By a `denoting phrase' I mean a phrase such as any one of the following: a man, some man, any man, every man, all men, the present King of England, the present King of France, the center of mass of the solar system at the first instant of the twentieth century, the revolution of the earth round the sun, the revolution of the sun round the earth. Thus a phrase is denoting solely in virtue of its form. We may distinguish (...) three cases: (1) A phrase may be denoting, and yet not denote anything; e.g., `the present King of France'. (2) A phrase may denote one definite object; e.g., `the present King of England' denotes a certain man. (3) A phrase may denote ambiguously; e.g. `a man' denotes not many men, but an ambiguous man. The interpretation of such phrases is a matter of considerably difficulty; indeed, it is very hard to frame any theory not susceptible of formal refutation. All the difficulties with which I am acquainted are met, so far as I can discover, by the theory which I am about to explain. (shrink)

By a `denoting phrase' I mean a phrase such as any one of the following: a man, some man, any man, every man, all men, the present King of England, the present King of France, the center of mass of the solar system at the first instant of the twentieth century, the revolution of the earth round the sun, the revolution of the sun round the earth. Thus a phrase is denoting solely in virtue of its form. We may distinguish (...) three cases: (1) A phrase may be denoting, and yet not denote anything; e.g., `the present King of France'. (2) A phrase may denote one definite object; e.g., `the present King of England' denotes a certain man. (3) A phrase may denote ambiguously; e.g. `a man' denotes not many men, but an ambiguous man. The interpretation of such phrases is a matter of considerably difficulty; indeed, it is very hard to frame any theory not susceptible of formal refutation. All the difficulties with which I am acquainted are met, so far as I can discover, by the theory which I am about to explain. (shrink)

_'Philosophy, from the earliest times, has made greater claims, and acheived fewer results than any other branch of learning... I believe that the time has now arrived when this unsatisfactory state of affairs can be brought to an end'_ - _Bertrand Russell_ So begins _Our Knowledge of the Eternal World_, Bertrand Russell's classic attempt to show by means of examples, the nature, capacity and limitations of the logico-analytical method in philosophy.

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)

Alfred North Whitehead was a prominent English mathematician and philosopher who co-authored the highly influential Principia Mathematica with Bertrand Russell. Originally published in 1919, and first republished in 1925 as this Second Edition, An Enquiry Concerning the Principles of Natural Knowledge ranks among Whitehead's most important works; forming a perspective on scientific observation that incorporated a complex view of experience, rather than prioritising the position of 'pure' sense data. Alongside companion volumes The Concept of Nature and The Principle of Relativity, (...) it created a framework for Whitehead's later metaphysical speculations. This is an important book that will be of value to anyone with an interest in the relationship between science and philosophy. (shrink)

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 thing or the other at random? Some philosophers regard this as a reductio of the very notion of a boundary, which should accordingly (...) be treated a mere façon de parler. In this paper I resist this temptation and examine some ways of taking the puzzle at face value within a realist perspective—treating boundaries as ontologically on a par with (albeit parasitic upon) extended parts. (shrink)

A taxonomy of part‐whole or meronymic relations is developed to explain the ordinary English‐speaker's use of the term “part of” and its cognates. The resulting classification yields six types of meronymic relations: 1. component‐integral object (pedal‐bike), 2. member‐collection (ship‐fleet), 3. portion‐mass (slice‐pie), 4. stuff‐object (steel‐car), 5. feature‐activity (paying‐shopping), and 6. place‐area (Everglades‐Florida). Meronymic relations ore further distinguished from other inclusion relations, such as spatial inclusion, and class inclusion, and from several other semantic relations: attribution, attachment, and ownership. This taxonomy is (...) then used to explain cases of apparent intransitivity in merological syllogisms, and standard form syllogisms whose premises express different inclusion relations. The data suggest that intransitivities arise due to equivocations between different types of semantic relations. These results are then explained by means of the relation element theory which accounts for the character and behavior of semantic relations in terms of more primitive relational elements. The inferential phenomena observed are then explained by means of a single principle of element matching. (shrink)

I shall attempt in what follows to show how mereology, taken together with certain topological notions, can yield the basis for future investigations in formal ontology. I shall attempt to show also how the mereological framework here advanced can allow the direct and natural formulation of a series of theses – for example pertaining to the concept of boundary – which can be formulated only indirectly (if at all) in set-theoretic terms.

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. (shrink)

Whitehead, in his famous book "Process and Reality", proposed a definition of point assuming the concepts of “region” and “connection relation” as primitive. Several years after and independently Grzegorczyk, in a brief but very interesting paper proposed another definition of point in a system in which the inclusion relation and the relation of being separated were assumed as primitive. In this paper we compare their definitions and we show that, under rather natural assumptions, they coincide.

A logic of intervals is proposed akin to the one published by Hamblin (Hamblin (1969) and (1971)). Like Hamblin's, the present system is also based on a single primitive. However, the work presented here differs from Hamblin's in a number of respects. Most importantly, the present system is explicitly based on mereological ideas in such a way that not only are the two notions of abutment and temporal order involved in Hamblin's primitive two-place relation "abuts at the earlier end" distinguished (...) ; the temporal ordering itself is built up from a symmetric mereological primitive. The present system is shown to be complete. (shrink)

We are used to regarding actions and other events, such as Brutus’ stabbing of Caesar or the sinking of the Titanic, as occupying intervals of some underlying linearly ordered temporal dimension. This attitude is so natural and compelling that one is tempted to disregard the obvious difference between time periods and actual happenings in favor of the former: events become mere “intervals cum description”.1 On the other hand, in ordinary circumstances the point of talking about time is to talk about (...) what actually happens or might happen at some time or another. We talk about ‘now’ and ‘then’ in an effort to put some order in our description of what goes on. And since different events seem to overlap in so many different ways, a full account of their temporal relations seems to run afoul of a reductionist strategy. This raises two philosophical questions. The first is whether we can actually go beyond time, as it were, i.e., whether we can take events as bona fide entities and deal with them directly, just as we can deal with spatial entities such as physical bodies or masses without confining ourselves to their spatial representations. This is a controversial issue (though probably not as controversial as it used to be), and ties in with a number of unsettled problems concerning, e.g., the structure of causality or the definition of adequate identity and individuation criteria for events. 2 The second question is whether we can perhaps do without time, i.e., whether we can dispense with time points or intervals as an independent ontological category and focus only on actual or potential happenings, in opposition to the form of reductionism mentioned above—in short, whether we can account for the temporal dimension in terms of suitable relations among events. This is also a highly controversial issue, and relates to the classical dispute concerning relational vs. absolutist conceptions of (space and) time.3 It is this second question that we intend to focus on here.. (shrink)

The perception of spatial bodies is at least in part a perception of bodily boundaries or surfaces. The usual mathematical conception of boundaries as abstract constructions is, however, of little use for cognitive science purposes. The essay therefore seeks a more adequate conception of the ontology of boundaries building on ideas in Aristotle and Brentano on what we may call the coincidence of boundaries. It presents a formal theory of boundaries and of the continua to which they belong, of a (...) sort which allows a resolution of certain Zeno-style paradoxes. The theory proves to be applicable not only in the cognitive science field but also in regard to problems relating to the ontology of geographical and geopolitical boundaries. (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.