{
  "id": "1012.4341",
  "version": "v1",
  "published": "2010-12-20T14:20:29.000Z",
  "updated": "2010-12-20T14:20:29.000Z",
  "title": "Leibniz's Principles and Topological Extensions",
  "authors": [
    "Marco Forti"
  ],
  "comment": "16 pages",
  "categories": [
    "math.GN",
    "math.LO"
  ],
  "abstract": "Three philosophical principles are often quoted in connection with Leibniz: \"objects sharing the same properties are the same object\", \"everything can possibly exist, unless it yields contradiction\", \"the ideal elements correctly determine the real things\". Here we give a precise formulation of these principles within the framework of the Topological Extensions of [8], structures that generalize at once compactifications, completions, and nonstandard extensions. In this topological context, the above Leibniz's principles appear as a property of separation, a property of compactness, and a property of analyticity, respectively. Abiding by this interpretation, we obtain the somehow surprising conclusion that these Leibnz's principles can be fulfilled in pairs, but not all three together.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-12-20T14:20:29.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "topological extensions",
      "ideal elements correctly determine",
      "leibnizs principles appear",
      "real things",
      "yields contradiction"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1012.4341F"
    }
  }
}