Online research in philosophy

What are the relationships between an entity and the space at which it is located? And between a region of space and the events that take place there? What is the metaphysical structure of localization? What its modal status? This paper addresses some of these questions in an attempt to work out at least the main coordinates of the logical structure of localization. Our task is mostly taxonomic. But we also highlight some of the underlying structural features and we single out the interactions between the notion of localization and nearby notions, such as the notions of part and whole, or of necessity and possibility. A theory of localization--we argue--is needed in order to account for the basic relations between objects and space, and runs afoul a pure part-whole theory. We also provide an axiomatization of the relation of localization and examine cases of localization involving entities different from material objects.

A region-based model of physical space is one in which the primitive spatial entities are regions, rather than points, and in which the primitive spatial relations take regions, rather than points, as their relata. Historically, the most intensively investigated region-based models are those whose primitive relations are topological in character; and the study of the topology of physical space from a region-based perspective has come to be called mereotopology. This paper concentrates on a mereotopological formalism originally introduced by Whitehead, which employs a single primitive binary relation C(x,y) (read: x is in contact with y). Thus, in this formalism, all topological facts supervene on facts about contact. Because of its potential application to theories of qualitative spatial reasoning, Whitehead's primitive has recently been the subject of scrutiny from within the Artificial Intelligence community. Various results regarding the mereotopology of the Euclidean plane have been obtained, settling such issues as expressive power, axiomatization and the existence of alternative models. The contribution of the present paper is to extend some of these results to the mereotopology of three-dimensional Euclidean space. Specifically, we show that, in a first-order setting where variables range over tame subsets of R 3, Whitehead's primitive is maximally expressive for topological relations; and we deduce a corollary constraining the possible region-based models of the space we inhabit.

Through an analysis of conditions under which the question of spatial anisotropy can be raised, the present paper brings out intimate conceptual relationships between the scientific concept of space and the concepts of entities, behavior, and explanation specified by scientific theories. Thus scientific departures from ordinary usage (or from usage in other scientific theories) of the term "space" entail corresponding shifts in the use of other terms not generally seen to be connected. As a case study of the relations between these terms, and of the refusal to allow the possibility of spatial anisotropy, Newtonian mechanics is examined.

Ordinary reasoning about space--we argue--is first and foremost reasoning about things or events located in space. Accordingly, any theory concerned with the construction of a general model of our spatial competence must be grounded on a general account of the sort of entities that may enter into the scope of the theory. Moreover, on the methodological side the emphasis on spatial entities (as opposed to purely geometrical items such as points or regions) calls for a reexamination of the conceptual categories required for this task. Here we offer some examples of what this amounts to, of the difficulties involved, and of the main directions along which spatial theories should be developed so as to combine formal sophistication with some affinity with common sense.

Think of “locations” very abstractly, as positions in a space, any space. Temporal locations are positions in time; spatial locations are positions in (physical) space; particulars are locations in quality space. Should we reify locations? Are locations entities? Spatiotemporal relation- alists say there are no such things as spatiotemporal locations; the fundamental spatial and temporal facts involve no locations as objects, only the instantiation of spatial and temporal relations. The denial of locations in quality space is the bundle theory, according to which particulars do not exist; facts apparently about particulars really concern relations between universals. A “space”, in our abstract sense, consists of a set of objects, together with properties and relations defined on those objects. The objects are the locations of the space, and the distribution of the properties and relations over the locations defines the space’s structure. All spaces are thus quality spaces; when the relations are thought of as spatiotemporal then the space is also a spatiotemporal space. By not reifying locations one denies that these abstract spaces isomorphically represent the real world. The real world does in some sense have a structure that can be non-isomorphically represented by a space (or, more likely, a class of spaces), but the locations in those spaces do not correspond to anything real. We will examine modal considerations on reifying locations. Denying the existence of spatiotemporal locations excludes certain possibilities for spatiotemporal reality. Denying the existence of qualitative locations excludes certain possibilities for qualitative space. In each case the excluded possibilities are pre-analytically possible. Some of the possibilities can be reinstated by modifying the locationless theories, but at the cost of an unattractive holism. Do these modal considerations mandate postulating locations? That depends on whether modal intuition can teach us about the actual world..

Here are two ways space might be (not the only two): (1) Space is “pointy”. Every finite region has infinitely many infinitesimal, indivisible parts, called points. Points are zero-dimensional atoms of space. In addition to points, there are other kinds of “thin” boundary regions, like surfaces of spheres. Some regions include their boundaries—the closed regions—others exclude them—the open regions—and others include some bits of boundary and exclude others. Moreover, space includes unextended regions whose size is zero. (2) Space is “gunky”.1 Every region contains still smaller regions—there are no spatial atoms. Every region is “thick”—there are no boundary regions. Every region is extended. Pointy theories of space and space-time—such as Euclidean space or Minkowski space—are the kind that figure in modern physics. A rival tradition, most famously associated in the last century with A. N. Whitehead, instead embraces gunk.2 On the Whiteheadian view, points, curves and surfaces are not parts of space, but rather abstractions from the true regions. Three different motivations push philosophers toward gunky space. The first is that the physical space (or space-time) of our universe might be gunky. We posit spatial reasons to explain what goes on with physical objects; thus the main reason..

I discuss the relations between God and spatial entities, such as the universe. An example of a relation between God and a spatial entity is the relation,causes. Such relations are, in D.M. Armstrong’s words, ‘realm crossing’ relations: relations between or among spatial entities and entities in the realm of the spatially unlocated. I discuss an apparent problem with such realm crossing relations. If this problem is serious enough, as I will argue it is, it implies that God cannot be the creator of the universe I also discuss that if God cannot be the creator of the universe, then God does not exist.

Common-sense reasoning about space is, first and foremost, reasoning about things located in space. The fly is inside the glass; hence the glass is not inside the fly. The book is on the table; hence the table is under the book. Sometimes we may be talking about things going on in certain places: the concert took place in the garden; then dinner was served in the solarium. Even when we talk about “naked” (empty) regions of space—regions that are not occupied by any macroscopic object and where nothing noticeable seems to be going on—we tipically do so because we are planning to move things around, or because we are thinking that certain actions or events did or should take place in certain sites as opposed to others. The sofa should go right here; the aircraft crashed right there. Spatial reasoning, whether actual or hypothetical, is typically reasoning about spatial entities of some sort. One might—and some people do—take this as a fundamental claim, meaning that spatial entities such as objects or events are fundamentally (cognitively, or perhaps even metaphysically) prior to space: there is no way to identify a region of space except by reference to what is or could be located or take place at that region. (This was, for instance, the gist of Leibniz’ contention against the Newtonian view that space is an individual entity in its own right, independently of whatever entities may inhabit it.) It is, however, even more interesting to see how far we can go in our understand-.

Standard theories in mereotopology focus on relations of parthood and connection among spatial or spatio-temporal regions. Objects or processes which might be located in such regions are not normally directly treated in such theories. At best, they are simulated via appeal to distributions of attributes across the regions occupied or by functions from times to regions. The present paper offers a richer framework, in which it is possible to represent directly the relations between entities of various types at different levels, including both objects and the regions they occupy. What results is a layered mereotopology, a theory which can handle multiple layers (analogous to the layers of a lasagna) of spatially or spatiotemporally coincident but mereologically non-overlapping entities. Keywords: Ontology, mereology, mereotopology, qualitative spatial reasoning, map layers, dynamic GIS..

I argue that relations between non-collocated spatial entities, between non-identical topological spaces, and between non-identical basic building blocks of space, do not exist. If any spatially located entities are not at the same spatial location, or if any topological spaces or basic building blocks of space are non-identical, I will argue that there are no relations between or among them. The arguments I present are arguments that I have not seen in the literature.