This has been a particularly difficult section for me. Please forgive me if things sound opaque, but Kant is a particularly difficult writer and my reading is hurt by the fact that it isn't occurring in an institutional setting. But enough disclaimers.

I'll start by backing up a bit and providing my reading of the preceding few sections, namely a summary of the transcendental deduction, the explanation and outline of book two, The Analytic of Principles, and the ensuing introduction. Against this background I'll present my trouble with chapter one, Of the Schematism of the Pure Concepts of the Understanding.

We've just completed the Analytic of Concepts, where we were informed of the necessity that the Pure Concepts of the Understanding strictly refer to sensible intuitions, thereby composing possible (which is to say sensible) experience, owing to the elementary unity of original apperception. Put differently, if it is the case that your particular experience of the world uniquely belongs to your singular, and therefore unitary, consciousness, then it must be the case that experience is composed by some kind of knowledge about objects prior to any actual experience. Or another formulation: if it is possible for me to say that my own or another person's thoughts or perceptions are subjective, then it has to be the case that the structure of subjectivity is objective, and it is this precise structure that Kant illustrates for us in the Analytic of Concepts, specifically the transcendental deduction, and which objectively provides the conditions of possibility for experience, Kant defining experience as determinate knowledge of appearances (I think I needed a semicolon somewhere in there but I'm not sure; also, please free to correct me where you think my readings are inaccurate).

So now Kant moves to Book II, the Analytic of Principles. The purpose now is to explain just how the pure concepts of the understanding are applied to or provide rules for determining appearances, for so far he has only described the necessity that they refer to sensuous objects by way of the transcendental unity of original apperception, the bare fact of consciousness. Judgement is the faculty tasked with "distinguishing whether something falls under a given rule or not." Transcendental logic can assist here by pointing out "the case to which each rule is to be applied."(B175, A136) So the first chapter of Book II "will treat of the sensible condition under which alone pure concepts of the understanding can be used, that is, of the schematism of pure understanding."(B175, A136) Still following? To recap, given that we possess pure, a priori concepts that necessarily and strictly refer to sensible objects, how does a non-empirical and non-sensible thing like a pure concept interact with a sensible object?

This where things get weird.

Kant tells us in the first chapter that, given the heterogeneity of pure concepts and sensible intuitions, there must be some third thing which mediates their interaction. This thing would have to be, on the hand, pure and non-empirical, but on the other hand intellectual and sensible at the same time. Kant titles the thing that satisfies these conditions a "transcendental schema". But just what is a schema? Kant replies:

After what has been said in the deduction of the categories, we hope that nobody will hesitate in answering the question whether these pure concepts of the understanding allow only of an empirical or also of a transcendental use; that is, whether, as conditions of a possible experience, they refer a priori only to appearances, or whether, as conditions of the possibility of things in general, they may be extended to objects in themselves (without any restriction to our sensibility). For there we saw that concepts are quite impossible, and cannot have any meaning unless there be an object given for them or, at least, for the elements of which they consist; and that therefore they cannot apply to things in themselves (without regard as to whether and how things are given to us). We likewise saw that the only way in which objects can be given to us is by modification of our sensibility; and lastly, that pure a priori concepts, besides the function of the understanding in the category itself, must also a priori contain formal conditions of sensibility (particularly of the inner sense), namely, conditions which contain the general condition under which alone the category can be applied to any object. We shall call this formal and pure condition of sensibility, to which the concept of the understanding is restricted in its use, the schema of the concept; and the procedure of the understanding with these schemata we shall call the schematism of the pure understanding.

The schema in itself is always only a product of the imagination; but as the synthesis of the imagination does not aim at a single intuition, but only at the unity in the determination of sensibility, the schema ought to be distinguished from the image. Thus, if I place five points one after the other, . . . . ., this is an image of the number five. If, on the contrary, I think a number in general, whether it be five or a hundred, this thought is rather the representation of a method of representing a multitude (for instance a thousand) in an image in accordance with a certain concept than the image itself. Indeed, in the case of a thousand I could hardly take in the image and compare it with the concept. This representation of a general procedure of the imagination by which a concept receives its image, I call the schema of this concept.

[...]The schema of a pure concept of the understanding, on the contrary, is something which can never be brought into any image whatsoever, for it is nothing but the pure synthesis determined by a rule of unity according to concepts in general, a synthesis expressed by the category; it is a transcendental product of the imagination, a product which concerns the determination of inner sense in general, according to the conditions of its form (time), with respect to all representations, insofar as these representations are to be joined a priori in one concept, in accordance with the unity of apperception. (B178 - B182, A139 - A142)

Now, the key to my reading of all this, which is what is in question after all, lies in nature of inner sense. Kant tells us earlier that inner sense lacks content but not the form of sensibility in general, which is time. Space is the condition of external sensibility but all intuitions are subject to the condition of time. It is owing to this strange situation of inner sense that Kant controversially claims that our self-image, or how we see ourselves, is a fabrication: your inner sense is empty, but still receptive of sensation. But its a law of the understanding that anything sensibly intuited has to be combined into a unitary appearance. So the understanding fabricates the unity of your self-image in order to make-up for this strange shortcoming of inner sense. But the same operation appears again in the context of the schemata, but what subtly distinct way? Inner sense is receptive, but possesses only the formal condition of time as its whole sensibility (which is receptivity). Time, however, turns out to fulfill the general condition of a schema: it is pure and non-empirical since it belongs to transcendental aesthetic as an a priori condition of sensibility, and so is not only intellectual but also sensible as the element of all sensation generally. Subsequently Kant will explain that the schemata are nothing "a priori determinations of time according to rules" but remember that the understanding can't provide such without provocation on the part of sensibility.

So could it be that Kant answers the question "how do pure concepts interact with sensible intutions?" in the following way?: Because we sense perturbations in time, which is purely formal, and time is primarily registered by inner sense, which is empty of content, the schemata are the way our minds cohere (or unify) the manifold of this kind of intuition, these perturbations in time on the part of external objects (distinct from their peturbations in space); that is, our sense of time is the mediating plane between sensations and concepts.

Do I have this correctly? Can anyone suggest corrections to my reading? This was probably overly long and could've been shorter, but I'm not really sure where I would've even begun making that kind of edit (some pointers would be very helpful, thank you). I guess I leave it up to y'all now. I hope I make some kind of sense.

  • I think I can re-write this more concisely. Dont' be surprised if you answer this and find a huge re-edit in its place.
    – Benoît
    Nov 17, 2011 at 22:12
  • 1
    Can you tell me which translation you're using?
    – stoicfury
    Nov 19, 2011 at 3:53
  • The translation is Marcus Weigelt's revision of Max Muller's original translation
    – Benoît
    Nov 22, 2011 at 4:05
  • Ah yes, I use the Guyer/Wood translation; I noticed your passages were slightly different. I can't really speak to the quality of that one, though it doesn't seem too much different.
    – stoicfury
    Nov 26, 2011 at 17:44
  • I am reading this section of Critique now. It is difficult to make sense out of it. I was curious what you are thinking about it now since you have had the benefit of three years to think about it.
    – Lenz
    Oct 24, 2014 at 4:02

2 Answers 2


You cover a lot of ground in your question, and at points it's hard to really figure out what your question is. It seems your major question is:

How do pure concepts interact with sensible intutions?

To start from the beginning: The pure concepts of understanding are a priori, and thus not abstractions from our perceptions. They are not derived from empirical concepts but rather they are intrinsic to the way our minds are formed. For anything to be thought in our minds, a pure concept must have at some point formed it into something coherent for us. I will state that again to be clear: Only when an a posteriori sensible intuition is translated via the pure concepts of understanding can an object or thought exist in our minds. Anything you think has to have gone through the categories.

However, these pure concepts of the understanding cannot be related to any particular objects or pictures in your mind, because they are the pure concepts, and any relation of them to a particular empirical intuition would inappropriate; the mere association of a pure concept with a sensible intuition would cause it to be "impure" (it would lose objectivity).

The question which thus arises is how the two are connected; there has to be some way to connect the concept of pure understanding with sensible intuitions. For example, when we look at plate, how is the pure concept of a circle related to the circularness of the plate? If pure concepts never interact with sensible intuitions, what causes us to make that judgment (that the plate is circular)?

For Kant, the answer is transcendental schema. To start, Wikipedia gives a decent overview:

Schemata that mediate between empirical (a posteriori) concepts or mathematical (pure sensuous) concepts and perceptions are similar to adapters. Just as adapters are devices for fitting together incompatible parts, schemata connect empirical concepts with the perceptions from which they were derived. Schemata are rules for the production of images. As rules, they are related to concepts. As image–producers, they are related to perceptions. "While the concept belongs to the understanding and its instance to perception, the schema has, so to speak, a foot in either domain. As rules for the production of images the schemata … are linked to the understanding; as rules for the production of images they are linked to perception." The "adapter" simile is even more apt in the case of transcendental schemata. This is because pure concepts of the understanding (Categories) are totally unrelated to perceptions. The pure concepts or Categories are original constituent components of the understanding and are not derived from empirical sense perceptions.

Other than saying that "the schema in itself is always only a product of the imagination", it doesn't appear it goes into much more depth than that. I think the paragraph in The Critique of Pure Reason just before the one you listed is most crucial for comprehending the concept of schema:

The concept of the understanding contains pure synthetic unity of the manifold in general. Time, as the formal condition of the manifold of inner sense, thus of the connection of all representations, contains an a priori manifold in pure intuition. Now a transcendental time-determination is homogeneous with the category (which constitutes is unity) insofar as it is universal and rests on a rule a priori. But it is on the other hand homogenous with the appearance insofar as time is contained in every empirical representation of the manifold. Hence an application of the category to appearances becomes possible by means of the transcendental time-determination which, as the schema of the concept of the understanding, mediates the subsumption of the latter under the former.

This paragraph is somewhat challenging to parse; it's clear he wants to say that a time-determination is that which connects the gap between sensible intuitions and pure concepts, but it's still not obvious how that works. Wikipedia has a small section on it, although from some quick searching it's not clear Kant ever actually answered this in a completely satisfactory manner. It seems others have suggested before that this is a problem Kant never fully solved.

  • There's a lot going on in my original formulation only because I wanted to contextualize my understanding: Kant is obsessively systematic, so it's difficult to discuss one section without a clear understanding of preceding developments.
    – Benoît
    Nov 22, 2011 at 4:15
  • Is this a constraint of StackExchange? I'd like to write multi-paragraph comments but pressing 'Enter' just submits what's written as a a comment. I guess we'll all just have to soldier on through a wall of text. So: I think that the real gamble I'm taking in my original and very rough formulation is this challenge to the distinction between pure concepts and sensible intuitions, bridged by the medium of time. Granted that Time "contains an a priori manifold in pure intuition", the problem is how this manifold turns into a determination.
    – Benoît
    Nov 22, 2011 at 4:30
  • Kant very explicitly tells us that in the Deduction that that our intuition of ourselves (how we see ourselves at a given moment in time) is not intrinsic to original apperception, to the bare fact of the "I think". He says that the intuition of ourselves is in fact a kind of fabrication caused by the emptiness of inner sense as regards content, but not form, since time, which is purely formal, is the only a priori intuition available to inner sense (Kant tells us that outer sense doesn't intuit time, see A118-119).
    – Benoît
    Nov 22, 2011 at 4:44
  • The problem is that, if I turn my attention to myself, which is to say my inner sense, the Understanding then meets with the situation of combining purely formal intuition, which Kant says through numerous examples is impossible without resorting to synthetically producing images (we can't conceive time without the image of a line). We literally borrow from outer sense the spatial orientation (images) to make time conceivable. So, confronting the pure, homogenous magnitude of time in inner sense in intuiting ourselves, we fabricate an image of ourselves for the purposes of representation.
    – Benoît
    Nov 22, 2011 at 4:52
  • But Kant also says that we can produce this imagination of ourselves with the help of the categories... which also run into the same situation, though this time obscured by words like 'a priori' and 'rules' (keywords for describing the Understanding, but not very explanatory when it comes to grasping the schemata). The Understanding still has to come to grips with combining the purely formal intuition of time, but Kant just tells us that this operation has always-already happened (a priori) according to a rule (alluding to the role of Understanding but not a specific operation)
    – Benoît
    Nov 22, 2011 at 4:58

“The project on which I am now working … must be completed, or else a gap will remain in the critical philosophy.” (Kant to C. Grave, September 21, 1798b, AK 12:257).


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