concepts and ideas, then, though themselves part of the given, yet at the same time take us beyond the given. thus, they make it possible to determine also the nature of the other modes of cognitive activity.

by means of a postulate, we have selected a special part out of the given world-picture, because it is the very essence of knowledge to proceed from a part with just this character. thus, we have made the selection solely in order to be able to understand knowledge. but, we must clearly confess to ourselves that by this selection we have artificially torn in two the unity of the given world-picture. we must bear in mind that the part which we have divorced from the given still continues, quite apart from our postulate and independently of it, to stand in a necessary connection with the world as given. this fact determines the next step forward in the theory of knowledge. it will consist in restoring the unity which we have destroyed in order to show how knowledge is possible. this restoration will consist in thinking about [320]the world as given. the act of thinking about the world actually effects the synthesis of the two parts of the given world-content—of the given which we survey up to the horizon of our experience, and of the part which, in order to be also given, must be produced by us in the activity of cognition. the cognitive act is the synthesis of these two factors. in every single cognitive act the one factor appears as something produced in the act itself and as added to the other factor which is the pure datum. it is only at the very start of the theory of knowledge that the factor which otherwise appears as always produced, appears also as given.

to think about the world is to transmute the given world by means of concepts and ideas. thinking, thus, is in very truth the act which brings about knowledge. knowledge can arise only if thinking, out of itself, introduces order into the content of the world as given. thinking is itself an activity which produces a content of its own in the moment of cognition. hence, the content cognised, in so far as it has its origin solely in thinking, offers no difficulty to cognition. we need only observe it, for in its essential nature it is immediately given to us. the description of thinking is also the science of thinking. in fact, logic was never anything but a description of the forms of thinking, never a demonstrative science. for, demonstration occurs only when there is a synthesis of the products of thinking [321]with a content otherwise given. hence, gideon spicker is quite right when he says in his book, lessing’s weltanschauung (p. 5): “we have no means of knowing, either empirically or logically, whether the results of thinking, as such, are true.” we may add that, since demonstration already presupposes thinking, thinking itself cannot be demonstrated. we can demonstrate a particular fact, but we cannot demonstrate the process of demonstrating itself. we can only describe what a demonstration is. all logical theory is wholly empirical. logic is a science which consists only of observation. but if we want to get to know anything over and above our thinking, we can do so only with the help of thinking. that is to say, our thinking must apply itself to something given and transform its chaotic into a systematic connection with the world-picture. thinking, then, in its application to the world as given, is a formative principle. the process is as follows. first, thinking selects certain details out of the totality of the given. for, in the given, there are strictly no individual details, but only an undifferentiated continuum. next, thinking relates the selected details to each other according to the forms which it has itself produced. and, lastly, it determines what follows from this relation. the act of relating two distinct items of the world-content to each other does not imply that thinking arbitrarily determines something about them. thinking [322]waits and sees what is the spontaneous consequence of the relation established. with this consequence we have at last some degree of knowledge of the two selected items of the world-content. suppose the world-content reveals nothing of its nature in response to the establishment of such a relation, then the effort of thinking must miscarry, and a fresh effort must take its place. all cognitions consist in this, that two or more items of the given are brought into relation with each other by us and that we apprehend what follows from this relation.

without doubt, many of our efforts of thinking miscarry, not only in the sciences, as is amply proved by their history, but also in ordinary life. but in the simple cases of mistake which are, after all, the commonest, the correct thought so rapidly replaces the incorrect, that the latter is never, or rarely, noticed.

kant, in his theory of the “synthetic unity of apperception,” had an inkling of this activity of thought in the systematic organisation of the world-content, as we have here developed it. but his failure to appreciate clearly the real function of thinking is revealed by the fact, that he believes himself able to deduce the a priori laws of pure natural science from the rules according to which this synthetic activity proceeds. kant has overlooked that the synthetic activity of thinking is merely the preparation for the discovery of natural laws properly so-called. suppose we select two [323]items, a and b, from the given. for knowledge to arise of a nexus according to law between a and b, the first requirement is that thinking should so relate a and b, that the relation may appear to us as given. thus, the content proper of the law of nature is derived from what is given, and the sole function of thinking is to establish such relations between the items of the world-picture that the laws to which they are subject become manifest. the pure synthetic activity of thinking is not the source of any objective laws whatever.

we must inquire what part thinking plays in the formation of our scientific world-picture as distinct from the merely given one. it follows from our account that thinking supplies the formal principle of the conformity of phenomena to law. suppose, in our example above, that a is the cause, b the effect. unless thinking were able to produce the concept of causality, we should never be able to know that a and b were causally connected. but, in order that we may know, in the given case, that a is the cause and b the effect, it is necessary for a and b to possess the characteristics which we mean when we speak of cause and effect. a similar analysis applies to the other categories of thought.

it will be appropriate to notice here in a few words hume’s discussion of causality. according to hume, the concepts of cause and effect have their origin solely in custom. we observe repeatedly that one event follows [324]another and become accustomed to think of them as causally connected, so that we expect the second to occur as soon as we have observed the first. this theory, however, springs from a totally mistaken view of the causal relation. suppose for several days running i observe the same person whenever i step out of the door of my house, i shall gradually form the habit of expecting the temporal sequence of the two events. but, it will never occur to me to think that there is any causal connection between my own appearance and that of the other person at the same spot. i shall call in aid essentially other items of the world-content in order to explain the coincidence of these events. in short, we determine the causal nexus of two events, not according to their temporal sequence, but according to the essential character of the items of the world-content which we call, respectively, cause and effect.

from this purely formal activity of our thinking in the construction of the scientific picture of the world, it follows that the content of every cognition cannot be fixed a priori in advance of observation (in which thinking comes to grips with the given), but must be derived completely and exhaustively from observation. in this sense, all our cognitions are empirical. nor is it possible to see how it could be otherwise. for, kant’s judgments a priori are at bottom, not cognitions, but postulates. on kant’s principles, all we can [325]ever say is only this, that if a thing is to become the object of possible experience, it must conform to these laws. they are, therefore, rules which the subject prescribes to all objects. but, we should rather expect cognitions of the given to have their source, not in the constitution of the subject, but in that of the object.

thinking makes no a priori affirmations about the given. but it creates the forms, on the basis of which the conformity of phenomena to law becomes manifest a posteriori.

from our point of view, it is impossible to determine anything a priori about the degree of certainty belonging to a judgment which embodies knowledge thus gained. for, certainty, too, derives from nothing other than the given. perhaps it will be objected that observation never establishes anything except that a certain nexus of phenomena actually occurs, but not that it must occur, and will always occur, in like conditions. but, this suggestion, too, is in error. for any nexus which i apprehend between elements in the world-picture is, on our principles, nothing but what is grounded in these elements themselves. it is not imported into these elements by thinking, but belongs to them essentially, and must, therefore, necessarily exist whenever they themselves exist.

only a view which regards all scientific research as nothing but the endeavour to correlate the facts of experience by means of [326]principles which are subjective and external to the facts, can hold that the nexus of a and b may to-day obey one law and to-morrow another (j. s. mill). on the other hand, if we see clearly that the laws of nature have their source in the given, and that, therefore, the nexus of phenomena essentially depends upon, and is determined by, them, we shall never think of talking of a “merely relative universality” of the laws which are derived from observation. this is, of course, not to assert that any given law which we have once accepted as correct, must be absolutely valid. but when, later, a negative instance overthrows a law, the reason is, not that the law from the first could be inferred only with relative universality, but that it had not at first been inferred correctly. a genuine law of nature is nothing but the formulation of a nexus in the given world-picture, and it exists as little without the facts which it determines, as these exist without it.

above, we have laid down that it is the essence of the cognitive activity to transmute, by thinking, the given world-picture by means of concepts and ideas. what follows from this fact? if the immediately-given were a totality complete in itself, the work which thinking does upon it in cognition would be both impossible and unnecessary. we should simply accept the given, as it is, and be satisfied with it as such. cognitive activity is possible only because in the given something [327]lies hidden which does not yet reveal itself so long as we gaze at the given in its immediacy, but which becomes manifest with the aid of the order which thinking introduces. prior to the work of thinking, the given does not possess the fulness of its own complete nature.

this point becomes still more obvious by considering in greater detail the two factors involved in the act of cognition. the first factor is the given. “being given” is not a quality of the given, but merely a term expressing its relation to the second factor in the act of cognition. this second factor, viz., the conceptual content of the given, is found by our thought in the act of cognition to be necessarily connected with the given. two questions arise: (1) where are the given and the concept differentiated? (2) where are they united? the answer to these two questions is to be found, beyond any doubt, in the preceding discussions. they are differentiated solely in the act of cognition. they are united in the given. thence it follows necessarily that the conceptual content is but a part of the given, and that the act of cognition consists in re-uniting with each other the two parts of the world-picture which are, at first, given to it in separation. the given world-picture thus attains its completion only through that mediate kind of givenness which thinking brings about. in its original immediacy the world-picture is altogether incomplete. [328]

if the conceptual content were from the first united with the given in our world-picture, there would be no cognition. for, no need could ever arise of transcending the given. so, again, if by thinking and in thinking we could create the whole world-content, once more there would be no cognition. for, what we create ourselves we do not need to cognise. hence, cognition exists because the world-content is given to us originally in a form which is incomplete, which does not contain it as a whole, but which, over and above what it presents immediately, owns another, no less essential, aspect. this second aspect of the world-content—an aspect not originally given—is revealed by cognition. pure thinking presents in the abstract, not empty forms, but a sum of determinations (categories) which serve as forms for the rest of the world-content. the world-content can be called reality only in the form which it acquires through cognition and in which both aspects of it are united.