| But as a sufficient criterion of truth, it has no further utility or authority. |
| For the fact that no cognition can be at variance with this principle without nullifying itself, constitutes this principle 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 content--which 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 = A, 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 "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. |
| SECTION II. Of the Supreme Principle of all Synthetical Judgements. |
| The explanation of the possibility of synthetical judgements 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 judgements a 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 judgement I do not go beyond the given conception, in order to arrive at some decision respecting it. |
| If the judgement 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 judgements, 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 judgement cannot be discerned merely from the judgement 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 judgements? |
| It is only a complex in which all our representations are contained, the internal sense to wit, and its form a priori, time. |