CPR: The Analytic of Principles, The Schematism

Concepts and Principles

The higher cognitive powers can be divided like so:

Analytic of Concepts: Pure concepts
Analytic of Principles: Judgements

Reason and inferences will be dealt with in the Dialectic.

Here in the Analytic of Principles, we’re concerned with the categories in action.

The Analytic of Principles is also called the Transcendental Doctrine of The Power of Judgement.

It is made up ofanalyses of:

• The sensible condition under which the categories can be used: Schematism
• The synthetic judgements that are made on the basis of the categories, under the condition above: System of Principles

Judgement

There’s an interesting parallel with Wittgenstein.

...whereas understanding is capable of being taught and equipped by rules, the power of judgement is a particular talent that cannot be taught at all but can only be practiced.

It is a “power”, or “faculty”. And Wittgenstein in On Certainty wrote,

124. I want to say: We use judgments as principles of judgment.

Meaning that we do not first learn the rules of judgement and then apply them to the world. Rather, the rules are manifest in the judgements themselves, and it is by actually judging that we learn the skill of judging.

The Schematism

The Deduction showed that experience is subject to the categories, but now kant wants to show how the categories apply to experience.

Here are some of the ways to describe the schemata:

• The transcendental condition under which the imagination brings appearances under concepts.
• The rules by which this takes place.
• The set of transcendental time determinations. [B177]
• The universal procedures of the imagination for providing concepts with their images.
• The rules for determining our intuition in accordance with a general concept. [B180]
• The phenomenon of an object in harmony with the category. [B186]
• The way in which objects are subsumed under concepts
• The adaptor between pure concepts and intuitions
• The formal and pure condition of sensibility to which the concept of understanding is restricted in its use. [B179]

But some of these apply only to certain kinds of schemata. Kant mentions three:

• Schemata for sensible (mathematical) concepts
• Schemata for the categories (the transcendental schemata)
• Schemata for empirical concepts

This only becomes clear after reading the whole of it, though. It proceeds like this:

Sensible Concepts

At the beginning of the schematism he says that when an object is subsumed under a concept, these must be homogeneous with each other. Homogeneous here means of the same kind or (of the concept) containing what is presented in the object. In Kant’s example of the plate, this would be roundness. The concept here is a circle, which is a sensible, mathematical concept.

Pure Concepts

But the problem of the schematism is how the pure concepts come to be applied to intuitions. In this case, Kant says [2nd para], the concepts are heterogeneous from intuitions. So there must be something so far left out of the account, a “third thing” [3rd para]. This is the transcendental schema. What is it—this adaptor—and how does it work?

Time is the universal form of intuition in which all objects of experience are presented (space only applies to some objects). A “transcendental time determination”, i.e., a presentation defined in time, or conditioned as temporal, is homogeneous with both sides:

• It is homogeneous with the category in that it is universal and rests on an a priori rule (a rule of judgement?)
• It is homogeneous with the appearance in that it contains time, which is the form common to all appearances

Imagination

A schema is a product of the imagination. But we should not take from this that a schema is merely an image. Kant gives the dots example here, the schema here being the method for presenting a multitude in an image—not the image itself. This is why the schema for a concept is “a universal procedure of the imagination for providing a concept with its image”. [B180]

Sensible Concepts Again

He applies this to sensible concepts. The image of a triangle is not adequate to the concept of a triangle as such, because such an image is always an image of a particular triangle; we cannot have an image of a universal triangle, but only this or that triangle.

Empirical Concepts

He does the same with empirical concepts now, with the example of the concept dog.

A Secret Art

This schematism of our understanding, i.e., its schematism regarding appearances and their mere form, is a secret art residing in the depths of the human soul, an art whose true stratagems we shall hardly ever divine from nature and lay bare before ourselves. Only this much we can say: the image is a product of the productive imagination’s empirical ability.

Seems like Kant has been mocked for this passage. He says he’s going to solve the problem of how pure concepts apply to sensible experience, but then appears to throw his hands up and say we’ll never know. But surely there are other ways of interpreting this? When he says “from nature” it suggests to me that he is saying we’ll never know exactly how the schemata operate in terms of empirical psychology—or even, to bring it up to date, neuroscience. What he can do is reveal the transcendental elements of the power of judgement, i.e., what it is that our brains etc. must achieve for us to be able to make judgements—in yet other words, the structure and functions of the way in which concepts are applied to experience.

This interpretation fits with what he says about judgement being something that is practiced, not taught. It is an innate skill, basic to our form of life, as Wittgenstein might say.

Note also that the productive imagination has an “empirical ability”. This might seem surprising because previously it was the _re_productive imagination which was that side of the imagination that dealt with the empirical. Pluhar notes that the latter is about the empirical only, whereas the productive imagination deals with both the empirical and the (pure) a priori.

Exhibition of the Transcendental Schemata

Kant goes on [B182] to “exhibit” the transcendental schemata according to the categories. I’ll look at two of them only.

Quantity

Image: space or time or both
Schema: number

Therefore number is nothing other than the unity in the synthesis of the manifold of a homogeneous intuition as such, a unity that arises because I myself produce [i.e., synthesize] time in apprehending the intuition.

I don’t see that number is “nothing other” than this, because surely the other schemata can be described in the same way. (Possibly an uncharitable reading)

Causality

Schema: the manifold’s succession insofar as this is subject to a rule — such that whenever a real thing is posited (i.e., a thing in time), something else always follows

Kant doesn’t give an image for causality, but maybe there is one. In improvising on the saxophone, I often seem to have some sort of image of tension and release, or of decay, or of descent into chaos, and other basic “images” with which I might build a solo. Isn’t there something similar with causality?

Substance

Schema: permanence of the real in time.

Variation of appearances occurs in time, and this means that time itself does not change. There is must be something real in intuitive presentations that corresponds to this permanence. It must be the substrate of all objects, i.e., that which undergoes change but which itself does not vary: substance.

Summary

Following are what the schema of the categories contain and are responsible for: [B184]

Schema of magnitude:
The production (synthesis) of time itself in the successive apprehension of an object

Schema of quality:
The synthesis of sensation (perception) with the presentation of time, i.e., the filling of time

Schema of relation:
The relation of perceptions to each other in time

Schema of modality:
Time itself as the correlate of the determination of an object as to whether and how it belongs to time

This all shows that the schemata are a priori time determinations according to rules.