David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Journal of Philosophical Logic 39 (3):229 - 254 (2010)
Mereotopology is that branch of the theory of regions concerned with topological properties such as connectedness. It is usually developed by considering the parthood relation that characterizes the, perhaps non-classical, mereology of Space (or Spacetime, or a substance filling Space or Spacetime) and then considering an extra primitive relation. My preferred choice of mereotopological primitive is interior parthood . This choice will have the advantage that filters may be defined with respect to it, constructing “points”, as Peter Roeper has done (“Region-based topology”, Journal of Philosophical Logic , 26 (1997), 25–309). This paper generalizes Roeper’s result, relying only on mereotopological axioms, not requiring an underlying classical mereology, and not assuming the Axiom of Choice. I call the resulting mathematical system an approximate lattice , because although meets and joins are not assumed they are approximated. Theorems are proven establishing the existence and uniqueness of representations of approximate lattices, in which their members, the regions, are represented by sets of “points” in a topological “space”.
|Keywords||Approximate lattice Filter Mereology Mereotopology Spacetime Ultrafilter|
|Categories||categorize this paper)|
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library|
References found in this work BETA
Roberto Casati, Barry Smith & Achille C. Varzi (1998). Ontological Tools for Geographic Representation. In Nicola Guarino (ed.), Formal Ontology in Information Systems (FOIS). Ios Press. 77--85.
Bowman L. Clark (1985). Individuals and Points. Notre Dame Journal of Formal Logic 26 (1):61-75.
Bowman L. Clarke (1981). A Calculus of Individuals Based on ``Connection''. Notre Dame Journal of Formal Logic 22 (3):204-218.
Theodore de Laguna (1922). Point, Line, and Surface, as Sets of Solids. Journal of Philosophy 19 (17):449-461.
Peter Forrest (2007). Mereological Summation and the Question of Unique Fusion. Analysis 67 (295):237–242.
Citations of this work BETA
No citations found.
Similar books and articles
Kathrin Koslicki (2007). Towards a Neo-Aristotelian Mereology. Dialectica 61 (1):127–159.
Jeffrey Sanford Russell (2008). The Structure of Gunk: Adventures in the Ontology of Space. In Dean Zimmerman (ed.), Oxford Studies in Metaphysics: Volume 4. Oxford University Press. 248.
Gabriel Uzquiano (2014). Mereology and Modality. In Shieva Kleinschmidt (ed.), Mereology and Location. Oxford University Press. 33-56.
Aaron J. Cotnoir (2010). Anti-Symmetry and Non-Extensional Mereology. Philosophical Quarterly 60 (239):396-405.
Peter Roeper (1997). Region-Based Topology. Journal of Philosophical Logic 26 (3):251-309.
Aaron J. Cotnoir & Andrew Bacon (2012). Non-Wellfounded Mereology. Review of Symbolic Logic 5 (2):187-204.
Paul Hovda (2009). What Is Classical Mereology? Journal of Philosophical Logic 38 (1):55 - 82.
Maureen Donnelly & Barry Smith (2003). Layers: A New Approach to Locating Objects in Space. In W. Kuhn M. F. Worboys & S. Timpf (eds.), Spatial Information Theory: Foundations of Geographic Information Science. Springer.
Achille C. Varzi (1996). Parts, Wholes, and Part-Whole Relations: The Prospects of Mereotopology. Data and Knowledge Engineering 20:259–286.
Ian Pratt-Hartmann & Dominik Schoop (2002). Elementary Polyhedral Mereotopology. Journal of Philosophical Logic 31 (5):469-498.
Added to index2010-04-03
Total downloads86 ( #19,409 of 1,692,771 )
Recent downloads (6 months)2 ( #108,992 of 1,692,771 )
How can I increase my downloads?