Abstract
I will examine what counts as necessary in the Copernican world, primarily as presented in Book I of De revolutionibus orbium coelestium (1543). In doing so, I will consider how Copernicus offers his system as an idea mundi, such that the intellectual vision of the astronomer converges with the divine vision of necessity. My reading here owes a particular debt to Georg Joachim Rheticus (1514–1574) and Johannes Kepler (1571–1630) and to the astronomical frontispieces of Oronce Fine (1494–1555). I also ask what necessities Copernican astronomy imposes on material bodies. I argue that Copernicus presents matter as perfect—perfectly incarnating geometry—at the cosmographical-astronomical scale. Material contingency, for him, arises only at smaller scales. My analysis of these issues extends to numerous points within Copernicus’s context and within the sixteenth-century reception of his work.
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Notes
- 1.
- 2.
Neugebauer (1975, 146).
- 3.
Copernicus used parallax for distance calculations. See Swerdlow and Neugebauer (1984, 232–271). For a discussion of the Copernican distances in light of Ptolemy’s Planetary Hypotheses (of which Copernicus, like all sixteenth-century European astronomers, was unaware), see Ibid., 472–479.
- 4.
- 5.
Robert Westman has made certainty of planetary distances the underlying motivation for Copernicus. For Westman, Copernicus wished to establish such certainty in order to shore up astrology against attacks from Pico della Mirandola. Westman (2011).
- 6.
- 7.
As Noel Swerdlow puts it, “He was in the situation—not infrequent in the sciences, in scholarship, in law—of being certain that he was right, but lacking conclusive proof.” Swerdlow and Neugebauer (1984, 21).
- 8.
Ibid., 144–45.
- 9.
For a review of Copernicus’s physical ideas and their Scholastic precedents, see Omodeo (2014, 197–233). For the humanist side of Copernicus’s physical ideas, see Knox (2005). For an overview of Copernicus’s sources, see Goddu (2010). For a comprehensive analysis of the internal logic of Book I, see Szczeciniarz (1998).
- 10.
Duhem (2004 [1908]).
- 11.
Ibid. 89–90.
- 12.
“Copernic conçoit le problème astronomique comme le conçoivent les physiciens italiens dont il a été l’auditeur ou le condisciple; ce problème consiste à sauver les apparences au moyen d’hypothèses conformes aux principes de la Physique. […].” Ibid., 84.
- 13.
- 14.
Swerdlow relies on his discovery of a page of notes, handwritten by Copernicus, in a manuscript held by the Library of Uppsala. As mentioned, these notes show Copernicus working through calculations for what would become the Commentariolus. Swerdlow (1973).
- 15.
In several articles, Edward Rosen reacted violently against Swerdlow’s argument. For Rosen’s Copernicus, planetary orbs are hollow, mutually penetrable, and intersecting. Rosen (1976, 302).
- 16.
Nicholas Jardine asks how Copernicus’s earth, surrounded by air, could attach to a solid orb. Jardine prefers to see the orbs as impenetrable and non solid. Jardine (1982, 177). Edward Grant has written that there was no explicit rule during the Middle Ages and the Renaissance as to the exact qualities of the celestial orbs. Their solidity or fluidity was never a “genuine issue,” although they were certainly corporeal. Copernicus, according to Grant, fits very well within the medieval mold, insofar as he does not present his “explicit opinions about the rigidity or fluidity of the orbs” Grant (1987, 172–173). Grant’s observation seems backed up by the fact that Copernicus never employs the word “solidus” to describe sphaerae or orbes. The celestial spheres were often described as crystalline in medieval philosophy, but according to Goldstein and Barker, “crystalline” was meant primarily to convey that the spheres had crystal’s transparency. Goldstein and Barker (1995, 392).
- 17.
KGW viii, 84, n.1.
- 18.
Jardine (1984, 70).
- 19.
KGW iii, 73: “Ergo idem orbis solidus (quos opinatur COPERNICVS) in quo haeret PIaneta, tardus est, cum Planeta orbe vectus incedit ex D in E [apogee to a point in the nearest quadrant]; velox, cum it ex E in F [to perigee]. Totus ergo orbis solidus jam velox jam tardus est. Quod COPERNICVS ut absurdum rejicit.” Swerdlow marshals both this passage and the passage from Kepler’s Apologia for support, in Swerdlow (1976, 131–132).
- 20.
KGW viii, 84 (n. 1): “Nostris Philosophis assentitur COPERNICVS. Intellige de spatio Orbium Geometrico: de materia enim, hoc est, de corpulentia adamantina ne PTOLEMAEVS quidem adeo crasse philosophatur.”
- 21.
“So let us come now to our principal subject. It is known that the planetary paths are eccentric. And hence the received judgment among natural philosophers (physicis), which establishes that the orbs be as thick as is required for the demonstrated variety of movements. And so far as this, Copernicus agrees with our philosophers.” KGW i, 47: “Igitur vt ad principale propositum veniamus: notum est, vias planetarum esse eccentricas: et proinde recepta physicis sententia, quòd obtineant orbes tantam crassitiem, quanta ad demonstrandas motuum varietates requiritur. Et hactenus quidem nostris Philosophis assentitur COPERNICVS.”
- 22.
Here is the quote in its fuller context. KGW i, 48: “Quae haec Naturae luxuries? Quam inepta? Quam inutilis? Quam minime ipsi vsitata? Atque ex hoc videre est, in COPERNICO nullum orbem ab alio tangi, sed ingentia relinqui systematum interualla vtique plena coelesti aura, sed ad neutrum tamen propinquorum systematum pertinentia.”
- 23.
KGW i, 48: “Orbibus ipsis tantam relinquo crassitiem, quantam requirit ascensus descensusque planetae […]”
- 24.
For the idea mundi in the Mysterium cosmographicum, see KGW i, 23–26. Kepler uses the variant spelling “idaea.”
- 25.
From the Mysterium onward, he believed that planets slowed as they grew further from the Sun because the Sun exerted a force that weakened with distance. He turned this intuition into a principle of his celestial physics.
- 26.
Knox (2002, 403–405).
- 27.
Copernicus and Rheticus (1959, 145). KGW i, 104 (this is the Latin reprinting of the Narratio appended to the first edition of the Mysterium cosmographicum).
- 28.
See Söderlund (2010, 177–187).
- 29.
- 30.
See sections 6–8 of Cicero (1977). De universitate was first printed in 1485 in a volume including De fato and Topica, with commentary by Giorgio Valla. De universitate was reprinted a handful of times in the sixteenth century.
- 31.
“Nam haec astrologiae pars: tota ferme imaginaria effectrixque est. Et haud secus quod rerum sapientissimus optimusque opifex veros coelos & veros motus divinae mentis opificio producit: mens nostra sui semper aemula parentis (cum ignorantiae labes plusculum detergitur) effictos coelos effictosque motus intra se profert verorumque motuum simulachra quaedam in quibus ut in vestigiis divinae mentis opificii depraehendit veritatem. Est igitur astronomi mens cum coelos coelorumque motus gnaviter effingit: similis rerum opifici coelos coelorumque motus creanti. […] Iterum mens similis est oculo in quo aetherei orbes orbiumque motus sine confusione repraesentantur.” Lefèvre d’Étaples (1517, f. a1v). Duhem provides a problematic translation of the above text. Besides his anachronistic reading of “imaginary,” the main problem is that he translates “effictus” as “fictif.” This is a stretch, as “effictus” usually refers to a copy taken from life, as in a portrait.
- 32.
For more on the humanist themes at play in Copernicus’s preface dedicated to the Pope, see Westman (2011, 133–40).
- 33.
- 34.
“[…] dans la perspective de la théologie astrale qu’Aristote développe dans le De philosophia et qui demeurera, encore qu’épurée, le fondement de toute sa spéculation théologique, l’astronomie nous fournit une expérience immédiate du divin; elle représente, si l’on peut ainsi parler, l’aspect expérimental de la théologie” (Aubenque 1962, 329).
- 35.
Ptolemy (1984, 37).
- 36.
Peuerbach (1515, f. 1v).
- 37.
This earth-planted sphere can also be seen in the frontispiece of Regiomontanus’s Epytoma in Almagestum Ptolomei.
- 38.
I have followed Isabelle Pantin’s translation. She cites the Aeneid, VII, 88, where incubuit refers to the priest reposing and awaiting prophetic dreams. Pantin (2009, 69).
- 39.
Sacrobosco (1527).
- 40.
Copernicus (1543, f. 3r).
- 41.
Likewise, in a wide swath of Scholastic and Renaissance thought, the necessity expressed by heavenly bodies is generally linked with their formality, regularity, predictability, and uniformity. In Book X of the Republic, Plato has all the celestial orbs turning around the spindle of necessity (ἀνάγκη). Plato (1935, 616c, 500–501). In Aristotle, the heavens are incorruptible, unwavering, and eternal. Averroes grants them necessity because they are “eternal and never fail to produce their effect.” Belo (2007, 170). As Pietro Daniel Omodeo notes in his chapter, Aquinas ascribes necessity to the celestial bodies because they are dominated by form, in contrast with sublunar matter, whose inherent mutability is the root of contingency. Such examples could be multiplied ad nauseum.
- 42.
- 43.
- 44.
“In aethere autem astra volvuntur, quae se et nisu suo conglobata continent et forma ipsa figuraque sua momenta sustentant; sunt enim rutunda, quibus formis, ut ante dixisse videor, minime noceri potest.” Cicero (1933, II 46).
- 45.
De caelo, II 4. For Cicero, presenting the Stoic cosmos, celestial bodies are composed of a flame that is close to the living and divine fire (ignem) or pneuma.
- 46.
For example, Oresme (1968, 440 114c).
- 47.
This was known long before Copernicus. Theon of Smyrna writes about it in his compendium of mathematical knowledge for reading Plato. If we scaled down the earth to the size of a foot in diameter, says Theon, the highest mountains would be smaller than one fortieth the diameter of a millet seed.
- 48.
Ptolemy (2000, 60).
- 49.
“Par le discours des sainctes lettres, et de l’histoire de Moyse, on void que la terre au commencement de sa creation estaoit toute couerte et enclose de l’estendüe des eaux, iusqu’a ce qu’elles se retirrent, partie sur la terre s’espandant, laissant neantmoins place commode aux hommes et animaux terrestres pour leur demeure, et aux plantes qui deuoyent seruir de pasture et soustien à tout ce qui a vie […] La mer donc des ce iour n’eut point sa situation naturelle, ains estant retiree en la partie opposite de ceste masse terrestre, a autaunt redoublé sa profondeur, comme elle a descouuert de la terre. Cest profondeur s’appelle Ocean, la saincte Escriture la tomme [tehom], c’est à dire, grand’ abysme: à sçauoir, où il y infinie assemblee d’eaux […]” I have cited from the French translation, Münster (1575, 6).
- 50.
- 51.
The work was first published by Apian as Cosmographicus liber (1524). It was expanded by Frisius, who appended to the work several of his own treatises. The Apian-Frisius Cosmographia went through many editions and translations.
- 52.
“[…] au centre de la figure, la représentation (« paysagère ») de la Terre comme sphère unique, ontologiquement homogène, composée sans solution de la continuité des éléments de la terre et de l’eau.” Besse (2003, 16).
- 53.
On this distinction, between the ideal of geometrical form and the imperfections inherent in real bodies, see section (2) of Pietro Omodeo’s contribution to this volume, Practices and Theories of Contingency in Renaissance Approaches to Nature.
- 54.
Copernicus (1978, 18).
- 55.
KGW iii, 28, 10–15. Kepler (1992, 58–59).
- 56.
- 57.
- 58.
Hooykaas (1987).
- 59.
Knox (2005, 205–208).
- 60.
Copernicus (1543, f. 6v).
- 61.
For the important cohesive role of water, see Bruno (1830, 60–62). “Oltre, che il simile si vede ne le gocce impolverate, pendenti e consistenti sopra il piano: per che l’intima anima, che comprende et è in tutte le cose, per la prima fa questa operazione, che secondo la capacità del suggetto unisce, quanto può, le parti: e non è, per che l’acqua sia o possa essere naturalmente sopra o circa la terra, più che l’umido di nostra sustanza sia sopra o circa il nostro corpo.” Ibid., 60–61.
- 62.
“Je ne veux aussi poursuivre ce qui est de la fermeté et stabilité de la terre, voiant que l’escriture saincte mesme nous la fait hors de mouvement, et enclose sous la concauité, et voulte admirable des cieux: et ne veux mettre en auant l’opinion fantastique, et trop gaillard de Copernique, qui pour se monstrer des plus habiles, a voulu contredire à tous philosophes, et prouuer que la terre est mobile, et par consequent elle a ses mouuemens qui vont suiuant celle cadence et harmonie admirable des parties du monde qui la ceignent et entourent, et reçoit par ce moien plus à son aise les influences des corps celestes […]” See first page of Belleforest’s preface de cest oeuvre au lecteur in Münster (1575).
- 63.
- 64.
Stahl et al. (1977, 3). I have lightly altered their translation.
- 65.
“The Earth, then, which by some great necessity, even by a virtue innate, evident, and conspicuous, is turned circularly about the Sun, revolves; and by this motion it rejoices in the solar virtues and influences, and is strengthened by its own sure verticity, that it should not rovingly revolve over every region of the heavens. The Sun (the chief agent in nature) as he forwards the courses of the Wanderers, so does he prompt this turning about of the Earth by the diffusion of the virtues of his orbes, and of light. And if the Earth were not made to spin with a diurnal revolution, the Sun would ever hang over some determinate part with constant beams, and by long tarriance would scorch it, and pulverize it, and dissipate it, and the Earth would sustain the deepest wounds; and nothing good would issue forth; it would not vegetate, it would not allow life to animals, and mankind would perish.” Gilbert (1958, 224). Also see, Regier (2017).
- 66.
Gatti (1999, 121).
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Regier, J.N. (2019). “Qualis alio modo reperiri non potest.” A Few Words on Copernican Necessity. In: Omodeo, P.D., Garau, R. (eds) Contingency and Natural Order in Early Modern Science. Boston Studies in the Philosophy and History of Science, vol 332. Springer, Cham. https://doi.org/10.1007/978-3-319-67378-3_6
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