Immanuel Kant - The Schema

I found some papers I wrote in grad school and thought I would share. This one was from a class I took on Kant's Critique of Pure Reason. It explains the concept of the schema. I remember this was a strange concept when I first learned it. I would later learn Slavoj Zizek would sometimes use the schema to explain how fantasy works. I hope you find this helpful. I am using the Cambridge edition, citing A/B version of the Critique.

The purpose of this paper is to investigate Immanuel Kant’s critique of abstract concepts. For Kant, to unravel an abstract concept is to know the determinate rules for human cognition; that is, to uncover the forms of judgment that allows one to conceptualize an object of experience. Empiricist philosophers such as Hume and Locke have tried to solve the problem of abstract concepts but without the employment of a priori conditions. The starting point for both Hume’s theory of impressions and Locke’s theory of ideas is the realm of experience. However, for Kant, experience as a starting point cannot demonstrate what is universal and necessary for the possibility of a priori judgments. To solve the problem of abstract concepts, Kant introduces the notion of a schema which is a determinate rule that mediates the relationship between appearances and the categories. There are three problems of abstract concepts associated with the schema: empirical concepts (in relation to the universal and particular), pure sensible concepts, and pure concepts of the understanding. In this paper I will explain the problem of empirical concepts in regards to the particular and universal, which the empiricist philosophers could not solve, and show how the employment of the schema solves the problem of abstract concepts.

 

In the section on transcendental deduction, Kant demonstrated how the combination of the transcendental aesthetic (the conditions of time and space) and the pure concepts of the understanding present the possibility of experience. Per Dieter Henrich, Kant’s transcendental deduction is a two steps process in a single deduction, exemplifying the connection between the intellectual and sensible conditions of human knowledge. The importance of the transcendental deduction is that it demonstrates the objective validity of the categories for the possibility of experience. Objective validity is vital for Kant’s transcendental deduction because it establishes the necessary truth for the possibility of judgments. 

 

The transcendental deduction, however, only tells us the story on how forms and structures operate within the mind. Kant’s next endeavor must present the empirical side of the story in order to fully proclaim his Copernican Revolution; that is, objects conform to our knowledge. To fully solve the problem of abstract concepts, we must understand how content is employed within the forms of the mind, because, as Kant states, “Thoughts without content are empty, intuitions without concepts are blind” [ B75/A51]. Without the employment of content, the categories of understanding would remain idle. 

 

Kant posits that general logic cannot supply the rules or forms for the power of judgment, noting that “General logic contains no precepts at all for the power of judgment, and more over cannot contain them” [B171/A132]. For instance, everyone can learn how to interpret a type of triangle or square, such as a right angle or a rhombus; but the power of judgment through the lens of general logic cannot state that this particular triangle or square is universally correct. Paul Guyer explains in Kant and the Claims of Knowledge, “If rules were needed to apply concepts, which are themselves rules, then further rules might be needed to apply concepts, which are ad infinitum” (162). General logic cannot inform what the determinate rules or precepts are for the power of judgment. Applying one rule to another rule under general logic leads to an infinite regress and not what is necessary and universal. 

To avoid the problem of an infinite regress Kant argues that there must be determinate rules (forms and structures) for the power of judgment. The transcendental deduction alone cannot produce an object of experience. The combination of the manifold of intuition and the categories require an additional mechanism to direct the appearances in order to produce an object of experience. Kant notes, “[T]he function of the understanding in the category must also contain a priori form conditions of sensibility … that contain the general conditions under which alone the category can be applied to any object” [B179/A140]. For Kant, there must be something “homogeneously contained” in the representation of the object in order to arrive at the concept of an object such as a dog or a plate. Kant notes, “In all subsumption of an object under a concept the representations of the former must be homogeneous with the latter” [A137/B176]. The notion of subsumption posits something particular in the representation that is homogeneous with the object. In other words, properties of objects are represented by predicates, and what links the predicates to the categories is what Kant terms the schema.  

 

The schema is a determinate rule that mediates that relationship between appearances and the categories. The schema is pure a priori and is also sensible because its application to the category is transcendental time-determinate. Kant notes, “[An] application of the category to appearances become possible by means of transcendental time-determination which, as the schema of the concept of understanding, mediates the subsumption of the later under the former” [B178/A139]. The transcendental deduction cannot mediate the appearance to the categories because pure concepts have they no time determination. It is the schema as a transcendental time-determinate that links the appearance to the categories. Every sensory application must contain time; and because time is a prior, the schema is therefore a transcendental procedure.

 

Kant demonstrates the notion of the schema through the concept of a plate. Our arrival at a concept of plate (as an empirical image) is because we have a concept of circularity or roundness which subsumes under the concept of plate. That is to say, the concept of plate homogeneously contains a mark of roundness. The predicate “roundness” delineated by the schema links the categories to the concept of a plate. 

 

One can also think of the schema as a theatre usher. We have the patrons which represent the unperceived data of the manifold. The manifold (the patrons) are ordered and filtered through the doors to the theatre in regards to time and space; and, lastly, the aisles acts as the categories with each seat being a mode under the tables of categories. The schema is the third element that ushers or mediates each patron into their seat or mode under the categories. The usher would be the only one who knows where to seat the patrons. 

As noted earlier, one of the three problems of abstract concepts associated with the schema is empirical concepts (the relationship to the universal and particular). Particularities are concepts we come to know in the phenomenal world such as a dog or a plate. Universals are forms that are rule governed and are the workings behind the scene that allow the particular to emerge. Empirical philosophers have not been able to provide a theory on how we can formally know an object of experience because their starting point is the particular not the universal. Philosopher such as Hume and Locke have argued theories that relate to empirical concepts, but nothing that demonstrates universality on how we come know an object of experience. For instance, Hume’s theory of impressions posits the mind can know, for example, the concept of dog based on one’s past experience of various breeds of four-footed animals. For Hume, the mind constructs a judgment based on resemblance, contiguity and causation. And over time, the mind creates a building block of this past experience. For example, I can know the difference between a Poodle and a Bulldog because my mind compares and contrasts with those particular breeds based on past experiences. That is to say, Hume’s theory works with the relations of the particular based on past judgments of dogs. But particularity cannot arrive what is necessary and universal. Hume’s theory of impressions cannot solve the problem of abstract concept because it does not provide a general rule for human cognition on how one comes know the concept of dog. 

 

Moreover, empiricist philosophers could not solve the problem of abstract concepts because they were working from what Kant calls the reproductive image (the empirical image). For Kant, empirical images cannot produce a proper theory of knowledge because it represents particularity, not universality. As Kant notes, “The concept of dog signifies a rule for in accordance with which my imagination can specify the shape of a four-footed animal in general, without being restricted to any single particular shape that experience offers me or any possible image that I can exhibit in concreto” [B181]. The schema solves the problem of abstract concept because the predicate “a figure of four-footed animal,” as rule is subsumed in the empirical concept of dog. The schema constrains the categories because it is impossible for the mind to think of all types of dogs in one given thought. The problem the empirical philosophers wrestled with was they were working from the image itself. The empirical image cannot be a determinate rule because, as pointed out with general logic, it is always relative. Kant states, “The schema is in itself always only a product of the imagination; but since the synthesis of the later has as it aim on individual intuition but rather only the unity in the determination of sensibility, the schema is to be distinguished from an image” [B179/A140]. The schema is not the conclusion (the empirical image), but is the procedure (pure a priori) that allows the conclusion (the concept of dog) to emerge. As Norman Kemp Smith notes in Commentary to Kant’s “Critique of Pure Reason” second edition, “Images become possible only through and in accordance with the schemata, but can never themselves be identified with them… Images are always particular; schemata are always universal" (338). It is the schema that mediates between appearances and the categories that makes the image of a dog or any object of experience possible. 

 

The notion of the schema debunks the empiricist’s problem of abstract concepts because it demonstrates a universal and transcendental procedure for the power of judgment. And because the schema is transcendental, it aligns with Kant’s Copernican revolution that object must conform to our knowledge. Thus, the schema is a transcendental time-determinate mechanism that mediates between appearances and the categories and thus, employs the form of judgments.