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Boundaries: An essay in mereotopology

In Lewis H. Hahn (ed.), Philosophy of Roderick Chisholm (Library of Living Philosophers). Open Court. pp. 534--561 (1997)

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  1. Boundaries and Things. A Metaphysical Study of the Brentano-Chisholm Theory.Gonzalo Nuñez Erices - 2019 - Kriterion: Journal of Philosophy 33 (2):15-48.
    The fact that boundaries are ontologically dependent entities is agreed by Franz Brentano and Roderick Chisholm. This article studies both authors as a single metaphysical account about boundaries. The Brentano-Chisholm theory understands that boundaries and the objects to which they belong hold a mutual relationship of ontological dependence: the existence of a boundary depends upon a continuum of higher spatial dimensionality, but also is a conditio sine qua non for the existence of a continuum. Although the view that ordinary material (...)
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  • Fiat and Bona Fide Boundaries.Barry Smith & Achille C. Varzi - 2000 - Philosophy and Phenomenological Research 60 (2):401-420.
    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 (...)
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  • The Formal Structure of Ecological Contexts.Barry Smith & Achille C. Varzi - 1999 - In Paolo Bouquet, Patrick Brezillon, Francesca Castellani & Luciano Serafini (eds.), Modeling and Using Context. Proceedings of the Second International and Interdisciplinary Conference. Springer. pp. 339–350.
    This is an informal presentation of the theory of niches understood as ecological contexts. The first part sets out the basic conceptual background. The second part outlines the main principles of the theory and addresses the question of how the theory can be extended to aid our thinking in relation to the special types of causal integrity that characterize niches and niched entities.
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  • Mereotopology: A Theory of Parts and Boundaries.Barry Smith - 1996 - Data and Knowledge Engineering 20 (3):287–303.
    The paper is a contribution to formal ontology. It seeks to use topological means in order to derive ontological laws pertaining to the boundaries and interiors of wholes, to relations of contact and connectedness, to the concepts of surface, point, neighbourhood, and so on. The basis of the theory is mereology, the formal theory of part and whole, a theory which is shown to have a number of advantages, for ontological purposes, over standard treatments of topology in set-theoretic terms. One (...)
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  • Boundaries: A Brentanian Theory.Barry Smith - 2000 - Brentano Studien 8:107-114.
    According to Brentano's theory of boundaries, no boundary can exist without being connected with a continuum. But there is no specifiable part of the continuum, and no point, which is such that we may say that it is the existence of that part or of that point which conditions the boundary. - An adequate theory of the continuum must now recognize that boundaries be boundaries only in certain directions and not in others. This leads to consequences in other areas, too.
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  • The Cornucopia of Formal-Ontological Relations.Barry Smith & Pierre Grenon - 2004 - Dialectica 58 (3):279–296.
    The paper presents a new method for generating typologies of formal-ontological relations. The guiding idea is that formal relations are those sorts of relations which hold between entities which are constituents of distinct ontologies. We provide examples of ontologies (in the spirit of Zemach’s classic “Four Ontologies” of 1970), and show how these can be used to give a rich typology of formal relations in a way which also throws light on the opposition between threeand four-dimensionalism.
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  • Confini. Dove finisce una cosa e inizia un’altra.Achille C. Varzi - 2007 - In Andrea Bottani & Richard Davies (eds.), Ontologie regionali. Mimesis. pp. 209–222.
    Ci imbattiamo in un confine ogni volta che pensiamo a un’entità demarcata rispetto a ciò che la circonda. C’è un confine (una superficie) che delimita l’interno di una sfera dal suo esterno; c’è un confine (una frontiera) che separa il Maryland dalla Pennsylvania. Talvolta la collocazione esatta di un confine non è chiara o è in qualche modo controversa (come quando si cerchi di tracciare i limiti del monte Everest, o il confine del nostro corpo). Talaltra il confine non corrisponde (...)
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  • Fiat Objects.Barry Smith - 2001 - Topoi 20 (2):131-148.
    Human cognitive acts are directed towards entities of a wide range of different types. What follows is a new proposal for bringing order into this typological clutter. A categorial scheme for the objects of human cognition should be (1) critical and realistic. Cognitive subjects are liable to error, even to systematic error of the sort that is manifested by believers in the Pantheon of Olympian gods. Thus not all putative object-directed acts should be recognized as having objects of their own. (...)
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  • Kognitionsforskningens topologiske grundlag.Barry Smith - 2003 - Semikolon 3 (7):91-105.
    The paper introduces the concepts at the heart of point-set-topology and of mereotopology (topology founded in the non-atomistic theory of parts and wholes) in an informal and intuitive fashion. It will then seek to demonstrate how mereotopological ideas can be of particular utility in cognitive science applications. The prehistory of such applications (in the work of Husserl, the Gestaltists, of Kurt Lewin and of J. J. Gibson) will be sketched, together with an indication of the field of possibilities in linguistics, (...)
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  • La Possibilité de Contact.Olivier Massin - 2008 - Swiss Philosophical Preprints.
    Deux choses sont en contact s'il n'y a rien entre elles (ni volume, ni ligne, ni point) et qu'elles ne se chevauchent pas (en un volume, un ligne ou un point). Le contact est la limite de proximité des choses : si deux choses sont en contact, deux autres choses ne peuvent être pas être plus près l'une de l'autre sans se pénétrer.
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  • Métaphysique et Ontologie.Kevin Mulligan - 2009 - Swiss Philosophical Preprints.
    Les mots « métaphysique » et « ontologie » se disent de façons multiples à l’intérieur de la philosophie analytique et ailleurs dans la philosophie du vingtième siècle. Ils sont souvent employés pour parler de la théorie ou l’analyse de ce qu’il y a, des espèces principales de ce qu’il y a et de leurs rapports. Mais les positivistes viennois, par exemple, appelaient « métaphysiques » les philosophies qu’ils n’aimaient pas (Carnap 1985, Campbell 1976 ch. 2)1. Et si Quine parle (...)
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  • Metafisica e ontologia.Kevin Mulligan - 2009 - Swiss Philosophical Preprints.
    Le parole “metafisica” e “ontologia” si dicono in molti modi diversi nella filosofia del XX secolo, tanto all’interno della filosofia analitica quanto altrove. Sono spesso usate per parlare della teoria o dell’analisi di ciò che c’è, delle specie principali di ciò che c’è e dei loro rapporti. Ma i positivisti viennesi, per esempio, chiamavano “metafisiche” le filosofie che non amavano (Carnap, 1985; Campbell, 1976, cap. 2); e se Quine parla dell’impegno ontologico o ontico di una teoria, non intende con ciò (...)
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  • Brentanian Continua.Olivier Massin - forthcoming - Brentano Studien.
    Brentano’s theory of continuity is based on his account of boundaries. The core idea of the theory is that boundaries and coincidences thereof belong to the essence of continua. Brentano is confident that he developed a full-fledged, boundary-based, theory of continuity1; and scholars often concur: whether or not they accept Brentano’s take on continua they consider it a clear contender. My impression, on the contrary, is that, although it is infused with invaluable insights, several aspects of Brentano’s account of continuity (...)
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  • The Niche.Barry Smith & Achille C. Varzi - 1999 - Noûs 33 (2):214-238.
    The concept of niche (setting, context, habitat, environment) has been little studied by ontologists, in spite of its wide application in a variety of disciplines from evolutionary biology to economics. What follows is a first formal theory of this concept, a theory of the relations between objects and their niches. The theory builds upon existing work on mereology, topology, and the theory of spatial location as tools of formal ontology. It will be illustrated above all by means of simple biological (...)
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  • Nisza.Achille C. Varzi & Barry Smith - 2000 - Filozofia Nauki 3:5–30.
    The concept of niche (setting, context, habitat, environment) has been little studied by ontologists, in spite of its wide application in a variety of disciplines from evolutionary biology to economics. What follows is a first formal theory of this concept, a theory of the relations between objects and their niches. The theory builds upon existing work on mereology, topology, and the theory of spatial location as tools of formal ontology. It is illustrated above all by means of simple biological examples, (...)
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  • The Impossibility of Relations Between Non-Collocated Spatial Objects and Non-Identical Topological Spaces.Jeffrey Grupp - 2005 - Axiomathes 15 (1):85-141.
    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.
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  • Ontological Tools for Geographic Representation.Roberto Casati, Barry Smith & Achille C. Varzi - 1998 - In Nicola Guarino (ed.), Formal Ontology in Information Systems (FOIS). Ios Press. pp. 77--85.
    This paper is concerned with certain ontological issues in the foundations of geographic representation. It sets out what these basic issues are, describes the tools needed to deal with them, and draws some implications for a general theory of spatial representation. Our approach has ramifications in the domains of mereology, topology, and the theory of location, and the question of the interaction of these three domains within a unified spatial representation theory is addressed. In the final part we also consider (...)
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  • Basic Problems of Mereotopology.Achille C. Varzi - 1998 - In Nicola Guarino (ed.), Formal Ontology in Information Systems. Ios Press. pp. 29–38.
    Mereotopology is today regarded as a major tool for ontological analysis, and for many good reasons. There are, however, a number of open questions that call for an answer. Some are philosophical, others have direct applicative import, but all are crucial for a proper assessment of the strengths and limits of mereotopology. This paper is an attempt to put sum order in this area.
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  • A Theory of Divides.Barry Smith - 1999 - The Analytic-Continental Divide Conference.
    Some would conceive philosophy as being divided into Analytic and Continental. This, as John Searle points out, is rather like conceiving America as being divided into Business and Kansas. Searle’s wise saying has not, as yet, received the theoretical attention it deserves. In both cases we have a certain domain, which is conceived as being divided into two parts, one defined in spatial terms, the other defined in terms of objects, practices or features widely spread through some spatial area. We (...)
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  • Basic Concepts of Formal Ontology.Barry Smith - 1998 - In Nicola Guarino (ed.), Formal Ontology in Information Systems. IOS Press. pp. 19-28.
    The term ‘formal ontology’ was first used by the philosopher Edmund Husserl in his Logical Investigations to signify the study of those formal structures and relations – above all relations of part and whole – which are exemplified in the subject-matters of the different material sciences. We follow Husserl in presenting the basic concepts of formal ontology as falling into three groups: the theory of part and whole, the theory of dependence, and the theory of boundary, continuity and contact. These (...)
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  • Spatial Reasoning and Ontology: Parts, Wholes, and Locations.Achille C. Varzi - 2007 - In Marco Aiello, Ian E. Pratt-Hartmann & Johan van Benthem (eds.), Handbook of Spatial Logics. Springer Verlag. pp. 945-1038.
    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.
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  • Introduzione. I confini delle cose.Luca Morena - 2002 - Rivista di Estetica 42 (20):3-22.
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  • The Spatiality of Being.Tim Ireland - 2015 - Biosemiotics 8 (3):381-401.
    Space is a product of semiosis. It is a condition pertinent to an organism’s semiotic freedom, which is articulated by the organism as a consequence of its capacity to manipulate the world in the course of its unfolding interaction with its environment. Spatial configuration is thus the result of agency inherent in the organism-in-its-environment. Space, a consequence of social cohesion, is effected through constraints and processes of enaction which are semiotic. These processes are productive and offer architects a novel means (...)
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  • Inconsistent Boundaries.Zach Weber & A. J. Cotnoir - 2015 - Synthese 192 (5):1267-1294.
    Mereotopology is a theory of connected parts. The existence of boundaries, as parts of everyday objects, is basic to any such theory; but in classical mereotopology, there is a problem: if boundaries exist, then either distinct entities cannot be in contact, or else space is not topologically connected . In this paper we urge that this problem can be met with a paraconsistent mereotopology, and sketch the details of one such approach. The resulting theory focuses attention on the role of (...)
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