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. 

Joker and Film Theory

This year I used Joker as an example of introducing film theory and wanted to share.

A few things to note:

Theory is hard. It requires you to read and re-read. It is not ready-made. But don't be overwhelmed. It takes time to learn the terminology. But it is a rewarding process.

Theory is not "good" or "bad" criticism. That's for movie reviewers, or what is known as evaluative criticism. I LOVE Siskel and Ebert, but no thumbs-up or thumbs-down when writing theoretically about film. You want to write critically which involves theory...

What insights does Joker offer for film theory?

Auteur Theory: Todd Phillips is probably not someone we think of as an auteur (evaluative). The Hangover movies or Old School did not garner Academy Award nominations.

 

But good and bad taste is not relevant here. As long as the director has a body of work, you can conduct an auteur analysis. 

 

You can also write about unconscious themes of a director's work - that is, themes the director did not know were showing up throughout their films. 

 

But this also raises an important point about writing theory. Rhetoric. Can you persuade me that Phillips is an auteur?

 

Genre: We all know genres. Joker not only challenges our expectations of the superhero genre, but even those who have played the Joker. 

 

 

Why does Joker challenge our expectations?

 

For one, the film is a slow burn, moving toward Arthur Fleck's transformation. Fleck is also an unreliable narrator, something we often don't see in superhero movies.

 

Could Joker impact future movies the way Pulp Fiction did in 1994? 

 

 

 

Genre theory often investigates how genres develop over time. Rick Altman's semantic/syntactic approach is key to explaining this. 

 

 

Altman's analysis moves away from bad and good judgement, and points us toward the evolution of genres, looking at how a film articulates the traits of a given genre and the deeper meanings it can convey. The two are interconnected.

As time passes, we may look back at Joker and other superhero films and try to understand why they were so popular with audiences.

Art Cinema and Narrative Theory: Joker shares many traits of art house cinema, such as ambiguity, loose narrative cause and effect, and digressions. 

 

To understand art house cinema traits, we have to weigh them against classical narrative, which often entails strict cause and effect, little or no ambiguity, and closure. See David Bordwell's article "The Art Cinema as a Mode of Film Practice.

 

Joker is not a strict cause and effect narrative, as the entire film is told through Fleck's perspective. It has digressions, such as the bathroom dance sequence and Fleck dancing down the steps. 

 

 

Joker has ambiguity. Early in the film we think Arthur is dating Sophie. But this is not true, because there is little indication we are inside of Arthur’s mind. It is not surprising that Joker has been compared to Martin Scorsese's Taxi Driver.

 

 

Semiotics: The study of signs. A key component of semiotics is inventorying signs—looking for patterns in a movie. A key theorist is Roland Barthes. His work draws our attention to a film's literal and figurative meanings.

 

Consider Arthur's dance down the stairs. There are multiple meanings. It is not only literally him going up and down, but a sign of his transformation.

 

 

At the start of the film he lumbers up the stairs after he is fired as a clown. On his way to Murray's talk show, toward the end of the film, he dances down the stairs, going into full Joker mode.

 

Realism and Formalism: One of the central questions early film theory took up was whether cinema has an essence. That is, is there something inherently significant about movies.

 

Andre Bazin argues it is cinematic space (mise-en-scene) that is significant to cinema. He loved movies that allow you to look within the frame, movies that try to mimic the structures of reality. Long takes and deep focus photography are techniques he championed in cinema.

 

Joker shares certain aspects of Bazanian realism, particularly its emphasis on the grittiness of the city. In many ways, the grittiness of the film captures Arthur's uncertain state of mind.

 

 

These are just some examples of how Joker can be a good way to begin film theory. I also recommend Kevin McDonald's excellent book.

 

 

The Seventh Seal and Ingmar Bergman

When I first taught world cinema, I knew I wanted to assign Ingmar Bergman's The Seventh Seal (1957). But when the time came to put my lecture together, I was surprised by how difficult this film was to teach. After finding some very good articles (see below), I found teaching this classic film by one of my favorite directors to be very rewarding.

 

Strangely, this past winter I taught The Seventh Seal right before Covid-19. It was also around the same time Max Von Sydow passed away - one of the stars of the film. Even before Covid, I would offer guiding questions to consider current films or television shows involving a plague or dystopia setting. Before I get to that, here are some points I addressed in the film. This lecture was structured from Birgitta Steene's and Marilyn Johns Blackwell's writings on the film.

Interior Landscape 

Bergman’s films often focus on an interior landscape, a reflection of a state of mind. Here we can see the impact of German Expressionism. Think of the expressive settings of The Cabinet of Dr. Caligari and how they embody the dark psyche of Cesare and Dr. Caligari.

 

Likewise, expressionism informs The Seventh Seal when the Knight is tormented by his own doubts. Bergman captures the Knight's interior through the harsh, rigid, and Gothic landscape that opens the film when he encounters Death.

Compare the film's opening to Jof, the traveling performer, who has a vision of The Virgin Mary. Here the angelic and serene landscape is much different from the dark and ominous opening of Death's arrival on the beach. Both scenes demonstrate Bergman's expressive use of mise-en-scene in capturing an interior landscape.

 

Art Cinema

The Seventh Seal is a classic example of European art house cinema, demonstrated by its loosely structured narrative and bleak ending. It is a film that intellectually challenges us. The film is not a strictly goal orientated film. Rather it is structured by the reprieve Death offers the Knight. The looseness of the story allows Bergman to digress the narrative into some interesting moments, particularly the flagellation scene.

 

At the same time, Bergman’s journey narrative has a purpose. This is certainly the case for the Knight. There are random events, but they do lead to his self-confrontation in the form of death at the end of the film. See David Bordwell's article on art house cinema.

(Notice how the geometric patterns entrap the Knight, suggesting he cannot escape death.)

 

Philosophy

Existentialism is often discussed in the context of The Seventh Seal. As Steene writes, "The Seventh Seal is an allegory with a theme that is quite simple: man, his eternal search for God, with death as his only certainty" (62). And Blackwell notes, "A major impetus behind the international fascination with The Seventh Seal lay in the political climate of the mid-1950s (576)."

The Seventh Seal engages with the existential view that a human life is decided in the choice of action.  Relevant here is French philosopher and writer Jean-Paul Sartre’s notion that “existence precedes essence.” In other words, essence is not predetermined but manifested through our choices and actions. Here, Blackwell makes reference to social concerns of the late 1950s, particularly the threat of nuclear Armageddon. And we can see how the dark themes of Bergman’s film could grab hold of the viewer’s imagination during that time.

I build upon this point by having students think about what current shows and movies invoke dark or dystopia themes. Answers I often get are The Walking Dead  and The Handmaid's Tale. I often cite post 9/11 films such as Children of Men or Cloverfield.

 

 

The famous final image of The Seventh Seal is the dance of death, which is taking from a painting.

 

 

The painter in this scene is based on Albertus Pictor who was a famous medieval Swedish painter. His dance of death church wall painting of Death playing chess directly informs the opening and ending of the film.

 

 

The Seventh Seal is a complex film on many levels. It is expressionistic, it demonstrates the art cinema mode of filmmaking, it engages with philosophy and also speaks to its current moment in the late 1950s. 

 

 

Perhaps more importantly, The Seventh Seal is a personal film for Bergman who was working through his own demons. As Peter Cowie puts it: “Bergman is exorcising his own demons, his own dread of the eternal darkness, and to his surprise and delight this process has appealed to audiences in practically every corner of the world” (cited from the Criterion disc).

 

Here are some other books and movies to discuss in relation to The Seventh Seal:

The Stand by Stephen King. King talks about the energy crisis at the time he wrote the novel.

PD James's Children of Men. For the movie, I often bring up social concerns post 9/11. For the book, which was published in 1990, I think it is more relevant to AIDS.

 

Sources:

The Seventh Seal” from Ingmar Bergman by Birgitta Steene, pp.61–69

The Seventh Seal: Cinematic Form and Cultural Criticism” in Film Analysis (Second edition) by Marilyn Johns Blackwell, pp.574–592­