## 1. Problems



> 
> *'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'.*
> --Ende (1974/1985: 24)
> 




Hole representations--no matter whether veridical--appear to
be commonplace in human cognition. Not only do people have the
impression of seeing holes; they also form a corresponding concept,
which is normally lexicalised as a noun in ordinary languages. (Some
languages even discriminate different types of hole, distinguishing
e.g. between superficial *hollows*, inner *cavities*,
and see-through
*perforations*.) Moreover, data from developmental psychology
and the psychology of perception confirm that infants and adults are
able to perceive, count, and track holes just as easily as they
perceive, count, and track paradigm material objects such as cookies
and tins (Giralt & Bloom 2000; Nelson & Palmer 2001; Horowitz
& Kuzmova 2011). These facts do not prove that holes and material
objects are on equal psychological footing, let alone on equal
metaphysical footing. But they indicate that the concept of a hole is
of significant salience in the common-sense picture of the world,
specifically of the spatiotemporal world.




If holes are entities of a kind, then, they appear to be
spatiotemporal particulars, like cookies and tins and unlike numbers
or moral values. They appear to have a determinate shape, a size, and
a location. ('These things have birthplaces and histories. They
can change, and things can happen to them', Hofstadter &
Dennett 1981: 6-7.) On the other hand, if holes are particulars,
then they are not particulars of the familiar sort. For holes appear
to be *immaterial*: every hole has a material
"host" (the stuff around it, such as the edible part of a
donut) and it may have a material "guest" (such as the
liquid filling a cavity), but the hole itself does not seem to be made of
matter. Indeed, holes seem to be *made of nothing*, if anything
is. And this gives rise to a number of conundrums. For example:


1. It is difficult to explain how holes can in fact be perceived. If
perception is grounded on causation, as Locke urged (*Essay*,
II-viii-6), and if causality has to do with materiality, then
immaterial bodies cannot be the source of any causal flow. So a causal
theory of perception would not apply to holes. Our impression of
perceiving holes would then be a sort of systematic illusion, on pain
of rejecting causal accounts of perception. (On the other hand, if one
accepts that absences can be causally efficacious, as urged by Lewis
2004, then a causal account could maintain that we truly perceive
holes; see Sorensen 2008 and 2015 along with Siegel 2009, Farennikova 2013, 
and Calabi 2019.)
2. It is difficult to specify identity criteria for holes--more
difficult than for ordinary material objects. If holes are immaterial,
we cannot account for the identity of a hole *via* the identity
of any constituting stuff. But neither can we rely on the identity
conditions of the hole's material host, for we can imagine
changing the host--partly or wholly, gradually or
abruptly--without affecting the hole. And we cannot rely on the
identity conditions of its guest, for it would seem that we can empty
a hole of whatever might partially or fully occupy it and leave the
hole intact. (Indeed, both "host" and "guest"
are relative notions. Doesn't their proper application
presuppose that we already know how to identify holes in the first
place? See Meadows 2015.)
3. It is equally difficult to account for the mereology of
holes. Take a card and punch a hole in it. You have made one hole. Now
punch again next to it. Have you made another hole? In a way, yes: now
the card is doubly perforated. But what prevents us from saying that
we still have one hole, though a hole that comes in two disconnected
parts? After all, material objects can be disconnected: a bikini, your
copy of the *Recherche*, a token of the lowercase letter
'i'. Perhaps holes may be disconnected, too? If so,
perhaps we have just punched a single, disconnected hole? (Casati
& Varzi 2004, 2021)
4. It is also difficult to assess the explanatory relevance of holes.
Arguably, whenever a physical interaction can be explained by appeal to
the concept of a hole, a matching explanation can be offered invoking
only material objects and their properties. (That water flowed out of
the bucket is explained by a number of facts about water fluidity,
combined with an accurate account of the physical and geometric
conditions of the bucket.) Aren't these latter explanations
enough?




Further problems arise from the ambiguous status of holes in
figure-ground displays (Bozzi 1975). Thus, for example, though it
appears that the shapes of holes can be recognized by humans as
accurately as the shapes of ordinary objects, the area seen through a
hole typically belongs to the background of its host, and there is
evidence to the effect that background regions are not represented as
having shapes (Bertamini & Croucher 2003; Bertamini & Casati
2015). So what would the shape of a hole be, if any?


## 2. Theories




These difficulties--along with some form of *horror
vacui*--may lead a philosopher to favor ontological parsimony
or revisionism over naive realism about holes. A number of options are
available: 


1. One may hold that holes do not exist at all, arguing that all
truths putatively about holes boil down to truths about holed objects
(Jackson 1977: 132) or, more generally, that all sentences that seem
to imply the existence of holes can be paraphrased by sentences that
lack the implication but could in principle be used for all the same
purposes as the original (van Inwagen 2014). This view calls for a
systematic way of producing the relevant paraphrases. For instance,
the sentence 'There is a hole in the carpet' can be
treated as a mere grammatical variant of 'The carpet is
perforated'; the sentence 'There are three round holes in
that piece of cheese' as a variant of 'That piece of
cheese is triply-roundly-holed', etc. (Challenges: Can every quantification over holes be analyzed this way? Consider: 'There are as many holes in my cheese as crackers on my plate'; Lewis & Lewis 1970: 207. Can a language
be envisaged that contains all the necessary shape predicates? Consider: 'There are two interlocking toroidal cavities in that piece of cheese'; Casati & Varzi 1994: 180. Can
every hole-referring noun-phrase be de-nominalized? Consider:
'The hole in the tooth was smaller than the dentist's
finest probe'; Geach 1968: 12.)
2. One may hold that holes do exist, but they are nothing over and
above the regions of spacetime at which they are found (Wake *et
al.* 2007). Surely they are not just regions of space, for holes can
move, as happens any time you move a donut, whereas regions of space
cannot. But as regions of spacetime, holes can be said to move in
virtue of having different temporal parts follow one another in
different places. (Challenge: Take the doughnut and spin it
clockwise. Take a wedding ring, put it inside the hole in the
doughnut, and spin it the other way. The two holes are spinning
in opposite directions, but the relevant temporal part of the little
hole is a spatiotemporal part of the bigger one. Would it be spinning
in *both* directions? See Lewis & Lewis 1970: 208.)
3. One may hold instead that holes are *qualified* portions of
spacetime (Miller 2007). There would be nothing peculiar about such
portions as opposed to any others that we would not normally think of
as being occupied by ordinary material objects, just as there would be
nothing more problematic, in principle, in determining under what
conditions a certain portion counts as a hole than there is in
determining under what conditions it counts as a dog, a statue, or
whatnot. (Challenge: What if there were truly unqualified portions of
spacetime, in this or some other possible world? Would there be truly
immaterial entities inhabiting such portions, and would holes be among
them?)
4. One might also hold that holes are *ordinary* material
beings: they are neither more nor less than superficial parts of what,
on the naive view, are their material hosts (Lewis & Lewis
1970; Mollica 2022). For every hole there is a hole-lining and for every
hole-lining there is a hole; on this conception, the
hole *is* the hole-lining. (Challenge: This calls for an
account of the altered meaning of certain predicates or
prepositions. Would holes *surround* themselves? Would filling a hole amount to filling space *outside* it? Would expanding the hole-lining
amount to *enlarging* the hole?)
5. Alternatively, one may hold that holes are "negative"
parts of their material hosts (Hoffman & Richards 1985). On this
account, a donut would be a sort of hybrid mereological
aggregate--the mereological sum of a positive pie together with
the negative bit in the middle. (Again, this calls for an account of
the altered meaning of certain modes of speech. For instance, making a
hole would amount to *adding a part*, and changing an object to
get rid of a hole would mean to *remove a part*, contrary to
ordinary usage.)
6. Yet another possibility is to treat holes as
"disturbances" of some sort (Karmo 1977). On this view, a
hole is to be found *in* some object (its "medium")
in the same sense in which a knot may be found in a rope or a wrinkle
in a carpet. (The metaphysical status of such entities, however, calls
for refinements. Simons 1987: 308 suggested construing them as
Husserlian moments that continuously change their fundaments, but this
seems to suit knots and wrinkles better than holes.)
7. Finally, it may be held that holes are not the particulars they
seem to be. Perhaps they are properties, viz. spatial qualities of their owners (O'Shaughnessy 2000: 333), or ways
things are (Meadows 2013), or relational entities whose fundamental
mode of being is being-in (McDaniel 2010). Perhaps holes are
ways the world is, viz. non-abstract, localized absences that can serve as truth-makers for negative existentials or
false-makers for positive existentials (Martin 1996). Or perhaps holes are genuine negative facts, viz. anti-instantiations of material properties by material things: an absence of F-stuff constitutes a hole insofar as it is surrounded by the presence of F-stuff (Barker & Jago 2012).




On the other hand, the possibility remains of taking holes at face
value, which is to say as *bona fide* immaterial particulars. Any such undertaking would have to account, not only for the general
features mentioned in section 1, but also for a
number of additional peculiarities (Casati & Varzi 1994). Among
others:


1. Holes are ontologically parasitic: they are always *in*
something and cannot exist in isolation. ('There is no such
thing as a hole by itself', Tucholsky 1931: 100; 'Take away the thing, and the hole goes too', Heath 1967: 524). This is why there cannot exist a world consisting only of holes (Coggins 2010: 71).
2. Holes are fillable. You don't necessarily destroy a hole by
filling it up (except perhaps when the filling is homogeneous with the hole-lining); you don't create a new hole by removing the
filling.
3. Holes are locationally gracious. When you fill or put something in a hole, the hole does not squeeze to the side; it shares its location with its guest (and if the guest has a hole, you get two co-located entities of the same kind).
4. Holes are mereologically structured. They have parts and can bear
part-whole relations to one another (though not to their hosts and not to their guests).
5. Holes are topologically assorted. Superficial hollows are
distinguished from internal cavities; straight perforations are
distinguished from knotted tunnels.




As is often the case, the choice between all these
alternatives--whether holes are to be subjected to Ockham's
razor, reduced to other entities, or taken at face value--will
depend on one's general metaphysical inclinations (Lewis &
Lewis 1996). It may also depend on controversial details concerning
the nature of space and spacetime, e.g. whether they are relational or
substantival (Braddon-Mitchell & Miller 2015). It is, more
generally, an instance of the sort of decision philosophers have to
make when they scrutinize the ontology inherent in the common-sense
picture of the world and the concepts, words, and purposes through
which it is described and apprehended.