{
  "id": "1605.03501",
  "version": "v1",
  "published": "2016-05-11T16:27:00.000Z",
  "updated": "2016-05-11T16:27:00.000Z",
  "title": "Is Leibnizian calculus embeddable in first order logic?",
  "authors": [
    "Piotr Blaszczyk",
    "Vladimir Kanovei",
    "Karin U. Katz",
    "Mikhail G. Katz",
    "Taras Kudryk",
    "Thomas Mormann",
    "David Sherry"
  ],
  "comment": "22 pages, to appear in Foundations of Science",
  "doi": "10.1007/s10699-016-9495-6",
  "categories": [
    "math.LO",
    "math.HO"
  ],
  "abstract": "To explore the extent of embeddability of Leibnizian infinitesimal calculus in first-order logic (FOL) and modern frameworks, we propose to set aside ontological issues and focus on procedural questions. This would enable an account of Leibnizian procedures in a framework limited to FOL with a small number of additional ingredients such as the relation of infinite proximity. If, as we argue here, first order logic is indeed suitable for developing modern proxies for the inferential moves found in Leibnizian infinitesimal calculus, then modern infinitesimal frameworks are more appropriate to interpreting Leibnizian infinitesimal calculus than modern Weierstrassian ones. Keywords: First order logic; infinitesimal calculus; ontology; procedures; Leibniz; Weierstrass; Abraham Robinson",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-05-11T16:27:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03B10",
      "26E35",
      "01A45"
    ],
    "keywords": [
      "first order logic",
      "leibnizian calculus embeddable",
      "interpreting leibnizian infinitesimal calculus",
      "set aside ontological issues",
      "first-order logic"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Springer"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}