Are Visual Illusions Misrepresentations?

1. Introduction

A central question of philosophy of perception is whether visual states have a nature

similar to beliefs about the world, whether they are essentially representational.

According to the content view, visual states are, at their core, representations with

contents that can be assessed for accuracy vis-à-vis the scene before the eyes. A familiar

line of reasoning in favor of the content view is that it offers the best overall account of

visual illusion (Burge 2005 and Byrne 2009). Illusion is taken to be nothing more than

misrepresentation at the sensory level. I call this the misrepresentation model of visual

illusion.

I accept a version of the content view, but I am going to raise a worry about this

way of defending the view. I introduce a novel way of thinking about illusion, what I call

the metamer model of visual illusion. This alternative to the misrepresentation model is

neutral on the issue of whether visual states are essentially representational.

Consequently, more work needs to be done to establish that the content view provides

the best overall account of illusion. We need reason to think that the misrepresentation

model is preferable to the metamer model.

Part of the interest of the metamer model, then, is its relevance to the ongoing

debate between proponents of the content view and naïve realists. Naïve realists like

Campbell (2002), Martin (2004), and Fish (2009) suppose that visual states are

fundamentally different in kind from beliefs and other paradigmatic representational

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states. Accordingly, they are committed to rejecting the misrepresentation model of 1

visual illusion and require an alternative. The model I introduce is, I believe, an

attractive option for these theorists.

I am attracted to the metamer model for yet a different reason. I endorse

Dretske’s (1988) familiar version of the content view. In Dretske’s framework,

misrepresentation is tied to failure to fulfill a biological function. Some visual illusions

are plausibly taken to be consequences of biological malfunction, and the

misrepresentation model is well suited to handle these cases. It is highly doubtful,

however, that all illusions involve biological malfunction. I will suggest that the

metamer model offers just what is needed to supplement Dretske’s approach to illusion.

Sections two and three are devoted to the misrepresentation model and the

metamer model, respectively. Although the metamer model can be cast in theoretically

neutral terms, I will sometimes presuppose Dretske’s version of the content view,

thereby preparing the way for the discussion in section four of Dretske’s way of handling

illusion.

2. The Misrepresentation Model

Mental representations are supposed to afford a distinctive explanation of successes and

failures of goal-directed activities. The idea is that success or failure in attaining a goal is

sometimes due to representational success or failure. Suppose you want to grab your

keys as you leave for an outing. Your belief about the location of the keys can help to

1 In what follows I set aside skepticism about the representational theory of mind. For reasons to take skepticism seriously, see Ramsey 2007.

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explain success or failure in your goal-directed activity of fetching the keys. For

example, success in collecting the keys on the way out the door might be due, in part, to

representational success. You succeed in gathering your keys because you have an

accurate belief about their location. Alternatively, you may fail to gather them because

your belief misrepresents the location of the keys.

Visual illusion can also give rise to errors in goal-directed behavior. I am going to

focus on visual illusions in insects because it is plausible that these illusions can occur in

the absence of any associated cognitive states like belief. The task errors associated

with these illusions are to be explained at the sensory level. The misrepresentation 2

model of visual illusion assimilates these errors to the kinds of mistakes that issue from

false belief: in each case the behavior is explained in terms of representational error.

The standard way of showing that an animal is susceptible to visual illusion is

through conditioning experiments. In a reward paradigm the animal comes to prefer

some stimulus type over others because it has been paired with something the animal

needs or wants (e.g. food), while in a punishment paradigm the animal comes to

disprefer a stimulus type because it has been paired with something unpleasant or

otherwise undesirable (e.g. electric shock). The animal is thereby trained either to

pursue or to avoid a given stimulus type. These pursuit and avoidance responses can be

2 Nanay (2013: 23-28) thinks we can identify behavior directly attributable to visual states in human subjects. In his example the subject’s beliefs do not explain successes or failures of visually guided behavior because the subject does not believe that things are as they visually appear. I set this strategy aside because it is too difficult to rule out the possibility that some other cognitive state is serving as an intermediary. Perhaps the visually guided response is directly controlled by a partial belief about the display, a rejected interpretation of the display, a belief about one’s visual evidence… 

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triggered in the absence of the relevant stimulus if the animal is susceptible to visual

illusion.

This general strategy has revealed susceptibility to familiar illusions in a wide

variety of animals, including insects, fish, and birds. Two recent studies on the

Ebbinghaus illusion (Salva et al. 2013, Sovrano et al. 2015) will serve to illustrate the

approach. These studies demonstrate that four-day-old domestic chicks (Gallus gallus)

and redtail splitfins (Xenotoca eiseni) are vulnerable to the Ebbinghaus illusion. The

birds and fish were trained to find food either at the larger or the smaller of two

presented circles. The animals were then presented with two equal-sized circles in a

standard Ebbinghaus display. Animals trained to go to larger circles preferred the circle

surrounded by smaller discs, while animals trained to go to smaller circles preferred the

circle surrounded by larger discs.

Insects are prone to a number of familiar visual illusions, including the

Müller-Lyer, the Craik-O’Brien-Cornsweet, the Kanizsa, the Benham disk, and the

waterfall illusion. As with the experiments on fish and birds just described, the

experiments revealing visual illusion in insects rely on operant conditioning. On one

prominent model of visual conditioning in bees due to Horridge (2009a, 2009b), bee

responses are driven by low-level feature detectors with no role for mediating cognitive

states. Task error due to visual illusion is to be explained at the sensory level.

There are reasons to doubt that Horridge’s approach can adequately address all

visually guided behavior in bees. Some visual learning in bees is remarkably

sophisticated and difficult to make sense of without acknowledging a role for cognitive

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factors (Zhang and Srinivasan 2004, Dyer 2012, Giurfa and Menzel 2013). Nonetheless,

Horridge’s model remains highly plausible as an account of the conditioned responses

that reveal the presence of illusion in bees. There is no obvious role for cognitive states

in the production of these relatively simple conditioned responses. 3

It is plausible, then, that some task errors in bees are directly attributable to their

visual states without a role for mediating cognitive states. According to the

misrepresentation model of visual illusion, these errors are akin to errors which result

from mistaken beliefs. They are best explained on the assumption that visual states can

have inaccurate representational content. In the following section I offer an alternative

way to think about these task errors.

3. The Metamer Model

The task errors discussed in the previous section are errors in a type of matching task.

The animal is trained to seek the closest match with a previously encountered stimulus

type and picks something physically distinct from the target. This is a familiar practice.

Psychologists routinely use matching tasks to determine the presence and strength of

illusions. Gilchrist’s (2006: 267-8) attempt to define error in lightness perception (i.e.

perception of surface reflectance) is a helpful illustration:

I will define a lightness error as the difference between the actual reflectance of a

target surface and the reflectance of the matching chip selected from a Munsell

chart… [M]y definition does not strictly require that the chart itself be perceived

3 Although Carruthers (2005) believes that honeybees have a belief-desire psychology, he allows that this cognitive architecture is not required to account for simple conditioned responses to stimuli.

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with no error at all. It does, however, require that errors in perception of the

chart be small relative to the errors one is trying to measure.

In this framework lightness illusion or error (these are not distinguished from one

another) is present when distinct reflectances are a perceptual match. The strength of an

illusion is simply a matter of how great the divergence is between the target and the

matching sample.

Matching tasks are particularly useful here because they can provide evidence

that the visual system is lumping together physically distinct stimuli. And when the

visual system is lumping together physically distinct stimuli, we can have visual illusion.

For example, suppose you are asked to find a match for a shade of grey presented

against a background darker than the target and the samples for matching are viewed

against a background lighter than the target. More likely than not you will succumb to

an achromatic contrast illusion and choose a sample that is lighter (higher in

reflectance) than the target.

The importance of matching tasks for investigating illusion is not limited to

research on color vision; it is equally important for research on spatial vision. Suppose

we want to know which factors influence the presence and strength of the Müller-Lyer

illusion. The standard way of testing for the presence and potency of a spatial illusion is

to devise a matching task. In the case of the Müller-Lyer subjects would be asked to find

a match in length for the target. Matching tasks along these lines have revealed

numerous errors in our perception of size, shape, distance, and the rest.

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So far we been focusing on matching tasks as tests of illusion, but physically

different stimuli can also match thanks to limitations of sensitivity. Every visual system,

natural or artificial, is limited in its sensitivity to differences in electromagnetic energy.

Most fundamentally, visual systems are limited in sensitivity to differences in intensity

(limitations of contrast sensitivity) and differences in wavelength (metamerism). These

types of limitation can be manifest in a matching task. Suppose your task is to create a

match in color for a patch of light. You are asked to create your own patch of light by

adjusting the mixture of three lights. The match you create may be physically rather

different from the target. For example, your matching patch might be composed of three

lights differing in wavelength while the target is monochromatic.

A metameric matching experiment along these lines can show that a visual

system is lumping together physically different stimuli. The same is true of failures in

discrimination tasks. Suppose a test patch differs in luminance from its surround, but

the difference lies below threshold. The visual system is once again lumping together

physically distinct stimuli.

When lumping together of physically distinct stimuli is due to limitations of

sensitivity, there is little temptation to regard the visual system as misrepresenting the

stimuli in question. But why is that, exactly? Why do limitations strike us as different

from illusions in this respect?

I begin with a couple suggestions that can be quickly dismissed. First, one might

suggest that the difference between illusion and limitation is one of degree. Limitations

often give rise to rather minor errors: the resulting percepts are still approximately

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correct. Illusions, on the other hand, are more significant departures from reality. This

suggestion is clearly unsatisfactory. As our illustration of metamerism above illustrates,

metamers can be physically very different from one another. Second, one might suggest

that what separates limitation from illusion is the fact that in cases of limitation it would

be arbitrary to prefer one of the matching percepts over another. For example, there

would seem to be no basis for supposing that only one of a pair of metamers is

accurately perceived. Which one and why? The problem with this suggestion is that the

same can plausibly be said about the contrast illusion described above.

So why, exactly, is it unnatural to think of limitations in terms of representational

error? Perceptual error or illusion is generally measured relative to conditions where

task error is minimized. (Gilchrist’s definition of lightness error above serves as an

illustration of this general point.) Performance on a matching or discrimination task

counts as incorrect relative to performance under optimal viewing conditions (e.g. the

conditions under which subjects make the greatest number of discriminations and

matches). Unlike illusory matching, metameric matching arises even under conditions

optimal for matching. Accordingly, there is an obvious obstacle to understanding how

metameric matching (under optimal conditions) could involve representational error.

Relative to what standard is color vision falling short? Yes, we can construct any number

of standards. But is there any relevant standard of correctness relative to which

metameric matching might fall short? Of course, what counts as a relevant standard will

depend on what assumptions are looming in the background, so I want to be explicit

about some of the theoretical assumptions I inherit from Dretske.

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On Dretske’s view, visual states are fundamentally states that have the biological

function of carrying information about states of the environment. I set aside the details 4

of Dretske’s theory about what it is for a signal to indicate or carry information. (For an

attractive theory inspired by Dretske’s theory, see Scarantino 2015.) What is important

for our purposes is Dretske’s attempt to explain the source of perceptual error. Error is

possible only when a visual state has the function of indicating. The function of an

indicating state is determined historically, either through evolution or through the

learning history of the organism. When a state has the function of indicating something

about the environment, it is possible for that state to occur as a result of malfunction.

Malfunction can take various forms. Sometimes visual systems decline in function

through senescence. Other times malfunctions arise because an organism is placed in

abnormal circumstances. Whatever form it takes, malfunction can have the consequence

that a visual state indicates when it is not supposed to. We have perceptual error or

misrepresentation.

Within this framework for understanding representational error, it is clear that

metameric matching (under optimal conditions) is not a product of representational

error. Metamerism is not due to abnormality or defect. Metamerism is a straightforward

consequence of the biological structures underlying all color vision in the natural world.

Biological color vision depends on the visual system’s integration of signals from a

limited number of opsin-based receptors. These receptors can be stimulated in the same

4 For a fascinating overview and critique of Dretske’s approach to vision, see Burge 2010. I have raised objections to Burge’s alternative to Dretske’s view elsewhere [citation omitted for purposes of blind review].

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ways by lights differing in spectral composition. Metamerism is a product of perfectly

normal functioning not only across species but across phyla.

More generally, limits of sensitivity as we are thinking of them are distinct from

failures of function. They are aspects of normal functioning. For example, some limits

on contrast sensitivity are inevitable consequences of the very biological substrates that

make detection of luminance differences possible in the first place. Optical and neural

factors combine to generate constraints on how well organisms can discern differences

in light intensity. These basic limits are not plausibly regarded as having their source in

malfunctions or defects; they are among the contours that serve to define an organism’s

visual capacities.

So how are we to think about metamerism if it is not a matter of

misrepresentation? If we want to hold on to the idea that visual states carry information

about the organism’s physical environment, our best option is to allow that the

information conveyed by the visual system is relatively coarse-grained (Dretske 1995:

88-93, Hilbert 1987: 81-100, Tye 1995: 147). Relative to our best measuring devices and

methods, biological visual systems categorize stimuli in a coarse-grained manner.

Relative to the fine-grained kinds discovered by physics (e.g. specific reflectance curves),

color vision reveals coarse-grained physical properties (types of reflectances).

Remarking on human color vision, Byrne and Hilbert (1997: 266) write: “The

reflectance-types that the human visual system represents objects as having are

considerably coarser than the maximally specific colors.” Although the stimuli for color

vision are specific reflectances, biological visual systems are not equipped to represent

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these specific physical kinds. Color vision lumps reflectances together into types of

reflectances. These types are the physical properties represented by color vision.

A distinguishing feature of illusion is that it is inextricably tied with compromised

performance on visual tasks. While metameric matching need not fall short of any

relevant standard of correctness, illusory matching necessarily falls short of the

standard set by performance under conditions optimal for fine-grained matching.

(Otherwise we lose our grip on the distinction between illusion and limitation of

sensitivity.) The question we are interested in is the following: What are illusions such

that they give rise to errors in visual tasks?

The misrepresentation model and the metamer model offer different accounts of

these errors in performance. On the misrepresentation model, error in performance is

attributed to representational error at the sensory level. Performance falls short because

the guiding visual state has an inaccurate content. The metamer model accounts for

error in performance without invoking error at the sensory level. Instead it invokes

coarse-grained content. First consider a case where two physically distinct items match

in appearance. According to the metamer model, the property represented is a

coarse-grained type of physical property. There is no error because the matching items

in fact share the property in question. Next consider a case where two items with the

same physical property fail to match in appearance. (Think of standard presentations of

the Müller-Lyer.) On the metamer model, this is simply a case where vision is

representing two overlapping coarse-grained kinds, i.e. types that include the same

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fine-grained physical kind. In this way the model is able to capture the truism that

illusions are apt to mislead and it does so without positing any error at the sensory level.

The metamer model is an especially natural fit with the wide variety of illusions

made manifest through matching tasks. These illusions fit naturally with the metamer

model because they are instances of metamerism broadly conceived. Following Freeman

& Simoncelli (2011), I will use the phrase “visual metamers” to refer to “stimuli that

differ physically but look the same.” Matching tasks used to determine the presence and

strength of illusion are simultaneously tests of visual metamerism.

Suppose some illusions are best understood along the lines I have sketched. The

idea is that these illusions have the same underlying nature as limitations of sensitivity

like metamerism. Visual metamerism has the same underlying source whether it occurs

in optimal or illusory viewing conditions, namely, the coarse-grained character of our

visual perception of the physical environment. We can still allow for a distinction

between illusions and limitations of sensitivity, but the distinction will have to do with a

difference at the behavioral level. Generally speaking, illusion compromises

performance on visual tasks as compared to performance under optimal conditions.

I have cast the metamer model in representational terms, but doing so is entirely

optional. Any plausible theory of perception ought to allow for the possibility of

coarse-grained perception of the physical environment. The metamer model can fit with

most any theory that acknowledges this possibility. The metamer model comes with very

little in the way of theoretical baggage. 5

5 The metamer model has some straightforward advantages over other alternatives to the misrepresentation model. First, it avoids the extreme conclusion defended by Antony (2011) and Rogers (2010) that there are no illusions. Second, it straightforwardly extends to illusions in very different

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I mentioned at the outset that some theorists recommend the content view on the

grounds that it provides the best explanation of illusion. Previous arguments along these

lines are incomplete. We need some reason to think that the misrepresentation model is

preferable to the metamer model. I will explore this matter further in the following

section.

4. Illusion without Malfunction

Dretske’s account of misrepresentation makes good sense of some visual illusions. I will

follow Dretske and endorse the misrepresentation model for these cases. Other illusions

indicate that Dretske’s approach to perceptual error is incomplete as it stands. I will

suggest that the metamer model is the addition needed to fill in the gap.

Recall that Dretske takes visual misrepresentation to be a product of biological

malfunction. This approach readily accommodates perceptual errors that arise either

through deterioration of the sense organ or under what Dretske calls unnatural

circumstances. By “unnatural circumstances” Dretske has in mind viewing conditions

that divorce a visual system from “the habitat in which it developed, flourished, and

faithfully serviced its possessor’s biological needs” (Dretske 1988: 68). An Ames room

illustrates this point. Illusion occurs thanks to the subject’s unusually restricted

viewpoint on an artificially constructed environment. Placed in these unnatural

conditions, the subject misrepresents the space as rectangular.

creatures like insects. The accounts of Brewer (2008) and Genone (2014) are less satisfying in this respect.

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Dretske offers a plausible diagnosis of these kinds of cases. There is some reason

to prefer the misrepresentation model over the metamer model when we are dealing

with standard cases of malfunction. I agree with Dretske that performance in natural or

normal conditions provides a relevant standard for thinking about how a sensory system

is supposed to work, that normal conditions have genuine normative significance.

Accordingly, I accept that the misrepresentation model is the best account of some

illusions. I will not dwell on this point, however, because my main goal is to establish a

role for the metamer model.

I think we need the metamer model to accommodate the pervasive and

systematic illusions which occur in virtually all human perception of natural scenes.

Psychophysical studies have revealed a variety of errors in our perception of color and

spatial properties under entirely normal viewing conditions. There is little or no 6

temptation to suppose that these ubiquitous errors are products of biological

malfunction. Yes, the errors can be avoided under optimal viewing conditions.

(Otherwise they would count as limitations rather than illusions.) But optimal

conditions do not have any normative significance in Dretske’s framework. Malfunction

does not occur with the shift from optimal to normal viewing conditions. Rather, visual

malfunctions are apt to occur as we move from the organism’s natural habitat to

unnatural circumstances. Optimal performance can itself be an artifact of the unnatural

conditions of the psychophysics lab, so we have to be especially wary of taking

suboptimal performance as evidence of biological malfunction. These considerations

6 I take it that the errors I have in mind are different in kind from what Mendelovici (2013) calls reliable misrepresentations. The errors I have in mind are illusions, and Mendelovici explicitly distinguishes reliable misrepresentations from illusions.

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suggest that the misrepresentation model of illusion cannot, by itself, provide a

comprehensive treatment of illusion. My proposal is that we invoke the metamer model

to account for these errors that occur in the absence of malfunction.

The ubiquitous distortions of spatial perception under normal viewing conditions

have received considerable attention in recent philosophical work, so I will set these 7

aside and focus on errors of achromatic color perception. Natural scenes differ from

optimal viewing conditions in a couple of obvious ways. First, natural scenes include

variations in illumination like shadows, and differences in illumination give to

perceptual errors. Surfaces viewed in weaker-than-optimal illumination take on a darker

appearance and surfaces viewed in brighter-than-optimal illumination take on a lighter

appearance. Here is Gilchrist on the pervasive and systematic matching errors brought

on by variations in illumination:

...every change in illumination, especially every spatial change, causes at least

some error. Surfaces on the brighter side of the illuminance border appear lighter

than they are, or surfaces on the darker side appear darker than they are, or

both… Surfaces tend to be lightened in high illumination and darkened in low

illumination… (2006: 275)

Second, in natural scenes surfaces are viewed against a variety of backgrounds.

Differences in background colors give rise to contrast illusions: “Targets on dark

backgrounds appear lighter and targets on light backgrounds appear darker.” (Gilchrist

2006: 277)

7 See, e.g., Hatfield 2009: 169 ff., Masrour 2015, and Masrour (forthcoming). For numerous references to relevant psychological literature, see Bingham et al. 2000.

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As we move from optimal to normal viewing conditions, we get new metamers.

Shades of grey distinguishable under optimal conditions come to match in appearance.

These illusions occur under natural viewing conditions, the very conditions in which we

thrive as biological organisms. We would be hard pressed to identify any biological

malfunction at work, so the misrepresentation model is ill-equipped to accommodate

these illusions. Meanwhile, the metamer model is ideally suited to handle these cases of

visual metamerism. The idea is that we are confronting something already familiar in

optimal viewing conditions: coarse-grained visual perception of the physical

environment.

Plausibly the same kinds of points can be made about illusions found in visual

systems that have evolved independently, like the Ebbinghaus and Müller-Lyer

illusions. In these sorts of cases we have reason to think that we are dealing with basic

ways that biological visual systems sort things. As with metamerism and other

limitations of sensitivity, we should hesitate to suppose that biological malfunctions are

at work. So once again we seem to be dealing with illusion in the absence of

malfunction. But illusion without malfunction is a problem for Dretske’s approach only

on the assumption that all illusions conform to the misrepresentation model. I am

inclined to reject this assumption and acknowledge a role for the metamer model within

Dretske’s framework.

Some readers may worry about giving up on the idea that illusions have a shared

nature. I do not share this worry, however. The phenomena that get lumped together

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under the label “illusion” differ considerably in their aetiology. It would be somewhat

surprising if a single model proved to be sufficient.

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