Summary
To what extent does holism in the philosophy of today’s physics break with the Cartesian tradition in modern philosophy of nature? To prepare the ground for an answer to this question, I show in this chapter that Cartesian philosophy of physics admits of a sort of holism. I take up the interpretation according to which Descartes and Spinoza consider matter and the continuum of physical, three-dimensional Euclidean space to be the same thing [6.1, 6.2]. Based on this identification we reach a holism which can be called “holism about matter as holism about space”: the parts of matter are identical with the points or regions of space. All physical properties are properties of points or regions of space. What makes something a point or a region of space is relational properties or relations to other points or regions within the whole of space. If the physical things are the points or regions of space, then any physical property can only be instantiated if there are many material things (points or regions of space) which extend as far as the whole material realm (the whole space) [6.3]. A theory of motion and change can be included in holism about space [6.4]. Finally, I examine whether holism about space (or space-time) can be directly applied to today’s physics. It is suggestive to try this holism out on general relativity. There is a programme for a further development of general relativity that amounts to a concrete elaboration of this holism, namely the geometrodynamics of Wheeler. However, this programme failed. We do not have a physics at our disposal which is not committed to physical systems over and above space-time. Even if we lay stress on the fact that Descartes’ and Spinoza’s philosophy of physics admits of a sort of holism, we cannot avoid a revision of Cartesianism in today’s philosophy of nature [6.5].
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References
As to a comparison between Spinoza’s holism and quantum holism, see also Shimony (1999).
Principles, part II, §§ 20, 34; Météores I (Descartes (1965–1973), Volume 6, pp. 238–239); letter 537 to More, 5 Feb. 1649 (Descartes (1965–1973), Volume 5, p. 273 ).
Diels and Kranz (1960/61), Volume 2, fragments 68 A 37, A 57, B 141.
Blumenberg (1988), p. 189. Translation adopted from Blumenberg (1991), pp. 167–168. See furthermore p. 241 (p. 211 in the English translation).
Synopsis of the Meditations (Descartes (1965–1973), Volume 7, pp. 13–14). Translation adopted from Cottingham, Stoothoff and Murdoch (1984–1991), Volume 2, p. 10. See furthermore Principles, part II, § 4, and letter 266 to Regius, Jan. 1642 (Descartes (1965–1973), Volume 3, p. 505 ).
Compare Nason (1946), pp. 455, 468; Treder (1982), p. 279; Cottingham (1986), pp. 84–85; Curley (1988), pp. 17–18, 32–33.
Cum Cartesius et alii dicunt omnium corporalium unam esse substantiam, intelligent unam similem naturam nec (puto) volunt, quod omnia corpora unum vere substantiam confient. Et sane aggregatum esse Mundum, ut grex aut machina, res ipsa ostendit.“, Leibniz, letter 31 to de Voider, 30 June 1704 (Gerhardt (1875–1890), Volume 2, p. 271, linesl-4). Compare Woolhouse (1993), p. 23.
Kant, Critique of Pure Reason A 185/B 228. Translation according to Kant (1998).
Brown (1989), by contrast, maintains in the first part of his paper that there is a material substratum underlying extension. But see Principles, part I, § 63, and consider what, if not extension, could be the property by virtue of which this substratum is a material substratum.
Principles, part II, §§ 10–12. Compare Garber (1992), p. 132.
Compare Keeling (1934), §§ 8–9; Hesse (1961), p. 103; Graves (1971), pp. 82–83; Hartz (1989), pp. 23–24; Kobayashi (1993), p. 61. As regards opposition to this interpretation, see especially the argument by Woolhouse (1994), in particular pp. 30–33.
Kobayashi (1993), pp. 14, 98, 124–125, 127–128, makes use of the term “holism” in his interpretation of Descartes’ philosophy of nature. By employing this term, he intends that all phenomena are referred to the whole system of the world.
See Ethics, part I, definition 4. For this interpretation, compare Bennett (1988), § 16, and the thorough discussion by Glauser (1994).
Ethics, part I, proposition 14 corollary 2; proposition 15 scholium (Spinoza (1925), Volume 2, p. 57, lines 22–23); part II, propositions 1–2.
See especially Ethics, part I, proposition 25 corollary; part II, definition 1.
See, for instance, Ethics, part I, proposition 15 scholium, and compare Ethics, part I, proposition 25 corollary; part II, definition 1.
On criticism of Descartes’ notion of extension, see furthermore letter 81 to Tschirnhaus, 5 May 1676 (Spinoza (1925), Volume 4, p. 332, lines 15–21); letter 83 to Tschirnhaus, • 16 July 1676 (Spinoza (1925), Volume 4, p. 334, lines 22–26 ).
See especially Ethics, part I, proposition 15 scholium (Spinoza (1925), Volume 2, p. 57, lines 13–14); Ethics, part II, definition 1; Descartes’ Principles Demonstrated in Geometrical Manner, part II, proposition 2 and corollary. Compare Lecrivain (1986), pp. 34–39.
Compare Descartes’ Principles Demonstrated in Geometrical Manner, part II, proposition 5 with Ethics, part I, proposition 15 scholium (Spinoza (1925), Volume 2, p. 59, line 35 — p. 60, line 5) (water example) and letter 6 to Oldenburg (Spinoza (1925), Volume 4, p. 29, lines 12–17). On Spinoza’s rejection of atomism, see Rice (1975), pp. 200–201; Lecrivain (1986), pp. 37–38.
Ethics, part I, proposition 15, scholium in Spinoza (1925), Volume 2, pp. 57–60: substantia extensa: p. 57, line 22; p. 58, lines 22, 30–31; p. 60, line 13. substantia corporea: p. 57, lines 25, 28; p. 58, lines 8,12,14–15,18,34–35; p. 59, lines 7, 11, 19; p. 60, line 2. quantitas: p. 59, line 25. materia: p. 59, lines 32–34; p. 60, line 7.
Ethics, part I, proposition 15, scholium (Spinoza (1925), Volume 2, p. 58, line 34–p. 59, line 1 and p. 59, lines 29–30). On the substance being infinite, see Ethics, part I, proposition 8. On its being unique (unicus), see Ethics, part I, proposition 14 and corollary 2; but see also letter 50 to Jelles, 2 June 1674 (Spinoza (1925), Volume 4, p. 239, line 16–p. 240, line 5). On its indivisibility, see Ethics, part I, proposition 13 and corollary. See furthermore letter 12 to Meyer, 20 April 1663 (Spinoza (1925), Volume 4, p. 56, lines 12–15 ).
Ethics, part I, proposition 15 scholium (Spinoza (1925), Volume 2, p. 59, lines 3–9). Translation adopted from Curley (1985), p. 423. See furthermore letter 12 to Meyer, 20 April 1663 (Spinoza (1925), Volume 4, p$155, line 11 - p. 56, line 4 ).
See especially Ethics, part I, proposition 15 scholium (Spinoza (1925), Volume 2, p. 59, lines 11–12).
Ethics, part I, proposition 15 scholium (Spinoza (1925), Volume 2, p. 59, line 32 — p. 60, line 5). Translation adopted from Curley (1985), p. 424.
quod si una pars materiae annihilaretur, simul etiam tota extensio evanesceret,“ letter 4 to Oldenburg (Spinoza (1925), Volume 4, p. 14, lines 19–20). See furthermore Short Treatise on God, Man, and His Well-Being, part I, Chapter 2, § 20 (Spinoza (1925), Volume 1, p. 25, line 19–p. 26, line 6).
Descartes’ Principles Demonstrated in Geometrical Manner, part II, definition 6 as well as proposition 2, corollary and demonstration.
But the reference in Ethics, part I, proposition 15 scholium (Spinoza (1925), Volume 2, p. 59, lines 16–17) (elaboration of the claim that there is no empty space) is apparently meant to be a reference to Descartes’ Principles Demonstrated in Geometrical Manner, part II, proposition 3.
Bennett (1988), Chapter 4. Rombach (1966), pp. 9–97, especially pp. 29–33, 42–43, 88–89, and Sachs (1976), especially p. 130, are, to a certain extent, forerunners of Bennett’s interpretation. See also Harris (1973), pp. 52–54. For interpretations which take up Bennett’s view, see Matthews (1989), pp. 5–6; Rohs (1996), Chapter 2.
See, for instance, the criticism of Curley (1991) and the reply of Bennett (1991). For Curley’s own position, see Curley (1969), Chapter 2; Curley (1988), Chapter 1. For a criticism of the identification of matter with space in the context of relating Spinoza’s philosophy of physics to today’s philosophy of physics, see Paty (1986), p$1269/Paty (1988), pp. 184–185; van Zandt (1986), p. 258.
For an argument that points are limits of extended parts of space and not parts of space themselves, see Hoffman and Rosenkrantz (1994), pp. 100–113, 188–193.
Diels and Kranz (1960/61), Volume 2, fragments 68 A 6, A 37.
Diels and Kranz (1960/61), Volume 2, fragment 68 A 6.
Newton (1952), question 31, p. 403. See furthermore Clarke, letter 1 to Leibniz, § 3; letter 2 to Leibniz, § 3 in Gerhardt (1875–1890), Volume 7.
Letter 3 to Leibniz, § 3; letter 4 to Leibniz, §§ 8–10, 15, 41; letter 5 to Leibniz, §§ 36–48, 79–82.
Bennett (1988), § 26.3. See furthermore §§ 26.4, 49.4. Clifford (1876) and Broad (1933), p. 158, already consider such an account of motion.
Compare, in the context of this implication, Redhead (1983), p. 77.
For a reliable and easily accessible introduction to the conceptual features of special and general relativity, see the papers in Audretsch and Mainzer (1988). The paper of Audretsch (1988) treats gravitation and the curvature of space—time.
For a definition of a local space—time theory see Earman and Norton (1987), pp. 517–518.
Compare in this context Shimony, “The Methodology of Synthesis: Parts and Wholes in Low-Energy Physics” (1987), in Shimony (1993), p. 209.
Compare Mellor (1981), pp. 128–132. See also Butterfield (1985).
As regards this terminology, compare Broad (1933), pp. 141–166, especially pp. 141–148. Lewis (1986b), pp. 202–204, uses the terms “endurance” and “perdurance” which relate to continuants and occurents respectively.
Russell (1954), pp. 286–288; Russell (1956), p. 329; Russell (1969), Chapter 14; Quine (1960), § 36. See furthermore Smart (1972). For a recent elaboration of such an ontology, see Heller (1990). Lewis (1986b), pp. 202–204, also endorses such an ontology; but he does not invoke the physics of relativity.
For instance, this is the way in which Putnam reads Quine. See, e.g., “Realism with a Human Face” in Putnam (1990), p. 26; “Is Water Necessarily H2O?” in Putnam (1990), pp. 65–66. See also Lemmon (1967), pp. 98–99, on Davidson.
See, for instance, Mellor (1981), pp. 66–72.
Compare, for instance, Strawson (1959), pp. 56–57; Geach (1972), Chapter 10.2; Mellor (1981), pp. 127–132; Hacker (1982).
Compare Graves (1971), pp. 316–317.
Teller (1987), pp. 430–431; Teller (1991), p. 382. See furthermore Auyang (1995), § 20.
For instance, Suppes (1985), p. 184.
See Wheeler (1962a), in particular pp. XI—XII, 8–87, 129–130, 225–236. For an overview, see Wheeler (1962b). See furthermore Graves (1971), Chapters 4 to 5, in particular pp. 236, 312–318; Kanitscheider (1976), Chapter 10. Clifford (1876) can be considered as a precursor of Wheeler’s programme.
Graves (1971), pp. 79–101; Campbell (1976), pp. 100–104; Mathews (1989), pp. 5–6.
See Misner (1974), pp. 12–14. Compare furthermore Earman (1972), pp. 644–646.
See Wheeler (1962a), in particular pp. 25–31, 45–66.
See Stachel (1974), pp. 33–39; Kanitscheider (1976), Chapter 12.
See Stachel (1974), pp. 45–46; Cao (1997), pp. 110–111.
See Misner, Thorne and Wheeler (1973), § 44.3–4, in particular p. 1205.
Misner, Thorne and Wheeler (1973), § 44.4.
In this context, the so-called hole argument is relevant. For an introduction, see Earman and Norton (1987); Earman (1989), Chapter 9; Butterfield (1989a); Nerlich (1994), Chapter 9.
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Esfeld, M. (2001). Cartesianism in Physics and Holism about Space Or Space-Time. In: Holism in Philosophy of Mind and Philosophy of Physics. Synthese Library, vol 298. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-1787-8_6
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