1 According to this principle, therefore, everything is referred to a common correlate, that is, the whole possibility, which, if it (that is, the matter for all possible predicates) could be found in the idea of any single thing, would prove an affinity of all possible things, through the identity of the ground of their complete determination. The determinability of any concept is subordinate to the universality (universalitas) of the principle of the excluded middle, while the determination of a thing is subordinate to the totality (universitas) or the sum total of all possible predicates.
2 The observations and calculations of astronomers have taught us much that is wonderful; but the most important is, that they have revealed to us the abyss of our ignorance, which otherwise human reason could never have conceived so great. To meditate on this must produce a great change in the determination of the aims of our reason.
3 This ideal of the most real of all things, although merely a representation, is first realised, that is, changed into an object, then hypostasised, and lastly, by the natural progress of reason towards unity, as we shall presently show, personified; because the regulative unity of experience does not rest on the phenomena themselves (sensibility alone), but on the connection of the manifold, through the understanding (in an apperception), so that the unity of the highest reality, and the complete determinability (possibility) of all things, seem to reside in a supreme understanding, and therefore in an intelligence.
4 Read nothwendig instead of unmöglich. Noiré.
5 A concept is always possible, if it is not self-contradictory. This is the logical characteristic of possibility, and by it the object of the concept is distinguished from the nihil negativum. But it may nevertheless be an empty concept, unless the objective reality of the synthesis, by which the concept is generated, has been distinctly shown. This, however, as shown above, must always rest on principles of possible experience, and not on the principle of analysis (the principle of contradiction). This is a warning against inferring at once from the possibility of concepts (logical) the possibility of things (real).
6This conclusion is too well known to require detailed exposition. It rests on the apparently transcendental law of causality in nature, that everything contingent has its cause, which, if contingent again, must likewise have a cause, till the series of subordinate causes ends in an absolutely necessary cause, without which it could not be complete.
7Not theological Ethics; for these contain moral laws, which presuppose the existence of a supreme ruler of the world, while Ethico-theology is the conviction of the existence of a Supreme Being, founded on moral laws.
8 Read ausgeschossen.
9 Read keiner instead of keine.
10 Instead of alle read als.
11 The early editions read transcendenten, instead of transcendentalen, which is given in the corrigenda of the Fifth Edition; it is not impossible, however, that Kant may have meant to write transcendenten, in order to indicate the illegitimate use of these concepts.
12 The advantage which arises from the circular shape of the earth is well known; but few only know that its flattening, which gives it the form of a spheroid, alone prevents the elevations of continents, or even of smaller volcanically raised mountains, from continuously and, within no very great space of time, considerably altering the axis of the earth. The protuberance of the earth at the equator forms however so considerable a mountain, that the impetus of every other mountain can never drive it perceptibly out of its position with reference to the axis of the earth. And yet people do not hesitate to explain this wise arrangement simply from the equilibrium of the once fluid mass.
13 This was a name given by the old dialecticians to a sophistical argument, which ran thus: If it is your fate that you should recover from this illness, you will recover, whether you send for a doctor or not. Cicero says that this argument was called ignava ratio, because, if we followed it, reason would have no use at all in life. It is for this reason that I apply the same name to this sophistical argument of pure reason.
14 After what I have said before about the psychological idea, and its proper destination to serve as a regulative principle only for the use of reason, there is no necessity for my discussing separately and in full detail the transcendental illusion which leads us to represent hypostatically that systematical unity of the manifold phenomena of the internal sense. The procedure would here be very similar to that which we are following in our criticism of the theological ideal.
15 Instead of der Erscheinungen read die Erscheinungen.
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Critique of Pure Reason
II
Method of Transcendentalism
The Method of Transcendentalism
If we look upon the whole knowledge of pure and speculative reason as an edifice of which we possess at least the idea within ourselves, we may say that in the Elements of Transcendentalism we made an estimate of the materials and determined for what kind of edifice and of what height and solidity they would suffice. We found that although we had thought of a tower that would reach to the sky, the supply of materials would suffice for a dwelling-house only, sufficiently roomy for all our business on the level plain of experience, and high enough to enable us to survey it: and that the original bold undertaking could not but fail for want of materials, not to mention the confusion of tongues which inevitably divided the labourers in their views of the building, and scattered them over all the world, where each tried to erect his own building according to his own plan. At present, however, we are concerned not so much with the material as with the plan, and though we have been warned not to venture blindly on a plan which may be beyond our powers, we cannot altogether give up the erection of a solid dwelling, but have to make the plan for a building in proportion to the material which we possess, and sufficient for all our real wants. This determination of the formal conditions of a complete system of pure reason I call the Method of Transcendentalism. We shall here have to treat of a discipline, a canon, an architectonic, and lastly, a history of pure reason, and shall have to do, from a transcendental point of view, what the schools attempt, but fail to carry out properly, with regard to the use of the understanding in general, under the name of practical logic. The reason of this failure is that general logic is not limited to any particular kind of knowledge, belonging to the understanding (not for instance to its pure knowledge), nor to certain objects. It cannot, therefore, without borrowing knowledge from other sciences, do more than produce titles of possible methods and technical terms which are used in different sciences in reference to their systematical arrangement, so that the pupil becomes acquainted with names only, the meaning and application of which he has to learn afterwards.
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Method of Transcendentalism
Chapter I
The Discipline of Pure Reason
Negative judgments, being negative not only in their logical form, but in their contents also, do not enjoy a very high reputation among persons desirous of increasing human knowledge. They are even looked upon as jealous enemies of our never-ceasing desire for knowledge, and we have almost to produce an apology, in order to secure for them toleration, or favour and esteem.
No doubt, all propositions may logically be expressed as negative: but when we come to the question whether the contents of our knowledge are enlarged or restricted by a judgment, we find that the proper object of negative judgments is solely to prevent error. Hence negative propositions, intended to prevent erroneous knowledge in cases where error is never possible, may no doubt be very true, but they are empty, they do not answer any purpose, and sound therefore often absurd; like the well-known utterance of a rhetorician, that Alexander could not have conquered any countries without an army.
But in cases where the limits of our possible knowledge are very narrow, where the temptation to judge is great, the illusion which presents itself very deceptive, and the evil consequences of error very considerable, the
negative element, though it teaches us only how to avoid errors, has even more value than much of that positive instruction which adds to the stock of our knowledge. The restraint which checks our constant inclination to deviate from certain rules, and at last destroys it, is called discipline. It is different from culture, which is intended to form a certain kind of skill, without destroying another kind which is already present. In forming a talent, therefore, which has in itself an impulse to manifest itself, discipline will contribute a negative,1 culture and doctrine a positive, influence.
That our temperament and various talents which like to indulge in free and unchecked exercise (such as imagination and wit) require some kind of discipline, will easily be allowed by everybody. But that reason, whose proper duty it is to prescribe a discipline to all other endeavours, should itself require such discipline, may seem strange indeed. It has in fact escaped that humiliation hitherto, because, considering the solemnity and thorough self-possession in its behaviour, no one has suspected it of thoughtlessly putting imaginations in the place of concepts, and words in the place of things.
In its empirical use reason does not require such criticism, because its principles are constantly subject to the test of experience. Nor is such criticism required in mathematics, where the concepts of reason must at once be represented in concreto in pure intuition, so that everything unfounded and arbitrary is at once discovered. But when neither empirical nor pure intuition keeps reason in a straight groove, that is, when it is used transcendently and according to mere concepts, the discipline to restrain its inclination to go beyond the narrow limits of possible experience, and to keep it from extravagance and error is so necessary, that the whole philosophy of pure reason is really concerned with that one negative discipline only. Single errors may be corrected by censure, and their causes removed by criticism. But when, as in pure reason, we are met by a whole system of illusions and fallacies, well connected among themselves and united by common principles, a separate negative code seems requisite, which, under the name of a discipline, should erect a system of caution and self-examination, founded on the nature of reason and of the objects of its use, before which no false sophistical illusion could stand, but should at once betray itself in spite of all excuses.
It should be well borne in mind, however, that in this second division of the transcendental critique, I mean to direct the discipline of pure reason not to its contents, but only to the method of its knowledge. The former task has been performed in the Elements of Transcendentalism. There is so much similarity in the use of reason, whatever be the subject to which it is applied, and yet, so far as this use is to be transcendental, it is so essentially different from every other, that, without the warning voice of a discipline, especially devised for that purpose, it would be impossible to avoid errors arising necessarily from the improper application of methods, which are suitable to reason in other spheres, only not quite here.
Method of Transcendentalism
Section I
The Discipline of Pure Reason in its Dogmatical Use
The science of mathematics presents the most brilliant example of how pure reason may successfully enlarge its domain without the aid of experience. Such examples are always contagious, particularly when the faculty is the same, which naturally flatters itself that it will meet with the same success in other cases which it has had in one. Thus pure reason hopes to be able to extend its domain as successfully and as thoroughly in its transcendental as in its mathematical employment; particularly if it there follows the same method which has proved of such decided advantage elsewhere. It is, therefore, of great consequence for us to know whether the method of arriving at apodictic certainty, which in the former science was called mathematical, be identical with that which is to lead us to the same certainty in philosophy, and would have to be called dogmatic.
Philosophical knowledge is that which reason gains from concepts, mathematical, that which it gains from the construction of concepts. By constructing a concept I mean representing a priori the intuition corresponding to it. For the construction of a concept, therefore, a non-empirical intuition is required which, as an intuition, is a single object, but which, nevertheless, as the construction of a concept (of a general representation) must express in the representation something that is generally valid for all possible intuitions which fall under the same concept. Thus I construct a triangle by representing the object corresponding to that concept either by mere imagination, in the pure intuition, or, afterwards on paper also in the empirical intuition, and in both cases entirely a priori without having borrowed the original from any experience. The particular figure drawn on the paper is empirical, but serves nevertheless to express the concept without any detriment to its generality, because, in that empirical intuition, we consider always the act of the construction of the concept only, to which many determinations, as, for instance, the magnitude of the sides and the angles, are quite indifferent, these differences, which do not change the concept of a triangle, being entirely ignored.
Philosophical knowledge, therefore, considers the particular in the general only, mathematical, the general in the particular, nay, even in the individual, all this, however, a priori, and by means of reason; so that, as an individual figure is determined by certain general conditions of construction, the object of the concept, of which this individual figure forms only the schema, must be thought of as universally determined.
The essential difference between these two modes of the knowledge of reason consists, therefore, in the form, and does not depend on any difference in their matter or objects. Those who thought they could distinguish philosophy from mathematics by saying that the former was concerned with quality only, the latter with quantity only, mistook effect for cause. It is owing to the form of mathematical knowledge that it can refer to quanta only, because it is only the concept of quantities that admits of construction, that is, of a priori representation in intuition, while qualities cannot be represented in any but empirical intuition. Hence reason can gain a knowledge of qualities by concepts only. No one can take an intuition corresponding to the concept of reality from anywhere except from experience; we can never lay hold of it a priori by ourselves, and before we have had an empirical consciousness of it. We can form to ourselves an intuition of a cone, from its concept alone, and without any empirical assistance, but the colour of this cone must be given before, in some experience or other. I cannot represent in intuition the concept of a cause in general in any way except by an example supplied by experience, etc. Besides, philosophy treats of quantities quite as much as mathematics; for instance, of totality, infinity, etc., and mathematics treats also of the difference between lines and planes, as spaces of different quality, it treats further of the continuity of extension as one of its qualities. But, though in such cases both have a common object, the manner in which reason treats it is totally different in philosophy and mathematics. The former is concerned with general concepts only, the other can do nothing with the pure concept, but proceeds at once to intuition, in which it looks upon the concept in concreto; yet not in an empirical intuition, but in an intuition which it represents a priori, that is, which it has constructed and in which, whatever follows from the general conditions of the construction, must be valid in general of the object of the constructed concept also.
Let us give to a philosopher the concept of a triangle, and let him find out, in his own way, what relation the sum of its angles bears to a right angle. Nothing is given him but the concept of a figure, enclosed within three straight lines, and with it the concept of as many angles. Now he may ponder on that concept as long as he likes, he will never discover anything new in it. He may analyse the concept of a straight line or of an angle, or of the number three, and render them more clear, but he will never arrive at other qualities which are not contained in those concepts. But now let the geometrician treat the same question. He will begin at once with constructing a triangle. As he knows that two right angles
are equal to the sum of all the contiguous angles which proceed from one point in a straight line, he produces one side of his triangle, thus forming two adjacent angles which together are equal to two right angles. He then divides the exterior of these angles by drawing a line parallel with the opposite side of the triangle, and sees that an exterior adjacent angle has been formed, which is equal to an interior, etc. In this way he arrives, through a chain of conclusions, though always guided by intuition, at a thoroughly convincing and general solution of the question.
In mathematics, however, we construct not only quantities (quanta) as in geometry, but also mere quantity (quantitas) as in algebra, where the quality of the object, which has to be thought according to this quantitative concept, is entirely ignored. We then adopt a certain notation for all constructions of quantities (numbers), such as addition, subtraction, extraction of roots, etc., and, after having denoted also the general concept of quantities according to their different relations, we represent in intuition according to general rules, every operation which is produced and modified by quantity. Thus when one quantity is to be divided by another, we place the signs of both together according to the form denoting division, etc., and we thus arrive, by means of a symbolical construction in algebra, quite as well as by an ostensive or geometrical construction of the objects themselves in geometry, at results which our discursive knowledge could never have reached by the aid of mere conceptions.
What may be the cause of this difference between two persons, the philosopher and the mathematician, both practising the art of reason, the former following his path according to concepts, the latter according to intuitions, which he represents a priori according to concepts? If we remember what has been said before in the Elements of Transcendentalism, the cause is clear. We are here concerned not with analytical propositions, which can be produced by a mere analysis of concepts (here the philosopher would no doubt have an advantage over the mathematician), but with synthetical propositions, and synthetical propositions that can be known a priori. We are not intended here to consider what we are really thinking in our concept of the triangle (this would be a mere definition), but we are meant to go beyond that concept, in order to arrive at properties which are not contained in the concept, but nevertheless belong to it. This is impossible, except by our determining our object according to the conditions either of empirical, or of pure intuition. The former would give us an empirical proposition only, through the actual measuring of the three angles. Such a proposition would be without the character of either generality or necessity, and does not, therefore, concern us here at all. The second procedure consists in the mathematical and here the geometrical construction, by means of which I add in a pure intuition, just as I may do in the empirical intuition, everything that belongs to the schema of a triangle in general and, therefore, to its concept, and thus arrive at general synthetical propositions.
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