A conversation with Achille C. Varzi
I met with Prof. Achille C. Varzi a few weeks before Christmas, in 2023 – i.e., more than a year ago. (Yes, I took my time transcribing this one.) Achille is Professor of Philosophy at Columbia University in New York, USA. He has published many papers on topics such as boundaries, maps, logic, facts (the naming), and more. Together with Roberto Casati, he has also published a book on the metaphysics of holes, among other topics. In this interview we talked about holes, how to create them, how to destroy them, and how the small things can sometimes be of great importance. Also, many thanks to Sofija A. Kozlova for help with transcribing. — Emils Zavelis
Everyone from the Tvērums editor team is delighted to publish this interview.
Emil: So, what was it that made you start looking into holes more seriously from a metaphysical side?
Achille: Historically, it went like this. Many years ago, I think in 1991, there was a summer school. Kit Fine was there, lecturing, and I was there, lecturing, and Roberto Casati, who is the co-author of the work on holes, was also attending the school.
Kit’s lectures were about ordinary objects and their metaphysics, and one day he mentioned holes as a problematic case because they are made of nothing and, therefore, tend to be very elusive. Roberto and I—who met there for the first time—became very fascinated by the topic. We realized that it can be a fantastic entry point into a number of deep and broad philosophical issues, such as constitution, causation, mereology (parts and wholes), coming into being and going out of existence, persistence through change, etc. Moreover, we were fascinated by the fact that holes are parasitic entities. They depend for their existence on there being some material host. But the fact that they are dependent doesn’t mean that they are reducible to those other entities.
This, indeed, is also the reason why Stephanie and David Lewis published their beautiful dialogue between Argle and Bargle, entitled “Holes”. In the dialogue, the issue was the ontology of holes—whether or not there are such things. Argle is a materialist nominalist who wants to say, “No there aren’t any.” Bargle, by contrast, is a realist about all sorts of entities. They’re about to have dinner and are eating snacks with cheese and crackers. Then Bargle says: “There are remarkably many holes in this piece of cheese.” Argle says: “You’re right, there are!” And then Bargle says: “Aha, gotcha! Because now you’ve said there are many holes in the cheese, therefore there are holes. But that’s inconsistent with your materialist nominalism.” And then, of course, Argle responds.
It’s a beautiful illustration of how an ontological debate proceeds. For example, think of the medieval debates on the problem of universals. That dialogue between Argle and Bargle—which, of course, we had read at the time when Roberto and I were discussing these issues—exemplified what we also thought was fascinating about the topic, namely, that it’s an entry point into very deep and difficult questions. It’s also fun. Because there are many intrinsically interesting questions about holes over and above the deep ones I just mentioned.
Emil: What’s also really fun is the fact that you were approached by CNN in the year 2000 to talk about holes. So how did that go?
Achille: It was actually a very interesting experience. On election day, late in the evening, one already roughly knew what the situation was. On the one hand, the incumbent Vice President and Democratic nominee, Al Gore, was comfortably ahead in various states for a total of 250 electoral votes. The Republican candidate, George W. Bush, in turn, was winning in other states, for a total of 246. So, 250 for Gore, 246 for Bush. But to win the election, you needed 270. There were three states that were, as the Americans say, too close to call. We didn’t know yet who was winning in those states. Two of those, I think Oregon and Wisconsin, were not important, because they would only bring a few votes altogether. So, it all boiled down to the third state, Florida, which brings some 25 electoral votes. That meant the winner of the election would depend on the winner of the state of Florida.
It turned out that the winner in Florida was George W. Bush, but by a very small margin, around 1700 votes, which is well below the margin of error tolerated by the state law. When the margin is so small, the law says a manual recount is required. Now, here comes the story.
In Florida—not everywhere in the States—they vote by punching a hole into the ballot next to the name of your favorite candidate. The idea is that once you’ve punched a hole, it’s hard to move it or to delete it. It’s supposed to be a very robust way of expressing your opinion. But unfortunately, not everybody punches holes as effectively as they’re supposed to. So, when the canvassing officials started the manual recount, they realized that many ballots had “quasi-holes”. For example, some had the famous “hanging chads”—the little piece of paper that didn’t fully detach from the ballot—while others showed signs of two attempts, and so on.
The manual recount turned out to be very complicated. It was going very, very slowly, and the newspapers were filled with photographs of the canvassers holding up the ballots and doing what they called the “sunshine test”. They would put the ballot in front of a light source to see if the light went through. If it did, there was a hole, otherwise there wasn’t.
One evening, I was watching the news, and the President of the Recounting Commission was asked by a journalist: “Why is it taking so long? We’re all waiting to know who’s the winner of the elections.” And the Commission President replied: “Well, you know what the real problem is? No one here is an expert on holes.” The next morning, I got a phone call from CNN saying: “We understand you’re a hole expert.”
By that time the book with Roberto Casati had been published and they probably Googled us or something. So, I ended up being on TV with Jeanne Moos, talking about holes and trying to explain that the destiny of the United States—if not the destiny of the entire world—depended on our criteria for identifying holes. I was doing the sunshine test, of course, with a slice of Swiss cheese and asking, “What happens in this case?” Alas, they didn’t listen. Gore unfortunately conceded soon afterward. They should have listened more carefully! (Both laugh) Okay, no, I’m kidding.
That’s a beautiful truth: the fact that even something so seemingly insignificant and unimportant as a hole in a piece of paper can be extremely consequential. When we do philosophy, we should not ignore the small things.
Emil: You know, given this background of voting and ballots, it would seem that holes are, in some sense, among the things in the world. (Brief pause.) Or so we say. We count them, we say, “There’s a hole”, like in the dialogue of the Lewises, which starts with Argle and Bargle pointing out that there are many holes in the cheese. So, what are holes? Objects, properties, or perhaps—nothing at all? How would you answer that?
Achille: First of all, I would draw a distinction here between the strict ontological question—whether we want to take holes seriously, whether they exist—and the metaphysical question about the nature of such entities—what kind of entities are they? For example, the dialogue between Argle and Bargle starts with the ontological question. Argle’s strategy—since he doesn’t believe holes exist—is to say that whenever we seem to be talking about holes, we are actually talking about holed or perforated objects. So, for instance, to say “There are holes in this piece of cheese” is to talk about the cheese itself and to say that it is perforated. In other words, for Argle the phrase, “there are holes in”, is not a quantification. It’s just a shape predicate, like “is a dodecahedron” or “is triangular”.
In our book, Roberto and I take an initial conditional realist attitude about holes. We provide some arguments—as much as we love Argle—that Argle’s position cannot really be pursued. And so, we move to a different question: “Okay, let’s suppose there are such things. In that case, what kind of things are they?” This is now a metaphysical question. You mentioned a few options—they could be properties, they could be objects, perhaps they could be modes of being. Our view is that they are objects. They are particulars, located in space and time, just like ordinary material objects. They change over time. For example, they can get larger or smaller. Indeed, it’s interesting that developmental psychology tells us that children in prelinguistic stage, i.e., infants, tend to reify holes and shadows alongside material objects, precisely because they have all these features that I’ve just mentioned. So, we take them to be particulars, but of course they are very peculiar particulars, because they are immaterial. They are, if you like the expression, made of nothing. I prefer to put it in terms of being part of the immaterial complements of material objects. In the book, we say that they are made of space, but that’s a long story. I don’t think we need to go into that.
Let’s say they are immaterial objects. Secondly, they are parasitic entities that don’t exist on their own. They cannot even be separated from their host. So, you cannot go to a store, buy a doughnut, and say: “Keep the hole!” I mean, if you buy the doughnut, you’re going to get the hole with it. And neither can you buy the hole and leave the doughnut there. You simply cannot remove the hole from the doughnut.
There are many entities that are parasitic in this sense, such as boundaries and surfaces. In the Middle Ages, some philosophers were wondering whether an omnipotent God could separate the surface of an object from the object itself. Only late medieval philosophers, such as Francisco Suárez, would agree to that. Otherwise we say: “No, it’s impossible, because surfaces are dependent entities.” And so, even though the saying goes, “There’s no doughnut without a hole,” ontologically speaking, there’s no hole without a doughnut around it (so to speak).
That’s in the end what we think holes are: immaterial, spatial-temporal particulars that depend for their existence on something else but are not thereby reducible to something else.
Because of these peculiarities, it turns out we need to revisit many theories. For example, we see holes, we count them. How can we see holes if they are immaterial? Even today, the best theory of perception we have is a causal theory: there is a causal flow from the object of perception to the perceiver. But causation is supposed to be a relation that obtains between material entities. That’s the standard view. Some people today have revisited that intuition and say: “No, you can also have absence causation, for instance, or immaterial causation.” That’s one way to go. But perhaps another way to go is to say that we can see things indirectly. For example, by seeing the doughnut, we see the hole inside it.
Emil: Yeah, the causal power of absences is an interesting topic. There is this odd non-standard philosophy paper maybe, you know it…
Achille: Yes, yes, by Tyron Goldschmidt. Yes, yes, yes, the Causal Power of Absences.
Emil: Exactly! It’s just the title page, and then the paper is blank. It has nothing, and of course yes, quite amusingly, it has received responses from others.
Achille: It’s a beautiful provocation. I personally disagree with the intended moral that we should draw, namely, that the absence of text has causal powers in so far insofar as the reader reacts with surprise. I don’t think it’s an absence that is causally responsible for the surprise. I think it’s something that is present, namely, a white page. We expected something else—we expected some text—thus we are surprised. But what we see is not the absence of text; we see a white page.
Sartre has this beautiful story in his Being and Nothingness. He has an appointment with a friend named Pierre at a café. Pierre is always on time. Sartre ends up getting there 15 minutes late. He’s worried, looks around. And then, all of a sudden, he has this very vivid perception of Pierre’s absence—Pierre’s not there. Typically, debates on this topic are based on whether or not Sartre’s experience should be described as the visual experience of an absence—the absence of Pierre. It’s not that Sartre saw that Pierre was absent. He’s supposed to have seen the absence.
It’s an interesting case because absences—like holes—are also parasitic. An absence is always an absence of something. It’s the absence of Pierre that Sartre supposedly saw. But most importantly, all of these sorts of experiences seem to depend on certain expectations that we have. It is because we expect to see something and that expectation is frustrated that we can perhaps put it in terms of seeing or perceiving an absence. Sartre expected Pierre. Pierre wasn’t there. So, Sartre saw Pierre’s absence (we are told). But suppose that Simone de Beauvoir also entered the café, and suppose she didn’t expect Pierre to be there. She had no expectation, therefore no frustrated expectation. Hence, she wouldn’t have seen the absence of Pierre.
Emil: Yes, there seems to be something psychological going on in these examples.
Achille: Yes, exactly. Of course, many other people were absent there. For example, you were not there. I wasn’t there. Paul Valéry wasn’t there. Napoleon wasn’t there. But Sartre didn’t see their absences because he didn’t expect them to be there. So, yes, there is something psychological, phenomenological. This is similar to what goes on with holes. The difference is that Roberto and I don’t think that holes are absences. We think they’re presences. They’re just immaterial, but they’re there.
Emil: So would you be willing to say that holes can have causal powers? Like when I explain water leaking from a bucket by saying it happens because there is a hole on the bottom of the bucket.
Achille: Yes, and no. Surely, we have causal explanations that appeal to the presence of holes. But a causal explanation is one thing; the report of a causal transaction is another. I don’t want to make this too complicated. The point is: whether holes themselves can be causes is a strictly metaphysical question.
Your example of a hole in the bucket letting the water flow out seems to be a good case of causal power. Notice that if you put it in terms of explanation, it’s easy. Why is the water flowing out? Because there is a hole in the bucket. This is an explanation. It has the form P because Q. That’s very different from a causal report, which is that the hole causes something. That’s an atomic statement. It’s a relational claim between two things or two states of affairs. I believe there are holes, so I’m open to hole causation.
Emil: Yes, I quite like that view myself. But never mind my metaphysical sympathies. Let’s say I want to create a hole. Is it just as simple as taking a sheet of paper and punching a pencil through it? Will that suffice?
Achille: Yes, with a couple of qualifications. Roberto and I think there are different kinds of holes. One standard, prototypical type of hole is a perforation—something that goes through, like a tunnel. Maybe the tunnel is very short, e.g., when you perforate a piece of paper, the thickness of paper doesn’t justify calling it a tunnel. But that is a topological hole because the topology is, strictly speaking, altered. The second type of hole is an internal cavity, e.g., a little bubble inside a wheel of cheese. That it’s hidden inside the cheese is, again, topologically significant, but it’s different from a perforation. And the third is simply a superficial hollow, as when you start digging into the ground, or when you press your finger into a piece of soft plasticine.
Now, because of this variety of holes, which are different species of the same ontological kind, there are different ways of making holes. Even within each kind there may be different ways of holemaking. For example, a superficial hollow can be made in two ways. Either by pressing and deforming the shape of what ends up being the material host without changing its topology, or perhaps by digging and removing some stuff. The case you mentioned, like punching a hole through a ballot, is still a different operation and yields only holes of the first type—perforations.
So, if I take a piece of paper and I… (Achille picks up a sheet of paper) let me do it this way… (brief pause, the paper won’t give) Oops. Ah! (The paper rips.) …I punch a hole through it, the piece of paper is still there, attached to the rest. This is a classic example of a hanging chad. I have broken the continuity of the surface and now there is a hole. But I haven’t removed any matter. It’s just that the shape is different.
The bubble inside—that’s more complicated. Kurt Tucholsky, a German writer from the 1930s, famous for his ironic style, wrote a little piece called Where do the holes in cheese come from? Of course, the answer is: it’s pure chemistry. It’s a process where, when you prepare the cheese, some bubbles of air generate inside, like in a glass of champagne, where there are plenty of little bubbles, etc. Those seem to have a birth that is due to natural causes.
So, you see, there are different ways of bringing holes into existence due to the fact that there are different kinds of holes. Some of them, as I said, involve changing the topology of the object. Some do not.
Of course, you can fill a hole completely without destroying it. If you fill a hole in the ground, for example with water or with cement, then the hole is still there. It’s just that it’s filled. So there, in addition to the host, we also have a guest. Holes, being immaterial, can be filled. In fact, we take this to be another important property in the metaphysical characterization of holes: they are fillable entities that have this dispositional property of admitting a guest.
Emil: They can spatially coincide with other objects.
Achille: Yes, exactly. It’s another example of a deep issue that is well illustrated by this case study. Holes can be located exactly where other things are located—for instance, their fillers. In fact, perhaps holes are even a good example of entities that can be co-located with other entities of the same kind. If you have a hole with a filler, those are entities of two kinds: one is immaterial, the other is material. But suppose you take, say, a ring and a doughnut and place the ring inside the bigger hole in the donut. Now the hole within the ring is going to occupy a proper part of the space occupied by the larger hole. So, we have a small hole co-located partly with a large hole. And they are entities of the same kind.
Emil: Yes, that is very interesting. But now it seems to me, however, that it’s quite difficult to make a whole go away once we have it. Because, as you said, we cannot really fill it up to make it go away, except maybe, if the material we fill it up is homogeneous with the material of the host.
Achille: Exactly so, exactly so. Which is why in Florida they thought that punching a hole in a ballot is a good way to have a robust vote. The main way to “kill” a hole is to fill it up with material that’s homogeneous with the host. When the guest and the host merge and are made of the same kind of stuff, the hole goes away. Another possibility is available, but only for one of the three kinds I listed earlier. Not perforations or tunnels, nor internal cavities, but hollows or indentations. You can simply deform the host in such a way as to gradually make the hole go away. Suppose you have a piece of black, soft plasticine. You press your finger into it and you thereby create a hole, but when you remodel it again, the hole goes away. When there is no topological change, you can simply reshape the host. When there is topological change, you have to fill the hole in the host with a guest that’s homogeneous with the host.
Emil: I’m also thinking, couldn’t I make a hole go away in the following way? Say, I take a sheet of paper, and punch one hole through it. Then I keep perforating it and do it so many times that at some point all the different bits of paper become detached from one another. Something like that.
Achille: That would work. Here’s another example. Let’s go back to this hole in the paper. I can do this:
At this point, one might be inclined to say that the hole is gone. In fact, I would say that now we have two holes. We have one here on the left, which is an indentation, not a perforation, and another one here on the right.
But you’re right. There are other ways, including cutting the host in various ways, that would result in the disappearance of the hole.
Another big question is whether there are such things as half-holes, or whether every hole with an H is a whole with a W.
Also, suppose I punch… and then I punch again… (Pause; many punches are slowly being made.) Sorry, I should have taken an easier paper. But you know what I’m talking about. If I punch, and I punch again, the question is: how many holes did I make?
The intuitive answer is, of course, two. I dare say that this is almost culturally universal. I have asked this question everywhere on the globe. Everybody would say two holes, no matter what their cultural background is, no matter what their language is.
But you could also say that I made one hole that has two disconnected parts. There are, after all, disconnected objects. For instance, every lowercase inscription of the letter ‘i’ is a disconnected object. Every copy of Principia Mathematica is a disconnected object in three volumes. Maybe this is a disconnected hole with two parts, as opposed to two holes.
How we count holes is itself a very difficult question. Perhaps the ordinary notion of a hole would deliver an answer, but as you know, when you start thinking about such issues, sooner or later you find yourself departing from common sense. That’s when you start elaborating a theory.
Emil: Thanks for that answer. I think we should wrap up to keep the conversation relatively short. But before we finish I should ask you: is there anything you would like to add that you maybe wanted to mention, but didn’t?
Achille: No, thank you. This was actually a very nice conversation, which shows in what way philosophy is a good thing. You take two people who have never met before, who are both speaking in a language that is not their native tongue, and who apparently share the same passion for philosophy—and they immediately start talking about apparently crazy things. And (A) they’re having fun, (B) they understand each other. They come up with new ideas as they talk. They find interesting applications, or ramifications, or complications. And this is the beauty of philosophy, and I think we are lucky to be able to do this.
Emil: Well said, well said. Yes, I enjoyed our conversation immensely, too. Thank you for that.
Achille: Thank you.