Aesthetics for Birds

Aesthetics and Philosophy of Art for Everyone

Seven Puzzles of Pictorial Content


What follows is a guest post by Gabriel Greenberg. Gabriel is Assistant Professor of Philosophy at University of California, Los Angeles. He is interested in the variety of representation, from symbols to images, and everything in between. He is the author of “Beyond Resemblance,” Philosophical Review 122/2 (2013).

In this post I want to pose seven puzzles about the representational content of pictures.  By “pictures” I mean, roughly, perspectival images like architectural and figurative drawings, photographs, or maps.  All the puzzles here presuppose that pictures have content.   This is a natural idea: a picture represents the world as being a certain way; how it represents the world as being is its content.  The fact that pictures have content is what makes them useful for communication, problem solving, and entertainment.

The puzzles here focus especially on the kinds of properties that are attributed in pictorial content.  The very first puzzle brings to the fore how rich and complex such attribution can be.  The remainder zero-in on relatively low-level spatial properties.   As you’ll see, there is no shortage of perplexity, even at this very basic stratum.  As far as I know, these puzzles represent basically open questions.

To characterize the content of a picture, I’ll typically use a sentence of the form “Picture P depicts Object O as Property P.”  The property in this case is attributed by the picture to the object.  I’ll call the object which is having properties attributed to it the “subject” of the picture.  When the geometry of a picture fits perfectly with the basic geometry of the scene (no matter if it happens to be misleading), I’ll call the depiction “perfectly accurate”.  (For those who’d like to get into more detail about these terminological decisions, I’ve included an appendix at the end.)

To the reader:

  1. What are your intuitive judgements about these puzzles?
  2. How does your favorite theory of depiction come down on these issues?
  3. Is there an analogous issue in the philosophy of perception, and how has it been resolved or debated there?

Pencil drawing of Lady Gaga
“Lady Gaga” by Vania

1. The Portrait of Lady Gaga

Context. Here is a fan-art portrait of Lady Gaga.  For the sake of argument, let’s suppose it was drawn from life.

Puzzle. Does this portrait of Lady Gaga depict her as…

  • having nose, eyes, and mouth?
  • having lungs?
  • having feet?
  • being a person?
  • sitting for a portrait?
  • being a musician?
  • having sung the song “Telephone”?
    having sung the song “Pokerface”?

A grey cube


2. Two Views of a Cube

Context. I’ve got a favorite cube. You can see it on the right. I put the cube on my desk and then make two perfectly accurate line drawings of it, from two different views. The first view is from an angle off one corner of the cube. From this view I produced Picture A. The second view is from directly overhead. From this view I produce Picture B.


A 3D line drawing of a cube
Picture A
A line drawing of a square
Picture B

Puzzle. It’s natural to think of Picture A as depicting its subject as being cube-shaped.  But does Picture B depict its subject as being cube-shaped?

If no, then what grounds the difference in content between the two pictures?  If yes, then I invite you to the next puzzle…

3. The Cube and the Rectangular Box

Context. I’ve got a favorite cube and a favorite rectangular box.  

Here they are:

A small cube and an elongated cuboid

Now, I place my favorite cube before me, and assume a viewpoint directly across from it.  I proceed to make a line drawing of the cube, without any of the background included.  I produce Picture C.   Later on, I place my favorite rectangular box before me, and assume a viewpoint directly across from one of its short faces.    Now I make a line drawing of the box, again without any of the background included. I produce Picture D.   Both drawings are perfectly accurate from their respective viewpoints.  As it happens, the two pictures are type-identical.

A line drawing of a square
Picture C
A line drawing of a square
Picture D

Puzzle. Does Picture C depict its subject as being cube-shaped?  Does Picture D depict its subject as being rectangular-box-shaped

If the answer to both questions is yes, what grounds the difference in content between the two pictures? 

If the answer to both questions is no, then what properties do these pictures attribute to their subjects?

4. The Ames Room

Context. An Ames Room is a room with bizarre geometry, carefully designed so that, when viewed from a standard viewing position, it appears to have the rectilinear geometry of a normal room. The diagram on top illustrates (pretty crudely) the difference between a normal rectilinear room and an Ames room.

Diagram of the geometry of an Ames room
A line drawing of a small room, with a grid on the floor
Picture E

While walking down a hallway in strange building, I peer through a tiny peep-hole in a door.  Inside I see a room.  The room appears to have the geometry of a rectilinear room, and this is what I come to believe. I draw what I see, producing Picture E above.  In fact, unbeknownst to me, the room is an Ames room, and I am looking at it from the standard viewing position.

Puzzle. Does Picture E depict its subject as having Ames geometry? or as having rectilinear geometry? or does it attribute some other geometry to the room?

5. Two Rooms

Context. One day I knowingly visit my local Ames Room, and draw it from the standard viewing position. I produce Picture F.  Picture F is perfectly accurate, given the viewpoint.  The next day I knowingly visit my local Normal Room, which has rectilinear geometry, and draw it from some viewpoint.  I produce Picture G.  Picture G is perfectly accurate, given the viewpoint.  As it happens, the two pictures are type-identical.

A line drawing of a small room, with a grid on the floor
Picture F
A line drawing of a small room, with a grid on the floor
Picture G

Puzzle. Does Picture F depict its subject as having Ames geometry?  Does Picture G depict its subject as having rectilinear geometry?

If the answer to both questions is yes, what grounds the difference in content between the two pictures?

If the answer to both questions is no, then what properties do these pictures attribute to their subjects?

Line drawing of 3D cube. One edge curves either outwards or inwards.


6. Unsteady Hands

Context. I have occasionally unsteady hands.  I set out to draw my favorite cube perfectly accurately, and do pretty well, but add one superfluous curve to an otherwise accurate drawing.

A square with a outward curve next to a square with an inward curve.

Puzzle. What is the precise spatial content of my picture?  Assuming it does not depict its subject as simply being cube-shaped, then…

Does it depict it as having a flat front face that protrudes above its top corners (pictured at left below)?

Or as having an indented front faces that does not protrude (pictured at right below)? Or something else?

A line drawing of a 3D cube

7. The Absent Cube

Context. I sit down at my empty desk, pop some acid, and soon hallucinate a perfect but unfamiliar cube sitting on the desk before me.  I proceed to create the drawing at right, which I believe perfectly accurately depicts the situation before me. (Alternatively: I draw the surface of my desk from memory, not life.  I have a false memory that there was a cube on the desk.  I believe my drawing accurately depicts the situation I remember.)

Puzzle. Does this depict my desk as having a cube sitting on it? 

Yes is the natural answer, but why? 

If it is because of the artist’s beliefs or intentions, did you also give artist’s beliefs or intentions primacy in Puzzles 4, 5, and 6?

Addendum on Terminology

It can be useful to standardize the way we talk and think about pictorial content, especially since using language to describe pictorial content can be an awkward fit.

We can divide pictorial content into pictorial reference and pictorial attribution.   What a picture refers to are the things that the picture is of or about.  What properties a picture represents its referents as instantiating is what it attributes.  This distinction is reflected in the common “depiction as” formulation for describing pictorial content.  I use the formulation in sentences such as these:

  1. The picture depicts Ponyo as walking across the street.
  2. The picture depicts the president as waving her hand.
  3. The picture depicts the cube as being a cube.

All of these have the format

[picture] depicts [object] as [property]

where the thing denoted by the term in the [object] position is a referent of the picture, and the thing denoted by the term in the [property] position is a property attributed by the picture to its referent.  No single “depicts as” sentence, at least none of readable length, will capture the entire content of a picture.   Each such sentence offers only a partial characterization of a picture’s content.

Any singular term can fill the [object] position, such as a name in (1) above, or definite description in (2) and (3).  As I choose to fix things, I’ll never take a definition description in the [object] position to express what properties the picture itself is attributing.  (Natural language may be less rigid in this regard.)   Thus (2) above does not characterize the picture’s content as attributing the property being the president.  For the same reason (3) is not a triviality.

A picture may have many referents.  To avoid the philosophical burdens of the term “reference”, I call the referents of a picture its “subjects”.  When one such subject is especially salient, I call this “the subject” of the picture.


  1. “Yes is the natural answer, but why? If it is because of the artist's beliefs or intentions, did you also give artist's beliefs or intentions primacy in Puzzles 4, 5, and 6?” Yes! Best, Ben.

  2. Hey Ben, if I understand your answer, you think that the picture in #4 attributes rectilinear geometry? but the first picture in #5 (which is type-identical) attributes Ames geometry? (both refer to Ames rooms, only the belief is changed)— I guess I find that surprising. Obviously they are picture of Ames rooms (in the referential sense), but same attributive content?

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  4. Fun stuff!

    I don't have clear intuitions to the problem as posed. Rather, my impulse is to think that “[picture] depicts [object] as [property]” misleadingly suggests that depiction is just a property of picture. I'm more inclined to think in terms whether pictures are taken to depict such-and-so, which becomes “[agent] takes [picture] to depict [object] as [property]”. We can ask whether agents out to take a particular picture to depict such-and-so. That will typically depend on the conditions under which the picture is produce, which might include intentions. But it may also depend on facts about the object.

    So I am inclined to say that the Ames room pictures depict a room as rectilinear, precisely because Ames rooms are constructions which are indented to appear rectilinear. They are more like a lie than like sarcasm.

    Regarding your initial question, about the relation between my intuitive judgements and my preferred theory of depiction, I am to much of a philosopher to be able to make a clear distinction any more.

  5. it sounds quite complicated.
    I think a photograph ( which is an image to begin with ) before being a photograph is about the content and about the photographer. Assuming that a photographer is more likely to take a photograph rather than just a mere image.
    I think you photograph certain things among a millions of other things/situations that you could choose from. It is about the content that you are photographing and about your emotions with which you charge the photograph, to say it like this. These emotions can make you compose in a certain way or see things in a certain way, even though the content is the same content for two given photographers.
    When the content is very powerful, I think things are a bit more clear. Hopefully.

    a more poetic photographer will photograph differently, he might see ordinary situations ( a cloud, a leaf falling, a piece of paper in the wind, etc) as being interesting. The content is the same for me as well, but I simply can not see his situations, his compositions even though I might like them.

    It might be quite different with drawings/paintings or technical drawings.
    But an image might be just a mere representation of the content, of what is in front of me without any interpretation of the person who took the image/ made the image.

  6. Very interesting post. With respect to your third question for the reader, I think the literature in philosophy of perception about how things look — e.g., whether/in what sense a round coin looks elliptical or looks round — might be relevant.

  7. Thanks for posting this, Gabe.

    Most of your puzzles, as I’m sure you know, have their own histories. The first is very Wollheim (my favorite example: 1998, 224). Most of those in the middle evoke Gombrich’s discussion of gates and the Ames room in _Art and Illusion_. One question, then, is whether you see these puzzles, in the distinctive way you present them, as pushing in directions previous discussions do not. They cluster around two issues: the pictorial attribution of qualities—being a cube, being red—and the pictorial reference to individuals like Gaga and your favorite cube. You can ask both kinds of question about pictures, but which of the _answers_ do you think tell us about what makes depiction distinctive? I tend to think that answers to questions of the latter sort cut across representational kinds, and thus don’t help us understand what makes pictorial representation distinctive. Questions of the former sort are where the action is. I assume you disagree here, because you introduced both kinds of puzzle as puzzles about pictorial content.

    Your Gombrich puzzles (2-6) all have a similar structure. Making that clear can help see one way to handle them, and perhaps by extension the Lady Wollheim puzzle.

    Cases 4-6 present two mutually-incompatible options for qualities pictorially attributed to the subject (Ames/ rectilinear, bulging in/ bulging out). Cases 2 and 3 are similar, except that in 2 the question is whether the subject is represented as a cube, or simply not represented that way. Notice, first, that we could multiply our options in each case. Many Ames-like distortions are possible, as are curvy options behind lenses. Second, not anything goes: a feathery, aesthetic bird-like creature is not an option. So, what makes a scene a good candidate?

    First suggestion: all good candidates share projective invariants with the picture itself. That’s how the picture manages to constrain the range of possibilities. Second suggestion: that set of projective invariants is a kind of pictorial content, close to what John Haugeland called ‘skeletal content’ (1991). What makes pictures distinctive is not that they have skeletal contents, but that they _instantiate_ their skeletal contents (among other things). Also distinctive in part is how pictorial skeletal contents are fleshed out to the ordinary contents, like cubes, Ames rooms, and so on.

    Fleshing-out is complicated. In part, it is a deeply perceptual process, which could involve the deployment of recognitional abilities, experiences of resemblance, or any of a number of other things. That’s what I think makes our uses of pictures highly perceptual. But, like recognition responses and experiences of resemblance, this process is highly context- and habit-bound. These contexts and habits are not just tuned to lighting and other low-level aspects of the environment, but also to the fact that we are dealing with representations, which carry their own norms with them. This helps see the important point behind both Ben B’s and PDM’s comments. To pick up on one of Gombrich’s points from _Art and Illusion_, if Ames rooms were as common as rectilinear ones, we might very well interpret your examples as depicting Ames rooms, or being indeterminate between the two, but as it stands, we don’t.

  8. Hey P.D.—

    Thanks for your comment! I like the idea of adding a parameter, the question is who or what fills this role? Lets say its a parameter for audience members, not artists. Then we should ask— is depiction relative to mere individuals, or is there some population that is that natural parameter? The individual idea seems to track what we are talking about when we say “to me, it depicts this… to her, it depicts something else”. But intuitively there is a more general notion of “depicts” which (if this general line is right) would have to be resolved to a population. So that is one question— who is the population and how are they defined?

    Another issue has to do with what kind of reaction is relevant on the part of the audience. Take Picture B in #2— the square picture of a cube. The visual system alone won't get you from a square to a cube. You'd have to import some further background knowledge of the context of creation if you want to say that it depicts its subject as a cube. But how much background knowledge is admissible? If you allow in too much, then you end up saying that the picture of Gaga depicts her as having written “Telephone”, which sounds implausible to me.

  9. P.S. I'd be curious to hear what your colleague Robert Howell has to say about this. He has some very interesting technical papers on pictorial representation from the 70's.

  10. Thanks for the reply.

    I'm not entirely sure how to fill in the relation, but the “[agent] takes [picture] to depict [object] as [property]” allows for uses that are both idiosyncratic and population-level. Fill it in with an individual, and you get something like “Gabriel takes 2b to depict a thing as cubical.” Use quantifiers or generic constructions, and you get something like “A typical Londoner would take 1 to depict Lady Gaga as grotesque.”

    Like you, I don't think it would be right to say that 1 depicts Gaga *as* having written “Telephone”. However: Suppose the artist intended for it to depict Gaga just after having written the song. Then it would sound fine to me to say “The picture depicts Gaga, just having written 'Telephone'.”

    For what it's worth, I think the real puzzle about 1 is whether or not it depicts Gaga as having two eyes.

  11. Thanks Amy! That certainly sounds like a promising area of connection. Though I suspect that that particular issue, round v. elliptical, cuts across the issues here. For example, in the drawing of the Ames room, all parties agree that, in the picture, the floor lines converge, and that this represents distance. If anything, the contrast between surface features and represented features is more stark in the picture case.

  12. Hey John–

    Thanks so much for the detailed comments and questions. Really thought provoking. Before giving any responses, I want to say that I started thinking about all these cases in large part because of the distinction you introduced between bare-bones and fleshed-out content in your book. (I realize there are traces of the idea in Haugeland.) As you argue, bare-bones content can be giving a very precise geometrical definition. We disagree about the exact role of the geometry here, but that's a matter of detail. The gnarly questions all have to do with how this bare-bones content is “fleshed-out”. Most *philosophical* discussions of this kind of problem focus on fleshing-out with either individuals, or very high-level properties like “being a person.” But I was worried about how low-level spatial properties get fleshed out. (After all, bare-bones content as you define it does not even include distance features.) All of these puzzles are intended to bring to the fore how challenging that task is.

    Now, onto some particular responses, in the order that you raise them.

    Re: History. I'm very happy to get better historical rooting here. The very first puzzle I got from Malinas' 1991 “A Semanitcs for Pictures”… but it seems like a very natural set of questions to ask, and I assume there are passages from Wollheim that predate it. (Right?) I'm going to have to go revisit the Gombrich passages and think about the points of similarity and disimilarity here– but thanks for the pointer.

    Re: Attribution v. Reference. There are a couple issues here to sort out. I think we agree that there is a distinction between pictorial attribution and reference. I think that both are components of *pictorial content*; I think you agree here too. I have absolutely no view about which “makes depiction distinctive”, so I'll hold my tongue there.

    So far so good. But now I want to disagree about your characterization of the puzzles, as chiefly contrasting reference and attribution. That point is taken for granted. Instead, I think of these as puzzles directly about attribution (“fleshing-out”). Sometimes the referent is relevant because our intuitions about what properties get attributed is sensitive to the referent. For example, in Puzzle 4, there is something strange about the idea that an artist could perfectly execute a drawing of a room– making no mistakes– yet nevertheless create a picture whose content was inaccurate of that room.

    Re: Common structure. I think if I understood the basic common structure of 2-6, I would be clearer about their resolution. Perhaps you can offer some help here? But basically all result from generating mis-matches of: the content that is naturally derived by the visual system / the kinds of scenes which geometrically project to the image / the beliefs or intentions of the artist. Pictorial content seems relatively clear when these dimensions are aligned. But, at least for me, it becomes murky when they are mis-aligned. Which if any of these deserves the title “content”?

  13. Re: first suggestion. As I flagged before, I want to take on your idea of bare-bones content, and also your characterization of it in terms of projection. I don't agree about the invariance idea. But that is a longer debate, perhaps for another time. (Curvlinear projection etc.) But even if we set that aside, yes, I think bare-bones content puts a constraint on possible contents, and that is what is great about it. It rules out the aesthetic bird. Unfortunately, it doesn't resolve the puzzles posed here, which is why they came to seem puzzling to me in the first place.

    Re: fleshing-out. As I said in response to PDM, I like the idea, which again you propose in your book, that audience reaction has something to do with fleshed-out content. (Even tho they don't use that idiom, I take it that Schier and Lopes hold analogous views.) But at that point things get tricky. I don't think its enough to say “well, it's highly contextual”. Contextual how? What are the principles and mechanisms?

    As I understand it, answering this question is hard because it must navigate between two perils. The first Peril is revealed by Puzzle #1. It shows is that not all facts which are compatible with an image being accurate are part of its content. Even though we know Gaga sung “Telephone”, and we know its a picture of Gaga, we don't think it represents her as having sung “Telephone”. So the interpretive process cannot be too open-ended. For example, you can't get the content of a picture by intersecting its bare-bones content with your general world-knowledge. This might make one think that fleshing-out is not really the domain of general inference, but is fixed by something lower-level in the visual system.

    The second peril is that the visual system itself appears to be quite rigid and modular. (Gombrich's empirical claims about Ames rooms seem dubious for this reason. *Perhaps* if the world were full of Ames rooms we would respond to the pictures differently. But the construction of the Ames room exploits perceptual principles which are probably as old as animal eyes– i.e. very very old, long before the arrival of mammals, hence long before the arrival of rooms.) The Ames room always looks like an normal room, no matter what you know. So the visual system is quite resistant to contextual information outside of its specific purvey.

    Should pictorial content simply go with the visual system? In that case, all of the Ames rooms drawings have the same content— rectilinear room. And the square drawings from #2 and #3 do not depict their subjects as a cube (or a box), because the visual system does not extract this information. This leads to the unfortunate conclusion that despite making no mechanical error, the artist has created pictures whose contents are inaccurate, in each case. Furthermore, there is the oddity, I think, of saying that the picture, though constructed correctly, depicts an Ames room as a rectilinear room.

    On one hand, pictorial content can't just be everything we can figure out given a picture. On the other hand, pictorial content can't just be everything the visual system can figure out given a picture. Finding a principled path between the constraints strikes me as very hard.

  14. Two follow up points.

    (1) We should be careful about what it means for an agent to “take” a picture to depict such and such. If “take” means “compute by the visual system” we'll get one set of answers (for individuals and the population); if “take” means “come to believe” we'll get a different set of answers. Relativizing to agents seems like progress, but doesn't let us settle many of the key issues.

    (2) Watch out in your “Telephone” example that you are not slipping into an idiom of pictorial *reference* rather than attribution. I agree its find to say “The picture depicts Gaga, just having written 'Telephone'.” But this might just be a de re way of fixing the time and place of the referent of the picture. It need not thereby ascribe telephonic content to the picture. (See my note in the terminology section about the “president” sentence.)

  15. The first puzzle.

    the picture depicts Lady Gaga in her signature style from “Pokerface”. You can not say it is from “Telephone” because the picture does not indicate this.
    It is straightforward.

    Also, for someone who is not familiar with Lady Gaga and who she is, the picture represents a girl, albeit a distinctive one, as having different features comparing to other girls you know. But not Lady Gaga.

    I think the content of a picture, after the final image is produced is what is important.
    Some photographers, for instance, believe that their pictures express more than they do. ( in pictures which are quite clear, not the ones that are more ambiguous). Beginner photographer go through this, but not only.

    But I think a really good artist is capable of expressing more complex ideas and also make them ambiguous to the viewer.
    But not one that is not good.

  16. I see your points more clearly, Gabe. Very helpful. Specifically, you say that deploying the idea of bare-bones content does not “resolve the puzzles posed here”. I was thinking that it does, at least for the most part, because I have a different sense of what the puzzles are. It’s puzzling that reasonably straightforward pictures admit of such questions about their contents. Other kinds of representation do not. Bare bones content, and the need to flesh out, give shape to the questions, and explain why some are compelling (Ames room or ordinary room?) and others (ordinary room or aesthetic bird?) are not. As far as giving a specific answer to whether it’s an Ames room or something else that’s depicted, the answer is: it depends. The Task is then to articulate on what it depends. Because I think one can get very far understanding what makes depiction a distinctive kind of representation in terms of the skeletal/fleshed-out distinction, the Task seems interesting, but tangential to my core concerns.

    That being said, you are right: it might be that the Task exposes some important philosophical ground, and that’s why I asked whether you see yourself as pushing these puzzles in a specific direction. Your two perils help me a bit with that, but let me frame one issue in that neighborhood.

    As you suggest, there are analogous and long-standing perils in the philosophy of perception. Very roughly, what we perceive is not the sum total of what we can infer from what we see, but it seems to outstrip the simplest qualities about which the visual system carries information. One might think that a path through the perils of perception yields a path through their pictorial analogs.

    But depiction is a kind of symbolization, albeit one that leans heavily on perception. Habit can play a role here that it might not be able to play in perception. This might make finding a “principled path between these constraints” impossible, because there need be no terribly principled path between them. This needn’t be worrying unless one’s account of depiction requires such a path.

  17. You reply to case #1 by saying, “the picture depicts Lady Gaga in her signature style from 'Pokerface'. You can not say it is from 'Telephone' because the picture does not indicate this. It is straightforward.”

    That struck me as the right thing to say.

    However, imagine if the artist had the false belief that the depicted style is the signature from 'Telephone' and had intended the picture to depict Lady Gaga singing 'Telephone'. Honestly, my intuitions then just pull in both directions.

  18. why would you want to imagine that the artist had a false belief of depicting something else that he actually depicted in the picture when you see what the content of the picture is?

  19. Yeah. In case four you believe the room is rectilinear and you intend to draw it as you believe it is, so you intend to draw it as rectilinear, and this intention determines the content (as long as I'm able to recognize that as your intention, which I can with the background story).
    In the first case in five you believe it is not rectilinear and you intend to draw it as you believe it is, so you intend to draw it as not rectilinear, and this intention determines the content (as long as I'm able to recognize that as your intention, which I can with the background story).
    So although the two pictures look just the same, there is a difference in attributive content. But this doesn't seem to me at all surprising – just one more counterexample to the sufficiency of resemblance for depiction.

    Thinking about it a bit more thoroughly though, I can sympathize with someone who thinks that a picture's content depends in part on the scene which caused it In a way, I think it does too, but this happens because the content of the drawer's intention depends in part on the scene which caused it, via the dependence of the content of the perception on the scene.

    That means that in case seven, I have to tell some complicated story about how it is that I have a perception as of a cube, even though there is no cube there. Whatever this complicated story is, someone who favors a causal-historical account of the content of the picture, can apply this complicated story directly to the picture, and so escape the need to go via the intention.

    So my answer to the questions were mainly motivated by the fact that I'm already sympathetic to an intentional account. But I don't think the examples force you to move in that direction. Someone sympathetic to a causal account should in principle have some story to tell – presumably, the same story they would tell in the case of perception.

  20. actually, I think you meant that it is true as being the only possibility that the artist has a false belief that he depicted the style from “Telephone” when he/she actually depicted the style from “Pokerface”.
    The picture does not show this though but the artist sees as it actually depicts the style from “Telephone”? That is what a false belief means.
    But would you not rather conclude that he is wrong according to what you see in the picture? In what sense the artist false belief is important?

  21. I find it lamentable that otherwise extremely intelligent people are still struggling with questions that have already been resolved by the work of Australian artist and art theorist Donald Brook. Brook has been published numerous articles and papers in the British Journal of Aesthetics and many other places since the late 1960's. Perhaps you should do a little more research.

  22. CHRISTY COMMENT: Jim, no doubt Donald Brook's work, especially (1969, 1983, 1986, & 1997), stands as a significant contribution to the debate on the nature of depiction. However, that's a far cry from your ridiculously bombastic and sweeping claim not only that Brook had already thoroughly and satisfactorily settled that debate but that all of those working in this area for at least the last 15 years or so ought to be ashamed of themselves, not just for wasting everyone's time but for their individual and collective research neglect/ignorance of Brook's work, be it willful or otherwise.

    Of course, that's utter bullshit that, other than you, absolutely no one's queuing up to shovel…not even The Great Resolver himself: Donald Brook.

  23. Thanks Christy, perhaps that was over assertive on my part – for which I apologise – but your doing a quick google search doesn't make you an expert on Brook's work. If you want to back up your apparently hollow erudition with substantive evaluation of even one or two of Brook's principal ideas I'd happy to thrash the issues out with you and if it turns out that you do indeed understand some of his insights then I'd be very happy to offer you a full apology for my imperiousness.

  24. CHRISTY COMMENT: Jim, let me get this straight: You will apologize for irresponsibly saying what was obviously false on the condition that I prove to your satisfaction that I had certain justificatory reasons for saying what was obviously true? How generous of you!

    While I'm no Brook scholar, I do know enough to realize two things:

    1) I have zero desire to debate the less-than-obvious merits of appeals to fuzzy quasi-conventional perceptual-failure based notions of simulation as a means by which to resolve putative puzzles of pictorial content with a hostile Brook acolyte who thus far has shown himself prone to gross exaggeration in service to the belittlement of others as well unable to utter even the most basic of apologies absent some further insult. In fact, I'm not quite sure which is more insulting: a) your ridiculous demand that I show you my credentials, or b) that I do so as a condition on receiving the honor of “thrashing out” a view that you and you alone endorse.

    2) It's my fucking blog, asshole. In no possible world does this end well for you.

    Perhaps you should have done a little more research.

  25. Fair enough Christy, you probably won't post this and perhaps it doesn't really matter. Consider it a private apology and if you want to post it then consider it a full public apology. I'm not so proud and I didn't intend to get your back up to quite such an extent – though I admit I wanted to be a little provocative. I'm just a bird spouting ornithology after all.

  26. Thank you, Jim. I appreciate the apology, and it certainly came at the right time. Gabe's doing some pretty awesome stuff on pictorial depiction and I suspect my caterwauling wasn't the best method of promoting it.

  27. This comment has been removed by the author.

  28. OK, a bit of background – because credibility seems to count, even among the birds. I’ve been making, talking about and teaching art for the vast majority of my life and in that time I’ve read, debated and taught a wide variety of theories of representation. I’m very familiar with resemblance theories, theories of illusion and theories of photographic transparency (fine art photography being my primary field of teaching). I’ve read Wollheim, Gibson, Arnheim, Gombrich and several other theorists often starting with “G”. It’s true that I’m convinced that I have encountered a theory that I think better explains representation than any other and if this makes me an acolyte of Donald Brook I’m guess I’m ok being defined as such. I consider myself to be an acolyte of James Clerk Maxwell by the same token.

  29. Brook’s theory is what is known in educational theory as a Threshold Concept which means that it is particularly difficult to get across and to acquire, not least because the other theories are so deeply embedded despite their many well documented and easy to exemplify deficiencies.

    Pictorial representation is a culturally evolved phenomenon. We need only look at history to see the clear evidence for this fact. Despite the tendency of many theorists to assume that reality ‘looks’ like pictures depict it, there is overwhelming evidence that prior to the discovery of perspective and the development of mirror and lens technology the ways that artists represented the world was often very unlike what we now think of as ‘realistic’ depiction.

    Pictures are not a simple form of representation by any means and they employ several different strategies of representation (which is why it’s often so difficult to explain what’s going on).

    Brook defines 3 principal forms of representation: Matching, Simulation and Symbolisation. For brevity I’m going to stick to Simulation because it’s the hardest to deal with and is most implicated in the Ames examples.

    In accounts of our perceptual abilities, much is made of the successes of our perceptual system but the systematic limitations are often thought of as anomalies. However, the properties of optics do something very particular to light which is profoundly exploitable for depth perception. We say “The distant ornithologist looks small” yet we know she is not small.
    Ruskin took the view – derived from his interest in Berkeley – that the child draws what she knows not what she sees. This philosophy is still promoted in schools throughout the world every time a teacher says “Look at the apparent shape.”

    Of course, it often helps, when trying to draw, to close one of your eyes. Imagine the medieval artist though, trying to improve their art and with no available example of what depiction is capable of? We can’t know what we don’t know and it is simply illogical to say that naïve artists don’t know how to see (although philosophers of perception are still inclined to make this ridiculous claim – as I heard just the other day at a conference in Glasgow). As it turns out, what naïve artists don’t know are the strategies of pictorial representation that would lead to what we now think of as realistic images. One of these strategies is to close one eye as you look at the world. Now imagine the medieval artist thinking to herself, “How can I improve my drawing? Oh, yeah, I know I’ll just close one eye and diminish my perceptual experience, that should help.”

    That’s a wee aside. Back to the exploitable characteristics of our optical system. Due to these characteristics we are able to substitute small things in the foreground for large things in the background. Choose any of the innumerable notional picture planes between you and an object and its possible to occlude any object perfectly with a flat representation so long as you control the circumstances very carefully. It is this exploitable perceptual regularity – that allows the substitution of flat small things in the foreground for 3d things in the distance that enables our cultural use of simulating representation (not to be confused with pictures per se).

    The reason the two Ames room depictions are a bit of a puzzle (but not for Brook’s theory) is because they are Matching representations of one another. They are not Matching representations of the room, they are Simulating representations of the room and as such they are deficient in certain respects. For an analogy, which I hope is more illuminating than confusing, the two images are like visual versions of the utterances “Be” and “Bee”. Humans are highly attuned to contextual cues in order to help us determine the meaning of representations.

  30. about the 4 case, the Ames Room.
    You produced Picture E which depicts a rectilinear room although it is not a rectilinear room.
    You took yourself as the subject who is experiencing what he sees.
    Even more, you were accurate in depicting exactly what you saw.
    We also know that a room has to have a certain geometry, standard.
    I assume there are some universal rules that make sense for producing a room.
    It is like a pattern.

    You did not know it was an Ames room. In that case, you would had liked to draw the room accordingly, right?
    I find it interesting though. I could draw what I see which is a mistake but so beautifully and convincingly misleading and what the reality actually is, all at once. Even though what I see is false, it is still convincingly haunting for my eyes.
    Unless something happens to give you further indication of the fact that it is an Ames room, there is no way you could figure it out.
    You will draw what you see because the intention was to be fooled.

    In the case 5, you know it is an Ames room. I find no excuse why you ended up drawing a rectilinear room when you knew it was not a rectilinear room. what was the purpose?

  31. Thanks John– I think we are now coordinated on the problems.

    If your concern is primarily to identify what is distinctive about pictures, then I can see why it may not be necessary to push beyond bare-bones content. If your concern is to explain why pictures have the semantic properties they do, then pushing beyond seems necessary.

    There is one sense in which the problem in perception is easier. We seem to have much clearer judgments about, and explanation of, perceptual content. For example, the perceptual content generated by looking at the Ames Room is clearly of a rectilinear room. That's why the Ames Room was constructed. But for some reason the judgments, at least for me, are less clear in the picture case.

    I agree that a “principled path” in the sense of a very clean and path may not be obtainable. Still, it seems like we all owe ourselves an account of what is habit and what is perception, and how on earth the two interact. The interaction question is especially challenging given the wealth of evidence that vision is impenetrable to high-level processes.

  32. Hey Jim, I'd like to get some specifics on this. Can you point to which Brook papers you think resolve particular issues. Since you are clearly quite familiar with his work, maybe you can join the conversation by explaining how his positions come down on the questions raised.

  33. Hi Jim, I'm afraid that explanation didn't really elucidate the matter for me. The current debate is being conducted in the framework of the theory of representation– in other words, the debate is about what kinds of CONTENT are assigned during interpretation. Exactly what CONTENT, according to brooks, are assigned to the two Ames rooms depictions. Let's get very concrete and clear about this.

    I also think that it is false to claim that the two Ames rooms drawings are representations of one another in any sense. They are each representations of a room, not a picture. They may happen to match each other. But they are not representations of each other.

    Some of what you are saying here simply recapitulates basic vision science. It's not really a profound mystery why a flat object could cause a percept of depth. It reflects an array of light which triggers depth perception mechanisms in the visual system. In a way, this side of visual perception is relatively well understood. (The fact that the percept is triggered by a line drawing adds complications which are not so well understood.)

  34. I also want to say that the ideas of “resemblance”, “looking like reality”, and “realistic depiction” play absolutely no role in the generation of the puzzles. The relevance of resemblance is widely debated in the literature on depiction. And virtually all parties to the debate recognize its culturally evolved dimension. So again, I'm not seeing the revelatory force of the Brooksian analysis.

  35. Thanks Ben— that is a clear position. As I understand your view, the attributive content of the picture is whatever the artist intends, so long as the picture resembles what they intend. I assume you need the latter clause to forestall crazy intentions from determining content.

    But how do you deal with #6 (Unsteady hands). The artist intended to draw a cube; the picture doesn't resemble a cube in the relevant sense. And I would have thought, intuitively, that the picture does *not* depict its subject as being cube-shaped. So how do you deal with cases where intentions and resemblance come apart?

  36. I also share the intuition that the picture depicts Gaga as having been the artist of “Pokerface”, but not of “Telephone”. But I think it is very interesting to try to figure out why this is. The picture includes no text or other explicit references to “Pokerface”. It simply shows Gaga in her “signature style” from Pokerface. Yet we all know that the person who made “Pokerface” was also the person who made “Telephone”. So, to repeat a point that has come up before, the content of the picture is not just what we can infer from it. Because then we would say yes to “Telephone”. There must be some less flexible evidential link which relates the picture to its content. I'm not sure what this is.

  37. Hi Gabriel,

    As I said, it’s not an easy argument to make by any means and it will take some work on your part to fit the pieces together because spelling it out word for word could drive us both crazy. I’m willing to stick this out but you will need to invest some time in thinking it through as well and maybe doing some homework on Brook’s theory (1969, 1983, 1986, & 1997 as Cristy has already cited). It will be worth it though I assure you.

    Brook's theory of pictorial representation dates back to the early 1960s when he was researching visual perception for a doctoral thesis at the University of Northern Australia, Canberra. During this time he began to notice that discussions of sculpture (and objects in general) tend to employ two distinct categories of description – what Brook then termed “Picture Accounts” or “Object accounts”. Picture accounts invariably emphasise views, contours and aspects of things seen from particular viewpoints whereas object accounts emphasise qualities of texture, mass, solidity and form. Our commonplace descriptions of things also incorporate combinations of both categories of descriptive account.

    As a consequence of this initial research Brook realised that two distinctly different systematic species-wide perceptual limitations underlie Picture Accounts and Object Accounts. Moreover, it soon became clear to Brook that these same perceptual limitations are responsible for two fundamentally different forms of representational strategy which enable all pictorial representation.

    In several journal articles and papers published between 1969 and 1997 Brook outlined these different representational strategies as Matching and Simulation. A third form of representational strategy was also incorporated into this theory to accommodate symbolic representation (of which language is an prototypical example)

    Matching and simulating representations are dependent on demonstrably different forms of perceptual failure/limitation/vulnerability/felicity. Matching relies on the fact that thing A can be used to represent thing B because two things are – for all we can tell (i.e. for all our perceptual faculties permit) – genuinely alike in one or more respects. One piece of paper from a ream of A4 sheets can be used to represent another from the same ream because they are genuinely alike in a variety of respects. The same piece of paper can also be used to represent any other piece of A4 paper in respect of size and shape even though in many other respects they might be very different (colour, texture, thickness etc). A coin could be used to serve as a matching representation of a wheel for instance since it would match in respect of circularity. Where it would definitely not match though would be in respect of scale and this is where simulating representation comes in.

  38. If you look at a wheel and hold up a coin, even if the wheel is at an angle to your field of vision, it is possible to align the coin in such a way that it perfectly obscures the wheel. Artists often use a very similar technique in order to produce observational drawings.

    Despite the fact that this technique is well documented the perceptual flaw that enables it remains unnamed, presumably because it is not believed to be a flaw but a straightforward characteristic of our perceptual makeup/constitution.

    The important perceptual flaw that makes it possible to perfectly obscure one thing with another of demonstrably different size is radically different from the perceptual flaw that leads us to say that two things are identical. Identicality is dependent either on the objective fact that two things share exactly the same quality or on our lack of perceptual resolution. For example, two pigments may be judged by all members of one species to have the same colour yet turn out to be easily discriminable by another species with a more finely discriminating perceptual makeup. So, Matching is dependent on either the objective fact that some things are genuinely alike or that a species of perceivers are unable to differentiate between different things due to a systematic lack in perceptual discrimination at the level of resolution.

    Simulation, on the other hand, is fully dependent upon the circumstances of presentation. The Ames room is dependent upon the careful control of the circumstances of presentation to the same degree. It exploits the fact that we find it impossible in curtain circumstances and in certain respects to discriminate between things that are easily discriminated between when the circumstances are not strictly controlled.

    As an aside, and in response to your question about the two depictions. It is beyond question that the two images are indiscriminable in almost all respects (aside from spatio-temporal location) and are thus symmetrically available for use as Matching representations of one another. Many theorists have noted that two duplicate photographs “resemble” one another more than they resemble their referent. The reason they do so is because resemblance plays no part. They are Simulating representations of their referent and Matching representations of one another.

    And as another aside. Terms like “looks like” and “appearance” are examples of how language has assimilated non-verbal representational strategies into its lexicon. When I say that such and such a thing “looks like” such and such other thing, what I am saying is that I believe it would be accepted as a viable representation by others of our species.

  39. ” Yet we all know that the person who made “Pokerface” was also the person who made “Telephone”.

    the person who made “Pokerface” and “Telephone” is not the artist who is depicting Lady Gaga. The artist chooses to depict her the way she likes. Doesn't this has any importance?

    why did you say that “the content of the picture is not just what we can infer from it. Because then we would say yes to “Telephone”.
    I simply do not understand what you mean and it seems to be vital for your entire thought process.

    other than that, maybe the artist made the drawing right after “Pokerface” video was made, so long before “Telephone” was released.
    what do you say about this?

  40. I'm kind of late to the party, but wanted to (a) express appreciation for another awesome post and (b) spout off on some of the questions Gabe poses to readers. Probably in many sections, because I have the blathers. I am coming from poetry, where representation obviously looks really different. (And totally not-aesthetics, not-mind bits of philosophy: ethics, metaphysics, formal epistemology.)

    My favorite theory of depiction is Kendall Walton's theory of truth in fiction: what is true according to a picture is what the picture prescribes imagining. Therefore, you can change what is true according to the picture by, e.g., putting a caption in. I would add that what the picture prescribes imagining is something like what a reasonable person would infer the author intended. (I think we can capture PD's ternary “X takes Y to depict Z” in this framework as “X takes the Y to have intended to prescribe imagining Z”. Walton's account does something like filling in “the normative viewer” for X.)

    My intuitive judgments on Gaga are that the picture:

    * Does depict her as having nose, mouth, and at least one eye. (I am uncertain about that other eye; maybe the picture is ambiguous.)
    * Does depict her as having an ordinary human body that extends beyond the frame, but doesn't depict her as having lungs and doesn't depict her as having feet. (Which means that there is some weird hyperintensional something going on. Also, what the heck do I mean by “the frame”?)
    * Does depict her as being a person.
    * Does not depict her as sitting for a portrait.
    * Does depict her as being a musician, and I'm not sure whether it depicts her as having sung “Telephone” and “Pokerface”.

    I think these intuitions are all consistent with Walton's theory. It had better be the case that one can have a prescription to imagine P without a prescription to imagine all the analytic consequences of P; otherwise I'm in trouble with the lungs and feet.

    Moar soon.

  41. Hopefully part 1 is just in moderation and was not eaten by the spamulator. My answer to questions 2-7 is that the answer depends entirely on context. And I think this is entailed by what I said in part 1 + reasonable background assumptions. Example pictures with exactly the same physical appearance may depict cubes or long boxes (or just squares, or be ambiguous); may depict Ames rooms or regular rooms (or just lines, or be ambiguous); and may depict cubes that are distorted in one of two ways (or just regular cubes drawn badly) depending on stuff like captions and surrounding conventions.

    This means I have to disagree with JVK above (I think) when he says “all good candidates share projective invariants with the picture itself”, at least if that's meant to be a universal generalization about all art. A cartoon doesn't necessarily depict its subject as cartoon-shaped; Medieval paintings often depict things as big because they're important and not because they're any combination of close by and big. (I'm puzzled about Escher prints: is an impossible staircase even a candidate for “projective invariant of impossible staircase picture”?) But maybe JVK meant that suggestion to apply to a large subset of visual art, including the pictures in the examples, in which case I can accept that he's right. I can also accept that the visual properties of a picture are important in determining its content, i.e., what a reasonable viewer should think the artist has prescribed to be imagined.

    Looking forward to more discussion. Must go do proper work now.

  42. That's right. I have to add that the intention is successful. That means not just that the picture has the property in respect of which it is intended to resemble the subject, but that the intention does not cause the resemblance via some deviant causal chain…

    In case #6, that means I can't say the cube is depicted as perfectly straight-sided because although you intended the line to be straight, this intention failed. Nor can I say that that side of the cube is depicted as curved, because although the line is curved, you didn't intend that.

    What I think I can say is that as well as intending that the line be straight, you also thereby intended it to be approximately straight, and this intention was successful, as it is approximately straight. So you did succeed in depicting the cube as being approximately straight-sided.

    Just to clarify, by saying that you depicted it as approximately straight-sided, I don't mean that you depicted it as not straight-sided. That's because, strictly speaking, being straight-sided is one way to be approximately straight-sided.

    What if your hands were even shakier, so it didn't even approximately resemble a cube? In that case, I think it fair to say that you didn't succeed in depicting it as cube shaped at all – not even approximately… it would just have ended up as a meaningless scribble.

    Thanks for posting this! I've really enjoyed reading the other threads as well.

  43. Did someone say “Intention”? Why if you're interested in the role of intention in determining pictorial content, then you should check out this new book Art & Art-Attempts (OUP 2013) about all sorts of cool and surprising shit that follows from taking intention-dependence seriously as a substantive necessary condition for being art—though I also hear its author is a shameless self-promoter, albeit a devilishly-handsome one.

  44. One last try because I think Donald Brook’s theory is worth serious consideration and because it is clear that nobody here has picked up on its explanatory force.

    Yesterday, in a lecture I briefly mentioned Brooks theory in a discussion of some related ideas about the 1958 debate between Elizabeth Anscombe (a leading light on the subject of intention as it happens) and J. L. Austin over the question of pretend anger.

    After the lecture a graduate student mentioned that she thought Brook was wrong. I asked why and she said that she ‘felt’ that there were more than three kinds of representation.

    The response is one that I have encountered before in relation to Brook’s theory. People tend to assume that it’s easily refuted but in fact I haven’t yet encountered a single decent refutation of even one small aspect of the theory.

    Most responses attempt to undermine Brook’s theory by claiming that it’s not new or, as in the above case, that it oversimplifies the facts. Those who claim that the theory is not new seem to be under the mistaken impression that Brook’s research is somehow lacking in some vital area and that their own superior knowledge of failed theories or partial explanations easily counts against someone who has been sharpening the theory for several decades through public discourse amongst theorists at the very forefront of these issues.

    As for the notion that there must be more than three kinds of representational strategy available to evolved creatures – this is like using the preposterous observation that there are many different kinds of sunrise and sunset as proof that the sun circles the earth. Copernicus failed to convince anyone of what we now know is the simple fact of the matter. The proof didn’t arrive until 46 years after his death following extensive observation and calculation on the part of Kepler.

    When it comes to explaining non-verbal representation we can look at perspectival diagrams and speculate until the proverbial bovines return to their dwelling place about content, intention, signification, illusion, denotation and resemblance. Such strategies of explanation stack caveat upon complexity upon ramified foundation but rarely provide anything more than partial explanations (often linguistically derived I hasten to add).

    All I can say is that for anyone hoping to make serious headway with these issues Brook’s theory is by far the most elucidatory and opens up significant potential for other fields of enquiry that are currently largely unexplored or poorly understood.

    When Anscombe mentioned to her teacher that it was understandable that people would think that the sun revolves around the earth because that’s what it looks like, Wittgenstein replied “And how else would you expect it to look?”

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