Abstract
This essay I argue that for Leibniz, bodies, are in an important sense not geometrical. Instead, I will argue, geometrical extension, which Leibniz characterizes as “ideal” and radically distinct from concrete reality, is something external to the concrete world of bodies which we apply to them. As part of the argument I will explore the sense in which continuous extension is ideal for Leibniz, and why, for him, it is metaphysically impossible that real bodies could instantiate continuous extension.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsNotes
- 1.
A VI, 4, 1504 (L 365). Cf. Discours de métaphysique § 12, A VI, 4, 1545 (AG 44). (English translations, when available, are given in parentheses following the original language citations). There are many other passages in which Leibniz claims that our ideas of extension contain something imaginary. See, e.g., A VI, 4, 1622 (RA 315); A VI, 4, 1465; A VI, 4, 1612–13; etc.
- 2.
GM VI 236–37 (AG 119–20). Cf. the account given in the earlier draft, Leibniz (1982, p. 66). A very similar account is given in an unpublished essay dated May 1702; see GP IV 395 (AG 252).
- 3.
GM VI 237 (AG 120).
- 4.
GM VI 237 (AG 120).
- 5.
Leibniz to Johann Bernoulli , 18/28 November, 1698, A III, 7, 944 (AG 169).
- 6.
GP IV 395 (AG 252).
- 7.
GP IV 395 (AG 252).
- 8.
Leibniz to Arnauld , 9 October 1687, A II, 2, 251. This is generally thought to be a later addition to the letter.
- 9.
“Specimen demonstrationum catholicae seu apologia fidei ex ratione,” A VI, 4, 2326.
- 10.
Adams (1994, p. 349ff.), discusses passages like these as part of an argument that Leibniz was an idealist in the period under discussion. However, the fact that extension can be separated from force only supernaturally makes these passages problematic for his case.
- 11.
A VI, 4, 1504 (L 365).
- 12.
On Descartes ’ conception of body, see Garber (1992, Chap. 3).
- 13.
GP IV 364 (L 390).
- 14.
LDV 72–73. Leibniz repeats the same basic argument a number of times in his correspondence with de Volder : see LDV 224–25, 304–305, 322–23. It is also found in later writings, e.g. GP IV 393–4 (AG 251) and GP VI 584 (AG 261).
- 15.
Physica VI 231a 18–28 (Aristotle (1984, vol. 1 p. 390)).
- 16.
A VI, 3, 537 (RA 149).
- 17.
A VI, 4, 668; cf. A VI, 4, 393, 565, 637, 1002, etc.
- 18.
A VI, 3, 563 (RA 205).
- 19.
GP IV 491 (AG 146).
- 20.
Ibid.
- 21.
Ibid.
- 22.
There is also an echo of this discussion in Leibniz to de Volder , 19 January 1706, LDV 332–33.
- 23.
GP IV 568 (L 583).
- 24.
Hobbes (1655, Chap. 7 §2).
- 25.
- 26.
A VI, 6, 50 (AG 292–93).
- 27.
LDV 302–3.
- 28.
GP VII 564.
- 29.
LDV 320–21.
- 30.
LDV 332–33.
- 31.
LDV 338–39.
- 32.
A II, 2, 185–86 (M 121).
- 33.
LDV 262–63
- 34.
A II, 2, 184 (M 120).
- 35.
A II, 2, 114–15 (M 88).
- 36.
A II, 2, 121 (M 94).
- 37.
A II, 2, 122 (M 95).
- 38.
This view is developed in detail in Garber (2009, Chap. 2).
- 39.
A II, 2, 251 (M 154).
- 40.
A II, 2, 249 (M 151).
- 41.
A II, 2, 154 (M 108).
- 42.
A II, 2, 184–85 (M 120–21).
- 43.
A II, 2, 186 (M 122).
- 44.
LDV 338–39.
- 45.
LDV 320–23.
- 46.
LDV 302–3.
- 47.
GP IV 491–92 (AG 146–7).
- 48.
GP IV 569 (L583).
- 49.
GP VII 564.
- 50.
Here I am agreeing with Vincenzo De Risi ’s claim that for Leibniz geometrical space is a genuine mathematical structure. See De Risi (forthcoming).
- 51.
A VI, 4, 1622 (RA 315).
- 52.
A VI, 4, 1648 (AG 34).
- 53.
Leibniz to Sophie , 1 October 1705, GP VII 563–4. There is a good discussion of this passage in Hartz and Cover (1988, p. 501). Although I would claim that Leibniz ’s metaphysics of body and the ultimate make-up of substance is somewhat different when he wrote this letter than it was earlier in the 1680s and early 1690s, the view expressed in the passage quoted is very much continuous with the earlier period.
- 54.
Some commentators have been tempted to read the no-exact-shape argument as an attempt to establish the claim that the world is made up of non-extended simple substances, and that the extension of bodies is an illusion in a strong sense. See, e.g., Adams (1994, pp. 229–32) and Sleigh (1990, pp. 112–14). But I think that it is more plausible to see Leibniz ’s intention here to point out the difference between what Sellars has called the manifest view of the world, the world as it appears to us, bodies with real geometrical shapes, and the scientific image of the world, bodies of infinite complexity, beyond our power to grasp in sense. See the excellent discussion of their views in Levey (2005, pp. 84–92).
- 55.
The claim that Leibniz ’s metaphysics in the so-called “middle years,” the 1680s and most of the 1690s was grounded in corporeal substance, and not in monads is discussed and argued at great length in Garber (2009). Among many problems with the view is the relation between corporeal substance regarded as the union of active and passive force and corporeal substance regarded as living individuals with souls (form) and bodies (matter). These two models for the corporeal substance are not obviously compatible with one another. Even so, it seems clear that Leibniz held both conceptions during the middle years, and that he thought that they were alternative developments of the same basic metaphysics. Again, see Garber (2009) for a fuller discussion of these issues.
- 56.
A II, 2, 751.
- 57.
Leibniz to L’Enfant , 25 November/5 December 1693, A II, 2, 753. It is interesting to observe that even though L’Enfant had written Leibniz about body, his reply is quite clearly about substance.
- 58.
Leibniz to Bossuet , 2/12 July 1694, A I, 10, 143–4 (Leibniz (1997, p. 30)).
- 59.
On the introduction of monads into Leibniz ’s thought, see Garber (2009, Chap. 8) and Garber (forthcoming).
- 60.
Leibniz to de Volder , 30 June 1704, LDV 306–7.
- 61.
De Risi (2007, p. 174).
- 62.
De Risi (2007, pp. 173–4).
- 63.
De Risi (2007, p. 320).
- 64.
De Risi (2007, p. 321).
- 65.
De Risi (2007, p. 323).
- 66.
De Risi (2007, p. 325; cf. pp. 324, 383–4).
- 67.
De Risi (2007, p. 341).
- 68.
De Risi (2007, p. 399; cf. pp. 396, 401).
- 69.
LDV 260–61. I have altered Paul Lodge ’s translation here slightly, substituting “the passive power” for “a passive power”.
- 70.
LDV 264–65.
- 71.
LDV 260–61. Here bodies (and their derivative forces) are taken to be phenomenal in the sense that their unity as aggregates is contributed by the mind: individual monads are substances, but it is the mind that makes an aggregate of monads a thing by considering them together. In general, for Leibniz to say that some being is phenomenal is to say that it is in some way or another constituted by a perceiver. For the different senses of the phenomenal and the different ways in which Leibniz understands bodies and their forces to be phenomenal, see Garber (2009, Chap. 7).
- 72.
LDV 262–63.
- 73.
LDV 336–37. In this context, though extension and the derivative forces are clearly dependent on perceivers, it is not clear that Leibniz means to say that extension and the derivative forces are phenomenal in exactly the same sense that he meant them to be in the passages above from the letter of 20 June 1703. On this see again Garber (2009, Chap. 7).
- 74.
LDB 224–25.
- 75.
LDB 366–67.
- 76.
Ibid.
- 77.
LDB 370–71. I have slightly altered the translation by Look and Rutherford .
- 78.
LDV 302–303. I have slightly altered Lodge ’s translation here, substituting “unit” for “unity” in the first sentence quoted.
- 79.
LDB 34–35. I presume here that the monads that he finds in every part of matter are the souls of the plants and animals (corporeal substances) contained there.
- 80.
Monadology §§ 67, 69–70 (AG 222).
- 81.
For a fuller development of the idea of Leibniz ’s philosophy as modular, albeit in a rather different context, see Garber (2014).
References
Adams, R. M. (1994). Leibniz: Determinist, theist, idealist. New York: Oxford University Press.
Aristotle (1984). In J. Barnes (Ed), The complete works of Aristotle (Vol. 2.). Princeton: Princeton University Press.
De Risi, V. (2007). Geometry and monadology: Leibniz’s analysis situs and philosophy of space. Basel, Boston and Berlin: Birkhäuser.
De Risi, V. (forthcoming). Leibniz on the parallel postulate and the foundations of geometry.
Garber, D. (1992). Descartes’ metaphysical physics. Chicago: University of Chicago Press.
Garber, D. (2009). Leibniz: Body, substance, monad. Oxford: Oxford University Press.
Garber, D. (2014). Monads and theodicy: Reading Leibniz. In L. Jorgensen & S. Newlands (Eds.), New essays in Leibniz’s theodicy (pp. 218–232). Oxford: Oxford University Press.
Garber, D. (forthcoming). Monads on my mind. In A. Nita (Ed.), Leibniz’s metaphysics and the adoption of substantial forms. Dordrecht: Springer.
Hartz, G. A., & Cover, J. A. (1988). Space and time in the Leibnizian metaphysic. Noûs, 22, 493–519.
Hobbes, T. (1655). Elementorum philosophiae secio prima de corpore. London: Andrew Crooke.
Hobbes, T. (1656). Elements of philosophy the first section concerning body. London: Andrew Crooke.
Leibniz, G. W. (1849–1863). In C. I. Gerhardt (Ed.), Leibnizens mathematische Schriften (Vol. 7). Berlin: A. Asher (References include volume and page. So ‘GM VII 80’ is volume 7 p. 80. Abbreviated ‘GM’).
Leibniz, G. W. (1875–1890). In C. I. Gerhardt (Ed.), Die philosophischen Schriften (Vol. 7). Berlin: Weidmann (Abbreviated ‘GP.’ References include volume and page. So ‘GP VII 80’ is volume 7 p. 80).
Leibniz, G. W. (1923-). Sämtliche Schriften und Briefe. In Deutsche Akademie der Wissenschaften zu Berlin (Ed.), Berlin: Akademie-Verlag (Abbreviated ‘A’. References include series, volume, and page. So ‘A VI, 4, 1394’ is series 6, volume 4, p. 1394).
Leibniz, G. W. (1967). The Leibniz-Arnauld correspondence (H. T. Mason, Ed. & Trans.). Manchester: Manchester University Press (Abbreviated ‘M’).
Leibniz, G. W. (1976). Philosophical papers and letters (2nd ed) (L. E. Loemker, Ed. & Trans.). Dordrecht: Reidel. (Abbreviated ‘L’).
Leibniz, G. W. (1982). Specimen dynamicum (H. G. Dosch, G. W. Most, E. Rudolph, & J. Aichelin, Eds. & Trans.). Hamburg: Meiner.
Leibniz, G. W. (1989). Philosophical essays (R. Ariew & D. Garber, Eds. & Trans.). Indianapolis: Hackett (Abbreviated ‘AG’).
Leibniz, G. W. (1997). Leibniz’s ‘New system’ and associated contemporary texts (R. S. Woolhouse & R. Francks, Eds. & Trans.). Oxford: Oxford University Press.
Leibniz, G. W. (2001). The labyrinth of the continuum: Writings on the continuum problem, 1672–1686 (R. Arthur, Ed. & Trans.). New Haven: Yale University Press (Abbreviated ‘RA’).
Leibniz, G. W. & B. Des Bosses (2007). The Leibniz-Des Bosses correspondence (B. Look & D. Rutherford, Eds. & Trans.). New Haven: Yale University Press (Abbreviated ‘LDB’).
Leibniz, G. W. & B. de Volder (2013). The Leibniz-de Volder correspondence (P. Lodge, Ed. & Trans.). New Haven: Yale University Press (Abbreviated ‘LDV’).
Levey, S. (2005). Leibniz on precise shapes and the corporeal world. In D. Rutherford & J. A. Cover (Eds.), Leibniz: Nature and freedom (pp. 69–94). Oxford: Oxford University Press.
Sleigh, R. C. (1990). Leibniz and Arnauld: A commentary on their correspondence. New Haven: Yale University Press.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this paper
Cite this paper
Garber, D. (2015). Leibniz’s Transcendental Aesthetic. In: De Risi, V. (eds) Mathematizing Space. Trends in the History of Science. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-12102-4_10
Download citation
DOI: https://doi.org/10.1007/978-3-319-12102-4_10
Published:
Publisher Name: Birkhäuser, Cham
Print ISBN: 978-3-319-12101-7
Online ISBN: 978-3-319-12102-4
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)