Abstract
Pierre Gassendi (1592–1655) is often viewed mostly as an antiquarian because of his interest in reconstructing Epicurean philosophy. Admittedly, Gassendi was one of the main actors in the revival of atomism in the seventeenth century, but he was also a supporter of Copernican cosmology, and he proposed a groundbreaking theory of space: not only did he depart from the Aristotelian notion of place, but he even proposed a new ontological conception of space as neither a substance nor an accident. For Gassendi, space was a homogeneous, infinite, three-dimensional entity which could be filled with bodies but was independent of them and could remain void. This new conception of space was elaborated not only as a revival of Epicureanism, or as a foundation for the new science, but also through a re-elaboration of the scholastic notion of imaginary spaces. The aim of this paper is to unravel some of Gassendi’s unacknowledged scholastic sources and explore how Gassendi, a staunch anti-Aristotelian, relied on a reinterpretation of this scholastic notion for his construction of a cosmological system immune to theological criticisms otherwise directed at the Epicurean and Brunian infinitist worldviews. This reinterpretation directly paved the way for a geometrical conception of space.
Research for this article was made possible by a Veni grant (275-20-042) awarded by NWO (the Netherlands Organisation for Scientific Research). All translations are the author’s except where otherwise noted.
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Notes
- 1.
- 2.
Koyré 1957a, 176: “il lui a apporté l’ontologie ou, plus exactement, le complément d’ontologie, dont elle avait besoin.”
- 3.
For an account of the various conceptions of place and space in antiquity see Algra’s Chapter 2 in this volume.
- 4.
That space is neither substance nor accident is a statement that can already be found in Francesco Patrizi’s Nova de universis philosophia. Patrizi, however, remained trapped in a rather confused ontology in which he claimed space to be “an incorporeal body, and a corporeal non-body,” Patrizi 1591, 65. On Patrizi’s conception of space, see Henry 1979; Muccillo 2010; De Risi 2016; Ribordy’s Chapter 7 in this volume. Gassendi acknowledged his debt to Patrizi in the Syntagma philosophicum: see Gassendi 1658, vol. 1, 246a. Raffaele Aversa even anticipated the position adopted by Gassendi and Patrizi according to which space is neither substance nor accident. But contrary to Gassendi, for Aversa, space did not have extension or magnitude: “Hoc spatium [sc. imaginarium] non est quicquam reale & positivum, neque substantia, neque accidens, neque extensio seu magnitudo,” Aversa 1625, 788a.
- 5.
- 6.
See Brundell 1987.
- 7.
- 8.
- 9.
See, for example, LoLordo 2007, 35: “None of the great diversity of views within late scholasticism is apparent from Gassendi’s treatment of Aristotelianism , either in the Exercitationes or in his later work. He almost never identifies individual scholastics or discusses their disagreements.”
- 10.
LoLordo 2007, 122.
- 11.
- 12.
Gassendi 1658, vol. 6, 4b: “Imprimis ergo, mi Galilee, velim sic tibi persuasum habeas, me tanta cum animi voluptate amplexari Copernicaeam illam tuam in Astronomia Sententiam, vt exinde videar mei probè iuris factus, cùm soluta, & libera mens vagatur per immensa spatia, effractis nempe vulgaris Mundi sistematisque repagulis.” (“First, my dear Galileo , I would like you to be convinced that I receive your Copernican opinion in astronomy with such pleasure in my soul that I seem honestly to be in my right when my mind, detached and free, wanders through immense spaces, now that the common barriers and systems of the world have been broken.”). This might recall Lucretius in De rerum natura, book I, 72–74.
- 13.
Gassendi to Peiresc , 26 February 1632, in Peiresc 1893, 258: “je ne rapporte pas à un petit bonheur d’avoir fait ceste observation de Mercure devant le Soleil; elle est tres importante tant pour estre la premiere qui a esté faite de ceste façon, que pour devoir servir à ceux qui viendront apres nous soit pour determiner la grandeur et l’esloignement, soit pour regler les mouvements de ce planete.” On Gassendi’s activities as an astronomer, see Humbert 1936. On his observation of Mercury’s transit before the Sun, see Gassendi 1632; 1658, vol. 4, 499–510.
- 14.
Peiresc 1893, 259: “suivant l’opinion de Copernicus je conçoy le Soleil logé au centre du monde, et là tournant sur son propre escieu dans l’espace de quelques vint huit jours [...].” Indeed the rotational period of the Sun viewed from the Earth is approximately 28 days. The fact that Gassendi located the Sun at the center of the world suggests that the world or the solar system is finite – what is infinite has no center – but this does not exclude the existence of an infinity of worlds or of an infinite universe. In that case the center of the world, where the Sun is located, would only be relative to the solar system.
- 15.
Gassendi 1658, vol. 6, 54a.
- 16.
See Brundell 1987, 30–47. In the Syntagma philosophicum Gassendi claimed that the Ptolemaic system is the “least probable” of all three cosmological systems. The Copernican one “seems clearer and more elegant.” But on scriptural grounds, the Tychonic system should be preferred because, according to the decree of the Church, the sacred texts attribute real motion to the Sun and real immobility to the Earth, and do not deal only with appearances: Gassendi 1658, vol. 1, 149a. Zittel claims that there is no evidence in Gassendi’s Life of Tycho Brahe (Paris: widow of Mathurin Dupuis, 1654) of his support of the Tychonic system, while Gassendi reported appraisals of the Copernican system from Catholics in his Life of Copernicus: see Zittel 2015, 260–261. In the latter text, Gassendi also briefly rebuked traditional objections against the Earth’s motion: see Gassendi 1658, vol. 5, 502b–503b. Be that as it may, the text from the Syntagma philosophicum I have just referred to displays Gassendi’s explicit support of the Tychonic system.
- 17.
- 18.
Gassendi 1641–1642, f. 442r. On this see Brundell 1987, 42.
- 19.
Gassendi 1642–1643, f. 627r.
- 20.
In the Institutio astronomica the geocentric Ptolemaic system was presented in a schematic way which is “the figure [schema] according to which the disposition of the world’s parts, such as they are commonly conceived and taught, are represented,” Gassendi 1658, vol. 4, 2a. This system corresponds to the “commonly received opinion,” ibid., 2b: “receptam vulgo sententiam.” The Tychonic and Copernican systems, by contrast, were presented as having gained the favor of “noble supporters,” ibid. But Gassendi did not state which system he favored. On the chair of mathematics at the Collège Royal, see Pantin 2006.
- 21.
See Morin 1631.
- 22.
Regarding his early realist interpretations of astronomical phenomena, Gassendi was clearly in alignment with Copernicus and Tycho Brahe . In his Life of Copernicus, Gassendi defended the realist import of Copernicus’ theory against Osiander’s interpretation: see Gassendi 1658, vol. 5, 510b, 514a. On Gassendi’s later positions, see Gassendi 1642–1643, f. 653v; 1658, vol. 1, 630a.
- 23.
The idea of “saving the phenomena” was expressed in his Institutio astronomica (1647): see Gassendi 1658, vol. 4, 25a. See also his Syntagma philosophicum in Gassendi 1658, vol. 1, 615a, 617b, 630a. On Gassendi’s move from a realist to a hypothetical approach to astronomy, and from a Copernican to a Tychonic cosmology after Galileo ’s 1633 condemnation, see Brundell 1987, 30–47.
- 24.
See Palmerino 2004a.
- 25.
For Bruno ’s infinitism see also Granada’s Chapter 8 in this volume.
- 26.
See Bakker’s Chapter 3 in this volume.
- 27.
Gassendi 1636, f. 161r–v: “Atque haec duo [sc. the infinity of spaces and infinity of bodies] quidem sunt, quae defendere nihil obstat. Aliud superest, quod planè non liceat, videlicet non modò plureis praeter hunc asserere Mundos; sed concedere etiam per inane illud immensum infinita corpuscula, ex quibus vel creati sint, vel creari adhûc plures Mundi possint. Sane et sacra fides id respuit, et ratio etiam naturalis, qua infrà edocebimur fabulosam penitùs esse, quam Epicurus adstruit constituendi Mundi rationem.”
- 28.
Ibid.
- 29.
See Helden 1985.
- 30.
Gassendi 1658, vol. 1, 141a–144b; 1641–1642, ff. 461r–463v.
- 31.
Let us recall that Copernicus conceived the universe as being immense but finite. As for Galileo , he seems to have leant toward a conception of an infinite universe, but in his letter to Ingoli (1624), he only claimed that it was uncertain (and would most probably remain so for the human sciences) whether the world was finite or infinite. See Galileo 1896, 529; Koyré 1957b, 95–99.
- 32.
See Sturlese 1987, 123; Canone 1993, xxxi, referred to in Del Prete 2000, 57 n1. See Gassendi 1658, vol. 1, 140a where he explicitly refers to Giordano Bruno in a marginal note, evoking the model of an infinite universe composed of worlds which communicate with one another (which is distinguished from the Epicurean model in which worlds are separated by void space).
- 33.
See Del Prete 2000.
- 34.
- 35.
- 36.
Gassendi 1637, f. 201v. Chapter 4 is entitled thus: “Vt concipiendum Spatium, in quo Ratio loci consistat.” Gassendi 1637, f. 202r: “Itaque suppono imprimis esse extra mundum spatia illa, seu interualla, quae imaginaria vulgὸ adpellantur.” The early reference to imaginary spaces in book XIV of De vita et doctrina Epicuri overturns Brundell’s statement according to which the introduction of this notion in the Syntagma philosophicum might result from a reaction to Descartes’ Principia philosophiae; see Brundell 1987, 68.
- 37.
Gassendi who usually explicitly mentions all his sources did not do so with regard to imaginary spaces. At best, he mentioned “Aristotle ’s supporters” (Gassendi 1637, f. 203v: “Aristotelis Sectarores”), “us,” that is to say the Catholics (Gassendi 1637, f. 206v: “nos”), or “the Doctors of the Church” (Gassendi 1658, vol. 1, 183b: “Sacrorum Doctorum”). There is no explicit reference to late scholastics in his discussions on space, but some passages are conceptually and textually so close to some scholastic texts on the topic that it is almost impossible to deny that Gassendi read some of them. Given, on the one hand, his early philosophical training and his teaching position in philosophy in Aix-en-Provence, and on the other hand, his fierce rejection of Aristotelianism , it should come as no surprise that Gassendi was knowledgeable about late scholastic texts but avoided claiming them among his sources.
- 38.
See Grant 1981, 108–181.
- 39.
Conimbricenses 1596, book VIII, chap. 10, qu. 2, art. 4, vol. 2, col. 519: “In hoc igitur imaginario spatio asserimus actu esse Deum: non vt in aliquo ente reali, sed per suam immensitatem: quam quia tota mundi vniuersitas capere non potest, necesse est etiam extra coelum in infinitis spatiis existere.”
- 40.
See Grant 1981, 123–124, 143.
- 41.
Gassendi 1637, f. 202v: “haud-dubiè imaginantur spatia jampridem existentia, in quibus creanda collocari possint [...].” Ibid., ff. 202v–203r.
- 42.
Ibid., f. 202v: “Heinc etiam hunc mundum concipimus fuisse in hac determinata parte infiniti spatij a Deo constitutum; qui in alia quauis parte constitui potuerat, & in quam adhûc posse agi intelligitur, hac ipsa stante inuariabili; cùm siue illi aduenerit, siue ab illa recesserit mundus, ipsa semper eadem constet.”
- 43.
This is the solution adopted, for example, by Albert of Saxony , see his Quaestiones in Aristotelis De Caelo, book I, qu. 11 in Albert of Saxony 2008, 139: “bene tamen concedo quod, quando crearetur lapis extra mundum, crearetur spatium extra mundum [...].”
- 44.
Gassendi would address this objection in the Syntagma philosophicum; Gassendi 1658, vol. 1, 189b–190a: “Respondebunt Deum, siue hunc Mundum ampliet, siue nouum creet, creaturum simul spatium, quod à superaddita huic, aut à tota alterius mole occupetur; seu potiùs quod noua ipsa moles, eiúsve extensio, dimensióque sit; neque enim esse aliud spatium volunt, quàm extensionem corpoream, ipsásve corporis dimensiones. Verumtamen, praeter iam dicta, vt constet nihil esse opus creare nouum spatium, & confirmetur dari extensionem, dimensionésque non corporeas, quae Inani spatio competant; cùm possit Deus pro lubitu aut propè, aut procul ab isto nouum Mundum condere, condat tantâ distantiâ ab hoc dissitum, quantum est, v.c. milliare; quaeso, ista distantia ecquid aliud erit, quàm spatium?”
- 45.
Gassendi 1637, f. 206v (my emphasis): “at spatium sive Intervallum non modo est locato prius, sed ab aeterno etiam est. Postremὸ requiri heic potest, sit-ne Interuallum reale, an-non? [...] Instabis, erit igitur aliquid reale, quod Deus non produxerit? Sed ne inuidiose id vrgeas, adtende vt heic nihil ampliùs dicamus, quàm qui ex nostris Spatia Imaginaria vulgò concedunt. Caeterùm enim et nos quoque, quicquid reale vulgo concipiunt, hoc est omneis substantias, omniaque accidentia Deum verum habere autorem fatemur. Quid quod res saltem videtur esse longè tolerabilior communi doctorum virorum Scholarumque sententia, quae statuit rerum essentias esse & aeternas, & a Deo vt improductas, sic independenteis, cum sint tamen id, quod est in substantiis, accidentibusque praecipuum?” Raffaele Aversa already identified this kind of position as potentially risky from a theological point of view: “Si hoc spatium esset ens reale & positivum, vel esset aeternum, & improductum, ac independens a Deo: & hic esset grauis error in fide, ac etiam contra rationem [...].” It cannot be something produced, either, because then it could be destroyed, but God would be able to create bodies in the place which was occupied by this space, which would lead to an absurdity. Consequently Aversa, contrary to Gassendi, concluded that imaginary space “non est quid improductum nec productum,” Aversa 1625, 788b. One finds the same kind of statement in Goclenius ’ Lexicon philosophicum about imaginary space; Goclenius 1613, 1067b: “Non enim est verum Ens, quia nec creatum est; nec increatum Ens [...].” The Coimbrans also stated that space is uncreated and has always existed, but that it is not a positive being; Conimbricenses 1596, vol. 2, 518: “Item, nec esse vllum aliud reale ac positivum ens, cum nihil tale praeter Deum ab aeterno fuerit; hoc verò spatium semper extiterit, semperque esse debeat.”
- 46.
Questiones super Physicam, IV, 6 in Oresme 2013, 458: “Quarta conclusio <est> quod capiendo vacuum primo modo, in infinitum spatium vacuum est extra mundum. Probatur ex descriptione, quia vacuum primo modo est: ubi non est corpus et potest esse; sed conceditur quod Deus, qui est omnipotens, posset ibi facere unum corpus aut unum mundum absque creatione novi loci, ergo ibi est vacuum primo modo.” Oresme 2013, 459: “Tertio, quicumque ponunt mundum generatum esse, necessario habent ponere vacuum esse, ubi factus est mundus; sed secundum veritatem ponendum est quod mundus factus est, ergo etc.” This agrees with a passage in Aristotle , De caelo, III, 2, 301b31–302a9.
- 47.
See Buridan 1509, book IV, qu. 2, f. 68r, col. 1–2.
- 48.
See Summa theologiae, part 1, question 46, article 1.
- 49.
See Grant 1981, 111.
- 50.
Gassendi 1649, 200: “Nam quòd nonnulli quidem dicunt, si Deus crearet mundos alios, spatia quoque alia, in quibus collocarentur, creaturum esse; inextricabilem profectò difficultatem subeunt, quae illis obiicitur de interiecto spatio inter duos quoslibet mundos; cum id cadere in mensuram valeat, & per maiorem, minoremve distantiam possit explicari.”
- 51.
On the appeal to annihilatio mundi in medieval philosophy, see Suarez-Nani 2017. See Henry of Ghent 2007, 3–10; Olivi 1922, 590; Richard of Middleton 1591, vol. 2, 186, col. 2; Duns Scotus 1895, 441b; Ockham 1980, 45–46; Buridan 1509, book III, qu. 15, f. 57r col. 2-f. 57v col. 1; Bradwardine 1618, 177–178; Oresme 1968, 166; Oresme, Questiones super Physicam, IV, 6 in Oresme 2013, 458; Albert of Saxony 2008, 132, 135, 136; Aversa 1625, 787a. Suárez , Disputationes metaphysicae, disp. XXX, section VII, 34 in Suárez 1861, 106a: “Deinde, quis neget posse Deum conservatis coelis annihilare totam sphaeram rerum generabilium et elementorum, vacuo manente toto spatio medio.” See Patrizi 1591, f. 65r; 1943, 240. For the role of the annihilatio mundi thought experiment in Suárez and Patrizi, see Ribordy’s Chapter 7 in this volume.
- 52.
Gassendi 1637, f. 203r (my emphasis): “Cogitemus quippe vniuersam Aristotelis elementarem regionem, corpora dico terrae, aquae, aëris, & ignis, sic in nihilum redigi, vt concaua illa coeli Lunae superficies nullum prorsùs contineat, an-non semper cogitamus spatium, in quo illa corpora fuerint? & in quo denuò collocari possint? an-non tanta ibi est longitudo, latitudo, ac profunditas, quanta fuerit anteà? Non-ne semper cogitamus eundem circumferentiae diametrum? Nonne centrum concipimus in hujus diametri dimidio? Non-ne semper imaginamur vbi regiones elementorum discriminitae fuerint? Quae foret distantia duorum corporum si in hoc spatio collocarentur? & id genus similia.”
- 53.
Ibid., f. 203r: “Dices fortè suppositionem esse impossibilem: at neque impossibilis est ijs qui posse vacuum vi diuina in rerum naturam induci concedunt [...].”
- 54.
- 55.
Gassendi 1637, f. 203v: “Tale Spatium, non Interiorem continentis corporis superficiem esse Locum.”
- 56.
- 57.
Gassendi 1658, vol. 1, 304a–b: “Non posse porrò esse Deum, nisi Infinitum, prorsúsque immensum, ex eo probatur, quòd si diuina Substantia limites aliquos haberet, eo ipso imperfecta esset; quoniam quantumvis ingens foret, finibus tamen concluderetur; haberi posset pro nihilo, comparatione infinitatis, infinita foret varietas locorum, in quibus agere nihil posset; in quibus quid vel ageretur, vel non ageretur, nesciret; cohiberetur quasi vi quadam, ne se se vltrà protenderet, cùm etsi vellet, non tamen posset.”
- 58.
In a letter to Sorbière of 30 January 1644, Gassendi even reversed the conceptual order between God and space usually observed by the theologians. Ibid., vol. 6, 179a: “so that by reasoning on that [sc. place or the dimension of length, width, and depth], we conceive God as immense, and by reasoning on this [sc. time] as eternal” (“adeò vt ratione illius concipiamus Deum Immensum, & ratione huius Æternum”).
- 59.
Ibid., vol. 1, 131b: “Spatium non potest limitari reipsâ, quasi vlteriùs spatium non sit; sed designatione, seu positione dumtaxat. Spatium ex se infinitum est, concipitùrque etiam diffusum vltra fineis Mundi.”
- 60.
On the importance of Gassendi’s work on Epicurean philosophy for the genesis of his cosmology and conception of space see Rochot 1944, 145–151.
- 61.
Gassendi 1658, vol. 1, 139–144.
- 62.
Ibid., vol. 6, 158a: “Quo loco cùm infinitudo spatiorum tolerari possit, si quidem & nostri plaerumque admittunt esse vltra Mundum infinita spatia quae Imaginaria appellant, in quibus fatentur Deum posse condere innumeros Mundos: non perinde tamen tolerari potest infinitudo corporum.” See also Gassendi 1649, 200, 234–235.
- 63.
- 64.
- 65.
See Westfall 1962, 172–173.
- 66.
- 67.
Gassendi certainly borrowed from Francesco Patrizi this radical exclusion of space and time from the Aristotelian categories of substance and accident. Gassendi acknowledged his debt to Patrizi in the Syntagma philosophicum, recognizing his perfect agreement with Patrizi’s conception of three-dimensional space; see Gassendi 1658, vol. 1, 246a. But Gassendi managed to remove the ontological confusion between space and body that still pervaded Patrizi’s theory. Concerning time, this amounted to a radical break from Epicurus , who considered time an accident of bodies and void. On Gassendi’s evolution regarding the ontological status of time, especially his departure from the Epicurean conception and the role of Galileo ’s mechanics within it, see Bloch 1971, 181–194.
- 68.
Gassendi 1658, vol. 1, 182a: “Nobis porrò, quia videtur, etsi nulla essent corpora, superfore tamen, & Locum constantem, & Tempus decurrens; ideò videntur Locus, & Tempus non pendere à corporibus, corporeáque adeò accidentia non esse. Neque verò idcircò sunt accidentia incorporea, quasi incorporeae cuipiam substantiae accidentium more inhaereant, sed incorporea quaedam sunt genere diuersa ab iis, quae Substantiae dici, aut Accidentia solent.” On time as an entity that would continue to flow independently of the existence of bodies, and on time as a continuous entity in which it is not possible to distinguish parts, see Disquisitio metaphysica, Against Meditation III, Doubt IX, art. 2, in Gassendi 1658, vol. 3, 346b–347b.
- 69.
Ibid., vol. 1, 182a: “Id nempe, quia nulla substantia, nullum accidens sit, cui non competat esse alicubi, seu quopiam in loco; & esse aliquando, seu aliquo tempore; atque ita quidem, vt, tametsi talis substantia, taléve accidens pereat; non ideò minùs constare Locus, aut fluere Tempus perseueret. Ex hoc verò fit vt Locus, & Tempus haberi res verae, Entiáve realia debeant; quòd licet tale quidpiam non sint, quale vulgò habetur aut Substantia, aut Accidens; reverâ sint tamen, neque ab Intellectu, vt Chimaerae dependeant, cùm seu cogitet Intellectus, seu non cogitet, & Locus permaneat, & Tempus procurrat.”
- 70.
Ibid., vol. 1, 182a: “Interuallum triplici dimensione, longitudinis, <latitudinis> & profunditatis constans, in quo corpus recipi, aut per quod transire corpus possibile sit”; “incorpoream Quantitatem.” “Latitudinis” is a correction found in the 1727 edition of Gassendi’s Opera omnia; see Gassendi 1727, vol. 1, p. [li].
- 71.
Gassendi 1658, vol. 1, 183a: “Quaeso autem in hac Inani regione, cùm orbiculare Lunae Caelum sit, nonnè accepto vno in concaua illius superficie puncto, concipimus esse ab illo in punctum oppositum certam intercapedinem, seu distantiam? Nonne haec distantia longitudo est quaedam, incorporea puta, ac inuisibilis linea, quae regionis diameter sit, & in cuius medio sit punctum, quod sit regionis, ac Caeli centrum, quódque priùs centrum ipsius Terrae exstiterit? Nonnè subinde intelligimus quantum regionis circa hoc centrum occupatum priùs fuerit à Terra, ab Aqua, ab Aëre, ab Igne? Nonne designamus mente quantum cuiusque superficiei, quantum profunditati vniuscuiusque respondent? Nonnè proinde ibi supersunt, quas apprimè imaginemur, dimensiones longitudinis, latitudinis, & profunditatis. Profectò, vbicumque concipere licet intercapedinem, aut distantiam aliquam, ibi & dimensionem concipere licet; quatenùs talis intercapedo, aut distantia determinatae mensurae est, siue cadere in mensuram potest. Huiusmodi ergo dimensiones sunt, quas & incorporeas dicimus, & spatialeis.”
- 72.
Mersenne to Descartes , 28 April 1638, in Descartes 1996, vol. 2, 117: “supposé que Dieu n’eût rien créé, [Roberval ] prétend qu’il y aurait encore le même espace solide réel, qui est maintenant, et fonde la vérité éternelle de la Géométrie sur cet espace, tel que serait l’espace où sont tous les corps enfermés dans le Firmament, si Dieu anéantissait tous ces corps.”
- 73.
See Descartes to Mersenne , 27 May 1638, in Descartes 1996, vol. 2, 138; 1991, 102–103: “You ask whether there would be real space, as there is now, if God had created nothing. At first this question seems to be beyond the capacity of the human mind, like infinity, so that it would be unreasonable to discuss it; but in fact I think that it is merely beyond the capacity of our imagination, like the questions of the existence of God and of the human soul. I believe that our intellect can reach the truth of the matter, which is, in my opinion, that not only would there not be any space, but even those truths which are called eternal – as that ‘the whole is greater than its part’ – would not be truths if God had not so established, as I think I wrote you once before [...].”
- 74.
Syntagma philosophicum in Gassendi 1658, vol. 1, 183b–184a: “Neque enim illa Imaginaria dici concedunt, quòd merè ab imaginatione, Chimaerae instar, pendeant, sed quòd illorum dimensiones instar corporearum, quae in sensum cadunt, dimensionum, imaginemur. Non vertunt autem incommodo dici ea Spatia improducta, independentiáque à Deo, quoniam positiuum nihil sunt, hoc est, neque Substantia, neque Accidens; qua vtraque voce comprehenditur quicquid rerum est à Deo productum” (“Indeed, [the Doctors of the Church] allow these spaces to be called imaginary, not because they would depend merely on the imagination, like the chimera, but because we imagine their dimensions like corporeal dimensions which fall under the senses. But they are not deterred because of the inconvenience there would be to say that these spaces are neither produced by God nor dependent on him, since they are nothing positive, that is to say they are neither substance nor accident, two words which include any thing that was produced by God”). Gassendi did not make explicit what kind of independence space has with regard to God. One way to downplay the heterodox flavor of such a statement would be to consider that Gassendi envisaged this independence as independence from God’s will, which would not exclude some kind of dependence regarding God’s intellect. But Gassendi never formulated a clarification of this kind.
- 75.
Gianni Paganini identified this tension in Gassendi’s conception of space in the Syntagma philosophicum. In the 1649 Animadversiones, although Gassendi claimed that space and time are things (res), are something real (aliquid reale), and do not simply depend on the imagination like a chimera, he did not present them as entia realia that would be even more fundamental than substance and accidents; Gassendi 1649, 614, 616. See Paganini 2005, 2008. However, as early as 1649, Gassendi did claim that space “is not only prior to what is located, but also to everything since the dawn of time,” Gassendi 1649, 622: “non modo est locato prius, sed omni etiam ab aevo est.”
- 76.
Suárez , Disputationes metaphysicae, disp. LI, section I, 24, in Suárez 1861, 979a–b: “Itaque, quatenus hoc spatium apprehenditur per modum entis positivi distincti a corporibus, mihi videtur esse ens rationis, non tamen gratis fictum opere intellectus, sicut entia impossibilia, sed sumpto fundamento ex ipsis corporibus, quatenus sua extensione apta sunt constituere spatia realia, non solum quae nunc sunt, sed in infinitum extra coelum […]. Ubi etiam annotavimus, cum corpus dicitur esse in spatio imaginario, illud, esse in, sumendum esse intransitive, quia non significat esse in alio, sed esse ibi ubi, secluso corpore, nos concipimus spatium vacuum, et ideo hoc, esse ibi, revera est modus realis corporis, etiamsi ipsum spatium ut vacuum vel imaginarium nihil sit.” For Suárez, there is no middle ground between real being and being of reason. If something is not a real being, it can only be a being of reason: “si ens reale non est, quale ens esse potest, nisi rationis, cum inter haec non sit medium,” disp. LI, section I, 24, in Suárez 1861, 979a. In themselves, imaginary spaces are nothing; disp. LI, section I, 12, in ibid., 975b: “Sed nihilominus sufficienter videtur posse convinci illud spatium, prout condistinctum a corpore continente et contento, revera esse nihil, quia neque est substantia, neque accidens, neque aliquid creatum aut temporale, sed aeternum.” On late scholastic Jesuit conceptions of imaginary spaces, see Leijenhorst 1996.
- 77.
Conimbricenses 1596, vol. 2, col. 518: “Spatium hoc non esse ens rationis[.]” Oresme refused to assimilate space to a chimera: “non est sicut chimera aut hircocervus,” Questiones super Physicam, IV, 6, in Oresme 2013, 461. Conimbricenses 1596, vol. 2, col. 518: “Item, nec esse vllum aliud reale ac positivum ens, cum nihil tale praeter Deum ab aeterno fuerit [...].”
- 78.
Conimbricenses 1596, book VIII, chap. 10, qu. 2, art. 4, vol. 2, col. 518–519: “Spatium hoc non esse ens rationis, cum ab eo reipsa absque opera intellectus intra mundum corpora recipiantur, & extra mundum recipi queant, si illic a Deo creentur. Quare eius dimensiones non idcirco imaginariae dici consueuerunt, quod fictitiae sint, aut a sola mentis notione pendeant, nec extra intellectum dentur; sed quia imaginamur illas in spatio, proportione quadam respondentes realibus ac positiuis corporum dimensionibus.” That those spaces are called ‘imaginary’ not because they are fictitious, but because they are imagined, was also stated by Aversa : “Et ideo vocatur imaginarium, quia ita imaginatione nostra apprehenditur. At non per hoc est penitus fictitium, sed verè datur,” Aversa 1625, 788a. This can also be found in Fonseca , see Fonseca 1589, 605: “Non est igitur spatium, quod & corporibus occupatur, & extra caelum infinite in omnem partem distentum est, quantitas ulla vera & realis, sed imaginaria. Non, quia ipsum spatium ex imaginatione pendeat, quasi nullum sit vsquam nisi cum nos illud omnino fingimus; sed quia spatium, quod re vera suo modo est, semperque fuit, ac erit, non est vera quantitas, sed ficta quantitas.”
- 79.
Contrary to what Paganini claims, this apprehension of space by the imagination is not something that appears only in the Animadversiones: see Paganini 2008, 189. Gassendi 1637, ff. 202v–203r: “Et dicito has dimensiones aliquid non realeis, sed imaginarias; reuerâ tamen, ac nemine cogitante sunt, quantumuis ipsas ex corporearum comparatione imagineris.” See also Gassendi 1649, 199: “Primùm, nihil esse videtur, quod obstet asserere spatia vltra hunc mundum infinita. Quippe Doctorum etiam nostrorum quam-plurimi illa defendunt, Imaginaria appellitantes, quod in iis longitudinis, latitudinis, altitudinis dimensiones, illis, quae in corporibus sunt, consimileis imaginemur”; ibid., 616: “Etenim constat nomine Spatij, Dimensionumque Spatialium, nihil intelligere nos aliud, quàm quae Spatia vulgò Imaginaria nominant, qualiáque Sacrorum Doctorum maxima pars dari admittit vltra Mundum: Neque enim illa Imaginaria dici concedunt, quòd merè ab imaginatione, chimaerae instar, pendeant, sed quòd illorum dimensiones instar corporearum, quae in sensum cadunt, dimensionum, imaginemur.” This passage is reproduced in the Syntagma philosophicum (see fn. 80). This undermines Paganini’s interpretation of the Animadversiones as downplaying the reality of space in comparison both with book XIV of De vita et doctrina Epicuri and the Syntagma philosophicum; see Paganini 2005, 298, 332.
- 80.
Gassendi 1658, vol. 1, 183b: “Etenim constat nomine Spatij, dimensionúmque Spatialium, nihil intelligere nos aliud, quàm quae Spatia vulgò Imaginaria nominant, qualiáque Sacrorum Doctorum maxima pars dari admittit vltra Mundum. Neque enim illa Imaginaria dici concedunt, quòd merè ab imaginatione, Chimaerae instar, pendeant, sed quòd illorum dimensiones instar corporearum, quae in sensum cadunt, dimensionum, imaginemur.” Ibid., 189b: “Hoc sanè, vt iam aliquoties insinuauimus, nihil aliud est, quàm quae pars maxima Doctorum vocat, admittitque spatia Imaginaria, quippe Imaginaria dicunt, reputantque, non quòd non reuerâ seclusaque imaginatione non sint, sed quòd eas, quae in ipsis dimensiones spatiales sunt, instar corporearum, quae in corporibus familiare est obseruare, imaginemur.”
- 81.
The apprehension of space by the imagination as it is here stated by Gassendi might seem to contradict one of his later claims, namely that we have no sensation or imagination of the infinite. Gassendi indeed appealed to infinite spaces and times as that which goes beyond the limits of the imagination and is seized only by the intellect. He was thus able to justify the existence of a human intellect having some kind of autonomy in relation to the imagination because it relates to some specific objects. Ibid., vol. 2, 452b: “quid verò, quod etiam dari spatia imaginaria vltra Mundum disserimus, quae ratio omni fine carere, infinitave esse ostendat; & constat nihilominùs nullam in nobis speciem, imaginemve infiniti esse; ac nostram proinde Imaginationem longè esse, vt tantam illorum spatiorum, quanta est magnitudinem, extensionem, vastitatem capiat? Imaginatio quidem nostra aliquovsque vltra Mundi amplitudinem exporrigitur; at breui tamen terminatur, soláque ratio superest, quae superesse spatia absque vllo termino concludat. Sic et cùm profitemur Deum Mundos per illa spatia infinitos posse producere, Imaginatio quidem nostra adnititur aliquovsque hanc multitudinem prosequi: at quàm breui quaeso, resistit, soláque Intellectus vis est, quae superesse vltra omnem imaginabilem numerum innumerabilem multitudinem arguat.” This seeming contradiction can be solved if one considers that space as a whole escapes the imagination due to the fact that its infinity cannot be apprehended by the imagination. But its dimensions can be imagined, i.e. some specific (namely geometrical) determinations can be apprehended by the imagination.
- 82.
Conimbricenses 1596, book VIII, chap. 10, qu. 2, art. 4, vol. 2, col. 518: “Hoc spatium non esse veram quantitatem, trina dimensione praeditam; alioqui non possent recipi in eo corpora, cùm plures eiusmodi dimensiones in eodem situ naturae viribus simul esse nequeant.” Grant 1981, 164: “To identify imaginary, infinite space with God’s immensity and also to assign dimensionality to that space would have implied that God Himself was an actually extended, corporeal being […] [and] such a move would have been completely unacceptable in medieval and early modern scholasticism.”
- 83.
See Grant 1981, 156, 162–163.
- 84.
Conimbricenses 1596, book IV, chap. V, qu. 1, art. 2, vol. 2, col. 31: “Sciendum igitur est […] dari extra coelum spatium quoddam infinite patens; quod non est aliquid reale, sed imaginarium, in quo concipere fas est puncta, lineas, & superficies in eodem imaginario intervallo permanentes [...].” Note that the relation between extramundane void space and mathematics can be dated back to the medieval period. Albert of Saxony already presents the idea that the parts of such void spaces could be distinguished by distance; see Albert of Saxony 2008, 131: “Quia Deus extra mundum talem lapidem creatum posset movere motu recto, et facere eum distare plus ab ultimo caelo quam prius; sed non posset talia facere nisi per spatium”; “si tales lapides non essent sibi invicem immediati, sicut Deus posset eos creare, tunc unus videretur distare ab alio, et per consequens extra caelum videretur esse distantia per quam tales lapides creati distarent.”
- 85.
Toletus 1593, book IV, chap. V, qu. 8, ff. 121v-122r: “Est autem notatu dignum, locum, seu spacium imaginarium bifariam nos posse considerare. Vno modo, vt sit res ficta omnino, & fingamus esse, quod non est, vt extra caelum, vel in vacuo, vt diximus. Altero modo, in communi abstrahendo ab hoc, vel illo spacio vero singulorum corporum, spacium in communi totius mundi, in quo modo sunt corpora, abstrahendo, inquam, ab hoc, vel illo corpore: & haec consideratio non est ficta, sed vera […]. Sic ergo imaginamur illud spacium in communi totius mundi, tanquam quiescens, id est, abstrahendo a motu eiusdem, & a particularibus subiectis: & in communi similiter in eo distantiam consideramus, & situm in communi, & singularium partium eius positionem, omnia abstrahendo in communi, vt Mathematicus figuras […]. Et hinc est, quod spacium in communi omnes sic abstrahunt, quia vident illa accidentia in communi remanere, nam quamuis mutetur spacium, hoc tamen manet spacium, & aequale spacium.” See also Albert the Great’s Commentary on Aristotle’s Physics in Albert the Great 1651, vol. 2, 177a: “vacuum non dicatur esse nisi dimensiones mathematicae [...].”
- 86.
Gassendi 1658, vol. 1, 232a: “At verò, quia Materia, ac per ipsam corpus omne naturale, caeteras inter proprietates praeditum est Magnitudine, Quantitatéve, quae extensione, dimensionéve trina, vt putà longitudinis, latitudinis, & profunditatis consistit; ideò, Geometra, Mathematicúsve proprietatem hanc deligens, ipsam à materia mente separat, separatamque considerat, & de separata demonstrationes texit: Et quia dimensio profunditatis reliquas duas complectitur, talísque est, qualis inesse intelligitur; ideò ipsa quoque appellatur corpus, sed Mathematicum tamen, seu Geometricum, & de genere quantitatis, non item verò de genere substantiae, seu materiae, à qua intelligitur mente, considerationéve abstractum. Heinc est proinde, cur dici audias spectari à Geometra lineam, quasi longitudinem expertem latitudinis, & superficiem, quasi latitudinem, quae sit expers profunditatis; tametsi in re ipsa, hoc est in materia, materialíve corpore, nulla longitudo sine latitudine sit; nulla latitudo sine profunditate.”
- 87.
Ibid., 219a: “Quinetiam Aristoteles non videtur posse aliâ ratione dicere duas superficies contiguas simul esse, seu pro vna eademque haberi, quàm quia illae sint incorporeae; quod quidem dici etiam potest de pluribus concurrentibus seu punctis, seu lineis; ac sanè tantò faciliùs, quantò puncta, lineae, superficies, aliud sunt à profunditate, cui tribuitur corporis nomen.”
- 88.
Ibid., 183a: “quoquoversùm cum suis dimensionibus prolatatum in infinitum.”
- 89.
Ibid., 184b: “potest illius portio maior, minórque designari, inque mensuram cadere, ac omneis prorsùs comparationes, quas ipsummet corpus, vt quantum est, habere.”
- 90.
For the Coimbrans see fn. 82. See Fonseca 1589, book V, chap. XIII, qu. 7, section 1, 603–606.
- 91.
See Grant 1981, 122–127. Henry of Ghent and Jean de Ripa are noteworthy exceptions.
- 92.
Gassendi 1658, vol. 1, 190a: “poterit sanè recta linea vel per Geometricum postulatum, ab vno puncto ad aliud duci, seu quasi ducta intelligi, quae & vlnâ, aliáve mensurâ applicitâ possit definiri: Quare & licet inter illa duo puncta nullum intercipiatur corpus; intercipitur nihilominus extensio, seu dimensio, quae incorporea sit [...].”
- 93.
Ibid., 220a.
- 94.
Ibid., vol. 1, 183b: “in Spatio, eiusque dimensionibus vox Incorporei nihil aliud sonet, quàm negationem corporis, corporearúmve dimensionum; non autem praetereà positiuam vllam naturam, cuius facultates, actionésve sint; quippe cùm […] spatium neque agere, neque pati aliquid possit; sed habeat solùm <non> repugnantiam, qua sinat caetera transire per se, aut se occupare.” The latter part of the quotation corresponds exactly to the Epicurean definition of body and void; see Lucretius , De rerum natura, book I, 440–444. I correct the 1658 edition by adding non before repugnantiam, just as in the text of the Animadversiones (Gassendi 1649, 616): “sed habeat solùm non repugnantiam, qua sinat caetera transire per se, aut se occupare.” This is consistent with the following passage: “corporeae <dimensiones> sine resistantia recipiantur in incorporeis,” Gassendi 1658, vol. 1, 219a. See also Fonseca 1589, 606: “est non repugnantia quaedam capiendorum corporum commensurata corporibus locandis” and Goclenius 1613, 1068a: “Spatium Inane non est verum Ens, sed capedo quaedam corporum, sed quid corporum capedo? nihil aliud, quam repugnantiae negatio ad capienda corpora.” Gassendi is here at variance with Bartolomeo Amico , who had dismissed the very idea that imaginary space was the negation of body, i.e. vacuum. On Amico, see Grant 1981, 168–169.
- 95.
Fonseca 1589, book V, chap. XIII, qu. 7, section 1, 605–606.
- 96.
As Mamiani remarks, “il suo spazio è una quantità pura dotata di dimensioni autonome e assolute,” see Mamiani 1979, 103.
- 97.
Gassendi distinguished between corporeal quantity, which is divisible and separable, and incorporeal quantity, which can be determined but is not really divisible. Gassendi 1649, 621: “Dicendum est, quantitatem aliam esse corpoream, aliam incorpoream; ac proprium quidem esse corporeae, ita posse diuidi, vt partes abs se mutuò distrahantur; quod verò ad incorpoream, spatialemve attinet, ea nec diuidi, nec, vt ita loquar, discontiuari vlla vi potest; sed licet dumtaxat designatione dicere, hanc spatij partem non esse illam.”
- 98.
Gassendi 1658, vol. 1, 131b: “Sin quidpiam ita extensum quoquouersum est, vt ipsius partes concipi non possint à se inuicem distrahi, neque esse capaces contactus, atque resistentiae, appelletur Spatium.”
- 99.
Ibid., 224b: “Locus vi nulla interrumpi potest, sed immobiliter continuum, idemque semper permanet […].”
- 100.
Ibid., 219b: “Heinc, cùm vrgent praeterea interuallo conuenire, vt quantitas sit, & quantitatem diuidi posse; dicendum est, quantitatem aliam esse corpoream, aliam incorpoream; ac proprium quidem esse corporeae, ita posse diuidi, vt partes abs se mutuò distrahantur; quod verò ad incorpoream, spatialémve attinet, ea nec diuidi, nec, vt ita loquar, discontinuari vlla vi potest; sed licet dumtaxat designatione dicere, hanc spatij partem non esse illam.” The similitude between place and what is placed is a similitude of dimension, see ibid., 219a. Their dimensions are superimposable.
- 101.
Disquisitio metaphysica, in Gassendi 1972, 254: “It is false that the ideas of geometric figures are not drawn from the senses and that they can exist in the world as they are conceived by geometers, namely indivisible.”
- 102.
Ibid., 257: “but that triangle composed of indivisible elements cannot exist except mentally and by hypothesis.”
- 103.
Gassendi 1658, vol. 1, 341a–b: “An proinde est ad eas responsurus, negando illam tam potestate, quàm actu infinitatem partium; & concedendo insectilia, non Mathematica illa, atque infinita; verùm Physica, finitáque, ac numero solùm per mentem incomprehensibilia? Declaratum certè est quoque iam ante & infinitatem illam partium in continuo, & insectilitatem Mathematicam in rerum natura non esse, sed Mathematicorum hypothesin esse, atque idcirco non oportere argumentari in Physica ex iis, quae natura non nouit.” On this see Bloch 1971, 179–180; Palmerino 2011, 305–306. Contrary to Bloch, I do not see a tension between the Syntagma philosophicum and the letter to Sorbière of 30 January 1644. Contrary to Bloch, in the latter Gassendi did not claim that space or place was “infinitely divisible” but that space had innumerable parts, i.e. that there were more parts in space than one could enumerate or count. Gassendi 1658, vol. 6, 179a: “Vtrumque [tempus et locus] etiam habens parteis inexhaustas” (“Both [place and time] have innumerable parts”). This is coherent with the passage just quoted from the Syntagma philosophicum, in which Gassendi suggested that the continuum could be made of finite physical indivisibles whose number went beyond the understanding (“numero solùm per mentem incomprehensibilia”).
- 104.
The study of the notion of imaginary spaces I have presented here is therefore in agreement with Olivier Bloch ’s more general statement about the use of theological arguments in Gassendi’s philosophy. See Bloch 1971, 316–317.
- 105.
See Palmerino 2011.
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Bellis, D. (2018). Imaginary Spaces and Cosmological Issues in Gassendi’s Philosophy. In: Bakker, F., Bellis, D., Palmerino, C. (eds) Space, Imagination and the Cosmos from Antiquity to the Early Modern Period. Studies in History and Philosophy of Science, vol 48. Springer, Cham. https://doi.org/10.1007/978-3-030-02765-0_11
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