CPR: The Transcendental Deduction (The “B” Deduction)

The notes on the A deduction are a real mess, and these might be too. I do plan to post something that weaves it all together, though whether it’s here or in a finished essay on critique-of-pure-reason.com I’m not sure.

This post covers the transcendental deduction in the second edition, i.e., the “B” deduction.

§ 15: On The Possibility of a Combination As Such

Synthesis is a Spontaneous Act of The Understanding

Kant begins by defining synthesis, but describes it as combination for a while before introducing that word.

First of all, there’s a manifold of uncombined presentations in purely sensible intuition. The combination of that manifold cannot likewise come through the senses and it cannot be part of that which is given shape by the pure forms of intuition. Why? Perhaps for the same sort of reason as Hume used to demonstrate the lack of justification for the attribution of causation to series of events. There is a profusion of sense impressions in perception, with nothing intrinsic to them which can supply the combination as such, the grouping together of these impressions into intelligible objects. We cannot sense combination. Our eyes respond appropriately to light, our nostrils to certain kinds of molecules, but the combination of these sensations to form presentations is not this passive receptivity or affection, but active interpretation (loosely speaking). Therefore synthesis/combination is not on the side of receptivity but of spontaneity, i.e., the understanding.

For this combination is an act of spontaneity by the power of presentation; and this power must be called understanding, in order to be distinguished from sensibility [B130]

Incidentally, I had been wondering about the difference between presentations and appearances, but if Kant is serious about placing presentations firmly in the realm of the understanding (though I’m not sure if this is consistent with other things he has said), then perhaps we can split it along with sensibility / understanding, such that appearances are to presentations as sensibility is to understanding? This interpretation might be a difficult one to pull off, because presentations for Kant are any number of different kinds of things at various levels of his structure.

The combination of manifold, whether of intuitions or of concepts, is an act of the understanding, though not always (or even usually) a conscious one.

NOTE: It might be tempting to think of this synthesis or combination as the result of the pure forms of intuition, space and time. This is not so. The manifold is given in sensible intuition, and the pure forms are given a priori, but the combination is separate from both of these: it is not given at all, but is actively constructed.

Analysis is the opposite of synthesis. It is the breaking down into parts. It presupposes the spontaneous act of synthesis. This is reasonable. After all, the identification of properties and parts of objects is surely an act of the understanding.

Q. But why does Kant bring up analysis here? Is it simply to complement his use of synthesis? From what we know of his habit for system, it would seem that way. But it is also important in helping to show how nature—as that which is studied by physicists, engineers, mechanics, and so on—is nature as understood in spontaneous acts of the subject beyond mere receptivity.

Q. My main question is how Kant can say that synthesis must be an act of the understanding. A. Well, what else could it be? We know that experience is nothing but a bundle of unconnected impressions (but do we really?) so how does it become bundled up in the way that it is. This logically (esp. transcendentally logically) must be more than receptivity.

Q. How can the pure form of intuition be described as part of a merely receptive faculty, when synthesis is spontaneous?

Unity of Synthesis

But if we think about how appearances must be combined in experience, there’s actually more to combination than just the synthesis of the manifold: there’s the unity of the manifold. Hence…

Combination is effectively (the presentation of) the synthetic unity of the manifold

But the presentation of this unity cannot just arise straight from the combination: it is added to the manifold (the manifold as presentation). And this preceding addition is what makes possible the concept of combination in the first place.

What is interesting here is that Kant is talking of the presentation of the manifold, the presentation of the combination, and the concept of combination. One would think that he could have said just that the addition of unity makes possible the combination of the manifold, but that is not the sense that he is trying to make clear here — Q. though surely he would also agree with that?

Combination is presentation of the synthetic unity of the manifold. Hence the presentation of this unity cannot arise from the combination; rather, by being added to the presentation of the manifold, it makes possible the concept of combination in the first place.

So, the concept of combination presupposes combination itself, naturally enough. It presupposes the presentation of the synthetic unity of the manifold.

But this unity is not the category of unity, because the judgements—through which the categories are applied—already presuppose this unity in experience: this unity is “already thought” [B131]

Hence a category already presupposes combination. We must therefore search for this unity … still higher up, viz., in what itself contains the basis for the unity of different concepts in judgements, and hence contains the basis for the possibility of understanding…

While it may have been tempting to think of the categories as the highest conditions of experience, it seems that even they depend on a ground of unity and synthesis. But what is this basic, supreme, unity?

What is the basis for, or source of, the synthetic unity of the manifold in intuition, as a general concept?

Let’s see…

§ 16: On The Original Synthetic Unity of Apperception

The I think must be capable of accompanying all my presentations.

The I think is not the statement “I think”, but is the concept or presentation, or perhaps rather the consciousness that one is thinking the presentation, whether this presentation is an intuition or is itself just a concept.

Kant is saying that…

  1. The I think is a precondition for a presentation’s thinkability. More accurately, to think something is to at least be capable of holding in one’s mind the concept that one is thinking of the presentation, which is in turn the presentation I, as the subject of this experience.
  2. Therefore, if the I think did not at least potentially accompany every presentation, then there could be presentations that were not thinkable, “which is equivalent to saying that the presentation either would be impossible, or at least would be nothing to me.”

In using “must be capable of accompanying”, Kant is indicating that not all presentations are objects of awareness at all times. We can see things and do things without their coming to the forefront of our minds. But what is important to Kant is that without the potential to be thought, they are nothing at all. This is interesting, because it seems to take thinking as primordial, even though we are not conscious of everything—a fact which on the face of it indicates that it is not the rational which is basic at all. Kant seems, like Descartes, to be saying that a human being is a thinking thing or is not an I at all.

But we know that there are given presentations prior to all thought — these are called intuitions — and these must, therefore — if they are to be anything at all — have a “necessary reference” to the I think that belongs to the same subject as the subject of the intuitive manifold.

Hence everything manifold in intuition has a necessary reference to the I think in the same subject in whom this manifold is found.

We can see where Kant is going. In the last section, Kant identified the synthetic unity of the manifold as having a basis which is the highest concept of unity on which all combination must depend. It’s looking like the I think has something to do with it, i.e., self-consciousness.

The I think is a spontaneous presentation, and not something that is found in sensibility.

I think = pure apperception = original apperception

This I think is by nature one, and this unity is called the transcendental unity of apperception. The transcendental bit indicates that it is a condition for a priori knowledge.

The manifold of intuition is mine or it is nothing. There cannot be presentations that do not belong to a united self-consciousness — that is almost contained in the meaning of the concept of a presentation, and if there were any other sort of presentation then it would not be the presentations that concern us here. Therefore they must necessarily conform to the condition under which presentations can be presentations belonging to “one universal self-consciousness”.

Next, Kant states that this identity, this unitary transcendental apperception, is possible only through the consciousness of the synthesis of presentations. This is, I think, a fascinating way to look at things. Against Hume, he believes in this necessary a priori I as a legitimate concept, but with Hume he believes that it cannot be derived straight from experience alone. So we end up with an I think, that is, a self which is knowingly examining itself for signs of a unified persistent self, and finding nothing but intuitions and concepts, or in Hume’s language (I suppose, not having read him), impressions and ideas. But…

  1. This thing that makes possible the I think is the very thing that the I is looking for! The thing that is looking for the I is of course the I itself. But empiricism is not able to say anything definite about it other than that it is a helpful habit of mind, and must look only to empirical consciousness, which isn’t up to the task, i.e., it cannot justify the positing of a persistent self. Kant, on the other hand, takes this as the clue to its necessity, which, however, can only be found with a transcendental philosophy (as he has done here already).
  2. And this is precisely what the I think must do to be an I at all, i.e., the I think is possible only through the consciousness of the synthesis of the manifold given in intuition. To find yourself, look at what you are experiencing.

In other words, the way in which we fail to find the self in our survey of sensible experience is the very thing that makes it possible in the first place, namely by means of the united consciousness of the objects of experience found therein. This is a nice demonstration of the power of transcendental philosophy and the weakness of empiricism.

Empirical Consciousness

But Kant mentions this “empirical consciousness”, which can’t be the key that he’s looking for because it’s “sporadic” and with no “reference to the subject’s identity.” [B133] And as mentioned in (1) just above, this is the consciousness of this or that object. Here Kant is again agreeing with Hume on one side, while positing his own innovation of the transcendental consciousness.

Now, the aforementioned “reference” to the subject’s identity, i.e., the reference to original apperception, comes about through the act of combining all these presentations of intuition,, “not through my merely accompanying each presentation with consciousness.”

Without the transcendental unity of apperception, a united empirical consciousness of object A is not necessarily linked with a united empirical consciousness of object B.

Thus it is only because a manifold of presentations can be combined in one consciousness that there can be a presentation of the identity of consciousness across these presentations. In other words, the I think depends on the reference of the manifold to a single consciousness. This seems so close to tautology, but I think it’s more like tiny little steps.

I.e., the analytic unity of apperception is possible only under the presupposition of some synthetic unity of apperception. [B133-B134]

Ah. So basically, we can see our consciousness as consisting of a manifold of presentations only thanks to a preceding synthesis, such that there is a single consciousness that has all these presentations in the first place. But again, it seems so close to stating the obvious.

It is more like this. Consciousness is united across presentations, spanning the manifold, but it is when this fact itself becomes a presentation, the I think, that we can talk of the transcendental unity of apperception. But, crucially, we could not even have the consciousness united across presentations without this “higher”, second-order consciousness as a basis.

I.e., only because I can comprise the manifold of the presentations in one consciousness, do I call them one and all my presentations. For otherwise I would have a self as many-colored and varied as I have presentations that I am conscious of. [B134]

Kant then reasserts that combination is an act of the understanding,, and…

... understanding itself is nothing more than the power to combine a priori and to bring the manifold of given intuitions under the unity of apperception — the principle of this unity being the supreme principle in all human cognition. [B135]

So, this principle is the principle of the necessary unity of apperception. Kant admits that it’s merely an analytic proposition. Perhaps this is why I got the stink of tautology back there.

So what is most interesting about this section for me is the idea that consciousness must be consciousness of something — or rather, a bunch of things. Or should it rather be seen as a second or third order consciousness, namely either the consciousness of my empirical consciousness, or else the consciousness of that, i.e., the awareness of the presentation I think?

Anyway, what it comes down to is that without a bunch of stuff to be conscious of, I wouldn’t be conscious, because that is what it means to be conscious. But be careful. Saying “that is what it means” is lazy. It might lead one to think that there’s no more to it: consciousness is consciousness of things. But this is not so. Kant’s point is both that there is an original, transcendental, necessary, and in a way independent and prior consciousness which is the condition for the combination of presentations in intuition; and also that the presentation of this consciousness — this presentation being the I think — depends on an always possible connection between this and the manifold in intuition, such that there is no absolutely independent original consciousness, so to speak.

Consciousness, then, is very much embedded in the world, and is not something that can fly off spirit-like to some non-sensible realm.

§ 17: The Principle of The Synthetic Unity of Apperception

The supreme principle for the possibility of intuition with reference to sensibility:

Everything manifold in intuition is subject to the formal conditions of space and time.

The supreme principle for the possibility of intuition with reference to understanding:

Everything manifold in intuition is subject to the conditions of the original synthetic unity of apperception.

Defn. Synthetic unity of apperception: the a priori synthesis of the manifold of presentations given to me in intuition.

All manifold presentations of intuition are subject to the first principle insofar as they are _given_to us. They are subject to the second principle insofar as they must be capable of being combined in one consciousness. [B136-B137]

Which is to say, they are subject to the second principle insofar as they are capable of being thought and known.

Understanding

Kant describes the understanding now as the power of cognitions, or in Weigelt the faculty of knowledge. Cognition or knowledge is a…

... determinate reference [or relation] of given presentations to an object. And an object is that in whose concept the manifold of a given intuition is united. [B137]

In other words, the manifold of a given intuition is united in a concept, namely the concept of an object.

But all unification of presentations requires that there be unity of consciousness in the synthesis of them.

Therefore the aforementioned reference of presentations to an object, as well as their objective validity and their status as congitions/knowledge — these consist solely of the unity of consciousness.

And this means that the “very possibility of the understanding” rests on the unity of consciousness. And this is why the synthetic unity of apperception is supreme: it is the “primary pure cognition/knowledge of understanding, on which the entire remaining use of the understanding is based.”

... in order to cognize .. a line .. in space, I must draw it; and hence I must bring about synthetically a determinate combination of the given manifold, so that the unity of this act [of synthesis] is at the same time the unity of consciousness (in the concept of a line), and so that an object (a determinate space) is thereby first cognized.

The synthetic unity of consciousness is, therefore, an objective condition of all cognition.

To see that this follows, connect “object” with “objective”. For me to know an object outside me, which is thereby an objective determination, I must perform a synthesis whose required unity (for it to be an object of my experience) depends on or even consists in the unity of consciousness. So this can be described as an “objective condition”.

Not only do I myself need this condition in order to cognize an object, but every intuition must be subject to it in order to become an object for me. [B138]

Kant then adds that without the synthetic unity of consciousness the manifold would not be united, but again says that this is analytic, because all it says is that for presentations to be mine they must be subject to the condition under which I can regard them as mine, or more specifically as belonging to my one identical self, thereby allowing me to “collate” them through the I think.

Kant then imagines possible kinds of understanding that would not require this principle of the synthetic unity of apperception. He points out that the principle is only required by an understanding in which the original apperception does not yet contain any given manifold of intuition. The other, imaginary kind of understanding that would not require the principle would be one that already had something given to it. The principle would not be required because no synthesis would be required to produce a unity of consciousness — and we have already seen that it is only through the synthetic unity of the manifold that there can be a unity of consciousness.

Human beings require that synthesis, and because it is the supreme or first principle, we can’t conceive (using our understanding) of any other sort of understanding.

§ 18: The Objective Unity of Self-Consciousness

In this section he contrasts the objective and transcendental unity of self-consciousness with the subjective and empirical unity of consciousness.

Empirical, subjective, consciousness is “a determination of inner sense time whereby that manifold of intuition … is given empirically.” But time itself, as the pure form of intuition, is subject to the objective unity of consciousness through the necessary relation/reference of the manifold within it to the self, the I think.

And only this original or higher unity of consciousness is objectively valid (he uses “self-consciousness” in the section title but mostly just “consciousness” in the text). The empirical unity of apperception “is only derived from the orginal unity under given conditions _in concreto” and is only subjectively valid.

Q. Why is this the case?
A. Well, the manifold in intuition can be chopped up any which way depending on contingent circumstances, and the unity in this empirical consciousness might only go for one person and no-one else, so cannot be objective.

Here’s a better way of thinking about it…

Whether I can be conscious empirically of the manifold as simultaneous or as sequential depends on circumstances or empirical conditions. [B140]

But the original unity of consciousness is what makes this possible, and this ground of possibility is not dependent on “circumstances or empirical conditions.”

The transcendental unity of apperception is “the unity whereby everything manifold given in an intuition is united in a concept of the object“, and this is what makes it objective.

Empirical unity of consciousness, on the other hand, is a determination of inner sense whereby that manifold given in intuition — and which is united in a concept objectively in the transcendental unity of apperception — is given empirically.

In other words, transcendental unity of consciousness is that which unites the manifold in a concept (or in an object, or in the concept of an object), and the empirical unity of consciousness is that which unites the manifold in intuitions. [I think that’s right]

I’m also thinking of the objective unity as taking place through the self that looks inward as Hume did, to find the self. This enquiring self is the transcendental or original apperception, and the self in various states of receptivity is what it finds, wherein there is the subjective unity that depends on circumstances.

Recall above somewhere for the meaning of “empirical consciousness” as “the consciousness of this or that”. In the present section it is the unity he’s focussing on, and whether it is objective or not. There is unity in both, but owing to their natures as described already, the unity of empirical consciousness is not the unity that enables a concept of the object and is therefore not objective.

And we can perhaps now see why he flips between self-consciousness and plain consciousness. In transcendental apperception one is conscious of being (empirically and maybe otherwise) conscious. So empirical consciousness is not yet self-consciousness.

NOTE: Derk Pereboom in Kant’s Metaphysical and Transcendental Deductions, describes Kant’s “empirical consciousness” as “consciousness according to Humean psychological theory”

§ 19: The Logical Form of All Judgements Consists in The Objective Unity of Apperception of The Concepts Contained in Them

Before I read it through, I’ll try to guess what this section is doing. Effectively this amounts to a deciphering of its title.

I think Kant is going to argue here that above and beyond the technicalities of logic, what judgements intrinsically are is something else. The form of judgements consists in the objective unity of apperception, insofar as this is a consciousness of the concepts which are used in those judgements. That is to say, judgements are intrinsically judgements of or by a single consciousness — because the objective unity of apperception of whatever is possible only through the original unity of consciousness itself. Something like that perhaps. We’ll see…

... a judgement is nothing but a way of bringing given cognitions to the objective unity of apperception. This is what the little relational word is in judgements intends [to indicate], in order to distinguish the objective unity of given presentations from the subjective one. [B141-142]

We say that the Moon is round and not only that it seems round. The latter would be expressing empirical, subjective consciousness. The judgement, in which we use is, thereby belongs to the transcendental unity of apperception and is objective.

For this word indicates the reference of the presentations to original apperception and its necessary unity. [B142]

Example: bodies are heavy [B142]

Although the judgement might be empirical and thereby contingent, there is still always a reference to the necessary unity of (or in) original apperception. A judgement relates presentations to one another, but it is only valid objectively, i.e., it is only fully a judgement at all, through the reference to original apperception and its necessary unity.

By this I do not mean that these presentations [bodies and weight] belong necessarily to one another in the empirical intuition. Rather, I mean that they belong to one another by virtue of the necessary unity of apperception in the synthesis of intuitions

they belong to one another according to principles of the objective determination of all presentations insofar as these presentations can become cognition/knowledge — all these principles being derived from the [supreme] principle of the transcendental unity of apperception.

Kant has shown that the synthesis of intuitions depends on the necessary unity of apperception. And the presentations belong to one another — i.e., there is always a reference to the necessary unity in apperception — not because all bodies that we’ve experienced in the past have been heavy, but because objective determinations are in play any time the understanding is involved, when the concept of an object is made available through the act of uniting the manifold given in intuition. And this all depends on the transcendental unity of apperception, or the principle thereof.

The main point is that judgements are valid objectively, expressed in the is. The relation of the relevant presentations that matters is their relation to each other according to principles of the understanding and ultimately the unity of consciousness in which the concepts are thought. On the other hand, the relation of the presentations to each other according merely to to “laws of association” is only subjectively valid:

According to these laws, all I could say is: When I support a body, then I feel a pressure of heaviness. I could not say: It, the body, is heavy — which amounts to saying that these two presentations are not merely together in perception … but are combined in the object, i.e., combined independently of what the subject’s state is. [B142]

NOTE: This empirical function of association is what is happening in the synthesis of reproduction in imagination. [A100, see the last post]

§ 20

The title is:

All sensible intuitions are subject to the categories, which are conditions under which alone their manifold can come together in one consciousness

Having argued in §17 that the intuitive manifold necessarily comes together in one consciousness — in Kant’s terms, the manifold given in a sensible intuition is subject necessarily to the original synthetic unity of apperception — Kant wants to prove further that the categories are conditions of this possibility (and thereby that the categories are the conditions of the objects of experience).

And he argued in §19 that the general logical function of judgements is to bring the manifold under one apperception.

Therefore the manifold given in an empirical intuition is “determined” in regard to one of the particular logical functions of judgements, these functions being the categories.

Thus the manifold in a given intuition is subject necessarily to the categories.

This section is a crucial turning point. Everything up till this point has concerned intellectual intuition and has thus been objective — concerning objects as thought (in which we use the is to express more than the subjective what seems) — and from now on he’s examining the subjective. He needs to show that empirical intuitions actually are given.

Thus, sections 21 to 26 provide justification for the supposition that empirical intuition is given. Intellectual intuition can be seen s either (a) intuition as given directly to the understanding, or (b) intuition as such, i.e., intuition as given representations, without presuming in what way they are given. That’s all very well, Kant thinks, but to show that the categories actually do apply, he must show that the mere possibility of the understanding’s application to intuition really does take place in the context of human understanding. I.e., he must show that the understanding and the sensibility are connected.

In what follows [cf. Section 26] it will be shown, from the mode in which the empirical intuition is given in sensibility, that its unity is no other than that which the category (according to Section 20) prescribes to the manifold of intuition in general [B144-5]

See G. J. Mattey’s lecture notes here

§ 21

This section is for orientation. He tells us where he’s up to and what’s left to do. Established so far…

Rather like intuition, so consciousness:

Empirical intuition —— subject to ——> pure a priori intuition
Empirical consciousness —— subject to ——> pure a priori self-consciousness

Through the synthesis of understanding, a manifold contained in an intuition that I call mine is presented as belonging to the necessary unity of self-consciousness, and this presenting is done by means of the category.

But he says that this, though it’s an important result, is just the beginning of the deduction.

I must still abstract … from the way in which the manifold for an empirical intuition is given, in order to take account solely of the unity that the understanding contributes to the intuition by means of the category.

Q. I am not clear on this. How exactly have the foregoing sections not yet abstracted fully from “the way in which the manifold” is given?

Anyway, he says that after doing that he will have to show (§ 26), again from the way in which the intuition is given in sensibility, that the intuition’s unity is just the unity assigned to the manifold in intuition by the category. And this will establish the objective validity of the categories regarding all objects of the senses, which will be the deduction completed.

But here is where he mentions a problem that he hasn’t been able to address. So, for us to experience in the way we do requires the categories. But why does our understanding have this requirement? Why is the unity of apperception — consciousness itself — brought about only through the categories, and the specific ones we have (and he has listed in the table)?

— for this no further reason can be given, just as no reason can be given as to why we have just these and no other functions in judging, or why time and space are the only forms of our possible intuition.

CORRECTION: It’s the other way around. The foregoing stuff has been abstract, concerned with any intuition. Now it remains to see how this happens with human sensible intuition.

§ 22: A Category Cannot Be Used For Cognizing Things Except When it is Applied To The Objects of Experience

Maybe this next step illuminates my confusion in the previous section. All argument hitherto has presupposed the objects of experience, but doing it that way you can hardly establish that such objects are the only possible objects. You have to “abstract” away from experience to consider the understanding alone — for a while at least.

Right. Now, the categories can be used to know things only when applied to the objects of experience.

Cognition, or knowledge, involves two components:

  1. The category through which an object is thought
  2. The intuition through which the object is given

There can be thoughts without objects, but without those objects, we have no way to tell if our thoughts apply to anything, so those empty thoughts cannot amount to cognition or knowledge.

Kant then emphasizes [B146] that our intuition is sensible to distinguish it from a thinkable intellectual intuition. This seemed odd to me, because from the Aesthetic onwards he has been talking of intuitions as intrinsically of the senses. But if we use an alternative definition of intuition as a presentation, a certain determination, of some sort of given, then one can imagine that some sort of consciousness could directly apprehend or perceive things without the means of the senses. Effectively this would be an extra sensory perception. The relevant examples would perhaps be Plato’s forms or Leibniz’s monads — that is, knowledge of these things would require this intellectual intuition.

Stephen Palmquist’s definition might be useful:

Intuition: the passive species of representation, by means of which our sen sibility enables to have sensations. By requiring appearances to be given in space and time, intuitions allow us to perceive particular relations between representations, thereby limiting empirical knowledge to the sensible realm.

But this merely shows that Kant is using “intuition” in two ways, one as what intuition actually is or must be for human knowledge and experience, and the other is a more cautious definition of just some sort of determination of a given — without asking how this given is given, i.e., a passive presentation tout court.

The latter way of speaking, which is what Kant is doing presently, is appropriate in terms of his plan as described in his orientation section §21, where he said he would have to further abstract from the sensibility to focus on understanding on its own, making no assumptions.

Anyway, back to the argument. So without intuitions we’d have thoughts but no objects for them to apply to, which means no knowledge.

Hence in us, thinking an object as such by means of a pure concept of the understanding can become cognition only insofar as this concept is referred to objects of the senses. [B146]

Now remember that although all our intuition is sensible, there are two types: pure and empirical. In pure intuition (“by determining pure intuition”) we can know objects in terms of their form — this is what’s gong on in mathematics. In empirical intuition we know things in space and time through perceptions. Incidentally, Kant here defines a perception as a presentation accompanied by sensation.

NOTE: perception then looks very close to intuition, so maybe a perception is just an empirical intuition. Works for me.

Now, going back to mathematics for a moment. What I said might indicate that mathematics can give us knowledge even though it can apply merely to the forms of intuition. But Kant stresses that it can only give us knowledge insofar as the thought mathematical objects are possible objects of experience. But he’s not quite clear:

... all mathematical concepts are, by themselves, no cognitions [items of knowledge] — except insofar as one presupposes that there are things that can be exhibited to us only in accordance with the form of that pure sensible intuition. [B147]

In other words… I can think a triangle and know that one can enclose a space with three straight lines. It also seems natural to suppose that you could do this even if you hadn’t seen a triangle before. But for this to be proper knowledge it must be possible for the shape of this object of thought to be an actual empirical object — or perhaps I should rather say that, for it to be knowledge, the triangle must be taken to be a possible empirical object. But I don’t see how presupposing makes all the difference between empty thought and knowledge. It’s probably a side-issue, but no doubt important for Kant’s philosophy of mathematics.

Consequently the pure concepts of the understanding, even when they are (as in mathematics) applied to a priori intuitions, provide cognition only insofar as these intuitions — and hence, by means of them, also the concepts of the understanding — can be applied to empirical intuitions.

Therefore the categories supply us with knowledge not through intuition as such (recalling the cautious definition above), but only through empirical intuition.

I.e., the categories serve only for the possibility of empirical cognition. Such cognition, however, is called experience.

Therefore, the categories cannot be used to gain knowledge of anything except for the objects of experience.

§ 23

Kant picks up this idea of a thinkable intellectual intuition again, which is a thought that results from considering the understanding on its own terms, abstracted from the sensibility — which he had stated was a necessary step in proving their objective validity, § 21.

The application of the pure intuitions of space and time is restricted to objects of the senses.

But the application of the pure concepts of the understanding can apply to “objects of intuition as such”, i.e., objects of intuition no matter how these intuitions have been given to us.

(+) However, if there is no intuition given in sensation then there is nothing to which the synthetic unity of apperception could be applied to determine an object.

So this extended domain of application “is of no benefit to us whatsoever” [B148], because the concepts are thereby empty, mere forms without objective reality.

Surely for this argument to work as it stands, he would have had to prove, in support of (+), that there can be no such thing as a synthesis of a non-sensible manifold. I think he must have done this, or at least considers that he has, because somewhere else (maybe forthcoming) he describes intellectual intuition and a cognition on such a basis as not requiring any synthesis. Certainly this seems acceptable, because the whole notion of synthesis is about the synthesis of what is given in sensation, and synthesis is a response to the empiricist challenge to the effect that perceptions cannot supply necessary and universal laws or a concept of the self.

A possible solution to this might be in Kant’s emphasis of our, which I was about to ignore but which is probably quite important:

But this further extension of the concepts beyond our sensible intuition is of no benefit to us whatsoever.

Solely our sensible and empirical intuition can provide them with meaning and significance. [B149]

I just realized that this can be read in two ways: “our” meaning “my” or “your”; or “our” meaning belonging to human beings or rather subjects like us. I think the latter is what he’s getting at, and that fis with how I’ve been reading this section and suggests I wasn’t so wrong in wanting to ignore it. But here is where I need to consult a commentary

Right, after having a look at Douglas Burnham’s commentary, I have a slightly clearer view of this. We can imagine, in merely thinking an object, that we are thinking an object that could be given in some nonhuman sensible intuition. We can do this, of course, because the categories are not restricted to what is given in sensibility, i.e., our sensibility. But for knowledge and “meaning and significance” the categories effectively are restricted.

If we suppose a nonsensible intuition then we cannot in the mind predicate anything of it positively but only negatively, i.e., we can only say of the object what it is not. It is not extended, it does not change, etc. This is just to say that the categories must apply to sensible intuition.

NOTE: See §17 above. That is where it’s already established that there is no such thing as intellectual intuition.

§ 24: On Applying The Categories to Objects of The Senses As Such

Burnham notes that after the last two clarifying sections, Kant returns to the central problem of the deduction in this section.

First, yet more stuff which is relevant to my foregoing discussions:

The pure concepts of the understanding refer, through mere understanding, to objects of intuition as such — i.e., we leave undetermined whether this intuition is ours or some other, although it must be sensible intuition.

It must be sensible intuition. So I’ve been confusing two thoughts. One is the thought of an intellectual intuition and the other is the thought of a sensible intuition which belongs to a nonhuman consciousness.

Q. Is the former impossible in principle and the latter possible as far as we know but not something we can know? A. Well, I’m not sure. Maybe something like this: intellectual intuition is thinkable, because we can abstract completely from the senses when considering the functions of the understanding, but only sensible intuition is possible, because it has already been established what intuition actually is, that is, passive receptivity to sensations. But this thinkability of intellectual intuition is what allows the slightly more compelling thought of a sensible intuition that works in a different way from ours.

Forging on…

The categories are forms of thought, and abstracted as we’ve been doing for the past few sections we can consider them just as this and no more, i.e., ...

... through which as yet no determinate object is cognized. [B150]

Kant summarizes the conclusions from earlier sections:

A priori knowledge, that rests on the understanding (as cognition in fact does (but the “in fact” is what Kant has been avoiding, which is why in transcendental fashion he has all the “insofar as” qualifications)), is based on the synthesis in the pure concepts as referred to the unity of apperception.

In other words, a priori knowledge is based on the synthesis in the pure concepts as belonging as one experience to me.

This synthesis (^), the synthesis of the manifold in the concepts, is transcendental, and only intellectual. But the intellectual is not the end of the story, of course. The manifold that is synthesized is that which is, first of all, conditioned by the pure forms of intuition, and which is given by the senses.

That is, the understanding determines objects of sensible intuition, applying its pure concepts to them, in accordance with the synthetic unity of apperception, i.e., applied to the synthetic united manifold. Thereby the understanding and the sensibility are brought together for knowledge, specifically then empirical knowledge, which is another term for experience.

Our intuitions being necessarily subject to this synthetic unity of apperception, the pure concepts of the understanding, “as mere forms of thought”, have objective reality, which is another way of saying they apply to objects (objects that can be given in intuition).

But they [the categories] apply to these objects only as appearances; for only of appearances are we capable of having a priori intuition. [B151]

... because the a priori intuitions apply to sensible intuitions, and the senses, of course, supply us only with appearances.

This solves the problem of how the understanding relates to our specific human sensibility: it can do so because the forms in which these sensations take shape as objects are within us. Objects are appearances, and appearances being within us there can be no problem in relating the understanding to objects.

Figurative & Intellectual Synthesis

In the foregoing, Kant has presumed a distinction which he now goes on to clarify:

This synthesis of the manifold of sensible intuition, which is a priori possible and necessary, may be called figurative synthesis. This serves to distinguish it from the synthesis that would be thought, in the mere category, in regard to the manifold of an intuition as such [I.e., sensible or intellectual]; this latter synthesis is called combination of understanding (synthesis intellectualis). [B151]

It’s odd that he says “This synthesis”, because above at (^) it is intellectual synthesis that he’s talking about, i.e., in the concept of an object. I suppose that the figurative synthesis is covered once he brings in sensible intuition.

Well, yes. As I was saying, the understanding can apply to sensibility because sensibility is moulded by the forms of intuition. The synthesis of the manifold of our sensible intuition makes this work, and this is the figurative synthesis.

Both these types of synthesis…

  1. Are a priori
  2. And “are the basis for the possibility of other a priori cognition.”

Therefore they are both transcendental.

What is the intellectual synthesis? Burnham describes it as “the synthesis as the understanding alone conceives it.” Burnham also points out that up till now, especially with the abstraction away from sensibility, Kant has been talking about intellectual synthesis, and is now going to introduce and explain figurative synthesis and argue that the latter must come under the former.

It looks to me as if the figurative synthesis is what does the work, and the intellectual synthesis is the same thing but thought, as if they’re two ways of looking at the same thing. Yes, I think this is right, and here is another way to say it: the figurative synthesis is the synthesis of intuition in its actual, human form.

Imagination

In any case, the figurative synthesis is called the transcendental synthesis of imagination.

It looks again like the imagination enters to act as a bridge between the understanding and the sensibility.

Possible essay question: Describe why Kant needs the imagination to make the argument of the deduction complete.

It can do this because, as Kant says next, it (imagination) is in one respect of the sensibility and in another respect of the understanding. It belongs to the sensibility because it gives intuitions to the understanding to correspond with the latter’s concepts. On the other hand, it belongs to the understanding because the synthesis of imagination is an act of spontaneity, “which is determinative, rather than merely determinable, as is sense.” [B151-152]

hence this synthesis can a priori determine sense in terms of its form in accordance with the unity of apperception.

This means that imagination is a power of determining sensibility a priori.

The imagination carries out the transcendental synthesis upon sensibility, and this is the starting point for the understanding’s application to what is given. This is very close to my idea of a bridge, of course. Another way to think of it is that, because the imagination is distinct from the understanding, it is that in us which the understanding uses to reach intuitions and apply the categories to them.

And again he reminds us that this synthesis — the transcendental synthesis of imagination — is the figurative synthesis, distinct from intellectual synthesis. Why now, I don’t know.

But next is something interesting. I haven’t looked into the reasons for Kant’s rewriting of the deduction, and I don’t yet have a decent grasp of how they differ. He now refers to the difference between productive and reproductive imagination, a distinction that appeared in the first edition. He points out that he has been talking here in the second edition mainly about the productive imagination, and that the reproductive is just subjective and empirical. Again I’ll try to explain the difference myself…

Reproductive imagination is our power of bringing to mind all at once different successive appearances, combining them to form a bundle that belongs together. It is subject only to empirical laws, the “laws of association”, and therefore it is not the basis that we need to find to establish the possibility of objects appearing as objects in the first place.

Productive imagination is this faculty considered transcendentally as the bare possibility of a single instance of the production of a synthesis, i.e., it is the power of imagination that makes possible its application according to the laws of association. It is imagination abstracted and seen in terms of the understanding’s spontaneity, rather than in terms of the various sensible intuitions that might or might not be associated.

Then, for the purpose of tidying up loose ends, he explores a paradox that Burnham describes as a “side issue”. I may come back to it, but right now I’m going to pursue the central argument of the deduction, which picks up again at § 26.

I will just comment on part of it though. At B154 Kant describes how we always perceive the need for figurative synthesis in ourselves.

We cannot think a line without describing it [i.e., in thought]. We cannot at all present the three dimensions of space without placing three lines perpendicularly to one another from the same point. [B154]

This suggests what perhaps should have been obvious, that by “figurative” he means what he says. He’s talking about actual figurative representations of the imagination, as when we imagine a circle or some lines.

§ 26: Transcendental Deduction of The Universally Possible Use in Experience Of The Pure Concepts of Understanding

In § 24 he provided the bridge between the sensibility and the understanding, namely the imagination. But this was a bridge between the understanding and the forms of intuition, rather than the particular objects, the actually given manifolds.

We must now explain how it is possible, through categories, to cognize a priori whatever objects our senses may encounter — to so cognize them as regards not the form of their intuition, but the laws of their combination — and hence, as it were, to prescribe laws to nature, and even to make nature possible. [B159]

This is supposed to be the last step in the deduction, the one missing piece of the puzzle.

Kant introduces the synthesis of apprehension, which first appeared in the “A” Deduction. It is …

that assembly of the manifold in an empirical intuition whereby perception, i.e., empirical consciousness of the intuition (as appearance), becomes possible. [B160]

Crucially, even this most empirical of the syntheses depends on the categories. He shows this by arguing that because space and time are intuitions as well as forms thereof, and these intuitions are characterized by unity of synthesis, there is a transcendental act of apprehension in which the categories are operative.

So, Kant uses the example of a house to show that there is an underlying unity stemming from the understanding. The empirical intuition of a house takes place through the apprehension of the intuition’s manifold, and the intuition’s manifold is a part of the entire field of spatial manifolds, which is given as a unitary thing itself, i.e., an intuition. This is the meaning of Kant’s insistence that space is both a pure intuition and a form of intuition. So, this apprehension is based on “the necessary unity of space and of outer sensible intuition as such.” [B162]

This unity, “if I abstract from the form of space”, is the category of magnitude. That is, it is only through the concept of magnitude that the unity of space is apprehendible.

NOTE: See the Aesthetic, esp. space as an infinite given magnitude, as unitary, etc. Here in the deduction Kant reveals what he did not touch on back then, namely that the very unity of space is an instantiation of one of the pure concepts of the understanding.

I think it’s important to note that this sort of synthetic unity is prior to the thingness of things: there is a prior unity in the perceivable features of Kant’s house [B162] before it becomes a house for us.

This synthetic unity, however, can be none other than the unity of the combination, conforming to the categories but applied to our sensible intuition, of the manifold of a given intuition as such in an original consciousness. [B161]

Steps in the 'B’ Deduction

  1. Derive the categories from the sorts of judgements we make [Metaphysical deduction, tables]
  2. Show that the unity of apperception is a requirement for all experience. [§ 21? 22?]
  3. Show that this unity of apperception operates through a synthesis according to the categories, which thereby apply with necessity to intuition as such, i.e., intuition from the understanding’s point of view, abstracted from its human condition (sensibility). [§ 21? 22?]
  4. Provide the bridge of imagination linking the categories to the forms of intuition, and show that space and time as forms of intuition fall under the notion of 'intuition as such’, therefore that they are necessarily subject to apperception and the categories. [§ 24]
  5. Finally, show that the actual objects of experience and their associations, i.e., the particular ways in which appearances are combined, and hence the actual laws of nature, are dependent on the categories. [§ 26]

[must include the figurative synthesis and other stuff]