What makes these a priori judgments hold for the restricted range of objects? Objects of experience are subject to conditions necessary for their being represented in intuition. That is, they are subject to the forms of intuition, space and time. Outer objects are side-by-side in space because it is only as in space that they are intutited by us. It is a property of human beings that we intuit things this way, though Kant could not say why. He also was doubtful about whether any other creature has this form of intuition, though he held it to be possible in the sense that there is no contradiction in the concept of such a being.
Now I want to say more about the nature of space itself. In the last lecture, I characterized the two opposing points of view prevelant at Kant's time. The Newtonians ("mathematical students of nature) held that space is a has a real existence (subsistence) in its own right, while the Leibnizians ("metaphysical students of nature") held that it is derivative from properties of bodies (inherent). Kant believed that both positions are wrong, but that each has something right about it. (This is characteristic of Kant's attitudes toward his predecessors.)
The Newtonian view is metaphysically wrong. The problem is that the concept of space is unintelligible: "they have to admit two eternal and infinite self-subsistent non-entities (space and time), which are there (yet without there being anything real) only in order to contain in themselves what is real" (A39/B56). (See Berkeley's version of this criticism for a clearer account of what is wrong here.)
The Leibnizian view is epistemically faulty. If space is derivative from bodies, then it can be known only through bodies, and therefore a posteriori. But Kant held that space cannot be known empirically, since our knowledge of it is knowledge of necessity. The key to the criticism is that space was thought to be a confused mode of representation, a mere "creature of the imagination," a fiction. This fiction could only be the product of experience by way of abstraction. Thus any general truths about space are only valid of those bodies which one has experienced, not all bodies one could experience.
The Newtonian view does not contain this epistemic defect. Since space is something in its own right, it is not absolutely necessary that it be known through experience. One might know a priori the characteristics of space, since space is not an object of perception and could be known only through the pure intellect. But Kant denied that such knowledge is possible for humans, so he had to look elsewhere to explain how our knowledge of space is a priori. (It should be noted, however, that the purported a priori status of space has not gone down well with posterity. The application of non-Euclidean geometry in relativistic physics has been taken to show that the properties of space are known empirically.)
What is correct in the Leibnizian view was its anti-metaphysical stance. Space and time do not exist in and of themselves, but in some sense are the product of the way we represent things. The are ideal, though not in the sense in which Leibniz thought they are ideal (figments of the imagination). The ideality of space is its mind-dependence: it is only a condition of sensibility.
Still, the Leibnizian view had its metaphysical elements. He held that bodies have real properties, their place relative to other bodies, and it is this reality which is converted into the fiction of space. Suppose two bodies switch positions with each other. Each is in a different place relative to the other, but it seems natural to say that one is in the same space as the other. Thus space is what we believe to stay the same when positions change. But there is in reality nothing that remains identical through change of position.
In his early work, Kant rejected the view that all the "spatial" properties of a thing are based on its place alone. Two objects may be identical with respect to relations of place, yet have different spatial properties. The example mentioned in the last class, a right hand and a left hand, illustrate this difference. If God were to create a single hand and nothing else, that hand would have to fit equally well on either side of the human body, which is impossible. ("Concerning the Ultimate Ground of the Differentiation of Directions in Space," 1765) Kant concluded that the differences in direction (right and left, up and down, front and back) which we find in bodies care only possible on the assumption of absolute space. He added the pregnant corollary, "absolute space is not an object of outer sensation; it is rather a fundamental concept which first of all makes possible all such outer sensation."
It is clear that the ideality of space is fundamental in Kant's doctrine. By making space a form of intuition, Kant was able to explain how it can be known a priori and at the same time be "objectively valid," applying to all objects of intuition. Those objects are appearances and not things in themselves. We know these things only through sensibility, so they are things in relation to our mode of intuition. A thing in itself would be a thing apart from this relation. Sometimes Kant called it a thing in general, at other times he called it an object of the pure understanding or noumenon. But this concept harbors many difficulties. As one of Kant's early critics, F. H. Jacobi, put the matter: "Kant cannot live with the thing in itself, but he cannot live without it."
Empirically real outer objects depend entirely on space for their properties. Their primary qualities (if you will), extension, motion and rest, attraction and repulsion, all are spatial; without space, they would have no properties at all. If this is right, then when we attempt to think away the spatial properties of outer objects, we are left with nothing. Are things in themselves, then, nothing? Or are appearances mere fabrications?
An obvious criticism of Kant's doctrine is that by claiming that things in space are appearances, he means that they are only apparently spatial. This Kant denied most vehemently. Mere seeming (Schein) occurs when we are deceived by an object of experience, e.g. by thinking we see water when there is only the hot desert sand. But appearance, (Erscheinung) is real; it has what Kant called empirical reality.
On the other hand, appearances are transcendentally ideal. They are a priori conditions of sensibility. (The word 'transcendental' was used by Kant officially to refer to what pertains to the a priori.) What would be transcendentally real is objects which are independent of these conditions, things in themselves. But we have no intuitive access to such things. In fact, the belief that we can know things in themselves gives rise to a special kind of illusion, transcendental illusion, which will be discussed later in the course.
This ends our discussion of space as such, and we now turn to the other form of intuition, time. Much of the argumentation pertaining to space is applicable, mutatis mutandis, to time, so I will not rehearse the arguments. As space is the form of outer intuition, so time is the form of inner intuition. We represent our own mental states as succeeding one another in time. Whereas space is three-dimensional, time is one-dimensional.
The bifurcation of the objects of space and time in to outer and inner appearance, respectively, raises an important question. How can Kant say that outer objects are in time? The answer is a bit convoluted. Since we represent objects in space through outer intuition differently as objects occupy different positions, there is a succession of mental states of representation. We must represent these as in time, so we indirectly subject the outer objects to time. "But since all representations, whether they have for their objects outer things or not, belong, in themselves, as determinations of the mind, to our inner state; and since this inner state stands under the formal condition of inner intuition, and so belongs to time, time is an a priori condition of all appearances whatsoever" (A34/B50).
So time is the mode by which we represent our inner states, and through those state the states of things outside us. Time is ideal, a form of inner sense, and the self which we experience (the "empirical self") is thus an appearance, not a thing in itself. This doctrine gave rise to Lambert's objection, discussed in the "Elucidation." Since change depends on time, then the self, as a thing in itself, is not subject to change, or, if it is, it is real. But time is said to be ideal. In response, Kant claimed that time is real, it is "the real form of inner intuition." Still, this leaves Kant in the position of having to admit that if we were able to know ourselves as things in themselves, we would not be able to attribute change to ourselves. And this raises the troublesome question of why Kant could appeal to the successiveness of our activity of representing, as he does later in the Critique.