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Notes
1A very useful account of the evolution of Galileo's ideas on this topic can be found in W.R. Shea, ‘Galileo's Atomic Hypothesis’, Ambix, 17 (1970), 13–27.
2Galileo, Discorsi e dimostrazioni matematiche intorno a due nuove scienze in Le Opere di Galileo Galilei, edited by A. Favaro, 20 vols (Florence: Barbera, 1890–1909), vol. 8 – henceforth referred to as EN. English translation by S. Drake, Two New Sciences (Madison: University of Wisconsin Press, 1974) – henceforth referred to as TNS. In subsequent footnotes references to the English translation of the text are followed by the EN page reference in brackets.
3See ‘The Assayer’, in The Controversy on the Comets of 1618, edited and translated by S. Drake and C. D. O'Malley (Philadelphia: University of Pennsylvania Press, 1960), 313: ‘Since, then, the presence of fire-corpuscles does not suffice to excite heat, but we need also their movement, it seems to me that one may very reasonably say that motion is the cause of heat.’
4 TNS, 12 [EN, 50].
5 TNS, 12 [EN, 51].
6 EN, 62.
7See M. Clavelin, ‘Le problème du continu et les paradoxes de l'infini chez Galilée’, Thalès, 10 (1959), 1–26.
8 TNS, 22 [EN, 61]: ‘I shall tell you first how to separate the force of the void from other [forces], and then how to measure it.’
9 TNS, 22 [EN, 61].
10 TNS, 22 [EN, 61].
11 TNS, 12 [EN, 51].
12 TNS, 27 [EN, 67].
13The theory of the tiny voids interspersed in matter and the subsequent problem of their number is introduced in Galileo's text as follows (TNS, 27 [EN, 66]): ‘Who knows that there are not other tiny voids operating on the most minute particles, so that the same coinage as that with which the parts are joined is used throughout?’
14 TNS, 28 [EN, 67].
15 TNS, 27 [EN, 66].
16 TNS, 28 [EN, 67].
17This word is prudently not introduced in the Discourses by Salviati, as someone might expect, but by Sagredo (TNS, 28 [EN, 67]).
18The history of this paradox can be found in I. E. Drabkin, ‘Aristotle's Wheel: Notes on the History of a Paradox’, Osiris, 9 (1950), 162–98.
19 TNS, 33 [EN, 71].
20 TNS, 33 [EN, 72].
21 TNS, 33 [EN, 72].
22 TNS, 33 [EN, 72].: ‘But imagining the line resolved into unquantifiable parts – that is, into its infinitely many indivisibles – we can conceive it immensely expanded without the interposition of any quantified void spaces, though not without infinitely many indivisible voids.’
23The problem of the existence of an extended or separate vacuum (vacuum separatum) has been studied (mainly in its medieval context) by E. Grant, Much Ado about Nothing: Theories of Space and Vacuum from the Middle Ages to the Scientific Revolution (Cambridge: Cambridge University Press, 1981), 99sq. Medieval natural philosophy rejected the existence of such a vacuum and Galileo implicitly is referring to this rejection when he is treating the problem of the dilatation of matter (TNS, 33 [EN, 72]).
24 TNS, 54 [EN, 93].
25 TNS, 53 [EN, 92].
26 TNS, 44–45 [EN, 82–3].
27 TNS, 46 [EN, 83].
28 TNS, 47 [EN, 85].
29 TNS, 48 [EN, 86].
30 TNS, 47 [EN, 85].
31Descartes has stressed this point in an objection formulated in his letter to Mersenne of 11 October 1638 (Œuvres de Descartes, edited by C. Adam and P. Tannery, 13 vols (Paris: Léopold Cerf, 1887–1913), vol. 2, 383).
32 TNS, 34 [EN, 73].
33See, for example, H. E. Le Grand, ‘Galileo's Matter Theory’, in New Perspectives on Galileo, edited by R. E. Butts and J. C. Pitt (Dordrecht: D. Reidel Publishing Company, 1978), 197–208 (206).
34 TNS, 57 [EN, 96].
35S. Nadler, in his book Spinoza: A Life (Cambridge: Cambridge University Press, 1999), 111, conjectures that Spinoza had lessons in the new science and Galileo's physics in Van den Enden's school.
36A. J. Servaas van Rooijen, Inventaire des livres formant la bibliothèque de Bénédict Spinoza, publié d'après un document inédit (La Haye – Paris: W. C. Tengeler – Paul Monnerat, 1888).
37References to Propositions of the Ethics (abbreviation: E) will be given as follows: E I 15 (this refers to Proposition 15 of the first part of the Ethics). Translations are those of E. Curley, The Collected Works of Spinoza, volume I (Princeton: Princeton University Press, 1985), henceforth referred to as ‘Curley’. G refers to Spinoza Opera, edited by C. Gebhardt, 4 vols (Heidelberg: Carl Winters, 1925), cited with volume and page.
38Spinoza's Letter 64 provides the necessary metaphysical context of the status of motion and rest (immediate infinite mode of the attribute of extension), but motion and rest do not literally appear in the passages of the Ethics (E I 21–3) where the theory of the infinite modes is introduced.
39On the radical distinction between the infinite and the finite, see the first Scholium of E I 8.
40See the sixth Definition of the first part of the Ethics (Curley 409; G II 45): ‘By God I understand a being absolutely infinite, i.e., a substance consisting of an infinity of attributes, of which each one expresses an eternal and infinite essence.’
41 E I Definition 6, Explanation (G II 46).
42Definition 4 of the first part of the Ethics (Curley 408; G II 45).
43Proposition 8 of the first part of the Ethics (Curley 412; G II 49): ‘Every substance is necessarily infinite.’
44We should keep in mind, and Spinoza indeed refers to this Definition in the demonstration of E I 8, that according to the second Definition of the first part of the Ethics, a finite thing is limited ‘by another of the same nature’ (Curley 408; G II 45).
45On this point, see Axioms 2, 4 and 5 of the first part of the Ethics. In the fifth Axiom we are in front of a conjunction of the way things are and the way things are understood; this Axiom explicitly relates the way the concepts of things are understood to causal connections which bind the things as they are in themselves.
46This deductive chain goes as follows: from E I 7 to the Corollary of E I 6 and then to E I 6 and to E I 3.
47 E I 15 (Curley 420; G II 56): ‘Whatever is, is in God, an nothing can be or be conceived without God.’
48Scholium of E I 15 (Curley 421; G II 57).
49Scholium of E I 15 (Curley 423; G II 58).
50See Scholium of E I 15, (Curley 423; G II 59): ‘And indeed it is no less absurd to assert that corporeal substance is composed of bodies, or parts, than that a body is composed of surfaces, the surfaces of lines, and the lines, finally, of points.’
51See M. Grene's relevant remarks in her ‘Introduction’, in Spinoza: A Collection of Critical Essays, edited by M. Grene (New York: Anchor Books, 1973), xi–xviii (xvi).
52Scholium of E I 15 (Curley 423; G II 59).
53On this point see Spinoza's Letter 4 (Curley 172; G IV 14);: ‘[I]f one part of matter were annihilated, the whole of Extension would also vanish at the same time.’ See also Spinoza's Short Treatise on God, Man, and His Well-Being, part I, chapter 2.
54Scholium of E I 15 (Curley 424; G II 59).
55Scholium of E I 15 (Curley 424; G II 60).
56Curley 424; G II 60.
57See the ‘Preface’ (written by L. Meyer and approved by Spinoza) of the Principles of Descartes' Philosophy (Curley 230; G I 132); see also Spinoza's Letter 12 and the first part of the Ethics.
58Letter 12 (Curley 205; G IV 60–61).
59Letter 12 (Curley 205; G IV 60–61).
60Letter 12 (Curley 205; G IV 60–61).
61Scholium of E I 15 (Curley 423; G II 59).
62 TNS, 28 [EN, 67].
63See the geometrical example analysed by Spinoza in his Letter 12: Curley 204; G IV 59 (Curley translates the term multitudo as ‘multiplicity’).
64Scholium of E I 15 (Curley 424; G II 59). For Galileo's position see TNS, 12 [EN, 51].