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Hobbes on Space as Imaginary Space

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Empiricist Theories of Space

Part of the book series: Studies in History and Philosophy of Science ((AUST,volume 54))

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Abstract

Hobbes’s first elaboration of his doctrine of space is directed against the traditional discussion of spatium imaginarium which Thomas White is indebted to in his De mundo dialogi tres (1642). Breaking with the scholastic mode of conceiving spatium imaginarium that considers it as an extracosmic space, Hobbes’s Anti-White (1642–1643) introduces a radically new notion of imaginary space, which identifies it with the very nature of any mental image. From this viewpoint, the paper outlines a difficulty in Hobbes’s criticism of White’s cosmology. In the Anti-White’s construction of the definition of space, the admission of an indefinite image of the whole world runs up against the problem that images are always particular for Hobbes, not universal. The author points out Hobbes’s attempts in De corpore (1655) to address this problem in the Anti-White’s definition. The paper emphasizes that, in connection with De corpore’s reshaping of the definition of space as imaginary space, the late scholastic dyad spatium imaginarium/spatium reale surviving in the Anti-White the redefinition of imaginary space against its traditional meaning is abandoned. Instead, the author argues, ‘real’ space is used in De corpore as a polemic tool against the identification of space with extension in White’s De mundo and Descartes’s Principia philosophiae. Accordingly, interpretations of Hobbes’s doctrine of space viewing it as the same from the Anti-White to De corpore distort Hobbes’s approach to the definition of space required as the first principle for natural philosophy.

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Notes

  1. 1.

    See Southgate (1993, chs 1, 4).

  2. 2.

    Malcolm (2002. 17). References to the Latin manuscript (late 1642-early 1643) of the so-called Anti-White, abbreviated AW, are given in Hobbes 1973

  3. 3.

    References to De corpore, abbreviated DCo, are given in Hobbes 1999.

  4. 4.

    See AW, ch. 9, § 16 (Hobbes 1973, 169–170).

  5. 5.

    See AW, ch. 27, § 1 (Hobbes 1973, 312–314).

  6. 6.

    See AW, ch. 27, § 1; ch. 34, § 2 (Hobbes 1973, 314; 381–382).

  7. 7.

    See Descartes (1964a, 172–174).

  8. 8.

    On Hobbes’s reshaping of Aristotelian ontology, see Pécharman (1992, 1995a, b). For a comparison with Gassendi, see Paganini (2008).

  9. 9.

    This draft, NLW MS 5297, and these notes, Chatsworth MS A10 and its variants in Harleian MS 6083, are published in appendix to Hobbes 1973. See Malcolm (2002, chs 1, 4).

  10. 10.

    See Hobbes (1973, 449–450; 474).

  11. 11.

    See NLW MS 5297 (Hobbes 1973, 450). Cf DCo, ch. 7, § 2: “id quod appellamus Spatium, imaginarium quidem, quia merum phantasma” (Hobbes 1999, 76).

  12. 12.

    See AW, ch. 3, § 1 (Hobbes 1973, 116–117).

  13. 13.

    DCo, ch. 8, § 5: “Spatium autem (qua voce semper intelligo imaginarium)…” (Hobbes 1999, 85 - this formula is inserted as the first member in the definition of place, locus).

  14. 14.

    Concerning the scholastic meaning of spatium imaginarium, associating imagination and extracosmic space, see Grant (1981, chs 6, 7). For possible sources of Hobbes’s doctrine of space in late scholastic philosophy, see Leijenhorst (1996) or Leijenhorst (2002, ch. 3, 101–123).

  15. 15.

    See White (1642, 26).

  16. 16.

    See Hobbes (1889, ch. 2).

  17. 17.

    The Elements of Law, ch. 2, § 5 (Hobbes 1889, 4).

  18. 18.

    Ibid.

  19. 19.

    AW, ch. 3, § 1 (Hobbes 1973, 116).

  20. 20.

    Ibid.

  21. 21.

    Ibid.

  22. 22.

    See AW, ch. 3, § 4 (Hobbes 1973, 119). When he summarizes White’s argumentation, Hobbes replaces the locution spatium imaginarium with the phrase spatium quod imaginamur esse extra mundum.

  23. 23.

    AW, ch. 3, § 1 (Hobbes 1973, 116).

  24. 24.

    See AW, ch. 30, § 4 (Hobbes 1973, 350). Cf. The Elements of Law, ch. 3, § 1 (Hobbes 1889, 8).

  25. 25.

    AW, ch. 3, § 1 (Hobbes 1973, 117).

  26. 26.

    Ibid.

  27. 27.

    For the demonstration of this thesis (which makes Hobbes’s nominalism quite radical), see AW, ch. 2, § 6 (Hobbes 1973, 112–113).

  28. 28.

    AW, ch. 2, § 2, § 3 (Hobbes 1973, 110, 111).

  29. 29.

    AW, ch. 27, § 5, § 6 (Hobbes 1973, 317). See also AW, ch. 40, § 1 (Hobbes 1973, 434). Leviathan takes on in 1651 the same canonical definition: “the Universe, being the Aggregate of all Bodies, there is no reall part thereof that is not also Body; nor any thing properly a Body, that is not also part of (that Aggregate of all Bodies) the Universe” (Hobbes 2012, vol. 3, ch. 34, 610). Cf DCo, ch. 26, § 1(Hobbes 1999, 281).

  30. 30.

    See AW, ch. 28, § 1 (Hobbes 1973, 331). Cf DCo, ch. 7, § 12 (Hobbes 1999, 80).

  31. 31.

    AW, ch. 3, § 1: “Spatium igitur imaginarium nihil aliud est quam imago, sive phantasma corporis” (Hobbes 1973, 117).

  32. 32.

    Ibid.: “Corporis dico simpliciter”.

  33. 33.

    Ibid.: “dicemus spatium esse imaginem corporis, quatenus corporis”.

  34. 34.

    See also AW, ch. 27, § 1: “concepta omnis corporis imago est spatium” (Hobbes 1973, 312).

  35. 35.

    Hobbes 1973, 449.

  36. 36.

    Ibid.

  37. 37.

    The Elements of Law, ch. 1, § 8 (Hobbes 1889, 2). Cf DCo, ch. 7, § 1 (Hobbes 1999, 75).

  38. 38.

    On degrees of individuality in Hobbes’s philosophia prima, see Pécharman (1995b).

  39. 39.

    AW, chapter 3, § 1 (Hobbes 1973, 117). I correct the Jacquot-Jones edition, which reads: “deficiente mundo, modo non una deficiat, existet tamen immotum spatium”. The Latin manuscript actually reads: “deficiente mundo, modo non una deficiat imaginatio, existet tamen immotum spatium” (Bibliothèque Nationale, Paris, MS 6566 A, f. 15r). Both the English translation “if the world were to vanish, then unmoved space, provided that it did not disappear at the same time, would still exist” (Hobbes 1976, 41) and the Italian translation “quando venga meno il mondo, purchè non scompaia tutto insieme, sussisterà tuttavia lo spazio immoto” (Hobbes 2010, 150) misunderstand the argument.

  40. 40.

    See for this proof Aristotle, Physics, Δ, 1, 208b 1–8.

  41. 41.

    Aristotle, Physics, Δ, 1, 208b 28.

  42. 42.

    See The Elements of Law, ch. 2, § 7–8 (Hobbes 1889, 5–6).

  43. 43.

    See, for example, AW, ch. 3, § 1: “sun by acting upon the eye makes it see a bright circle” (Hobbes 1973, 116). Against the belief that this “bright circle” is the sun in the sky, Hobbes demonstrates the non inherence of images in external bodies.

  44. 44.

    Descartes (1964a, 181).

  45. 45.

    See DCo, ch. 25, § 2–3 (Hobbes 1999, 268–270). Cf AW, ch. 30, § 3 (Hobbes 1973, 350).

  46. 46.

    See DCo, ch. 7, § 1 (Hobbes 1999, 75). Cf NLW MS 5297 (Hobbes 1973, 449).

  47. 47.

    DCo, ch. 7, § 1 (Hobbes 1999, 76). Cf NLW MS 5297 (Hobbes 1973, 450) and Cavendish’s notes, which are more concise (Hobbes 1973, 474 [1]).

  48. 48.

    See DCo, ch. 7, § 2, ch. 8, § 1 (Hobbes 1999, 76, 82). Cf NLW MS 5297 (Hobbes 1973, 450, 452). Also see Cavendish’s notes (Hobbes 1973, 476 [1]) for a passage corresponding word for word to DCo, ch. 8, § 1.

  49. 49.

    Hobbes 1973, 450. See Payne’s and Cavendish’s notes (Hobbes 1973, 474 [2]) and the final version in DCo, ch. 7, § 2 (Hobbes 1999, 76–77): in Cavendish’s notes and the final version, the tense of the verb appear is changed from past to present.

  50. 50.

    See Hobbes 1973, 474 [2].

  51. 51.

    Hobbes 1973, 450.

  52. 52.

    See DCo, ch. 7, § 2 (Hobbes 1999, 76).

  53. 53.

    Ibid. See, reciprocally, the commonly accepted definition of body as ‘that which occupies a space’ in AW, ch. 27, § 1 (Hobbes 1973, 312); see also Leviathan, ch. 34: “The Word Body, in the most generall acceptation, signifieth that which filleth, or occupyeth some certain room, or imagined place” (Hobbes 2012, 610).

  54. 54.

    Later in his Philosophia prima (DCo, ch. 8, § 5), Hobbes uses another argument to prove that place is immovable - a confirmation of his definition of place as a phantasm: if a place were carried away when a body moves from some place to another, then this would require ad infinitum a place of a place, now this is impossible (see Hobbes 1999, 85; also Hobbes 1973, 454). Cf Aristotle, Physics, Δ, 1, 209a 23–26, for Zeno’s relating the same absurdity to the assertion that place exists: if place exists it must have a place to exist in, and so on ad infinitum.

  55. 55.

    See DCo, ch. 8, § 1 (Hobbes 1999, 82 - already in the 1643–4 draft and in Cavendish’s notes: see Hobbes 1973, 452 and 476 [1]).

  56. 56.

    Place can be defined only after body is defined, and body itself is defined on the basis of the definition of space. See DCo, ch. 8, § 5 (Hobbes 1999, 85). Cf. Hobbes 1973, 453 and 477 [5].

  57. 57.

    See Hobbes (1994, 381): Letter 103, [30 November/]10 December 1656, François Peleau to Hobbes.

  58. 58.

    See Schuhmann (1998, 84).

  59. 59.

    The definitions of space and place quoted by Cavendish in his Letter to Jungius (“spatium est corporis simpliciter phantasma”; “locus cujus libet corporis est spatium, quod cum illo corpore coincidit”) are not the definitions verbatim of his notes on an early draft of De corpore (“spatium est phantasma rei existentis simpliciter, quatenus existentis”; “locus est corporis cujus cumque spatium imaginarium, quod cum ipsa corporis magnitudine coincidit”: Hobbes 1973, 474 [2]; 477 [5]).

  60. 60.

    See Schuhmann (1998, 85 - my emphasis).

  61. 61.

    DCo, ch. 8, § 5 (Hobbes 1999, 85). See NLW MS 5297: “Space (which I always understand imaginary)” (Hobbes 1973, 453).

  62. 62.

    DCo, ch. 8, § 4 (Hobbes 1999, 84). Cf. NLW MS 5297: “The extension of a body is the same with the magnitude or that which some call real space” (Hobbes 1973, 453). The published version of De corpore retains the formulation of NLW MS 5297, which prohibits the double usage of the term ‘space’. See, in contrast, the notes by Payne and by Cavendish (Hobbes 1973, 477 [4]).

  63. 63.

    DCo, ch. 8, § 4 (Hobbes 1999, 84).

  64. 64.

    See DCo, ch. 7, § 2, ch. 8, § 4 (Hobbes 1999, 75, 82).

  65. 65.

    For the disparity between spatium and spatium reale in Hobbes’s final doctrine, see DCo, ch. 8, § 9 (Hobbes 1999, 87). Strikingly, from the three occurrences of spatium reale in the Philosophia prima of De corpore (ch. 8, § 4, § 5, § 9), the two latter get a purely negative or critical function: see Hobbes (1999, 84, 85, 87).

  66. 66.

    AW, ch. 3, § 2 (Hobbes 1973, 117).

  67. 67.

    Ibid.

  68. 68.

    Ibid.

  69. 69.

    For corporeitas see AW, ch. 27, § 1, § 8; ch. 34, § 2 (Hobbes 1973, 312, 319, 381). For extensio and magnitudo, see AW, ch. 7, § 6 (Hobbes 1973, 149).

  70. 70.

    For late scholastic uses (Suarez, Fonseca, the Conimbricenses) of the dyad spatium imaginarium/spatium reale in defense of the opinion that God is omnipresent in an extracosmic infinite space, see Grant (1981, 153–163). Schuhmann (1992) has suggested that Hobbes’s doctrine of space shares important features with late scholastic commentaries on Aristotle. Leijenhorst (1996, 374–380) has demonstrated that in some sense of his doctrine of spatium imaginarium, Hobbes is close to Suarez, and in another sense closer to Toletus. However, Schuhmann and Leijenhorst do not differentiate Hobbes’s position in De corpore from his position in the Anti-White. I argue, instead, that the two positions are not identical, and that the analogy between Hobbes’s doctrine of space and the late scholastic dyad spatium imaginarium/spatium reale does not suit Hobbes’s mode of argumentation in De corpore.

  71. 71.

    See AW, ch. 7, § 6; ch. 27, § 8 (Hobbes 1973, 149, 319). Cf AW, ch. 5, § 2: “extension or quantity”, together with figure and colour, is a part of the image of a body (Hobbes 1973, 129). In the Anti-White, extension, as well as space, is considered twice, in the mind and in the body conceived by the mind.

  72. 72.

    AW, ch. 27, § 1, § 8 (Hobbes 1973, 312, 319).

  73. 73.

    See DCo, ch. 8, § 2 (Hobbes 1999, 83). Cf NLW MS 5297: “whence it is that of a body one part appears here and another there? it is answered…by reason of the extension” (Hobbes 1973, 452) and Cavendish’s notes (Hobbes 1973, 476 [2]).

  74. 74.

    DCo, ch. 3, § 3 (Hobbes 1999, 33). Cf Payne’s notes (Hobbes 1973, 466).

  75. 75.

    Surprisingly, when Schuhmann (1992, 71) writes: “L’espace réel est […] l’essence du corps”, his reference is to DCo, ch. 8, § 23, which reads: “extension is said to be the essence of a body” (see Hobbes 1999, 92). Schuhmann feels authorized to substitute systematically in Hobbes’s first philosophy spatium reale for extension and to read De corpore according to the doctrine of space in the Anti-White. To my eyes, Hobbes’s use of the notion of spatium reale in chapter 8 of De corpore is no longer the positive use found in chapter 3 of the Anti-White.

  76. 76.

    See AW, ch. 3, § 3 (Hobbes 1973, 118).

  77. 77.

    See DCo, ch. 8, § 4 (Hobbes 1999, 84). NLW MS 5297 is comparable with the published version: see Hobbes (1973, 453).

  78. 78.

    Ibid.

  79. 79.

    DCo, ch. 8, § 5 (Hobbes 1999, 85). Cf NLW MS 5297; Payne’s and Cavendish’s notes (Hobbes 1973, 453, 477).

  80. 80.

    Ibid. The enumeration reproduced in Payne’s notes is not as worked out as in Cavendish’s notes or in NLW MS 5297: see Hobbes (1973, 453–454, 477).

  81. 81.

    Ibid. Cf NLW MS 5297 (Hobbes 1973, 454). This per absurdum demonstration is not developed in Payne’s and Cavendish’s notes.

  82. 82.

    DCo, ch. 8, § 5 (Hobbes 1999, 85). Cf NLW MS 5297 (Hobbes 1973, 454). No corresponding passage in Payne’s and Cavendish’s notes.

  83. 83.

    See Descartes (1964b, 45). For Hobbes’s reception of Descartes’s Principia philosophiae according to the Cavendish-Pell correspondence, see Brandt (1928, 179).

  84. 84.

    Principia philosophiae, II, art. 10. About Descartes’s doctrine of space/place in articles 10–12, see Garber (1992, 134–136; also 149–150 for a comparison with Toletus).

  85. 85.

    DCo, c. 8, § 5: Hobbes (1999, 85).

  86. 86.

    For this ‘ubicatio’ argument, see White (1642, 27).

  87. 87.

    White (1642, 28).

  88. 88.

    See White (1642, 32–33).

  89. 89.

    See AW, ch. 4, § 2 (Hobbes 1973, 126–127).

  90. 90.

    DCo, ch. 8, § 5 (Hobbes 1999, 85).

  91. 91.

    DCo, ch. 7, § 2 (Hobbes 1999, 77).

  92. 92.

    For the demonstrations to which Hobbes alludes in this passage, see Principia philosophiae, II, art. 21 (Descartes 1964b, 52); De mundo, Dialogus I, Nodus III (White 1642, 26).

  93. 93.

    See DCo, ch. 8, § 9 (Hobbes 1999, 87).

  94. 94.

    Ibid.

  95. 95.

    Ibid.

  96. 96.

    See Descartes (1964b, 50).

  97. 97.

    Ibid. For that reason, “what would happen if God did remove from some vessel all the body contained in it and did not permit another body to occupy the place of the body removed”, is for Descartes that “the sides of the vessel would be therefore contiguous to each other”.

  98. 98.

    See White (1642, 29). Cf AW, ch. 3, § 7 (Hobbes 1973, 121): Hobbes criticizes the sliding from contiguity to conjunction in White’s argumentation.

  99. 99.

    AW, ch. 3, § 3 (Hobbes 1973, 118).

  100. 100.

    See Schuhmann (1992, 71, n. 41).

  101. 101.

    See Leijenhorst (1996, 378).

  102. 102.

    The attribution to De corpore of the scholastic distinction between real space and imaginary space is first found in Grant (1981, ch. 8). My question applies to his reading too: see Grant (1981, 226 and 401, n. 255).

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    Martine Pécharman

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    Laura Berchielli

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Pécharman, M. (2020). Hobbes on Space as Imaginary Space. In: Berchielli, L. (eds) Empiricist Theories of Space. Studies in History and Philosophy of Science, vol 54. Springer, Cham. https://doi.org/10.1007/978-3-030-57620-2_2

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