Substance is one of the twelve categories or concepts of the understanding. Its correlate is the concept of accident. In the Table of Categories, it is classified as a category of relation, specifically as inherence and subsistence (substantia et accidens) (A80/B106). In the Prolegomena, the category is referred to simply as “substance” (Ak IV, 383).
Inherence is the existence of accidents of a substance, while subsistence is the existence of the substance itself. Accidents are defined as the determinations of a substance, while a substance is that which is determined by accidents.
Substance/accident is an a priori pair of concepts, in that it cannot be removed in thought from our empirical concept of any object (B6).
If from your empirical concept of any object whatever, corporeal or incorporeal, you omit all properties that experience has taught you, you still cannot take away from the concept the property through which you think the object either as a substance or as attaching to a substance (even though this concept of substance is more determinate than that of an object as such. Hence you must, won over by the necessity with which this concept of substance forces itself upon you, admit that this concept resides a priori in your cognitive power. (B6)
The basis for the concept of substance is to be found in logic, specifically in the logical concepts of subject and predicate, which together with the copula make up a form of judgment. As a “form of thought,” substance is that which “can exist as subject but never as mere predicate” (B149). Correspondingly, an accident would be that which exists as predicate but never as subject.
We cannot apply the concepts substance/accident to any object but appearances, objects in space and/or time. For example, we might try to apply it to ourselves as thinking beings.
Now in all our thought the I is the subject wherein thoughts inhere only as determinations, and this I cannot be used as the determination of another thing. Hence everyone must necessarily regard himself as the substance, but regard thought as being only accidents of his existence and determinations of his state. (A349)This application of the category of substance is empty, however, unless it states something about the persistence of substance over time. Hence, it is of value only when applied to myself as appearance. The mere presentation of ourselves as thinking does not yield any information about our temporal properties. (This is argued in the First Paralogism.)
The application of the category of substance to appearances takes place only insofar as the category has a “schema” connecting it with time. The schema of substance is permanence, i.e., persistence through time. Correspondingly, accidents are the transitory. So to bring appearances under the concept of substance, we think them as consisting of persisting beings with transitory states. That we are justified in so thinking them, and indeed must think appearances this way, is argued in the First Analogy. For a discussion of this argument, see the lecture notes for the First Analogy
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