Acta Analytica

, Volume 24, Issue 1, pp 11–15

Generalizing the Disappearing Act: A Reply to István Aranyosi


    • Department of PhilosophyWashington University

DOI: 10.1007/s12136-008-0041-1

Cite this article as:
Sorensen, R. Acta Anal (2009) 24: 11. doi:10.1007/s12136-008-0041-1


In “The Reappearing Act” István Aranyosi postulates a new way of seeing to solve a puzzle posed in “The Disappearing Act;” an object that is exactly shaded can be seen simply by virtue of its contrast with its environment – just like a shadow. This object need not reflect, refract, absorb or block light. To undermine the motive for this heretical innovation, I generalize the puzzle to situations involving inexact shading. Aranyosi cannot extend his solution to these variations because he needs to conserve principles of camouflage. On the bright side, the solution to the puzzle that I propose in my book Seeing Dark Things does extend to these variations.



In the early universe, glowing plasma uniformly illuminated everything. All was white.

This universal ganzfeld changed color in the same sequence as cooling white-hot steel. From white, the universe went yellow, then red, then dark.

The Dark Age began 400,000 years after the Big Bang. The plasma, which had been sole source of illumination, cooled into atoms (mostly hydrogen and helium). There were now, loosely speaking, clouds of hydrogen. Collectively, the melee of atoms constituted an all-encompassing fog. This fog was co-extensive with the darkness.

1 Exactly Shaded Objects

Was the universal fog an exactly shaded object? It meets István Aranyosi’s requirement of lacking a surface in contact with light. It meets his condition of being in a region that could have been illuminated. However, Aranyosi also requires that an exactly shaded object prevent the formation of a shadow. There were no shadows in the Dark Age because there were no sources of light.

The first shadow had to wait a half billion years for the clouds to condense into stars. Although the universe was still too inhospitable for observers, there were visible shadows. There were also visible objects. The stars could be seen by virtue of the light they emitted. The planets and their moons could be seen by virtue of the light they reflected or absorbed or blocked. Material objects are seen by virtue of how they interact with the light.

István Aranyosi disagrees. He thinks that exactly shaded objects can be seen as shadows are seen – solely in virtue of their contrast with their illuminated environment.

Wait! We conceal objects by putting them in shadows. In “The Disappearing Act”, a truncated brick is constructed to mimic a shadow cast under a cone (see the diagram reprinted in Aranyosi’s article). As the brick penetrates that shadow, more and more of the brick is hidden under the cover darkness. The darkness is not shadow because no shadow can penetrate an opaque object. The shadow recedes, never commingling with the penetrating brick.

At the instant the darkness completely covers the brick, I say (on page 70 of Seeing Dark Things, Sorensen 2008) that the whole brick is invisible because every part of it is in the dark. Aranyosi says the opposite; at the instant the brick is completely covered, all of the previously hidden brick becomes visible. But István Aranyosi’s spectacle is fragile. If the darkness were to stray slightly beyond the brick, continues Aranyosi, the brick reverts to invisibility.

Aranyosi insists on exact shading because he wishes to preserve principles of camouflage. If you want to prevent only a part of an object from being seen, then prevent light from making contact with that part.

Why doesn’t concealing all the parts amount to concealing the whole object? Aranyosi answers: If the darkening only extends as far as the object, then there is a visual match with the object – the sort of match sufficient for seeing a silhouetted object. True, a silhouetted object differs in that it interacts with the light (by blocking it). But the exactly shaded object is sustaining the visual match by virtue of its delicate positioning. Wiggle the brick and you wiggle the image. The influence of the brick would be more salient if it slid around to keep under a moving cone. Its light-avoiding behavior would be needed to explain appearances.

Aranyosi needs to concede disanalogies with silhouettes. An exact mach is not a necessary condition for seeing silhouetted objects. When you see the silhouette of a mother holding her baby, you see each of them despite the commingling of their darkness.

Mixed viewing is also possible. The left half of a firefighter can be seen in silhouette from the light of the harvest moon while his right half is seen by the light it reflects from the fire.

In the case of cast shadows, an exact match (with respect to shape and size) fails to be a sufficient condition for seeing the caster of the shadow. In silhouette portraiture, the subject of the portrait casts a shadow congruent with the subject. But seeing the shadow does not count as seeing the subject. We do not change our verdict even after being reminded how much influence the subject has over his shadow; the subject must sit exactly in profile to establish a faithful representation.

2 Inexact Variations

When formulating “The Disappearing Act,” I emphasized the exactness of the match. This is sufficient to create the puzzle, but it is not necessary.

Suppose that the truncated cone extends deep into the earth. The shaded region only extends to ground level. There is no exactly shaded object.

Nor does Aranyosi’s principle apply if a foreign shadow makes contact with the brick as in Fig. 1.
Fig. 1

Contact with foreign shadow

There is a brick under the left cone, but only shadow under the right cone. The brick is shaded, but the shade is bigger than the brick. Therefore, it is not visible by Aranyosi’s condition of exact shading. So what are we seeing on the left? Is it the brick, a shadow cast by the left cone or some third thing? The original puzzle has re-appeared.

As more alien shadows make contact, the shape of the shade no longer even roughly matches the shape of the cone. This loss of an approximate match makes us less inclined to think that the truncated cone is visible. The brick becomes akin to a fugitive hiding in a big shadow (who Aranyosi acknowledges cannot be seen).

Aranyosi’s exact shading principle also fails to apply in some situations in which there is an exact visual match between the dark volume and the object. Suppose the brick grows a protuberance that is seen by virtue of absorption as in Fig. 2?
Fig. 2

Dark protrubence

Although the brick matches the shape of the black region, the black region is a composite of shade and a little light absorbing brick (the bit that sticks out into the light).

3 Two Categories of Visibilia

When something is cloaked by a shadow, we still see the “cloak.” I use scare quotes because the shadow is in a different category than an object (such as a garment). Shadows belong with visibilia that frame the limits of object perception: space, contours, the vanishing point, the horizon, the sky, darkness. These subservient visibilia are like the grid of a microscope. Although the function of the grid is to facilitate observation of the specimen, the grid can itself be seen.

Subservient visibilia guide the perception of objects. This gives them hegemony over objects; they are easier to see than objects because they structure the realm of visible objects. When the visual system marks an object as invisible because it is enveloped in shadow, the visual system does not need to mark the shadow as itself visible.

Nominally, subservient visibilia might be described as harder to see. For we frequently restrict the domain of discourse to objects. This is a special case of us limiting the domain of discourse to the objects of interest. Markers typically are not included in reports of what is seen; their presence is trivial. If a microscopist views a slide that lacks a specimen, he will report that the sees nothing even though he sees the grid. Similarly, we say we see nothing when we see only darkness or shadows or the horizon.

Shadows are holes in the light. Charting these holes helps the eye navigate. If a shadow exactly shades an object, then we see the shadow not the object. In a lunar eclipse, the shadow of the earth is cast on the moon. If the eclipse were perfect, then the moon would not be seen. Only the shadow of the earth would be visible. In a solar eclipse, the moon is active rather than passive; instead of merely being darkened by the earth, the moon blocks the light and so is seen in silhouette.

In a lunar eclipse, the shadow-body extends from the earth to the moon over a distance of more than 350,000 km. In “The Disappearing Act,” there is no shadow-body when the brick is parked under the cone. The shadow cast by the cone is an abstract shell.

Sounds strange? Yes, but we are in a category of notoriously strange visibilia. Aranyosi finds it bizarre that we can see something as empty as a hollow shadow. But filling up a hollow shadow (by shrinking the brick) does not make it any more visible. The inner darkness is not like black velvet (which absorbs light).

‘Shadow’ is both a count noun and a mass noun (as in ‘Skyscrapers cast more shadow than churches’). Aranyosi might assume that the count noun applies only if the mass noun applies, that a shadow must have shadow. This principle may work for nouns designating objects, but it does not hold in general. [‘I can give three justifications (count noun) for this thesis that lack justification (mass noun).’]

The breakdown of the familiar implication from count noun reading to the mass noun reading extends to holes in general. Consider a crack in a granite slab. Both faces of the separate chunks of granite are in complete contact. Roberto Casati and Achille Varzi (1994, pp 79-81) correctly classify this fracture as a thin hole. I add the claim that it is a hole that lacks any hole. If the crack is completely inside the slab, then Casati and Varzi classify the internal crack as a two-dimensional cavity. I add the assertion that it is a cavity without any cavity. Holes need not have volume.

(Yuri Balashov (1999, pp. 253–254) distinguishes between absence of a quantity and a quantity having a measure of zero. So perhaps Balashov would say the crack has a limiting amount of hole or volume; a zero quantity. The distinction does not make a crucial difference in the present situation.)

Filling a shadow with light destroys it, for a shadow is a hole in the light (specifically, one that is due to blockage). However, holes can survive being filled with heterogeneous matter. A dental cavity can be filled with gold.

A shadow can be filled with darkness that is not shadow. For instance, the shadow might be filled with darkness due to destructive interference or a para-reflection. (Note that Aranyosi’s object-oriented analysis also fails to extend to these variations of “The Disappearing Act.”) The shadow exists by virtue of there being the right sort of process rather than by its characteristic product (a mass of shadow).

Methodologically, we should consolidate mysteries. By crediting the shadow with visibility we avoid complicating the theory of object perception. In particular, we preserve the principle that objects are seen only by virtue of their interaction with the light.


I thank Francis Jeffry Pelletier and Mark Steen for their counsel on mass terms.

Copyright information

© Springer Science+Business Media B.V. 2008