## 1. Introduction: philosophical questions about space and time



In the context of interpreting Kant's views concerning space and
time, a number of philosophical questions are relevant. Kant himself
provides a litany of these questions in his so-called *Inaugural
Dissertation* of 1770, a text in which he broke with his previous
broadly "Leibnizian" views from the pre-critical period
(Hatfield 2006, 72-6). He writes:



> 
> Space is not something objective and real, nor a substance, nor an
> accident, nor a relation; instead, it is subjective and ideal, and
> originates from the mind's nature in accord with a stable law as
> a scheme, as it were, for coordinating everything sensed externally.
> (Ak 2: 403)
> 



In this one pithy sentence, we find a list of many important early
modern questions concerning space. Is space "real," or is
it "ideal" in some sense? Is it a substance in its own
right, a property of some substance, or perhaps neither? Is it somehow
dependent on the relations among objects, or independent of those
relations? What is the relationship between space and the mind? And
finally, how do these various issues intersect with one another?



The passage from the *Inaugural Dissertation* hints at five
distinct questions or issues concerning space and time. First, there
is the question of the ontology of space and time considered within
the framework of what Kant would regard as the dogmatic metaphysics of
the seventeenth century. This framework might suggest that if space
and time are to exist, or to characterize the physical world, they
must be considered either substances in their own right, or else
properties of some substance. Neither option seems particularly
attractive. Space and time seem distinct from substances because they
are causally inert, causally inaccessible--their aspects or
properties cannot be altered by interacting with any other
substance--and imperceptible. Since they are often regarded as
infinite, moreover, some thinkers have doubted that they could be
substances, as God is often thought of as the sole infinite substance
(Descartes may have conceived of space as "indefinite" for
this reason). However, it is also difficult to think of space and time
as properties of any substance, for then they would presumably be
dependent on that substance for their existence. If we regard them as
dependent on any contingent substance, it seems that we would be
committed to the idea that space and time could fail to exist, or
could disappear, depending on the happenings of that contingent
substance. One might think instead that space and time depend on the
one necessary substance, but this obviously raises a host of other
issues. To think of space and time as properties of God is potentially
to regard God as spatiotemporal, which is *verboten* from the
point of view of many seventeenth-century thinkers (Janiak 2008,
chapter five).



A second topic arises if we consider the ontology of space and time
independently from the substance-property metaphysical framework,
e.g. by considering the relationship of space and time to
physical objects. Following Newton's discussion in the first
(1687) edition of the Scholium following the Definitions in the
*Principia*, the modern debate concerning space's
ontology has been centered on two overarching conceptions: absolutism
(now sometimes called "substantivalism," although that
label raises certain issues), the view that space and time exist
independently of all possible objects and object relations, or perhaps
the view that space-time points exist; and relationalism, the view
that space and time depend for their existence on possible objects and
relations, or perhaps the view that space-time points do not exist
(DiSalle 2006; Messina 2018).



Leaving aside questions about ontology, there is a distinct--or
at least potentially distinct--issue regarding space and time:
what is the origin of our representation of space and of time? This
third issue arises from the sense in the early modern period that our
idea or representation of space and time must somehow be importantly
distinct from our idea or representation of ordinary physical objects.
Many believed that space and time are causally inert and therefore
imperceptible--how then are we are able to represent space and
time at all? Few are willing to deny that we have a representation,
not merely of spatial and of temporal objects, but also of space and
time themselves, so there is a genuine puzzle lurking here.



The fourth topic follows on the heels of the third: what is the
content of our idea or representation of space and time? From
Kant's point of view, the content of a representation might
provide us with a guide to its possible origin. Alternatively, we
might be able to consider the origin of a representation as providing
us with a clue as to what its content might be. In the case of space,
there may be reason to think that the content of our representation
must somehow reflect what we know about space from Euclidean
geometry.



The fifth and potentially final topic is closely connected with the
third and fourth, and indeed, connects all four previous topics with
one another: what is the relationship between space and time, on the
one hand, and the human mind, on the other? This question obviously
cries out for clarification. Part of what this question might mean can
be characterized by the third and fourth questions above: if we think
of the mind as representing space and time in a certain way, then
perhaps this is part of our understanding of the mind's
relationship with space and time themselves. But within the context of
Kant's work, there is, at least *prima facie*, another
issue lurking here--are space and time somehow dependent upon the
mind for their existence? It may be that some kind of dependence is
suggested by the origin--or by the content--of our
representation of space and time (or perhaps by these two jointly).
But Kant also seems to think that a view recognizing the dependence of
space and time on the mind might offer advantages in addressing the
ontological problems mentioned above.



Each of these five philosophical issues concerning space and time is
relevant for understanding Kant's views. As we will see below,
part of the difficulty in interpreting Kant arises from the fact that
he evidently transforms various aspects of the early modern debates
concerning space and time through the perspective presented in the
first *Critique* (Allison 2004, 120-1). Within the context of
the first issue raised above, the view that space and time are
*real* may mean that space and time are substances in their own
right, rather than merely properties; yet within the context of the
absolutism-relationalism debate, if space and time are *real*,
they exist independently of all objects and relations. But Kant uses
the terms *real* and *ideal* to express views concerning
the relation between space and time and the mind, leaving aside any
views concerning objects and relations. This entry aims to clarify
matters by separating these various considerations.


## 2. The background to Kant's views in the *Critique*


### 2.1 Leibniz and Newton



There is no doubt that the debate between the Leibnizians and the
Newtonians concerning the status of space and time forms part of the
essential background to Kant's views throughout his career.
Although Newton originally formulated his conception of space and time
in response to Descartes's views in the *Principles of
Philosophy* (1644), by the turn of the eighteenth century, Newton
and his followers were embroiled in an extensive debate with Leibniz
and his supporters on the Continent. This reflected, in part, the
famous priority dispute regarding the calculus, but it also reflected
some of Leibniz's fundamental criticisms of Newton's views
of space, time and motion in *Principia mathematica* (1687,
1713--second edition). Leibniz raised many of those criticisms in
his correspondence with Samuel Clarke, who defended Newton's
ideas. Kant mentions this debate frequently in the
*Critique* (see, e.g., A23/B37, A39/B56, & A46/B64).
Broadly speaking, Newton and his followers argued for the importance
of thinking of space, time and motion as "absolute" or at least from
an absolute point of view. This means that one regards space and time
as existing independently of matter and relations amongst material
bodies. As Newton (1999, 408) puts it, "Absolute space, of its own
nature without reference to anything external, always remains
homogeneous and immovable." So absolute space, or space regarded from
an absolute point of view, has a nature and has the properties of
homogeneity and immovability independently of anything else. Since
space on this conception has a nature and has properties independently
of any relations, Newton was often interpreted as saying that space is
a being or perhaps a substance. To the chagrin of many philosophers,
Newton avoided using these categories in the *Principia*
itself, although in a famous unpublished manuscript he denied that one
should think of space as either a substance or as an
accident (Newton 2014, 35-36). In his correspondence with Clarke
(1715-1716), Leibniz then argued that Newton's conception of
space and time conflicts with the principle of sufficient reason: if
space were to exist independently of all matter and material
relations, then there could be no reason for God to have chosen to
create matter in one location rather than any other; independently of
matter, all locations are indistinguishable (see L 5: 3-4). In part to
solve this problem involving the principle of sufficient reason,
Leibniz then argues that space is merely the order of relations
amongst material bodies. So on his view, space depends on objects and
their relations, which solves the problem: since space does not exist
independently of matter, God never faced the question of "where" to
place bodies in space. To create a bunch of matter just is to create
space.



Many interpreters have thought that in the *Critique of Pure
Reason*, and particularly in its first section, the Transcendental
Aesthetic, Kant attempts to engage the Leibnizian
"relationalist" and the Newtonian "absolutist"
conceptions of space with transcendental
 idealism.[1]
 As Charles Parsons puts it, "the issue between what are now
called absolutist and relationalist conceptions of space and time,
represented paradigmatically by Newton and Leibniz" represents
"the background to all of [Kant's] thinking" about
space and time (Parsons 1992, 67; cf. Torretti 1999, 105). In the
beginning of the Transcendental Aesthetic, Kant frames his view by
contrasting it with the failures of the Leibnizians and the Newtonians
to conceive of space appropriately:



> 
> Now what are space and time? Are they actual entities [wirkliche
> Wesen]? Are they only determinations or also relations of things, but
> still such as would belong to them even if they were not intuited? Or
> are they such that they belong only to the form of intuition, and
> therefore to the subjective constitution of our mind, without which
> these predicates could not be ascribed to any things at all?
> (A23/B37-8).
> 



The view that space and time are actual entities is meant to represent
the Newtonian position, and the view that they are determinations or
relations of things, the Leibnizian position (but cf. Hatfield 2006,
77-8). Later in the Transcendental Aesthetic, he refers to the
Newtonians as the "mathematical investigators" of nature,
who contend that space and time "subsist" on their own,
and to the Leibnizians as the "metaphysicians of nature,"
who think that space and time "inhere" in objects and
their relations (see A39-40/B56-57).



While Kant does clearly allude to this theoretical background, it is
noteworthy that views of the sort he defends in the
Aesthetic--that space and time are transcendentally ideal, that
they are mere "forms" of intuition, that they depend upon
the "subjective constitution of the mind," and so
on--do not obviously make contact with the Leibniz/Newton debate.
This raises questions about Kant's use of the Leibniz-Newton
background. First, how does Kant understand the Leibnizian and the
Newtonian conceptions of space and time? Does he think of them solely
as views on what I have called the status of space vis-a-vis
objects and relations, or does he think that they contain, or perhaps
entail, views on other topics, such as the character of our
representations of space and time? Does Kant regard himself as needing
to undermine either, or both, of these prior conceptions in order to
support his conclusion that space and time are transcendentally ideal?
Does Kant's rejection of *both* the Leibnizian and the
Newtonian conceptions as types of "transcendental realism"
illuminate what he means by transcendental idealism? And finally, is
Kant on secure ground in characterizing his predecessors' views
in this way? These questions will help to guide the discussion
below.



The fact that Kant focuses on the debate between the Leibnizians and
the Newtonians is perplexing given his evident lack of interest,
within the context of the *Critique*, in problems concerning
motion. One of Newton's principal reasons for distinguishing
between an "absolute" (or "mathematical") and
a "relative" (or "common") conception of space
is to ground a distinction between true and merely relative motion.
Newton construes the true motion of an object, as opposed to its
merely "apparent" motion, not in terms of its change in
relations to other objects, as Descartes had done in his
*Principles*, but in terms of its change of absolute place
(Janiak 2008, chapter five). So the very idea of absolute or
mathematical space helps to express what true motion is. Discovering
the true, as opposed to the merely apparent, motions of objects, so
that one can then determine the forces that cause these true motions,
represents one of the principal goals of Newton's
*Principia*.



Kant is perfectly well aware of these details from the Scholium to the
*Principia*, but he makes it clear in the Transcendental
Aesthetic that he wishes to bracket questions concerning the motion of
objects. The reason is that he regards <motion> as an
empirical concept, and the Aesthetic aims to articulate a purely *a
priori* conception of space (see A 41/B 58; also MFNS, 4: 482).
Instead, Kant tackles physical motion in the *Metaphysical
Foundations*, where he contends that one can distinguish true from
relative motion by determining the center of mass frame of the solar
system (4: 482, 487, 555-6, 559-63), thereby avoiding the postulation
of Newton's mathematical (absolute) space.



But what if we abstract away from questions of physical motion? What
if we consider motion within a much more abstract context: for
instance, can the motion of a *mathematical point* through
space be considered in the Aesthetic? Kant makes it clear that this
remains empirical because the concept of motion itself is empirical,
and so should still be deferred to the *Metaphysical
Foundations*. Indeed, the latter begins with a consideration of
motion in abstraction from various physical questions like the mass of
the objects and then slowly progresses by adding further physical (or
empirical) elements.



Kant does discuss the important notion of the "motion of the
subject" in a famous footnote in SS26 of the Transcendental
Deduction. Is that kind of motion under discussion, perhaps
implicitly, in the context of the Aesthetic? Kant does not think that
the "motion of the subject," for instance in drawing a
circle, is empirical, but he does think that it requires--indeed,
it apparently exemplifies--the unity of the manifold of intuition
imposed by the unity of consciousness. Whatever this doctrine may
mean, it seems clear that from Kant's own perspective it cannot
be dealt with in the Aesthetic, for the latter text abstracts from all
contributions of understanding and therefore abstracts from any
consideration of the unity of the manifold imposed by the unity of
understanding. (This seems to be closely related to Kant's point
in SS26 that it is only from within the point of view of the
Transcendental Analytic that one is able to make a distinction between
what he calls space as a *form of intuition* and space as a
*formal intuition*.) So from Kant's point of view,
although various kinds of motion are considered in the critical
philosophy--including the so-called motion of the subject in
describing a space, the motion of a mathematical point through space,
and the motion of a body through space--no kind of motion can be
considered within the context of the Aesthetic (see Pollok 2006).



This seems to suggest that Kant's interest in the
absolutism-relationalism debate does not originate with his concern to
discuss *motion* in any sense of the term. In what follows,
then, one goal is to specify why Kant remains focused in the Aesthetic
on the views of Leibniz and Newton (and their respective followers).
It may be that Kant's interest derives from his general interest
in the views of what he calls the "metaphysicians," the
Leibnizians, and of what he calls the "mathematicians,"
the Newtonians. Throughout the pre-critical and critical periods, Kant
evinces considerable interest in various attempts to reconcile certain
aspects of Leibnizian metaphysics with the Newtonian view of nature
(Friedman 1992, 1-52). But there is also more to be said about
Kant's focus on the absolutism-relationalism debate (see
especially Messina 2018), which we do below.


### 2.2 Kant's understanding of representation



In a famous passage in the first *Critique*, Kant helpfully
discusses his notion of representation (A320/B376-77):



![figure 1](figure1.jpg)

Figure 1.




Kant regards an intuition as a conscious, objective
representation--this is strictly distinct from sensation, which
he regards not as a representation of an object, property, event,
etc., but merely as a state of the subject. Whereas sensations do not
represent anything distinct from the sensing subject (including
perhaps the state of the subject's body), intuitions are
objective
 representations.[2]
 Recent scholarship emphasizes the importance of his distinction
between sensation and intuition (Allais 2015, 145-47, 154,
159-60).



The distinction between sensation and intuition in Kant's
thinking is fundamental to his overarching conception of space and
time. This is the case for several reasons, not least because one
should avoid thinking that Kant takes us to have a sensation of space;
we have, rather, an intuition of it (see Carson 1997). The distinction
has many facets, but the basic idea is as follows. Sensations are
subjective in the sense that they do not represent objects, they are
modifications of the subject. A good example of a sensation would be
an itch that I feel. Of course, an itch might be caused (e.g.) by some
flour that fell on my nose while baking cookies, but the itch does not
represent the flour, or indeed anything outside myself; the itch is
simply what I feel. If we felt only sensations, we would lack
representations of things other than ourselves, even if such things
caused or helped to cause our sensations. Perhaps sensations would
enable us to avoid injury or pain--one might, say, jump back when
feeling heat from a fire. But without intuition, we would lack spatial
awareness: that is, we would lack an awareness of things in spatial
locations around us. In order to represent things other than
ourselves, we require intutition, which Kant regards as a singular,
immediate, objective representation (where sensations are merely
subjective, as we have seen). In what sense is intuition an objective
representation that is singular and immediate? That complex idea
means, for starters, that intuition represents particulars, i.e.,
things with some spatial location vis-a-vis me and also other
things. So when I feel an itch, I have a sensation; when I see the
pile of flour in front of me next to the bowl on my counter, I have an
intuition, a representation of something in space with a location
relative to me and to other things. However, although intuition
can represent flour on the counter next to the bowl, it does not
represent it *as* flour. For that, one would require a
 *concept*.[3]




As is well known, the distinction between concepts and intuition is
also fundamental to Kant's thought. Whereas intuitions are
singular, immediate representations, concepts are general, mediate
ones (Engstrom 2006). Each item represents properties, objects, or
states of affairs, but they do so distinctly. Unfortunately, there is
no consensus on the right way to understand this
 idea.[4]But
 roughly speaking, intuition represents some *X*--where
*X* might be an object, a property, or perhaps even an
event--as one represents *X* in perception. Thus it
represents *X* as, for instance, *that
 there*.[5]In
 contrast, a concept represents *X*--where, again,
*X* might be a property, an object, or perhaps even an
event--by placing *X* within one or more classes. Suppose
that I want to represent my desk, at which I am sitting right now. To
represent my desk in intuition is to represent it as something I point
to, as *that there*. This does not indicate, of course, that
this is a desk, my desk, a piece of furniture, made of wood, etc., but
it does pick out a particular, something with a spatial location
relative to me and to other things (like the carpet on the floor). It
does so *immediately* at least in the sense that it makes use
of no other representation. To represent my desk with a concept is to
represent it as a *desk*, or as a *piece of furniture*,
or as a *wooden thing*, etc. From Kant's point of view,
this is to represent my desk *mediately* at least in the sense
that the concept, <desk>, represents an object through other
concepts, such as
 <furniture>.[6]
 It is also important to remember that in representing my desk through
intuition, i.e., in representing it as a thing with some spatial
location but not yet *qua* desk, I am *perceiving* the
desk but not *judging* it to be a desk (or anything else). In
order to *judge* that there is a desk in front of me, or
indeed, in order to judge that there is something in front of me, I
require concepts and the complex machinery discussed in the famous
Transcendental Deduction, a key section of the *Critique* that
arrives after the arguments of the Transcendental Aesthetic have been
presented. Intuition alone is akin to perception--it plays a role in
judgment, but it is not itself akin to 
judgment.[7]



One of Kant's surprising ideas is that each type of objective
representation, intuition and concept, can be either empirical or
*a priori*. The idea that some concepts are not empirical may
not be surprising because of the famous early modern
tradition concerning innate ideas. Of course, Kant's
conception of the *origin* of such concepts--outlined in
what he calls the "metaphysical deduction" (B159,
B377)--contains surprises because he does not embrace innate
ideas (Longuenesse 1998). But leaving that complication aside, it is
surely very surprising to hear that intuition, which in some regards
is akin to perception (Parsons 1992, 65-66; Allais 2015,
147*ff*), can also be empirical or *a priori* in
character. Here it helps to recall that Kant distinguishes sensation
from intuition. There remains a question, however, of how we are to
understand the very idea that we can have pure--or *a
priori*, i.e., non-empirical--intuition at all. This idea
comprises a central piece of Kant's views on space and time, for
he famously contends that space and time are nothing but forms of
intuition, a view connected to the claim in the Transcendental
Aesthetic that we have pure intuitions of space and of time. This
means, as we have seen, that we have non-empirical, singular,
immediate representations of space and of time. One goal of this entry
is to clarify this idea. It is not a stretch to contend that it
represents one of Kant's most distinctive contributions to
modern philosophy. Characteristically, it is profoundly difficult to
grasp.


## 3. The "Metaphysical Exposition"


### 3.1 What is a metaphysical exposition?



What Kant calls the Metaphysical Exposition of the Concept of Space
presents the first arguments of the Transcendental Aesthetic. Kant
defines the "exposition" of a concept as follows:
"By an exposition (*expositio*) I understand the clear
(if it is not explicit) representation of what belongs to a concept;
it is metaphysical if it contains what the concept presents as *a
priori* given" (A23/B38). By a concept (*Begriff*) in
this context I take Kant simply to mean a
 representation.[8]
 So his goal is to characterize the content of the representation of
 space. For Kant, an "exposition" is different from a definition: he
 is not undertaking a definition of space, the word
 'space,' or the concept <space> (for helpful
 discussion, see Dunlop 2012). In this regard, Kant follows a long
 tradition emanating from Newton's Scholium following the
 Definitions in the
*Principia*, where Newton explains that space, time and motion
are familiar to everyone and therefore will not be defined in his
work, unlike unfamiliar technical concepts like mass or
impressed force, which are defined (Newton 1999, 408). Unlike
Newton, however, Kant focuses primarily on our representation of
space, rather than on space itself. That seems to be expressed by his
notion of an exposition.


### 3.2 The origin of our representation of space



In the first argument of the Metaphysical Exposition, Kant suggests
that the representation of space cannot be empirical:



> 
> 1. Space is not an empirical concept which has been derived from outer
> experiences. For in order that certain sensations be referred to
> something outside me (that is, to something in another region of space
> from that in which I find myself), and similarly in order that I may
> be able to represent them as outside and alongside one another, and
> accordingly as not only different but as in different places, the
> representation of space must already underlie them [dazu muss die
> Vorstellung des Raumes schon zum Grunde liegen]. Therefore, the
> representation of space cannot be obtained through experience from the
> relations of outer appearance; this outer experience is itself
> possible at all only through that representation (A23/B38).
> 



One might wonder what type of view is at issue here. One potential
target is a classic empiricist account of our idea of space, such as
that found in Locke. Acknowledging in the *Essay* that the idea
of space seems to be "remote" from our perception of
objects, Locke contends nonetheless that its origin lies in experience
(*Essay*, 2.13.2-4): perceivers observe objects in close
proximity to one another, including the distance between objects, and
then repeatedly add the ideas of these distances together, thereby
obtaining an idea of as large a single space as they please. According
to Locke's view, a version of which was also defended by Hume
(*Treatise*, 1.2.3), we obtain a representation of
space--not of places, but of the one all-encompassing space,
which *may* be akin to geometric space--from the
perception of spatial relations.



Kant may be focusing attention on the starting place of Locke's
view. It seems that for Locke, we begin with an idea of the distance
between any two bodies; this would presumably involve an idea of these
two bodies as being in different places. Kant may be contending that
in order to represent objects as in different places from one another,
I must represent them as in space. But if this were true, then I would
already have, as it were, the representation of space, and therefore
could not obtain it in the way Locke outlines.



Daniel Warren clarifies this argument in an especially helpful way
(Warren 1998; cf. Allison 2004, 100-104). Certainly, it is not true in
general that in any order to represent any two entities, A and B, as
related in some way, I must represent them as falling into a larger
"space" of some relevant character. Warren gives a useful
example: in order to represent A as "brighter than" B, I
need not represent A and B as being part of a larger
"brightness" space. I *could* do so: I could
represent A and B via the "brightness" relation precisely
by representing A as lying at one end of a brightness spectrum, and B
as lying near its other end. But I need not do so: I could simply
represent A and B themselves, and represent A as brighter than B, as I
might do with two lights (Warren 1998, 200*ff*). The suggestion
is that in order to represent A and B as bearing a *spatial*
relation with one another--say, to represent them as being some
distance apart--I must represent A and B as *in space*. In
that sense, the representation of objects as spatially related may
presuppose the representation of space. The problem for Locke is that
he begins with my perception, or idea, of a distance between two
objects, and then proceeds to construct my idea of space from that
initial point. But if my representation of a distance relation between
any two objects already presupposes a representation of those objects
as in space, then the former cannot be the beginning point of a
process that issues in the latter.

 Some commentators have noted
that Locke--or another classical empiricist--may not be the
only focus for Kant's first argument. At some moments, Leibniz
seems committed to the view that the representation of space is
constructed from particular perceptions of distance relations (and the
like). For instance, in a famous passage in his final letter to
Clarke, Leibniz claims that in order to obtain a representation of
space, one can consider a system of objects, some of which are in
motion, and abstract the notion *same place* from that
 system.[9]
 For A and B to occupy the same place is for them to have the same
relation to the same bodies in space at different times. Space is what
encompasses all such
 places.[10]
 Kant's first argument may have some bite against the view in
this passage as well. Whether Kant's argument also undermines
Leibniz's relationalism about space is a separate issue, and a
matter of
 controversy.[11]

Some commentators have thought that Kant's second argument in
the Metaphysical Exposition is intended specifically to undermine
Leibniz's relationalism (cf. Parsons 1992, 68-9):



> 
> 2. Space is a necessary *a priori* representation that
> underlies all outer intuitions. One can never forge a representation
> of the absence of space, though one can quite well think that no
> things are to be met within it. It must therefore be regarded as the
> condition of the possibility of appearances, and not as a
> determination dependent upon them, and it is an *a priori*
> representation that necessarily underlies outer appearances.
> (A24/B38-9)
> 



Kant claims that although we can represent space as empty, we cannot
represent to ourselves the absence of space. This point would
undermine Leibnizian relationalism if the relationalist claim that
space is not independent of objects is, at least in part, founded on
the claim that the very idea of space existing independently of
objects is incoherent. If one held such a view, one could raise doubts
about relationalism by contending, as Kant does, that we can in fact
conceive of space to be devoid of objects.



The view that space cannot exist independently of objects at any given
instant does seem to entail that space cannot be utterly devoid of
objects. Leibniz thinks that space is the order of the actual and
*possible* relations among objects, so he has the resources to
say that space can contain empty sectors--see *New
Essays*, 127, and L 5: 43--but it seems he cannot claim that
space is *altogether* empty, for then object relations would be
absent. Yet this view seems perfectly compatible with the idea that we
can *conceive* of empty space. Leibniz himself makes repeated
and explicit use of the thought of such a situation when attempting to
undermine the Newtonian view that space is absolute. Instead of
arguing that the idea that space could be independent of objects is
incoherent, Leibniz contends that it violates the principle of
sufficient reason (see L3: 5; L 5: 53), a principle Clarke himself
defends in a distinct version. The "fiction" (L5: 29; cf.
L5: 55) that space could exist independently of objects violates the
principle because the homogeneity and uniformity of space prevent
there from being any reason for God to place the objects of the
universe with one particular orientation within absolute space rather
than with any other possible orientation. The idea that God could
place objects within a pre-existing absolute space with one
orientation rather than another is evidently not incoherent; rather,
God would lack a *reason* for doing this. Similarly, Leibniz
contends that absolutism violates the principle of the identity of
indiscernibles (L4: 16) and that it bears theological difficulties
(L4: 10).



This is not to deny that Leibniz's relationalism intersects with
his understanding of the representation of space. He thinks that we
must not be fooled by the fact that we can think of space as empty of
objects into concluding that space itself is something independent of
objects and their relations. As with all mere abstractions, we must
not reify
 space.[12]



One might read Kant's second argument instead as
straightforwardly targeting the view that the representation of space
is empirical. Kant claims that we cannot represent the absence of
space, but that we can represent space as empty of objects. His point
may be that empiricist philosophers who contend that the
representation of space is obtained from the perception of objects
must bear the burden of explaining how it is possible for us to
conceive of space as empty of such objects. This consideration appears
to be rather weak. But the further contention that one cannot
represent the absence of space may be more difficult for an empiricist
to accept. *Prima facie*, it is difficult to see why, if our
representation of space is indeed empirical in origin, we should lack
the ability to conceive of space's *absence*. This might
be read as Kant's *prima facie* point against an
empiricist view of the representation of space.



In these first two arguments, Kant considers, perhaps among other
things, the origin of our representation of space, concluding that it
is not empirical. It seems, though, that these first two arguments
leave open the question of the *content* of our representation
of space in two important senses. First, Kant's first two
arguments do not explicate what properties we represent space as
having. Do we represent it, for instance, as finite or infinite, as
homogeneous or not? And so on. Second, the first two arguments in the
Transcendental Aesthetic apparently leave it open that the content of
our representation of space could be conceptual. That is, they leave
it open that our representation of space could be a concept, rather
than an intuition--it could be either a general, mediate
representation, or a singular, immediate one. We simply know--if
Kant's arguments are successful--that the representation is
not empirical. And Kant certainly thinks that a non-empirical
representation could be either a concept or an intuition; that is, he
thinks that we have both *a priori* concepts and pure
intuition. Since the idea of pure intuition is puzzling in a way that
the idea of an *a priori* concept may not be, one interpretive
goal is to clarify this idea in the course of understanding the second
two arguments of the Metaphysical Exposition.


### 3.3 The content of our representation of space



In the third and fourth arguments, Kant contends that the
representation of space has a specifiable content that is incompatible
with it being a conceptual representation. That is, he argues that our
representation of space is not a concept, but is in fact an
intuition--it is a singular, immediate representation. As we have
seen, the distinction between sensation and intuition indicates that
this claim does not amount to the idea that we have a sensation of
space (for reasons adduced above). Instead, it amounts to the claim
that we have an objective representation of space, but one that is
singular and immediate.



In order to understand the two arguments intended to establish the
conclusion that we have a singular, immediate representation of space,
it is helpful to recall Kant's attitude toward concepts. From
his point of view, whereas to fall "under" a concept means
to be part of a concept's extension, to fall
"within" a concept means to be part of its intension. Just
as significantly, the extension of a concept, in Kant's way of
thinking, is not the things that instantiate the concept, or the set
of things to which the concept "applies"; rather, it is
the class of concepts that function as sub-groupings falling under
this more general heading. This idea requires clarification.



Consider the *extension* of
 <being>:[13]



![figure 2](figure2.jpg)

Figure 2.




The extension of <being> is those concepts on the conceptual
tree that fall "under" <being>--those concepts
are species of the genus, <being>. Kant speaks of a series of
genus-species relations inhering between the members of the class of
concepts that serve as a given concept's extension; whether a
concept serves as a genus or a species is relative. The concept
<created> is a genus with respect to its species
<material> and <immaterial>, but a species with respect to
the genus <being>. The *intension* of a concept consists
of those concepts that collectively constitute it. Hence the concept
<human> has this intension: "rational animate material
created being." The concepts that collectively constitute a
given concept are often called "Merkmale" or
"Teilbegriffe," or what might be called its conceptual
parts ("Vienna Logic," Ak 24: 913). To construct the
concept <human>, one puts together the concepts
<rational>, <animate>, *<*material>,
<created>, and <being>. To formulate or to grasp the
concept <human*>* just is to grasp these
constituents.



With these distinctions in mind, we can consider Kant's third
argument in the Metaphysical Exposition. In this argument, Kant
concentrates on the intension (in his sense) of a concept.



> 
> 3. Space is not a discursive, or as one says, general concept of
> relations of things in general, but a pure intuition. For, firstly,
> one can represent only one space, and if one speaks of many spaces,
> one thereby understands only parts of one and the same unique space.
> These parts cannot precede the one all-embracing space as being, as it
> were, constituents out of which it can be composed, but can only be
> thought as *in it*. It is essentially one; the manifold in it,
> and therefore also the general concept of spaces, depends solely on
> limitations. It follows from this that an *a priori* intuition
> (which is not empirical) underlies all concepts of space. Similarly,
> geometrical propositions, that, for instance, in a triangle two sides
> together are greater than the third, can never be derived from the
> general concepts of line and triangle, but only from intuition and
> indeed *a priori* with apodictic certainty. (A24-5/B39-40; cf.
> "Anticipations of Perception" at A169-70/B211)
> 



The suggestion here is roughly this: if the representation of space
were a concept rather than an intuition, one ought to be able to
construct it by placing its parts together. This seems to require that
it is possible to represent the parts independently of representing
the concept to be constructed. This is the case with other concepts:
it is possible to represent any of the parts of the intension of
<human>, such as <material being>, without *ipso
facto* representing the whole concept, <human>. Kant is
claiming that this will not work in the case of the representation of
space because we obtain the representation of places only by
delimiting some subsection of our representation of the one
all-encompassing space. To put the point in a way that highlights a
parallel with the first argument of the Metaphysical Exposition: the
representation of any place presupposes the representation of space.
Thus we cannot represent any of the "parts" of
space--any place--without *ipso facto* representing
space itself. The idea, then, is that the part-whole relation of the
representation of space is distinct from the part-whole relation that
obtains for concepts.



It is not clear that this argument is successful. It seems, e.g., to
conflate the following: (1) the relation between space and its parts;
and, (2) the relation between the representation of space and its
constituents. Without this conflation, it is not clear why we should
expect to construct our concept of space from our concept of place. It
would seem more sensible to construct our concept of space from other
concepts, such as that of infinity, or that of a magnitude, and so on,
rather than from the concept of a place. The claim of the conflation
is predicated on the notion that Kant's third argument concerns
the representation of space rather than space itself. This notion, in
turn, may conflict with the letter, although perhaps not with the
spirit, of the first sentence of the third argument, which mentions
that "Der Raum," or space, is not a concept, but rather is
an intuition. If one follows the letter of the argument, one can avoid
this apparent conflation. But the price is somewhat high: what does it
mean to wonder whether space itself is a concept, and who held
something like that view? On the face of it, such a view may seem
rather odd to the contemporary
 reader.[14]
 One way to make progress in understanding this view is to re-read
Leibniz. It is possible to read Leibniz as arguing that space itself
is a kind of abstraction, rather than a real entity or substance, and
perhaps it is not a stretch to contend that space must be a conceptual
abstraction, like the entities of what Leibniz might call pure
mathematics. That is, space itself, on this view, is a kind of
conceptual abstraction in the way that an isosceles triangle is an
abstraction, or a line is an abstraction, rather than a real entity or
substance. Of course, this requires us to understand Leibniz's
position through a Kantian lens. Even so, if the view in focus is that
space itself is a kind of concept, it remains unclear why one
wouldn't say that this concept is dependent on other
constitutive concepts, such as the concept of infinity or that of
homogeneity, which Kant himself tackles in the next numbered argument.
Perhaps the best answer here is to read Kant as engaging specifically
with Leibniz's argument in his last (fifth) exchange with
Clarke, mentioned above. The idea is that Leibniz's argument
might be understood as involving the claim that the concept of place
is constitutive of the concept of space, and that space itself is
really nothing but a kind of concept, which licenses the exclusive
focus on the concept of space. Then the claim would be that the
Leibnizian view that space itself is a conceptual abstraction obtained
through some process of perceiving objects occupying various places is
wrong on both counts.



Just as Kant's second argument attempts to shore-up the idea,
presented in the first argument, that the representation of space is
*a priori*, his fourth and final argument attempts to shore-up
the idea, presented in the third argument, that the representation of
space is not conceptual in character. Here both the extension and the
intension of concepts seem to be at issue:



> 
> 4. Space is represented as an infinite *given* magnitude. Now
> one must think every concept as a representation which is contained in
> an infinite number of different possible representations (as their
> common mark), and which therefore contains these *under
> itself*; but no concept, as such, can be thought as if it
> contained an infinite number of representations *within
> itself*. It is in this latter way, however, that space is thought
> (for all the parts of space are simultaneous in infinity [denn alle
> Teile des Raumes ins Unendliche sind zugleich]). Therefore the
> original representation of space is an *a priori intuition*,
> not a *concept* (B40).
> 



Kant claims that since we represent space as containing an infinite
number of places within it, our representation of space cannot be
conceptual. Why should that be? The idea is that although concepts can
have an infinite extension--a potentially infinite number of
subordinate concepts *under* them--they cannot have an
infinite intension, an infinite number of representations
*within* them. A concept that is infinite in the latter sense
could not be grasped by a finite
 mind.[15]
 For a concept to have an infinite extension would be for it to have
an infinite number of species, i.e. for it to be possible to
distinguish an infinite number of sub-types "under" it on
the conceptual tree. This does not harm our ability to grasp any
concept within the tree, for to grasp any arbitrarily chosen concept
within the tree, I merely need to grasp its constituents (those
concepts *within it*), and those would be "above"
it on the tree. But our ability to grasp concepts would be affected if
they could contain an infinite number of constituents *within
themselves*: if, say, <fish> contained an infinite number of
constituents--if there were an infinite number of higher-level
conceptual taxa "above" <fish> on the tree--it
could not be grasped, and might even lack determinate content. Or at
least, to specify its content would take an infinite number of
steps.



According to Kant, however, we represent space as having an infinite
number of constituents, namely
 places.[16]
 If our representation of space were conceptual, we would be required
to represent each of these constituents *in order to represent
space itself*, just as we are required to represent metal in order
to represent gold (for <gold> catergorizes gold as a metal). Yet
we cannot represent every place within space in an effort to represent
space itself. If we can take it as settled that we represent space,
and as settled that we represent it as having an infinite number of
places within it, then our representation of space presumably cannot
be conceptual in Kant's sense. The third argument in the
Metaphysical Exposition seems to imply, as we have seen, that the
representation of any place presupposes the representation of space
itself. This fourth argument makes a distinct point: if the
representation of space itself were to require the representation of
each part that we represent space as having, then we could not
represent space at all. Since we do represent space, and since we do
represent it as having an infinite number of places within it, our
representation of space is not conceptual in Kant's sense. Of
course, Kant's readers may deny one of his apparent assumptions
here, viz., that we represent space as infinite. Readers with broadly
empiricist sympathies in particular may be skeptical of this
assumption.



Kant's view that we have an intuition, rather than a concept, of
space can be seen to raise a difficult problem: space is not an
object, and yet intuition seems to provide us with something akin to a
perception of something. As Lucy Allais puts it, intuition involves
"presence to consciousness of an object" (Allais 2015,
197*ff*), and yet space is not an object. It is difficult to
see why we should think of ourselves as perceiving space at all. It is
easy enough to understand the idea that some ordinary thing, like a
tomato, is an object that is present to my consciousness, say when I
look at the tomato on a farm stand. There are, of course, many
philosophical theories of perception, and these theories will differ
in their discussions even of simple cases of perception such as this
one. But it seems uncontroversial to suppose that the tomato is
present to my consciousness as an object at least in the sense that
the tomato is one of the things that I'm looking at. And it also
seems uncontroversial to think that there are many other things,
besides tomatoes, that might be present to my consciousness in a
similar way, from clouds to fog to rainbows, even though they are not
"objects" in the simple sense in which a tomato is an
object. However, it certainly seems like a stretch to say that space
itself might be one of those things. That is not merely because space
is not an object in any clear sense; it is also because space itself,
in this historical and philosophical context, is not something that
has a causal impact on me. So it remains doubly difficult to see how I
might conclude, with Kant, that I have something akin to a perception
of space. Kant assures us, of course, that we have an *a
priori* intuition of space, so although he is discussing something
akin to perception in one sense, in another sense what he is
discussing is supposed to be quite distinct from ordinary perception.
Whether that assurance helps to clarify this issue for his readers is
a matter of debate. What is clear, however, is that this aspect of
Kant's conception of space remains one of the most
controversial, and most difficult, aspects of his theoretical
philosophy.



Kant may have other reasons for thinking that our representation of
space is not a concept. If we recall Kant's view that concepts
are general, mediate representations, and his view of how these facts
are reflected in the conceptual trees discussed above, then there is
indeed at least a *prima facie* puzzle as to how we could have
a concept, in Kant's sense, of space. Consider a contrast class.
Even if we think that <God> represents only a single entity,
that fact does not undermine Kant's view that this concept is a
general, mediate representation (cf. Thompson 1972, 318-19, 328-29).
For we represent God, in Kant's view, by representing it through
other concepts: for instance, God is a necessary substance
(A678/B706), so <God> is a mediate representation. This is
distinct from the way in which an intuition represents something. And
the concept <substance>--which is one of the
categories (A80/B106)--is a representation that we can grasp
independently of grasping <God>. Hence <substance> is a
constituent of <God>, but not *vice versa*. Moreover,
<God> is a *general* representation because it places God
within another class, namely the class of substances. It will then be
a matter of some dispute whether the *generality* criterion and
the *mediacy* criterion amount to the same thing (cf. Parsons
1992, 63-6). But the key point here is this: the fact that
<God> picks out a single individual--and perhaps even,
*can pick out only a single individual*--does not entail
that this concept is not general or mediate. This suggests, in turn,
that Kant's point in the Metaphysical Exposition cannot be that
our representation of space picks out a single individual and
therefore cannot be a concept. Rather, he presumably thinks that we do
not represent space either: (1) by representing its constituents,
namely places; or (2) by representing it *through* other
concepts. We have discussed (1) above; what about (2)?



Concerning (2), note that to represent space by representing it
through other concepts may require one to take a (usually
controversial) stand on the ontology of space in one of the senses
outlined above. For instance, if one wishes to place <space>
somewhere on the conceptual tree, one must presumably find a place for
it under some concept such as <substance> or <being>. But
there is no accepted view of space's ontology: some regard it as
a substance (or a being), others as a network of relations, others as
a property of God, etc. Because of these long-standing, unresolved
disputes, it seems reasonable to regard an approach that depends on
their resolution as unpromising. Kant highlights the accepted fact
that we represent space as an infinite Euclidean magnitude--this
can be widely accepted, despite the dispute concerning space's
ontology.



Another way to clarify Kant's arguments regarding conceptuality
is to consider what opponent he has in mind for the second two
arguments. It seems unlikely that Locke's views are at issue in
these arguments--instead, Kant probably had Leibniz in mind.
Leibniz held the view that the idea (or representation) of space hails
from the pure understanding, which he contrasts with the kind of
Lockean view noted above. He writes in the *New Essays*:



> 
> 
> PHILALETHES: The ideas the perception of which comes to us "by
> more than one sense, are of space, or extension, figure, motion and
> rest."
> 
> 
> 
> THEOPHILUS: These ideas, which are said to come from more than one
> sense - like those of space, figure, motion - come rather
> from the common sense, which is to say, from the mind itself; for they
> are ideas of the pure understanding, though ones which relate to the
> external world and which the senses make us perceive, and so they
> admit of definitions and demonstrations. (*New Essays*, 128;
> see Leibniz 1840, 230)
> 
> 
> 



Leibniz may have in mind the idea that our perceptions cannot give us
the idea of a continuum, and he certainly thinks of space as a
continuum. The senses, for instance, cannot give us the idea of
something that is infinitely divisible. Elsewhere in the *New
Essays*, Leibniz makes a related point by saying that space is
akin to the entities of "pure mathematics."



One question here is whether Leibniz and Kant agree sufficiently in
their views of concepts for Kant's arguments to have any bite
against the kind of view Leibniz expresses in the *New Essays*,
a text that Kant read sometime after it was first available in 1765
(Vaihinger 1922, 2: 133, 414 and 428-9). Leibniz, famously, has the
idea of a complete concept of a substance, and it seems that such as
concept would contain an infinite number of constituents--God
grasps the complete concept of a substance by grasping all its
constituents. Given this view, it may be that the considerations
adduced in Kant's fourth argument in the Metaphysical Exposition
are unlikely to worry Leibniz, since he would simply accept the idea
that the representation of space, as with any concept, might have an
infinite number of constituents (Posy 2000). However, the third
argument may have more bite: if Kant is right in contending that the
representation of any place presupposes the representation of space
itself, then perhaps that representation lacks the ordinary part-whole
structure of a concept. Leibniz may in fact accept that general
conception of the part-whole structure of concepts. If so, this third
argument may present a problem for his view.



Yet the first and second arguments of the Exposition are not merely
opportunities to contend with empiricist views like those of Locke;
nor are the third and fourth arguments merely aimed at challenging
rationalist views like those of Leibniz. On the contrary, the claim
that the representation of space is neither empirical nor conceptual
is important in general for Kant's transcendental idealism and,
in tandem, it is significant for understanding what he regards as the
philosophical mistakes embodied in transcendental realism, and in what
Kant will later call "dogmatic idealism," both of which he
strongly opposes. These are discussed in the next section.


## 4. The "Transcendental Exposition" and Kant's "conclusions"


### 4.1 What is a transcendental exposition?



In the B (1787) edition of the *Critique*, SS2 of the
Transcendental Aesthetic, the Metaphysical Exposition, is followed by
SS3, the Transcendental Exposition. Whereas the Metaphysical
Exposition deals, as we have seen, with the origin and the content of
the representation of space, its transcendental cousin apparently
attempts to provide an explanation of what Kant takes to be the
synthetic a priori knowledge (or cognition) available to us in
geometry. This raises very difficult interpretive issues that arise
with Kant's philosophy of mathematics--such issues are
dealt with in a separate entry in this *Encyclopedia* (see Lisa
Shabel's entry on
 Kant's philosophy of mathematics).
 However, Kant may also be raising a related point in this
section--consider the following passage, which is inserted within
the discussion of geometry (cf. section 2-b above):



> 
> Now how can an outer intuition inhabit the mind, which precedes the
> objects themselves, and in which the concept of the latter can be
> determined *a priori*? Obviously not otherwise than insofar as
> it has its seat solely in the subject, as its formal constitution for
> being affected by objects, and thereby gaining *immediate
> representation*, i.e., *intuition*, of them, therefore only
> as the form of outer *sense* in general. (B41)
> 



We have seen in the Metaphysical Exposition that we have a pure (or
*a priori*) intuition of space, that is, a non-empirical,
singular, immediate representation of space. But how is such a
representation so much as possible? If we are considering an
*empirical*, singular, immediate representation, we can easily
understand that in cases of ordinary perception, we can (e.g.) see a
rose in a vase in front of us. Hence our perception may include a
singular, immediate representation--that is, we may represent
*that there*, an object with a spatial location. This empirical
case is reasonably clear, but what does it mean to contend that we
have a non-empirical, singular, immediate representation? This cannot
be akin to a case of seeing an object directly in front of us, for one
of Kant's points in the Metaphysical Exposition, as we have
seen, is that the representation of places, and of objects as bearing
spatial relations, *presupposes* the (non-empirical)
representation of space. But if our representation of space is not
akin to seeing something directly in front of us, then what makes it
immediate and singular? Kant's suggestion in the passage above
appears to be that intuition must somehow have its seat in the
subject--it must somehow be a "form" of the mind, or
more precisely, of what Kant calls here "outer sense".
This obviously brings us very close to the formulation of
transcendental idealism--that view is stated explicitly for the
first time in the *Critique* in the very next paragraph of the
Transcendental Aesthetic. But the paragraph quoted above, coupled with
Kant's discussion of what a Transcendental Exposition is meant
to be, suggests that part of Kant's goal here is to *explain
how a non-empirical, singular, immediate representation of space is
possible*. (This is parallel to explaining how synthetic *a
priori* knowledge within geometry is possible.)



Similarly, some commentators have noted that the
"conclusions" following the Transcendental Exposition (in
the very next paragraph following the one quoted above) are given no
additional argumentative support, and are therefore intended to follow
from the arguments within the Metaphysical Exposition and the
Transcendental Exposition. That is, the view that the representation
of space is an a priori intuition is supposed to entail the rather
robust conclusions about space that Kant reaches in the Transcendental
Aesthetic. His first such conclusion--labeled "a" and
followed by another conclusion labeled "b"--is rather
startling:



> 
> Space represents no property at all of any things in themselves, nor
> any relation of them to one another, i.e., no determination of them
> that attaches to objects themselves and that would remain even if one
> were to abstract from all subjective conditions of intuition. For
> neither absolute nor relative determinations can--prior to the
> existence of the things to which they pertain, thus *a
> priori*--be intuited. (A26/B42)
> 



Among other things, Kant returns here to the debate concerning space
and time between the Leibnizians and the Newtonians mentioned at the
outset of the Transcendental Aesthetic. It seems that Kant intends his
view to be contrasted with the Newtonian view of space, which
apparently tells us something about its "absolute"
determinations, and also with the Leibnizian view, which apparently
tells us something about its "relative" determinations.
Perhaps Kant is suggesting here that the Newtonian and Leibnizian
views of space and time, despite their evident differences along
various dimensions, each indicate that the representation of space
cannot be a non-empirical, singular, immediate representation, or
perhaps they tacitly suppose that it cannot be such a representation.
If he is suggesting that idea, one wonders why that would be the case.
I discuss this issue in the next section.



In the next few paragraphs of the Transcendental Aesthetic, Kant
reaches the famous conclusions that we can speak of space "only
from the human standpoint" (A26/B42) and that space has
"transcendental ideality" (A28/B44). This is the heart of
one of Kant's main positions in the *Critique of Pure
Reason*. In order to clarify these ideas, I first follow
Kant's suggestion in the passage above that he intends his
position to be contrasted in some respects with the positions of
Leibniz and of Newton. This maneuver will place us in a position to
understand transcendental idealism in a bit more depth.


### 4.2 Absolute/relational vs. real/ideal



Various confusions can plague one's understanding of the modern
debate between absolutism and relationalism about space and
time--some of these confusions are especially pervasive in
discussions of Kant's views. For instance, absolutism is
sometimes conflated with realism, and idealism with relationalism. One
reason for the first conflation may be historical in nature. In their
celebrated correspondence, which forms part of the essential
background to Kant's work on space and time in the
*Critique*, Clarke and Leibniz often consider the proposition:
*space is real*. By our lights, realism and anti-realism
concern the question of whether something is in some sense dependent
on the mind. We ask this question about tables and chairs, numbers and
sets, and all manner of other things. But when Leibniz and Clarke
discuss the "reality," or the "absolute
reality," of space, they are typically concerned with the
question of space's status vis-a-vis objects. This is
clearly the case when Leibniz and Clarke consider one of the principal
questions of their correspondence, whether their common acceptance of
the principle of sufficient reason entails that one of them holds the
correct conception of space (cf. L3: 4 and C 3: 4-5). Leibniz
contends, while Clarke denies, that if space were independent of
objects, God would lack a sufficient reason for placing the objects of
the universe into space with one orientation rather than another.
Leibniz concludes from this that space lacks "reality" or
that it lacks "absolute reality" (see L5: 29 and L5: 36).
*Based on precisely the same considerations*, Leibniz denies
that space is "absolute" (L3: 2-3, L3: 5, L4: 16, L4:
9-10) and contends that it is "relative" (L3: 4).
Hence in this context, for space to be *real* is for space to
exist independently of objects and relations.



Likewise, Leibniz's contention that space is *ideal* (L5:
33) serves as his response to Clarke's claim (C4: 7) that there
can be "extramundane" space, that is, space beyond the
boundaries of the object-universe. Here, too, the contention that
space is ideal--or that it lacks reality--amounts to the
contention that it *cannot exist independently of objects*.
This is evident in a passage from Leibniz's last letter:



> 
> I have demonstrated that space is nothing other than an order of the
> existence of things observed in their simultaneity. And therefore the
> fiction of a material finite universe, moving forward in an infinite
> empty space, cannot be admitted. It is altogether unreasonable and
> impracticable. For, besides that there is no real space out of the
> material universe, such an action would be without any design in it:
> it would be working without doing any thing...It would produce no
> change which could be observed by any person whatsoever. These are
> imaginations of philosophers who have incomplete notions, who make of
> space an absolute reality [realite absolue] (L 5: 29).
> 



Note that by "real space out of the material universe"
Leibniz does not mean space *independent of the mind*, but
rather, space *independent of objects*.



This is not to say that there is no discussion of space's status
relative to the mind in the correspondence. Leibniz asserts in his
last letter that relations are "ideal" because they are
neither substances nor accidents, and are therefore not elements of
reality (L5: 47). As he writes in the *New Essays*, in reality
there are only substances and properties of substances; the mind
"adds" relations (*New Essays*, 2.12; cf. also
2.30.4 and 2.25.1). Since space is the order of the possible relations
of objects, it is presumably ideal in the sense of being
mind-dependent. But Leibniz's point here seems to be that just
as people reify relations, thinking they exist independently of
objects, they reify space, thinking it too exists independently of
objects. So even when Leibniz discusses the ideality of space, he does
so to indicate that we need not think of relations and of space as
absolute in order to account for the tendency toward reification.



The ideality and reality of space bear a different significance for
Kant than they do for Leibniz and Clarke. For Kant, asking whether
something is real or ideal concerns its status vis-a-vis the
mind. One of Kant's most explicit discussions of realism and
idealism appears in the Fourth Paralogism (A368-380), where he is
concerned with the possible mind-dependent status of objects and with
the status of our knowledge of their existence. Although it is clear
that Kant is discussing the status of spatial objects vis-a-vis
the mind, *in part by discussing the relation of space and time to
the mind*, there is no treatment here of the status of space and
time vis-a-vis objects *per se*.



> 
> But I understand under the *transcendental idealism* of all
> appearances the doctrine according to which they are all together to
> be regarded as mere representations, and not as things in themselves,
> and accordingly that space and time are only sensible forms of our
> intuition, but not determinations given for themselves, or conditions
> of objects as things in themselves. This idealism is opposed by
> *transcendental realism*, which considers space and time as
> something given in themselves (independent of our sensibility). The
> transcendental realist therefore represents outer appearances (when
> one grants their reality) as things in themselves, which would exist
> independently of us and our sensibility, and therefore also would be
> outside us according to pure concepts of the understanding. (A369)
> 



In light of these points, consider the following table:




|  |  |
| --- | --- |
| **Realist relationalism**1. Space is the order of possible relations among objects
2. Relations are mind-independent
 | **Idealist relationalism**1. Space is the order of possible relations among objects
2. Relations are mind-dependent
 |
| **Realist absolutism**1. Space is an object-independent framework for object relations
2. Space is mind-independent
 | **Idealist absolutism {?}**1. Space is an object-independent framework for object relations
2. Space is mind-dependent
 |



A realist can be a relationalist if she thinks space is the order of
actual and possible relations among actual (and maybe possible)
objects and she thinks those relations are *real*. This
indicates, incidentally, that realists about space need not think of
it as a kind of *object*: it can be perfectly real *and*
the order of possible relations among objects. Indeed, Kant himself
may have held this view in his *Physical Monadology* of 1755:
he still accepted Leibinzian relationalism, but he rejected the
Leibnizian construal of relations, holding them to be aspects of
 reality.[17]
 Similarly, some contemporary defenders of relationalism seem to hold
the view that space is the order of actual and possible relations
among actual and possible objects, and those relations are perfectly
real, that is, they are not dependent on the mind in any sense.



Absolutism raises other difficulties. It is possible to think of space
as an instantaneous framework projected onto reality by the
 mind.[18]
 If space is such a mind-dependent framework, it could still be
thought of as independent of objects. At any rate, if absolutism
indicates that space is independent of all objects and relations, and
if that is held to entail that it must be independent of the mind as
well, we probably require some clarification of this entailment, for
it is not obvious (Ishiguro 1972, 109). In fact, Kant may have
defended an absolutist-idealist conception of space in the
*Inaugural Dissertation* of 1770 (Friedman 1992, 29-31).
Clarity can be achieved only if one avoids conflating these myriad
views.



Kant consistently writes in the *Critique* of ideality and
reality in the more familiar modern sense, where mind-dependence is at
issue. His usage serves to shift the philosophical discussion
concerning space from a focus on relationalism and absolutism to one
on idealism and realism. Hence when he reflects on the Newtonian and
Leibnizian conceptions of space and time in general terms in the
Transcendental Aesthetic, he eschews a discussion of the relative
merits of absolutism and relationalism in favor of discussing the
common mistake of his predecessors. For instance, after outlining his
conception of space and time, Kant claims: "Those, however, who
assert the absolute reality [*absolute Realitat*] of space
and time, whether they take it to be subsisting or only inhering, must
themselves come into conflict with the principles
[*Principien*] of experience" (A39/B56). The former
group, also called "the mathematical investigators of
nature," is clearly identified with the Newtonians, and the
latter, the "metaphysicians of nature," with the
Leibnizians (cf. Shabel 2005, 31, 45-9). So transcendental idealism is
articulated as a kind of *replacement* for the Leibnizian and
Newtonian conceptions of space and time, but it is not their status as
relationalist and absolutist conceptions, respectively, that calls for
their replacement. Rather, it is their status as representatives of a
separate and overarching conception of space, a conception according
to which space (like time) is said to bear an "absolute
reality." This occurrence of 'absolute' clearly
cannot have the meaning that Leibniz and Clarke intend.



This raises a difficult question. Kant contends that transcendental
idealism as a general conception of space is to be contrasted with
transcendental realism, a position he attributes both to Newton and to
Leibniz. Yet from Leibniz's point of view, the only elements of
reality are substances and their properties. Relations, which are
neither substances nor properties, are not among such elements, if we
are speaking with metaphysical rigor. This is evident in a number of
texts; for instance, in response to his Lockean interlocutor, Leibniz
writes in the *New Essays*: "This division of the objects
of our thoughts into substances, modes, and relations is pretty much
to my liking. I believe that qualities are nothing but modifications
of substances and the understanding adds relations
[l'entendement y adjoute les relations]." He adds that
relations are "the work of the understanding" (*New
Essays*, 145). Since space for Leibniz is just the order of object
relations, and relations are ideal, space too is ideal in some sense
(*New Essays*, 145; cf. Cassirer 1902, 248). That is to say,
there is a sense in which spatiality does not characterize reality
(Adams 1994, 254-5). These views are to be found in the letters to
Clarke and in the *New Essays*, both of which Kant read, and
Kant himself explicitly mentions some of
 them.[19]
 The obvious obstacles to understanding Leibniz as a realist
complicate the interpretation of transcendental idealism, since Kant
clearly thinks it is an alternative to both Leibniz's and
Newton's allegedly realist views. This problem is tackled
in the next section.


## 5. What is transcendental realism?


### 5.1 Kant's criticisms of Leibniz



Why might Kant characterize Leibniz as holding some version of the
"transcendental realist" perspective that he also
attributes to Newton? This characterization is puzzling, as we have
seen. If we return to the conceptual matrix above, it is not merely
that Leibniz considers space to be the order of the possible relations
among objects, and therefore to be dependent upon objects and their
relations; it is also the case that he explicitly adopts the common
early modern view that relations are *ideal* in the sense that
they are somehow dependent upon the
 mind.[20]
 So *prima facie*, if space is a relational order, or dependent
upon relations, and relations, in turn, are dependent upon the mind,
then it seems that space is itself dependent upon the mind. Thus
Leibniz appears to deny that space is *real* in a
*Kantian* sense. Denying that space is real can be equivalent
to denying that space is absolute; but Leibniz's relationalism,
*coupled* with his familiar early modern view of relations (an
independent metaphysical thesis), seems to entail that space is
*also* not real in the sense that it is not independent of the
mind. In what sense, then, can Leibniz be called a transcendental
realist? *Prima facie*, it is unfair to interpret him in this
way.



We might return to the first description in the *Critique* of
the Leibnizian position regarding space and time, which appears just
before Kant begins the Metaphysical Exposition of Space. He asks of
space and time: "Are they only determinations or also relations
of things, yet such as would belong to things even if they were not
intuited?"
 (A23/B38).[21]
 This may suggest what Kant has in mind when he contends that the
Leibnizians think of space and time as bearing an "absolute
reality." Perhaps what he means is that for Leibniz, space has a
reality *independent of intuition*, or that space exists
independently of intuition *per se*, even though it may not be
independent of the mind *per se*. But then what might this idea
mean in more detail?



In his extensive discussion of Leibniz in the so-called Amphiboly,
Kant suggests that Leibniz's transcendental realism might be
expressed in his view that space and time are *phenomena bene
fundata*:



> 
> Fourth, the famous *doctrine of time and space*, in which he
> intellectualized these forms of sensibility, arose solely from this
> very same deception of transcendental reflection. If I would represent
> outer relations of things through mere understanding, this can be done
> only through a concept of their reciprocal effect, and if I should
> connect a state of one and the same thing with another state, then
> this can only be done in the order of grounds and consequences. Thus
> Leibniz thought of space as a certain [gewisse] order in the community
> of substances, and of time as the dynamic sequence of their states.
> The uniqueness and independence from things, however, which both of
> these seem to have in themselves, he ascribed to the
> *confusion* of these concepts, which made that which is a mere
> form of dynamical relations be taken for a single intuition subsisting
> by itself and preceding the things themselves. Thus space and time
> became the intelligible form of the connection of things (substances
> and their states) in themselves (A275-6/B331-2).
> 



Space is the order of the actual and possible relations of objects;
since objects reflect the order of substances (in some
very-difficult-to-specify sense), space itself reflects the order of
substances, albeit in a confused manner (see Langton 1998, 68-96).
Whereas a conceptual representation of this circumstance would provide
one with a representation of the monadic order, sensibility
misrepresents space as an independent entity. Hence space is
independent of intuition in that it is the order of relations, and
that order reflects or expresses the order of substances, which itself
is independent of
 intuition.[22]
 Hence space is viewed as "a certain order in the community of
substances," a variant of which Kant himself defended in the
pre-critical period (see Friedman's introduction to
*Metaphysical Foundations*, 174).



This indicates, in turn, how to interpret the idea that transcendental
realism can involve different portrayals of space's relationship
with objects. One may think that space is independent of intuition by
claiming that it supervenes on the order of substances (which itself
is independent of intuition); or, one may think that space is
independent of intuition by claiming that space is an independently
existing entity. The former is the Leibnizian view, the latter the
Newtonian. Kant suggests as much in the Transcendental Aesthetic:



> 
> We dispute all claim of time to absolute reality [absolute
> Realitat], namely where it would attach to things absolutely as a
> condition or property even without regard to the form of our sensible
> intuition. Such properties, which pertain to things in themselves, can
> also never be given to us through the senses. Therefore herein lies
> the *transcendental ideality* of time, according to which, if
> one abstracts from the subjective condition of our sensible intuition,
> it is nothing at all, and can be considered neither as subsisting nor
> as inhering in the objects in themselves (without their relation to
> our intuition). (A36/B52)
> 



The absolutist construal of transcendental realism contends that space
and time "subsist" on their own, i.e., independently of
objects. The relationalist construal of transcendental realism
contends that space and time "inhere" in the objects, that
is, they do not exist independently of them. And as we have seen,
Leibniz would also contend that ordinary objects themselves somehow
inhere in the monadic
 order.[23]



But how does Leibniz's conception of the representation of space
square with Kant's reading? In his latter letter to Clarke,
Leibniz attempts to show that we can form an idea of space without
relying on the notion that space is somehow independent of the
relations of objects (L 5: 47). Since he talks of people
"observing" various objects and their relations to one
another, it can sound as if he thinks that the idea of space is
obtained through sensory experience of object relations. But which
idea of space does he have in mind? In other words, what is the
content of the idea of space that he has in mind? He may mean that one
can gain a rough and ready idea of space--of a three-dimensional
magnitude that is not itself a property of any object or grouping of
objects--in the way that he describes. But surely one cannot gain
the mathematical view of space in this way, for several reasons that
Leibniz expresses in the *New Essays* (as noted above): (a)
space and time are entities in pure mathematics; (b) space is a
continuum, and one certainly cannot obtain that notion from the sense
perception of object relations; and, (c) sense perception will
generate a confused idea, but to have a clear and distinct idea of
space, one indicating its properties as a mathematical entity,
requires something other than sense perception. So it seems reasonable
to distinguish between an ordinary, everyday conception of
space--one in which we need not consider whether it is infinite
or finite, infinitely divisible or finitely divisible, or perhaps
whether the parallel postulate holds, etc.--and our geometric
conception of space. There can be little doubt that Kant has our
geometric conception of space in mind throughout the Transcendental
Aesthetic--this is clear in the third argument of the
metaphysical exposition and throughout the transcendental
exposition.



So for Leibniz, <space>confused arises from our
perceptual experience with objects, but <space>clear &
distinct could not possibly so arise. Kant himself emphasizes,
not only in the Amphiboly, but also in the Aesthetic itself, that the
Leibnizians are committed to the view that
<space>confused arises from our perceptual experience
of objects and their relations. In SS7 of the Aesthetic (in the B
edition), he writes:



> 
> If they take the second position (as do some metaphysicians of
> nature), and hold space and time to be relations of appearances (next
> to or successive to one another) that are abstracted from experience,
> though confusedly represented in this abstraction, then they must
> contest the validity or at least the apodictic certainty of *a
> priori* mathematical doctrines with respect to actual things
> (e.g., in space), since this certainty does not at all occur *a
> posteriori*, and according to this view the *a priori*
> concepts of space and time are only creatures of the imagination, the
> origin of which must actually be sought in experience, out of whose
> abstracted relations imagination has made something that certainly
> contains what is general in them but that cannot occur without the
> restrictions that nature has attached to them. (A39/B56-A40/B57)
> 



We might read Kant's Leibniz as committed to the following
claims:



(1)
<space>confused arises from our perceptual
 experience, as outlined in the last letter to Clarke; and,
(2)
<space>clear & distinct arises when we
 remove the confused perceptual elements from
 <space>confused, thereby obtaining a clear and
 distinct idea, that is, a conceptual representation of
 space.

We can then see the first two arguments in the Metaphysical Exposition
as attempting to undermine (1), and the second two arguments as
attempting to undermine (2). Thus Leibniz denies that we have an *a
priori*, singular, immediate representation of space. Instead, he
thinks we begin with an empirical representation of space, remove the
confused elements of that representation, and thereby obtain a clear
and distinct idea, i.e., a conceptual representation of an abstract
mathematical
 entity.[24]



This discussion is reminiscent of Kant's fundamental
disagreement with the Leibnizians regarding what Kant calls
"sensibility" and "understanding." In the
General Remarks on the Aesthetic, we read:



That, therefore, our entire sensibility is nothing but the confused
representation of things, which contains solely that which pertains to
them in themselves, but only under a heap of marks and partial
representations that we can never separate from one another
consciously, is a falsification of the concept of sensibility and of
appearance, which renders the entire theory of them useless and empty.
(A43/B60)



Kant wishes to oppose this Leibnizian attitude toward
sensibility--which he goes on to label an "entirely unjust
perspective" (A44/B62)--in a general but thoroughgoing way
in the Aesthetic and elsewhere in the *Critique*. In the
Amphiboly, for instance, he complains that Leibniz "left nothing
for the senses but the contemptible job of confusing and upsetting the
representations" of the understanding (A276/B332). Thus Kant
does not merely think that we have a non-empirical, singular,
immediate representation of space. He thinks--if we borrow
Leibnizian terminology--that our clear and distinct
representation of space is singular and immediate. For Kant, intuition
can be a genuine source of clear and distinct representations.



If we return to Kant's fundamental conception of representation,
according to which sensation is a representation of the
subject's state, and intuition is an "objective"
representation, we might characterize Kant's critical attitude
toward the Leibnizians as follows: they conflate intuition with
sensation, or construe intuition as a kind of sensation. The
Leibnizians fail to recognize that intuition is a kind of objective
representation, rather than a merely confused representation, one that
is confused because it actually represents a state of the subject
while purporting to represent objects. According to
*Kant's* Leibniz, when I have a red book in front of me,
and then have a sensation of redness, my senses represent the book as
having a property that is similar to my sensation, when in fact it
bears a distinct property (say, a surface texture of some kind). This
*may* be the right view of the sensation of secondary
qualities--the Leibnizian error lies instead in assimilating all
cases of perception to this kind of case, and thereby concluding that
perception presents us only with confused ideas. If we rigorously
distinguish sensation from intuition a la Kant, then we open
the possibility of objective representations that are akin to
perceptions. We do not have a *sensation* of an infinite
Euclidean magnitude (!), but we do have a singular and immediate
representation of it. The Leibnizians lack room for this option.


### 5.2 Kant's criticisms of Newton



Kant focuses most of his critical gaze in the Aesthetic on Leibniz and
the Leibnizians. This may reflect the fact that Leibniz held, as we
have seen, well-developed views concerning space and time and their
representation. Newton did not hold extensive views about the
representation of space and time (although he had a minimal
perspective on such matters). It may also reflect the fact that Kant
held various broadly "Leibnizian" positions throughout the
pre-critical period, breaking rather substantively with Leibniz in the
Inaugural Dissertation of 1770. But this is not to say that Kant
focused exclusively on Leibniz and his followers in the Aesthetic. He
also presents two broad sorts of criticism of the Newtonian position.
First, he criticizes the Newtonians for holding a transcendental
realist position concerning space and time--his arguments against
transcendental realism presumably hold, if they are successful,
against both the Leibnizian "inherence" view and the
Newtonian "subsistence" view of space and time. Second, he
contends that their perspective, unlike Leibniz's, is marred by
a set of serious metaphysical problems. When discussing the Newtonian
position, Kant often emphasizes those problems. In SS7 of the
Aesthetic (in the B edition of 1787), Kant describes the
transcendental idealist conception of space and time, and then
characterizes the relevant contrast class:



> 
> Those, however, who assert the absolute reality [absolute
> Realitat] of space and time, whether they take it to be
> subsisting or only inhering, must themselves come into conflict with
> the principles [Principien] of experience. For if they decide in favor
> of the first (which generally is the position of the mathematical
> investigators of nature), then they must assume two eternal and
> infinite self-subsisting non-entities (space and time), which are
> there (yet without there being anything actual) only in order to
> comprehend everything actual within themselves.
>  (A39/B56-A40/B57)[25]
> 



Kant contends that the Newtonians conceive of space as a kind of
quasi-object. He seems to return here to the classical discussion of
the ontology of space mentioned at the outset of this entry. He
emphasizes that on the Newtonian view, space and time are akin to
substances--in that they are independent of all objects and
relations, on the one hand, and independent of the mind (and of
intuition), on the other--and yet lack causal relations. They are
also imperceptible, and certainly in the case of space, infinite. Thus
for Kant, the Newtonians regard space as an infinite substance-like
entity that is imperceptible and causally inert, a view that Kant
regards as absurd on general metaphysical grounds. Numerous
philosophers throughout the eighteenth century, from Leibniz to
Berkeley to Du Chatelet, concurred. Kant adds that the Newtonian
view seems to conflict with what he calls "the principles of
experience" (see Shabel 2005, 46-7). Perhaps the idea behind
this second criticism can be discerned from Kant's comments
elsewhere in the *Critique* and in the *Metaphysical
Foundations of Natural Science*--in those texts, Kant notes
that absolute space is not an object of possible experience and that
one cannot prove its existence by appealing to
 experience.[26]
 In this way, Kant's criticisms of the Newtonian view seem to
rest on very general metaphysical and epistemic
considerations--they seem to be largely divorced from the sort of
specific views of intuition and of representation that played a
substantial role in Kant's criticisms of Leibniz.


## 6. What is transcendental idealism?



Transcendental idealism is obviously too complex to clarify simply by
discussing Kant's views of space and time. A full discussion of
it would have to range over his critical writings in metaphysics,
aesthetics, teleology, and ethics. But as we have seen, Kant himself
indicates in the Transcendental Aesthetic that transcendental idealism
is closely related to his conception of space and time, and so some
clarity concerning Kant's overarching philosophical position can
be achieved in the context of this entry. The *modus operandi*,
as above, will be to probe Kant's own discussions of the views
of space and time articulated by his predecessors in order to clarify
his own position. In particular, Kant's remarks concerning
Berkeley are especially helpful in this context, in addition to his
remarks on Leibniz and Newton.


### 6.1 Kant's criticisms of Berkeley



We have seen above that from Kant's point of view, both Leibniz
and Newton--and perhaps some of their followers--defend
versions of "transcendental realism." This is due to their
support of the view--or perhaps commitment to the view (on other
grounds)--that space and time are independent of intuition in
some sense. They may also be adherents of this realist position on the
grounds that they do not articulate the view Kant defends in the
Metaphysical Exposition, viz. that we have a non-empirical, singular,
immediate representation of space and time. But what does it mean for
Kant to say that space and time are somehow dependent on intuition?
One way of achieving some clarity in this domain is to fill out what
Kant regards as the relevant conceptual landscape by looking to his
characterization of another idealist position, that of Berkeley (as he
understands him). So suppose that space is not a property of objects
independent of intuition in any sense--it does not even
*supervene* on properties of objects that are independent of
intuition (recall that for Leibniz, space supervenes on the monadic
order because objects and relations supervene on that order). On the
view I want to consider, space does not supervene on properties of
objects that are independent of intuition because there are no such
properties. Suppose that space is indeed dependent on intuition, but
on *empirical* intuition. I take this to represent *one
possible construal* of Berkeley's phrase, *esse est
percipii*. This consideration suggests that, *prima facie*,
Kant should not interpret Berkeley as a transcendental realist. And if
that is right, what prevents Berkeley from being understood as a
transcendental idealist? Correlatively, what prevents one from
understanding transcendental idealism as some kind of Berkeleyan
idealism about space and time? These sorts of question can help to
clarify what Kant understands by *transcendental* idealism, for
Kant seems to view Berkeley as a fellow idealist, but one who does not
defend a transcendental variety of this position.



Ironically, the view that Kant is--perhaps despite his fervent
denials--an idealist of the Berkeleyan variety arose in one of
the first critical appraisals of the *Critique*, the so-called
Garve-Feder review of
 1782.[27]
 In the *Prolegomena*, written directly after the review, Kant
 is concerned to distinguish his version of idealism from
 Berkeley's; one point he emphasizes hinges on their differing
 conceptions of space. In considering the question of why his early
 critics Garve and Feder interpreted him as a Berkeleyan idealist, he
 writes:



> 
> The solution to this difficulty rests upon something that could have
> been very easily seen from the context of the work, if one had wanted
> to. Space and time, along with what they contain, are not things, or
> properties of things, in themselves, but belong merely to the
> appearances of such things; thus far I am in agreement with the
> previous idealists. But these idealists, and among them especially
> Berkeley, saw space as a merely empirical representation, a
> representation which, just like the appearances in space together with
> all of the determinations of space, would be known to us only by means
> of experience or perception; I show on the contrary, first, that space
> (and time too, to which Berkeley gave no attention), along with all
> its determinations, can be cognized by us *a priori*, for
> space, as well as time, inheres in us before all perception or
> experience as a pure form of our sensibility and makes possible all
> intuition from sensibility, and therefore all appearances (Ak 4:
> 374-5).
> 



So from Kant's point of view, Berkeley rejects transcendental
realism--he rejects the notion that space is a thing in itself,
or a property of things in
 themselves.[28]
 He presumably also rejects the idea that space and time are
independent of intuition. In the Transcendental Aesthetic, Kant admits
that one cannot "blame" Berkeley for falling into a
radical version of idealism in an attempt to avoid the
"absurdities" of transcendental realism, absurdities into
which Kant takes the Newtonians to have fallen (B70-1)--these are
the very absurdities discussed above in the section on Kant's
criticisms of Newton. Kant seems to be suggesting with this remark
that Berkeley--who was himself a fierce critic of the Newtonian
idea of absolute or mathematical space--defended the view that
space and time are dependent on intuition, that they are not
"transcendentally real," in order to evade the Newtonian
conception. And just before the Refutation of Idealism, Kant
emphasizes again that Berkeley avoids transcendental realism
(B274--see Wilson 1999, 276-93). From Kant's point of view,
Berkeley correctly avoids transcendental realism, but does so by
falsely claiming that space is dependent on *empirical*
intuition. This is a mistake, as we have seen, because Kant thinks
that the representation of space cannot be empirical. It is precisely
this sort of view, in turn, that Kant cites when concluding that space
must be dependent on *a priori* intuition in some sense. So
perhaps transcendental idealism is *transcendental*--and
not merely *idealist*--because it contains the view that
our representation of space is non-empirical as an essential
component.



What, then, of Kant's famous contention that endorsing
transcendental realism commits one to empirical idealism (A368-9)? It
would seem, *prima facie*, that Berkeley ought to be committed
to empirical idealism, and yet Kant interprets him as
*rejecting* transcendental realism. I take it that Berkeley
avoids transcendental realism, and therefore merely empirical
idealism, by defending a more radical *dogmatic* idealism
(B274-5). According to that view, there are no objects or properties
that are independent of
 intuition.[29]
 In contrast, Kant interprets the Leibnizians as thinking both that
the order of substances is transcendentally real, i.e. independent of
intuition *per se*, and also as thinking that well-founded
phenomena and their relations are not real--the latter emerge
from our misrepresentation of the underlying non-relational monadic
reality. The phenomenal world of objects bearing spatial and causal
relations is merely ideal. It is perhaps in *that* sense that
the Leibnizians are committed to empirical
 idealism.[30]


### 6.2 Conclusions



The reading (provided above) of what makes transcendental idealism
*transcendental* hints at a further way of clarifying
Kant's overarching position. His view is not just that space is
not a property of things independent of intuition *per se*, but
that space is not a property of things independent of *a
priori* intuition. That distinguishes Kant's conception from
the idealism of a thinker like Berkeley, for Kant denies, as we have
seen, the view that space is somehow dependent upon *empirical*
intuition. This point, in turn, highlights a significant parallel
between the first and second arguments of the Metaphysical Exposition
and its third and fourth arguments. Just as the latter two arguments
allow Kant to distinguish his idealism from Leibniz's based on
the notion that the representation of space is non-conceptual, the
former two arguments allow him to distinguish his idealism from
Berkeley's based on the notion that the representation of space
is non-empirical. Hence the "dogmatic" idealism of
Berkeley and the "empirical" idealism of Leibniz are each
ruled out by considering the content and origin of the representation
of space. That, at least, would seem to form part of Kant's
intention in the Transcendental Aesthetic, especially in the
Metaphysical Exposition. This indicates that Berkeleyan and Leibnizian
idealist views can be construed as conceptions of the relation between
space and intuition. Whereas Berkeley takes space to be dependent on
*empirical* intuition, Leibniz takes it to be independent of
intuition *per se*. This illuminates Kant's concern in
the Transcendental Aesthetic with our representation of space:
considering that representation in particular allows Kant to tackle
other conceptions of the relation between space and intuition.



Finally, transcendental idealism, in so far as it concerns space and
time, has the following essential component: we have a non-empirical,
singular, immediate representation of space. Part of Kant's
innovation is to introduce into the philosophical lexicon the very
idea that we can have non-empirical intuition. It is improbable that
we can interpret this idea correctly unless we remind ourselves that
Kant rigorously distinguishes between sensation and intuition. That
distinction, in turn, forms a crucial component in Kant's
extensive rejection of the Leibnizian doctrine of perception. It is
only with the rejection of that doctrine that we can understand
Kant's break with the Leibnizian view of space and time in the
right light.