(3) The only intellectual heir of Kant: Schopenhauer
Before we continue, I have to make a remark. Schopenhauer is, aside from Kant, in my conviction, the greatest philosopher of all times. He has brought philosophy in a completely new orbit, and has powerfully led it further, animated by the upright desire to bring humanity closer to the truth. But in his system lie the most incompatible contradictions in such amount, that it’s already a huge task, to discuss them just briefly. This task is fundamentally made harder, because he himself doesn’t strictly respect his own definitions and designates one and the same issue first right, then wrong. (...)
Thus the Understanding brings about, through its function (law of causality) and its forms (space and time), due to the changes in the sensory organ, the visualizable world, and the reason extracts from these empirical visualizations its concepts. Schopenhauer had to reject the whole Analytic of Kant. From the standpoint of the Understanding he couldn’t accept the Synthesis of the diversity, since the Understanding, without help of the reason, brings about the visualization; from the standpoint of reason he had to assail the Categories, since concepts rely only on empirical visualizations and therefore a concept a priori is a contradiction in adjecto. The Synthesis however and the categories form the content of the Analytic.
I absolutely agree with the rejection of the Categories, as pure concepts a priori: a concept a priori is impossible; however it is false, that the Understanding, without help of the reason, can construct the visualizable world.
Before I can justify this view, which has the irrefutable right part of the Transcendental Analytic on its side, the Synthesis of the diversity of the visualization, I have to clarify the reason and in general the complete cognition.
The reason has one function and one form. Schopenhauer gives it no form and a function, which doesn’t include its full being. He places its function in the building of concepts; I however say: the function of the reason is simply Synthesis, its form the present.
It has three helping faculties. The first one is the memory. Its function is: preservation of the impression in the mind, as long as possible. The second helping faculty is the judgement-power. Its function is: assembling what is homogenous. He thus have 1) assembling of homogenous partial-representations of the Understanding, 2) assembling similar objects, 3) assembling concepts, according to the laws of thought. The third helping faculty is the imagination. Its function is merely, to hold the composed visualization together as image.
The completed cognition, so sense, the Understanding, judgement-power, imagination, memory and reason come together in a center: the mind (called by Kant pure original apperception and by Schopenhauer subject of perception) whose function is the self-consciousness. Everything comes together in the self-consciousness’ center, and conversely it crosses through all its faculties with its function and gives their actions consciousness. The table of the mind is according to this as follow.
From the different nuances of the mind follows, that the placement of single cognitive faculties is not an idle affair. Where is sensibility, there is also mind, but how could the difference between an animal and a human indicated than by this, that certain activities of the mind are denied the animal? Without disassembling the mind in its single capabilities (faculties) we would be limited to complete meaningless general expressions, such as, the intelligence of this animal is less than that one. If we dissemble, we can indicate much better what is lacking, and so to say, lie the finger on the source point of the distinction.
Kant was therefore right to dissemble the mind; also the dissembling is necessary for the critical philosophy.
The reason proceeds now on the domain of the Understanding in two distinct types of compositions, which Schopenhauer completely overlooked. He recognizes only one type: the building of concepts; he doesn’t recognize the other one: composition of partial-representations into objects and connection of objects under each other.
The second type is more original than the others, we will first observe the building of concepts.
That the building of concepts rests upon the Synthesis only, will everyone accept after a short moment of thinking. The judgement-power provides the reason a similar diversity, which assembles it and designates it with one single word. The judgement-power assembles only the homogenous: in this act immediately lies the separation. The reason unifies the homogeneity, as well as its remainder. For example, all horses are unified in the concept horse un that which is separated (oxen, donkeys, insects, snakes, humans, houses etc.) in the concept not-horse. Always it appears synthetically.
Its act is also always the same, if it has innumerous, or only a few objects, or properties, activities, relationships etc. to bring under a concept. Only the spheres of concepts are different. Further: the less specific a concept is, the more it has under it, and the more specific a concept is, the more empty it is.
Through this way the complete experience of humans, inner and outer, is reflected in concepts. The reason then works them further in composition of concepts to judgements and in the connection of judgements (premises), to find from it a divided lying judgement, which Logic and Syllogism are about.
If we follow the reason on its other path, we enter a domain, where the Understanding is excluded from, and which we, after Kant, will call the domain of the inner sense, until we have we know it more precisely. We have touched upon it in the preliminary discussion of time. There we found, that fulfilled moments get connected. But what is the role of reason in this operation? Its own form, the present, becomes a problem for it. It is conscious of its own changes in the inner sense, through the memory, but has nevertheless only the present, which is constant and yet always is. Now it guides with increasing attention the always continuing point of present and lets the imagination hold on the vanished points: this way it preserves the first fulfilled transition from present to present, i.e. the first fulfilled moment, then the second, the third etc. and through that the consciousness of succession or the concept of time. The always continuing point of present describes in the imagination so to speak a line. The reason connects moment with moment, and the imagination always hold that which is connected. The imagination itself doesn’t connect, like Kant wants.
The reason, which is conscious of the unconstrained continuation of its Synthesis and the incessantly the present affecting inner state, connects also the lost moment with the upcoming moment. This way the original image of time emerges: a point between two moments, two connected wings.
The by the reason constructed time should not be confused with the aprioric form present. It is a composition a posteriori. The underlying unity is the fulfilled moment.
The Synthesis of the reason doesn’t depend on the time. The reason connects in the continuation of the present and lets the imagination of the connected take over in every new moment fully and completely. Therefore time is also not the prerequisite of the perception of objects, who are always fully and completely in the present. But time is a prerequisite for the perception of motion.
Like the world is always only a on our eyes lying colored plane, without the space, so would, without time, our knowledge be deprived of all development; since, with the words of Kant, without time
a composition of contradictorily opposed determinations in one and the same object would be impossible to grasp.
But it would a great error, to assume, that development itself depends on the prerequisites of time: only the knowledge of the development, not this itself, depends on time.
Kant and Schopenhauer are in regard to time, while they first make it to an apriopric form, then since they let the real motion depend on it, trapped in the most rare deception.
Furthermore Kant first lets time float, then lets it stand still:
Coexistence is not a mode of time itself; for none of the parts of time coexist; they are all in succession to one another. ^(191D,214E)
Time, whose continuity is ordinarily designated by the term flowing or flowing away. ^(181D,204E)
On the other hand:
Time in which all change of appearances has to be thought, remains and does not change. ^(190D,213E)
At this last sentence Schopenhauer takes great umbrage; but does he put the restless time in a better light by taking away its ground, the real succession, with which it stands or falls? He says, in reaction to the last sentence:
That this is fundamentally false, is proven by the in us all existing firm certitude, that, if all things in heaven and on earth would suddenly stand still, time would continue its course unaffected. (Perarga)
And why would in this case time continue its course? Only because, one thing on earth, which has this firm certitude, does not stand still.
To use an image to make the state of affairs more clear, the point of present can be compared to a cork ball, which moves upon a steady moving flow. The wave, which carries the ball, is the inner state, a wave among countless others, which all have the same course. If we give the ball consciousness disappear under water, then it doesn’t remain at the same place, but floats further. With humans it’s the same. If we faint, or in sleep our consciousness is completely defunct and the time rests; but our inside doesn’t rest, but unstoppably moves itself further. Upon awakening, through our state amid the general development of the world we remark at first, that a certain time has passed and subsequently construct it. If we consider, an individual who has slept uninterruptedly for 50 years and meanwhile has naturally been changed; nevertheless he doesn’t feel the ailments of old age, and his chamber hasn’t changed since the moment he fell asleep, then he would, upon awakening, first believe, that he has slept only one night. A look through the winder, a look at the mirror immediately change his view. Due his grey hairs and facial features he’ll be able to “approximately” measure the time, which has since then passed by; better methods would tell him the minutes, i.e. the covered way of the complete world-wave determines the time, which has since then passed by.
Time certainly stands Still. It is an imagined fixed line, whose positions are immovable. The past year 1789 and the future year 3000 take a fully determined place on it. What however floats, always floats, floats restlessly, is the present, carried by the point of motion.
Before everything we must research, if the Understanding, with its function (law of causality) and its forms (space and time) can construct the whole real world, which lies before our eyes, alone; the reason really doesn’t provide anything for visualization: according to the Schopenhauerian theory.
First and foremost we encounter Schopenhauer’s inexcusable misuse of the law of causality. For him it’s “a girl for everything”, a magic horse, on whose back he swings into the drunkenness, when the obstacles seem too difficult for thought.
We remember us, that the law of causality doesn’t mean anything more, than the transition of the sensuous sensation to its cause. It expresses therefore only the causal relation between outside world and subject, or better: the Schopenhauerian “immediate object”, the body, and this constraint becomes even more limited because, it’s always the transition of the effect to the cause, never vice versa. Has the intellect found the cause for the change in the sensory organ, as well as brought it into a relation to time (I follow Schopenhauer’s line of thought) then its job is done.
The knowledge of the operation itself is not a work of the Understanding. It relies on thinking and is therefore a late ripe fruit of the reason.
The clear state of affairs of above now first gets darkened by Schopenhauer, while he grants the intellect the transition of cause to effect. Because he says:
Understanding has everywhere the same simple form: knowledge of causality, transition from effect to cause, and from cause to effect. (WaWuV 1, § 6)
This is false in two directions. First the Understanding doesn’t know, like I said above, the transition of effect to cause, since it is exclusively the affair of the thinking (the Understanding knows as little its function, as the stomach knows, that it digests); secondly its function is exclusively the transition of effect to cause, never vice versa. Schopenhauer adjudges here the Understanding an impossibility, i.e. thinking and earns the criticism he accused Kant of, namely to bring the thinking in the visualization.
Meanwhile with this darkening he isn’t finished yet, the darkness isn’t intensive enough, full darkness must occur:
But in every case the business of the Understanding is invariably to apprehend directly causal relations: first, as we have seen, those between our own body and other bodies; then those between these objectively perceived bodies among themselves. (4fold R, § 21)
This is fundamentally false, and the simple aprioric law of causality is strongly violated, in order to serve the goals of Schopenhauer. It doesn’t require special sharpness, to see which motives led him; since it’s clear, that the objective world relies on the Understanding alone and support of the reason is not needed, only if the Understanding “immediately grasps” the whole causal net, which encompasses the world. Is the last case not possible, then the reason must be called upon. Through this however came (as Schopenhauer assumed without any reason), the thinking in the visualization and also causality would not be through and through aprioric, but only the causal relation between my own body and the other bodies would be aprioric, which would wipe out the baselines of the Schopenhauerian system.
Everyone will see, that Schopenhauer has also here effectively brought the thinking in the visualization. The Understanding goes only from the effect in the sensory organ to the cause. It executes this transition without support of the reason, since it’s its function. But this transition gets known only due the thinking, i.e. due the reason. The same knows furthermore the transition of the cause to effect in the sensory organ and eventually it knows the body as object among objects and gains by this the knowledge of causal relations between bodies among themselves.
From this becomes clear, that causality, which expresses the causal relation between object and object, is not identical with the law of causality. The first one is a more broad concept, which contains the law as a more narrow concept. So the causality in Kantian sense, which I have called general causality, should not be confused with the Schopenhauerian law of causality. The last one only expresses the connection of a certain object (my body) to other bodies, which cause changes in me, and indeed, and like I have to repeatedly emphasize: the one-sided relation of effect on cause.
The proof for the apriority of causality, in which Kant was totally unsuccessful, like Schopenhauer brilliantly showed, is therefore also not finished by Schopenhauer, since the law of causality lies indeed in us before all experience, but it doesn’t cover causality. Meanwhile Schopenhauer acts as if he has really proven the apriority of causality; furthermore, as if the Understanding grasps all causal relations immediately. The last one is, as we have seen, a subreption (obtaining by false pretenses), since these relations can only be known by thinking and the Understanding can’t think.
When we hear Schopenhauer talk about causality, which I will touch upon again below, then we know from now on, first that it’s not identical with the law of causality, secondly, that the law’s apriority can’t give it the same nature. It is a connection a posteriori.
After this preview I go back to our actual research, if the forms space and time are really enough, to generate the visualizable world.
We can put time aside; since it is, as I’ve shown, not a form of visualization, but a composition a posteriori of the reason. Suppose by the way, that it is a form of visualization, then it’s obvious, that it can only the bring the finished objects in a relation, by giving its states of being duration. Superfluously, I want to remind us of Kant’s striking remark:
Time cannot be a determination of outer appearances; it has to do neither with shape nor position.
Therefore only space remains and it indeed gives the object shape and position, by precisely bounding the sphere of force and determining its place. However is the object finished, when I have its mere outline, when I know, that it is extended this and that long in length, width, depth? Certainly not! The main issue: its colors, hardness, smoothness or roughness etc. short, the sum of its activities, which space can only place to its boundaries, can’t be determined by space alone
Let us remind ourselves, how Kant dealt with these ways of activity of bodies. In the Transcendental Aesthetic he disdainfully made them mere sensuous sensations, which could rely on no transcendental principle in the sensuousness, and in the Transcendental Analytic he brought them by the skin of his teeth under the Category of Quality, according to the rules of Anticipation of Experience, for which he gave a wondrous proof.
Schopenhauer dealt with them with even greater harshness. In his first works he calls them specific sensuous impression, the specificly determined way of activity of the bodies too, from which he immediately jumps off, to arrive at the mere abstract activity in general. Only in his later works he comes closer to the matter. He says:
The nerves of the organs of sense impart to the phenomenal objects color, sound, taste, smell, temperature, so the brain imparts to them extension, form, impenetrability, the power of movement, in short all that can only be presented in perception by means of time, space. (WaWuV 2, § 2)
Furthermore in Parerga:
I have expressed, that all forms (space, time and causality) are the brain’s share of the visualization, like specific sensuous impression in the respective organs of sense.
Like it is our eye, which brings forth green, red and blue; so it is our brain, which brings forth time, space and causality (of which matter is the abstractum). My visualization of a body is the product of my sensuous and brain function.
This last sentence will fulfill every friend of the Schopenhauerian philosophy with displeasure; because by it the intellectuality of the visualization gets a mortal wound. As we know, he originally let the only function of the senses be, delivering the poor material for visualization; the senses are “the under-workmen of the Understanding” and in that, which they deliver it, doesn’t lie “anything objective”. And therefore our visualization is through and through intellectual, not sensuous. How does this suddenly change, if I look back at the passages above! Now the Understanding partially visualizes, partially the sensory organs visualize: the visualization is thus partially sensuous, partially intellectual, and the pure intellectually of the visualization is irretrievably lost. (In order to prevent misconceptions, I remark, that according to my cognition theory, the visualization isn’t intellectual but rather spiritual: a work of the complete mind. The merit of Schopenhauer lies in the fact, that he denied the senses the ability to visualize in Fourfold Root.)
Why did Schopenhauer fall in this unfortunate contradiction with himself? Clearly because he could as little as Kant, find a form of Understanding, on which the manners of activity in question can be brought back as a whole. Here he and Kant have left a big gap in the cognition theory, and to fill it has been a task granted to me. Namely, the form which the Understanding uses as support, is matter.
Matter too we have to imagine us a point with the ability of objectifying the specific way of activity of a body (the sum of its activities). Without this aprioric form of the Understanding visualization would be impossible. Even space would lie uselessly in us, since it can only place the boundaries of a specific activity. As little as the upside down turned image of a house for example on our retina, can become, without the law of causality and space, an upright standing object, so little can the in the sensory organ generated blue color for example be transferred to an object, without the Understanding and its second form matter. Matter is therefore a prerequisite for experiencing objects and is as such aprioric.
(…)
Generally expressed, matter is that form of Understanding, which objectifies the certain and specially determined way of activity of a body. Without it the outside world, despite senses, law of causality and space, would be closed for us. All activities, all forces must first become material (substantive), before it becomes something for us. Schopenhauer is right that matter is the carrier of forces and for our knowledge the vehicle of qualities and forces of nature, but well-understood: it is in our head, the force remains outside and independent of the head. Every force is for our knowledge material, in the object they are inseparable. However force is, independent from subject, not material: it is only force, or according to the brilliant teachings of Schopenhauer, only will.
Here I remark, that the marvelous Locke found himself on the right way to the truth, but, looking ahead in the distance, was deceived. Namely, instead of summarizing the by him so astutely detached secondary qualities under the concept matter and determining the thing-as-it-is as pure force, he let them wander as mere sensuous sensations and made matter to thing-as-it-is. He put turned the affair on its head.
This is the right place, to highlight a merit of Schopenhauer, which I much prefer to do, since it’s the best way to wipe out the painful impression which his fruitless struggle with the Matter has to make on us: that is, delivering the true theory about colors. He did so in his marvelous work: “On vision and colors”, which I consider to be among the most important ones, to have ever been written.
(…)
After these necessary side-discussions we return to the Synthesis of the reason. We remember us the great composition, time, which it, on the domain of the inner sense, accomplished by the itself moving point of present.
As object of research we take a blooming apple tree at such a distance of us, that it fully emerges on our retina. According toSchopenhauer it stands as exclusive work of the Understanding completely finished before us, according to Kant we have without the reason (with him the Understanding) only a “rhapsody of perceptions”, “a bustle of single appearances”, which do not constitute a whole. I will prove, that Kant was right.
Schopenhauer takes an aristocratic glance at and coldly rejects the profound teaching of Kant of a composition of a diversity of the visualization and complains, that Kant didn’t properly explain, nor demonstrated, what then this diversity of the visualization, should be before the composition by the reason. The complaint is however justified by nothing and it seems, as if he intentionally ignores the clearest passages of the Transcendental Analytic. I remind of the passage cited above, namely this one:
It is accepted, that the senses deliver not only impressions, but also put them together and provide images of objects, to which without doubt besides the receptiveness of impressions something more is needed, namely a function of Synthesis of the same.
If only Kant had always written this clearly: a lot of wondrous and lunatic stuff wouldn’t have come on the market!
Discussing the Synthesis in more detail, Schopenhauer deems that: all things are in space and time, their parts are originally unseparated, instead they are united. Therefore everything already originally appears as continuum. If however one wants to lay the Synthesis in it
the different sense-impressions of one object to this one only (…) is rather a consequence of the knowledge a priori of the causal nexus (…), by virtue of which all those different effects upon my different organs of sense yet lead me only to one common cause of them. (WaWuV I, appendix)
Both are false. We have already seen, that time originally isn’t a continuum, rather must be composed into such by reason; mathematical space, which we will soon get to know, is likewise composed. Furthermore the Understanding can, by virtue of its function, only search the cause to a change in the sensory organ; it can however not recognize, that diverse activities originate from one object, since it’s not a composing an thinking force. Besides that this is about different composition.
The great considerateness which Schopenhauer manifested, by asking: how do I come to it at all, that I search the cause of a sensuous impression not in myself, but rather outside of me and effectively moving it outwards – this question which made him find the aprioric law of causality -, he left it completely as he went to the construction of the outer world. Here he took the objects as they appear for adults and didn’t ask: must this visualization not likewise at first be learned as child, like the visualization of the right place of an object. But now let us come to business!
We contemplate our blooming apple tree while paying full attention to our eyes, then we will find, that they are in constant movement. We move them from downside to upside, from upside to downside, from right to left and vice versa, short, we palpate the whole tree with our eyes, who use the lighting rays as long feelers, as Schopenhauer strikingly says.
In examining (perlustrare) an object, we let our eyes glide backwards and forwards over it, in order to bring each point of it successively into contact with the center of the retina, which sees most distinctly: we feel it all over with our eyes. (Fourfold Root, § 21)
Before we do this at all, we already have the tree completely before us, it is already a united object, and we palpate it merely, because those parts, which lie on the sides of the center point of the retina, are not clearly seen by us. This happens at lightning speed, so that we can be conscious of the unquestionable Synthesis of the obtained clear representation only with the greatest attentiveness. Our imagination holds upon the clear parts, which if they belong to an object, reason tirelessly composes, and by this we obtain a clear image of the full tree.
This Synthesis always takes place, although we might have seen this tree a thousand times. It is however essentially made easier by the fact, that we, as adults, presume the concept of whole concepts and grasp a new object immediately, in a very short moment, as whole, to precisely observe its parts is our only task.
I started with the hardest example, in order to obtain a sketch of the process. Now we want to let a part of the tree meet the retina and for this goal we place ourselves close to it. If we focus our eyes straight forwards we see a piece of the trunk. We immediately know, that we have a tree before us, but we don’t know its figure. Now we starts from downside and go up to the top, contemplate it from right to left too and always we lose the contemplated parts from our eyes. In spite of that we have the complete tree in the imagination. Why? Because our reason composes the parts and the imagination always holds on to what is composed. Here the Synthesis manifests itself already very clearly.
Most clearly it becomes, when we leave the eyes and limit ourselves to touch; since the eye is the most perfected sensory organ and functions with incomparable speed, so that we can capture its procedure only with great effort. Touch is completely different; here our wings are cut off. Let us imagine, that our eyes are closed and we are given an empty frame of a picture. We find an edge, then move our hand until we find another edge, under it another one, until we come to our starting point. What has actually happened? The Understanding has applied the first impression of my fingertip’s nerves to a cause, has placed the boundaries of this cause with help of space, and has given the expanded cause, with help of matter, a determined manner of activity (like complete smoothness, certain temperate and density). It can’t do anything else. This procedure is repeated with the second impression, with the third on etc.; always it starts again: connection of the effect to a cause and the structure according to its forms, space and matter. By this manner it produces partial-representations, which are, without reason, even if the imagination holds onto them, nothing more than a “rhapsody of perceptions”, which can’t become an object. But the reason is meanwhile not inactive. Exercising its function, it composes the partial-representations and the imagination follows, as loyal follower, always holds the partial-representations together. Finally we lift the frame and the Understanding gives it a certain weight and the object is finished.
Reason can’t process the impressions of the sense, the Understanding can’t unify/compose the sensuous impression: only together they can generate objects and Kant is right, when he says:
Understanding and sensibility, with us, can determine objects only when they are employed in conjunction, ^(252D,274E)
but, I add, without Categories, which have become completely superfluous.
Reason composes the partial-representations, which are by space determined according to depth (elevation, deepening, size), length and width, into a figure of space and the special activity of the partial-representations, which matter objectifies, into quality of space, and the object is finished, without help of the Categories of Quantity and Quality. This manner of Syntheis has nothing to do with concepts.
While Schopenhauer recorded only on side of the function of the reason: creation of concepts, he overlooked the other side: Synthesis of a diversity of visualization into objects, and moreover very rightly judged, that thinking can contribute to visualization really nothing (or as also Kant very fittingly says: the visualization doesn’t require the functions of thinking in any way), believed to bring the reason however only thinking in the visualization, he rejected the profound teaching of the Synthesis of a diversity by the Understanding (reason), i.e. he cut off the best part of Kant’s cognition theory. Thinking however doesn’t come in any way in the visualization by the composition of a diversity by the reason.
Let’s turn back to our apple tree. The composition of single visualization happen successively. The reason composed and the imagination held upon what was composed at all times. All this found place on the always continuing point of present and the succession in the composition was in no way considered. This is meanwhile accidental, since reason is already in possession of time and, while the Synthesis had to link its attentiveness fully on the succession. By this it has given the tree, as long as the contemplation lasted, brought the contemplation itself in a time-relation and has given it duration.
Likewise changes of places (like for example the motion of a branch of our tree) be recognized upon the point of motion, when they are such, that they, can be perceived as moving compared to resting objects. On the other hand, changes of places, where this isn’t the case, can only be recognized with help of time. The same happens with development, which completes together with the concept change of places, the sphere of the concept of motion (motion covers both concepts). We imagine us that we stand again before our apple tree in autumn. Right now it bears fruit. We have the same tree and nevertheless not the same. A composition of the opposing predicates (blooming and bearing fruit) in the same objects is only possible due time, i.e. it is very well possible, to visualize the blooming tree to one time and the fruit bearing tree to another time.
Thus we owe time, as we can see very well from this point, an extraordinary great extension of our knowledge. Without it we would always be limited to the present.
This is also the right place, to say something about the cognition of the higher animals. Schopenhauer assigned them only Understanding and denied them reason. He had to do this, since he lets the reason only think, not compose, and it’s certain that animals know no concepts. My explanation of reason as an ability, of achieving two very different ways of compositions, which relies on a single function (in essence I merely free the gold of a brilliant thought of Kant from an on it poured heap of worthless soil), proves itself here to be very fertile. Every day, animals give proofs, that they are not completely limited to the present, and people break their head about it, how they come to their actions. Sometimes they are assigned only reason, i.e. the capability of thinking in concepts, or everything is put under instinct. Both are false. They merely have a one-sided reason. They compose; compose therefore images on the always continuing point of present, short, they can think in images.
Let’s look back! The visualizable world is ready. Object stands next to object, they rest of move themselves, they all develop themselves and they stand in a relation to time, which is not an infinite pure visualization a priori, rather a composition a posteriori grounded upon the floating aprioric point of present.
The next thing which we have to discuss is mathematical space.
As I have shown above, is pace, as form of Understanding, a point with the ability, to place the boundaries of the spheres of activity of the objects into three directions. As it is and for itself space has no expansion, although all expansion can only objectify itself by it. It is the reprehensible game of the frivolous reason, to take the space away from the hands of the Understanding (which uses it only for the determination of objects), to extend it, in unhindered continuation of its Synthesis, to unify empty space-particles (which can only exist in our fantasy) in an empty objective space, whose dimensions extend into infinity.
On the other hand it is nevertheless correct, that every object works into three directions. Not the size of this activity depends on the point-space – it is present independent from our head – but never we would be able, to perceive it, without the point-space, which lies in us for this goal and therefore is a prerequisite a priori for the possibility of experience.
Since this conformity exists, I can say of every body, before I know it, thus a priori, say, that it works into three directions. Now the from its content separated pure form is suited, to essentially expand human knowledge. The reason is justified, to synthetically shape it.
This is the case with mathematical space; since no one will question its utility. The reason composes, like partial-representations into objects, fantasized space-particles into mathematical space.
That it’s a composition is clear. As little as I have with an object immediately as a whole, so little is the mathematical space given me as prepared, as visualization. Or with the words of Kant:
Appearances are all without exception magnitudes, indeed extensive magnitudes. As intuitions in space or time, they must be represented through the same synthesis whereby space and time in general are determined. ^(175D,198E)
It is hardly necessary, to mention, that mathematical space has only scientific and indirectly practical worth and that the visualization of objects fully and completely is independent from it. They only come about with support of the form of Understanding space, the point-space. By this time essentially distinguishes itself from mathematical space; since knowledge of many changes of places and all developments are without time impossible.
Posted Mar 22, 2017, 1:03 PM UTC · edited