Reason is the source of transcendent principles. A principle is transcendent when it explicitly applies to objects which cannot be experienced, as opposed to immanent principles (those of the analytic), which are explicitly limited to empirical objects. These principles are concocted by reason in its effort to unify the principles of the understanding by completing them. They employ Ideas, concepts whose intended objects are, as it were, free-standing, and which provide a foundation for the objects of experience. The idea of the soul is that of the seat of all our representations; that of the world is the idea of the totalit of the universe; that of God is the idea of the ground of the possibility of all objects in general. Corresponding to these three ideas are three sections of the Dialectic: the Paralogisms, the Antinomy, and the Ideal, respectively.
The three-fold division corresponds exactly to the three objects of Wolffian "special metaphysics." The basis of Wolff's division was this. Theology deals with the necessary being (God), while the other two deal with contingent beings. Psychology's object is the soul, which is a special kind of contingent being. Cosmology concerns the world, which is the aggregation of all contingent beings which exist. Kant's systematization of the three areas of special metaphysics follows a three-fold division of types of syllogism in Aristotelian logic. The categorical, hypothetical and disjunctive syllogisms correspond to the doctrines of the soul, the world and God, respectively. This division is universally condemned as being so artificial as to be useless.
The Idea of the soul is that of a single simple substance in commerce with a body. Not surprisingly, the four predicates determining the Idea of the soul are said to correspond to the four types of category: quantity, quality, relation and modality, respectively. In the first edition, this yields a division of the Paralogisms into four. In the second edition, Kant dropped the soul/body connection in favor a a generic description of the soul as that which thinks. Thus the soul is that which thinks, and that which thinks is a single, simple substance. Since we have dealt with the contet of the first edition Fourth Paralogism above, we will follow the lines of the second edition treatment of the Paralogisms.
The doctrine of the soul begins with the fundamental datum that I think. As Kant had emphasized in the Analytic, the judgment that I think must at least be possible in order for me to make any judgment at all. It is the "vehicle" of all representations. Kant adds in the Paralogism that 'I think' is an existential judgment, that I exist thinking. So there is something which thinks. But what is this something? There are three ways in which it might be represented: 1) as the object of inner intuition, 2) as the subject of judgments, 3) as an object which underlies the object of inner intuition, i.e., as a thing in itself which is a thinking thing.
I represent myself as an object of inner intuition by representing successive states in time. As we saw in the Refutation of Idealism, such a representation is not that of a permanent substance, so the soul as construed by metaphysics is not given through inner intuition. It is only the appearance of an unknown something = x. As Kant construes the Paralogisms, one starts with a set of analytic truths about a thinking subject and concludes from them properties of the soul as a thing in itself. We think ourselves as a simple subject which is identical through time, but this has nothing to do with anything but ourselves as appearance.
To say that I think myself as subject is nothing more than to say that I think myself as that which thinks. This judgment is patently analytic. If it is added that this subject is substance, the judgment is again analytic, if the concept of substance thus attributed is that of a subject which is not a predicate of any other subject (this is the "logical" meaning of the category of substance). A mistake occurs when attributes permanence to the subject, i.e., makes a "real" use of the category of substance. For permanence applies only to objects in time, but the metaphysical subject, the thing in itself, is not in time. We are unable in particular to infer from the substantiality of the I which thinks to the immortality of the soul.
Perhaps immortality follows from the simplicity of the subject. The Wolffian argument was that because the soul is a simple subject, it cannot be dissolved into parts, and hence cannot be destroyed by any force in nature. The simplicity of the soul is said (by Kant) to be analytic in this sense: that the I which thinks a complete thought is the same I which thinks each component of the thought. But this unity is merely formal: it has nothing to do with any underlying reality. All it says is that we cannot think any multiplicity in the single 'I.' But this is only because the representation of the 'I' is empty, "the poorest of all representations."
Although we cannot infer from the unity of the bare representation 'I' to the real simplicity of a substance, we can at least state that whatever the 'I' is, it is not material. This is because matter is merely outer appearance, quite distinct from the object of inner intuition, which is not in space. However, it is quite possible that the objects of both inner and outer intuition share a common substratum. And the substratum may be a composite, in which case the soul may be divisible after all. So the immortality of the soul cannot be inferred from its immateriality.
The final property attributed to the soul is that of unity through change. From this is inferred its personality. But again, the initial inference from the 'I' to its unity is merely analytic. The 'I' is the subject of our thinking, of our representation, and time is the form of inner intuition. Thus time itself depends on the 'I,' which therefore must be regarded as being the same at all times. But this unity is merely subjective: I cannot from my own point of view represent myself as anything other than a unity. But objectively, I might be a succession of substances, each passing along the content of thinking as a series of balls in contact with one another pass along motion when one end is struck. In this case, there would be no metaphysical unity and no basis for personality.
In summary, the problem of the Paralogisms is that the unity of consciousness, of the 'I think' is conflated with the unity of an object. The only way in which we are given to ourselves as object is through inner intuition, and as such we are subject to the categories. But the categories do not determine the unity of consciousness; the unity of consciousness is a condition for the application of the categories. And time does not determine the unity of consciousness; the unity of consciousness is a necessary condition for the represention of objects in time.