Introduction

Summary

I: On the difference between Pure and Empirical Knowledge

With respect to time, all knowledge begins with experience. However, this does not necessarily mean that all knowledge arises from experience. The question is, can there be knowledge independent of experience? Knowledge of this kind is called a priori, while that which is derived from experience is called a posteriori.

A priori knowledge is not simply that which may be known before some experience occurs; it is that which is absolutely independent of all experience whatsoever. Pure a priori knowledge has no empirical elements mixed up with it, whereas impure a priori knowledge has some relation to experience. Knowledge that is a posteriori - that is, empirical - is only possible through experience. For instance, “every change has a cause” is an impure a priori proposition, because the concept of change is derived only from experience.

II: The Human Intellect, even in an Unphilosophical State, is in Possession of Certain Cognitions “a priori”

How can we distinguish between a pure and an empirical cognition? The two tests for purity are that of necessity and universality. The empirical can never provide either, for experience cannot tell us that some phenomenon must be of some way, or that all phenomena are of some way. Empirical universality is an arbitrary extension of validity from most cases to all cases. In contradistinction, pure (a priori) cognition is characterized by its necessity and strict universality. Both need not be established for a cognition to be deemed pure; and it is enough to demonstrate only one, as neither one is a feature of the empirical.

That humans possess judgements that are necessary and strictly universal can be demonstrated by any mathematical proposition. But also, scientific propositions like “every change has a cause” (although being an impure a priori proposition) possesses both necessity and universality due to the conception of a cause necessarily and universally being connected to an effect, since a cause would not be a cause if it had no effect. Furthermore, empirical judgements could not acquire any degree of certainty if the principles they are based on are themselves also empirical. Finally, there are also concepts that remain after we have stripped away all that is empirical, such as the concepts of body and substance.

III: Philosophy stands in need of a Science which shall Determine the Possibility, Principles, and Extent of Human Knowledge “a priori”

Some human cognitions seem to extend the range of judgements beyond that of possible experience, by means of concepts with no corresponding object of experience. This transcendental, or supersensible, realm of thought holds problems of reason which are of great importance to humans and of which doubt or indifference does not restrain us from inquiring into. These include God, the freedom of the will, and immortality. The science which deals with these problems is called metaphysics. It has been dogmatic from the beginning because it has taken on this task without first investigating its capacity to do so.

Since it deals with questions outside the safe ground of experience, the foundations of metaphysics ought to be investigated before going any further. But humans have a natural desire to expand their knowledge on these important questions, and so go about doing so (and very quickly) without knowing whether this is possible. At any rate, mathematics has had such undeniable success as an a priori science, that metaphysics is taken to have the same fruitfulness. Just as a dove, flying through thin air, may believe it would fly even more effortlessly if it were to be in airless space, metaphysicians see in the independence from experience a freedom for limitless thought. Indeed, outside of experience, metaphysics encounters very little resistance to rapid and complex theorizing.

But regardless of all the effort and enthusiasm, there has been no real progress in metaphysics. Every new metaphysical theory is another attempt to blindly stumble around in the dark. Part of this has to do with the desire to finish the edifice of knowledge as quickly as possible, and only reflect upon the foundations when absolutely required to. But also, a great deal of the operations of reason consist in the analysis of concepts, which does not introduce any new matter or content (but merely clarifies that which was already contained in the concepts). However, reason unconsciously slips into a second mode of function, where it connects foreign concepts to each other, without knowing how these are connected. These two modes are explored in the next section.

IV: Of the Difference Between Analytical and Synthetical Judgements

In all judgements where the relation between the subject and the predicate is cogitated, this relation is possible in two ways: either the predicate belongs to the subject and is contained within the conception of the subject, or the predicate lies outside of the subject, though it stands in connection with it. The former judgement is termed analytical, the latter synthetical.

Analytical judgements are those in which the connection is cogitated through identity and can be called explicative; synthetical judgements are cogitated without identity and can be called augmentative. An example analytical judgement might be “all bodies are extended”, because extension is built into the concept of body. An example synthetical judgement might be “all bodies are heavy”, as the concept of weight is not contained in the concept of body, but nevertheless is related to it by means of experience.

In this way, all judgements of experience are synthetical, since analytic judgements have no recourse to go outside of the sphere of conceptions with the application of the principle of contradiction. The principle of contradiction is what establishes a priori knowledge as necessary and universal. Whereas synthetical judgements conjoin concepts contingently as part of a whole, which is called the synthesis of intuitions.

Analytical judgements are always a priori (pure), but synthetical judgements are not always a posteriori (empirical). A synthetic a priori judgement would occur without the aid of experience; indeed, it is the characteristic of an a priori judgement to be necessary and universal, which cannot be established through experience. All speculative knowledge, such as metaphysics, is synthetic a priori.

V: In all Theoretical Sciences of Reason, Synthetical Judgements “a priori” are contained as Principles

All mathematical judgements are a priori synthetical. Consider the proposition 7 + 5 = 12. This is not an analytic proposition, as the number 12 is not contained in the concept of the sum of 7 and 5, i.e. (7 + 5 = SUM) is not the same proposition as (7 + 5 = 12). In order to derive 12 from the sum of 7 and 5, we need to resort to an intuition corresponding to one of the concepts, such as the fingers on a hand. This becomes more clear when doing more complex mathematical operations. The same can be said of the proposition that a straight line is the shortest distance between two points. The concept of shortest is not contained in the concept of line, and so is a wholly new addition to the concept, the synthesis of which is achieved through an intuition.

Natural philosophy (physics) also contains synthetical a priori judgements as principles. For instance, the propositions that the quantity of matter in the universe remains constant, or that an action must equal a reaction in terms of motion, are both synthetic. The necessity and universality of these claims is clear, so they are indeed a priori. But they are also synthetical, as they involve concepts that do not share an identity, e.g. matter with permanency.

Metaphysics, too, must contain synthetic a priori judgements. It must not simply clarify the concepts we have of things, but actually extend the knowledge we have of them to regions beyond possible experience. A metaphysical proposition like “the world must have a beginning” involves necessity, so it is a priori. And the concepts of world and beginning are not contained within one another, so a judgement using them must be synthetic, which requires an intuition as its ground. But since the judgement is a priori, it cannot appeal to experience for this ground, so some other intuition must be used for the judgement to be valid.

VI: The Universal Problem of Pure Reason

It can be advantageous to put a number of different investigations under a single question; for the purposes of this essay, the question is this: how are synthetical a priori judgements possible? The entire existence or downfall of the science of metaphysics depends on the answer to this single question.

The reason metaphysics has vacillated for so long with no progress is because the distinction between analytical and synthetical judgements was never properly drawn. David Hume was the closest to suggesting it, but he failed to accept that certain propositions - like those containing the concept of causality - could be possible, because he thought they were simply confused notions borrowed from experience and habit. However, had he applied his skepticism universally, he would have had to reject all mathematics, which would have been absurd.

Because mathematics and natural philosophy have undeniably made progress in the extension of our knowledge, the aforementioned question can be asked for them as, “how are they possible?”, since it is already evident that they are. But with metaphysics, which has made such miserable progress, the question is rather, “is metaphysics possible?” Metaphysics as a natural and powerful human disposition is certainly possible, but the real question is whether metaphysics is possible as a science; that is, whether we can possess knowledge of the objects in which it treats.

The critique of (pure) reason is what can lead to the establishment of this science. It is not a large science, as its object of study is only Reason itself. Once Reason understands itself, it can determine the limits of its application, namely to that of objects outside of experience. This is a completely different procedure to any other done in the past; the focus is on determining how the concepts used in metaphysics come about a priori. Although metaphysics has consistently failed in the past, it is indispensable to human reason, so it is prudent to assess what the limits of reason are with respect to this science.

VII: Idea and Division of a Particular Science, under the Name of a Critique of Pure Reason

The science which deals with all that has been said is called the Critique of Pure Reason, since reason is the faculty which provides the principles of knowledge a priori. The Critique is a propaedutic to the complete system of pure reason, which would be called transcendental philosophy. The term transcendental here means all knowledge which is occupied not with objects, but with the mode in which we cognize these objects, as far as this mode is a priori. For the purposes of this essay, the focus will only be the principles of a priori synthesis, as a guide and preparation for a complete transcendental organon. The Critique of Pure Reason is the complete idea of a transcendental philosophy, but not the science itself. There must be nothing empirical involved in its concepts, for its subject is pure reason.

It is divided into two parts: a Doctrine of the Elements, and a Doctrine of the Method. The former is subdivided into two parts, which deal with the two sources of human knowledge, sense and understanding. Objects of sense are given, while objects of understanding are thought. The conditions under which objects are given must precede the conditions under which objects are thought, so the conditions of sensibility will be addressed first.

Questions:

• In V, Kant says

Arithmetical propositions are therefore always synthetical, of which we may become more clearly convinced by trying large numbers.

Is this appeal to our psychological limitations appropriate for a transcendental argument?

• In V, Kant says

Some few principles preposited by geometricians are, indeed, really analytical, and depend on the principle of contradiction. They serve, however, like identical propositions, as links in a chain of method, not as principles [...] What causes us here to commonly believe that the predicate of such apodeictic judgements is already contained in our conception, and that the judgement is therefore analytical, is merely the equivocal nature of the expression.

What does Kant mean here? This paragraph was very confusing to me.

What does Kant mean here? This paragraph was very confusing to me. — darthbarracuda

This is what I think. When an arithmetic calculation is performed, the answer is not in the adding or subtracting numbers, but it comes from the intuition of the mind . IOW intuition must work to come up with the answer for arithmetic calculations, therefore it is a synthetic judgment process. One does not notice it when it is a simple calculation such as 1+1=2.  But when there are larger (complex) numbers such as 756 + 243 = 999, it is evident that, intuition is called for to come up with the answer.

Geometry is based on the contradiction principle.  Contradiction principle says that, A cannot be "not A" .i.e. a circle cannot be "not circle", a triangle cannot be "not triangle", and geometrical items have their definitions already contained in the concepts. a triangle is a 3 sided polygon and the total of the 3x internally formed angle is 180 degrees.  The definition covers all the triangles in the universe. There is no triangle in the universe, which does not fall in the definition. If it doesn't then it is not a triangle. Therefore geometric judgments are analytical.

“....Some few principles preposited by geometricians are, indeed, really analytical, and depend on the principle of contradiction.....

Yet, the analytic is conditioned by the....

“....Analytical judgements are therefore those in which the connection of the predicate with the subject is cogitated through identity....

Hard to reconcile this apparent mischaracterization. But assuming Kan knew what he wanted to say, the reconciliation must be possible. If that weren’t tough enough.....

“....Mathematical judgements are always synthetical.....

Given that geometricians are mathematicians, and all mathematical propositions are synthetic judgements, the “preposited” principles by geometricians must not be mathematical propositions covered by synthetical judgements. That being the case is supported by....

“....and depend on the principle of contradiction. They serve, however, like identical propositions, as links in the chain of method, not as principles—for example, a = a, the whole is equal to itself, or (a+b) —> a.....

Why not change a little teeny-weeny thing, and call it identity propositions? So if the “preposited” principles of geometricians that depend on the principle of contradiction, are really just the first links in a chain of a method, and if that method Is just formal logic, not mathematics, then it follows that it is only logical that the geometrician work with one figure in order to gain something from it, and he would not work with any other kind of figure, for working with trapezoids would necessarily contradict what he wanted to discover about a triangle. Hence, the preposited principle of contradiction relates to what figure he works on, but the real mathematical propositions remain synthetical, which relates to how he works with the figure.

Formal logic consists in conceptions by their similar identities, Kantian analytics consists in conceptions by their similar relations, within a given proposition. If conceptions can be conceived as relating without any additional conceptions supplementing that which is given in the proposition, or, which is the same thing, no additional conceptions are necessary to derive a truth from that proposition, it is analytical. This is a two-aspect system, the conceptions avail themselves to mere analysis for their similarity.

If the conceptions in a proposition cannot be related to each other without the addition of another conception, it is synthetical, and is a three-aspect system. The conceptions in this system avail themselves, not to analysis, but to synthesis, by means of which the additional conceptions are derived.

“....merely the equivocal nature of the expression.”

.....the expression being any considered analytical judgement, and the equivocation residing in the dual nature of, on the one hand, identity, and on the other, contradiction. Therefore, even geometrician’s judgements with respect to their profession alone, is nonetheless synthetic. And “...mathematical judgements are always synthetical...”, survives unscathed.

Dunno if that helps or not......

Mathematical judgements are always synthetical — Mww

Some simple ones are 100 or 99 per cent synthetic and the more complex they get the greater the analytical proportion of it. Any educational psychologist or person that is being helped with specific learning differences will tell you that much.

As for the a priori part that is on a sliding scale as well. Husserl who followed Kant quite a bit, found there are three sequences to perception alone (which apply whether priori / posteriori / synth. / analy.)

I like the thread, thanks for posting the notes.

Ok. Good to know.

I did my nightly CPR readings last night, and picked out some contents from the Transcendental Aesthetic.

Empirical intuition
"The effect of an object upon the faculty of representation, so far as we are affected by the said object, is sensation. That sort of intuition which relates to an object by means of sensation is called an empirical intuition.

The undetermined object of an empirical intuition is called phenomenon."

Pure intuition
"I call all representations pure, in the transcendental meaning of the word, wherein nothing is met with that belongs to sensation. And accordingly we find existing in the mind a priori, the pure form of sensuous intuitions in general, in which all the manifold content of the phenomenal world is arranged and viewed under certain relations. This pure form of sensibility I shall call pure intuition."


Form
"That which in the phenomenon corresponds to the sensation, I term its matter; but that which effects that the content of the phenomenon can be arranged under certain relations, I call its form.
But that in which our sensations are merely arranged, and by which they are susceptible of assuming a certain form, cannot be itself sensation. It is, then, the matter of all phenomena that is given to us a posteriori; the form must lie ready a priori for them in the mind, and consequently can be regarded separately from all sensation."

"Thus, if I take away from our representation of a body all that the understanding thinks as belonging to it, as substance, force, divisibility, etc., and also whatever belongs to sensation, as impenetrability, hardness, colour, etc.; yet there is still something left us from this empirical intuition, namely, extension and shape. These belong to pure intuition, which exists a priori in the mind, as a mere form of sensibility, and without any real object of the senses or any sensation. The science of all the principles of sensibility a priori, I call transcendental aesthetic." - The CPR, Transcendental Aesthetic

I understand Transcendental as "before experience or prior to experience", and Aesthetic as "sensory perception" in the CPR. So, transcendental aesthetic denotes a priori sensory perception or knowledge, which are non experiential sensory perception or knowledge .i.e. metaphysical perception or knowledge such as on God and Souls.

My understanding and interpretation on the CPR texts I am reading, might be wrong, different from yours or the formal views in the commentary books.  If you see or spot any points wrong, different, unclear, or simply points for discussions, please let me know. Thanks.

I've scarcely read this sort of thing anywhere except in SpLD literature (and the odd hint in Husserl commentaries, and, more vaguely, Max Black's comments in The nature of mathematics dealing with intuitionism). This supports Kant's point against his usual opponents, but I wonder if he was too brief. I'm not actually reading CPR yet (so shall probably stay out from now on) but shall enjoy referring to this thread when I do.

What supports Kant against his usual opponents? Max Black’s comments? Is it Black that says what you wrote...

Some simple ones are 100 or 99 per cent synthetic and the more complex they get the greater the analytical proportion of it. — Fine Doubter

If so, that opposes Kant rather than supports him, insofar as Kant makes no mention of the varying degrees of analytic/synthetic with respect to mathematical judgements. Maybe nowadays, folks have added their own interpretations to Kantian metaphysics, but that shouldn’t detract from what the man himself says.

And Kant was brief about the analytic/synthetic dichotomy, because all he was trying to prove was the possibility of synthetic a priori cognitions. In order to do that, he first had to distinguish the conditions synthetic cognitions must have, from the other kinds of cognitions there are, then determine whether such cognitions were indeed possible a priori.

It turns out he was so brief, because it was so simple and easy to prove. In fact, he chastised Hume....gently of course..... for not having thought of it already.

Anyway.....drop in when you feel like it, bearing in mind there are no proper Kantian scholars here. Or, if there are, they’re being awful damn quiet.

It supports Kant, but others say it opposes him because they only see the cases where it isn't (much) the case. I think developmental experience supports Kant plenty: if grouped neatly and nearly enough, we can take in five objects as five. If we're quick at it, two groups of five as ten. But sets of sets of sets (which claims to be based on the same maths) isn't so obvious. My shades of grey / spectrums / continuums outlook tends to resolve false dichotomies and affirms more viewpoints, hence is epistemically successful.

I don't think Black criticised Kant for his brevity on that. The spectrums / continuums is something I added because I found they are very successful for me in various circumstances in all fields of knowledge.

I got The nature of mathematics in a second hand shop ages ago, didn't understand it totally, but Black is basically juxtaposing several viewpoints or camps in maths. Godel's findings were new at that time but surely it was always obvious that maths is an ideal / a fiction / an approximation? Even at the everyday level we have the paradox of one, two or three oranges (integers) versus 1.35694027 (continuums). And right angled triangles are right enough. This all fascinated me since infant school, and indeed it doesn't get spelt out enough (imagination isn't appealed to enough). At the greengrocer he didn't slice an apple when we asked for a pound of apples: it was over or under.

I've now downloaded the same book as free PDF.

I think zero is an approximation, and infinite and infinitesimals are approximations to approximations.

I expect this is only a small part of Kant's story and I don't want to make the thread subject small or partial. A site based partly on Fries, and which appreciates Kant somewhat, that I stumbled upon is www.friesian.com

surely it was always obvious that maths is an ideal / a fiction / an approximation? — Fine Doubter

Yeah....a take-off on the old “is math invented or discovered” dichotomy. There are those that say math is ideal because there are no numbers in Nature, that math is a fiction because there are no mathematical laws in Nature, and that math is an approximation because the possibility exists that other rational agencies have different maths. Not to mention, any mathematical formulation predicated on pi must necessarily be an approximation.

What is sets of sets of sets?

numbers in Nature ... sets of sets of sets — Mww

There are numbers in Nature in the form of recursions, which a lot of prominent personalities make great show of "not" understanding. When they are calculated, they are calculated approximately.

Page 35 of a book I greatly like, 50 mathematical ideas you really need to know by Tony Crilley, describes imaginary numbers as grouping several pieces of maths together to be done at the same time. Reportedly quaternions are a very advanced form of this. Reputedly sets are a greatly more complicated development from that. And models are a greatly more complicated development from that. "Model theorists" claim not to be modelling anything > sigh < Once we can't see it at all, it stops being even 1 % synthetic or a priori and one no longer has assumptions one can consciously critique or adjust.

There never was anything wrong with approximations being approximations, or honesty about ideals being ideals.

There are numbers in Nature in the form of recursions — Fine Doubter

Hmmm. How does infinite reflections in paired mirrors prove numbers are contained in Nature?

If counting is a recursive procedure, the procedure itself cannot show numbers are already contained in Nature, for numbers must be presupposed in order for the procedure to even occur.

But....maybe neither of those are what you meant by recursive. In which case, I don’t understand what you do mean.

I compiled all my notes for the Transcendental Aesthetic and found that I had quite a bit of questions. I have used bracketed numbers in my notes to point to the associated question.

I: Transcendental Doctrine of Elements [0]

Summary:

First Part. Transcendental Aesthetic

I: Introduction

Intuition is the only means in which our knowledge immediately [1] relates to objects [2]. 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. The receptivity of the mind for representations through various modes is called sensibility. Objects are thought by the understanding, from which arise conceptions; but all thought must relate in some way to intuitions, and therefore sensibility [5].

Sensation is the means in which an object affects the faculty of representation [6]. Intuitions which relate to objects by means of a sensation are called empirical intuitions. The undetermined object of an intuition is called a phenomenon [7]. Within the phenomenon are its matter and its form; the matter corresponds to the sensation, and the form corresponds to the rules for the way the matter is represented. The matter of a phenomenon is given a posteriori, while the form is given a priori, for the form cannot be a sensation itself.

A representation is pure when nothing in it belongs to sensation. The form of phenomena is a pure representation which arranges the manifold content [8]. This pure form of sensibility can be shortened to simply pure intuition. There is no real object of sensation corresponding to a pure intuition, as this is a requirement for its purity.

The science of the principles of sensibility a priori is called transcendental aesthetic (the term “aesthetic” is referencing the first half of the ancients’ division of objects of cognition into the sensible and the conceivable). This forms the first science of the transcendental doctrine of elements, the second being the transcendental logic, which is the science of the principles of pure thought. To get to the forms of pure sensibility, which is the focus of transcendental aesthetic, sensibility must first be isolated from the understanding by stripping away all concepts; the raw empirical intuitions must then be stripped of all sensation. There are two pure forms which remain after all this has been done: space and time. Space will be investigated first.

Section I. Of Space

2. Metaphysical Exposition of this Conception [9]

A metaphysical exposition of a concept is a simple and clear representation of what belongs to the concept when it is given a priori. Space is the external sense of the mind, that being which permits the mind to represent to itself objects that are not itself. On the other hand, time is the internal sense of the mind, that being which permits the mind to contemplate itself and its states. Thus the focus here will be on determining what belongs to humans’ external sense - space - when this is given without any sensation.

1. Space is not given through outward experience, because the very notion of outward-ness (objects being separate from the mind and separate from each other) necessarily involves spatiality. Space must be prior to any outward experience for there to be any outward experience at all.

2. Thus space is a necessary condition, and not a determination, of all outward experience. To further illustrate the previous point: we cannot imagine objects that are not in space, but we can imagine space without any objects [10].

3. Space is not a discursive (or general) conception of the relations between things, but is rather a pure intuition, because there is only one all-encompassing space, which is prior to all of its parts [11].

4. Space can also be known to be an intuition, because it is given as an infinite quantity; while concepts can have infinite representations under it (it applies to an infinite number of representations), they cannot have an infinite number of representations within it (it must be defined by a finite number of representations), and the opposite is true for intuitions.

3. Transcendental Exposition of the Conception of Space

A transcendental exposition of a concept is an explanation of how other synthetical a priori cognitions are made possible through the concept. In order to do so, it must be shown that these cognitions are actually conditioned by the given conception, and further that this is only possible if the given conception is of a certain way.

Geometry will be the other synthetical a priori cognition used here, since it is the science which determines the properties of space in this way. Because geometry involves synthetic propositions, its subject matter - space - cannot be a concept, since no concepts alone cannot yield synthetic knowledge; thus space is an intuition. And because geometry is apodictic, space cannot be empirical, as apodicticity entails necessity and universality, which cannot be found through experience; thus space is a pure intuition which precedes the perception of objects. A pure intuition of external objects that is anterior to the objects themselves can only come from the subject is just what is meant by a form of sensibility - in this case, the form of the external sense.

4. Conclusions from the foregoing Conceptions

a. Space is not a property of things as they exist apart from the mind; it is a condition for the experience of external objects, and not a determination of these objects, since a determination of an object cannot precede the existence of the object it is determined by.

b. 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.

Joining the limitation of a judgement to the conception of a subject gives it universal validity. For instance, the proposition “all objects are beside each other in space” is applicable only when they are taken to be objects of intuition, whereas the proposition “all things, as external phenomena, are beside each other in space” does not suffer this deficiency. Thus the expositions before demonstrate the empirical reality (objective validity) of space with respect to objects of sensibility, but the transcendental ideality of space with respect to things-in-themselves [12].

Space is the only subjective representation that has objective validity with respect to sensible intuitions; there is no other representation from which we can derive synthetical a priori propositions, like we do in geometry. Sensations are subjective but not ideal [13], and give no cognition of objects as intuitions do. They are not properties of things, but changes in the subject, which may be different across people, and so cannot ground any objective validity.

Section II. Of Time

5. Metaphysical Exposition of this Conception

1. Similar to that of space, the focus here will be on determining what belongs to humans’ internal sense - time - when this is given without any sensation or inner states.

2. Time is a priori, for neither coexistence nor succession would be perceptible to us if it was not in relation to time. Thus time is not empirical, as the notion of change requires there be time.

3. Time is a necessary representation, because we cannot think of phenomena apart from time, but we can think of time as apart from phenomena [14].

4. Since time is necessary, it is also possible to make apodictic judgments regarding it, such as “different times are not coexistent but successive” (just as different spaces are not successive but coexistent). Neither necessity nor universality can be derived from experience, so time is a priori.

5. Time is not a discursive conception, but a pure form of sensible intuition. Just like what was said for space, time is given as a single object that is prior to its parts, and only an intuition can relate to a single object. Also, the proposition that different times cannot be coexistent is synthetical, which prevents time from being a concept [15].

Each part of time is given as a limitation of the one unlimited time, just as space is. But conceptions can only furnish a partial representation [16], so time must be an intuition.

6. Transcendental Exposition of the Concept of Time

The conception of change and the conception of motion (change of place) is possible only through the representation of time; if this were not an internal, a priori intuition, no conception could make the conjunction of contradictorily opposed determinations in the same object comprehensible. Time allows for this in terms of succession, by placing one determination after another.

7. Conclusions from the above Conceptions

a. Time is not a property of things as they exist apart from the mind. For if it were real in itself, it would not present to the mind any real object; and it belonged as a determination to objects, it could not be their condition, and we could not form synthetical a priori propositions about it.

b. Time is the form of the phenomena of internal sense, and nothing more. It does not concern objects of external sense (those in space), but rather with the relations of representations in our internal state. These representations have no spatiality, so we use analogies to help describe them (such as a linear line extending into infinite). All of its relations can be expressed in an external intuition, which is yet another reason why time is an intuition [18].

c. Time is the formal condition of all phenomena, both internal and external. All representations of objects, external or internal, are determinations of the mind. They belong to our internal state, which is subject to the formal condition of internal intuition. Thus all phenomena stand necessarily in relation to time; immediately if they are internal, and mediately if external.

And just as with space, time has objective validity and a priori universality only with respect to objects of sensibility, and not with things as they are in themselves. Since all intuition is sensuous, no object can ever be presented in experience that is not conditioned by time. It is empirically real, that is to say, it has objective validity with respect to all objects of sense; but it is transcendentally ideal, that is to say, it is nothing outside of this domain.

8. Elucidation

One common objection to the aforementioned argument for the empirical reality and transcendental ideality of time is this: change is real, and is only possible through time, so time must be real as well. It is true that time is real, but only as the subjective internal sense; that is to say, it is a mode of representation of the self as an object, and not an object itself. However, that which is represented to humans by time does not stand in a necessary relation to time; if we (or another being) could intuit ourselves without time, there would be no change. Thus change is only real if time is real, and that which is represented through change need not be represented as such if time is not the condition of inner sensibility.

The reason why this argument is brought up so often is because time is taken to be an easier target than space. Objects in space cannot be proven to be absolutely real, due to the possibility of skeptical idealism; but objects of the inner sense are taken to be undeniably real. However, this ignores the nature of both objects, which is that they are phenomena. Phenomena have two aspects: the object considered in-itself, and the form of our intuition of the object. The form of phenomena as intuitions applies only because the form is provided by the subject. Space and time are the only forms of sensuous intuition, and they allow us to make synthetic a priori judgements, such as what is done by mathematics with space. Most importantly, they are only applicable to objects considered as sensuous phenomena, and not with the thing-in-itself.

If space and time are absolutely real (subsistence), then they must be eternal and infinite and exist (without being any object themselves) in order for all other real entities to exist, which results in absurdities when the understanding attempts to go beyond them. And if space and time are relational (inherence), then they are an abstraction from experience; in which case, apodictic propositions, like those of mathematics or physics, would be invalid, for experience cannot ground the necessity or universality that is required for apodicticity. Neither flaws are present for the theory of the transcendental ideality of space and time.

The Transcendental Aesthetic has only two components, space and time. All other representations of sensibility require experience. Even motion, which unites both, presupposes that there be an object (in space and time) that can move. Space and time have no such requirements. They are pure forms of intuition, and therefore require no empirical sensation for their representation.

9. General Remarks on Transcendental Aesthetic

I. In order to avoid misunderstanding, all that has been said so far with respect to sensuous cognition will be summarized. Our intuitions are nothing but the representation of phenomena; the things and the relations that we intuit are not the same (in themselves) as our representation of them in intuition. These representations - and crucially including their spatial and temporal properties - are dependent upon the subject, and are nothing without it. The nature of the thing-in-itself that is represented to us through intuition is completely unknown and can never be known; nor can it be known how it is represented to other perceptive beings with different receptivities.

Space and time are the pure (a priori) forms of intuition, the matter of which being provided by sensation. They alone can be cognized independently of experience, and in fact are given antecedently to all actual perception [18]. Only the pure forms can provide apodictic knowledge by grounding necessity and universality; empirical (a posteriori) sensations are contingent and can only provide it relatively. And no accumulation of empirical knowledge will ever yield any knowledge of the thing-in-itself, but only knowledge of our own sensibility.

[19]

The distinction between essential and accidental properties of phenomena is merely empirical, and does not represent any property of the thing-in-itself, as the transcendental object remains entirely unknown. When viewing a rainbow through a sunny shower, the empirical distinction might be to assign the rainbow as an accidental feature (dependent upon things like the geometric orientation of the person), while the raindrops are the essential feature (because they exist regardless of the rainbow existing). But the transcendental distinction would be to assign both the rainbow and the raindrops (including their spatial and temporal properties) to mere phenomena - that is, representations that are inseparable from sensibility - while the thing-in-itself remains unknown.

The theory of the Aesthetic must not just be plausible, but undeniably certain, if it is to serve as an organon for a greater Transcendental Philosophy. To do so, it will be helpful to assume an opposite view; that space and time are in-themselves objective and conditions for the possibility of objects as things-in-themselves. From where do we cognize the apodicticity of synthetic a priori propositions concerning these forms, as we do in geometry or physics? It can only be through intuition or conceptions given a priori or a posteriori. Empirical concepts founded on empirical intuitions cannot provide the necessity nor the universality required for apodicticity, so space and time must be a priori.

But conceptions by themselves cannot render synthetic propositions; the only possibility remaining is for space and time to be a priori intuitions - that is to say, intuitions are given to us by ourselves, and not through sensation. Yet if they are a priori intuitions, but did not belong to a faculty of intuition, then it would be impossible to formulate any synthetical propositions regarding external objects [21] whatsoever, because there would be no way to know if the necessity of your representation being the way it is, is also found with the object of the representation as it is in-itself. If space and time are forms of the external sense, however, then while the thing-in-itself is still unknowable, the objective validity of phenomena is retained.

II. In further demonstration of the ideality of space and time, it will be noted that all of our cognition belonging to intuition contains nothing more than mere relations (feelings of pain and pleasure, as well as the will, are exempted, since they are not cognitions [22]). The relations for space are: extension (of place), motion (change of place), and the forces of motion (the laws in which this change of place is determined). Time contains the relations of the successive, the coexistent, and the permanent (the successive and the coexistent). The things that are involved with these relations are not given through intuition. Relations themselves cannot give any knowledge of a thing-in-itself, so the forms of intuition only contain the relation between the object and the subject, and not the object in-itself.

A representation that precedes all thought of an object is an intuition, and when it contains nothing but relations, it is a form of intuition. The form presents us with no representation itself except when something else is placed in the mind [23]; in other words, the form can only be the way in which the mind presents itself with representations and is affected by itself. The subject is represented to itself as a phenomenon through the internal sense, time, and not as it is in-itself, were it to be intuited spontaneously (intellectually).

The question at hand is, how can the subject have an internal intuition of itself? It will be noted that apperception (the consciousness of the self) is the basic representation of the “ego”; and if by it every representation of the manifold in the subject were spontaneously given, then the internal sense would indeed be intellectual. But for a human, this consciousness requires an internal perception of the manifold representations which were previously given in the subject, the manner of which is called sensibility (which is the absence of spontaneity). Self-consciousness can only apprehend what is in the mind if it can affect the mind and produce an intuition of the self, which is only a phenomenon arranged by the internal sense, or time.

III. To say that intuition of objects through the forms of space and time represents objects as phenomena is not to say that they are mere illusions. A phenomena is that which is never found in the object itself, and only and always with the relation of the object with the subject and the representation of it by the subject. Phenomena truly are given, and are objective with respect to the conditions in which they are given. They are only illusory when these predicates are applied outside of this domain [24].

IV. The object of God (which can never be an object of intuition to us [25]) must have spontaneous intuitions as his only means of cognition, since thought always involves limitation [26]. This intuition must not involve the conditions of space and time [27]. But if space and time are forms of objects as things in themselves, they would also be the conditions of the existence of God, which would seem to contradict the idea of God being infinite. But if space and time are not objective forms of things, then they must be subjective and be the forms of our intuition, which is sensuous, by which we mean the subject is affected by an object that already exists.

Even if all beings have the same forms of sensibility, this universality would not change the fact that it is still sensuous, and not intellectual (it is deduced, not original [28]), which seems to only belong to God. But this is only an illustration of the Aesthetic, and not a proof of it.

10. Conclusion of the Transcendental Aesthetic

This concludes one part of the solution to original problem formulated in the Introduction, that being: “how are synthetical propositions a priori possible?” It has been demonstrated that we are in possession of pure intuitions (space and time), which allow us to pass beyond a given conception and connect it with a foreign representation during an a priori judgement, and thereby form a synthesis. These judgements, however, do not apply to anything but the objects of our senses, and are only objectively valid when considered in relation to possible experience.

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?
3. How does an intuition happen, if not in time? Unless it is that the affection of an object upon the sensibility happens "in time" (with respect to our sensibility), but "happens" in-itself in a way that we cannot conceive?
4. What does "given" mean here?
5. Kant says "But all thought must directly, or indirectly, by means of certain signs, relate ultimately to intuitions". What does he mean by "signs"?
6. What does "representation" mean here? I have seen it used to describe both intuitions and conceptions. Is a representation just anything that we are aware of?
7. Does this mean the undetermined object of an intuition just is the intuition, or does the intuition contain an undetermined object? i.e. is intuition phenomena, or does intuition contain phenomena?
8. Why does Kant use this term, "manifold content", how is it different than just "matter", i.e. sensation?
9. Why does Kant call it a conception, when space is an intuition?
10. Can we imagine space without any objects? I can imagine a black, empty void, but the fact that it is black means that it is not simply extension.
11. I don't think Kant explains here why space being essentially one makes it an intuition, and not a conception. I know that he claims that that which relates to a single object is an intuition, but I guess I don't understand why concepts can't do that too.
12. To clarify, objective reality with respect to objects of sensibility basically means intersubjective agreement upon certain properties of these objects?
13. How is ideal different from subjective? Is it like essential vs accidental?
14. See 10. I don't know if we can imagine time without any phenomena.
15. Why is this proposition synthetic? I understand the difference between analytic and synthetic propositions, but sometimes I find it hard to tell if a proposition is analytic or synthetic.
16. What is a "partial representation", is it related to how concepts require an intuition for synthesis?
17. Redacted.
18. What exactly does it mean for something like time to be given "antecedently" to all actual perception. How do I conceive of this apart from some analogy to time?
19. I genuinely have no idea what this paragraph meant: "To say, then, that all our sensibility is nothing but the confused representation of things containing exclusively that [...] " Any help?
20. Redacted.
21. I'm not sure if I follow the last step of this argument. Why would it be impossible to formulate synthetic propositions regarding external objects if space and time are real, objective conditions of things-in-themselves?
22. Kant asserts this is the case, but does not argue for it. Why are they not cognitions?
23. If forms do not present us with representations except when matter is given, then why does Kant say that we can conceive of space and time as empty of objects?
24. I'm not sure if I wholly follow why Kant thinks transcendental realism leads to skeptical idealism.
25. Why can't God be an object of intuition? Because this would place him in space and time, which would mean he would be limited?
26. Why does thought always involve limitation?
27. Why not?
28. What does Kant mean by "deduced" and "original"?

I understand Transcendental as "before experience or prior to experience", and Aesthetic as "sensory perception" in the CPR. So, transcendental aesthetic denotes a priori sensory perception or knowledge, which are non experiential sensory perception or knowledge .i.e. metaphysical perception or knowledge such as on God and Souls. — Corvus

I think transcendental has different meanings depending on the context. There seem to be at least two different meanings:

• Knowledge pertaining not to objects, but with the mode in which we perceive objects; as opposite of empirical, which pertains to objects of experience. Basically a "meta" discourse.
• That which is independent of the conditions of human sensibility.

But in general, the term transcendental is connected to the conditions of human sensibility. The pure forms of human sensibility are transcendentally ideal, and the thing-in-itself is transcendentally real.

I don't know if I would describe transcendental as before or prior to experience. That would just be a priori, I think. The Transcendental Aesthetic is one part of the general question, "how are synthetic a priori judgements possible?", and it focuses on the conditions of sensibility, whereas the Transcendental Logic focuses on the conditions of thought.

Damn!! No wonder you been absent so long.

For one post, those are a lot of questions. :smile:

26. Why does thought always involve limitation? — darthbarracuda

Since I take this to be self-evident, I’ll comment: Thought devoid of aboutness, devoid of some given it is about, could be meaningfully classified as thought in which sense? Even in thinking about possible cases of such type of thought, I’m thinking about the addressed topic. This aboutness then will be literally limited, or bounded, to that which it is about. Here, then, one obtains the conclusion that all thought, in order for it to be meaningfully classified as such, will be limited and, hence, in some way finite.

The sole alternative to this conclusion is that there can occur thoughts that are literally unlimited, or unbounded, in all ways: an infinite thought. But such loses all semblance of what the term “thought” refers to, in part because it would be a thought devoid of aboutness which, again, is always in some way limited to that which is addressed, to that which the thought is about. Because a literally boundless, or limitless, aka infinite, thought is nonsensical, one again concludes that thought always involves limitation. Differently expressed, that it is always finite.

I should further comment:

IV. The object of God (which can never be an object of intuition to us [25]) must have spontaneous intuitions as his only means of cognition, since thought always involves limitation [26]. — darthbarracuda

What I don't get is how one can envision a plurality of intuitions that are unlimited, or infinite. Quantity is always finite, limited. And plurality entails quantity - hence a multitude of finite intuitions, since they're quantifiable. So, by my appraisals, these spontaneous intuitions would themselves then not be infinite, instead being bounded one from the other. And they would themselves entail that God's cognition (assuming the hypothesis of such God) consists in some manner of limitations, rather than being infinite (in the sense of literally devoid of limits/boundaries). Thereby resulting in the conclusion that such God is in fact in some way limited, rather than infinite.

I think transcendental has different meanings depending on the context. There seem to be at least two different meanings: — darthbarracuda

Excellent work on your posts, looks interesting and a lot to go over in them. :up:
Sure, I appreciate your points on "transcendental". Will read and reflect on them, and get back if there are further queries. cheers.

0. The whole is not the same as its parts.
1. Immediate merely indicates systemic successions. Everything starts somewhere.
2. Because object herein relates to intuition, they are real, physical existences with the capacity to affect the senses. They are distinguished thereby, from objects of reason, objects of experience, ideas, notions, transcendental objects in general which do not affect the senses.
3. It is enough to say the time of the affect on the senses by objects, is sufficient for how intuitions happen. Intuitions do happen in time, but that doesn’t say how they happen. For that, we really don’t have an explanation, nor do we need one.
4. Intrinsic Kantian dualism. Given to us here means that which we do not give to ourselves. That which is a perception vs that which is merely thought.
5. Keep in mind the perspective. This has all to do with the empirical side of reason, thus objects here are the real physical things in the world. Signs are the matter of objects in accordance with the mode of their affect. One kind of sign of an object is its odor, another sign is its shape.....and so on. Like any sign, it is a preliminary indication of that which is to understood by means of it, but in this case, a preliminary indication of the phenomenon it should become. Thought must relate just says the conceptions synthesized to intuitions must be imagined as necessarily belonging together. In other words, it is inconsistent to synthesize a conception belonging to smell, to a sign given from the sense of sight.
6. Representations are not all present to awareness, but that which is present to awareness, is a representation. Intuition and conceptions are representations, as are ideas, sensations, even perceptions themselves. As unsatisfying as it may be, representations are the means by which reason explains itself.
7. In this system, an object of intuition just indicates any object of perception in general, that is as yet merely an appearance. An undetermined object of intuition, per se is that which follows from the operation of that faculty, which is therefore a phenomenon, a particular determinable representation. Intuition can be said, if anything, to contain the forms of objects, insofar as such forms reside a priori in this faculty. The CofJ gives a more inclusive exposition of this part of the system....changes in subjective conditions, and all that. Aesthetic vs empirical judgements. Productive vs reproduction imagination. Seriously complex methodology, needless to say.
8. It is safe to say manifold content is the matter of the object, because all sensation is with respect to it. Technically, that which in phenomena is arranged according to forms, is the manifold content of them, and they correspond to the sensation from which they are given. The inference being, if the matter of objects were that which is arranged, they would be determined by that arrangement. It follows that if object were to be determined merely from the arrangement of its matter, there would be no need of any synthesis with conceptions in order to experience an object as a certain thing, and the entire transcendental system immediately becomes untenable.
9. Space is an intuition....a pure intuition only....because it is considered to be the necessary condition for the experience of objects. Space is a conception insofar as it must first be thought as both justified for, and logically consistent with, the role it plays in a theoretical system. If space could not be thought, it could never be a conception. If never a conception, never a possibility. If never a possibility, never a necessity. If never a necessity, never a necessary condition. If never a necessary condition, never a logically justified domain in which objects are to be found, because we already know with absolute certainty where they are not. If no logically justified domain in which they are to be found, no logically justified possibility of being known. A contradiction.
10. That space is necessary for objects, and objects are necessary for color, it follows that empty space will be absent any color, which is merely our conception of black, which is contingent on objects in space, not the space they are in. Extension is shape, neither extension nor shape is a property of black. Space doesn’t have shape, insofar as all parts of space are each themselves just space, and the shape of objects is merely the limits of the space it is in. To imply space as black or that black is extended, are a transcendental illusions of mischaracterized reason.

Enough.

What I don't get is how one can envision a plurality of intuitions that are unlimited, or infinite. Quantity is always finite, limited. And plurality entails quantity - hence a multitude of finite intuitions, since they're quantifiable. — javra

I recall a discussion of the infinite in Allison's book that made the point that the concept of infinite need not involve the actual presentation of an infinite number of representations, but instead just the presentation of "limitlessness", e.g. there is always more to be had, the supply of possible representations will never run out. This is how space and time are presented, as a single unified whole which can be broken down into infinitely smaller parts.

Thanks very much for your response, I'll read through them more thoroughly later when I have more time.

Fractals – the example with which you illustrate your point – have boundaries, thereby being bounded, and thereby being subject to limits. We can discern one type of fractal from another because of the boundaries of each.

God is supposed to not be subject to any boundaries, for these impose limits, as well as to be divinely simple, i.e., not consisting of any parts; “infinite”, or "limitless", in this specific sense; rather than that of a qualified infinity (one which is restricted or limited) - for example, the infinite length of a geometric line that assumes endless constituent points bounded by their particular alignment.

I re-read your previous question and I'm not sure if I have the prerequisite knowledge to offer a proper response. I will say that a spontaneous intuition is intellectual, not sensible, and I seem to recall that the intellectual intuition of an object brings this object into being. Also, while it might not make sense to us to conceive of an infinite manifold of intuition, attempting to do so would involve thought, no? And thought inherently involves limitation. If God is infinite, but cannot be given through intuition, then the only other way to apprehend God is through thought, which will never achieve a full cognition of it.

But this is getting into deep waters (for me at least), I could be completely off the mark here.

Hm, I agree. I guess in the back of my mind is the neo-Platonic notion of the "the One" as g-d. Which is likely not what Kant had in mind. But I don't want to digress the thread with this. BTW, kudos for a really well thought out appraisal for and list of questions to Kant's critique.

I think transcendental has different meanings depending on the context. There seem to be at least two different meanings:

Knowledge pertaining not to objects, but with the mode in which we perceive objects; as opposite of empirical, which pertains to objects of experience. Basically a "meta" discourse.
That which is independent of the conditions of human sensibility.

But in general, the term transcendental is connected to the conditions of human sensibility. The pure forms of human sensibility are transcendentally ideal, and the thing-in-itself is transcendentally real.

I don't know if I would describe transcendental as before or prior to experience. That would just be a priori, I think. The Transcendental Aesthetic is one part of the general question, "how are synthetic a priori judgements possible?", and it focuses on the conditions of sensibility, whereas the Transcendental Logic focuses on the conditions of thought. — darthbarracuda

I did some reading on the NKS commentary to the CPR for this points. NKS summaries 3 different definitions on transcendental of Kant in the CPR.

"1. Transcendental" is primarily employed by Kant as a name for a certain kind of knowledge. Transcendental is knowledge not of objects, but of the nature and condition of our a priori condition of them. In other words, a priori knowledge must not be asserted, simply because it is a priori, to be transcendental ; this title applies only to such knowledge as constitutes a theory or science of the a priori. Transcendental knowledge or transcendental philosophy must therefore be taken as coinciding ; and as thus coincident, they signify the science of possibility, nature and limits of a priori knowledge. The term similarly applies to the subdivisions of the Critique. The Aesthetic is transcendental in that it establishes the a priori character of the forms of sensibility ; the Analytic in that it determines the a priori principles of understanding, and the part which they play in the constitution of knowledge ....

But later in the critique Kant employs the term transcendental in the a second sense, namely, to denote a priori factors in knowledge. All representations which are a priori and yet are applicable to objects are transcendental. The term is then defined through its distinction from the empirical on the one hand, and from the transcendent on the other.

2. An intuition or conception is transcendental when it originates in pure reason, and yet at the same time goes to constitute an a priori knowledge of objects. The contrast between the transcendental and the transcendent, as similarly determined upon by Kant, is equally fundamental, but is quite of different character. That is transcendent which lies entirely beyond experience ; whereas the transcendental signifies those a priori elements which underlie experience as its necessary conditions. The transcendent is always unknowable. The transcendental is that which by conditioning experience renders all knowledge, whether a priori or empirical, possible. The direct opposite of the transcendent is the immanent, which as such includes both the transcendental and the empirical. ....

3. The third meaning of the term transcendental arises through its extension from the a priori intuitions and concepts to the processes and faculties to which they are supposed to be due. Thus Kant speaks of the transcendental syntheses of the apprehension, reproduction, and recognition, and of the transcendental faculties of imagination and undertaking. In this which render experience possible. And in as much as processes and faculties can hardly be entitled a priori, Kant has in this third application of the term departed still further from this first definition of it." - NKS Commentary to the CPR pp. 73-76 1922

I have based my interpretation of transcendental from the 2nd definition in NKS commentary to the CPR.

"The transcendental is that which by conditioning experience renders all knowledge, whether a priori or empirical, possible. The direct opposite of the transcendent is the immanent, which as such includes both the transcendental and the empirical."

That was a critical point, on which my understanding of transcendental in Transcendental Aesthetics was based.

The condition of experience must be prior / before to experience logically, otherwise it is not condition at all. If it is the same as experience then it would be experience itself, if after experience, then it would be the effect / result of experience.

Experience must always be the experience of something of someone. So it must have the subject of experience, and also the object of experience too. Experience in general before the real experience by the subject about something is a blank concept which has no meaning on its own, because there is no such an object which stands for experience in the real world. All experience is mental and has its subject and object to be meaningful.

Therefore the term a priori is also prior / before to experience to be meaningful, because on its own without matching real world experience of someone about something, it also is just a blank concept.

That was my understanding, but of course I imagine that it is subjective, and do expect possible criticisms.

Nice work here, thanks for sharing. So in summary, transcendental can mean:

1. any knowledge that is about the a priori conditions of experience and thought of objects (such that, the representation of space is not transcendental, but the knowledge that the representation of space is a priori and a condition for experience is),

2. a representation that is a priori and a condition for experience and thought of objects (such that, the representation of space is transcendental - though not transcendent, i.e. pertaining to the thing-in-itself),

3. not sure if I follow this last point.

Thanks again for the responses, much appreciated :pray:

1. Immediate merely indicates systemic successions. Everything starts somewhere. — Mww

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

Given to us here means that which we do not give to ourselves. That which is a perception vs that which is merely thought. — Mww

"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?

Space is an intuition....a pure intuition only....because it is considered to be the necessary condition for the experience of objects. Space is a conception insofar as it must first be thought as both justified for, and logically consistent with, the role it plays in a theoretical system. If space could not be thought, it could never be a conception. — Mww

Okay, so just to be sure I follow, the intuition of space is not identical to the conception of space. The conception of space is just the thought of the intuition of space.

Extension is shape, neither extension nor shape is a property of black. Space doesn’t have shape, insofar as all parts of space are each themselves just space, and the shape of objects is merely the limits of the space it is in. To imply space as black or that black is extended, are a transcendental illusions of mischaracterized reason. — Mww

I get that space is not colored, but I still don't see how Kant can say we can imagine space as empty without objects. How do I imagine space without something in it? How do I imagine a representation with no object? I understand space and the objects that are in it are distinct, but it is not clear to me that space can precede objects; i.e. space and objects seem to be given always together.

@darthbarracuda You can imagine an empty room I’m sure.