Kant does not argue for the rationalist position that all knowledge is produced by reason, nor does he argue for the empiricist position that all knowledge is produced by experience. He agrees with the empiricist position that all knowledge begins with experience and that there cannot be any innate ideas in the mind prior to experience, but he does not agree that this position supports the claim that experience must be the only source of all knowledge. Instead, he explains why reason and experience may be combined to produce valid knowledge.

The Critique of Pure Reason is divided into three main sections: "Introduction," "Transcendental Doctrine of Elements," and "Transcendental Doctrine of Method." In the Introduction, Kant discusses the difference between pure and empirical knowledge, and the difference between analytic and synthetic judgments. He also explains the need for a new science (which he calls a "critique of pure reason") in order to determine the possibility, principles, and extent of a priori knowledge.

In the transcendental doctrine of elements, Kant discusses the transcendental aesthetic (of space and time), the transcendental analytic, and the transcendental dialectic. The transcendental analytic includes the analytic of concepts and the analytic of principles. The transcendental dialectic is the logic of pure reason, which may produce transcendental judgments (concerning objects beyond the limits of possible experience). According to Kant, the transcendental dialectic includes three kinds of dialectical arguments: (1) paralogisms, (2) antinomies, and (3) ideals. Each of these dialectical arguments reveals that irresolvable conflicts may be created when principles of pure understanding are applied beyond the sphere of possible experience. Thus, the transcendental dialectic demonstrates that misuses of reason may lead to philosophical error.

In the transcendental doctrine of method, Kant discusses the discipline, canon, architectonic, and history of pure reason.

Kant distinguishes between a priori knowledge (which is based on reason) and a posteriori knowledge (which is based on experience). A priori knowledge may be pure (if it has no empirical element) or impure (if it has an empirical element). A priori truths are logically necessary truths, while a posteriori truths are empirical, conditional truths. A priori judgments are characterized by logical necessity and by strict universality, but a posteriori judgments are not characterized by logical necessity or by absolute universality.

Analytic judgments are also to be distinguished from synthetic judgments. An affirmative analytic judgment is one in which a predicate is affirmed to belong to a subject, and in which the predicate is contained by, or belongs intrinsically to, the concept of the subject. An affirmative synthetic judgment is one in which a predicate is affirmed to belong to a subject, and in which the predicate does not belong intrinsically to the concept of the subject. Analytic judgments may explain a subject, or may analyze it into its predicates, but do not add to the subject any predicates that are not already contained within the concept of the subject. Synthetic judgments, on the other hand, may augment a subject by adding new predicates to the concept of the subject.

According to Kant, all analytic judgments are a priori. Synthetic judgments may be a posteriori or a priori. A priori judgments may be analytic or synthetic. A posteriori judgments are always synthetic. According to Kant, synthetic a priori truths include the truths of mathematics and the truths of natural science (physics). All mathematical judgments are synthetic, and all proper mathematical judgments are a priori.

In order to explain how synthetic a priori judgments are possible, Kant discusses the nature of time and space. He explains that space is a necessary, a priori representation that provides the foundation for all external intuitions.¹ Space does not represent a property of things as they are in themselves. Furthermore, time is a necessary, a priori representation that provides the foundation for all internal intuitions. Time does not belong to things as they are in themselves. Space and time are pure (a priori) intuitions, and they are subjective conditions of the sensibility that establish a foundation for all other intuitions.

Knowledge may arise from two main sources: the sensibility and the understanding. The sensibility is the faculty of receiving impressions, while the understanding is the faculty of producing representations. Sensibility produces intuitions, and understanding produces concepts. Thus, intuitions and concepts are elements of all cognitions, and they are elements of all a priori and a posteriori knowledge.² Intuitions and concepts may be a priori or a posteriori. A priori concepts are pure concepts of the understanding, while a posteriori concepts are derived from sensory intuitions.

While the transcendental aesthetic is the science of the laws of sensibility, transcendental logic is the science of the laws of the understanding.³ Transcendental logic may be divided into transcendental analytic and transcendental dialectic.

Transcendental analytic may be divided into the analytic of concepts and the analytic of principles. In order to schematically illustrate the analytic of concepts, Kant provides a table of the logical function of the understanding in judgments, in which judgments are grouped according to their (I) quantity (universal, particular, singular), (II) quality (affirmative, negative, infinite), (III) relation (categorical, hypothetical, disjunctive), and (IV) modality (problematic, assertoric, apodictic).⁴

The analytic of concepts may also be schematically illustrated by a table of the categories, which provides a catalogue of twelve pure (a priori) concepts of the understanding. The table of the categories shows that pure concepts of the understanding may de divided into four groups: (I) of quantity (unity, plurality, totality), (II) of quality (reality, negation, limitation), (III) of relation (of inherence and subsistence, of causality and dependence, of community), and (IV) of modality (possibility or impossibility, existence or nonexistence, necessity or contingency).⁵

The categories (or pure concepts of the understanding) are a priori concepts that define conditions of possible experience. The categories also define conditions under which the manifold content of intuitions and representations may be unified by the understanding.

Knowledge may be attained by the combined operation of the sensibility and the understanding. Sensibility produces intuitions that may be the source of empirical concepts. Imagination may also provide representations of objects if these objects are not present for intuition. Synthesis of intuitions and concepts is an act of the understanding.

Understanding may unite manifold intuitions and representations. The synthetic unity of intuitions and representations is necessary a priori for the understanding. The understanding produces a unity that cannot be attained merely by the faculty of intuition.

Apperception is an act of self-consciousness that may accompany any act of representation. Apperception may also unite the manifold content of intuitions. The synthetic unity of apperception may thus connect many intuitions and representations within a single consciousness.

Apperception may be pure (a priori) or empirical (a posteriori). It may have an analytic or synthetic unity. It may have an originally synthetic unity, and thus its synthetic unity may be a condition for its analytic unity. It may also have a subjective (empirical) unity and an objective (transcendental) unity.

Every cognition consists of two elements: (1) an intuition, and (2) a concept. A concept is given its object by an intuition. Every concept of an object is based on a corresponding intuition of that object. A concept that has no object is a thought, but it is not an element of cognition. Cognition is made possible by the combined operation of intuition and conceptual thought.

All intuitions are sensory, according to Kant. Sensory intuition may be empirical or non-empirical. Space and time are pure intuitions that are non-empirical, because they do not correspond to objects of experience. Space and time are thus a priori intuitions that establish conditions for possible experience.

Faculties of cognition include: intuition, understanding, judgment, and reason.⁶ Intuition may be classified as a lower faculty of cognition, while understanding, judgment, and reason may be classified as higher faculties of cognition. Intuition is the faculty of receiving impressions. Understanding is the faculty of producing rules or concepts. Judgment is the faculty of determining whether a rule or concept is subsumed under other rules or concepts. Reason is the faculty that produces principles, and it may be regarded as the highest faculty of cognition.

The analytic of principles may be schematically represented by a table of principles of the pure understanding, according to which all principles may be classified as axioms of intuition, as anticipations of perception, as analogies of experience, or as postulates of empirical thought. These four categories of principles may be further classified according to their form, since the first two categories are mathematical, while the second two categories are dynamic.⁷ The mathematical principles of the understanding are constitutive principles of intuition, while the dynamic principles of the understanding are regulative principles of intuition.⁸

Each of the categories in the table of principles represents a principle of the application of the pure understanding. The principle of axioms of intuition is that all intuitions have a quantity (or degree) of extensity. The principle of anticipations of perception is that the reality of phenomena has a quantity (or degree) of intensity. The principle of analogies of experience is that experience is a synthetic unity of perceptions. The principle of the postulates of empirical thought is that there are formal, material, and universal conditions of experience.

All a priori cognitions are given their objective reality by their possibility of experience. All a posteriori cognitions are given their objective reality by objects of experience.

Kant divides objects of cognition into phenomena and noumena. Phenomena are objects of possible experience, but noumena are not objects of possible experience. Noumena do not have any objective reality. The concept of a noumenon is problematic, since a noumenon is not an object of sensory intuition. Thus, the existence of noumena can be neither affirmed nor denied by the sensibility or the understanding.

The transcendental dialectic is the logic of the relation between sensibility and understanding. Kant explains how philosophical error may be caused by the unobserved influence of the sensibility on the understanding. He also tells us how the subjective basis of a judgment may be confused with the objective basis of a judgment. He also explains how philosophical error may occur when regulative principles of the understanding are confused with constitutive principles of the understanding.

Representations and concepts may be pure (a priori) or empirical (a posteriori). An "idea" may be defined as a pure concept that transcends the possibility of experience. An idea of pure reason transcends any empirical object, says Kant. Thus, an idea of pure reason may also be described as a transcendental idea.

Philosophical error may occur if we attempt to apply the principles of understanding to objects that are beyond the limits of possible experience. Thus, immanent principles (which may be applied only within the limits of possible experience) must be distinguished from transcendent principles (which may be applied beyond the limits of possible experience). The principles of the pure understanding are immanent, and they are not transcendent. They are not applicable to objects that are beyond the limits of possible experience. Thus, Kant also distinguishes between transcendental and transcendent principles by explaining that principles of pure understanding may be transcendental in their mode of a priori cognition or transcendent in their application beyond the limits of possible experience.

Kant describes three kinds of sophistical arguments for the validity of transcendental ideas: (1) paralogisms of pure reason, (2) antinomies of pure reason, and (3) ideals of pure reason. The paralogisms of pure reason assert that, given the manifold nature of the thinking subject, there is an absolute (unconditioned) unity of the thinking subject. The antinomies of pure reason propose that, given the totality of conditions for a particular phenomenon, there is an absolute unity of the conditions for that phenomenon. The ideals of pure reason propose that, given the totality of conditions for all objects of thought, there is an absolute (unconditioned) unity of all objects of thought.

Kant also presents a table of four cosmological ideas that categorize the conditions of possibility of phenomena. The four cosmological ideas are of (I) the absolute completeness of the composition of all phenomena, (II) the absolute completeness of the division of a given totality in a phenomenon, (III) the absolute completeness of the origin of a phenomenon, and (IV) the absolute completeness of the dependent existence of whatever is changeable in a phenomenon.⁹

According to Kant, transcendental idealism can provide a solution to the cosmological problem of whether all phenomena in space and time are conditioned by our perceptions of them. Transcendental idealism affirms that the world is real insofar as it is an object of possible experience, and it also affirms that the reality of the world cannot be separated from the world’s existence as an object of mind. Realism, on the other hand, affirms that the world is real independently of whether it is an object of possible experience, and it affirms that the reality of the world does not depend on whether the world is an object of mind.

Transcendental ideas include concepts of the soul, concepts of ultimate reality, and concepts of God. Psychology (the study of the soul), cosmology (the study of ultimate reality), and theology (the study of God) are thus concerned with the ideals of pure reason. The nature and existence of these ideals cannot be proved empirically, because they transcend empirical cognition. No empirical concept of these ideals of pure reason can adequately represent them. Thus, any concept of the soul or of ultimate reality is problematic, since an empirical concept cannot adequately represent an idea of pure reason.

Transcendental ideas (pure concepts of reason) may also be regulative principles for the understanding. They are not constitutive principles of the empirical world, because they are not based on empirical cognition. Indeed, philosophical error may occur when regulative principles of the understanding are confused with constitutive principles of the understanding. However, although transcendental ideas are not ideas of empirical objects, they may still be applied to the empirical world, and they may guide the understanding. Thus, pure reason may act as a regulative principle to guide the production of representations and concepts.

¹ Immanuel Kant, Critique of Pure Reason, translated by J.M.D. Meiklejohn (Amherst: Prometheus Books, 1990), p. 24.
²Ibid., p. 44.
³Ibid., p. 45.
⁴Ibid., p. 56.
⁵Ibid., p. 62.
⁶Ibid., p. 97.
⁷Ibid., p. 114.
⁸Ibid., p. 360.
⁹Ibid., pp. 235-6.

Kant, Immanuel. Critique of Pure Reason. Translated by J.M.D. Meiklejohn. Amherst: Prometheus Books, 1990.