As a preface to comprehending Kant’s conception of space I turn first to the notion of the Erscheinung which is often translated as “appearance” and which I render with “specter.” When this is understood I think it is easier to grasp Kant on space.

The specter is immediately an object which we see as actual, and indeed as much as we feel the touch of one hand on the other, and yet which is actually only within us. An easy example of an everyday use of the term specter is the face that we occasionally spy in a cloud. Often times one person will see a face in a cloud and not be able to get another person to see it. This face is actually on our retinas, on our skin as Schopenhauer was wont to say.*

[* A good example of a specter is the projection of a bunch of straight line on a page into a cube, e.g.,

Even though the lines are flat on the screen or page, we nonetheless see it projected into space. The straight lines are what are "really" here and the box or cube is a specter of our looking.]

Now there is a deeper usage of this term, namely that everything we see about us, our hands, those trees, this table, all things visible are actually just specters on our retinas. This is not to say that there are no hands, trees and tables on their own out in space beyond our eyes, but merely that what we actually see immediately is on our retina, and these objects are not things on their own that exist on their own the way we see them.

Consider this example that the arch skeptic David Hume confronted.* When you look at your table close up it is big and takes up a large part of your retina, and when you see it at a distance it is small and takes up a small part of your retina. Now if what we saw were a thing on its own, then to be logical we would have to say the table itself changes size on its own and merely in tandem with our sightings of it. But since we don’t speak this way but say rather: the table is constant in its size and being, and it only looks like it is changing size because we are seeing it from different distances; this means that we know that we are dealing actually with mere specters of the table and not with the table on its own. [Hume, by the way, never was able to account for this phenomenon, i.e., he could not imagine how he could have come to think that the table did not change in size since in every sighting it (the spectral image) did in fact change.]

[* See Hume's Enquiry Concerning Human Understanding , Section 118 (back button must be used to return here).]

And so we see that what has happened is this: we have taken these retinal specters and we have imagined something which is not spectral, namely the object on its own, e.g., Hume’s table, and we utilize that thing, which we think of as independent of us and uniform in its existence, in order to transform the specters in our eyes from things on their own (which get larger and smaller on their own) into images, i.e., projections on our retina of things which exist apart from us in space. Using this terminology we can now say that the face in the cloud is a specter and the cloud itself is an image (a projection of the cloud on the retina), and that the rainbow we see is a specter/Erscheinung and the rain is an image. But that is everyday talk. On the deeper level we need to understand that even the rain itself is actually a specter, i.e., all that we know about the rain comes to us through some organ of sense, e.g., the sight for the shape of the raindrops on the retina, the hands to tell that the rain is wet and cool or warm via our organs of touch.

And so we can now see a bit better where Kant is coming from, for he is interested in how it is that people came to consider the myriad of specters which appear to us, and to make the differentiation between the rainbow and the rain, for example, for when you think about it there is really no reason why the rain and all things might not come and go out of existence just like the rainbow does and the face in the cloud does. Now we don’t think that way and so how is it that we came to make that jump? This jump means that it is a synthetic contribution to the world that we ourselves make and since it is this synthesis which we ourselves produce, it behooves the philosopher to inquire as to how it is that this synthesis has any validity and indeed what validity itself is supposed to mean.

In brief then how then do we go from the subjective to the objective since all that is ever given us is spectral, i.e., within us, and thus which is entirely subjective? That is the question that Kant will undertake to answer. And the clue is Hume’s table: solve Hume’s problem with his table and you have answered this question.

We are now ready to take Kant on with regard to his conception of space. What must space be in order that we are able to solve Hume’s problem? As a first step Kant wants to show that space is not a notion which we obtain empirically through exposure. This is called the Metaphysical Deduction of space. There are four points that Kant will make here.

1. In the first place we notice that Hume was already seeing his table in space (and in time, which must also be examined), namely he is seeing it as close to, and then also as far away from, himself. Now on its own the table, being merely spectral, is not in space at all, but merely larger and smaller (this size being the proportion of the retina taken up by the sighted table); and so it is already a synthetic addition to the sightings of the table to notice the distance from the viewer, and this is contributed by us ourselves. In fact Kant indicated that you could look at something all day long and notice its color, size, shape, etc., etc., and never notice that it is apart from you, for that “apart from you” has a reference to you and so is not an aspect of the table. And so it seems that our conception of space cannot be something that we glean from experience, but rather is more something that we add to experience.

2. In addition we must recognize that space is different from all empirical, experienced-based objects in that while we can utilize space to imagine the absence of any such object, we cannot imagine the absence of space. We can picture an object in a given space and then again we can picture that same space as devoid of that object, but then for us to be able to imagine the absence of space this means we would have to have a super space, as it were, in order then to imagine the absence of this given space, and that is impossible. And so the concept of space is of a different sort than all empirical concepts.

3. Furthermore space is also not an intellectual invention inspired in the empirical way of multiple exposures to some object. Typically we come to the general notion of a table, for example, by considering this table and that table and noting what is common (an elevated surface suitable for writing or eating or something like that) and ignoring what is different (the size or shape or color of the individual tables). But you cannot come to the notion of space in this empirical way. For you cannot be exposed to a part of space and then to another part of space, and then put these two parts of space together into a concept of space such that each is a part. For each of these parts is originally a space and is seen that way, and so space must always be presupposed before you can formulate the notion of a part of space. Hence space is merely an envisagement, i.e., a way of looking at and considering things.*

[* If space is merely a way of looking at things, then it would follow that the born blind would have no conception of space. Now the blind can certainly tell when they are being affected by something which is independent of them, and that is called the external sense. But space is the form of this external sense and it is seated only in beings of sight. Thus the blind have a sense of the external, but there is no form to that sense as it is with seeing humans.]

4. Finally Kant wanted to show that space is thought of in a way that no empirical object could ever be considered, namely as infinite and yet at the same time as entirely given, for it is the mark of the infinite that it can never be given. Take for the example an infinite straight line. If you approached the concept of this line empirically you would merely come to the conclusion that no matter how far you examined it, there always remained something yet to examine. But this could not possibly tell you that there would always be yet something to examine, for by means of an empirical inspection you would never see the fact that it were infinite, for you could not tell what would be the case with a further inspection.*

[* How then do we actually come to this recognition? We must do something like this: we imagine a straight line of indefinite length. And then we imagine ourselves looking at some segment of that line, and we imagine that this segment is the second of three equal parts of that line, and finally we imagine that this new, longer segment made up of the three equal parts is itself the second of three equal parts of an even longer segment, and that this property always holds. And now we need go no further, for we can already tell that this imagined line must be thought of as given and yet nonetheless be infinite. And so no empirical inspection is necessary at all.]

Now we have completed Kant's Metaphysical Deduction of Space. But all that Kant has done so far is merely to show that what we know and mean about space cannot have arisen to us though any experience. Now he turns to validate space positively by showing that certain things we know we could only know if space were the way we have of looking at things, and one of those things that we know and which is made possible by space being a way of looking at things is experience itself. This is called the Transcendental Deduction of Space.

First Kant notes that mathematics is one of these things that we could know only if space is a way of looking at things. Consider this: a characteristic of any and all triangles is that any two sides together are longer than the remaining side. How can we make such a statement? There are only two ways: 1. either by inspection via an envisagement; or 2. analytically by means of an analysis of what we actually and already think when we consider a triangle. Now if we knew this only empirically, like we come to know tables in general through inspection, then the most we could ever say is that so far every examined triangle has possessed this property of any two sides being greater than the third. But since we in fact know this holds of all triangles, even those not yet examined, it is clear that this knowledge does not arise empirically.

But our knowledge of this property of triangles is also not analytical, as though we could just think of a three sided figure and not only conclude that it had three angles (every two sides making an angle) but also that every two of the three sides were greater than the third. But that information can never be deduced from the concept of triangles as every one can tell for himself by just thinking about triangles (and not attending to their picture).

To solve this problem Kant utilizes the notion of the Anschauung or envisagement (although most translators use “intuition” to render this notion). An envisagement can be empirical, as when we take a look at a given table or a given triangle, or it can be a pure envisagement which is devoid of any empirical object. Kant will find his solution in this latter

A pure envisagement in space is basically a figure which we trace out in space, like pantomimicly describing a circle in mid air as a mime artist might do. We do the same thing with regard to the triangle, and so we take a look at this imaginary creature of our own making. And we notice that as we shorten the length of any two sides they progressively approach the third side, and we see that if they were equal to, or shorter than, the third side, the triangle itself would vanish by turning into parts of that third side and we would have no triangle at all. And so we are able to see in a single glance that all triangles would be subject to the rule that any two sides together are greater than the third, and this recognition is only possible because we know that triangles are not things on their own at all, but rather our own envisagements, and this knowledge is only possible because space itself is a pure envisagement, merely the way we have of looking at external things.*

[* To say that space is merely the way we look at things does not mean that things are not in space, but merely that we could not know that things are in space except by means of this subjectively seated way of looking at things. In other words the space that we are familiar with and in which we see all external things is a product of our own minds and is not gleaned from experience.]

Our validation of space with regard to the specters we have already considered, namely in the same way that we see the triangle in space, we see the specters in space and it is by means of that that we are able finally to come with Hume to the question as to the tandem with which the distance varies with the size of object; and in the same way that we can draw a triangle and see it in space before our eyes (which is a pure envisagement/Anschauung) we can also draw an object in our imagination and put it not only into space but also into different distances from us in that space and notice that when the object remains the same size, the projected image varies. In fact Schopenhauer said that the eye is the first object that we really come to know; it is only with reference to the eye that there can be any meaning to “distance from” and “looks like”.*

[* By the way the notion of specter/Erscheinung has an immediate reference to sight, but Kant uses the term more generally to denote any object which is on a sense organ, e.g., the tones that a car horn makes or the smell from a rose.]

We can conclude now: human science and experience is valid because we are able to put all external specters into space* and distinguish them as the rainbow and the rain, specter and image, but also at the same time, since space and time are merely the ways we look at things, they only hold for things we can look at, and so therefore do not hold for things on their own without regard to our looking. For example, if there is a God or angels, then since they cannot be looked at, we are not able to say that they are in space and are subject to the conditions of space.

[* Kant makes a similar case for the internal specters, e.g., feelings and thoughts, namely that we consider them in time with this time also being a subjectively seated envisagement/Anschauung.]

Conclusion: even though space is our own contribution to experience, it is valid for it makes experience possible, but it makes no contribution to our understanding of things on their own at all, and does not hold or condition them.

It might be worthwhile now to consider how it is that Kant got interested in the notion of specter and envisagement in the first place. There were in his time two schools of thought regarding the sources and nature of human knowledge. There was the empirical school and there was the rational school. The former was exemplified by David Hume. Hume sought to explain all knowledge as either analytical in that he (wrongly, it turns out) thought math to be or else as empirical, i.e., developing expectations based on exposure to objects. The former knowledge is certain, the latter iffy. If math were developed through exposure, we would never be able to say that 7+5 is 12 but merely that so far 7+5 has been found to equal 12. And so, since for him there was only the analytical and the empirical, he thought the information was analytical. But he was wrong in this, for when you merely analyze the notion of 7+5 you never come to 12 (any more than the analysis of the triangle could reveal that any two sides were greater than the third); the most you could do would be to think about the notion of a unification of seven and five but not what that unifying number was.* And so analytically the 12 does not arise. The way we actually come to this knowledge of 12 is via a pure envisagement, namely taking the seven in mind and using the visual picture of the five fingers and progressively increasing the 7 at the same time with the exhaustion of all five fingers, i.e., 8 9 10 11 and then finally 12.

[* One imaginable and intuitive way of unifying them might be to notice that 7 contains a five in its concept, and so we might think that 7 and 5 were unified in the 7; but which of course is not what we mean with addition at all.]

And so Hume fails to explain mathematics.

As far as empirical knowledge goes we have these iffy expectations, e.g., that a struck billiard ball will move, but not that it has to, and for all we know the next time a struck billiard ball might remain stationary. But then, as we have already mentioned, Hume realized that by his own theory of growing expectations it would be impossible to know that his table did not get smaller at a distance, for all that would ever be given to him via empirical inspections would be that it did get smaller at a distance. And the iffy part means this: since we know only what we have observed thus far (and that “thus far” is the mark of empirical knowledge) and not at all that things have to be the way they are, it is conceivable that for all we know the next time we looked at the table from a greater distance it might be the same size (in the retina) or even larger. An interesting flaw in Hume's theory which he did not grasp was this: if our knowledge of the behavior of billiard balls and tables were empirical, then if ever a billiard ball did not move upon being struck of if a table did not get smaller when viewed from a distance, we would have no reason to imagine anything "out of whack," for since the knowledge is empirical and conditioned always by the "thus far" we would merely accumulating additional information about these objects in the continuing march of the exposures to these objects.

And so Hume’s system failed in every regard and it took Kant to explain the sources of the assurance we have with regard to both mathematics and the illusion of the varying size of the table.

The other school was the rationalist school. And to cover this briefly, its leading exponent, the brilliant Leibniz (inventor of calculus, independently of Newton), had to assume that space did not exist on its own, but only in relationship to real things, for on its own it could not be real, for on its own space is actually nothing at all. But Kant realized that if this were true, then since two hands could be imagined as utterly alike so that the description of the one were identical with the description/conception of the other, then you could not tell whether you had two left hands, or two right hands or a left and a right hand; and so the only way that you could tell that your two hands were different would be by taking a look at the two hands in space together, and then, if they were left and right, you would see that even though their parts were identical and even substitutable with each other point for point, still they could not occupy the same space, i.e., the left glove will not fit the right hand. In other words, by his own system, since space were not real but merely the relationship of real things, Leibniz would not have been able to tell his left hand from his right (except by feeling) and would never have been able to understand why sometimes his gloves fit and sometimes not, even as Hume with his system would never be able to realize that his table did not get larger and smaller on its own.

The next step in grasping Kant’s thought with regard to our experiential and scientific knowledge is to understand his notion of time (which parallels his conception of space) and then to move on to consider his concept of the object which will take us to the deduction of the categories. I hope to do this before too much longer.

As a preview of sorts, time is treated pretty much the same way as space, and we find that the only way that we can recognize an alteration is that we are able to recall a prior image and have it in mind in the present, but not consider it as present (although it certainly is subjectively to the mind), but to account it as earlier. In this way we came to see that there is a present state of some object and an earlier state of that same object and so therefore there has been an alteration. For example, the table is small now, but it was large earlier and so there has been an alteration. We have this a priori capacity of forming an objective time line such that depictions, though merely present to the mind at the present moment, are seen as affixed sooner on that line. Without this the most you could say is "the table is small" and not relate it to another image except by similarity, e.g., the small table which is vivid now and the depiction of a large table (which is actually the same table seen earlier and closer) which is faint (being merely a memory) have a similar shape and color.

The object of human experience is entirely spectral and as such exists empirically only in our actual sighting of it. The table is not smaller and larger on its own, but only in the human eye. These sighted objects are not real things at all, but merely our organal responses to stimuli, like the sighted table being merely an image on the retina. Empirically then we would never have come to the notion that there were an object which were independent of all this spectral material (and thus invisible and without the feeling of resistance in our touch) such that this impressions on our sense organs might be understood too be images and not things on their own.

Now the source of our knowledge of empirical objects is the perception. But the perception is a product of a mind which serves as a device for unifying diverse depictions in various ways into a single consciousness, e.g., a total of many individuals. The form of this mind is categorical, and the categories are the different ways we have of unifying depictions. The categorical mind is always awake to a possible connections of depictions, and for this reason finds coincidences intriguing. When two sensations occur in some sort of tandem in the mind, there is a reaction which is the perception. This reaction consists in taking a "second look", namely of recreating one element of the two sensations in order to see the other also arises. Kant called this perception the Wahrnehmung which is built upon "care" and "taking", i.e., carefully noticing. In this way the mind dismisses some coincidences as simply coincidences and considers others which show signs of connection, i.e., a replication. Once the material for a possible connection is obtained through perception the mind seeks to conceive of some object such that this intriguing coincidence would be a natural phenomenon. This object, arising as it does through the categorically unifying mind, is so conceived that it not only explains the phenomenon but does so in a consistent fashion with all other explanations. Thus a unity is provided a priori by the mind such that not only perception is first made possible, but the perceptions arises under the presupposition of a unity with all other possible perceptions, much as the one, a priori sighting of the triangle enables us to speak in a way that will be consistent with everything else we ever come to say about the triangle.