Do Holes Exist?


Imagine someone being asked to create a list of every object that exists. What would the list look like? Depending on who its author is, it may look different in several ways. Take, for example, the size of the list. Some authors might reason that in addition to familiar objects such as keys and tables, there are also objects which are fusions of other objects. Just as fusions of wood planks can be tables, so too can keys and tables make a fusion of their own. Consider the klable: an object that is part key, part table. Why shouldn’t there be klables? If objects can be distributed in space (e.g., a bikini), and if fusion is possible (e.g., from wood planks), then there is no reason to think that there aren’t klables. Granted, klables matter for little over and above keys and tables. Nevertheless, no complete list of objects can leave them out!

Unsatisfied with the justification for klables, a different author may wish to exclude fusions from his list altogether. Alternatively, he may wish to include some fusions but not others.

How else might any two object lists differ? One possibility even for lists of the same size is that their entries don’t correspond to one another. Discrepancies of this kind may have a familiar explanation: a difference of opinion regarding the existence of souls, gods, numbers, sets, possible worlds, properties, fictions, experiences, tropes, natural kinds, etc.

The titular question identifies a further class of objects which might be controversial: holes. Do holes exist? Either way, what are they? Do they belong on an object list?

One reason for thinking that they do not belong on an object list has to do with the way that a hole is defined. Take the following definition for example: a hole is an empty region in some material. To illustrate, see how the hole of a doughnut is a region of emptiness within a lump of dough. What would it mean for the hole of a doughnut to exist? On this definition, it would mean that there is a thing which is the empty region of a doughnut. But how could such a thing be a thing if it is completely empty? Even if a doughnut has air where its hole is, the air is incidental to the hole and not part of it. To prove this, imagine a doughnut in a perfect vacuum and see that it still has a hole.

This reasoning is confused, you might assert: the doughnut has no hole either way, since holes do not literally exist! If holes do exist, they would have to be constituted by nothing. What is the difference between something that is constituted by nothing, and something which is nothing? It seems that there is no difference. So, holes are nothing, i.e., they do not exist.

As cogent as this reasoning sounds, there are at least two serious problems with it.

First, things that exist have holes as parts, even as necessary parts. Consider the true statement that shirts exist and shirts have holes in them. This seems undeniable, does it not? But then the hole-denier finds himself in a dilemma. Either shirts exist and holes do, or neither holes nor shirts exist. This disjunction follows from the simple principle that no existing object has non-existing parts. If shirts exist, then all of their parts exist. If shirts have holes, then their holes exist along with them. Surely, acknowledging holes is preferable to denying shirts!

If this isn’t convincing, notice a second property of holes. Holes can have causal relationships. If I step in a hole, it might cause an injury to my foot—something no non-existing object can do. If you think the causal explanation for this hypothetical injury is exhausted by the properties of the ground beneath the hole, then ask: what causes my foot to strike the ground beneath the hole? The answer to this unavoidably refers to the hole above the dirt. In addition to causing things, holes can also be the effect of things. Digging makes a hole deeper, and filling a hole makes it go out of existence.

For reasons of parthood and causation, it appears difficult to deny that holes exist. Grudgingly acknowledging holes, you might wonder about one last thing. Perhaps holes exist, but they can be defined in a way that avoids any weirdness—the source of which seemed to be the idea that holes are constituted by emptiness. Can holes be defined in a way that doesn’t refer to emptiness, or to a synonym? Here I do not have an answer. Instead, let’s consider one proposal as a heuristic.

Perhaps we might identify holes with their geometry. Specifically, a hole in x might be understood as a spatial boundary bisecting x and non-x where that boundary forms an enclosed shape. Let us illustrate this definition by returning to the doughnut example. For any doughnut, we can define its hole as that circular boundary which bisects its doughy region from a different, non-doughy region.

This is a bit clunky, but perhaps it will work. To find out, we ought to take a closer look at what a boundary is. This is because if holes exist and if holes are identical to boundaries, then boundaries exist, too. What does a commitment to boundaries entail? A boundary is a kind of plane. What then is a plane? A plane is a set of lines; but what are lines? A line is a set of points; but what are points? Here it seems we have reached a dead end without a further answer. Is there anything that constitutes a ‘point’ apart from its location? It seems not. Having made this discovery (that holes are points at bottom) compare it to our earlier definition of a hole as a region of emptiness:

If holes (under the original definition) exist, the following is true:

  • At location L, something constituted by nothing exists.

If boundaries exist, the following is true:

  • At location L, something constituted by nothing in addition to its location exists.

It seems to me that if our goal was to eliminate metaphysical weirdness, no progress has been made. The only difference between the two propositions above is a redundant locational reference. In view of this, I suggest that we simply accept the first definition on account of its simplicity, and that we count holes among things that exist.

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