The postulates of empirical thought, which correspond to the categories of modality, are stated as follows:

"1. That which agrees with the formal conditions of experience (according to perception and conceptions) is possible.

2. That which is connected with the material conditions of experience (sensation) is actual.

3. That of which the connexion with the actual is determined according to universal conditions of experience is necessary (exists necessarily)."[1]

These principles, described as only 'explanations of the conceptions of possibility, actuality, and necessity as employed in experience', are really treated as principles by which we decide what is possible, what is actual, and what is necessary. The three conceptions involved do not, according to Kant, enlarge our knowledge of the nature of objects, but only 'express their relation to the faculty of knowledge'[2]; i. e. they only concern our ability to apprehend an object whose nature is already determined for us otherwise as at least possible, or as real, or as even necessary. Moreover, it is because these principles do not enlarge our knowledge of the nature of objects that they are called postulates; for a postulate in geometry, from which science the term is borrowed (e. g. that it is possible with a given line to describe a circle from a given point), does not augment the conception of the figure to which it relates, but only asserts the possibility of the conception itself.[3] The discussion of these principles is described, contrary to the terminology adopted in the case of the preceding principles, as 'explanation' and not as 'proof'. The discussion, however, certainly includes a proof of them, for it is Kant's main object to prove that these principles constitute the general character of what can be asserted to be possible, actual, or necessary respectively. Again, as before, the basis of proof lies in a theory of knowledge, and in particular in Kant's theory of knowledge; for it consists in the principle that everything knowable must conform to the conditions involved in its being an object of possible experience.

To understand these principles and the proof of them, we must notice certain preliminary considerations. In the first place, the very problem of distinguishing the possible, the actual, and the necessary presupposes the existence of distinctions which may prove open to question. It presupposes that something may be possible without being actual, and again that something may be actual without being necessary. In the second place, Kant's mode of approaching the problem assumes that we can begin with a conception of an object, e. g. of a man with six toes, and then ask whether the object of it is possible, whether, if possible, it is also actual, and whether, if actual, it is also necessary. In other words, it assumes the possibility of separating what is conceived from what is possible, and therefore a fortiori from what is actual,[4] and from what is necessary. Thirdly, in this context, as in most others, Kant in speaking of a conception is thinking, to use Locke's phraseology, not of a 'simple' conception, such as that of equality or of redness, but of a 'complex' conception, such as that of a centaur, or of a triangle in the sense of a three-sided three-angled figure. It is the apprehension of a 'complex' of elements.[5] Fourthly, what is said to be possible, real, or necessary is not the conception but the corresponding object. The question is not, for instance, whether the conception of a triangle or of a centaur is possible, actual, or necessary, but whether a triangle or a centaur is possible, actual, or necessary. Kant sometimes speaks loosely of conceptions as possible,[6] but the terms which he normally and, from the point of view of his theory, rightly applies to conceptions are 'objectively real' and 'fictitious'.[7] Lastly, Kant distinguishes 'objectively real' and 'fictitious' conceptions in two ways. He speaks of establishing the objective reality of a conception as consisting in establishing the possibility of a corresponding object,[8] implying therefore that a fictitious conception is a conception of which the corresponding object is not known to be possible. Again, he describes as fictitious new conceptions of substances, powers, and interactions, which we might form from the material offered to us by perception without borrowing from experience itself the example of their connexions, e. g. the conception of a power of the mind to perceive the future; and he says that the possibility of these conceptions (i. e. the possibility of corresponding objects) cannot, like that of the categories, be acquired a priori through their being conditions on which all experience depends, but must be discovered empirically or not at all. Of such conceptions he says that, without being based upon experience and its known laws, they are arbitrary syntheses which, although they contain no contradiction, have no claim to objective reality, and therefore to the possibility of corresponding objects.[9] He implies, therefore, that the object of a conception can be said to be possible only when the conception is the apprehension of a complex of elements together with the apprehension—which, if not a priori, must be based upon experience—that they are connected. Hence a conception may be regarded as 'objectively real', or as 'fictitious' according as it is the apprehension of a complex of elements accompanied by the apprehension that they are connected, or the apprehension of a complex of elements not so accompanied.

It is now possible to state Kant's problem more precisely. With regard to a given complex conception he wishes to determine the way in which we can answer the questions (1) 'Has the conception a possible object to correspond to it', or, in other words, 'Is the conception 'objectively real' or 'fictitious'?' (2) 'Given that a corresponding object is possible, is it also real?' (3) 'Given that it is real, is it also necessary?'

The substance of Kant's answer to this problem may be stated thus: 'The most obvious guarantee of the objective reality of a conception, i. e. of the possibility of a corresponding object, is the experience of such an object. For instance, our experience of water guarantees the objective reality of the conception of a liquid which expands as it solidifies. This appeal to experience, however, takes us beyond the possibility of the object to its reality, for the experience vindicates the possibility of the object only through its reality. Moreover, here the basis of our assertion of possibility is only empirical, whereas our aim is to discover the conceptions of which the objects can be determined a priori to be possible. What then is the answer to this, the real problem? To take the case of cause and effect, we cannot reach any conclusion by the mere study of the conception of cause and effect. For although the conception of a necessary succession contains no contradiction, the necessary succession of events is a mere arbitrary synthesis as far as our thought of it is concerned; we have no direct insight into the necessity. Therefore we cannot argue from this conception to the possibility of a corresponding object, viz. a necessarily successive series of events in nature. We can, however, say that that synthesis is not arbitrary but necessary to which any object must conform, if it is to be an object of experience. From this point of view we can say that there must be a possible object corresponding to the conception of cause and effect, because only as subjected to this synthesis are there objects of experience at all. Hence, if we take this point of view, we can say generally that all spatial and temporal conceptions, as constituting the conditions of perceiving in experience, and all the categories, as constituting the conditions of conceiving in experience, must have possible objects. In other words, 'that which agrees with the formal conditions of experience (according to perception and conceptions) is possible'. Again, if we know that the object of a conception is possible, how are we to determine whether it is also actual? It is clear that, since we cannot advance from the mere conception, objectively real though it may be, to the reality of the corresponding object, we need perception. The case, however, where the corresponding object is directly perceived may be ignored, for it involves no inference or process of thought; the appeal is to experience alone. Therefore the question to be considered is, 'How do we determine the actuality of the object of a conception comparatively a priori, i. e. without direct experience of it[10]?' The answer must be that we do so by finding it to be 'connected with an actual perception in accordance with the analogies of experience'[11]. For instance, we must establish the actuality of an object corresponding to the conception of a volcanic eruption by showing it to be involved, in accordance with the analogies (and with particular empirical laws), in the state of a place which we are now perceiving. In other words, we can say that 'that which is connected with the material conditions of existence (sensation) is actual'. Finally, since we cannot learn the existence of any object of experience wholly a priori, but only relatively to another existence already given, the necessity of the existence of an object can never be known from conceptions, but only from its connexion with what is perceived; this necessity, however, is not the necessity of the existence of a substance, but only the necessity of connexion of an unobserved state of a substance with some observed state of a substance. Therefore we can (and indeed must) say of an unobserved object corresponding to a conception, not only that it is real, but also that it is necessary, when we know it to be connected with a perceived reality 'according to universal conditions of experience'; but the necessity can be attributed only to states of substances and not to substances themselves.'

Throughout this account there runs one fatal mistake, that of supposing that we can separate our knowledge of things as possible, as actual, and as necessary. Even if this supposition be tenable in certain cases,[12] it is not tenable in respect of the objects of a complex conception, with which Kant is dealing. If we know the object of a complex conception to be possible, we already know it to be actual, and if we know it to be actual, we already know it to be necessary. A complex conception in the proper sense is the apprehension of a complex of elements together with the apprehension of, or insight into, their connexion.[13] Thus, in the case of the conception of a triangle we see that the possession of three sides necessitates the possession of three angles. From such a conception must be distinguished Kant's 'fictitious' conception, i. e. the apprehension of a complex of elements without the apprehension of connexion between them. Thus, in the case of the conception of a man with six toes, there is no apprehension of connexion between the possession of the characteristics indicated by the term 'man' and the possession of six toes. In such a case, since we do not apprehend any connexion between the elements, we do not really 'conceive' or 'think' the object in question, e. g. a man with six toes. Now in the case of a complex conception proper, it is impossible to think of a corresponding individual as only possible. The question 'Is a triangle, in the sense of a figure with three sides and three angles, possible?' really means 'Is it possible for a three-sided figure to have three angles?' To this question we can only answer that we see that a three-sided figure can have three angles, because we see that it must have, and therefore has, and can have, three angles; in other words, that we see a triangle in the sense in question to be possible, because we see it to be necessary, and, therefore, actual, and possible. It cannot be argued that our insight is limited to the fact that if there are three-sided figures they must be three-angled, and that therefore we only know a triangle in the sense in question to be possible. Our apprehension of the fact that the possession of three sides necessitates the possession of three angles presupposes knowledge of the existence of three-sided figures, for it is only in an actual three-sided figure that we can apprehend the necessity. It may, however, be objected that the question ought to mean simply 'Is a three-sided figure possible?' and that, understood in this sense, it cannot be answered in a similar way. Nevertheless, a similar answer is the right answer. For the question 'Is a three-sided figure possible?' really means 'Is it possible for three straight lines to form a figure, i. e. to enclose a space?' and we can only answer it for ourselves by seeing that a group of three straight lines or directions, no two of which are parallel, must, as such, enclose a space, this insight presupposing the apprehension of an actual group of three straight lines. It may be said, therefore, that we can only determine the possibility of the object of a complex conception in the proper sense, through an act in which we apprehend its necessity and its actuality at once. It is only where conceptions are 'fictitious', and so not properly conceptions, that appeal to experience is necessary. The question 'Is an object corresponding to the conception of a man with six toes possible?' presupposes the reality of man and asks whether any man can have six toes. If we understood the nature of man and could thereby apprehend either that the possession of six toes was, or that it was not, involved in one of the possible differentiations of man, we could decide the question of possibility a priori, i. e. through our conceiving alone without an appeal to experience; but we could do so only because we apprehended either that a certain kind of man with six toes was necessary and actual, or that such a man was impossible and not actual. If, however, as is the case, we do not understand the nature of man, we can only decide the question of possibility by an appeal to experience, i. e. to the experience of a corresponding object, or of an object from which the existence of such an object could be inferred. Here, therefore—assuming the required experience to be forthcoming—we can appeal to Kant's formula and say that we know that such a man, i. e. an object corresponding to the conception, is actual, as being connected with the material conditions of experience. But the perception which constitutes the material conditions of experience in the case in question is only of use because it carries us beyond possibility to actuality, and appeal to it is only necessary because the object is not really conceived or, in other words, because the so-called conception is not really a conception.

Kant really treats his 'objectively real' conceptions as if they were 'fictitious', even though he speaks of them as complete. Consequently, his conceptions not being conceptions proper, he is necessarily led to hold that an appeal to experience is needed in order to establish the reality of a corresponding object. Yet, this being so, he should have asked himself whether, without an appeal to perception, we could even say that a corresponding object was possible. That he did not ask this question is partly due to the fact that he attributes the form and the matter of knowledge to different sources, viz. to the mind and to things in themselves. While the conceptions involved in the forms of perception, space, and time, and also the categories are the manifestations of the mind's own nature, sensations, which form the matter of knowledge, are due to the action of things in themselves on our sensibility, and of this activity we can say nothing. Hence, from the point of view of our mind—and since we do not know things in themselves, this is the only point of view we can take—the existence of sensations, and therefore of objects, which must be given in perception, is wholly contingent and only to be discovered through experience. On the other hand, since the forms of perception and conception necessarily determine in certain ways the nature of objects, if there prove to be any objects, the conceptions involved may be thought to determine what objects are possible, even though the very existence of the objects is uncertain. Nevertheless, on his own principles, Kant should have allowed that, apart from perception, we could discover a priori at least the reality, even if not the necessity, of the objects of these conceptions. For his general view is that the forms of perception and the categories are only actualized on the occasion of the stimulus afforded by the action of things in themselves on the sensibility. Hence the fact that the categories and forms of perception are actualized—a fact implied in the very existence of the Critique—involves the existence of objects corresponding to the categories and to the conceptions involved in the forms of perception. On Kant's own principles, therefore, we could say a priori that there must be objects corresponding to these conceptions, even though their nature in detail could only be filled in by experience.[14]

[1] B. 265-6, M. 161.