Metaphysics, as Aristotle defined in his eponymous book, is the study of being qua (“as,” “in terms of,” “as being”) being. This vague definition could be sharpened by considering a paradigmatic example of metaphysical inquiry: the existence (being) of holes. This entry aims to sketch answers to the question “Do holes exist?” and objections to them.
What are we talking about?
To begin, consider the following syllogism for the existence of holes (which we all accept, I assume):
P1(i): There are holes in this cheese.
P2(i): If there are holes, then holes exist.
C(i): Holes exist.
For hole-deniers (we will soon see why some philosophers are attracted to this position), P1(i) or P2(i) must be rejected (or, in rare cases, both). Disputing P1(i) is an ontological dispute since it directly concerns the ontological structure of the world. You can think of an ontological structure like a book of the world that catalogs all of the world’s objects. The question P1(i) poses is thus: are holes enlisted in this book? Or: are holes a part of the world’s ontological structure?
Disputing P2(i) is a meta-ontological dispute since it concerns rules we follow in figuring out answers to ontological questions. Does it follow from “there are Xs” that “Xs exist”? This is a “meta” question since it is about ontology, and in some sense more fundamental than ontology. In other words, even if we have settled every single ontological dispute (metaphorically: we have figured out the book’s entire content), we may still dispute on the meta-ontological level about what it means (or what it is) to be a part of the book. Is book-membership good enough for existence?
Most philosophers answer positively (i.e., they think P2[i] is true). This view, originating from W. V. O. Quine, is sometimes called the standard view of meta-ontology. I will take P2(i) for granted as well. (However, followers of Rudolf Carnap or Alexius Meinong will disagree and reject P2(i). For more on meta-ontology, see Ontology and Metaontology by Francesco Berto and Matteo Plebani)
At this point, I can imagine you asking: how can anyone reject C(i)? What are these philosophers thinking?
Well, here are two syllogisms about why holes can be very problematic:
P1(ii): Materialism states that only material things exist.
P2(ii): Holes exist and holes are not material.
C(ii): Materialism is false.
P1(ii) is a definition; the only disputable part of P2(ii) is whether holes are material (for the hole supporter); C(ii) is unacceptable (how can materialism be rejected so easily?). It seems to me that holes are not material. While they are usually filled with some substance (air, for instance), holes exist in space and space is immaterial (are holes identical to space? See Theory 3).
Another one:
P1(iii): Our perception of holes is caused by holes.
P2(iii): Holes are made of nothing.
C(iii): Our perception of holes is caused by nothing.
A similar structure: P1(iii) seems good; P2(iii) takes the existence of holes for granted and elaborates on their properties; C(iii) is entailed by P1(iii) and P2(iii) but is unacceptable.
Over time, philosophers have proposed various answers to these arguments against holes. Good answers are labeled “theories,” and we will consider 3 of them now.
Theory 1: Holes don't exist
Theory 1 (popularized by Quine) says: By “There are holes in this cheese,” I only mean “This cheese is perforated.” Every time I say a sentence with holes, I can paraphrase holes out of it. Thus, I don’t need to commit to the existence of holes to say true sentences about them.
However, Theory 1 faces problems when the sentences containing holes become increasingly complex. For instance, how do you paraphrase “There are as many holes in my cheese as crackers on my plate,” or “The hole in the tooth was smaller than the dentist’s finest probe”?
Theory 2: Holes exist, as material
Theory 2 (popularized by David Lewis) says: For every hole, there is a hole-lining (whatever material surrounds the hole). Why don’t just identify the hole with its hole-lining? That way, I can believe in holes while still maintaining materialism.
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However, consider this childishly simple syllogism:
P1(iv): Hole-linings can be sweet.
P2(iv): Holes can’t be sweet.
C(iv): Holes aren’t hole-linings.
Lewis has more to say on Theory 2, but I will leave it for the reader to explore.
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Theory 3: Holes exist, as space-time
Theory 3 says: We say that holes are nothing, but what we really mean is that holes contain nothing. That’s because holes are just regions of spacetime.
However, consider the following syllogism:
P1(v): Spacetime can’t move.
P2(v): Holes can move.
C(v): Holes aren’t spacetime.
Further defending Theory 3 requires us to get into the theories of spacetime (especially theories of time) that are beyond the scope of this entry.
Theory N: ???
Theories of holes are numerous and can get very complex. Here are some:
Holes are non-abstract, localized truth-makers for negative existentials.
Holes are anti-instantiations of material properties?
Holes are Husserlian moments that continuously change their fundaments?
Indeed, the existence of holes, just like most questions in metaphysics, remains an open question. I hope this entry gave you a taste of what doing metaphysics is like, and clarified somewhat it is to study being qua being.