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ABSTRACT In the ‘Critique of Pure Reason’ Kant aims to prove that space is nothing but a

form of one’s internal intuition. To support his theses, he starts by writing a few arguments in the

‘Metaphysical Exposition on Space’. There, in his second premise Kant argues that since one can

imagine empty space, space must be a form of one’s intuition. First, I will argue that it is not

possible to imagine an empty space. Later, using early Wittgenstein’s view, I will argue that

Kant’s premise can be revalidated by paraphrasing it, so it will argue that one’s notion of space

does not depend on any particular object.

1. Kant’s Metaphysical exposition on space

In the ‘The Transcendental Aesthetic’ chapter, in his book “Critique of Pure Reason”, Immanuel

Kant is using this next argument as the second premise of the Metaphysical exposition for the

definition of space:

“Space is a necessary representation, a priori, that is the ground of all outer

intuitions. One can never represent that there is no space, though one can very

well think that there are no objects to be encountered in it. It is therefore to be

regarded as the condition of the possibility of appearances, not as a

determination dependent on them, and is an a priori representation that

necessarily grounds outer appearances.” (Kant, 1999, p. 175)

Kant is using this argument in order to show that space is idealistic, and its concept can be

invoked only with regards to objects of human intuition; that space exists only by means of

human sensibility, and not by itself. Therefore, that space is a form of our intuition. I will now

rearrange the argument in my own words:

P1: One cannot have an outer representation of no space.

P2: One can think of a space with no objects to be encountered in it.

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C: Space is an a priori representation which acts as the condition of the possibility of all

appearances or outer intuitions.

Kant does not elaborate on either one of his premises, and he takes it for granted that they will be

obvious to any reader. Now, I can agree with his approach immediately considering P1, but as

I’m not certainly clear on what Kant meant to describe in P2, I would like to dwell a bit longer

on it.

In the above quote, Paul Guyer chose to translate Kant’s second premise, which I reformulate

into P2, like this: “One can [...] think that there are no objects to be encountered [in space]”1.

Whereas Guyer used the word ‘think’, in the Hebrew translation, Yirmiyahu Yovel chose the

word “imagine” (Kant, 2013, p. 138). Looking into Kant’s original wording, we can find that he

chose to use the word “denken“2 (Kant, 1919, p. 79), which can be translated as ‘to reason’ or

‘to think’. In Kant’s proposition (P2), the verb is being used to invoke the mental action, which

performing it in a certain way, enables one to refer to a space with no objects in it. Thus, the key

to understand P2 is located in finding which mental action according to Kant, will allow one’s

cognition to form the relation with an empty space. Since my goal is to find Kant’s intentions,

concentrating my analysis on the meaning of the word “denken” as defined by any dictionary,

will be a non-philosophical method. Instead, I will try to see whether I can extract any

intelligible meaning for the verb by analyzing Kant’s epistemology as described in “Critique of

Pure Reason”.

2. Clarifying Kant’s usage of the term space

1 My emphasis

2 The full sentence is: “Man kann sich niemals eine Vorstellung davon machen dass kein Raum sei, ob man sich

gleich ganz wohl denken kann, dass leine Gegenstände darin angetroffen”.

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To begin with, I wish to exclude the possibility that by using the term ‘space’, Kant might have

referred to any kind of space. Any kind of space can refer to a room, the earth or the Milky Way.

By definition, the meaning of each one of these spaces is being constructed using boundaries

which are being defined by objects. Therefore, using in P2 a general version of the term ‘space’

(a term that might invoke several different spaces) will not satisfied Kant’s argument. Because,

once a space is being defined by objects, Kant will not be able to conclude C - that space is prior

to the object, and hence internal; a conclusion which is crucial to the Copernican Revolution that

Kant is aiming at. To invoke only a space that has the possibility of being in the state of ‘empty

from objects’, the proposition must refer to an infinite space.

My point can also be understood from Kant’s third Metaphysical premise on space:

”[O]ne can only represent a single space, and if one speaks of many spaces,

one understands by that only parts of one and the same unique space. And

these parts cannot as it were precede the single all-encompassing space as its

components (from which its composition would be possible), but rather are

only thought in it.” (Kant, 1999, p. 175)

According to Kant, even when one refers to a certain space, as for example a space of a

room, it is only being thought as a separated space. But, as Kant argues, we forced by

our understanding to consider this space as part of the infinity space. Therefore, to

establish a general theory of space, Kant’s must refer to infinite space in P2.

3. Imagining empty space

After establishing that in P2 Kant refers to an infinite space, I will try to see which possible ways

exist for perceiving it as empty. In P2, Kant is referring to infinite space that should be empty

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from objects. It is only natural that if the space can be defined as being in ‘empty from objects’,

it should also have the ability to contain objects. Now, since objects in Kant’s philosophy are

products of post-synthesis and conscious state of our understanding, the mental action that

Kant’s invokes in P2 cannot be transcendental. Hence, thinking of an ‘empty from objects’

space, should be something that anyone can do at any time. And since probably the ‘empty from

objects’ kind of space will not be available near us, one will have to imagine it. So now, I will

turn to my imagination faculty, and see what I can pull from it. Logically thinking, it seems to

me that after we will empty the entire imagined space, object after object, two things will be left:

the empty space, and us, the thinkers. But still, using my imagination, I cannot grasp how exactly

I should imagine an ‘empty from objects’ space; and, as long as I will not know how to imagine

‘empty from objects’ space, I will have to consider P2 as impossible, and therefore, as wrong.

One can suggest that we should simply imagine the ‘empty from objects’ space as a pitched

black space; similar to what one sees when closing one’s eyes, and seals one’s visual senses from

outer objects. But this as well, will be problematic. Because according to Kant, judging

something as black means that a category made by our understating is being used (Kant, 1999, p.

205). This means that we will have to consider space as an object of the empirical experience,

and that consideration is unacceptable according to Kant. Space cannot be an object of the

empirical experience, according to Kant, since space is not an object; it is one of the two forms

of our intuition, which through them, objects are being generated for the understanding.

Therefore, ‘empty from objects’ space cannot be imagined as an empty black horizon.

4. Defining Inner and Outer space

Since Kant wishes to prove that space is not something that exists externally to us, but rather as a

part of our mind, and as a form of intuition, it is important to indicate the fact that we do not

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need an actual outer space3 in order to imagine objects. We have the ability to think of, let’s say,

a triangle, and by thinking I mean that we have the ability to draw or produce an imaginary

triangle in front of our consciousness. It does not matter whether we shut our eyes or keep them

open, in either case I can still perceive cognitively signals from my imagination that make me fill

like it is a triangle that is perceived by me. It also does not matter whether I imagine the side of

Giza’s pyramid or just a general abstract triangle shape; the shape is still there to be perceived. It

is important to distinguish the abstract triangle, which belongs to inner intuition, from a visual

triangle, which belongs to empirical intuition. As one does not use a visual sense in order to see

the imagined triangle, one does not depend on the existence of outer space in order to perceive

the triangle. This separation between the visual and the abstract is a crucial point for Kant. Kant

wishes to redefine space and show us that space itself is not an outer thing, but an inner thing. He

writes about the connection between outer and inner objects in A48:

“You thus give yourself an object in intuition; but what kind is this, is it a pure

a priori intuition or an empirical one? If it were the latter, then no universally

valid, let alone apodictic proposition could ever come from it: for experience

can never provide anything of this sort. You must therefore give your object a

priori in intuition, and ground your synthetic proposition on this. If there did

not lie in you a faculty for intuiting a priori; if this subjective condition

regarding form were not at the same time the universal a priori condition under

3 Although Kant is giving the term ‘space’ a total new meaning, one will still need to use the same word when

referring either to space as was considered before Kant’s copernican revolution, or to space as considered by Kant in his critique. Which means, that a term that might be considered as paradoxical in Kant’s view, such as ‘outer space’ (since space should always be regarded as internal intuition, and never as something that exists externally to us), might not be paradoxical if one understand the term as belonging to a pre-Kantian era. I used the ‘outer space’ term to refer to the pre-Kantian ‘space’, so I’ll be able to compare it with Kantian usage of ‘space’. I would use the term ‘physical space’ whenever I will wish to refer to the natural physical outer space, that is valid also for Kant.

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which alone the object of this (outer) intuition is itself possible; if the object

(the triangle) were something in itself without relation to your subject: then

how could you say that what necessarily lies in your subjective conditions for

constructing a triangle must also necessarily pertain to the triangle in itself? for

you could not add to your concept (of three lines) something new (the figure)

that must thereby necessarily be encountered in the object, since this is given

prior to your cognition and not through it.” (Kant, 1999, p. 188)

Kant argues this in order to support the same conclusion as C (the conclusion of P1 and P2).

Space is a mere form of our intuition, which contains the a priori conditions for all empirical

forms whatsoever. We can say that for Kant space is not a visible or sensible thing, but rather

inner thing, which is being used as the ground for all objects; and therefore, allows us the ability

to have an a priori knowledge about objects. When we visually perceive the Giza’s pyramid, we

actually see our inner space intuition being filled by outside sensible material. It is possible to

use our inner space and image a triangle while perceiving simultaneously Giza’s pyramid with

our visual sense. This means that the inner space can be separated in some sense from the outer

space. But, as long as we perceive with our senses the Giza’s pyramid, we will not be able to

empty our inner space. Eventually, the only difference between the inner and the outer space,

between seeing and imaging a triangle, is our consideration towards its existence (a subject

which discussed by Kant in the transcendental logic). When we see an imaginary triangle, we

know it is not really there; its actual existence depends on us, whereas the Giza’s pyramid’s

existence does not; we can say that other people can see it as well.

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5. Empty inner space

In the previous chapter I established that for Kant outer space is foundationally equal to inner

space. The outer space is an extension of the inner space, and once it is being filled with sense-

data, our inner sense is being filled as well. Based on that, I can now suggest a different

interpretation to P2. If for Kant space is an inner thing, he is arguing that one can think of an

object without the need for an outer sense or physical space. Therefore, arguing that we can think

of a space with no objects to be encountered in it (P2) means that we can think or feel that our

inner space is empty. But, since physical space is constructed over, and conditioned by, the inner

space, to think of an empty inner space means simultaneously to think of an empty physical

space and to argue for this ability might raise some issues.

In the chapter “Refutation of Idealism”, Kant is trying to show that Descartes, in his idealism,

assumes wrong. Kant is trying to show that the state which Descartes describes, where the

existence of all outer objects is being questioned and put on hold, is impossible. He write in

B275:

“The proof that is demanded must therefore establishes that we have experience

and not merely imagination of outer things, which cannot be accomplished unless

one can prove that even our inner experience, undoubted by Descartes, is possible

only under the presupposition of outer experience.” (Kant, 1999, p. 326)

Kant needs to prove that the cogito cannot exist unless outer things will truly exist as

independent. Kant insists that the possible imaginary scenario, like Descartes describes in his

meditations, where we refer to objects as outer things when they are actually nothing but objects

that are being generated by our own mind, is impossible. The autonomy of the existence of outer

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objects is a necessary condition that has to be satisfied in order for the Cartesian cogito to exist.

In order to establish the proof, Kant uses the concept of time. As was already established in “The

Transcendental Aesthetic”, time is not an empirical concept, but it is rather somehow being

drawn from our experience. Moreover, time is a necessary representation that grounds all

intuitions, inner or outer. Kant starts the argument by stating in B275 that “I am conscious of my

existence as determined in time” (Kant, 1999, p. 188). This is his version for the Cartesian

cogito. We can only define ourselves as this thing that stays identical while time changes.

Therefore, to be able to know ourselves and to be conscious of ourselves we have to have a

concept of time along with the knowing of ourselves. But, as Kant determines, in order for the

concept of time to exist in us, and in order for us to be able to use it for judgments and

determinations, there has to be a thing that persists through time; something that stays one with

itself. And since only by the existence of this persisting thing, one can identify himself, this

persisting thing cannot be an inner or imaginary thing. If it would have been so, consciousness

would never exist. Now, since I established above that by thinking of an empty inner space, one

would also be required to think of an empty physical space, Kant’s argument (P2) becomes

impossible to perform. Judging by what Kant establishes in the “Refutation of Idealism”, the

experience of thinking of an empty inner space (which will always be accompanied by an empty

physical space) will never occur simultaneously with a self-consciousness of the performer.

Once the state of ‘thinking of an empty inner space’ will be achieved, no self awareness will

subsist, and therefore no memory of the experience will be left. Hence, one cannot perform any

conscious thinking of an empty space, to match or to experience Kant’s argument as worded in

P2.

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6. A Wittgensteinian notion of space

Ludwig Wittgenstein, in his book ‘Tractatus Logico-Philosophicus’ (Wittgenstein, 2010) has

also used the empty space scenario, but for a slightly different purpose. Unlike Kant,

Wittgenstein does not intend to have metaphysic conclusions using the empty space scenario, but

rather, only to draw the boundaries of human understanding. Wittgenstein believes that human

understanding is being reflected through the boundaries of logic in general, and through the

boundaries of language in particular, as an instance of logic. According to Wittgenstein, an

object in human logic equals the sum of all the possibilities of its occurrence in states of affairs.

Therefore, when dealing with human understanding, every state of affairs of every object should

be considered as part of the object itself. Thus, according to Wittgenstein, the only way to refer

to an object is when it occurs in one of its states of affairs, and not when it is separated from

them. To prove this, Wittgenstein writes:

“2.0121 Just as we cannot think of spatial objects at all apart from space, or

temporal objects apart from time, so we cannot think of any object apart from

the possibility of its connexion with other things.” (Wittgenstein, 2010, p. 25)

Few propositions later, we find that Wittgenstein is using quite similar wording to what

Kant has used in P2:

“2.013 Every thing is, as it were, in a space of possible atomic facts. I can think

of this space as empty, but not of the thing without the space.” (Wittgenstein,

2010, p. 26)

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Wittgenstein proposes that space can exist for the human understanding without a

specific object (doesn’t matter which one), as long as there will be other objects to

perceive through one’s senses. And, a certain object cannot exist without its specific

space. This is because, once an object disappears, its space disappears with it. Whereas,

the space of other perceived objects still exists, continuing to create the notion of space

in our understanding. Wittgenstein recognizes that in addition to the fact that a spatial

object cannot exist separated from space, the space of a spatial object cannot exist for

our understating without the object it belongs to. Again, a notion of space will exist

even after a certain object will vanish, but only as long as other spatial objects are being

perceived. This notion of space cannot be considered identical to the space that was

involved in the state of affairs of the vanished object, but rather space that is being

assembled from the state of affairs of the rest of the existing spatial objects.

In the successive proposition, Wittgenstein reinforces this by stating:

2.0131 […] A speck in a visual field need not be red, but it must have a colour;

it has, so to speak, a colour space round it. A tone must have a pitch, the object

of the sense of touch a hardness, etc.” (Wittgenstein, 2010, p. 26)

This means that we can speak of, or understand what is, an empty space. But, only when

the space is in relation with existing objects. For example, we can speak of the empty

space that exists between objects, but it has no properties or existence without the

objects that he situated between. The empty space will have the colors of the objects

that are located in the depth of our sight. This is why, our vision has only two

dimensions; the third is being added only rationally. This is the crucial point here.

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Kant’s argument (P2), as it is worded, seems to suggest that one can imagine and refer

to space alone (since it is empty) without referring to any other objects at the same time.

The inability of one to perform such an action does not mean that C cannot be deduced,

but just that P2 needs to be paraphrased in accordance with Wittgenstein’s theory.

Instead of having P2 referring at the same sentence to the transcendental space, and to

the conscious ability of our understanding, the argument needs to be rearranged, and to

refer to things only from the perspective of our understanding.

So, it seems to me now, that implementing Wittgenstein’s view on P2 will validate

Kant’s argument. Paraphrasing P2 will look like this:

P1: One cannot have an outer representation of no space.

New P2: One cannot think of an object without its space, but can think of space without

the same object.

C: Space is an a priori representation which acts as the condition of the possibility of all

appearances or outer intuitions.

Conclusion

In this paper, I started by outlining the fact that on Kant’s second argument, in the

metaphysical exposition of the concept of space, it is not clear how one should be able

to perceive an empty space. At first, I tried to see whether one can imagine an empty

space. From this effort I came to the conclusion that this space must not have any color

at all, or it will exceed Kant’s definition, by being considered as an object. Later, after

arguing that according to Kant outer space is always being constructed over inner space,

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imagining an inner space will cause simultaneously an empty outer space. Using the

‘Refutation of Idealism’ chapter, I concluded that as long as our outer space will be

empty, no conscious mental action is possible, and hence Kant’s argument is not

performable. Then, to resolve Kant’s not performable argument, using Wittgenstein’s

view, I suggested considering the term space as part of the spatial objects one perceives.

Therefore, we cannot argue that an empty space as a whole is possible for imagining,

but only that we can think of space without a specific spatial object, whereas we cannot

think of a spatial object without space.

References

Kant, I. (1999). Critique of pure reason. (P. Guyer, & A. W. Wood, Trans.) Cambridge

University Press.

Kant, I. (2013). Critique of pure reason. (Y. Yovel, Trans.) Israel: Kibutz Poalim.

Kant, I., & Valentiner, T. (1919). Kritik der reinen Vernunft. Leipzig : F. Meiner.

Wittgenstein, L. (2010, October 22). Tractatus Logico-Philosophicus. (C. K. Ogden, Trans.)

Retrieved from Project Gutenberg: https://www.gutenberg.org/files/5740/5740-pdf.pdf