Second Book. Of the dialectical conclusions of pure reason
First Chapter. Of the Paralogisms of pure reason
General note on the transition from rational psychology to cosmology
Second Chapter. The Antinomy of pure reason
First Section. System of cosmological ideas
Second Section. Antithetic of pure reason
First Antinomy
Second Antinomy
Third Antinomy
Fourth Antinomy
Third Section. Of the interest of reason in these conflicts
Fourth Section. Of the transcendental problems of pure reason and the absolute necessity of their solution
Fifth Section. Sceptical representation of the cosmological questions in the four transcendental ideas
Sixth Section. Transcendental idealism as the key to the solution of cosmological Dialectic
Seventh Section. Critical decision of the cosmological conflict of reason with itself
Eighth Section. The regulative principle of pure reason with regard to the cosmological ideas
Ninth Section. Of the empirical use of the regulative principle of reason with regard to all cosmological ideas
I. Solution of the cosmological idea of the totality of the composition of phenomena of an universe
II. Solution of the cosmological idea of the totality of the division of a whole given in intuition
Concluding remarks on the solution of the transcendental mathematical ideas, and preliminary remarks for the solution of the transcendental dynamical ideas
III. Solution of the cosmological ideas of the totality of the derivation of cosmical events from their causes
Possibility of causality through freedom
Explanation of the cosmological idea of freedom in connection with the general necessity of nature
IV. Solution of the cosmological idea of the totality of the dependence of phenomena with regard to their existence in general
Concluding remarks on the whole antinomy of pure reason
Third Chapter. The ideal of pure reason
First Section. Of the ideal in general
Second Section. Of the transcendental ideal
Third Section. Of the arguments of speculative reason in proof of the existence of a Supreme Being
Fourth Section. Of the impossibility of an ontological proof of the existence of God
Fifth Section Of the impossibility of a cosmological proof of the existence of God
Discovery and explanation of the dialectical illusion in all transcendental proofs of the existence of a necessary Being
Sixth Section. Of the impossibility of the physico-theological proof.
Seventh Section. Criticism of all theology based on speculative principles of reason
Appendix to the transcendental Dialectic
Of the regulative use of the ideas of pure reason
Of the ultimate aim of the natural Dialectic of human reason
II. Transcendental Doctrine of Method
Introduction
First Chapter. The discipline of pure reason
First Section. The discipline of pure reason in its dogmatical use
Second Section. The discipline of pure reason in its polemical use
Of the impossibility of a sceptical satisfaction of pure reason in conflict with itself
Third Section. The discipline of pure reason with regard to the hypotheses
Fourth Section. The discipline of pure reason with regard to its proofs
Second Chapter. The canon of pure reason
First Section. Of the ultimate aim of the pure use of our reason
Second Section. Of the ideal of the Summum Bonum, as determining the ultimate aim of Pure Reason
Third Section. Of trowing, knowing, and believing
Third Chapter. The architectonic of pure reason
Fourth Chapter. The history of pure reason
Supplement IV
Introduction
I
Of the Difference between Pure and Empirical Knowledge
That all our knowledge begins with experience there can be no doubt. For how should the faculty of knowledge be called into activity, if not by objects which affect our senses, and which either produce representations by themselves, or rouse the activity of our understanding to compare, to connect, or to separate them; and thus to convert the raw material of our sensuous impressions into a knowledge of objects, which we call experience? In respect of time, therefore, no knowledge within us is antecedent to experience, but all knowledge begins with it.
But although all our knowledge begins with experience, it does not follow that it arises from experience. For it is quite possible that even our empirical experience is a compound of that which we receive through impressions, and of that which our own faculty of knowledge (incited only by sensuous impressions), supplies from itself, a supplement which we do not distinguish from that raw material, until long practice has roused our attention and rendered us capable of separating one from the other.
It is therefore a question which deserves at least closer investigation, and cannot be disposed of at first sight, whether there exists a knowledge independent of experience, and even of all impressions of the senses? Such knowledge is called a priori, and distinguished from empirical knowledge, which has its sources a posteriori, that is, in experience.
This term a priori, however, is not yet definite enough to indicate the full meaning of our question. For people are wont to say, even with regard to knowledge derived from experience, that we have it, or might have it, a priori, because we derive it from experience, not immediately, but from a general rule, which, however, has itself been derived from experience. Thus one would say of a person who undermines the foundations of his house, that he might have known a priori that it would tumble down, that is, that he need not wait for the experience of its really tumbling down. But still he could not know this entirely a priori, because he had first to learn from experience that bodies are heavy, and will fall when their supports are taken away.
We shall therefore, in what follows, understand by knowledge a priori knowledge which is absolutely independent of all experience, and not of this or that experience only. Opposed to this is empirical knowledge, or such as is possible a posteriori only, that is, by experience. Knowledge a priori, if mixed up with nothing empirical, is called pure. Thus the proposition, for example, that every change has its cause, is a proposition a priori, but not pure: because change is a concept which can only be derived from experience.
II
We are in Possession of Certain Cognitions a priori, and even the Ordinary Understanding is never without them
All depends here on a criterion, by which we may safely distinguish between pure and empirical knowledge. Now experience teaches us, no doubt, that something is so or so, but not that it cannot be different. First, then, if we have a proposition, which is thought, together with its necessity, we have a judgment a priori; and if, besides, it is not derived from any proposition, except such as is itself again considered as necessary, we have an absolutely a priori judgment. Secondly, experience never imparts to its judgments true or strict, but only assumed or relative universality (by means of induction), so that we ought always to say, so far as we have observed hitherto, there is no exception to this or that rule. If, therefore, a judgment is thought with strict universality, so that no exception is admitted as possible, it is not derived from experience, but valid absolutely a priori. Empirical universality, therefore, is only an arbitrary extension of a validity which applies to most cases, to one that applies to all: as, for instance, in the proposition, all bodies are heavy. If, on the contrary, strict universality is essential to a judgment, this always points to a special source of knowledge, namely, a faculty of knowledge a priori. Necessity, therefore, and strict universality are safe criteria of knowledge a priori, and are inseparable one from the other. As, however, in the use of these criteria, it is sometimes easier to show t
he contingency than the empirical limitation8 of judgments, and as it is sometimes more convincing to prove the unlimited universality which we attribute to a judgment than its necessity, it is advisable to use both criteria separately, each being by itself infallible.
That there really exist in our knowledge such necessary, and in the strictest sense universal, and therefore pure judgments a priori, is easy to show. If we want a scientific example, we have only to look to any of the propositions of mathematics; if we want one from the sphere of the ordinary understanding, such a proposition as that each change must have a cause, will answer the purpose; nay, in the latter case, even the concept of cause contains so clearly the concept of the necessity of its connection with an effect, and of the strict universality of the rule, that it would be destroyed altogether if we attempted to derive it, as Hume does, from the frequent concomitancy of that which happens with that which precedes, and from a habit arising thence (therefore from a purely subjective necessity), of connecting representations. It is possible even, without having recourse to such examples in proof of the reality of pure propositions a priori within our knowledge, to prove their indispensability for the possibility of experience itself, thus proving it a priori. For whence should experience take its certainty, if all the rules which it follows were always again and again empirical, and therefore contingent and hardly fit to serve as first principles? For the present, however, we may be satisfied for having shown the pure employment of the faculty of our knowledge as a matter of fact, with the criteria of it.
Not only in judgments, however, but even in certain concepts, can we show their origin a priori. Take away, for example, from the concept of a body, as supplied by experience, everything that is empirical, one by one; such as colour, hardness or softness, weight, and even impenetrability, and there still remains the space which the body (now entirely vanished) occupied: that you cannot take away. And in the same manner, if you remove from your empirical concept of any object, corporeal or incorporeal, all properties which experience has taught you, you cannot take away from it that property by which you conceive it as a substance, or inherent in a substance (although such a concept contains more determinations than that of an object in general). Convinced, therefore, by the necessity with which that concept forces itself upon you, you will have to admit that it has its seat in your faculty of knowledge a priori.
Supplement V
Empirical judgments, as such, are all synthetical; for it would be absurd to found an analytical judgment on experience, because, in order to form such a judgment, I need not at all step out of my concept, or appeal to the testimony of experience. That a body is extended, is a proposition perfectly certain a priori, and not an empirical judgment. For, before I call in experience, I am already in possession of all the conditions of my judgment in the concept of body itself. I have only to draw out from it, according to the principle of contradiction, the required predicate, and I thus become conscious, at the same time, of the necessity of the judgment, which experience could never teach me. But, though I do not include the predicate of gravity in the general concept of body, that concept, nevertheless, indicates an object of experience through one of its parts: so that I may add other parts also of the same experience, besides those which belonged to the former concept. I may, first, by an analytical process, realise the concept of body, through the predicates of extension, impermeability, form, etc., all of which are contained in it. Afterwards I expand my knowledge, and looking back to the experience from which my concept of body was abstracted, I find gravity always connected with the before-mentioned predicates, and therefore I add it synthetically to that concept as a predicate. It is, therefore, experience on which the possibility of the synthesis of the predicate of gravity with the concept of body is founded: because both concepts, though neither of them is contained in the other, belong to each other, though accidentally only, as parts of a whole, namely, of experience, which is itself a synthetical connection of intuitions.
Supplement VI
V
In all Theoretical Sciences of Reason Synthetical Judgments a priori are contained as Principles
1. All mathematical judgments are synthetical. This proposition, though incontestably certain, and very important to us for the future, seems to have hitherto escaped the observation of those who are engaged in the anatomy of human reason: nay, to be directly opposed to all their conjectures. For as it was found that all mathematical conclusions proceed according to the principle of contradiction (which is required by the nature of all apodictic certainty), it was supposed that the fundamental principles of mathematics also rested on the authority of the same principle of contradiction. This, however, was a mistake: for though a synthetical proposition may be understood according to the principle of contradiction, this can only be if another synthetical proposition is presupposed, from which the latter is deduced, but never by itself. First of all, we ought to observe, that mathematical propositions, properly so called, are always judgments a priori, and not empirical, because they carry along with them necessity, which can never be deduced from experience. If people should object to this, I am quite willing to confine my statement to pure mathematics, the very concept of which implies that it does not contain empirical, but only pure knowledge a priori.
At first sight one might suppose indeed that the proposition 7 + 5 = 12 is merely analytical, following, according to the principle of contradiction, from the concept of a sum of 7 and 5. But, if we look more closely, we shall find that the concept of the sum of 7 and 5 contains nothing beyond the union of both sums into one, whereby nothing is told us as to what this single number may be which combines both. We by no means arrive at a concept of Twelve, by thinking that union of Seven and Five; and we may analyse our concept of such a possible sum as long as we will, still we shall never discover in it the concept of Twelve. We must go beyond these concepts, and call in the assistance of the intuition corresponding to one of the two, for instance, our five fingers, or, as Segner does in his arithmetic, five points, and so by degrees add the units of the Five, given in intuition, to the concept of the Seven. For I first take the number 7, and taking the intuition of the fingers of my hand, in order to form with it the concept of the 5, I gradually add the units, which I before took together, to make up the number 5, by means of the image of my hand, to the number 7, and I thus see the number 12 arising before me. That 5 should be added to 7 was no doubt implied in my concept of a sum 7 + 5, but not that that sum should be equal to 12. An arithmetical proposition is, therefore, always synthetical, which is seen more easily still by taking larger numbers, where we clearly perceive that, turn and twist our conceptions as we may, we could never, by means of the mere analysis of our concepts and without the help of intuition, arrive at the sum that is wanted.
Nor is any proposition of pure geometry analytical. That the straight line between two points is the shortest, is a synthetical proposition. For my concept of straight contains nothing of magnitude (quantity), but a quality only. The concept of the shortest is, therefore, purely adventitious, and cannot be deduced from the concept of the straight line by any analysis whatsoever. The aid of intuition, therefore, must be called in, by which alone the synthesis is possible.
[It is true that some few propositions, presupposed by the geometrician, are really analytical, and depend on the principle of contradiction: but then they serve only, like identical propositions, to form the chain of the method, and not as principles. Such are the propositions, a = a, the whole is equal to itself, or (a+b) > a, that the whole is greater than its part. And even these, though they are valid according to mere concepts, are only admitted in mathematics, because they can be represented in intuition.9] What often makes us believe that the predicate of such apodictic judgments is contained in our concept, and the judgment therefore analytical, is merely the ambiguous character of the expression. We are told that we ought to join in thought a certain predicate to a given concept, and this necessity is inherent in th
e concepts themselves. But the question is not what we ought to join to the given concept, but what we really think in it, though confusedly only, and then it becomes clear that the predicate is no doubt inherent in those concepts by necessity, not, however, as thought in the concept itself, but by means of an intuition, which must be added to the concept.
2. Natural science (physica) contains synthetical judgments a priori as principles. I shall adduce, as examples, a few propositions only, such as, that in all changes of the material world the quantity of matter always remains unchanged: or that in all communication of motion, action and reaction must always equal each other. It is clear not only that both convey necessity, and that, therefore, their origin is a priori, but also that they are synthetical propositions. For in the concept of matter I do not conceive its permanency, but only its presence in the space which it fills. I therefore go beyond the concept of matter in order to join something to it a priori, which I did not before conceive in it. The proposition is, therefore, not analytical, but synthetical, and yet a priori, and the same applies to the other propositions of the pure part of natural science.
3. Metaphysic, even if we look upon it as hitherto a tentative science only, which, however, is indispensable to us, owing to the very nature of human reason, is meant to contain synthetical knowledge a priori. Its object is not at all merely to analyse such concepts as we make to ourselves of things a priori, and thus to explain them analytically, but to expand our knowledge a priori. This we can only do by means of concepts which add something to a given concept that was not contained in it; nay, we even attempt, by means of synthetical judgments a priori, to go so far beyond a given concept that experience itself cannot follow us: as, for instance, in the proposition that the world must have a first beginning. Thus, according at least to its intentions, metaphysic consists merely of synthetical propositions a priori.
VI
The General Problem of Pure Reason
Much is gained if we are able to bring a number of investigations under the formula of one single problem. For we thus not only facilitate our own work by defining it accurately, but enable also everybody else who likes to examine it to form a judgment, whether we have really done justice to our purpose or not. Now the real problem of pure reason is contained in the question, How are synthetical judgments a priori possible?
Critique of Pure Reason Page 68