(2) Visualizations

We have to remind us again, that the composition of a diversity can never come to us through the senses, that it however

is an affair of the understanding alone, which itself is nothing but the faculty of combining a priori, and of bringing the diversity of given representations under the unity of apperception. ^(131D, 154E)

If I can now give evidence with sentences of Kant, that the infinite space and the infinite time do not originally lie in the sensuousness as essential, all-embracing, pure visualizations, but that they are the product of an in infinity advancing Synthesis of the Understanding, then we don’t assail that space and time aren’t properties of the things-as-they-are –this most lustrous philosophical acquisition!- but instead that Kant’s space and Kant’s time are, as pure visualizations a priori, completely untenable, and the sooner they are removed as our aprioric forms, the better it is.

It is not hard for me, to give the proof. I cite the most concise passages, and I don’t want to left it unsaid, that Kant removed the first two from his second edition of the Critique: for good reasons and with purpose.

• Passages from the First edition of the Critique:

The Synthesis of apprehension must now also a priori , that is, in visualizing representations, that are not empirical, be exercised. Then without this synthesis we could not have a representation of space, nor of time a priori, because these could only be generated through the Synthesis of the diversity, which the sensuousness offers in its original receptiveness.

It is clear that, when I draw a line in thought, or think the time of an afternoon to another, or just want to imagine a certain number, that first I’ll necessarily have to link one of this diversity to the other. However if I would lose that what precedes (the first part of the line, the preceding part of time, or the after another imagined units), if I would always lose them in my thoughts, and not reproduce them, when I continue to the proceeding part, then I could never have a complete representation and the above mentioned thoughts, yes, not even the purest and first principle-representations of space and time could arise.

• Passages from the Second edition of the Critique:

Representations as visualizations in space and time must be represented through the same Synthesis, whereby space or time can be determined at all.

Similarly with all times, however small. In these I think to myself only that successive advance from one moment to another, whereby through the parts of time and their addition a determinate time-magnitude is generated. ^(175D,198E)

The most important passage is this:

Space, represented as object (as we are required to do in geometry), contains more than mere form of visualization; it also contains combination of the diversity, given according to the form of sensibility, in a visualizable representation, so that the form of sensuousness gives only diversity, the formal visualization gives unity of representation. ^(147D, 170nE)

It’s as if we’re dreaming! I ask everyone to put these passages next the sentences cited from the Transcendental Aesthetics, especially those who are represented with the great certitude:

Space is a pure form of visualization. We can imagine one space only and if we speak of many spaces, we mean parts only of one and the same space. Nor can these parts be considered as antecedent to the one and all-embracing space and, as it were, its component parts out of which an aggregate is formed, but they can be thought of as existing within it only.

Certainly it’s impossible to imagine a more pure, complete contradiction. In the Transcendental Aesthetic is form of visualization always identical with pure visualization; however here they are separated in the most strict way, and Kant emphasizes, that space as pure visualization is more than space as mere form, that is, composition of a diversity, through the Synthesis of the Understanding, which is nothing more, than the capability to compose a priori.

From this it becomes irrefutably clear, that the unlimited time and the unlimited space, as such, aren’t forms of the sensuousness, but compositions of a diversity, which, like all compositions, are the work of the Understanding, therefore belong to the Transcendental Analytic and indeed under the category of quantity. Kant implicitly says this too in the Axioms of visualization.

The mathematics of space (geometry) with its axioms is based upon this successive synthesis of the productive imagination in the generation of figures. ^(176D,199E)

to which he connects the pure mathematics in its complete precision on the objects of experience.

Meanwhile we want to put all this aside and research, how space and time, as visualizations, are generated. Kant says in the mentioned passages of the first edition of the Critique:

Space and time can only be generated through the Synthesis of the diversity, which the sensuousness offers in its original receptiveness.

What is this diversity of original receptiveness of sensuousness? That we have to deal with a composition before all experience is clear; since it would be the shaking of the Kantian philosophy in its foundations, if space, which we want to consider first, if it would be the composition of an a posteriori given diversity. But how can it be possible, that it is the composition of a diversity a priori? Which space-part, as unit, does the sensuousness offer a priori to the imagination, through which the infinite space by continuous composition is generated? Is this unit a cubic inch? a cubic foot, a cubic rod, cubic mile, cubic sun-width, cubic Sirius-width? Or is it no unit at all but instead the most diverse space-parts which the imagination puts together?

Kant remains silent about this!

A posteriori the composition isn’t difficult. There I have a monstrous sea of air which offers itself to the imagination. Who thinks about it that in it a force manifests itself? A clumsy objection! Air and space are exchangeable concepts. The greatest mind, as well as the most narrow-minded peasant talks about space, which contains a house, a room; Kant says at the top of his “Metaphysical Foundations of Natural Science”: “Matter is the movable in space”; the poet lets the eagle fly “drunk of space” his circle, and only the imagination should be questionable? No! To the space, which the air offers, are added the space-parts of houses, trees, humans, the whole earth, the sun, the moon and all stars, which the thinking subject had cleansed it from all the it fulfilling activity. Now it continues the gained monstrous space-part into infinity in a similar way, a standstill is impossible, since there are no boundaries in the continuation.

A posteriori can this way, with open or closed eyes, an infinite space be constructed, i.e. we don’t have a single entity, but only the assurance, that in this progress of the Synthesis we won’t ever find a hindrance.

But are we allowed to make this composition? Not even the purest space-particle of cubic line can be provided to us a posteriori, i.e. through experience. The smallest space-part, as well as the largest, results only because, that I think away the it fulfilling force. Where a body stops to work, another one begins to work/with its activity (“workness”). My head is not in space , as Schopenhauer once remarks, but in the air, which certainly isn’t identical with space. Likewise matter isn’t the movable in space, but substances move in substances and motion is in general only possible due the different bodies’ so-called states of matter, not because an infinite space contains the world.

Would the world be composed of solid substances only, then motion would only be possible through the simultaneous shift of all bodies, and the representation of a space would not arise in a human’s head. Really, a movement in liquid elements is considered by no one as a motion in space. We don’t say: the fish swim in space, but: they swim in water. The unlimited view into distance and the reason which has gone astray (perverse ratio) are the generators of the infinite space. In the world there are only forces, no space-parts, and the infinite space exists as little, as the smallest space-part.

It is very remarkable, that in the pre-Kantian time, where things were granted space just like that, that this state of affairs was recognized by Scotus Erigena correctly. Although his world does lie in the infinite space, which contains everything, which doesn’t move itself, but inside the boundaries of the world there is no space: there, there are only bodies in bodies. This isn’t doesn’t get changed by the fact that Scotus sometimes bring back space in the world; he didn’t have the critical mind of Kant, and no one, even today, will misjudge the difficulty of the investigation. (By the way, one time Scotus makes the remark, that space exists only in the human mind.) He says in his De Divisione Naturae:

(…)

The free unbounded view through the absolutely transparent element is also the reason, why everyone, the greatest as well as the most limited human,

can never represent to himself the absence of space, though we can quite well think it as empty of objects.

Meanwhile, we should not jump to conclusions. Should air and the perverse reason really be enough, to generate the infinite space? Certainly not! Only due to an aprioric form they can. Which one is it however? We will find it immediately.

First we have to come back to our question, if space can be the composition of a diversity a priori? We have already seen, that Kant leaves us completely in the dark about it, which parts of the space should be composed a priori. So we ask: Is it possible at all to have the representation of a certain space-part in us before all experience, or with other words, can we arrive at visualization of a space-part, before having seen or felt an object? The answer to this is: no! it isn’t possible. Space either lies in us as pure infinite visualization, before all experience, in me, or it’s found a posteriori, through empirical ways: for it is as hard to let the smallest space-part lie, as pure visualization a priori, in our sensuousness, as the infinite space. Is this however the case, then it would be the most foolish torture, to attain through Synthesis homogenous parts, what I can have immediately as a whole.

Here does also lie the cause, why Kant makes with no further ado of space pure visualization and doesn’t let it be generated through a composition of spaces first, through which also the Synthesis would enter the sensuousness, while it should be only a function of the Understanding, resp. the blind imagination.

Could space only be generated by an a priori given diversity; is it however likewise impossible to discover in us a partial-space, as the complete space, then it follows, that the infinite space cannot at all be generated a priori, that there is given no space, as pure visualization a priori.

I summarize: There is, according to our investigations, no infinite space outside my head, in which the things are contained, nor is there an infinite space inside my head, as a pure visualization a priori. Likewise there are no limitations of space, space-parts outside my head. However there is an infinite space in my head (attained through Synthesis of an a posteriori given diversity), which is moved outwards. I also have a through empirical way obtained, from the perverse reason, infinite fantasy-space. Likewise I have its limitations, so space-parts of arbitrary size, fantasy-spaces.

Consequently, as I remarked on the first page of this criticism, Kant has done nothing more, than definitively moving the outward fantasy-space, which is normally seen as an independent from subject existing objective space, into our head. Hereby he has freed the things-as-the-are from space, which is precisely his immortal merit. His fault was, that he attacked, that the infinite space is of empirical origin, and he put it, as pure visualization, before all experience, in our sensuousness. A second merit is, that in the Transcendental Analytic he separated space as form from space as object (pure visualization). While he thereby came to an unsolvable contradiction with the teachings of the Transcendental Aesthetic, he nevertheless demonstrated, that he had fully fathomed the problem of space and gave possible successors an invaluable indication to the right way. We will follow this indication.

What is space as form of visualization, which (we will follow Kant’s line of thought for now) lies a priori in our sensuousness.

In negating way the question has already been answered: space, as form of visualization is not the infinite space. What is it then? It is, generally expressed, the form through which the objects’ boundaries of activity are set. Thereby it is a prerequisite for the possibility of visualization and its apriority determined above all doubt. Where a body stops to work, there space sets the boundary for it. Even though the special activity of a body (its color) can set its boundaries (I don’t consider touch), but this could only happen into height and width, and all bodies would be perceived as planes, even if all in my vision lying planes could would move in parallel and their distance from me = 0. They lie so to speak on my eyes. With help of the space’s dimension of depth the Understanding determines (after Schopenhauer’s masterful exposition [TN; in Fourfold Root]), on basis of the most miniscule data, the depth of the object, their distance to each other etc.

This form is only imaginable as the image of a point, which has the ability, to expand itself to three dimensions in undetermined wideness (in indefinitum). It is the same, if the sensuousness lies it at a grain of sand or at an elephant, if its third dimension uses for the determination of distance a 10 feet from me standing object or the moon. It itself is no visualization, mediates however all visualization, like the eye itself doesn’t see itself, the hand can’t grab itself.

By this it becomes clear, how we come to a fantasy-space. Through experience we learn to use the point-space – otherwise it would lie dead in us – and the subject may expand it to its liking, into three dimensions, without giving it an object, as wide as he wants. Through this way we soar through the “infinite space of heaven” without content, and proceed always further without any obstacle. Without this always ready in us lying form the perverse reason wouldn’t be able to generate the infinite space, with only the unlimited view into the wide. However the possibility of the unlimited view relies already on the aprioric form space (point-space). – I still want to remark, that the right use of space demands a long first stadium. Little children try to grab everything, the moon, as well as images on walls. Everything floats before their eyes: they haven’t learned how to use the third dimension. The same has been observed, as is known, with operated blind-born.

The consequences of the point-spice are extremely important. Is the infinite space a pure visualization a priori, then it is without doubt that the thing-as-it-is possesses no expansion. To see this, only short reflections is needed; since it’s clear, that in this case every Thing has its expansion only as a loan from the general infinite space. Is space however not pure visualization, but only a form for visualization, then the expansion doesn’t rely on the space, but only its perceptibility, the knowledge of expansion depends on the subjective form. Should there be somewhere a path to the things-as-they-are (which we still have to investigate), then it’s certainly also expanded, i.e. it has a sphere of activity, although the space a priori, as subjective form, lies in us.

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In relation to time the questions are the same.

1. Is time generated through the Synthesis of diversity, which the sensuousness offers in its original receptiveness? Or

2. does it result through the Synthesis of a diversity, which the sensuousness offers a posteriori?

Kant says:

Time determines the relation of representations in our inner state. ^(72D, 77E)

So the inner state is what we have to take as foothold. If we take a look inside of us, under the condition that the outside world is still completely unknown to us and has made no impression on us, and also, that our inside offers no changes, then we would be practically dead, or inside the deepest dreamless sleep, and a representation of time would not appear in us. The original receptiveness therefore can’t give us the most insignificant datum [TN; singular form of data] for the generation of time, whereby the first question is answered negative.

If we think of a change of sensation in us, yes merely the experience of our breath, the regular ejection of air after inhaling, then we have a set of fulfilled moments, which we can connect to each other. Thus only a fulfilled time is perceivable, and the fulfillment of moments is only possible through the data pf the Experience. It would come up in no one’s mind, to say, that our inner state doesn’t belong to the experience and can’t be given a posteriori.

How is the infinite time however generated, which is after all imagined as empty? In a similar way as the infinite space. The thinking subject abstracts the content of every moment. The from its content deprived transition from present to present is the unit, which the imagination will hand over to the Synthesis. Since however an empty moment is in no way an object of visualization, so borrow we from space

and represent the time-sequence by a line progressing to infinity, in which the diversity constitutes a series of one dimension only; and we reason from the properties of this line to all the properties of time, with this one exception, that while the parts of the line are simultaneous the parts of time are always successive. ^(72D, 77E)

Thus the infinite time lets itself be constructed a posteriori, i.e. we don’t have a specific visualization of it, but only the certitude, that the progress of the Synthesis will nowhere be restrained. But we ask here, just like with space, are we allowed to such a Synthesis? Not the smallest imaginable time can be delivered unfulfilled to us by the experience. Let’s nevertheless try to one time, to provide ourselves an empty moment. Throw away everything from the rapid transition between two presents, then we have at least fulfilled the smallest time-magnitude in our thoughts.

We conclude now as we did by space. Is the infinite time only generable through the Synthesis of an a priori given diversity; is in our original sensuousness no smallest unfulfilled time to be found, then the infinite time a priori can’t be generated a priori, it can then also not, lie as pure visualization a priori in our sensuousness.

According to this there is no infinite space in outside head, which devours the things, nor is there an infinite time in my head, which should be a pure visualization a priori. However there lies an infinite space (consciousness of a unconstrained Synthesis) in my head, obtained through the connection of a posteriori given fulfilled moments, whose content is violently robbed.

Thus we have a through empirical way surreptitious infinite fantasy-time, whose being is through and through succession, which transports everything, the objects as well as our consciousness, in restless progress with itself. Kant banned the infinite space from our head, i.e. he took the things-as-they-are away from it, freed them from time. To this great merit he stands on the other side the fault, that he laid down the time, as pure visualization a priori, in our sensuousness. A second merit was, that he discerned time as form from time as object (infinite line).

And now we stand before the important question: What is time, as form of visualization, which lies a priori in our sensuousness? In negating way it has already been answered. The time, as form of visualization, is not the infinite time. What is it then? As form of the sensuousness can it be only the present,a point, like with space, a point which is always becoming but never is, always moving, a floating point.

As present the time has really no influence on the visualization or, as Kant says it:

Time cannot be a determination of outer appearances; it has to do neither with shape nor position.

I’ll say it openly: time is no form of the sensuousness.

Like we remember us, Kant brought them there via a detour, as he explains:

All representations, whether they have or have not external things for their objects, still in themselves, as determinations of the mind, belong to our internal state,

which falls under the formal prerequisite of time. The inner state is however never a visualization, but feeling, and where this one, the inner motion, affects the mind, there lies the point of present.

Through this a peculiar light falls upon the complete Transcendental Analytic. In it the sensuousness wasn’t dealt with, that the Aesthetics did. Only the diversity of the sensuousness, the material for the categories, wanders above the Analytic, to be composed and Connected. The Analytic self solely deals with the Understanding, the categories, the Synthesis, the imagination, the consciousness, the apperception and always and always again the time. The transcendental schemata are time-determinations, the generation of extensive and intensive magnitudes happens in the progress of time, the Analogies of experience sort similar appearances according to their relation in time. Therefore I said above, we can open a page of the Analytic and always we’ll encounter the Synthesis of a diversity and time, and called both of them the immortal crowns on the corpse of the categories. How is it possible, that Kant couldn’t bring about the Analytic without a form of sensuousness, without time? Precisely because time is not a form of sensuousness, no aprioric original form at all, but only and solely a composition of the reason. About this I will talk in extensive detail later; but the passage where we are now, is the most suitable to introduce Schopenhauer, the only intellectual heir of Kant.

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Schopenhauer’s position to the Transcendental Aesthetic and Analytic is: unconditional acceptance of one, unconditional rejection of the other. Both are inacceptable.

He accepted readily, without any criticism infinite space and infinite time as pure visualizations a priori, and he ignored the strict investigation of Kant on the forms of the visualization completely. It was for him a clear matter, that space and time lie, before all experience, as forms of visualization, in our cognition. He denied, therefore, with Kant the recognizability of the thing-as-it-is, between it and the perceiving subject stand always these forms, according to which the sensuous impressions are processed.

Nevertheless he has, with most high human prudence, improved a part of Kant’s cognition-theory and irrefutably proven his improvements. The first question, which he asked himself, was: “How can we come to a visualization from outward objects at all? how arises this complete, for us so real and important world in us?” With right he wasn’t satisfied with the meaningless expression of Kant: “the empirical of the visualization is provided to us from outside”. The question itself is extremely meritorious; since nothing seems more self-evident, as the emergence of objects. They are here at the same time of a simple glance with the eyelids; which complex process should happen in us, to generate them?

Schopenhauer didn’t let himself be misled by this “at the same time”-ness. Like Kant, he started with the sensory impression, which is the first point of reference on subjective ground for the development of visualizations. He examined it precisely and found, that it’s certainly given, but not that the visualization can originate from the senses, like Kant wants; since

for sensation is and remains a process within the organism and is limited, as such, to the region within the skin ; it cannot therefore contain any thing which lies beyond that region, or, in other words, anything that is outside us. (Fourfold Root § 21)

Should the sensation become visualization, then the Understanding must become active and exercise its one and only function, the law of causality:

for, in virtue of its own peculiar form, therefore a priori, i.e. before all experience (since there could have been none till then), the Understanding conceives the given corporeal sensation as an effect (a word which the Understanding alone comprehends), which effect, as such, necessarily implies a cause.

The law of causality, the aprioric function of the intellect, which he first needs to learn as little, as the stomach digesting, is therefore nothing more, than the transition of the effect in the sensory organ to cause. I request to remember this well, because Schopenhauer will, as we will see later on, bow it into different directions and openly violate it just in order to be able to reject Kant’s complete Transcendental Analytic

Simultaneously it summons to its assistance Space, the form of the outer sense, lying likewise ready in the intellect (i.e. the brain), in order to remove that cause beyond the organism ; for it is by this that the external world first arises. This intellectual operation does not however take place discursively or reflectively, in abstracto, by means of conceptions and words ; it is, on the contrary, an intuitive and quite direct process. For by it alone, therefore exclusively in the Understanding and for the Understanding, does the real, objective, corporeal world, filling Space in its three dimensions, present itself and further proceed, according to the same law of causality, to change in Time, and to move in Space.

Thus the Understanding has to deliver the objective world, and our empirical visualization is an intellectual one, not a merely sensuous one.

Next Schopenhauer proves with success the intellectuality of the visualization (turning the in the retina wrongly standing image upright; single view of the doubled visual sensations, (…)) and masterfully shows, how the Understanding makes from the merely planimetric sensation, with use of the third dimension of space, a stereometric visualization, while constructing with the different gradations of light and dark the single bodies and then its location, i.e. its distance from each other, with use of visual angle, linear perspective and air-perspective.

According to Schopenhauer the Kantian pure visualizations, space and time, are no forms of our sensuousness, but forms of the Understanding, whose only function is the law of causality. To this improvement of Kant’s cognition theory the other is added, that the separated the intuitive knowledge from abstract knowledge, the Understanding from the reason; then by this our knowledge is freed from the pure concepts a priori, an extremely harmful and confusing, without justification entered wedge.

With Kant the sensuousness visualizes, the Understanding (faculty of concepts and judgements) thinks, the reason (faculty of conclusions and ideas) concludes; with Schopenhauer the senses only provide the material for visualization (although he grants them too visualization-capability, about this later), the Understanding visualizes, the reason (faculty of concepts, judgements, conclusions) thinks. The reason, whose only function is the construction of concepts, according to Schopenhauer, doesn’t help in any way the production of the phenomenal world. It only repeats it, mirrors it, and next to the intuitive knowledge it adds the distinctly different reflective knowledge.

The visualizable and, so far as material content is concerned, empirical knowledge, which Reason — real Reason works up into conceptions, which it fixes sensuously by means of words ; these conceptions then supply the materials for its endless combinations through judgments and conclusions, which constitute the weft of our thought-world. Reason therefore has absolutely no material, but merely a formal, content,

In reflecting, Reason is absolutely forced to take its material contents from outside, i.e., from the intuitive representations which the Understanding has created. Its functions are exercised on them, first of all, in forming conceptions, by dropping some of the various qualities of things while retaining others, which are then connected together to a conception. Representations, however, forfeit their capacity for being intuitively perceived by this process, while they become easier to deal with, as has already been shown. — It is therefore in this, and in this alone, that the efficiency of Reason consists ; whereas it can never supply material content from its own resources. (Fourfold Root § 34)