The topic at hand is Kant’s basic argument for the claim that synthetic a priori judgments bringing objects of experience under the categories apply to those objects. Reference will be made to the Critique of Pure Reason (CPR).
Kant’s nonbasic argument may perhaps be considered the entire Critique, or at any rate every deduction and aesthetic treatise that precedes the argument presented in what follows. So, in my account of this topic, I believe an achievement of something like a narrow clarity may be ambitious enough. Therefore the aim is to describe Kant’s strategy for the argument and then to retrace his steps in moving through it. No attention or space will be given to a critical examination of the argument.
I will avoid giving a lengthy account of the categories of understanding, though they are mentioned in the topic. It should be sufficient to say that they are not “categories” in a taxonomical sense, but may be thought of as universal predicates — the twelve categories of understanding are meant to be Kant’s account of all possible qualities of general objects of intuition as they can possibly be experienced. Their function in his scheme is to help to circumscribe the realm of possible experience and limit a priori knowledge to those objects of possible experience (CPR B166-167). The difficulty Kant means to address arises from the fact that synthetic a priori judgments necessary to bring objects of experience under the categories are ampliative mental functions which are meant to unify concepts in consciousness; they do not seem to be “entitled” to apply to objects of experience directly.
At this point I will begin outlining the argumentative strategy given in the Critique. Kant claims that the possibility of pure (a priori) synthetic judgments will be found in, and found necessary, by way of three grounds, which are: first, inner sense and its a priori form, time, because in time are contained all representations, second imagination, because imagination spontaneously synthesizes representations, and thirdly the unity of apperception, because all representations are unified in relation to a constant self or consciousness (CPR B195, footnote on B162-164). His goal is to link these three concepts to empirical knowledge, and then to show that the conditions of the possibility of experience (from which we gain empirical knowledge) are the same as those conditions for the possibility of objects of experience. This, he argues, will show that these conditions “possess objective validity in a synthetic a priori judgment” (CPR B197). Which is to say that, if he succeeds, synthetic a priori judgments made under the conditions of the possibility of experience (i.e., in space and time) will have objective weight in that they can legitimately regard the objects of experience (spatio-temporal objects). This would justify his claim and solve a problem of critical import to the Critique.
In the dense section spanning B194-B196, Kant first attempts to link the three grounds to the possibility of empirical knowledge in general. Kant first argues that knowledge in general gains sense and meaning by its reference to objects, and then applies this notion to concepts; concepts must have reference to actual objects or they are merely representational playthings. This of course includes even pure concepts, such as space and time. So Kant claims that the representation of space and time (in consciousness) is a “mere schema” through which the reproductive imagination works to “call up and summon the objects of experience.” This has the effect of connecting pure concepts of the understanding, which are constructed a priori and housed in sensibility to the empirical realm.
Kant then argues that without a synthesis according to rules, these objects of experience would only amount to a “rhapsody of perceptions” — no unified experience, no knowledge. However, since we do admit the possibility of experience (which entails a unified apperception!), it must be the case that there are rules governing the synthesis of our perceptions, rules that have objective reality. In one sense, this could be a much easier answer to why a priori synthetic judgments apply to objects, but it is not one that seemed to satisfy Kant in this passage. In these two preceding sections he seems to have completed the first half of his task – establishing a link between the three grounds and a possible empirical knowledge.
He makes a further argument, beginning at the bottom of B196, that our secured a priori synthetic judgments about space have a mediate relation to possible experience because space is one of the conditions under which experience can occur — and he claims alone this anchors those judgments in objective validity. In the paragraph that follows, when Kant claims that “experience is in its possibility the only kind of knowledge that imparts reality to all other syntheses,” I take this to mean that we only conceive as real, and thus eligible for synthesis in experience, those objects which we know are possibly real. This amounts to an a priori synthetic judgment about what is strictly required for a synthetic judgment to occur – that “every object is subject to the necessary conditions of synthetic unity of the manifold of intuition in a possible experience” (CPR B197). It seems that this completes the second half the task that Kant has undertaken in this passage.
The Kantian argument, presented above, is meant to substantiate the claim that synthetic a priori judgments apply to objects of experience to be brought under the categories. Kant first had to show how pure concepts of the understanding can refer to empirical entities as they are spontaneously generated by the imagination. He then argued that experience must be synthesized according to rules because without such rules, our perceptions would be anarchic and any kind of intersubjective discourse would be impossible. He concluded by showing that the a priori conditions of experience are such that every object presented to us in the manifold of intuition must be subjected to a synthesis that accords with those a priori conditions.