Leibniz’s Theory of Space

Foundations of Science 18 (3):499-528 (2013)
  Copy   BIBTEX

Abstract

In this paper I offer a fresh interpretation of Leibniz’s theory of space, in which I explain the connection of his relational theory to both his mathematical theory of analysis situs and his theory of substance. I argue that the elements of his mature theory are not bare bodies (as on a standard relationalist view) nor bare points (as on an absolutist view), but situations. Regarded as an accident of an individual body, a situation is the complex of its angles and distances to other co-existing bodies, founded in the representation or state of the substance or substances contained in the body. The complex of all such mutually compatible situations of co-existing bodies constitutes an order of situations, or instantaneous space. Because these relations of situation change from one instant to another, space is an accidental whole that is continuously changing and becoming something different, and therefore a phenomenon. As Leibniz explains to Clarke, it can be represented mathematically by supposing some set of existents hypothetically (and counterfactually) to remain in a fixed mutual relation of situation, and gauging all subsequent situations in terms of transformations with respect to this initial set. Space conceived in terms of such allowable transformations is the subject of Analysis Situs. Finally, insofar as space is conceived in abstraction from any bodies that might individuate the situations, it encompasses all possible relations of situation. This abstract space, the order of all possible situations, is an abstract entity, and therefore ideal

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 90,616

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Similar books and articles

The 'Properties' of Leibnizian Space: Whither Relationism?Edward Slowik - 2012 - Intellectual History Review 22 (1):107-129.
Space and relativity in Newton and Leibniz.Richard Arthur - 1994 - British Journal for the Philosophy of Science 45 (1):219-240.
On the space-time ontology of physical theories.Kenneth L. Manders - 1982 - Philosophy of Science 49 (4):575-590.
Leibniz on force and absolute motion.John T. Roberts - 2003 - Philosophy of Science 70 (3):553-573.
Leibniz and Newton on Space.Ori Belkind - 2013 - Foundations of Science 18 (3):467-497.
Identity, space-time, and cosmology.Jan Faye - 2008 - In Dennis Dieks (ed.), The Ontology of Space-Time II. Amsterdam: Elsevier. pp. 39-57.
On field's argument for substantivalism.Jerzy Gołosz - 1999 - International Studies in the Philosophy of Science 13 (1):5 – 16.

Analytics

Added to PP
2012-03-31

Downloads
151 (#115,859)

6 months
9 (#145,127)

Historical graph of downloads
How can I increase my downloads?

Author's Profile

Richard T. W. Arthur
McMaster University

References found in this work

Leviathan.Thomas Hobbes - 1904 - Harmondsworth,: Penguin Books. Edited by C. B. Macpherson.
Leviathan.Thomas Hobbes - 2006 - In Aloysius Martinich, Fritz Allhoff & Anand Vaidya (eds.), Early Modern Philosophy: Essential Readings with Commentary. Blackwell.
New Essays on Human Understanding.Gottfried Wilhelm Leibniz - 1981 - New York: Cambridge University Press. Edited by Peter Remnant & Jonathan Bennett.

View all 25 references / Add more references