Talking about nothing
What if there is something that isn't there?
Our world is full of gaps. Something is missing everywhere. We have holes in our socks. There are gaps in arguments. Shadows. Trenches are gaps in the ground. Valleys are places where the mountain is missing. Silences are stretches of time in which nothing is said. Talking about what is not there belongs in our conversations like the gaps in a picket fence. Something is missing after every slat.
We owe a peak of grotesque-comic poetry to Christian Morgenstern (1871-1914), the master of eccentricity. His famous poem "Der Lattenzaun" (The picket fence), published in the Galgenlieder (Gallows songs) in 1905, is less about the peculiarities of the instrument for garden or property demarcation, than about the withdrawal of "nothingness" - so to speak:1
The picket fence
One time there was a picket fence
with space to gaze from hence to thence.
An architect who saw this sight
approached it suddenly one night,
removed the spaces from the fence,
and built of them a residence.
The picket fence stood there dumbfounded
with pickets wholly unsurrounded,
a view so loathsome and obscene,
the Senate had to intervene.
The architect, however, flew
to Afri- or Americoo.
Memories also have gaps and do not differ so much from picket fences. Some pickets are prominent, jutting out like sore thumbs, while others are smaller, blending in with the background. The gaps between the pickets can be vast and wide, leaving plenty of room for forgetfulness or uncertainty. Our identity - what we believe ourselves to be - is like a continuous fence built by trying to fit the pickets and gaps together to delimit a field in which an I is at home.
Everyone's picket fence is different. Some people have many pickets closely spaced, while others have pickets that are far apart. My own fence of memories has few pickets that are loosely connected by large areas of nothingness. At times, this can be a curse, making it difficult to tell stories about myself since there is little material to work with. However, it can also be a blessing, as the baggage is lighter, and it's easier to move the fence when I need to.
One incident that I still vividly recall dates back to the 1980s, around 1986 or 1987. Allow me to share the story with you.
A conversation at the beach
One beautiful summer day, a few friends from my high school class decided to go for a swim together. As we lay on the beach, we found ourselves contemplating the meaning of a "hole." I can no longer recall how the topic came up, whether it was prompted by one of us digging a hole in the sand or meditating on a slice of cheese or or maybe someone was wondering why trouser legs have an inside and an outside. Whatever it was, the question had taken hold of us and refused to let go.
At first glance, holes seem like such a simple phenomenon, made up of conceivable simple components, easy to identify. You can see them, point to them, even describe and depict them because right there, where something is missing, there is a hole. That's the frustrating thing about holes. How can there be something that is not?
Holes certainly exists. They are a part of our world. They have a certain size and spatial topography. They have a dimension both in space and in time. Holes can arise and disappear. We are able to point to them, count them. We can create and destroy holes. Holes are a part of the causal network of our world. We can dig, punch, drill, or cut them. They collect water or let light in.
Holes have already existed long before us. And holes are useful: sieves, funnels, handles on beer cases, windows, doors, and trouser legs. How could we even exist without holes? Holes are not fictions but real. They are everywhere. Physics even speaks of "black holes," but that's another story.
What then are holes? We came up with various possibilities. A hole - we started with the obvious - is something where there is nothing. But this seemed contradictory. Something cannot be nothing!
Another one was that a hole is something that is (partially) enclosed by something else. Holes are things that have a boundary. That also seemd obvious and sounded much better. But then we saw a ball floating on the water. Obviously, this was something (a ball) that was partially enclosed by something else (water). But there was no hole. Just a ball in the water.
The ball, however, made a dent in the surface of the water - we also saw dents as holes. If we could freeze the water in its current state and remove the ball, then we would see a hole, in a certain sense.
Holes can be filled, but not every filling is acceptable. Holes are picky. We then thought that it could have to do with the density of the materials. A hole exists when a denser material partially encloses a less dense material. The "dimple" in the water is a hole because water is denser than air and partially encloses the air.
But that can't be right either. We can make a hole in Styrofoam and then pour water into it. We would still have a hole in the Styrofoam, but the filling (the water) is denser than what surrounds it (the Styrofoam).
If I remember correctly, we finally agreed that if we assume that there are only three states of matter (gaseous, liquid, solid) that are ordered in this sequence, then a hole is a region consisting of a substance in a lower state of matter than the substance that partially surrounds it.
Clouds that consist partly of liquid water are therefore not holes, but they can have some, if the water is missing. If we submerge a solid object in water, we don't have a hole at that point. A hole would only exist if we’d replace the solid object with air (provided that the water remains in the same configuration). A drop of oil floating on the water surface and making a small dent is also not a hole. And if we stuff an apple-filled goose at Christmas and then roast it, it doesn't have a hole, but a filling.
This definition seemed useful to us and we moved on to the more mundane things that young people do at the beach in good weather.
Today I think, that our reasoning had some weaknesses. We weren’t talking about holes, but about something else. The most obvious problem is that a hole is not identical to what it fills. If we go into the garden and dig a hole with a spade, then we substitute one volume of earth with one volume of air. But the hole is not that air! We could fill it with water afterwards, another substitution, but this doesn’t change the identity of the hole. It remains the same.
The second problem is that holes are also not identical to what surrounds them. A hole in a piece of cheese is where cheese is missing. A piece of non-cheese, so to speak. So we had tried to characterize holes by what they are not.
Let’s call the thing or material that surrounds a hole the host of a hole. The host is what the hole is “in”. Every hole is inside something, as all holes are filled with something.2 Let's call that filling the guest of the hole. A hole - every hole, therefore, has a host as well as a guest, but it is neither one nor the other. A hole is where there is a host that can accommodate a guest. It’s a gap, a possibility of substitution.
In most cases, it is easy to locate a hole. It is there, and yet, it is not what it consist of. Are holes (or shadows, moments of silence, valleys, the gaps of a picket fence) therefore nothing? Places that are defined by the absence of something? Nonthings that exist?
Piggeldy’s plan
The probably most philosophically interesting (and interested) pigs in children's literature, Piggeldy and Frederick, have extensively circled around holes.3 “What are holes?” the piglet Piggeldy asks his big brother Frederick, after which the peripatetic but equally clueless Frederick invites his little brother for a walk with the words: "Nothing easier than that. Come with me."
The two set out and first try to approach the problem phenomenologically, searching for examples of holes (sock holes, mouse holes, puddles) and their qualities (you can fall into them).
But Piggeldy is dissatisfied with the result of the search. Because in the puddle there is water, in the mouse hole there is a mouse, and in the sock hole there is still more sock than hole. “Always a hole is something where something else belongs,” he complains, “a hole is never just a hole.”
To which his brother Frederick replies: “There will never be a hole without something around it." "Aha,” Piggeldy rejoiced, “a hole is only a hole because there is always something around it.” Frederick nodded. He could have quoted Kurt Tucholsky to support his insight:4
There is no such thing as a hole by itself, as sorry as I am to say.
“When I grow up,” said Piggeldy ignoring his bigger brother as well as Tucholsky, “I will invent a hole without anything around it.”
Piggeldy seems to have an absurd plan, and his remark makes us smile. I think, however, Piggeldy might be onto something. We could make a distinction between a criterion for holes, which could include their host, and what holes themselves are - as holes, ontologically speaking.
Without a host, we cannot identify holes, but they themselves are something else. Think of a mother. It is not possible to identify a mother without considering her offspring. A mother is always a mother of someone. There is no such thing, Frederick and Tucholsky would say, as a mother by herself.
But wait a moment! Isn't a mother herself a female person who exists at a specific space-time location, independent of her offspring? This example highlights the difference between identifying mothers and defining what mothers are, in and of themselves.
Similar things apply to holes. To identify a hole in a cheese, we need to consider the cheese. But not a single particle of a hole in a cheese is made of cheese! It seems, therefore, that Piggeldy wouldn't need to invent holes without something around them. Holes already are excluding the stuff that surrounds them. But, hey, what the heck are we talking about here?
Having clarified this, the question remains: What are holes? Unsurprisingly, there is a philosophical debate about this issue. There are always philosophical debates. But this one is especially interesting. Let’s dive in.
Hole Ontologies
If we assume that there are holes, then they seem to be specific to a certain place and time, similar to concrete physical objects like mountains or pencils, and unlike abstract entities such as numbers or values. They possess a particular shape, size, and location, and they have origins and histories. They can undergo changes and be subject to various events.
If we view holes as particulars (lets call this position naive realism about holes), which seems to be an obvious move, then we run into a diffuculty: holes are different from more familiar particulars. Holes seem to be immaterial, not made of matter but rather made of nothingness, if they are made of anything at all.
To accept a naive realism about holes, therefore, means to acknowledge the existence of concrete immaterial objects (let’s call them nothings).5 Given this challenge, most philosophers lean towards a reevaluation of commonly held beliefs abut holes rather than accepting a straightforward realist view.
So we are now entering the field of the ontology of holes, where all kinds of fruits grow. Some of these fruits could be given classical names, such as nominalism, materialism, physicalism, or universalism, as they recycle ideas from these currents. I will not discuss these positions as such, but will only examining the different strategies for avoiding the assumption of concrete nothings and what costs these strategies have. There are always some costs …
Holes don’t exist
What if there are no holes at all, but only perforated objects? Instead of saying that a cheese has a hole, we could just as well say that it is perforated. That would imply that there is cheese. Perhaps that it has properties, such as being yellow, having a certain weight, or being perforated. It would, however, not imply that there are holes. Certainly not that there are nothings!
That’s the old strategy of nominalism. If I say that my sock has a hole, then I am referring to my sock only. And my utterance would be true, if it would be correct to apply the predicate “has a hole” or “is perforated” to my sock. Let's imagine two sheets of paper. Now, let's take a hole puncher and perforate one of them. In what way do the two sheets differ? Instead of saying that one has a hole and the other does not, we could say instead that one is perforated and the other is not.
One might object that these predicates can only be correctly applied if there really is a hole in my sock or in the sheet of paper. A nominalist would respond that we do not need to assume this, but can simply stop at establishing norms of language usage.
This strategy comes down to the claim that all sentences that seem to imply the existence of holes could be rephrased to eliminate the implication of the existence of holes, while still being able to serve the same purposes as the original sentences.
The philosophical debate about holes started in 1970 when David Lewis and his wife Stephanie published a paper about this problem.6 This paper was presented in a unique format - that of a fictitious dialogue between two philosophers named Argle and Bargle, who engage in a thought-provoking discussion about the holes in a piece of Gruyère cheese.
Argle defends the position of nominalism:
When I say that there are holes in something, I mean nothing more nor less than that it is perforated. The synonymous shape-predicates “… is perforated” and “there are holes in …” – just like any other shape-predicate, say “… is a dodecahedron” – may truly be predicated of pieces of cheese, without any implication that perforation is due to the presence of occult, immaterial entities.
Argle doesn't hold out for long, however. Bargle points out that we can count holes and compare the number of holes with other, more common objects. While we could paraphrase a sentence like "The cheese has two holes" as "The cheese is doubly perforated," we would have to assume that our language has an infinite number of such predicates (doubly perforated, triply perforated, etc.) to account for all holes. Besides this, we would have to explain how we could learn such a language that includes so many words. This leads to a dead end.
Moreover, we can compare the number of holes in a cheese with the number of other ordinary objects, such as the crackers on the plate next to it: "The cheese has the same number of holes as there are crackers on the plate." A nominalist should prohibit such sentences. And that is the price we would pay if we deny the existence of holes. We would have to restrict our language concerning holes massively, and this would probably render it useless.
Holes are portions of spacetime
Another strategy is to hold that holes are just regions of spacetime rather than material objects. Wake, Spencer, and Fowler, for instance, argue that the traditional view of holes as objects with a physical boundary is problematic because it raises questions about what exists on either side of the hole's boundary. By contrast, the authors propose that a hole should be understood as a region of spacetime in which the properties of matter and energy differ from the surrounding spacetime.7
According to this view, a hole is not a thing, but rather a region in which the properties of things are different.
One could object that we want to know more about these different properties. Not every region of spacetime that differs from the surrounding region is a hole. In front of me is a chest. It occupies a certain region of spacetime and its properties differs from its surroundings. But my chest is a chest and not a hole.
Remember our day at the beach? We spoke about regions with different properties as well and were pondering what this difference consists in (density or state of matter for instance).
This criticism is, however, not entirely fair, as we could argue that the exact nature of these differences only matters in identifying holes, not in determining what holes are. Once we have identified a hole, what it is, could be just a region in space and time.
This means that there is nothing special about the portions of spacetime that constitute a hole, compared to other portions of spacetime that are occupied by ordinary material objects. It is not fundamentally more difficult to determine the conditions under which a portion of spacetime should be considered a hole than it is to determine the conditions under which it should be considered a pencil, a mug of coffee, or any other kind of object.
A more important objection to this position has to do with the fact that regions of spacetime can overlap or that one region can be part of another region. Let's take a toilet paper roll. It has a hole. Now let's turn it clockwise. The hole moves with it. We could now insert another, narrower toilet paper roll into this one and turn it counterclockwise. The spacetime region of the hole in the smaller roll is a part of the spacetime region of the larger roll. Does the smaller hole now rotate both clockwise and counterclockwise?
The problem - expressed more generally - is that regions that overlap cannot have mutually exclusive qualities in the area where they overlap. If one region is completely black and another is completely white, they do not overlap; they cannot have common parts. This has to do with the identity of regions of spacetime.
Holes, however, can contain other holes, and it seems that it doesn't matter whether the properties of the individual holes exclude each other or not. Does it follow that holes are, therefore, not spacetime regions?
Holes are ordinary things
Argle has another card up his sleeve. Holes are ordinary objects, he says:8
The matter isn’t inside the hole. It would be absurd to say it was: nobody wants to say that holes are inside themselves. The matter surrounds the hole. The lining of a hole, you agree, is a material object. For every hole there is a hole-lining; for every hole-lining there is a hole. I say the hole-lining is the hole.
Be prepared: Argle isn’t claiming that this is what we would say. A hole in a cheese is where there is no cheese. We would say that the host doesn’t belong to the hole. The hole starts where the host ends.
What Argle is proposing instead, is that we should say that a hole is identical with its lining. This would avoid the assumption of concrete nothings, but presumably preserves everything what we want to say about holes, because there’s a 1:1 relation between a hole and its host.
What would it mean to identitfy holes with their hosts? First of all, we could no longer say that hosts (partially) surround or enclose a hole. “Surround” and “enclose” would mean something else (“identity”) when we speak about holes.
Then, we would have to change our language with regard to to what we say about what’s inside a hole. A point on a hole-lining would then be inside the hole, but the filling wouldn’t.
Moreover, ordinarily speaking, holes and hole-linings often have different volumes. When we were children at the seaside, we sometimes looked for so-called chicken gods. These were stones that had one or more holes. Often the stones were more voluminous than the holes they had. If a hole is the same as the surrounding material - here the stony material - then we would have mostly been wrong in our assessment of the size of the holes back then.
Or let's imagine we make a small hole in a piece of paper. Then we cut off some of the paper outside the hole. Have we made the hole smaller by that? Would expanding the hole-lining amount to enlarging the hole?
The next difficulty concerns counting. Suppose we have a piece of cheese with two holes. Wouldn't Argle have to say that there is only one hole and not two? That it is impossible for a connected thing - a sieve, for example - to have multiple holes? Argle could respond - and he does - that we do not have one piece of cheese in front of us, but rather two pieces of cheese that overlap each other. Each one is identical to a hole. With a sieve, there would be more overlaps accordingly.
But how do we decide how many overlappings there are? Look at a roll of toilet paper. How many holes does it have? One? Two? Three? How many overlapping parts does the roll consist of? It's hard to say.
It seems that identifying holes with material things is even more costly than simply denying their existence altogether.
Holes are mind-dependent things
In the article "What Angles Can Tell Us About What Holes Are Not," P.J. Meadows challenges the idea that holes can be understood as individual objects or things in their own right.9 He argues that holes are better understood as properties or relations between objects, rather than as entities that exist independently.
Meadows explores the role of angles in understanding holes, arguing that the way we perceive holes is shaped by the angles of the surrounding objects. He suggests that holes are not objective features of the world, but are instead mind-dependent in the sense that they are created through our perceptions and interpretations of the world.
It might be worth noting that Meadows' focus on angles as a key factor in understanding holes may not be universally applicable. The way we perceive holes may also be influenced by other factors, such as lighting, color, texture, and depth perception, among others. But we’re not talking about perceiving holes here.
The central problem with this view, in my opinion, seems to be that the conclusion that Meadows draws isn’t following from his premises. While it is true that our perception of holes is influenced by our surroundings, it does not necessarily follow that holes, therefore, cannot be understood as objects in their own right. For example, one could argue that a hole in a bucket is a physical object and the cause of the water running out, even if its existence is dependent on the material around it. Even if we can’t perceive the hole in the bucket without perceiving the bucket.
Holes are real but not quite
Maybe, there’s some middleground. Maybe that there are not only things that exist and things that don’t. Some things could be more or less real. And possibly holes are such sorts of things.
McDaniel, for instance, examines the concept of almost nothingness and argues that it is a meaningful and important aspect of human experience.10 He suggests that although we often focus on the substantial and concrete aspects of reality, such as physical objects and events, there are also many instances where we encounter something that is not quite nothing, but also not quite something in a substantial sense.
McDaniel tries to clarify his view that holes are things with a kind of diminished reality. Considering the nominalist project, he writes:11
Suppose that we cannot paraphrase statements about holes and other almost nothings in terms of statements about ‘positive’ entities alone. Perhaps this is because of the limits of our language: there are no infinitely long sentences in English, and the only way to paraphrase talk about holes would be via infinitely long constructions. However, suppose we can conceive of how such a paraphrase might go in an augmented version of English. I think this is the case with holes. If we think this augmented version of English would be a metaphysically better language to speak than ours, … then we have a reason to think that holes are mere beings by courtesy. Ontological reduction, on this picture, amounts to identifying some entity as a mere being by courtesy. Ontological elimination, by contrast, consists in denying any sort of reality to the entity in question.
Assuming that it makes sense to talk about different types of things that are differently real, and that holes belong to the things that exist but not quite (beings by courtesy), in contrast to chairs or mountains, then it seems that we can have our cake and eat it too. We could calm our skepticism regarding the existence of immaterial things without having to assume that holes don’t exist or aren’t entities in their own right.
Another possibility is that holes are genuine absences or negative spaces in the world. While they are not physical objects or properties, they can still have an impact on our understanding of the world. C.B. Martin, for instance, argues that entities are not the only things that exist in the world.12 We can conceive of absences and voids as ‘ways things are not,’ and that they can be just as real and important as entities.
He uses the example of a hole in the ground to illustrate his point, arguing that the hole is not just the absence of dirt, but a real and meaningful part of the world. Martin contends that recognizing the ontological status of absences and voids can help us to better understand and explain certain phenomena, such as the behavior of subatomic particles in quantum mechanics.
McDaniel and Martin's views lead to an inflated ontology, where everything that is not present is treated as a separate entity. That makes the question of the existence of holes appear like a decision.
That reminds me a little bit of my six-year-old daughter. She's afraid to go to her room at night when the light is off. That's completely normal at her age. She says there are ghosts in her room. Sometimes I suggest that we could just check to see if that's true. And then she says: Ghosts can't be seen because they're only there in the dark. So ghosts are "almost nothings." They're there, but not really. Not like chairs or socks that we can see even in the light.
Which language do you speak?
If I'm to be completely honest, none of the approaches presented just now impresses me, not even naive realism. Don't get me wrong: I wouldn't say they're wrong with regard to holes. It’s rather that they introduce different ways of speaking. And we are free to chose one. We could roll the dice and deceide to speak as each individual author presented and thereby accept the costs that would come with that.
Alternatively, we could go back to the beginning of the story and see if we've made a mistake somewhere along the line. I think we have.
Let's think again of a sheet of paper with a hole cut into it. If we could give a complete physical description of the sheet, including the hole, we wouldn't find anything astonishing. Molecules, atoms, and subatomic particles are in various relationships to each other and are in different states.
Perhaps the sheet has not only a hole but also a fold and a small dirt stain somewhere. Surely, it's not cut completely straight, the edges are a bit frayed here and there. While this will make our physical description more complicated, it doesn't mean that we would discover any strange entities that don't fit into our physical description.
With this type of description, the sheet itself is no more or less real than the hole in its center. This is because, when we speak about "the world" in our daily lives, we rely on abstractions. When we talk about sheets, we leave out all the folds, holes, indentations, unevenness, etc. in which different things, which we also call sheets, differ from each other. Once we've abstracted over these differences, we can bring them back into the picture by making more detailed descriptions. And this is where slits, gaps, folds, holes, etc. come into play.
Similar considerations apply to mountains. No mountain is like any other. Physically speaking, the concept of a mountain is an abstraction. That's practical. If we want to know more, we bring valleys, cuts, slopes, etc. into play. But that doesn't mean that valleys are less real than mountains. It's just more practical to talk about mountains and valleys than to make a complete physical description of a section of the world.
Holes are like folds or frayed corners - concepts that compensate for the idealizations we've made with other concepts. If I go into the garden and dig a hole, I "transform" a prototypical garden into a less prototypical garden. Strictly speaking, there are neither prototypical gardens nor holes. Or, there are in a certain sense.
We could start with more complicated geometric constellations instead of flat surfaces. Suppose we start with undulating surfaces. A prototypical garden would then look like a stormy ocean. Instead of digging holes, I could then go out and remove accumulations that have formed on its surface. I probably wouldn’t dig a hole then. I would say that this way of categorizing things would result in a less efficient language, but it wouldn't change the world one bit.
Our everyday language is an efficient way of talking about the world, but it's certainly not the only way. We could divide the world according to other criteria and make corresponding - different - adjustments.
So to summarize, holes are deviations from an ideal that exists just as little and as well as the ideal itself. A gap in an argument is a deviation from an ideal argument. A gap in a garden fence is a deviation from the ideal of a continuous, fully closed surface. A hole in a sheet of paper is a deviation from an ideal sheet of paper. One could just as well say that a sheet of paper is an ideal hole filled with cellulose - provided that we adjust our language accordingly in other areas too.
Naive realism about holes is not naive because it assumes the existence of immaterial objects, but because it regards the way we categorize the world in everyday life as unalterable. And nominalism is not rejected because it denies the existence of certain things which seem to “be there,” but because it sees our everyday way of dividing the world as fundamentally wrong. As if it were possible to distinguish a "correct" way of division from a less correct one.
Are holes real now? I would say that this is not a meaningful question. A sheet of paper with a hole is just as real as a sheet of paper without a hole. They are simply two differently filled regions, or - rather - two regions with different correct descriptions within the same language.
What we could do is to consider what kind of deviation holes are. After all, there are not only holes. We also know gaps, shadows, silences, dents, valleys, and so on. As a final suggestion to contribute something constructive here, I would propose the following:
A hole is a spaciotemperal region R such that
(i) R is a real part of a larger region R*,
(ii) R and R* consist of different largely homogeneous stuff S and S*, and
(iii) S is more easily substitutable by another stuff S’ compared to S*.There are as many holes in a region R* as there are unconnected regions R1, R2, … that fulfill conditions (i) to (iii).
The most interesting part of this account is condition (iii) which is about substitutability (or removability). A hole contains stuff that that can be removed easily compared to its surroundings. The chest in front of me is not a hole in the space which surrounds it. It is easier to substitute the air around the chest than the chest itself. Imagine a sheet of paper within a larger region R*. It’s usually difficult to replace the space the sheet lives in with something else. So, the space the sheet fills out is not a hole.
But we could make a wooden box that can precisely accommodate the sheet inside. In this case, it would be easier to replace the space occupied by the sheet with something else - another sheet of paper for instance - than to replace the space occupied by the box. In this case, the space occupied by the sheet of paper could be considered a hole.
Condition (iii) also adds a modal dimension to holes. Holes are regions in which replacement or substitution is (easily) possible. For water to flow out of a bucket, there needs to be a spot on the surface of the bucket that can be easily replaced by water. If we dig a hole in the garden, we can fill it with potatoes. If there were still soil in the spot, it would be difficult bring in the potatoes.
It would certainly be interesting to investigate this type of modality further. I suppose it won't be quite so easy, and I won’t do it here. Instead, I would like to test my suggestion a little bit. It is, of course, an empirical hypothesis about our language usage, and not about what our world is made of.
It can, nevertheless, turn out to be false. With the assistance of a set of questions, I recently tested my hypothesis. My objective was to determine whether substitutability is a valid criterion for identifying holes. As a guest at a large party, I distributed a questionnaire containing the following items. (The percentage figures refer to the relative frequency with which the respective answers were selected by the guests.)
Imagine we have a piece of styrofoam, about 10 mm thick and as large as an A4 sheet. Now we cut a circular hole in the center of the styrofoam with a knife. Consider the following cases:
We insert a wooden rod with the same diameter as the hole and about 50cm long into the hole and move it back and forth.
A) The hole still exists. (57%)
B) The hole no longer exists. (35%)
C) I don't know what to say. (7%)
We now shorten this rod to 1cm length, insert it into the hole so that the ends exactly match the edge of the styrofoam, and leave it in place.
A) The hole still exists. (57%)
B) The hole no longer exists. (35%)
C) I don't know what to say. (7%)
We remove the wood and take a round, transparent glass rod of 1cm length and insert it into the hole so that we can see through it.
A) The hole still exists. (64%)
B) The hole no longer exists. (29%)
C) I don't know what to say. (7%)
We remove the glass and insert the cut-out piece of styrofoam into the hole.
A) The hole still exists. (36%)
B) The hole no longer exists. (50%)
C) I don't know what to say. (14%)
Now we take out the styrofoam again, smear the edges with glue, put it back into the hole, and wait for the glue to dry.
A) The hole still exists. (14%)
B) The hole no longer exists. (86%)
C) I don't know what to say. (0%)
We take a new, similar piece of styrofoam and cut another hole into it. Now we slit the styrofoam from one side so that the slit reaches from the edge of the styrofoam to the edge of the hole.
A) The hole still exists. (64%)
B) The hole no longer exists. (36%)
C) I don't know what to say, (0%)
Now we also slit the styrofoam from the other side so that this second slit reaches from the opposite edge of the styrofoam to the other edge of the hole. We could separate the two sides of the styrofoam, but we keep them together.
A) The hole still exists. (43%)
B) The hole no longer exists. (57%)
C) I don't know what to say. (0%)
Now we take the two sides of the styrofoam apart and lay them on the table at some distance.
A) The hole still exists. (14%)
B) The hole no longer exists. (86%)
C) I don't know what to say. (0%)
A new piece of styrofoam. We cut another hole into it. At some distance from it, we cut a second hole. Now we take a knife and slit the styrofoam from one hole to the other, connecting them.
A) The first hole still exists. (86%)
B) The first hole no longer exists. (14%)
C) I don't know what to say. (0%)
We create another hole. Then we take the knife and cut away a piece from the edge of the hole all around, making it larger - for example, 20 mm in diameter.
A) The original hole still exists. (50%)
B) The original hole no longer exists. (43%)
C) I don't know what to say. (7%)
The first thing that should strike you is that the concept of a hole - like most everyday concepts - is vague. That means that the intuitions of different speakers can differ slightly from each other, especially in borderline cases.
In questions 1 through 5, I tested the effects of the presence of a "solid" guest on our conception of holes. Slightly more than half of the participants indicated that a wooden filling - regardless of whether it fitted the host or not - had no impact on the continued existence of the hole. A transparent filling slightly increased this tendency.
When the filling, however, was the same material as the host, significantly fewer participants assumed that the hole would continue to exist than that it would disappear. If the filling was difficult to substitute (case 5), then most participants changed their assumption from the existence of a hole to its absence.
I have a suspicion that the correlation between the answers to case 1 and case 2 could be explained by consistency considerations. Some of the participants told me that they found it difficult to answer the questions. It might have been better, therefore, to distribute several different questionnaires to neutralize this effect. However, this would have required more participants than I had.
I find the comparison between case 4 and case 5 interesting. Even if the hole has the same filling, the easiness of substitutability seems to be crucial for the conception of holes. If the guest is firmly attached to the host, only very few people seem to want to consider the presence of a hole.
I have no idea how to explain the significant difference in the answers between case 6 and case 9. In both cases, the host is partially penetrated and either connected to its edge or the edge of another hole. While in the first case only 64% assumed that the hole would continue to exist, in the latter, it was a whopping 86%. This was a big surprise.
What surprised me as well - albeit to a lesser extent - is the difference between 6 and 7. Similar case 10. There is - at least in German - a linguistic ambiguity regarding the situation as described in 10. If we remove stuff from the edge of the host a bit, we can express this activity in two different ways:
a) We create a larger hole.
b) We make the hole bigger.
In the fist description we assume that the resulting hole is another hole than the one we started with. The second description assumes a continuity of the hole. The answers to case 10 might reflect this ambiguity more or less.
What this shows is that a hole is not simply a region, but perhaps rather a maximally extended sub-region that possesses a certain characteristic. For people who prefer the second description, a property of the hole has changed (its size). For people who would rather use the first formulation, the identity of the hole has changed, which would mean that the size was not seen as a feature, but as a criterion for the identity of holes.
I had a conversation about this topic with some of the guests (a qualitative field study, so to speak). Most of them had not thought about holes and could not tell me exactly what they are and how they can be individuated. One conversation partner said that, "for him," there are only holes when the host is solid and the guest is gaseous. When I asked if he meant that there are also holes in clouds, he denied it. Another guest said that there are only holes where something is "broken." A woman believed that holes always had to be continuous, with two "entrances." If something only had one exit, like a cave, then it was not a hole in the rock, but rather a pit.
This small experiment shows that there is no consistent everyday theory about holes. This is not surprising. After all, there is also no consistent everyday theory about chairs, containers, or porridge.
This also shows that it doesn't make much sense to ask what holes are. I tried to explain how it comes about that we use this concept. We use it because, when we speak, we initially overlook details and use concepts that contain abstractions and idealizations. Holes are therefore interruptions of "things" because such interruptions are not initially provided for the things we talk about.
We live like Platonists in a world full of ideal forms: an ideal stone has no dents; an ideal leaf has no fringes, and an ideal bucket has no holes. Ideal stones, ideal leaves, and ideal buckets, however, do not exist. Therefore, we need holes (dents, gaps, scratches, bumps, creases) too.
Morgenstern, Christian. Gedichte. Galgendichtung, Berlin 1905
It is, of course, possible that a hole is "filled" with a vacuum. Although this is not a "substance" in the literal sense, it is a filling nevertheless.
Loewe, Elke and Dieter. Die schönsten Geschichten von Piggeldy und Frederick, Ravensburg 2008
Tucholsky, Kurt. “Zur soziologischen Psychologie der Löcher” (signed Kaspar Hauser), Die Weltbühne, March 17 1931, p. 389
Casati and Varzi argue persuasively that claims about the existence of holes cannot be paraphrased away. We are committed to the literal truth of ‘∃x x = a hole’, and this implies that we are ontologically commited to assume that holes exist. (cf. Casati, R., and Varzi, A. C. Holes and Other Superficialities, Cambridge 1994, pp. 178–184)
Lewis, David and Stephanie. “Holes”, Australasian Journal of Philosophy 48 (1970): 206–212
Wake, A., Spencer, J., and Fowler, G. “Holes as Regions of Spacetime”, The Monist 90 (2007), 372–378
Lewis, David and Stephanie (1970)
Meadows, P. J. “What Angles Can Tell Us About What Holes Are Not”, Erkenntnis 78 (2013), 319–331; see also: Meadows, P. J. “Holes Cannot Be Counted as Immaterial Objects”, Erkenntnis 80 (2015), 841–852
McDaniel, K. “Being and Almost Nothingness’”, Noûs 44 (2010), 628–649
McDaniel 2010, p. 644
Martin, C. B. “How It Is: Entities, Absences and Voids”, Australasian Journal of Philosophy 74 ( 1996), 57–65