utility or authority. For the fact that no cognition can be at variance with this principle without nullifying itself, constitutes this principie the sine qua non, but not the determining ground of the truth of our cognition. As our business at present is properly with the synthetical part of our knowledge only, we shall always be on our guard not to transgress this inviolable principle; but at the same time not to expect from it any direct assistance in the establishment of the truth of any synthetical proposition.

There exists, however, a formula of this celebrated principle --a principle merely formal and entirely without contentwhich contains a synthesis that has been inadvertently and quite unnecessarily mixed up with it. It is this :-"It is impossible for a thing to be and not to be at the same time.” Not to mention the superfluousness of the addition of the word impossible to indicate the apodeictic certainty, which ought to be self-evident from the proposition itself, the proposition is affected by the condition of time, and as it were says: "A thing=4, which is something=B, cannot at the same time be non-B." But both, B as well as non-B, may quite well exist in succession. For example, a man who is young cannot at the same time be old; but the same man can very well be at one time young, and at another not young, that is, old. Now the principle of contradiction as a merely logical proposition must not by any means limit its application merely to relations of time, and consequently a formula like the preceding is quite foreign to its true purpose. The misunderstanding arises in this way. We first of all separate a predicate of a thing from the conception of the thing, and afterwards connect with this predicate its opposite, and hence do not establish any contradiction with the subject, but only with its predicate, which has been conjoined with the subject synthetically,-a contradiction, moreover, which obtains only when the first and second predicate are affirmed in the same time. If I say: "A man who is ignorant is not learned," the condition "at the same time" must be added, for he who is at one time ignorant, may at another be learned. But if I say: "No ignorant man is a learned man," the proposition is analytical, because the characteristic ignorance is now a constituent part of the conception of the subject; and in this case the negative proposition is evident immediately

from the proposition of contradiction, without the necessity of adding the condition "at the same time."-This is the reason why I have altered the formula of this principle,—an alteration which shows very clearly the nature of an analytical proposition.

THE SYSTEM OF THE PRINCIPLES OF THE PURE UNDER

STANDING.

SECTION SECOND.

Of the Supreme Principle of all Synthetical Judgments. THE explanation of the possibility of synthetical judgments is a task with which general Logic has nothing to do; indeed she needs not even be acquainted with its name. But in transcendental Logic it is the most important matter to be dealt with,-indeed the only one, if the question is of the possibility of synthetical judgments à priori, the conditions and extent of their validity. For when this question is fully decided, it can reach its aim with perfect ease, the determination, to wit, of the extent and limits of the pure understanding.

In an analytical judgment I do not go beyond the given conception, in order to arrive at some decision respecting it. If the judgment is affirmative, I predicate of the conception only that which was already cogitated in it; if negative, I merely exclude from the conception its contrary. But in synthetical judgments, I must go beyond the given conception, in order to cogitate, in relation with it, something quite different from that which was cogitated in it, a relation which is consequently never one either of identity or contradiction, and by means of which the truth or error of the judgment cannot be discerned merely from the judgment itself.

Granted then, that we must go out beyond a given conception, in order to compare it synthetically with another, a third thing is necessary, in which alone the synthesis of two conceptions can originate. Now what is this tertium quid, that is to be the medium of all synthetical judgments? It is only a complex,* in which all our representations are contained, the internal sense to wit, and its form à priori, Time.

The synthesis of our representations rests upon the imagi nation; their synthetical unity (which is requisite to a judgment), upon the unity of apperception. In this, therefore,

* Inbegriff

to be sought the possibility of synthetical judgments, and as all three contain the sources of à priori representations, the possibility of pure synthetical judgments also; nay, they are necessary upon these grounds, if we are to possess a knowledge of objects, which rests solely upon the synthesis of representations.

If a cognition is to have objective reality, that is, to relate to an object, and possess sense and meaning in respect to it, it is necessary that the object be given in some way or another. Without this, our conceptions are empty, and we may indeed have thought by means of them, but by such thinking, we have not, in fact, cognized anything, we have merely played with representation. To give an object, if this expression be understood in the sense of to present the object, not mediately but immediately in intuition, means nothing else than to apply the representation of it to experience, be that experience real or only possible. Space and time themselves, pure as these conceptions are from all that is empirical, and certain as it is that they are represented fully à priori in the mind, would be completely without objective validity, and without sense and significance, if their necessary use in the objects of experience were not shewn. Nay, the representation of them is a mere schema, that always reiates to the reproductive imagination, which calls up the objects of experience, without which they have no meaning. And so is it with all conceptions without distinction.

The possibility of experience is, then, that which gives objective reality to all our à priori cognitions. Now experience depends upon the synthetical unity of phænomena, that is, upon a synthesis according to conceptions of the object of phænomena in general, a synthesis without which experience never could become knowledge, but would be merely a rhapsody of perceptions, never fitting together into any connected text, according to rules of a thoroughly united (possible) consciousness, and therefore never subjected to the transcendental and necessary unity of apperception. Experience has therefore for a foundation, à priori principles of its form, that is to say, general rules of unity in the synthesis of phænomena, the objective reality of which rules, as necessary conditionseven of the possibility of experience-can always be shewn in experience. But apart from this relation, à priori synthetical

propositions are absolutely impossible, because they have ao third term, that is, no pure object, in which the synthetical unity can exhibit the objective reality of its conceptions.

Although, then, respecting space, or the forms which productive imagination describes therein, we do cognize much à priori in synthetical judgments, and are really in no need of experience for this purpose, such knowledge would nevertheless amount to nothing but a busy trifling with a mere chimera, were not space to be considered as the condition of the phænomena which constitute the material of external experience. Hence those pure synthetical judgments do relate, though but mediately, to possible experience, or rather to the possibility of experience, and upon that alone is founded the objective validity of their synthesis.

While then, on the one hand, experience, as empirical synthesis, is the only possible mode of cognition which gives reality to all other synthesis;* on the other hand, this latter synthesis, as cognition à priori, possesses truth, that is, accordance with its object, only in so far as it contains nothing more than what is necessary to the synthetical unity of experience.

Accordingly, the supreme principle of all synthetical judgments is: Every object is subject to the necessary conditions of the synthetical unity of the manifold of intuition in a possible experience.

A priori synthetical judgments are possible, when we apply the formal conditions of the à priori intuition, the synthesis of the imagination, and the necessary unity of that synthesis in a transcendental apperception, to a possible cognition of experience, and say: The conditions of the possibility of experience in general, are at the same time conditions of the possibility of the objects of experience, and have, for that reason, objective validity in an à priori synthetical judgment.

*Mental synthesis.-T.

SYSTEM OF THE PRINCIPLES OF THE PURE UNDER

STANDING.

SECTION THIRD.

Systematic Representation of all Synthetical Principles thereof.

That principles exist at all is to be ascribed solely to the pure understanding, which is not only the faculty of rules in regard to that which happens, but is even the source of principles according to which every thing that can be presented to us as an object is necessarily subject to rules, because without such rules we never could attain to cognition of an object. Even the laws of nature, if they are contemplated as principles of the empirical use of the understanding, possess also a characteristic of necessity, and we may therefore at least expect them to be determined upon grounds which are valid à priori and antecedent to all experience. But all laws of nature, without distinction, are subject to higher principles of the understanding, inasmuch as the former are merely applications of the latter to particular cases of experience. These higher

principles alone therefore give the conception, which contains the necessary condition, and, as it were, the exponent of a rule; experience, on the other hand, gives the case which comes under the rule.

There is no danger of our mistaking merely empirical principles for principles of the pure understanding, or conversely; for the character of necessity, according to conceptions which distinguishes the latter, and the absence of this in every empirical proposition, how extensively valid soever it may be, is a perfect safeguard against confounding them. There are, however, pure principles à priori, which nevertheless I should not ascribe to the pure understanding-for this reason, that they are not derived from pure conceptions, but (although by the mediation of the understanding) from pure intuitions. But understanding is the faculty of conceptions. Such principles mathematical science possesses, but their application to experience, consequently their objective validity, nay the possi bility of such à priori synthetical cognitions (the deduction thereof) rests entirely upon the pure understanding.

On this acco int, I shall not reckon among my principles