A a priori judgment is such that it cannot be falsified by experience. So a true a priori judgment, if it applies to objects of experience, is necessarily true with respect to those objects. This does not mean that it is necessarily true in any absolute sense, however. That is, one may be able to conceive of a state of affairs outside the realm of possible experience which falsifies the a priori judgment, so that it is possible that it is false. But it remains necessary relative to the objects of experience. This notion of relative necessity is fundamental to Kant's metaphysics. Kant held that it was the failure to so restrict the claims of metaphysics that was responsible for its sorry state.
There is still something strange-sounding about Kant's thesis, however. For why should anyone think that we can make judgments independently of experience which nonetheless are necessary only relative to objects of experience? Here Kant states that he has revolutionized metaphysics in a manner analogous to Copernicus' revolution. The prevailing view was that the truth of metaphysical judgments required that they conform to objects. Kant's revolutionary alternative was to suppose that objects conform to our way of representing them.
With respect to intuitions, if it "must conform to the constitution of the objects, I do not see how we could know anything of the latter a priori; but if the object (as object of the senses) must conform to the constitution of our faculty of intuition, I have no difficulty in conceiving such a possibility" (Bxvii). The same idea applies to the use of concepts. The understanding supplies rules to which objects of experience must conform. Kant called this switch Copernican because of the change in perspective it involves (though unlike Copernicus' hypothesis, Kant's puts the human subject in the "center" of things).
Kant made another analogy, this time with the ancient mathematicians who converted geometry from an empirical science (useful in surveying after the annual flooding of the Nile) to an a priori science. They did so by recognizing that the objects of geometry are constructed. In Euclid's Elements, the proofs proceed by the construction of various figures (straight lines and circles) and reasoning about the consequences of the construction. Thus if the geometician "is to know anything with a priori certainty he must not ascribe to the figure anything save what necessarily follows from what he has himself set into it in accordance with his concept" (Bxii).
At this point, we may return to the discussion of synthetic judgments a priori. We can now see why Kant believed that mathematical judgments are a priori. Besides the fact that they are necessary, they depend not on a given object but on the construction of their objects. The fact that the objects are constructed is the reason why judgments about them are synthetic. One cannot by comparison of the concepts 'straight' and 'shortest' infer that a straight line is the shortest distance between two points. "The true method . . . was not to inspect what he discerned either in the figure, or in the bare concept of it, and from this, as it were, to read off its properties; but to bring out what was necessarily implied in the concepts that he had himself formed a priori, and had put into the figure in the construction by which he presented it to himself" (Bxi-xii). It is the manner of construction of the straight line which insures that it is the shortest distance between two points. Arithemetic also proceeds by the construction of its objects, i.e., of numbers. The sum of 7 and 5 is a number which must be constructed by the successive addition of unit to unit.
We can now say that the X which unites subject and predicate in a mathematical judgment is the construction of the mathematical object. In a priori synthetic judgments applying to the objects of experience, e.g. that every event has a cause, the X will be the construction of the empirical object. This is a tricky notion to understand, involving as it does mysterious faculties such as the "transcendental imagination," which is discussed in the most difficult section of the book, the Transcendental Deduction of the Categories.
We will begin our examination of the construction of objects with intuitions. And once again we run straightaway into a puzzling situation. For it is to intuition that objects are given to the mind. Yet in order that there be a priori synthetic judgments true of those objects, the obejcts must be constructed. The solution is to distinguish between the form and matter of intuition. It is the matter of intuition which is given to the mind, while the mind supplies the forms of intuition. The matter is a "manifold" that corresponds to sensation, and the forms of intuition are space and time, which bring a certain order to the manifold.
Insofar as the mind supplies the forms independently of the the experience of given objects, these forms are a priori. Space is the form of outer sense (which represents bodies), and time of inner sense (which represents our own mental states). Momentarily, I shall begin discussing space, but I must note that the tension between the givenness of objects and their construction has only been papered over at this point. A compelling dilemma will be revealed at the end of this lecture.
Kant was concerned with the metaphysics of space from early in his career. The issue was hotly contested, as it pitted the two giants Newton and Leibniz squarely against each other. The debate was carried out in a series of papers exchanged between Leibniz and Samuel Clarke, a disciple of Newton -- a debate which ended with the death of Leibniz. Much of the exchange was sterile, reflecting the radically opposing points of view of the two philosophers of nature.
Newton was the partisan of absolute space, a metaphysical reality in its own right. Properties of bodies, such as extension, figure, motion and rest depend on their being in space, according to Newton. (For more, click here.) At the opposite end of the spectrum was Leibniz, who denied both Newtonian theses. Space is relative to bodies in it, having no reality of its own. Instead, space is an ideal thing, a fiction. And the properties of bodies are complete without any reference to space at all. Bodies have relational properties, their places, but place is not a relation of a body to space. (For more, click here.)
Kant had rejected the Leibnizian doctrine of space earlier in his career. In 1765 he published an article ("Concerning the Ultimate Ground of the Differentiation of Directions in Space,") purporting to prove that there is absolute space. If Leibniz were right, relations of place or position are enough to account for all the spatial properties of a given body. Thus two bodies, all of whose parts stand in exactly the same position relative to one another. "If one looks at one of them on its own, examining the proportion and the position of its parts to each other, and scrutinizing the magnitude of the whole, then a complete description of the one must apply in all respects to the other, as well." But this description leaves out the fact that one object (say a right hand) cannot occupy the same area of the other (a left hand of the same size and shape). So, Kant concluded, the directional properties of things involve a reference to something else: absolute space.
Against Newton, Kant held that space is not a metaphysical reality in its own right. It is neither a substance or a property of a substance. However, it is something upon which bodies depend for their properties. This again seems inexplicable, but Kant holds that it is possible because bodies are appearances, not things in themselves. As appearances, bodies can depend on a space which is not a metaphysical reality, because they themselves are not metaphysical realities in their own right. Thus space is a form of human intuition, a product of our sensibility, which gives order to a manifold presented by sensation. "Since we cannot treat the special conditions of sensibility as conditions of the possibility of things, but only of their appearances, we can indeed say that space comprehends all things that appear to us as external, but not all things in themselves, by whatever subject they are intuited, or whether they be intuited or not" (A27/B43). In a sense, Kant tried to carve out a niche between the Newtonian and Leibnizian theories of space. With Newton he accepted the view that the properties of bodies depend on space, rather than vice-versa. With Leibniz he accepted the notion of space being dependent on the human mind, though of quite a different sort than the fictitious product of a confused sensibility that Leibniz had described. There is also something Leibnizian in the view that space provides unity to a manifold given in sensation.
The notion that space is a form of intuition special to the human subject led naturally to Manuel Vargas's question in class. If the subject were to be changed in some fundamental way, say by a major alteration in its body, would the "appearances" for it change as well? First, it must be noted that Kant believed that sensibility is a faculty of the human mind, and that it is independent of the body. So no alteration of the body could result in a "deformation" of our faculty of sensibility.
But immediately a troublesome point arises. What are we to make of the notion of "sensibility" or of the mind being "affected" by its objects if sensibility is not, even in part, a bodily faculty. The senses themselves -- the eyes, ears, nose, etc. with their associated neural circuitry -- are all parts of the body. But bodies themselves are appearances, and hence the products of affection. And if it is not through our bodies that we are affected, how are we affected? The same question can be asked about Kant's claim that in inner sense (under the form of time), the mind affects itself.