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Resemblance and Representation

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Ben Blumson

1. Introduction

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The fact is that on that night I laughed at the axiom Quae sunt aequalia uni tertio sunt aequalia inter se (“Things which are equal to a third thing are equal to each other”), for the portrait resembled M. M. and it also resembled the strumpet, and the latter did not resemble M. M. Murray admitted it, and we spent an hour philosophizing.
Giacomo Casanova, History of My Life, volume 4, chapter 10

1It’s a platitude – which only a philosopher should dream of denying – that whereas words are connected to what they represent merely by arbitrary conventions, pictures are connected to what they represent by resemblance. The most important difference between my portrait and my name, for example, is that whereas my portrait and I are connected by my portrait’s resemblance to me, my name and I are connected merely by an arbitrary convention. The first aim of this book is to defend this platitude from the apparently compelling objections raised against it, by analysing depiction in a way which reveals that it really is mediated by resemblance.

2It’s natural to contrast the platitude that depiction is mediated by resemblance, which emphasises the differences between depictive and descriptive representation, with an extremely close analogy between depiction and description, which emphasises the similarities between depictive and descriptive representation. Whereas the platitude emphasises that the connection between my portrait and me is natural in a way the connection between my name and me is not, the analogy emphasises the contingency of the connection between my portrait and me. Nevertheless, the second aim of this book is to defend an extremely close analogy between depiction and description.

3The main strategy of the book is to generalise ideas from the philosophy of language to encompass pictures. Depiction is representational in the same sense as description, except whereas the latter is mediated by convention, the former is by resemblance. It turns out, I will argue, that many ideas from the philosophy of language apply directly to depiction, with only superficial amendments or the incorporation of resemblance. And it turns out that the apparently compelling objections raised against the platitude that depiction is mediated by resemblance are merely manifestations of, and amenable to the same solutions as, familiar problems from the philosophy of language.

4This chapter introduces the central themes of the book. The first section clarifies the subject with an ostensive definition of depiction. The second section introduces the analysis of resemblance as sharing properties and explains how it underlies the most compelling objections to the platitude that depiction is mediated by resemblance. The third section provides a brief taxonomy of kinds of representation, and discusses the place of depiction within this taxonomy. The fourth section elaborates and defends the method of analysis, which is the central method of the book. The fifth section outlines the remaining chapters of the book.

1.1 An ostensive definition of depiction

5Depiction is a distinctive kind of representation. Figurative painting and drawing are the paradigm example, but figurative sculpture, photographs and maps are also central examples. Language is the paradigm of non-depictive representation, but symbolic notation – whether in mathematics or music – and indication – as when clouds represent rain or smoke represents fire – are also central examples. In contrast, material objects such as rocks, tables and planets are not examples of either kind of representation, but are at most degenerate cases of indication. The rest of this section clarifies and defends this ostensive definition.

6Three clarifications. First, although figurative painting and drawing is the paradigm example of depiction, defining depiction as a kind of representation means that not all paintings and drawings are depictions. Although figurative and abstract painting, for example, have much in common, abstract paintings are not counterexamples to the thesis that depiction is mediated by resemblance, because figurative and abstract paintings intuitively don’t belong to the same kind of representation (Lopes, 1996, 5-6). Figurative and abstract paintings are similar because they are flat surfaces marked with paint, not because they represent in the same way.

7Second, defining depiction as a kind of representation means depictions may belong to any media (Hopkins, 1994, 1; Kulvicki, 2006, 106-114). Although sculptures, for example, are not flat surfaces marked with lines or colour, this does not disqualify sculptures from being depictions, since it is plausible that figurative sculptures and pictures represent in the same way. Similarly although most music, for example, is neither depictive nor representational, program music is an important exception. Most dance is not representational, but mime is depiction in the medium of movement. And movies are plausibly depictions in the medium of film (Currie, 1995, 2).

8This point is methodologically important. John Hyman, for example, begins a very different inquiry when he writes “Is an apple red because of the visual sensation it produces in us when we see it, or does it produce this sensation in us because it is red? All pictures – whatever kind of substance they are made of – consist of colour distributed on a plane. So this is the right way for a study of depiction to begin” (Hyman, 2006, 7). If the subject of inquiry is a kind of representation, rather than a representational medium, the right way to begin is not to inquire into the nature of perception and colour, but into the nature of representation in general.

9Third, while depictive and descriptive representation are distinct kinds, I allow that they may overlap. Take, for example, a picture of a signboard which reads ‘danger’. The picture both represents a signboard and represents danger. But whereas the signboard is represented depictively, danger is represented merely descriptively, since it is represented by the appearance of the word ‘danger’ within the picture. Similarly the Soviet flag represents a hammer and sickle as well as representing the Soviet Union: the hammer and sickle are represented depictively, but the representation of the Soviet Union is arguably merely conventional (Peacocke, 1986, 383).

10Allegorical representation is the reverse of this pattern. The words of the fiction are paradigmatically descriptive, but the events described also represent a real situation. While the representation of the fiction is descriptive, the representation of the real situation is depictive, and plausibly mediated by resemblance. Animal Farm, for example, describes in language the takeover of a farm by pigs (Orwell, 1945). The events described in turn depict the Russian Revolution, perhaps in virtue of the resemblance between the events of the story and the events of the revolution. So allegorical stories are plausibly a kind of depictive representation.

11If it’s insisted that depiction must be a kind of visual representation, then this could be accommodated by substituting resemblance below for resemblance in visible respects. Although Animal Farm and the Mona Lisa, for example, have in common that they both represent what they do by resemblance, they differ because whereas the Mona Lisa resembles Lisa in respects which are visible, the story of Animal Farm resembles the revolution in respects which are invisible. So although the analysis below does not distinguish between depictions in different media, it can be easily modified if it’s desirable to do so (Abell’s (2009) analysis, for example, adopts this suggestion).

12One objection. Beginning with an ostensive definition of depiction which – whether by accident or design – classifies all and only representations which are mediated by resemblance as depictions might be thought to beg the question in favour of the platitude that depiction is mediated by resemblance. If the main objections against the resemblance theory were about which representations it classifies as depictions, then this objection would be right: choosing figurative painting and drawing as paradigm examples of depiction would stack the deck in favour of the platitude that depiction is mediated by resemblance.

13But the most compelling objections against the platitude that depiction is mediated by resemblance aren’t merely about its classification of different kinds of representation, but purport to show that it’s impossible for any kind of representation to be mediated by resemblance. If successful, these objections would show that depiction is not mediated by resemblance, no matter which representations are classified as depictions and no matter how depiction is ostensively defined. So in the context of rebutting these objections, beginning with an ostensive definition of depiction doesn’t beg the question in favour of the platitude that depiction is mediated by resemblance.

14Beginning with an ostensive definition of depiction which – whether by accident or design – classifies all and only representations which are mediated by resemblance as depictions may also be thought to beg the question against other theories of depiction, according to which what is distinctive of depiction is a distinctive kind of perceptual experience (Wollheim, 1980; 1987), a special kind of syntactic and semantic structure (Goodman, 1968; Kulvicki, 2006), or a peculiar kind of perceptual processing (Schier, 1986; Currie, 1995; Lopes, 1996; Newall, 2011). Since these theories disagree in their classifications, my choice of examples may also stack the deck against them.

15But if a different choice of ostensive definition leads to a different final classification, and thence to a different theory, this only shows that the different definition ostended a different class of things, for which a different theory is appropriate. If, for example, one begins with an ostensive definition of depiction which includes abstract painting and excludes figurative sculpture, then one will end with a different classification and a different theory of depiction. But that theory of depiction would not disagree with the theory I argue for here, because it has a different subject matter. Beginning with an ostensive definition doesn’t beg the question, but merely describes the subject.

16Because different theories of depiction – whether or not they agree about which things they classify as depictions – are not obviously inconsistent with each other, I will not adopt a last man standing approach, which seeks to establish the resemblance theory by first refuting every other plausible theory, and mention alternative approaches only when they’re relevant to the exposition of my own. If there’s an analysis of depiction in terms of resemblance which captures the classification outlined here, discovering that analysis suffices for success. If there are other analyses or theories in other terms which capture other classifications, discovering them is an even greater success.

1.2 The analysis of resemblance as sharing properties

17The naïvest analysis of depiction in terms of resemblance simply assimilates depiction to resemblance (Goodman, 1968, 3). According to it:

(1) Something depicts another if and only if the former resembles the latter.

18The Mona Lisa, for example, is supposed to depict Lisa simply because the Mona Lisa resembles Lisa. Counterexamples to the necessity and sufficiency of this analysis illustrate some of the most compelling objections to the platitude that depiction is mediated by resemblance.

19In turn, the naïvest analysis of resemblance simply assimilates resemblance to having properties in common. According to it:

(2) Something resembles another if and only if the former has a property in common with the latter.

20Peas in a pod resemble each other, for example, because they have the properties of greenness, roundness and yuckiness in common. So according to the naïvest analyses of depiction and resemblance, the nature of depiction ultimately depends on the nature of properties.

21But there are rifts in our conceptions of properties. A first is the rift between sparse and abundant conceptions of properties (Lewis, 1983a; 1986, 59-69). According to an abundant conception of properties there’s a property corresponding to each (possible) predicate, and so the number of properties is the number of (possible) predicates. Just as there’s a property of being white which corresponds to the predicate ‘is white’, for example, there is also, according to abundant conceptions of properties, a property of being a raven or a writing desk, corresponding to the predicate ‘is a raven or a writing desk’. So properties, according to the abundant conception, are ubiquitous.

22(A predicate is just a sentence with a name removed. The predicate ‘is white’, for example, results from removing ‘snow’ from ‘snow is white’. Likewise, the predicate ‘is a raven or a writing desk’ results from removing ‘Edgar’ from the sentence ‘Edgar is a raven or a writing desk’. The semantic value of a predicate is often thought of as a property: the semantic value of ‘is white’, for example, is the property of being white, whereas the semantic value of ‘is a raven or a writing desk’ is the property of being a raven or a writing desk. So abundant conceptions of properties are motivated in part by the need to find a semantic value for every (possible) predicate.)

23Sparse theories of properties deny there is a property corresponding to every possible predicate, and so deny the number of properties is the number of possible predicates. Which predicates correspond to properties, according to sparse theories, is revealed a posteriori by total science (Armstrong, 1978b, 7-9). Whether the predicate ‘is white’ corresponds to a property of being white, for example, is an a posteriori question; the existence of the property of being white cannot be deduced from the existence of the predicate ‘is white’, and no property of being a raven or a writing desk corresponds to the predicate ‘is a raven or a writing desk’.

24Whereas an abundant conception of properties is considered most appropriate for the analysis of predication, it’s the sparse conception which is considered appropriate for the analysis of resemblance. As David Lewis, for example, writes “Because properties are so abundant, they are undiscriminating. … Thus properties do nothing to capture facts about resemblance. That is work more suited to the sparse universals” (Lewis, 1983a, 13). But it’s almost as difficult to square the analysis of resemblance as having properties in common with a sparse as with an abundant conception of properties. So, until chapter ten, I’ll attempt to stay neutral on this issue.

25A second is the rift between the subjective and objective conception of properties. According to subjective conceptions of properties, whether a particular instantiates a property is dependent on us, whereas according to objective conceptions of properties, whether a particular instantiates a property is a fact independent of us. According to a subjective conception of colours, for example, whether a particular is red depends on whether it is disposed to appear red to us under certain conditions, whereas according to an objective conception of colours, whether a particular is red depends on whether it is disposed to reflect light of a certain wavelength.

26The platitude that depiction is mediated by resemblance is often associated with an objective conception of properties. In his criticism of the resemblance theory, Michael Newall, for example, says “I will call all theories that hold that a viewer-independent resemblance between a picture and its referent is necessary for depiction resemblance theories. … Viewer-independent resemblances involve identity in some respects – a sharing of viewer-independent properties… Viewer-independent resemblance is close to the everyday meaning of the term ‘resemblance’, and it is this that resemblance theorists employ” (Newall, 2011, 67).

27Likewise, in his defence of the resemblance theory, Hyman writes “I shall argue that there is a strict and invariable relationship between the shapes and colours on a picture’s surface and the object which it depicts, which can be defined without referring to the psychological effect the picture produces in a spectator’s mind…” (Hyman, 2006, 73). But although it’s natural to combine the platitude that depiction is mediated by resemblance with an objective conception of properties and resemblance, the platitude that depiction is mediated by resemblance is equally compatible with the subjective conception, and so I will also attempt to stay neutral on this issue.

28In light of the analysis of resemblance as having properties in common, the necessity of the first analysis is not obvious, because it’s not obvious which properties pictures have in common with what they represent. As Robert Hopkins, for example, writes: “Resemblance must be resemblance in certain respects. If two things resemble, they must do so in respect of some property or other, perhaps in respect of many. Unfortunately, when we ask in what respect picture and object resemble, it is easier to find difference than likeness” (Hopkins, 1998, 11). Whereas most pictures are flat and rectangular, most of the things they represent are neither flat nor rectangular.

29But although explicitly specifying the respects of resemblance between many pictures and what they represent is difficult (see Hyman (2006, 73-112) and Newall (2011, 66-94) for detailed discussion of particular examples), whether there is an in principle problem for the necessity of resemblance for depiction depends on one’s conception of properties. If it’s combined with a sparse theory of properties – according to which whether there is a property corresponding to each (possible) predicate is revealed by a posteriori scientific investigation – the problem is severe. I will return to the problem posed by sparse conceptions of properties in chapter ten.

30But if it’s combined with an abundant theory of properties – according to which there is a property corresponding to each (possible) predicate – the analysis of resemblance as sharing properties entails that everything resembles everything in some respect, so the necessity of resemblance for depiction is guaranteed. If properties are abundant, then a raven resembles a writing desk, for example, because the raven and the writing desk both fall under the predicate ‘is a raven or a writing desk’. Likewise, the Mona Lisa resembles Lisa because the Mona Lisa and Lisa both fall under the predicate ‘is the Mona Lisa or Lisa’. In this case, the problem of necessity evaporates.

31The insufficiency of the first analysis is obvious, because resemblance is ubiquitous. Members of the same family resemble each other, but do not depict each other; twins resemble each other almost exactly, but still do not depict each other. Automobiles from the same assembly line resemble each other very closely, but rarely represent each other. Most paintings bear a closer resemblance to other paintings than they do to what they represent (Goodman, 1968, 4-5). And all white things resemble each other in virtue of sharing the property of being white, but not all white things depict each other. Sharing a property is sufficient for resemblance, but not depiction.

32If it’s combined with an abundant theory of properties – according to which there is a property corresponding to each (possible) predicate – then the analysis of resemblance as sharing properties entails everything resembles everything in some respect, which exacerbates the insufficiency of resemblance for depiction. Although if properties are abundant the Mona Lisa is guaranteed to resemble Lisa, for example, since the Mona Lisa and Lisa both fall under the predicate ‘is the Mona Lisa or Lisa’, a raven is also guaranteed to resemble a writing desk because both fall under the predicate ‘is a raven or a writing desk’. But ravens do not depict writing desks.

33Since resemblance is not obviously necessary and obviously insufficient for depiction, it might be thought that an analysis of depiction should specify some relevant respects in which all depictions resemble what they represent. Hopkins, for example, writes “One reaction would be to abandon hope that there is any one respect in which all pictures are experienced as resembling their objects. Sometimes colour is the key, sometimes tone, sometimes shape. However, it is clearly desirable to resist this retreat if possible. Supposing that we still hope for a single respect relevant to all depiction, where should we look for it?” (Hopkins, 1998, 51-52).

34But the quixotic search for a specification of a relevant respect in which all depictions resemble what they represent is superfluous to defending the platitude that depiction is mediated by resemblance. If depiction is mediated by resemblance, every depiction resembles what it represents in some relevant respect. But it doesn’t follow that there is some relevant respect in which all depictions resemble what they represent, because the respects relevant to each different depiction may be different. And even if there is a relevant respect in which all depictions resemble what they represent, a specification of the respect cannot establish the sufficiency of resemblance for depiction.

35Two counterexamples, which rely on the reflexivity and symmetry of resemblance, illustrate this point. First, Aristotle resembles himself, but Aristotle does not depict himself. Moreover, since all things share all of their properties with themselves, it follows from the definition of resemblance as sharing properties that resemblance is a reflexive relation: everything resembles itself. In contrast, depiction is not a reflexive relation: not everything depicts itself. So the insufficiency of resemblance for depiction follows simply from the fact that resemblance is reflexive whereas depiction is not (Goodman, 1968, 4).

36Just as resemblance is reflexive, so is resemblance in specific respects. Resemblance in respect of colour, for example, is reflexive, because everything is the same colour as itself. In general, everything shares its own properties with itself, so everything resembles itself in respect of every kind of property. So just as resemblance simpliciter is not sufficient for depictive representation, no specific respects of resemblance are sufficient for depictive representation either: even if there were a relevant respect in which all depictions resembled what they represent, resemblance in that respect would not provide a sufficient condition for depiction.

37Second, just as the Duke of Wellington’s portrait resembles the Duke, the Duke resembles his portrait. But while the portrait depicts the Duke, the Duke does not depict his portrait. Since whenever one thing shares a property with a second, the second shares that same property with the first, resemblance is symmetric: whenever one thing resembles a second, the second resembles the first. In contrast, depiction is not a symmetric relation: not all things depict the things which depict them. So the insufficiency of resemblance for depiction follows merely from the fact that resemblance is symmetric whereas depiction is not (Goodman, 1968, 4).

38Just as resemblance is symmetric, so is resemblance in specific respects. Resemblance in respect of being green, for example, is symmetric, since if one pea shares the property of being green with another pea, then the second pea must also share the property of being green with the first. In general, if something shares a property with another, then the latter shares that property with the former, so if something resembles another in some respect, then the latter resembles the former in that same respect. So specifying particular respects in which depictions resemble what they represent can’t exclude examples of insufficiency arising from the symmetry of resemblance.

39So analysing depiction in terms of respects of resemblance is inadequate not because there’s no relevant respect in which all depictions resemble what they represent, but because no respect of any kind could be sufficient for representation. A similar point is made by Nelson Goodman in Languages of Art, where he writes that: “The plain fact is that a picture, to represent an object, must be a symbol for it, stand for it, refer to it; and that no degree of resemblance is sufficient to establish the requisite relationship of reference” (Goodman, 1968, 5). An adequate analysis of depiction in terms of resemblance must combine resemblance with representation.

40But effecting a combination of resemblance with representation is not straightforward. The simplest way to effect the combination is simply to conjoin resemblance with representation, leading to the following analysis (Schier, 1986, 3):

(3) Something depicts another if and only if the former resembles and represents the latter.

41This analysis accommodates the point that depiction is a kind of representation straightforwardly since, according to it, the Mona Lisa, for example, depicts Lisa not merely because the Mona Lisa resembles Lisa, but also because the Mona Lisa is a representation of Lisa.

42This analysis also escapes the obvious counterexamples to the sufficiency of the first. Members of the same family and cars off an assembly line do not depict each other, since although they resemble each other, they don’t represent each other. Paintings resemble each other more than what they represent, but they still do not depict each other unless they represent each other. Aristotle does not depict himself, since he does not represent himself. And although the Duke of Wellington resembles his portrait as much as it resembles him, the Duke does not depict his portrait, since only the portrait represents the Duke, and not vice versa.

43But there are less obvious counterexamples to the sufficiency of the second analysis, which show that it doesn’t escape the problems of the first. The sign-language sign for a rabbit, for example, resembles a rabbit, but it does not depict a rabbit because the resemblance of the sign to the rabbit is noticeable only if one already knows what it represents (Lopes, 1996, 16). Similarly, all onomatopoeic words resemble what they represent, but not all depict what they represent, because the resemblances responsible for their origin have ceased to be relevant: the resemblance of ‘woof’ to a dog’s bark, for example, is no longer relevant to its representation of a dog’s bark.

44Likewise, if properties are abundant, the analysis of resemblance as sharing properties entails every representation resembles what it represents in some respect. But even if properties are abundant, not every representation is a depiction. If properties are abundant, then the name ‘rosemary’ resembles rosemary, for example, since both the name ‘rosemary’ and rosemary fall under the predicate ‘is ‘rosemary’ or rosemary’, and so have the corresponding property of being ‘rosemary’ or rosemary. But even if properties are abundant, the name ‘rosemary’ does not depict rosemary. Resemblance and representation, like resemblance simpliciter, is insufficient for depiction.

45Moreover, there are counterexamples to the combination of representation with any specific respect of resemblance. The phrase ‘this phrase’, for example, both represents and resembles itself, so the analysis predicts that it depicts itself. Furthermore, since resemblance is reflexive, the phrase ‘this phrase’ resembles itself in every respect. Nevertheless, ‘this phrase’ is obviously not a depiction of itself, since the fact that it resembles itself is merely incidental to the fact that it represents itself. So simply conjoining resemblance and representation cannot escape the basic problem posed by the insufficiency of resemblance (Goodman, 1970, 437).

46A simple way to attain sufficiency would be to stipulate that the resemblance of a symbol to what it represents is not incidental to how it represents. Take, for example, the following analysis (Sachs-Hombach, 2003, 171):

(4) Something depicts another if and only if the former represents the latter in virtue of the former resembling the latter.

47Since ‘this phrase’ does not represent itself in virtue of resembling itself, this version of the analysis escapes the insufficiency of the second analysis by guaranteeing a non-incidental connection between resemblance and representation.

48Likewise, although onomatopoeic words resemble what they represent, but do not all depict what they represent, this is because they have ceased representing what they do in virtue of resembling it, and now represent what they do merely conventionally: the resemblance of ‘woof’ to a dog’s bark, for example, is not any longer relevant to its representation of a dog’s bark, and so ‘woof’ does not represent a dog’s bark in virtue of resembling it. And even if the name ‘rosemary’ resembles rosemary in respect of the property of being ‘rosemary’ or rosemary, it’s obviously not in virtue of this resemblance that ‘rosemary’ represents rosemary.

49But although this analysis escapes insufficiency, it’s not an informative response to the objection. The objection, supported by examples such as ‘this phrase’, claims that resemblance is in general incidental to the way that symbols represent what they do. By defining depiction as that kind of representation in which resemblance plays a non-incidental role, this version of the analysis states there is a non-incidental role for resemblance in depictive representation, but it doesn’t elaborate on what that role is. An informative analysis, in contrast, would specify what the non-incidental role of resemblance in depictive representation is as well as stating that it has one.

1.3 An intuitive taxonomy of representation

50Representation is not a fundamental feature of the world, which suggests it should be analysable in terms of more fundamental features. In order to effect this reduction, it’s helpful to divide representation into various kinds. The broadest division into kinds of representation is between natural and non-natural representation. Intuitively, natural representation divides into depiction and indication, and non-natural representation divides into conventional and intentional representation. Conventional representation is analysed in terms of intentional representation, whereas intentional representation is analysed in terms of natural representation.

51It’s common to combine the platitude that depiction is mediated by resemblance with the thesis that depiction is a kind of natural representation. The following passage, for example, neatly exemplifies the intuitive connection that many feel between the two theses: “As opposed to conventional symbols there are the so-called natural symbols, in which there is some non-conventional or natural relation (usually either of resemblance or causal connection) between the symbol and the thing symbolized” (Hospers, 1946, 30). Depiction, this suggests, is a kind of natural representation, and the role of resemblance is analogous to the role of causation in indication.

52The paradigmatic example of natural representation is indication. Whereas depiction is mediated by resemblance and language by convention, indication is mediated by causation. Smoke is a natural representation of fire, for example, because smoke is caused by fire. Similarly, clouds naturally represent rain because rain is caused by clouds. And the number of rings in a tree’s trunk is an indication of the age of the tree because of the causal connection between the number of rings and the age of the tree. If indication is simply causation, then indication is ubiquitous, since nearly everything physical is causally connected to something.

53So the obvious way to analyse depiction as a kind of natural representation is to argue that just as indication is simply causation, depiction is simply resemblance. But this naïve suggestion – as the last section argued – cannot offer sufficient conditions for depiction, and so cannot support the platitude that whereas description is mediated by convention, depiction is mediated by resemblance. This suggests that unless one’s willing to accept the consequence that just as resemblance is ubiquitous, depiction is ubiquitous, depiction should not be analysed as a kind of natural representation, like indication, but as a kind of non-natural representation, like description.

54Even if it’s denied that depiction is a kind of natural representation, photography – an important kind of depiction – plausibly is. Since there’s a causal connection between photographs and what they represent, photographs are indications. This suggests that depiction must be analysed at least partially in terms of indication or causation: just as painting and drawing might be analysed by combining resemblance with non-natural representation, photography can be analysed by combining resemblance with natural representation. I’ll argue in section 3.3 that this suggestion cannot be carried through: photographs are depictive only insofar as they are non-natural.

55Just as natural representation is traditionally – but incorrectly – divided into depiction and indication, non-natural representation is traditionally – and correctly – divided into conventional and intentional representation. Language is the paradigm example of conventional representation, but there are numerous other examples, such as Morse code and semaphore, musical and mathematical notation, and various traffic signals or gestures. The hallmark of conventional representation is arbitrariness: my name, for example, is conventional, because my name was chosen arbitrarily; if my parents had chosen another name, it may have suited me just as well.

56It’s natural to combine a close analogy between depiction and description with the thesis that depiction is a kind of conventional representation, so I have to emphasise this is not my position: whereas my name and I, for example, are connected merely by an arbitrary convention, the connection between my portrait and me is non-arbitrary – my portrait represents me because it resembles me. Although some depictive symbol systems are partly mediated by convention – it’s a convention, for example, that the top of a map represents the north – I will argue in section 5.2 that not every depictive symbol system is mediated (even in part) by convention.

57Although depiction is not a kind of conventional representation, chapters four and five argue that there’s a close analogy between depictive symbol systems and conventional language: if the component of the analysis of conventional language which ensures its arbitrariness is substituted for resemblance, then it applies instead to depictive symbol systems. And if the component of the analysis of conventional language ensuring its arbitrariness is removed altogether, it applies not just to depictive symbol systems but to symbol systems in general, including those – such as innately known languages or symbol systems – which are mediated by neither convention nor resemblance.

58The fact that linguistic expressions may be used non-literally, with meanings which differ from those attached to them by convention, attests conventional representation is not the only kind of non-natural representation (Grice, 1957, 215). If, for example, I said, pointing into the sky, ‘that aeroplane is a kilometre long’, then I would typically only mean that it was much longer than the usual aeroplane, though the conventional meaning of the sentence is that the aeroplane is a whole kilometre in length. This type of representation is not mediated by convention, but by the intentions and purposes of the representation’s perpetrator.

59Although the paradigm example of intentional representation is non-literal language, there are numerous other examples. Whereas it’s a convention for an audience to clap (or to knock on the table) to express appreciation, it’s not a convention for speakers to clear their throats in order to signal they’re about to begin, since because a clear throat is a prerequisite of speaking, an audience can recognise a speaker’s intention to speak by hearing them clear their throat. I will argue in chapters two and three that depiction is a kind of intentional representation, and the role of the resemblance of depictions to what they represent is to facilitate the expression of intention.

1.4 The methodology of analysis

60The central method of this book is philosophical analysis, which calls for clarification in order to avoid some common misunderstandings and misgivings. An analysis is a statement of equivalence between an analysandum and analysans. The following, for example, is an analysis of bachelors: bachelors are unmarried men. The analysis says what bachelors are by stating that bachelors, the analysandum, are equivalent to unmarried men, the analysans. Similarly, an analysis of depiction should state an equivalence between depiction, the analysandum, and a combination of resemblance and intentions, the analysans.

61An analysis of depiction should not only state an equivalence between depiction and something else, but should state the conditions under which something depicts another. The Mona Lisa, for example, should not merely be classified as a depiction, but as a depiction of Lisa. That suggests that the analysis should be in the form of a biconditional stating that something depicts another if and only if…, where the ellipsis on the right hand side is replaced by the analysans. The first analysis above, for example, replaced the ellipsis on the right with ‘resembles’ to form the statement that something depicts another if and only if the former resembles the latter.

62Biconditional analyses should be interpreted as strict biconditionals, which state necessary equivalences between the analysandum and the analysans, rather than material biconditionals, which merely state a contingent coincidence between the analysandum and analysans. The biconditional ‘snow is white if and only if grass is green’, for example, is not an adequate analysis of snow’s being white in terms of grass’ being green, since although ‘snow is white’ and ‘grass is green’ are the same in truth-value, it isn’t necessary that this is so. Illuminating analysis requires a necessary and not merely contingent coincidence between the analysandum and the analysans.

63Even a strict biconditional does not always suffice for an illuminating philosophical analysis: it is a simple matter to find strict biconditionals which fail to provide an analysans which illuminates the nature of the analysandum. Take, for example, the analysis: something depicts another if and only if the former depicts the latter. This analysis obviously states a necessary equivalence between the analysandum and the analysans, since its left and right side cannot differ in truth-value. But because the analysandum and the analysans are stated in exactly the same terms, the analysis is uninformative: it contributes nothing to a philosophical understanding of depiction.

64The fourth analysis above – which states that something depicts another if and only if the former represents the latter in virtue of resembling the latter – displays a similar defect, despite being a strict biconditional. In this case the terms of the analysans are distinct from terms of the analysandum. But the analysis is insufficiently illuminating since what is sought from a philosophical analysis of depiction – an explanation of how something may represent another in virtue of resembling it – is not provided in the analysans, but simply assumed to be available. An adequate analysis of depiction, in contrast, can be expected to provide an explanation of how depictions represent.

65Some analyses are illuminating but uninteresting. No doubt it’s possible, for example, to analyse bottles in terms of the purely physical. But the analysis would not be worth the difficulty of obtaining it: although an analysis of bottles in terms of the physical would show bottles are physical, the physical nature of bottles is not something we’re inclined to doubt. An illuminating analysis of depiction in terms of resemblance, in contrast, would be interesting, because – as the objections raised against it show – the platitude that whereas description is mediated by convention, depiction is mediated by resemblance is something we’re inclined to doubt.

66The illumination of analysandum by analysans may be of two kinds: an analysis may be either reductive or reciprocal, depending on its goals. Reductive analyses require the terms of the analysans to be metaphysically, epistemologically or conceptually prior to the terms of the analysandum, whereas reciprocal analyses are just required to illuminate how the analysandum and analysans are interrelated (Avramides, 1989, 19-24). Defending the platitude that depiction is mediated by resemblance and a strong analogy between depiction and description requires merely a reciprocal analysis of depiction in terms of resemblance and intention.

67Nevertheless, the analysis of non-natural meaning in terms of intentions and beliefs is generally considered as the first stage of a larger reduction of all representation – mental, descriptive and depictive – in terms of the physical (Schiffer, 1972, xi-xxix). If the second stage of this reduction – the analysis of intentions and beliefs in terms of the physical – is successful, then the analysis of depiction in terms of intentions and beliefs could likewise be considered as a step towards reductive physicalism, which would establish the epistemic, metaphysical or conceptual priority of mental over depictive representation. This is desirable, but not a requirement of success.

68In particular, it’s often objected that analyses of depiction in terms of resemblance and intention cannot be epistemologically reductive, since the terms of the analysans are not epistemologically prior to the terms of the analysandum: the resemblance of a depiction to what it represents and the intentions of its perpetrator, according to the objection, are only discoverable because the depiction represents what it does, rather than the reverse (Lopes, 1996, 16-20). The analysis below isn’t committed to the epistemic priority of intention over representation, but merely, I will argue in section 2.2, to the epistemic priority of resemblance over depiction.

69Four objections. First, analysis is often misleadingly called “conceptual analysis”, as if the analysandum were a concept and the analysans were the conditions for the application of that concept. This leads to the idea that the subject of investigation is not depiction itself, or whatever is being analysed, but merely the concept of depiction, or the concept of the analysandum. Given that one might easily have had a different concept of depiction and that it’s possible that not everyone expresses the same concept using the word ‘depiction’, this suggests analysis is merely an exercise in autobiography, rather than a method of philosophical inquiry.

70But analyses, on the face of it, state equivalences between analysanda and analysans, rather than conditions for the application of concepts. So there’s no reason to suppose that concepts, rather than analysanda themselves, are the subject of investigation. It might be true, and explain the use of the title “conceptual analysis”, that knowledge that an analysis is true is based on grasping the concepts expressed in the analysis. But even if this epistemology of analysis is correct, it needn’t follow that concepts are the subject of analyses. So it needn’t follow that analysis is merely an exercise in autobiography, rather than a method of philosophical inquiry.

71Second, analysis is often criticised on the grounds that it leads to dialectical deadlock, where it becomes impossible to assess rival positions. Robert Hopkins, for example, writes that “Provided that rival views avoid obscurity and obvious failure to cover more than a fraction of picturing [depiction], there is little to help us choose between them. At most they may differ about quite where the boundaries of depiction lie. The debate between them will then reduce to trading intuitions about which peripheral cases do or don’t count as depiction. Experiences of such discussions elsewhere in philosophy suggest that they are rarely productive” (Hopkins, 1998, 23-24).

72It is true that rival analyses disagree on the classification of which examples count as depictions. But this is no different from the disagreement of rival scientific theories over how to interpret the results of particular experiments: one theory may discard as noise what another regards as extremely significant. Just as it’s still possible to assess rival scientific theories which disagree over the results of particular experiments by conducting further experiments and appealing to theoretical virtues such as simplicity, rival analyses may still be assessed by appeal both to further examples and, when only peripheral examples remain, to general theoretical virtues.

73Third, continued disagreement between proponents of rival analyses even after all examples and theoretical considerations are taken into account sometimes indicates verbal disagreement about what the terms of the analysandum refer to, rather than substantive disagreement about its nature. If this is the case, it’s better to resolve the dispute by accepting both analyses as successful accounts of distinct analysanda (as I suggested in section 1.1). But philosophical progress may continue by assessing the consequences of each analysis for the further questions they were intended to resolve, so that the method of analysis is able to resolve substantive questions even in the presence of verbal disagreement (Chalmers, 2011a).

74So even if the dispute about whether depiction is mediated by resemblance turns out to be a merely verbal dispute about which kind of representation ‘depiction’ refers to, it does not follow that there are no substantive questions which an analysis of depiction – or of one disambiguation of what ‘depiction’ refers to – in terms of resemblance can resolve. In particular, there is substantive disagreement about the question of whether any kind of representation at all is mediated by resemblance, so disagreement over whether depiction is mediated by resemblance could continue even if it were discovered the original disagreement is partly verbal.

75Fourth, it might be objected that most philosophical analyses are unsuccessful. There are nearly always counterexamples which show that the truth of the sentences on each side of the biconditional used to give an analysis may differ, so that the two sides are not equivalent. Furthermore, this usually proves to be the case independently of the complexity of the analysis or the number of revisions it has undergone. Given this history, it is very unlikely that an analysis of depiction which is both informative and truly necessary and sufficient will ever be given. If this is the case, then it seems that analysis is a poor choice of method for examining the nature of depiction.

76But failure comes in degrees. Some counterexamples damage the succinctness of an analysis, but don’t interfere with its ability to clarify the issues it’s proposed in order to resolve. It’s sometimes pointed out, for example, that colours cannot be analysed in terms of reflectance properties, because stained glass windows have their colour due to filtering rather than reflecting light (Hyman, 2006, 15). But this counterexample does not affect the spirit of the analysis, since it’s not an obstacle in principle to the project of analysing colours in terms of their effect on light or, more generally, in terms of whatever physical properties are normally correlated with colours.

77But some counterexamples show, not just that the analysis of a given thing is likely to be cumbersome, but that it is in principle impossible to give an analysis of that thing in the relevant terms. The existence of a possible world, for example, which is a physical duplicate of our own but lacks conscious experience, is a counterexample to any analysis of consciousness in physical terms, regardless of the complexity of such an analysis (Chalmers, 1996). The example, if successful, shows that the analysis of consciousness in terms of the physical is not merely cumbersome, but impossible in principle.

78An adequate analysis of depiction should not be vulnerable to this second kind of counterexample. There may be counterexamples which show the correct analysis must be cumbersome and unwieldy, but there should be no counterexamples which show it’s impossible in principle to analyse depiction in terms of resemblance and intentions in parallel with the analysis of non-natural meaning. So although the analysis of depiction below is unlikely to be more than approximately true, it may still be sufficiently close to the truth to support a strong analogy between depiction and description and to defend the platitude that depiction is mediated by resemblance.

1.5 Conclusion

79The following chapters pursue an analysis of depiction which combines the platitude that depiction is mediated by resemblance with a close analogy between depiction and description. The second chapter argues for defining depiction as a kind of intentional representation, by adapting a Gricean analysis of meaning and communication (this part of the book shadows Abell 2005a; 2009, as well as Blumson 2009). Chapter three defends this analysis from familiar objections to intentionalism in philosophy of art. I argue that these objections are really objections to intentionalism in general, and have already been answered by proponents of the Gricean program.

80The Gricean program in the philosophy of language employs a strategy of divide and conquer by distinguishing speaker meaning, which is analysed in terms of intention, from sentence meaning, which is analysed in terms of convention. Whereas chapters two and three extend the Gricean analysis of speaker meaning in terms of intention to encompass depiction, chapters four and five modify the Gricean analysis of sentence meaning in terms of convention by jettisoning arbitrariness in favour of resemblance to form an analysis of depictive symbol systems. By jettisoning resemblance as well, chapter five extends this analysis to symbol systems in general.

81Languages are striking for their compositionality: the meaning of sentences depends upon the meanings and arrangement of their parts. Chapters six and seven pursue the analogy between depiction and description to its extreme by arguing that depictive symbol systems, like languages, are compositional. Chapter six argues that both depiction and description have compositional structure and chapter seven argues that compositional structure has the same role in the interpretation of both depiction and description. The platitude that depiction is mediated by resemblance is neglected in these chapters, but the pursuit of a strong analogy between depiction and description continues.

82The platitude that depiction is mediated by resemblance is often doubted because it’s not obviously consonant with the possibility of depicting inexistents, the possibility of depicting something without depicting something in particular, and the possibility of depictive misrepresentation. In chapter eight, I argue that these problems are merely manifestations of the problem of intentionality in general and, in chapter nine, I argue that the analysis of content in terms of possible worlds resolves this problem in a way which is consonant with the platitude. Chapter nine also addresses problems raised by pictures in perspective, and the possibility of depicting impossibilities.

83Just as it’s a platitude that depiction is mediated by resemblance, it’s a platitude that a picture is realistic to the degree to which it resembles what it represents (in relevant respects). But if properties are abundant and degrees of resemblance are proportions of properties in common, then the degree of resemblance between different particulars is constant (or undefined), which is inconsonant with the platitude. Chapter ten argues this problem should be resolved by revising the analysis of degrees of resemblance in terms of proportion of properties in common, and not by accepting a sparse theory of properties or denying the platitude.

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