Holes

In this paper I take up the task, begun by Lewis and Lewis in their seminal paper on the topic, of offering a theory of holes according to which a hole is simply its hole-lining. I begin by motivating the theory, arguing that it holds interest even absent its original animating concerns of nominalism and materialism, and present desiderata any such theory must satisfy. With this in place, I offer a definition both of a lining and of hole sameness, arguing (...) that these can overcome the most prominent standing objections to identifying holes with linings. Finally, I present a more powerful counterargument in the spirit of Casati and Varzi, and conclude with an emended version of the theory meeting all our earlier desiderata. I conclude by dispelling some possible worries about the nominalist and materialist credentials of my theory. (shrink)

The following argument is widely assumed to be invalid: there is a pain in my finger; my finger is in my mouth; therefore, there is a pain in my mouth. The apparent invalidity of this argument has recently been used to motivate the conclusion that pains are not spatial entities. We argue that this is a mistake. We do so by drawing attention to the metaphysics of pains and holes and provide a framework for their location which both vindicates the (...) argument's validity and explains why it appears invalid. To this end, we show that previously proposed explanations for the apparent invalidity of the argument fail. Moreover, we show that our account accommodates and explains seemingly opposing linguistic data. We conclude that the ‘pain-in-mouth argument’ does not undermine the view that pains are spatial entities. (shrink)

The U.S. presidential election of 2000 was crucially decided in Florida. And, in Florida, the election hinged crucially on a peculiar sort of question: Does this ballot have a hole? “Yes, it does”, so the ballot is valid and ought to be counted. “No it doesn’t”, and the ballot must be discarded. If only one could tell! Where were the hole experts when we needed them? Eventually the matter was thwarted by the Supreme Court and we all gave up. But (...) we did learn something. We learned that even the destiny of a Presidential Election, if not more, might ultimately depend on one’s criteria for identifying holes—not their material surroundings, which everyone could detect, but the holes themselves. (shrink)

A new type of impossible picture is presented and described. The picture involves an object along with its reflection in a plane mirror, delivering two apparently irreconcilable views of the object itself when seen simultaneously in its flesh and in the mirror. Contrary to other, more familiar impossible pictures, its interpretation requires explicit reasoning about the represented reality. It is a slow impossible picture.

A brief introduction to the main philosophical problems and theories about the nature of holes and such-like nothingnesses.

This paper discusses attributively limited concrete objects such as disturbances (holes, folds, scratches etc), tropes, and attitudinal objects, which lack the sort of spatial location or part structures expected of them as concrete objects. The paper proposes an account in terms of (quasi-Fregean) abstraction, which has so far been applied only to abstract objects.

There is no doughnut without a hole, the saying goes. And that’s true. If you think you can come up with an exception, it simply wouldn’t be a doughnut. Holeless doughnuts are like extensionless color, or durationless sound—nonsense. Does it follow, then, that when we buy a doughnut we really purchase two sorts of thing—the edible stuff plus the little chunk of void in the middle? Surely we cannot just take the doughnut and leave the hole at the grocery store, (...) as we cannot just eat the doughnut and save the hole for later. But then, again, surely when we eat a doughnut we do not also eat the hole. Or do we? (shrink)

Metaphysics is largely an a priori business, albeit a business that is sensitive to the findings of the physical sciences. But sometimes what the physical sciences tell us about our own world underdetermines what we should think about the metaphysics of how things actually are, and even how they could be. This chapter has two aims. The first is to defend a particular conception of the methodology of a priori metaphysics by, in part, exemplifying that methodology and revealing its results. (...) The second is to present a new account of holes. These two aims dovetail nicely. We are independently interested in providing a better analysis of the concept <hole> that yields a more plausible metaphysical story about holes. But focusing on holes is also a good way to explore the methodology we endorse: for this is an area of metaphysics that is sufficiently self-contained and narrow in focus that it provides a manageable case study, while at the same time raising interesting and deep issues about the nature of space. Ultimately we defend a new, functionalist, analysis of holes, which, unlike its rivals, neither misidentifies nor renders us implausibly eliminativist about holes under various different metaphysical suppositions about the nature of space. In the process, we set out the complex relations between the intension of “hole,” and its extension at various worlds under different suppositions about the nature of space. In explicating these relations our account exemplifies what we take to be the core methodology in a priori metaphysics. (shrink)

In this paper I argue that the theory that holes are immaterial objects faces an objection that has traditionally been thought to be the principal difficulty with its main rival, which construes holes as material parts of material objects. Consequently, one of the principal advantages of identifying holes with immaterial objects is illusory: its apparent ease of accounting for truths about number of holes. I argue that in spite of this we should not think of holes as material parts of (...) material objects. This is because the theory that holes are properties does not face the same difficulties as either of these theories that construe holes as objects of some sort. (shrink)

Here, we clarify the relationship among three space-time conditions of interest: geodesic completeness, hole-freeness, and inextendibility. In addition, we introduce a related fourth condition: effective completeness.

Let’s start with compositional pluralism. Elsewhere I’ve defended compositional pluralism, which we can provisionally understand as the doctrine that there is more than one basic parthood relation. (You might wonder what I mean by “basic”. We’ll discuss this in a bit.) On the metaphysics I currently favor, there are regions of spacetime and material objects, each of which enjoy bear a distinct parthood relation to members of their own kind. Perhaps there are other kinds of objects that enjoy a kind (...) of parthood relation other than the ones enjoyed by material objects and regions of spacetime. Perhaps, for example, there are facts; I’ve been wavering over whether to embrace these entities for years now. However, I’m reasonably confident that if there are facts than the kind of parthood relation that facts bear to that which composes them is not the kind of parthood relation enjoyed by material objects or regions of spacetime. More on why I am reasonably confident later. (shrink)

In this engaging and wide-ranging new book, Nikk Effingham provides an introduction to contemporary ontology - the study of what exists - and its importance for philosophy today. He covers the key topics in the field, from the ontology of holes, numbers and possible worlds, to space, time and the ontology of material objects - for instance, whether there are composite objects such as tables, chairs or even you and me. While starting from the basics, every chapter is up-to-date with (...) the most recent developments in the field, introducing both longstanding theories and cutting-edge advances. As well as discussing the latest issues in ontology, Effingham also helpfully deals in-depth with different methodological principles and introduces them alongside an example ontological theory that puts them into practice. This accessible and comprehensive introduction will be essential reading for upper-level undergraduate and post-graduate students, as well as any reader interested in the present state of the subject. (shrink)

Slot theory is the view that (i) there exist such entities as argument places, or ‘slots’, in universals, and that (ii) a universal u is n-adic if and only if there are n slots in u. I argue that those who take properties and relations to be abundant, fine-grained, non-set-theoretical entities face pressure to be slot theorists. I note that slots permit a natural account of the notion of adicy. I then consider a series of ‘slot-free’ accounts of that notion (...) and argue that each of them has significant drawbacks. (shrink)

In this paper I argue that holes are not objects, but should instead be construed as properties or relations. The argument proceeds by first establishing a claim about angles: that angles are not objects, but properties or relations. It is then argued that holes and angles belong to the same category, on the grounds that they share distinctive existence and identity conditions. This provides an argument in favour of categorizing holes as one categorizes angles. I then argue that a commitment (...) to the existence of properties to be identified with holes provides sufficient resources to account for true claims about holes. (shrink)

Firstly I define a hole as a dependent matter-less endurant, which is a little modification of Casati and Varzi’s definition. Adopting this definition, holes seem to invite three problems about causation: (1)causal closure, (2)ungrounded disposition and (3)causal overdetermination. I will defend my definition against all these problems by showing that holes are limiting cases of physical endurants rather than their opposition and that they have causal powers in a broad sense.

Minor entities provide an interesting testbed for metaphysical theories, but also for investigating the structure of concepts, as their concepts appear to be tributary of different representational systems.

This issue of The Monist is devoted to the metaphysics of lesser kinds, which is to say those kinds of entity that are not generally recognized as occupying a prominent position in the categorial structure of the world. Why bother? We offer two sorts of reason. The first is methodological. In mathematics, it is common practice to study certain functions (for instance) by considering limit cases: What if x = 0? What if x is larger than any assigned value? Physics, (...) too, often studies the (idealized) initial and boundary conditions of a given system: What would happen in the case of a perfect sphere, or a perfectly black body? In the cognitive sciences, research often thrives on the analysis of cognitive errors, perceptual illusions, brain pathologies. Also in logic one can learn a lot by studying special, anomalous scenarios such as those exhibited by the paradoxes: it is unlikely that we actually find ourselves in a soritical context, or in a liar-like situation, but the fact that we might—or simply the fact that we can conceive of such a possibility—is important enough to deserve careful consideration. In short, the odd, the unfamiliar, the extra-ordinary, the limit cases are perfectly at home in scientific and more broadly intellectual discourse at various levels, where they can be fruitfully engaged in a sophisticated way (witness the existence of specific confining and managing strategies for dealing with them); and they are important precisely because they instruct us concerning the normal, the obvious, and the paradigmatic. The same goes for metaphysics, we submit. Although its major concern is, naturally, with such core entities as substances, properties, or hunks of solid matter, a lot may be learned by paying attention to those limit cases where we find ourselves dealing with entities of much lesser kinds, whether real or putative. (shrink)

This paper defends a view that falls somewhere between the two extremes of inflationary and deflationary accounts of holes, and it does so by rejecting the initial conceptualisation of holes in terms of absences. Once we move away from this conception, I argue, we can see that there are no special metaphysical problems associated with holes. Rather, whatever one’s preferred metaphysics of paradigm material objects, that account can equally be applied to holes. This means that like the deflationist, I am (...) entity monist: I reject the idea that there are any immaterial beings. On the other hand, like the inflationist I reject the idea that we should identify holes with parts or surfaces of paradigm objects. Like the inflationist, I hold that there exist entities in roughly the regions of space-time where pre-theoretically we would say there exist holes, and those entities are holes. Call this latter part of the view—that where the folk are apt to claim there is a hole, that hole has roughly the dimensions that the folk attribute to it—hole-instinctivism (the view that our instincts about hole location/dimension are roughly right). Ultimately I embrace hole conventionalism, a view that includes commitment to both entity monism and hole-instinctivism. According to hole conventionalism, holes are no more ontologically problematic than statues, nor are they of a fundamentally different ontological kind from statues. (shrink)

This paper defends a view that falls somewhere between the two extremes of inflationary and deflationary accounts, and it does so by rejecting the initial conceptualisation of holes in terms of absences. Once we move away from this conception, I argue, we can see that there are no special metaphysical problems associated with holes. Rather, whatever one’s preferred metaphysics of paradigm material objects, that account can equally be applied to holes. This means that like the deflationist, I am entity monist: (...) I reject the idea that there are any immaterial beings. On the other hand, like the inflationist I reject the idea that we should identify holes with parts or surfaces of paradigm objects. Like the inflationist, I hold that there exist entities in roughly the regions of space-time where pre-theoretically we would say there exist holes, and those entities are holes. Call this latter part of the view—that where the folk are apt to claim there is a hole, that hole has roughly the dimensions that the folk attribute to it—hole-instinctivism (the view that our instincts about hole location/dimension are roughly right). Ultimately I embrace hole conventionalism, a view that includes commitment to both entity monism and hole-instinctivism. According to hole conventionalism, holes are no more ontologically problematic than statues, nor are they of a fundamentally different ontological kind from statues. (shrink)

We discuss the view that a hole is identical to the region of spacetime at which it is located. This view is more parsimonious than the view that holes are sui generus entities located at those regions surrounded by their hosts and it is more plausible than the view that there are no holes. We defend the spacetime view from several objections.

Argle claimed that holes supervene on their material hosts, and that every truth about holes boils down to a truth about perforated things. This may well be right, assuming holes are perforations. But we still need an explicit theory of holes to do justice to the ordinary way of counting holes--or so says Cargle.

In classical topology the only part of a doughnut that matters is the edible part. Here I review some good reasons for reversing the order and focusing on the hole instead. By studying the topology of the hole one can learn interesting things about the morphology of the doughnut (its shape), and by studying the morphology of the hole in turn one can learn a lot about the doughnut’s dynamic properties (its patterns of interaction with the environment). The price--of course--is (...) that one must be serious about reifying voids. (shrink)

Considering topology as an extension of mereology, this paper analyses topological variants of mereological essentialism (the thesis that an object could not have different parts than the ones it has). In particular, we examine de dicto and de re versions of two theses: (i) that an object cannot change its external connections (e.g., adjacent objects cannot be separated), and (ii) that an object cannot change its topological genus (e.g., a doughnut cannot turn into a sphere). Stronger forms of structural essentialism, (...) such as morphological essentialism (an object cannot change shape) and locative essentialism (an object cannot change position) are also examined. (shrink)

The methodological anarchy that characterizes much recent research in artificial intelligence and other cognitive sciences has brought into existence (sometimes resumed) a large variety of entities from a correspondingly large variety of (sometimes dubious) ontological categories. Recent work in spatial representation and reasoning is particularly indicative of this trend. Our aim in this paper is to suggest some ways of reconciling such a luxurious proliferation of entities with the sheer sobriety of good philosophy.

Italian translation of "Holes and Other Superficialities" (1994).

Argle. I’ve said it before and I’ll say it again: all things are material. Either holes are somehow material, or else there are no such things. Maybe a hole is the material hole-lining that, as we so misleadingly say, “surrounds” the hole; or else whatever ostensible reference we make to holes is secretly some other sort of language-game altogether, or it’s fictitious reference, or it’s just plain mistaken.

This is a revised and extended version of the formal theory of holes outlined in the Appendix to the book "Holes and Other Superficialities". The first part summarizes the basic framework (ontology, mereology, topology, morphology). The second part emphasizes its relevance to spatial reasoning and to the semantics of spatial prepositions in natural language. In particular, I discuss the semantics of ‘in’ and provide an account of such fallacious arguments as “There is a hole in the sheet. The sheet is (...) in the drawer. Ergo *there is a hole in the drawer”. (shrink)

Holes are a good example of the sort of entity that down-to-earth philosophers would be inclined to expel from their ontological inventory. In this work we argue instead in favor of their existence and explore the consequences of this liberality—odd as they might appear. We examine the ontology of holes, their geometry, their part-whole relations, their identity and their causal role, the ways we perceive them. We distinguish three basic kinds of holes: blind hollows, perforating tunnels, and internal cavities, treating (...) these uniformly as immaterial bodies. We develop a morphology of holes, focusing on the way a hole can be filled, and then look at the main properties of the resulting conceptual framework: holes are parasitic upon the surfaces of their hosts; holes can move, fuse into each other, split; they can be born, develop, and die. Finally, we examine how some morphological features of holes are represented in perception, including the conditions whereby we have the impression that we see, feel, or even hear a hole. The book has over 150 pictures and is completed by a formal appendix, a section with puzzles and exercises, and a extensive annotated bibliography. (shrink)