Part three of my commentary on Deleuze’s Kant seminars
Deleuze’s fourth seminar on Kant looks in more detail at how the correspondence between conceptual and spatio-temporal determinations, touched on at the end of Part Two, is established, through what he calls “two great operations of knowledge.” These operations; the “synthesis strictly speaking” and the schema, are acts of the productive imagination, the faculty that determines “a space and a time in conformity to a concept, but in such a way that this determination cannot flow from the concept itself.” The synthesis and the schema are not in themselves judgments of what is before us, rather they connect, in different ways, the concept to the diversity, so we can say what is before us through our faculty of understanding.
The schema and the synthesis strictly speaking (“synthesis” from now on) are both synthetic operations, i.e. they bring heterogeneous elements together. They differ from each other in their relation to time and in the order in which the concept and the space-time diversity are brought together. The synthesis operates on the here and now of the spatio-temporal diversity, a process of apprehension and reproduction, through which we recognise what is before us. In the moment of recognition we apply the concept to the diversity, we say what it is; “its a table.” While the synthesis works from the diversity, the schema starts from the concept, as such it is valid at all times and not just here and now as with the synthesis. Also, unlike the synthesis, which is governed by the rule of recognition, the schema operates under the rule of production.
Deleuze turns once more to geometry to demonstrate the schema in operation, starting from two judgments of a straight line. The first says: “the straight line is a line equal in all its points,” this a definition which gives us the concept of the straight line. The second judgment says: “the straight line is black,” this gives us a judgment based on experience, i.e. an empirical or a posteriori judgment. He then goes onto a third judgment: “the straight line is the shortest path from one point to another.” Unlike the previous judgments the line here, despite appearances, is not associated with a predicate, i.e. that it is black or equal in all its points. Instead the shortest path is a rule of production (cf synthetic a priori judgments in Part One), it tells us how to produce a straight line in space and time; hidden behind which is the “Archimedean theme of the… smallest angle which is formed by the tangent and the curve,” the calculus of exhaustion. Therefore the shortest path is not a predicate of a line given in a conceptual judgment, but a rule by which I produce a straight line in space and time. It is the schema by which the concept of the straight line is connected to what appears; the straight black line.
Deleuze now goes on to examine the schema of a circle, starting again with its concept: “where points are situated at equal distance from a common point named centre” (4, 6). The experience of the circle can be found all around “the sun, a plate, a wheel.” But what is between them that allows a connection to be made between the concept and these spatio-temporal diversities, i.e. what is the schema of the circle?
Deleuze’s answer to this is: “the round,” (le rond), which, rather than being an attribute of the circle, is, like “take the shortest.” a rule of production. “The round is what allows us to make a circumference,” which in turn “allows us to make certain materials round.” Like the shortest path, the round is experienced as a dynamic process, an operation in which “something in experience is rounded.” The round, as the schema of a circle, is “a process of production of the circumference-type which allows the production in experience of things corresponding to the concept circle” (4, 6). The schema determines space and time in conformity with the concept, but without the intervention of the concept, i.e. it is an act of the productive imagination.
Deleuze develops this further by asking what is the schema of a lion? Again we start with the concept, using the scholastic method of genus and specific difference: lion, genus: mammal, specific difference (not wholly seriously): with a mane that growls. Its appearance in space and time can be thought as the illustrations or images we make of lions; “a small lion, a big lion, a desert lion, a mountain lion.” The lion’s schema is to be found between these, in its spatio-temporal rhythms or dynamisms: “the way in which it produces a spatio-temporal domain in experience in conformity with its own concept.” The lion is productive in its movement through its environment, the paths and traces that it leaves in its domain, “the times that it uses a particular path.” i.e. the way it inhabits space and time, which we can never derive from its concept. We can also get something of this from a single tooth, we can see that it is a carnivore. From this Deleuze concludes that the schema of an animal “is its spatio-temporal dynamism” (4, 7)