Plato Lets Us Off Too Easily

What do you see when you play this movie? If your vision is at all intact, you perceive motion, and you almost certainly also recognize that there is structure and coherence to the motion. In other words, you probably feel fairly confident that the motion you observe is not random, but reflects some underlying process — that there is an explanation of some sort that accounts for what you are seeing. And you would be right. Congratulations — that's no small achievement.

But how much more can you say about what the process actually is? It could be a lot of things, right? You don't really know, other than that it's structured motion, as already stipulated. But you might take the evident periodicity of the motion to be suggestive of rigid body rotation, and you'd be right about that. This inference might be reinforced if you recognize the shiny blue thing to be some kind of semitransparent glass or crystal, in which case you might conclude that it either contains or stands in front of the rotating rigid body. And knowing this would allow you to further deduce that some of the evident curvature of the rotating object might be a mere "trick of the light" as light is refracted and reflected within the glass. And if you can get as far as dismissing the curvature as artifactual, then you may find that some of the angles suggest something vaguely cube-like in nature. And you'd be right there too.

As shown in the second movie, the source of motion is in fact a rotating wire-frame cube, which happens to be located a considerable distance behind the spherical glass, and illuminated from behind.



What I am trying to get at here is how difficult it can be to get to the "truth" of the matter — to describe the way things really are. You might protest that "actually, it wasn't that difficult at all." Maybe you instantly detected a rotating cube behind or within a glassy substance. Well, OK. But remember that besides the unusual wire-frame cube (whose actual structure I assume you did not guess from the first movie) there was nothing spectacularly alien about the scene. Identifying an object lit from behind and viewed through heavy glass is not categorically different than identifying an object lying under a few feet of moving water in a river or creek, something we are fairly good at most of the time. (To make the example stronger, try to imagine the appearance of the cube after being refracted or reflected through a series of heterogeneous materials, rather than just one piece of glass.)

My point is this: Plato's Allegory of the Cave paints our epistemological challenge as one of inferring the true structure of reality from a linear projection of that reality into a lower-dimension subspace. Information is lost in this projection, since features which exist independently in the real world are collapsed together in our perception, just as in the allegory three dimensions are collapsed into two dimensions (shadows on the wall). However, by invoking an analogy involving mere linear projection, Plato lets us off the hook too easily. Indeed, one might protest that Plato's shadows actually yield a good deal of information about the structure of the real world. Provided we know the manner in which the shadows are produced and that we have the capacity (!!) to conceive and reason about a third dimension, we denizens of the cave could probably make some fairly good inferences about what goes on in the three dimensional world beyond our experience.

For example, imagine the simple 2-dimensional projection (shadow) of the rotating wire-frame cube. Seeing this shadow on a wall, you would very quickly deduce the structure of the actual 3-dimensional object, because this projective mapping is very simple. [We of course have to note the inevitable presence of inductive ambiguity that arises when dimensional information is lost. In the case of the wire-frame shadow, the direction of rotation will be underdetermined because the "front" and "back" of the cube cannot be distinguished in the shadow.]

A naive extrapolation of Plato's analogy might therefore lead one to believe that the problem of ontology is just figuring out how many actual physical dimensions are linearly projecting into the three dimensions of our experience, and then making inferences about what actual n-dimensional entities correspond to the 3-dimensional entities we observe in our perceptual subspace. We then end up with a naive "Flatworld" ontological attitude, which holds that what actually exist in the world are n-dimensional entities which project linearly (or worse, orthogonally) into our own three dimensions. So, in this view, while we do not perceive the real world, we perceive a subspace of the real world in which objects have a fairly simple relationship to their actual n-dimensional counterparts.

The problem is that there is no reason a priori to think that the world of our experience is a simple linear projection of some higher-dimensional reality. This is what I am trying to illustrate with the movies. What if, like the image of the cube refracted through heavy glass, the entities in your observational subspace are related to actual entities in the world in some highly-complex manner, and that the actual nature of this relationship is utterly unknown to you? This is our actual epistemological situation. It is certainly reasonable to think, like Plato, that the objects of our experience are related to some broader reality beyond our perception. But it is wrong to think that we know anything about the structure of that relationship. Indeed, how can we ever characterize the properties of that relationship without first knowing something about the broader reality itself. One cannot characterize a relationship between two sets of entities when only the properties of one set are actually known. And yet...