Achille C. Varzi

Fiat and bona fide boundaries

There is a basic distinction, in the realm of spatial boundaries, between bona fide boundaries on the one hand, and fiat boundaries on the other. The former are just the physical boundaries of old. The latter are exemplified especially by boundaries induced through human demarcation, for example, in the geographic domain. The classical metaphysical problems connected with the notions of adjacency, contact, separation, and division can be resolved in an intuitive way by recognizing this two-sorted ontology of boundaries. Bona fide boundaries yield a notion of contact that is effectively modeled by classical topology; the analogue of contact involving fiat boundaries calls, however, for a different account, based on the intuition that fiat boundaries do not support the open/closed distinction on which classical topology is based. In the presence of this twosorted ontology it then transpires that mereotopology-typology erected on a mereological basis-is more than a trivial formal variant of classical point-set topology.

Fiat and Bona Fide Boundaries: Towards on Ontology of Spatially Extended Objects

Human cognitive acts are directed towards objects extended in space of a wide range of different types. What follows is a new proposal for bringing order into this typological clutter. The theory of spatially extended objects should make room not only for the objects of physics but also for objects at higher levels, including the objects of geography and of related disciplines. It should leave room for different types of boundaries, including both the bona fide boundaries which we find in the physical world and the fiat (or human-demarcation-induced) boundaries with which much of geography has to deal. Two distinct axiomatic theories of boundaries are accordingly presented, and the need for both is examined in some detail. The resultant dual framework is shown to have application above all for our understanding of issues involving contact, division, and separation, issues which have posed serious difficulties for the ontological theories of boundaries that have been proposed hitherto.

Boundaries, Continuity, and Contact

There are conflicting intuitions concerning the status of a boundary separating two adjacent entities (or two parts of the same entity). The boundary cannot belong to both things, for adjacency excludes overlap; and it cannot belong to neither, for nothing lies between two adjacent things. Yet how can the dilemma be avoided without assigning the boundary to one or the other thing at random? Some philosophers regard this as a re- ductio of the very notion of a boundary, which should accordingly be treated a mere facon de parler. In this paper I resist this temptation and examine some ways of taking the puz- zle at face value within a realist perspective—treating boundaries as ontologically on a par with (albeit parasitic upon) voluminous parts.

A note on the transitivity of parthood

That parthood is a transitive relation is among the most basic principles of classical mereology. Alas, it is also very controversial. In a recent paper, Ingvar Johansson has put forward a novel diagnosis of the problem, along with a corresponding solution. The diagnosis is on the right track, I argue, but the solution is misleading. And once the pieces are properly put together, we end up with a reinforcement of the standard defense of transitivity on behalf of classical mereology.

Words and Objects

When we set ourselves to draw up an inventory of the world — a catalogue of all there is, was, and will or could be — we have to face two tasks. First, we have to figure out what sorts of things there are, i.e., we must identify and characterize the categories under which the items in the inventory will fall. For example, we might want to draw a distinction between such things as chairs and tables, on the one hand, and conferences, hurricanes, and stabbings, on the other. And we may wonder what to do when it comes to such things (if such there be) as numbers, jokes, haircuts, smiles, souls, shadows, and so on. The second task is to figure out, for each category, how many different things there are, i.e., how many individual items must be included in that category. Is this chair the same as the chair that was here yesterday? Is it something over and above the mereological fusion of the molecules that constitute it? Am I the same as my body? Is Brutus’s stabbing of Caesar the same event as his killing of Caesar? Is it the same as the assassination of Caesar? Is it the same as the violent assassination of Caesar? And so on.

Reasoning about Space: The Hole Story

Much of our naive reasoning about space involves reasoning about holes and holed objects. We put things in holes, through holes, around them; we jump out of a hole or fall into one; we compare holes, measure them, enlarge them, fill them up.

Perdurantism, Universalism, and Quantifiers

I argue that the conjunction of perdurantism (the view that objects are temporally extended) and universalism (the thesis that any old class of things has a mereological fusion) gives rise to undesired complications when combined with certain plausible assumptions concerning the semantics of tensed statements.

Modes of Connection

In recent years there has been a proliferation of theories for representing space and time in a qualitative way based on a primitive notion of topological connection. In previous work, we have commenced the construction of a unified framework. Independently of any foundational or applicative concerns, we attempt to delineate the space iof mereotopological theories based on an account of their intended models and to place some existing theories into this framework. This paper extends this work by considering a second, orthogonal dimension along which varieties of topological connection can be classified: the strength of the connection.

Inconsistency without Contradiction

1. Genuine worlds, ersatz worlds David Lewis has argued that impossible worlds are nonsense. 1 If there were such worlds, one would have to distinguish between the truths about their contradictory goings-on and contradictory falsehoods about them. One would have to distinguish between, say, the alleged truth (1a) In so-and-so world pigs can fly; and in that world pigs also cannot fly, and the contradictory falsehood (1b) In so-and-so world pigs can fly; and it is not the case that, in that world, pigs can fly. But this—Lewis argues—is preposterous: there is no such distinction to be drawn. (1a) and (1b) are equivalent. Of course, Lewis does distinguish between the following: 2 (2a) In the world of Sherlock Holmes, Watson limps; and in that world Watson also does not limp. (2b) In the world of Sherlock Holmes, Watson limps; and it is not the case that, in that world, Watson limps. (2b) is contradictory. But (2a) is, in a sense, true: there is a discrepancy in Conan Doyles writings. In one of the Holmes stories, Watson limps because

Surrounding Space – The Ontology of Organism-Environment Relations

The history of evolution is a history of development from less to more complex organisms. This growth in complexity of organisms goes hand in hand with a concurrent growth in complexity of environments and of organism-environment relations. It is a concern with this latter aspect of evolutionary development that motivates the present paper. We begin by outlining a theory of organism-environment relations. We then show that the theory can be applied to a range of different sorts of cases, both biological and non-biological, in which objects are lodged or housed within specific environments, or niches. Biological science is interested in types — for example in genotypes, phenotypes, and environment types — and in regularities that can serve as the basis for the formulation of laws or general principles. Types, however, can exist only through their corresponding tokens. Our theory of token environments is meant to plug this gap and to provide a first step towards a general theory of causally relevant spatial volumes.