Abstract
Hobbes scholars have often remarked on the friendship between Hobbes and Marin Mersenne, sometimes emphasizing his role in promoting De cive. Yet little attention has been given to the intellectual relationship that formed between the two and that had growing importance during the most philosophically productive years of Hobbes’ life. Studies about Mersenne have tended to emphasize Hobbes’ contribution to the development of Mersenne’s thinking; but, though there are several studies about Hobbes in Mersenne’s works, little attention has been given to Mersenne’s possible influence on Hobbes.
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Notes
- 1.
See Robertson 1886, 37–38. Fritjof Brandt noted ‘that a philosopher with Mersenne’s qualities as compiler could have exercised any decisive influence on such fundamental and daring thinker as Hobbes we consider little probable’, though admitting Mersenne ‘has been able to awaken interests in Hobbes, and certainly his criticism too has acted guidingly, a fact which is indicated by the autobiography’. (Brandt 1928, 160). Moreover, he noted some elements common to both authors, such as their interest in Galileo and speculations in the fields of optics and music (ibid., 154–160). See also Tönnies 1925, 19. Arrigo Pacchi argued that both could be counted, in a sense, as followers of ‘constructive scepticism’. See Pacchi 1965, 63 ff. and 179 ff. Aldo Gargani contrasted two different approaches to scientific knowledge: that of Galileo, Descartes, and Hobbes against that of Mersenne and Gassendi. According to Gargani, for the former group, the mechanism was the tool to reduce the sensible qualities of objects in their mathematically quantifiable objective reality, whereas Mersenne considered it only a descriptive model. In this interpretation ‘An operation of ordering phenomena, with sensory appearances within the schemes of mathematic legality, is the limit beyond which man’s powers of knowledge can legitimately operate’. Gargani 1971, 176–182).
- 2.
- 3.
- 4.
Many scholars have assumed that Mersenne might have influenced Hobbes’ thought, in particular regarding the foundation of epistemology of knowledge, against the sceptics. On this topic see, in particular, Tuck 1988.
- 5.
Hobbes makes special mention of the meetings in the Minims cloister in the 1640s. See, for example Six Lessons, EW, VII, 340–343. On Mersenne’s circle, see Lenoble 1943, 590 ff. Armogathe 1992, esp. 135 ff.; Taton 1994; Beaulieu 1995, 63 ff. and 176–185; Maury 2003, 154–156; Lewis 2006, 110 ff. See also Jullien 2006. On the French academies in seventeenth century see also Fumaroli 2015.
- 6.
- 7.
Mersenne’s relationship with scepticism has been a point of debate, opened by an interesting and still relevant article by Popkin; see Popkin 1957.
- 8.
- 9.
Mersenne 1625, Preface (p. not numbered, fifth page of the preface): ‘Je desire seulement pour toute satisfaction qu’un chacun fasse son profit de la verité, laquelle étant venuë de Dieu doit estre rapportée à son honneur, c’est pourquoy je treuve mauvais, de ce qu’il y en a qui ont si peu d’esprit, & de jugement, qu’ils croient que la verité des Mathematiques est inutile, & qu’elle ne peut servir à la pieté, & à la Religion: je m’assure que cette opinion ne vient que de l’ignorance, & qu’ils n’auront pas si tost compris ce que j’ai traité dans cette œuvre, qu’ils avouront librement: qu’il n’y a rien dans ces sciences qui ne soit tres-utile pur l’intelligence de l’écriture sainte, de saincts peres, de la Theologie, de la Philosophie, & de la Jurisprudence, & qui ne nous puisse servir pour nous élever à la connaisance, & à l’amour de Dieu. Car il n’y a point de sciences, apres la Theologie, qui nous proposent, & nous fassent voir tant des merveilles comme font les Mathematiques, lesquelles élevent l’esprit par dessus soy-mesme, & le forcent de reconoistre une divinité; car la Statique, l’Hydraulique, & la Pneumatique produisent des effets si prodigieux, qu’il semble que les hommes puissent imiter les œuvres les plus admirables de Dieu…’.
- 10.
Scholars who particularly focused on the mathematics’s dominance over physics in Mersenne’s intellectual horizon included Dear (see Dear 1988, 48 ff., who maintains that Mersenne cleaved to a certain interpretation of Aristotelism, of which Mersenne’s thinking kept the main concepts), and Daniel Garber (see Garber 2004, 148 ff.). Garber argues that the notion of mixed mathematics is fundamental to understanding Mersenne’s relationship with Galileo and the new science, because—according to Garber—Mersenne considered Galileo a kind of ‘mixed mathematicians’, rather than a natural philosopher.
- 11.
Mersenne 1625, 51.
- 12.
Ibid., 52.
- 13.
Ibid. On this link between logic and metaphysics and the concept of metaphysics in Mersenne’s thinking in general, see Marion 1994, esp. 139 ff.
- 14.
Mersenne 1625, 135 and 148–149. Optics covers about forty columns in Quaestiones in Genesim. See Beaulieu 1995, 28. Mersenne also links this to Claude Mydorge’s experiments on parabolic mirrors (see Mersenne 1623, col. 488–538). However, as Lenoble has noted, Mersennes here again refers to light as a visible quality (Ibid., col. 472), and it was not until later works that we would see a significant evolution in Mersenne’s optics. See Lenoble 1943, 479. Mersenne was also concerned with establishing what light is, defining it as accidens incorporeum. (Mersenne 1623, col. 737–739). See also Beaulieu 1982b, 311; Cozzoli 2007, 31–3 and Cozzoli 2010, 11–14.
- 15.
Mersenne 1625, 148–149.
- 16.
Ibid., 206.
- 17.
Mersenne 1625, 212–213: ‘Or quelques Phenomenes qu’on puisse proposer dans la Philosophie, il ne faut pas penser que nous puissions penétrer la nature des individus, ni ce qui se passe interieurement dans iceus, car nos sens, sans lesquels l’entendement ne peut rien conoître, ne voyent que ce qui est exterieur; qu’on anatomise, & qu’on dissolve les corps tant qu’on voudra soit par le feu, par l’eau, ou par la force de l’esprit, jamais nous n’arriverons à ce point que de rendre notre intellect pareil à la nature des choses, c’est pourquoy je croy que le dessein de Verulamius est impossible, & que ces instructions ne seront causes d’autre chose que de quelques nouvelles experiences, lesquelles on pourra facilement expliquer par la Philosophie ordinaire.’ Mersenne spent an entire chapter of Verité on discussing Bacon’s philosophy (chapt. 16), presenting the Baconian division of the Eidola, (ibid., 206 ff.). Mersenne’s interest in Bacon’s philosophy is also seen in his many mentions of his work (including in Quaestiones in Genesim and Cogitata), and, especially, in the translation that Mersenne did and never published (from 1626 to 1628) of the second century of Sylva Sylvarum. See Buccolini 2002. On Mersenne’s relationships with Bacon, see also Fattori 2000.
- 18.
Mersenne 1625, 207. Popkin focused on this aspect, arguing that Mersenne’s giving up the aspiration to master the inner nature of things opens a kind of a third way of a propositional nature that diverges from dogmatic realism and from radical scepticism alike. See Popkin 1957. Interesting observations by Crombie join Popkin’s article. He argued that as Mersenne reflected on the sceptics, he gave up scientific realism and developed instead (especially after 1634) a complex dialectic between the theoretical element and experimental observation. See Crombie, ‘Marin Mersenne (1588–1648) and the Seventeenth-Century Problem of Scientific Acceptability’ (1975), now in Crombie 1990, 399–417, 402. However, on the concept of hypotheses in modern natural philosophy, it is key to keep in mind Sophie Roux’s critical comments on Popkin’s essay. See Roux 1998. Roux notes out that even with those writers often considered as ‘dogmatic’, such as Descartes, hypotheses have a fundamental role in the context of physics.
- 19.
Mersenne 1625, 221–222 (my trans.): ‘…car encore que les sens soient la porte des obiects, ils ne sont pas la porte des conclusions, ni des conseils, qui se prennent dans le cabinet secret de l’entendement, lequel se moque souvent de leur suggestion, parce qu’il a une plus vive, & plus excellente lumiere, par le moyen de laquelle il découvre leur erreur, quand ils se trompez: par exemple les yeus sont deçeus, quand ils jugent que le bâton droit veu dans l’eau est rompu, mais la raison s’y oppose, parce que la lumiere de la Dioptrique luy fait reconoistre qu’il est droit.’
- 20.
Ibid., 222.
- 21.
Ibid., 192. On the role of entendement in La Verité, in relationship to scepticism, see Paganini 2008, 144 ff.
- 22.
Mersenne 1625, 220 (my trans.): ‘…il faut consulter l’experience, afin de la conjoindre avec la raison, depeur que nous soions deceus par les imaginations de notre esprit, quand l’experience nous manque: mais quand l’un[e] est conjointe avec l’autre, il ne faut plus craindre de donner son consentement en faveur de la verité: il ne faut plus dire
, il faut recevoir la verité dans notre entendement, comme l’ornement, & le plus grand thresor, qu’il puisse recevoir, autrement il sera en des tenebres perpetuelles, & n’aura aucune consolation.’ - 23.
Ibid., 224. On the importance of mathematical and geometric elements regarding creation and universal harmony, see Fabbri 2003, 142 ff.
- 24.
- 25.
Mersenne 1625, 203.
- 26.
See Buccolini 1997, 10–11.
- 27.
See Mersenne 1625, 722–724. Cf. Clavius 1591, 20. Scholivm: ‘Vt autem videas, plurès demonstrationes in vna propositione contineri, placuit primam hanc propositionem resolvere in prima sua principia, initio facto ab vltimo syllogismo demonstrativo. Si quis igitur probare velit, triangulum A B C, constructum methodo praedicto, esse aequilaterum, utetur hoc syllogismo demonstrante…’. On the role given mathematics in Clavius and other sixteenth-century authors, such as Piccolomini, Barozzi, and Mazzoni, see Galluzzi 1973, esp. 53–54. See also Crapulli 1969. On the next century, Sergio 2006.
- 28.
See Clavius 1591, Prolegomena, not num.: ‘Theorema autem appellant eam demostrationem, quae solùm passionem aliquam proprietatemve unius, vel plurium simul quantitatum perscrutatur. Vt si quis optet demonstrare, in omni triangulo tres angulos esse aequales duobus rectis, vocabunt talem demonstrationem Theorema, quia non iubet, aut docet triangulum, aut quippiam aliud construere, sed contemplatur tantummodo trianguli cuiuslibet constituti passionem hanc, quodanguli illius duobus sint rectis aequales. Unde a contemplatione ipsa, haec demonstratio theorema dicitur. In theoremate fieri nulla ratione potest, contradictionis utraque pars vera ut sit. Si enim quis demonstret, omnes angulos trianguli cuiuslibet duos esse rectis angulis aequales, nullo poterit modo fieri, ut inaequales quoque sint duobus rectis.’
- 29.
On the conception of mathematics as a certain science in Mersenne’s thought, see Lenoble 1943, 33 ff.
- 30.
Mersenne 1625, 225–226: ‘Apres avoir discouru des sciences en general, & apres avoir montré que nous ne devons pas suspendre notre jugement à tout propos, ni sur toutes choses, ie veus maintenant vous faire voir que les mathematiques sont des sciences tres-certaines, & tres-veritables, es quelles la suspension ne treuue pas lieu: or auant que de vous apporter le demonstrations desquelles elles se servent, il faut que vous sçachiez qu’elles ont la quantité intellegible pour leur obiect, car elles ne considerent point le sensible que pour accident, & ce pour nous faire tumber en quelque façon sous les sens ce qui est releué par dessus l’incertitude de la matiere’.
- 31.
Buccolini has correctly pointed out a clear comparison between this passage and a corresponding one in the work of Giuseppe Biancani in De mathematicarum natura dissertatio (1615). See Buccolini 1997, 10–11.
- 32.
Mersenne 1625, 226–227: ‘La Physique traite aussi de la quantité, mais entant qu’elle est sensible, & que ses proprietéz se peuvent cognoistre par quelque sorte de mouvement, selon lequel elle est sujette à divers changemens; mais la quantité Mathematique est invariable, car il ne peut se faire qu’un triangle ne sois compris par trois lignes, & par trois angles conjoints par trois points indivisibles: n’importe qu’il ni ayt aucun triangle parfait au monde, il suffit qu’il puisse estre pour établir la verité de cette science, & que la nature nous represente dans ses individus sensibles les figures de Mathematique le plus parfaictement qu’elle peut, comme la ronde dans le cieus, dans les astres, & dans les élemens, sans mettre en ligne de conte tout ce qui est produit par les élemens ayant la figure Spherique, ni tous les artifices qui ont été inventé par les Mechaniques’.
- 33.
Popkin , in particular, stressed mathematics’ character of conventional certainty in opposition to the hypothetical nature of physics in Mersennian thought. See Popkin 1979, 138.
- 34.
According to Grosseteste, physics is within the limits of the probable, whereas mathematics achieves certain, rigorous knowledge. Roger Bacon considered the primary knowledge from which all other knowledge came (see Bacon 1897–1900, pars IV, II, 1, Vol. 1, 109–111). However, it was William of Ockham who gave a great deal of attention to physical science, though he did consider it in probabilistic terms, based on restoring the validity and generality of scientific statements, adopting a principle of the uniformity of nature and the analysis of the linguistic matrix of scientific discourse, sometimes in terms consistent with the positions that Thomas Hobbes would take, as Aldo Gargani has noted. See Gargani 1971, 151 ff. See also Crombie 1953, 219 ff.
- 35.
Buccolini has correctly noted that Mersenne’s thought follows in the tracks of speculations around Quaestio de certidudine mathematicarum, a considerable presence in the sixteenth-century Paduan philosophical milieu as well. Some authors have highlighted the prospect of establishing the value of mathematical demonstration specifically on their being able to be tied to the form of the scientific syllogism, which was considered a demonstratio potissima. See Buccolini 1997, 13. The author is mainly referring to Opusculum de certitudine mathematicarum (1560) by Francesco Barozzi and also noted Mersenne’s privileged source in De mathematicarum natura dissertatio by Biancani.
- 36.
Mersenne discusses geometry in the work’s fourth book and introduces the topic, restating that the validity of geometric demonstration is attested to by the fact that after almost 2000 years, the propositions in Euclid’s Elementa still remain universally valid. See Mersenne 1625, 717 ff.
- 37.
Nonetheless, according to Buccolini, though ‘the mathematical method is hypothetical, based on suppositions, on hypotheses that are the intellect’s constructions, mathematics is applied to physics because it is in accordance with experience, and, indeed, learning mathematics comes from experience itself’. Buccolini 2015, 73. Buccolini also emphasizes some parallels between Objectiones mersenniane e quelle hobbesiane alle Meditazioni by Descartes (ibid., 61–62). The topic needs specific detailed analysis beyond the scope of this study.
- 38.
On this topic, see Buccolini 1997, 28 ff. Buccolini also pointed at the consistency between the concept of ressemblance and Gassendi’s similitudo (ibid., 29).
- 39.
See Mersenne 1625, 149. See Aristotle, De anima, III (Γ) 8, 432a. For the Latin expression: ‘Nihil est in intellectu quod prius non fuerit in sensu’, see Thomas Aquinas, Quaestiones disputatae de veritate, q. 2, art. 3, 19.
- 40.
Mersenne 1625, 141 ff.
- 41.
Ibid., 148–149 (my trans.): ‘…l’Optique, dans laquelle nous ferons paroistre que nous sçavons asseurément ce qui appartiens aus couleurs, & à la lumiere. Je diray seulement ici que nous ne nous fions pas a un seul sens, ni même à tous le sens pris ensemble, car nous nous servons de la raison, qui ne laisse rien qu’elle n’examine: or il n’est pas veritable que l’entendement ne comprenne rien que ce qui entre par les sens exterieurs, car il cognoît qu’il y a de l’air, & milles autres choses que le sens exterieurs ne sçauroient appercevoir.’ In his analysis of Mersenne’s optics, Cozzoli neglects La verité des sciences. See Cozzoli 2007, 2010.
- 42.
Questions inouyes, Question XVIII, now in Mersenne 1985, 53.
- 43.
Ibid.
- 44.
Regarding mathematics, Mersenne writes that ‘…si on leur oste la posibilité de la quantité, il semble qu’on leur oste le fondement, sur lequel elles establissent leurs demonstrations, et qu’elles ne peuvent tout au plus user que de la moindre demonstration que l’on appelle à posteriori; quoy que l’on puisse dire qu’il n’est pas necessaire que leur suject, ou leur object soit possible, d’autant qu’elles peuvent proceder conditionnellement, et conclure absolument: par exemple, encore qu’il n’y eust point de quantité possibles, les Mathematiciens peuvent dire, s’il estoit possible de faire un triangle rectangle, c’est chose asseurée que l’hypotenuse ou la soustendante de l’angle droit seroit un quarré egal aux quarrez des deux autres costez: de là vient que l’on peut dire que la pure Mathematique est une science de l’immagination, ou de la pure intelligence, comme la Metaphysique, qui ne se soucie pas d’outre object que du possible absolu, ou conditionné’. (Ibid., 54).
- 45.
Mersenne 1625, 51.
- 46.
Carraud pointed out this shift, as he considered the close relationship between mathematics and metaphysics in Mersennian thought. See Carraud 1994, esp. 156–157.
- 47.
Questions Inouyes, Question XIX. In Mersenne 1985, 56. The same argument extends to morality.
- 48.
Question XXVIII. In Mersenne 1985, 77–78. On Mersenne’s relationship with chemistry, see Beaulieu 1993; Clericuzio 2000, 47–50. Mersenne’s Alchemist is clearly a chemist and alchemist at once. It was only during the seventeenth centuries, with the development of iatromechanics, that chemistry began to distinguish itself from alchemy. See Califano 2010, I, 65–69.
- 49.
On Mersenne’s interest in Galileo, see Lenoble 1943, 39 ff. and 391 ff.; Beaulieu 1984, 1995, 106–117. On the reception of Copernicanism in Mersenne, see Hine 1973, who argued that though it had garnered Mersenne’s favor, he would have considered it no more than a mere mathematical hypothesis. A different interpretation was given by Pierre Costabel, who stressed the correspondence with Jean Rey (1631–1632), where Mersenne focused at length on the defense of the Copernican hypotheses. See Costabel 1994. The issue of the impact of the Galileo affaire in seventeenth-century France has been extensively discussed. See Beaulieu 1984 and esp. Lerner 2001; Fabbri 2005; Lewis 2006; Pantin 2011. On Mersenne’s general relationships with Italy and Galileo’s pupils, see Beaulieu 1986, Beaulieu 1989, 1992.
- 50.
- 51.
Crombie , in particular, focused on this topic, see Crombie, ‘Marin Mersenne (1588–1648) and the Seventeenth-Century Problem of Scientific Acceptability’. In Crombie 1990, 402–405.
- 52.
We will return to this topic. See below, Chap. 2, §§ 8 ff.
- 53.
Mersenne 1636a, Livre II (Du Mouvement des Corps), 112, Corollaire I: ‘Je doute que le sieur Galilee ayt fait les experiences des cheutes sur le plan, puis qu’il n’en parle nullement, & que la proportion qu’il donne contredit souvent l’experience: & desire que plusieurs esprouvent la mesme chose sur des plans differens avec toutes les precautions dont ils pourront s’aviser, afin qu’il voyent si leurs experiences respondront aux nostres, & si l’on en pourra tirer assez de lumiere pour faire un Theoreme en faveur de la vitesse de ces cheutes obliques, dont les vitesses purroient estre mesurees par les differens effets du poids, qui frappera dautant plus fort que le plan sera moins incliné sur l’horizon, & qu’il approchera davantage de la ligne perpendiculaire.’
- 54.
See Raphael 2008.
- 55.
On the experimental element, which is far from devoid of theory in Mersenne, see Crombie’s statement: ‘His insistence on the careful specification of experimental procedures, use of controls, repetition of experiments as well as those calculated from theory, recognition and approximations, and estimation of experimental errors marked a notable step in experimental method’. ‘Marin Mersenne (1588–1648) and the Seventeenth-Century Problem of Scientific Acceptability.’ In Crombie 1990, 407–408. On Mersenne’s relationship with the culture of experimentation, see also Beaulieu 1995, 265 ff.; Blay 1994; Nardi 1994, and Maury 2003, 211 ff. On the insistence on empirical confirmation in Galilelian observations, see Lewis 2006, 119 ff. Raphael argues that in translating Galileo’s Discorsi, Mersenne identified two different types of ‘experiences’: universal and individual (or singular), see Raphael 2008, 32. However, Raphael argues that Mersenne did not consider the experimental element within the horizon of the scientific method (ibid., 35–36).
- 56.
The first volume of Harmonie Universelle appeared in 1636, precisely when Hobbes was in Paris.
- 57.
- 58.
Mersenne 1634, 58.
- 59.
Ibid., Preface et advertissement au lecteur, 31 (my italics).
- 60.
Ibid., 32.
- 61.
- 62.
Mersenne 1636a, Livre II, 149–150.
- 63.
Ibid., Livre III: Des mouvemens & du son des chordes, 167 (my trans.): ‘… je suis bien esloigné de vouloir demonstrer tout ce que je prouve par l’experience, qui sera suivie de tous ceux qui la feront, parce qu’il faut convaincre l’entendement par la raison evidente pour la contraindre d’embrasser une demonstration: ce que je desire que l’on remarque une fois poure toutes, afin que l’on ne croye pas que j’use tousjours de la diction demonstrer, ou demonstration dans un sens Mathematique; ce que ceux-là concluront aysément qui sçavent la difficulté qui se rencontre à demonstrer aucune chose dans la Physique, dans laquelle il est tres-difficile de poser d’autres maximes plus avantageuses que les experiences bien reglées et bien faites ...’
- 64.
Mersenne 1637, Nouvelles observations physiques et mathématiques, 8: ‘Il est difficile de rencontrer de principes ou des veritez dans la Physique, dont l’objet appartenant aux choses que Dieu a crées, il ne faut pas s’estonner si nous n’en pouvons trouver les vrayes raisons, & la maniere dont elles agissent, & patissent, puis que nous ne sçavons le vrayes raisons que des choses que nous pouvons faire de la main, ou de l’esprit; & que de toutes les autres choses que Dieu a faites, nous n’en pouvons faire aucune, quelque subtilité & effort que nous y apportions, joint qu’il les a pû autrement faire.’ See also Lenoble 1943, 384.
- 65.
Hobbes agreed with this idea, but it was actually common in the earlier philosophical tradition, in particular in the late Paduan Aristotelism in the seventeeth century.
- 66.
Lenoble 1943, 386. In describing the Mersennian position, Lenoble argues that: ‘Cette idée que nos systèmes sont seulement des modèles possibles des choses, n’était certes pas inconnue des Scolastiques. Ce qu’il y a de plus nouveau dans le cas de Mersenne, c’est bien la valeur même attribuée à la science pragmatiste: elle se suffit désormais à elle-même, sans regrets bien vifs d’une science plus parfaite.’
- 67.
See Syntagma. In Gassendi 1658, 95a–95b: ‘Philosophamur de iis instar quarum ipsi Authores sumus.’ See also: ibid., 122b–123b. On this topic, see Bloch 1971, 150–151; Gregory 2000, 157–189; 174. On Gassendi’s epistemology see Fisher 2005, 89 ff. On the role of mathematics in Gassendi’s thought, see also Rochot 1957.
- 68.
See MLT, XXX, 10, 352–353.
- 69.
See EL, Part I, chap. II, § 2, 3: ‘Originally all conceptions proceed from the action of the thing itself, whereof it is the conception’.
- 70.
MLT, XXX, 3, 349; Eng. Trans. 364.
- 71.
Mersenne 1625, 149.
- 72.
Ibid.
- 73.
Ibid., 222.
- 74.
Ibid., 148.
- 75.
The classical opinion that vision is the noblest of the senses is shared not only by Descartes (see La Dioptrique, AT, VI, 81), but is found often throughout the history of philosophy as well as in Plato (Timaeus, 45b–47b) and Aristotle (Metaphysics, I, I, 980a)
- 76.
- 77.
See De cive, Epistle dedicatory, OL, II, 136–137.
- 78.
See MLT, Chap. 23, § 1, 269–270.
- 79.
See Hobbes to Sir William Cavendish, Earl of Newcastle, from Paris, July 29/Aug. 8 1636, CH, I, 33.
- 80.
Ibid.
- 81.
This argument, found in Mersenne and Hobbes, seems to confirm Laudan’s (odd) hypothesis, according to which the ‘hypotheticsm’ of certain philosophies of the modern era are the result of a corpuscolar concept of matter, which would be tied to impossibility of verifying these microparticles’ behavior. See Laudan 1981, 44. See on the topic, Sophie Roux’s critical doubts in Roux 1998, 16 ff.
- 82.
See Pacchi 1965, 10. As we have noted, Popkin attributed mitigated scepticism to Mersenne and Gassendi (Popkin 1979, 148). Lenoble 1943 and Beaulieu 1995, in contrast, considered Mersenne a champion of mechanism and a fervent supporter of modern science. Dear 1988; Garber 2004, 2013, 15–16 argue that Mersenne had, on the whole, kept true to Aristotelism. It is, however, significant that Popkin’s position presented both elements at once that appear dichotomous in other interpretations. For a comprehensive overview of Mersenne’s relationship with scepticism see Paganini 2008, 129–147.
- 83.
This topic will be discussed in depth below. See below, chap. II, § 8.
- 84.
Hobbes, EL, Part I, chap. II, § 9, 7.
- 85.
Hobbes to Sir Charles Cavendish, from Paris, [Jan 29.] Feb. 8. 1641, CH, I, Letter 31, 83: ‘And if a man could make an Hypothesis to salue that contraction of ye sun yet such is the nature of naturall thinges, as a cause may be againe demanded of such Hypothesis, and neuer should one come to an end, wthout assigning the Immediate hand of God. Whereas in mathematicall sciences wee come at last to a definition wch is a beginning or Principle, made true by a pact and consent amongst our selues’.
- 86.
On the image of scientific theories as mere hypotheses that serve to ‘save the phenomena,’ see Duhem 2003, esp. 120 ff.
- 87.
Hobbes to Sir Charles Cavendish, from Paris, 29 Jan. [8 Feb.] 1641, CH, I, 83.
- 88.
Malcolm had originally dated the text to early 1640 (suggesting it as the latest date by which Hobbes left his native land in November 1640). See Malcolm, ‘General Introduction’, in CH, I, lii-lv. More recently, Raylor and Malcolm himself have suggested December 1640 as the earliest date and April 1643 (with August 1642 most likely) as the latest date that the manuscript was prepared by a Parisian copyist. See Raylor 2005, and Malcolm 2005.
- 89.
See TO II, chap. I, § 1, f. 193 r/147.
- 90.
The division of sciences into certain and probable ones can also be found in Six Lessons to the Professors of the Mathematics, EW, VII, 183–184. On this topic, see esp. Giorello 1990. see also Médina 2013a, 86–87. On the concept of mathematics in Hobbes, in general, see Breidert 1979; Grant 1996a, b, and especially Jesseph 1999. See also Sergio 2001, 87–226, and Sergio 2006, 207–254.
- 91.
Syntagma. In Gassendi 1658, I, 286a–286b: ‘Si dum aliqua causa invenitur, & tanquam vera, germanaque effertur, ac divenditur, quae verisimilis dumtaxat, ac forte quoque spuria sit, non habeamus, quo respicientes diiudicare illam possimus. Sane & hoc quoque est valde iucundum, nisi assequamur veram causam, verae specie non decipi; & qualiscumque reperta sit, tribuere illi posse legitimum pretium. Hac ratione. Dum causam venati, de alicuius inventae veritate diffidimus, sit nobis occasio invendi, arripiendique aliam viam, iuxta quam fortassis foeliciores simus: nataque adeo exinde est, quae dici Problematica solutio, responsiOve (sic) solet, cum vatiae causae proponuntur, ut singulae solum verisimiles, quo aut uberius disquiratur, aliqua ne earum sit vera; aut insinuetur, praeter allatas, requiri quampiam aliam posse.’ Gassendi, however—unlike Hobbes—is sceptical about the possibility of establishing a demonstrative science per causas. See Gregory 2000, 174–175. See also Fisher 2005, 117, and 2008.
- 92.
TO II, chap. I, § 1, f. 193 r./147.
- 93.
Ibid. My translation.
- 94.
On this topic in Bacon, see Rossi 1974, esp. 3–17; Gaukroger 2001, 6–36 and 132 ff. On the multiple senses of the study of nature in Bacon, see also Fattori 2012, 191–212. For an overview of similarities and differences between Bacon’s and Hobbes’ models of natural philosophy, see Sergio 2003. See also Bernhardt 1985b, 449–457, Terrel 2015; Milanese 2015; Jacquet 2015; Marquer 2015; Dubos 2015; Ducrocq 2015; Berthier 2015. See also Moreau 1989, 39–47. On the direct relationship between Bacon and Hobbes, an essential text is Bunce 2003.
- 95.
Hobbes 2012, 74: ‘Reason is the pace; Encrease of Science, the way; and the Benefit of mand-kind, the end.’
- 96.
- 97.
- 98.
Mersenne 1625, 226–227.
- 99.
Ibid.
- 100.
Objectiones ad Cartesii meditationes, (henceforth Objectiones) OL, V, 271–272: ‘Si triangulum nullibi gentium existat, non intelligo quomodo naturam aliquam habeat: quod enim nullibi est, non est: neque ergo habet esse, seu naturam aliquam. Triangulum in mente oritur ex trinagulo viso, vel ex visis ficto. Cum autem semel rem, unde putamus oriri ideam tranguli, nomine trianguli appellaverimus, quanquam perit ipsum trangulum, nomen manet. Eodem modo, si cogitatione nostra semel conceperimus angulos trianguli omnes simul aequari duobus rectis, et nomen hoc alterum dederimus triangulo, habent tres angulos aequales duobus rectis: etsi nullus angulus existeret in mundo, tamen nomen maneret, et sempiterna erit veritas propositionis istius, triangulum est habens tres angulos duobus rectis aequales … Unde constat essentiam, quatenus distinguitur ab existentia, nihil aliud esse praeter nominum copulationem per verbum est.’
- 101.
Mersenne 1625, 227.
- 102.
- 103.
As we know, Hobbes decided not to publish his critique of Thomas White’s De Mundo and many of the ideas developed in this work can be found later in De corpore (1655). See Jacquot 1952a, b. On the reasons for this decision and the importance of De motu, loco et tempore in the development of Hobbes’ philosophy, see Paganini 2010a, esp. 24 ff.
- 104.
MLT, XXVI, 2, 309; Eng. trans. Hobbes 1976, 305.
- 105.
See Objectiones, OL, V, 257–258: ‘Quid jam dicimus, si forte ratiocinatio nihil aliud sit quam copulation et concatenatio nominum sive appellationum perverbum hoc est? Unde colligimus ratione nihil omnino de natura rerum, sed de earum appellationibus: nimirum, utrum copulemus rerum nomina secundum pacta, quae arbitrio nostro fecimus circa ipsarum significationes, vel non. Si hoc sit, sicut esse potest, ratiocinatio dependit a nominibus, nomina ab imaginatione, et imaginatio forte, sicut sentio, ab organorum corporeorum motu: et sic mens nihil aliud erit praeterquam motus in partibus quibusdam corporis organici’.
- 106.
MLT, XIV, 1, 201–202: Philosophia vera, plane idem est quod vera, propria & accurata rerum nomenclatura, consistit enim in cognitione differentiarum; differentias autem rerum nosse is solus videtur qui singulis rebus suas appellationes proprias attribuere didicerit; praeterea ratiocinatio recta, quae philosophorum opus est, nihil aliud est quam recta verarum propositionum in syllogismum combinatio, vera autem propositio constat ex recta copulatione nominum, nimirum subiecti & praedicati secundum proprias & adaequatas earum significationes; ex quo colligitur philosophiam veram esse non posse, quae fundamentum non habeat in adaequata rerum nomenclatura.’
- 107.
According to Hobbes, the truth or falseness of philosophical claims depend only on propositions, which in turn depend only on the meaning of the names. See MLT, XXX, 17, 357: ‘veritas autem & falsitas, idem sunt quod vera & falsa propositio’. On the formal and syllogistic concept of reason in Hobbes, see Zarka 1989 and esp. Minerbi Belgrado 1993, 63 ff.
- 108.
See Mersenne 1625, 199 and 203.
- 109.
The names themselves are determined by human will, and there is no connection between the name and the thing it describes. According to Arrigo Pacchi, in his nominalism, Hobbes ‘goes beyond Abelardian conceptualism, and even positions more radical than Occamism: indeed, for Occam, the universal has no mental reflection, being an intentio animae … Hobbes, in contrast, removes this final concrete quality from the universal and sweeps away any kind of predetermined relationship between individual things. They no longer have any need for the constraints of Aristotelian hierarchy of genus and species, or of any hierarchy; any connection between the names of things is thus purely arbitrary’. See the footnote by Arrigo Pacchi in Hobbes 1968, 36. On Hobbes’ nominalism and conceptualism, see Dal Pra 1962, 411–433. Zarka ( 1999, 85–93) discusses at length the comparison between Ockham and Hobbes. See also Jesseph 2013, 380–383.
- 110.
MLT, I, 1, 105; Eng. trans. Hobbes 1976, 23.
- 111.
MLT, XXX, 22, 358; Eng. trans. Hobbes 1976, 377.
- 112.
On the particular status that geometry has in Hobbes’ philosophical system, see Sacksteder 1980, 1992. Hanson 1991 underscores the extension of the geometric method to all realms of knowledge as a uniquely Hobbes’ conventionalism, by highlighting also the underlying relationship with scepticism, inherent to the problem and Mersenne’s interest in Hobbes’ philosophy. Ibid., 636 ff.
- 113.
MLT, I, 1, 106: ‘Alia pars philosophiae considerat spatii ad spatium, temporis ad tempus, figurae ad figuram, numeri ad numerum relationes; atque haec pars constituit Geometriam et Arithmeticam, quae solent ambo comprehendi uno nomine Mathematicae, cuius appellationis causa est quod scriptores Geometriae agnoscerentur docuisse, id est manifestum fecisse discipulis et lectoribus suis doctrinam quam tradiderunt esse veram, omnemque eis dubitationem ademisse, qui ideo non modo audiisse sed certo didicisse aliquid dicerentur, ideoque
, id est discere, vocabant Geometriam et Arithmeticam scientias mathematicas.’ - 114.
Ibid., 106.
- 115.
Ibid., Eng. trans. Hobbes 1976, 24, modified.
- 116.
Ibid., MLT, I, 2, 106.
- 117.
MLT, I, 3, 107; Eng. trans. Hobbes 1976, 26.
- 118.
These concepts were much used in the school of Padua and by its leading sixteenth-century exponents, such as Agostino Nifo and Jacopo Zabarella. See Randall 1961, 30–31, and Crombie 1953, 228–230. On Renaissance Aristotelianism, see Schmitt 1985, and Bianchi 2003. On Hobbes’ relationship with humanistic and Renaissance thought, in addition to the mentioned studies by Skinner, see Schuhmann 1985, 1990; Paganini 1999, 2006c, 2007, 2010b.
- 119.
Mersenne 1625, 203 (my trans.): ‘… car l’Analyse nous conduit si admirablement depuis le sommet de chaque science jusques aus premiers principes, & les tres-simples élemens, & la voye de composition,
, nous meine si parfaictement, & si asseurément depuis les premiers principes des sciences jusques à leur perfection ...’ (my translation). - 120.
In particular, Gargani gave Agostino Nifo the credit for having formulated an interpretation of the two methods, especially fruitful for developing the scientific-philosophical disciplines, which was also particular to Hobbes’ intellectual paradigm. Gargani 1971, 33–38; esp. 34: ‘According to Nifo, scientific research starts from cognition of the objects of the sensory experience, on the basis of which the resolutive method arrives at the discovery of cause, a process named demonstratio signi. This is the start of the conceptual elaboration (intellectus negotiatio) phase, involving an operation of composition and division of the induced or discovered causal term or “discovery” of the resolutive technique.’
- 121.
MLT, XXX, 10, 352–353; Eng. trans. Hobbes 1976, 368–369, subtantially modified.
- 122.
De corpore, VI, 10, OL, I, 70: ‘Interea manifestum est quod in causarum investigatione partim methodo analytica partim synthetica opus est. Analytica, ad effectus circumstantias sigillatim concipiendas, synthetica ad ea quae singulae per se efficiunt in unum componenda.’ In De corpore itself, Hobbes does, in fact, seem to make a distinction between the two methods (chap. III, § 9 and chap. VI, § 13), resolving the problem of the quoted passage. On the combination of compositio and resolutio in Hobbes’ philosophy, see Jesseph 2006, 123–124; See also Médina 2013a, b, 105.
- 123.
MLT, VII, 1, 145–146: ‘Methodus autem inquirendi unica videtur esse posse, nempe ea quae incipit a varietate phantasmatum sive imaginum quae a rebus ipsis in sensoria agentibus efficiuntur, sine quibus imaginibus inquirere de re qualibet aeque potest lapis atque homo. Quoniam igitur ea immutata esse dicimus quae eodem modo apparent ac prius, et mutata quae aliter; mutation rerum in eo consistit quod sensoriis immutatis ipsae tamen eandem non efficiant speciem, seu imaginem in animo, hoc est consistit in motu aliquo partium obiecti adventitio.’
- 124.
MLT, VII, 4, 147–148: ‘Cum ergo corpus sive materia prima mutari potest, & per partes moveri modis innumerabilibus, et per motus huiusmodi efficere innumerabilia phantasmata in animis sentientium, hoc est specierum innumerabiles varietates, & impossibile sit scire quos motus habeant totius mundi singulae particulae, sequitur etiam impossibile esse ut sciamus quot sunt rerum varietates, & proinde an sint in coelo corpora nostris analoga, necne. Potest fieri ut sint; potest fieri ut omnes chimaerae & monstra imaginationis humanae habeant in coelis res ipsis analogas, potest etiam fieri ut non sit ibi ullum grave aut leve, ullus homo, aut animal aut arbor, quippe quae horum nihil scire possumus, propterea quod non operentur in sensus nostros a tanta distantia.’ Cf. Galilei, Dialogo sopra i due massimi sistemi, OG, VII, 86.
- 125.
Hobbes returns to a quite similar discussion of lunar motions whose causes are particularly difficult to investigate. See MLT, XXIV, 1, 289–290; See also De homine, II, 6, OL, II, 16. See Bitpol-Hespériès 2005, 166, who quotes a passage as an example of the absolute predominance of rational demonstration over experimental observation.
- 126.
See Giudice 2016, 92 ff.
- 127.
Objectiones, Objectio IV, OL, V, 258: ‘…mens nihil aliud erit praeterquam motus in partibus quibusdam corporis organici’.
- 128.
- 129.
See Paganini 2003, 29 ff. See also Paganini 2004a. I find Paganini’s argument convincing, as he says that it is much more probable that Hobbes discovered sceptical themes through the translation of Montaigne’s Essais in John Florio’s version (as well as Mersenne and Gassendi’s writings, which problematize some of Aenesidemus’ tropes), rather than by reading the works of the Spanish writer Francisco Sanchez (as Lupoli maintains. See Lupoli 2004, 2006, 74 ff.
- 130.
See De corpore, XXV, 9, OL, I, 325–327.
- 131.
Ibid., VIII, 2, 91–92.
- 132.
On the process of reducing palpable qualities to mere perceptions, see Leijenhorst 2002, 84–89, developing interesting ideas both about Hobbesian natural philosophy’s debt to late scholasticism (on the concepts of space and time, body and accident), and analyzing how these concepts were absorbed and fit into the framework of a mechanical philosophy.
- 133.
De corpore, VIII, 2, OL, I, 92.
- 134.
- 135.
See Paganini 2003, 31–32. Paganini gives a lengthy discussion of Hobbes’ relationship with both ancient and modern scepticism. See also Paganini 2004a, 2008, 171–227, and Paganini 2015. Popkin had already briefly discussed the topic (see Popkin 1982, 133–48, republished with a lengthy appendix in Popkin 1992, 9–26 and 27–49). Richard Tuck had emphasized Mersenne and Hobbes’ shared proposition of providing the certain foundations of knowledge with an ‘anti-sceptic’ function (see Tuck 1988). I find it difficult to support Sorell’s position on the subject, as he argues that Hobbes’ thought is essentially far from sceptical topics (see Sorell 1993, 121–135.
- 136.
See Popkin 1957, 65 ff.
- 137.
Mersenne 1625, 13–15: ‘…tout ce que vous apportez contre l’Aristote monstre seulement que nous ne sçavons pas le dernieres differences des individus, & des especes, & que l’entendement ne penetre point la substance que par les accidens: ce qui est veritable, car nous nous servons des effets pour nous élever a Dieu, & aus autres substances invisibles, comme si les effets étoient des cristaus à travers lesquels nous apperçeussions ce qui est dedans: or ce peu de science suffit pour nous servir de guide en nos actions … c’est donc assez pour avoir la science de quelque chose, de sçavoir ses effets, ses operations, & son usage, par lesquels nous la distinguons de tout autre individu, ou d’avec les autres especes: nous ne voulons pas nous attribuer une science plus grande, ny plus particuliere que celle-là’.
- 138.
Ibid., 150.
- 139.
Syntagma. In Gassendi 1658, I, 207b: ‘Ea nempe nostrae perspicaciae, cognitionisque conditio est, ut, cum pervidere naturas rerum intimas non possimus, aliquos effectus possimus; contentos nos esse oporteat, si hariolati quidpiam circa illas ex quibusdam effectibus, nostras qualescumque de ipsis notiones adnitamur aliis effectibus accomodare, cum eorum causas poscimur, seu quomodo a suis naturis originem habeant, rogamur.’ On this topic see also Fisher 2005, 19 ff. and 346 ff.
- 140.
See Mersenne 1625, 151.
- 141.
See ‘Marin Mersenne (1588–1648) and the Seventeenth-Century Problem of Scientific Acceptability,’ in Crombie 1990, 405.
- 142.
See below, chap. 2, § 2.
- 143.
- 144.
The concept of cause is the common denominator linking matter, the reality of bodies in motion and the phenomenal world of phantasms that define our perceptions and, as a result, our concepts as well. On the idea of cause in Hobbes, see Leijenhorst 2005, who underscores that this is the bridge between the subjective world of our phantasmata and the objective world of bodies in motion (ibid., 90). It is used with the same meaning in Malherbe 1984, 84 ff. and Paganini 2008, 213–217. Zarka prefered a more distinctly formal sense, an interpretive principle more than as a law governing the phenomena of reality (see Zarka 1999, 73 ff.).
- 145.
See De homine, X, 5, OL, II, 93.
- 146.
- 147.
Questions theologiques, physiques, morales, et matematiques. In Mersenne 1985, Epître dédicatoire, 202: ‘…il semble que la capacité des hommes est bornée par l’écorce, et par la surface des choses corporelles, et qu’ils ne peuvent penetrer plus avant que la quantité, avec une entiere satisfaction. C’est pourquoy les anciens n’ont pu donner aucune demonstration de ce qui appartient aux qualités, et se sont restreints aux nombres, aux lignes, et aux figures, si l’on excepte la pesanteur, dont Archimede a parlé dans ses Isorropiques’. See also Lenoble 1943, 353 ff.
- 148.
See Lewis 2006, 118.
- 149.
In several passages of Mersenne’s works, he expressly calls Galileo a ‘philosophe’ and not a mere mathematician. See, for example the advertissement placed at the end of the first book of Harmonie Universelle, which introduces the topic of the second book, titled: Des mouvements de tovtes sortes de corps: Mersenne 1636a, Livre I, 84. Lenoble had also already discussed the topic. See Lenoble 1943, 357. I believe that Mersenne, broadly speaking, followed the principles of ‘Galilean’ philosophy, though his epistemological perspective differs from Galileo’s, and in some respects is much closer to that of Gassendi, as Popkin has suggested. I do not think that Mersenne considered Galileo a mere mathematician or just an acute observer of reality, as Garber suggests (Garber 2004) and Massimo Bucciantini, following Garber. See Bucciantini 2007, 44 (conversely, I agree with Bucciantini that this was, more or less, the idea that Descartes had of Galileo).
- 150.
Hobbes’ materialism is marked by his metaphysical perspective, which greatly reduces the scope of his so-called conventionalism (as we will discuss further below, by comparing Hobbes’ position with that of Galileo). On the topic, see Malherbe 1989, 24, diverging from the more Ockhamist interpretations of Hobbesian philosophy suggested by Bernhardt and Zarka (See Bernhardt 1985a, and Zarka 1985). See also Milanese 2013, 53 ff.
- 151.
My interpretation of Hobbes’ perspective diverges from that of Malet, who emphasizes its distance from Galileo’s methodology and epistemology. See Malet 2001, 319 ff.
- 152.
Mersenne, Questions théologiques, physiques et mathématiques, in Mersenne 1985, 279: ‘Ce qui est si ridicule, et si inepte qu’il n’y a plus que les vieilles, et les trop credules qui ne s’en moquent comme d’une pure fable: car outre que l’experience fait voir que ces graveures, et ces figures n’ont nulle force, ou aptitude pour determiner, et pour attirer les vertus des Astres, la raison y repugne entierement, qui mesme persuade que les astres n’ont pas la force, ni les influences qu’on leur attribuë, car chaque astre n’a point d’autre force sur nous que celle qu’il exerce avec sa lumiere, et sa chaleur; de sorte que si l’on disposoit autant de chandelles autour de la terre, comme il y a d’estoiles au Ciel, dont elle fust aussi illuminée, et échauffée, comme elle est par lesdites estoiles, nous sentirions les mesmes influences.’ In Mersenne 1634, the question III, (see Mersenne 1985, 565–588), Mersenne refutes the principles of astrology and judicial astrology.
- 153.
Mersenne 1636a, Livre II, 99. The idea that the phenomenon of visual perception is created only by a moving column of air has very deep similarities with Hobbes’ optical theory, which we will discuss further below.
- 154.
Ibid., 299–300. In Chapter 24 of De motu, loco et tempore, Hobbes adds a paragraph (21) with a title that would seem to contradict Mersenne: ‘Why not all influence do constitute light’, in which he argues that the earth’s rotation motion can influence the motion of light though without producing heat (cf. MLT, XXIV, 21, 303–304). However, this aspect of Hobbes’ thoughts should be evaluated in light of his and Mersenne’s astronomical perspectives, that we will discuss below.
- 155.
Mersenne 1636a, Livre II, 300: ‘…l’on est contraint d’avoüer que l’homme n’est pas capable de sçavoir la raison d’autre chose que de ce qu’il peut faire, ny d’autres sciences, que de celles, dont il fait luy-mesme les principes, comme l’on peut demonstrer en considerant les Mathematiques.’
- 156.
Ballistica et acontismologia, in Mersenne 1644, Praefatio utilis ad lectorem (p. not num., first page of the preface).
- 157.
MLT, XXXVI, 2, 397: ‘…an fortuita dependeant ab astris, pertinet ut aliquid dicatur de modo quo procedere possit operatio ad res longinquas; omnis quidem actio, ut dictum saepe est, est motus, nimirum motus localis, quies enim nihil mutat, id est nihil efficit. Quando vero ex motu effectum aliquem produci oculis videmus, ibi operationem & motum, eandem rem esse facile omnes consentimus; sed quando effectum vident, motum autem non vident, ibi motum esse negant plerique, et operationem, qua effectus producti sunt, secundum differentias quas homines in seipsis sentiunt diverse appellant, modo calorem, modo frigus, modo humorem, modo siccitatem, modo lumen; et quando haerent, sympathiam aut antipathiam, aut occultam qualitatem, aut denique influentiam, sed nunquam motum; quasi qualitates naturae, et potentiae corporum eodem modo infunderentur in corpora, quo aqua, aut alia res fluida infunditur, vel influit in vasculum. Sciendum igitur est motum a corpore ad corpus propagari in quantacunque distantia per continuam proximi et contigui corporis protrusionem, ita ut producendo effectui non sit opus corpus aliquod, sive partem astri aliquam euclare ad terram.’
- 158.
Galilei, Dialogo sopra i due massimi sistemi del mondo, OG, VII, 486. Eng. trans. Galilei 1967, 462: ‘Ma…più mi meraviglio del Keplero che di altri, il quale, d’ingegno libero ed acuto, e che aveva in mano i moti attribuiti alla Terra, abbia poi dato orecchio ed assenso a predominii della Luna sopra l’acqua, ed a proprietà occulte, e simili fanciullezze.’ On the difference between Galileo’s and Kepler’s epistemologies, see Bucciantini 2003.
- 159.
We will later discuss this subject at length. See below, chap. 2, § 4.
- 160.
Hobbes noted that Galileo had not taken into account the lunar motions coinciding with the tides, and, therefore, had developed a flawed explanation of the phenomenon that did not involve the moon. See MLT, XVI, 2, 211.
- 161.
Ibid., XXIV, 1, 289; Eng. trans. Hobbes 1976, 278.
- 162.
TO I, OL, V, 218–220; TO II, chap. I, §§ 4–8, ff. 193v–197r/148–150.
- 163.
MLT, IX, 2, 161–162.
- 164.
Ibid., XXIV, 21, 303–304; Eng. trans. Hobbes 1976, 297.
- 165.
Questions Inouyes, question XXXVII. In Mersenne 1985, 102.
- 166.
MLT, XXIV, 21, 303–304: ‘Poterit quis interrogare quare terra non sit per se lucida ut sol, si quidem enim lux (quae solis est influentia) fiat per solum motum expansivum, terra autem influentiam in lunam exerceat per similem expansionem, erit quoque terrae virtus illa expansiva lux. Dicendum igitur [est] influentiam quidem eorum quorum natura per omnes particulas minimas, et ut ita dicam, mathematice homogenea est, lucem esse eamque fortem aut debilem pro velocitatis gradu quo se dilatant. In corporibus vero heterogeneis, quale est terra, et quodlibet aliud corpus cuius partes motus specificos habent et proprios sibi; et pugnantes cum motibus particularum adiacentium, etsi unaquaeque pars, ac proinde totum, motum habeat illum quem diximus expansionis sive dilatationis, [dico] non tamen illum motum esse lucem, sed influentiam a luce differentem, et quia corpora essentialiter inter se differunt per motum internum partium et innumerabiles sunt differentiae corporum specificae, innumerabiles quoque esse differentias influentiarum.’
- 167.
Ibid., XIX, 7, 246; Eng. Trans. Hobbes 1976, 221, modified.
- 168.
Leijenhorst gave the theory of the diurnal rotation of the earth that appears in De motu, loco et tempore as evidence of the influence of Campanella’s pansensism and panpsychism, on Hobbes’ philosophy. See Leijenhorst 1997, 120. See also Sergio 2006, 207–208; Sergio 2007, 311; Sergio 2016, 86. On Campanella’s pansensism, see especially the first chapters of the second book of De sensu rerum et magia: Campanella 2007, 33–64. See also Ernst 2010, 108 ff.
- 169.
Paganini noted the mechanical explanation of sensation and animal motions in Hobbes, highlighting the similarities with Gassendi’s arguments. See Paganini 1990, 369 ff. Cf. Syntagma. In Gassendi 1658, II, 328a–b; see also ibid., 345b. Gassendi, like Hobbes, believes that animals are endowed with the faculty of reason. See, for example, his Objectiones to Descartes’ Meditations (See Objectiones Quintae, AT, VII, 271. See also Exercitationes paradoxicae adversos Aristoteleos, Praefatio. In Gassendi 1658, III, 102; ibid., 202b–203a). As Gregory has noted, this topos is common in scholastic anthropocentrism, as well as in libertine literature, such as in La Mothe Le Vayer, and Cyrano de Bergerac. See Gregory 2000, 51, and 102–104. See also Bloch 1971, 368 ff.
- 170.
Mersenne, Questions théologiques, physiques et mathématiques. In Mersenne 1985, 341–342 (my trans.): ‘Puisque la terre a besoin du Soleil, elle doit l’aller chercher, comme nous cherchons le feu, dont nous avons besoin: car si nous ne desirons pas que les villes, et les campagnes se tournent, quand nous montons au haut des tours pour les contempler, aussi, ne devons nous pas desiderer que le Soleil et les estoiles se tournent pour envisager la terre.’
- 171.
Horstmann saw interesting similarities between Kepler and Hobbes’ writings, from Tractatus opticus II, to Decameron physiologicum. See Horstmann 1998, 142 ff.
- 172.
Ibid., 138.
- 173.
In fact, an argument very similar to that in Mersenne and Hobbes is also seen in William Gilbert’s De Magnete, where, when discussing the earth’s rotation, he seems to suggest that the earth’s motion is seeking the light from the sun and the benefits of that light. See Gilbert 1600, 224. See also Westfall 1971, 27.
- 174.
MLT, XVIII, 15, 238; Eng. Trans. Hobbes 1976, 211.
- 175.
Ibid.: ‘Quod si voluntaria dicatur conversio esse animalium, nihil obstat hoc quin terrae conveniat quanquam enim in terra motus ille voluntarius non sit, tamen in animalibus voluntas illa, sive appetitus caloris motus est, videtur igitur terra ideo convertere se ad solem, hoc est, moveri motu diurno, propterea quod partes a sole aversae ad conservandam naturam, sive motum suum essentialem ad solem accedant, partes vero soli proximae calore solis saturatae in eodem loco non amplius se bene habeant, & proinde ut motus illorum naturalis liberius exerceatur rursus se recipient, atque hoc moto fit conversio ea qua definitur dies, ideoque diurna appellatur.’
- 176.
- 177.
De corpore, OL, I, 315–334. On the topic of animal reactions to a heat source, Hobbes’ explanation is much like Descartes’ in L’homme, though Descartes certainly did not apply this explanation to human beings like Hobbes did. (See Descartes, AT, XI; 187 ff. See also ibid., AT, XI, 119–120. Bitpol-Hespériès drew a comparison between Hobbes’ De homine and Descartes’ L’homme, identifying similarities in content and focusing on the fact that both discussed the phenomenon of vision. See Bitpol-Hespériès 2005. The analogy of the animal-machine is also found in the Discours de la méthode. See Descartes, Discours de la méthode, AT, VI, 46 ff. See also Traité de l’homme, AT, XI, 119–120. On the animal machine theory in Descartes, see Morris 2000; Gaukroger 2002, 196 ff.
- 178.
In De corpore, XXV, 5, OL, I, 320, Hobbes writes: ‘Etsi autem sensio, uti diximus, omnis fiat per reactionem, ut tamen quicquid reagit sensiat necessario non est’, referring to a form of pansensism very similar to that of Telesio and Campanella: ‘Scio fuisse philosohos quosdam, eosdemque viros doctos, qui corpora omnia sensu praedita esse sustinuerunt; nec video, si natura sensionis in reactione collocaretur, quo modo refutari possint.’
- 179.
MLT, XXIV, 11, 299; Eng. trans. Hobbes 1976, 291, modified.
- 180.
MLT, XXIV, 11, 299: ‘Itaque et terra habet motum talem materiae internum per quem est terra. Rursum omne corpus durum, si pars eius aliqua ab alio corpore incurrente impellatur, hanc proprietatem habet ut & se plus vel minus, prout durities sua & vis incurrentis maior vel minor est, restituat, & liberando se; si aliter non possit, resilit, ut constitutionem suam specificam conservet, non ut agens sensibile quod cognoscit quid sui sit conservativum, sed ut turbo rotatus velociter & impingens contra parietem statim resilit non ex appetitu conservandi motum circularem, sed ex vi illius ipsius motus qui materiam ad figuram certam determinverat quae cum impactu in parietem consistere non potuit. Itaque et terra eam quoque habet proprietatem, ut si agens aliquod in ipsam ita agat, ut ea actione motus ille eius internus, per quem est terra, impediatur, statim se recipiat.’
- 181.
Ibid., XXIV, 13, 300.
- 182.
See Baldin 2017.
- 183.
See Hobbes to Mersenne for Descartes, February 7, 1641, AT, III, 302. Descartes replied by arguing that these motions were the cause of the softness of bodies. He also maintained that the hardness of a given object was due to the internal cohesion of its parts. (AT, III, 321–322).
- 184.
- 185.
See Sapientia, XI, 20
- 186.
See Fabbri 2003, 158–170.
- 187.
- 188.
- 189.
See Mersenne 2003, 41
- 190.
Questions physiques et mathématiques, Question 35. In Mersenne 1985, 405: ‘Il faut seulement remarquer qu’il n’y a quasi nul corps dans toute la nature qui n’ayt un son particulier … l’on peut dire que toutes les impressions que les objects font sur nos sens, ne sont autre chose qu’une espece de sons puisque elles consistent dans un mouvement, par lequel les corps nous communiquent leurs proprietez, et nous enseignent ce qu’ils peuvent, et ce qu’ils sont, et toute que sorte de mouvement faict un son, ou plustost que le son, et le mouvement sont une mesme chose.’
- 191.
Ibid., 406: ‘Si l’on cognoissoit la vistesse de la lumiere, et du mouvement qu’elle fait dans l’air, et dans l’œil, et le mouvement, ou l’impression que les autres objects impriment sur nous, l’on pourroit determiner, et expliquer leurs raisons, et leurs Analogies par le moyen des sons; d’où l’on infereroit leurs vertus, et leurs proprietez; et parce que les raisons sont mieux cognuës, et plus aysées à concevoir, à veriffier, et à expliquer dans les sons, que dans les autres objects, l’on en tireroit de la lumiere pour toutes les autres sciences’. A basic form of the analogy was already seen in the Traité from 1627, but here, Mersenne maintained that investigation was easier in the field of optics, because sound, unlike light, is invisible. See Mersenne 2003, 20. On Mersenne’s musical and acoustic theories, see Bailhache 1994, and esp Fabbri 2003.
- 192.
Brandt had already advanced the theory that the ideas about optics and music in Harmonie universelle could have been very interesting for Hobbes. See Brandt 1928, 158–160.
- 193.
- 194.
Mersenne 1636a, Livre I, (De la nature & des proprietez du son), 15: ‘…la lumiere s’estend dans toutes la sphere de son activité dans un istant, ou si elle a besoin de quelque temps, il est si court que nous ne pouvons pas le remarquer: mais le Son ne peut pas remplir la sphere de son activité que dans un espace de temps, qui est d’autant plus long que le lieu où se fait le Son est plus esloigné de l’oreille.’ The Harmonicorum libri explain how light and sound are different and similar in the Propositiones V and VI (2 and 3).
- 195.
Mersenne 1636a, Livre I, 18. The issue is addressed again on page 24 where Mersenne seeks to provide an explanation of the propagation of sound through solid bodies and finds the it in the air vibrations in the pores of solid bodies.
- 196.
- 197.
Mersenne 1636a, Livre I, 45.
- 198.
- 199.
- 200.
Mersenne 1636a, Livre I, 46.
- 201.
Ibid., 47–48 (my trans.): ‘Le mouvement de la lumiere est ce semble plus subtile que celuy des Sons, & penetre plus avant dans la substance de l’air, qu’il remplit d’une certaine liqueur semblable à de l’huile tres-subtile & tres-claire, qui se meut de telle sorte qu’elle affecte l’œil & le nerf optique, qui commence à descouvrir tous les objets exterieurs, si tost que l’air esmeu s’est introduit dans ses pores pour imprimer un semblable mouvement à l’air interieur de la membrane qu’on appelle aranée.’
- 202.
Here, as elsewhere, we can see the influence of the image of light as ‘very spirited, tenuous, and fast substance’, that Galileo suggested in his Copernican letters (see Galilei, Letter to Mons. Pietro Dini, March 23, 1615, OG, V, 301–303), and Descartes’ conception of subtle matter, which he describes as ‘matiere fort subtile et fort fluide, qui s’estende sans interruption depuis les Astres iusques à nous.’ Descartes, La dioptrique, AT, VI, 87. On the Descartes’ concept of light, see Roux 1997, 49–66.
- 203.
Mersenne 1636a, Livre I, 49: ‘Or encore qu’il soit tres-difficile de s’imaginer comment toute la lumiere qui passe par le plan BC, (quoy qu’on la suppose aussi large que le Ciel) peut estre rassemblée dans un point, attendu qu’il n’y a nul point dans ladite surface qui n’en soit couvert & rempli, & consequemment que ladite lumiere est continuë sans aucuns pores & sans aucune vuide, & que ce rassemblement au point e ne se peut faire sans penetration d’une infinité de rayons qui se condensent jusques à l’infini, neantmoins il est ce me semble encore plus difficile de comprendre comment tout le solide de l’air qui va frapper la glace aCB, se reflechit au point e; car l’on peut dire que la lumiere est un accident qui n’est pas tellement determiné aux lieux, qu’il ne puisse occuper & couvrir tantost un plus grand lieu, & tantost un moindre: mais l’air est un corps, dont les differentes parties ne peuvent naturellement se penetrer: & bien qu’il eust une infinité de petits espaces vuides, neantmoins il ne peut estre reduit à un point comme la lumiere.’
- 204.
- 205.
See below, Appendix.
- 206.
Hobbes’ first mention of a theory of light that considers only the transmission of motion in the medium is in the letter to William Cavendish, Earl of Newcastle, mentioned above several times, from October 16/26, 1636.
- 207.
Hobbes says on several occasions that he started considering the nature of light around 1630. See, for example, Mersenne’s letter for Descartes from March 1641 (Hobbes to Marin Mersenne, March [20/] 30, 1641, CH, I, 102–103), and the mention in the First Draught. See Hobbes, FD, not num. (f. 3 r) / 76–7. On the authorship of the Short Tract see the appendix, below.
- 208.
Hobbes, Appendix ad Leviathan, in Hobbes 2012, 1185 (OL, III, 537): ‘Memini tamen quod Corpus putarem aliquando id solum esse, quod Tactui meo vel Visui obstaret. Itaque speciem quoque corporis in speculo, aut somno, aut tenebris apparentem, quanquam miratus, corpus tamen esse arbitrabar. Sed consideranti postea Species illas evanescere, ut quarum existentia dependeret non a seipsis, sed a natura animata, non amplius mihi visae sunt reales, sed Phantasmata & effectus rerum in organa sensuum, agentium; & proinde esse incorporeas.’ Karl Schuhmann quotes this passage in support of his theory that the Short Tract was written by Hobbes, see Schuhmann 1995b, 20. In Hobbes 1988a, b, 38, we read indeed that: ‘Species are substances’.
- 209.
Hobbes to William Cavendish, Earl of Newcastle, CH, I, 37–38. Jean Bernhardt and Yves Charles Zarka have noted that some of Hobbes’ theories (such as that light is only motion, that its propagation is instant, and the rejection of any concept of species) were already found in Descartes’ Dioptrique (See Bernhardt 1979, and Zarka, 1988, 86–87), which Hobbes only received in October 1637, as shown by the letter he sent to Sir Kenelm Digby on October 4/14 1637 (See Sir Kenelm Digby to Hobbes, October 4/14, 1637, CH, I, 51), which means we can say that Hobbes formulated his theory independently. See also Marquer 2005, 15–16. On the controversy between Descartes and Hobbes about Meditations, see Curley 1995, 97–109; Guenancia, 1990. See also Marion 2005. The controversy continued later as well, as Gianluca Mori has well demonstrated, see Mori 2010a, 2010b, 166–172. On Hobbes’ materialism in Objections, see Terrel 2016, 13–31.
- 210.
EL, Part I, chap. II, 3–7.
- 211.
TO I, OL, V, 217: ‘…in visione, neque objectum, neque pars ejus quæcunque transit a loco suo ad oculum.’
- 212.
Ibid., 217–218: ‘Ut motus possit motum generare ad quamlibet distantiam, non est necessarium ut corpus illud a quo motus generatur, transeat per totum illud spatium per quod motus propagatur; sufficit enim ut parum, imo insensibiliter motum, protrudat id quod proxime adstat; nam id quod adstat, pulsum suo loco, pellit quoque quod est proximum sibi, atque eo modo motus propagabitur quantum libueris…’
- 213.
Ibid., 218 (my italics).
- 214.
Ibid., 219–220 (my trans.): ‘Nam quo instante incipit motus a B versus C, necesse est ut incipiat motus a C versus D, et a D versus E, et ab E prorsum. Quare si statuatur oculos in qualibet distantia a sole, puta in E: quo istante incipit sol dilatare se in B, eodem ferietur oculus in E. Unde propagabitur motus ad retinam, et inde per conatum retinae nervum optimum usque ad cerebrum: et hoc fit eodem instante, quo motus incipit in B.’ See also Prins 1996, 133 ff.
- 215.
TO I, OL, V, 221.
- 216.
In Mersenne 1636b, 3, Mersenne writes that, though both light and sound are propagated ‘in orbem’. Nevertheless, ‘soni non solum linea recta, seu directis radiis, sed etiam circularibus, ellipticis, parabolicis, & aliis, quibusvis lineis feruntur ad aurem; lux vero solummodo rectis lineis fertur ad oculum, sive directis, sive reflexis, sive refractis.’
- 217.
TO I, OL, V, 222: ‘Quoniam enim radius est via per quam motus projicitur a lucido, neque potest esse motus nisi corporis: sequitur radium locom esse corporis, et proinde habere tres dimensiones. Est ergo radius spatium solidum.’
- 218.
Ibid., 221–222 (my trans.): ‘Radium appello, viam per quam motus a lucido per medium propagatur. Exempli gratia: sit lucidum AB, a quo moto ad CD pars medii quae interjacet inter AB et CD, protrudatur ad EF: et a parte medii quae erat inter CD et EF, promota ulterius ad GH, propellatur pars illa quae erat inter EF et GH, ulterius ad IK, et sic deinceps, sive directe sive non, puta versus LM. Spatium jam quod continetur inter lineas AIOL, et BKM, est id quod voco radium, sive viam per quam motus a lucido per medium propagatur.’
- 219.
TO II, chap. II, § 2, f. 204v/p. 160: ‘Cum vero directa haec motus a lucido propagatio, non sit ipsum Corpus per quod motus propagatur (nam differentia magna est jnter ipsum aerem et motum in aere) neque aliud corpus praeter ipsum, non potest radius lucis dici corpus, ut radius rotae ligneae lignum, sed tantum via motus propagatio.’
- 220.
Ibid.
- 221.
TO I, OL, V, 222–223: ‘Lineam unde radii latera incipiunt: exempli gratia, lineam AB, unde incipiunt latera AI et BK: appello lineam lucis simpliciter. Linearum autem quae a linea lucis continua protrusione derivantur, quales sunt CD, EF etc., unamquamque appello lineam lucis eousque propagatam’.
- 222.
- 223.
- 224.
TO I, OL, V, 228. See also Shapiro 1973, 160–161.
- 225.
TO II, chap. II, § 2, f. 204v/160 (my trans.): ‘Rursum quoniam motus intelligi non potest nisi in corpore, habeatque omne Corpus, tres dimensiones, Longitudinem, Latitudinem, et crassitiem, necesse est ut etiam via motus constet dimensionibus iisdem, Non est ergo radius longitudo sine latitudine, sed solidum, cuius longitudo terminatur superficie corporis lucidi sive radiantis; quanquam possit interdum illa considerari non ut superficies, sed ut punctum, nimirum cum ratiocinatione, obiecti sive lucidi magnitudo non consideratur; neque dicitur aliquid punctum vel linea, vel superficie mathematica propterea quod dimensionibus careat, sed quia in argumentum non assumuntur.’
- 226.
Ibid. (my trans.): ‘In radiatione vero considerabimus longitudinem, et latitudinem non autem Crassitiem; haec enim intelligitur ex sumpta latitudine per omnes positiones; Exempli causa, si fiat radiatio cylindrice, secundum longitudinem AB vel CD, latitudo erit BD, vel EF, vel GH, cum autem quod demonstratur de una latitudine, demonstretur de omnibus, intelligetur ex una latitudine quomodo tota radiatio solida progredietur, ut non opus sit in radiationis contemplatione, plures dimensiones considerare quam longitudinem et latitudinem. Rursum quamquam radiationem hic considero eam quae fit a qualibet minima et imperceptibile parte lucidi, tamen quia et sic ambae dimensiones aliquando contemplandae sunt, dabo omni irradiationi latitudinem conspicuam, quantum sufficit adscriptioni notarum, sive literarum, quibus commodius omnis dimensio distingui et nominari possit, quam latitudinem, finita demonstratione, ad exilitatem linearem revocare imaginatione sua unusquisque potest; radiationem ergo vocabimus longitudinem quae est ab A.
- 227.
See Shapiro 1973, 161.
- 228.
It is not necessary to analyze the refraction phenomenon in detail here, as there is an extensive thorough literature on it (see Médina 1997, 40–41; Giudice 1999, 70 ff.; Horstmann 2000. We can simply remark that in considering refraction, Hobbes argued that when a ray of light propagates uniformly, whether it be dense or rare, it behaves like a cylinder, but when one part of the ray propagates less easily than the other, as in refraction, it behaves like a ‘truncated cone’. Giudice 1999, 72. See also Giudice 2015, 156.
- 229.
TO I, OL, V, 245.
- 230.
Ibid., 228.
- 231.
See TO II, chap. II, § 2, f. 204v/160 The topic is discussed in more detail in First draught, see FD, fol. 13 ff./122 ff. See also Stroud 1983, 39 ff.
- 232.
TO I, OL, V, 225.
- 233.
Ibid., 226 (my trans.): ‘Possumus ergo considerare radium ABCD sine latitudine, hoc est ut linea mathematica. Sed incidentia obliqua, ubi operatio ab F ad planum in H in majori est distantia quam ab E in G, non potest considerari EFGH ut linea mathematica: quia sic consideratur EF ut punctum mathematicum, quod tamen consideratur uno termino operari longius quam altero, hoc est, consideratur ut habens terminos, hoc est, non ut punctum. Itaque si consideraremus lineam oblique incidentem ut mathematicam, consideraremus EF ut punctum et non punctum, quod est absurdum.’
- 234.
TO II, chap. II, § 1, f. 204r/159–160.
- 235.
Ibid., chap. II, § 3, f. 205r/160.
- 236.
Ibid.
- 237.
See MLT, II, 8, 114.
- 238.
Ibid. My translation.
- 239.
Ibid., 114–115.
- 240.
- 241.
See Médina 2015, 82.
- 242.
See De homine, X, 5, OL, II, 93. As Médina has demonstrated, Hobbes’ definition of mixed mathematics follows that of Aristotle (See Aristotle, Posterior analytics, I, 13, 79a 7–10; Physics, II, 194a 10). See Médina 2015, 56.
- 243.
De corpore, I, 8, OL, I, 9.
- 244.
De corpore, VI, 5, OL, I, 62: ‘Causae autem universalium (eorum quorum causae aliquae omnino sunt) manifestae sunt per se sive naturae (ut dicunt) nota … causa enim eorum omnium universalis una, est motus; nam et figurarum omnium varietas ex varietate oritur motuum quibus construuntur.’ The words that François du Verdus wrote on the subject to Hobbes in December 1655 are of interest: ‘…puis que les Corps agissent selon [leurs grandeurs et leurs figures altered to leur grandeur et leur figure] et par leurs mouvemens qui sont les Objects de la Géometrie et des Mécaniques, il est impossible d’estre Philosophe a moins que d’estre Géométre Et aussi tot j’ai veu ces Gens-là (which he had termed ‘Pédans’ and ‘perroquets’) s’éfaroucher croyans qu’une Philosophie Geometrique c’est a dire la vraye Philosophie [tendit deleted > tende] a renverser les verités les plus importantes. Mesmes quand je luy ay allegué que du vray on ne peut rien inferer que de vray [Et que mesmes je leur ay fait deleted > jusqu’a leur faire] voir dans l’Écriture Sainte la Nécéssité qu’il y a d’estre Geométre pour estre Philosophe où il est dit Que Dieu á fait toutes choses En poids En nombre En mesure. Car (dis-je a ces Messieurs là) la Mesure veut dire l’étenduë et la grandeur du Corps, le nombre veut dire en Effect le nombre de ses Angles, qui fait la figure; Et le Poids c’est l’effort a tendre vers quelque part.’ François du Verdus to Hobbes, from Bordeaux, December [13/] 23, 1655, CH, I, 217.
- 245.
- 246.
See Leijenhorst 2002, 84 ff.
- 247.
MLT, X, 9, 178; Eng. Trans. Hobbes 1976, 123 modified.
, il faut recevoir la verité dans notre entendement, comme l’ornement, & le plus grand thresor, qu’il puisse recevoir, autrement il sera en des tenebres perpetuelles, & n’aura aucune consolation.’
, id est discere, vocabant Geometriam et Arithmeticam scientias mathematicas.’
, nous meine si parfaictement, & si asseurément depuis les premiers principes des sciences jusques à leur perfection ...’ (my translation).References
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———. 1988b. Of Passions (British Library: Ms. Harl. 6083), ed. Anna Minerbi Belgrado. Rivista di Storia della Filosofia (4): 729–738.
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Baldin, G. (2020). Hobbes and Mersenne. 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_1
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