Description

• Title:
  Space, points and mereology. On foundations of point-free Euclidean geometry
• Creator:
  Gruszczyński, Rafał;
  Pietruszczak, Andrzej
• Description:
  This article is devoted to the problem of ontological foundations of three-dimensional Euclidean geometry. Starting from Bertrand Russell’s intuitions concerning the sensual world we try to show that it is possible to build a foundation for pure geometry by means of the so called regions of space.It is not our intention to present mathematically developed theory, but rather demonstrate basic assumptions, tools and techniques that are used in construction of systems of point-free geometry and topology by means of mereology (resp. Boolean algebras) and Whitehead-like connection structures. We list and briefly analyze axioms for mereological structures, as well as those for connection structures. We argue that mereology is a good tool to model so called spatial relations. We also try to justify our choice of axioms for connection relation.Finally, we briefly discuss two theories: Grzegorczyk’s point-free topology and Tarski’s geometry of solids.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2017 Logic and Logical Philosophy
• Date:
  2009.11.30
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion
• Language:
  English
• Source:
  Logic and Logical Philosophy; Vol. 18 No. 2 (2009); 145-188;
  Logic and Logical Philosophy; Tom 18 Nr 2 (2009); 145-188;
  2300-9802;
  1425-3305
• Format:
  application/pdf
• Publisher:
  Uniwersytet Mikołaja Kopernika w Toruniu
• Relation: https://apcz.umk.pl/LLP/article/view/LLP.2009.009/990
• Subject:
  space;
  points;
  mereology;
  pointless geometry;
  point-free geometry;
  geometry of solids;
  foundations of geometry;
  point-free topology
• Identifier: https://apcz.umk.pl/LLP/article/view/LLP.2009.009
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  text