What is Kantian Accounting?:
Kantian accounting refers to a general method of developing formal conditions with which one can think about the necessary in experience, or account for experience, or hold experience accountable for what it provides rather than what it already demanded to be given as it is (these all be taken to be equivalent in this case). These conditions aren't an addition to our a priori knowledge, but the result of an examination of experience to determine which concepts must be assumed in discussion about experience, as well as faculties that render the synthesis between these ways we must think our a priori concepts with our learned a posteriori concepts.
Employment of the Method:
The primary goal of the first half of the first critique (Transcendental Doctrine of Elements) is to provide a grasp of the elementary components in transcendental philosophy, and a consistent language to employ when talking about them. To do this a process of abstraction is employed; this is seen most clearly in the Transcendental Aesthetic with space and time.
In the Transcendental logic Kant still uses abstraction, but employs a structure to help him get an image of how he wants to tackle the division of pure concepts. That he already divided experience up into intuition and concept was important, because the focal point of the Transcendental logic was to account for the connection of concepts to experience, as well as the results of our employment of pure concepts alone to acquire new knowledge (Transcendental Dialectic). Judgments are what Kant calls what we employ to place objects under concepts, and so it was natural for him to base his division off a table of all judgments, which he provides on A70, B95.
If the table of judgments is a model that is successful or not is tested by seeing if the categories Kant develops off of it are sufficient for providing all of the pure modes in which we judge an objects, or objects under concepts. Further, the pure employments in combination of the categories, and the interesting limits that they set to our knowledge, provide fertile ground for additional development and work about a priori concepts.
The test of the completeness of the categories is beyond the scope of this blog post, but at least we can go one step further and notice an interesting addition to this that applies to Kant's entire architectonic.
Formal Accounts Are One and All Mutable:
In providing a formal account Kant does not also need to provide the sole or even normative way that something is talked about; as long as what is provided in an account is complete, then it is at least sufficient. The addition of more distinction and organization, which is available in abundance in Kant's architectonic, is not an addition from necessity to the demand of accounting, but a potential benefit for adoption of his architectonic. It is possible to find a clearer way of dividing up the roles of the a priori; this is not necessary, but certainly helpful, particularly in certain problem domains where the sheer quantity of distinctions Kant makes are unnecessary and even cumbersome.
The use of Kant's accounting is found in criticism of attempts to employ the concepts in the account outside of their proper realm. If a better system for such criticism is available, or better fits a mode of thought or discussion, it would seem a practical demand to adopt the account that better suits the purposes of the critique at hand. It does make sense to have a well developed set of concepts and terms that are well understood by many people so that much of our work will be the translation of one system to another, but I can only recommend Kant's system from my own familiarity with it, and am open to the idea that there may be a more subtle system possible either preexisting Kant's, entirely original or simply built on top of Kant's architectonic.