If holes are entities of a kind, then, they appear to be spatiotemporal particulars, like cookies and tins and unlike numbers or moral values. They appear to have a determinate shape, a size, and a location. (‘These things have birthplaces and histories. They can change, and things can happen to them’, Hofstadter & Dennett 1981: 6–7.) On the other hand, if holes are particulars, then they are not particulars of the familiar sort. For holes appear to be immaterial: every hole has a material “host” (the stuff around it, such as the edible part of a donut) and it may have a material “guest” (such as the liquid filling a cavity), but the hole itself does not seem to be made of matter. Indeed, holes seem to be made of nothing, if anything is. And this gives rise to a number of conundrums. For example:

existence | location and mereology | mereology | nothingness | object | ordinary objects | space and time: singularities and black holes | space and time: the hole argument

These difficulties—along with some form of horror vacui—may lead a philosopher to favor ontological parsimony or revisionism over naive realism about holes. A number of options are available:

On the other hand, the possibility remains of taking holes at face value, which is to say as bona fide immaterial particulars. Any such undertaking would have to account, not only for the general features mentioned in section 1, but also for a number of additional peculiarities (Casati & Varzi 1994). Among others:

Further problems arise from the ambiguous status of holes in figure-ground displays (Bozzi 1975). Thus, for example, though it appears that the shapes of holes can be recognized by humans as accurately as the shapes of ordinary objects, the area seen through a hole typically belongs to the background of its host, and there is evidence to the effect that background regions are not represented as having shapes (Bertamini & Croucher 2003; Bertamini & Casati 2015). So what would the shape of a hole be, if any?

As is often the case, the choice between all these alternatives—whether holes are to be subjected to Ockham’s razor, reduced to other entities, or taken at face value—will depend on one’s general metaphysical inclinations (Lewis & Lewis 1996). It may also depend on controversial details concerning the nature of space and spacetime, e.g. whether they are relational or substantival (Braddon-Mitchell & Miller 2015). It is, more generally, an instance of the sort of decision philosophers have to make when they scrutinize the ontology inherent in the common-sense picture of the world and the concepts, words, and purposes through which it is described and apprehended.

Holes are an interesting case study for ontologists and epistemologists. Naive, untutored descriptions of the world treat holes as objects of reference, on a par with ordinary material objects. (‘There are as many holes in the cheese as there are cookies in the tin.’) And we often appeal to holes to account for causal interactions, or to explain the occurrence of certain events. (‘The water ran out because the bucket has a hole.’) Hence there is prima facie evidence for the existence of such entities. Yet it might be argued that reference to holes is just a façon de parler, that holes are mere entia representationis, as-if entities, fictions.

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Hole representations—no matter whether veridical—appear to be commonplace in human cognition. Not only do people have the impression of seeing holes; they also form a corresponding concept, which is normally lexicalised as a noun in ordinary languages. (Some languages even discriminate different types of hole, distinguishing e.g. between superficial hollows, inner cavities, and see-through perforations.) Moreover, data from developmental psychology and the psychology of perception confirm that infants and adults are able to perceive, count, and track holes just as easily as they perceive, count, and track paradigm material objects such as cookies and tins (Giralt & Bloom 2000; Nelson & Palmer 2001; Horowitz & Kuzmova 2011). These facts do not prove that holes and material objects are on equal psychological footing, let alone on equal metaphysical footing. But they indicate that the concept of a hole is of significant salience in the common-sense picture of the world, specifically of the spatiotemporal world.