The Online Library of Liberty

A project of Liberty Fund, Inc.

• Dedication
• Preface 1
• Translator’s Preface
• Translator’s Preface to Second Edition
• Introduction [p. 1]
• I: The Idea of Transcendental Philosophy
• II: Division of Transcendental Philosophy
• I: The Elements of Transcendentalism
• Part I: Transcendental Æsthetic [p. 19]
• Section I: Of Space
• Section II: Of Time
• Part II: Transcendental Logic [p. 50]
• Introduction the Idea of a Transcendental Logic
• I: Of Logic In General
• II: Of Transcendental Logic
• III: Of the Division of General Logic Into Analytic and Dialectic
• IV: Of the Division of Transcendental Logic Into Transcendental Analytic and Dialectic
• Division I: Transcendental Analytic In Two Books, With Their Chapters and Sections
• Book I: Analytic of Concepts
• Chapter I: Method of Discovering All Pure Concepts of the Understanding
• Section I: Of the Logical Use of the Understanding In General
• Section II: Of the Logical Function of the Understanding In Judgments [p. 70]
• Section III: Of the Pure Concepts of the Understanding, Or of the Categories
• Chapter II: Of the Deduction of the Pure Concepts of the Understanding [p. 84]
• Section I: Of the Principles of a Transcendental Deduction In General
• Section II: Of the a Priori Grounds For the Possibility of Experience
• I: Of the Synthesis of Apprehension In Intuition
• II: Of the Synthesis of Reproduction In Imagination
• III: Of the Synthesis of Recognition In Concepts [p. 103]
• IV: Preliminary Explanation of the Possibility of the Categories As Knowledge a Priori
• Section III: Of the Relation of the Understanding to Objects In General, and the Possibility of Knowing Them a Priori [p. 115]
• Book II: Analytic of Principles
• Introduction of the Transcendental Faculty of Judgment In General
• Chapter I: Of the Schematism of the Pure Concepts of the Understanding [p. 137]
• Chapter II: System of All Principles of the Pure Understanding [p. 148]
• Section I: Of the Highest Principle of All Analytical Judgments
• Section II: Of the Highest Principle of All Synthetical Judgments [p. 154]
• Section III: Systematical Representation of All Synthetical Principles of the Understanding
• I: [of the Axioms of Intuition 1 Principle of the Pure Understanding
• II: [ Anticipations of Perception
• III: [ the Analogies of Experience
• IV: The Postulates of Empirical Thought In General
• Chapter III: On the Ground of Distinction of All Subjects Into Phenomena and Noumena
• I.: Identity and Difference
• II.: Agreement and Opposition
• III.: The Internal and the External
• IV.: Matter and Form
• Note On the Amphiboly of Reflective Concepts
• Division II: Transcendental Dialectic In Two Books, With Their Chapters and Sections [p. 293]
• Introduction: 1.
• Book I: Of the Concepts of Pure Reason [p. 310]
• First Section of Ideas In General
• Second Section of Transcendental Ideas [p. 321]
• Third Section System of Transcendental Ideas [p. 333]
• Book II: Of the Dialectical Conclusions of Pure Reason
• Chapter I: Of the Paralogisms of Pure Reason [p. 341]
• Chapter II: The Antinomy of Pure Reason
• Section I: System of Cosmological Ideas
• Section II: Antithetic of Pure Reason
• Section III: Of the Interest of Reason In These Conflicts [p. 462]
• Section IV: Of the Transcendental Problems of Pure Reason, and the Absolute Necessity of Their Solution
• Section V: Sceptical Representation of the Cosmological Questions In the Four Transcendental Ideas [p. 485]
• Section VI: Transcendental Idealism As the Key to the Solution of Cosmological Dialectic
• Section VII: Critical Decision of the Cosmological Conflict of Reason With Itself
• Section VIII: The Regulative Principle of Pure Reason With Regard to the Cosmological Ideas [p. 508]
• Section IX: Of the Empirical Use of the Regulative Principle of Reason With Regard to All Cosmological Ideas
• Chapter III: The Ideal of Pure Reason
• Section I: Of the Ideal In General
• Section II: Of the Transcendental Ideal ( Prototypon Transcendentale )
• Section III: Of the Arguments of Speculative Reason In Proof of the Existence of a Supreme Being
• Section IV: Of the Impossibility of an Ontological Proof of the Existence of God [p. 592]
• Section V: Of the Impossibility of a Cosmological Proof of the Existence of God [p. 603]
• Section VI: Of the Impossibility of the Physico-theological Proof
• Section VII: Criticism of All Theology Based On Speculative Principles of Reason [p. 631]
• Chapter I: The Discipline of Pure Reason
• Section I: The Discipline of Pure Reason In Its Dogmatical Use
• Section II: The Discipline of Pure Reason In Its Polemical Use
• Section III: The Discipline of Pure Reason With Regard to Hypotheses
• Section IV: The Discipline of Pure Reason With Regard to Its Proofs
• Chapter II: The Canon of Pure Reason [p. 795]
• First Section: of the Ultimate Aim of the Pure Use of Our Reason
• Section II: Of the Ideal of the Summum Bonum As Determining the Ultimate Aim of Pure Reason
• Section III: Of Trowing, Knowing, and Believing [p. 820]
• Chapter III: The Architectonic of Pure Reason [p. 832]
• Chapter IV: The History of Pure Reason [p. 852]
• Supplement I: Motto to Second Edition
• Supplement II: Preface to the Second Edition. 1787. [p. Vii]
• Supplement III: Supplement Iv
• Supplement V
• Supplement Vi
• Supplement V
• Supplement Vi
• Supplement Vii
• Supplement Viii
• Supplement Ix
• Supplement X
• Supplement Xi
• Supplement Xii
• Supplement Xiii
• Supplement Xiv
• Supplement Xv
• Supplement Xvi a
• Supplement Xvi B
• Supplement Xvii
• Supplement Xviii
• Supplement Xix
• Supplement Xx
• Supplement Xxi
• Supplement Xxii
• Supplement Xxiii
• Supplement Xxiv
• Supplement Xxv
• Supplement Xxvi
• Supplement Xxvii
• Supplement Xxviii

I

[OF THE AXIOMS OF INTUITION1

Principle of the Pure Understanding

I call an extensive quantity that in which the representation of the whole is rendered possible by the representation of its parts, and therefore necessarily preceded by it. I cannot represent to myself any line, however small it may be, without drawing it in thought, that is, without producing all its parts one after the other, starting [p. 163] from a given point, and thus, first of all, drawing its intuition. The same applies to every, even the smallest portion of time. I can only think in it the successive progress from one moment to another, thus producing in the end, by all portions of time and their addition, a definite quantity of time. As in all phenomena pure intuition is either space or time, every phenomenon, as an intuition, must be an extensive quantity, because it can be known in apprehension by a successive synthesis only (of part with part). All phenomena therefore, when perceived in intuition, are aggregates (collections) of previously given parts, which is not the case with every kind of quantities, but with those only which are represented to us and apprehended as extensive.

On this successive synthesis of productive imagination in elaborating figures are founded the mathematics of extension with their axioms (geometry), containing the conditions of sensuous intuition a priori, under which alone the schema of a pure concept of an external phenomenal appearance can be produced; for instance, between two points one straight line only is possible, or two straight lines cannot enclose a space, etc. These are the axioms which properly relate only to quantities (quanta) as such.

But with regard to quantity (quantitas), that is, with regard to the answer to the question, how large something may be, there are no axioms, in the proper [p. 164] sense of the word, though several of the propositions referring to it possess synthetical and immediate certainty (indemonstrabilia). The propositions that if equals be added to equals the wholes are equal, and if equals be taken from equals the remainders are equal, are really analytical, because I am conscious immediately of the identity of my producing the one quantity with my producing the other; axioms on the contrary must be synthetical propositions a priori. The self-evident propositions on numerical relation again are no doubt synthetical, but they are not general, like those of geometry, and therefore cannot be called axioms, but numerical formulas only. That 7+5=12 is not an analytical proposition. For neither in the representation of 7, nor in that of 5, nor in that of the combination of both, do I think the number 12. (That I am meant to think it in the addition of the two, is not the question here, for in every analytical proposition all depends on this, whether the predicate is really thought in the representation of the subject.) Although the proposition is synthetical, it is a singular proposition only. If in this case we consider only the synthesis of the homogeneous unities, then the synthesis can here take place in one way only, although afterwards the use of these numbers becomes general. If I say, a triangle can be constructed with three lines, two of which together are greater than the third, I have before me the mere function of productive imagination, which may draw the lines greater or smaller, and bring them together at various angles. The number 7, on the contrary, [p. 165] is possible in one way only, and so likewise the number 12, which is produced by the synthesis of the former with 5. Such propositions therefore must not be called axioms (for their number would be endless) but numerical formulas.

This transcendental principle of phenomenal mathematics adds considerably to our knowledge a priori. Through it alone it becomes possible to make pure mathematics in their full precision applicable to objects of experience, which without that principle would by no means be self-evident, nay, has actually provoked much contradiction. Phenomena are not things in themselves. Empirical intuition is possible only through pure intuition (of space and time), and whatever geometry says of the latter is valid without contradiction of the former. All evasions, as if objects of the senses should not conform to the rules of construction in space (for instance, to the rule of the infinite divisibility of lines or angles) must cease, for one would thus deny all objective validity to space and with it to all mathematics, and would no longer know why and how far mathematics can be applied to phenomena. The synthesis of spaces and times, as the synthesis of the essential form of all intuition, is that which renders possible at the same time the apprehension of phenomena, that is, every external [p. 166] experience, and therefore also all knowledge of its objects, and whatever mathematics, in their pure use prove of that synthesis is valid necessarily also of this knowledge. All objections to this are only the chicaneries of a falsely guided reason, which wrongly imagines that it can separate the objects of the senses from the formal conditions of our sensibility, and represents them, though they are phenomena only, as objects by themselves, given to the understanding. In this case, however, nothing could be known of them a priori, nothing could be known synthetically through pure concepts of space, and the science which determines those concepts, namely, geometry, would itself become impossible.

[1 ]Here follows, in the later Editions, Supplement XVI.