Front Page Titles (by Subject) Section II: Of the Highest Principle of all Synthetical Judgments [p. 154] - Critique of Pure Reason
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Section II: Of the Highest Principle of all Synthetical Judgments [p. 154] - Friedrich Max Müller, Critique of Pure Reason 
Immanuel Kant’s Critique of Pure Reason. In Commemoration of the Centenary of its First Publication. Translated into English by F. Max Mueller (2nd revised ed.) (New York: Macmillan, 1922).
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Of the Highest Principle of all Synthetical Judgments [p. 154]
The explanation of the possibility of synthetical judgments is a subject of which general logic knows nothing, not even its name, while in a transcendental logic it is the most important task of all, nay, even the only one, when we have to consider the possibility of synthetical judgments a priori, their conditions, and the extent of their validity. For when that task is accomplished, the object of transcendental logic, namely, to determine the extent and limits of the pure understanding, will have been fully attained.
In forming an analytical judgment I remain within a given concept, while predicating something of it. If what I predicate is affirmative, I only predicate of that concept what is already contained in it; if it is negative, I only exclude from it the opposite of it. In forming synthetical judgments, on the contrary, I have to go beyond a given concept, in order to bring something together with it, which is totally different from what is contained in it. Here we have neither the relation of identity [p. 155] nor of contradiction, and nothing in the judgment itself by which we can discover its truth or its falsehood.
Granted, therefore, that we must go beyond a given concept in order to compare it synthetically with another, something else is necessary in which, as in a third, the synthesis of two concepts becomes possible. What, then, is that third? What is the medium of all synthetical judgments? It can only be that in which all our concepts are contained, namely, the internal sense and its a priori form, time. The synthesis of representations depends on imagination, but their synthetical unity, which is necessary for forming a judgment, depends on the unity of apperception. It is here therefore that the possibility of synthetical judgments, and (as all the three contain the sources of representations a priori) the possibility of pure synthetical judgments also, will have to be discovered; nay, they will on these grounds be necessary, if any knowledge of objects is to be obtained that rests entirely on a synthesis of representations.
If knowledge is to have any objective reality, that is to say, if it is to refer to an object, and receive by means of it any sense and meaning, the object must necessarily be given in some way or other. Without that all concepts are empty. We have thought in them, but we have not, by thus thinking, arrived at any knowledge. We have only played with representations. To give an object, if this is not meant again as mediate only, but if [p. 156] it means to represent something immediately in intuition, is nothing else but to refer the representation of the object to experience (real or possible). Even space and time, however pure these concepts may be of all that is empirical, and however certain it is that they are represented in the mind entirely a priori, would lack nevertheless all objective validity, all sense and meaning, if we could not show the necessity of their use with reference to all objects of experience. Nay, their representation is is a pure schema, always referring to that reproductive imagination which calls up the objects of experience, without which objects would be meaningless. The same applies to all concepts without any distinction.
It is therefore the possibility of experience which alone gives objective reality to all our knowledge a priori. Experience, however, depends on the synthetical unity of phenomena, that is, on a synthesis according to concepts of the object of phenomena in general. Without it, it would not even be knowledge, but only a rhapsody of perceptions, which would never grow into a connected text according to the rules of an altogether coherent (possible) consciousness, nor into a transcendental and necessary unity of apperception. Experience depends therefore on a priori principles of its form, that is, on general rules of unity in the synthesis of phenomena, [p. 157] and the objective reality of these (rules) can always be shown by their being the necessary conditions in all experience; nay, even in the possibility of all experience. Without such a relation synthetical propositions a priori would be quite impossible, because they have no third medium, that is, no object in which the synthetical unity of their concepts could prove their objective reality.
Although we know therefore a great deal a priori in synthetical judgments with reference to space in general, or to the figures which productive imagination traces in it, without requiring for it any experience, this our knowledge would nevertheless be nothing but a playing with the cobwebs of our brain, if space were not to be considered as the condition of phenomena which supply the material for external experience. Those pure synthetical judgments therefore refer always, though mediately only, to possible experience, or rather to the possibility of experience, on which alone the objective validity of their synthesis is founded.
As therefore experience, being an empirical synthesis, is in its possibility the only kind of knowledge that imparts reality to every other synthesis, this other synthesis, as knowledge a priori, possesses truth (agreement with its object) on this condition only, that it contains nothing beyond what is necessary for the synthetical [p. 158] unity of experience in general.
The highest principle of all synthetical judgments is therefore this, that every object is subject to the necessary conditions of a synthetical unity of the manifold of intuition in a possible experience.
Thus synthetical judgments a priori are possible, if we refer the formal conditions of intuition a priori, the synthesis of imagination, and the necessary unity of it in a transcendental apperception, to a possible knowledge in general, given in experience, and if we say that the conditions of the possibility of experience in general are at the same time conditions of the possibility of the objects of experience themselves, and thus possess objective validity in a synthetical judgment a priori.