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”.))