The Shadow Problem as a Metaphilosophical Test Case

The shadow problem is a cute little puzzle about the metaphysics of shadows.

Consider four objects, L, A, B, and C arranged like this


where L is a lamp providing the only light, A and B are opaque objects, and no light is falling on C.

Consider also some non-controversial propositions concerning shadows, their casters, and shaded objects.

1. An object can cast a shadow only if it is opaque and light is falling on it.
2. Shadows cannot be cast through opaque objects
3. An object is in the shade only if some other object is casting a shadow upon it.

Here’s the problem: Is C in the shade? If it is, then by principle 3 either A or B must be casting a shadow on it. However, principle 1 rules out B as the shadow caster, since no light falls on B and principle 2 rules out A, since A’s shadow can’t be cast through B. We are led to the absurd conclusion, then, that C is not in the shade.

Further reflection may lead us to reject one or more of the three principles. Or increase their number to four or more. (Personally, I’m a shade and shadow eliminativist.)

While the shadow problem is fun to regard as a first-order philosophical problem, I like how it reflects on various higher-order problems, like: what are philosophical subject matters and methods? Or: when, if at all, do philosophers ever arrive at solutions to problems?

One thing I especially like these days about the shadow problem is how it illustrates to students what a philosophical problem is. It’s pretty clear, I think, that this isn’t going to be solved by simply opening the dictionary, or asking the scientists in the department of shadow studies.

Some other meta-philosophical issues I’ve been thinking about in connection with the shadow problem are:

What, if anything, is added by describing anything here as intuitive or as deliverances of intuition?

Would the methods of experimental philosophy do a damn bit of good here? Suppose that there were survey results demonstrating a small yet statistically significant difference in people’s willingness to abandon one of the propositions? Would that thereby make one solution to the problem better than another?

(My presentation of the shadow problem is adapted from the way Peter Suber formulates it [link]. (For other formulations and a brief history of the problem, see pp39-40 of Roy Sorensen’s 1999 J. Phil article “Seeing Intersecting Eclipses”.))

16 Responses to “The Shadow Problem as a Metaphilosophical Test Case”

  1. Rich says:

    That’s a neat puzzle, but I think it’s quite easily solved by rejecting assumption (3). Surely an object is in the shade if and only if there is no light falling on it? Then (C) is unproblematically in the shade. Being in the shade is a more generic state that being an object on which a shadow is cast, which (C) is not.

    The only problem is to specify what we really mean by “no light falling on an object”, since clearly an object can be in the shade without being in pitch blackness. Perhaps there has to be a straight line from a point on the object to a light-emitting point that’s unblocked by opaque objects?

    The problem of defining “in the shade” gets much worse with multiple light sources though…

  2. Pete Mandik says:

    Well, Rich, no light is falling on L but I doubt many people would want to regard it as in the shade.

    L is the sole light source with light traveling in straight lines away from it. If A, B, and C are removed or are totally absorptive, it’s guaranteed that no light is falling on L.

  3. A.G. says:

    It is a good example of a problem that shows what a philosphical problem is. I’m going to remember this for the future when i run into someone who tries to pose a problem as philosophical just because we don’t have the tools to answer the question emperically.

    my comment and stab at it. first, in #2, do non-opaque objects let shadows “pass through” them? I just took my vodka glass and put it in a shadow, and then substituted a box for a paint roller and can’t convince myself that there’s a difference.

    the motive for the “opaque” definition seems to stem from the counterfactual, “what if the piece of wood wasn’t there, then the light would pass through the vodka glass and the piece of fluff behind that wouldn’t be in the shade, therefore, since the wood is there, we can still say that the fluff is in the shade of the wood.”

    so it’s not that a shadow can pass through a non-opaque object, but that in a counterfactual, light can.

    But if that’s true, then it’s also true that in the counterfactual with the paint roller box and no wood, that the fluff is in the shade of the paint roller box.

    In both cases, we can say that the fluff is in the shade, but only by extending the analysis to counterfactual worlds. The slight of hand as presented, by implying that shade passes through non-opaque objects, makes it look like the anaylsis only takes into account the way things actually are, and so the possible work of object B is said not to count.

  4. Pete Mandik says:

    So, A.G., does A cast a shadow on C?

  5. A.G. says:

    ok, ok, ok;


    1) and 3) I still have no problem with, 2) is still the problem, but now I am changing my claim and saying that shadows are cast through cans and glass equally. “cast through” is clearly a metaphor and it is no more scientifically true that L “casts” a ’something’ on A than through B to C.

  6. Peter van Diest says:

    First, a remark about things being in the shade, but not in pitch darkness: in such cases light is reflected off of these things, which means that light must be falling on them. This light may not come directly from the (only) light source, but could be called ambient light; it is reflected from the surroundings or broken at the edges of things. I take it, from the way the shadow problem is stated, that we should not concern ourselves with these complications.

    Now, the main problem is that the puzzle is stated in terms of a shadow being something. If we say A casts a shadow on B, then we suggest that something is going from A to B. But a shadow is not something. On the contrary, it is the absence of something, namely light. This means that especially proposition two is a non-starter.

    There’s another problem in this puzzle, and it’s to do with how we perceive something being in the shade. Rich states that something is in the shade if there’s no light falling on it. Pete objects that there’s no light falling on L, but nobody would say that L is in the shade.

    The solution to this dilemma is to realize that something can only be said to be in the shade if there is no light coming from it - either by emission or reflection - instead of saying there is no light falling upon it. Now we can easily see that B and C are in the shade, whereas L and A are not. B and C are in the shade because they cannot reflect light from L and they do not emit light themselves. L is not in the shade because it emits light, and A is not because it reflects L’s light.

  7. Pete Mandik says:

    Thanks, Peter, for your remarks. There’s much in what you say that I like since it agrees with my shade and shadow eliminativism (namely, that there strictly speaking are no shades or shadows).

    I take it that you are revising the notion of shade so that there is no requirement of any light being blocked. I call this revisionary since it seems contrary to common usage to allow the existence of shades in the absence of blocked light.

    I’m not sure, though, what you think of the notion of shadow, and a lot of the puzzle can be formulated in terms of shadow without mention of shade. Is a shadow cast by A? If so, upon what is it cast? Is a shadow cast on C? If so, by what is it cast?

  8. Pete Mandik says:


    It’s sounding like 2 is not the only of the three that you have a problem with. If scientific truth is a guiding concern, then it’s likely you’d have to treat 1 and 3 as puzzling since they concern things that don’t exist or don’t ever happen.

  9. Peter van Diest says:


    In order to gain some fresh insight into this puzzle, allow me to recast it to another setting:

    Let S be a shower, under which we place U1 (an umbrella). Under U1 we place U2 (another umbrella), and under U2 we place C (a dry cat). Then we turn on the tap. Then we turn off the tap, retrieve the cat, place it under U2 again and this time sufficiently restrain it, and turn on the tap once more. The question is: does the cat stay dry, and if so, what protects it from getting wet? The answer is, of course, “yes” and “two umbrella’s”.

    Now consider the questions: “Is dryness cast upon the cat?” and “If so, what casts the dryness?” The obvious absurdity of these last two questions illustrates the awkwardness of our thinking about shadows. The whole conundrum rests on the illconceived notion, informed no doubt by the image that language imposes upon us, that a shadow is somehow a positively existing thing, whereas in reality it is just the opposite: the very absence of something.

    So, to your questions. Is a shadow cast by A? Language-wise the answer is yes, and it is cast on B. But analytically, nothing is actually emanating from A, it’s just that anything on the opposite side from the light shining on A is deprived of that light.

    Is a shadow cast on C? If so, by what is it cast? Again, language-wise, yes, a shadow is cast on C, because the light from L is blocked by everything between L and C. It is difficult to maintain that B casts a shadow if we keep using the imagery language imposes upon us. But analytically we can say that C is just as deprived of light as B is, and as soon as both A and B (”everything between L and C”) are removed, C will emerge out of the shadow, glaring at us like a wet cat.

  10. A.G. says:


    You’re right. my last sentence “it is no more scientifically true that L “casts” a ’something’ on A” means that I also don’t accept 1 contrary to my first sentence.

    I do have to say though that the scientific response seems like an easy victory, the real challenge it seems to me, using Peter’s terminology, to fix natural language with “analytical” language and see if this works out.
    If this is really a philosophical problem, then it has to be more difficult than getting the correct elements of nature right.

    Let’s eliminate shadows, and introduce the state of darkness, the lack of EMR caused by x absorbing or blocking EMR. Now we don’t have a problem of shadow language, but introduce the problem of causal language (maybe similar to declaring victory by letting C fibres firing substitute for pain).

    C is in the dark. but is C’s dark state caused by A reflecting or absorbing EMR? Peter’s cat is “protected” by “two umbrellas” but in the real state of affairs, is the second umbrella blocking water from hitting the cat? The idea of protection appeals to counterfactuals to include B. In the same way, A is blocking the light and C is in the dark because A blocks EMR. We can eliminate the absurdity of passing darkness or dryness through B to C, but behold, the problem remains.

    Imagine the cat is in a house. Imagine an umbrella placed on top of a house. Imagine the cat standing on the floor sharing the axis of the umbrella. If it rains, is the umbrella blocking the water from hitting the cat? Are the umbrella and the roof together, “protecting” the cat? The conceptual work done by the real world state of affairs begins losing intuitive ground. And it’s almost entirely counterintuitive to say the umbrella is blocking the water from hitting the cat, or even in conjuction with the house counterfactually, if we suppose the house is waterproofed by God. At that point, it seems as if the scientific description of the real world state of affairs is trivial and meaningless.

  11. Pete Mandik says:


    Prior to your last two paragraphs, I like everything you say, especially the remarks about the absurdity of the casting of drynesses. I think, however, that in the last two paragraphs, the attempted separation of what’s true analytically and what’s true language-wise isn’t working if shade and shadow conservation is your goal. I doubt, for example, that it’s correct to say “language-wise, yes, a shadow is cast on C, because the light from L is blocked by everything between L and C” since I doubt that, “language-wise”, all of the things intervening between L and C contribute to the blocking. B, in particular, is inert. It’s dubious, then that there’s a shadow for C to emerge from. The space C inhabits contains only C. No shadow shares it.

  12. Pete Mandik says:


    I think that attempts to be scientific here are neither easy nor trivial. Along these lines, I don’t think the introduction of states of darkness is either scientifically or philosophically promising, as is evident in the trouble you run into trying to describe causal relations between a state of darkness and a light-blocker. (Causal relations between negative states of affairs are sufficiently weird to avoid altogether. Is my not being shot causing my not bleeding to death?)

    How about instead a state of having light fall on something? That seems a better candidate for a causal relatum. It can, for instance, enter into causal relations with states of heating.

    So, what’s really going on in real reality? L is in a state of emanating light, A is in a state of having light fall on it, and B and C are in neither of those states.

  13. A.G. says:

    Pete says,

    “So, what’s really going on in real reality? L is in a state of emanating light, A is in a state of having light fall on it, and B and C are in neither of those states.”

    That seems to be true. And reflects the sentiment here (from which I read last night trying to get some better anyalitical tools for the job):

    “philosophers interested in analysing causal processes have tended to see the chief task to be to distinguish causal processes such as atoms decaying and billiard balls moving across the table from pseudo processes such as moving shadows and spots of light.”

    The question though I think is, “is real reality good enough?” If we eliminate shadows, what else would we need to eliminate?

    “If causation must involve a physical connection between a cause and its effect, than many everyday causal claims will not count as causation. ‘I killed the plant by not watering it..”

    Which urge theories such as,

    “Dowe and Armstrong hold that while such cases are not genuine causation, they count as a close relative, which Dowe variously calls causation* (1999, 2000) or ‘quasi causation’ (2001, compare Ehring 1997, pp 150-1). Persson (2002) coins the term ‘fake causation’. This relation is essentially a counterfactual about causation (see also Fair 1979, pp 246-7).”

    Well, it was along those lines that I apparently had tried to conjur up this on-target though somewhat fumbling attempt a few days ago:

    “then it’s also true that in the counterfactual with the paint roller box(B) and no wood(A), that the fluff(C) is in the shade of the paint roller box.”

    Contrast this with your response to Peter,

    “B, in particular, is inert. It’s dubious, then that there’s a shadow for C to emerge from.”

    Yes, it’s inert, but not across all possible worlds. If we’re willing to allow the counterfactual pseudo-cause, then c can said to in fact emerge from the shadows of A and counterfactual B and the question urges a false dilemma to make us choose one over the other. So it is also that the cat is “protected” by A and B.

    But perhaps there is something drastically wrong with the counterfactual pseudo-cause. Then we opt for the simplicity of the real cause which drives “real reality” as you described to me in your last response.

    But consider the cat in the universe Peter created. If the cat were restricted to thinking in terms of “real reality”, how would he satisfy himself the second umbrella he bought to protect himself from the horror of water wasn’t a waste of money?

    So it seems to me we have a choice. Either accept shadow talk as it is with contradictions and all, because more precise definitions won’t fix it, or go the “real reality” route and be left with a language that’s consistent, strips away pseudo-causes and objects, but not equipped to deal with everyday-life reality. Note that in this case, if everyday-life reality has truth content in any way, then physicalism on these terms is false.

  14. Pete Mandik says:

    Hi A.G.

    Sorry ’bout the delayed reply.

    I’ve got to say I don’t share your enthusiasm for contradictions. If I’m going to even consider embracing contradictory ontologies, there better be some pretty juicy reward for the effort, like the eternal salvation that accompanies affirmation of the Holy Trinity or at least the enlightenment that might be triggered by contemplating the sound of one hand clapping. But since all you’ve got on offer are concerns about the umbrella shopping habits of an imaginary cat, I’ll be waiting until further incentives are announced. In the meantime I’ll continue to regard contradictory entailments of existence claims as falsifications of those claims.

    Also in the meantime I’d like to raise a few questions about your parting remarks about physicalism. One question is: How can something admittedly contradictory have, as you claim, truth content? My view, and the classical one, is that contradictory contents are false, not true. Another question: even if some mind-bending-ly good reason could be given for reconciling truth contentfulness and contradictoriness of so-called everyday reality, why would this preclude physicalism? Why couldn’t physicalism similarly reconcile truth-contentfulness and contradictoriness?

    Back to shadows: we can live quite well without ‘em. So let’s do so.

  15. Neil Fitzgerald says:

    I don’t think we need to abandon any of the three statements. Can’t we solve the problem simplying by saying that the union of A and B is the ‘object’ casting a shadow on C?

    (I remember you once stated to me that the collection of all the air molecules within five miles of the Eiffel tower has ‘existence’ in precisely the same sense as any other entity. So a union of two objects shouldn’t be problematic ;-))

  16. Pete Mandik says:

    Hi Neil,

    If B is going to be part of the shadow caster even though B is causally inert with respect to the casting of the shadow, that raises some questions about how to decide which of various causally inert objects to consider as part of the shadow caster.

    Consider this scenario.


    or this one:


    by what principle does [B] but not [D] count as part of the shadow caster?