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ARTICLE
Spatial perception: The perspectival aspect
of perception
E.J. Green
1
|Susanna Schellenberg
2
1
Massachusetts Institute of Technology
2
Rutgers University
Correspondence
Susanna Schellenberg, Professor of
Philosophy, Rutgers University, Department of
Philosophy, 106 Somerset, 5th Floor, New
Brunswick, NJ 08901-4800, USA
Email: susanna.schellenberg@rutgers.edu
E.J Green, Assistant Professor, Department of
Linguistics and Philosophy MIT, 77
Massachusetts Ave, Cambridge, MA
0213904307, USA
Email: ejgr@mit.edu
Abstract
When we perceive an object, we perceive the object from a per-
spective. As a consequence of the perspectival nature of perception,
when we perceive, say, a circular coin from different angles, there is
a respect in which the coin looks circular throughout, but also a
respect in which the coin's appearance changes. More generally,
perception of shape and size properties has both a constant
aspect—an aspect that remains stable across changes in perspec-
tive—and a perspectival aspect—an aspect that changes depending
on one's perspective on the object. How should we account for
the perspectival aspect of spatial perception? We present a frame-
work within which to discuss the perspectival aspect of perception
and put forward three desiderata that any account of the perspec-
tival aspect of perception should satisfy. We discuss views on which
the perspectival aspect of perception is analyzed in terms of consti-
tutively mind‐dependent appearance properties as well as views on
which the perspectival aspect of perception is analyzed in terms of
representations of mind‐independent perspectival properties.
1|INTRODUCTION
When we perceive objects, we perceive them as having a multitude of spatial properties, including size, shape, and
location. While the study of spatial perception has a distinguished history in philosophy, the topic has received rela-
tively little recent attention compared with, say, the perception of color. This entry should help rectify this state of
affairs. We will focus on a specific question about spatial perception, namely, the question of how to account for
the perspectival aspect of perception.
When we perceive an object, we perceive the object from a perspective. As a consequence, when we perceive a
circular coin from different angles, there is a respect in which the coin looks circular throughout, but also a respect in
which the coin's appearance changes. Likewise, when we perceive two trees of the same size located at different
distances from us, there is a respect in which they look the same size, but also a respect in which they appear different
(e.g., Cohen, 2010; Peacocke, 1983; Schellenberg, 2008). More generally, perception of shape and size properties has
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© 2017 The Author(s) Philosophy Compass © 2017 John Wiley & Sons Ltd
Received: 15 May 2017 Revised: 31 July 2017 Accepted: 20 September 2017
DOI: 10.1111/phc3.12472
Philosophy Compass. 2018;13:e12472.
https://doi.org/10.1111/phc3.12472
wileyonlinelibrary.com/journal/phc3 1of16
both a constant aspect—an aspect that remains stable across changes in perspective—and a perspectival aspect—an
aspect that changes depending on one's perspective on the object. How should we account for the perspectival
aspect of spatial perception?
In Section 2, we present a framework within which to discuss the perspectival aspect of perception. In Section 3,
we put forward three desiderata that any account of the perspectival aspect of perception should satisfy. In Section 4,
we consider views on which the perspectival aspect of perception is analyzed in terms of constitutively mind‐
dependent appearance properties. In Section 5, we discuss views on which the perspectival aspect of perception is
analyzed in terms of representations of mind‐independent perspectival properties. Since the literature on spatial
perception has focused primarily on visual perception, we will be doing the same here. However, for recent discussions
of spatial perception in audition, see for example Casati and Dokic (2009) and O'Callaghan (2010).
2|PERSPECTIVAL PROPERTIES, APPEARANCE PROPERTIES, INTRINSIC
PROPERTIES, AND CONSTANCY PROPERTIES
To critically discuss different ways of accounting for the perspectival aspect of perception, it will be helpful to distin-
guish two kinds of properties in connection with both the perspectival aspect and the constant aspect of perceptual
experience.
Let's start with the perspectival aspect. There are external, mind‐independent properties that change as a
perceiver's location in relation to a perceived object changes ceteris paribus. We will call these mind‐independent per-
spectival properties or perspectival properties for short. In Section 5, we will distinguish several ways of analyzing these
perspectival properties. For now, it will suffice to say that they are mind‐independent relational properties that we can
be aware of when we perceive our environment. Note that perspectival properties involve relations to a perceiver's
location rather than relations to the perceiver or to her experience. Thus, such properties are mind‐independent rela-
tional properties, because they do not constitutively involve anything mental. We can contrast these external, mind‐
independent properties from properties of perceptual experience that change as a perceiver's location in relation
to a perceived object changes ceteris paribus. We will call these mind‐dependent appearance properties or appear-
ance properties for short. Since appearance properties are properties of the perceiver's experience, they are mind‐
dependent. However, it is possible that such mind‐dependent properties may be understood in terms of the
perceiver's awareness of certain mind‐independent properties—namely, perspectival properties. By analogy, the
property of being speckled is a mind‐independent property but the property of being aware of speckledness is
a mind‐dependent property.
In Section 4, we will discuss views on which appearance properties are not analyzed in terms of awareness of
mind‐independent perspectival properties but are rather analyzed as either monadic mind‐dependent properties or
alternatively in terms of awareness of mind‐dependent entities, such as phenomenal properties. On both
approaches, appearance properties are mind‐dependent all the way down. In Section 5, we will discuss views
on which appearance properties are analyzed in terms of awareness of perspectival properties. Changes in per-
spectival properties include changes in an object's distance and orientation with respect to the perceiver's location.
Changes in appearance properties include changes in phenomenal character and perhaps also perceptual
representation.
A distinction parallel to the distinction between perspectival properties and appearance properties can be made
with regard to the constant aspect of perceptual experience. There are external, mind‐independent properties that
remain the same as a perceiver's location in relation to a perceived object changes ceteris paribus. We will call these
mind‐independent intrinsic properties or intrinsic properties for short. We can contrast these external, mind‐independent
properties from properties of perceptual experience that remain the same as a perceiver's location in relation to a
perceived object changes ceteris paribus. We will call these mind‐dependent constancy properties or constancy
properties for short.
1
2of16 GREEN AND SCHELLENBERG
To focus the discussion, it will help to have a specific example in mind. Consider Sam. At time t1, Sam sees a
box from directly above (Figure 1.). Let's call this View 1. At time t2, he sees the same box from a different angle
(Figure 1b). Let's call this View 2. There is a sense in which the top of the box looks rectangular in both View 1
and View 2, but there is also a sense in which it looks different in Views 1 and 2. Some might say that in View 2,
the surface looks trapezoidal, though many will disagree with this description of the phenomenal character of
seeing a slanted box (Schellenberg, 2008).
2
The box's intrinsic properties remain the same, while its perspectival
properties differ in Views 1 and 2 relative to Sam's location. For example, the box's orientation relative to Sam's
line of sight changes, but its top remains rectangular. Sam's experience instantiates the same constancy property
but different appearance properties in Views 1 and 2. This is the sense in which the box both “looks different”and
“looks the same”between the two views.
The distinctions between perspectival and intrinsic properties as well as between appearance and constancy
properties allow us to formulate the following questions for any view of the perspectival aspect of spatial perception.
How should we understand the nature of perspectival properties? How should we understand the nature of appear-
ance properties? What is the relationship between perspectival properties and appearance properties? What is the
relationship between intrinsic properties and constancy properties? Finally, what is the relationship between appear-
ance properties and constancy properties?
3|THREE DESIDERATA FOR AN ACCOUNT OF PERSPECTIVAL
VARIATION
With the distinction among perspectival properties, appearance properties, intrinsic properties, and constancy prop-
erties in hand, we can formulate three desiderata for any account of the perspectival aspect of spatial perception:
Dual Aspect Desideratum: Perceptual experience is characterized by both appearance properties and constancy
properties, and these properties at least partially account for the phenomenal character
of spatial perception.
This desideratum captures the idea that when Sam perceives the box first in View 1 and then in View 2, there is a
sense in which the top surface of the box looks the same in both views and there is a sense in which it looks different
FIGURE 1 View 1 (a) and View 2 (b) of the box
GREEN AND SCHELLENBERG 3of16
in View 1 than it does in View 2. In both views, Sam's experience is characterized by the same constancy property;
however, the two experiences have different appearance properties. Note that a constancy property is a property
of a single experience, but multiple experiences can be characterized by the same constancy property. Of course
not all experiences instantiate the same constancy properties. For example, if Sam views a trapezpoidal surface from
directly above, then his experience will fail to instantiate the constancy property instantiated by his experiences of the
rectangular surface. A viable account of the perspectival aspect of perception should explain these features of Sam's
experience.
Consistency Desideratum: The perceptual content of subject's perceptual experience is not inconsistent as a conse-
quence of the subject perceiving an external, mind‐independent object from a perspec-
tive. This is the case even if perceptual content grounds both an appearance property
and a constancy property with regard to the same perceived object.
Let's assume for the sake of argument that the box perceived in View 2 looks trapezoidal to Sam. A view that
satisfies the consistency desideratum will be a view on which Sam's perceptual content is consistent despite the fact
that it grounds both the box looking trapezoidal and the box looking rectangular. On non‐representationalist views of
perceptual experience, the consistency desideratum needs to be reformulated in non‐representationalist terms.
3
On
such views, the reformulated consistency desideratum is satisfied if the fact that the box looks trapezoidal to Sam
in View 2 is not inconsistent with the fact the box looks rectangular to Sam. Either way, the consistency desideratum
accounts for the fact that the appearance and constancy aspects of one's perceptual experience are not incompatible
with one another.
Perspective without Illusion Desideratum: If a subject's perceptual experience is characterized by an appearance
property, this does not entail that the experience is illusory.
The top of the box is in fact rectangular. However, if there is a sense in which it looks trapezoidal when perceived
at a slant, this does not entail that it is being misperceived. If we assume that we perceive perspectival properties, then
accounting for the perspective without illusion desideratum will require showing that the fact that we perceive per-
spectival properties does not entail that perception is illusory.
In what follows, we will discuss a range of views of the perspectival aspect of spatial perception, examine whether
and how they satisfy these three desiderata, and discuss some problems facing each view. First, we will discuss views
that account for the perspectival aspect of spatial perception in constitutively mind‐dependent ways. We will
then discuss views that account for the perspectival aspect of spatial perception in terms of awareness of
mind‐independent perspectival properties.
4|SENSE DATA AND SENSATIONS
On all the views we will consider, the perspectival aspect of spatial perception is understood in terms of appearance
properties. However, we can distinguish views that analyze such appearance properties in terms of the awareness of
mind‐independent perspectival properties from views that instead analyze appearance properties in constitutively
mind‐dependent ways. In this section, we will consider views on which the perspectival aspect of spatial perception
is analyzed in constitutively mind‐dependent ways. There are two such approaches. On one approach, appearance
properties are analyzed in terms of awareness of mind‐dependent objects or properties. On a second approach,
appearance properties are treated as primitive to perceptual experience rather than as properties to be analyzed in
terms of awareness of something else, be it a mind‐dependent or a mind‐independent property (such as a perspectival
property).
4of16 GREEN AND SCHELLENBERG
4.1 |Sense data
Some have proposed that when Sam sees the box in View 2, he is aware of a mind‐dependent object—e.g., a sense
datum or an image—that is in fact trapezoidal (e.g., Ayer 1963; Broad, 1925; Robinson, 1994; Russell, 1912).
4
On this
type of view, shape and size appearance properties are analyzed in terms of awareness of intrinsic properties of sense
data. This view has its root in the British Empiricist notion of an idea (Hume, 1758/2007; Locke, 1690/1975). As it is
developed by sense data theorists, we infer information about the intrinsic shapes and sizes of external physical
objects (e.g., the rectangularity of the top of the box) from our immediate awareness of the shapes and sizes of
sense data.
The sense datum view satisfies the perspective without illusion desideratum. After all, sense data actually have
the shapes and sizes of which we are putatively aware. The sense datum you are aware of when viewing the box
at a slant really is trapezoidal. Thus, you are not under an illusion when you perceive it as trapezoidal.
Moreover the sense datum view satisfies the consistency desideratum for two reasons. First, many sense datum
theorists hold that the property of rectangularity does not in fact figure in one's perceptual experience of the box at all
but rather is inferred on the basis of awareness of the properties of sense data. Thus, there can be no contradiction
internal to experience between the properties trapezoidal and rectangular. Second, there is no contradiction between
perception and perceptual judgment, because the properties trapezoidal and rectangular are attributed to different
things. The former is attributed to a sense datum, while the latter is attributed (in judgment) to an external object.
Matters are less clear for the sense datum view when it comes to the dual aspect desideratum. Arguably when
Sam sees the box in View 2, he does not merely judge or infer that the box is rectangular. He experiences it as such.
5
This is what we have meant by the claim that perceptual experience instantiates constancy properties. However, on
standard versions of the sense datum view, Sam is not perceptually aware of the rectangularity of the box, but rather
judges that the box is rectangular (Ayer 1963; Broad, 1925). The theory holds that the properties of which Sam is
perceptually aware when he views the slanted box are properties of a trapezoidal sense datum that the box elicits.
But this sense datum cannot be both rectangular and trapezoidal. Thus, this version of the sense datum view does
not satisfy the dual aspect desideratum.
While the sense datum theory has been rejected on such grounds (e.g., Noë, 2005), the sense datum theorist
could in principle satisfy the dual aspect desideratum by positing that there are both sense data corresponding to cer-
tain perspectival properties and sense data corresponding to intrinsic properties. For example, one might hold that
when viewing a slanted box, we are aware of two separate sense data: A rectangular sense datum and a trapezoidal
sense datum, where the latter is supposed to correspond to some perspectival property of the box. Indeed, a sophis-
ticated version of sense datum theory might hold that there are sense data corresponding to intrinsic properties, but
also sense data corresponding to one or more of the mind‐independent perspectival properties that we'll consider in
Section 5.
The main reasons for rejecting the sense datum view are independent of satisfying our three desiderata. One
central problem concerns where sense data are located (see, e.g., Huemer, 2001: 149–168). If they are located in
physical space, then why can we not detect them by means of standard scientific instruments? If they are not located
in physical space, then how do we interact with or become sensorily aware of them? A further problem is that
standard versions of sense datum view are committed to mind‐body dualism and this view faces familiar difficulties
that we will not rehash here.
6
4.2 |Sensations
A different approach to accounting for the perspectival aspect of perception is to argue that perceptual experience is
characterized by sensations in addition to representing intrinsic properties (Peacocke, 1983; 2008). Consider again
Sam, who sees the slanted box (View 2) and represents the box's intrinsic shape as rectangular. The sensations
account posits that Sam's experience is characterized by a sensation or sensational property that accounts for the
GREEN AND SCHELLENBERG 5of16
trapezoidal appearance of the box. In this way, the “trapezoidal”aspect of the experience is explained by appeal to
mind‐dependent, non‐representational sensational properties, while the “rectangular”aspect is explained by appeal
to how the experience represents the box.
7
Since the sensation is a property of one's experience and the intrinsic property represented is a property of the
external object, the two cannot conflict. After all, sensations are not perceptually represented. Since sensations are
not part of perceptual content, they cannot be accurate or inaccurate and also cannot give rise to contradiction with
regard to the properties represented by experience. Thus, if appearance properties are accounted for in terms of sen-
sations while constancy properties are accounted for in terms of representations of intrinsic shape, the consistency
desideratum is satisfied. Moreover, assuming that sensations do not make perceptual phenomenology illusory, the
perspective without illusion desideratum is satisfied.
Proponents of the sensation account have a variety of options for understanding the relation between sensa-
tional properties and representational properties. One approach is to treat them as wholly separate. However, a dif-
ferent version of the sensation view would hold that phenomenal visual sensations are the means through which we
represent physical spatial properties. Hatfield (2009: ch. 6; 2016), for instance, holds that a slanted rectangular surface
causes a trapezoidal phenomenal visual appearance, and that this appearance is the way that we represent the
surface's rectangularity from our perspective. He also holds that physically parallel lines receding into the distance
elicit a phenomenal visual appearance in which the lines converge, and that this is the way that receding parallel lines
are represented in perception.
Many philosophers have rejected the sensation view because they believe that it fits poorly with the phenomenal
character of spatial perception and, thus, has problems satisfying the dual aspect desideratum. Harman (1990), for
example, has argued that when we introspect our visual experience, it seems to us as though the properties of which
we are aware are properties of external, mind‐independent objects rather than intrinsic features of our experience.
This is standardly referred to as the transparency thesis. If the transparency thesis is true, then when Sam perceives
the box first in View 1 and then in View 2, the change that he is aware of will seem to him to be a change in the box, or
in his relation to it, rather than an intrinsic change to his experience of the box. Those attracted to the transparency
thesis have thus argued that appearance properties should be analyzed in terms of awareness of external perspectival
properties rather than in terms of intrinsic features of experience (Hill, 2014: 212; Tye, 2002).
Moreover, there are properties of the box that change when Sam sees the box first in View 1 and then in View 2,
namely, properties that the box has in virtue of its relation to Sam's viewpoint. The sensations approach accounts for
the difference in Sam's experience between these views in terms of properties that are entirely mind‐dependent.
However, note that any perceiver occupying Sam's location would undergo a similar change in appearance properties,
and there are mind‐independent properties of the box that change between View 1 and View 2. One might argue that
these facts are reason enough to analyze the change in Sam's experience in terms of awareness of mind‐independent
properties.
8
There are constitutive regularities both between intrinsic properties and relevant constancy properties as
well as between perspectival properties and relevant appearance properties. By treating appearance properties as
entirely independent of awareness of perspectival properties, the sensations view does not account for these
regularities.
5|APPEARANCE PROPERTIES AS AWARENESS OF MIND‐INDEPENDENT
PROPERTIES
An alternative to treating appearance properties as constitutively mind‐dependent is to analyze appearance proper-
ties in terms of awareness of mind‐independent perspectival properties. On such views, the changes in Sam's spatial
experience as he adopts different viewpoints with respect to the box are analyzed in terms of his awareness of
changes in properties the box has relative to his viewpoint (e.g., Hill, 2014; Schellenberg, 2008; Tye, 2002). While
appearance properties are analyzed in terms of awareness of perspectival properties, constancy properties are
6of16 GREEN AND SCHELLENBERG
analyzed in terms of awareness of intrinsic properties. On this cluster of views, the focus is on the nature of perspec-
tival properties. To a first approximation, the perspectival properties of an object are determined by the object's intrin-
sic properties and the perceiver's location. Beyond this general characterization, there are several different ways of
analyzing perspectival properties. We will consider them in turn.
5.1 |Aspects
One way to account for the perspectival aspect of perception in terms of mind‐independent properties builds on the
basic observation that from different viewpoints, different portions of an object's surface become visible (where “xis
visible”means something like “xsupplies light to the retinas”). For instance, when you view a solid cube, at any given
time at most three of its faces will be visible, while the others will be occluded. Changes in viewpoint will bring some
of the faces that were previously hidden into view and hide some faces that were previously visible. More generally,
suppose that one occupies a particular viewpoint vwith respect to a polyhedral object o. From v, a particular config-
uration of o's edges and vertices will be visible. This configuration, along with the topological relations between the
edges, is called an aspect of o. The collection of o's aspects constitutes its view potential (see Koenderink, 1984;
Palmer, 1999: 446–447; Tarr & Kriegman, 2001; for recent philosophical discussions of aspects, see Briscoe, 2008;
Noë, 2004). If the same set of edges and vertices is visible from two distinct viewpoints, then the same aspect of o
is visible from those two viewpoints. If a different set of edges and vertices is visible from two distinct viewpoints,
then a different aspect of ois visible from those two viewpoints.
Aspects are a kind of perspectival property. On the aspect account, appearance properties can be analyzed in
terms of the awareness of aspects. We will assume that constancy properties are analyzed in terms of awareness of
intrinsic properties. How does the aspect account fare with respect to our three desiderata? Assuming we are aware
of both an object's aspect and its intrinsic spatial properties, the view satisfies the dual aspect desideratum.
9
It satisfies
the consistency desideratum since an object's intrinsic shape and an object's aspect given a perspective are two differ-
ent things, and so, an experience in which one represents or is aware of both will not be inconsistent. The view satisfies
the perspective without illusion desideratum: Since an object really does make different aspects visible to different
viewpoints, there is no illusion involved in being perceptually aware of different aspects from different viewpoints.
However, it is questionable whether the appeal to aspects can provide a complete account of the perspectival
aspect of perception. Aspects are simply too coarse‐grained to explain what makes rectangular surfaces at a slant
“look trapezoidal”(if in fact they do look that way). Thus, consider View 3 of the box (Figure 2), from a perspective
intermediate between Views 1 and 2. In whatever sense in which the top of the box looks trapezoidal in View 2, it
arguably also looks trapezoidal in View 3. However, Views 1 and 3 are associated with the same aspect of the object,
since the same configuration of edges and vertices is visible.
Thus, even if appeal to aspects supplies a partial explanation of the perspectival aspect of spatial perception, it is
unlikely to be the whole story. Aspects do not provide much by way of insight into the types of changes in appearance
properties that have generally occupied philosophers, for they do not explain why slanted objects look “compressed,”
or, for that matter, why far away objects look “smaller.”Moreover, while there is clearly a difference between the
aspects of an object that are directly visibly available to one and those that are not, arguably, we perceive three‐
dimensional objects as having back sides, and we perceive their shapes as being continuous even if the whole shape
is not directly visibly available to one.
5.2 |P‐shapes and solid visual angles
An alternative approach to analyzing appearance properties in terms of awareness of mind‐independent perspectival
properties involves direct appeal to the two‐dimensional projection of an object either onto the retina (e.g., Lowe,
1992: 87–88) or onto the frontal plane, that is, a plane perpendicular to the line of sight leading from one's viewpoint
to the object (Noë, 2004, 2005). Following Noë, we will refer to the shape of an object's projection onto the frontal
GREEN AND SCHELLENBERG 7of16
plane as its “P‐shape.”
10
On such a P‐shape proposal, perspectival properties are analyzed as two‐dimensional projec-
tions of an object's intrinsic spatial properties either onto the frontal plane or onto the retina. Appearance properties
in turn are analyzed in terms of awareness of such two‐dimensional projections. On such views, perceivers are aware
of both an object's projected spatial properties as well as its intrinsic spatial properties. The former accounts for the
appearance property, the latter for the constancy property.
It is widely accepted that two‐dimensional retinal projections play an important role in visual processing. It has
been argued, for example, that the visual system computes the shape of an object by first registering its
two‐dimensional retinal shape and then applying certain rules or “heuristics”for deriving three‐dimensional
structure (e.g., Pizlo, 2008). Moreover, it has been argued that an object is recognized by comparing its two‐
dimensional retinal projection with images of two‐dimensional retinal projections stored in memory (e.g., Edelman,
1999; Ullman, 1996). Even if two‐dimensional retinal projections play a role in visual processing, however, it is
questionable whether we are aware of them, or of P‐shapes, in standard cases of conscious perception.
A view similar to the P‐shape proposal has it that spatial appearance properties should be understood in terms of
awareness of the solid visual angles that perceived objects subtend (Jagnow, 2012; Tye, 2002). The solid visual angle
an object subtends relative to a viewpoint is fixed by the union of rays leading from that viewpoint to the boundary of
the object. A rectangle viewed at as slant subtends the same solid visual angle as a trapezoid viewed from directly
above on and an object subtends a progressively smaller visual angle as it moves farther away from your viewpoint.
Assuming P‐shapes do play a role in personal level conscious perception, the view would satisfy the consistency
desideratum. After all, P‐shapes and intrinsic shapes are different in kind, and so, awareness or representation of the
former will not be inconsistent with awareness or representation of the latter. Moreover, if appearance properties are
analyzed in terms of awareness of P‐shapes, then the view will moreover satisfy the perspective without illusion
desideratum. However, it is questionable whether appearance properties can be explained in this way while account-
ing for phenomenal character of spatial perception.
Several challenges facing the P‐shape proposal concern its consistency with spatial phenomenology and thus its
ability to satisfy the dual aspect desideratum. These challenges target the idea that P‐shapes even partially character-
ize the phenomenal character of spatial perception.
FIGURE 2 View 3 of the box
8of16 GREEN AND SCHELLENBERG
The P‐shape of a three‐dimensional volumetric object is planar and so flat, but there is arguably no sense in which
such objects look flat (Briscoe, 2008; Schellenberg, 2008; Schwitzgebel, 2006, 2011). Furthermore, it is not clear why
attributing a P‐shape Fto a region of the frontal plane should make an external object look F, nor is it clear why
perceptually representing an external object as being related to a certain P‐shape Fshould make that object look F.
For example, it is unclear why simply representing a slanted box as projecting a trapezoidal image on the frontal plane
should make the box look trapezoidal.
A further problem is that the distortions to an object's shape appearance as a result of slant are in general less
extreme than the distortions to its P‐shape (see Hatfield, 2009: ch. 6, Hatfield, 2016; Hill, 2014: Chapters 11–12; Hill
& Bennett, 2008; Thouless, 1931). Similarly, the reduction in apparent size as an object recedes into the distance is
less drastic than the reduction in the size of its projection onto a particular frontal plane—its “P‐size.”While the solid
visual angle view avoids the criticism that objects don't look flat, the view faces similar difficulties to the P‐shape pro-
posal (Hatfield, 2016; Hill, 2014). Namely, distortions to an object's shape appearance with increasing slant are in gen-
eral less extreme than distortions to its solid visual angle.
11
If the P‐shape theorist claims that the apparent shape or size of an object changes in direct proportion to its
P‐shape or P‐size, then these observations pose a serious difficulty for the view. The P‐shape theorist might accom-
modate these data by claiming that P‐shapes (or properties of projecting certain P‐shapes) are simply misrepresented in
experience and thus give up the perspective without illusion desideratum (see Hill, 2009: 164–165 for an argument
against this view). However, the P‐shape view will fail to satisfy either the dual aspect desideratum or the perspective
without illusion desideratum.
5.3 |Distance and slant
A third approach to analyzing appearance properties in terms of awareness of mind‐independent perspectival
properties is to appeal to the fact that as a perceiver shifts perspective on an object, the object's distance and slant
will change relative to the perceiver. The best known scheme for visually representing distance and slant is Marr's
2½‐D sketch. For each patch of a visible surface (up to a certain resolution), the 2½‐D sketch specifies (a) the distance
and direction of that patch from one's viewpoint and (b) the patch's orientation relative to one's line of sight (see Marr,
1982: 275–279) thus creating a depth map.
12
The distance‐and‐slant view analyzes appearance properties in terms of
awareness of an object's distance and slant, while constancy properties are analyzed in terms of awareness of intrinsic
shape and size properties (Briscoe, 2008; Hopp, 2013; Siewert, 2006; Smith, 2002).
How does the distance‐and‐slant view fare with respect to our desiderata? The view can satisfy the consistency
desideratum: There is no inconsistency between an object's intrinsic shape and its distance and slant relative to your
viewpoint, so there is no inconsistency in being aware of these properties concurrently. Moreover, it satisfies the per-
spective without illusion desideratum: Since an object's distance and slant really do change with changes in viewpoint,
there is no illusion involved in representing them as changing. Finally, if appearance properties are analyzed in terms of
the awareness of distance and slant properties while constancy properties are analyzed in terms of the awareness of
intrinsic properties, then the distance‐and‐slant view satisfies the dual aspect desideratum. It is highly plausible that
our awareness of intrinsic shape alongside distance and slant offers at least a partial account of the phenomenal char-
acter of spatial perception.
While the distance‐and‐slant view does well in satisfying our desiderata, it is been criticized on grounds that it
does not fully account for the phenomenal character of spatial perception. The distance‐and‐slant view does not
register any respect in which farther objects “look smaller”than closer objects. Farther objects, on this view,
simply look farther away. Similarly, the view does not register any respect in which a slanted rectangular surface
may “look trapezoidal.”Rather, it simply looks rectangular and at a slant. To the extent that one is attracted to
the intuition that slanted rectangles look trapezoidal or slanted circles look elliptical, one will not be attracted
to the distance‐and‐slant view.
GREEN AND SCHELLENBERG 9of16
There are at least two options available to the defender of the distance‐and‐slant view. Either she can deny that
slanted objects have compressed shape appearances and that farther away objects have smaller size appearances, or
she can embrace pervasive misrepresentation, and thus reject the perspective without illusion desideratum. The first
option is evidently endorsed by A. D. Smith: “[T]he suggestion that pennies, for example, look elliptical when seen
from most angles is simply not true…. Such a penny (usually) looks just the way it is: round and tilted away from
you”(Smith, 2002: 172; see also Siewert, 2006).
13
On this view, all that changes as regards the experience of an
object's spatial properties when it is slanted away from you is its perceived depth and slant properties—a slanted rect-
angle does not look trapezoidal in any respect nor does a slanted circle look elliptical.
How viable one finds this approach will obviously depend on how committed one is to the view that shape and
size appearances change depending on an object's orientation and distance. The idea that a slanted rectangular sur-
face looks in some way trapezoidal is readily grasped by participants in psychology experiments. When asked to
report the shape that an object “looks”or “appears”(rather than its real physical shape), participants will often indicate
a shape that is somewhat compressed relative to the object's real shape (Thouless, 1931; Wagner, 2006: ch. 6).
14
As
such, the “trapezoidal”appearance of a slanted box does seem to have psychological reality. In response, some pro-
ponents of the distance‐and‐slant view have argued that these compressed shape properties are not generally repre-
sented in perception. Instead, we represent them only as a result of taking up a special imaginative perspective on the
perceived object (Briscoe, 2008).
15
The second option is to combine the distance‐and‐slant view with a view on which physical shape and size are
systematically misperceived. On this option, when we perceive a rectangular surface at a slant, we perceptually rep-
resent it as being physically somewhat trapezoidal, and also as slanted relative to our line of sight. Likewise, when we
perceive train tracks that recede away from us, we perceptually represent them as physically converging in the dis-
tance. Consistent with this, there is psychological evidence that as objects get farther away, our perception of their
length along the depth dimension becomes progressively more compressed (e.g., Wagner, 1985, 2006: ch. 7; Loomis,
Da Silva, Fujita, & Fukusima, 1992). On this view, a circular object that is slanted in depth should look slightly elliptical,
because its perceived length from front to back will be compressed relative to its perceived length from left to right.
This proposal obviously requires giving up the perspective without illusion desideratum. At bottom, however, it is an
empirical question whether we are subject to pervasive geometrical illusions.
16
5.4 |Situation‐dependent properties
A fourth approach to analyzing appearance properties in terms of awareness of mind‐independent perspectival prop-
erties is to appeal to situation‐dependent properties (Schellenberg, 2008). Situation‐dependent properties are a kind
of perspectival properties. They are extrinsic, mind‐independent properties that are exclusively sensitive to and onto-
logically dependent on intrinsic properties and the situational features. Situational features are features of the envi-
ronment that determine the way an object is presented. For the perception of size, shape, and other spatial
properties, the perceiver's location in relation to the perceived object is the crucial situational feature that determines
how the object is presented. For the perception of color and shading, the lighting conditions and color context are
among the crucial situational features. A situation‐dependent property is determined by a (nonconstant) function of
an intrinsic property of the object and relevant situational features. This means that fixing the intrinsic properties
and the situational features fixes the situation‐dependent properties (Schellenberg, 2008: 57–60).
Consider again Sam who sees the box first in View 1 and so straight on and then in View 2. In both cases, the box
is presented in a certain way given his location. In View 2, one side of the box is closer than the other; one part faces
away from him. The box's shape is presented in an egocentric frame of reference, which in turn means that the object
and its parts are presented as standing in specific spatial relations to Sam. The way the box is presented to Sam's loca-
tion is on the suggested view an external and mind‐independent, albeit, situation‐dependent property of the world.
Any perceiver occupying the same location would, ceteris paribus, be presented with the same situation‐dependent
property—though perceivers differ with regard to which situation‐dependent properties are perceptually available
10 of 16 GREEN AND SCHELLENBERG
to them and they differ in how they represent situation‐dependent properties. On this approach, we represent both
intrinsic properties and situation‐dependent properties. Appearance properties are analyzed in terms of awareness of
situation‐dependent properties, while constancy properties are analyzed in terms of awareness of intrinsic properties.
The situation‐dependent properties approach easily satisfies the dual aspect desideratum. After all, we perceive
and are aware of both the perspectival properties and intrinsic properties in our environment. As a consequence our
perceptual experience is characterized by both appearance properties and constancy properties.
The situation‐dependent properties approach satisfies the consistency desideratum. To see why, consider
Peacocke's case of two same‐sized trees one of which is further away than the other. According to the situation‐
dependent properties approach, a subject who sees the trees represents two distinct properties: An intrinsic property
and a situation‐dependent property. While the representation of the intrinsic property grounds the sense in which
trees look the same size, the representation of the situation‐dependent property grounds apparent difference in size.
Since the intrinsic property and the situation‐dependent property are different in kind, the representational content is
not inconsistent. This is the case even if both properties are attributed to the same objects.
The situation‐dependent properties approach satisfies the perspective without illusion desideratum. After all,
appearance properties are analyzed in terms of awareness of mind‐independent situation‐dependent properties. So
there is nothing illusory about seeing situation‐dependent properties. Indeed, appealing to situation‐dependent prop-
erties allows us to analyze many cases as non‐illusory that philosophers—but not psychologists—typically treat as
visual illusions. Examples are the bent look of a stick partially immersed in water or the red look of a white wall
immersed in red light (Schellenberg, 2008: 74–75).
17
Aspects are a kind of situation‐dependent property, but situation‐dependent properties include more than just
aspects. In contrast to P‐shapes, situation‐dependent properties are not projections and are not two‐dimensional.
They are three‐dimensional. Schellenberg (2008) has argued that one important advantage of the situation‐dependent
property approach over the distance‐and‐slant approach is that the perceiver need not be aware of slants and
distances to perceive situation‐dependent properties. Perceiving slants and distances is, Schellenberg contends, an
intellectually sophisticated activity. If this is correct, then in contrast to the distance‐and‐slant approach, the situa-
tion‐dependent property approach does not over‐intellectualize perception. While situation‐dependent properties
are relational properties in that they are a function of intrinsic properties and situational features, they need not be
perceived as relational properties. Indeed, one may not be aware of the situational features in any way but may only
be aware of the property constituted by the intrinsic property and the situational features as if it were a monadic
property. Of course, even in this case the situation‐dependent property may not be perceived as a monadic property.
According to the situation‐dependent property view, we are normally aware of which property perceived is intrin-
sic and which is situation dependent, in that we are aware which property is constant and which is fleeting or relative
to situational features. There are, however, cases in which we mistake a situation‐dependent property for an intrinsic
property, such as when we mistake a white wall illuminated by red light to be a red wall. The situation‐dependent
property approach can easily account for such cases and moreover can easily account for why it is that we have some
reason to believe that the wall is red. After all, it is situation‐dependently red. To take an example involving spatial
properties, consider again Peacocke's trees. The representational content of a perception of the trees will be the
following.
(Tree
1
and Tree
2
are the same size′,Tree
1
and Tree
2
are different in size′′)
The single primed property is a situation‐dependent property, and the double primed property is an intrinsic prop-
erty. While the two properties represented differ in kind and while the representational content marks them as differ-
ent, perception need not represent these metaphysical facts. In extreme cases, the subject may just be aware that the
trees are somehow the same size and somehow different in size. In contrast to the distance‐and‐slant view, the situ-
ation‐dependent property approach can account for this while nonetheless satisfying the consistency desideratum.
One challenge for the situation‐dependent property view is raised by the fact that objects have myriad situation‐
dependent properties. There are many properties determined as a function of an object's intrinsic properties together
GREEN AND SCHELLENBERG 11 of 16
with its situational features. Further developments of the view are needed in order to specify which of these proper-
ties is prioritized by the visual system in any particular case. For example, if the slanted box has a trapezoidal shape
appearance, which specific situation‐dependent property accounts for this appearance? A proponent of the position
needs to answer this question in a way that also accommodates the data discussed earlier. For example, phenomenal
shape and size appearances do not seem to change in direct proportion with either P‐shapes or solid visual angles.
Thus, for the situation‐dependent property view to adequately capture these features of spatial phenomenology,
the situation‐dependent properties that account for shifts in shape and size appearance also should not change in
direct proportion to an object's P‐shape or solid visual angle.
6|CONCLUSION
We have discussed a variety of approaches to explaining the perspectival aspect of perception. We evaluated each
view with respect to three desiderata for a theory of perspectival variation. Now, it is an option to reject one or more
of these desiderata. Indeed, it has been argued that our experience of spatial properties is systematically inaccurate
(McLaughlin, 2016). A view on which experience of spatial properties is systematically inaccurate will reject the per-
spective without illusion desideratum.
In our discussion, we have focused primarily on views on which appearance properties are analyzed in terms of
(awareness of) properties or objects, which are distinct from an object's intrinsic spatial properties. A different sort
of view would hold that appearance properties are determined by perceptual modes of presentation of an object's
intrinsic shape and size (see, e.g., Burge, 2010). Thus, the “trapezoidal”aspect of Sam's experience when seeing the
slanted box in View 2 would be due to his perceptual mode of presentation of the table's rectangularity. This percep-
tual mode of presentation would be different when Sam views the box in other orientations.
As we have seen, a major fault line in disputes about how to account for the perspectival aspect of perception
concerns whether there is any respect in which a slanted box looks trapezoidal, or a slanted coin looks elliptical. While
some find this judgment inescapable, others do not. For those in the latter camp, the distance‐and‐slant view (perhaps
supplemented with the aspect view) is quite plausible. Those in the former camp have, on the other hand, encoun-
tered difficulty in developing a view of appearance properties, on which the three desiderata are satisfied while giving
an adequate account of phenomenal character and being sensitive to empirical data. Schellenberg (2008) has argued
that the situation‐dependent property approach provides the resources needed for an account of appearance prop-
erties that avoids such difficulties.
There are a variety of further issues surrounding spatial constancy and perspectival variation that we have not
addressed here. While we have discussed appearance properties and perspectival properties in detail, we have said
little about constancy properties, except that they may plausibly be accounted for in terms of perceptual awareness
of an object's intrinsic properties. However, even if this is correct, it raises a number of further issues. First, objects
have myriad intrinsic shape properties. A square object is also a rectangle, quadrilateral, and closed figure. Which of
these properties are represented in perceptual experience? On this issue, Green (2017) has argued that our perceptual
representation of intrinsic shape is layered at varying degrees of abstraction and that representations of abstract
shape play a critical role both in visual processing and during concept acquisition. Second, there are a number of ways
to understand the notion of perceptual constancy. For example, when we see a coin as circular both when viewed
straight on and when viewed at a slant, does this merely involve perceiving it as circular at two separate times, or does
it also involve perceiving it as remaining circular from one time to the next (Bennett, 2016; Green, forthcoming)?
Given the emphasis placed on perceptual constancy in recent work within the philosophy of mind and perception
(see Burge, 2010; Smith, 2002), it is important to investigate the various ways of understanding this capacity.
There are further issues regarding perceptual constancy that we have not addressed here. We have discussed the
fact that when we see an object, our perceptual experience manifests perceptual constancy as our viewpoint on the
object changes. There is strong evidence that perceptual experience manifests perceptual constancy in the face of
12 of 16 GREEN AND SCHELLENBERG
geometrical changes considerably more complex than mere changes in viewpoint. For example, many of the objects
that we perceive change their intrinsic shapes as they move. This is true of biological objects, such as human beings
and cats, but also of many artificial objects, such as staplers and reclining chairs. Nonetheless, such objects often per-
ceptually appear to retain key aspects of their overall structure as they move. Green (forthcoming) argues that percep-
tual experience manifests a kind of perceptual constancy, called structure constancy, in response to many nonrigid
objects of this sort. Green contends that structure constancy places important constraints on viable models of the rep-
resentational format and reference frame of visual spatial experience.
In addition to the nature of constancy properties, a question to be addressed in a further work is how (and
whether) perceivers transition from egocentric to allocentric frames of reference in perception, that is how they tran-
sition from perceiving objects in an egocentric frame of reference to perceiving them as having properties character-
ized in an allocentric frame of reference (Schellenberg, 2007). Another central question is how and if our visual
experience of spatial properties accords with consistent geometries of visual space. Some, such as Hatfield (2009:
ch. 5), take the perspectival aspect of perception to have crucial implications for questions about the geometry of
visual space. We plan to address these questions among others in a second paper.
ENDNOTES
1
Although we'll focus here on exercises of perceptual constancy across changes in perspective or viewpoint (where an
object's intrinsic shape remains constant), it is also plausible that there are aspects of perceptual experience that remain
constant across changes that alter an object's intrinsic shape, such as the normal walking motion of a human being (Green,
forthcoming).
2
The notion of “slant”is ambiguous, as it can refer either to the angle formed between a surface and some background sur-
face, such as a flat ground plane, or to the angle formed between a surface and the perceiver's line of sight. The first is
called geographical slant, while the second is called optical slant (see Bennett, 2016). When we speak of slant here, we'll
always have optical slant in mind.
3
Non‐represenationalist views have been defended by austere relationalists or naïve realists (Brewer, 2011; Campbell,
2002; Martin, 2002). Johnston (2004) has defended a non‐representationalist view that eschews many of the externalist
commitments of naïve realists.
4
This is not an obligatory view for sense datum theorists. For example, both Price (1932: 3) and Jackson (1977: 102–103)
claim that sense data are arrayed in three‐dimensional space, located at varying distances and angles relative to the
perceiver. It is open to a proponent of this version of sense datum theory to hold that when Sam is aware of the slanted
box, he is simply aware of a slanted rectangular sense datum, and so not aware of any trapezoidal object.
5
Some, however, have rejected this claim about shape experience (Hill, 2014: 229–230; Prinz, 2012: 74).
6
See Austin (1962) for a variety of arguments against the sense datum view.
7
In developing his view of sensations, Peacocke (2008) proposes that the trapezoidal sensational property of experience
when one views a slanted rectangle is the shape of a region of one's “visual field.”The visual field is characterized as
the curved plane in space that contains the retina of the (hypothetical) “cyclopean eye,”which occupies a position roughly
halfway between the two eyes (e.g., Hershenson, 1999: 20–21). But which region of this plane is relevant? A natural
answer is that it is the region of the plane occupied by the two‐dimensional projection of the distal rectangle. In this case,
sensational properties bear some similarity to Noë's “P‐shape”proposal, discussed below, though on the latter view, such
projective shape properties figure in an experience's representational content. As such, Peacocke's view is likely to face
similar problems to the P‐shape proposal in accounting for the phenomenology of apparent shape (e.g., an object can pro-
ject an image twice as large as another object onto the frontal plane yet not appear twice as large).
8
These facts do not strictly entail that appearance properties must be analyzed in terms of awareness of mind‐independent
properties. One could, for instance, hold that different perceivers are presented with the same mind‐dependent properties
and that these properties reliably covary with mind‐independent properties that the box has by virtue of its relation to the
perceiver's location.
9
It is an open question whether, and in what respect, a perceiver can be perceptually aware of those parts of an object that
are hidden from her viewpoint (e.g., an object's backside or occluded parts). The ability to fill in the hidden parts of an
object is called “amodal completion.”For recent discussions of amodal completion and perceptual experience, see
Nanay (2010) and Briscoe (2011).
10
See also Tye (2000: 78–79) for a version of the P‐shape account.
11
In light of these issues, Christopher Hill (2009, 2014, 2016; Hill & Bennett, 2008) proposes that shape and size appearance
properties involve awareness of “Thouless properties.”These are construed as complex relational properties of objects
GREEN AND SCHELLENBERG 13 of 16
determined as a function of their intrinsic properties along with their distance and orientation relative to the perceiver.
Thouless properties are supposed to represent a “compromise”between an object's intrinsic properties and its solid visual
angle.
12
Because the 2½‐D sketch is limited to describing the geometry of visible surfaces, it does not include any description of the
way surfaces complete behind occluders.
13
McLaughlin (2016) joins Smith in rejecting the view that slanted objects appear compressed in shape but endorses the
view that faraway objects appear smaller in size.
14
These are often called apparent instructions, to distinguish them from objective instructions, which require the participant
to indicate the spatial properties that an object actually has.
15
Similarly, Kelley (2008) suggests that while we can come to experience a slanted coin as having an elliptical apparent
shape, we cannot do this while also experiencing it as intrinsically circular.
16
See McLaughlin (2016) for arguments that perception is subject to pervasive geometrical illusions.
17
The bent stick case is sometimes referred to as an “optical”illusion rather than a visual illusion.
ORCID
Susanna Schellenberg http://orcid.org/0000-0002-5103-2438
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E. J. Green is Assistant Professor in the Department of Linguistics and Philosophy at MIT. He works in the philos-
ophy of mind and cognitive science, with a primary focus on perception. His specific research interests include our
perception of objects and their geometrical properties, the nature of perceptual reference, and the role of
GREEN AND SCHELLENBERG 15 of 16
hierarchical structure in perceptual representation. He has articles either in print or forthcoming at Noûs,Philoso-
phy of Science,The British Journal for the Philosophy of Science,Mind & Language, and Philosophical Topics. Prior to
his appointment at MIT, he was a Bersoff Faculty Fellow at NYU. He received his PhD from Rutgers University.
Susanna Schellenberg is Professor of Philosophy at Rutgers University. She holds a secondary appointment at the
Rutgers University Center for Cognitive Science (RuCCS). She works on a range of topics in philosophy of mind,
epistemology, and philosophy of language. The issues she has tackled include the nature of perceptual experience,
evidence, capacities, mental content, and imagination. Her work has appeared in Journal of Philosophy,Mind,Noûs,
and Philosophy and Phenomenological Research. Her book The Unity of Perception: Content, Consciousness, Evidence
(OUP) develops an integrated account of the phenomenological and epistemological role of perception in light of
the thesis that perception is constitutively a matter of employing perceptual capacities.
How to cite this article: Green EJ, Schellenberg S. Spatial perception: The perspectival aspect of perception.
Philosophy Compass. 2018;13:e12472. https://doi.org/10.1111/phc3.12472
16 of 16 GREEN AND SCHELLENBERG
