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  1. added 2019-08-06
    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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  2. added 2019-06-11
    Drawing Boundaries.Barry Smith - 2019 - In Timothy Tambassi (ed.), The Philosophy of GIS. New York: Springer. pp. 137-158.
    In “On Drawing Lines on a Map” (1995), I suggested that the different ways we have of drawing lines on maps open up a new perspective on ontology, resting on a distinction between two sorts of boundaries: fiat and bona fide. “Fiat” means, roughly: human-demarcation-induced. “Bona fide” means, again roughly: a boundary constituted by some real physical discontinuity. I presented a general typology of boundaries based on this opposition and showed how it generates a corresponding typology of the different sorts (...)
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  3. added 2019-06-05
    New Foundations for Qualitative Physics.Jean Petitot & Barry Smith - 1990 - In J. E. Tiles, G. T. McKee & C. G. Dean (eds.), Evolving Knowledge in Natural Science and Artificial Intelligence. London: Pitman Publishing. pp. 231-49.
    Physical reality is all the reality we have, and so physical theory in the standard sense is all the ontology we need. This, at least, was an assumption taken almost universally for granted by the advocates of exact philosophy for much of the present century. Every event, it was held, is a physical event, and all structure in reality is physical structure. The grip of this assumption has perhaps been gradually weakened in recent years as far as the sciences of (...)
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  4. added 2019-04-07
    De amore.Andrej Poleev - 2018
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  5. added 2019-01-28
    What Is the Validity Domain of Einstein’s Equations? Distributional Solutions Over Singularities and Topological Links in Geometrodynamics.Elias Zafiris - 2016 - 100 Years of Chronogeometrodynamics: The Status of the Einstein's Theory of Gravitation in Its Centennial Year.
    The existence of singularities alerts that one of the highest priorities of a centennial perspective on general relativity should be a careful re-thinking of the validity domain of Einstein’s field equations. We address the problem of constructing distinguishable extensions of the smooth spacetime manifold model, which can incorporate singularities, while retaining the form of the field equations. The sheaf-theoretic formulation of this problem is tantamount to extending the algebra sheaf of smooth functions to a distribution-like algebra sheaf in which the (...)
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  6. added 2018-12-17
    Fiat Objects.Barry Smith - 1994 - In Nicola Guarino, Laure Vieu & Simone Pribbenow (eds.), Parts and Wholes: Conceptual Part-Whole Relations and Formal Mereology, 11th European Conference on Artificial Intelligence, Amsterdam, 8 August 1994, Amsterdam:. Amsterdam: European Coordinating Committee for Artificial Intelligence. pp. 14-22.
    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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  7. added 2018-11-26
    A Topological Analysis of Space-Time-Consciousness: Self, Self-Self, Self-Other.Hye Young Kim - forthcoming - In When Form Becomes Substance. Power of Gesture, Grammatical Intuition and Phenomenology of Space. Basel, Switzerland:
    This paper attempts to explore a possibility to visualize the structure of time-consciousness in a knot shape. By applying Louis Kauffman’s knot-logic, the consistency of subjective consciousness, the plurality of now’s, and the necessary relationship between subjective and intersubjective consciousness will be represented in topological space.
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  8. added 2018-11-03
    Topological Foundations of Cognitive Science.Carola Eschenbach, Christopher Habel & Barry Smith - manuscript
    A collection of papers presented at the First International Summer Institute in Cognitive Science, University at Buffalo, July 1994, including the following papers: -/- ** Topological Foundations of Cognitive Science, Barry Smith -/- ** The Bounds of Axiomatisation, Graham White -/- ** Rethinking Boundaries, Wojciech Zelaniec -/- ** Sheaf Mereology and Space Cognition, Jean Petitot -/- ** A Mereotopological Definition of 'Point', Carola Eschenbach -/- ** Discreteness, Finiteness, and the Structure of Topological Spaces, Christopher Habel -/- ** Mass Reference and (...)
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  9. added 2018-06-06
    Poincaré on the Foundation of Geometry in the Understanding.Jeremy Shipley - 2017 - In Maria Zack & Dirk Schlimm (eds.), Research in History and Philosophy of Mathematics: The CSHPM 2016 Annual Meeting in Calgary, Alberta. Springer. pp. 19-37.
    This paper is about Poincaré’s view of the foundations of geometry. According to the established view, which has been inherited from the logical positivists, Poincaré, like Hilbert, held that axioms in geometry are schemata that provide implicit definitions of geometric terms, a view he expresses by stating that the axioms of geometry are “definitions in disguise.” I argue that this view does not accord well with Poincaré’s core commitment in the philosophy of geometry: the view that geometry is the study (...)
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  10. added 2017-12-19
    Quantum Gravity and Taoist Cosmology: Exploring the Ancient Origins of Phenomenological String Theory.Steven M. Rosen - 2017 - Progress in Biophysics and Molecular Biology 131:34-60.
    In the author’s previous contribution to this journal (Rosen 2015), a phenomenological string theory was proposed based on qualitative topology and hypercomplex numbers. The current paper takes this further by delving into the ancient Chinese origin of phenomenological string theory. First, we discover a connection between the Klein bottle, which is crucial to the theory, and the Ho-t’u, a Chinese number archetype central to Taoist cosmology. The two structures are seen to mirror each other in expressing the psychophysical (phenomenological) action (...)
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  11. added 2017-11-24
    Putting the World Back Into Semantics.Barry Smith - 1993 - Grazer Philosophische Studien 44 (1):91-109.
    To what in reality do the logically simple sentences with empirical content correspond? Two extreme positions can be distinguished in this regard: 'Great Fact' theories, such as are defended by Davidson; and trope-theories, which see such sentences being made the simply by those events or states to which the relevant main verbs correspond. A position midway between these two extremes is defended, one according to which sentences of the given sort are made tme by what are called 'dependence structures', or (...)
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  12. added 2017-08-24
    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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  13. added 2017-08-23
    Envisioning Transformations – The Practice of Topology.Silvia De Toffoli & Valeria Giardino - 2016 - In Brendan Larvor (ed.), Mathematical Cultures: The London Meetings 2012--2014. Zurich, Switzerland: Birkhäuser. pp. 25-50.
    The objective of this article is twofold. First, a methodological issue is addressed. It is pointed out that even if philosophers of mathematics have been recently more and more concerned with the practice of mathematics, there is still a need for a sharp definition of what the targets of a philosophy of mathematical practice should be. Three possible objects of inquiry are put forward: (1) the collective dimension of the practice of mathematics; (2) the cognitives capacities requested to the practitioners; (...)
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  14. added 2017-08-23
    An Inquiry Into the Practice of Proving in Low-Dimensional Topology.Silvia De Toffoli & Valeria Giardino - 2015 - In Gabriele Lolli, Giorgio Venturi & Marco Panza (eds.), From Logic to Practice. Zurich, Switzerland: Springer International Publishing. pp. 315-336.
    The aim of this article is to investigate specific aspects connected with visualization in the practice of a mathematical subfield: low-dimensional topology. Through a case study, it will be established that visualization can play an epistemic role. The background assumption is that the consideration of the actual practice of mathematics is relevant to address epistemological issues. It will be shown that in low-dimensional topology, justifications can be based on sequences of pictures. Three theses will be defended. First, the representations used (...)
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  15. added 2016-12-18
    The Logic and Topology of Kant's Temporal Continuum.Riccardo Pinosio & Michiel van Lambalgen - manuscript
    In this article we provide a mathematical model of Kant?s temporal continuum that satisfies the (not obviously consistent) synthetic a priori principles for time that Kant lists in the Critique of pure Reason (CPR), the Metaphysical Foundations of Natural Science (MFNS), the Opus Postumum and the notes and frag- ments published after his death. The continuum so obtained has some affinities with the Brouwerian continuum, but it also has ‘infinitesimal intervals’ consisting of nilpotent infinitesimals, which capture Kant’s theory of rest (...)
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  16. added 2015-06-09
    Global and Local.James Franklin - 2014 - Mathematical Intelligencer 36 (4).
    The global/local contrast is ubiquitous in mathematics. This paper explains it with straightforward examples. It is possible to build a circular staircase that is rising at any point (locally) but impossible to build one that rises at all points and comes back to where it started (a global restriction). Differential equations describe the local structure of a process; their solution describes the global structure that results. The interplay between global and local structure is one of the great themes of mathematics, (...)
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  17. added 2014-12-08
    On Classifying Material Entities in Basic Formal Ontology.Barry Smith - 2012 - In Interdisciplinary Ontology: Proceedings of the Third Interdisciplinary Ontology Meeting. Keio University Press. pp. 1-13.
    Basic Formal Ontology was created in 2002 as an upper-level ontology to support the creation of consistent lower-level ontologies, initially in the subdomains of biomedical research, now also in other areas, including defense and security. BFO is currently undergoing revisions in preparation for the release of BFO version 2.0. We summarize some of the proposed revisions in what follows, focusing on BFO’s treatment of material entities, and specifically of the category object.
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  18. added 2014-11-20
    Mereotopological Connection.Anthony G. Cohn & Achille C. Varzi - 2003 - Journal of Philosophical Logic 32 (4):357-390.
    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 (...)
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  19. added 2014-11-20
    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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  20. added 2014-11-20
    Boundaries, Continuity, and Contact.Achille C. Varzi - 1997 - Noûs 31 (1):26-58.
    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 (...)
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  21. added 2014-10-09
    Reasoning About Space: The Hole Story.Achille C. Varzi - 1996 - Logic and Logical Philosophy 4:3-39.
    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 (...)
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  22. added 2014-10-09
    Parts, Wholes, and Part-Whole Relations: The Prospects of Mereotopology.Achille C. Varzi - 1996 - Data and Knowledge Engineering 20:259–286.
    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 (...)
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  23. added 2014-08-10
    The Formal Ontology of Boundaries.Barry Smith & Achille C. Varzi - 1997 - Electronic Journal of Analytic Philosophy 5 (5).
    Revised version published as Barry Smith and Achille Varzi, “Fiat and Bona Fide Boundaries”, Philosophy and Phenomenological Research, 60: 2 (March 2000), 401–420.
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  24. added 2014-03-22
    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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  25. added 2014-03-21
    Topological Essentialism.Roberto Casati & Achille C. Varzi - 2000 - Philosophical Studies 100 (3):217-236.
    Considering topology as an extension of mereology, this paper analyses topological variants of mereological essentialism (the thesis that an object could not have different parts than the ones it has). In particular, we examine de dicto and de re versions of two theses: (i) that an object cannot change its external connections (e.g., adjacent objects cannot be separated), and (ii) that an object cannot change its topological genus (e.g., a doughnut cannot turn into a sphere). Stronger forms of structural essentialism, (...)
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  26. added 2014-02-10
    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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  27. added 2013-08-20
    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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  28. added 2013-07-04
    On Place and Space: The Ontology of the Eruv.Barry Smith - 2007 - In Christian Kanzian (ed.), Cultures: Conflict – Analysis – Dialogue. Ontos. pp. 403-416.
    ‘Eruv’ is a Hebrew word meaning literally ‘mixture’ or ‘mingling’. An eruv is an urban region demarcated within a larger urban region by means of a boundary made up of telephone wires or similar markers. Through the creation of the eruv, the smaller region is turned symbolically (halachically = according to Jewish law) into a private domain. So long as they remain within the boundaries of the eruv, Orthodox Jews may engage in activities that would otherwise be prohibited on the (...)
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  29. added 2012-09-23
    Ontology and the Logistic Analysis of Reality.Barry Smith - 1993 - In Nicola Guarino & Roberto Poli (eds.), Proceedings of the International Workshop on Formal Ontology in Conceptual Analysis and Knowledge Representation. Italian National Research Council. pp. 51-68.
    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.
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  30. added 2012-06-27
    The Contact Algebra of the Euclidean Plane has Infinitely Many Elements.Thomas Mormann - manuscript
    Abstract. Let REL(O*E) be the relation algebra of binary relations defined on the Boolean algebra O*E of regular open regions of the Euclidean plane E. The aim of this paper is to prove that the canonical contact relation C of O*E generates a subalgebra REL(O*E, C) of REL(O*E) that has infinitely many elements. More precisely, REL(O*,C) contains an infinite family {SPPn, n ≥ 1} of relations generated by the relation SPP (Separable Proper Part). This relation can be used to define (...)
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  31. added 2012-05-24
    Topology as an Issue for History of Philosophy of Science.Thomas Mormann - 2013 - In Hanne Andersen, Dennis Dieks, Wenceslao J. Gonzalez, Thomas Uebel & Gregory Wheeler (eds.), New Challenges to Philosophy of Science. Springer. pp. 423--434.
    Since antiquity well into the beginnings of the 20th century geometry was a central topic for philosophy. Since then, however, most philosophers of science, if they took notice of topology at all, considered it as an abstruse subdiscipline of mathematics lacking philosophical interest. Here it is argued that this neglect of topology by philosophy may be conceived of as the sign of a conceptual sea-change in philosophy of science that expelled geometry, and, more generally, mathematics, from the central position it (...)
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  32. added 2011-10-30
    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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