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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.
References
Anthony, L. 2011. The openness of illusions. Philosophical Issues 21: 25-44.
Bingham, G., Zaal, F., Robin, D., & A. Shull. 2000. Distortions in definite distance and
shape perception as measured by reaching without and with haptic feedback. Journal of
Experimental Psychology 26: 1436-1460.
Brewer, B. 2008. How to account for illusion. In A. Haddock & F. Macpherson (eds.).
Disjunctivism: Perception, Action, Knowledge. New York: Oxford University Press.
Burge, T. 2005. Disjunctivism and perceptual psychology. Philosophical Topics 33: 1-78.
Burge, T. 2010. Origins of objectivity. New York: Oxford University Press.
Byrne, A. & D. Hilbert. Colors and reflectances. In A. Byrne & D. Hilbert (eds.),
Readings on color vol. 1: The philosophy of color. Cambridge, MA.: MIT Press.
17
Campbell, J. 2002. Reference and consciousness. New York: Oxford University Press.
Carruthers, P. 2005. Consciousness: Essays from a higher-order perspective. New
York: Oxford University Press.
Dretske, F. 1988. Explaining behavior: Reasons in a world of causes. Cambridge, MA.:
MIT Press.
Dretske, F. 1995. Naturalizing the mind. Cambridge, MA.: MIT Press.
Dyer, A. 2012. The mysterious cognitive ability of bees: Why models of visual processing
need to consider experience and individual differences in animal performance. Journal
of Experimental Biology 215: 387-395.
Fish, W. 2009. Perception, hallucination, and illusion. New York: Oxford University
Press.
Freeman, J. & E. Simoncelli. 2011. Metamers of the ventral stream. Nature
Neuroscience 14: 1195-1201.
Genone, J. 2014. Appearance and illusion. Mind 123 490: 339-376.
18
Gilchrist, A. 2006. Seeing black and white. New York: Oxford University Press.
Giufra, M. & R. Menzel. 2013. Cognitive components of insect behavior. In R. Menzel
and P. Benjamin (eds.), Invertebrate learning and memory. London: Academic Press.
Hatfield, G. 2009. Perception and cognition: Essays in the philosophy of psychology.
New York: Oxford University Press.
Hilbert, D. 1987. Color and color perception. Stanford: CSLI.
Horridge, A. 2009a. Generalization in visual recognition by the honeybee (Apis
mellifera): A review and explanation. Journal of Insect Physiology 55: 499-511.
Horridge, A. 2009b. What does an insect see? Journal of Experimental Biology 212:
2721-2729.
Martin, M. 2004. The limits of self-awareness. Philosophical Studies 120: 37-89.
Masrour, F. 2015. The geometry of visual space and the nature of visual experience.
Philosophical Studies 172: 1813-1832.
19
Masrour, F. Forthcoming. Space perception, visual dissonance, and the fate of standard
representationalism. Nous.
Mendelovici, A. 2013. Reliable misrepresentation and tracking theories of mental
representation. Philosophical Studies 165: 421-443.
Nanay, B. 2013. Between perception and action. New York: Oxford University Press.
Ramsey, W. 2007. Representation reconsidered. Cambridge: Cambridge University
Press.
Rogers, B. 2010. Stimuli, information, and the concept of illusion. Perception 39: 285-288.
Salva, R., Rugani, R., Cavazzana, A., Regolin, L., & G. Vallortigara. 2013. Perception of
the Ebbinghaus illusion in four-day-old domestic chicks (Gallus gallus). Animal
Cognition 16: 895-906.
Scarantino, A. 2015. Information as a probabilistic difference maker. Australasian
Journal of Philosophy 93: 419-433.
Sorvano, V., Albertazzi, L. & R. Salva. 2015. The Ebbinghaus illusion in a fish (Xenotoca
eiseni). Animal Cognition 18: 533-542.
20
Tye, M. 1995. Ten Problems of Consciousness: A representational theory of the
phenomenal mind. Cambridge, MA.: MIT Press.
Zhang, S., & M. Srinivasan. 2004. Exploration of cognitive capacity in honeybees:
Higher functions emerge from a small brain. In F. Prete (ed.), Complex worlds from
simpler nervous systems. Cambridge MA.: MIT Press.
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