Abstract
The famous correspondence between Leibniz and Clarke deals with fundamental physical and metaphysical questions, such as the soul-body interaction, the freedom of will, the composition of matter, the possibility of a vacuum, miracles, gravity, and the nature of space and time. With respect to most of these issues the disagreement between Leibniz and Clarke results from their conflicting views on God’s role in the world. While Clarke blames Leibniz for turning God into a necessary agent, Leibniz accuses Clarke of having a wrong notion of God’s power and wisdom. The aim of this chapter is to show how theological, metaphysical and cosmological considerations shape Leibniz’ and Clarke’s respective theories of space. In his letters, Leibniz repeatedly invokes the Principle of Sufficient Reason and the Principle of the Identity of Indiscernibles in order to argue, against Newton and Clarke, that space cannot exist independently from, and prior to, physical bodies. Clarke, in turn, appeals to imaginary scenarios of medieval origin in order to show that the metaphysical principles that underlie Leibniz’s theory of space imply a limitation of God’s freedom. The chapter analyses in detail the role that imaginary scenarios play in the discussion concerning the ontological status of space, and attempts to provide a new interpretation of the function of the Principle of the Identity of Indiscernibles in the Correspondence.
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Notes
- 1.
Shapin 1981, 192.
- 2.
Discourse on Metaphysics, in Leibniz 1989, 36.
- 3.
Ibid., 39.
- 4.
Both in the text and in the footnotes I use the letters ‘C’ and ‘L’ to indicate the respective author of the letter, roman numerals to indicate the number of the letter, and Arabic numerals to indicate the paragraph. L.IV, post scriptum, Alexander 1956, 44.
- 5.
L.I.4, ibid., 12.
- 6.
C.IV.22–23, ibid., 50.
- 7.
C.II.1, ibid., 20.
- 8.
C.IV.15, ibid., 49.
- 9.
L.II.1, ibid., 16.
- 10.
Ibid.
- 11.
Clarke 1998, 74.
- 12.
CII.1, Alexander 1956, 21.
- 13.
Ibid., 20–21.
- 14.
L.III.5, ibid., 26.
- 15.
Cf. Rickles 2008, 33.
- 16.
L.III.5, Alexander 1956, 26.
- 17.
L.III.6, ibid., 27.
- 18.
C.III.2, ibid., 30–31.
- 19.
Ibid., 31.
- 20.
Arthur 2017, 118.
- 21.
C.III.4, Alexander 1956, 32.
- 22.
Chernoff 1981, 132.
- 23.
Ibid. E.J. Khamara writes, along similar lines: “Hence Clarke allowed the following suggestion (which I shall call Clarke’s hypothesis) to be a coherent logical possibility: that the material universe as a whole should, for any period of time and without any internal alterations, be in a state of uniform rectilinear motion along a certain absolute direction” (Khamara 2006, 99). See also Alexander 1956, xxvii.
- 24.
Grant 1981, 249.
- 25.
Quoted in Grant 1979, 230 (my emphasis).
- 26.
Grant 1996, 124. As Algra’s Chapter 2 in this volume recalls, the first extant version of this thought experiment is found in the work of the Stoic philosopher Cleomedes .
- 27.
Grant 1976, 241.
- 28.
L.IV.2, Alexander 1956, 36.
- 29.
Ibid.
- 30.
In the Confessio philosophi (1672–1673), Leibniz had admitted the possibility that two identical bodies, for example two eggs, might be distinguished only by their situation in space. In a letter to Casati , written in 1689, Leibniz used the same example of two eggs in order to argue that there are not two things in nature which differ only extrinsically. A close examination will reveal that two apparently identical eggs are discernible ‘in themselves.’ See Rodriguez-Pereyra 2014, 84–92.
- 31.
L.IV.4, Alexander 1956, ibid., 36.
- 32.
L.IV.6, ibid., 37.
- 33.
Dainton 2010, 178.
- 34.
Leibniz IV.13, Alexander 1956, 38.
- 35.
Leibniz IV.15-16, ibid., 38–39.
- 36.
Lin 2016, 455.
- 37.
Leibniz IV.13, Alexander 1956, 38.
- 38.
L.IV.21, ibid., 39–40.
- 39.
C.IV.21, ibid., 50.
- 40.
C.IV.13, ibid., 48.
- 41.
Arthur 2017, 120. See also Arthur 1994, 221 and Vailati 1997, 132–133. Newton ’s sixth corollary states that “If bodies are moving in any way whatsoever with respect to one another and are urged by equal accelerative forces along parallel lines, they will all continue to move with respect to one another in the same way as they would if they were not acted on by those forces,” Newton 1999, 423.
- 42.
L.V.29, Alexander 1956, 63–64.
- 43.
L.V.52, ibid., 74.
- 44.
C.V.26–32, ibid., 100–101.
- 45.
Ibid., 102.
- 46.
C.V.52-53, ibid., 104–105.
- 47.
- 48.
Rodriguez-Pereyra 2014, 120.
- 49.
Ibid., 25–26.
- 50.
L.III.5, Alexander 1956, 26.
- 51.
- 52.
L.IV.6, Alexander 1956, 37.
- 53.
Rodriguez-Pereyra 2014, 122.
- 54.
L.IV.15, Alexander 1956, 38–39.
- 55.
L.IV.4, ibid., 36.
- 56.
C.IV.3-4, ibid., 46.
- 57.
C.IV.15, ibid., 49.
- 58.
L.V.4-5, ibid., 56.
- 59.
Rodriguez-Pereyra 2014, 28.
- 60.
L.V.57, Alexander 1956, 76.
- 61.
L.V.58, ibid., 76–77.
- 62.
L.V.21, ibid., 60–61.
- 63.
L.V.25, ibid., 62.
- 64.
Rodriguez-Pereyra 2014, 124.
- 65.
L.V.58, Alexander 1956, 70–71.
- 66.
L.IV.13, ibid., 38.
- 67.
L.III.5, ibid., 26.
- 68.
L.IV.7, ibid., 37.
- 69.
Futch 2008, 50. Futch who, somewhat unexpectedly, does not discuss the thought experiment of God displacing the world in a straight line, maintains that according to Leibniz the PII is incompatible not only with Newtonian space, but also with empty space. Nicholas Rescher also attributes to Leibniz the view that void is impossible (Rescher 1967, 94).
- 70.
- 71.
Grant 1981, 412, n86.
- 72.
C.III.2, Alexander 1956, 31.
- 73.
L.V.29, ibid., 63 (my emphasis).
- 74.
L.V.33, ibid., 64.
- 75.
L.IV.21, ibid., 39–40; L.IV. post scriptum, ibid., 44.
- 76.
C.V.52–53, ibid., 104.
- 77.
For an analysis of various ancient versions of this thought experiment, see Ierodiakonou 2011.
- 78.
This and other Lockean thought experiments are discussed in Soles and Bradfield 2001.
- 79.
Locke 1975, 175–176.
- 80.
Leibniz 1996, 150–151.
- 81.
“Le véritable infini ne se trouve point dans un tout, composé de parties.” (Leibniz 1875–1890, VI.6, 7).
- 82.
- 83.
- 84.
Futch 2008, 24.
- 85.
L.V.31, Alexander 1956, 64.
- 86.
Khamara 2006, 42.
- 87.
C.V.52–53, Alexander 1956, 104.
- 88.
L.V.52, ibid., 74.
- 89.
L.V.53, ibid.
- 90.
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Palmerino, C.R. (2018). Space, Imagination and the Cosmos in the Leibniz-Clarke Correspondence . In: Bakker, F., Bellis, D., Palmerino, C. (eds) Space, Imagination and the Cosmos from Antiquity to the Early Modern Period. Studies in History and Philosophy of Science, vol 48. Springer, Cham. https://doi.org/10.1007/978-3-030-02765-0_12
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