1. Introduction

Some philosophers interested in perception who draw inspiration from empirical psychology and cognitive science have complained, with some justice, of a tendency in the philosophical literature to ignore empirical work on perception. In particular, anti-representationalists about perception have been accused of ignoring scientific work.1 There is more than one reason for anti-representationalist philosophers to pay attention to the empirical psychology of perception. For one thing, talk of ‘representations’ is ubiquitous in the field. Philosophers who hold that perception can be understood in non-representational terms owe an explanation of how their views are compatible with empirical discoveries which are often couched in representational vocabulary. There is a prima facie conflict which needs to be resolved. For another, empirical work on perception deals with a range of interesting perceptual capacities. Consideration of such work offers a broadening of horizons beyond the limited range of cases usually discussed in the philosophy of perception, and thus an escape from what Austin called the “constant obsessive repetition of the same small range of jejune ‘examples'” (Austin 1962, p. 3).

In this paper I examine one current debate in the empirical psychology of perception, one that revolves around talk of representation. I argue that non-representationalism is compatible with what has been discovered through empirical work in this corner of the field.

My argument is thus modest in two dimensions. First, I claim only compatibility: I do not argue that the empirical work I discuss shows that non-representationalism is true. Such modesty is justified by a context in which proponents of representationalism appeal to the use of representation talk in psychology in support of their position. That the findings of empirical psychology are neutral with respect to the philosophical issue is itself a substantive philosophical thesis.

Second, my conclusion, if valid, applies directly only to the specific issue at hand. There may, for all I say here, be considerations elsewhere in empirical psychology that do directly support representationalism. In mitigation, I hope that the line of thought pursued here may be applicable elsewhere. In any case, examination of specific issues in empirical psychology is what is required in order to rebut the representationalist accusation of indifference towards empirical work.

2. Representations and looks

In this section I establish a preliminary point about representationalism. Although, on the representationalist view, ascriptions of representational content explain the looks presented by objects in visual experience, one cannot infer content directly from correct descriptions of looks. Our primary concern here is with representations as defined by philosophers. Insofar as there are psychological uses of the term ‘representation’ which do not presuppose a commitment to the philosophical doctrine of representationalism, they are not part of my target.

What, then, is the philosophical doctrine? The representationalist claims, in the first instance, that to perceive an object is to represent it as being a certain way. To represent, in the relevant sense, is to token a mental state with veridicality conditions pertaining to the perceiving subject’s environment. The mental state defines conditions which may or may not be fulfilled by the way the environment is. Just as in making claims about the world we speak truly or falsely of it, in perceiving our environment we represent it either accurately or inaccurately.

Frege (1892) showed that at least some states defined by such truth or veridicality conditions – conspicuously, beliefs – are more fine-grained than the worldly states of affairs upon which their truth-values depend. The same situation can be veridically represented by states which have different veridicality conditions. It is plausible that, if veridicality conditions are ascribable also to perceptual experiences, those experiences will, like beliefs, be finer-grained than the states of affairs they represent. For the representationalist, then, the perceived environment may underdetermine the representational content of a perceiver’s perceptual states, even if we assume that the perceiver is perceiving veridically.

An example is provided by Christopher Peacocke’s (1992) discussion of representational content. All squares are regular diamonds, and vice versa. But one may represent a given object either as a square or as a regular diamond. Since the terms ‘square’ and ‘regular diamond’ mean different things, a claim that an object is a square is not a claim that it is a regular diamond. Similarly, a perceptual experience of an object as a square is not an experience of the object as a regular diamond. In this way, the representationalist can account for a striking fact about experiences of seeing such objects as square floor tiles. Depending on one’s perspective, the tiles may look either like squares or like regular diamonds. In neither case is one perceiving non-veridically. But the same tiles can on different occasions present different looks, and which look is presented on an occasion depends, the representationalist claims, on how the tiles are being represented on that occasion.

Peacocke’s example brings out an important aspect of the representationalist thesis: its approach to (in the visual case) looks. When we perceive an object, veridically or non-veridically, it presents a look to us. The floor tile presents either a square look or a diamond look, depending on our perspective. In cases of illusion, such as the case of the Müller-Lyer diagram, objects present looks to us which differ from the way they really are. The lines in the Müller-Lyer look, contrary to fact, to differ in length.

According to the representationalist, at least some differences between looks presented by objects call for explanation in terms of the contents of visual experience. The difference between the square and diamond looks presented by floor tiles is immediate and integral to the experience. The tiles present themselves to us in one way or another, so that one could see a tile as a square without realising that it can also be seen as a diamond. Since the tiles do not change between experiences of them, something in one’s experience must differ. Peacocke’s proposal is that different properties are represented in different visual experiences of the tiles. The representationalist claim is thus an explanatory one. The looks presented by objects are explained by the ways we represent them.

Nevertheless, the content of a visual experiences cannot simply be read off a correct description of the look presented. Any such description may underdetermine how we represent the object. It cannot be assumed that the veridicality conditions of the mental state that explains a given look are best described in the same terms as those which we use to describe the look itself.

This is so, in particular, because the way in which we describe the look may reflect our own interests and projects. Looks are important to us, in part, because of their epistemic value – what they enable us to know. Thus the way we describe them may reflect what we find epistemically valuable. Descriptions thus influenced by interests and values cannot be relied upon as guides to the cognitive machinery that enable us to perceive things as looking one way or another. Any example one might give is likely to be at least potentially controversial. But the following case is at least plausible, and will serve to explain the essential idea. We may describe a very dark cloud as looking like a raincloud. But a representationalist can perfectly well insist that the perceptual system merely represents the cloud as dark, and that in no way does rain enter into its representational content. We are inclined to describe the look in terms of the likeliness of rain, because of the importance for our lives on whether it is likely to rain or stay dry.

We would therefore be making a mistake if we inferred, from the existence of a rainy look, the involvement of rain in perceptual content. Still, there is a difference between clouds which have rainy looks and clouds which have not. This difference corresponds to a difference in perceptual content between experiences of rainy-looking and non-rainy-looking clouds, and this difference provides an explanation of the difference in looks. On the representationalist account, then, we must look beyond the way the world appears to us in order to determine just what the representational content of a mental state is. We must look to the cognitive machinery which enables us to perceive: we must, that is, do some empirical psychology.

3. Numerosity looks

Among the things in the world to which we are perceptually sensitive is the numerosity of collections of objects. This is especially so for small numbers: I can tell at a glance that there are four cups on the table, without having to count. But it is also true of the relative numerosity even of much larger collections of objects. Suppose that two flocks of birds are visible, both far too large for us to give a reasonable estimate of just how many birds are in either. We may still be able to say with confidence that one flock has more birds than the other.

Not only are we able to give secure judgements of relative numerosity; we do so on the basis of distinctive numerosity looks. Some collections of objects immediately strike us as more numerous than others. We are able to make these judgements only because they so strike us; because, that is, the collections present the numerosity looks they do. Since, on the representationalist view, looks are explained by the content of visual experiences, it is because our visual experiences have the contents they have that we are able to make the numerosity judgements we do.

What is meant by the claim that there are distinctive numerosity looks? One way to appreciate the point is to realise that numerosity perception, like the perception of size or colour, is prone to illusion. This has been demonstrated by empirical psychologists of perception, who have demonstrated adaptation effects on perceived numerosity and density. The basic fact is this: subjects will overestimate numerosities if they are first exposed to low numerosity arrays, and underestimate them if exposed to high numerosity arrays. Most strikingly: take a display consisting of two arrays of dots, of equal dimensions, one on the right and one on the left.2 The left array is much more numerous and dense than the right array. Subjects are asked to fixate on this display for thirty seconds; it is then replaced with a similar display, in which two identical arrays are shown, of medium numerosity and density.

In the second display, the left array strikes subjects as much less numerous and dense than the right. Having adapted to the numerous and dense left array in the first display, that in the second strikes them as particularly sparse. This is so despite another striking phenomenological fact. In the second display, the two arrays are not only equally numerous and dense, but are visibly identical. In a sense, they are obviously equal in numerosity and density, since one can take in straight away that the pattern of dots is the same in both. The demonstrated effect therefore has the character of a robust illusion. Robust illusions continue even when one discovers that they are illusions: even if one is perfectly aware of the real lengths of the lines in the Müller-Lyer diagram, one line will still look longer than the other. Indeed, this adaptation effect is an unusually striking example of a robust illusion, because it is not just that one knows that the two arrays are equinumerous. In some sense one sees that they are.

Empirical psychologists create illusions not primarily because they are interested in illusions per se, but rather because they believe that the conditions under which illusions are created sheds light on what occurs in perception in non-illusory cases. The assumption is that the same cognitive machinery that is in operation when we suffer from an illusion of low numerosity, is also in play when we veridically perceive a low numerosity. Thus, the factor that explains the illusion also explains perceptual success under different conditions. In the numerosity illusion, the left array looks less numerous than the right. It thus presents a look of relatively low numerosity to the perceiving subject. The interest in the illusion lies in this thought: the same look that is presented by the left array in the illusion is also presented by the less numerous array in non-illusory situations, when subjects achieve genuine perceptual sensitivity to numerosity.

4. Numerosity and density

In this section, I examine some hypotheses that have been put forward in the literature of empirical psychology to explain numerosity looks. These hypotheses differ in the types of perceptual content they ascribe to experiences in order to explain numerosity judgements. But, I will argue, it can be doubted that there is a fact of the matter about which hypothesis is correct. The assumption that there is such a fact of the matter arises not from examination of the empirical phenomena themselves but from a prior philosophical commitment to the representationalist view outlined in section two above.

We saw in section two above that the looks that are to be explained by positing representational content may underdetermine the content itself. On representationalist assumptions, the way we describe a look is not a reliable guide to the actual veridicality conditions of the mental state that explains the look. Our example of the two arrays of dots is a case in point. That a perceptual experience of the two arrays allows us (under normal circumstances) to make a judgement about their relative numerosity is not sufficient to entail that our experience represents relative numerosities directly. It is an elementary geometrical fact about such arrays that, so long as their area remains constant, their numerosity and density will vary together. Thus, of any pair of arrays of the sort discussed above, that array which is more numerous will also be more dense. Therefore, sensitivity to a difference in numerosity between two arrays could be explained by a capacity to perceptually represent either numerosity or density.

Which sort of representational content is in fact tokened by perceiving subjects when presented by numerosity looks? This issue has been the object of discussion in the recent psychological literature, with different researchers on perception taking different sides. Burr and Ross (2008, 2012) hold that numerosity is a directly perceptible property. We apprehend numerosities because we directly perceive them. Durgin (1995, 2008), on the other hand, thinks that our apprehension of numerosities is derived from our perception of another property of arrays: their texture density, the number of dots per unit area.

This is a difficult matter to decide. Psychologists study differential numerosity perception by testing subjects’ estimates of numerosity on the inspection of arrays of dots more or less like those we have described. If two such arrays are similarly sized, the more dense will also be more numerous. The two can only be distinguished by varying the size of the arrays. But doing so makes it unclear whether subjects’ perception of size are influencing their estimates of numerosity. On the other hand, to have a given density is not the same thing as to have a given numerosity, as is shown by the simple fact that larger arrays can be more numerous while being equally dense. Since numerosity and density are different properties, a representation of numerosity is not ipso facto a representation of density. That is, to ascribe content to an experience involving numerosity is different from ascribing content involving numerosity. If representationalism is true, these alternative ascriptions are in conflict. But, it is worth noting, absent representationalist commitments it is not obvious that perceiving density is a different from perceiving numerosity.

In what follows I will summarise briefly Durgin’s arguments for the primacy of density perception, and then those of Burr and Ross on behalf of the primacy of numerosity. Durgin (2008, p. R855) understands the issue as one of whether we need consider the visual system to “jump right to a numeric representation,” or whether the effect observed in the experiments can instead be explained with reference to more primitive sorts of representation. The implied contrast between relatively primitive and relatively sophisticated representations is a key theoretical commitment of Durgin’s. Intuitively, the apprehension of numerosity is a more cognitively demanding achievement than the apprehension of density. Density seems a more sensory quality, one whose apprehension requires only attention to the qualitative character of the object. This intuitive difference makes it tempting to suppose that the representation of density requires less cognitive processing than the representation of numerosity.

He also claims that cultures without a concept of number can still distinguish magnitudes, and speculates that subjects from such cultures will be subject to the adaptation effect. He takes this to indicate that subjects undergoing the effect do not do so in virtue of representing number.

That Durgin takes such considerations to be relevant reveals something of how he conceives the question: as one about the cognitive machinery involved in perceptual experiences of a particular sort. The question can then be formulated in this way: the experiments demonstrate that a particular sort of experience is possible for a subject. What sorts of representation are necessary for such an experience? What representational repertoire must a subject possess if she is to be capable of undergoing an experience of this sort?

This way of formulating the question leads immediately to a demand for representational parsimony. That is, no more kinds of representation should be attributed to subjects than is necessary for an adequate explanation of the subjects’ capacity to have the experiences they have. Durgin is thus committed to a certain direction of explanation: the experiences of a subject are explained by the subjects’ representational capacities. In particular, subjects’ representational repertoire is supposed to explain the character of their experiences. In Durgin’s experiments, subjects either notice a difference between A and B, or misperceive the difference between the two arrays, depending on the conditions in which they are placed. Some representational capacity is being drawn upon: as there are two apparent candidates, each of them explanatorily sufficient, the question is whether it is more parsimonious to choose density or numerosity.

Burr and Ross argue that the perception of numerosity is primary and not derived from a prior perception of texture density. They formulate the issue somewhat differently from Durgin, however. They argue (2008, p. 426) that we have a visual sense of number, just as we do of colour. They reformulate this thesis by saying that there are distinct “qualia” for numerosity. This invocation of qualia is problematic, since that term has been used with different connotations. It has been used, for example, to describe non-representational properties of experience (Block 1990). But Burr and Ross are committed to representational explanations of numerosity phenomena. Their claim is rather that there is a direct perceptual apprehension of number akin to that of colour. In representationalist terms, this is the view that numerosity enters into the representational content of perceptual experiences.

In contrast to Durgin, Burr and Ross (see for example their 2012) take the visual sense of number to be prior to the ability to apply number concepts, for example in counting. Infants and some other animals have this sense, though they cannot count. Indeed, appealing to research by Pelli and Tillman (2008) on object recognition, Burr and Ross take numerical conceptual capacities to be derived from the sense of number. Pelli and Tillman’s work concerns the visual conditions under which object recognition is possible. How must a subject’s visual field be arranged if the subject is to be capable of recognising an object? They demonstrate that objects must appear in an “uncrowded window” in the visual field in order to be recognised: for example, subjects will only recognise images of familiar people if they appear in this window. Again, printed words can only be read in the window. Indeed, correctly formed words can only be distinguished from nonsensical strings of letters when they lie within the window.

By contrast, the crowded visual field outside the window is characterised by textural properties, rather than by objects. “We see stuff (unnamed texture) and perceive space (the shape of the scene we are in)” (Perri and Tillman 2008, p. 1133). One sees indeterminate features of the scene (“stuff”) without being able to make out individual objects. For example, one is aware that there is a jumble of letters in some location in the visual field, without being able to tell whether these letters compose any words. Density is just such a textural feature: an array of dots outside the uncrowded window looks more or less dense, though the individual dots are not clearly in view. As Burr and Ross comment (2012, p. 197) “when object recognition fails, it is impossible to count objects or to estimate their number.” Objects need to be distinguished from their surroundings in order to be enumerated, that is, in order to have number concepts applied to them. Number concepts can therefore only be applied to items within the uncrowded field: outside of it, one sees not numerosities but only indeterminate quantities.

Counting and the estimation of numbers are cases par excellence of the application of number concepts. It is worth noting the generality of this claim. The everyday notion of counting covers a number of importantly different cognitive processes. Crucially, it includes both conscious processes of counting and subitizing – that is, the immediate recognition of small numerosities, as when one “just sees” that there are exactly three bottles on the wall. Again, “estimation” covers judgements of numerosity whether these are immediate or the result of conscious processes of reasoning. The claim, then, is that the application of number concepts to objects in a scene quite generally depends on the availability of the objects for perceptual recognition.

Inspecting the arguments of Durgin and Burr and Ross, we find a somewhat inconclusive dispute. The issue apparently cannot be settled directly by testing cognitive processing. The arguments rely rather on opposing views about a broader issue: the relation between the representational capacities involved in perception and higher cognitive faculties, such as the capacity to count. The mere fact that experimental research on numerosity perception cannot, at least as it has developed so far, decide the issue should make us alive to the possibility that there is no fact of the matter about whether numerosity or density is primarily being perceived in these cases. The possibility is at any rate not ruled out by what we know from empirical psychology. In the next section I explore this possibility.

5. Representations and looks again

Where does the demand for a decision about whether numerosity or density is perceived directly come from? I argued in the previous section that it comes not from empirical study of the phenomena of numerosity perception, but rather from prior representationalist commitments. It comes, that is, from the assumption that looks are to be explained by positing mental states with veridicality conditions. Because a representation of density is not ipso facto a representation of numerosity, it is then thought to follow that either one or the other property must enter into the representational content of the posited mental state.

Call a difference between two representations of a thing a representational difference. We can now express the argument of section two above in this way: representational differences are finer grained than differences between looks. The puzzle about numerosity arises from the fact that the difference between the numerosity and density of an array, area being constant, is a representational difference and not a difference between looks.

But we should also observe a corrollary of the argument so far. Which ascription of content is correct is not something that need be transparent to the perceiving subject. Whether numerosity or density is represented is not available to introspection. Indeed, representational content can perform its explanatory task, as outlined in section two above, whether or not it can be described in such commonsensical terms. For all that has been said so far, it might be the case that neither of these two familiar properties are represented in the experience.

Let us stipulate a mental state type which can be called sensitivity. One counts as sensitive to numerosity, for example, insofar as one is in a position to tell, of two arrays, which is the more numerous. Now, let us hold the areas of two arrays constant, as in Durgin’s experiment described in section three above. Sensitivity to numerosity will, in this case, just be sensitivity to density. There is no fact of the matter, no need to decide, to which of these two properties a subject is sensitive.

The point can be put in another way. Take two arrays of equal area, one on the left of the visual field and the other on the right. Once again, the left array is both more numerous and more dense than the right. We can stipulate a scalar predicate – call it ψ – which applies to both arrays and to which the perceiving subject is said to be sensitive. The left array is more ψ than the right, and a third array of the same area would be more ψ again if more numerous and dense. The ψ-property might, for all we have said, just be numerosity. It could also be density. But nothing forces us to choose between these two options. The experience can be described in terms of arrays which are more or less ψ, without that property being determinately either numerosity or density.

Similarly, the robust illusion described in section three above can be described in terms of the ψ property. In that illusion, the left array, though in fact more ψ than the right, is made to look less so. This description is wholly adequate as a description of the facts established in the experiment.

Just as nothing in the experiments allows us to conclusively decide between the proposals of Durgin and Burr and Ross, nothing in them rules out an account in terms of ψ. Thus it is open to the representationalist to argue as follows. What enables us to judge that the left array is more numerous is a perceptual experience that represents that array as more ψ. The content of the experence has form that L is more ψ than R. It is this content that does the explanatory work attributed to representations in section two above. To be sensitive to the numerosity or density of the arrays, is to represent them correctly as more or less ψ.

But if this route is taken, the specifically representational features of the posited token mental state are no longer doing any work. Instead of saying that an array looks to have a certain relative numerosity because the subject represents it as being some degree of ψ, we can with the same result simply say that the perceiving subject registers the numerosity look possessed by the array. That is, no compelling reason has been found to understand sensitivity as a matter of representation, since no compelling reason has been found to individuate the properties to which subjects are sensitive more finely than worldly states of affairs.

The difference between this route and representationalism is not a trivial one. As we have seen, the representationalist takes numerosity looks to be explained by the way in which the perceiving subject represents arrays. On the alternative, non-representationalist view now under consideration, the direction of explanation is reversed. It is only because the array already possesses numerosity looks that the subject registers them. In this sense, the non-representationalist approach attributes to the array itself the factors in virtue of which we are sensitive to numerosity.

It bears reiterating that I do not claim that these considerations show that representationalism is false. The claim is merely that a non-representational approach is possible and consistent with what we know about the psychology of numerosity perception. What the inconclusiveness of the debate concerning numerosity and density shows is that there is no compelling empirical reason to think of the perceiving subject as tokening mental states with determinate veridicality conditions. There is therefore no compelling empirical reason to think of the subject as tokening representations, in the philosophers’ sense of representation. The anti-representationalist still, however, owes an account of just what role the notion of representation plays in psychological explanation, however. What is it that psychologists are talking about, if not philosophers’ representations?

6. Cognitive processing

The thesis of the non-representationalist, as understood here, is that the mental states that are tokened when a subject perceives do not in themselves determine veridicality conditions. The thesis does not involve any denial that we must posit the tokening of some mental states in order to explain the operation of the perceptual system, or that interesting questions do arise for the psychologist about the nature of such states.

The debate between Durgin and Burr and Ross, discussed in section three above, centres around contrasting conceptions of cognitive processing. Given that a mental state of a certain sort is tokened when subjects register numerosity looks, it may be asked how the tokening of these states relates to the exercise of other cognitive capacities of the subject. To see the point, consider once again the arguments of these authors. Durgin takes it to be crucial that sensitivity to numerosity does not involve a grasp of number concepts. One does not have to be applying number concepts in order to be impressed with the relatively greater numerosity, or apparently greater numerosity, of the left array. This is a point about cognitive processing. If Durgin is right, the mental state that is tokened when a perceiving subject registers a numerosity look is independent of the mental states that are tokened when the subject applies number concepts, for example in counting or in thinking of specific numbers of items.

Burr and Ross point to the dependency of our sensitivity to number on a prior capacity to recognise distinct objects. The thought here is that only under those conditions in which we are able to recognise distinct objects are we sensitive to numerosity looks. This is again a point about cognitive processing: specifically, a point about the conditions under which the tokening of a certain sort of cognitive state is possible.

In neither case does anything essential depend on the tokened mental states determining veridicality conditions. On the contrary, it is open to us to suppose that determinate veridicality conditions are only attributed to perceptual states by us when we interpret those states by reference to the knowledge of the world they yield. Thus, insofar as our interest is in the numerosity of a collection, we will be disposed to describe the perceiving subject as sensitive to numerosity. Insofar as our interest is in the density of some area of a visual field, we will speak in terms of sensitivity to density.

In summary, sensitivity plays the role of representation without any requirement for determinate veridicality conditions more finely individuated than worldly states of affairs. Sensitivity to numerosity just is sensitivity to density, whereas representations of these properties must be distinguished. The switch from representation to sensitivity thus means that the distinction between density and numerosity pertains to our descriptions of perceptual states, and not to the perceptual states themselves.

7. Conclusion

I have not attempted to show here that perceptual states are not representational in the philosophers’ sense. But I have tried to show, for one sort of perceptual sensitivity, that psychological investigation can be carried on without presupposing such representational content. Insofar as the point generalises to other forms of perceptual sensitivity, showing this is enough to demonstrate that appeal to empirical psychology is not sufficient to establish representationalism in the philosophy of perception.

8. References

Block, Ned (1990). Inverted earth. In: J. Tomberlin (ed.) Philosophical Perspectives vol. 4. Atascadero: Ridgeview Publishing Co.

Burge, Tyler. (2005. Disjunctivism and perceptual psychology. Philosophical Topics 33: 1-78.

Burr, David and John Ross (2008) A visual sense of number. Current Biology 18: 425-428.

Burr, David and John Ross (2012) Number, texture and crowding. Trends in Cognitive Science 16 (4): 196-7.

Durgin, Frank (2005) Texture density adaptation and the perceived numerosity and distribution of texture. Journal of Experimental Psychology: Human Perception and Performance 21: 149-169.

Durgin, Frank (2008) Texture density adaptation and visual number revisited. Current Biology 18: R855-R856.

Frege, Gottlob (1892) Über Sinn und Bedeutung. Zeitschrift für Philosophie und philosophische Kritik 100 25-50.

Peacocke, Christopher (1992) A Study of Concepts. Cambridge, Mass.: MIT Press.

Pelli, Denis G and Katharine A Tillman (2008) The uncrowded window of object recognition. Nature Neuroscience 11 (10) :1129-1135.

1See Burge 2005 for a recent version of this complaint.

2This describes an experiment by Durgin 2005.