Abstract
Despite his inclination for the Geometrical Method and the mathematization of nature, the most markedly mathematical and geometrical works of Hobbes reveal his gaps of knowledge in these areas, earning him harsh criticism from British mathematicians and scientists.
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Notes
- 1.
- 2.
See White 1642, 204 ff. For a biographical and intellectual profile of White see Southgate 1993 (on White’s tendency to reconcile Aristotelianism and certain aspects of modern science, ibid., 5 ff.). On the circumstances surrounding the writing and publication of White’s De Mundo see Jacquot and Jones 1973, 9–70. On the Erastian spirit shared by Hobbes and the ‘Blackloists,’ that is, the English Catholics who revolved around White and wanted to abandon the realist faction to open separate talks with Cromwell, see Collins 2002, and Collins 2005, 139–141, and 178–180.
- 3.
According to Hobbes, the water of the sea or of a lake does not exercise any weight on an object on the bottom, but this is not because the object is in its natural place, but instead—according to Archimedean principles—due to pressure exercized on the mass of water by the object that has occupied its place. See MLT, XX, 3, 248–249.
- 4.
Ibid., XX, 8, 251–252.
- 5.
Ibid., 251–252, Eng. Trans. Hobbes 1976, 230, largely modified.
- 6.
On the Aristotelian idea that the persistence of movement requires a mover, see: Aristotle, Physics, VII, 241 b ff. Jean Bernhardt, who was the first to devote a short contribution to the presence of Aristotle physics in Hobbes, maintained that Hobbes’ principle of conservation of movement is Aristotelian (see Bernhardt 1989b). Nevertheless, it seems that in this and many other aspects, Hobbes owes a debt to Galileo’s physics and is also perfectly aware of the process of translating certain Aristotelian concepts in mechanistic terms, which is something that was undertaken by the Galileo and continued by Hobbes (in this regard, see the suggestion made by Spragens 1973, 53 ff.). On the presence of Aristotle and Aristotelianism in Hobbesian philosophy, see Leijenhorst 2002.
- 7.
Galilei, Dialogo sopra i due massimi sistemi del mondo, OG, VII, 52–53; Eng. trans. Galilei 2001, 32.
- 8.
See Camerota 2004, 446 ff.
- 9.
See Galilei, Le Mecaniche, OG, II, 180
- 10.
As underscored by Bucciantini, the Istoria is the ‘first’ Galilean text on ‘natural philosophy.’ See Bucciantini 2003, 217.
- 11.
Galilei, Istoria e dimostrazioni intorno alle macchie solari, OG, V, 134; Eng. trans. Finocchiaro 2008, 98.
- 12.
Galilei, Dialogo sopra i due massimi sistemi del mondo, OG, VII, 174; Eng. trans. Finocchiaro, 232.
- 13.
See Koyré 1966, 229–230. Westfall also adopts a similar position to Koyré. See Westfall 1971, 18–19. Geymonat’s position is different, maintaining that Galileo’s failure to explicitly set out the principle of inertia in no way implies that this princple is completely lacking from Galilean physics. On the contrary, it is implicit in his discussions of atronomy in the Dialogues and in his writings on physics and mechanics in the Discourses. See Geymonat 1957, 322–326. In contrast to Koyré’s interpretation, see also Drake, ‘Galileo and the Concept of Inertia’, in Drake 1970, 240–256; and Drake, ‘The Case Against ‘Circular Inertia”. Ibid., 257–278.
- 14.
Koyré’s views are supported by certain passages from the Dialogue, such as the following exchange of quips between Salviati and Simplicio. Galilei, Dialogo sopra i due massimi sistemi del mondo, OG, VII, 173–174; Eng. trans. Galilei 2001, 170–171: ‘Salv. … Now tell me, what do you consider to be the cause of the ball moving spontaneously on the downward inclined plane, but only by force on the one tilted upward? Simp. That the tendency of heavy bodies is to move toward the center of the earth, and to move upward from its circumference only with force; now the downward surface is that which gets closer to the center, while the upward one gets farther away. Salv. Then in order for a surface to be neither downward nor upward, all its parts must be equally distant from the center. Are there any such surfaces in the world? Simp. Plenty of them; such would be the surface of our terrestrial globe if it were smooth, and not rough and mountainous as it is. But there is that of the water, when it is placid and tranquil.’
- 15.
- 16.
Galilei, Discorsi e dimostrazioni intorno a due nuove scienze, OG, VIII, 268: ‘Mobile quoddam super planum horizontale proiectum mente concipio, omni secluso impedimento: iam constat, ex his quae fusius alibi dicta sunt, illius motum aequabilem et perpetuum super ipso plano futurum esse, si planum in infinitum extendatur.’
- 17.
Ibid., 243: ‘Attendere insuper licet, quod velocitatis gradus, quicunque in mobili reperiatur, est in illo suapte natura indelebiliter impressus, dum externae causae accelerationis aut retardationis tollantur, quod in solo horizontali plano contingit, nam in planis declivibus adest iam causa accelerationis maioris, in acclivibus vero retardationis: ex quo pariter sequitur, motum in horizontali esse quoque aeternum, si enim est aequabilis, non debilitatur aut remittitur, et multo minus tollitur.’
- 18.
The importance of the Galilean concept of inertia in Hobbes was first identified by Spragens, although he did not go into the matter in any great depth. See Spragens 1973, 60 ff.
- 19.
See MLT, XX, 8, 252, Eng. Trans. Hobbes 1976, 231.
- 20.
- 21.
MLT, XXI, 13, 262.
- 22.
Ibid.
- 23.
Here, as elsewhere, White keeps faith with his Aristotelian principles. His arguments against the existence of the vacuum are also based on Aristotelian and scholastic philosophy. Basing his theory on the Aristotelian definition of place, defined as an immobile surface of the body (Aristotle, Physics, IV, 212a, 20), he denied both the possibility of the vacuum and the plurality of worlds. In fact, if there were multiple worlds, we would be faced with the problem of justifying the vacuum inter mundia. See White 1642, 29 ff. White’s theory particularly echoes an argument linked to the theme of the annihilatio mundi, found in Jean Buridan, as in other fourteenth-century Parisian natural philosophers and some Mertonians. When reasoning upon issues concerning the potentia dei absoluta, medieval thinkers theorized about a miraculous intervention of God that would annihilate the cosmos, asking themselves whether empty space could be conceived as a place. On this subject see Grant 1981, esp. 86 ff.; Grant 1996a, b, 82–83; Funkenstein 1986, 117 ff.; Parodi 1981, 201 ff.; Bianchi 1997, 269–303. On the debate surrounding the vacuum during the Renaissance (esp. in Patrizi and Telesio) see: Schmitt, ‘Prove sperimentali sull’esistenza del vuoto’. In Schmitt 2001, 65–83.
- 24.
See Brandt 1928, 328. As regards the principle of inertia associated with circular motion, Mintz 1952 maintains that Hobbes absorbed a circular concept of inertial motion by reading Galilean texts. Henry has returned to this subject recently, underscoring the analogies between certain passages in Galileo’s Dialogue and Hobbes’ simple circular motion. See Henry 2016, esp. 13 ff.
- 25.
De Principiis (National Library of Wales, Ms 5297), MLT, Appendix II, 457: ‘Quod quiescit nisi ab externo moveatur semper quiescet. Quod movetur nisi ab externo impediatur semper movebitur.’
- 26.
See Paganini 2010, 34–35.
- 27.
Ibid. On the importance of the concept of cause in Hobbes see supra, chap. 2, § 7.
- 28.
See De corpore, VIII, 19, OL, I, 102.
- 29.
Ibid., IX, 7, 110; Eng. Trans. EW, I, 124.
- 30.
Ibid., 110–111; Eng. Trans. 125. As he continues, while not referring to it directly, Hobbes goes back to and criticizes White’s opinion, according to which rest is ‘more opposed’ to movement, than movement is opposed to the the rest.
- 31.
Ibid., XV, 3, 180.
- 32.
Ibid., XV, 7, pp. 182–183; Eng. trans. 216.
- 33.
Ibid., 183: ‘Et siquidem in pleno fiat, tamen cum conatus sit motus, id quod in via ejus proxime obstat removebitur, et conabitur ulterius, et hujus conatus removebit rursus id, quod sibi proxime obstat, et sic in infinitum. Pertingit etiam ad distantiam quantamcumque in instante; nam eodem instante, quo prima pars medii pleni removet partem sibi proximam, pars secunda partem rursus sibi proximam obstantem removet.’
- 34.
Ibid. Eng. Trans. EW, I, 217.
- 35.
Ibid. EW, I, 216
- 36.
Ibid.: ‘I do not here examine things by sense and experience, but by reason’ The position expressed by Hobbes in this passage recalls some of the declarations made by Galileo, who stated that the demonstrations ‘regarding my supposition lose nothing of their strength and conclusiveness; just as the demonstration of Archimedes is not diminished by the fact that in nature no moving body is found that moves in spiral lines.’ (Galileo to Giovan Battista Baliani, January 7, 1639, OG, XVIII, 12–13, my translation).
- 37.
See Koyré 1966, 314–317. Nevertheless, Carla Rita Palmerino has claimed, on the contrary, that in Gassendi the abovementioned principle is far from being formulated correctly and explicitly. See Palmerino 2004, esp. 150–151, and Palmerino 2008, esp. 160 ff. Paolo Galluzzi highlighted the central role played by Gassendi in the circulation of the Galilean laws of motion, so much so that his Epistolae de motu led to a second ‘affaire Galilée.’ See Galluzzi 1993, 86–119. Generally, on the links between the physics of Galileo and Gassendi, see Bloch 1971, 189–194; Festa 1999.
- 38.
Gassendi, Epistolae tres. De motu impresso a motore translato. In Gassendi 1658, III, 495b; Eng. Trans. in Palmerino 2004, 150: ‘Quaeres obiter, quidnam eveniret illi lapidi, quem assumpsi concipi posse in spatiis illis inanibus, si a quiete exturbatus aliqua vi impelletur? Respondeo probabile esse, fore, ut aequabiliter, indefinenterque moveretur; et lente quidem, celeriterve, prout semel parvus, aut magnus impressus foret impetus. Argumentum vero desumo ex aequabilitate illa motus horizontalis iam exposita; cum ille videatur aliunde non desinere, nisi ex admistione motus perpendicularis; adeo, ut quia in illis spatiis nulla esset perpendicularis admistio, in quacumque partem foret motus inceptus, horizontalis instar esset, et neque acceleraretur, retardereturve, neque proinde unquam desineret.’
- 39.
Gassendi, accused of plagiarism by Jean-Baptiste Morin (who claimed that some of the speculations in the Epistola de motu, published in 1642, had been taken from one of his own works printed the previous year), called up Hobbes as his witness in his response, specifying that the English philosopher had been aware of his ideas since 1640. See Gassendi, ‘Epistola III. In librum qui a viro Cl. Ioanne Morino’. In Gassendi 1658, III, 521b. See Leijenhorst 2004, 169.
- 40.
Lisa Sarasohn has claimed that the development of a ‘mechanical world-view’ in Hobbes was determined by the ideas of Pierre Gassendi, with whom the English philosopher came into contact during his Grand Tour. See Sarasohn 1985, esp. 368. What is more, the author supposes that a reciprocal partnership developed between the two philosophers in the 1640s, especially in the field of psychology and physics (ibid., 370–371). However, Paganini produced a detailed analysis of the relationship between Hobbes and Gassendi as regards psychology (see Paganini 1990) and physics (Paganini 2004b, 2008).
- 41.
TO I, OL, V, 219–220. See also Prins 1996, 133 ff.
- 42.
Leijenhorst can be credited with having identified the influence of Galilean momentum on Hobbes’ conatus. He produced an interesting and in-depth study dedicated to the reception of the Galilean law of falling heavy objects in Hobbes’ natural philosophy. See Leijenhorst 2004, 182–184.
- 43.
See Brandt 1928, 299–300, which draws upon some of Lasswitz’s analyses (see Lasswitz 1963, 214 ff.), who was the first to analyze the importance of the concept of conatus in Hobbes, comparing it to the earlier cogitations of Galileo and the later ones of Leibniz and Newton. A reference to this can also be noted in Malherbe 1984, 103–109. The concept of conatus was studied by Robinet 1990, and especially by Barnouw 1992. More recently, the topic has been returned to in Bertman 2001, Lupoli 2001, Pietarinen 2001, and Jesseph 2016.
- 44.
EL, Part I, chap. VII, § 2, 28: ‘This motion, in which consisteth pleasure or pain, is also a solicitation or provocation either to draw near to the thing that pleaseth, or to retire from the thing that displeaseth. And this solicitation is the endeavour or internal beginning of animal motion, which when the object delighteeth, is called APPETITE; when it displeaseth it is called AVERSION’. On the meaning of conatus in reference to the phenomenology of sensation, see Barnouw 1990, 116.
- 45.
See Brandt 1928, 299–300.
- 46.
See MLT, XIII, 2, 194–195.
- 47.
See Descartes, La Dioptrique, in AT, VI, 88. On the analysis of the notion of the determination of motion and other fundamental concepts in Descartes’ physics, see McLaughlin 2000, esp. 88 ff. For a detailed analysis of Descartes’ physics see Shea 1991 (on inclination, 232 ff.); Gaukroger 2002, which, however, focuses almost entirely on the Principia. On the connection between physics and mechanics in Descartes see Roux 2004.
- 48.
- 49.
TO I, OL, V, 220: ‘… unde propagabitur motus ad retinam, et inde per conatum retinae ad nervum opticus usque ad cerebrum’.
- 50.
MLT, XIII, 2, 195 (my trans.).
- 51.
See Baldin 2017.
- 52.
MLT, XIII, 2, 194–195.
- 53.
De corpore, XV, 2, OL, I, 177; Eng. trans. Hobbes 1976, 206. The English translation also adds ‘and in an instant or point of time.’
- 54.
De corpore, XXII, 1, OL, I, 271: ‘CONATUM definivimus supra cap. xv, art. 2, esse motum per longitudinem quidem aliquam, consideratam autem non ut longitudinem, sed ut punctum. Itaque sive quid conanti resistit, sive nil resistit, conatus tamen idem est’.
- 55.
- 56.
See Gargani 1971, 228.
- 57.
- 58.
See Galilei, Discorsi e dimostrazioni intorno a due nuove scienze, OG, VIII, 81 ff. The subject of the infinite division of matter, featured in his Discourses, will be discussed in depth in the next chapter.
- 59.
De corpore, XXIII, 1, OL, I, 287. Engl. Transl. EW, I, 351.
- 60.
See Leijenhorst 2004, 182.
- 61.
- 62.
- 63.
Galilei, Le Mecaniche, OG, II, 159.
- 64.
Ibid.: ‘… propensione ad andare al basso, cagionata non tanto dalla gravità del mobile, quanto dalla disposizione che abbino tra di loro diversi corpi gravi; mediante il qual momento si vedrà molte volte un corpo men grave contrapesare un altro di maggior gravità.’
- 65.
Ibid.
- 66.
Ibid.
- 67.
Ibid.: ‘Centro della gravità si diffinisce essere in ogni corpo grave quel punto, intorno al quale consistono parti di eguali momenti: sì che, imaginandoci tale grave essere dal detto punto sospeso e sostenuto, le parti destre equilibreranno le sinistre, le anteriori e le posteriori, e quelle di sopra quelle di sotto; sì che il detto grave, così sostenuto, non inclinerà da parte alcuna, ma, collocato in qual si voglia sito e disposizione, purché sospeso dal detto centro, rimarrà saldo. E questo è quel punto, il quale andrebbe ad unirsi col centro universale delle cose gravi, cioè con quello della terra, quando in qualche mezzo libero potesse discendervi.’
- 68.
- 69.
On this subject see Shea 1977.
- 70.
Mersenne 1634. Now in Mersenne 1985, 443 : ‘La pesanteur d’un corps est l’inclination naturelle qu’il a pour se mouvoir, et se porter en bas vers le centre de la terre. Cette pesanteur se rencontre dans le corps pesans à raison de la quantité des parties materielles, dont ils sont composez; de sorte qu’ils sont d’autant plus pesans qu’ils ont une plus grande quantité desdites parties souz une mesme volume.’
- 71.
Ibid., 444: ‘Le moment est l’inclination du mesme corps, lors qu’elle n’est pas seulement considerée dans ledit corps, mais coinjonctement avec la situation qu’il a sur le bras d’un levier, ou d’une balance; et cette situation fait qu’il contrepese souvent à un plus grand poids, à raison de sa plus grande distance d’avec le centre de la balance. Car cet éloignement estant joint à la propre pesanteur du corps pesant, luy donne une plus forte inclination à descendre: de sorte que cette inclination est composée de la pesanteur absoluë du corps, de l’éloignement du centre de la balance, ou de l’appuy du levier. Nous appellerons donc toujours cette inclination composée, moment, qui répond au ’
des Grecs.’ - 72.
Ibid.: ‘Le centre de pesanteur de chaque corps est le point autour duquel toutes les parties dudit corps son également balancées, ou équiponderantes: de sorte que si l’on s’imagine que le corps soit soustenu, ou suspendu par ledit point, les parties qui sont à main droite, contrepeseront à celles de la gauche, celles de derriere à celles de devant, et celles d’en haut à celles d’en bas, et se tiendront tellement en équilibre, que le corps ne s’inclinera d’un costé ni d’autre, quelque situation qu’on luy puisse donner, et qu’il demeurera tousjours en cet estat. Or le centre de pesanteur est le point du corps qui s’uniroit au centre des choses pesantes, c’est-à-dire au centre de la terre, s’il y pouvoit descendre.’
- 73.
De corpore, XXIII, 1, OL, I, 286.
- 74.
Ibid.; Eng. trans. EW, I, 351.
- 75.
Ibid.
- 76.
Ibid.
- 77.
The English Translation also adds ‘and is in the strait line by which the weight is hanged.’ Ibid., 352.
- 78.
Ibid. Compared to the translation, the Latin original offers a better understanding of the Galilean origin of the concepts expressed by Hobbes: ‘IV. Momentum est ponderantis, pro certo situ, certa ad movendum radium potentia. V. Planum aequilibrii est quo ponderans dividitur, ita ut momenta utrinque sint aequalia. VI. Diameter aequilibrii est duorum aequilibrii planorum sectio communis. VII. Centrum aequlibrii est duarum aequilibrii diametrorum commune punctum.’
- 79.
Ibid., XXIII, 4, 288; Eng. Trans. 353.
- 80.
Ibid. 287: ‘Pondus est aggregatum omnium conatuum, quibus singula puncta corporis, quod radium premit, in rectis sibi invicem parallelis conantur; ipsum autem corpus premens ponderans nominatur.’
- 81.
See Leijenhorst 2004, 183.
- 82.
Galilei, Discorsi e dimostrazioni intorno a due nuove scienze, OG, VIII, 202 (my italics); Eng. trans. Finocchiaro, 340.
- 83.
Ibid., 205.
- 84.
- 85.
De corpore, XXII, 1, OL, I, 271; Eng. Trans. EW, I, 333.
- 86.
De corpore, XV, 2, OL, I, 178; Eng. trans. 206. In the English edition, the discussion is broader and more detailed. The fact that Hobbes was well aware of Galileo’s speculations regarding uniformly accelerated motion has been widely demonstrated by Jesseph, who emphasized that the mathematical demonstrations present in chap. 16 of De corpore follow those of Galileo in the fourth day of his Discourses and Demonstrations. On the other hand, as Jesseph himself notes, John Wallis had observed the very close analogy between the geometric argument in § 9 of Chapter 16 of De corpore and Galileo’s speculations. See Jesseph 2004, 204 ff.
- 87.
On the connection between impetus/conatus and the importance of the concept of conatus in Hobbesian dynamics, see also Gaukroger 2006, 287 ff.
- 88.
Galilei, Discorsi e dimostrazioni intorno a due nuove scienze, OG, VIII, 280; Eng. Trans. Finocchiaro, 346: ‘Si aliquod mobile duplici motu aequabili moveatur, nempe horizontali et perpendiculari, impetus seu momentum lationis ex utroque motu compositae erit potentia aequalis ambobus momentis priorum motuum.’
- 89.
- 90.
Galilei, Discorso intorno a le cose che stanno in su l’acqua e che in quella si muovono, OG, IV, 68: ‘Momento appresso i meccanici significa quella virtù, quella forza, quella efficacia, con la quale il motor muove e ’l mobile resiste; la qual virtù depende non solo dalla semplice gravità, ma dalla velocità del moto, dalle diverse inclinazioni degli spazii sopra i quali si fa il moto, perché più fa impeto un grave descendente in uno spazio molto declive che in uno meno. Ed in somma, qualunque si sia la cagione di tal virtù, ella tuttavia ritien nome di momento.’ See Galluzzi 1979a, b, 241.
- 91.
MLT, XXI, 12, 260.
- 92.
In this passage, Hobbes once again argues against White, using the Galilean arguments from the ‘second day’ of the Dialogue (see Galilei, Dialogo sopra i due massimi sistemi del mondo, OG, VII, 182), where Galileo stated that a heavy body dropped by a man on horseback will not stop its motion immediately, but will be braked progressively by the friction of the earth with which it comes into contact.
- 93.
MLT, XXI, 12, 260.
- 94.
Ibid., 261: ‘Idem enim est impetus quod motus sive velocitas, non causa eius neque effectus.’
- 95.
Ibid.
- 96.
The concept of impetus as virtus derelicta was introduced in European Latin world during the Middle Ages by the Scotist Francesco de Marchia, but it is primarily in Jean Buridan that the term acquires fundamental importance in physics. Buridan claims, in contrast to the Aristotelian theory of antiperistasis (on which, see infra), the projectile has an impetus, a force, or a quality, proportional to its mass and motion (see Jean Buridan, In De Caelo, III, q.). Buridan also uses impetus to explain the phenomenon of the increased velocity of heavy bodies in free fall, claiming that impetus increases with the speed of the projectile (Ibid, II, 1. 12). See Crombie 1953, 250 ff. For an extensive and detailed discussion of impetus in medieval philosophy: Maier 1968, 113 ff. See also Grant 1996a, b, 93 ff., who underscores the Arabic origin of the notion of impetus, which is rooted in the concept of mail, advocated by Avempace. On the influence of Avempace on Galileo, the following classic study is always useful: Moody 1951. On the elements present among medieval physicists, also common to Galileo, see Clavelin 1968, 75–126. See also Hooper 1996, which presents two different interpretations of the word in Galileo’s work: one, from his youth, closer to the interpretation of Francesco de Marchia and a second later one, from his maturity, closer to the meaning attributed to it by Buridan (ibid., 159).
- 97.
De corpore, XV, 2, OL, I, 178; Eng. Trans. EW, I, 207.
- 98.
See supra, chap. 1, § 4.
- 99.
TO II, chap. 1, § 11, f. 198v/152–153: ‘… notandum id quod experientia Certissimum est, in cribro sic moto grana, paleis et scrupis permixta ea agitatione segregari, et haec inter se in medium locum congregari.’
- 100.
Ibid.
- 101.
MLT, X, 11, 180 (my trans.).
- 102.
See Leijenhorst 2004, 167 ff.
- 103.
MLT, X, 11, 180.
- 104.
Ibid.: ‘Qui quaerunt itaque quae sit causa gravitatis, hoc quaerunt quo motore saxum, vel aliud corpus descendit per aërem, vel premit manum vel aliam rem qua sustentatur. Primum igitur satis iam plerisque philosophis manifestum esse puto, ipsum saxum non movere seipsum; habet ergo motorem externum.’
- 105.
Ibid.
- 106.
Ibid, 180–181 (my trans.).
- 107.
Ibid, 181.
- 108.
Hobbes to Mersenne for Descartes, 7 February 1641, AT, III, 302: ‘...spiritus subtiles et liquidos, vehementia motus sui, posse constituere corpora dura, ut adamantem, et lentitudine, alia corpora mollia, ut aquam vel aërem.’
- 109.
MLT, X, 11, 181. In this passage, Hobbes seems to refer to the Baconian discussion of the theme of corruption of bodies, which is caused by the spirits leaving the body. See, for example: Bacon, Historia Vitae et Mortis, in Bacon 2007, 172.
- 110.
MLT, X, 11, 181 (my trans.).
- 111.
Ibid.
- 112.
Ibid.
- 113.
Ibid. (my trans).
- 114.
See Leijenhorst 2004, 171 ff.
- 115.
See Palmerino 2004.
- 116.
- 117.
See Aristotele, Physics, IV, 215a ff., see also ibid., VIII, 266b; De Caelo, III, 301b. As we know (see supra, footnote 96), this Aristotelian theory was criticized by Buridan, who demonstrated the contradictory implications of the explanation proposed by the Greek philosopher: firstly, that which offers resistence to motion (that is to say air) cannot also be its mover. Moreover, it is not explained how air, which is so easily divisible, ‘supports a stone weighing ten pounds for any length of time’. Buridan, In de Caelo, III, 2, my translation. On this subject, see Crombie 1953, 250 ff.
- 118.
MLT, X, 11, 181.
- 119.
See ibid., XXI, 10, 259; and XXIV, 10 ff., 298 ff.
- 120.
Ibid., XIII, 2, 195 (my trans.).
- 121.
See Baldin 2017.
- 122.
Ibid. See Mersenne 1637, Livre III. Des Mouuemens & du son des chordes, 165 and Bernier 1684, II, 309–309. See also Gassendi to Jean Chapelain, in Gassendi 1658, III, 466b. As we know, Gassendi attributed atoms with an innate tendency to movement. On the concept of matter in the philosophy of Gassendi, see Bloch 1971, 210–229; Messeri 1985, 74–93; Osler 1994, 180 ff., and Gaukroger 2006, 262–276. Clericuzio focuses heavily on materia actuosa in Gassendi, a concept that—according to the author—removes Gassendi from a strictly mechanistic perspective. See Clericuzio 2000, 63 ff.
- 123.
In the Dialogus physicus he refers to a steel blade or a crossbow and explains that the return of the two bodies to their initial position is ‘itself a local motion, but within an imperceptible space, and no less very fast, so as to cause a very fast movement’ (Dialogus physicus, OL, IV, 248, my translation). Nevertheless, this recovery movement cannot take place in a straight line because motion of this type would necessarily cause the moving object to move in its entirety, ‘therefore it is necessary for the movement to be circular, so that every point of the body that is dilated completes a small circle’ (ibid., 249).
- 124.
See Palmerino 2004, 149.
- 125.
See Gassendi, ‘Epistolae de proportione qua gravia decidnetia acceleratur’. In Gassendi 1658, III, 572 ff.
- 126.
De corpore, XXX, 2, OL, I, 414: ‘Appetitum aliquem esse putarent internum’.
- 127.
Ibid.
- 128.
Ibid.
- 129.
Ibid.
- 130.
Ibid.
- 131.
Ibid., 415.
- 132.
Ibid., XXX, 5, 417–418. The law of falling heavy objects makes its appearance in a letter from Galileo to Paolo Sarpi dated October 16, 1604, (OG, X, 115). However, here the increase in velocity is deemed to be proportional to space and not to time. It was in his Dialogue that Galileo presented the scientific community with the correct law of falling heavy bodies (See Galilei, Dialogo sopra i due massimi sistemi del mondo, OG, VII, 248).
- 133.
Galilei, Discorsi e dimostrazioni intorno a due nuove scienze, OG, VIII, 209–210. For a detailed analysis of the mathematical and geometrical discussion of naturally accelerated motion in Galileo’s texts, see Clavelin 1968, 285 ff.
- 134.
De corpore, XXX, 5, OL, I, 417–418; Eng. Trans. EW, I, 514.
- 135.
- 136.
See De corpore, XVI, OL, I, 184 ff.
- 137.
Ibid., 184–185; Eng. Trans. EW, I, 218–219.
- 138.
Ibid., 186–187.
- 139.
Ibid., XVI, 9, 196; Eng. Trans. EW, I, 232.
- 140.
See Galilei, Discorsi e dimostrazioni, OG, VIII, 272 ff.
- 141.
In the Theorema III, Propositio III (OG, VIII, 282), Galileo writes: ‘momenta autem celeritatis sunt inter se ut spatia, quae iuxta ipsa momenta eodem conficiuntur tempore.’
- 142.
In an article on the physics that Descartes outlines in his exchange of letters with Mersenne (which differs from the essentially ‘narrative’ physics of the Principia due to its markedly mathematical dimension), Garber claims that gravity as a ‘natural tendency of heavy bodies to fall towards the centre of the earth’ is a fundamental element of Galileo’s ‘paradigm’ (in the meaning coined by Kuhn 1962, esp. 30 ff.), but that it could not have been shared by Descartes: ‘because they contain nothing over and above extension, bodies can have no innate tendencies at all’. See Garber 2000, esp. 122. Nevertheless, in the light of Galileo’s criticism of Kepler with regard to the phenomenon of tides, it is difficult to believe that a concept of an innate tendency in bodies (which is therefore foreign to the principles of mechanism) was present in Galileo’s epistemology. As we observed in the previous chapter and as we shall see even more clearly in the following chapter, Galileo made an ongoing effort to explain every physical phenomenon in mechanistic terms, including the structure of matter.
- 143.
See Galilei, Dialogo sopra i due massimi sistemi del mondo, OG, VII, 248.
- 144.
Galilei, Istoria e dimostrazioni intorno alle macchie solari e loro accidenti, Letter III, OG, V, 187.
- 145.
This should not lead us to believe that metaphysical and theological problems were alien to Galileo’s thinking, as extensively demonstrated by the Copernican letters. On this subject see, for example, Redondi 1997.
- 146.
See Leijenhorst 2004, 177–179.
- 147.
Hobbes adopts an identical model to explain the phenomenon of magnetism. See De corpore, XXX, 15, OL, I, 427 ff.
- 148.
See supra, chap. IV, § 4.
- 149.
See Seven Philosophical Problems EW, VII, 7–13; and also Decameron physiologicum, EW, VII, 147–151. In his Dialogus physicus sive de natura aeris, Hobbes simply observes that gravity ‘is a conatus direct from every place towards the center of the Earth.’ (Dialogus physicus, OL, IV, 250, my translation).
- 150.
See Seven Philosophical Problems, EW, VII, 7–9 (Problemata Physica, OL, IV, 306).
- 151.
Decameron physiologicum, EW, VII, 147: ‘It is certain that when any two bodies meet, as the earth and any heavy body will, the motion that brings them to or towards one another, must be upon two contraries ways; and so also it is when two bodies press each other in order to make them hard; so that one contrariety of motion might cause both hard and heavy, but it doth not, for the hardest bodies are not always the heaviest; therefore I find no access that way to compare the causes of different endeavours of heavy bodies to descend.’
- 152.
Decameron physiologicum, EW, VII, 147: ‘And further, the motion of the stone downward shall continually be accelerated according to the odd numbers from unity; as you know hath been demonstrated by Galileo. But we are nothing the nearer, by this, to the knowledge of why one body should have a great endeavour downward than another. You see the cause of gravity is compounded motion with exclusion of vacuum.’
- 153.
Ibid.
- 154.
Ibid. (my italics): ‘It may be it is the figure that makes the difference. For though figure be not motion, yet it may facilitate motion, as you see commonly the breadth of a heavy retardeth the sinking of it.’
- 155.
Ibid., 148–149.
- 156.
See MLT, X, 11, 180.
- 157.
See Descartes, La Dioptrique, AT, VI, 88.
- 158.
De corpore, XV, 1, OL, I, 176; Eng. trans. EW, I, 204–205: ‘…velocitatem esse motum consideratum ut potentiam, qua mobile tempore certo certam potest transmittere longitudinem. Quod est brevius enunciari potest sic, velocitas est quantitas motus per tempus et lineam determinata.’
- 159.
Ibid., XV, 2, 178: ‘…impetum esse ipsam velocitatem, sed consideratam in puncto quolibet temporis in quo fit transitus.’
- 160.
Ibid.
- 161.
Ibid., 177; Eng. Trans. 206. ‘…conatum esse motum per spatium et tempus minus quam quod datur, id est, determinatur, sive expositione vel numero assignatur, id est, per punctum.’
- 162.
EW, I, 207.
- 163.
Ibid.
- 164.
Ibid., 271; Eng. Trans. EW, I, 333: ‘motum per longitudinem aliquam, consideratam autem non ut longitudinem, sed ut punctum’.
- 165.
MLT, XIII, 2, 195.
- 166.
MLT, XXI, 12, 260 (my italics): ‘Sciendum autem est motum & impetum eandem rem esse, vocari autem impetum, atque etiam vim.’
- 167.
In the English edition Hobbes adds the concept of quickness. See EW, I, 212: ‘I define Force to be the impetus or quickness of motion multiplied either into itself, or into the magnitude of the movent, by means wherof the said movent works more or less upon the body that resists it.’
- 168.
De corpore, XV, 2, OL, I, 179: ‘…vim definiemus esse impetum multiplicatum sive in se, sive in magnitudinem moventis, qua movens plus vel minus agit in corpus quod resistit.’
- 169.
MLT, XXI, 12, 260: ‘Ex quo sequitur illud omne quod mobilis magnitudini aliquid contribuit, eiusdem etiam impetui contribuere.’
- 170.
De corpore, XV, 4, OL, I, 181; Eng. Trans. EW, I, 215.
- 171.
Ibid. Eng. 214–215: ‘excessus motus corporis moventis super motum vel conatus corporis resistentis.’
- 172.
See Galilei, Discorsi e dimostrazioni intorno a due nuove scienze, OG, VIII, 154–155.
- 173.
De corpore, XXIII, 1, OL, I, 287; Eng. Trans. EW, I, 351: ‘Momentum est ponderantis, pro certo situ, certa ad movendum radium potentia.’
- 174.
Howard Bernstein observed that Leibniz, who is unanimously considered one of the fathers of infinitesimal calculus, used the concept of conatus in his early writings with the same meaning coined by Hobbes. See Leibniz, ‘Vorarbeiten zur theoria motus abstracti’ in Leibniz 1923—, VI, 2, 171 ‘Omnis actio corporis est motus, omnis motus est in tempore. Motus autem in tempore minori quolibet dato, intra spatium minus quolibet dato est conatus’. See Bernstein 1980, esp. 26. The analogy between Hobbesian conatus and the ideas of Leibniz was also suggested by Watkins 1965, 123–132.
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Baldin, G. (2020). Galileo’s Momentum and Hobbes’ Conatus. 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_3
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