Abstract
In the first day of his Discourses and Mathematical Demonstrations Relating to Two New Sciences, Galileo illustrates the theme of the ‘first new science,’ which concerns the ‘resistance which solid bodies offer to fracture.’ This is the most comprehensive and complex discussion left to us by the Italian scientist regarding his concept of matter, in which the passages devoted to the paradoxes of the infinite are particularly noteworthy. Galileo tackles the subject of the composition of the continuum by focusing the argument on a geometric problem: in order to be divisible into infinitely divisible parts, the line and every continuum must necessarily be composed of an infinite number of indivisibles ‘and if the parts are infinite in number, we must conclude that they are not finite in size, because an infinite number of finite quantities would give an infinite magnitude.’ Galileo writes:
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Notes
- 1.
Galilei, Discorsi e dimostrazioni matematiche intorno a due nuove scienze, OG, VIII, 47.
- 2.
See, in this regard: Biener 2004, esp. 266 ff.
- 3.
- 4.
See Palmerino 2000, 290. The subject of the mathematical and physical composition of the continuum was explored extensively in the ancient and medieval world. See Murdoch 1982. William of Ockham took the Aristotelian theory up again, firmly denying the real existence of mathematical points (see, for example, Ockham, ‘Expositionis in libros artis logicae Proemium et Expositio in librum Porphyrii de praedicabilibus.’ In Ockham 1974–1988, II, 205 ff; McCord Adams 1987, I, 201 ff). Ockham’s position was shared by Jean Buridan and Albert of Saxony, as well as by the Mertonians Thomas Bradwardine and William Heytesbury (see Murdoch 1982, 573–575), while the existence of indivisibles was upheld by Henry Harclay, Walter Chatton, Gerard Odon and Nicolas Bonet (ibid., 575–576). See also Murdoch 2009. On the problem of the continuum and the minima naturalia in the Middle Ages see Maier 1984, 271 ff.
- 5.
Galilei, Discorsi e dimostrazioni matematiche intorno a due nuove scienze, OG, VIII, 80; Eng. trans. Galilei 2003, 34.
- 6.
Ibid.; Eng. Trans. 34, slightly modified.
- 7.
- 8.
Galilei, Discorsi e dimostrazioni matematiche intorno a due nuove scienze, OG, VIII, 85; Eng. trans. Galilei 2003, 36–37, slightly modified.
- 9.
Ibid.; Eng. Trans. 37, slightly modified.
- 10.
Ibid., 85–86 (my italics); Eng. trans. 37, slightly modified.
- 11.
See Baldini 1977a, 20–21. On the subject of the structural isomorphism of the universe as an endemic feature of some seventeenth-century philosophies and on the importance of the concept in modern science, see Palmerino 2011. On Galileo: 309 ff. On corpuscularism and its importance in modern science (particularly in Italy), see Baldini 1977b.
- 12.
TO II, chap. I, § 13, fol. 200v/154 (my italics, my trans.): ‘Corporum in universum duo sunt genera; unum quorum partes inter se ita cohaerent ut non facile separentur, qualia sunt quae vocantur Dura, alia magis, alia minus; alterum quorum partes ad omnem motum impressionem diffluunt et aliae ab aliis dirimuntur, quod vocant fluidum. Utrum vero sit corpus aliquod ita fluidum ut quaemadmodum cogitatione in semper divisibilia dividi, ita re ipsa in semper separabilia separari possit, id hoc loco non est disputandum.’
- 13.
De corpore, XXVI, 4, OL, I, 347; EW, I, 426.
- 14.
A number of analogies between the handling of fluids in Galileo and Hobbes have been observed by Thomas Holden. See Holden 2004, 18.
- 15.
On this subject see primarily Giudice 1997. The question of the corpuscular composition of fluid and the theme of atomism will be discussed in greater depth in the next paragraph.
- 16.
See Samuel Sorbière to Hobbes, from Paris, [23 January/] 2 February 1657, CH, I, 433–435.
- 17.
Hobbes to Samuel Sorbière, from London, 6 [/16 February] 1657, CH, I, 443, Eng. trans. Noel Malcolm, 445.
- 18.
De corpore, XXVI, 3, OL, I, 340: ‘Neque causa apparet major, quare materia mundana interpuncta debeat esse, ad admittendum motum, spatiis vacuis quam spatiis plenis, plenis inquam sed fluidis’. What is more, regarding the nature of fluid, he added that those who uphold the vacuum, ‘… dum naturam fluidi contemplantur, constare ilud imaginantur tanquam ex duri granulis, quomodo farina fluida fit e frumento molito; cum tamen fluidum concipere possibile sit tanquam natura sua aeque homogeneum, ac est ipsa atomus vel ipsum vacuum.’
- 19.
Hobbes to Samuel Sorbière, from London, [February 6/16] 1657, CH, I, 443; Eng. trans. 446.
- 20.
On the subject of fluid in the Dialogus physicus see primarily Shapin and Schaffer 1985, 115 ff.
- 21.
See, for example, Decameron physiologicum, EW, VII, 108–109 and 138–139.
- 22.
Dialogus physicus de natura aeris, OL, IV, 244–245: ‘Ego, contra, distinctionem non capio inter fluida et non fluida, quam sumitis a magnitudine partium; nam si caperem, ruina illa, sive rudera illa, quae jacent in ecclesia Paulina, mihi dicenda essent fluida’.
- 23.
Ibid. Eng. trans. Shapin and Schaffer 1985, 354.
- 24.
Lasswitz had already drawn attention to Galileo’s atomism, see Lasswitz 1963, II, 37 ff. Further significant contributions on this topic include: Shea 1970; Le Grand 1978. Baldini 1977a broadly develops the issue, comparing the Discourse on Bodies in Water (1612) with the Discourses and Mathematical Demonstrations (1638). Baldini maintains that Galileo’s ‘corpuscularism’ is key to the distinction between primary and secondary qualities (ibid., 16–17), although he affirms that the Galilean position differs clearly from the modern imitators of atomism such as Gassendi. Pietro Redondi considered three phases of the Galilean concept of matter: an initial moment linked to a personal interpretation of certain Aristotelian theories taught at the Collegio Romano; a phase characterized by physical atomism, which reached its peak in 1623 with the publication of The Assayer, and, lastly, a third period, after 1634, when Galileo’s atomism was characterized by a mathematical and geometrical concept of the continuum, which culminates in his Discourses. See esp. Redondi 1985. The question of atomism is also central to his well-known Galileo’s eretico. See Redondi 2009, esp. 16–31. Redondi deems that the ‘shift’ from a physical interpretation of atomism to the geometrical one of the Discourses was also due to reasons of a ‘theological’ nature). Nonnoi 2000 claimed that in the first day of the Discourses Galileo did not develop the problem in a definitive and complete manner and insisted on the difference between the concept of minima and that of atoms. See, also Biener 2004, Gómez Lopez 2001, and Gómez Lopez 2008.
- 25.
See Galluzzi 2011, 36–37. As Galluzzi observed (taking up some observations already made by Redondi, see Redondi 1985, 537–539), some Galilean passages concerning the subject of matter and atomism present profound analogies with the observations sketched out by Paolo Sarpi in some of his Pensieri, which the Servite presumably composed in around the 1580s (Galluzzi 2011, 70 and note). We we will be returning to this subject later on.
- 26.
Baldini also focused on this. See Baldini 1977a, 6 ff. The author also claims that the Discourse is the first text in which Galileo criticizes not only individual aspects of Aristotelian physics, but disputes the very foundations of Aristotle’s natural philosophy (ibid., 9).
- 27.
See Palmerino 2000, 292 ff.
- 28.
Galilei, Discorso intorno alle cose che stanno in su l’acqua e che in quella si muovono, OG, IV, 106.
- 29.
- 30.
Galluzzi maintains that this excerpt represents a further step forward by the scientist towards developing a ‘binary’ concept of atomism, which contemplates two levels (equivalent, symmetrical, and interchangeable) at the same time: physical and mathematical. See Galluzzi 2011, 6.
- 31.
Galilei, Il saggiatore, OG, VI, 350; Eng. trans. Drake 1957, 277.
- 32.
This idea had already been put forward by Galileo some years earlier, as recorded by the scientist’s correspondence. In a letter from as early as 1619 he refers to shape, size and motion as characteristics typical of the smallest parts that make up bodies and are the fundamental components of the phenomenology of the sensation that Galileo would go on to develop in The Assayer. In a letter to Galileo dated 8 August 1619, Giovanni Battista Baliani expressed his doubts regarding the theory of matter that Galileo had set out through the pen of his pupil Guiducci in the Discourse on Comets. At the bottom of the page, Galileo had noted that the only real characteristics that can be attributed to bodies are shape, size and motion. See Giovanni Battista Baliani to Galileo, 8 August 1619, OG, XII, 475. See also Galluzzi 2011, 68 ff.
- 33.
Galilei, Il saggiatore, OG, VI, 350: ‘E come ai quattro sensi considerati ànno relazione i quattro elementi, così credo che per la vista, senso sopra tutti eminentissimo, abbia relazione la luce, ma con quella proporzione d’eccellenza qual è tra ‘l finito e l’infinito, tra ‘l temporaneo e l’istantaneo, tra ‘l quanto e l’indivisibile, tra la luce e le tenebre.’
- 34.
Ibid., 352; Eng. Trans. Drake 1957, 278.
- 35.
Baldini 1977a emphasized that in a letter to Fortunio Liceti, dated 25 August 1640, Galileo openly disputed the position that had been attributed to him by the Aristotelian philosopher La Galla, who accused him of claiming light to be a material and corporeal substance (see Galileo to Fortunio Liceti, 25 August 1640, OG, XVIII, 233–234). Nevertheless, he considered it to be composed of infinite corpuscules, so that it could be defined as something ‘simultaneously’ corporeal and incorporeal.
- 36.
However, we must observe that in the Discourses of 1638, Galileo would claim that light has no instantaneous velocity, but moves in time. See Galilei, Discorsi e dimostrazioni matematiche intorno a due nuove scienze, OG, VIII, 88–9.
- 37.
See Galluzzi 2011, 76–78.
- 38.
- 39.
Galilei, Postille alle esercitazioni filosofiche di Antonio Rocco, OG, VII, 745 (my italics).
- 40.
Ibid. See Galluzzi 2011, 87.
- 41.
- 42.
On the discussion of the rota aristotelis in the Discourses and the importance of the geometrical problem in reference to the concept of the continuum developed by Galileo, see Dijksterhuis 1961, 421–423.
- 43.
Galilei, Discorsi e dimostrazioni matematiche intorno a due nuove scienze, OG, VIII, 95–96: ‘… gl’infiniti lati indivisibili del maggior cerchio con gl’infiniti indivisibili ritiramenti loro, fatti nell’infinite istantanee dimore de gl’infiniti termini de gl’infiniti lati del minor cerchio, e con i loro infiniti progressi, eguali a gl’infiniti lati di minor esso cerchio, compongono e disegnano una linea eguale alla descritta dal minor cerchio, contentente in sé infinite sovrapposizioni non quante, che fanno una costipazione e condensazione senza veruna penetrazione di parti quante, quale non si può intendere nella linea divisa in parti quante, quale è il perimetro di qualsivoglia poligono, il quale, disteso in linea retta, non si può ridurre in minor lunghezza se non col far che i lati si sovrapponghino e penetrino l’un l’altro.’
- 44.
- 45.
Galilei, Discorsi e dimostrazioni matematiche intorno a due nuove scienze, OG, VIII, 71; Eng. trans. Galilei 2003, 28, slightly modified.
- 46.
Ibid., 72; Eng. Trans. 25.
- 47.
Ibid.: ‘… risoluta in parti non quante, cioè nei suoi infiniti indivisibili.’
- 48.
Ibid.
- 49.
Ibid. (my italics).
- 50.
Ibid., p. 96. As underscored by Galluzzi, the first day of the Discorsi marks the completion of the process undertaken by Galileo since the years of the Pisan De motu, in which he considers the mathematical and physical interpretation of the natural world to be perfectly equivalent and comparable. See Galluzzi 2011, 84.
- 51.
OG, VIII, 96; Eng. Trans. Galilei 2003, 51.
- 52.
Ibid., 86.
- 53.
See Cavalieri 1632.
- 54.
Galilei, Discorsi e dimostrazioni matematiche intorno a due nuove scienze, OG, VIII, 86 (my italics).
- 55.
In a letter dated 2 October 1634, Cavalieri wrote to Galileo that his position did not force him to uphold the continuum composed of indivisibles (OG, XVI, 136–138, esp. 138). Subsequently, the two scholars discussed the composition of the continuum and indivisibles. See Cavalieri 1989, 725–769. On the discussion between the two and Cavalieri’s contribution to the development of the Galilean theory, see Giusti 1980, 40 ff.; Galluzzi 2011, 109–111; Jullien 2015, and Palmerino 2010. See also Brunschvicg 1913, 162–167; Baroncelli 1992; Festa 1992; Radelet-De Grave 2015.
- 56.
Descartes to Mersenne, 11 October 1638, AT, II, 383. Upon examining the Discourses and Mathematical Demonstrations, Descartes deemed the Galilean plan to ‘examine matters of physics with mathematical reasons’ to be laudable and declared himself to be in total agreement with Galileo regarding this matter (ibid., AT, II, 380). Despite this, he made some detailed criticisms of Galileo’s work. See Shea 1978, especially as regards the problem of the continuum and indivisibles: 152 ff.
- 57.
Ibid., AT, II, 384 (my trans.)
- 58.
Ibid., AT, II, 382 (my trans.).
- 59.
Galilei, Discorsi e dimostrazioni matematiche intorno a due nuove scienze, OG, VIII, 67; Eng. Trans. Galilei 2003, 19: ‘…le sottilissime particole del fuoco, penetrando per gli angusti pori del metallo (tra i quali, per la lor ristrettezza, non potessero passare i minimi dell’aria né di molti altri fluidi), col riempiere i minimi vacui tra esse fraposti liberassero le minime particole di quello dalla violenza con la quale i medesimi vacui l’una contro l’altra attraggono, proibendogli la separazione; e così, potendosi liberamente muovere, la lor massa ne divenisse fluida, e tale restasse sin che gl’ignicoli tra esse dimorassero; partendosi poi quelli e lasciando i pristini vacui, tornasse la lor solita attrazione, ed in conseguenza l’attaccamento delle parti.’
- 60.
Descartes illustrates his conception of the microscopic structure of solids, distinguishing it from that of water, in Descartes, Les Météores, AT, VI, 233; Eng. Trans. Garber 2009, 115: ‘I assume that the small particles of which water is composed are long, smooth, and slippery like little eels, which are such that however they join and interlace, they are never thereby so knotted or hooked together that they cannot easily be separated; and on the other hand, I assume that nearly all particles of earth, as well as of air and most other bodies, have very irregular and rough shapes, so that they need be only slightly intertwined in order to become hooked and bound to each other, as are the various branches of bushes that grow together in a hedgerow.’ On the structure of matter in Descartes see: Gaukroger 2002, 130–134.
- 61.
Hobbes to Mersenne for Descartes, 7 February 1641, AT, III, 302.
- 62.
Ibid., AT, III, 302–303.
- 63.
In response to the objections made by Descartes, who did not agree that Hobbes’ subtle fluid was comparable to his subtle matter, Hobbes set out his theory more clearly. See AT, III, 302, CH, I, 63: ‘Neque enim ego dixi durescere corpora per ingressum spirituum, neque mollescere per exitum eorundem; Sed spiritus subtiles & liquidos, vehementiâ motûs sui, posse constituere corpora dura, ut adamantem; & lentitudine, alia corpora mollia, ut aquam vel aërem.’
- 64.
In De corpore, XXVIII, OL, I, 384–385, Hobbes considers various causes for bodies becoming hard: freezing; the cohesion of atoms within a coherent whole (ibid., 386–7); the ‘exhalation’ of fluid particles from the body, thanks to which the remaining hard particles become compacted (ibid., 388) and, lastly, Hobbes considers his old explanation, which contemplates the fast, whirling motion of particles (ibid.).
- 65.
The idea that the hardness of bodies can be attributed solely to internal motion is also found in TO II, 154, and in MLT, XXIV, 11, 299).
- 66.
- 67.
As we know, until February 1648 Hobbes had admitted the possibility of a vacuum interspersum (see Hobbes to Marin Mersenne, from Saint Germain, 7[17] February 1648, CH, I, 165) and his attitude towards the vacuum changed, starting in May of the same year (see Hobbes to Marin Mersenne, from Saint Germain, 15 [25] May 1648, CH, I, 172).
- 68.
- 69.
Hobbes was forced to admit the existence of these small empty spaces due to his model of light propagation. This emerges clearly in the Tractatus Opticus II and returns in De motu, loco et tempore (MLT, IX, 2, 161) where Hobbes confirms that the movement of the light source is not admissible, ‘sine vacuo, vel spatiolis vacuis inter partes interiectis; sed quia neque impossibile est vacuum immaginari, neque possibile probare quòd omne spatium sit corpore aliquo repletum, nihil impedit quin partes solis motum talem habere possint’. In the First Draught Hobbes tackles the objection that motion within the light source cannot take place without the existence of the vacuum. See FD, fol. 6–7/96: ‘I suppose, that there is a vacuity made by such dilatation, but find no impossibility, nor absurdity, nor so much as an improbability in admitting vacuity, for no probable argument hath ever beene produced to the contrarie, unlesse wee should take a space or extension for a body or thing extended and thence conclude because space is everywhere imaginable, Therefore bodie is in every space, For who knowes not that Extension is one thing and the thing extended another …’
- 70.
Hobbes’ relationship with atomism has been explored since the nineteenth century, with the important study by Lasswitz (see Lasswitz 1963, II, 224 ff.) in which the author maintained that Hobbes’ theory of fluids was what made it so difficult to place the author in the history of atomism. The issue was also taken up again by Pacchi in particular, who had already underscored the irreconcilability of atomism and antivacuism (see Pacchi 1965, 238–242, and primarily Hobbes 1978). See also Kargon 1966, 54–62. The difficulty involved in reconciling Hobbesian antivacuism with atomism was reiterated by Giudice (Giudice 1997). On the other hand, Agostino Lupoli, making particular reference to a passage from the Decameron physiologicum, in which Hobbes seems to suggest the existence of atoms that are created hard by an eternal cause (EW, VII, 134), maintains that Hobbes’ concept of atoms is compatible with his fluidism, if we suppose a sort of physical indivisible. See Lupoli 1999, esp. 597 and Lupoli 2006, 539–554.
- 71.
De corpore, VII, 13, OL, I, 89; Eng. trans. EW, I, 100.
- 72.
Ibid., XXII, 17 ff., OL, I, 283 ff.
- 73.
Dialogus physicus de natura aeris, OL, IV, 244; Eng. Trans, Shapin and Schaffer 1985, 353.
- 74.
Ibid.; Eng. Trans, Shapin and Schaffer 1985, 354.
- 75.
Ibid., 283; Eng. Trans, Shapin and Schaffer 1985, 387.
- 76.
Ibid.; Eng. Trans, Shapin and Schaffer 1985, 388.
- 77.
Ibid, 284.
- 78.
Ibid, 285. The phenomenon was explained in a different manner in the first chapter of De homine, where Hobbes maintained that the generation of flesh in the human body is produced in different stages: firstly, with the digestion of food, then with circulation that carries the transformed matter to the nerves and, lastly, this matter, filtered through the nerves, becomes flesh. See De homine, I, 2, OL, II, 2–5. See also Médina 2013b, 160–162. The idea, derived from Galen, that animal spirits present in the nerves are like an air or a very subtle wind ‘qui, venant des chambres ou concavités qui sont dans le cerveau, s’escoule par ces mesmes tuyaux dans les muscles’, is present, in different terms, not only in Descartes’ Dioptrics (AT, VI, 110), but also in Campanella 2007, 47 ff. See Ernst 2010, 26 and 108 ff.
- 79.
Dialogus physicus de natura aeris, OL, IV, 245; Eng. trans, Shapin and Schaffer 1985, 389–390.
- 80.
According to Lupoli, this reveals the not only conceptual, but real and ontological priority of the fluid over the prime hard body. See, in this regard Lupoli 2006, 549 and 553–534. Lupoli maintains that Hobbes thought of the existence of a primordial fluid matter, which would in some way predate ‘creation’ and was entirely lacking in motion, which it would acquire through the intervention (in a sort of creative act) of a primary corporeal mover, which would cause atoms to come together. In reality, I believe that Hobbes’ hypothesis presents fewer ‘metaphysical’ connotations, as we shall see below.
- 81.
See Galilei, Discorsi e dimostrazioni matematiche intorno a due nuove scienze, 86–87; see Galluzzi 2011, 96.
- 82.
De corpore, VII, 13, OL, I, 89; EW, I, 100.
- 83.
Examinatio et emendatio mathematicae hodiernae, OL, IV, 56: ‘Divisio est opus intellectus’.
- 84.
- 85.
Descartes, La dioptrique, AT, VI, 86–87: ‘y ayant plusieurs pores en tous les corps que nous apercevons autour de nous, ainsy que l’expérience peut monstrer fort clairement; il est necessaire que ces pores soyent remplis de quelque matière fort subtile & fort fluide, qui s’estende sans interruption depuis les Astres jusques a nous.’
- 86.
De corpore, XXVI, 3, OL, I, 340; EW, I, 417.
- 87.
Ibid.
- 88.
See White 1642, 31 ff.
- 89.
MLT, III, 12, 124.
- 90.
Ibid.
- 91.
Ibid., III, 9, 123.
- 92.
Ibid.
- 93.
Ibid.
- 94.
Ibid., XI, 8, 185.
- 95.
On the interpretation of indivisibles in Hobbes and his criticism of Torricelli’s demonstration of the construction of the ‘acute hyperbolic solid’ through the application of the indivisible method, see Giorello 1990, 237–239; Mancosu and Vailati 1991, 67–68; Jesseph 1993. Jesseph demonstrates that Hobbes did not reject the indivisible method outright and, indeed, that he reflected extensively upon Cavalieri’s work, drawing some observations from it (contained in a manuscript now conserved in Chatsworth House: Hobbes C.1.5). What is more, in chap. 26 of De corpore, Hobbes proposed a demonstration taken from Propositio 23 of Cavalieri’s Exercitationes Geometricae Sex (ibid., 183–186). See also Jesseph 1999, 185–189; Holden 2004, 96–99. On Torricelli’s indivisibles, see De Gandt 1989, 1992; Bortolotti 1989; Bascelli 2015.
On the subject of indivisibles and the transition from the concept of indivisible to the Leibnizian concept of infinitesimal: Malet 1996, esp. 11–50. On the ‘prehistory’ of the concept of indivisibile, see Celeyrette 2015.
- 96.
Six Lessons, EW, VII, 201.
- 97.
See Examinatio et emendatio mathematicae hodiernae, OL, IV, 55–56.
- 98.
See De Principiis et Ratiocinatione Geometrarum, OL, IV, 391–392.
- 99.
De corpore, XXVI, 5, OL, I, 347–348; Eng. Trans. EW, I, 426.
- 100.
See Seven Philosophical Problems, EW, VII, 38: ‘But for one general cause of hardness it can be no other than such an internal motion of parts as I have already described, whatsoever may be the cause of the several concomitant qualities of their hardness in particular.’ See, in general, Chap. 5, which discusses ‘hard and soft’. Ibid., 32–38.
- 101.
Decameron physiologicum, EW; VII, 133: ‘But yet this is most certain, that nothing can make a hard body of a soft, but by some motion of its parts.’
- 102.
Ibid., 133–134.
- 103.
Ibid., 129.
- 104.
Ibid., 134.
- 105.
Galilei, Discorsi e dimostrazioni matematiche intorno a due nuove scienze, OG, VIII, 66–67; Eng. Trans. Galilei 2003, 19, slightly modified.
- 106.
Descartes, Les Météores, AT, VI, 237.
- 107.
Ibid. The image of particles of water resembling small eels was also cited critically in the second treatise on optics. See TO II, chap. I, § 21, fol. 202v/158.
- 108.
Decameron physiologicum, EW, VII, 133: ‘For the parts of the hardest body in the world can be no closer together than to touch; and so close are the parts of air and and water, and consequently they should be equally hard, if their smallest parts had not different motions.’
- 109.
The work was published posthumously in 1682, but written in 1668, as Hobbes writes in the preface, where he indicates that he had composed it 10 years prior to Bramhall’s text The Catching of Leviathan, published in 1658. See An Answer to a book published by Dr. Bramhall, EW, IV, 282.
- 110.
An Answer, EW, IV, 309–310.
- 111.
In MLT, III, 3, 118, the place is defined in these terms: ‘Quoties autem corporis alicuius spatium reale coincidet cum parte aliqua spatii imaginarii, illam partem, qua cum coincidit, vocamus corporis illius, locum. Quod si cum spatio aliquo imaginario, corporis nullius spatium reale coincidat, tum vocamus spatium illud imaginarium vacuum.’
- 112.
In chap. 7 of De corpore, entitled Place and Time, Hobbes does not provide a definition of place (see De corpore, OL, I, 81 ff.), since it was already present in the previous chapter (De corpore, VI, 6, 62–63): ‘locus est spatium quod a corpore adaequate impletur vel occupatur, ignorare non potest; et qui motum concipit, nescire non potest quod motus est loci unius privatio et alterius acquisitio.’ In the aforementioned manuscript De Principiis, however, the definition was more in keeping with the language used in De motu. See De Principiis, (National Library of Wales, Ms 5297), MLT, Appendix II, 453: ‘Space (which I always understand imaginary) which is coincident with the magnitude of any body is called the place of that body, and then the body is said to be placed.’ Regarding the distinction between real space and imaginary space and the importance of these concepts in Hobbesian philosophy, see Schuhmann 1992.
- 113.
See Aristotle, De generatione et corruptione, I, 5, 328a. On the problem of substantial change or mixture see below, section 4.
- 114.
Descartes, Les Météores, AT, VI, 238–239. On the differences between the Cartesian concept and the atomistic theory of matter, see De Buzon 2013, 243 ff.
- 115.
De corpore, XXVII, 1, OL, I, 364; EW, I, 448 (my italics). Lupoli drew attention to this passage and believes that the Hobbesian concept of fluid has a ‘metaphysical’ dimension. It could be identified, in some way, with a sort of ‘primordial’ prime matter. See Lupoli 1999, 588; Lupoli 2006, 540–541. However, in my opinion Leijenhorst quite rightly objected that in the cited passage Hobbes does not identify the two terms at all, but simply limits himself to comparing them (see Leijenhorst 2004, 90 ff.). He also maintains that Hobbes is referring here to the traditional Aristotelian concept of prime matter, which is considered inert (ibid., p. 91), but Hobbes, on the contrary, proposes a radically different conception of prime matter, which he identifies with corporeality in general. What is more, in reference to the identification of divinity with the corporeal spirit or fluid proposed by Lupoli, Leijenhorst (ibid., 81–88) cites some passages from Hobbesian works that are difficult to reconcile with this idea. For the differences between the Hobbesian concept of prime matter and the one specific to the Aristotelian tradition see Leijenhorst 2002, 150–155, where the author also makes an interesting comparison with Zabarella’s idea of prime matter.
- 116.
MLT, VII, 3, 146.
- 117.
Ibid., 147 (my trans.).
- 118.
See supra, chap. 2, § 2.
- 119.
MLT, XXVII, 1, 312 (my trans.).
- 120.
Id., De Principiis (National Library of Wales, Ms 5297), MLT, Appendix II, 457.
- 121.
See Aristotle, De generatione et corruptione, I, 5, 320 b; Metaphysics, 1029 b.
- 122.
See De corpore, VIII, 24, OL, I, 105; EW, I, 118–119, slightly modified.
- 123.
Ibid.
- 124.
On the atomistic motifs present in the philosophy of Galileo, please make special reference to the cited studies by Shea, Redondi and Galluzzi. For a detailed and accurate comparison with the philosophy of Lucretius and the De rerum natura, see the interesting contribution by Camerota 2008.
- 125.
- 126.
Campanella maintains that Galileo and Sarpi were both ‘Democritean’ in a letter to Peiresc. See Campanella to Nicolas-Claude Fabri de Peiresc, in Campanella 2010, 454: ‘io son certissimo ch’il signor Galileo in molte cose, massime nei principii, è con Democrito, e dal discorrer c’ha fatto meco in Roma, e da quel che scrive nell’opuscolo De natantibus e nel Saggiatore, el padre Castelli [e]t monsignor [C]iampoli e condiscepoli così [per] tal lo difendeno. El fra Paolo ab antiquo si sa essere stato democritico, perché Giovan Battista Porta suo amico quando stava in Napoli fra Paolo, e col quale han fatto molte operazioni chimiche, me l’ha narrato. El signor Galileo conversò con lui, quando eravamo in Padua nel 1593.’ See also Ernst and Canone 1994, esp. 363–364. See also the interesting observations made by Favino 1997, where the author also shows Ciampoli’s warm support for the atomistic doctrines of his master Galileo. On Ciampoli see Favino 2015. There are numerous interesting analogies between the thinking of Ciampoli and the texts by Gassendi. As regards the link between Galileo and Sarpi, it is superfluous to underline that during his period in Padua, Galileo had the opportunity to work in collaboration with the Servite friar, who presumably contributed to the discoveries that Galileo published in his Sidereus Nuncius. In this regard see Cozzi 1979, 164 ff.; Sosio 1995, and Bucciantini, Camerota and Giudice, 24–43. Favaro’s classic study is also useful. See Favaro 1966, II, 69 ff. See also Frajese 1994, 63 ff. Wootton maintains that Sarpi was a materialist, but not an atomist, because ‘he believed that matter could be changed: it was not made up of unalterable unitary atoms, but would be compressed, expanded and so on.’ See Wootton 1983, 15. However, see the following note.
- 127.
Galluzzi 2011, 82 emphasizes the profound analogy between this passage from Galileo’s Discourses and the idea that features in one of Paolo Sarpi’s Pensieri. See the ‘Pensiero 111’ in Sarpi 1996, 130: ‘La materia delle cose naturali è corpo, perché, facendosi le trasmutazioni, il corpo è quello che sempre resta e non trasmutasi mai, e li suoi termini sono superficie, linea e punto, co’ quali terminato acquista figura.’ In my opinion, an equally significant mention is made in another pensiero, in which Sarpi criticises the Aristotelian notion of transmutation, just as Galileo would do. See the ‘Pensiero 332′, ibid., 267: ‘la nutrizione si può far, senza alcuna trasmutazione, solo per congragazion e separazione.’ Sarpi’s concept of matter is extremely similar to that of Hobbes, with whom he shares the same ‘Galilean root,’ as I have emphasized in Baldin 2013, esp. 105–111. On the similarities between Sarpi and Hobbes on the political aspects, see also Baldin 2016a, and Baldin 2015.
- 128.
Decameron physiologicum, EW, VII, 132: ‘Transubstantiation of bodies by mixture’.
- 129.
Ibid.: ‘Mixture is no transubstantiation’.
- 130.
Hobbes considered transubstantiation a mere absurdity and, in fact, in Chap. 8 of his Leviathan he places the concept of transubstantiation in the category of insignificant speech (see Hobbes 2012, 122). Negative references to this dogma also appear elsewhere, as in Historia Ecclesiastica, OL, V, 404.
- 131.
It is interesting to observe that Hobbes’ statements seem to ‘confirm’ Orazio Grassi’s accusations made against Galileo, according to whom Galileo’s ‘Democritean’ concept of matter is incompatible with the dogma of transubstantiation. Sarsi 1626, OG, VI, 486–487: ‘Galilaeus vero diserte asserit, calorem, colorem, saporemque ac reliqua huiusmodi, extra sentientem, ac proinde in pane ac vino, pura esse nomina: ergo, abscedente panis ac vini substantia, pura tantum qualitatum nomina remanebunt. Quid ergo perpetuo opus miraculo est, puris tantus nominibus sustentandis? Videat ergo hic, quam longe ab iis distet, qui tanto studio harum specierum veritatem ac durationem firmare conati sunt, ut etiam divinam huic operi potentiam impenderint. Scio equidem lubricis ac versutis ingeniis videri posse, patere hinc etiam effugium aliquod, si fas sit sanctissimorum fidei praesidium dicta ad libitum interpretari, eaque a vero et communi sensu alio detorquere.’ See also Shea 1970, 21, but above all Redondi 2009, 244 ff., who claims that this was the real reason for Galileo’s condemnation.
- 132.
Aristotle, De generatione et corruptione, I (A), 10, 328a.
- 133.
Indeed, in De corpore, I, 8, OL, I, 9, Hobbes claims that ‘Subjectum Philosophiae, sive materia circa quam versatur, est corpus omne cujus generatio aliqua concipi, et cujus comparatio secundum ullam ejus considerationem institui potest.’
- 134.
MLT, Appendix II, 457 (my trans.).
- 135.
See White 1642, 329.
- 136.
See MLT, XXXIII, 7, 379.
- 137.
De corpore, XXVI, 1, OL, I, 336; Eng. Trans. EW, I, 412–413. See Paganini 2008, and, above all, Paganini 2015. I disagree with Arrigo Pacchi, who in numerous articles, maintained that a philosophical concept of God as the prime mover represents the necessary foundation for the existence of the universe in Hobbes’ system. See Pacchi 1984 (now also in Pacchi 1998, 53–65), and Pacchi 1988. The question is also taken up again in another contribution by Pacchi, in which he compares the different interpretations of Hobbesian theology that emerged during the twentieth century with a number of philosophical and theological reflections made by Hobbes. See Pacchi 1990. I do not find Lupoli to be convincing either, who—starting with the claim that Hobbes’ statements against the creation of the world made in De motu, loco et tempore and De corpore are limited to upholding the impossibility of philosophical argument in favour of creation, without reaching an all-out denial of it—maintains that it is possible to state that the eternity of the world is ‘undoubtedly denied by Hobbes’ (Lupoli 2006, 554 and 566–574). It is true that Hobbes incidentally states in ‘Appendix ad Leviathan’ (in Hobbes 2012, 1147; OL, III, 513), that the world was made ‘without doubt from nothing’, but he also indicates that this is deemed to be the truth because it is written in the Holy Scriptures and not on the basis of reasoning or philosophical exploration. In fact, it is necessary to bear in mind that Hobbesian statements on matters of faith are sometimes incoherent or even openly contradict his own philosophical arguments. For example, in De motu, loco et tempore, Hobbes, so as not to attribute materiality to God, maintains that the existence of incorporeal substances is a dogma of faith (MLT, IV, 3, 127), something that is openly denied in his later works, where the very concept of incorporeal substance is held to be a mere absurdity.
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Baldin, G. (2020). The Paradoxes of Matter. In: Hobbes and Galileo: Method, Matter and the Science of Motion. International Archives of the History of Ideas Archives internationales d'histoire des idées, vol 230. Springer, Cham. https://doi.org/10.1007/978-3-030-41414-6_4
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