Constructing a Geometry of Thinking, Research Time, 30/11/2017

Let's actually get a little bit into this idea of a geometry for philosophy. I talked yesterday about what a plane of immanence is – now let’s get into how particular planes work.

So Gilles Deleuze’s term, plane of immanence, is a map of concepts, a map of their mutual possibility. If you can develop a coherent philosophy out of a set of concepts, then that set all exists on the same plane of immanence.

That they can cohere means that their components and structures can all fit together without internal contradictions that make nonsense of the conceptual machinery. But that’s just one philosophical system that fits on the plane.

Imagine that you’re Bernhard Riemann. Sitting in your office, doing mathematics, like a mathematician would. You’re setting up some guidelines for how a particular type of space would work. You can extrapolate from those mathematical rules what types of shapes can exist in your space.

Deleuze: "The components of the schema are as follows:
1) the "I think" as an ox head wired for sound, which
constantly repeats Self=Self; 2) the categories as universal
concepts (four great headings): shafts that are extensive
and retractile according to the movement of; 3) the
moving wheel of the schemata; 4) the shallow stream of
Time as form of interiority, in and out of which the wheel
of the schemata plunges; 5) space as form of exteriority;
the stream's banks and bed; 6) the passive self at the bottom
of the stream and as junction of the two forms; 7) the
principles of synthetic judgments that run across spacetime;
8) the transcendental field of possible experience,
immanent to the "I"; 9) the three Ideas or illusion of
transcendence (circles turning on the absolute horizon;
Soul, World, and God).
A shape that fits a spherical-section space – space curved like a planet – will flay apart, unable to hold itself together, on a negatively-curved space – curved like a saddle. Same goes for shapes that work on saddle spaces splitting apart on spheres.

Now imagine that instead of setting up the boundary conditions for this geometric space, you had to figure out its parameters by trial and error. Try constructing different kinds of shapes and see whether they can exist together. If they can’t, then they each project from themselves a different type of space.

Well, that’s Gilles Deleuze sitting in his office, doing philosophy. But instead of shapes and spaces, he’s working with concepts – frameworks of organizing perceptual and cultural thought to understand our experiences and lives in different ways.

In philosophy, there’s no function to set the boundary conditions for the concepts you develop first. Philosophical concepts have many components organized in complicated ways. Check out this example of Kant’s philosophy. It’s a ridiculous-looking diagram, but it’s a genuinely pithy description (and depiction) of his concept of subjectivity.

Analyze this concept. Think about all of its components and their dynamic relationships with each other. How does this concept help us understand our own subject-hood, mind, personality, and experience? Once you understand all the concept’s components, internal dynamics, and practical effects, then you can start the next step in the process.

Yeah, I know. You’re not even done after all that work. At least this is only one possible process for philosophical thinking – it might be the most admirable, if you consider only the dedication to such a strange and difficult task. So here’s the next step.

Figure out its plane of immanence. Extrapolate from those components, dynamics, and practical affects what other concepts are compatible with this particular way of thinking. If you’re lucky, the thinker you’re studying has done a lot of the work for you. Like Kant, who developed concepts in morality, aesthetics, theology, and philosophy of science alongside his central concept of subjectivity.

Maybe you’re a bit less lucky, and the map expands across the work of many thinkers. You might study a particular tradition of thinkers, like the Abbasid-era Aristotelians.

Or maybe you do comparative philosophy, looking for conceptual compatibilities across cultures and civilizations – analyzing structures of thought developed in Chinese Legalism of the Warring States period and contemporary authoritarian philosophies like those of Carl Schmitt, Giovanni Gentile, or Vladimir Lenin.

Most terrifying task of all in mapping planes of immanence – straight-up creating concepts from near-scratch and testing them for mutual compatibility. If they fit, you have another few points on the map. If not, rinse and repeat.

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