Leibniz on the Logical Order of Time

Abstract

As regards the question of the nature of time, Leibniz's account of monads raises the question of whether they have a temporal order and what this temporal order derives from. His account is generally taken to be an attempt to ground the asymmetric direction of time in a non-temporal sequence, such a chain of causes or reasons. The problem is whether such chains can ground temporal sequences without presupposing what it is that they are supposed to ground. Is his attempt circular, as many commentators have argued? A case can be made that monadic states can be individuated without presupposing time, which would enable him to account for temporal sequences in terms of a non-temporal one.

Notes

¹ G.W. Leibniz, Leibnizens mathematische Schriften, edited by C.I. Gerhardt (Berlin: H.W. Schmidt, 1849–1863), vol. 7, 18. Henceforth cited as GM, followed by volume and page number.

² See R. Arthur, ‘Leibniz's Theory of Time’, in The Natural Philosophy of Leibniz, edited by K. Okruhlik and J.R. Brown (Dordrecht: Reidel, 1985), 301–303 are especially relevant.

³ J.A. Cover, ‘Non-Basic Time and Reductive Strategies: Leibniz's Theory of Time’, Studies in the History and Philosophy of Science, 28 (1997): 289–318. Arthur and Cover have provided the most extensive and historically-sensitive interpretations along these lines, but others can be found in J. Earman, World Enough and Space-Time (Cambridge, MA: MIT Press, 1989); L. Sklar, Space, Time, and Spacetime (Berkeley, CA: University of California Press, 1977); and B.C. Van Fraassen, An Introduction to the Philosophy of Space and Time (New York, NY: Random House, 1970).

⁴ B. Russell, The Philosophy of Leibniz (London: Routledge, 1997), 52–53.

⁵ Russell, The Philosophy of Leibniz, 52–53.

⁷ I. Kant, Selections, edited and translated by L.W. Beck (New York, NY: Macmillan, 1988), 401.

⁶ ‘Here I may add that the concept of alteration, and with it the concept of motion, as alteration of place, is possible only through and in the representation of time; and that if this representation were not an a priori (inner) intuition, no concept, no matter what it might be, could render comprehensible the possibility of an alteration, that is, of a combination of contradictorily opposed predicates in one and the same object, for instance, the being and the not-being of one and the same thing in one and the same place. Only in time can two contradictorily opposed predicates meet in one and the same object, namely, one after the other’, I. Kant, Critique of Pure Reason, translated by N.K. Smith (New York, NY: St. Martin's Press, 1965), A32/ B48.

⁸ J. Bennett, ‘Leibniz's Two Realms’, in Leibniz: Nature and Freedom, edited by D. Rutherford and J.A. Cover (Oxford: Oxford University Press, 2005), 140.

⁹ Bennett, ‘Leibniz's Two Realms’, 140.

¹⁰ Bennett, ‘Leibniz's Two Realms’, 140.

¹¹ G.W. Leibniz, Die philosophischen Schriften von Gottfried Willhelm Leibniz, edited by C.I. Gerhard (Berlin: Weidmann, 1875–1890), vol. 4, 568. Hereafter, this work is cited as G, followed by volume and page number. This passage can also be found at page 583 of G.W. Leibniz, Philosophical Papers and Letters, translated and edited by L.E. Loemker, second edition (Dordrecht: Kluwer Academic Publishers, 1989), hereafter cited as L.

¹² G.W. Leibniz, Opuscules et fragments inédits de Leibniz, edited by L. Couturat (Paris: Félix Alcan, 1903), 476, hereafter cited as C.

¹³ G.W. Leibniz, Sämtliche Schriften und Briefe (Darmstadt and Berlin: Berlin Academy, 1923–2001), series 6, vol. 4, 2769, hereafter cited as AK, followed by series, volume, and page numbers.

¹⁴ AK 6.4.1439.

¹⁵ AK 6.4.398.

¹⁷ AK 6.4.628.

¹⁸ AK 6.4.568.

¹⁹ AK 6.4.390.

¹⁶ C 480.

²⁰ AK 6.4.569.

²¹ G.W. Leibniz, Textes inédits, edited by G. Grua (Paris: Presses Universitaires de France, 1948), 323, 512, hereafter cited as Gr. For this same definition, see also AK 6.4.569.

²² AK 2.498.

²³ AK 6.4.1437. As late as his exchange with Clarke, Leibniz characterizes the principle of contradiction as expressing the truth that ‘a proposition cannot be true and false at the same time’. Consistent propositions will therefore be those that can be true, at the same time. See Leibniz's second letter, first paragraph, to Clarke, in G.W. Leibniz, Leibniz and Clarke Correspondence, edited by R Ariew (Indianapolis, IN: Hackett, 2000).

²⁴ GM 7.18.

²⁵ AK 6.4.401.

²⁶ AK 6.4.401.

²⁷ GM 7.18.

²⁸ G 4.568/L 583.

³⁰ Gr 547.

³¹ AK 6.4.629.

³² AK 6.4.568. See also the related claim that ‘if two incompatible things exist, they differ by time […] If two propositions are true, which appear contradictory […] they differ by time’ (AK 6.4.390).

²⁹ Kant, Critique of Pure Reason, A32/ B48.

³³ Kant, Critique of Pure Reason, A32/ B48.

³⁴ A state, according to Leibniz, is either some aggregate of predicates or properties denoted by those predicates (C 473). We will further refine this definition below.

³⁵ AK 6.1.483.

³⁶ AK 6.4.937.

³⁷ D. Rutherd, Leibniz and the Rational Order of Nature (Cambridge: Cambridge University Press, 1995), chapter 5. See also R. Adams, Leibniz: Determinist, Theist, Idealist (Oxford: Oxford University Press, 1994), chapter 4.

³⁸ C 471.

³⁹ G.W. Leibniz, Vorausedition zur Reihe VI (Philosophische Schriften) in der Ausgabe der Akademie Wissenschaften der DDR (Münster: Leibniz-Forschungsstelle der Universität Münster, 1982–1991), 1253.

⁴⁰ As Mates puts it, ‘The concept A is contained in (or is included in) the concept B, and B involves A, if and only if it is absolutely impossible for there to be an object falling under B but not under A’. B. Mates, The Philosophy of Leibniz: Metaphysics and Language (Oxford: Oxford University Press, 1986), 87. In this sense, the concept ‘animal’ is an immediate requisite of the concept ‘horse’: it is prior by nature to it, and nothing can fall under the latter concept that does not fall under the former, i.e. to fall under the latter is eo ipso to fall under the former. On the other hand, a condition that is causally necessary for an effect might be necessary for that effect only relative to a certain ‘mode of production’, or law of nature or principle of order.

⁴¹ AK 6.4.998.

⁴² AK 6.4.569, emphasis added.

⁴³ R. Sleigh, The Leibniz-Arnauld Correspondence (New Haven, CT: Yale University Press, 1990), 64.

⁴⁴ ‘In this complete concept of possible Peter, which I concede is observed by God, are contained […] essential or necessary items, namely, those that flow from an incomplete or species concept, and are demonstrated from terms so that the contrary implies a contradiction’, Gr 311.

⁴⁶ AK 6.2.499, C 473.

⁴⁵ AK 6.2.499, C 473.

⁴⁷ AK 6.2.499, C 473.

⁴⁸ This last proviso is added to ensure that we do not include essential properties in states. If some property results from essential properties alone, then that property must itself be essential.

⁵¹ AK 6.4.390.

⁴⁹ For instance, Leibniz maintains that even though the action and passion of two substances may come to be at the same moment (‘eodem momento producanter’), the former is still prior by nature – and therefore provides a reason for the latter – even if it is not prior by time; AK 6.2.489. See also Theodicy, Section 66, where Leibniz writes that relations of action and passion pertain to coexisting things. G.W. Leibniz, Theodicy, edited and translated by E.M. Huggard (La Salle, IL: Open Court Press, 1996).

⁵⁰ AK 6.4.390.

⁵² AK 6.2.499.

⁵³ C 473, emphasis added.

⁵⁴ C520/L 268.

⁵⁵ G.W. Leibniz, The Discourse on Metaphysics, edited and translated by G. Montgomery (La Salle, IL: Open Court Press, 1995), 19–21.

⁵⁶ Mates, The Philosophy of Leibniz, 87.

⁵⁷ Mates, The Philosophy of Leibniz, 91.