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Leibniz's Theory of Universal Expression Explicated

Published online by Cambridge University Press:  01 January 2020

Ari Maunu
Ari Maunu*
Affiliation:
University of Turku, FIN-20014 Turku, Finland
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Extract

According Leibniz's thesis of universal expression, each substance expresses the whole world, i.e. all other substances, from its particular, unique viewpoint, or, in other words, the complete individual notion of a substance — the comprehensive notion which includes, in internal terms, everything truly attributable to a substance — is such a universal expression of, or ‘involves,’ every other substance, or, as Leibniz also frequently states, from any given complete individual notion one can ‘deduce’ or ‘infer’ or ‘demonstrate,’ or from it ‘follows,’ or it ‘leads to,’ (all truths about) the whole world. On the other hand, in Leibniz's view each (created) substance is internally individuated, self-sufficient and independent of other (created) substances, and the complete individual notion of a substance is such that it respects this requirement. Leibniz also says, with an apparent intention of pronouncing his doctrines of expression and self-sufficiency at the same time, that each substance is ‘as if a world apart,’ or like a ‘multiplication’ or ‘concentration’ of the world.

Type
Research Article
Information
Canadian Journal of Philosophy , Volume 38 , Issue 2 , June 2008 , pp. 247 - 267
Copyright
Copyright © The Authors 2008

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References

References

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D'Agostino, F.B. 1976. ‘Leibniz on Compossibility and Relational Predicates.’ Philosophical Quarterly 26: 125-38. Reprinted and cited from Leibniz: Metaphysics and Philosophy of Science, ed. R. S. Woolhouse. Oxford: Oxford University Press 1981, 89–103.CrossRefGoogle Scholar
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Koistinen, O. and Repo, A. 1999. ‘Compossibility and Being in the Same World in Leibniz's Metaphysics.’ Studia Leibnitiana 31: 196–214.Google Scholar
Kulstad, M. A. 1977. ‘Leibniz's Conception of Expression.’ Studia Leibnitiana 9: 55–76.Google Scholar
Kulstad, M. A. 1980. ‘A Closer Look at Leibniz's Alleged Reduction of Relations.’ Southern Journal of Philosophy 18: 417-32. Reprinted and cited from Gottfried Wilhelm Leibniz: Critical Assessments, Vol. 2, ed. R.S. Woolhouse. London: Routledge 1994, 213-30.CrossRefGoogle Scholar
Look, B. 2002. ‘On Monadic Domination in Leibniz's Metaphysics.’ British Journal for the History of Philosophy 10: 379-99.CrossRefGoogle Scholar
Mates, B. 1968. ‘Leibniz on Possible Worlds.’ In Logic, Methodology, and Philosophy of Science III, ed. Rootselaar, B. van and Staal, J.F.. Amsterdam: North-Holland, 507-29. Reprinted and cited from Leibniz: A Collection of Critical Essays, ed. H.G. Frankfurt. Notre Dame: University of Notre Dame Press 1972, 335-64.CrossRefGoogle Scholar
Mates, B. 1986. The Philosophy of Leibniz: Metaphysics and Language. Oxford: Oxford University Press.Google Scholar
Maunu, A. 2004a. ‘Leibnizian Soft Reduction of Extrinsic Denominations and Relations.’ Synthese 139: 143-64.CrossRefGoogle Scholar
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Mugnai, M. 1992. Leibniz’ Theory of Relations. Stuttgart: Steiner. (= Studia Leibnitiana, Supp. 28.)Google Scholar
Parkinson, G.H.R. 1965. Logic and Reality in Leibniz's Metaphysics. Oxford: Clarendon.Google Scholar
Ramsey, F.P. 1929. ‘Theories.’ In Ramsey, F.P. 1990, Philosophical Papers, ed. Mellor, D.H.. Cambridge: Cambridge University Press, 112-36.Google Scholar
Rescher, N. 1967. The Philosophy of Leibniz. Englewood Cliffs: Prentice-Hall.Google Scholar
Rescher, N. 1979. Leibniz: An Introduction to His Philosophy. Oxford: Blackwell.Google Scholar
Rescher, N. 1981. ‘Leibniz on Intermonadic Relations.’ In Truth, Knowledge and Reality: Inquiries into the Foundations of Seventeenth-Century Rationalism, ed. Parkinson, G.H.R.. Wiesbaden: Steiner. (= Studia Leibnitiana, Sonderheft 9.) Reprinted and cited from Rescher, N., 1981, Leibniz's Metaphysics of Nature: A Group of Essays. Dordrecht: Reidel, 56–83.Google Scholar
Russell, B. 1937. A Critical Exposition of the Philosophy of Leibniz, Second Edition. London: Routledge 1992. (First edition: 1900.)Google Scholar
Rutherford, D. P. 1995. Leibniz and the Rational Order of Nature. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Sleigh, R. C. 1990. Leibniz and Arnauld: A Commentary on Their Correspondence. New Haven: Yale University Press.CrossRefGoogle Scholar
Strawson, P.F. 1959. Individuals: An Essay in Descriptive Metaphysics. London: Methuen.Google Scholar
Wong, D. 1980. ‘Leibniz's Theory of Relations.’ Philosophical Review 89: 241-56.CrossRefGoogle Scholar
(A) Sämtliche Schriften und Briefe (Reihe 1-8), hrsg. Berlin-Brandenburgischen Akademie der Wissenschaften et al. Berlin et al.: Akademie Verlag et al., 1923f. Cited by series, volume and page (e.g. ‘A VI, 4, 308’ refers to series VI, volume 4, page 308).Google Scholar
(AG) Philosophical Essays, ed. and trans. R. Ariew and D. Garber. Indianapolis: Hackett 1989.Google Scholar
(C) Opuscules et fragments inédits de Leibniz, ed. L. Couturat. Paris: Alcan 1903.Google Scholar
(DM) Discours de métaphysique (1686), A VI, 4, 1529-88 / AG 35-68. Cited by section number.Google Scholar
(DSR) De Summa Rerum: Metaphysical Papers 1675-1676, ed. and trans. G.H.R. Parkinson. New Haven: Yale University Press 1992. (Latin original (from A VI, 3, 391-7, 399-400, 461-84, 490-1, 504-28, 572-88) and English translation on facing pages.)Google Scholar
(G) Die philosophischen Schriften von Gottfried Wilhelm Leibniz (Bände 1-7), hrsg. C. I. Gerhardt. Berlin: Weidmann, 1875-90. Reprinted, Hildesheim: Olms, 1960-1. Cited by volume and page (e.g. ‘G2 249’ refers to volume 2, page 249).Google Scholar
(GI) Generales inquisitiones de analysi notionum et veritatum (1686), A VI, 4, 739-88 / P 47-87. Cited by section number.Google Scholar
(Gr) Textes inédits d'apres les manuscrits de la bibliothèque provinciale de Hanovre, ed. G. Grua. Paris: Presses Universitaires de France 1948.Google Scholar
(H) Theodicy: Essays on the Goodness of God, the Freedom of Man and the Origin of Evil, ed. A. Farrar, trans. E.M. Huggard. La Salle: Open Court 1985.Google Scholar
(L) Philosophical Papers and Letters (Second Edition), ed. and trans. L. Loemker. Dordrecht: Reidel 1969.Google Scholar
(LA) The Leibniz-Arnauld Correspondence (1686-91), G2 11-138 / AG 69-90 (in part) & LAM. Cited by page number in G2 (given marginally in LAM).Google Scholar
(LAM) The Leibniz-Arnauld Correspondence, ed. and trans. H. T. Mason. Manchester: Manchester University Press 1967.Google Scholar
(LC) The Leibniz-Clarke Correspondence (1715-6), G7 345-440 / AG 320-46 (in part) & L 675-717. Cited by letter and section number.Google Scholar
(LH) The Leibniz Manuscripts in Niedersächsische Landesbibliothek, Hanover, cited by Bodemann's numbering (as given in Die Leibniz-Handschriften der Königlichen öffentlichen Bibliothek zu Hannover, hrsg. E. Bodemann; Hannover 1889; reprinted, Hildesheim: Olms 1966) and page. References to LH 4.3.5c 2r and LH 4.8 61r are to texts printed in Mugnai (1992, pp. 26 (n. 47) and 158, respectively).Google Scholar
(M) Monadologie (1714), G6 607-23 / AG 213-25. Cited by section number.Google Scholar
(MP) Philosophical Writings, ed. G.H.R. Parkinson, trans. M. Morris and G.H.R. Parkinson. London: Dent 1973.Google Scholar
(NE) Nouveaux essais sur l'entendement humain (c. 1704), A VI, 6, 43-527 / NERB. Cited by section number and parenthetically by page number in A VI, 6, (given marginally in NERB).Google Scholar
(NERB) New Essays on Human Understanding, ed. and trans. P. Remnant and J. Bennett. Cambridge: Cambridge University Press 1981.Google Scholar
(P) Logical Papers: A Selection, ed. and trans. G.H.R. Parkinson. Oxford: Clarendon 1966.Google Scholar
(PNG) Principes de la Nature et de la Grace, fondés en raison (1714), G6 598-606 / AG 207-13. Cited by section number.Google Scholar
(Schr) Monadology and Other Philosophical Essays, ed. and trans. P. Schrecker and A. M. Schrecker. Indianapolis: Bobbs-Merrill 1965.Google Scholar
(SN) Système nouveau de la nature et de la communication des substances … (1695), G4 477-87 / AG 138-45. Cited by paragraph number.Google Scholar
(T) Essais de Théodicée sur la bonté de Dieu, la liberté de l'homme et l'origine du mal (1710), G6 21-462 / H. Cited by section number (in the main essays), with the abbreviation: k = Remarques sur le Livre de l'origine du mal …. (E.g. ‘t 291’ refers to Section 291 of the main essays and ‘t k14’ to Section 14 of the Remarques.)Google Scholar
(WF) Leibniz's ‘New System’ and Associated Contemporary Texts, ed. and trans. R. S. Woolhouse and R. Francks. Oxford: Clarendon 1997.CrossRefGoogle Scholar
Adams, R.M. 1979. ‘Primitive Thisness and Primitive Identity.’ Journal of Philosophy 76: 5–26.CrossRefGoogle Scholar
Adams, R.M. 1994. Leibniz: Determinist, Theist, Idealist. Oxford: Oxford University Press.Google Scholar
Bennett, J. 2001. Learning from Six Philosophers: Descartes, Spinoza, Leibniz, Locke, Berkeley, Hume, Vol. 1. Oxford: Oxford University Press.Google Scholar
Broad, C.D. 1950. Leibniz: An Introduction, ed. Lewy, C.. Cambridge: Cambridge University Press 1975.Google Scholar
Brown, C. 1990. Leibniz and Strawson: A New Essay in Descriptive Metaphysics. Munich: Philosophia Verlag.Google Scholar
Brown, G. 1987. ‘Compossibility, Harmony, and Perfection in Leibniz.’ Philosophical Review 96: 173-203. Reprinted and cited from Gottfried Wilhelm Leibniz: Critical Assessments, Vol. 2, ed. R. S. Woolhouse. London: Routledge 1994, 261-87.CrossRefGoogle Scholar
Burdick, H. 1991. ‘What Was Leibniz's Problem about Relations?’ Synthese 88: 1–13.CrossRefGoogle Scholar
Cover, J.A. and O'Leary-Hawthorne, J. 1999. Substance and Individuation in Leibniz: An Essay in Metaphysics. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
D'Agostino, F.B. 1976. ‘Leibniz on Compossibility and Relational Predicates.’ Philosophical Quarterly 26: 125-38. Reprinted and cited from Leibniz: Metaphysics and Philosophy of Science, ed. R. S. Woolhouse. Oxford: Oxford University Press 1981, 89–103.CrossRefGoogle Scholar
Furth, M. 1967. ‘Monadology.’ Philosophical Review 76: 169–200.CrossRefGoogle Scholar
Hintikka, J. 1969. ‘Leibniz on Plenitude, Relations, and the ‘Reign of Law.’’ Ajatus 31: 117-44. Reprinted (in a slightly revised form) and cited from Reforging the Great Chain of Being: Studies of the History of Modal Theories, ed. S. Knuuttila. Dordrecht: Reidel 1981, 259-86.Google Scholar
Ishiguro, H. 1972. ‘Leibniz's Theory of the Ideality of Relations.’ In Leibniz: A Collection of Critical Essays, ed. Frankfurt, H.G.. Notre Dame: University of Notre Dame Press, 191–213.Google Scholar
Ishiguro, H. 1990. Leibniz's Philosophy of Logic and Language, Second Edition. Cambridge: Cambridge University Press. (First edition: 1972.)Google Scholar
Koistinen, O. and Repo, A. 1999. ‘Compossibility and Being in the Same World in Leibniz's Metaphysics.’ Studia Leibnitiana 31: 196–214.Google Scholar
Kulstad, M. A. 1977. ‘Leibniz's Conception of Expression.’ Studia Leibnitiana 9: 55–76.Google Scholar
Kulstad, M. A. 1980. ‘A Closer Look at Leibniz's Alleged Reduction of Relations.’ Southern Journal of Philosophy 18: 417-32. Reprinted and cited from Gottfried Wilhelm Leibniz: Critical Assessments, Vol. 2, ed. R.S. Woolhouse. London: Routledge 1994, 213-30.CrossRefGoogle Scholar
Look, B. 2002. ‘On Monadic Domination in Leibniz's Metaphysics.’ British Journal for the History of Philosophy 10: 379-99.CrossRefGoogle Scholar
Mates, B. 1968. ‘Leibniz on Possible Worlds.’ In Logic, Methodology, and Philosophy of Science III, ed. Rootselaar, B. van and Staal, J.F.. Amsterdam: North-Holland, 507-29. Reprinted and cited from Leibniz: A Collection of Critical Essays, ed. H.G. Frankfurt. Notre Dame: University of Notre Dame Press 1972, 335-64.CrossRefGoogle Scholar
Mates, B. 1986. The Philosophy of Leibniz: Metaphysics and Language. Oxford: Oxford University Press.Google Scholar
Maunu, A. 2004a. ‘Leibnizian Soft Reduction of Extrinsic Denominations and Relations.’ Synthese 139: 143-64.CrossRefGoogle Scholar
Maunu, A. 2004b. ‘Extrinsic Denominations and Universal Expression in Leibniz.’ Dialogue: Canadian Philosophical Review 43: 83–97.CrossRefGoogle Scholar
Mugnai, M. 1992. Leibniz’ Theory of Relations. Stuttgart: Steiner. (= Studia Leibnitiana, Supp. 28.)Google Scholar
Parkinson, G.H.R. 1965. Logic and Reality in Leibniz's Metaphysics. Oxford: Clarendon.Google Scholar
Ramsey, F.P. 1929. ‘Theories.’ In Ramsey, F.P. 1990, Philosophical Papers, ed. Mellor, D.H.. Cambridge: Cambridge University Press, 112-36.Google Scholar
Rescher, N. 1967. The Philosophy of Leibniz. Englewood Cliffs: Prentice-Hall.Google Scholar
Rescher, N. 1979. Leibniz: An Introduction to His Philosophy. Oxford: Blackwell.Google Scholar
Rescher, N. 1981. ‘Leibniz on Intermonadic Relations.’ In Truth, Knowledge and Reality: Inquiries into the Foundations of Seventeenth-Century Rationalism, ed. Parkinson, G.H.R.. Wiesbaden: Steiner. (= Studia Leibnitiana, Sonderheft 9.) Reprinted and cited from Rescher, N., 1981, Leibniz's Metaphysics of Nature: A Group of Essays. Dordrecht: Reidel, 56–83.Google Scholar
Russell, B. 1937. A Critical Exposition of the Philosophy of Leibniz, Second Edition. London: Routledge 1992. (First edition: 1900.)Google Scholar
Rutherford, D. P. 1995. Leibniz and the Rational Order of Nature. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Sleigh, R. C. 1990. Leibniz and Arnauld: A Commentary on Their Correspondence. New Haven: Yale University Press.CrossRefGoogle Scholar
Strawson, P.F. 1959. Individuals: An Essay in Descriptive Metaphysics. London: Methuen.Google Scholar
Wong, D. 1980. ‘Leibniz's Theory of Relations.’ Philosophical Review 89: 241-56.CrossRefGoogle Scholar