Sunday, November 27, 2016

Deriving the Table of Pure Concepts from the Table of Judgments

This is a brief attempt to show the relationship between the table of judgments and the table of pure concepts (categories). I will assume that the reader is already familiar with the table of judgments and categories, and generally what the categories are for.
The table of judgments is a clue for the discovery of the categories. The clue works in the following way: all of our judgments (of objects) can be described formally by their quantity, quality relation and modality. For example, "The cat is blue", is a singular (quantity), affirmative (quality), categorical (relational) and assertoric (modal) judgment.
Because we can identify these possible descriptors for all judgments, we can separate the content of the judgments from these formal marks. We can abstract the content from our above example and leave the form, which gives us, "the X is A." This judgment is still singular, affirmative, categorical and assertoric. The X now represents an object in general. From this point we can make much greater sense of how the table of judgments serve as a clue.
This object in general (X) doesn't represent a distinct object but is a stand in for any object that could replace it (e.g., 'cat'). When we only know X, we have no content to consider what X may be, but we do know that whatever the X may be, it will participate in judgments that have a form knowable in advance (quantity, quality, relation and modality). The pure concepts serve to describe X so far as we will be able to relate it to the form of judgments possible for Xs.
The categories represent the manner in which appearances are unified such that there can be judgments about them. (Would it make sense to call the pure concepts an algebra between appearance and judgment?)