Leibniz, Gottfried Wilhelm


Gottfried Wilhelm Leibniz (1646–1716) was a German philosopher, mathematician, physicist, scientist, politician, diplomat, historian and librarian. He is known as the last universal genius and as one of the most famous philosophers of his time. Leibniz invented a mechanical calculator, developed the infinitesimal calculus, anticipated modern computational science and paved the way for the discovery of the principle of the conservation of energy in physics. He was one of the first to solve mechanical problems by self‐regulating systems, anticipated modern geology in claiming that the earth has a molten core and paved the way for the distinction between conscious and subconscious states. Leibniz exchanged more than 15 000 letters with both intellectual and political persons of distinction, among them two German emperors, Tsar Peter the Great and almost all important scientists and philosophers of his time.

Key Concepts:

  • Monads are indivisible, mind‐like entities, which the late Leibniz considered as the fundamental building blocks of reality.

  • Divine machines, for Leibniz, are the bodies of living beings. The term refers to the functional organisation of the body of living beings which, contrary to that of artificial machines, Leibniz thought to be infinite.

  • ‘Pre‐established harmony’ is Leibniz's term for the relation between substances, most notably for the relation between mind and body.

  • Optimism is a Leibnizian position according to which this world is the best of all possible worlds.

  • Corporeal substances are living beings with a body.

  • The Stepped Reckoner is a digital mechanical calculator designed to execute all four basic arithmetic operations.

Keywords: Leibniz; monads; divine machine; calculating machine; pre‐established harmony; mind; body; possible world; optimism; corporeal substance

Figure 1.

Prototype of Leibniz's Stepped Reckoner. Gottfried Wilhelm Leibniz Library, Hanover. Gottfried Wilhelm Leibniz Bibliothek (library) – Niedersächsische Landesbibliothek, Hannover. © Gottfried Wilhelm Leibniz Bibliothek.



Blumenfeld D (1995) Leibniz's ontological and cosmological arguments. In: Jolley N (ed.) The Cambridge Companion to Leibniz, p. 353–382. New York and Cambridge: Cambridge University Press.

Davis M (2000) The Universal Computer: The Road from Leibniz to Turing. New York: B&T.

Descartes R (1641) Meditations on First Philosophy, translated by John Cottingham, Cambridge: Cambridge University Press. 1996.

Descartes R (1644) Principles of Philosophy, translated by VR Miller and RP Miller, II: 1–25. Dordrecht: Reidel. 1983.

Des Chene D (2000) Spirits and Clocks: Machine and Organisms in Descartes. Ithaca, NY: Cornell University Press.

Fontenelle B (1731) Eloge de M. Leibnitz. Eloges des Académiciens avec l'Histoire de l'Académie Royale des Sciences en MDCXCIX. Hague. Reprinted, Brussels: Culture et Civilisation (1969).

Garber D (1995) Leibniz: physics and philosophy. In: Jolley N (ed.) The Cambridge Companion to Leinbniz, p. 270–353. New York and Cambridge: Cambridge University Press.

Hobbes T (1651) Leviathan. In: Curley E (ed.) Leviathan with Selected Variants from the Latin Edition from 1668, IV, xlvi. Indianapolis: Hackett. 1994.

Kulstad MK and Carlin L (2008) ‘Leibniz's philosophy of mind'. In Zalta EN (ed) The Stanford Encyclopedia of Philosophy, Fall 2008 edn. Available at: http://plato.stanford.edu/archives/fall2008/entries/leibniz-mind/ (accessed on 12 September 2013).

Look B (2002) On monadic domination in Leibniz's metaphysics. British Journal for the History of Philosophy 10(3): 379–399.

Nachtomy O (2007) Possibility, Agency, and Individuality in Leibniz's Metaphysics. Dordrecht: Springer.

Phemister P (2005) Leibniz and the Natural World: Activity, Passivity, Corporeal Substances in Leibniz's Philosophy. Dordrecht: Springer.

Rutherford D (1995) Leibniz and the Rational Order of Nature, p. 271–272; 282. Cambridge: Cambridge University Press.

Rutherford D (2009) Simple substances and composite bodies. In: Busche H (ed.) Gottfried Wilhelm Leibniz: Monadologie, p. 35–49. Berlin: Akademie Verlag.

Smith JEH (2011) Divine Machines: Leibniz and the Sciences of Life. Princeton: Princeton University Press.

Voltaire (1953–67) Correspondence. 107 vols. Besterman T (ed.) Vol. 22, p. 434. Geneva: Institut et Musée Voltaire Les Delices.

Voltaire (1966) Candide, or Optimism, translated by RM Adams, New York: Norton.

Wilson C (1989) Leibniz's Metaphysics: A Historical and Comparative study, Manchester: Manchester University Press.

Primary Sources for Leibniz with Abbreviations

Further Reading

Antognazza MR (2011) Leibniz: An Intellectual Biography. Cambridge: Cambridge University Press.

Duchesneau F (1998) Les modèles du vivant de Descartes à Leibniz. Paris: Vrin.

Fichant M (2003) Leibniz et les machines de la nature. Studia Leibnitiana 35: 1–28.

Garber D (2009) Leibniz: Body, Substance, Monad. New York and Oxford: Oxford University Press.

Hartz GU and Wilson C (2005) Ideas and animals: the hard problem of Leibnizian metaphysics. Studia Leibnitiana 37: 1–19.

Jolley N (ed.) (1995) The Cambridge Companion to Leibniz. Cambridge: Cambridge University Press.

Look B (2010) Leibniz's metaphysics and metametaphysics: idealism, realism and the nature of substance. Philosophy Compass 5(11): 871–879.

Nachtomy O (2007) Possibility, Agency, and Individuality in Leibniz's Metaphysics. Dordrecht: Springer.

Smith JEH (2006) The Problem of Animal Generation in Early Modern Philosophy. Cambridge: Cambridge University Press.

Smith JEH and Nachtomy O (eds) (2011). Machines of Nature and Corporeal Substances in Leibniz. Dordrecht: Springer.

Contact Editor close
Submit a note to the editor about this article by filling in the form below.

* Required Field

How to Cite close
Tietz, Sarah(Oct 2013) Leibniz, Gottfried Wilhelm. In: eLS. John Wiley & Sons Ltd, Chichester. http://www.els.net [doi: 10.1002/9780470015902.a0025062]