Immanuel Kant’s Critique of Pure Reason (1781) is an examination of the sources of human knowledge, and of the relation of a priori knowledge to empirical knowledge. Kant explains how a priori knowledge can be provided by pure reason, and how reason and experience can be combined to produce valid principles of human knowledge and understanding.

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 how reason and experience may be combined to produce valid knowledge.

Kant’s 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, the difference between analytic and synthetic judgments, and the need for a new science (which he calls the Critique of Pure Reason) 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 of 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).

The Transcendental Dialectic includes three kinds of dialectical arguments: paralogisms, antinomies, and ideals. These dialectical arguments reveal 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 the misuse of reason can lead to philosophical error.

Finally, 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, contingent truths. A priori judgments are characterized by logical necessity and by strict universality. A posteriori judgements are not characterized by logical necessity or by absolute universality.

Kant distinguishes between analytic and 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 which 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 either 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 mathematic judgments are synthetic, and all proper mathematic judgments are a priori.

To explain how synthetic a priori judgments are possible, Kant examines the nature of time and space. Kant explains that space is a necessary, a priori representation which 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 which 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 are subjective conditions of the sensibility which establish a foundation for all other intuitions.

Kant says that knowledge arises from two main sources: the sensibility and the understanding. The sensibility is the faculty of receiving impressions, and the understanding is the faculty of producing representations. Sensibility produces intuitions, and understanding produces concepts. Thus, intuitions and concepts are elements of all forms of knowledge.² Intuitions and concepts may be either a priori or a posteriori. A priori concepts are pure concepts of the understanding. 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. The Analytic of Concepts is represented by a table of the logical function of the understanding in judgments, according to which judgments may be grouped by their I) Quantity (Universal, Particular, Singular), II) Quality (Affirmative, Negative, Infinite), III) Relation (Categorical, Hypothetical, Disjunctive), or IV) Modality (Problematic, Assertoric, Apodictic).⁴

The Analytic of Concepts is also represented by a Table of the Categories, which is 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 Non-Existence, Necessity or Contingency).⁵

The categories are a priori concepts which define conditions of possible experience. The categories also define conditions under which the manifold content of intuitions and representations can be unified by the understanding.

Knowledge is attained by the combined operation of the sensibility and the understanding. Sensibility produces intuitions which are the source of empirical concepts. Imagination may also provide a representation of an object when the object is not present in intuition. Synthesis of intuitions and concepts is an act of the understanding.

Understanding may unite manifold intuitions and representations. According to Kant, the synthetic unity of intuitions and representations is possible and necessary a priori for the understanding. The understanding produces a unity which cannot be attained merely by the faculty of intuition.

Apperception is an act of self-consciousness which 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 may be empirical (a posteriori). Apperception may have an analytic unity or a synthetic unity. According to Kant, apperception has an originally synthetic unity, and thus its synthetic unity is a condition for its analytic unity. Apperception may also have a subjective (empirical) unity, or an objective (transcendental) unity.

Kant explains that every cognition consists of two elements: an intuition and 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 which has no object is a thought, but is not an element of cognition. Cognition is made possible by the combined operation of intuition and conceptual thought.

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

Faculties of cognition include: intuition, understanding, judgment, and reason.⁶ Intuition is classified as a lower faculty of cognition, while understanding, judgment, and reason are 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 highest faculty of cognition, and is the faculty which produces principles.

The Analytic of Principles is represented by a table of principles of the pure understanding, according to which all principles may be classified as either: I) Axioms of Intuition, II) Anticipations of Perception, III) Analogies of Experience, or IV) Postulates of Empirical Thought. Kant says that these four categories of principles may be further classified according to their form, since the first two categories are mathematic, while the second two categories are dynamic.⁷ The mathematic 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.

Kant argues that 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. 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 by 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. Kant also explains 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 either pure (a priori) or empirical (a posteriori). A pure concept which transcends the possibility of experience is referred to by Kant as an "idea." An idea of pure reason transcends any empirical object. Thus, an idea of pure reason may also be defined as a transcendental idea.

Kant argues that philosophical error may by caused by attempting to apply the principles of understanding to objects which are beyond the limits of possible experience. Thus, he distinguishes between immanent principles (which are within the limits of possible experience), and transcendent principles (which may be applied beyond the limits of possible experience). He also distinguishes between transcendental and transcendent principles, by saying that principles of pure understanding may be transcendental in their mode of a priori cognition or may be 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 propose 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 presents a table of four cosmological ideas, which categorize the conditions of possibility of phenomena. The four 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 what is changeable in a phenomenon.⁹

Kant says that Transcendental Idealism is a key to a solution of the cosmological problem as to whether all phenomena in space and time are conditioned by our perceptions of them. According to Kant, Transcendental Idealism is a philosophy that the world is real insofar as it is an object of possible experience, and that therefore the reality of the world cannot be separated from the world’s existence as an object of mind. Realism, on the other hand, asserts that the world has an independent reality, and that the reality of the world does not depend on whether the world is an object of mind.

Transcendental ideas, according to Kant, include ideas of the soul, of ultimate reality, and 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, says Kant, cannot be proved empirically, because they transcend empirical cognition. No empirical concept of these ideals of pure reason can adequately represent them. Any concept of ultimate reality, or of God, is problematic, since an empirical concept cannot adequately represent an idea of pure reason.

Transcendental ideas may also be regulative principles for the understanding. Transcendental ideas, according to Kant, are not constitutive principles of the empirical world, because they are not based on empirical cognition. Transcendental ideas are pure concepts of reason. Kant explains that philosophical error may occur when regulative principles of the understanding are confused with constitutive principles of the understanding. Transcendental ideas are not ideas of empirical objects, but they may be applied to the empirical world to guide the understanding. Thus, they are regulative rather than constitutive ideas. Pure reason is a regulative principle, which acts to unify the empirical concepts of the understanding.

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.