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)

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 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 two-sorted ontology it then transpires that mereotopology—topology erected on a mereological basis—is more than a trivial formal variant of classical point-set topology. (shrink)

Both early analytic philosophy and the branch of mathematics now known as topology were gestated and born in the early part of the 20th century. It is not well recognized that there was early interaction between the communities practicing and developing these fields. We trace the history of how topological ideas entered into analytic philosophy through two migrations, an earlier one conceiving of topology geometrically and a later one conceiving of topology algebraically. This allows us to reassess the influence and (...) significance of topological methods for philosophy, including the possible fruitfulness of a third conception of topology as a structure determining similarity. (shrink)

This paper expands on the theory of event structures put forward in previous work by further investigating the subtle connections between time and events. Specifically, in the first part we generalize the notion of an event structure to that of a refinement structure, where various degrees of temporal granularity are accommodated. In the second part we investigate how these structures can account for the context-dependence of temporal structures in natural language semantics.

Each phenomenon contains variable components, which are conservative. Because of their conservation, they accumulate. Present phenomena contain constituents of phenomena, belonging to the past which form the present and the future, and their dependence on time is an exponential one - S = Sₒe^t-tᵖ. We assume that before and after tₒ = t-tᵖ = 0 the change pertains to phenomena of one type. The dependency is for each defined phenomenon of one and the same type. The concrete aspect of the (...) change S will depend on the type of the phenomenon. We show in our study how in some cosmological phenomena, the exponential dependence on time is present. The processes of radioactive disintegration of atomic nuclei, are also phenomena of this type. We present the real phenomena as a sum of exponents. Each phenomenon originates, develops and is destroyed. In reality most phenomena are formed as a composition of exponential dependencies of the change. (shrink)

The paper outlines a model-theoretic framework for investigating and comparing a variety of mereotopological theories. In the first part we consider different ways of characterizing a mereotopology with respect to (i) the intended interpretation of the connection primitive, and (ii) the composition of the admissible domains of quantification (e.g., whether or not they include boundary elements). The second part extends this study by considering two further dimensions along which different patterns of topological connection can be classified - the strength of (...) the connection and its multiplicity. (shrink)

Of Chisholm’s many signal contributions to analytic metaphysics, perhaps the most important is his treatment of boundaries, a category of entity that has been neglected, to say the least, in the history of ontology. We can gain some preliminary idea of the sorts of problems which the Chisholmian ontology of boundaries is designed to solve, if we consider the following Zeno-inspired thought-experiment.

A critical survey of the main philosophical theories about events and event talk, organized in three main sections: (i) Events and Other Categories (Events vs. Objects; Events vs. Facts; Events vs. Properties; Events vs. Times); (ii) Types of Events (Activities, Accomplishments, Achievements, and States; Static and Dynamic Events; Actions and Bodily Movements; Mental and Physical Events; Negative Events); (iii) Existence, Identity, and Indeterminacy.

A critical review of the main themes arising out of recent literature on the semantics of ordinary event talk. The material is organized in four sections: (i) the nature of events, with emphasis on the opposition between events as particulars and events as universals; (ii) identity and indeterminacy, with emphasis on the unifier/multiplier controversy; (iii) events and logical form, with emphasis on Davidson’s treatment of the form of action sentences; (iv) linguistic applications, with emphasis on issues concerning aspectual phenomena, the (...) telicity/atelicity distinction, the treatment of statives, and temporal quantification. (shrink)

We can see mereology as a theory of parthood and topology as a theory of wholeness. How can these be combined to obtain a unified theory of parts and wholes? This paper examines various non-equivalent ways of pursuing this task, with specific reference to its relevance to spatio-temporal reasoning. In particular, three main strategies are compared: (i) mereology and topology as two independent (though mutually related) chapters; (ii) mereology as a general theory subsuming topology; (iii) topology as a general theory (...) subsuming mereology. Some more speculative strategies and directions for further research are also considered. (shrink)

A critical survey of the fundamental philosophical issues in the logic and formal ontology of space, with special emphasis on the interplay between mereology (the theory of parthood relations), topology (broadly understood as a theory of qualitative spatial relations such as continuity and contiguity), and the theory of spatial location proper.

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.