Philosophy
The Metaphysics of Holes and the Problem of Spatial Boundaries
Quick fact
Some philosophers have argued that a hole is not a physical object at all, but rather a 'negative entity'—a region of space defined by the material that surrounds it, which challenges our standard assumptions about spatial boundaries.
Why this is interesting
Holes are everywhere—in donuts, cheese, and fabric—but are they actually part of the furniture of reality? Could a hole be said to exist in the same way a donut does?
Read the full explanation
Understanding The Metaphysics of Holes and the Problem of Spatial Boundaries
We all know what a hole is: a gap in a material object. But when we try to account for holes in our ontology, they become puzzling. A hole is not made of matter like the dough of a donut; it's defined by the absence of the dough in a specific region. Yet we can count holes (e.g., 'a donut has one hole'), and we can describe their shapes and sizes. This raises a fundamental question: should holes be included in our list of what exists? Consider a donut. The donut's material forms a ring, and the empty air inside is what we call the hole. Now, where is the boundary of that hole? It's not a surface of matter; it's an abstract interface between the air and the dough. So, the hole's boundary is a purely geometric concept, not a physical one. This fact lies at the heart of the philosophical problem.
A deeper explanation
The metaphysical problem of holes was famously brought to prominence by David Lewis and Stephanie Lewis in their paper 'Holes' (1970). They asked: if holes exist, what kind of entities are they? The natural answer is to think of them as located regions of space—like the Air in the donut's center. But that would make holes identical to the air, which seems wrong, because we could remove the air and still have a hole. Conversely, if we think of holes as 'negative parts' of the object, we run into paradoxes: a hole is not a part like a chunk of matter, and the same hole can be shared by different objects (e.g., a ring and a torus). Another view, 'hole-eliminativism,' denies that holes exist at all. It treats statements like 'That donut has a hole' as merely shorthand for 'The donut is shaped in a certain way.' This avoids ontological commitment but seems to ignore the fact that we can compare holes—e.g., 'This hole is bigger than that one.' The debate highlights the problem of spatial boundaries: boundaries are supposed to be properties of objects, but holes have boundaries that are not material. This forces us to decide whether we need to accept non-material boundaries and negative entities in our ontology, which in turn has implications for how we understand material constitution and the nature of space itself.