It seems indisputable that there are holes. For example, there are keyholes, black holes and sinkholes; and there are holes in things such as sieves, golf courses and doughnuts. We come into the world through holes, and when we die many of us will be put into specially dug holes. But what are these holes and what are they made of? One of the big philosophical questions about holes is whether they are actually things themselves or, as the German-Jewish writer Kurt Tucholsky suggested in ‘The Social Psychology of Holes’ (1931), whether they are just ‘where something isn’t’. To help us investigate this issue, let us first dissect the anatomy of the hole.

So, imagine a doughnut – the classic kind that is round with a hole in the middle, rather than the jam-filled kind. The dough of the doughnut is an example of what is called the ‘host’ of the hole – the stuff that surrounds the hole. Now imagine you put your finger through the hole in the doughnut, and wear the doughnut like a ring. Your finger is then an example of what is called a ‘guest’ in the hole – the stuff that is inside the hole. But now consider the doughnut in an early stage of its creation in a factory, about to get the hole cut out of the dough. What do we call the part of the dough that gets removed to create the hole? Should it be called a guest-in-residence, about to be evicted? These parts of the dough have been branded by food merchandisers as ‘Timbits’ and ‘Munchkins’, and are marketed as the actual hole of the doughnut. Yet surely they are not, as the hole is created by the Timbits’ or Munchkins’ removal, rather than being identified with what gets removed.

Now, if we do not take the removed dough to be the hole, then what do we take the hole to be? Are holes material things, where material things are physical (like tables and chairs), or are holes immaterial things, where immaterial things are not physical (like abstract entities)? Or are holes not even things at all?

This issue is discussed in the paper ‘Holes’ (1970) by the American philosophers Stephanie and David Lewis, which contains a dialogue between the characters Argle and Bargle. Argle is a materialist, that is, someone who rejects the existence of anything immaterial. Materialism could be seen as a plausible position for Argle to hold, since it doesn’t commit Argle to the existence of potentially weird entities that go above and beyond the material; in other words, it is ontologically parsimonious. Like Madonna, Argle is a material girl living in a material world, where all the things that exist are physical material objects.

Bargle, on the other hand, challenges Argle’s materialism by introducing two further plausible positions, namely, that holes exist and that such holes are immaterial objects. It is plausible that holes exist: we seem to perceive holes; we refer to them in our language; and they seem necessary for the existence of other things. It is also plausible that holes are immaterial things since our intuitive view of holes is that they are not tangible objects but rather seem more like gaps, and so are not material things themselves but are rather, as Tucholsky described, where the material things are not. Argle and Bargle’s debate is therefore over which of the following individually plausible but collectively inconsistent claims to reject:

(1) There are no immaterial objects.

(2) There are holes.

(3) Holes are immaterial objects.

These are inconsistent because (1) says there are no immaterial objects, yet (2) and (3) together entail that immaterial holes exist: if there are holes, and if holes are immaterial objects, then immaterial holes exist. So which should we reject? We could reject (1), which says that there are no immaterial objects, and instead hold that there are immaterial things in the world, including holes. But this option is not available to Argle, since Argle is a committed materialist and so doesn’t want to say that any immaterial things exist.

What about rejecting (2), then, which says that there are holes? The problem with this is that we say (or sing) things such as: ‘There’s a hole in my bucket, dear Liza,’ and so we refer to holes. When we utter (or sing) such a sentence (or lyric), our words (and maybe our fingers too) point to the hole in the bucket. If there are no holes, and so no such hole for our fingers or words to point at, then we need to reinterpret such sentences without making reference to holes. For example, we could make do with the language of objects being perforated, rather than objects having holes, as such: ‘My bucket is perforated, dear Liza.’ Now this doesn’t have quite the same ring to it as the original, but the meaning seems to be preserved. In this paraphrased sentence, we point to the bucket rather than to a hole, and describe that bucket as having a certain perforated shape. It is the bucket that is hole-y shaped, rather than there being actual holes in the bucket. But can every truth about holes be reinterpreted and systematically paraphrased as truths about perforated host objects? And does the eliminability of the word in our language really provide us with evidence regarding the thing’s actual existence? Ordinarily, we do not think that, by simply not talking about something, it ceases to exist.

As for (3), which says that holes are immaterial objects: can that be rejected? Could holes be material rather than immaterial? Well, this was our central issue. If holes are material, which material thing are they? Could they be the guest? No, for similar reasons as to why the TimBits and Munchkins are not the holes themselves. Could they be part of the host, perhaps the lining of the hole? Maybe. But how thick is the lining for the hole? Should we take one millimetre thickness of the doughnut around the hole as constituting the hole? Or the entire width of the doughnut, namely, the entire host? Or even somewhere in between those thicknesses of the lining? There are so many candidate linings of the hole, and it seems there is no reason to choose one over another, leaving it an arbitrary matter as to which lining we define and identify the hole with. And if we did not pick one of the linings, leaving a multitude of linings, then there would be a multitude of holes, one per each lining, all somewhere within the one doughnut. This seems like far too many holes in one place! It also leads to further oddities. For example, we do not think that we eat the hole of a doughnut when we eat the host lining of dough, do we? Again, this is further food for thought.

But why does all this matter? What’s in a hole? Well, one case that the hole expert Achille Varzi, professor of philosophy at Columbia University, cites is that of recounting holes in ballots during the 2000 US presidential election. In Varzi’s words: ‘All of a sudden, we realise that the destiny of the United States, if not the destiny of the entire world, depends on our criteria for counting holes.’ And in order to count the holes, we need to know how to identify and individuate them, and thus we need to know what they are. Granted, this is an unusual case. But a better understanding of where holes lie on the material/immaterial and thing/nothing divides should fill a gap in our knowledge of reality.

This Idea is part of a project that has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme, under grant agreement number 679586.