What are holes?
By Collin Ng
That there are holes is uncontroversial. There are holes in Swiss cheese, doughnuts, tunnels, drains and pipes. Holes can also seemingly cause physical phenomena: “The hole in the mug caused my tea to spill all over the floor.”
Indeed, our use of language commits us to the existence of holes. Every time we utter statements about holes— for example, “There is a hole in this doughnut”— we’re saying there must be such a thing as holes, and one exists inside that doughnut.
However, upon closer examination, holes are bizarre and troubling entities.
The materialist thesis
The materialist holds that there is only matter and that everything that exists is reducible to matter. This seems to be the metaphysical thesis presupposed by the natural sciences, and, considering the sciences’ successes at explaining the natural world, the only agreeable metaphysical thesis. I assume most of us are materialists; this seems to me the prima facie metaphysical theory endorsed by most of us.
However, holes pose a challenge to the materialist: intuitively, holes are an absence of matter— they exist where something is not— yet they exist. Thus, we have one of three individually plausible but collectively contradictory theses:
There are no immaterial objects (the materialist thesis)
There are holes
Holes are immaterial objects
Against holes
A materialist could deny thesis 2 and say there are no holes. Simply doing away with holes is easy and elegant — a virtue in metaphysics, in keeping with Ockham’s Razor, the principle that we should prefer the simplest explanations for phenomena.
But if this position can be coherently maintained, it must have to produce a way of referring to holes without being committed to their existence.
They can do this by treating holes as a property (adjective) of an object (noun). “There is a hole in this doughnut,” which has “hole” as the noun, could be paraphrased to have “doughnut” as the noun, if “hole” is treated as an adjective: “the doughnut is holed” (however awkward this may sound). Now the sentence refers to an object with a property of “hole-ness” and not a hole, so the need to posit holes existing is removed.
But if this is so, every statement about holes must be ultimately paraphrasable as statements about holed objects.
Unfortunately, this is not so. A statement like “the hole in the tooth was too small for the dentist’s probe” cannot be paraphrased using this method: if we try, we get “the holed tooth was smaller than the dentist’s probe”. The paraphrase means something different than the original, and we are again forced to posit holes.
Holes exist
Another materialist response could be to deny thesis (3) and say holes are somehow reducible to matter. If so, what material objects would they be?
Could holes be the matter occupying the space where the hole is? A hole in swiss cheese would be nothing more than air. Let us consider a doughnut in the vacuum of space, where there is no air or matter. Do we, therefore, conclude that there is no hole in the doughnut? Further: in an empty mug, the hole would be air, I can then fill the mug, and the hole is now water according to this account. What makes one thing cease to be the hole and the other suddenly become the hole? This indicates that holes are something over and above whatever stuff occupies them.
Then, could holes be the matter lining or surrounding the hole? After all, for every hole, there is something material surrounding it. A hole in swiss cheese would be cheese since the matter lining the hole is cheese. This again would mean altering the way we speak of holes— the hole-lining is said to “surround” the hole. But evidently, things don’t surround themselves.
This thesis raises further questions. How thick ought the lining of the hole be? A millimetre-thick lining around the hole? The entire mass surrounding it? Somewhere in between those thicknesses? Both (or any other thickness) seem arbitrary. Additionally: do we eat the hole of a doughnut when we eat the dough? Would adding more stuff around the hole mean enlarging the hole?
It seems holes are not reducible to any matter internal or external to them. In fact, saying that holes are reducible to any material thing violates our fundamental intuition about them, that they exist where something is not.
Holes exist immaterially
Must we then bite the proverbial bullet? Must we deny materialism and accept the existence of holes as immaterial objects? But positing this thesis is, too, wrought with problems.
First, how do we perceive holes? We perceive the world through physical data from our senses: green wavelengths of light reflect off grass, enter our eyes, and we perceive that it is green. Airborne molecules from flowers enter our noses, and we perceive that it smells fragrant. The interaction of physical bodies with our sense organs causes our perceptions. But how do we perceive holes if holes are immaterial, non-physical entities?
An immaterial entity should have no power to cause or interact with material things (including our sense organs) since they have no mass, form, location or motion. Something immaterial cannot cause a material event: I can’t move a box by my thought of moving it.
However, it is the case that holes have the power to interact with the world and cause events, as noted at the beginning of this article. We can cause holes to come into being (I can create holes using a hole puncher) and cease to be (I can eat a doughnut and the hole disappears too). Holes cause physical events (the hole in the mug caused my tea to spill all over the floor).
Our perceptions of holes and their seeming ability to affect the world are impossibilities if indeed holes are immaterial objects.
It is worth pointing out that holes aren’t like the immaterial objects whose existence philosophers squabble over — the Platonic Forms, mathematical objects, possible worlds, God, souls — because of those properties that make them closer to material objects: for example, their ability to interact with physical objects, and their spatiotemporal existence (existing within space and time).
Conclusion
Where are we now… we’ve reasoned our way to a dead end. Holes are not reducible to any matter, the thesis that they are immaterial things is untenable, and the thesis that they don’t exist at all can’t be coherently maintained. Holes seem like some unique type of entity somewhere in between the physical and non-physical; having material properties but existing immaterially.
This is still a troubling conclusion for materialists out there; what other bizarre immaterial entities must they postulate next to make sense of the world? And this raises interesting questions: are there different ways of existing?
Further reading
Casati, R., & Varzi, A. (1996, December 5). Holes. Stanford Encyclopedia of
Philosophy. https://plato.stanford.edu/entries/holes/
Lewis, S., & Lewis, D. (1970). Holes. Australasian Journal of Philosophy,
48(2), 206-212. https://doi.org/10.1080/00048407012341181