Abstract
Suppose we take a picture containing a full image of a duck and slice it right through, leaving some of the duck image (including its head) on one slice and some of it on the other. How many duck images will we be left with? Received theories of pictorial representation presuppose that a surface cannot come to contain new images just by changing its physical relations with other surfaces, such as physical continuity. But as it turns out, this is in tension with received theories’ approach to incomplete images. I address three views with respect to the circumstances in which incomplete images of X represent X. 1. A liberal, non-restrictive view: ‘Iff they meet relevant requirements posed by received theory of pictorial representation.’ 2. Moderate restrictions of this view (‘iff they meet requirements posed by theory of pictorial representation and...’) and 3. A fully restrictive view (‘never’). After investigating challenges for the liberal view, I end up supporting it. The main challenges rest on the fact that only the fully restrictive view can plausibly accommodate some principles that seem inherent to our theory of representation. For instance: only this view accommodates received theories’ presupposition that the representational properties of a surface depend on its configurational properties such that new images may appear on a surface only if its configurational properties have changed. Since the liberal view is overall more plausible than the restrictive view, I reject this presupposition and bear the consequences.
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Notes
Usually supplemented by additional conditions which do not supervene on configurational properties, like the picture maker’s intention to depict X; a certain kind of a causal connection to X (in the case of photographs). These conditions, which Newall (2011) terms ‘correctness conditions,’ will be taken into account below. Versions of (1) (combined with (2)) are defended by Hyman (2006) and Hopkins (1998). For (2) see Wollheim (e.g. 1980, chapter 5). For (3), see Lopes (1996) and Schier (1986). Newall (2011, chapter 3), combines elements of accounts (1), (2) and (3) on this account: “A surface [S], depicts [X] iff (i) [S] can occasion a non-veridical seeing of [X] and (ii) this non-veridical seeing accords with appropriate standards of correctness.” Newall (2011, p. 43) Except for the above accounts, it’s worth mentioning a fourth account: (4) ‘S depicts X iff (Part of) S denotes X’, originally put forward by Goodman (1976). Unlike the rest, this criterion all by itself doesn’t tell us why pictures represent what they do. I will not mention it when discussing factors that seem to play a role in determining what a picture represents. A novel version of (4) which combines elements of (2) was defended by Kulvicki (2006).
‘Image’ is not usually used to stand for some part of the surface of a picture; It’s often used to denote something in purely phenomenal space. But I couldn’t think of a more suitable term for what I wish to talk about. (One can follow Schier 1986 and use ‘icon’ to refer to what he calls a pictorial-part of the picture, and say that an image of X necessarily exemplifies an icon of X, without this implying that this is the only icon it exemplifies).
And factors like the intentions of the artist.
This doesn’t mean that qualitatively identical surfaces cannot represent different things, as in the case of distinct photographs of Elvis and his doppelganger (respectively) that share all of their configurational properties. It only means that once its content is determined, changing what a surface represents requires changing its configurational properties (or, as in a case in which some picture is chosen to be part of a collage, changing the relevant intentional background).
It may be motivated by the fact that many overlapping parts of the surface are sufficient for eliciting the relevant recognitional response. Recalling Unger’s (1980) problem of the many, one may similarly be inclined to consider every object consisting of a table minus any of its molecules to be a table, given that it meets relevant requirements (it looks like table, could be used as a table etc.) But then there would be millions of tables in almost the same region in which we ordinarily take there to be one and this is extremely counterintuitive. The idea of many overlapping images is perhaps less repugnant than the idea of many overlapping tables. But theoretical alternatives to the former view can be inspired by analogical solutions to the problem of the many. Upholding the alternative view that there is only one image of the duck in Fig. 3 (as I do), one still has to face the new puzzle raised in this paper. This view is consistent with all three approaches to incomplete images explored below (the liberal, the moderate and the restrictive approach).
And other principles discussed below.
And do not have anything to do with “correctness conditions” (e.g. artist’s intentions, or causal relation to the represented object, in the case of photographs); factors that are not acknowledged by up-to-date theories of pictorial representation.
Setting the more prosaic reasons for focusing on photographs aside: since I’m trying to make a general point, I find some idiosyncrasies of non-photographic forms of pictorial representation rather distracting in the present context. Let me introduce two such features. First, I do not want to discuss cases that seem to require special treatment, like the duck/rabbit image (in which the same image can be seen as a rabbit from one aspect and as a duck from another). Given that the right kind of causal relation to X is necessary for photographically representing X, photographic images of a duck will not represent a rabbit (or a duck/rabbit) even if they resemble a rabbit from a certain aspect. Second, it may be argued that paintings give us independent reasons to reject the idea (discussed below) that the mereological sum of a picture’s slices does not contain images that never appeared in the picture before it was sliced. For instance, slices of a sketch of a face can be re-organized to jointly represent a tree which wasn’t represented in the original picture. Slices of a photograph of a face, on the other hand, will never photographically represent a tree, if they lack the relevant causal connection to a tree.
Non-photoshopped, nor manipulated by dark room constructions, double exposures etc.
So, for example, if there’s any sense in which a photograph can be said to represent a fictional character (on top of representing an actress dressed as one), it’s not the sense of representation that interests me here.
For a causal theory of photographic representation see e.g. Walton (1984).
This will be further discussed below (Sect. 5).
The charge does not apply to a liberal view that considers every part of a surface that can become a duck-image on some possible-slicing to already (actually) be a duck-image. This, in effect, would save ‘no new duck-image created’ at the expense of taking each duck to be represented extremely many times in the original photo. Though conceptually possible, this will not be the liberal view I defend. So I find the objection appropriate.
If this needs to be motivated: on an informal pole (among friends and colleagues), ‘three’ turned out by far the most popular answer to ‘how many duck images are there in Fig. 5?’
Some symbols represent only in the context of a larger whole (these are what Schier 1986 calls ‘sub-iconic’ symbols). So the moderate view will allow that some images may be destroyed upon slicing.
And despite the fact that each of the ducks is recognizable.
One might object that PhotoCons is still much less plausible than the idea that images cannot be created upon slicing. But, dialectically, taking the restrictive view to depend on an objection to PhtoCons is not necessary. Since the point of this section is to take the moderate view off the table, I’ll move on to a stronger argument, which is based on the fact that the restrictive view is compatible with PhotoCons.
“And for each duck, part of some slice (.../elicits a recognitional response) for it”. (Although restrictivists can even adopt a principle that doesn’t include this qualification).
I’m using ‘+’ for the arithmetical sum and ‘\(+\)’ for the mereological sum.
The fact that the slices used to belong to the same photograph (trace back to the same photographic event) can be used to motivate the idea that, unlike a collection of photographs, each of which is similar to a certain slice respectively, say, the slices may jointly represent something which they do not represent distributively.
Notice that the liberal view cannot offer a similar move: if each of the slices individually contains duck-images so that the number of duck images appearing on individual slices is, e.g. 6 (as in the dotted-lines case) the slices cannot plausibly jointly contain less duck images than that (e.g. 3).
Sure, pointy is an illegitimate idealization, and so is ‘the smallest part that still carries photographic content’. For the sake of discussion suppose moderate-theorists can make sense of it.
If one is afraid the photographic content will be ruined along the way, the same reductio can be achieved without repeated-slicing of the same copy, but with slicing a number of copies differently instead.
It might seem that the restrictive view faces a similar problem: supposedly, it’s unintuitive to say that a picture of a duck minus a tiny part of the tail does not depict a duck, whereas a picture of a duck including that bit does. But restrictivists can afford two responses: 1. they can follow similar views in metaphysics and say that as opposed to what the moderate view offers, the difference between complete and incomplete images “jumps right out” (compare Merricks (2005, p. 628) on composite objects). 2. More convincingly perhaps, they can take ‘complete image’ to be vague. They may need to add that an image of X is definitely incomplete if (roughly) the parts of X that are outside the scope are sufficient for generating an X-image; seeing all of them can .../elicit a recognitional response for X. (this way, as opposed to the liberal view, restrictivism still accommodates PhotoCons). Since restrictivism need not bother with accommodating P2, vagueness shouldn’t be a problem; there’s no need to insist that the appearance of an image in the series is “abrupt”. Unlike the restrictive view, as long as the moderate theory relies on the advantages of accommodating P2, it has to embrace a sharp-cut-off view with respect to the sorites series: it cannot be a vague matter whether a certain slice contains an image of X or not. For if, in a certain case, the number of duck-images on each of two slices cannot be determined, and the number of the duck-images on the picture of which they are the only slices is, e.g., determinately three (a case that could easily arise from any no-sharp-cut-off-account of the series), P2 is lost.
And a duplicate of it.
If the image is not a point on the photographed ring, the essential right-kind-of-causal-relation between the ring and its image is absent.
‘continuous’ is, in this context, continuously as condense as required for pictorial representation.
Not much hangs on it. Considering other sorts of pictures will just somewhat complicate formulations. I think non-manipulated photographs do not represent objects more than once. (Following Meskin (2000) I think that an image of an image of X is not thereby an image of X).
For presentation of the Moorean challenge in terms of philosophical methodology (as I do here), see Kelly (2005).
The following explanation by Newall (2011, p. 71) may be helpful: “An easy way to grasp what occlusion shape is, is to take a pane of glass and place it between oneself and the object in question. One then looks through the glass at the object and traces the object’s outline on the glass. The resultant outline, from that point of view, will have the same occlusion shape as the traced object. If this outlined shape were to be filled in with an opaque material such as paint, provided one’s point of view had not moved, it would precisely occlude the outlined object.”
Given that Hyman is open to adjust his criterion in light of other unintuitive consequences (see 2006, p. 95) I assume that in light of the examples above he would also be inclined to adjust his criterion to better match our pretheoretical judgments, which other theories surveyed here already approve.
Another view that is perhaps worth considering (call it ‘the revised restrictive view’) is the view that only incomplete images that were, at some point, part of a complete (and continuous) image, never qualify as X-images. This view will not have the ad-hoc problem: the difference between incomplete images that used to be part of a complete X-image and partial images that represent X is that only the latter were intended to represent X when they were created. The view will also accommodate Slice/Part and PhotoCons. However, adopting it means taking similar pieces of photographic paper, with relevantly similar causal history to represent different things because one of them is a slice, and the other is a photograph. On all other views, slices represent what they do in the nearest possible world in which they are photographs. On the revised restrictive view, seeing a piece of photographic paper (and knowing everything about the scene in which it was taken) will not be enough to determine what it represents. One will also have to know whether that piece is a slice or a whole photograph.
Each principle deserved an independent treatment, because the implications of denying each are different. The principles are logically independent. As we have seen, the moderate view accommodates PhotoCons without accommodating Slice/Part. In the other direction: we can imagine a view that accommodates Slice/Part, but which takes a photograph to be ruined upon slicing, so that if there was anything which was jointly represented by the parts, on top of what they individually represented, it is no longer represented once the picture is sliced (think of Fig. 11 for instance).
Perhaps other ways of addressing this will be found compelling. One might be inclined to say that what we have really shown is that there are abundantly many images of the same duck in Fig. 16, for instance (so it is represented many times over, albeit in the same phase, by different parts of the photo). This will obviously result in a version of the liberal view. However, the argument in this section shows that the liberal view has other options. In particular, it shows that even if we take ‘being-an-X-image’ to be a maximal property (roughly, such that large parts of an X-image are not themselves X-images), the liberal view can be forcefully defended. The reasons for taking ‘being an X-image’ to be a maximal property are similar to the reasons for taking ‘being a table’ to be a maximal property (see Sider 2001a, b for the latter view) and one may find them equally compelling. Showing that the liberal view can live with this constraint on theories of representations is therefore significant. Considering other theoretical alternatives for the liberal view can be thought of as applying Unger’s (1980) “problem of the many” to the case of images (see footnote 5). I’ll leave a comprehensive discussion on the matter for another day.
One may add the following point in favour of the liberal view: when parts of a photo are attached, anyone able to recognize the state of affairs in each part can generate an interpretation of the whole based strictly on this ability. But when the parts are detached, this will not necessarily be so (we can recognize something as a right half of a duck in such-and-such circumstances, and something else as a left half of that duck in such-and-such circumstances, without thus realizing that both are of halves of that duck in the very same circumstances). One may take this to imply that when parts are detached, the picture is ruined (see Schier 1986, pp. 66–67) This is a step towards recognizing that the slices are just new pictures that, pace restrictivism, do not jointly represent anything over and above what they represent individually.
Unless, of course, in light of some distinctive intentional act which would make them form a picture.
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Acknowledgments
I wish to thank Ron Aboodi, Dan Baras, Meir Buzaglo, Ravit Dotan, Katherine Hawley, Ran Lanzet, Ofer Malcai, Andy Peet, Dawn Phillips, Amnon and Yaron Pitkovski and Gil Sagi. I also wish to thank anonymous referees for ‘Synthese’ for very helpful comments and suggestions. Special thanks to Aviv Hoffmann and Sonya Roca-Royes for extensive and valuable discussions and comments.
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Pitcovski, E. Getting the big picture. Synthese 194, 941–962 (2017). https://doi.org/10.1007/s11229-015-0981-0
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DOI: https://doi.org/10.1007/s11229-015-0981-0