[quote="darthbarracuda;586027"
]That which is independent of the conditions of human sensibility.[/quote]

You mean an objective reality? God(s) is (are) transcendental in this sense. So is the dual stuff in the magic trinity theory of consciousness.

Space is the form of the phenomena of external sense, and nothing more. It is what makes possible external intuition, and its given-ness precedes that of objects of external intuition. Outside of the subjective point of view of a human mind, space has no meaning, it is nothing. It is a predicate that is applicable only to objects of human sensibility, that is, phenomena. The form of the external sense of other beings cannot be known. — darthbarracuda

That's what HE thinks.

Because the Transcendental Logic is much longer than the Aesthetic, and also in order to more frequently visit this forum, I will try to break my notes down into smaller, more digestible chunks.

Second Part. Transcendental Logic

Introduction. Idea of a Transcendental Logic

Summary

I. Of Logic in general

Human knowledge has two sources: the capacity to receive impressions from objects through affection (sensibility), and the capacity to cognize [0] by means of these representations (understanding); objects are either given through our faculty of receptivity, or thought via the production of conceptions by the faculty of spontaneous [1] cognition.

With respect to sensation, both intuitions and conceptions can be either pure or empirical. Sensation is the matter of sensuous cognition. When an intuition is independent of all matter (sensation), it is a pure intuition, containing only the form of an intuition; and when a conception is independent of all matter (sensation), it is a pure conception, containing only the form of the thought of an object. Thus only pure intuitions and conceptions are possible a priori; the empirical only a posteriori.

Our nature is such that intuitions are never not sensuous; they must always appertain to the way in which objects affect us [3]. Through the understanding, the objects of these intuitions are thought. Only through the unification of intuition and conceptions can a cognition happen; thoughts without content are void, and intuitions without concepts are blind. The mind must make conceptions sensuous by joining them with the objects of intuitions, and it must also make its intuitions intelligible by bringing them under these concepts.

The science of the laws of sensibility is called aesthetic, and the science of the laws of understanding is called logic. Logic may be classified as either general or particular. General (or elemental) logic contains the absolutely necessary principles (forms) of thought, without which the understanding is useless. Particular logic concerns the laws of correct thought with respect to some specific class of objects; it is an organon for a science and arrives late in the maturity of the science on account of its requirement for an extensive knowledge of its objects.

General logic itself may be classified as either pure or applied. Pure general logic is that which abstracts from all empirical causes from which cognitions arise; things like sensations, imagination, memory, habit, inclinations, etc. Pure general logic contains only a priori principles which can be applied to either empirical or transcendental content [4]. Applied general logic is that which concerns the use of the understanding under subjective empirical conditions; in other words, it is a broad and general psychology of logic, a representation of the understanding within the context of empirical conditions, which concerns things like attention, doubt, conviction, etc. Only the pure logic of general logic is a proper science [6], concerning nothing but the forms of thought, without reference to its content (empirical or transcendental), or psychological factors. The relationship of pure and applied general logic is analogous to the relationship of pure and practical ethics.

II. Of Transcendental Logic

General logic is concerned with the form of the understanding, without distinction of the origin of its representations; it does not merely abstract from all sensation (as was done for the transcendental aesthetic), but all content, pure and empirical. Not all a priori cognitions are transcendental; only those that are directed at the a priori possibility and use of cognition are transcendental. Thus the representation of space is a priori but not transcendental, while the knowledge that the representation of space is a priori, is transcendental. The distinction between the transcendental and the empirical is applicable only to the critique of cognitions, and not to the relation of these with their objects.

The science of transcendental logic is concerned with the principles of pure understanding, by which we cogitate objects entirely a priori. It is a subset of general pure logic, applying only to the a priori relations in thought of objects.

III. Of the Division of General Logic into Analytic and Dialectic

If truth is the accordance of a thought with its object, then the object of a (valid) thought must be able to be distinguished from other objects. As such, to ask for a universal criteria for truth is self-contradictory, because it is to ask for a criteria that is valid for all objects, without distinction of content, the relation to which is precisely what truth amounts to. So in terms of the matter (content) of a cognition, no universal test of truth can be given. However, with respect to the pure form of a cognition, logic presents us with universal and necessary laws of understanding which can be used for such a necessary, though not sufficient criteria of truth - for a self-consistent thought may nevertheless disagree with its object.

The study of the principles involved in this negative test of truth can be called analytic pure general logic. Thought must be at least self-consistent if it is to be true; only after this is established can the content be scrutinized. Analytic logic has applicability only to the form of thought, and not to its matter. It cannot be used to determine if the content of a cognition is true, although it is tempting to do so. When this is done - that is to say, when general pure logic is used to try to extend our knowledge of objects - it is called dialectic. Dialectic, or general logic as an organon of thought, is the art of producing ignorance!, for it improper to be applied in this way and yields absolutely no knowledge when it is

IV. Of the Division of Transcendental Logic into Transcendental Analytic and Dialectic

Just like what was done in the Transcendental Aesthetic with sensibility, the Transcendental Logic must isolate the understanding and focus only on that which originates from it. The Transcendental Analytic is the critique of the principles of pure understanding, without which no object can be thought of, and thus is also a logic of truth. But this pure cognition requires that objects be given to it, to serve as the matter of application. When we apply these cognitions by themselves and to regions beyond experience, we make judgements of objects with no material distinction to provide the objective validity required for truth. The Transcendental Dialectic is the critique of this mistaken use of understanding and reason.


Questions:

0. Cognize, this term is used a lot, but without any definition. For a lot of these terms, I think I have a fuzzy grasp of what they mean, though a precise definition would be better.
1. Spontaneous, what does this mean?
2. Redacted.
3. How can Kant claim to know this, except by experience, e.g. it has been the case that all of my intuitions that I can remember have been sensuous up until the present.
4. By transcendental content, I take Kant to mean space and time?
5. Redacted.
6. What makes pure logic a proper science and applied logic not?

You can imagine an empty room I’m sure. — I like sushi

The room is still an object, with walls that have color.

Nice summary. Thank you.

3. not sure if I follow this last point. — darthbarracuda

It had a few spelling errors in that paragraph. When I used the spell checking software, it even replaced the words into some other words from its whim. Sorry. Now I have checked them, corrected the badly spelled words, and also added a little more sentences from the NKS commentary into 3.

I think what it says is that Kant's 3rd definition of transcendental is much different from the 1st, in that thranscendental preconditions the mental activities and concepts arising from a priori intuitions such as apprehension, reproduction, and recognition and even imagination and understanding, which render experience possible. But these faculties of mind cannot be themselves equated / called (titled) as a priori, which make the 3rd definition much more distant from the 1st.

Walls are walls because of the empty space between them. What’s your point? I can imagine a space that contains no objects.

According Kant space and time are ‘Intuitions’. Think of them as the canvas upon which cognition emerges. His view here is that mentally we ‘know’ (I prefer ‘ken’) only by way of space and time. We cannot imagine without placing something in a spaciotemporal frame.

The use of ‘transcendental’ will become more clear in later sections. He basically argues for and against different elements throughout the book so don’t take any of it as a ‘conclusion’ (so to speak).

Amend above to ‘pure intuitions’.

It’s a boom where you’ll constantly find yourself rereading previous sections once the next reveals something. Enjoy :)

0. In the Introduction, Kant says that the Critique is not a doctrine; yet here he calls part of it the Doctrine of Elements (and later the Doctrine of Method). Why? — darthbarracuda

0. "Lehre" vs. "Doktrine" (Transzendentale Elementar l e h r e in German). Both are translated as doctrine. "Lehre" can also mean something like "teaching", "(basic) lesson" or "basic knowledge" (I'm not a native speaker of German).


The following excerpt is from the "Jäsche Logic", Kant's lectures on Logic which were published in 1800 (Kant was still alive then). It can help to clarify the basic terms and distinctions:

"Of concepts

§1

The concept in general and its distinction from intuition

All cognitions, that is, all representations related with consciousness to an object, are either intuitions or concepts. An intuition is a singular(1) representation (repraesentatio singularis), a concept a universal (repraesentatio per notas communes) or reflected(2) representation (repraesentatio discursiva).
Cognition through concepts is called thought (cognitio discursiva).

Note 1. A concept is opposed to intuition, for it is a universal representation, or a
representation of what is common to several objects, hence a representation insofar as it can be contained in various ones.

2. It is a mere tautology to speak of universal or common concepts - a mistake that is grounded in an incorrect division of concepts into universal, particular, and singular. Concepts themselves cannot be so divided, but only their use."

https://cdchester.co.uk/wp-content/uploads/2018/05/Lectures-on-Logic-The-Cambridge-Edition-of-the-Works-of-Immanuel-Kant-in-Translation-Immanuel-Kant.pdf p.589

Questions:

0. In the Introduction, Kant says that the Critique is not a doctrine; yet here he calls part of it the Doctrine of Elements (and later the Doctrine of Method). Why?
1. What does "immediately" mean here? Independently of thought, as in, we don't have to reflect upon it?
2. What does "object" mean here? — darthbarracuda

0. In the Introduction, Kant says that the Critique is not a doctrine; yet here he calls part of it the Doctrine of Elements (and later the Doctrine of Method). Why?
I think this is the common complaint of the commentators of the CPR such as NKS, Paton and D. P. Dryer.  They all seem to agree that Kant was not consistent in the CPR in some of the definitions of the concepts and also the points. NKS even says the CPR is a patch work of shifting contents from Kant's previous publications.  Still the significance and importance of the CPR cannot be denied in the history of philosophy.  There are far more interesting and significant philosophies in the CPR than the minor inconsistencies that one should worry about. 
 
But for me, when Kant says Doctrine, that means they are the points he accepts as principles, and follows. For critique, I would understand as something still to be investigated, analysed and come to a conclusion.

1. What does "immediately" mean here? Independently of thought, as in, we don't have to reflect upon it?
I would have thought, because independently of thought, it must be sensory perception or the content of the sensory perception.  Sense perception of objects would not need intuitions for perception, because it doesn't need a thinking process. It would be direct perception such as bodily sensations?

2. What does "object" mean here? (An intuition can only happen [3] if an object is given [4] to us, which can only occur if the object can affect the mind.)
Some objects are general concepts, which have no particular reference to them. In that case, even if they are given to us, we have no concrete idea what they are.  These objects don't relate or activate intuitions.  For objects to affect our mind and relate to intuition, they must be particular objects such as the real objects that we see, hear and can touch etc. Or the objects from the past memory that we have directly experienced and acquainted with, then they do relate to the intuitions, which enable our mind think, reflect and imagine etc.

These are just notes from my thoughts on the points.  Could be totally different from others' points of course, which I would be interested to hear and reflect again.

Walls are walls because of the empty space between them. What’s your point? I can imagine a space that contains no objects.

According Kant space and time are ‘Intuitions’. Think of them as the canvas upon which cognition emerges. His view here is that mentally we ‘know’ (I prefer ‘ken’) only by way of space and time. We cannot imagine without placing something in a spaciotemporal frame. — I like sushi

I am not disagreeing with Kant's claim that space is an a priori intuition, or that we can't imagine objects not in space. All I am saying is that I don't find this particular argument (that we can imagine space without objects) compelling because it's not clear to me that this is actually the case. I don't seem to be able to conceive of "extension" apart from having there be an object that is extended; while extension and the properties of the object are distinct, and may have different origins, they nevertheless appear to be inseparably conjoined when it comes to actually presenting themselves to the mind.

Yes, there is empty space between the walls, but take away those walls, what is there? A black void, which nevertheless is still something on account of it possessing color. Again I am not saying that space possesses color, just that I can't conceive of space without applying color. Obviously this will be different for someone who is blind, I just happen to depend heavily on visual sensation when thinking about objects. Point being, some kind of sensation seems to be required for space to have any presentation, probably because it is just a form, and how do you conceive of a form (relations) without anything that takes part in the relation?

0. "Lehre" vs. "Doktrine" (Transzendentale Elementar l e h r e in German). Both are translated as doctrine. "Lehre" can also mean something like "teaching", "(basic) lesson" or "basic knowledge" (I'm not a native speaker of German). — waarala

Cool, thanks that makes a lot more sense.

NKS even says the CPR is a patch work of shifting contents from Kant's previous publications. Still the significance and importance of the CPR cannot be denied in the history of philosophy. There are far more interesting and significant philosophies in the CPR than the minor inconsistencies that one should worry about. — Corvus

Yeah, I'm realizing that we can really get side-tracked by hairsplitting comparatively minor issues. Probably I need to ease off the perfectionism a bit and settle more on understanding the whole rather than each individual itty bitty detail. Those can come later with time.

I would have thought, because independently of thought, it must be sensory perception or the content of the sensory perception. Sense perception of objects would not need intuitions for perception, because it doesn't need a thinking process. It would be direct perception such as bodily sensations? — Corvus

I figured something along the same lines, immediate meaning there being no other further representation that relates to the object. The object is given by sensations, sensation is the the initial way in which objects come into awareness. After which, forms and concepts are applied to sensation, thus indirectly (not immediately) to the object.

Yeah, I'm realizing that we can really get side-tracked by hairsplitting comparatively minor issues. Probably I need to ease off the perfectionism a bit and settle more on understanding the whole rather than each individual itty bitty detail. Those can come later with time. — darthbarracuda

This is important for this book. VERY important. Like I said, you’ll find yourself jumping back and forward through the text countless times.

Yeah, I'm realizing that we can really get side-tracked by hairsplitting comparatively minor issues. Probably I need to ease off the perfectionism a bit and settle more on understanding the whole rather than each individual itty bitty detail. Those can come later with time. — darthbarracuda

I think both ways are all valuable exercises. I am reading with a few different commentaries on the CPR (NKS, H.J. Paton, D.P. Dryer, S. Gardner, W. Sellars, H.W. Cassirer, Allison, P.F. Strawson, Walker, Bennett, Ewing) and it makes the reading painfully slow. But will try to catch up. I am not sure if it would be better for me just concentrating on the Kant's CPR first without the commentaries. But then, I would have less or more vague understanding of the text.

Damn, that's a heavy lift. I feel a bit foolish for having started Allison's book without reading the CPR alongside it. Unfortunately, while what I have read of Allison's book has made some of the CPR easier to understand, I find myself at times reading the CPR through the lens of Allison's book. Oh well.

Allison's book is very good, and I am also using it. I was looking for the best commentaries, and keep getting one after another, and ended up with 7- 8 different copies. But on the hind sight, maybe should have stick to 1 - 2. I find D.P. Dryer's book also very good.

I don't understand what you mean by systemic successions, could you clarify this? — darthbarracuda

Systemic successions is just me, keeping the theoretically mandated order of the particular influences of the particular elements involved, between the perception of an object and the experience of it.
————-

"Give to ourselves" - I take this to not mean things like memory or imagination (which we present to ourselves without an external stimuli), but rather that which does not have its original origin in us? — darthbarracuda

Backwards. Given to us means has its origin external to us; given to ourselves means has its origin internally within us. Thus, “give to ourselves” does mean things like memory, imagination. Technically, every facet of the representational cognitive system we give to ourselves. The world only gives to us the things on which the system is used.
—————

the intuition of space is not identical to the conception of space. — darthbarracuda

Space is not an intuition, because all intuitions have sensuous origins, and we never sense space. Space for us is never a phenomenon. Space is called a pure intuition just to provide a condition under which objects of perception can be said to be located relative to us or to each other. As a conception, it allows the concept of motion to have meaning. Just as time as a concept allows change to have meaning.
————-

How do I imagine space without something in it? — darthbarracuda

By imagining where some object would have to be, if there was one. Don’t forget, in Kantian-ese, you’re imagining a transcendental ideal, not a thing. Just hold out your hand, palm up, and imagine a Mars bar sitting there. Now think away the Mars bar, and imagine the space it was in, which you should be able to do. Now....just for fun....try thinking away the space the bar was in. You can’t, because there wasn’t, and never could be, anything relative to that empty space. There no such thing as an empty thought, you cannot think of that which may take the place of the space you thought away, therefore it is impossible to think it away in the first place. That’s why, along with time, Kant calls them ideals, because they are not themselves conditioned by anything. Instead, they are the conditions. Speculative epistemological metaphysics.

Besides, I don’t see a problem with imagining the empty space between two objects a foot apart. Elementary particle physics aside, of course, which we don’t care about anyway, but people like to try proving Kant wrong by bringing up such nonsense.
————

The book is a critique of reason. Reason is what the show is all about. Transcendental is a perspective, one of four, that reason takes with respect to what it is doing at any given time, the others being empirical, rational and judicial, or, moral. Reason examines....we can examine using reason in these various perspectives....everything from one or more of those perspectives, and some require all of them, re: freedom of the will. The most noteworthy being, of course, the so-called Copernican Revolution....something Kant never said by the way....in which reason is said to look at things from a different point of view. The ultimate transcendental perspective.

Reason is what the show is all about. — Mww

:100: :up:

0. There really isn’t a definition qua certain criterion, for cognition as such. There are fly-by’s, like, “thought is cognition by means of conceptions”, or, “(truth is) the accordance of a cognition with its object”. Cognition, in and of itself, is hidden in this passage: “...the unity of the act of arranging diverse representations under one common representation....” (A68/B93), in which it may be surmised cognition is the culmination (the unity) of the act (the logical “function”) of the understanding in synthesizing a series of conceptions under a general representation.

1. Spontaneity. Which makes more sense....that there exists in some faculty of the human mind a repository of all possible conceptions, even for that of which there is as yet no thought, or, a certain faculty of human reason brings up new conceptions pursuant to a circumstance in which no extant conception is sufficient? If the former, there would be no need to conceive anything at all, for the conception of it, no matter what it is, is already present in the mind. But then we would need a mechanism by which the mind, which is itself not part of the cognitive system, picks and chooses the proper conception out of every possible standing iteration resident in the repository, and then gives the conception to understanding, which most certainly is part of the cognitive system. Now, such could be the case, but parsimony suggests the simplicity of just letting understanding be that faculty by which conceptions arise, and that only and always in conjunction with something else already given by the system, re: phenomenon, because in that way, the system remains a unified procedure, operating by and within itself, without the influence of that which is not contained in it.

Again....transcendental philosophy. We aren’t talking about what we know. We talking about how it is possible to know, which presupposes not knowing. It follows that T.P. concerns itself with that instance between the absence of and the acquisition of, knowledge. In other words, the first ever instance of it. People are fond of missing the implication, instead complicating it by insinuating the effect of extant knowledge, when the cognitive system is most effective in, and absolutely necessary for, the absence of it. From the conception of “wheel” to the conceptions of “quark”, it’s all done the same way, the only difference being the time of it.

3. “Our nature is such that intuitions are never not sensuous; they must always appertain to the way in which objects affect us”

How can Kant claim to know this, — darthbarracuda

He doesn’t claim to know it; he claims that according to transcendental philosophy, such is a necessary hypothesis such that the philosophy is internally consistent and logically coherent. There is never an empirical proof for speculative metaphysics. What may be said that he does know, is that if intuitions are in some case not of sensuous origin, the entire treatise is worthless.

4. “Pure general logic contains only a priori principles which can be applied to either empirical or transcendental content.”

By transcendental content, I take Kant to mean space and time? — darthbarracuda

No. Logic has to do with understanding, as phenomena has to do with sensibility. Kantian dualism. The transcendental content of the logic of understanding, are the categories, which provide “.....unity to the different representation in a judgement...”. Space and time, as pure intuitions, are that which makes representations of objects possible, but has nothing to do with either the empirical content of phenomena, nor with judgements respecting the unity of those representations. Space and time, on the other hand, as conceptions, are deduced transcendentally, which merely indicates their objective reality and logical validity are thought absent any empirical influence in the formulation of their respective representations, and, their employment is completely a priori. This does not, however, make them transcendental conceptions, but only indicates the manner of their production.

An a priori principle takes the form of conceptions such as “cause”. While we have no logical need of cognizing a cause for the possibility of objects of sense, we certainly must append the conception of space to them necessarily, as a pure a priori intuition, as a means to justify the invocation of the system in the first place. “....for mere intuition does not in any respect stand in need of the functions of thought...” (A91/B123)

6. The answer to that is in the notes.

Space is not an intuition, because all intuitions have sensuous origins, and we never sense space. Space for us is never a phenomenon. — Mww

Not sure if I agree with this exactly, since Kant says in many places that space and time are intuitions, albeit pure; they provide the form, sensation provides the matter. They aren't concepts, and because of the dichotomy between concepts and intuitions, they must be intuitions. I agree they aren't phenomena, since they aren't appearances given to us by sensation. Space is given by us in order for phenomena to be given to us.

How I am understanding things as of now is that representations can be either concepts or intuitions, and can be either pure or empirical; but a representation cannot be both a concept and an intuition for they have a different nature.

Now think away the Mars bar, and imagine the space it was in, which you should be able to do. — Mww

I only find myself able to do so if I continue to image my hand (in space), and perhaps some sense of a geometric outline of where the Mars bar used to be. If I imagine extension in its most simplest form, I think of a grid or sorts. Hasn't Kant by this point already said that geometry requires the use of intuition (lines, graphs, etc) even though it studies the pure form?

I agree that I cannot imagine objects without space, and I think that this by itself can be turned into an argument for its a priority and therefore ideality, due to its universality.

Elementary particle physics aside, of course, which we don’t care about anyway, but people like to try proving Kant wrong by bringing up such nonsense. — Mww

Yes I have heard much about non-Euclidean geometry and particle physics as arguments against the Kantian view. Got any reading suggestions on this topic?

The book is a critique of reason. Reason is what the show is all about. Transcendental is a perspective, one of four, that reason takes with respect to what it is doing at any given time, the others being empirical, rational and judicial, or, moral. Reason examines....we can examine using reason in these various perspectives....everything from one or more of those perspectives, and some require all of them, re: freedom of the will. — Mww

Very interesting, I'm not familiar with this distinction of four perspectives. Is it raised later in the CPR?

Now, such could be the case, but parsimony suggests the simplicity of just letting understanding be that faculty by which conceptions arise, and that only and always in conjunction with something else already given by the system, re: phenomenon, because in that way, the system remains a unified procedure, operating by and within itself, without the influence of that which is not contained in it. — Mww

So, spontaneity refers to the capacity for the understanding to produce new and original conceptions that were never previously thought, when given the material to work with by phenomena.

Thanks again for all the detailed responses, I am grateful.

I'm not familiar with this distinction of four perspectives. Is it raised later in the CPR? — darthbarracuda

(Sigh) Ya know, I often frown upon subjectively, and sometimes chastise objectively, those who take some passage and reinvent it. So...here I am, unceremoniously busted for doing exactly that. From this little bit in the B introduction at xxviii.....

“.....For pure speculative reason has this peculiarity about it, that it can and should measure its own capacity according to the different ways for choosing the objects of its thinking, and also completely enumerate the manifold ways of putting problems before itself, so as to catalog the entire preliminary sketch of a whole system of metaphysics; because, regarding the first point, in a priori cognition nothing can be ascribed to the objectsd except what the thinking subject takes out of itself, and regarding the second, pure speculative reason is, in respect of principlese of cognition, a unity entirely separate and subsisting for itself, in which, as in an organized body, every part exists for the sake of all the others as all the others exist for its sake, and no principle can be taken with certainty in one relation unless it has at the same time been investigated in its thoroughgoing relation to the entire use of pure reason....”

.....I unceremoniously took it upon myself to substitute perspective for relation. But there’s enough support for the substitution, elsewhere and throughout the text, I think, to make it at least not inconsistent. Kant is notorious for saying stuff like, understanding views all its conceptions....., or, imagination reaches for its synthesis....., which just makes it seem like these faculties have a sort of capacity to reflect or look at their objects, which is, for all intents and purposes, a perspective these faculties possess, relative to the mode by which objects are presented to them.

So rather than a reification of abstract ideas on my part, which is usually considered an argumentative fallacy, I think the use of perspective as more along the lines of a rhetorical device, which is sort of allowed. Still, CPR can be successfully studied without the notion of perspectives. Whatever suits the student, right?
—————

Space is not an intuition.....
— Mww

Not sure if I agree with this exactly....(...)
......but a representation cannot be both a concept and an intuition for they have a different nature. — darthbarracuda

Point to you. I should have said, “space is not an empirical intuition”, insofar as all intuitions are of appearances and space does not appear in sensations. It is easy to see that space is necessary for the determinations of sensible objects, insofar as objects must be in space in order to be a perception for us. This from the metaphysical exposition of the conception of space. As such, we represent to ourselves a condition which pertains to all objects, as opposed to intuitions respecting the dissimilar matter of them. I suppose Kant means to say that whenever something is represented about an object, the representation of its space must have already been given, from which is deduced that space is then the form of sensibility, or, “....that which effects that the content of phenomena can be arranged under certain relations...”. All this means is, we cognize one end of this undetermined object as “tail” and the other end as “head”, with absolute certainty, because one is intuited as being in a different spatial relation from the other, and all that such that the conception of “dog” doesn't contradict itself. And while this seems like an awful lot of trouble to go through every time, the methodology of the system as a whole, just wouldn’t work without doing exactly that.

On the other hand, from the transcendental exposition of the same conception...Kantian dualism once more....in the case of synthetic a priori cognitions in which there are determinations on objects that are not of sensibility, re: geometric figures, which give to us a representation of the determinable space these figures enclose, it is found that this space is necessarily intuited as well, but not under empirical conditions. Kant says of this, “....What, then, must be our representation of space, in order that such a cognition of it may be possible? It must be originally intuition...” (added in B41, omitted in A).

Apparently, a representation can be both an intuition and a conception, albeit from different perspectives. Space is represented here as an intuition, there as a conception, but always a priori.

There’s a very good examination of the background history of Kantian critical philosophy in the introduction by Guyer/Wood, found here: http://strangebeautiful.com/other-texts/kant-first-critique-cambridge.pdf . Damn thing is 80 pages long, just as a measly intro, but there’s a lot of interesting commentary in it. You might find it useful.

I have already read past the first book of the Transcendental Analytic, though the consolidation of my notes is lagging a bit.

Transcendental Logic. First Division

Transcendental Analytic

1.

The goal of the Analytic is to study the principles underpinning pure understanding; to accomplish this, the concepts contained in the Analytic must be pure (and not empirical), belong to thought (and not sensibility), elementary (and not deduced), and belong to a complete table of pure concepts. This completeness can only come from an idea of the understanding as a self-sufficient united system, whose parts cannot be added or removed.

The Analytic is divided into two books: the first covers the concepts of pure understanding, while the second covers the principles of pure understanding.

Book I

2. Analytic of Conceptions

This will not be focused on the analysis of some class of concepts, but on the faculty of understanding itself, which alone gives the possibility of a priori conceptions.

Chapter I. Of the Transcendental Clue to the Discovery of all Pure Conceptions of the Understanding

3. Introductory

When we think about the faculty of cognition, we usually do so in a haphazard and unsystematic way; doing so cannot lead to any certainty of judgement thereof, because it does not give any sense of unity or necessity to the conceptions thought, and is dependent on chance. Transcendental philosophy has the advantage that its concepts are pure and unified, and therefore connected by a single idea, which gives us a rule to follow during our investigations.

Section I.

4. Of the Logical Use of the Understanding in general

The understanding is non-sensuous (independent of sensation), and because of this it must not contain any intuitions, since it is in our nature for intuitions to be sensuous. And because there are only two modes of cognition (intuitions and conceptions), the understanding must cogitate through conceptions, that is to say, it is discursive [0], and not intuitive.

Since intuitions are sensuous, they require affection by an object, and so also on the receptivity of the sensibility to impressions. Conceptions, on the other hand, require that different representations be arranged under one common representation (the act of which is called a function), and so also on the spontaneity of thought.

The understanding uses concepts only in order to judge [1] by means of them. Since only intuitions relate immediately to an object, conceptions relate to them mediately (indirectly) as representations of a representation of an object. Judgements are therefore functions of unity, in that many possible representations are joined under one. As the faculty of judgement, the understanding is a faculty of thought (since thought is the cognition by conceptions), and conceptions are predicates of possible judgements. As such, all of the functions of the understanding can be found through the functions of thought, since the understanding just is the faculty of judgement, this being the faculty of thought.

Section II.

5. Of the Logical Function of the Understanding in Judgements

The function of thought in every judgement, when abstracted from all content, has four heads, each of which can be of three moments:

• Quality of judgements
  - Universal
  - Particular
  - Singular
• Quality
  - Affirmative
  - Negative
  - Infinite
• Relation
  - Categorical
  - Hypothetical
  - Disjunctive
• Modality
  - Problematical
  - Assertorical
  - Apodeictical

The following observations will be made to avoid any unnecessary confusion [2]:

1. Singular judgements are not the same as general judgements, so they can be considered to be entirely different from universal judgements.
2. In transcendental logic, infinite judgements are not the same as affirmative judgements, though this is the case in general logic.
3. All judgements are either categorical, hypothetical or disjunctive.
4. The modality of a judgement is peculiar in that it provides no additional content (since this is exhausted by quantity, quality and relation), but is only concerned with the copula (“is”). Problematical judgements may be false, yet still facilitate our cogitation of truth. Problematical judgements concern possibility (objective validity), assertorical judgements concern actuality (objective reality), and apodeictical judgements concern necessity. The mind judges things in this order.

Section III.

6. Of the Pure Conceptions of the Understanding, or Categories.

While general logic abstracts from all content (and expects it to be provided elsewhere in order for it to transform it into conceptions), transcendental logic contains the a priori manifold of intuition, which is used as the matter for pure concepts. Since space and time are the condition of sensibility, they affect how objects are conceived in thought, since these concepts are void without any sensible content, and no concept pertaining to its content can arise before the content is given.

Once this sensibility is delivered to the mind, however, the process called synthesis occurs, in which different representations are examined and joined together into a single cognition. Synthesis in general is merely the operation of the imagination, which is indispensable as a function of thought, yet nevertheless usually not well-understood. The understanding reduces the product of the synthesis to conceptions, from which we attain a proper cognition.

The duty of transcendental logic is to reduce to conceptions, not representations, but the pure synthesis of representations. The diversity of the manifold of pure intuition is first given, then the imagination synthesizes it, before pure conceptions are applied by the understanding to give this synthesis unity, and therefore transform it into a cognition [3].

The pure conceptions of the understanding are the functions which gives unity to both the representations in a judgement, and the synthesis of representations in an intuition. These conceptions, through analytic unity, give rise to the logical forms of judgement, but they also introduce transcendental content through the application of the synthetic unity of the intuitive manifold [8]. Thus there are exactly the same number of pure concepts as there are logical forms, to which they correspond, and are given the name categories. They are:

• Of Quantity
  - Unity
  - Plurality
  - Totality
• Of Quality
  - Reality
  - Negation
  - Limitation
• Of Relation
  - Of Inherence and Subsistence (substantia et accidens)
  - Of Causality and Dependence (cause and effect)
  - Of Community (reciprocity between the agent and patient)
• Of Modality
  - Possibility - Impossibility
  - Existence - Non-existence
  - Necessity - Contingence

It is through these, and only these, pure conceptions that the manifold of intuition is made conceivable - that is to say, thought as an object of intuition. While Aristotle tried to make a catalogue of his own, he went about it unsystematically, and the result was not only uncertain to be correct, but actually indeed contained elements that should not have been included. In comparison, this catalogue has been arrived at by abiding by a rule [4], and so the result is guaranteed to be correct and complete. These pure conceptions themselves have deduced conceptions (called predicables), however these are not included in the present work, as it would distract from its overall purpose, however they would belong in a complete transcendental philosophy.

7.

Here are some observations related to the pure conceptions:

I. The table of categories can be divided into two classes: the first of which relates to objects of intuition (deemed mathematical), the second to the existence of these objects in relation to each other and/or to the understanding (deemed dynamical). Only the latter has correlates [5].

II. There are always three members of each of the four classes. The third is always a product of the combination of the second and first members; but this third member is not a deduced category because of this, since a particular function is required for the first and second members to produce the third.

III. [6]

8.

Ancient transcendental philosophy contained a fifth categorical division, the members of which were the one, the true, and the good (unity, truth, perfection). This would augment the number of categories, which cannot be, because there is a one-to-one relation between a category and a logical function of thought. These supposed-categories are really just surreptitious names for the categories of quantity (unity, plurality and totality) when viewed as general laws of consistency of cognition. In every cognition of an object there is a unity of the manifold (qualitative unity); the truth (objective reality) of a cognition can be indicated by the number of true deductions that are sourced from it (qualitative plurality); and finally when this plurality is fully in accordance with the conceptual unity, it is perfect (qualitative completeness) [7].

Questions/Thoughts

0. By "discursive", I take Kant to mean the process in which the understanding organizes objects by concepts according to their marks.
1. By "judgement", I take Kant to mean basically the mental process of deciding if something is the case.
2. This part was fairly dense to get through, and I felt it was not as important to focus on, so I brushed over some of the parts I found confusing.
3. I don't really understand what the difference is between the synthesis of the imagination (conjoining intuitions) and the operation of the understanding (putting this synthesis under a concept to give it unity). This part was a bit dense for me.
4. It is unclear to me what this rule exactly is.
5. What does Kant mean by "correlate"?
6. Kant's discussion about community and disjunctive judgements is dense, but I recall in Allison's book a good deconstruction of the argument, so I will defer the summary of it to there.
7. I found this section to be incredible dense in areas, though I think I grasp the general idea.