1

(This is a draft of a paper that will appear in corrected form in Philosophical Psychology . Please contact

the author for the final draft before citing.)

Representing the Impossible

Jennifer Matey

ABSTRACT: A theory of perception must be capable of explaining the full range of

conscious perception, including amodal perception. In amodal perception we

perceive the world to contain physical features that are not directly detectable by

the sensory receptors. According to the active-externalist theory of perception,

amodal perception depends on active engagement with perceptual objects. This

paper focuses on amodal visual perception and presents a counter-example to the

idea that active-externalism can account for amodal perception. The counter-

example involves the experience of so-called ‘impossible objects’, objects

experienced in perceptual character as having geometrical properties that no

physically real object can have.

1. Introduction

In recent years, interest in enactive approaches to perception among both

philosophers and cognitive scientists has grown considerably1. Arguably, much of

the recent interest in enactivism can be attributed to the work of Alva Noë. Noë

advances the view that perception depends on active physical engagement with

perceptual objects rather than on representations and internal computations2.

Following others, I will refer to this view as active-externalism. This paper discusses

a counter-example to active-externalism involving the experience of a so-called

‘impossible object’. Impossible objects are objects experienced in visual character as

having geometrical properties that no physically real object can have. A brief

discussion of active-externalism will be presented in sections 1 and 2, followed by

the introduction of the counter-example in section 3.

1 Early forms of ecological, embodied and enactive theories of perception can be

found advanced in the work of Heidegger (1927) Sartre (1943) Merleau-Ponty

(1943) and Gibson (1966, 1979). 2 In addition to Alva Noë’s defense of active-externalism in Action in Perception

(2004) and Out of Our Heads (2009), the view has been recently defended in Noë,

Pessoa and Thompson (2000), and also O’Regan and Noë (2001). A number of other

contemporary philosophers have put forward externalist theories of perception.

Some examples include, M. Rowlands (1999, 2003, 2006), A.J. Jacobson (2008), and

S. Hurley (2002). The recent interest in active-externalism has also generated a

mass of critical literature. Some of the better known critical works include, Aizawa

(2007a, 2007b) and Rupert (2004).

2

Active-externalism is a theory about conscious perceptual experience. The present

discussion will focus on visual perception but conclusions about visual perception

here should make the point about perception in general. In the case of conscious

vision, discrimination of objects and their properties occurs in virtue of an

experience with phenomenal character. Phenomenal character can be a difficult

concept of convey. One way to bring out what it means for an experience to have

phenomenal character is to say that there is something-that-it-is-like to have the

experience3.

It is assumed that every experience with phenomenal character will have a material

substrate or vehicle, which is to say that there is some material property or

properties that are both necessary and sufficient for the experience to be

instantiated. Arguably, the popular view is that substrates of visual experiences are

just neural states of the brain; to have a given visual experience E one need only be

in the right neural state. Noë rejects the view that neural states are sufficient for

perceptual experiences. On active-externalism, the substrates of visual experiences

consist of aspects of the subject’s body and his or her environment.

The view that the substrates of visual experience extend into the environment

results from a particular understanding of the nature of what Noë refers to as

‘sensorimotor knowledge’ and its role in visual perception. On Noë’s view, in order

for, “mere stimulation to constitute perceptual experience, that is, for it to have

genuine world presenting content, a perceiver must possess and make use of

sensorimotor knowledge”4. Sensorimotor knowledge is counterfactual knowledge of

the way in which the sensory appearance of a perceptual object would change in

response to movement vis-à-vis the object5.

3 Following Nagel (1974) 4 Out Of Our Heads pp. 10. 5 Noë considers several empirical cases where perceivers come to master

knowledge of the ways movement influences sensory stimulation only by actively

engaging with perceptual objects. One study involves use of inverting lenses. When

subjects are fitted with glasses that cause an inversion of normal information to the

perceptual system so that sensory stimulation usually coming from the right

stimulates the left and vice versa, the initial effect is not an inversion of

representational character but rather wholly distorted visual experience. Images

only become correct after the perceiver actually moves around, learning the effects

of movement on visual sensation (see Stratton 1897, Kohler 1951, Taylor 1962).

Noë also discusses a case that he calls ‘experiential blindness’. After congenitally

blind individuals with cataract caused blindness have corrective surgery, they do

not have normal vision immediately. Their experiences do not begin to become

normal until they move around and learn about the influence that movement has on

changes in sensation (see Gregory and Wallace 1963, Valvo 1971). It should be

noted that the characterization of the inversion experiments noted above that Noë

provides is itself controversial. Klein (2007) argues not only that Kohler’s work does

3

The active-externalist view assumes that acquiring sensorimotor knowledge

requires physically engaging with one’s environment. According to Noë,

sensorimotor knowledge is practical as opposed to theoretical knowledge and is

therefore more akin to a skill such as the ability to dance than it is to a set of

propositions. Noë writes, “even if, as a matter of fact, complex abilities- like the

ability to dance- are amenable to characterization by propositions, it would not

follow that being able to dance consists in knowing those propositions”6. Acquiring a

skill requires practice performing the activity in question. If sensorimotor

knowledge is practical ‘know-how’ knowledge, then active engagement with a

perceptual object is the only way to acquire sensorimotor knowledge. The fact that

sensorimotor knowledge depends on active engagement with perceptual objects,

leads Noë to assert that the substrate of that knowledge will consist in whatever

material features of the subject’s body and environment facilitate that engagement.

He writes,

What is the causal substrate of the experience of the wine’s flavor? Perhaps

this substrate is only neural, but perhaps it is not. For example, perhaps the

only way or the only biologically possible way to produce just the flavor

sensations one enjoys when one sips a wine is by rolling a liquid across one’s

tongue. In that case, the liquid, the tongue, and the rolling action would be

part of the physical substrate for the experience’s occurrence7.

Some have accused Noë of confusing the nomological necessity of the causal relation

for the sort of metaphysical necessity that ordinarily grounds claims about

constitution8. The fact that material feature F is causally responsible for experience

E does not entail that E metaphysically supervenes on F. But Noë believes that it is

misguided to carve nature’s joints based on metaphysical rather than natural

relations. We should therefore understand Noë as delineating material substrates by

nomological supervenience relations rather than by metaphysical supervenience.

On Noë’s view, given that certain material features M of the subject’s body and her

environment are necessary for producing experience E, M constitutes E’s substrate.

A theory of perception must endeavor to explain the full range of visual perception.

One particularly difficult aspect of visual perception that it must endeavor to explain

not actually show that learning the effect of movement is necessary to correct the

inverted images but that re-inversion, if it occurs at all, does not occur when the

enactivist predicts it would. Klein takes this to be evidence against active-

externalism. 6 Action In Perception pp. 120. 7 Action In Perception pp. 220. 8 For example, both Ned Block (2005) and Adams and Aizawa (2007a, 2007b)

accuse researchers like Noë of conflating causation with constitution. They argue

that the fact that perception depends causally on action does not mean that we

ought to consider causal conditions to be constitutive of those experiences.

4

is the phenomenon of amodal perception. The following section elaborates on

active-externalism in the context the difficult case of amodal perception.

2. Amodal Perception

Amodal perception is a ubiquitous feature of ordinary perception. In amodal visual

perception, we perceive the world to contain physical features that are not directly

detectible by the visual receptors. Although we seem to see the world to contain

these physical features, amodal features are not presented in the sensory character

of visual experience in the same way that directly sensed features of objects

normally are, as sensory features. Noë describes this latter phenomenon as

‘presence in absence’ and refers to the problem that amodal perception raises for

vision theory as the, ‘problem of perceptual presence’9.

There are a number of types of amodal perception. Noë includes among amodal

perception: amodal richness10, objection completion11, perceptual invariance or

constancies12, and the perception of objects as having voluminous three-

9 See Chapter 2 and pp. 128 of Noë (2005). 10 It seems that we visually perceive the world as being richly detailed. But based on

what we actually know about the construction and workings of the visual system,

along with evidence from studies on change blindness and inattentional blindness, it

is clear that the actual qualitative details comprising visual experience can

correspond neither to the richness of detail present in the actual world, nor to the

richness of detail that our visual experiences nevertheless represent the world to be

comprised of. See Noë (2002); Action In Perception pp. 67-71; and also Dennett

(1991); O’Regan et. al. (1996, 1997); Rensink et. al. (1997, 2000); and Simons and

Levin (1998). 11 We frequently see there to be whole objects despite the fact that we do not have

continuous sensory information corresponding to the entire object. Noë uses the

example of the Kansiza figure. We experience one triangle overlapping another

despite that only the three vertices of the obscured triangle are modally present. We

experience those three separate triangles as parts of a whole triangle. When

perceiving the Kansiza figure, we also experience the bottom triangle as being

obscured by a triangle in the foreground, whose three vertices are experienced as

obscuring 1/6th of each of three circles. We do not experience the obscured circles

as having the shape of pac-men, but rather as having the shape of quarters. 12 In vision, invariance or constancy can take a variety of forms. It commonly

pertains to an object’s color, size, or shape; when we view an object we see the

object to have an invariant size, shape and color. While the size, shape and color of

the image projected onto the retina may vary as we engage the object from different

perspectives and distances, in different lighting or different contexts, typically the

size, shape and color that we see the object to be remains invariant throughout

these qualitative changes. Noë refers to this as the dual aspect of perceptual content,

“There’s the way experience presents the world as being, as it were, apart from our

5

dimensional shapes. It would be interesting to explore each of these phenomena in

depth, but here we will focus just on the amodal example of three-dimensional

object perception. When we confront objects, we always confront them from a

particular perspective. Whatever perspective we adopt on the object, we are

presented with just a facing surface. But as Noë describes, “despite the fact that you

can only see part of the object’s surface, in looking at it we enjoy the experience of it

as a voluminous solid”13. This is a form of amodal perception because perceiving the

object to have a three-dimensional shape involves perceiving the object to have

physical aspects that continue out of direct view.

The virtues of active-externalism become particularly apparent, according to Noë, in

considering how well the theory handles the case of amodal perception. Consider

the amodal case of three-dimensional object perception. On Noë’s account, seeing an

object such as a tomato to be a voluminous solid requires that one implicitly

understand that moving around the object would bring into view parts of it that had

previously been occluded. Noë writes,

What explains the fact that you experience the tomato as voluminous and

three dimensionally extended is that in looking at the tomato, you implicitly

take it that were you to move your eyes a bit to the left or right or up or down

you would bring previously hidden or obscured parts of the tomato into

view…you visually experience parts of the tomato that, strictly speaking, you

do not see, because you understand, implicitly that your sensory relation to

those parts is mediated by familiar patterns of sensorimotor dependence14.

In the quote above, Noë states that one must know that there will be systematic

changes in sensory experience as one moves around the tomato, in order to see it to

be a voluminous solid. But importantly, amodal perception often involves, not just

experiencing objects as being voluminous, but experiencing them as having specific

kinds of shapes. Noë writes, “you do not merely experience the tomato as three

dimensionally extended, you experience it as possessing that characteristic, tomato-

like ovoid with a furrow shape”15.

perspective. This is one aspect of content. And there is the way the world is

presented in experience, a way that always incorporates some reference to how

things look or sound or feel from your vantage point. So, for example, your

experience presents you with the circularity of the plate, but also with the elliptical

shape it presents from here.” Action In Perception pp. 163. Hulbert (1998, pp. 283)

describes color constancy as an ability to detect invariant properties associated with

color experience such as the spectral reflectance of the object’s surface based on the

unstable qualitative impression, which varies under changing lighting conditions.

Noë discusses size and shape constancy in Action In Perception pp. 75-79 and color

constancy, pp. 123-132. See also Noë (2002). 13 Action In Perception pp. 76. 14 Action In Perception pp. 77. 15 Action In Perception pp. 77.

6

Moreover, although we certainly see some objects to have generic shape-types such

as a ‘tomato-like ovoid’, it is also possible to see objects as having the very specific

determinate shapes that they in fact have. This is evident in the fact that much of our

more nuanced sensorimotor engagements with objects presupposes that we have

more than just a general sense of how they are shaped16.

On Noë’s view, in order to perceive the object’s specific shape, we must understand

the precise way that the object’s sensory presentation would change in response to

specific movements. It is not enough to understand that our sensory experience of

the object would change as we or the object change position. To see the object’s

specific shape, we must understand precisely how that sensory information would

change with each new perspective on the object17. Noë refers to these specific

dependency relations between movements relative to the object and the sensory

information that such movements would bring about, ‘laws of sensorimotor

contingency’. Laws of sensorimotor contingency can be expressed as

counterfactuals prescribing what specific sensory character would result from

which specific movements,

When you experience something as cubical, you experience it as presenting a

definite sensorimotor profile. That is, you experience it as something whose

appearance would vary in precise ways as you move in relation to it, or as it

moves in relation to you. You have an implicit practical mastery of these

patterns of change. It is this implicit practical mastery in which, for the most

part, your eventual appreciation of the observational concept ‘cubical’

consists18.

Some writers have noted that Noë’s argument for active-externalism supports two

models that differ from one another in how they yoke perception to action19. On the

16 Just think about the detailed understanding that one has to have of the size and

shape of a car in order to parallel park in very small spaces. 17 Presumably there is a spectrum with respect to how precisely we visually

experience an object’s shape. The view under consideration can account for this by

allowing there to be differences in the amount of detail in the precision of our

sensorimotor knowledge. 18 Action In Perception pp. 117. 19 See Aizawa (2010). Also, in his recent paper, “Consciousness: Don’t Give Up On

The Brain”, K. Aizawa argues that Noë puts forth both a stronger and a weaker

version of his view. We are in agreement over what we both call Noë’s stronger

view. But we differ with regard to the way that we characterize the weaker view.

Aizawa does not characterize Noë’s weaker view as a form of externalism as it

seems to him that no actual active engagement is necessary on that view. On the

other hand, I take externalism to be an essential component of Noë’s view. A weaker

interpretation must therefore be an interpretation of the view that takes it not only

to be compatible with paralysis, but to still be a variety of externalism. I attribute to

7

one hand, Noë often talks as if sensorimotor knowledge just is the right kind of

skillful engagement with perceptual objects. On this view, if perception of amodal

properties depends on employment of sensorimotor knowledge, then we can only

perceive objects when we are actively engaging with them. This view seems to be

what Noë has in mind when he writes, “seeing is an activity of exploring the world”20

and also, “consciousness, like a work of improvisational music, is achieved in action,

by us, thanks to our situation in and access to a world we know around us”21.

Following others, I will call the view that we can only perceive objects to have

amodal properties when we are actively engaging with them, Noë’s strong view.

But at some points, Noë eases off the strong claim that perception is constituted by

occurrent physical engagement22. Take a paradigmatic example of a skill that is

based on procedural learning like bicycle riding; arguably, one can only acquire the

ability to ride a bicycle by actually riding one. Unlike propositional knowledge,

acquiring a skill requires actual practice performing the activity in question. But

once one acquires the skill, the acquired knowledge can then be generalized to other

relatively similar contexts. Knowledge of how to ride a bicycle can be generalized to

enable one to ride a motorcycle. Similarly, acquiring knowledge of the

counterfactual laws required to see a tomato to have a characteristic tomato-like

ovoid with a furrow shape involves physically engaging with an object with that

kind of shape. But once we acquire the sensorimotor knowledge unique to seeing

this shape, we might assume that that knowledge could then be generalized to

future encounters with similarly shaped objects. This version of the theory is

weaker insofar as it does not take perceiving an object to depend on occurrent

engagement with the perceptual object. But even this weaker view takes the

sensori-motor knowledge required for amodal perception to depend on some

present or past physical engagement with a like-shaped object23.

Noë’s weaker view the claim that sensorimotor knowledge is causally dependent on

active engagement and the weaker view the claim that sensorimotor knowledge is

causally dependent on active engagement and the further assumption that for Noë,

causal dependence can be the basis for claims about constitution or substrates. 20 Out Of Our Heads pp. 146. 21 Out Of Our Heads pp. 186. 22 For example Noë writes, “Paralysis is certainly not a form of blindness. But isn’t

that precisely what the enactive view requires, that the paralyzed be experientially

blind? No. The enactive view requires that perceivers possess a range of pertinent

sensorimotor skills. It seems clear that quadriplegics have the pertinent skill…more

important, paralysis does not undermine the paralyzed person’s practical

understanding of the ways movement and sensorimotor stimulation depend on each

other”. Action In Perception pp. 12. 23 This is a form of externalism about the substrates of experience provided that we

allow his contention that substrates can extend to the external properties that

nomologically necessary for the acquisition of sensorimotor knowledge constitutive

of perception.

8

I have just articulated the strong and weak versions of active-externalism because

other readers have also had difficulty deciding on which view Noë means to defend.

For the purposes of the present paper, it won’t be important to determine which

version of the view Noë has in mind as the objection presented here shows that

neither can be the right account of perception.

3. Impossible Objects

In this section I introduce a counter-example to active-externalism. The following

section discusses an objection to the counter-example that I find unpersuasive.

My counterexample is based on the visual experience of an impossible object. As I

use the term, ‘impossible object’ refers to an object that is experienced to have

paradoxical perceptible properties such as a three-dimensional shape with

inconsistent geometrical features. Because we experience the object to have a

voluminous three-dimensional shape, the experience is a form of amodal

perception. I intend to show that active-externalism cannot account for the visual

experience of impossible objects. This is ironic as the great strength of active

externalism was its alleged ability to provide a more satisfying account of amodal

perception than rival theories.

You have probably encountered a depiction of an impossible object. M.C. Escher

popularized such depictions in the early 20th century. Around the same time, Oscar

Reutersvard drew over twenty-five hundred impossible geometric forms. Roger

Penrose further elaborated some of these, like the triangle below. When we look at

the Penrose triangle below, we experience the depicted object as a voluminous solid.

But the object that we experience the figure to depict has geometrical properties

that are inconsistent with one another. The object is therefore impossible. This point

deserves fuller elaboration. I will borrow Mortensen’s (2009) description of the

impossible content of Penrose triangle experiences. Although this description may

not prove to be exhaustive of ways to formulate how such figures might be

differently construed as impossible in visual experience, the fact that it does justice

to some instances of experience with the Penrose triangle makes it sufficient for the

present purpose.

Consider the following depiction of the Penrose triangle.

9

Axis z is normal with the plane of the paper. One key intuition about the Penrose

triangle is that, if we begin at the bottom right vertex A and follow the figure

counterclockwise, each vertex of the figure appears to recede from the observer. As

Mortensen (2009) observes,

The corner A, considered in 3-D tilts into the page when it is traversed anti-

clockwise. This means that points further along the face AB are further away in

the z-direction than points not so far along. Thus we may deduce that:

(1) A is closer in the z-direction than B

(2) B is closer in the z-direction than C

By similar reasoning:

(3) C is closer in the z-direction than A

(4) Trans (closer)

(5) A is closer in the z-direction than A

But clearly, by observation (or by definition of closer):

(6) A is not closer (in the z-direction) than A

The statements (5) and (6) contradict one another. This is the proposed proof of

the paradoxicality of the triangle.24

24 Mortensen’s logical re-construction of the impossible content of visual

representations of the Penrose triangle is reinforced by a psychological account of

how such content is cognitively constructed (2009, 2010). Cowan and Pringle

(1978) asked participants to rate 18 of 27 four-sided figures in terms of geometrical

possibility/impossible on a 1-10 scale. Degree of impossibility turned out to reflect

judgments of parity of the figure’s corners as follows. Starting at the bottom right

corner, the corners of the figures are viewed in a counter-clockwise rotation. One

point is added for each time a corner seems to turn into the plane of the page, and

one point is subtracted for each time a corner seems to turn outward. Co-planar

corners are neutral. High rankings on impossibility correlate strongly with higher

mean parity scores. Mortensen takes the strong correlation between parity and

impossibility to reinforce the logical analysis of the paradoxical visual content

above, where the paradox involved premises articulating parity of the vertices. For a

10

Assuming as is customary that we can only perceive objects as they would appear in

Euclidean space, we experience the Penrose triangle to be an object with a three-

dimensional shape that no object could really have25. The shape that we see it to

have is a shape that could not exist in Euclidean space26.

It goes without saying that we cannot engage with impossible shapes. Since one

could not have ever engaged with the relevant shape, the experience of the Penrose triangle is a counter-example to Noë’s strong view that seeing an object to have a

specific voluminous shape requires that one be physically engaging with the

object27.

The experience of the Penrose triangle is also a counter-example to the weak

version of Noë’s view. On that view, perceiving an object to have a specific

voluminous shape does not require occurrent physical engagement with the

perceptual object. But on the weak view, experiences still supervene on external

features because at least some prior physical engagement with a like-shaped object

was necessary in order for the perceiver to have acquired the counterfactual

knowledge relevant to perceiving that exact shape28.

mathematical account consistent with Mortensen’s logical and psychological

account, see Mortensen (2010). 25 The argument doesn’t require that the concept of impossibility is represented in

the content of the visual experience here, although in some cases it might be. The

claim here is that the configuration of properties represented in visual experience

could not be co-instantiated in an actual physical object. 26 Although the assumption that it is possible to represent what is impossible is

controversial, there is already a precedent set for this assumption by Paul

Churchland (2005). Churchland demonstrates that it is possible to experience

‘chimerical colors’ which are color qualities that cannot exist. Churchland argues

that such colors can even be predicted from the assumptions of the standard color

opponency model of visual processing, which is a physical theory. 27 Note that we see the Penrose triangle depicted not just as having a voluminous

shape, but as having a very specific shape much as we see the cube to have a specific

shape (in the case of the Penrose triangle however it is a specific paradoxical shape).

The substantiation of this claim is made in section 4. 28 Mortensen and colleagues have attempted to construct a convincing animation of

a rotating Penrose triangle. The animation might be taken as equivalent to walking

around a figure. At a point in the rotation three tri-bars seem to connect up making a

Penrose triangle just as in the Perth construction. At another point, one tri-bar

appears to pass through another. If the animation were truly equivalent to a rotating

Penrose triangle, then this might suggest that we could acquire the relevant

counterfactuals necessary to see it to have an impossible shape by moving relative

to such an object (or by viewing the animation). But the animation only apparently

rotates an impossible figure. For one thing, the tri-bars do not connect up in the way

that they do in our visual representation of the impossible Penrose triangle, so the

11

I want now to add to the strength of this counterexample by highlighting some

additional problems that the impossible object poses for active-externalism.

Certain actual oddly constructed three-dimensional objects are commonly perceived

as real three-dimensional Penrose triangles. Consider the photograph of the

apparently impossible triangle below29.

When we are in the presence of this object, the object appears to have an impossible

three-dimensional shape. But the object’s actual shape is different from the shape

that it is commonly experienced to have. Its actual shape is revealed by the three

images below, which show the apparently possible object as it actually appears

when it is seen from different perspectives30,

Arguably, the best way to characterize our original experience of the apparently

impossible object above is by the concept of illusion. When a perceiver takes up the

perspective that the first photograph depicts the object from, the qualitative

impression on the retina made by the object is identical to the qualitative

impression that an actual impossible object (if there were such a thing) might make.

rotating object is not analogous to a rotating Penrose triangle in the relevant way.

Moreover, since the tri-bars do appear to connect up at a single point in the rotation,

we are left with our initial worry about how we can see the object to have this

impossible shape despite its not actually having the shape that we represent it to

have at that point. Finally, it is worth nothing that the tri-bars in the animation are

not continuous; they are composed of discontinuous cubes. 29 This construction by Brian McKay and Ahmed Abas is located at Claisebrook

Square in Perth, Australia. 30 Photographs by, Bjørn Christian Tørrissen.

12

In other words, the impression from this perspective is compatible with two ways of

resolving the image: as having the shape that the construction actually has, or as the

impossible shape of a Penrose triangle. But the perceiver generally does not

experience the object as having the disjunctive property of having one or the other

of the two shapes. Rather, the visual system selects one way of resolving the image

over the other and we experience the object as having the impossible shape.

The question arises, how should we explain the visual system’s selection of the

incorrect disjunct in this illusion? Noë presents the following explanation of

perceptual illusion, “one misperceives because one draws on the wrong

sensorimotor skills and expectations”31. Recall that according to Noë’s view, in order

to see an object to have a specific shape one must draw on the set of counterfactual

relations between movement and appearance that are specific to the shape that the

object is seen to have. If in perceiving an object, we draw on counterfactual

information specific to a different shape, then we will, on Noë’s view, see the object

to have the shape that corresponds with that counterfactual knowledge rather than

see it to have the shape that the object actually has.

Active-externalism, then, explains the illusion of the apparently impossible triangle

as resulting from the perceiver drawing on the wrong sensorimotor skills and

expectations. But drawing on the wrong sensorimotor knowledge still involves

drawing on some sensorimotor knowledge. Presumably, to see the object as the

apparently impossible triangle, we would have to draw on counterfactual

knowledge particular to the impossibly shaped object that we see it to be. But this

wouldn’t be possible on the active-externalist view. Recall that active externalism

has it that we can only acquire the laws of sensorimotor contingency pertaining to a

shape by actively engaging with that shape-type, either occurrently (strong view) or

at least at some point in the past (weak view). Given that we cannot interact with

impossible objects at all, we would not be able to acquire the particular

sensorimotor knowledge that would be necessary to account for this illusion. So

Noë’s active-externalism cannot explain the illusion of the apparently impossible

triangle.

Moreover, active externalism predicts that once perceivers come to master the

relevant laws of sensorimotor contingency, they will come to perceive the object’s

true shape. We perceive an object to have a specific shape by understanding the

counterfactual relations between movement and the sensory information pertaining

to the object. Acquiring the right sensorimotor expectations should enable us to see

the object’s shape correctly. But contrary to the predictions of active-externalism,

even after perceivers have learned how the appearance of the construction depicted

in the photographs above changes as it is viewed from different perspectives, on a

very basic visual level, the object continues to look to have an impossible shape

31 Action In Perception pp. 86.

13

when we adopt the relevant perspective32. The example resembles the Muller-Lyer

illusion where two lines that are really the same length appear to be different

lengths due to the presence of certain contextual factors, even after learning that the

lines are the same length. Although one can come to see the apparently impossible

object to have the unusual but entirely possible shape that it actually has, this

requires considerable effort; it is not automatic in the way that visual perception

generally is. The active-externalist theory is supposed to explain this automatic type

of visual perception. So the example shows that sensorimotor knowledge is actually

impotent when it comes to explaining the theory’s target.

The impossible figure counterexample is straightforward. But it would be advisable

to consider potential objections before making any final proclamations about the

plausibility of active-externalism based on the impossible triangle. I discuss several

versions of a promising objection in the following section. The objection has some

prima facae plausibility. Ultimately, however, the objection is unpersuasive.

4. Objection

One might object to the previous section’s counter-example to active-externalism on

the ground that I have incorrectly described the way that we experience the object.

Contrary to what I have claimed, it may be charged that we never actually visually

experience the Penrose triangle as having conflicting geometrical properties. Below

I elaborate several versions of this objection.

One weakness of arguments that rely on appeals to phenomenology is that people

often have different intuitions about phenomenal character. We disagree about

phenomenology. It therefore seems plausible that there would be disagreement

over the best way to describe the visual experience of the Penrose triangle. One

view might be that, rather than experiencing the triangle as having a precise shape

consisting of two conflicting geometrical properties, we visually experience the

Penrose triangle in a vague way, leaving the shape at least partially unspecified. One

who held this interpretation could also hold that we do not visually experience the

shape to be paradoxical, perhaps one of its conflicting features is not manifest in

experience.

If the only motivation to hold this alternative view about the experience of the

Penrose triangle turned out to be that it just seems introspectively apparent, then I

could disarm the objection by the claim that it is not consistent with what seems

most introspectively apparent to me when I view the figure. So it would help the

objection if there were some independent motivation for the claim that we visually

32 It may be that once perceivers learn the apparently impossible object’s actual

shape, they are unlikely to experience it in quite the same way as they had the first

time. But I think this is most likely due to their knowing that they are subject to a

visual illusion, rather than to a difference in the visual experience itself.

14

experience the shape vaguely. I’m going to go ahead and consider a possible

justification for this view on behalf of the objection and then evaluate its plausibility.

It is evident that we experience many ordinary objects to have shapes and sizes

where we leave those shapes partially unspecified. For example, consider the magic

scarf trick; a magician pulls an unexpectedly long silk scarf from a pocket. The first

time we see this trick it is likely to be accompanied by feelings of surprise and

perplexity. Arguably, this stems from the fact that our expectations about the length

of the scarf are violated when the magician removes the scarf from his or her pocket.

Our initial expectations about the size of the scarf can be explained by appeal to the

notion of object completion33. Object completion is a form of amodal perception. We

frequently see there to be whole objects despite the fact that we do not have

continuous sensory information corresponding to the entire object. When we first

perceive the magic scarf, we attribute to it a fairly specific three-dimensional size

and shape, even though we only make direct visual contact with a small portion of

the scarf. We expect that further visual contact with the scarf will confirm this.

When we see that the scarf’s actual size conflicts with our initial experience of it, we

are surprised.

After having seen the magic scarf trick a number of times, however, we no longer

react in the same way. We are not surprised. I think that this is because learning the

actual length of the scarf influences the way that we subsequently perceive the scarf.

But it isn’t that we come to see the scarf to be the particular size that it is. Rather, a

better explanation is that we no longer attribute any particular length to the scarf.

Consider another similar example. When we experience an oncoming train, we

make direct visual contact with just a small portion of the train. But arguably, we

still experience there to be a whole train. To see there to be a whole train is to

experience the train to have some determinate length. But what length do we

experience the train to be? We do not see the train as being the specific length that it

is. If we did, we would be surprised whenever a train turns out not to be the precise

33 An alternative description might be that we are surprised when we see the actual

length of the scarf because it conflicts with expectations that we have about its size

based on background beliefs that we have previously formed about the sizes of

particular objects. As evidence for this view one might point to the fact that learning

the actual length of the scarf has an impact on the way that the scarf is experienced

subsequently as evidenced by the fact that after exposure to the trick we are no

longer surprised. The fact that we are no longer surprised suggests that something

has changed. For those who believe that perception is not affected or penetrated by

experience or other mental states, the easiest way to account for the change would

be by the view that what has changed is some background belief about the scarf’s

size or shape. But while impenetrability may be used as evidence that something is

perceptual, it is far from established that all perceptual processing is resistant to

influence by other mental states. Moreover, even if one maintained this

disagreement regarding the scarf case, there are surely many other examples of

object completion that one could substitute here.

15

length that we had anticipated. But we are seldom surprised at discovering the

actual length of a perceived train. This cannot be because we always experience the

train to be the particular length that it is and we are always correct. That would be

surprising. The best way to explain our lack of surprise at the train and magic scarf

cases, I propose, is by the view that we experience each as having some determinate

length, a length that is left unspecified in experience. So it seems right that while we

often see objects as having determinate sizes and shapes, we do not necessarily see

those objects to have any particular size or shape.

This fact about ordinary perception of common objects might be used to bolster the

claim that we visually experience unordinary objects such as the Penrose triangle

vaguely as well. But I want to maintain, contrary to this objection, that we do not

experience the shape of the Penrose triangle in a vague and unspecified way. I

appealed to the fact that we are surprised when we learn the true length of the scarf

as evidence that we initially perceive the scarf to have a relatively specific size. We

are surprised at what we learn about the scarf’s length because it conflicts with our

expectations about its length based on the content of our visual representation of

the scarf. The Penrose triangle evokes feelings in us that are similar to surprise,

namely perplexity and confoundedness. It seems likely that these similar feelings

are also caused by the fact that the experience of the figure violates our

expectations.

But in the case of the Penrose triangle, the way that we experience the object to be

violates expectations about what sorts of perceptible objects there can be. This

supports the view that we experience the Penrose triangle as having an impossible

three-dimensional shape. In order to experience the object to have the paradoxical

shape that we experience it to have, we must see it to have a specific shape with two

inconsistent geometrical properties. On the other hand, when we experience objects

vaguely or indeterminately shaped, we would have expected the experience to be

accompanied by the sense that there are aspects of the object’s shape that are

unknown and yet to be revealed. But our experience of the Penrose triangle is not

accompanied by the sense that aspects of its shape are yet to be revealed. It

therefore seems better to say that we experience the Penrose triangle to have a

specific albeit impossible shape. So I don’t think that the counterexample I have

presented can be defused by redescribing the experience of the impossible figure as

of an object whose shape is only vaguely experienced.

I have been assuming that if one wanted to charge that I have misdescribed the

experience of the Penrose triangle as of an impossible shape, he or she should have

in mind an alternative description of the experience of the triangle where it is not

seen has having conflicting geometrical properties. Since the object depicted by the

drawing of the Penrose triangle does have conflicting geometrical properties, the

best alternative description will involve experiencing the object in an incomplete

way. Another alternative description is that we don’t experience the figure all at

once in visual character, but rather, different aspects of the object become more or

less salient at different times. This would call into question that we see the Penrose

16

triangle as paradoxical. For something to be seen as paradoxical, two contradictory

features of it must be presented alongside one another. On this hypothetical

alternative interpretation of the experience of the Penrose triangle, the triangle

would not be a counter-example to active-externalism.

I don’t think that this redescription of the case will do the trick either. If one

wanted to maintain that we do not see the Penrose triangle as having an impossible

shape, then they must provide an alternative account for why our experience of it is

accompanied by feelings of surprise, perplexity and confoundedness. I have been

maintaining that such feelings occur whenever we encounter something that

conflicts with expectation and that in the case of the Penrose triangle, these feelings

arise because what we see conflicts with our expectations about what sorts of

perceptible geometric forms there can be. If we really don’t see the Penrose triangle

as having the impossible shape, as this version of the objection maintains, then what

could it be that conflicts with expectation and evokes the feelings of surprise and

such? I think that there are two possibilities that someone raising this version of the

issue against my counter-example might appeal to. I don’t think that either will

work. Let’s consider each.

First, perhaps we feel perplexity and confoundedness at the Penrose triangle on

account of entertaining a thought or making a judgment to the effect that the various

geometrical properties that we individually see the object to have at different times

all belong to the same object. On this hypothetical account, it would be a thought

that has the paradoxical content rather than the visual experience itself, as I have

been suggesting. A judgment or thought is a cognitive state that involves

entertaining, if not endorsing, a proposition.

Here is why I do not find this explanation to be satisfying. When we come to see the

true shape of the apparently impossible object in the photograph in the previous

section, either by moving about the object or by viewing photographs of the object

taken from different perspectives as we have already done, we come to believe that

the apparently impossible object has an entirely possible actual shape. Yet, even

after we learn the object’s true shape, we are still subject to the illusion when we

return to the relevant perspective. If experiencing the object as having an

impossible shape were really the result of forming a judgment or entertaining a

thought about its shape with paradoxical contents, then after learning its true shape,

we would be entertaining two different propositions about the object which each

attribute to the object an entirely different three-dimensional shape; one

proposition attributes to the object its true shape and one attributes to it the

impossible shape (accounting for the illusion). But it seems unlikely that this would

happen. The rational thing would be to stop thinking about the object as having an

impossible shape upon learning otherwise. Either most perceivers are being

irrational, or we can visually represent objects to have impossible shapes. I find the

latter more likely to be the case.

17

Also, recall that when we view the apparently impossible construction from the

perspective depicted in the first photograph, the qualitative impression projected

onto the retina is compatible with at least two ways of reconciling the object’s

shape. We can experience the object to be shaped as an impossible Penrose triangle,

or we can experience it as having the shape that the construction actually has.

Rather than experience the object’s shape as this set of disjuncts, the visual system

selects just one disjunct, resolving it as an impossible object. The fact that learning

the construction’s true shape has no impact on how we resolve the visual

information suggests that the mechanism responsible is automatic and resistant to

influence from higher-level cognitions such as beliefs. These are properties that are

often ascribed to perceptual processing and not to personal level judgments34. I take

this as further evidence that experiencing the Penrose triangle to be impossible is

not a result of endorsing, or even just entertaining, a proposition.

I have been canvassing alternative accounts for how our experience of the Penrose

triangle could come to be accompanied by feelings of surprise, confoundedness and

perplexity. This is important because to object to my counterexample based on the

assumption that I have incorrectly described the case as one of instantiating

paradoxical perceptual content, one would have to show that there is an alternative

description for how we experience the impossible object that can account for the

experienced strangeness in viewing it. A final explanation that might be given is

that, based on having seen an individual part of the object such as a vertex or a

tribar, we form perceptual expectations about the object’s unseen parts that are

violated when we attend to those parts; here we have perceptual expectations about

what sorts of sensory changes will accompany movement even without

representing the object’s specific shape. So for example, when viewing the Penrose

triangle, our perceptual expectations might conform to the set of changes that would

be consistent with viewing a common three-dimensional triangle. Given past

experience with regular triangular objects, we should expect further visual exposure

to similar objects to conform to the sensorimotor contingencies of regular triangles.

As we scan the Penrose figure, however, the actual visual experience violates these

expectations and maybe this is what accounts for our feelings of perplexity and

surprise.

But I am skeptical that this alternative account will do. Note that in cases such as the

magic scarf, after we see the trick a few times, we are no longer surprised. We learn

to have new visual expectations about the scarf and experience conforms to this

new set of expectations. We should expect that once we become visually accustomed

to the Penrose triangle, something similar would happen. As we become familiar

with the object, expectations about how its sensory presentation would change as

we move our eyes over it would eventually come to conform to the actual visual

potential of the present shape. On the alternative description advanced above, as

34 I’m not claiming that all perception is belief-independent. Rather, belief-

independence can be evidence that something is a matter of perception rather than

thought.

18

our visual experience conforms to the actual shape of the object, the sense of

perplexity and confoundedness should dissipate. It is significant that this never

completely happens with the Penrose triangle. The object continues to evoke

feelings of perplexity and confoundedness when we view it. So the perplexity and

confoundedness that we experience in the case of the Penrose triangle cannot be

fully accounted for by the view that perceptual expectations are violated when we

view it. Rather, as I have already indicated, when we view the Penrose triangle, we

feel perplexity and confoundedness at the violation of our expectations about what

types of perceptible objects are possible. And this indicates that we see it as having

an impossible shape.

Conclusion

A theory of perception must be capable of explaining the full range of conscious

perception, including amodal perception. In amodal perception, we perceive the

world to contain physical features that are not directly detected by the visual

receptors. For example, in the case of three-dimensional object perception we see

objects as having voluminous shapes, backsides and other parts that remain out of

direct view. According to the active-externalist theory of perception, amodal

perception, including three-dimensional object perception, depends on active

engagement with perceptual objects.

Philosophers who have critically engaged with Noë’s view have noted that the

literature on active-externalism supports two versions of this view. According to

what I have referred to as Noë’s strong view, sensorimotor knowledge just is the

right kind of skillful engagement with perceptual objects. If amodal perception

depends on employment of this kind of sensorimotor knowledge, then we can only

perceive objects when we are actively engaging with them. Elsewhere it seems that

Noë has a weaker view in mind that does not take perceiving an object to depend on

occurrent engagement with perceptual objects. On the weaker view, the

sensorimotor knowledge constitutive of perception will have been acquired during

some present or previous physical engagement with a like-shaped object.

This paper discussed a counter-example to both the strong and weak versions of

active-externalism. The counter-example involves the visual experience of so-called

‘impossible objects’ such as the Penrose triangle. Impossible objects are objects

experienced in visual character as having geometrical properties that no physically

real object can have. I have argued that we visually experience such objects as

having impossible voluminous shapes. Since we see the object to have a shape that

we cannot ever have engaged with, perceiving objects to have specific three-

dimensional shapes cannot depend on actual active engagement with perceptual

objects. This is to say, then, that we have no reason for taking perception to

supervene on external features of the environment such as perceptual objects.

19

One may wonder, however, whether an even weaker enactivist (but not necessarily

externalist) theory might still be viable. Perhaps perception still depends on

sensorimotor knowledge, knowledge of the way that sensorimotor experience may

change as we take on different perspectives vis-a-vis the object of perception, but

sensorimotor knowledge does not depend on having ever physically engaged with a

perceptual object. It is worth noting that this enactivist view would not necessarily

be incompatible with the computational view of perception that Noë rejects. But

even so, could this watered down version of the theory hold out some promise?

To the contrary, I think that it is here where the impossible object counter-example

proves most interesting. Insofar as the impossible object’s shape is physically

impossible, there is no conceivable system of behavior that would enable one to

experience it to have the impossible shape. The inconsistencies in the apparent

geometry of the object would dictate incompatible courses of movement to go

through or around it. How then could seeing the Penrose triangle to have an

impossible shape depend on sensorimotor knowledge? The impossible object

counter-example therefore demonstrates that even the weakest form of the view

cannot adequately account for the phenomenon of amodal perception.

* The author would like to thank for their helpful comments, Benedicte Veillet,

Elizabeth Schechter, Esa Diaz-Leon, Heather Logue, Louise Antony, and an audience

at the University of Connecticut’s Philosophy department to whom an earlier

version of the present paper was presented.

References

Aizawa, K. and F. Adams (2007a) The Bounds of Cognition. Blackwell Publishers.

Aizawa, K. and F Adams (2007b) “Understanding the Embodiment of Perception”

Journal of Philosophy. 104, pp. 5-25.

Aizawa, K. (2010) “Consciousness: Don’t Give Up On The Brain”. Royal Institute of

Philosophy Supplement. 85: 263-284. Cambridge University Press.

Block, N. (2005) “Review of Action in Perception by Alva Noë” in Journal of

Philosophy. Vol CII Issue 5.

Churchland, Paul. (2005) “Chimerical Colors: Some Phenomenological Predictions from

Cognitive Neuroscience” in Philosophical Psychology. Vol. 18. No. 5 pp. 527-560.

Cowan, T., and Pringle, R., (1978) An Investigation of the Cues Responsible for Cube

Impossibility. Journal of Experimental Psychology: Human Perception and

Performance, 4: pp. 112-120.

Dennett, D.C. (1991) Consciousness Explained Boston, MA: Little, Brown & Co.

20

Gibson, J.J. (1979). The Ecological Approach to Visual Perception. Houghton Mifflin.

Gibson, J.J. (1966) The Senses Considered As Perceptual Systems. Boston: Houghton-

Mifflin.

Gregory, R.L. and J.G. Wallace. (1963) “Recovery From Early Blindness: A Case

Study”. Experimental Psychology Society. Monograph no. 2.

Heidegger, M. (1927) Being and Time. Trans. J. Macquarie. Oxford: Blackwell.

Hulbert, A.C. (1998) “Computational Models of Color Constancy” in Perceptual

Constancy. Ed. V. Walsh and J. Kulikowski. Cambridge: Cambridge University Press.

Hurley, S. (2002) Consciousness In Action. Harvard University Press.

Jacobson, A.J. (2008) “What Should a Theory of Vision Look Like?” Philosophical

Psychology. Vol. 21. Issue 5. Pp. 585-599.

Klein, C. (2007) “Kicking the Kohler Habit” Philosophical Psychology Vol. 20, No. 5:

pp. 609-619.

Kohler, I. (1951/1964) “Formation and Transformation of the Perceptual World”

Psychological Issues 3, no. 4: 1-173

Merleau-Ponty, M. (1943) The Phenomenology of Perception. London: Routledge.

Mortensen, Chris (2010) “Visual Paradox and Cognition” in Christiansen, Scheier and

Sutton eds. ASCS09: Proceedings of the Ninth Conference of the Australasian Society for

Cognitive Science 2010, Sydney: Macquarie Centre for Cognitive Science, 245-

249.

Mortensen, Chris. (2010) Inconsistent Geometry, College Publications.

Nagel, T. (1974) “What is it Like to Be a Bat?” Philosophical Review, pp. 435-450.

Noë, A., Pessoa, L. and Thompson E. (2000) “Beyond the Grand Illusion: What Change

Blindness Really Teaches Us About Vision.” Visual Cognition 7: 93-106.

Noë, A. (2002a) “Is the Visual World a Grand Illusion?” in, Is the Visual World a Grand

Illusion?, ed. A. Noë, 1-12. Thorverton, UK: Imprint Academic.

NoëA. (2009) Out of Our Heads: Why You Are Not Your Brain And Other Lessons

From the biology of Consciousness. Hill and Want.

21

O’Regan, J.K., Rensink, R.A., Clark J.J. (1999) “Change Blindness As a Result of

Mudsplashes” Nature 398 p. 34.

O’Regan, J.K., Rensink, J.A., Clark, J.J. (1996) “Mud Splashes Render Picture Changes

Invisible”. Invest. Ophlhalmol Vis Sci. 37, p. 213.

O’Regan, J.K. and Noë, A. (2001) “A Sensorimotor Account of Vision and Visual

Consciousness” Behavioral And Brain Sciences. 24: 5.

Palmer, Stephen E. (1999) Vision Science: Photons to Phenomenology. Cambridge, MA:

MIT Press.

Rensink, R.A., O’Regan, J.K., Clark, J.J. (2000). “On the Failure to Detect Changes in

Scenes Across Brief Interruptions” Visual Cognition.

Rensink, R.A., O’Regan, J.K. Clark J.J. (1997) “To See or Not to See: The Need for

Attention to Perceive Changes in Scenes” Psychological Science, 8 (5). Pp. 368-73.

Rowlands, M. (1999) The Body in Mind: Undersanding Cognitive Processes. Cambridge

University Press.

Rowlands, M. (2006) Body Language: Representation in Action. MIT Press.

Rowlands, M. (2003) Externalism: Putting Mind and World Back Together Again.

McGill-Queen’s University Press.

Rupert, R. ( 2004) “Challenges to the Hypothesis of Extended Cognition,” Journal of

Philosophy 101: 389-428.

Sartre, J.P. (1943) Being and Nothingness. Trans. H. Barnes. London: Methuen.

Simons, D.J. and Levin, D.T. (1998) “Failure to Detect Changes to People in a Real-

World Interaction” Psychonomic Bulletin and Review, 5 pp 644-9.

Stratton, G.M. (1897) “Vision Without Inversion of the Retinal Image” Psychological

Review 4: 341-360, pp 463-481.

Taylor, J.G. (1962) The Behavioral Basis of Perception New Haven, CT: Yale University

Press.

Valvo, A. (1971) Sight Restoration After Long-Term Blindness: The Problems and

Behavior Patterns of Visual Rehabilitation. New York: American Federation for the

Blind.