'The Swiss cheese is multiply-roundly-holed.'
Do holes exist? To answer this question we must first to think about what objects do exist. This is a tricky affair. For what does exist?! The answer isn’t obvious . . .
Imagine air gaps in swiss cheese (pictured), craters on the Moon, the leaves of a Monstera plant, silence in a song, and electron holes. A physicalist might argue none exist because they lack physicality.
The physicalist, however, might say that holes are defined by the absence of things which do exist in time and space: the lack of rock, the lack of cheese, the lack of plant cells, the lack of music, the lack of an electron. But this approach undermines itself since most of the Universe is empty space. Moreover—and this is more-philosophically problematic—it disregards things that might intuitively exist to us non-physically: mental health, numbers, beauty, God, morality, the institution of marriage . . . Of each of these, there is something immaterial and abstract we may not want to rule out from the definition of existence.
But we have to be careful, for we wouldn’t necessarily want to claim that mind-dependent fictions like Santa Claus, Lara Croft, and the One Ring also exist—would we?
The philosophy of fiction is a very real research area, wherein philosophers abandon literal truth in favour of making claims attached to wider fictions. Inspired by deflationism, logical operators for existential quantification are used like this: ‘According to the fiction of maths, numbers exist’. (There would be fictions for mental health, beauty, God, morality, and marriage, too.)
Similarly, holes are attached to other things—e.g. with shape predicates: ‘The Swiss cheese is multiply-roundly-holed’. But then we do not represent holes in themselves. Holes are in other things, whose existences are also hard to quantify!
Others would say all of this is absurd, that holes are regions in spacetime. After all, we can move things containing holes around; those holes move in different directions, in different places, at different speeds, giving them unique properties.
To quote Michael Ende from his fantasy novel The Neverending Story:
'No,' said the will-o'-the-wisp. 'Then there'd be a dried-up lake. But there isn't, where the lake used to be there's nothing—absolutely nothing.'
'A hole?' the rock chewer grunted.
'No, not a hole,' said the will-o'-the-wisp despairingly. 'A hole, after all, is something. This is nothing at all.'
Do holes exist? An innocent question with an indulgence of guilty answers.