cognition in form, not necessarily one that excludes all empirical content. What matters now is not the empirical matter of experience, but the formal structure that makes experience possible. In this sense, concepts such as causality, substance, and motion count as pure forms of a priori cognition.

Kant writes:

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 Kant had retained his initial, stricter understanding of “pure,” then only mathematics would qualify as genuinely pure a priori cognition.

After doing some digging, I found that Kant himself recognized this confusion and eventually clarified what he meant:

For in the first passage I had said: among the cognitions a priori, however, those are called pure in which nothing empirical is intermixed; and I had given as an example of the opposite the proposition: everything alterable has a cause. By contrast, I cite on p. 5 this same proposition as an example of a pure cognition a priori, i.e., one that is not dependent on anything empirical. Here we have two meanings of the word pure, of which I am only concerned with the latter in the whole work, though. (Emphasis mine)

• This clarification appears in Kant’s essay On the Use of Teleological Principles in Philosophy (as translated in the Cambridge Edition of Practical Philosophy).

Kant’s Subtle Shift — End

Kant continues:

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 arising from that association.

Kant contrasts his view with that of Hume, who argued that the notion of cause and effect is learned through experience alone. However, Kant shows that the judgment that an effect must follow a cause arises from a sense of necessity — something that experience by itself cannot explain. If causality were grounded merely in habit, as Hume proposed, it would exist only as a subjective expectation within the mind. Yet we experience causality as objective and universal — as a law of nature itself.

Thus, causality cannot be derived from experience alone; rather, it is one of the conditions that make experience possible. It must therefore originate a priori.

Furthermore:

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.

While Kant begins by analyzing judgments, he soon transitions to concepts. Consider a body, for example: if we strip the empirical concept of the body of everything derived from the senses — its color, texture, weight, and other sensible qualities — something still remains: space.

This also applies to the concept of substance:

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).

If we strip an object all its empirical features, we are still left with the notion of substance — something that underlies through change. (More of this will be explained later.)

Thus, necessity, universality, causality, space, and substance are all a priori conditions that make experience possible.

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

Kant continues:

… certain cognitions even abandon the field of all possible experiences, and seem to expand the domain of our judgments beyond all bounds of experience.

He explains that some cognitions appear to “abandon the field of all possible experience” and attempt to extend judgment beyond what experience can ever give. These are not transcendental cognitions, but transcendent ones — ideas like God, freedom, and immortality that reason generates when it tries to go beyond the limits of experience.

In this sense, Kant encounters a fundamental problem. The cognitions that “abandon the field of all possible experience” reflects the tendency of reason to transcend the bounds of experience:

These unavoidable problems of pure reason itself are God, freedom and immortality.

The concepts of God, freedom, and immortality concern things-in-themselves meaning that they can never be objects of possible experience. They are instead ideas of pure reason. These concepts are ideals that reason constructs to find an ultimate explanation. Let’s review them:

• God — the idea of a supreme being (theological reason)
• Freedom — the idea of the will as uncaused (cosmological reason)
• Immortality — the idea of the soul existing forever (psychological reason)

Kant writes:

But the science whose final aim in all its preparations is directed properly only to the solution of these problems is called metaphysics, 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.

Unlike the empirical sciences, which concern themselves with appearances — the world as it is given to us — reason asks about the ultimate grounds of those appearances. Reason seeks what lies beneath or beyond phenomena. Thus, Kant is not rejecting the ideas of God, freedom, or immortality; rather, he argues that before we can address these questions, philosophy must first undertake a critique of reason itself. Instead of asking Is there a God? Is the will free? Is the soul immortal? we must first ask: How is knowledge possible? What are the limits and capacities of reason?

Kant continues:

Now it may seem natural that as soon as one has abandoned the terrain of experience one would not immediately erect an edifice with cognitions that one possesses without knowing whence… without having first assured oneself of its foundation through careful investigations… And in fact nothing is more natural, if one understands by the word natural that which properly and reasonably ought to happen

For most of us, it seems obvious that before debating the existence of God or the immortality of the soul, we should first analyze the scope and limits of human reason itself. Yet earlier philosophers did not take this approach. Kant explains why for three reasons:

• First: “Mathematics gives us a splendid example of how far we can go with a priori cognition independently of experience.” The success of mathematics encouraged philosophers to assume that pure reason could achieve certainty in metaphysics. Since math works a priori, they believed other rational claims could too.
• Second: “… if one is beyond the circle of experience, then one is sure of not being refuted through experience.” Once a philosopher leaves the realm of experience, they cannot be disproven by any empirical evidence. It is a safe space to speculate.
• Third: “The charm in expanding one’s cognitions is so great that one can be stopped in one’s progress only by bumping into a clear contradiction.” It can be an enjoyable experience until one bumps into a contradiction. However, many clever thinkers simply invent new concepts to avoid contradiction.

At any rate, Kant gives us the metaphor of a bird in flight to describe philosophers who abandon the realm of experience. The bird feels the resistance of the air and imagines it could fly even better in empty space, failing to notice that this resistance is precisely what makes flight possible. Likewise, philosophers who attempt to reason entirely beyond experience believe they will ascend higher by discarding empirical constraints; yet in doing so, they lose the very medium that gives thought its possibility.

We must remember that Kant’s project is transcendental, not transcendent. Right now, he is not concerned with proving or disproving the existence of God, whether one has freedom, or the immortality of the soul. Rather, he is concerned with how reason operationalizes to examine ask these questions. This is why Kant turns to Plato as an example:

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.

Plato attempted to transcend into a realm of ideas (Forms) because he believed the world to be imperfect. This reach for a higher, transcendent unity is precisely Kant’s critique. Kant makes clear that legitimate a priori cognition does not just assume a concept readily-made beyond experience — it solely yields clarity and illumination.

IV. On the difference between analytic and synthetic judgments.

Kant continues to describe the difference between two kinds of judgments:

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.

Here, Kant explains how a subject relates to a predicate within a judgment. The subject is the concept being considered, while the predicate is the property or determination attributed to that concept. Kant notes that he will focus on affirmative judgments, where the structure is “A is B.” In contrast, negative judgments deny a predicate of a subject — “A is not B.” This has nothing to do with positive or negative feelings; it is a matter of logical form. Regardless, the important point is not the contrast between affirmative and negative judgments, but the different ways in which the subject and predicate can be connected within a judgment:

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 concept A, though to be sure it stands in connection with it.

Kant distinguishes between two kinds of judgments based on how the predicate relates to the subject:

Analytic judgments: These are cases in which “the predicate B belongs to the subject A as something that is (covertly) contained in the concept A.” In other words, the predicate is already built into the subject-concept. A classic example is: “All bachelors are unmarried.” The predicate “unmarried” is not new information; it is essential to the very concept of a bachelor.

Synthetic judgments: These are cases in which “the predicate B lies entirely outside the concept A,” even though it may stand in some relation to it. For example: “The coffee cup is on the table.” The predicate “on the table” does not belong to the concept coffee cup; it adds new information that must be supplied by experience. A coffee cup can be in many locations, so the predicate is not contained in the subject-concept itself.

Kant clarifies the distinction between the two types of judgments:

Analytic judgments (affirmative ones) are thus those in which the connection of the predicate is thought through identity, but those in which this connection is thought without identity are to be called synthetic judgments.

Kant calls analytic judgments judgments of clarification because they do not add anything new to a concept; they simply make clarify what is already contained within it. Such judgments clarify a subject by breaking it into different components, all of which are implicitly present from the start. For example, in the judgment “All bachelors are unmarried,” the predicate “unmarried” is part of the very definition of a bachelor. Likewise, “All bachelors are men” is analytic, since maleness is also contained in the concept bachelor (at least in the normative fashion). These judgments do not expand our knowledge, but only clarify what the concept already includes.

By contrast, Kant describes synthetic judgments as judgments of amplification, since they expand the subject-concept by adding something not already contained within it. In these judgments, the predicate introduces new information. Using the earlier example, “The coffee cup is on the table,” the predicate “on the table” is not contained within the concept coffee cup.. Likewise, we could say “The coffee cup is in San Francisco.” The location of the cup is not part of the concept coffee cup, and therefore such judgments amplify rather than merely clarify the concept.

Kant continues:

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 judgment, and therefore need no testimony from experience for that

Put simply, judgments of experience must be synthetic. To know that a coffee cup is on the table, for instance, one must appeal to actual experience — such as seeing it — because the predicate is not contained in the subject-concept. By contrast, if a judgment is analytic, it requires no experience at all, since the predicate is already included within the concept of the subject. Consider the analytic judgment “All triangles have three sides”: one does not need to encounter a triangle in experience to know this is true. Analytic judgments are therefore a priori, not judgments of experience.

He explains:

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 experience from which I had extracted this concept of body, I find that weight is also always connected with the previous marks, and I therefore add this synthetically as predicate to that concept.

Kant offers a specific example: the proposition “A body is extended.” In this case, experience is unnecessary, because extension is a defining mark already contained within the concept of a body. When we analyze the concept of the body, we find features such as extension, impenetrability, and shape — all of which are included a priori in the concept itself. By contrast, the judgment “A body is heavy” is synthetic, since weight is not a mark contained within the concept of a body. A body can easily be imagined as occupying space without possessing weight. Thus the predicate “heavy” can be added to the concept only through experience; it is through encountering bodies in the empirical world that we discover that they are connected with weight.

Kant moves to discuss the most difficult type of judgment: synthetic a priori judgments:

But in synthetic a priori judgments this means of help is entirely lacking.

If I am to go beyonds 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?

Synthetic a priori judgments are different from what Kant has discussed so far. Earlier, he showed that analytic judgments are a priori, since their predicates are contained within the subject-concept, and that many synthetic judgments are a posteriori, since they add new information taken from experience. Now, however, Kant turns to a third kind of judgment: synthetic a priori judgments. These judgments add new information to a concept (so they are not analytic), yet they are also known independently of experience (so they are not empirical).

Here we encounter a problem. In a synthetic a priori judgment, the predicate is not contained in the subject-concept and yet it also cannot come from experience, since the judgment is supposed to hold necessarily and universally, beyond what experience can ever justify. So how are such judgments possible? What would a judgment look like that is both synthetic and a priori? This is the central question Kant now poses.

Thankfully, Kant gives an example to clarify his pivotal move:

Take the proposition: “Everything that happens has its cause.”

In this judgment, the concept of a cause is not contained within the concept of something happening, which means the judgment is synthetic. Put simply, one can think the idea of an event or something happening without at all thinking the idea of a cause. “Cause” is not included in the subject-concept. When we analyze the concept “something happens”, we find certain analytic marks: a change occurs, something begins to be, something that was not now is. These features belong to the concept of a happening itself. But causality is different. A cause is not the change itself but something prior that determines the change according to a rule. This determining ground is not part of the concept of “something happening”; it is a distinct concept.

And yet, we judge the principle “Everything that happens has its cause” to be universal and necessary, which means it is a priori. Experience alone cannot justify such necessity or universality, since experience tells us only what has happened, not what must happen. For that reason, this synthetic judgment cannot be a posteriori. It adds a new predicate (“has a cause”) to a concept that does not contain it, but it does so independently of experience. Hence it is a synthetic a priori judgment.

Kant asks two important questions:

How then do I come to say something quite different about that which happens in general, and to cognize the concept of cause as belonging to it, indeed necessarily, even though not contained in it?

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?

Essentially, Kant asks what allows us to add a new predicate — such as “has a cause” — to a subject where that predicate is not contained, as in the concept “something happens,” and yet judge this addition as necessarily true without relying on experience. What enables such synthetic a priori judgments? Kant refers to this enabling ground as the “unknown = X.” He considers this problem to be of the greatest importance, because our most fundamental forms of knowledge — especially those found in mathematics, physics, and metaphysics — depend on synthetic a priori principles. The remainder of the Critique of Pure Reason is devoted to uncovering and explaining what this “X” is that makes synthetic a priori judgments possible at all.

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

Kant splits Section V into three different parts which will be labeled accordingly:

1. “Mathematical judgments are all synthetic.”

This proposition seems to have escaped the notice o f 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.

Prior to Kant, many philosophers believed that mathematics was rooted in analytic judgments — truths that follow simply from analyzing concepts. In other words, they thought mathematical propositions were true by definition. However, Kant argues that mathematics actually adds something to a concept and is therefore synthetic (what he terms “pure mathematics”). He explains why previous philosophers came to the conclusion that mathematics was an analytic judgment:

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

There are three main reasons Kant identifies for why earlier philosophers believed mathematical judgments were analytic. First, mathematics appears to rest on the principle of contradiction, the rule that a proposition and its negation cannot both be true at the same time (e.g., “A is A” cannot coexist with “A is not A”). Second, mathematical propositions appear to be apodictic: they possess absolute certainty. Third, mathematics proceeds entirely through strict deduction — proofs unfold with logical rigor in a progression of steps. Many philosophers took these three features as proof that mathematical judgments must be analytic.

However, Kant does find mathematics to exist as a priori judgments:

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.

Mathematical propositions are not empirical because they must be universally true and carry necessity — something experience can never provide. One might argue that we learn a truth like 2 + 2 = 4 by observing cases in the world, such as placing two red marbles next to two blue marbles and seeing that they make four. Experience can show only that these marbles happen to add up this way in this instance. It can never guarantee that 2 + 2 must always equal 4 in all possible cases, under all conditions, without exception. Thus the truth of mathematical judgments must be a priori.

Kant continues by giving the example of another math problem:

To be sure, one might initially think that the proposition “7 +5 = 12” 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 al thought what this single number is which comprehends the two of them.

Kant acknowledges that many people initially take arithmetic to be an analytic judgment. For example, the proposition “7 + 5 = 12” seems to suggest that twelve is already contained in the concept of “the sum of seven and five,” in the same way that “unmarried” is contained in the concept of “bachelor.” But Kant rejects this assumption. He argues that “the sum of 7 and 5 contains nothing more than the unification of both numbers in a single one,” meaning that the concept of the sum presupposes the combination of seven and five but does not yield the specific number twelve. The concept tells us that the two numbers are unified, but not what that unified number is.

To get the number twelve from “7+5,” Kant writes:

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.

Thus, mathematical propositions are a priori, since they possess universality and necessity — features that do not arise from experience. However, they are not analytic, because nothing in the concept “7 + 5” inherently contains the number twelve. The concept expresses only the idea of unifying seven and five, not what that unified number is. To arrive at twelve, we must go beyond the mere concept and employ intuition, constructing the sum through a temporal or spatial representation (e.g., counting one’s fingers). For this reason, mathematical judgments are synthetic a priori: they extend knowledge while still being known independently of experience:

The arithmetical proposition is therefore always synthetic…

Kant continues to discuss geometry:

Just as little is any principle of pure geometry analytic.

That the straight line between two points is the shortest is a synthetic proposition.

Again, many philosophers before Kant would have taken the proposition that “the straight line between two points is the shortest” to be an analytic judgment. Kant disagrees. The concept of a straight line tells us only how the line is drawn — namely, that it is free of curvature — but it tells us nothing about the quantity or length of the line. Thus the predicate “is the shortest” is not contained within the concept of a straight line and cannot be obtained by conceptual analysis. For this reason, the judgment cannot be analytic. As Kant writes:

Help must here be gotten from intuition, by means of which alone the synthesis is possible.

Furthermore:

To be sure, a few principles that the geometers presuppose are actually 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.

Here, Kant acknowledges that certain geometric propositions appear to be analytic. For example, the statement “a = a” is analytic in the strictest sense, since the predicate is contained within the subject. The same is true for a proposition like “(a + b) > a.” Yet Kant emphasizes that these are not genuine principles of geometry but rather logical rules that help mathematicians structure geometric proofs. Kant states:

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.

Mathematics, in Kant’s framework, requires construction in intuition. Kant notes that it is easy to mistakenly take synthetic judgments to be analytic ones. The example of the straight line between two points being the shortest illustrates this. In doing geometry, we often speak as though certain predicates naturally attach to concepts or belong to them inherently. But a distinction must be made. Although the predicate does belong to the concept necessarily, this is not because it is contained in the concept itself. Rather, the necessity arises only once an intuition. Intuition provides the connection that conceptual analysis alone cannot supply.

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

Next, Kant turns to the natural sciences (what he calls “physica”) as further proof of synthetic a priori judgments. Mathematics is not the only medium by which this proof is shown; physics also requires them. Kant uses two examples here:

1. The law of conservation of matter: “… In all alterations of the corporeal world the quantity of matter remains unaltered …”
2. Newton’s Third Law: “… In all communication of motion effect and counter-effect must always be equal.”

Both of these examples are synthetic a priori. They are not derived from experience, since no finite number of observations can ever prove such strict necessity; and they are not analytic, because their predicates are not already contained within their subjects. Kant clarifies this by detailing the concept of matter. Normally, when we discuss matter, we think of the filling of space, extension, and so on. But the notion of persistence or conservation of quantity is not something already contained in the concept of matter. The concept of matter alone does not tell us that, in every alteration, the quantity of matter must remain the same. Yet we nevertheless find this conservation to hold necessarily and universally, which means the principle is a priori rather than empirical.

The same goes for Newton’s Third Law. The concept of an object in motion, by itself, does not tell us that there must always be an equal and opposite reaction. That connection is not analytic; it adds something new to the concept of motion. And yet we take this law to be universally and necessarily true for all possible cases. Thus, like mathematics, the pure part of natural science rests on synthetic a priori principles.

3. “In metaphysics..”

Finally, Kant turns to metaphysics as another domain in which synthetic a priori judgments operate. Metaphysics does not simply analyze a priori concepts and clarify them analytically. Instead, Kant explains that metaphysics attempts to “amplify our cognition a priori,” meaning that it must add something to concepts that is not already contained within them. He notes that the scope of metaphysics is so expansive that “experience itself cannot follow us that far.”

Kant illustrates this with a straightforward example:

“The world must have a first beginning…”

This judgment cannot be derived from experience, since no one can ever experience the totality of the world or witness its origin. Yet it is also not analytic, because the concept of a first beginning is not contained within the concept of the world itself. The judgment adds something new while claiming necessity, and therefore qualifies as synthetic a priori. For this reason, Kant concludes that the aim of metaphysics is composed entirely of synthetic a priori judgments (judgments that extend beyond experience while still claiming universal and necessary validity).

VI. The general problem of pure reason.

Kant continues to explain the problem at hand:

The real problem of pure reason is now contained in the question: How are synthetic judgments a priori possible?

Once again, Kant’s emphasis on this question highlights its importance — it is the inquiry that structures the entire text. He writes:

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.

There has been no solution to this problem. Kant continues by discussing David Hume, noting that Hume is “among all philosophers [who] came closest to this problem,” yet ultimately fell short by “believing himself to have brought out that such an a priori proposition is entirely impossible.” This conclusion, Kant argues, is “destructive of all pure philosophy.” Had Hume possessed the distinction between analytic and synthetic judgments — along with the insight that “pure mathematics” itself contains synthetic a priori principles — he would not have drawn an illegitimate conclusion.

Kant explains that the central problem — How are synthetic a priori judgments possible? — is necessary for understanding the foundations of all human knowledge. If we can solve this problem, then we can determine how the pure use of reason is possible in any science that claims to know objects a priori. This allows us to answer two major questions:

1. How is pure mathematics possible?
2. How is pure natural science possible?

For mathematics and physics, these questions are legitimate because these sciences already exist; their actuality proves their possibility. The fact that they generate necessary and universal truths shows that a priori cognition is already operative within them. Kant’s task, then, is to uncover the transcendental conditions that make these sciences possible in the first place.

Metaphysics, on the other hand, is more complex. Because metaphysics has not produced necessary and universal truths — at least not with the kind of stable progress seen in mathematics and physics — we have legitimate reason to doubt whether metaphysics exists as a genuine science at all. Only by solving the problem of synthetic a priori judgments can we determine whether metaphysics is possible, or whether it is merely an illusion.

Kant adds an important detail to his analysis of metaphysics: even if metaphysics cannot yet be described as a genuine science, it nevertheless exists as a “natural predisposition.” Human reason is naturally inclined to ask metaphysical questions, and this speculative tendency is an essential part of what it means to be human. It will persist as long as reason persists. This leads Kant to ask:

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?

Put simply: why does human reason generate these metaphysical questions in the first place? At any rate, the thoughts, ideas, and arguments that come from our metaphysical inclination have produced all kinds of contradictions. Kant’s provides an example: reason can argue both that the world must have a beginning and that the world must exist from eternity. The same faculty yields opposing conclusions. Because of this, we cannot rely on metaphysical inclination as a basis for truth. So Kant insists that the real issue now is whether reason can answer these questions at all. This leads to two different possibilities:

1. Reason is capable of knowing its objects (the world, God, the soul, etc.), in which case metaphysics could be placed on a secure scientific foundation.
2. Reason is incapable of such knowledge, meaning we must establish clear and determinate limits for its use.

Whether metaphysical knowledge is possible at all depends entirely on the capabilities of reason. Kant continues by asking a new-found question:

This last question, which flows from the general problem above, would rightly be this: How is metaphysics possible as science?

Kant notes that the critique of reason “leads necessarily to science.” Only by subjecting reason to rigorous critique are we able to establish metaphysics as a genuine science. If reason is left unexamined, the only thing that would result is a relentless dogmatism, where “groundless assertions” are left unexamined. To clarify his project, Kant explains that his critique or pure reason is not an infinitely long project where it is necessary to examine every object that reason might think about or consider. Instead, his critique of reason analyzes the problem “entirely from its own womb.”

To conclude this section, Kant argues that all previous attempts at dogmatic metaphysics must be rejected. None of the older metaphysical systems succeeded in expanding synthetic a priori cognition, and yet each still claimed authority over the subject while remaining thoroughly dogmatic. Kant calls instead for a renewed philosophical approach — one that recognizes the difficulty of the task and seeks to cultivate metaphysics as a genuine science, rather than leaving it to grow unchecked and contradictory.

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

In this final section, Kant explains the direction of his project moving forward:

Now from all of this there results the idea of a special science, which can be called the critique of pure reason.

The science that he posits is the critique of pure reason. As explained earlier, understanding pure reason — and recognizing its potential limitations — allows us to examine and study metaphysics, rather than through the dogmatic systems that have previously led to contradiction and confusion. He writes:

For reason is the faculty that provides the principles of cognition a priori.

Hence pure reason is that which contains the principles’ for cognizing something absolutely a priori.

Here, Kant explains the distinction between reason and pure reason. Reason is the general faculty that supplies a priori principles — the basic rules or laws that structure how we can know things prior to experience (i.e., humans are born into reason). Because reason is defined this way, pure reason refers to the set of these principles themselves, the ones that allow us to cognize something entirely a priori. Pure reason is the source of the non-empirical conditions that make experience possible.

Kant continues:

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.

Here, Kant explains an essential term of his philosophy and its importance: transcendental. Transcendental cognition is not concerned with objects themselves, but with the manner in which objects are known — specifically, the a priori conditions that make such knowledge possible at all. In other words, transcendental inquiry examines the structures of the mind that must already be in place before any experience of objects can occur. He continues to describe his critique of pure reason:

Such a critique is accordingly a preparation, if possible, for an organon, and, if this cannot be accomplished, then at least for a canon…

This critique is understood as a “preparation,” one that would ideally allow us to establish an organon — a complete set of rules — that would make it possible to examine metaphysics as a genuine and fully developed science. If this cannot be accomplished, then at the least, we can establish the boundaries by which metaphysics becomes illegitimate (a canon).

To put his critique simply, Kant writes:

… our object is not the nature of things, which is inexhaustible, but the understanding, which judges about the nature of things…

Kant continues by explaining what constitutes transcendental philosophy:

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 certainty of all the components that comprise this edifice.

It is the system of all principles of pure reason.

Transcendental philosophy is the idea of a rigorous and complete science — one that would systematically lay out every principle of pure reason. This critique of pure reason serves as the architectural blueprint for this science: it sketches the overall structure according to principles so that the proper foundation for a genuine system of pure reason can be established.

Furthermore:

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 principles of synthesis, and if nothing is lacking in them in regard to this essential aim.

Kant adds that although this project may seem daunting, it becomes relatively straightforward once the fundamental principles have been established. Filling in the later details is nowhere near as difficult as securing the necessary a priori principles of pure reason themselves. To ensure that these principles remain accurate, Kant is clear in how he seeks to approach this task:

The chief target in the division of such a science is that absolutely no concept must enter into it that contains anything empirical…

… although the supreme principles of morality and the fundamental concepts of it are a priori cognitions, they still do not belong in transcendental philosophy …

Kant makes two points clear. First, no empirical content can enter this domain, since transcendental philosophy deals exclusively with a priori cognition. Second, even though the principles of morality are themselves a priori, morality cannot be included within transcendental philosophy. This is because moral concepts inevitably involve empirical elements. Motivation, intention, pleasure, and displeasure, etc. all rely on empirical observations and studies. Morality, instead, belongs to the domain of practical reason.

To conclude the introduction, Kant explains:

Now if one wants to set up the division of this science from the general 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.

… 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.

Transcendental philosophy can be divided into two major parts:

1. Doctrine of Elements — the basic components of pure reason; a priori structures

2. Doctrine of Method — how components of pure reason are used systematically.

Interestingly, Kant finishes the Introduction by emphasizing that human cognition has two distinct stems — which potentially arise from a common but unknown root. These two stems are sensibility and understanding. Through sensibility, objects are given to the mind; through understanding, objects are thought. Sensibility provides intuitions, while understanding provides concepts.

What makes the Critique of Pure Reason so remarkable is that the structure of the book mirrors the structure of human cognition itself. An object must first be given before it can be thought. For that reason, the Critique begins with the Transcendental Aesthetic, which investigates sensibility and its pure intuitions — space and time — before turning to the Transcendental Analytic, which examines the understanding and its pure concepts, where Kant will discuss the categories of the mind in detail.

Conclusion

Kant is one of the most well-known philosophers in history, and that reputation is unlikely to fade. His work is bold — he famously claims to be offering a Copernican Revolution in philosophy — and his solution to the rationalism versus empiricism debate remains one of the most influential philosophical developments of the modern era. While Kant has his critics and rivals, there is no doubt that the Critique of Pure Reason stands as one of philosophy’s most important and enduring texts.

(After all… you Kant go wrong with Kant!)