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Vae ex philosophia naturali ad institutionem nostram necessaria videbantur tamquam principia et hypotheses. Mundum videlicet sphaericum, immensum, similem infinito. Stellarum quoque fixarum sphaeram omnia continentem immobilem esse.
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Copernicus’s claim that natural philosophers have not achieved consensus on the extent of the universe in I, 8 echoes Pliny’s about inquiries into what is outside the world in II, I, 3–4. Pliny in II, VI, 32–35 confirmed Copernicus’s views about the ordering and periods of the superior planets, and Pliny is an example of an ancient author who placed Venus and Mercury below the Sun (II, VI, 36–40).93 Pliny may also have been one of Copernicus’s sources for the teleological definition of gravity, namely, the notion of gravity as a natural appetite or desire implanted in the parts so that they would join themselves into unified wholes in the form of a globe.94 We will examine some of these more substantive issues in chapters nine and ten. On the basis of annotations, comments, and the like, scholars have assumed that Copernicus also had access to works by Cicero, Macrobius, and Vitruvius. He annotated Ptolemy’s Geography, and either read Martianus Capella’s De nuptiis philologiae et Mercurii (in the 1499 edition from Vicenza or the 1500 edition from Mantua) or relied on some description of its geo-heliocentric account of Mercury and Venus.95 In Part III of this study we examine his knowledge of Aristotle in detail, noting here that we have discussed in chapter four standard scholastic commentaries that Copernicus would have heard as a student in Cracow. 7. Achillini Of the books we consider in detail, I turn now to a work by a professor teaching at Bologna while Copernicus studied there. Alessandro Achillini was an Averroist Aristotelian who attacked Ptolemaic
Caeterorum vero corporum caelestium motum circularem, sumatim recensuimus.” (Italics added). In Revolutions, Rosen placed the text in I: 11, 26, lines 37–42. 93 See Rosen’s index in his commentary to Revolutions for references to Pliny. 94 De revolutionibus I, 9; Pliny, Natural History II: 2. I owe this observation to Knox, “Copernicus’s Doctrine,” 189–193. 95 Goddu, “Annotations,” 204–206 and 222, identifies the correct copy of Ptolemy’s Geography in Uppsala, now catalogued as Copernicana 45. Copernicus’s annotations indicate that he used it, but it does not appear that it made an obvious contribution to arguments, although they explain why he was circumspect in his comments about the circumference of the world based on ancient calculations. The facts that he cites are used to support the conclusion about Earth’s sphericity, obviously an important fact related to its capacity for circular motion. On Martianus Capella, see Rosen, Commentariolus, n. 327; and Birkenmajer, Kopernik, 24. 267, 339, 560, and 565. One possible source is Macrobius, In somnium Scipionis I, 19.
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models, and argued for a strictly concentric astronomy. It is possible that Copernicus may have known him and his work De orbibus libri quattuor (1498). I summarize its contents briefly, noting passages that might have influenced Copernicus because some scholars think that Copernicus must have attended his lectures and known his work. The summary also indicates my doubts about these conjectures.96 In the four books of De orbibus, Achillini treats the matter, form, composition, and accidents regarding the heavens, all in scholastic style with many citations of Aristotle and Averroes. Book I considers three principal questions, whether there is matter in heaven, whether a star is specifically different from its orb, and whether there are eccentrics and epicycles. Book II treats intelligences and whether they undergo change. Book III asks whether heaven takes its being from intelligence, whether it undergoes change, whether it is actually finite in extent, and whether there is only one heaven. Book IV asks about the sphericity of heaven, whether it is essentially luminous, whether its motion is eternal and natural, and about what effects the celestial motions have on inferior bodies. Before we look at some details, we should observe the difficulty of distinguishing arguments that can be attributed specifically to Achillini from the views found in Averroes. In other words, we would have to find some distinctive expressions in Achillini that Copernicus echoes to conclude that he influenced Copernicus. My summary is selective, as it must be, focusing on the objections to eccentric and epicycle models, and selecting other passages that might have influenced Copernicus. The first objection to eccentrics is that the world has a unique center.97 The emphasis on this point is contradicted
96 Di Bono, Sfere, 62–64; idem, “Copernicus,” 153, n. 72, where he asserts that Copernicus “would have had to follow the lessons of Alessandro Achillini,” citing F. Barone’s edition of Copernicus’s Opere (Turin, 1979). I have been unable to obtain this edition and evaluate Barone’s evidence. See also Barker, “Copernicus,” 349–350. Granada and Tessicini, 433–435, on the other hand, seem to be less persuaded, emphasizing the deficiencies of Achillini’s work in astronomy, citing di Bono, Sfere, in support. 97 Achillini, De orbibus (1498), Book I, Dubium tertium, f. 10ra–b, and the argument concludes thus: “Contra quos ponuntur hec conclusio. Nullum corpus caeleste est excentricum et est conclusio Averrois 12 Metaphysice commento 45: excentricum autem et epiziclum dicere est extra naturam epiziclum autem est impossibile, ut sit omnino et secundo Caeli commento 32. Ex hoc apparet quod dicunt mathematici de excentricis est impossibile idem commento 35 et in suo libro Almagesti. Item secundo Caeli commento 62. Motus quos ponit Ptolomeus fundantur super duo fundamenta que non conveniunt scientie naturali excentricum et epiziclum quorum utrumque est falsum.” Barker, “Copernicus,” 357, n. 25, cites a form of this text from the 1545 edition.
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directly by Copernicus in his first postulate from Commentariolus. Does his first postulate, then, mean that he was responding to Achillini or Averroes, or that he had already accepted the need for eccentric and epicycle models, and, consequently, recognized that the motions of the celestial bodies have multiple centers? We will analyze the postulates in Commentariolus in more detail in the next section, but suffice it here to say that Copernicus seems to reject concentric models out of hand. There is no indication that he ever took them as a serious candidate for restoring astronomy. He may have considered them seriously on mathematical grounds later when more technically competent attempts became available, but it rather appears that he formulated his first postulate to dismiss concentric theories because he had already accepted the need for eccentric and epicycle models, not because he was responding to Achillini.98 There is evidence in Achillini’s text that he knew about Novara’s observation of the declination of the arctic pole.99 Evidence that they knew one another or one another’s work does not prove Copernicus’s direct acquaintance with Achillini’s work, but could rather indicate that Novara informed Copernicus of Achillini’s views. Over the next few folios, Achillini attempts to defend Averroes’s speculation about spherical models that generate a gyrational or spiral motion, rejects explicitly the metaphor about the Sun as a king in the middle, and also rejects any suggestion that the motion of the heavens moves other bodies by force or violence.100 In this context he cites the opinions of Eudoxus and Callippus, and defends Averroes as another author who tried to preserve the principles of Aristotelian natural philosophy.101
98 Granada and Tessicini, 435, focus on Achillini with respect to Commentariolus, and argue that Copernicus recognized the existence only of eccentric-and-epicycle astronomy at that time. It is true that there was not yet a technically competent concentric rival, but Copernicus seems to have been prejudiced by the failure of the ancient versions. 99 De orbibus I, 3um, f. 12vb. Birkenmajer, Kopernik, 516, also cites the text. 100 De orbibus, ff. 13r–15v. Achillini cites Averroes’s De substantia orbis (f. 14v), and also indicates familiarity with De sphaera, f. 14vb: “Patet etiam motuum caelestium catenationem esse nobilissimam et naturalissimam sine corporeis ligamentis sine raptu sine violentia a principio vitali naturaliter ligante corpora mobilia et ea ex desiderio rationali movente.” The rejection of raptus might also indicate that he influenced Capuano da Manfredonia whose commentary on De sphaera appeared in 1499, or the dependence of both on Sacrobosco or Averroes’s De substantia orbis. 101 De orbibus, f. 16vb.
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The kinds of expressions that Achillini uses, however, are not so specific to him as to confirm a connection with Copernicus. In the concluding section of his arguments regarding eccentric and epicycle models (ff. 15v–19v), Achillini launches into a skeptical attack against the reliability altogether of the observational basis of Ptolemaic astronomy. Pointing out the inaccuracy of observations is one thing, but attacking the reliability of the tradition of observational astronomy altogether is another matter. He argues against judgments about distances in principle,102 and about variations in the speed of the Sun during the course of a year,103 referring to perceptual distortions, visual errors, imprecise instruments, atmospheric variables, the deception of the senses, the falsity of measurements of the bounded elongations of Mercury and Venus, and the illusory observation of retrograde motion.104 Recall that Brudzewo had refuted Averroes’s objections and affirmed the basic reliability of the observations on which eccentric and epicycle models are based.105 If Copernicus read or heard Achillini’s arguments, it is hard to imagine a reaction other than shock and dismay. Achillini was right, of course, that there are observational difficulties, and, (Copernicus would have agreed) that we need to account for the observations in a natural way, but Achillini’s point, following Averroes, is that the observations are not to be explained but rather explained away.106 Of course, Copernicus read authors whose views he 102 De orbibus, f. 17rb: “Sed distantia et propinquitas non est sensibile proprium. . . . Ideo iudicare de propinquitate vel remotione per sensum exteriorem in valde magnis distantiis quales sunt in proposito non est certum iudicium de distantiis neque de aliis.” 103 Ibid. f. 17rb: “Preterea solis motus velocitatis celeritatemque vix orde explicatur quisquam potest, et tamen sensibilem temporis partem aponit postquam se nobis manifestari caepit.” 104 Ibid. f. 17rb–18ra: “Propter quam non firmum est etiam mathematicorum iudicium de quantitate diametri solis sive per instrumentis capiatur sive per eclipses et earum quantitates. . . . Ad primam confirmationem concessum est corpora caelestia aliquando apparentur maiora, immo luna nova arcualiter illuminata respectu visus nostri aliquando apparent cornua exire partem lune obscuram, ideo necesse est sensum decipi in istis casibus. . . . Et dicamus solem suo motu regulari quartas zodiaci in equaliter pertransire absque excentrico aut epiziclo aut inequali eius distantia a polis proprie spaere.” 105 As mentioned in chapter five, Świeżawski, “Matériaux,” in documenting references to Averroes in Cracow sources of the late fifteenth and early sixteenth century enumerated 213 citations to Averroes by comparison with 161 to Giles of Rome and 128 to Thomas Aquinas, for example. 106 Ibid. f. 18rb–19ra: “Tertio principaliter arguitur planete aliquando sunt stationarii et aliquando directi aliquando retrogradi quod non est possible sine excentricis et epiziclis. . . . Tertio illa sunt ponenda que longo tempore et infallibiliter sunt observata sine quibus apparentia salvari non possunt, sed epizicli et excentrici sunt huiusmodi. . . . Ad tertium negatur quia apparentium alias causas reddidimus, neque astronomi
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rejected, and in the early 1520s took the trouble to defend Ptolemy’s observations at the request of a friend (Letter Against Werner), but there is no indication of a reaction to Achillini’s attack on the observational basis of astronomy. In Book IV, possibly another book that Copernicus consulted, Achillini returns to more cosmological questions that we can assume would have interested Copernicus. They concern questions about the nature of heavenly spheres and their movers. In fact, these are the sorts of discussions that may have contributed to Copernicus’s reluctance to address or answer questions about the nature of spheres, the causes of their motions, the finiteness of the universe, and the like. These are, perhaps, the discussions that he had in mind, which in De revolutionibus he characterizes as exercises in logic, yet when he makes that comment, he refers specifically to Aristotle.107 All of that said, and despite my skepticism, I also urge a careful reading of Achillini’s treatise, and more consideration of his possible influence on Copernicus, even if dialectical. Copernicus knew the Averroistic objections to Ptolemaic astronomy, and at this point in his career tended to dismiss concentric approaches without much reflection. It could be that Achillini’s diatribe prejudiced him against concentric hypotheses, but that would still leave us to explain his use of models in Commentariolus that appear to derive from mathematical solutions developed to address objections to Ptolemaic models. It is clear that Copernicus had available to him summaries and translations of the opinions of ancient authorities. There can be little doubt that these are the works that he scoured to find predecessors, alternative views, and even arguments that may have inspired him to formulate the geokinetic hypothesis. They provided him at the very least with arguments in support of the hypothesis once he formulated it. Some experts have inisisted that strictly astronomical and mathematical considerations led him to the heliocentric theory, but formulating the geokinetic hypothesis explicitly required a virtually simultaneous dialectical re-evaluation of geocentric assumptions.108 To the extent that we can separate these steps or moments, we maintain
excentricos aut epiziclos demonstrant aliquo genere demonstrationis secundo caeli commento 35 et 62, quia non a priori videlicet neque a posteriori.” 107 De revolutionibus I, 8. 108 The most important representative of the technical, mathematical route to heliocentrism, of course, is Swerdlow, “Derivation,” 423–511.
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that qualitative (not technical) mathematical issues led him to adopt heliocentrism with its geokinetic consequences. Those consequences, however, entailed a refutation or, at least, critical evaluation of geocentric principles. In other words, his major innovation was cosmological (heliocentric and geokinetic), for which only qualitative mathematical considerations sufficed. All of the above steps (astronomical, mathematical, heliocentric, and geokinetic) necessarily occurred before he wrote Commentariolus, but can we establish with any certainty exactly when he read which text for the first time, whether before Commentariolus or later before he composed Book I of De revolutionibus? 8. Commentariolus In this section I will argue that the date of the composition of his earliest work should be set in or around 1510, hardly a risky or original conclusion inasmuch as several experts have settled on that year as well. I offer further circumstantial evidence in support of that conclusion. I will further argue that Copernicus relied certainly not only on Regiomontanus’s Epitome but also Bessarion’s In calumniatorem, Valla’s De expetendis, and Pliny’s Natural History, and very probably on Part I of Ficino’s translation of Plato’s Works. He probably also used Part II, but we have no compelling reasons for thinking that his acquaintance with the dialogues in that part were indispensable for the writing of Commentariolus. We begin with a brief summary of Commentariolus. Copernicus began Commentariolus controversially with “petitiones” that he also called “axioms.” If we set aside the personal attacks by some commentators, the experts agree, even if inadvertently, that he did not mean the word “axiom” in the sense of self-evident principles but rather in the sense of assumptions or common notions.109 As Copernicus himself made abundantly clear, the rest follows only if the seven postulates or assumptions are granted him. It is evident that he arrived at these seven propositions by working his way back to them as the ones necessary and sufficient from which to derive the remaining propositions. In the version later owned by Tycho Brahe from which two other copies derive, Commentariolus is very brief, written on twelve folios, 109 Rosen, Commentariolus, 92; Swerdlow, “Derivation,” 437; and Schmeidler, “Leben,” 11–17, esp. 12. See Knorr, “Notes,” 203–211, for additional comments and reflections.
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recto and verso.110 We may think of it as a first or working draft—there is no evidence that Copernicus intended it for publication. Its character and style are similar to what we find in the Theorica literature, so perhaps he intended Commentariolus as his brief version of the more popular and less technical works like Peurbach’s Theoricae novae or Albert of Brudzewo’s Commentariolum, both of which could be used as texts in university instruction. There were evidently at least two copies, a fact that suggests that he distributed or had it distributed for comment. If it was to serve as an outline for a complete work intended to replace Ptolemy’s Almagest, he abandoned that notion by 1515.111 The publication of the Latin Almagest in 1515 made it possible for him to model the complete work on Ptolemy himself. His annotations in the copy of the 1515 edition that he used show that he spent a lot of time correcting it and trying to sort out the corruptions and confusions. It seems that this process went on for several decades, probably not completed until he received a copy of the Greek edition. The introduction of Commentariolus sets out a brief and sketchy history of the work of his predecessors. They assumed a large number of celestial spheres to account mainly for planetary motions by means of the principle of uniformity. Heavenly bodies that are perfectly spherical should move uniformly. By linking and combining uniform motions, they hoped to account for the apparent motions of the bodies.112 In a few lines Copernicus reports that Eudoxus and Callippus tried to construct an account by means of concentric circles, but such models
110 Rosen, Commentariolus, 75. See Goddu, “Reflections,” 37. See also Dobrzycki and Szczucki, “On the Transmission,” 25–28. 111 It was probably in 1515 that Copernicus made the relevant observation. See Birkenmajer, Kopernik, 78, on the observation of 1512 as setting the tempus ante quem, which would move the date up two years from the documented fact of its mention in the collection of Matthew of Miechów in 1514. Schmeidler, “Leben,” 12–14, seems to agree that observations begun in 1512 indicate that Commentariolus was completed, and that Copernicus was starting to work on the observations needed for the promised full-length study with demonstrations. See also Biskup, Regesta, 58, No. 76. But see Swerdlow, “Derivation,” 430, for a correction. I accept 1514 as the tempus ante quem for reasons stated below. 112 In summarizing and paraphrasing the text, I have consulted both the Rossmann Latin edition that was reprinted in Copernicus, Das neue Weltbild, and Prowe’s edition in Coppernicus, 2, but I followed Rosen’s translation except in cases noted. Zekl did not use Rosen’s emendations, but at this time the critical editions have yet to appear.
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failed, leading others to construct eccentric and epicycle models, the solution adopted by most scholars. The latter is the system associated principally, of course, with Ptolemy. His models were consistent with the numerical data, but a number of difficulties remained. The eccentric-epicycle models do not work without adding an equant model on which the planet (or center of the epicycle) moves with uniform velocity. But that means that the planet is not moving uniformly on the deferent sphere or on its own epicycle relative to the center of the epicycle, but to some other point. To Copernicus this adjustment was neither sufficiently absolute nor sufficiently pleasing to the mind.113 These defects, he says, led him often to consider a more reasonable arrangement of circles that would account for every apparent irregularity and that would move uniformly as required by the rule of perfect motion. It was a difficult and almost insoluble problem, but after some time (at length) he hit on a suggestion that could solve the problem by means of fewer and much more suitable constructions than those put forward by his predecessors if some “petitiones” were granted him. As we all know, Copernicus accepted, indeed, insisted on the ancient principles of uniform, circular motion. The equant model, he implies, was the first indication that something was seriously wrong. But how he got from that realization to his solution is hidden in the expression “at length.” How long? By means of what additional steps? What else or what other problems or difficulties did he recognize or encounter? Can we reconstruct those steps? We will work towards answers to those questions. Here are the “petitiones”:114 1. All of the celestial orbs or spheres do not have one unique center. (To anyone familiar with the inadequacy of concentric models and with the eccentric-epicycle models, this might appear to be self-evident, but some astronomers continued to pursue concentric solutions.)115
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Commentariolus, Rosen tr., 81. Rosen translates “petitiones” as “postulates,” Zekl uses the German word “Forderung,” which connotes “claim.” Swerdlow also uses “postulate.” I have usually followed Rosen and Swerdlow here, but occasionally “claim” strikes me as the appropriate sense. 115 For example, concentrists and Paduan homocentrists, about whom more below. As we saw in chapters four and six, the first postulate was commonly held at Cracow, and it appears in the Epitome, but Copernicus was evidently the first to interpret it 114
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2. The center of Earth is the center of gravity and of the lunar sphere; it is not the center of the universe. (Ptolemaic astronomers adopted a physical system of spheres or orbs in which eccentric-epicycle models were embedded, and thereby constructed a compromise that seemed to preserve both eccentrics and Earth as the center of each of the total spheres and the center of the starry vault.) 3. All of the spheres go around the Sun, which is near the center of the universe and, hence, is in the middle of them all. (This does not contradict postulate 1, but it seems little more than a solar version of the geocentric compromise rejected in postulate 2.) 4. The distance between Earth and Sun is imperceptible in relation to the distance between Earth-Sun and the stars. (It is as if the distance between Earth and Sun were reduced to a point in relation to their distances from the stars. The absence of stellar parallax is a result of this relatively small distance between Earth and Sun.) 5. Earth’s daily axial rotation causes the observed apparent daily motions of the stars, thus leaving the stars immovable. 6. Likewise, the motion of Earth on its sphere around the Sun causes the observed apparent annual motion of the Sun. (A sphere moves Earth annually around the Sun, hence Earth has more than one motion. Copernicus is not explicit here about a third motion of Earth.) 7. Earth’s orbital motion causes the observed apparent retrograde motions of the planets. The motions of the planets, then, are always direct. The motion of Earth suffices to explain many apparent irregularities in the heavens. (Note that Copernicus is not explicit here about the bounded elongations of Mercury or Venus, or about the ordering of the planets according to sidereal periods.) From these postulates, Copernicus proposes to show to what extent the uniformity of the motions can be saved in a systematic way. The mathematical demonstrations will appear in the larger work that he plans to write. Here the lengths of spherical radii or semidiameters will suffice to indicate to competent mathematicians how well his arrangement of circles agrees with the numerical data and observations.
as an assumption that together with other assumptions leads to the conclusion that Earth orbits the Sun.
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He distinguishes his effort from that of the Pythagoreans because their assertions about the motion of Earth are not based on mathematical considerations but rather belong to natural philosophy. Natural philosophers, however, base their conclusions about Earth’s immobility for the most part on appearances. But if Earth’s immobility is caused by an appearance, Copernicus implies, only a mathematical analysis can reveal the cause. Notice here that Copernicus is aware from the start that he must refute geocentric assumptions. He does not, however, say that the mathematical analysis has to be technically detailed; indeed in Commentariolus, the mathematics is of a more qualitative nature, relying primarily on estimates of orbital radii. Then follows without further preparation his announcement of the order of the spheres, beginning with the outermost sphere of the fixed stars. In providing the ordering according to sidereal periods, Copernicus supplies a number for Mars that he took evidently from Valla’s De expetendis XVI, 1.116 In the following section on the apparent motion of the Sun another notable peculiarity is Copernicus’s restriction of axial rotation to Earth alone. The spherical nature of other bodies did not lead Copernicus to ascribe an axial rotation to them, probably because he had no observational evidence of such rotations. As spheres they would be capable of axial rotation; however, as Copernicus’s training in logic had taught him, “a posse ad esse non valet consequentia,” that is, an inference from possibility to actuality is invalid. As is well known, Copernicus concluded that Earth has three motions, motivated by his aim to show which apparent celestial motions can be replaced by motions of Earth. As for the apparent motion of the Sun and fixed stars, the Sun’s annual motion, the universe’s daily rotation, and precession of the equinoxes can be replaced by respectively three motions of Earth.117 Then Copernicus notes explicitly for the first time disagreements in measurements and observations, namely, for the length of the tropical year based on the interval from vernal equinox to vernal equinox. The variation based on reliable observations leads inevitably to error.118 As
116 Rosen, Commentariolus, 94, n. 48. The exact reference in Valla, contrary to Rosen, is f. sig. bb7v, lines 12–13. 117 Rosen, notes, nn. 38, 56, 66, and 83. 118 In other words, because the different observations are reliable, the differences are not due to faulty observations. This is the sort of statement that supports my suggestion that Achillini’s skeptical critique of observations would have appalled him.
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a result of differences and what Copernicus believed to be a variability in the precession of the equinoxes, he proposed a derivation of the solar year from the fixed stars as more accurate, that is, the sidereal year as opposed to the tropical year.119 Finally in this section, Copernicus asserts that the apsides maintain a constant position among the stars. This claim will lead him to propose models that he later abandoned after he realized, probably around 1515, that the apsides move relative to the stars.120 For the Moon, Copernicus describes a double-epicycle model as “truer” than Ptolemy’s in accounting both for its non-uniform motion and its variations in distance. Copernicus’s first objection to Ptolemy’s theory was that the Moon’s epicycle center moved uniformly relative to Earth but non-uniformly relative to the eccentric’s center.121 Regiomontanus pointed out the problem with the variation in distance resulting from Ptolemy’s model in Epitome V, 25.122 The three outer planets have similar models, that is, double-epicycle models on a concentric deferent. Their spheres enclose the sphere on which Earth moves with its Moon. Copernicus implies that the observation of their retrograde motions is an optical illusion caused by the motion of Earth relative to the motions of the outer planets, the fourth appearance explained by one of Earth’s motions.123 Furthermore, their retrograde arcs increase in size according to their nearness to Earth. Accordingly, the arcs for Saturn are the smallest, and the arcs for Mars the largest.124 In accounting for variations in latitude, Copernicus says that the Earth’s motion “causes” the apparent latitudes to change for us. He imagines an oscillating motion along a straight line, a motion that can be produced by a combination of two spheres.125 119 Several attributions show that Copernicus relied on Epitome III: 2 for an incorrect statement, although Copernicus seems to have misread or misinterpreted Regiomontanus in part. See Rosen, Commentariolus, n. 93. 120 On the observation and the calculation, see Biskup, Regesta, 65, No. 98; p. 66, No. 102 (a calculation made in 1516); and Swerdlow, “Derivation,” 430. See also Rosen, Commentariolus, n. 110. See Birkenmajer, Kopernik, 78, for the emphasis on the observation of 1512; compare Schmeidler, “Leben,” 12–14. See also Goddu, “Reflections,” 47, n. 6. 121 Rosen, Commentariolus, n. 136; and Swerdlow, “Derivation,” 461. 122 Albert of Brudzewo, Commentariolum, 54–56 and 67–69, points out other defects in Ptolemy’s lunar model, but not this one. See also Rosen, Commentariolus, n. 140. 123 Rosen, Commentariolus, n. 192. 124 Copernicus expresses these numbers in terms of the ratio of the great orb’s semidiameter to the semidiameters of the respective planetary spheres. 125 See Rosen, Commentariolus, n. 233, on the so-called Tusi couple.
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Finally on the superior planets, Copernicus compared the sizes of a planetary sphere to the fixed length of the great orb’s eccentricity, twenty-five units.126 If Copernicus thought that the epicycles are also spheres, then it is apparent that spheres do penetrate one another, for the secondary epicycle penetrates the space occupied by the primary epicycle, and the primary epicycle penetrates the space occupied by the deferent sphere. Of course, if Copernicus regarded the spheres as the spaces in which epicycles move, then we must suppose that the epicycles represent only circles on which planets move with these circles somehow “attached” to or “embedded” in the sphere.127 Before attempting solutions to numerous textual and historical problems, we complete the essential parts of the summary. Copernicus’s description of the motions of Venus, unaccompanied as it is by either figures or geometrical demonstrations, is challenging. For our purposes, we may merely note that he accounts for its bounded elongation and its retrograde motion as appearances caused by Earth’s motion on its great orb outside of Venus’s orb. Again he resorts to a double-epicycle model to account for motion in longitude.128 Similar to the outer planets, he resorts again to an oscillating motion along a straight line as produced by a combination of two concentric spheres with oblique axes to account for its motion in latitude.129 Mercury poses the most serious problems for a mathematical astronomer. Copernicus proposes another double-epicycle on a concentric deferent, but difficulties arise in accounting for motions both 126 Rosen, Commentariolus, n. 169. Cf. Swerdlow, “Derivation,” 426–429; idem, “Summary,” 201–213, esp. 203 for the explanation of Copernicus’s rounding off the solar eccentricity of 26;28 to 25 units. The references are to the “Uppsala Notes,” for which see Czartoryski, “Library,” 366, item 2c. The “Uppsala Notes” are in Copernicana 4, Uppsala University Library, folios 270r-285v, esp. fol. 284v (fol. 15v of the “Notes” themselves). The notes are sometimes foliated separately with the folio in question numbered 15v, but in the codex it is folio 284v, as one can plainly see in the photograph. A detailed analysis with plates and tables appears below. 127 Compare Rosen, Commentariolus, nn. 172 and 174; Swerdlow, “Derivation,” 470– 478. See also Rosen, n. 200, where Rosen shows dependence on Pliny’s Natural History II: 59. Rosen questions whether Copernicus had yet read or studied Epitome XII: 1–2. See Swerdlow, who claims that the proposition dealing with an eccentric model for the second anomaly leads to the heliocentric theory. Compare Goldstein, “Copernicus and the Origin,” 221–222; Goddu, “Reflections,” 39–41; see also Rosen’s very long note 200, esp. p. 113. Apollonius’s theorem is the issue here, namely, a method that determines the stations and the length of the retrograde arc between them by the planets’ moving either on an epicycle or on an eccentric. The details appear below. 128 In De revolutionibus V, 20–25, he will replace these with an eccentreccentric. 129 Rosen, Commentariolus, 88 and n. 274.
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in longitude and latitude. Unlike the other four planets Copernicus here resorts to an oscillating motion by two small interlocking spheres to account for the planet’s approach and withdrawal in longitude. Similarly, its deviation in latitude also requires a combination of two concentric spheres with oblique axes. Commentariolus concludes with an enumeration of the circles sufficient “to explain the entire structure of the universe and the entire ballet of the planets.”130 Some questions will be reserved for later chapters, that is, technical philosophical details are left to Part III, where I will treat Copernicus as logician, natural philosopher, and mathematical cosmologist. Through enormous industry, and often with brilliant insights, previous scholars have laid the groundwork for what follows. My effort to reconstruct Copernicus’s path to the heliocentric theory in this section identifies the assumptions and establishes the conclusions that Copernicus would later strengthen with the arguments presented in De revolutionibus. Where there is substantive overlap between Commentariolus and De revolutionibus we may assume that the fundamental principles were already at hand as he wrote Commentariolus.131 Here I focus on Copernicus’s sources to try to reconstruct his steps to the heliocentric theory in its first form. Part of this discussion requires engagement with the secondary literature. I hope thereby to produce the likeliest account of the following issues—the method by which he arrived at his postulates, the decision to adopt double-epicycle models, the source of his models to account for planetary oscillations, and the year in which he completed his draft. Scholars have provided evidence that for the composition of Commentariolus Copernicus used the Epitome of Regiomontanus, Giorgio Valla’s De expetendis, the Almanach perpetuum of Alfonso de Corduba Hispalensis, the so-called “Uppsala Notes,” Cicero’s De natura deorum, Pliny’s Natural History, and Martianus Capella’s De nuptiis philologiae et Mercurii.132 To these I propose to add Plato’s Parmenides. There are apparently additional sources that no one has yet identified or found.
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Rosen, Commentariolus, 90, and nn. 319–324. The question of “solid” spheres is treated in chapter ten, as well as questions about the reality of spheres, orbs, and circles. 132 Goldstein, “ Copernicus and the Origin,” 223–231, also considers Aristotle’s De caelo, Averroes’s commentary, Proclus (in Valla), and Vitruvius. See also Rosen, Commentariolus, nn. 326–327. On Cicero and Pliny, see Knox, “Copernicus’s Doctrine of 131
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It is, of course, possible, even plausible, that Copernicus arrived at his postulates last. That is to say, once he decided what he wanted to “prove” or “demonstrate,” he worked his way back from conclusions to the postulates that he would need to make the derivations work. Even though Copernicus does not provide precise mathematical demonstrations in this work, the conclusions and what details he supplies must follow from his assumptions. If we accept this, however, then that shifts the question to how he arrived at the conclusions. Copernicus himself tells us generally how, and it is in its essentials the same explanation he provides later in the Preface to De revolutionibus. In Commentariolus he tells us that he accepted the ancient assumption that the motions of the heavenly bodies are to be accounted for by using spheres that move uniformly. As anomalies arose, combinations of circles were introduced and became more complicated, and finally circles were postulated that violated the principle of uniform motion relative to its deferent sphere and even its own epicycle center. As a consequence, he began to search for a more reasonable arrangement of circles that would account for every apparent irregularity without violating the principle of uniform motion with respect to a sphere’s or circle’s proper center. At this point, his account becomes vague, informing us that somehow he hit on models that worked better, provided one accepted his seven postulates. He adopted one fundamental assumption as self-evident—uniform circular motion of perfectly spherical celestial bodies. From that point on, he describes a dialectical process, the stages of which he learned as a student and that Plato’s Parmenides reinforced and guided at least in one crucial respect. For there Copernicus encountered the advice to “test” every relevant hypothesis both affirmatively and negatively. The “self-evident” assumption was adopted because its contradictory was deemed absurd. He compared uniform motion and non-uniform motion; circular motion and non-circular motion; concentric models and eccentric models; eccentric models with epicycle models, concentric models with double-epicycle models, and eccentric with epicycle and equant models; geocentric and heliocentric models; geostatic and geokinetic models.
Gravity,” 189–193. I also think it likely that Bessarion’s In calumniatorem Platonis inspired Copernicus to appreciate Plato’s dialectical method of inquiry.
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By a series of questions he was led to his postulates. Here I arrange the questions in the order corresponding to the postulates. Do the celestial spheres have one center or many centers? If many, then Earth cannot be the center of the universe but only of gravity and of the lunar sphere. Why are the models for all planetary spheres related to the position of the Sun? If their motions are relative to the Sun, then let us suppose that the planetary spheres encircle the Sun approximately in the middle of their motions. If Earth’s distance from the Sun is very small in comparison to the Sun’s distance from the stars, then could we perceive Earth’s motion relative to the Sun or the stars? If not, then which motions are merely apparent and due to Earth’s motions, and which are the proper motions of the spheres? Do the stars and the entire universe rotate once a day around Earth east to west, or does Earth rotate on its axis west to east? Does the Sun orbit Earth once a year or does Earth orbit the Sun once a year? Do the planets really move backwards and then forwards, or does Earth’s orbital motion account for these apparent irregularities? The conclusions that natural philosophers reach about the immobility of Earth rest on appearances, but Earth’s immobility is itself an appearance. When confronted with two appearances that contradict one another, by what principles, standard, or criterion shall we remove the contradiction? We have seen that the assumption of geocentrism has led to the violation of uniform motion relative to the deferent center and epicycle center, and accounted for irregularities in motions and distances by resorting to non-uniform motions. By means of his seven postulates, Copernicus claims that he can account for every apparent irregularity while keeping everything else moving uniformly. Above all he can determine the order of the spheres between the fixed stars at the periphery and the stationary Sun near the center according to sidereal periods with the Moon orbiting Earth between the spheres of Mars and Venus.133
133 Now, an objective reader would have legitimate objections about the claimed uniform circular motions. Copernicus’s resort to an oscillatory motion introduces rectilinear motions into the heavens, and he has made the terrestrial celestial. But compare with Rheticus, Narratio prima, Rosen tr., 130 and 138, who also emphasizes Copernicus’s achievement as establishing the perpetual and consistent connection and harmony of celestial phenomena, and that the order and motions of heavenly spheres agree in an absolute system.
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Noel Swerdlow’s critique of the postulates and their ordering is persuasive.134 I conclude that their order does not correspond to the dialectical process by means of which Copernicus arrived at the heliocentric cosmology. I have reconstructed the stages elsewhere;135 here I reformulate them as a series of questions that correspond to his reflections in De revolutionibus I, 4, conclusions in I, 10, and criticisms of predecessors in the Commentariolus and the Preface to De revolutionibus. Both texts have the following in common: acceptance of the axiom of uniform motion, rejection of the equant model as a violation of the axiom, and the recognition that each of the heavenly motions has a proper center. That is to say, taken singly the heavenly motions do not have a single center. Taken together, however, the heavenly spheres rotate around one center. In following the Platonic advice to examine dichotomies, Copernicus in his statements suggests that the following questions led him to propose the motions of Earth. 1. Why are the planetary spheres ordered around Earth according to two different principles—sidereal periods for Mars, Jupiter, and Saturn; a zodiacal period of one year for Mercury and Venus? Should not the heavenly spheres rotate around one common center according to one common principle? 2. Why do some authorities place Mercury and Venus above the Sun (Plato), around the Sun (Martianus Capella), and below the Sun (Ptolemy)? Why are Mercury and Venus subject to bounded elongation and hence move with the Sun in one year? 3. Why does Mars have such a conspicuously large epicycle, such a large retrograde arc, and such great variations in distance by comparison with the other superior planets?136 134 Swerdlow, “Derivation,” 437–438. See also Martin Clutton-Brock, “Copernicus’s Path,” 197–216. 135 Goddu, “Reflections,” 41–46. 136 Ptolemy rounds the ratios in the Almagest off to 7 : 1 for Mars, and 104 : 16 for Venus, as compared with 88 : 34 for Mercury, 37 : 23 for Jupiter, and 7 : 5 for Saturn. The same gaps are reflected, of course, in the cosmological distance scale in Planetary Hypotheses, the results of which were available in the theorica literature known to Copernicus and in the Epitome. The variations in distance are about the same in Copernicus’s system. From Copernicus’s statements it is often very difficult to distinguish a clue from an afterthought. I have sometimes suggested that the variations
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4. Why does Venus along with Mercury fill such a large space between the Sun and the Moon, and why is Venus’s retrograde arc larger than Mercury’s? My claim is that starting from his assumptions and by answering these questions consistently, Copernicus was led by a process of elimination to his conclusion that the Sun is the cosmological center of the heavenly spheres, that the Earth with its Moon orbits the Sun, and that Earth rotates on its axis leaving the very distant stars at rest. If the planetary spheres are ordered around the center according to one principle, than Earth cannot be the cosmological center of their motions. Some experts speculate that Copernicus anticipated a Tychonic arrangement that he would have rejected because of the interpenetration of the spheres of the Sun and Mars.137 In fact, the spheres of Mercury and Venus, even in the Capellan arrangement, penetrate the sphere of the Sun, yet Copernicus says nothing about it.138 He refers to Martianus Capella merely to cite a predecessor who put at least two planets in motion around the Sun. Copernicus, I contend, never got as far as a Tychonic arrangement, because the Capellan arrangement proposed two centers (Sun and Earth) with necessarily two different principles of arrangement, which would not have answered the first
for Mars and Venus were a clue, but perhaps after he imagined the Earth in orbit, Copernicus realized that it would explain retrograde motion, eliminating the need for epicycles to account for that observation. Earth’s motion explains in part the large variations in distance, and renders the large epicycles for Mars and Venus superfluous. The only functions left for epicycles were to adjust the motions of the planets and to account for variations in latitude, for which epicyclets sufficed. 137 Swerdlow, “Derivation,” 478. 138 I owe this observation to Martin Clutton-Brock in a private communication. He believes that Victor Thoren was the first to notice this apparent result. Not even Tycho Brahe raised this objection, which leads me to suspect that he thought of the orbits of Mercury and Venus around the Sun as epicycles of the Sun, and probably did not regard them as spheres. Thoren does comment on the relation between the comet of 1577 and the penetration of the spheres of Mercury and Venus, and he says that Tycho seems to have realized this consequence only some years later. See Thoren, “Tycho Brahe,” 3–21, esp. 8. Compare Jarrell, “Contemporaries,” 22–32; Schofield, “Tychonic World Systems,” 33–44; and Schofield, Tychonic World Systems. For an illuminating discussion of the alternatives, see Gingerich and Westman, Wittich Connection.
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question satisfactorily.139 Copernicus clearly assumed that there should be one center with one principle of arrangement.140 The Capellan arrangement did suggest an arrangement around the Sun as center. This is very likely the suggestion that inspired Copernicus to imagine Earth with its Moon in orbit around the Sun, necessarily outside the orbit of Venus, filling the large space between the Moon and Sun, and inside the orbit of Mars, thus explaining the large retrograde arcs of Venus and Mars, the large Martian epicycle and variations in distance, and all the planetary spheres ordered around the Sun, after some calculation,141 according to sidereal periods. By drawing on the consequences of the dichomoties and questions, he arrived eventually at a heliocentric, geokinetic system with eccentric-epicyle models as preserving the principles of uniform and circular motions while accounting for observed non-uniformities in motion and variations in distance. The double-epicyle models in Commentariolus constituted an intermediate stage. The Platonic method of examining dichotomies likely led him to resolve other questions in principle, although he does not address these in Commentariolus. The universe is either a whole or it is not. If not, then it is disordered, an unacceptable consequence, hence it must be an ordered whole. The elemental motions are natural or violent. If violent, then the elements would be disordered, also unacceptable. If the spherical body on which elements exist has a circular motion, then the natural motion of elemental bodies must also be circular. The rectilinear motion that we observe in the case of a falling body must be a compound motion. A rectilinear falling motion cannot be unnatural, hence such motions are an expression, as it were, of a natural tendency in such bodies to be united with their whole, and the most rapid motion is rectilinear. In De revolutionibus Copernicus
139 In the Tychonic arrangement, all of the planets can be ordered from the Sun according to sidereal periods, but they are still ordered zodiacally (Mercury and Venus) and sidereally (superior planets) from Earth. One could calculate the mean distance of the planets from the Sun, but the mean distance of each planet from Earth is necessarily the Earth-Sun distance. 140 Goldstein, “Copernicus and the Origin,” 220–222; Goddu, “Reflections,” 40–41. 141 For a reconstruction of the computation, see Goldstein, “Copernicus and the Origin,” 230. Copernicus calculated the sidereal priods from the synodic periods, the numbers for which he probably derived from Regiomontanus’s Epitome. See Table 3 for a simple modern computation of Mercury’s and Venus’s sidereal periods from their synodic periods.
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compares their condition while falling or striving to be united with the whole as a condition of sickness compared to their healthy condition when united with the whole. Sickness, on this view, is natural, tending towards health. I will address the logic in chapter eight, natural philosophy in chapter nine, and cosmological details in chapter ten; here I simply remark that the annotation in Parmenides fits Copernicus’s argumentative strategies developed to support the greater probability of his hypotheses over those of his geocentric, geostatic predecessors and contemporaries.142 The decision about which hypotheses to accept or reject requires a thorough evaluation of all of the consequences. It was, I suggest, Plato’s Parmenides that emboldened him to undertake the dialectical inquiry with its mathematical details and that led, in Commentariolus, to the rearrangement in the form of seven postulates. Admittedly, this suggestion extracts a great deal from one annotation, but the reconstruction illuminates the sort of reasoning that guided his treatment of hypotheses. The comment, brief as it is, reflects the impression that the text made on him. The same criticisms of predecessors with the same assumptions we find once again in De revolutionibus.143 As in his later qualitative account in De revolutionibus, Book 1, Copernicus leaves detailed exposition for later. As expressed in the Commentariolus, the motions of Earth cause the regular non-uniformities and variations in distance, thus eliminating or explaining some of the most peculiar non-uniformities. Even when he agrees that the motions of heavenly bodies are circular or composed of circles, he is anticipating Earth’s motions. Earth’s rotation on its axis eliminates the diurnal rotation of the entire universe. Earth’s annual motion around the Sun explains the regularity of the seasons, the direct motions of all of the planets, and the planets’ varying distances from Earth. In short, he is far from mentioning the complications of the geometrical models but is rather content to insinuate the Earth’s motions as providing an initial approximation of the solutions and explanations of the observed non-uniformities. 142 Rosen, Revolutions, Commentary, 359. Knox, “Ficino and Copernicus,” 413– 418, and idem, “Copernicus’s Doctrine,” discusses Copernicus’s doctrine of elemental motion and its sources. Again, Rheticus, Narratio prima, Rosen tr., 131, presents Copernicus’s discovery as the end of a critical inquiry, the results of which compelled him to assume other hypotheses or theories. 143 In chapter ten, I explain how in De revolutonibus I, 4–10, Copernicus completed his analysis of spheres, orbs, and their arrangement.
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To summarize the observational data, then, we need refer only to the following. The sizes of the retrograde arcs and distances of the planets from Earth vary. For the planets that move with the Sun in the geocentric system, the retrograde arc for Venus is greater than Mercury’s retrograde arc. For the planets seen in opposition, the variation and the size of the retrograde arcs are greater the closer the planet is to Earth.144 In other words, Mars exhibits the greatest variation and Saturn the least. Next, Copernicus knows that the Capellan arrangement explains the observation of bounded elongation. By calculating the sidereal periods of Mercury and Venus from their synodic periods, he realizes that Venus’s sidereal period is more than Mercury’s and less than the Sun’s. When he places Earth where the Sun is, the entire system falls into place. Even geocentrists had concluded that Mars, Jupiter, and Saturn follow the distance-period principle, yet the periods for Mercury and Venus were measured by the zodiacal period of the Sun, one year. That is the case if one places the Sun in the middle between the inferior and superior planets. But if one places Earth between the inferior and superior planets, then all of the planets follow the same principle. The reason for the variations in distance, in the sizes of the retrograde arcs, and the sizes of the planetary epicycles in the Ptolemaic system becomes clear. Earth is a planet, and the planets are arranged according to their sidereal periods. Most of the details and the principal conclusions I have provided elsewhere, but here for the sake of completeness I include a photograph of the crucial folios (Plates 2 and 3) from Copernicus’s “Uppsala Notes” (referred to as U).145 The first shows the verso of the last printed table in Copernicana 4, on which Copernicus began to write the results of his calculations. For reasons that we do not know for sure, he stopped writing and turned to a later folio, on which he repeated the first word and completed writing the results. That folio reports the calculations used in Commentariolus. Following Plate 3 are tables summarizing Copernicus’s calculations (Table 1), a comparison between Ptolemy and Copernicus on linear distances (Table 2), and a modern computation of Mercury’s and Venus’s sidereal periods from their synodic periods (Table 3).
144 Those facts alone might suggest that Earth is closest to Venus and Mars, as Copernicus emphasizes near the conclusion of De revolutionibus I, 10. 145 Following Swerdlow, “Derivation,” 426–429.
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Plate 2—Detail of Uppsala, Copernicana 4, folio 269v.
Plate 3—Uppsala, Copernicana 4, folio 284v, also identified as folio 15v of the “Uppsala Notes,” referred to as U.
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Table 1—Copernicus’s Calculations in Uppsala Notebook In Uppsala Notebook, f. 284v (also identified as f. 15v of the notes themselves), Copernicus calculated the radii (semidiameters) of the planetary spheres according to two units. At the top of the folio he used 10,000 units to represent the radius of a planetary sphere, and compared it to the size of the planet’s eccentricity, that is, the Earth’s orbital radius relative to the planet’s orbital radius. In the bottom half of the folio he compared planetary orbital radii to Earth’s orbital radius scaled to 25 units. Scaled to 10,000 units, the planet’s orbital radius to the eccentricity of the planetary model or Earth’s orbital radius:
Scaled to 25 units, the planetary orbital radius to Earth’s orbital radius:
Mars = 6583 Jupiter = 1917 Saturn = 1083
Mars = 38 Jupiter = 130 Saturn = 230 5/6
10,000:6583 = 1.52 10,000:1917 = 5.22 10,000:1083 = 9.23
38:25 = 1.52 130:25 = 5.2 230.833:25 = 9.23
[Copernicus reversed the ratio for the inferior planets.] [Venus = 7200 7200:10,000 = .72]* Venus = 18 Mercury = 376[0]** 3760:10,000 = .376 Mercury = 9 2/5
18:25 = .72 9.4:25 = .376
The eccentricity of the planetary model is in the left-hand column. In Copernicus’s system the eccentricity is equivalent to Earth’s planetary orbital radius scaled to 10,000. Note that the ratios correspond approximately to the ratios of the orbital radii in Copernicus’s system with Earth’s orbital radius set at 1: Mercury = .376, Venus = .723, Mars = 1.523, Jupiter = 5.203, and Saturn = 9.234. * Venus is omitted at the top of the folio. ** The folio records two different numbers for Mercury’s “eccentricity,” 2256, but in the left-hand margin appears 376. The first number is normed to 6,000, a variation of Regiomontanus’s Tabella sinus recti. The number in the margin is normed to 1,000, which I have changed to 10,000 for the sake of consistency. (Sources: Copernicana 4, containing Tabule Alfonsi regis (Venice, 1492), Tabula directionum perfectionumque (Augsburg, 1490), Tabella sinus recti, and The Uppsala Notebook, ff. 270r–285v, Uppsala University Library; and De revolutionibus V, 9, 14, 19, 21, and 27.)
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Moon Sun Planet
Least Distance
Greatest Distance
33 Earth radii 1,160 Earth radii
64 Earth radii 1,260 Earth radii
Ratio of Greatest to Least Distance (rounded off )
Mercury Venus Mars Jupiter Saturn
88 : 34 104 : 16 7:1 37 : 23 7:5
(From Almagest, IX–XI. Approximately: (R – r – e) : (R + r + e) where R designates the deferent radius, r the epicycle radius, and e the eccentricity.)
Cosmological Distance Scale Least Distance Greatest Distance (Earth radii) (Earth radii) (minimum distance × ratio = maximum distance) Moon Mercury Venus Sun Mars Jupiter Saturn
33 64 166 1,160 1,260 8,820 14,187
64 166 1,079 1,260 8,820 14,187 19,865
(64 × 88/34 = 166) (166 × 104/16 = 1,079) (1,260 × 7 = 8,820) (8,820 × 37/27 = 14,188) (14,187 × 7/5 = 19,862)
(Source: James Evans, The History and Practice of Ancient Astronomy, 387–388.)
Copernicus’s Orbital Radii, Sidereal Periods, and Mean Distances of Planets in Terrestrial Radii Mercury .376 88d (.24 yr) 430 E.R.
Venus
Earth
Mars
Jupiter
Saturn
.723 225d (.616yr) 822
1.00 1yr 1142
1.523 1.88yrs 1736
5.203 11.86yrs 5960
9.234 29.46yrs 10,477
(The figures approximate the results in De revolutionibus V, 9–30; the mean distances are from Swerdlow and Neugebauer, Mathematical Astronomy, II: 539, Table 12.) The significance of Copernicus’s numbers, however, is not so much their differences from Ptolemy’s, but the explanation for the greater variations for Mars. The closer the orbits of two planets are, the greater the variations in distance between them.
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Table 3—Calculation of a Sidereal Period from a Synodic Period If Copernicus assumed that Mercury and Venus are inferior planets, then to determine their sidereal periods and which is faster, we can use the following formula with Sn standing for the synodic period of the planet and Sd for its sidereal period: 1 = 1/Sd – 1/Sn. We know from Regiomontanus’s Epitome that Copernicus could have calculated Mercury’s Sn at 115.78. Earth’s sidereal period, of course, is 1 year or 365.25 days; therefore, 115.78/365.25 = .317. (1) 1 = 1/Sd – 1/Sn. (2) 1 = 1/Sd – 1/.317. (3) 1 = 1/Sd – 3.16. (1/.317 = 3.16) (4) 1 + 3.16 = 1/Sd. (5) 4.16 = 1/Sd. (6) 4.16 Sd = 1. (7) Sd = 1/4.16. (8) Sd = .24 years. (9) Sd = 88 days (.24 × 365.25 = 88) From Regiomontanus’s numbers for Venus, its Sn = 584.4 days. 584.4/365.25 = 1.6. 1/1.6 = .625; therefore, Sd = 1/1.625. Beginning at step 7 as above: (1) Sd = 1/1.625. (2) Sd = .615. (3) Sd = 224.63 days (.615 × 365.25 = 224.63) In Commentariolus, Copernicus calculated Mercury’s Sd as 88 days, and Venus’s as 7 and 1/2 months (7.5 × 30 = 225 days).
One more issue requires our attention. Already in Commentariolus Copernicus adopted something like a Tusi couple to account for planetary oscillations. In chapter five, I proposed that he might have developed his solution independently of Arabic sources by relying on suggestions that he could have encountered in Poland. Such a possibility, in my view, is supported by Mario di Bono’s critical evaluation of the literature that assumes that Copernicus must have been acquainted with Maragha models. Here is the appropriate place to consider the technical details at least sufficiently to understand the solution at which Copernicus arrived.146
146
See di Bono, “Copernicus, Amico,” esp. notes 1–7 for the scholars who have
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Because Giovan Battista Amico (1536) used this device, Noel Swerdlow suggested that the transmission of the model came through Italy. Hieronymus Fracastoro (1538) provided a demonstration of a similar reciprocation device.147 Di Bono’s critique is based on the way in which modern mathematical translations can obscure important differences and exaggerate marginal similarities.148 The Tusi device has one circle carrying a second circle whose radius is half its size and that rotates in the opposite direction at twice the velocity of the first. The initial point of contact (for example, at the top of the first circle) will generate a straight line (the diameter of the first circle) down to the opposite point and back to the original point.149 The 1:2 ratio is crucial, as we will see later. Furthermore, a description of the device as a circle that “rolls inside another twice its dimension” obscures the fact that the physics of that era precluded such a rolling in reality because there is no void in the heavens.150 Despite such objections, Tusi’s mechanism is a physical, not a simple, geometrical construction. Arabic asronomy attempted to find a physical structure for the Ptolemaic system that reconciled the mathematical constructions and physical reality.151 Di Bono goes on to describe three different versions of the device. The first is called a “rectilinear version,” which di Bono calls, more precisely, “the spherical version with parallel axes and radii in the ratio of 1:2.”152 This version is designed to solve those problems dealing with the non-uniform motion of the deferents of the Moon and the planets, that is, the problem of the equant. See Figure 1. The second version, called the “curvilinear version” and “spherical version,” di Bono, again more precisely, describes as the “spherical
made contributions to this topic. According to di Bono, n. 2, Dreyer seems to have been the first (1906) to show that Copernicus’s theorem was already known to Nasir al-Din al Tusi. Di Bono, n. 74, rejects the Cracow connection. 147 See di Bono, nn. 3–4, for the details. Cf. Swerdlow, “Aristotelian Planetary Theory,” 36–48, esp. 37. 148 In addition, Aristotle rejected the very idea that a rectilinear motion can be compared with, let alone composed by, circular motions. See di Bono, n. 14. 149 See di Bono, 134, figure 1. He adopted the figure from Saliba, “Astronomical Tradition,” 67–99, esp. 79. 150 This is, of course, another Aristotelian objection. 151 Ragep, Nasir al-Din al-Tusi’s Memoir, 1: 41–53. 152 Di Bono, 135–136. Compare Ragep, “Two Versions,” 329–356. Di Bono took his first figure from Saliba, “Astronomical Tradition,” 68–69 and 74–81.
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Figure 1—Tusi’s device: spherical version with parallel axes and radii in the ratio of 1:2. (From Saliba, p. 79)
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version with oblique axes and equal radii.” This version is designed to generate an oscillation between two points on a great circle arc (not a straight line). This device solves problems such as deviation in latitude, variable precession, and variation in the obliquity of the ecliptic.153 See Figure 2. George Saliba then identified a third version called “the plane version with equal radii.” This version of the device is composed of two identical circles in a single plane, one of which “rides” on the circumference of the second and moves in the opposite direction at a uniform speed that is twice the speed of the second. This version solves the problem of motion in latitude, not the problem of the equant for which the Tusi device (first version) would later have to be applied. See Figure 3. Di Bono’s description of Copernicus’s devices is complicated by obscurities in the texts and differences between Commentariolus and De revolutionibus.154 Di Bono says that the version Copernicus used in Commentariolus for deviations in latitude for the superior planets and Venus is the spherical version with oblique axes and equal radii (that is, the second version). The result, then, would be an oscillation on a great circle arc.155
153 Di Bono took the figure from Saliba and Kennedy, “Spherical Case,” 285–291, esp. 288. 154 We might also add that it is complicated by Edward Rosen’s commentary to Commentariolus, which is often a lengthy, running attack on Swerdlow’s translation and interpretation. Di Bono apparently ignored Rosen and followed Swerdlow, although di Bono’s reading concludes (140) with a paradox about how to interpret the solutions in Commentariolus. 155 Rosen’s translation, 87–88 and nn. 227–254. In fact, Copernicus says that the motion of libration or the oscillatiing motion occurs “along a straight line.” See Zekl, 24–26: “Accidit etiam motu telluris in orbe magno latitudines visibiles nobis variari, ita sane propinquitate et distantia visibilis latitudinis angulos augente et minuente, sicut mathematica ratio exposcit. Siquidem hic motus librationis secundum lineam rectam contingit, fieri autem potest, ut ex duobus orbibus huiusmodi motus componatur, qui cum sint concentrici, alter alterius deflexos circumducit polos et inferior contra superiorem duplici velocitate polos orbis epicyclos deferentis, et hi quoque poli tantam habeant deflexionem a polis orbis mediate superioris, quantum huius a polis supremi orbis. Et haec de Saturno, Iove et Marte ac orbibus terram ambientibus.” If he was thinking of plane circles, then the result is a straight line. But if he was thinking of spheres, the result is an oscillation on a great circle. But see Swerdlow, “Derivation,” 488–489, who interprets the equal radii as “degenerating” an ellipse into a straight line. Di Bono evidently follows Swerdlow’s interpretation, whereas Rosen takes Copernicus at his word that the oscillating motion occurs along a straight line, not an arc, because the “orbs” are functioning in a plane.
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Figure 2—Tusi’s device: spherical version with oblique axes and equal radii. (From Saliba and Kennedy, p. 288)
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Figure 3—Tusi device: plane version with equal radii. (From di Bono, p. 137)
Copernicus then introduces the “spherical version with parallel axes and radii in the ratio of 1:2” (that is, the first version) to account for variation in the distance of Mercury from the center of the deferent.156 In his account, di Bono then shifts to the devices as described in De revolutionibus. First, he describes a plane version with two circles of equal radii, the second turning in the opposite direction and at twice the velocity of the first. By means of this device, a point will oscillate back and forth along a diameter of the larger circle that contains both of the smaller circles. Their oscillation is rectilinear. This is clearly the 156 Di Bono, 138–139. This is what Rosen takes to be a variation in longitude. See Rosen, 89 and n. 293. Again, Copernicus says that by composite motion “the centers of the larger epicycle are carried along a straight line, just as I explained with regard to the oscillating latitudes.” Copernicus seems to have focused on a plane version, and he apparently saw no difference between the version with oblique axes of equal radii and one with parallel axes of unequal radii. What is more, he suggests “solving” the latitude problem for Mercury in the same way as that of the other planets.
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third version, and this is the version that Copernicus demonstrates in De revolutionibus III, 4. See Figure 4. Why did Copernicus change from spherical versions to the plane version in De revolutionibus? Di Bono concludes from III, 5, that because the “differences between the arcs and the chords in the cases under consideration are minimal,” Copernicus used the plane version with equal radii, not the spherical version with oblique axes, to account for all variations. That is, the plane version accounts for variability in precession, variability in the obliquity of the ecliptic, the variations in latitude of all planets, and the variation in longitude for Mercury.157 After describing devices in texts of Amico (eds. 1536, 1537, and 1540) and Fracastaro, di Bono takes up the question of transmission or re-discovery. First, he asserts, the claim that the drawings in Tusi’s Tadhikira (in Ms. Vatican, Greek 211) and De revolutionibus are identical is false. The first version of the device (1:2 ratio) is in Tadhikira and the third (equal radii) is in De revolutionibus. Second, contrary to the claim, the letters in the figures are not identical, and even where they are, such a coincidence can be explained by mathematical conventions of nomenclature in geometrical figures. In any case, the drawings are different. As far as De revolutionibus is concerned, it is possible that Copernicus relied on Proclus (published in 1533). But for Commentariolus he either would have had to see a manuscript, or he might have encountered among Paduan homocentrists the idea of a reciprocation device as a variation of the hypothesis of Eudoxus and Callippus.158 Copernicus may have seen some manuscript with the Tusi device, but that would explain his use of the first version in Commentariolus for Mercury, not his use of the second version for the latitudes of the planets. His demonstration and use of the third version in De revolutionibus suggests independent elaboration. Di Bono advances a second hypothesis:
157 So do I interpret di Bono’s remark, 141: “Our opinion is that he does so in all other cases including Mercury.” This conclusion may explain why Rosen interpreted the examples in Commentariolus as plane versions generating a rectilinear motion. In addition, Swerdlow, “Derivation,” 489, states the condition under which the line generated will be a straight line, namely, a case where the angle between a point on the circumference of the lower circle and the point on the circumference of the upper circle is small enough so that the point on the upper circle generates a straight line. Swerdlow goes on to point out problems with this supposed solution. 158 Copernicus pointedly says in Commentariolus that their concentric circles failed. Di Bono, n. 74, dismisses the possible Cracow sources as too different in content and purpose to have inspired Copernicus to his solution.
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Figure 4—Reciprocation mechanism in Copernicus. (From holograph of De revolutionibus III, 4, Opera omnia I, fol. 75r) Copernicus, starting from criticisms of the Ptolemaic system (among them the problems of the equant and uniform circular motion, which were certainly known to him and which his stay at Padua would have reinforced) and working on the solution of the double epicycle, found himself in practice starting from the same presuppositions, and operating with the same objectives and the same methods, as the Arab astronomers. This being so, it is by no means remarkable that he obtains results very similar to those of his predecessors—leaving out of consideration the fact, which is not at all cosmologically irrelevant, that the Arab models maintained the immobility of the Earth. From this viewpoint, the reciprocation device, even if prompted by the discussions with the Paduan Aristotelians, could equally well have derived from an independent reflection on these same problems.159 159
He goes on to discuss Amico and Fracastoro, arguing for a revival of the hypoth-
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With that comment I conclude my summary of di Bono’s critique. If Copernicus did arrive at the first two versions independently, and showed no awareness of the third version in writing Commentariolus, then the question comes down to what could have prompted him to hit on a reciprocation device. Di Bono thinks that discussions with Paduan Aristotelians may have prompted him, but he concedes that independent reflection on problems with the equant and uniform circular motion may have led him to his solutions. If independent, however, then we must also consider any source that described a geometrical solution, for the problem emerged, as we encountered it in Commentariolus, in accounting for deviations in latitude of all planets and, additionally, in longitude for Mercury. By that time Copernicus had already committed himself to solving all of the problems by use of uniformly moving circles alone. Any oscillation model using spheres or circles, regardless of content, context, and purpose, would have been a suitable candidate for solving the problem. In other words, scholars should again look at the Cracow sources through “Copernican eyes.” There he may have encountered an oscillation model, whatever its source and whatever its purpose, that he later adapted in the forms in Commentariolus and De revolutionibus.160 * * * While still residing in Lidzbark, Copernicus did record at least two astronomical observations—one in 1504 and the other in early 1509, at least one of which was on the Cracow meridian, suggesting that Copernicus was either in Cracow or Frombork, not Lidzbark.161 Later when he wrote De revolutionibus, Copernicus referred all of the observations
esis of Eudoxus, a characteristic feature of Paduan homocentrism. Schmeidler, Kommentar, 184, decisively rejects Copernicus’s direct knowledge of Arabic works: “Die von Swerdlow und Neugebauer vorgebrachten Vermutungen, daß Copernicus direkte Kenntnis von Originalschriften islamischer Astronomen gehabt haben könnte, sind wenig überzeugend.” 160 See Appendix VI for an excursus on transmission and suggestions for a reconstruction based on late medieval sources at Cracow. 161 Rosen, “Biography,” 333. Copernicus observed the conjunction of Saturn and Jupiter on 12 May 1509, an observation not recorded by Biskup, Regesta, 46–47. Biskup, 52, no. 59, records the lunar eclipse of 2 June 1504 on the Cracow meridian, also in Rosen, “Biography,” 334. Rosen based his comment about the conjunction of 1509 on a report by Marcin Biem of Olkusz in a marginal note to his copy of John Stöffler’s Ephemeris. There was correspondence between Martin and Copernicus about the event. The letter was lost, but Starowolski testifies to having seen it. See Hilfstein, Starowolski’s Biographies, 87, and Hilfstein’s comments, 55–58.
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that he made in Frombork to the Cracow meridian because he believed Frombork to lie on the same meridian as Cracow.162 Evidently Copernicus did visit Frombork on occasion before he moved there permanently in 1510. It does not appear that Copernicus used any of the observations recorded during the period in Lidzbark prior to 1509 in De revolutionibus. This suggests that he had not yet decided to compose a major mathematical work with models and tables that required being checked against observations. He was still at an early stage where he was making observations to compare them against the predictions in current ephemerides, as Rosen suggested. If that judgment applies to the observation of early 1509, then this leads me to conclude that Copernicus had not yet arrived at the resolution to compose a major work on astronomy, and that he had not yet begun to write Commentariolus.163 In 1510 Copernicus came to the conclusion that he could not follow Uncle Lucas’s plans for the advancement of his ecclesiastical career any longer. He would continue to perform his duties as a canon and remain engaged, at times heavily, in the administration and even defense of Varmia. Were he to become a bishop, however, all hope of completing a major and arduous reformation of astronomy would have been futile. By the autumn of 1510 Copernicus was transferred from Lidzbark to the cathedral chapter at Frombork. It seems that he was far enough at work on the Commentariolus to realize the need for a thorough reworking of Ptolemaic astronomy, such that would require years of calculations and observations to complete. He may have already completed the text in 1510, or shortly after the move to Frombork. The break with his uncle probably caused him some anguish, but it was sweetened by the knowledge that he had helped his uncle through a serious illness and, most of all, by a sense of relief from the burdens of higher church office. As for the selection of Frombork, it was the site of the chapter, its library especially with his additions was better
162 Modern geographers place Cracow at 50.04N and 19.57E, Frombork at 54.21N and 19.40 or 19.41E, and Lidzbark at 54.08N and 20.35 or 20.34E. Compare Times Index-Gazetteer, 441 for Kraków and 276 for Frombork, with Oxford Atlas for the alternate coordinates. 163 See Rosen tr., 82, where Copernicus alludes to his intention to write a larger work.
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stocked than Lidzbark’s for his purposes, and from the observations made there already he probably recognized its superiority as a place for relatively undisturbed observations. In brief, it was superior as a workplace in most respects.164 He remained involved in the business of the chapter and in Varmia, but he had escaped a potentially allconsuming job for the comparatively lighter duties of a canon and its sufficient income.165 He may also have wondered about his freedom to pursue a controversial project as a bishop. Even under the circumstances he delayed as long as he could, and perhaps would never have published De revolutionibus but for Georg Joachim Rheticus’s intervention. Judging from some annotations in his copy of Pontanus’s works and Bessarion’s defense of Plato, we perceive a figure who cherished the solitude and leisure to indulge his taste for the contemplative life. These were inclinations that he probably began to form as a young student. They were deepened by his contacts with humanists and academics at Cracow, and confirmed in Italy. Uncle Lucas had evidently seen promise in Nicholas at an early age, but little did he suspect that he had helped to form an intellectual, not a full-time administrator. In 1510, then, he informed his uncle that he could not follow his wishes. Could he have made such a personally difficult decision—one that he knew would disappoint his uncle—unless he had already recognized the absolute necessity of a break with him? I conclude, then, that he began to write Commentariolus after May 1509 and completed it in 1510. To sum up yet another long chapter, we have concluded that Copernicus acquired and developed the philosophical assumptions and techniques that he deployed for the remainder of his life in reforming ancient astronomy by 1510. His education and the books
164
This is not to say that Copernicus made extensive observations in Frombork. In fact, his instruments and the visibility from his tower were limited, and Frombork is very far north and also affected by fog from the lagoon. See Hamel, 177–184, for the limitations under which Copernicus labored. With some justice it may be said that Copernicus did not fully appreciate the need for new and more accurate observations to the extent that Regiomontanus and, later, Tycho Brahe did. As we shall see in the concluding chapter, even Rheticus was dismayed by Copernicus’s willingness to settle for inaccurate observations. 165 In fact, Copernicus was extremely busy administering church property, participating in the struggles against the Teutonic Knights, making himself available for medical advice, and engaging himself in economic and monetary policies, as a glance at Biskup’s Regesta demonstrates.
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that he acquired and used allowed him to formulate the fundamental assumptions and conclusions that he had reached by means of the qualitatively astronomical, mathematical analysis that led him to the heliocentric and geokinetic hypotheses. In U and in Commentariolus we see the first efforts to transform Ptolemy’s geocentric models into heliocentric, heliostatic ones. We turn now in Part III to the elaboration of Copernicus’s philosophy.
PART THREE
COPERNICUS AS PHILOSOPHER
CHAPTER EIGHT
COPERNICUS AS LOGICIAN 1. Introduction In an earlier effort to uncover the logical principles behind Copernicus’s arguments in De revolutionibus, I focused attention on his likely education in logic at Cracow. Because an examination of his arguments indicated that he had been trained in logical reasoning and argumentation, it was plausible to assume that he learned logic and dialectic as an undergraduate at Cracow.1 Today the formal study of logic has been relegated to mathematical technicalities and its practical study reduced to exercises in critical thinking. We can hardly appreciate the extent to which medieval universities trained their students in logic, devoting about twenty percent of courses to the study of works on logic. Accordingly, I described the instruction in logic at Cracow in the 1490s, and tried to show how his teachers influenced Copernicus to develop the arguments presented in the Preface and Book I of Revolutions. I stand by the analysis and principal conclusions of the articles that appeared in 1995 and 1996. My subsequent examination of Copernicus’s education in law at Bologna and his reading of Neoplatonic supporters of Plato and of some Platonic dialogues, however, has led me to a deeper appreciation for Copernicus’s attention to indispensable methodological principles and his participation in the reform of ancient astronomy.2 By 1510 he formulated his answers to the principal foundational questions, and concluded what issues required a definite solution and which questions he could leave for others to answer. There is already sufficient evidence in Commentariolus to identify Copernicus’s argumentative strategies. However, he did not articulate them more fully until the 1520s in Book I of Revolutions 1
Goddu, “Consequences,” 137–188; idem, “Logic,” 28–68. The details are in chapters three, four, and seven. Earlier scholastics introduced a doctrine rejecting the paradoxes of strict implication that in practical disciplines like law was applied to evaluate conditional propositions. Even so, some Cracow logicians gave the doctrine a peculiar emphasis by stressing relevance as a condition of validity. 2
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and even later (1542) in the Preface. As far as strictly philosophical, dialectical, and methodological issues and argumentative strategies are concerned, Copernicus resolved the principal issues well before 1520. We turn from a chronological examination of his intellectual development to analyses of Copernicus as logician, natural philosopher (chapter nine), and mathematically trained cosmologist (chapter ten). Around 1546–1547, Giovanni Tolosani alleged that Copernicus was ignorant of logic and natural philosophy.3 We do not have a detailed critique from Tolosani, but we may surmise that he possibly had two issues in mind. First, Tolosani was probably referring to Copernicus’s obscure statement in the Preface to Pope Paul III about the relationship between hypotheses and conclusions. Copernicus’s statement suggests that by 1542 he may have thought that he was leaning on Aristotle. “If the hypotheses assumed by them were not false,” he says, “everything [that] follows from their hypotheses would be confirmed beyond any doubt.”4 According to a standard scholastic formula (cited in chapter three), the true agrees with the true and cannot follow from the false.5 Among other standard scholastic accounts, however, Tolosani seems to have ignored the view of Thomas Aquinas that results may follow from hypotheses that we cannot demonstrate are true. In other words, they may be false, yet we can derive the appearances from them.6 Second, Tolosani may have been referring to Copernicus’s overturning of the traditional relation in the arts between mathematics and natural philosophy.7 This is the sort of criticism made by Luther 3 Tolosani, Opusculum quartum, 31–42. See Garin, Rinascite e rivoluzioni, 283–295, esp. 288. I treat Tolosani’s complete argument in the conclusion in the context of the reception of the heliocentric theory. Compare Lerner, “Aux origins,” 681–721, which provides another edition with French translation. 4 On the Revolutions, tr. Rosen, 4. 5 Perhaps it was Rheticus who reminded Copernicus of this formula. In Narratio prima, tr. Rosen, 142–143: “Aristotle says: ‘That which causes derivative truths to be true is most true’. Accordingly, my teacher decided that he must assume such hypotheses as would contain causes capable of confirming the truth of the observations of previous centuries, and such as would themselves cause, we may hope, all future astronomical predictions of the phenomena to be found true.” As Rosen notes, the quotation from Aristotle is found in Metaphysics I minor, 993b26–27. The relevant Latin passage in Rheticus, Narratio prima, ed. Hugonnard-Roche, 58 reads: Aristoteles inquit: Verissimum est id quod posterioribus, ut vera sint, causa est. As pointed out in chapter three, Aristotle used similar language in Nicomachean Ethics I, 8, and in Prior Analytics II, 2–4. 6 Thomas Aquinas, Summa theologiae IaIae, q. 32, art. 1, reply to objection 2. 7 Tolosani, Garin ed. 35–36. See Epilog for the text. Notice that in addition to criticizing Copernicus for his ignorance of Scripture and the potential theological danger
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about 1541 and that is echoed in Andreas Osiander’s “Letter to the Reader.”8 The first objection, expressed in modern terms, has come to be known as the problem of induction. The problem, of course, can be traced to Aristotle, and in modern philosophy of science it is linked with the intractable logical dilemmas of the hypothetico-deductive method.9 The consensus among philosophers is that induction and hypothetico-deductive method are not compatible with classical logic. In classical logic it is not possible to show that evidence confirms a hypothesis, because even irrelevant consequences follow just as logically from an antecedent. Some logicians have proposed relevance as a condition of validity and, accordingly, have attempted to develop a relevance logic that is otherwise just as formally valid as classical logic.10 The response of scientists seems for the most part to go on with their work, ignoring the objections of logicians. In effect, what they have adopted is some form of relevance logic, even if intuitively, and they have left it to the logicians to argue among themselves about the validity of relevance logics.11 A careful reading of Copernicus’s texts shows that he too adopted relevance between consequents and their antecedents (hypotheses) as a condition of validity for astronomical hypothetical propositions. In the previous publications mentioned above I showed that Copernicus could have encountered discussions by philosophers at Cracow, who held just such views about relevance. Furthermore, their use of
of his work, he especially emphasizes the point that there is no arguing with those who deny the first principles of a science. Tolosani adds that an inferior science receives its principles by which its conclusions are proved from the superior science. 8 Copernicus, Revolutions, XX, translated by Rosen as “Foreword by Andreas Osiander.” 9 The comments by Johannes Kepler in this regard are instructive. See Kepler, New Astronomy, II, 21: 294, “Why, and to what extent, may a false hypothesis yield the truth?” I will return to Kepler in my conclusion. Here I quote only the first sentence of Kepler’s remarks: “I particularly abhor that axiom of the logicians, that the true follows from the false, because people have used it to go for Copernicus’s jugular, while I am his disciple in the more general hypotheses concerning the system of the world.” 10 The literature on these topics is vast. For an introductory orientation, see Goddu, “Consequences,” 140–152. For more recent discussions of the logical issues, see Waters, “Relevance Logic,” 453–464; Achinstein, Book of Evidence; Koutras, “Aristotle,” 153–160; and Read, “Formal and Material Consequence,” 233–259. 11 Achinstein, Book, 86–94, for instance, does not find relevance either necessary or sufficient to meet his criteria for veridical evidence.
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traditional topics to support relevance corresponds closely to Copernicus’s arguments in De revolutionibus. Subsequently, however, I discovered that as a law student at Bologna, Copernicus would have encountered the very same doctrine about relevance in legal dialectic. Chapter six summarizes that doctrine, which now leads me to suggest that experts in their disciplines modified the rules of formal classical logic defended by some philosophers. They adopted relevance as a condition of validity for inferences in their professional domains partly as a matter of common sense based on assumptions about causal connections or, when causal connections were uncertain, other relationships based on topics, such as part and whole. In short, as an undergraduate at Cracow and a law student at Bologna (and perhaps as a medical student at Padua),12 Copernicus took it as a matter of course that relevance between hypotheses and consequences is a condition of validity, and irrelevance provides a justification for rejecting alternative hypotheses. In addition, the discovery of Copernicus’s annotation to Plato’s Parmenides in Ficino’s translation of that dialogue further confirms Copernicus’s attention to philosophical and logical issues regarding hypotheses.13 The annotation is very brief, but its context suggests that the advice to consider hypotheses thoroughly from both constructive and deconstructive points of view influenced Copernicus’s consideration and evaluation of hypotheses in astronomy as a methodological principle. His familiarity with topics provided the logical tools for the construction of his arguments. This reading is consistent with the view, supported by Copernicus’s explicit statements, that he regarded his hypotheses as more probable than those of his predecessors, and
12
His education in Padua, however, seems to have consisted mostly of gathering information about medications, drugs, regimen, and their effects with little concern about methodology. See chapter six for the details. 13 See chapter seven. We may also note here that in his annotation, Copernicus replaced Ficino’s word “suppositio” with “hypothesis.” See Goddu, “Copernicus’s Annotations,” 208 and Plate 42. In Narratio prima, Rheticus (Rosen tr. 162–165) confirms Copernicus’s reflection on hypotheses and reliance on Plato for his approach to hypotheses, but he does not refer to Parmenides. In Rheticus’s reconstruction, he refers to the Epinomis, a title, however, that does not appear in the table of contents of Ficino’s translation of Plato’s works in the 1484 edition. See Goddu, “Copernicus’s Annotations,” Plate 41. Rheticus is at pains here to emphasize Copernicus’s reliance on divine guidance; the reference to Epinomis confirms Rheticus’s emphasis.
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that he recognized that he had no strictly demonstrative proof of the Earth’s motions.14 Here I focus on the principal topics used by Copernicus to support his arguments. Plato’s advice in Parmenides about how to treat hypotheses provided Copernicus with methodological guidelines that we can articulate and exemplify. I discuss the logical issues involved in his use of mathematics and astronomy to justify the instances where he proposes mathematical grounds for arriving at conclusions in natural philosophy. In this regard I will consider the views of Luther and Osiander about the liberal arts. Finally, I examine the logical issues in my reconstruction of Copernicus’s “discovery” of the heliocentric theory. I follow the problems that he identified in the theories of his predecessors. His critique led him to propose the Sun’s stability and Earth’s motions as the solutions to the problems that prevented his predecessors from accounting for the observations on the assumption that the celestial bodies move uniformly in circles. In chapter seven I argued that he arrived at his theory from the recognition of various centers and varying distances. I showed that his grounds were partly aesthetic, but more importantly, he made epistemic claims supporting the greater likelihood of his hypotheses as compared with those of his predecessors. 2. The Sources of Dialectical Topics, 1490–1550 During the period of Copernicus’s formal university education and the publication of his major treatise, 1490–1543, humanist critics of scholastic logic placed such emphasis on rhetoric that the arguments of early modern authors are sometimes dismissed as little more than emotional appeals for a new ideology. The greater emphasis on rhetoric obscures the extent to which humanists included logic and dialectic in their broader and more comprehensive understanding of rhetoric. This chapter analyzes Copernicus’s discourse in a way that shows how
14 Thus, I reject an alternative interpretation by de Pace based on a speculative reconstruction of Copernicus’s supposed reading of Plato’s Phaedo, according to which Copernicus did have a demonstration of the heliocentric theory based on his interpretation of Plato. The method in Phaedo corresponds roughly to that in Parmenides, emphasizing generally accepted opinions and the need to test theories, adopting the theory that seems the soundest, and achieving truth insofar as the human mind can attain it.
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he took full advantage of the new rhetorical strategies by discovering arguments that made extensive use of dialectical topics. The vast majority of arguments in most disciplines are dialectical or probable. Although demonstration is undoubtedly the ideal that all strive to achieve, only some proofs in mathematics and logic start from premises that have the self-evidence, primacy, immediacy, necessity, and universality requisite to the construction of a strict demonstration in the Aristotelian sense. Other arguments even in mathematics and logic and nearly all arguments in other disciplines start from hypothetical assumptions or from the opinions generally accepted by the experts in that field, and whatever results emerge from them, the conclusions have only the degree of probability or plausibility and the persuasive force that characterize the premises. The connections between premises or hypotheses and conclusions may be necessary, that is, the conclusions may follow necessarily from the premises or hypotheses, but as long as the premises or hypotheses remain at best probable or plausible, then so do the conclusions that follow from them.15 As we saw in chapter three, techniques of dialectical, probable, and plausible reasoning have a long history in the west. By examining arguments against the background of the teaching of dialectical topics, we will find, I believe, that the authors whom we read were trained in techniques of argumentation, and that they were trained in their specialized disciplines to use and develop the assumptions, warrants, and backing that the community of scholars in their disciplines used as a matter of course. What we also find is that scholars adapted or changed traditional warrants to support new conclusions, developed new warrants, and also rejected some traditional warrants as irrelevant.16 Copernicus’s education and his writings were influenced by late medieval and Renaissance contexts. There is abundant evidence that the ancient and medieval traditions of dialectical argumentation continued to be transmitted and developed throughout the Renaissance.17 Although humanists had generally nothing good to say about scholas-
15 For excellent summaries of the background and explanations of the terminology, see Moss, Novelties, 1–23; Serene, “Demonstrative Science,” 496–517; Jardine, “Humanist Logic,” 173–198. 16 On the terminology, see Toulmin, Uses of Argument, and Bird, “Rediscovery,” 534–540. In chapter three, see section 1. See also Spruyt, “Peter of Spain,” 3. 17 Risse, Logik.
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tic logic, their criticisms were often consistent with the views of late medieval scholastic authors who viewed logic and argumentation in terms broader than demonstration and the syllogism. When authors like Lorenzo Valla (1407–1457) and Rudolf Agricola (ca. 1443–1485) shifted emphasis from the syllogism and formal validity to a variety of techniques for settling a matter that is in doubt, they were continuing trends that reflect late medieval thinking about topical invention.18 The humanist revival of rhetoric and the tendency to blend rhetorical with dialectical topics has contributed to the impression that the humanists had little regard for logic, and that they were only interested in persuasion by appeal to the emotions. Although some scholastic authors overreacted to humanist critiques by returning to emphasis on the syllogism and formal validity, others accorded dialectical topics a very important role in the construction of arguments. The evidence of their teaching suggests as well that their views exercised an important influence on students, even students, who, we know, responded positively to the new humanist dialectic and rhetoric. Copernicus was one of those students, and as we turn to him, we may focus briefly on the sorts of texts that were available to him during the period of his formal education (1491–1503) and of his major writings (1510–1543). As we also saw in chapter three, the standard sources for teaching dialectical topics to students were Aristotle’s Topics and Peter of Spain’s Tractatus better known as the Summulae logicales.19 I summarize briefly the main relevant points of chapter three here. When Copernicus entered the University of Cracow in 1491, the leading and most influential teacher of logic there was John of Glogovia. Copernicus very likely attended lectures and exercises on logic taught by John or by a colleague whom John had trained. The relevance of these considerations to Copernicus’s major work is relatively straightforward. In his commentaries on texts of Peter of Spain, John of Glogovia rejected the paradoxes of strict implication (from the impossible anything follows and the necessary follows from anything), and in his analysis argued that the validity of consequences
18 On Valla and Agricola, see Jardine, “Lorenzo Valla,” 253–286. On Agricola, see Mack, 227–256. 19 Some scholars also returned to Boethius, who again became popular in the early modern period. I owe this observation to Jennifer Ashworth. In fact, Johannes Caesarius is an example of an author who evidently did return to the texts of Boethius. See below for a summary of Caesarius’s version of topics.
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depends on rules of reasoning supplied by dialectical topics. We do not know whether Copernicus ever read or used the commentary by John. As we shall see below, however, the use of dialectical topics as rules evaluating consequences and as warrants for discovering arguments, and John of Glogovia’s reasons for rejecting the paradoxes of strict implication fit Copernicus’s argumentative strategies perfectly.20 Other important sources of dialectical topics that would have been available to Copernicus are Rudolf Agricola’s De inventione dialectica written around 1479 but first published in 1515, and Johannes Caesarius’s Dialectica first published in 1520. There were also other texts, but those of Agricola and Caesarius were widely influential and published in many editions. Both of these works applied Cicero’s topics as well, and would, therefore, have been complementary to the education in law that Copernicus received at Bologna between 1496 and 1501.21 Agricola studied at Erfurt and Cologne in the 1450s, but his major work on dialectic, De inventione dialectica, was evidently influenced more by his studies in Italy.22 Although the work is often disparagingly classified among works of rhetorical logic, the title clearly suggests that it is a topics-logic treatise. Agricola’s work was an effort to put Valla’s innovations into a textbook form.23 As such, it depends on the use of topics to construct arguments, and it assigns a subsidiary role to syllogistic argument as artificial and not suited to practical arguing and persuasion. If we were to locate Agricola’s work in the scholastic debates of the Middle Ages, we would include it among those approaches that viewed logic as an art rather than as a science. Accordingly, it stresses informal reasoning over formal inference, practical uses over theory, and persuasion over formal validity. It is a work that employs topics in the discovery of arguments for the purpose of securing or confirming belief about something that is in doubt.24 Expressed in that way, the purpose of Agricola’s work is consistent with the Boethian tradition of dialectical topics.
20 See chapter three. See Boh, “John of Glogovia’s Rejection,” 373–383; Goddu, “Consequences,” 152–163; idem, “Logic,” 36–61. 21 Rosen, Copernicus, 65–75; and see chapter six. 22 Jardine, “Lorenzo Valla,” 257. 23 Mack, 244–250, but also notes fifteen ways in which Agricola departs from Valla, showing how Agricola accepted the basis of Aristotelian metaphysics. 24 Jardine, “Humanist Logic,” 181–184; Mack, 233–237. Cf. Green-Pedersen, Tradition, 330; and Ashworth, Language, 10–14.
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Among the authors influenced by Agricola and who contributed to the popularity of Agricola’s approach to dialectic after 1530 was Johannes Caesarius. His Dialectica was published in over thirty editions between 1520 and 1579, and it became one of the most popular textbooks at Cologne, where it was first published, and subsequently in Cracow, Erfurt, Tübingen, and in Italy. Following the lead of Agricola, Caesarius argued for a revival of the approach to philosophy that places dialectic as the art of invention at the heart of the philosophical enterprise. Be that as it may, the work begins with a summary of standard Aristotelian and scholastic topics—predicables, predicaments, propositions, syllogism, demonstration, and definition and division. In the treatises on the categorical syllogism, hypothetical syllogism, and consequence, Caesarius considered disputations, topics, and dialectic argument, drawing a close connection between dialectical arguments and enthymemes. Treatise IX on dialectical topics draws on Boethius and Rudolph Agricola to emphasize the importance of topics for constructing arguments to secure belief about something that is in doubt. Caesarius’s influential textbook provides another example of a manual intended to teach students how to use dialectical topics to construct plausible arguments, and it does so in a way that makes Agricola’s new emphasis consistent with Aristotelian logic. As we did for Peter of Spain’s Summulae in chapter three and Appendix I, we may set down Caesarius’s scheme or list of topics as presented in the Dialectica. Caesarius divided topics into maxims and differentiae, and he divided the differentiae into intrinsic, extrinsic, and intermediate.25 (I) Intrinsic topics are further divided into (A) from the substance: (1) from the definition, (2) from the description, (3) from the interpretation of the name; and (B) from things that accompany the substance of the thing: (4) from the whole, (5) from the part, (6) from the cause, (7) from the effect, (8) from generation, (9) from corruption, (10) from uses, and (11) from concomitant accidents.
25 Caesarius, Dialectica, ff. X 7v–Bb3; the scheme is presented on f. Y 8v. Compare with Green-Pedersen, Tradition, 46–54, for Boethius’s list. Compare with the list from Peter of Spain above in chapter three. See Appendix I.
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(II) Extrinsic topics: (12) from authority, (13) from similar things, (14) from equal or equivalent things, (15) from proportion, (16) from what is less, (17) from what is more, (18) from opposites, (19) from contradictory opposites, (20) from transumption, and (21) from changed proportion. (III) Intermediate topics: (22) from inflections, (23) from coordinates, and (24) from division. The differences between the lists of Peter of Spain and Caesarius can be easily explained in most cases. Where Peter distinguished the intrinsic topic from the whole into six subspecies, Caesarius simply mentioned one, “from the whole.” Peter distinguished “from the cause” into the four Aristotelian causes, and he distinguished “from opposites” into four types, not just two. These differences suggest that Caesarius used the list as it appears in Boethius. On the other hand, Caesarius introduced “from equals or equivalents” and “from changed proportions,” which suggest mathematical examples. It does not seem that Caesarius’s list was as useful as Peter’s. In fact, one gets the impression that Caesarius merely summarized, in a schematic way, categories and distinctions with which everyone was already familiar. Peter of Spain’s Summulae, Agricola’s De inventione dialectica, and Caesarius’s Dialectica are representative texts of the Copernican era. They all drew on Aristotle and Boethius; Agricola and Caesarius borrowed directly from Cicero as well. In reading the arguments of an author like Copernicus, we can reconstruct the rules or warrants on which Copernicus relied by asking ourselves how his arguments are structured and how they depend on dialectical topics. The dialectical topics cited below are mostly what we could call commonplaces, that is, the standard sorts of rules that any well-educated person of the era would have known. Experts in the fields of natural philosophy and astronomy would have known the topics specific to those fields. In some instances, we can see that Copernicus is clearly and deliberately challenging some of the commonly held assumptions of his era. Even as he does so, however, he tries to persuade the reader by critiquing the commonly accepted view while at the same time arguing for the plausibility or reasonableness of his alternative. The last strictly logical source that we may mention is the teaching of legal dialectic at Bologna. As we saw in chapter six, Pietro Andrea Gammaro, a student of teachers at Bologna who taught at the univer-
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sity during the period that Copernicus attended the university, wrote an important work on legal dialectic. Although he probably learned logic as an undergraduate in Cracow, Copernicus would also have learned how to apply dialectical techniques to the analysis of legal cases. Legal dialectic of the era was dominated by the concept of topics as the seat of arguments. Topics from similitude and from authority were the most applicable and used in law, but legal dialecticians also emphasized the topic from the whole. What is remarkable about legal dialectic is the way in which jurists routinely assumed connection or relevance as a condition of validity for consequences. In other words, it is altogether possible that Copernicus’s intuition here was a common view in specialized disciplines where scholars either assumed the need for restrictions on logical theory or ignored the technicalities defended by some experts in logic. They no doubt viewed such technicalities as theoretical and not practical or applicable to the real cases with which they were concerned. Because of the unique importance of one topic in particular, from an integral whole, I beg the reader’s indulgence as I turn to yet another summary, this one devoted to part/whole relations in the western tradition.26 3. Mereology—Logic and Ontology Up to this point I may have given the impression that ancient and medieval discussions of logic were completely free of ontological assumptions or commitments. That is a false impression as the following discussion illustrates. “Mereology” is a major subject of discussion in late antique and medieval philosophy.27 Derived from the Greek méros (part), mereology is the “science” of part/whole relations. Medieval thinkers analyzed relationships between parts and wholes with great acuity.28 The first
26
Much of what follows is in Goddu, “Copernicus’s Mereological Vision.” Liddell and Scott’s Greek-English Lexicon (Oxford, 1883) lists “part” as only one of the many meanings of méros. Varzi, “Mereology,” 1–5, provides a variety of meanings for “part” and “whole” in both technical senses and in ordinary language. 28 King, “Medieval Mereology.” The bibliography on mereology is extensive and can be found in the following: Henry, Medieval Mereology; Burkhardt and Dufour, “Part/Whole I: History”; Simon, Parts. 27
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explicit analysis of part/whole relations in western thought appears in Plato. In Parmenides (137a–145e) Plato pursues the consequences of contrary assumptions. If being has parts, then what is the relation of the whole to the parts? Is the whole just the collection of the parts or more than the sum of the parts? In Theaetetus (202e–205e) Plato notes the difference between a syllable and the letters in it. A syllable is formed from letters yet is distinct from them, for it has its own peculiar form or arrangement. Plato also concludes that there is a difference between a sum and a whole.29 In other words, an arithmetical sum is not the same as a whole that possesses unity (hólon or súnolon). Aristotle took up these issues in several texts, too many to summarize briefly.30 I select texts essential for the results that follow, namely, those regarding integral whole and parts and the texts where Aristotle draws conclusions about the order of the universe and the natural motions of bodies. Although Aristotle did not discuss part/whole relations in a systematic way, his discussion of concrete wholes in Topics (VI, 13, 150a22–b36) forms the basis for the later dialectical topics from an integral whole and from an integral part: “The whole perishes when the parts do, but the parts do not necessarily perish when the whole has perished.” This assertion is the basis for the consequences, “If the whole is, then the part is; if the part is not, then the whole is not.” But the following are not valid: “If the whole is not, then the part is not; if the part is, then the whole is.”31 Aristotle adds that a whole compounded of parts in a particular way is not just a totality, sum, or collection of parts. In other words, a quantity (posón) is not what he understands by a composite whole (súnolon). Metaphysics (V, 15–16) clarifies this qualification by using the word “total” (hólon) to describe a quantity the parts of which can change
29
Additional texts from Plato: Phaedrus 265d-266b, Philebus 16c-17a, Sophist 260e261d. Burkhardt and Dufour, “Part/Whole,” 663–664; King, “Medieval Mereology,” 2. 30 Topics V, 5; VI, 11, 13–14; Physics I, 1, 4; II, 4; III, 5–6; IV, 5; De caelo I, 3; II, 14; Metaphysics I, 5; IV, 2, 5; V, 2–3, 23, 25–27; VII, 2; VIII, 1, 6; X, 1; XI, 10; XII, 8, 10; and XIII, 8; Parts of Animals 640b1–5; 646a25–30; Rhetoric II, 24.2.1401a23–b5; and Poetics, 6 and 12. In the analytical indexes of technical terms in his translations of Metaphysics and Physics, Richard Hope provides many more references to méros, mórion (pars, particula), hólon (totum), and súnolon (a composite or integral whole, sometimes also rendered totum in Latin and totum integrale). 31 Rhetoric II, 24, 1401a23–b5 supports these qualifications, but also points out examples of syllogisms that are not genuine, for example, from a whole action that is wrong concluding that each part is wrong.
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position without affecting the aggregate. A total, in turn, is distinguished from organic substances composed of homogeneous parts such as tissue, flesh, and bone, thus generating the distinctions (Parts of Animals II, 1, 646a1–647b9) among three sorts of substantial composition: elemental, uniform (bone, flesh, and tissue), and non-uniform (organs). Things in which the whole is not like a heap or lump have some uniting factor (Metaphysics VIII, 6, 1045a8–12). Such texts are connected to the teleological dimension in Aristotle’s biological thinking but they have echoes in his cosmological views of Earth and the celestial spheres as primary beings—the world is a cosmos, a definite something, all things ordered together around a common center (Metaphysics XI–XII). We commonly divide the Aristotelian cosmos into two spheres (celestial and terrestrial), but Aristotle allows for many ways in which the celestial influences the terrestrial. For example, the motions of higher bodies are transmitted to lower bodies even down to the rotation of the upper terrestrial atmosphere, the Sun warms Earth, and many continued to believe in the astrological influences of the qualities and motions of celestial bodies. In Metaphysics IV, 5, 1010a28–32 Aristotle criticizes his predecessors for having attributed to the whole that which is true only of the part: We should add another criticism against those who hold these views: they have been reporting what they observe in only a few sensible things as if it were true of the whole cosmos. For it is only the region of what is sensible round about ourselves that is continually in process of destruction and generation; but this is, so to speak, not even a small part of the whole, so that it would have been more just to acquit this small bit because of the whole than to condemn the whole because of this small bit.32
Aristotle himself concluded that the heavens were made of an element different from the elements in the sublunar realm. For him, each simple body or element has only one natural motion, and the whole of an element, if united, and the part move naturally in the same direction, as, for example, the whole Earth together and a small clod (De caelo I, 3, 269b30–270a13). De caelo II, 14, 296b27–297a7 summarizes the argument succinctly:
32
Hope translation, 79–80.
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chapter eight If it is inherent in the nature of earth to move from all sides to the centre (as observation shows), and of fire to move away from the centre towards the extremity, it is impossible for any portion of earth to move from the centre except under constraint; for one body has one motion and a simple body a simple motion, not two opposite motions, and motion from the centre is the opposite of motion towards it. If then any particular portion is incapable of moving from the centre, it is clear that the earth itself as a whole is still more incapable, since it is natural for the whole to be in the place towards which the part has a natural motion.33
It should be noted, however, that constructive arguments from part to whole depend on the conception of a natural whole thing. By concluding that the heavens are made of a different fifth element, the aether, with a distinctive natural motion in circles around the center of the cosmos, Aristotle cut off arguments that the celestial motion follows the same patterns as terrestrial motion. Although they departed from Aristotle on their notions of the relation between God and the created world, Neoplatonic and medieval authors devoted much attention to part/whole relations.34 Their motives varied, but a number of puzzles caught their attention. For Neoplatonists like Proclus, the whole is hierarchically related to the parts, an idea that could be easily adapted to Aristotle’s arrangement of the spheres down to the center of Earth. Boethius, sympathetic to such schemes, summarized and interpreted Aristotle’s doctrines on topics and division. As we indicated above, he devised in particular the formulas that would be repeated down to the Copernican era. With regard to whole/part topics, Boethius organized the topics into rules for the discovery of arguments. He adopted Cicero’s division of topics, two of which are from the whole and from the enumeration of the parts. In discussing parts, Boethius distinguished between two ways: parts taken as species or as members. By “members” Boethius meant “real parts.” He discussed inferences from whole to parts and from parts to whole, often referring to examples of integral whole and integral parts.35 The scholastics adopted this category of topic, introducing a number of distinctions by way of ever more sophisticated examples. From the existence and non-existence of whole and parts, they devel33
Guthrie, tr. Aristotle on the Heavens, 245–247. King, “Medieval Mereology,” 2–3; Charles-Saget, L’Architecture. I owe the latter reference to Dilwyn Knox. 35 Stump, tr. De topicis differentiis, 37, 51–52, and 65; Boethius, De divisione liber, ed. and tr. Magee, 38–41. 34
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oped rules for valid and invalid constructive and destructive inferences respectively. Already implicit in Aristotle, who, however, had applications to organic substances pre-eminently in mind, the consequences that we owe to Cicero and Boethius are the ones found later in Peter of Spain with the typical example of the house:36 (1) (2) (3) (4)
If the house exists, then the parts (roof, walls, foundation) exist. If the house is not, then the parts are not. If the parts are, then the house is. If the part is not, then the house is not.
Everyone agreed that (1) and (4) are valid, although some authors added qualifications. For example, Abelard regarded an integral whole as identical with a unique set of parts including the arrangement that individual parts have. (2) is then qualified to read: (2´) If the house is not, then the parts-of-this-house are not (which in this form is valid). Although (3) remains invalid, in the following sense it is valid: (3´) If the parts-of-this-house are, then the house is potentially. Later scholastics emphasized integral wholes that are actually composed out of their parts, implicitly recognizing that not all parts of a whole (totum) are plausibly parts of an integral whole (totum integrale), otherwise a monster results. For example, cobbling together hands, feet, and a head does not make up a human being.37 The claim about unique arrangement of parts can generate other puzzles noted by medieval philosophers. If I repair a house by replacing some parts, is it still the same house? Some changes (renovation) may indeed produce a new, different house. Such considerations led medieval philosophers to a variety of solutions. Some distinguished between principal (or vital) parts and less principal (non-vital) parts, one consequence of which is that the destructive application from the integral part (If the part is not, then the house is not) holds only for principal parts. For things that change, move, grow, or diminish, the distinction provides a way of preserving identity over time and for distinguishing between principal and less principal parts.38 36
Peter of Spain, Tractatus, V, 64. King, “Medieval Mereology,” 16–18. 38 King, “Medieval Mereology,” 24; Henry, Medieval Mereology, 54–57, 82–84, 334–336; Simon, Parts, 198–204. 37
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Answers to questions about the composition of homogeneous and heterogeneous substances, and about continuous, contiguous, and discrete things often depended on how authors interpreted Aristotle. Aristotle thought the cosmos qua unified thing “has” a nature in the sense that the parts are ordered according to the substantial or qualitative forms that they possess as inferred from their observed motions and behaviors. Where Aristotle observed contrary simple motions (up and down), he concluded that the contrary motions must be due (aside from their generating cause) to contrary qualitative forms that account for a natural directionality in the things possessing those qualities. The observed circular motions of celestial bodies must be due to a form that has no contrary thus revealing a different substance the nature of which is to move in circles. Aristotle’s metaphysical analysis also led him to the existence of immaterial intelligences that are the cause of eternal circular motion. The contiguity of the celestial spheres is revealed in the way that the circular motions influence the motions of lower spheres down to comets in the upper atmosphere and even to the circular motion of the Earth’s atmosphere.39 To situate Copernicus’s dialectical strategies in this context, I focus now on simpler kinds of dilemmas. For example, the topics from an integral whole and from an integral part seem to imply that if, for example, Socrates loses a hand, then Socrates does not exist. One strategy for dealing with this apparently absurd consequent is to define an integral part as the kind of part that cannot be removed without destroying the whole. As we saw above, authors who applied this strategy made distinctions between vital parts (applicable only to organisms) and less vital parts, or between principal as opposed to less principal parts. Or, to put it negatively, a non-integral part is one that we can remove and still have the same individual. This criterion does not remove all ambiguity. We could attempt to find some nonarbitrary criterion, but we would obscure an important lesson from these examples. The answer that we would give to such a question reveals our view of what it is to be an individual and of what constitutes the identity of an individual. Copernicus’s mereological vision of the universe refers to an intuition about the universe as a composite or integral whole. By analyzing the intuition held by him and his followers, we can reveal features of
39
De caelo I, 2; Metaphysics XII, 7–9.
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their heliocentrism that otherwise remain obscure. We will also discover why they believed that their conclusions were more probable and likely than those of geocentrists. Finally, we will also appreciate (in the conclusion and epilog) why Michael Mästlin and Johannes Kepler found Copernicus’s answers persuasive, even compelling. 4. Logic in the Commentariolus In Commentariolus Copernicus proceeds in the following way: He follows a brief recitation of the principles of ancient astronomy and the failures of his predecessors with the postulates that, he claims, preserve the principles, and solve the problems that his predecessors were unable to solve. The first result that he announces is the order of the celestial spheres and of the planetary spheres according to sidereal periods. He then proceeds to treat the motions of the planets, providing a largely qualitative account that relies for the most part on the ratios of spheres and circles to convey the image of the harmonious cosmic ballet that results from the adoption of his postulates. I proposed in chapter seven that he arrived at the postulates initially by means of a dialectical exercise, identified conclusions, formulated the postulates that he needed to derive the conclusions, and then reorganized them. Copernicus asserts as his first postulate or claim that there is no one center of all motions. He no doubt regarded this claim as a premise for the conclusion that Earth is not the center around which all bodies revolve. The true Sun in his system is also not the unique center of all heavenly motions. There are several centers, and even for the motions of the planets’ epicycles it is the center of Earth’s orbit, not the true Sun, that is the center of their motions. The Moon accompanies Earth in its annual motion around the Sun, but the center of the Moon’s motion is Earth, not the Sun, and the center of the Earth’s motion is not the true Sun but the mean Sun. What Copernicus asserted as his first postulate seemed obvious to him indeed, not because of his heliocentrism but as the result of a review of Ptolemaic geocentrism. In that system all bodies circulate around Earth, but with exception of the Sun, they do so in epicycles, and in every model there are eccentrics and equants that serve as centers of circles. Copernicus concluded that it is obvious that there is no one center of all heavenly motions, hence he tried to persuade his readers to begin with that obvious fact and proceed to other claims or likely hypotheses.
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chapter eight 5. The Use of Topics in the Preface of De revolutionibus
This summary begins with the structure of the dedication to the Pope, and then suggests and makes reference to the standard dialectical topics that Copernicus seems to have used. The analysis used here is typically represented by the following scheme:40
W
G
according to these rules or principles
C support
The grounds
the claim.
As the scheme indicates, evidence is linked to a claim or conclusion by way of rules. The rules include standard and common logical relationships that one finds in Aristotle’s Topics or in the handbooks described above. Additional rules are supplied by the standard discussions in a discipline, that is, by what experts in the field regard as warrants in that field. In the analysis that follows, I will characterize the parts of the argument G (grounds), W (warrants), and C (claim) according to the above scheme. The scheme does have weaknesses. For
40 Note Spruyt’s formulation of the general idea, “Peter of Spain,” 3. The scheme and variations on it can be found in Toulmin, Uses, 99; and Toulmin, Rieke, and Janik, Introduction to Reasoning, 49. Some experts criticized Toulmin’s books severely, and objected that Toulmin’s scheme merely reintroduced Aristotelian syllogistic with premises in a way that is deficient from a formal perspective. See, for example, Booth, Colomb, and Williams, Craft, 90. I have not included the “qualifications” that often need to be inserted between the grounds or evidence and the claim. In general, Copernicus’s qualifications come in the form of statements where he characterizes his conclusions as more probable than those of his predecessors. Note Booth’s comments and his reference to Toulmin, 268, especially to Freeman, Dialectics, and to van Eemeren, Grootendorst, and Kruiger, Handbook. Defenders have countered that Toulmin’s scheme is less artificial and less formal from a stylistic perspective. In Appendix VII, however, I have provided syllogistic versions of the most important of Copernicus’s arguments, most of which have the structure of enthymemes requiring us to supply the missing premises.
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example, it is sometimes difficult to distinguish between grounds and warrants. In some cases, warrants are premises that provide a middle term linking two extreme terms as in a categorical syllogism. The warrants that serve as rules or principles cannot always be found among the strictly dialectical topics but come from principles of a specific discipline such as astronomy or natural philosophy. Finally, Copernicus occasionally adapts warrants involving metaphysical criteria such as ontological superiority or dignity. In what follows below I will specify in the footnotes which of the above corresponds best with Copernicus’s warrants.41 Before I analyze its logic in detail, however, I consider three important studies of the Preface. Robert Westman’s most important articles offer innovative and illuminating revisions of the standard approaches.42 The dominant note is about Copernicus’s appeal to and participation in reform (humanist, ecclesiastical, calendrical, and astronomical). The persuasive strategies that Copernicus adopted and the HorationErasmian rhetoric uncovered by Westman fit the clerical-humanist audiences that he was addressing. Following on Westman’s groundbreaking work, Peter Barker and Bernard Goldstein proposed an alternative interpretation that focuses on the intended patron.43 They argue that Copernicus’s original intention was to dedicate De revolutionibus to Duke Albrecht of Prussia. The argument rests largely on the role that Georg Ioachim Rheticus played in finally bringing the book out in print. I cannot repeat all of the details or evidence here, but the argument goes something like this. Although Rheticus addressed the Narratio prima to Johann Schöner of Nuremberg, the book concludes with a long encomium directed to the Duke of Prussia (Encomium Prussiae). As Barker and Goldstein see it, Rheticus and Copernicus’s friend, Tiedemann Giese, developed a strategy to secure the Duke’s support and remove Copernicus from a potentially damaging court case in Frombork. They conclude, then, that dedicating De revolutionibus to the Duke was part of the strategy. Why, then, did Copernicus dedicate it to Pope Paul III? According to Barker and Goldstein, Giese persuaded Copernicus to dedicate the work to the Pope without Rheticus’s knowledge. The
41
Critics of Toulmin’s scheme complained about all of these weaknesses. Westman, “Proof,” and idem, “La préface.” Compare with Westman, “Astronomer’s Role.” 43 Barker and Goldstein, “Patronage.” 42
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evidence supporting the reconstruction is partial for not all correspondence has survived. In my view, however, the story is implausible. They do not explain adequately the grounds that would authorize a dedication to the Pope. A dedication was not just the decision of the writer but a kind of negotiation. In other words, the writer required an intermediary through whom he could approach the Pope, and thus know that the dedication of the book would be welcome.44 Second, their account implies that Giese and Copernicus were duplicitous in their treatment of Rheticus. Now, there is some evidence that the failure to mention Rheticus’s role in the publication of the book had troubled Rheticus, yet Rheticus seems to have accepted Giese’s excuse that Copernicus was old and infirm when he wrote the dedication. There is no indication that he was surprised that it had been dedicated to the Pope.45 It also seems consistent with the facts in their account to suppose that Rheticus and Giese developed a strategy that from the start entailed the dedication of the Narratio to the Duke and of De revolutionibus to the Pope, precisely to cover both Protestant and Catholic interests. In the most recent important discussion of the Preface, Miguel Granada and Dario Tessicini raise similar objections to the account by Barker and Goldstein, and devote a good deal more attention to addressing the question of the intermediary between Copernicus and the Pope.46 One detail that they emphasize also ties their explanation to Girolamo Fracastoro’s homocentric models as an alternative to Ptolemaic astronomy. Contrary to his comments in Commentariolus where he dismisses concentric alternatives, Copernicus refers explicitly to
44 They argue, 358, that because Copernicus had become a client of Duke Albrecht, an approach to the Pope would be credible. What connection did the Duke have with the Pope? 45 Burmeister, Rhetikus, I, 57–62, and III, 55–59 (Giese’s letter of 26 July 1543) emphasizes the fact that Rheticus remained until his death Copernicus’s true disciple. Rheticus’s letter to Giese that prompted the response is not extant, but Giese was presumably responding to a remark by Rheticus, yet there is no indication in it that the dedication to the Pope surprised Rheticus. Burmeister also points out that in the Narratio, Rheticus refers to Copernicus consistently as “my teacher,” never by name. Burmeister suggests that later authors have invented a problem or exaggerated it, for there is not the slightest indication that Rheticus was inconsolable about the matter. Rosen, “Biography,” 400–402, implies that Rheticus knew about the dedication to the Pope, and says that it was Rheticus who omitted the Introduction. That suggests that Rheticus knew enough about the Preface to realize that the Introduction was no longer appropriate. 46 Granada and Tessicini, “Copernicus and Fracastoro,” esp. 437–447.
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homocentric attempts in the Preface.47 In the absence of an exhaustive examination of the texts from 1490 to 1540, it is difficult to evaluate the significance of the terms concentric and homocentric. If Granada and Tessicini are right, then they have pointed out an important difference between Commentariolus and De revolutionibus that suggests that part of the motive for the Preface involved eliminating a rival. In my opinion, it is far from clear that Copernicus ever took concentric or homocentric alternatives as a serious rival. He seems to have dismissed them out of hand in both texts as theories that cannot be made to fit the phenomena.48 They have, however, strengthened Westman’s case for the dedication to the Pope. All of that said, I must conclude that it is premature to draw any confident conclusions about the more speculative reconstructions. Westman’s argument, by contrast, is more secure. What emerges from it is a picture of Copernicus interested in reform of the calendar, concerned about objections to his theory based on Sacred Scripture, and motivated to frame his decision to publish such an unconventional cosmological proposal so as to address a clerical audience steeped in a humanist-artistic culture of reform. As Westman has shown in this and other contexts, Michael Mästlin’s later comments on De revolutionibus provide clues about Copernicus’s strategies. Although I had developed my arguments prior to noticing Mästlin’s observations, I introduce these comments here to emphasize the relation between rhetoric and dialectic. I will return to these themes explicitly in section six below and also in the conclusion of this work. Here I turn to the task of explaining the logical or dialectical features of Copernicus’s Preface. In the introductory section of the Preface to Pope Paul III, Copernicus’s rhetorical strategy is to anticipate rejection and acknowledge the outrageous nature of his proposals.49 This leads him, then, to explain
47 Westman, “Proof,” 179 and 198, n. 45, also noted “homocentrics” as a reference to Paduan Averroism. 48 Copernicus seems to have been unaware of Regiomontanus’s interest in concentric astronomy. See Shank, “Regiomontanus,” idem, “Regiomontanus and Ptolemy,” and Swerdlow, “Regiomontanus’s Concentric-Sphere Models.” 49 Westman, “Proof,” 167–205. Note Westman’s emphasis on poetics and its relation to Copernicus’s humanistic credentials. All of these devices support Copernicus’s claims as they relate to his character and the moral aim of achieving perfection. My relative neglect of these features of his arguments is due to the focus on strictly logical criteria.
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what led him to adopt the new ideas, beginning with the inadequacies of, first, narrowly homocentric astronomy and of, second, the Ptolemaic geostatic alternative. Aside from observational problems with the first (non-confirming results) and theoretical problems with the second (contradiction of first principles of uniform motion), the principal problem was that Ptolemaic hypotheses failed to elicit the “structure of the universe and the [commensurability] of its parts.” The principal criterion is that the method of Ptolemaic astronomers is unsound, for they “omitted something essential” or they “admitted something extraneous or wholly irrelevant.”50 To resort to the scheme sketched at the beginning of this section, the hypotheses (G) should yield by virtue of an essential relation or be relevant to (W) the structure of the universe and the commensurability of its parts (C).51 The warrants of essential relation and relevance suggest that Copernicus may have relied on the following standard, common topics to support the argument: W1: from an integral whole, which supports the inference from a composition of parts having quantity to the existence of the part in a quantitative relation to the whole, as Copernicus exemplifies by comparing a portrait in which the parts are taken from different individuals resulting in a monster with a portrait of a single individual; W2: from the description, inasmuch as the reference to an essential relation suggests that he is referring to essential properties.52
50 Copernicus, De revolutionibus, Gesamtausgabe 2: 4. The translation is, with one emendation, from Revolutions, tr. Rosen, Complete Works 2: 4. I will cite the translation, as in this case, by page number. The Latin expression used by Copernicus: “aliquid necessariorum, vel alienum quid, et ad rem minime pertinens, admisisse inveniuntur.” 51 This argument and all those following can be recast as a hypothetical syllogism. See Appendix VII, Example 1. The model for this version of the argument is in Slomkowski, Aristotle’s Topics, 53. Although Slomkowski’s is a controversial interpretation, the examples suggest how the arguments can be rendered syllogistically. 52 These correspond to the topics in the Summulae (as numbered in Appendix I) to I, B, 6 and I, A, 2 respectively; and in the Dialectica to I, B, 4 and I, A, 2 respectively. We noted in Chapter 3 that Peter of Spain simplified the logic of part/whole relations. Copernicus follows such a simplified version, and was evidently unaware of technical difficulties. Copernicus’s use of mereological (part/whole) topics requires a separate and detailed analysis. His intuitive view suggests a solution of a more precise question. I will indicate some consequences below, but see Goddu, “Copernicus’s Mereo-
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Although less likely and appropriate in my view, the topics from definition, from universal whole or genus, or from the formal cause may also have played a role here, but the above warrants seem to fit the best.53 The argument presented by Copernicus clearly possessed aesthetic and rhetorical appeal as well, and which he proceeds to exploit even more effectively in the next section of the Preface. Copernicus returns the reader’s attention to his state of mind by describing the frustration that he felt over the centuries-long failure to discover the true arrangement of the parts created by the “best and most systematic Artisan of all.” Copernicus relies here above all on the topic from efficient cause and its maxim: “that is good whose efficient cause is good as well.”54 He immediately uses this equally theological warrant as the explanation why he reread the sources to see if anyone had proposed any other motions of the spheres. The extrinsic topic from authority justifies the serious consideration of a heliocentric alternative, for some respectable ancient authors did so.55 Hence, Copernicus implies, he might not be insane after all, and when one considers the motion of the Earth seriously, otherwise incidental observations follow necessarily and naturally from the hypothesis. The structure of the argument is as follows: From the assumption that God is a systematic artist (G), we may conclude by virtue of the topic from efficient cause (W), that God arranged the parts of the world machine in a definite and unique order (C).56 Because God created the system for our sakes (G), we may suggest by virtue of the topic from efficient cause as well (W), that we are capable of discovering the definite and unique order in which God arranged the parts (C). Because God created us with a desire to know (G), we are permitted by virtue of the topic from authority (W), to consider alternatives proposed by the ancients (C). Because some ancient authors were free to imagine
logical Vision,” for the complete analysis. The Conclusion and Epilog summarize the results. 53 Compare Summulae, topics I, A, 1; I, B, 4; and I, B, 14; Dialectica, topics I, A, 1; I, B, 4; and I, B, 6. 54 Revolutions, 4. Cf. Summulae, topic I, B, 12; Dialectica, topic I, B, 7. 55 Cf. Summulae, topic II, b, 29; Dialectica, topic II, 12. 56 See Appendix VII, Example 2. There were several sources from which Copernicus might have adopted the expression machina mundi. In chapter seven, we noted Bessarion’s use of the expression. Baroncini, “Note,” 12–18, cites over a dozen relevant passages, including one from Lactantius, Divinae institutiones 2, 5, 7–37, a passage where Lactantius also refers to God as artifex mundi. Rosen, Commentary, 359, to 22:7, also refers to Lactantius for Copernicus’s expression visibilem Deum.
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any circles whatever (G), Copernicus contends by virtue of the topic from authority and, he implies, out of fairness (W), that he too should be permitted “to ascertain whether explanations sounder than those of [his] predecessors could be found for the revolution of the celestial spheres on the assumption of some motion of the earth” (C).57 By attributing certain motions to the Earth (G), by intense study, correlation of the motions of the other planets with the orbiting of Earth, and by computation (W), Copernicus finds that the otherwise incidental observations follow necessarily and naturally (C). The final argument of a substantive nature is this: Because “the order and size of all the planets and spheres, and heaven itself is so linked together” (G), by virtue of the topic from an integral whole (W), it follows “that in no portion of it can anything be shifted without disrupting the remaining parts and the universe as a whole” (C).58 After this argument in the Preface, Copernicus describes the order of De revolutionibus, in which he seems to be telling the reader that he adopted the topic from the whole, more specifically from an integral whole, as a model for the book:59 Accordingly in the arrangement of the volume too I have adopted the following order. In the first book I set forth the entire distribution of the spheres together with the motion which I attribute to the earth, so that this book contains, as it were, the general structure of the universe. Then in the remaining books I correlate the motions of the other planets and of all the spheres with the movement of the earth so that it may thereby determine to what extent the motions and appearances of the other planets and spheres can be saved if they are correlated with the earth’s motions.
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Revolutions, 5. Revolutions, 5. See Appendix VII, Example 3. 59 Revolutions, 5. On the importance of this topic at Cracow, see Chapter 3. Copernicus’s use of the topic from an integral whole is constructively valid and destructively invalid. His evaluation of from an integral part is constructively invalid and destructively valid. On the other hand, he does speculate that gravity is a tendency implanted in all bodies in the universe, a constructive application of part to whole. This is strong evidence for concluding that the whole, as Copernicus understands the cosmos, is a heterogeneous, not a homogeneous, whole. Furthermore, his conception of cosmos indicates that he regarded it as an integral and essential quantitative whole. As an artifact of the divine Artisan, the cosmos possesses as its foundation a design and an idea of construction. For details and precedents, see Burkhardt and Dufour, “Part/Whole I,” 663–673, esp. 669–671. 58
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He hopes that astronomers will examine his derivations, and he seems optimistic that if they do so, they will agree with him. He concludes the Preface with remarks suggesting why he dedicated the book to the Pope. It seems that Copernicus anticipated Scriptural objections, and was trying to fend off theological objections and perhaps even censure. He dismisses objections based on Scripture bluntly as incompetent, but he softens the blow by also suggesting that his work may contribute to reform of the ecclesiastical calendar. Copernicus was apparently aware that in the past some medieval authors had considered the motion of the Earth, but in the absence of observational proof and in the face of Aristotelian natural philosophy, they had allowed Scripture to settle the matter.60 In other words, passages in Scripture were admitted as legitimate warrants supporting the conclusion that the Earth is stationary at or near the center of the universe. In the conclusion of the Preface, Copernicus challenges the legitimacy of using passages from Scripture as warrants for conclusions in astronomy and natural philosophy. Passages from the Bible are irrelevant. To propose a major change in a discipline requires an author to use the warrants accepted by contemporary experts, but it is virtually impossible to propose such a change without also challenging the legitimacy or relevance of some warrants. Throughout the Introduction to Book I (analyzed in detail below), Copernicus uses some warrants in an uncontroversial way, but he also reinterprets others or applies them in an original way, and there are yet others that he replaces or dismisses altogether. He uses rhetoric to frame the argument, which itself relies on dialectical topics, the warrants acceptable in natural philosophy and astronomy, and the geometrical means available to mathematicians allowing them to show that the observations or results are consistent with the hypotheses. The discursive strategy adopted by Copernicus is to frame dialectical arguments in a rhetorically persuasive humanistic style. By means of rhetoric Copernicus provides the structure and motives for the arguments. In the arguments Copernicus arranges the objections, evidence, and warrants supporting the conclusion, in the first half of the
60 Nicole Oresme is the best-known example, but direct acquaintance with Oresme’s works, especially one written in French (Livre du ciel et du monde), is difficult to prove. On the other hand, Copernicus may have heard of Luther’s reaction to his proposal even before the work appeared. On Luther’s remarks, see Norlind, “Copernicus and Luther,” 273–276.
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Preface, that the Ptolemaic theory has failed to elicit the structure of the universe and the commensurability of its parts. That conclusion, in turn, leads to the more satisfying solution provided by the heliocentric view, according to which the observations follow naturally and necessarily from the observations with the parts arranged commensurately in the structure of the whole. Copernicus achieves this conclusion by the blending of rhetorical persuasion, poetic image, aesthetic pleasure, theological ethos, mathematical consistency, and the use of dialectical topics. Some have suggested that the aesthetic dimension of Copernicus’s arguments excludes epistemic claims.61 But this is a mistake. The aesthetic dimension involves structure and coherence, both of which provide Copernicus some justification for believing in the truth of his principal hypotheses. Furthermore, the claim that some observations follow naturally (not in an ad hoc manner) is an epistemic claim.62 The further study and understanding of Copernicus’s discourse requires attention to all of these techniques and strategies. 6. The Rhetorical Framework of Book I In the 1543 edition of De revolutionibus, Copernicus or Rheticus suppressed the Introduction that is found in the holograph. After Copernicus wrote the Preface in 1542, he and Rheticus may have felt that the Introduction was redundant, and perhaps also realized that its tone was not entirely consistent with that of the Preface. The aesthetic and moral appeals of the Introduction follow Ptolemy in part and seem almost pagan by comparison, whereas the Preface is clearly addressed to a clerical-humanist audience. Despite its suppression, I examine it here because it does reveal important motives at an earlier stage of composition.
61 Kokowski, Copernicus’s Originality, 8, tries to force an either-or choice between aesthetic criteria and epistemic criteria in support of his claim that Copernicus’s criteria were exclusively epistemic. 62 McMullin, “Rationality,” 55–78, esp. 70–75, where McMullin argues that “naturalness,” that is, coherence is epistemic, not aesthetic. In explaining his statement, however, he says that coherence is not just a matter of taste, suggesting that it is partly aesthetic but primarily epistemic, for the claim is that “a theory that makes causal sense of a whole series of features of the planetary motions is more likely to be true than one that leaves these features unexplained.” Compare with Kokowski, who cites McMullin to deny that coherence is aesthetic at all.
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Copernicus begins the Introduction by reminding the reader of the motives for studying astronomy—it is an appeal to the entire tradition of classical learning and its appreciation for mathematics and astronomy in the formation of the liberally educated individual. Copernicus portrays himself as part of this tradition, and he affirms his desire to continue this tradition, putting himself at the service of its noble tasks, which includes bringing astronomy closer to perfection and completion, not overturning and destroying it.63 As is well known and as we have tried to elucidate by focusing on the dialectical strategies adopted by Copernicus, he placed great emphasis on such criteria as harmony, symmetry, and commensurability. These criteria have been interpreted primarily as aesthetic in nature, and thus as appealing primarily to the emotions in a rhetorical fashion. As a result, Copernicus’s arguments tend to be dismissed as not strictly rational. The aesthetic role of ideals of harmony in astronomy has been a commonplace theme, but one of those commonplaces that we somehow have not adequately fathomed. The relation between ideas of harmony and science seems mysterious and even mystical, and so the connection has remained elusive, unpersuasive, and unsatisfying, at least from a modern scientific and secular point of view. By coming to grips explicitly with the rhetorical purpose of Copernicus’s turn to traditional ideals and his exploitation of aesthetic design, we can elucidate the role that dialectical argumentation plays in Book I. He used dialectic to persuade astronomers and philosophers that his proposals will achieve the goals set by Ptolemaic astronomers that their methods have failed to achieve. We mean many things when we refer to “aesthetics.” In using the term, we are usually referring to something that we regard as possessing beauty, elegance, and simplicity. We are also often thinking of the mental pleasure that comes from solving problems in an elegant way. By extension we may mean the realization, wonder, and recognition at having found some new understanding of what we always knew but had never quite appreciated completely, that is, the sense of having plumbed the depths of some vast mystery. At the same time, Copernicus claimed to have solved an age-old problem in a way that achieved its goal. We may also reflect on the peace of mind that may accompany the completion or perfection of a work, as if somehow
63
Compare with Moss, 49–51.
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a restless energy has found its fulfillment. It is, I think, fair to say that Copernicus was motivated to construct an astronomical system that was well composed and well organized, that mirrored the perfect, complete, and unified whole that is the universe, as a product fitting of a divine artisan.64 It is striking, by contrast, to read the opening paragraphs of the Introduction. While appealing to the liberal tradition of learning and reminding us of its goals, Copernicus seems anxious to allay the fears that his proposals would, he knew, engender. His solution was frightening to some. In an age of violent reform, even Luther of all people complained that Copernicus was just another innovator who would turn the whole art of astronomy upside down.65 To such, Copernicus’s ideas threatened destruction and fragmentation. His vision implied to many that the universe was possibly boundless and hence with no true center. In solving one major and long-standing problem, Copernicus was creating another that perhaps had no solution because the universe that emerged from his mind might be devoid of wholeness and meaning altogether. For Copernicus, then, it did not go without saying; rather, he had to affirm his continuity with the tradition, with the traditional vision of a finite universe that was a complete and unified whole, and above all with the fulfillment of traditional goals. Indeed, to judge by the recent standard accounts of the Copernican Revolution, Copernicus was entirely successful in his effort to persuade readers that his vision was traditional and conservative.66 By using such language, I do not mean to imply that Copernicus was insincere. His affirmation of traditional beliefs seems genuine. Still, the structure of his text reveals the following pattern: proclamation of traditional goals followed by enumeration of the shortcomings of Ptolemaic astronomy. The contrast could hardly be clearer. Throughout Book I, the pattern is agreement 64 As Danielson, First Copernican, 74–76, emphasizes, there is a similar tone in Rheticus’s Narratio linking the metaphor of harmony, poetic metaphors, and musical analogy to scientific models. 65 On Luther’s reaction, see Norlind. One can get a picture of the anxiety provoked by Copernicus’s proposal in the sixteenth and seventeenth centuries in Crowe, Theories, 174–188. 66 See, for example, Swerdlow and Neugebauer, Mathematical Astronomy, 1: 54–64 and 70–85. Of course, Swerdlow’s judgment reflects his understanding of the technical mathematics in Copernicus and his predecessors; still, such focus tends to minimize the broader cosmological impact of Copernicus’s hypotheses.
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with what is right in Ptolemy, compared with what has failed and does not fit. When he proposes his own solution, the contrast, then, is with what succeeds and does fit. The suggestions that follow are neither exhaustive nor exclusive of other explanations. They expose the logic of Copernicus’s arguments without excluding other readings and possible sources. They confirm that Copernicus was attentive to the logical strategies that could move a reader to assent. What we may observe is that many of the dialectical topics summarized above have counterparts among the rhetorical topics. This observation suggests that the differences between some dialectical and rhetorical topics depend on their purpose and function. Aristotle saw rhetoric as the counterpart of dialectic—rhetoric aims specifically at persuasion while dialectic provides the strictly logical arguments.67 Throughout the Rhetorica Aristotle refers the reader to the Topica.68 Later in Book I, Aristotle says of rhetoric that it is an offshoot of both dialectic and ethical studies.69 The context here suggests that because its aim is persuasion, the purpose of rhetoric is not only speculative but also practical. The division of rhetoric into political, forensic, and ceremonial seems advisory more than scientific, that is to say, someone writing a political speech, for instance, would do well to follow Aristotle’s advice. In analyzing a text, however, we may not find the same distinctions very helpful or illuminating. In whatever way we use the Rhetorica, we may observe that the lengthy enumeration of
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Aristotle, Rhetorica I, 1, 1354a1–15. For modern interpretations of Aristotle on the relation between dialectic and rhetoric and on enthymemes, see van Eemeren and Houtlosser, Dialectic and Rhetoric, 3–11. Note the editors’ comment related to Aristotle’s adoption of the term enthymeme to refer to rhetorical proof, 10. I paraphrase their very complicated formulation. Authors take a perspective that is primarily dialectical when they advance arguments in order to resolve a difference of opinion, and adopt a procedure to test the acceptability of the opinion at the core of the difference in terms of its tenability in the light of critical reactions. Authors take a perspective that is primarily rhetorical when they view the argument as aimed at achieving agreement by having the audience agree on the acceptability of the opinion. “In this way in the former case the resolution of the difference of opinion is firstly associated with the dialectical aim of valuing opinions and in the latter case with the rhetorical aim of creating consensus.” It is clear that Copernicus tried to achieve both aims. 68 There are at least ten explicit references to the Topica in the three books of the Rhetorica. 69 Rhetorica I, 2, 1356a20–30.
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twenty-eight topics in Book II is very reminiscent of several topics in the Topica, and so confirms the close relationship between the two.70 Although Renaissance authors like Valla and Agricola reacted against scholastic academic structures, in some respects they seem more faithful to the spirit of Aristotle’s reflections on rhetoric and dialectic. Their blending of the two suggests that they adopted a point of view similar to Aristotle’s, whether they saw themselves as Aristotelian or not. Later readers like Caesarius and Melanchthon, just to mention two prominent examples, found Agricola’s ideas on dialectic and rhetoric consistent with Aristotelian logic. In a similar way, Copernicus saw himself as an interlocutor in ancient traditions, Ptolemaic and Aristotelian. As he adopted their goals and methods, he simultaneously adapted them to new ends thus transforming the traditions to which he was contributing. 7. The Use of Topics in Book I As we proceed, then, to analyze Book I of De revolutionibus, we will suggest the topics that seem to link grounds and conclusions and the arguments themselves together, keeping in mind that they may serve a rhetorical function or a dialectical function or both. For the Introduction, I use the same scheme as I did for the Preface—ground (G), warrant (W), and claim (C). The ground and claim are taken from Copernicus’s text. Where the warrant is also in the text, it is in parentheses (W), but where I supply what appears to be the warrant linking the ground to the claim, it is in square brackets [W]. Because heaven is the most beautiful natural thing (G), by virtue of its position close to God and its nearly divine disposition [W], it is the most deserving to be known (C). Almost all of the other branches of mathematics support it (G), by virtue of the relation of function or purpose [W] astronomy represents the consummation of mathematics, the summit of the liberal arts, and the most worthy of a free man (C). Because all of the good arts serve to draw man’s mind away from vice and lead it to better things (G), by virtue of its higher position [W], astronomy can perform this function best (C). Because contemplation of the best stimulates one to do the best and to admire the
70
Rhetorica II, 23, 1397a7–1401a1.
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Maker of everything (G), by virtue of efficient cause [W], we achieve extraordinary intellectual pleasure and are made glad (C). Because mathematics and astronomy confer great benefit and adornment on the commonwealth (G), we may appeal to authority [W], where Plato commends it to keep the state alert and attentive to festivals and sacrifice, as necessary for the teacher of higher learning, and to become and be called godlike (C). Principles and assumptions (hypotheses) have been a source of disagreements, many observations do not agree with Ptolemy’s predictions, and the aids assisting our enterprise have grown with time (G). We may thus conclude from the progress that has been made [W], that we may still through our efforts bring astronomy to perfection (C). The warrants in the Introduction seem to be rhetorical for the most part. As we noted above, the assertions here are intended to assure readers of Copernicus’s conservatism. Copernicus draws on his reader’s belief in God, on recognition of the importance of mathematics for training the mind, on the traditional aim of perfecting the science over time, and on the relation of this activity to the achievement of self-perfection. He intends all of these appeals to make the reader sympathetic to his efforts. There is a hint of the idea that bringing astronomy to perfection may require a radical move, but for the most part the Introduction is reassuring, not threatening. Having established a reassuring mood, Copernicus maintains that mood for the next four chapters. He does so by following the structure of Ptolemy’s own introduction, drawing on the ideas in Ptolemy that Copernicus supports, again providing at best only a hint of how he will bend these to his own purpose. In concluding in Chapter 1 that the universe is spherical (C), Copernicus appeals, it seems, to common wisdom [W], in citing a variety of metaphysical, physical, and mathematical grounds. A sphere is the most perfect form and a complete whole, a sphere is the most capacious or efficient of geometrical solids, all have observed the universe to be of this shape, and wholes strive, as it were, to be circumscribed in a sphere (G). Chapters 2 and 3 confirm the conclusion that Earth is a sphere (C). The conclusion is based empirically [W] on well-known observations (G), for example, standard astronomical observations, observations of Earth’s curvature made on ships or of approaching ships as seen from a coast, the fact that water flows downward and forms a single sphere with Earth.
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There is a note of progress in Chapter 3 with respect to new geographical knowledge, but it is expressed so subtly as to be more re-assuring than alarming. Spanish and Portuguese explorers have corrected and added to Ptolemy’s Geography, which Copernicus uses immediately to support his conclusions: that land and water together press upon a single center of gravity; that the earth has no other center of magnitude; that, since earth is heavier, its gaps are filled with water; and that consequently there is little water in comparison with land, even though more water perhaps appears on the surface.71
It is, however, tempting for us to see in this correction of Ptolemy an additional (though suppressed) argument: If Ptolemy was wrong about the geography of Earth (an object close enough to us to test claims about it), then why could not Ptolemy be wrong about astronomy? Just as new explorations have added to and corrected Ptolemy’s understanding of geography, so, we may see Copernicus implying, can we add to and correct Ptolemy’s astronomy. After he draws his conclusions about Earth and water, Copernicus concludes Chapter 3 by listing and correcting all of the errors made by the most prominent ancients about the shape of Earth. Chapter 4 affirms Copernicus’s commitment to circular motion (C) as the motion most appropriate or proper to (W) a sphere and its form (G). There are several variables, such as direction, size, etc., with each sphere possessing a circular motion proper to its shape. In some cases, we must imagine circular motions compounded of several circles (C), because their “nonuniformities recur regularly according to a constant law” (G), which would not happen unless their motions were circular, “since only the circle can bring back the past” (W).72 Copernicus hints at some discomfort here, for he takes it as established that “a single heavenly body cannot be moved by a sphere nonuniformly,” and supports the commonly accepted view with a counterfactual argument. If there were such non-uniformity in the motion of a sphere, “it would have to be caused either by an inconstancy . . . in the moving force or by an alteration in the revolving body.”73 71
Copernicus, Revolutions, 10. Copernicus, Revolutions, 11. See Appendix VII, Example 4, for the general form of the argument. In this case the warrant appears to be a premise that links two extreme terms by means of a middle term. 73 Copernicus, Revolutions, 11. 72
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From these considerations (G), it follows from geometrical principles [W] that their uniform motions appear non-uniform to us (C). There can be by virtue of geometrical principles [W] two causes of this result (C), the circles of the heavenly bodies may have poles different from Earth’s or Earth is not at the center of the circles about which they revolve (G). Observation (G) shows us by measurement [W] that the distances of objects from the observer vary (C). This variation (G), in turn, makes their motions appear unequal in equal times (C) as a result of geometrical principles [W]. We must, then, examine the relation of Earth to the heavens carefully (G); otherwise we may make the error of attributing to the heavens what belongs to Earth (C) by violating the rule that permits only a negative inference from part to whole [W]. That is to say, the error here would be to attribute to the whole what belongs only to one of its parts.74 Copernicus, we may see in retrospect, is easing the transition to the idea that Earth moves. The structure of these chapters corresponds roughly to the first three postulates from his earliest known work on this subject, the Commentariolus. The first four chapters of Book I show us how Copernicus’s argument improved since that first effort from around 1510. With Chapter 5, Copernicus makes his first proposals about the motion and position of Earth. Earth is a sphere (G), so we must ask whether its shape as a sphere entails (W) its motion in a circle (C), and what place it occupies in the universe (C´). The reason, Copernicus seems to imply, is that spheres, as we have seen [W], can occupy any place in the universe (C). Copernicus knows, of course, what the common-sense view is, but he urges his reader to be open-minded to seeing that the problem has not yet been solved. On the correct answers to the questions about the Earth’s motion and position depends the correct explanation of what is seen in the heavens. The next paragraph reminds the reader of the familiar principle of relativity and applies it to the observation of daily rotation. Already here, Copernicus suggests that Earth’s rotation on its axis (G) would account for the observation of daily rotation (C). He challenges the reader to consider why motion should not be attributed to the enclosed
74 These are complex examples that involve a topic proper to natural philosophy (relativity of motion) and the topic from the part. See Appendix VII, Examples 5a and 5b. These arguments are linked together with the argument in Example 6 below.
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rather than to the enclosing [W], to the thing located in space rather than to the framework of space [W]. He cites several ancient authorities [W] in support of the hypothesis.75 In the previous arguments, Copernicus raised doubts about whether the part moves or the whole moves. With this argument he now provides a reason why we should attribute motion to the part rather than to the whole. The next question concerns Earth’s position in the whole universe and in relation to the Sun and planets. As for the sphere of the fixed stars, its distance is so great (G) as to make Earth’s distance from the center (C) insignificant by comparison (W). Earth’s variable eccentricity in relation to the Sun and planets (C) has been demonstrated observationally and mathematically (G) by measurement and geometrical reasoning [W], so the only serious question is whether the explanation is that only the planets approach and withdraw or that Earth approaches to and withdraws from them. In other words, the suggestion following from the above observations (G) is that aside from daily rotation, Earth would move as a planet among the planets (C), as the authority of Philolaus (and Plato) confirms (W).76 This argument now challenges the reader to accept Earth’s orbital motion as an explanation for the variation of Earth’s eccentricity and distances in relation to the Sun and planets. But many believe it possible to prove by geometrical reasoning [W] that Earth is in the middle of the universe (C), serving as a center, relatively speaking, and is motionless (C' ) because when a body rotates, the center remains unmoved and things nearest to the center move most slowly (G). With Chapter 6, Copernicus begins his refutation of the commonsense view by attacking the warrants or principles used to confirm Earth’s centrality. Because the universe is so immense and the size of Earth is a point in relation to it (G), it is impossible to say whether Earth is the exact geometrical center of the universe. If we cannot prove that it is the center (G), then we cannot prove that it is at rest in the middle.
75 See Appendix VII, Example 6. The warrant in this example appears to be a topic proper to metaphysics, namely, ontological superiority or dignity. 76 This argument now challenges the reader to accept Earth’s orbital motion as an explanation for the variation of Earth’s eccentricity and distances in relation to the Sun and planets. See Appendix VII, Example 7. The entire series of arguments appears to rely on the topic from the whole, a warrant that is proper to natural philosophy (relativity of motion, and an application of the principle of economy).
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That an immensely vast universe should rotate in twenty-four hours is more astonishing (W) than a rotation of a small body like Earth. Because they were unable to provide observational and mathematical proof, the ancients resorted to physical arguments to prove that Earth is at the center. Copernicus summarizes these arguments in Chapter 7. The arguments are standard Aristotelian claims based on the absoluteness of Earth’s heaviness and on the association between heaviness and simple rectilinear motion. The “natural” motion of a heavy body is rectilinear and downwards towards the center of Earth. Any motion of a heavy body contrary to rectilinear or down (upwards, sideways, circular) is contrary to nature or “violent.” The rotation or circular motion of a heavy body like Earth, then, would be violent and contrary to nature. Chapter 8 refutes these arguments and shows them to be inadequate. Copernicus’s response is a masterpiece of dialectical reasoning. If Earth does in fact rotate (G), reasons Copernicus, then surely someone would regard its circular motion as natural (C). What is natural has natural effects, namely, they are well ordered and preserve Earth in its best state (W). What is violent would have violent effects and eventually would cause disintegration. If Earth does rotate, and rotation is its natural motion, then Ptolemy need not have feared the consequences.77 The point here is that what is called “natural” depends on identifying or defining the nature of a thing correctly. If Earth in fact rotates, then rotation is natural to it. How Earth in fact behaves must be determined before we can conclude what its nature is and what is natural to it. Rather than worry about the motion of tiny Earth, Copernicus chides Ptolemy, why was he not more worried about the motion of the heavens? It must be very swift, so swift in fact that we would expect it to be driven by centrifugal action farther and farther to infinity and so would its speed, then, also have to increase to infinity. But, as we all know from Aristotelian physics, the infinite cannot be traversed or moved in any way (W), so it follows that the heavens must be stationary (C).
77 The warrant here appears to be the topic from the cause. See Appendix VII, Example 8.
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There are several other questions about whether the heavens and the universe are finite or infinite, which lead to more questions that are better left to natural philosophers to discuss. Copernicus seems to imply here that trying to answer empirical questions by reasoning alone does not settle the questions.78 We can perhaps settle questions about Earth. The principle of relativity shows us that the motion of Earth accounts for observations of the heavens. Can its motion account for other observations? The motions of clouds, air, or falling bodies would be affected by Earth’s axial rotation (G), but we can assume that objects close to Earth share in Earth’s motion and move with it (W). The motion of rising and falling bodies would be compounded of both circular and rectilinear motions (C). Rectilinear motion, far from being natural, is the motion that we attribute to bodies that have been thrust from their natural place: Therefore rectilinear motion occurs only to things that are not in proper condition and are not in complete accord with their nature, when they are separated from their whole and forsake its unity.79
Rectilinear motions are not simple, constant, and uniform, but change— accelerating or decelerating according to variable circumstances. Circular motions are uniform and eternal, but rectilinear motions vary and are limited, for when a body reaches its natural place, it is no longer heavy or light, and its motion stops. Circular motion belongs to wholes, rectilinear motion to parts, and they are relative to one another. Immobility is nobler and more divine than change and instability (G), and what has greater dignity should be the least moved (W), hence it makes more sense to attribute motion to Earth than to the universe (C). It is more absurd to attribute motion to the framework of space (G) or to what encloses the whole of space than to that which is enclosed and occupies some space (W), and so it makes more sense to attribute motion to Earth (C). Finally, the planets approach Earth and recede from it (G), which means that if Earth were the center, then the planets move at times
78 If this is what Copernicus meant to suggest here, it is an objection that could be raised against his own speculations. What is more, Copernicus dismisses or sets aside the physical questions as ones that perhaps can be settled only after the correct framework is adopted. 79 Copernicus, Revolutions, 17.
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away from and at other times towards the middle. Variations in distance argue against the Earth in the middle [W]. It makes more sense, then, to understand “motion around the middle” in a more general way, namely, as a motion that encircles its own center (C): You see, then, that all these arguments make it more likely that the earth moves than that it is at rest. This is especially true of the daily rotation, as particularly appropriate to the earth. This is enough, in my opinion, about the first part of the question.80
Because nothing prevents Earth from moving (G), we can consider in Chapter 9 whether it has other motions and can be regarded as one of the planets.81 Earth is not the center of all of the revolutions (G). The non-uniform motions and varying distances of the planets indicate this (W). There are many centers, a fact that leads us to ask whether the center of the universe is identical with the center of terrestrial gravity or with some other point (C). Gravity, in fact, seems to be a quality proper to all spheres (G), some tendency placed in them by God (W) that gathers the parts together into a unity and a whole in the form of a globe (C). The other observed motions are also relative. If Earth has an orbit around the Sun (G), then, according to the principle of relativity [W], the appearances of the daily rising and setting of the stars, Sun, Moon, and planets would be the same (C). The retrograde motions of the planets are not proper to them (C' ) but an effect of their proper motions (G) relative to Earth’s motion [W]. It will then be seen that the Sun occupies the middle of the universe (C" ). All these facts are disclosed to us by the principle governing the order in which the planets follow one another, and by the harmony of the entire universe, if only we look at the matter, as the saying goes, with both eyes.82
80 Copernicus, Revolutions, 17. See Appendix VII, Example 9. The warrant here is the fundamental hypothesis of ancient astronomy accepted by Copernicus. 81 In Narratio prima, Rosen tr. 148, Rheticus refers to Aristotle, De caelo II, 14: When one motion is assigned to Earth, it may properly have other motions. Aristotle was referring to the assumption of its orbital motion and its shared diurnal motion with the starry vault, and objects that its proper motion would then be along the ecliptic, not the equator. Despite the conclusion, Copernicus may have been leaning on Aristotle here in moving from consideration of one motion to other motions. 82 Copernicus, Revolutions, 18. See Appendix VII, Examples 10a and 10b.
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Copernicus’s procedure in using the available facts to answer the questions about Earth’s position and its motions is to analyze the order of the heavenly bodies and to use the available clues. He has assumed from the outset that a question about a part can be answered affirmatively only by establishing the order of the whole [W]. From the existence of the order of the whole we can infer the order of one of its parts.83 Everyone agrees that the fixed stars are the farthest, followed by Saturn, Jupiter, and Mars. The planets were arranged (C) according to the duration of their revolutions (G) on the assumption that duration corresponds to the size of the orbit (W). Therefore, those that take the most time are probably the farthest (C). With respect to Mercury and Venus, however, there are differences of opinion, because these planets exhibit bounded elongation from the Sun. Copernicus recounts the different arguments that have been proposed. Plato’s opinion is based on observational considerations, such as the failure to observe phases and eclipses, which support the opinion that Mercury and Venus must be above the Sun. Ptolemy’s opinion is based on the vast space that is left between the Sun and Moon if the first opinion were correct. Because such a space seems unfitting, Ptolemy placed Mercury and Venus between the Sun and Moon. The failure to observe phases and eclipses is explained by the following assumptions. These planets are not opaque and so would not exhibit phases and would not eclipse the Sun and, anyway, they are so small in comparison to the Sun, they are not visible against the bright light of the Sun. Even these conclusions, however, mean that Venus has a huge epicycle, which raises again the objection against a vast empty space. Ptolemy’s argument that the Sun must move in the middle between the planets that show every elongation from it (Saturn, Jupiter, and Mars) and those that do not (Venus and Mercury) is unpersuasive. The Moon too shows every elongation from the Sun, yet Ptolemy did not place the Moon in an orbit beyond the Sun. As for those who locate Venus and Mercury below the Sun in a different order around Earth, they violate the principle based on the
83 Although he expresses the point differently, Rose, Italian Renaissance, 127–129, also emphasizes the connection between the principle of uniformity and the idea of a well-ordered universe.
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duration of the orbits. If they are correct, then only two alternatives are left—either Earth is not the center of the heavenly spheres or there is no principle of arrangement. (Copernicus suppresses the conclusion here that because there is a principle of arrangement, then Earth cannot be the center of the heavenly spheres.) Copernicus turns to the Capellan arrangement (W) to support the notion that Mercury and Venus orbit the Sun, thus explaining the observations of their bounded elongations. If we link Saturn, Jupiter, and Mars to the Sun, and that they are nearest to Earth when in opposition to the Sun and farthest when in conjunction with the Sun (G), then the Sun seems to be the body around which all of the planets execute their revolutions (C).84 This arrangement also yields a vast space between Mars and Venus, which is large enough to contain both Earth and its Moon (G). Copernicus at last bites the bullet and proposes that Earth with its Moon makes an annual revolution around the Sun (C' ). Here Copernicus appeals to the principle of economy or simplicity (W)85 to argue for the conclusion that many of the observed motions thought to be proper to the stars, planets, and Sun can be reduced to the effects created by the motions of Earth (C" ). Copernicus realizing that the conclusion is shocking turns immediately to the first principle accepted by virtually everyone, namely, that the sizes of the spheres correspond to the durations of their revolutions (G). From that commonly accepted view he establishes their order beginning with the highest: the fixed stars, Saturn, Jupiter, Mars, Earth and Moon, Venus, and Mercury with the Sun near the center or, as he puts it, in the middle of everything (C). With the fixed stars and Sun immovable, the ordering principle is the sidereal period of the planets around the Sun (W). That principle establishes the order of the
84
Copernicus clearly recognized that the Capellan arrangement also explained the observation of bounded elongation, but it also would explain their retrograde motions. Copernicus’s models for the superior planets required small epicycles (epicyclets) to make them more accurate and to account for their motions in latitude, but his focus here is on the architectonic structure of the whole and the principle of arrangement of the whole, not on the possibility that an effect may be explained by introducing an ad hoc assumption. He does not use the epicyclets to account for retrograde motion. The planets move on the epicyclets in such a way as to generate a slightly oval orbit. For Venus and Mercury, in De revolutionibus, he uses eccentreccentrics rather than epicyclets. 85 He does not use the principle here to argue for a reduction in the number of circles or spheres.
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whole, from which we may determine the order of any part [W]. The ordering also enables us to explain (G), not just describe or merely account for, the observed retrograde motions of the other five planets and the observed bounded elongations of Mercury and Venus (C). Left with the failure to observe stellar parallax, Copernicus can only suppose that the fixed stars must be much farther than anyone had ever imagined before (G). This huge gap with its vast space is a problem, but as with the twinkling of the stars, he argues that there had to be a great difference between what moves and what does not (W) in order to distinguish the planets from the stars (C). “So vast, without any question, is the divine handiwork of the most excellent Almighty.”86 It appears that Copernicus accepted the view of numerous late mediaeval philosophers that the principle of economy does not necessarily apply to God and his creative activity. Elsewhere in Revolutions Copernicus also makes arguments and uses dialectical topics. Probably the most controversial involve claims about the truth of alternative models. In these cases he was relying on the topic from division, but in retrospect we can now see that he was optimistic to think that the alternatives were exhaustive. In fact, we shall see in chapter ten that Copernicus was not always certain which hypothesis or model was correct. 8. Hypotheses in Copernicus’s Method In chapter ten I will examine Copernicus’s hypotheses in the context of his cosmological principles and mathematical models. Here I focus briefly on the logical and methodological issues. Copernicus, I have argued, read and annotated Ficino’s translation of Plato’s Parmenides. That dialogue in particular impressed Copernicus with the method of dialectical inquiry regarding hypotheses. Genuine philosophers must test all of the main theories and hypotheses affirmatively and nega-
86 Copernicus, Revolutions, 22. See Appendix VII, Examples 11a and 11b. In these linked arguments Copernicus draws the connection between distances and periods by appealing to natural explanation as opposed to a merely ad hoc account of observations. See Rheticus, Narratio prima (Rosen tr. 138) for emphasis on the absolute system and (187) on Copernicus’s reluctance to depart from ancient philosophers except for good reasons and when the facts themselves coerced him. See also Rose, Italian Renaissance, 127.
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tively for all of their consequences, selecting only those that are sound and rejecting those that are inconsistent with the sound hypotheses. Copernicus understood that the ancients distinguished hypotheses that they believed to be true from ones they assumed for the purpose of demonstrating the appearances. The ancient principles and hypotheses that they regarded as fundamental and true include principles of uniform and circular motion, geocentrism, geostability, and the circular motion of the fixed stars. In his famous “Letter to the Reader,” Osiander in speaking of the “novel hypotheses” of Copernicus’s work referred explicitly to the Earth in motion and the Sun at rest. Osiander departed from Copernicus in conflating these hypotheses with mathematical models as all imaginary and fictitious. Osiander claimed to regard the geometrical hypotheses of the ancients as equally fictitious. Yet Osiander was silent about the geocentric hypothesis, which he implicitly took for granted, not on philosophical grounds, but on scriptural grounds, for only in revelation, he asserted, do we find anything certain.87 Copernicus accepted the principles of uniform, circular motion, but rejected the others as false because from those assumptions his predecessors failed to deduce the structure of the universe. Other hypotheses, however, clearly refer to the devices of the geometrical models. In geometrical contexts, Copernicus referred consistently to the hypotheses of circles by means of which the ancients demonstrated the appearances. In their demonstrations, he alleged, they omitted something necessary or essential and admitted something extraneous and wholly irrelevant. “The necessary and essential that they omitted” probably refers to one or more of the fundamental propositions of natural philosophy. The extraneous and irrelevant refer most likely to a mathematical model that violates a fundamental hypothesis. The word translated as “extraneous” is alienum, exactly the word he used to criticize the models that have the epicycle center moving uniformly on an extraneous circle (in circulo alieno). Although we have been chastised by modern mathematical experts for misunderstanding the technical issues here, Copernicus said and repeated on several occasions that the defect in the ancients’ assumptions was that their hypothesis of combinations of circles was neither suitable enough nor adequate (IV, 2). The principal example that he provides is always of the same sort,
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Revolutions, XX.
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namely, while they claim that the motion of the epicycle’s center is uniform around the center of Earth or some other point, it is nonuniform on its own eccentric:88 Therefore, the epicycle’s motion on the eccentric described by it is nonuniform. But if this is so, what shall we say about the axiom that the heavenly bodies’ motion is uniform and only apparently seems nonuniform, if the epicycle’s apparently uniform motion is really nonuniform and its occurrence absolutely contradicts an established principle and assumption? But suppose you say that is enough to safeguard uniformity. Then what sort of uniformity will that be on an extraneous circle on which the epicycle’s motion does not occur, whereas it does occur on the epicycle’s own eccentric?
So here he refers explicitly to the violation of an axiom, an established principle and assumption.89 His solution is to propose another arrangement or system of circles that he claims does not violate the axiom. I will return to the technical issues in chapter ten with a discussion of Copernicus’s “hidden” equant, but I proceed here with the recitation of Copernicus’s comments. One of the principal achievements of Book V is to show how the motion of Earth and the motions of the planets account for retrograde motion better than the assumption of motion on an epicycle around a stationary Earth. Here again in recounting the ancients’ theory, he complains that the motion of the epicycle is not uniform around the deferent center but around an extraneous and non-proper center (V, 2: circa centrum alienum et non proprium). He refers explicitly to the case of Mercury, and adds the comment:90 I have already adequately refuted this result in my account of the Moon. These and similar consequences furnished the occasion to consider the mobility of the Earth and other ways by means of which to preserve uniform motion and the principles of the science and to render the account of apparent non-uniformity more constant.
We will have to complete the discussion of mathematical hypotheses and models when we turn to those issues in chapter ten. For now I emphasize the logic of Copernicus’s reasoning and arguments. He
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Revolutions IV, 2: 176, lines 1–9. It is one thing to conclude that the resultant motion is noncircular and nonuniform but altogether another matter to conclude that the circular motions out of which it is composed are themselves non-uniform! See Revolutions V, 4. 90 My translation. 89
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adopted some hypotheses as fundamental, namely, the uniform, circular motions of the heavenly bodies. He examined and evaluated hypotheses such as geocentrism and geostability for their consequences or results, which, he concluded, were inconsistent with the fundamental hypotheses. That failure provided the license or warrant to consider alternative hypotheses, namely, the mobility of Earth and stability of the Sun. He claims that the results of these hypotheses are consistent with the fundamental hypotheses or principles, and he adds further consequences that provide natural explanations of observed phenomena. We will elaborate on other relevant details in chapters nine and ten, but here we may observe without deeper examination that his proposed hypotheses are natural-philosophical. Their justification depends on their consistency with the fundamental principles and hypotheses of astronomy (uniform, circular motions), and on the relation of the whole to the part. His reasoning depends on architectonic principles that subordinate natural-philosophical hypotheses to astronomical considerations. His argument from whole to part retains a dialectical character for it depends on the greater probability of his architectonic principles. 9. The Logical Issues in the Relation between Mathematics and Natural Philosophy In the previous section we alluded to the subordination of some natural-philosophical hypotheses to mathematical and astronomical hypotheses. When his contemporaries accused Copernicus of ignorance of logic and natural philosophy, and complained that his hypotheses threatened to turn the whole art of astronomy upside down and throw the liberal arts into confusion, they recognized that Copernicus had reversed the relation between mathematics and natural philosophy. Robert Westman has interpreted this reversal, rightly in my view, as the revolutionary move in the Copernican theory.91 I am not persuaded, however, that Copernicus intended this reversal as a general methodological principle. In other words, it was not his view that all natural-philosophical principles are to be subordinated to
91
Westman, “Astronomer’s Role,” 105–147.
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mathematical ones. In this section, I explore the logical background of this reversal, and I propose to identify the limitations or qualifications that Copernicus adopted in selecting those cases in which the reversal was legitimate as opposed to those that were not. Again, the main idea here is that he examined hypotheses for their conformity with more fundamental and sound hypotheses, rejecting hypotheses whose consequences were not consistent with the more fundamental ones.92 We have briefly discussed the Aristotelian background in chapter four on the relation between mathematics and natural philosophy. Aristotle set restrictions on the transition from one discipline to another in the prohibition of illicit metábasis. Metábasis means “transition,” and Aristotle objected to an illicit transition in a proof from one genus or species to another, based usually on ambiguity, which leads to fallacious arguments. Aristotle considered most, but not all, instances of sliding from one field to another in a proof or demonstration as an example of illicit metábasis. The arithmetical proof of a geometrical proposition is an example that he cited, but he did allow exceptions. In cases where a discipline is concerned with the collection of empirical facts while the other is concerned with discovering the reason for the fact, Aristotle judged the transition to be licit. There are cases where two disciplines are hierarchically ordered, for example, when physics provides the fact and mathematics the reason for the fact.93 In other 92 Rheticus, Narratio prima (Rosen tr. 140) confirms that there was widespread acquaintance with the importance of hypotheses and theories to astronomers, and with the difference between a mathematician and a physicist. Rheticus emphasizes the point that the observations and the evidence of heaven lead to the results, suggesting that God and mathematics will enable us to face and overcome every difficulty. These are ideas that he and Copernicus may have derived from the Neoplatonic tradition in authors like Bessarion and Ficino, both of whom revived a version of the illumination theory. According to such an account, God illumines the human intellect making it possible for us to reach the highest truths and to discover truths about the universe. On Ficino, see Platonic Theology, 4, Books XII–XIV. 93 The usually cited examples, we must however point out, are trivial by comparison with the examples that we find in Copernicus and Galileo. One of the most cited examples is from Posterior Analytics I, 13, 78a31–38 that the distance of stars causes their twinkling and the nearness of the planets causes their non-twinkling. See also Aristotle, On the Heavens II, 8, 290a17–23. Copernicus, in fact, cited this example in his Letter Against Werner, tr. Rosen, Complete Works, 3: 146. The Letter provides more evidence of Copernicus’s acquaintance with Aristotle, primarily to Metaphysics, Physics, and On the Heavens. See Rosen’s comments in his introduction, 134. I have not analyzed this treatise for the logic of its argumentation, because it is a critique of Johann Werner’s treatise, “On the Motion of the Eighth Sphere,” in which Copernicus devotes most of his effort to defending the reliability of Ptolemy’s data. The topics discussed are primarily relevant to questions about Copernicus’s direct acquaintance
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cases, the two disciplines are equal, for example, a geometrical proposition provides the reason why circular wounds heal more slowly than other wounds. In other texts, however, Aristotle suggested that two disciplines remain separate, and that the apparent transition is actually a matter of considering a particular case as primarily physical or primarily mathematical. In the Physics he prohibited the comparison between circular and rectilinear motions as involving an illicit transition because “circular” and “rectilinear” belong to different kinds of things, just as the sharpness of a pencil and the sharpness of a musical tone are incomparable. He may have had the problem of squaring the circle in mind, but his view placed severe logical and ontological constraints on mathematical analysis. Among the most important critics of Aristotle’s prohibition was William of Ockham. Ockham interpreted Aristotle as allowing for the subordination of a mathematical analysis to physical considerations, the subordination of a physical analysis to mathematical considerations, and even the partial subordination of one science to another. The consequence is that Ockham subdued the logical and ontological restrictions on mathematics, making it a suitable instrument for analyzing any problem that can be quantified or clarified logically by means of mathematics.94 There was a time when I thought that Ockham’s critique had survived in late medieval sources that indirectly reached Copernicus. In fact, it appears as if Ockham’s critique, even if adopted by a number of fourteenth-century scholars, fell into neglect. This is not to say that Aristotle’s prohibition disappeared, but later medieval sources suggest that Aristotelians were influenced by developments in mathematics and by the revival of Platonism.95 This leaves us, then, to seek another explanation for Copernicus’s conclusion that some natural-philosophical propositions are subordinate to some astronomical-mathematical ones. The explanation, in fact, is already at hand. Copernicus adopted the assumption about uniform,
with Aristotle’s texts, especially the three mentioned which we discuss further in chapters nine and ten. 94 This argument is developed more extensively in Goddu, “Impact,” 204–237. 95 Wallace, Domingo de Soto, has cited Jesuit authors of the sixteenth and early seventeenth centuries who advocated the greater use of mathematics in natural philosophy. Wallace’s claims that these approaches can be traced back to Thomas Aquinas are unconvincing. See McMullin’s review of Wallace’s Prelude to Galileo, 171–173; and Wallace’s response in Philosophy of Science, 504–510.
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circular motions as fundamental. If he ever subjected that assumption to questioning, he dismissed the questions as contrary to the whole tradition of astronomy. He evidently concluded from the regularity of celestial events that the motions of celestial bodies must be circular, uniform, and, therefore, must be represented by circles and combinations of circles.96 Copernicus may also have found encouragement in the fact that Aristotle himself used mathematics as a paradigm of science, and subordinated physics to mathematics to some extent in the mixed sciences of astronomy and optics.97 The next step, as we showed in the previous section, was to subject other hypotheses to scrutiny, namely, whether they produced results in agreement with the fundamental hypothesis of uniform, circular motions. Where such hypotheses failed, he rejected them. In chapter seven, we provided an account of how he arrived at the hypotheses that he accepted. This step is complicated for it involved simultaneous rejection of geocentrism and adoption of geokineticism, rejection of the motion of the Sun and adoption of heliocentrism, and recognition of the results that agreed with the fundamental assumptions and further results that strengthened the greater likelihood of his hypotheses. As we can see, then, Copernicus had to adopt some hypotheses as fundamental, select secondary ones in conformity with these, and select models that would satisfy both the fundamental and secondary ones. The secondary included cosmological and natural-philosophical assumptions that had to be subordinated to the fundamental astronomical-mathematical assumptions. The selection of further mathematical hypotheses and models had, in turn, to be subordinated to the cosmological, natural-philosophical assumptions while preserving the fundamental astronomical-mathematical assumptions. We consider the acceptance of the secondary hypotheses in chapter ten. Although he went further than Aristotle in subordinating physics to mathematics, like Aristotle, Copernicus did not make a complete subordination of physics to mathematical astronomy.
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Revolutions, I, 4: 11, lines 10–15. For recent emphasis on these points, see Hussey, “Aristotle and Mathematics,” 217–229, esp. 217–218, and note Hussey’s careful qualification (225) that Aristotle did not make a complete subordination of physics to mathematics. 97
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10. The Logical Issues in the Discovery of the Heliocentric Theory As we have suggested in the previous two sections, Copernicus adopted a dialectical methodology. What we wish to clarify here are the logical steps in his reasoning from problems with geocentric systems to the adoption of an alternative system, leaving the details of his critique of geocentricism to chapter nine and of his discovery to chapter ten. There are principally two facts that led Copernicus to reject his predecessors’ efforts, the problem of saving uniform motion by resort to an equant and the problem of the variations in the distances of the planets from Earth. In both cases Copernicus concluded that the systems violated the fundamental principles or, if they satisfied them, they did so by introducing hypotheses that failed the test of relevance. In chapter three we referred to three Aristotelian texts as possible sources for Copernicus’s view about the relation between hypothesis and results. Nicomachean Ethics I, 8, 1098b11–12 (“with a true view all the data harmonize, but with a false one the facts soon clash”), Prior Analytics II, 2–4, and Metaphysics I minor, 993b26–27 (“that which causes derivative truths to be true is most true”) agree broadly with Copernicus’s controversial statement in the Preface to Paul III. Because the text from Ethics refers to data, it seems the most relevant, but of all of the alternatives, there are reasons for thinking that Copernicus knew the text of the Metaphysics best. Rheticus refers to it explicitly in Narratio prima.98 Copernicus’s friend Tiedemann Giese wrote a commentary on the Metaphysics in the form of glosses, but I have found no evidence in Giese’s copy at Uppsala that Copernicus knew the commentary. Of course, he might have discussed the text and especially this passage with his friend. It is possible that they knew each other as early as 1503, but Copernicus did not transfer until 1510 to Frombork where Giese was also a canon.99 Perhaps more significant, we know that Copernicus either garbled or deliberately changed Aristotle’s meaning in a passage from Metaphysics not far from the text about truth. At 993b12–15, just fourteen lines earlier, Aristotle expresses gratitude to those who have spoken superficially, for they too have made contributions to the powers of
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Rosen tr. 142. On Giese, see Pociecha, “Giese,” PSB, 7: 454–456. Cf. Rosen, “Biography,” 340.
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thought. Copernicus either had a different version or he understood Aristotle to have been expressing gratitude to those who have committed errors for they too have contributed to the truth. Copernicus’s interpretation is not completely at variance with Aristotle’s dialectical method, but Giese’s commentary could not be the source for Copernicus’s interpretation.100 On the one hand, Copernicus’s comment suggests acquaintance with Metaphysics, but, on the other, it also suggests that he was relying on his memory in 1524. Hence, it seems likely to me that Copernicus knew all of the passages either from his teachers or his own reading prior to 1503. As he struggled with puzzles about the truth status of hypotheses in astronomy, he recalled them and arrived at his own strong views. His assertions in De revolutionibus, however, also demonstrate acquaintance with dialectical topics, a branch of philosophy that he learned in Cracow and probably reinforced in Bologna. In adopting the Aristotelian view about the relation of true premises to true conclusions, he expanded Aristotle’s criterion from causal (propter quid) demonstration to the somewhat weaker criterion of relevance. He further concluded that irrelevance was a ground for rejection of a cosmological theory on which Ptolemaic geocentric astronomy was based. Because their hypotheses introduced something extraneous and irrelevant, Ptolemaic astronomers failed to resolve the problems in accord with their own principles, and, consequently, failed to arrive at the true system of the world.
100 Copernicus, Letter Against Werner, Complete Works, 3: 145 and notes 11 and 12. I consulted Giese’s glosses on this text in Uppsala, Inc. 31:164, questions of Johannes Versoris on the Metaphysics with the complete text of Metaphysics (Cologne, 1493; Hain *16051). The book is annotated in several hands, but Giese owned the book, and there is no question that he wrote the comments on Metaphysics. On f. 13v, Aristotle’s text reads: “Non solum autem his dicere gratiam iustum est quorum aliquis opinionibus communicaverit. Sed his qui adhuc superficialiter enunciaverunt, etenim conservunt aliquid.” At the words “superficialiter enunciaverunt” Giese enters the comment “de veritate” between the lines. In other words, he interpreted Aristotle to be speaking of those who had spoken the truth but in a superficial way, not those who had spoken incorrectly. At the beginning of the chapter in question, Aristotle says that everyone says something true about the nature of things, and makes another striking comment just a little below it. At 993b7–11, he says: “Perhaps, too, as difficulties are of two kinds, the cause of the present difficulty is not in the facts but in us. For as the eyes of bats are to the blaze of day, so is the reason in our soul to the things which are by nature most evident of all.” It is hard to imagine Copernicus not being struck by such statements. I have again used the translation by Ross in Basic Works, 712–713.
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In the conclusion of this study, we will return yet again to the issue of true hypotheses. There is a problem with Copernicus’s view, yet he could hardly have been expected to see it. He had focused his attention on reforming astronomy within the confines of a natural philosophy and cosmology that were still broadly Aristotelian. In chapters nine and ten we articulate the consequences for Copernicus’s philosophy of nature and cosmology. In the conclusion we explain the momentous advance by Kepler about the understanding of hypotheses. 11. Concluding Remarks on Copernicus’s Relation to the Aristotelian Logical Tradition Copernicus became acquainted with Aristotelian philosophy in the context of late medieval schools of interpretation and transmission. Although we cannot prove that he attended classes in either Cracow or Bologna, his later treatises indicate that he had been trained in the techniques of dialectic, the means for discovering middle terms in syllogistic arguments. His arguments are, of course, not syllogisms, and he tried to model his style on humanistic or classical authors. There are, nonetheless, arguments, and they sometimes have the structure of enthymemes, leaving us to supply the warrants or premises on the assumption that his arguments are hypothetical syllogisms. In other, perhaps most, cases, his warrants are explicit. Aristotle regarded enthymemes as rhetorical proofs, but he also advocated analyzing them for their logical validity. In other words, we focus on dialectic to examine the logical validity of an argument, and on rhetoric to understand how the argument is supposed to move readers to assent.101 Copernicus’s views about hypotheses, however, derive from his reflections on the interpretation of hypotheses in the astronomicalmathematical tradition in which he was also trained, and from his reading of Ficino’s translation of Plato’s Parmenides. It would be anachronistic to characterize his method as hypothetico-deductive, but the arguments do share some of the features of such reasoning, and they encounter some of the same logical difficulties that modern logicians have raised about inductive reasoning and hypothetico-deductive method. We have pointed out some of these issues above, arguing
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Van Eemeren and Houtlosser, Dialectic and Rhetoric, 3–11.
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that Copernicus adopted the criterion of relevance in evaluating the validity of consequences in a discipline like astronomy. I have taken no position on the validity of such a strategy because these remain very controversial issues in the technical literature that deals with the logic of hypothetico-deductive method and inductive reasoning. We have argued that Copernicus’s strategy was controversial in his own day, yet there is evidence that it was taken for granted in specialized and practical disciplines that had to apply the standard logical criteria to the actual problems and issues of those disciplines. In such circumstances, scholars tended to regard the strictly logical criteria as theoretical, modifying them to make it possible for them to reach conclusions that were more reasonable than other alternatives. They could fall back onto Aristotle’s own statements about truths and derivative truths, a text on which Copernicus himself may have relied for his controversial statement about the true not following from the false. The texts provide abundant evidence that Copernicus was sensitive to logical issues, and that he gave serious thought to principles and criteria that would make it possible for astronomers to advance beyond the impasse that blocked the way to further progress in astronomy. That impasse, as he saw it, resulted from geocentric assumptions, and that fact was revealed to him by the failure of those assumptions to produce results in conformity with the fundamental principles of the discipline. That part of his argument is, I believe, indisputably logical. Whether, however, Copernicus’s hypotheses yielded the results that he claimed to achieve remains both historically and logically controversial to this day. We examine further historical dimensions of his philosophical assumptions and of his relation to the Aristotelian tradition in the remaining two chapters.
CHAPTER NINE
COPERNICUS AS NATURAL PHILOSOPHER 1. Introduction When two of the leading experts on Copernicus characterized him as an Aristotelian, they were without doubt referring to his retention of celestial spheres as the movers of the planets and to his views in natural philosophy.1 Although other experts have pointed to non-Aristotelian sources of Copernicus’s account of motion and natural elemental motion, I have concluded that Copernicus also drew on schools and communities of the Aristotelian tradition. He combined them into an uneasy synthesis with all of the ambiguities and inconsistencies that one would expect. Teachers and students within the Aristotelian tradition modified Aristotelian doctrine, often interpreting it in ways that combined the fundamental principles of other authors and JudaicChristian doctrines, and thereby created a synthesis that is difficult to
1 Rosen, Introduction to Letter, Complete Works, 3: 134, comments: “[F]amiliarity with Aristotle’s treatises does not of course make Copernicus an Aristotelian in the sense that he regarded the Stagirite as infallible. On the contrary, where he detected a flaw in Aristotle, as in the Stagirite’s division of simple motion into three mutually exclusive types, he did not hesitate to correct it. But he did not undertake to overthrow Aristotelianism, as he did the Ptolemaic astronomy. On the other hand, what he believed was sound in both systems, he retained with gratitude and affection, an attitude which some of our contemporaries would do well to consider.” Compare with the assertion of Swerdlow, “Copernicus,” 162–168, esp. 164–165: “For these physical problems raised by the motions of the earth, which should also affect the motion of birds, clouds, and projectiles, Copernicus made what he considered to be a minimal alteration of Aristotelian natural motion of the elements, such that the natural motion of a spherical body, whatever its substance, is to rotate in place by virtue of its form alone. The daily rotation of the spherical earth together with the surrounding water and air is, therefore, entirely natural; projectiles, birds, and clouds are simply carried along with the rotating earth; and heaviness (gravitas), the descent of heavy bodies to their natural place, the surface of the earth, in straight lines, is due to a ‘natural inclination placed in the parts’ to come together to form a globe. In proposing this explanation, Copernicus did not intend to overthrow or displace Aristotelian physics but to adapt it to the motion of the earth, unlike Galileo Galilei (1564–1642), who later used much the same principles as Copernicus for a devastating attack on Aristotle. In fact, the objections to the motion of the earth were not completely answered until Isaac Newton (1642–1727).”
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reconcile with genuine Aristotelianism. Be that as it may, this was the Aristotelianism that Copernicus encountered, and it is far from clear how much he realized or, for that matter, even cared about the authenticity of classical authors’ views. Or, to put it differently, his concern, shared by the authors of the Aristotelian tradition, was to arrive at the truth, and to adopt Aristotelian views where they agreed and adapt his views where they did not.2 2. Copernicus’s Critique of Geocentrism In chapter four, I summarized the principal Aristotelian cosmological assumptions and conclusions relevant to Copernicus’s arguments. From the point of view of natural philosophy and physics in particular, we have been conditioned to view Copernicus as having anticipated the successful mechanical principles enunciated definitively by Newton some one hundred and forty-four years after the appearance of De revolutionibus. Despite the successful historical revision of Copernicus’s astronomical achievements as a conservative continuation and even fulfillment of the goals of Ptolemaic astronomy, the topos of anticipation still dominates the standard representations of his vision of cosmology, natural philosophy, and physics.3 Even when some readers acknowledge the survival of Platonic and Aristotelian principles in Copernicus’s understanding of cosmology, they have still left the impression that he anticipated essentially antiAristotelian solutions to several problems and questions. Because of the success of the Newtonian program, such readings of Copernicus seem plausible.4
2
See chapter four on the Aristotelian tradition and on Aristotelian schools and sects. An excellent example is Pedersen and Pihl, Early Physics, 317. This text provides one of the best accounts of ancient and early modern astronomy but reads Copernicus’s intentions about natural philosophy from the viewpoint of contemporaneous negative reactions by Aristotelians and from the viewpoint of later physical astronomy. In his text, Birth, chs. 1–3, Cohen adopts for pedagogical purposes a portrayal of Aristotelian dynamics that was so incompatible with the Copernican theory that a new theory had to be developed. My own earlier essays, for example, Goddu, “Dialectic,” 95–131, at 125–131, also portray Copernicus as having left the physical questions for a later day, thus suggesting that Copernicus anticipated a non-Aristotelian solution. 4 Exceptions are Moraux, “Copernic et Aristote,” 225–238, and Swerdlow, “Copernicus,” 163. 3
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Several scholars in the Middle Ages criticized Ptolemaic astronomy on a variety of grounds. Still, no one in the Middle Ages through the fifteenth century proposed multiple motions of Earth as a solution to the problems found in Ptolemy’s theory. What, then, led Copernicus to suppose, contrary to common sense, to naked-eye observations of the stars, and to the geocentric principles of Ptolemaic astronomy and Aristotelian natural philosophy that the Earth has not only one, not just two, but three motions? As far as we know, Copernicus never recounted the process that led him to those conclusions. About thirty years after he proposed a heliocentric theory, the reasons that he provided may represent the evolution of his thought, but his statements in 1542 (the dedication to Pope Paul III) were clearly intended to persuade readers to suspend judgment until they saw the results. In other words, we do not know whether the account was rhetorical, autobiographical, or a little of both. In that account he tells us that he took the original aims and principles of astronomy as absolutely correct—to represent all of the known celestial phenomena with geometrical models that do not violate the principles of perfect uniformity and circularity. The models would thereby reveal the true, perfectly uniform and circular motions existing behind the phenomena. That was the challenge that Plato had supposedly presented to astronomers in the Republic. Expressed in his own words written probably in the mid-1520s, Copernicus saw his study as “concerned with the most beautiful objects, most deserving to be known.”5
5 De revolutionibus I, Introduction, 487, 1–3: “Nter multa ac varia literarum artiumque studia, quibus hominum ingenia nego[ci]antur ea praecipue amplectenda existimo: summoque prosequenda studio: quae in rebus pulcerrimis et scitu dignissimis versantur.” Plato’s challenge in the Republic appears at VII, 529a–530d. Plato’s view has been the subject of much controversy. See Bulmer-Thomas, 107–112, for a brief survey. Several scholars have rightly criticized the distinction between mathematical astronomy and physical astronomy, and rejected Duhem’s instrumentalist/ realist dichotomy. See, for example, Lloyd, “Saving,” and Goldstein, “Saving,” for their assessments and references to additional literature. Knorr, “Plato,” has also shown that Plato did not formulate the challenge about saving the phenomena, although later Neoplatonic authors and others did attribute it to him. See also Evans, “Simplicius.” For the interpretation of the text especially by astronomers, see Pedersen and Pihl, Early Physics, 26–30, 65–67. For these reasons, when I refer to it, I place it in quotation marks (“Plato’s axiom”) to indicate the spurious yet customary nature of the attribution. On chronology, see Birkenmajer, Mikołaj Kopernik, 350–389, esp. 352–354 and 362–373; Rosen, “When Did Copernicus,” 144–155. Compare Schmeidler, Kommentar, 1–5.
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He believed that God had created a perfect system and human beings capable of discovering that perfect system. From Plato, Aristotle, and Ptolemy, he accepted the belief that the motions of planets and stars are perfectly uniform and circular and so must be represented by circles and combinations of circles that preserve perfect uniformity and circularity. Sometime between 1496 and 1509—this is where his account of 1542 lacks details—he came to the following conclusion. All homocentric representations and the more complicated, but more adequate, epicycle-deferent models had failed to achieve the principal goal, namely, the representation of a coherent system using only circles that preserved perfect uniformity with respect to their proper centers. In spite of all the hypotheses and models they devised, all of his predecessors had failed. The next step in his account is far from clear. In chapter seven we presented a reconstruction of how Copernicus arrived at his theory, but the account underscores his silence and the differences among the experts. Somehow he began to wonder about the placement of Earth at the center of the system and to ask whether, perhaps, the Earth itself moves. Why he thought a moving Earth would remedy the mistakes of his predecessors is not at all clear. In addition to the questions and problems that led him to his cosmological theory, he presumably adopted the Earth’s motions initially as a working hypothesis. He evidently believed that models constructed according to a heliocentric hypothesis would preserve the principles and achieve the goal of representing celestial motions with circles that preserve perfect uniformity with respect to their proper centers. If we judge the results with the same severity that he judged those of his predecessors, we have to be puzzled why he thought that switching the positions of Sun and Earth and putting Earth in motion would work better.6 The alternatives are not perfectly equivalent, but neither was completely successful. Let me hasten to add, however, that his decision to work out the details is what separates his work from all earlier heliocentrists. Clearly, something else emerged that persuaded Copernicus that his hypotheses were right. In other words, although his initial reasons 6
Actually, the center of Copernicus’s cosmos is the center of Earth’s orbit, which is eccentric to the Sun. In other words, the center is the mean Sun, not the true Sun. Many experts have pointed this fact out, for example, Swerdlow and Neugebauer, Mathematical Astronomy, 1: 159–161, but for a clear exposition see Evans, History, 415.
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for proposing heliocentrism may have been frustrated, the results persuaded him that he had it basically right, regardless of the problems that remained. “The problems that remained” refers to the construction of completely equantless models that preserved uniform and circular motions. Copernicus’s planetary models required him to construct small epicycles to account for their motions in latitude and for the non-uniformity of the planets’ motions. In the models for the superior planets the resulting path of the planet is slightly oblong or, as he himself expressed it, “imperceptibly” not a perfect circle, and the problem of non-uniform motion is solved by what amounts to a hidden equant.7 The models for the inferior planets raise even more difficulties, but again there are hidden equants and other paradoxical results. Copernicus acknowledges that the path of a planet is not perfectly circular, but it is composed of uniformly moving circles.8 “Results” refers to the achievements that Copernicus himself either emphasized or clearly implied. First is the natural explanation of bounded elongation of Mercury and Venus and of retrograde motions of all the planets. Second is the ordering of the planets according to sidereal periods. Third is the estimate of relative distances of the planets from the Sun. Copernicus concluded that ordering the planets according to sidereal periods was the only way in which they could be ordered, otherwise the wonderful commensurability and harmony of the system would be destroyed. The planets had to be ordered in this way, and he knew that he was right about that even if he could not prove it. Alas, everything else was murkier. The experts have explained most of the astronomical difficulties adequately.9 Copernicus himself recognized, of course, that philosophers and theologians would likely reject out of hand his hypothesis of a moving Earth. While he did not compose a text of natural philosophy to accompany his mathematical treatise, he did address himself to the most serious objections. By and large, his approach was dialectical, that is to say, he raised questions
7 De revolutionibus V, 4: 366, 34–35: “Hinc etiam demonstrabitur, quod sidus hoc motu composito, non describit circulum perfectum iuxta priscorum sententiam mathematicorum, differentia tamen insensibili.” An excellent explanation is provided by Evans, History, 420–422. Cf. Swerdlow and Neugebauer, Mathematical Astronomy, 1: 295–297. 8 Swerdlow and Neugebauer, Mathematical Astronomy, 289–299, 372–374, 403– 415, 483–491, and 535–37; Evans, “Division,” 1009–1024. 9 Especially Swerdlow and Neugebauer.
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about some principles or about their application. This is why I will subordinate the analysis to his critique of geocentrism, for Copernicus was inclined to revise principles rather than reject them altogether. He rejected a number of assumptions, but his rejection of an assumption led him to revise, not reject, a principle. The result, then, was an adaptation to the heliocentric system. And the purpose was to delay the anticipated abrupt and unreflecting reactions of philosophers and theologians. If he could get them to take some questions seriously, perhaps he could move them to re-examine the issues from a fresh perspective. In other words, I subordinate the interpretation of his views in natural philosophy to the rhetorical and dialectical strategies adopted in Book I of De revolutionibus. There is a third alternative. After Copernicus concluded that only a heliocentric cosmology could achieve the goals of ancient astronomy, he drew inspiration from sources that he recognized as unconventional. As he produced his sketch of natural philosophy, he likewise drew inspiration from sources that he also recognized were unconventional while presenting its details as much as he could in a way that he thought that his contemporaries could assimilate. Later thinkers went further than what Copernicus had envisioned and in a manner that he tried to avoid, namely, by adopting principles and constructing arguments that would eventually entail the destruction of Aristotelian natural philosophy.10 The alternative, as I have expressed it, may seem to require only a subtle or nuanced modification of my thesis. What the alternative contributes in very clear terms—that the authors whom I have cited in support of a modification of Aristotelian principles fail to make clear—is the extent to which Copernicus relied on especially ancient unconventional and anti-Aristotelian sources to support his unconventional cosmology. We cannot simply argue, as Rosen and Swerdlow implied, that Copernicus altered Aristotelian principles as demanded by his theory without resorting to unconventional sources that were incompatible with genuine Aristotelianism. They all agree that Copernicus did not intend to overthrow, destroy, or displace Aristotelian or scholastic cosmology.11
10 This alternative depends on a private communication from Dilwyn Knox, which I have modified to emphasize the difference between cosmology and natural philosophy. 11 Knox, “Copernicus’s Doctrine,” 157–211.
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In chapter four I enumerated eight themes held by several medieval scholastics that are non-Aristotelian, some of which can be characterized as even anti-Aristotelian, yet such scholastics were perceived as Aristotelian and as carrying on the Aristotelian tradition. As I conceded in that chapter, several of Copernicus’s views in natural philosophy and cosmology are decidedly anti-Aristotelian and anti-scholastic. Heliocentrism and geokineticism are obviously contrary to scholastic Aristotelianism. Because there appears to be consensus that Copernicus did not intend to destroy Aristotelian natural philosophy altogether, we apparently agree that he intended to transform, modify, and adapt Aristotelian and alternative principles to a heliocentric cosmology. What means did he employ to fulfill this intention? He relied on ancient opponents of Aristotelian doctrine, and he exploited scholastic modifications to propose theories about nature, natural motion, elemental motions, spheres, celestial spheres, and the properties of celestial bodies that are compatible with his heliocentric cosmology. We cannot, however, overlook the fact that nearly all of his sources were also geocentrists. His conclusions were equally opposed to their cosmological views. The construction of an entirely new natural philosophy consistent with heliocentrism was beyond even Copernicus’s considerable imagination. He was freed but also limited by ancient and scholastic conceptions. He had seen Aristotelian principles rejected, transformed, and adapted in almost countless ways. He could not have proposed his transformations without ancient and scholastic critics of Aristotelian doctrine, but he had sufficient and even defensible reasons for questioning the dogmatic acceptance of Aristotelian principles that were incompatible with heliocentrism. The prevailing view was that the universe is an open system and behaves like an open system. If the Earth moves, then, we should be able to perceive it. Copernicus’s proposal implied that the universe is an open system, yet it behaves as if it were an enclosed system. Because Copernicus did not grasp this problem adequately, he thought that modifying ancient and scholastic principles would suffice to construct a sketch of a natural philosophy compatible with a heliocentric cosmology. The modifications were non-Aristotelian, some were anti-Aristotelian, yet they seemed to fit with transformations that Copernicus proposed without explicitly rejecting Aristotelian natural philosophy or the Aristotelian tradition. Again, these are further reasons why I am persuaded that his critique of geocentrism motivated his transformation of ancient and scholastic natural philosophy, Aristotelian and non-Aristotelian.
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Three important themes will serve to illustrate how the critique of geocentrism guided Copernicus to his principles of natural philosophy. The motions of celestial bodies, the motions of elemental bodies, and the question of whether the universe is finite or infinite will illustrate Copernicus’s principles and mutual dependence of his answers to these problems. These themes will also help us to solve some thorny problems of interpretation as well.12 In chapter ten, we will deal additionally with the problems of the existence of spheres and the nature of celestial matter. 3. The Motions of Celestial Bodies Aristotle assumed that the eighth sphere (the sphere of the fixed stars) has the daily, circular motion that we observe it to possess. Circular motion is simple; hence there must be an element that performs such a motion by its very nature. The circle is a more perfect figure than a straight line, and it follows that circular motion is more perfect than linear motion. Bodies that move in a circle are more divine than the elements of the sublunar region. The heavenly bodies that move in circles are eternal and uncreated, although the actuality of their movement can be traced back to the unmoved mover. The motion of the eighth sphere causes the motions of the lower planetary spheres. I have here combined accounts from De caelo, Physics, and Metaphysics, as scholastic readers were inclined to do, and as Copernicus himself suggests by his indirect references to Aristotle.13 Copernicus replaced the motion of the eighth sphere with the Earth’s daily rotation on its axis; hence he had to revise the Aristotelian account of the motions of the planetary spheres. In his theory, of course, Earth is a planet. How does he explain the motion of Earth? Everyone agrees that Earth is a sphere. It does not follow necessarily
12 Szczeciniarz, Copernic, has provided an alternative interpretation of motion and infinity in the Copernican theory that relies on supplying answers to questions about which Copernicus preferred to remain silent. 13 We do not know whether Copernicus consulted Aristotle’s texts or relied on references made by others, or was simply referring to Aristotle from memory. We know that in specific places he was referring to certain chapters of De caelo and Metaphysics, and generally to principles contained in the Physics. Here the relevant texts are De caelo I, 2–3, Metaphysics XII.6.1072a18–35, and Physics VIII, 5–10. On Copernicus’s knowledge of Aristotelian texts, see Moraux, “Copernic et Aristote.” See chapter four for late fifteenth-century commentaries at Cracow on natural elemental motions.
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from that fact that it moves, but if it moves, then surely there would be nothing unnatural about its moving in a circle. His explanation of the motion of a sphere is that such motion is natural to a sphere. That motion is not a property of all spheres, however, follows from his belief that the Sun and the sphere of the stars are motionless.14 Form is not the cause of motion, that is, the form of sphericity by itself does not cause a sphere to rotate. An external efficient cause may be necessary to put a sphere in motion or to remove an obstacle to motion, but once moved the sphere would move in a circle according to its nature. For Copernicus, then, “according to nature” indicates a potentiality in conformity with the form or shape of a thing, or to put it differently, the spherical shape of a body disposes it to move naturally in a circle, but its shape does not necessarily entail that the body revolves.15
14 Knox, “Copernicus’s Doctrine,” 172, n. 76, has quite rightly pointed out an ambiguity in the Latin text of De revolutionibus, where Copernicus seems to imply that the Sun may rotate. See De revolutionibus I, 9: 17, 3–8: “Equidem existimo, gravitatem non aliud esse, quam appetentiam quondam naturalem partibus inditam a divina providentia opificis universorum, ut in unitatem integritatemque suam sese conferant in formam globi coeuntes. Quam affectionem credibile est etiam Soli, Lunae, ceterisque errantium fulgoribus inesse, ut eius efficacia in ea qua se repraesentant rotunditate permaneant, quae nihilominus multis modis suos efficient circuitus.” Yet elsewhere, Copernicus decisively commits himself to the proposition that the Sun is stationary. De revolutionibus 1, 10: 19, 25–28: “Proinde non pudet nos fateri hoc totum, quod Luna praecingit, ac centrum terrae per orbem illum magnum inter ceteras errantes stellas annua revolutione circa Solem transire, et circa ipsum esse centrum mundi: quo etiam Sole immobili permanente, quicquid de motu Solis apparet, . . .” The text could be restricted only to the Sun’s annual motion, but surely he could have found an expression more ambiguous than Sole immobili permanente to express himself. In his astronomical models (De revolutionibus III, 15, 20 and 25), Copernicus entertains motions of the Sun, but these are references to the mean Sun, and they indicate his recognition of alternative mathematical models to account for the appearances. See Swerdlow and Neugebauer, Mathematical Astronomy, 1: 159–161, where they discuss these alternatives, and conclude that Copernicus believed the Sun to be immovable even though he could not prove it. 15 I owe the qualification at the end of the paragraph to a comment by Knox, which is intended to remove any ambiguity. See also Knox, “Copernicus’s Doctrine,” 170, n. 66. See also Wolff, “Impetus Mechanics,” 257–279, esp. 219–220. Compare with Kokowski, Copernicus’s Originality, 230–231. In the pages cited Wolff and Kokowski emphasize the distinction between form and cause of circular motion. See also Aristotle, Metaphysics XII, 6, 1071b3–25. Again, Szczeciniarz, 91–105, re-interprets the exceptions, leaving form as the cause of the motion of a sphere. Yet, on 254, n. 198, Szczeciniarz acknowledges a difficulty with Copernicus’s arguments. See chapter four on natural place and form, and on celestial spheres. Copernicus could have derived some features of his interpretation from Johannes Versoris. Cf. Goddu, “Sources,” 85–114, esp. 86–97; and idem, “Teaching,” 69–75. Versor also denies that shape is a cause of motion. Instead, he regards shape as a cause of speed.
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It is hard to keep the issues separate, but Copernicus evidently realized that the source of the problem was Aristotle’s associations of a natural motion with simplicity, and of simplicity with an element that by its nature performs the observed motion. First, the assumption is a simplification and generalization from observations of clearly more complicated motions. As Aristotle knew, actual elemental things are mixtures, yet he asserted the principle in a theoretically foundational way. Everyone acknowledged the principle of the relativity of motion; only Copernicus recognized it as a problem that no naked-eye observation, or commonsense experience, could resolve decisively.16 Second, if a decision about what is natural and what is contrary to nature is based on such a principle, we may commit a fatal error right at the start. Copernicus had no inkling of an account based on extrinsic, mechanical forces. His only recourse was to re-define the meaning of “natural.” The “nature” of a body suggests a capacity or a possibility, so he had to express it conditionally—if a sphere moves or is caused to move, then its motion in a circle would be “natural” to it. He may have believed that at the creation God set some spheres in motion, although he does not say so explicitly. He maintained that the circular motions of spheres continue uniformly and unfailingly because of their perfect constitution and inherent capacity for circular motion. The rotation of spheres causes the celestial bodies embedded in them to move in circles either by contact or by carrying them. There is no resistance, however, for spherical celestial bodies have a natural capacity for circular motion. Copernicus believed that Earth rotates on its axis because, as a sphere, it possesses the capacity to rotate, and to do so uniformly and unfailingly. He may have supposed, although he nowhere says so, that the great orb moving the Moon and Earth may cause Earth to rotate on its axis. Because Earth possesses a natural capacity for rotation, it offers no resistance. Copernicus could have employed the theory of impetus here, as Michał Kokowski believes, but this would have entailed the consequence that the motion of Earth requires an extrinsic force, violence,
16
Perhaps Nicole Oresme recognized the problem, yet he allowed Scripture to tip the balance of probability towards the geostatic view. Cf. Oresme, Le livre, II, 25: 536– 538. See chapter four for fifteenth-century views at Cracow on nature as an intrinsic principle of motion.
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or an unnatural cause.17 Copernicus is insistent on the idea that the rotation of the celestial spheres and of Earth on its axis is natural, a capacity that is actualized in such a way as to preclude any extrinsic cause or force. But if God put them in motion, then was not a force applied? Kokowski appeals to the Aristotelian maxim in its Latin form, “Omne quod movetur ab alio movetur.”18 But Aristotle also affirms this principle even in the case of self-moved bodies, and the principle constitutes a step in his demonstration of an unmoved mover. Furthermore, Helen Lang has interpreted the principle in the case of projectile motions as a matter of “handing over” the body.19 Although “carrying” for Aristotle is a species of violent motion, for Copernicus the “carrying” of bodies in circles by spheres is not a matter of impressing a force, but natural because spherical bodies are suited for circular motion. These considerations reveal complications in Aristotle’s discussions that lead to the more metaphysical parts of his natural treatises. Did Copernicus also accept the idea that the rotation of spheres is generated by an imitation of the unmoved mover? Copernicus does not speculate. He asserts that in those cases where a sphere rotates, its rotational motion is natural, and that God endowed bodies with the properties that they have. How the potentiality is actualized is not explained. His system requires an immobile center and an immobile periphery. One could speculate that God’s “activity” other than creation requires nothing more than the removal of obstacles, not the direct exercise of a force. Copernicus even used an Aristotelian principle here against Aristotle. Forced motions are of limited duration, gradually giving way
17 As Knox pointed out to me in his reaction to this assertion, Buridan and others argued that the impetus imparted into celestial bodies would constitute an intrinsic and natural principle of motion. Yet there is an ambiguity here. The imparted force or impetus is extrinsic, and is absorbed by the body, so that it seems that the cause of its initial motion is extrinsic even if its continued motion is due to the now intrinsic impetus. Buridan’s famous discussion in Quaestiones II, q. 12, is, as Richard Dales points out, full of conditionals and subjunctives. Buridan offers this speculation as an alternative to celestial intelligences. Furthermore, the motion of the heavenly bodies would be perpetual precisely because they encounter no resistance. If there were no resistance, why would they need a force to move them? This seems to be the sort of objection made by Oresme. Elsewhere, Buridan himself appears to accept Aristotle’s doctrines of heavenly motion without qualification. See Dales, “Medieval De-animation,” 547–549. I owe the reference to Dales to Knox. See also Funkenstein, “Some Remarks,” 329–348, esp. 342. 18 Kokowski, 229–231. Compare with Aristotle, De caelo I, 2, 268b14–269 b17. 19 Lang, “Inclination, Impetus,” 224–251. For a fuller summary, see chapter four.
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to natural motion.20 As a celestial sphere or Earth rotates, its rotation is uniform and enduring, again indicating that circular motion is natural to a celestial sphere. Copernicus otherwise retained all of the other attributes and metaphors of “perfection,” “dignity,” “continuity of motion,” and of quasi-eternity and quasi-infinity in the sense that a circle has no beginning and no end. We do not know whether Copernicus maintained a theory of impetus, or, if he did, whether he thought that a celestial sphere moves a body by means of impetus. It is also not clear whether he thought God moves spheres by means of impetus. He does not explain such details or answer the remaining questions because that is not his goal. Such speculation, in fact, misses the point. Copernicus argued dialectically against the Aristotelian conclusion that a motion of Earth would be contrary to nature, and would generate violent consequences. If Earth moves and we observe no such violent consequences, then its motion must be natural (De revolutionibus I, 8). A single sphere moves a celestial body uniformly (De revolutionibus I, 4). Circular motion is the only simple natural motion, for it is the only motion that is uniform and unfailing (De revolutionibus I, 8). A sphere cannot be the cause of observed non-uniformities in the celestial motions, for this would presuppose either that the moving force varies or that the body varies (De revolutionibus I, 4). Copernicus makes this argument to support the conclusion that the observed non-uniformities are a consequence of Earth’s motions (De revolutionibus I, 4 and I, 8–9). I now turn to Copernicus’s account of the motions of elemental bodies, and again take up the questions about impetus as they relate to his remarks on elements and elemental motions. Aside from the geokinetic hypothesis, the most serious obstacle for an Aristotelian interpretation of heliocentrism is Copernicus’s account of elemental motion. 4. Impetus and the Motions of Elemental Bodies My initial approach to this question is motivated by an effort to understand Aristotle’s views on natural elemental motions. I begin with a
20 De revolutionibus I, 8: 14, 19–21: “Quibus enim vis vel impetus infertur, dissolvi necesse est, et diu subsistere nequeunt: quae vero a natura fiunt, recte se habent, et conservantur in optima sua compositione.” For the doctrines at Cracow, see chapter four.
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brief review of Aristotle’s interpretation of mathematics, and turn to a brief discussion of the analysis that led Aristotle to his conclusions about the motions of elemental bodies. Physics II, 2 and Posterior Analytics I, 13 contain the famous discussions about astronomy and mathematics and their relation to natural philosophy. Mathematics ignores strictly physical characteristics, yet astronomy examines geometrical figures that are indeed mathematical, but deals with them not so much in their mathematical as in their physical aspects.21 Aristotle refers here to form and matter, evidently regarding the formal element in astronomy as mathematical, and hence says that natural philosophy must recognize both the formal and material aspects of nature. Yet, we know that Aristotle explains the natural motions of bodies as the result of the qualitative characteristics that bodies possess. Their mathematical characteristics and the mathematical descriptions of their motions follow from their natures as inferred from their motions. This reading is also consistent with the view he expresses in Metaphysics I, 2, 1001b–1002b, where he denies that mathematical entities are primary beings. A body cannot exist without mathematical properties, yet, we can conceive of mathematical properties in the abstract (1002a4–6).22 In rejecting geocentrism and the priority that Aristotle assigned to qualitative characteristics of bodies, Copernicus evidently reversed the priority of mathematics and natural philosophy at least with respect to questions about the order of the cosmos. In Physics III, 1 and IV, 1–9, Aristotle associated motion with place, and settled the question about the order of the cosmos by means of his doctrine of natural place. Aristotle developed Plato’s ideas on place and elements in a way that led to a major departure from Plato on the origin of the cosmos. Where Plato emphasized the collection of elements as a result of separation from one another according to the principle of “like to like,” Aristotle concluded that the motions of the elements are a part of their nature. Hence, Aristotle rejected Plato’s
21 Aristotle, Posterior Analytics I, 13, 79a1–16. I have substituted a reference to astronomy here for Aristotle’s reference to optics. 22 Edward Hussey has argued for the priority of mathematics over physics in Aristotle’s account, but Hussey is careful to exclude a discussion of motion. He adds, “Aristotle shows no sign of wishing to make a complete subordination of physics to mathematics.” See Hussey, “Aristotle and Mathematics,” esp. 218 and 225.
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hypothesis about the creation of the world.23 With the doctrine of creation, Christian Aristotelians reintroduced Platonic considerations in the doctrine of place, thus combining the two and reinforcing once again a Platonic reading of Aristotle. Copernicus, for his part, was compelled to make the immovable sphere of the fixed stars the place of the universe, and he ordered the remaining spheres by sidereal periods as measured from the Sun at the center. In what follows, I examine his use of the concept of impetus, its relation to the motions of celestial spheres and bodies, and its relation to the motions of elemental bodies. The last topic also requires us to consider his remarks on the elements, especially fire. As we have noticed elsewhere, Copernicus’s remarks are often dialectical, meaning that they make clear what he rejects in the view of a predecessor or opponent. His remarks seldom allow us to attribute to him a complete theory, and so the characterization remains tentative and incomplete. As we saw in chapter four, Cracow philosophers of the 1490s reported the theory of impetus but without adopting it, or, if they adopted it, they adapted it to conform to Aristotle’s doctrine. Perhaps this explains Copernicus’s cautious use of impetus. This is again a case where scholars driven by the logic of their own reconstructions have attributed to Copernicus opinions that are stated in too global and complete a form.24 In short, Copernicus does not work out the details. He is content to point out the weaknesses in the views of his opponents, and offer alternatives that are, at best, suggestive of
23 On the comparison of Plato and Aristotle on the place and motion of the elements, see Solmsen, Aristotle’s System, 127–129 and 266–269. 24 Wolff, “Impetus Mechanics,” provides the most thorough argument in support of Copernicus’s adoption of impetus mechanics. I agree with much in Wolff ’s analysis, but his thesis of continuity between impetus mechanics and classical inertial mechanics drives him to interpret Copernicus’s remarks as implicit adoption of impetus dynamics. Wolff ’s summary of Copernicus’s modifications of traditional impetus theory, 230–231, is superb. But the logic of his argument leads him (227–230) to force Copernicus’s clear restriction of impetus to account for forced or violent motions into Copernicus’s explanation of the natural motions of spheres and the motions of the bodies that they carry. Kokowski, 230, also concludes that Copernicus implicitly applied the theory of impetus to natural motions where he discusses an unfailing cause. For a superb review and critique of the now standard misconceptions about socalled impetus mechanics, see Sarnowsky, “Concepts of Impetus.” Although modest and tentative in his remarks, Drake, “Impetus,” 45–46, already in 1975 warned readers clearly and pointedly about converting the possibility of a relation between impetus and the discovery of the law of free fall into an actuality that is not supported by the documents. See also Goddu, “Impetus.”
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a solution. It is an obvious fact that he does not work out all of the details, but his restraint and caution have not deterred some scholars from developing a full-blown theory on his behalf and attributing their views to Copernicus. This is not to say that efforts to construct complete accounts on his behalf are worthless. On the contrary, they are instructive and informative, always providing evidence with possible sources, and thus contributing to a deeper understanding of Copernicus’s achievement. I have considered them carefully, and rejected them reluctantly. In two cases “rejection” is far too strong a word. I have revised and adapted the interpretations of Michael Wolff and Michał Kokowski to my interpretative framework, although they will likely find my reinterpretation unacceptable. In yet a third case, Dilwyn Knox, we will consider the most comprehensively documented analysis of Copernicus's doctrine of gravity.25 I would like to think that most of our differences are a matter of definition and qualification. I agree that Copernicus’s account is not Aristotelian. His theory requires a drastic re-interpretation of Aristotle’s principles, yet I will argue that Copernicus used other ancient authorities to exploit inconsistencies and ambiguities in Aristotle’s texts precisely to adapt them to a heliocentric cosmology. Let us return to Copernicus’s remarks in De revolutionibus. In I, 4, after characterizing the circular motion of the heavenly spheres as an expression of its form as the simplest body,26 he asserts that a simple sphere cannot move a simple heavenly body non-uniformly.27 The only way that a heavenly body could move non-uniformly, he adds, would be by means of an inconstant force (whether extrinsic or intrinsic) or a change in the revolving body.28 He rejects these alternatives because they are unworthy of objects that are constituted in the best order.29 He concludes the chapter by suggesting that the position and motion of Earth may be the cause of the observed non-uniformities. 25
Knox, “Copernicus’s Doctrine of Gravity.” Gesamtausgabe 2: 9, lines 21–23: “Mobilitas enim sphaerae, est in circulum volvi, ipso actu formam suas exprimentis in simplicissimo corpore, . . .” 27 Ibid. 10, ll. 11–12: “Quoniam fieri nequit, ut caeleste corpus simplex uno orbe inaequaliter moveatur.” 28 As Aristotle affirms in De caelo II, 6. Compare De rev. 10, ll. 12–14: “Id enim evenire oporteret, vel propter virtutis moventis inconstantiam, sive asciticia sit, sive intima natura, vel propter revoluti corporis disparitatem.” 29 As Aristotle asserts in De caelo II, 12, 292a15–28. See section 2 above, and compare De rev. 10, ll. 14–15: “Cum vero ab utroque abhorreat intellectus, sitque indignum tale quiddam in illis existimari, quae in optima sunt ordinatione constituta: . . .” 26
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Note that Copernicus assumes that the sphere exerts a constant moving force (virtus movens expressed negatively in context as virtutis moventis inconstantiam) on the celestial body. The application of the constant moving force generates a uniform motion, which suggests that the sphere, rotating uniformly, moves the body by contact with it or by carrying it. Copernicus follows Aristotle’s “natural” view that celestial bodies do not move themselves or have independent movers but are caused to move by the spheres in which they are fixed.30 There is no suggestion here that the sphere imparts a force or a quality to the body that keeps it moving.31 This is not the doctrine of impetus as espoused by Jean Buridan, who speculated that God imparted a noncorruptible impetus to a celestial sphere.32 As Edward Rosen notes, Copernicus’s expressions here are similar to Aristotle’s in De caelo II, 6, 288a28–288b8, and are a consequence of Aristotle’s principle that everything in motion is moved by another. Copernicus does not explain precisely what moves a sphere or how the sphere moves a celestial body. He apparently thinks that the uniformly rotating sphere carries the celestial body around—only that which is simple can move what is simple, and so it is impossible that its motion should be irregular. The conclusion also echoes the passage in De caelo II, 6.33
30 Of course, Aristotle proposed two theories about the motions of the heavenly spheres. 1) On the assumption that they are animate and their motions voluntary, he proposed intelligences or separate movers whose motions are caused by the prime mover as an object of desire. 2) On the assumption that they are natural, he proposed the fifth element whose nature is to move in a circle. 31 Kokowski, 229–230, assumes that “impetus,” “force,” and “moving force” are synonyms, thus justifying the conclusion that where Copernicus refers to an “unfailing cause” (causa indeficiens), he also means “impetus.” Likewise, Wolff, 218–231, interprets causa indeficiens as a permanent impetus transferred to a “natural” motion by the supposed connection between circular and rectilinear motion. But if “natural,” it needs no impetus or extrinsic force to move it. The body merely needs the “force” to actualize its natural potentiality for circular motion. 32 Again, Copernicus’s account is based on Aristotle, De caelo II, 8, 289b30–35. Buridan proposes the theory as an alternative to Aristotle’s moving intelligences. See Johannes Buridanus, Quaestiones II, q. 12, 180–181: “Posset enim dici quod quando deus creavit sphaeras caelestes, ipse incepit movere unamquamque earum sicut voluit; et tunc ab impetu quem dedit eis, moventur adhuc, quia ille impetus non currumpitur nec diminuitur, cum non habeant resistentiam.” Compare with the edition of Patar, Ioannis Buridani Expositio, 443, lines 81–85. 33 Rosen, Commentary, 349 to p. 11:17. See Kokowski, 221–222 and 229–231, where he reads “impetus” and “moving force” as synonyms. Although he cites the Aristotelian principle in the scholastic formulation (“Omne quod movetur ab alio movetur.”), he overlooks De caelo II, 6, and does not analyze the relation between the moving
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In De revolutionibus I, 8, however, Copernicus uses the word impetus four times. In the first (Gesamtausgabe, p. 14, line 19), he associates impetus with vis, and contrasts things to which force or impetus is applied with things that are moved according to nature. Things moved by an impetus, he says, soon disintegrate (dissolvi) and cannot subsist for long. By contrast, things moved by nature are well ordered and in their best state. From this text it is clear that Copernicus uses “impetus” to account for violent motion, but the rotation of Earth on its axis, he argues, is natural and so cannot be the result of force or violence.34 The next occurrence (14, line 28) is in a context that we may consider counterfactual. Copernicus chides Ptolemy for having overlooked
sphere and the moved body. Wolff, 219–220, similarly reinterprets these passages. As I have argued, Copernicus holds the view that celestial bodies are attached to or embedded in spheres—they carry the celestial bodies. Copernicus does not discuss the relation more specifically, and nowhere does he say that the sphere imparts or gives a force to the body, which continues to move the body. Copernicus also does not explain how bodies move on epicycles or eccentreccentrics; nor does he explain the cause of Earth’s rotation on its axis. It may be that Copernicus adhered to some version of the theory of impetus, but the text from I, 4 is consistent with De caelo II, 6. Kokowski juxtaposed the Latin text of De revolutionibus in the critical edition (Warsaw) and German, French, Polish, and English translations. Translations are interpretations, of course, and Kokowski’s juxtaposition shows that the translators usually rendered “impetus” as “force,” “power,” “violence,” or some such word. The translations are not inaccurate, but reflect the views of the translators, all of whom rejected the idea that Copernicus was an adherent of the medieval theory of impetus. Kokowski notes some similarity between Copernicus’s understanding of impetus and the view held by Nicholas of Cusa, but Kokowski does not assert that Cusa was Copernicus’s source. Rosen cites a text by Cusa in his commentary, 348, but also does not assert Copernicus’s familiarity with it. Unfortunately, we do not know whether Copernicus saw or read any of Cusa’s works. In my checking of the lists of books in the libraries at Lidzbark and Frombork, I could find no mention of Nicholas of Cusa. If there was a copy in either of those libraries, it did not end up in Sweden as far as we know. The library at the Jesuit College at Braunsberg lists a copy of the works of Cusa, but its provenance is unknown. See Hipler, ZGAE, 5: 384. 34 Kokowski, 222–231, cites this text but does not consider it separately from the others, overlooking the contrast between natural and violent. Moraux, 232, also notes in relation to this passage that Copernicus does not specifically invoke projectile motion here, and so Moraux distinguishes the use of the term from Buridan’s version of the theory. As I indicated above, Wolff does not address the question why a natural motion or a natural capacity would require an impetus. He does so, I believe, because he overlooks the alternative answer to the question of what the moving cause is. Copernicus does not explain the motion of those spheres that rotate. Perhaps God moved them or removed hindrances. The sphere carries a celestial body; there is no need of an extrinsic force in the form of impetus being transferred to the body. My remarks are repetitive, but that is because the same objection applies to the relevant steps in Wolff’s and Kokowski’s arguments.
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the tremendous centrifugal force that would be generated by a swiftly moving starry vault.35 The higher they would be carried by the impetus of their motion (motus impetu) the faster they would have to move because of the expanding circumference. Again, impetus is associated with a force that would lead to an infinite motion, which, he reminds the reader, contradicts an axiom of physics that the infinite cannot be traversed or moved. Indeed, the axiom is Aristotelian.36 The implication is clear that he associates impetus with violence and disruption, not with what moves according to nature.37 The third use of the word impetus (15, line 29) occurs in a context where Copernicus explains how air, clouds, and other things suspended in air share in Earth’s rotational motion. He speculates that air may mingle with watery or earthy matter and so by its proximity to Earth would share in its constant revolution without resistance. The air and things in it closest to the surface are tranquil unless the wind or some other impetus drives them this way and that.38 Again, Copernicus applies impetus to explain a motion that is contrary to nature. Copernicus uses impetus one last time (16, line 10) in a context where he explains the compound motion of falling and rising bodies, and why their motions have a rectilinear component. Their rectilinear motion is not simple, uniform, and equal (unvarying), for they cannot be regulated by their lightness or by the impetus of their weight.39 A
35 In fact, Copernicus misrepresents Ptolemy’s view here. I owe this observation to Knox. See Knox, “Copernicus’s Doctrine,” 174, n. 81. Perhaps this was another case where Copernicus was commenting from memory or an earlier misapprehension that he did not question, even though he had texts at hand. 36 For example, De caelo III, 2. 37 Kokowski, 222–231, notes that Copernicus “explicitly applied the term impetus in three places, where he considered the issue of violent motion” (emphasis in the original). Yet, he says, 230, “we must conclude that Copernicus implicitly applied the theory of impetus also in the case of natural motion in these contexts where he writes about causa indeficientia (sic) (‘unfailing cause’).” In his footnote 8, 231, he claims that Copernicus applied the concept of impetus to both violent and natural motions. As we see, however, at the beginning of I, 8, Copernicus contrasts natural motions with violent motions, and it is only with reference to the latter that he uses impetus. 38 De rev. 15, 28–29: “Proinde tranquillus apparebit aer, qui terrae proximus, et in ipso suspensa, nisi vento, vel alio quovis impetu ultro citroque, ut contingit, agitentur.” The 1543 edition, f. 6a, reads “agitetur” at the end. Kokowski, 221–231, overlooks this passage. 39 De rev. 16, 8–10: “Praeterea quae sursum et deorsum aguntur, etiam absque circulari, non faciunt motum simplicem uniformem et aequalem. Levitate enim vel sui ponderis impetu nequeunt temperari.” In De caelo III, 2, Aristotle himself speaks of the impulse of weight and lightness. And in III, 2, 301b17–302a9, he introduces some
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falling body moves slowly at first and increases its speed as it falls, and earthly fire we perceive to relax all at once after it has achieved a high altitude.40 This behavior shows that the cause is the violence applied to earthy matter. This passage does suggest that Copernicus may have adopted the notion that the weight of a body generates an accidental impetus that causes a falling body to accelerate. But he immediately adds that the cause is violent because the motion is not simple, uniform, and equal. A little further below, however, he reminds us that bodies moving with rectilinear motion retain a circular component, so their motions are partly natural (the simple and uniform circular component) and partly violent (the accelerated component of their rectilinear motions). Here we need to introduce more careful distinctions. A falling body has a compound, not simple, motion because its motion is both circular and rectilinear. But the rectilinear component itself is compound and not simple, for the motion produced by gravity is the result of a natural appetite instilled in bodies by God. That is to say, the rectilinear motion produced by gravity is natural. The acceleration, however, requires violence, an impetus.41 As soon as such bodies have reached their own place, they cease to be heavy or light, and their rectilinear motion ends. Circular motion belongs to wholes, rectilinear to parts. He adopts the metaphor that circular abides with rectilinear as being alive abides with sickness. Here the contrast seems to be between the more perfect and the less perfect or the natural and the less natural, not the natural and the violent or contrary to nature. In playing with such comparisons, Copernicus evidently intends to strengthen his conclusion that Aristotle’s division of simple motion into three types (towards the middle, away from the middle, and around the middle) is a rational, not a real, distinction.42 Although the passage contrasting
complications in his understanding of natural motion and how some natural motions are mixed with force or a violent impulse. 40 Knox, “Copernicus’s Doctrine,” 170, interprets in sublimis as “upwards,” one of its possible meanings, but the meaning is ambiguous, and it is not clear how high Copernicus thought fire moved, possibly higher than we can actually perceive. 41 I owe the distinction between the composite motions of a falling body and the composite motions of the rectilinear component of a falling body to Knox. 42 Kokowski, leaning on Markowski, also suggests that Copernicus may have been familiar with a work that derives from Jean Buridan or some other fourteenth-century terminist source. Copernicus uses the expression “ponderis impetu” to explain the acceleration of a falling body. Scholars often claim that medieval interpreters adopted the theory of impetus to account for the acceleration of a falling body. The theory
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being alive with sickness can be interpreted as a contrast between the natural and the violent, the comparison in Copernicus seems softer. As we will see in more detail below, there are reasons for thinking that Copernicus relied on the Suda here, but Copernicus’s rendering suggests that he either softened its contrast between natural and contrary to nature or he read it as intending to soften the contrast.43 Copernicus understood impetus to account for motions that require an extrinsic force and that are not simple, uniform, and equal.44 The motion of a part towards its whole, however, is not a completely violent motion. Such motions retain a circular component, and even the rectilinear component of falling bodies is the result of heaviness, which he calls a natural desire that God implanted in parts for the purpose of gathering them together in the form of a globe (I, 9: 17, lines 29–33). It appears that Copernicus’s doctrine of motion was undeveloped. Its ambiguous and apparently inconsistent features suggest that at this juncture in his argument he was less interested in developing a complete and coherent theory than in raising doubts about Aristotle’s theory.45 His statements are intended to reveal the arbitrariness in the application of the principles. He emphasizes the variations in the dissupposedly corrects Aristotle’s idea that the speed of a body is directly proportional to its weight and inversely proportional to the resistance of the medium (V α W/R, in modern form). Aristotle's apparent belief that one can calculate average speed in this way and the implicit claim that he was ignorant of the fact that a body accelerates as it falls are preposterous on the face of it. It is difficult to believe that observers seeing the different impacts caused by the same body falling over a greater distance or time would not conclude that the body has increased in speed, even if they were in doubt about whether or not the speed increased uniformly. In fact, in De caelo III, 2, 301b21–23, Aristotle asserts that a body accelerates as it falls, and explains that a force makes a falling body move more quickly downwards. The point here is that a force accelerates a natural motion. 43 Hooykaas, “Aristotelian Background,” 111–116, interprets Copernicus’s use of the analogy between healing and the rectilinear motion of a falling body in Aristotelian terms as not wholly natural and not unnatural or violent either. This reading seems to me to square with the ambiguity in Copernicus’s account. Hooykaas suggests that Copernicus could have developed this account by relying on scholastic commentaries, but as we shall see below, Knox has suggested an alternative source, and in my view, I believe that he has found the text on which Copernicus relied for this reading. 44 Perhaps this is what he understood by Aristotle’s remark that “force” is a cause in something else or it is in the thing itself regarded as something else. Weight in a heavy body seems to generate such a force. 45 In comments shared with me, Knox argues that the construction of an account of elemental motion was critical for the reception of Copernicus’s cosmology. The outcome, he argues, was a theory that was consistent, if tortuous and undeveloped. According to Knox, Copernicus intended to do more than raise doubts about Aristotle’s doctrine. It seems to me that its undeveloped character rather supports the
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tances of celestial bodies from Earth (I, 8 and I, 9) to refute the Aristotelian division between motion away from and motion towards the center. With exception of the stars, the observations confirm that all celestial bodies do both.46 He rejects the generalization that a simple body has a simple motion. His principal aim was to move readers to accept the greater probability of Earth’s motions. This still leaves us, however, to examine his remarks about elemental motions more closely. First, Copernicus adopts an account of the elements that diverges from Aristotle’s. The ultimate source seems to be Plato, but the analysis is driven by his recognition of the need to assimilate air to water and earth. He needs to explain how air shares in the motion of a globe that is earthly and watery. He may have rejected Aristotle’s views about elemental fire and aether, but his remarks are ambiguous (I, 7–8 and I, 10).47 He makes these remarks almost in passing. In the autograph he also refers to the theory of atoms to make a point about the immensity of the universe (I, 6), but it is not clear from the comment that he adhered to the theory.48 One may assume from his description of the Sun as a lamp and lantern that he believed it to possess fire, but he does not say so explicitly. Aleksander Birkenmajer pointed out that Copernicus’s reference to blazing smoke (“fumum ardentem”) comes from Aristotle, but he added that the reference to its explosive nature resembles a comment by the Stoic Cleanthes cited by Cicero. The Stoics did distinguish between terrestrial fire and the element fire that is proper to the Sun, an opinion refuted by Aristotle.49 Evidently, Copernicus rejected Aristotle’s speculation about aether, for he attributes the circular motion of a sphere to its geometrical form, not aether.50 In I, 8, he says that earthly fire is the only fire we see, but he refers in I, 10 (19, line 15) to “aether” in a place where we would normally see “fire,” and a little above (line 11), in the autograph, he rhetorical strategy of introducing doubts about Aristotle’s doctrine and suggesting alternatives that would reinforce those doubts. 46 But see the explanation by Johannes Versoris, Quaestiones de caelo et mundo I, [q. 11], f. 3vb. See chapter four, and Goddu, “Sources” and “Teaching.” 47 Rosen’s comment, 353 to p. 17:16, that Copernicus rejects the elemental fire of the traditional cosmology requires qualification. See also Kokowski, 55. 48 Someone, probably Copernicus himself, deleted the passage. See Rosen, 350 to p. 14:19, for comment. 49 Birkenmajer, 368 to p. 16, 27–29. He refers to De generatione II, 4, 331b25–26; and Meteorologica IV, 9, 388a2. 50 Rosen, 348 to p. 10:30.
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again uses “aether” as a synonym for what is called the “fiery element” (“. . . et si placet eitam aethera, quod igneum vocant elementum”).51 From all of these considerations and opinions I conclude that Rosen was hasty in claiming that Copernicus rejected fire as an element. Copernicus says that light bodies such as fire move upwards and in a straight line, but he also says that the motion is a compound of circular and straight. As it rises upwards, it suddenly relaxes, which suggests that once it has reached its proper place, its motion is circular. There are at least four possible sources for Copernicus’s account. The first source is Aristotle himself, in a passage that Rosen evidently overlooked. In Meteorology I, 3, 340b20–25, Aristotle says the following:52 So what is heaviest and coldest, that is, earth and water, separates off at the centre or round the centre : immediately round them are air and what we are accustomed to call fire, though it is not really fire : for fire is an excess of heat and a sort of boiling. But we must understand that of what we call air the partimmediately surrounds the earth is moist and hot because it is vaporous and contains exhalations from the earth, but that the part above this is hot and dry.
Note Aristotle’s distinction here between “fire” and “what we are accustomed to call fire.” He continues at 340b30–31: “We must suppose therefore that the reason why the clouds do not form in the upper region is that it contains not air only but rather a sort of fire.” And then a little below at 340b37–341a9 adds:53 It moves in a circle because it is carried round by the motion of the heavens. For fire [i.e. what we are accustomed to call fire] is contiguous with the element in the celestial regions, and air contiguous with fire, and their movement prevents any condensation; for any particle [of fire] that becomes heavy sinks down, the heat in it being expelled and rising into the upper region, and other particles in turn are carried up with the fiery exhalation : thus the one layer is always and continually full of air, the other of fire, and each one of them is in constant process of transformation into the other.
Copernicus’s statements seem to echo the ambiguity in Aristotle’s own account.
51 Opera omnia 1: fol. 8v, line 16. Copernicus evidently cancelled the word “aethera.” In Meteorologica I, 3, Aristotle allows for variety in the purity of ether. 52 I have relied here on Aristotle, Meteorologica, tr. Lee. 53 Ibid. The comments in brackets are supplied by Lee in footnotes.
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A second source is Pliny, Natural History II, III, 10–11, where he places fire in the region of the blazing stars, and echoes the Stoic theory of cosmic cohesion. We know that Copernicus relied on Pliny for some of the comments that he makes that reflect Stoic conceptions of force and constraint.54 Earthly fire is the only fire that we perceive, and in I, 10 Copernicus refers to “what is called ‘the element of fire’.” For the third source Dilwyn Knox argues that the usage derives ultimately from Plato (Timaeus 58d), and that Copernicus probably got it directly from pseudo-Plutarch, Placita philosophorum II, 7.55 In these passages we find distinctions between types of fire and also comparisons with explosion and expulsion. One could argue, however, that Copernicus followed standard conflations of Platonic, Aristotelian, and Stoic doctrines with little attention to inconsistencies. Commentators were more concerned with the general configuration of the cosmos than with the details for their own sake. Even if he relied on Pliny, Plato, and the Placita philosophorum, Copernicus may have interpreted them as roughly consistent with Aristotle’s own ambiguous remarks, but Copernicus used them to argue that the other elements share in the motion of the Earth. The Stoic sources served his purposes.56 This now brings us back to Copernicus’s account of elemental motion. There are clearly non-Aristotelian elements in Copernicus’s account. Wolff and Kokowski tend to regard Copernicus’s comments as anti-Aristotelian. Kokowski argues that Copernicus held some
54 Obrist, Cosmologie médiévale, 253–255, comments on Pliny’s reinforcement of Stoic doctrines. See also Knox, “Copernicus’s Doctrine,” 182–193, where he considers Aristotle, scholastic interpreters, Plutarch, Pliny, and Cicero as sources for Copernicus’s account of gravity. Knox’s distinction between a physical and teleological account of gravity is important. He rejects Krafft’s argument that Copernicus relied on Plutarch’s De facie. See Krafft, “Copernicus Retroversus II.” According to Knox, Pliny and Cicero were almost certainly Copernicus’s sources for his teleological doctrine, although he thinks that Cicero provided the closest doctrinal fit. See Pliny, Natural History II, II, 5, and II, LXV, 163–164. For Cicero, he cites De natura deorum II. xlv. 115–xlvi. 117. 55 Knox, “Ficino and Copernicus,” 412–413, note 54. Compare Kokowski, 55. I believe that Wolff, 221, goes too far in maintaining that “Copernicus intends to get rid of the five Arisotelian elements, . . .” 56 I have tried to conform my interpretation as much as possible to Knox’s authoritative acquaintance with the sources, but he emphasizes departures from Aristotle where, it seems to me, Copernicus has already subordinated his interpretation to the geokinetic theory.
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version of impetus theory that ultimately derives from Buridan.57 Birkenmajer and Moraux, on the contrary, have shown that Copernicus’s comments are not compatible with the details of Buridan’s account.58 Wolff maintains that Copernicus modified the traditional theory of impetus.59 Rosen has also emphasized the difference between Nicholas of Cusa’s “initial impulse” that God imparted to the celestial spheres and Copernicus’s explicit comments.60 Also by contrast, Knox has made a meticulous search for the sources of Copernicus’s comments, from which he has tried to reconstruct Copernicus’s theory of elemental motion. First, Knox argues that Copernicus relied on Pliny and/or Cicero, especially for the teleological doctrine of gravity. Second, he argues persuasively that Copernicus used the Suidae lexicon, and relied on it for the physical doctrine of gravity. Third, he contends that Copernicus’s doctrine of gravity has more in common with the idea presented in the Suda under the lemma kínesis than with any other supposed source. The version in the Suda may derive ultimately from Johannes Philoponus. Knox, of course, also emphasizes the differences, especially in details, between Aristotle’s and Copernicus’s conceptions. For example, Aristotle held that a piece of earth displaced from the center of the universe would return in a straight line to the center regardless of whether or not there was any Earth there already. Not that Aristotle admitted such a possibility really, but the point is that his doctrine of natural place established directionality as absolute, not relative. The same holds for the light element, fire, and for the “circular” element, aether. Copernicus, on the other hand, regards natural place as the whole to which a heavy body (water and earth) moves because God has implanted in the parts a natural desire to be reunited with their whole where they move only with circular motion. Air and presumably fire behave similarly.61 The principle of returning to their respective wholes applies, Copernicus conjectures, to the Sun, Moon, and all of the planets. Copernicus’s natural place, then, is relative, not absolute.
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Kokowski, 56 and 218–231. Birkenmajer, 368–370; compare Moraux, 232. 59 Wolff, 230–231. 60 Rosen, 348. 61 Knox, “Ficino and Copernicus,” 413–414. In fact, Copernicus argues that as elements return to their wholes, their motion is compounded of straight and circular components. Aristotle’s argument is in De caelo IV, 3. 58
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The idea of returning to a sphere rectilinearly where an element resumes its natural circular motion derives from several ancient sources. As Knox shows, it became a standard Neoplatonic doctrine. Philoponus adopted it, and it reappears in Nicole Oresme’s Livre du ciel et du monde, Nicholas of Cusa’s De docta ignorantia, and Giorgio Valla’s De expetendis et fugiendis rebus. As we saw in chapter seven, Copernicus used Valla’s book extensively, but Knox says that while its account of the doctrine does correspond to Copernicus’s version, it is brief and lacks the details found in Copernicus’s version.62 Next, Knox considers carefully but also eliminates Ficino as the source, concluding that a better fit is a quotation of presumably Philoponus’s account in the Suda under the lemma kínesis as we indicated above.63 I cite the Latin version of the Suda provided in the footnotes of the 1853 edition, and translate the relevant part here:64
62 Knox, “Ficino and Copernicus,” 415, n. 59. In “Copernicus’s Doctrine,” 194–208, esp. 199–201, Knox reviews in detail all of the relevant possibilities. 63 On Ficino and Neoplatonic sources in general, see Schmeidler, Kommentar, 184. 64 In “Copernicus’s Doctrine,” 194–208, Knox bases his analysis on editions of the Suda from 1499 and 1514, one or both of which Copernicus likely knew and used. His translation of the relevant passage is reasonably close in its essentials with one significant exception to my translation of the Latin translation that I used. Of course, readers should consult Knox’s more authoritative source and translation. See Suidae lexicon, columns 260–264. For the complete entry, see Appendix VIII. Here I quote only the translated passage: “ Motus etiam existit, cum res alium ex alio locum mutant.—Quae per orbem aguntur interitu vacant.—Aliter de motu. Non est, inquit [Aristoteles,] glebae naturale moveri deorsum, neque igni sursum ferri: neque enim talis motionis principium in se habent, sed extrinsecus ab alio moventur. unumquodque enim elementum in suo toto quiescit: quippe tota vel stare volunt vel in orbem moveri: est autem motio in orbem quies quaedam. Iam secundum naturam suam gleba cum movetur, in suo toto manet immobilis; quemadmodum hic ignis in sua sphaera. cum vero gleba vel aqua vel hic aer extra locum naturalem existit, singula ad totum suum tendunt, et quieti naturali restitui cupiunt. nam ab vi quadam externa ex loco naturali pulsa moventur ea via, quae est secundum naturam. quando quidem sic moventur, ut quae in alieno loco existant, et toto suo contra naturam privata sint. Non igitur motus ille secundum naturam est, quo res ad locum naturalem tendunt (alioquin enim ipsa tota sic moverentur), sed viae ad id quod est secundum naturam. Potest tamen etiam motus ille naturae consentaneus dici: eo nimirum sensu quo dicimus sanitatem esse secundum naturam, morbum vero contra naturam. illa ducit ad id quod est secundum naturam hic vero ad id quod est contra naturam. id enim quod primum movet, si quidem corpus sit, ipsum etiam movetur. movet enim baculum ianuam, et baculum manus, quae non manet immota, sed ipsa movetur. quod si primum movens sit incorporeum, nihil necesse est ipsum quoque moveri, dum alterum movet. nam deus, qui universum movet, ipse est immotus, utpote stabilem habens essentiam et facultatem et actionem.”
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chapter nine Motion also occurs when a thing moves from one place to another place.—Things that are moved in a circle are incorruptible.65—Another account of motion. It is not, says [Aristotle]66 natural for a clod of earth to be moved downwards, nor for fire to be carried upwards: for they do not have the beginning of such motion in themselves, but are moved by something extrinsic. For an element rests when it is together with the whole [of which it is a part]; in fact the whole either tries to remain at rest or to be moved in a circle: but motion in a circle is a kind of rest. When the clod of earth is moved according to its nature, it remains immobile when together with the whole [of which it is a part], just as fire does when it is in its sphere. But when earth, water, or air is outside of its natural place, each tends to its whole, and desires [is inclined] to be restored to its natural quiet. For things moved from their natural place by a certain external impulse are moved in a way that is according to nature. When things are so moved that they are in another place, they are deprived of their whole, contrary to nature. Therefore such a motion by which they tend to their natural place is not natural (otherwise the whole itself would be so moved), but the ways to those places are natural.67 Nevertheless the motion can be said to be consistent with nature: in the same way in which we say that health is natural and disease is contrary to nature. Health leads to that which is natural, but disease to that which is contrary to nature. For that which moves first, if it is a body, is itself moved. When a staff moves a door, and my hand, which does not remain unmoved, moves the staff, it is moved by itself. But if the first mover is incorporeal, it is not necessary for it to be moved itself while the other moves. For God, who moves the entire universe, is himself unmoved, for he has an immutable essence, power, and action.
The context of these assertions is the discussion of Aristotle’s De anima I by Philoponus. The issues concern self-moving beings, the motions of
65 I have interpreted the Latin passage by comparison with the Greek version, which my colleague Nathaniel Desrosiers translated for me. 66 The editors’ addition that the doctrine is from Aristotle is impossible. As Knox suggests in a note to his translation, presumably Philoponus is meant, and I agree. 67 As in Aristotle, De caelo III, 2, the implication here is that the cause, though in the body, is accidental to it, and hence not part of its essence. Knox, however, translates this part thus: “Therefore motion towards natural place is not by nature. For it is the wholes that produce these motions. Hence it is that these motions of parts are not according to nature but are paths to what is natural. It is possible to move ‘according to nature’ otherwise, as when we say that recovering health is according to nature and sickness is, so to speak, contrary to nature. For the former leads to what is according to nature, the latter to what is contrary to nature.” Even in Knox’s translation, however, there still appears to be an ambiguity inasmuch as we are told that “recovering health” is according to nature. It would follow that a body moving to its natural place would be analogous to recovering health, and so according to nature, and it is an ambiguity that Copernicus himself reflects.
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bodies, projectile motions, and the contrast between Plato and Aristotle. In my view, the passage along with other evidence confirms Knox’s speculation that Copernicus used it in his account of natural place and elemental bodies in De revolutionibus I, 8. The similarity between Copernicus’s remarks and the comments in the text are especially clear in the part that has to do with the tendency of bodies to be reunited with their wholes in their proper spheres. The same ambiguity arises about whether such motions are natural or violent. The motion by means of which a thing tends to its natural place is not natural, but the things to which they move are according to nature.68 The motion can be said to consent to nature in the sense in which we say that health is natural and disease contrary to nature. The one leads to that which is natural, the other to that which is contrary to nature, but recovering health is motion back to its natural state. By analogy, even the rectilinear component of a falling body is natural motion to the extent that it is a motion back to its natural state. Even in the case of a moving body, the first mover moves itself, and here the entry uses an example which is reminiscent of the theory of impetus. Yet it can also be read as a confirmation of Aristotle’s principle that everything moved is moved by another, as applied especially in De caelo III, 2.69 That said, we now consider the differences between the entry in the Suda and Copernicus’s comments. First, the body in its proper sphere remains at rest, for there is no suggestion here, except for the equivalence it proposes between motion in a circle and rest, that as a body achieves its natural place it moves in a circle. Motion in a circle is natural for the element fire (and perhaps air) in its sphere, but the natural motion of earth is rest at the center. Indeed, Copernicus requires an explanation for the circular motion of the air nearest to Earth, and here we saw him appeal to conformity of nature or proximity as possible explanations.70 Second, the entry in the Suda tends to regard the
68 This is the significant departure from the Greek to which I alluded earlier. In his comments on my chapter, Knox pointed out that there is no suggestion in the Greek that the path itself is natural. Rather is it the things to which they move that are according to nature. 69 Hooykaas, “Aristotelian Background,” again reads the comparison between recovering health and the rectilinear motion of a falling body in Aristotelian terms as a return to the natural perfection of a body’s Form. 70 Ingram, “Revolution,” 28 and 32, note 18, maintains that impetus helped to explain why falling bodies and airborne phenomena are not left behind by the rotation of Earth. Perhaps, but Copernicus does not appeal to impetus explicitly, rather
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motion of a body back to its whole as violent. Third, they move along a path to those things that are according to nature. Fourth, the entry is less ambiguous than Copernicus’s comparison in asserting that health is natural and sickness is contrary to nature. It may be, however, that Copernicus read the passage as softening the contrast, for Copernicus is insistent on the idea that motion in a circle is more natural than the compound motion of a falling body. And he reflects the same ambiguity in referring to its state as, not unnatural, but less natural. The rectilinear component requires a force, but Copernicus characterizes the tendency in things to return to their whole or sphere as implanted in them by God. This characterization suggests that the inclination is natural and that the motion, while not perfect, is partly natural. Because Copernicus must preserve its motion as compound and hence partly circular, it cannot be completely violent. Hence, he softens the contrast and makes it relative to conform to his theory. I believe that Copernicus combined it with Aristotle’s own account of the force involved in an upward or downward motion as partly natural and partly violent or less natural. Copernicus insists that circular motion is natural, and motion towards a whole is a compound of circular (natural) and rectilinear (partly violent and partly natural, or less natural) motion. Sickness for him is not contrary to nature but nature in a less perfect state. As in scholastic interpretations of Aristotle, Copernicus’s contrast between natural circular motion and rectilinear motion draws on the distinction between the essential and proper as opposed to the accidental and less proper.71 On the whole, then, I am inclined to agree with the view of Aleksander Birkenmajer. While claiming to recognize Copernicus’s reliance on several ancient and Renaissance sources, Birkenmajer nonetheless characterized Copernicus’s natural philosophy as a transformation of Aristotelian doctrine.72 He acknowledged Copernicus’s divergence from Aristotle—most of the differences are obvious, but he rightly distinguished between unavoidable departures from and explicit rejection
he refers to conformity in nature or proximity, indicating that he has not decided on a solution. 71 Compare with chapter four. 72 In fact, however, it is not at all clear to what extent Birkenmajer recognized Copernicus’s reliance on other sources for his doctrines in natural philosophy. In my view, Knox’s studies require us to take these sources far more seriously than any other account has to date.
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of Aristotle’s view.73 Knox has made the differences even clearer and persuaded me to reformulate the role of non-Aristotelian and nonscholastic sources in Copernicus’s accounts of gravity and elemental motion, but the passage in the Suda persuades me that Copernicus adopted the view presented there only in part and tried to reconcile it with his own conception of natural circular motion and the compound motions of rising and falling bodies. From the brief account that Copernicus provides, we are hardly able to construct a coherent physics of elemental motion, or attribute to him the traditional theory of impetus. As Copernicus wrote this chapter in the 1520s, he was probably mindful of disagreements among scholastics about the interpretation of De caelo III, 2 and perhaps Meteorology I, 3. Copernicus tried to move readers to reconsider the arguments in support of geocentrism. His principal aim was to reveal the arbitrariness in the application of his opponents’ own principles by adapting them to the heliocentric theory. Once he established the plausiblity of Earth’s rotation on its axis, he turned immediately in I, 9 to a consideration of other possible motions. All of that said, I beg the reader’s indulgence for the repetitiousness of the above summary and for the following attempt to render Copernicus’s theory as coherent as possible. Copernicus does not think of Earth as floating through space in an orbit; it is being carried with the Moon by a sphere in which it is embedded or to which it is attached.74 He nowhere explains any of this, namely, how the spheres carry or move the planets, probably because he simply took it over as a standard way of combining Ptolemy’s mathematical models with the doctrine of spheres. As he turns to the question of Earth’s rotation on its axis, he appeals to its form. But not all spheres rotate on their axes, or if he thinks so, he does not say so. He does not explicitly say that the Sun rotates on its axis, nor does the Moon, nor do the planets, probably because of the obvious fact that he has no observational evidence that they rotate. Observation shows that the planetary spheres move in circles around Earth in the geocentric system and around the Sun in his system. There is absolutely no explanation of the relation between the circular motions of the spheres and the motions of the bodies in the spheres
73 74
A. Birkenmajer, Études, 372. I will turn in detail to the role of spheres in Copernicus’s cosmology in chapter ten.
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other than the traditional belief and claim that the spheres carry and move the planets. His argument that Earth’s rotation is natural as following its form is dialectical. If it rotates and if there are no violent consequences, then it must be natural. As bodies fall, their motions must be compound, partly circular and partly rectilinear. His purpose in I, 8 was to raise doubts and questions about Aristotelian assumptions and conclusions, and to suggest how the concepts and distinctions could be linked together with other accounts in support of Earth’s axial rotation as more probable. All of that said, however, we still have to try to put this together into something that is at least apparently coherent. Copernicus does not explain how a celestial sphere moves the bodies in it. It appears that he intended his remark about form and spherical shape as a response to two objections. The first, about which he is explicit, is that the circular motion of a sphere is natural, not violent. The form or shape, however, indicates a potentiality, not necessarily actualized. The second objection that is rather implied than stated is more specific. How can a celestial sphere move a bulky object like Earth, a corollary to the objection against placing terrestrial elements in the heavens? By that move Copernicus seemed to shatter the division between celestial and terrestrial elements. He makes two responses to that objection. Ancient authorities, including Aristotle, did not make an absolute division between the celestial and terrestrial. The celestial influences the terrestrial by its circular motion, and there is ambiguity about elements such as aether and fire. Second, the emphasis on Earth’s spherical form means that it has a natural capacity for circular motion and rotation on its axis. The circular motion of the celestial sphere actualizes that potentiality just as the circular motions of the heavens move the bodies and elements below them in Aristotle’s system. Embedded as it is in a celestial sphere, Earth moves in a circle and rotates because its capacity for circular motion has been actualized. As in Aristotle, the higher can act on the lower, that is, the celestial sphere acts on the bodies embedded in it without violence. If correct, the answer is not completely satisfactory, for it does not explain why Earth specifically rotates on its axis.75 The argument from simplicity is
75 Of course, the answer to this question turns out to be very complicated, and was not addressed until cosmologists realized that the solution requires a historical reconstruction of the formation of the solar system.
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also a response to an objection, not a physical explanation. Of course, if Earth did not rotate on its axis, one side would always face the Sun and the other the night sky, so it must rotate, but that is not a physical explanation of its motion. That seems to be as far as Copernicus progressed in dealing with such questions. 5. Infinity and the Finiteness of the Cosmos A similar misunderstanding has arisen with regard to Copernicus’s views about whether the universe is finite or infinite. His system is properly called “heliostatic” for three reasons. (1) The Sun is stationary; (2) the center of Earth’s orbit is the mean Sun, eccentric to the Sun, that is, the center of Earth’s orbit is the geometrical center of his planetary models; and (3) the Sun is the center of the starry vault. He placed all of the stars at an equal distance from the center in the eighth sphere. The confusion about infinity has three sources. First, the failure to observe stellar parallax made the stars much farther than anyone had ever imagined, thus suggesting that the universe might be infinite. In the autograph copy of De revolutionibus, Copernicus said that the universe is infinite-like or similar to the infinite, meaning immense, not infinite pure and simple.76 And if he was referring to the space between the spheres of Saturn and the fixed stars, he suggested that God placed the stars at such a great distance so that we might more easily grasp the difference between planetary phenomena and the fixed stars. The planetary phenomena are effects of the Earth’s annual motion, but these phenomena do not appear in the fixed stars.77 The second source of confusion is a text by Copernicus himself where he raised the question about the infinity of the universe, and did
76 De revolutionibus, Appendix I, 490, 6–7: “Mundum . . . similem infinito.” The comment on the size of the universe appeared at the beginning of Book II, but in his translation Rosen added it with an explanation near the end of I, 11: 26, 39; the Warsaw edition places it at the beginning of I, 12. The same expression is used by Rheticus in Narratio prima. A similar expression appears in Pliny, Naturalis historia, II, 1: “[Mundum est] . . . finitus et infinito similis.” Szczeciniarz, 83–91, evidently believes that an infinite universe corresponds to Copernicus’s true view and his rhetoric. On 248 and elsewhere, Szczeciniarz notes Copernicus’s affirmation of a finite universe, implying that Copernicus contradicts himself. A similar problem arises with Szczeciniarz’s insistence that Copernicus proposed a homogeneous universe, a suggestion that he qualifies on 243 without qualifying his conclusion. 77 De revolutionibus I, 10: 21, 17–18.
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not settle it decisively, leaving it to natural philosophers to answer. We will return to that text momentarily. Third, the illustration accompanying the partial English translation of Book I of De revolutionibus by Thomas Digges in 1576 appeared to commit the theory to an infinite expanse of stars. Digges also retained the position of the Sun at the center, however, suggesting either that the illustration may not have represented his view or that he still did not quite grasp Copernicus’s mathematics or the idea in the radical way that Giordano Bruno proclaimed in 1584.78 The subsequent failure to observe stellar parallax with the telescopes available in the seventeenth century tended to support belief in the infinity of the universe. Copernicus’s intention is clear with exception of one text. His entire system with the stars located in the eighth sphere and the Sun at the geometrical center of the complete system fits a finite conception of the universe. Why, then, did he not answer his own question decisively? The text in question is about the space beyond the eighth sphere. Responding dialectically to objections against the Earth’s diurnal and annual motions, he wondered why geocentrists were not more worried about the centrifugal effects of a rapidly spinning eighth sphere contained by nothing. Would not the effect lead to an infinite expansion of the universe, in which case how could the eighth sphere move at all since, as every Aristotelian knows, an infinite space cannot be traversed in a finite time?79 With this answer he reflected the fact that natural philosophers were of several minds on the existence and nature of extra-cosmic void. If it existed, then did it possess matter of some sort? Was it like very attenuated air? Did space somehow fix the finite system of starry and planetary spheres? Even if there were nothing, it would be infinite in the sense of being without limit and capable of receiving bodies. Nearly everyone agreed that the universe itself did not move. After all, even Aristotle maintained that “heavy” bodies would have no natural motion in a void.80 The existence and nature of extra-cosmic void, then, were very much open questions in
78 Bruno, La cena de la ceneri (1584) and De l’infinito universo e mondi (1584). Nicholas of Cusa, De docta ignorantia II, 8, seems to affirm an infinite universe, but the subtle way in which he expressed it could be interpreted modally. It is possible from the point of view of God’s power that the universe could be greater. This conception of infinity is compatible with an actually finite universe. See Lai, “Nicholas of Cusa,” 161–167. On Digges, see also Granada, “Origins,” 518. 79 De revolutionibus I, 8. 80 Physics IV, 8, 215a5–18.
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the fifteenth and sixteenth centuries, and Copernicus reflected the lack of consensus. Whether the expanse beyond the eighth sphere is finite or infinite, it would make more sense to suppose the immobility of the eighth sphere and of the container of everything than to suppose that what is contained remains immobile.81 Copernicus demonstrated his dialectical ability to take Aristotelian principles and use them in support of his own view.82 Without maintaining that Copernicus would have remembered details of the teaching at Cracow on the subjects of place, void, and motion, I draw your attention to doctrines taught in the second half of the fifteenth century at the university. The discussions relevant to my inquiry begin with the problem of the place of the cosmos. Philosophers, astronomers, and theologians disagreed about the number of spheres, and some of them concluded that the last sphere, whatever its number, is not in place. The Cracow scholars who taught in the last decade of the century, however, maintained that the last sphere is in place not in the usual way but in an accidental sense, not per se.83 Cracow authors who held that view based it on the theological conception of the empyrean, the heaven that surrounded the last sphere proposed by philosophers and astronomers. Copernicus’s critique of the motion of the last sphere suggests that he was familiar with scholastic discussions and that he did not rely exclusively on the texts of Aristotle. It is not far-fetched to suppose that his speculations here may derive from the questions discussed at Cracow. Cracow natural philosophers were divided on the question of void. Some of them conceived of void as a place where bodies do not exist, but which is capable of receiving bodies. This combination of an Aristotelian with Platonic or Stoic conception, and the fact that one teacher devoted comments to other ancient conceptions, especially Plato’s, could very well have made an impression on Copernicus. For him the issue arises only with respect to the space beyond the eighth sphere. We do not know exactly which texts of Plato he may have read, but as late as 1542 he evidently regarded the diverse points of view about the
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The argument appears near the end of I, 8. Compare with Aristotle, De caelo I, 5. As Knox suggested in his comments on this chapter, however, this is another respect in which Copernicus would have found Stoic sources congenial. 83 The last sphere was said to be accidentally in place in one of three ways, in relation to bodies on either side, to bodies immediately inside, or to the center. See chapter four. 82
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existence of void and the infinity of space as equally probable because they had not yet been settled conclusively by natural philosophers.84 Copernicus decisively affirmed the finite extent of the planetary spheres up through the sphere of the stars as one, whole, spherical body with a definite geometrical center. Perhaps thinking of the discussions at Cracow and other speculations about the place of God and the place of the finite system of Sun, planets, and stars, he left the question about the infinity of the void beyond the eighth sphere to natural philosophers. Assembling the results of my analysis in the final chapter, however, will lead me to modify this provisional conclusion reached in the context of natural philosophy. 6. Summary In trying to solve the problems of Ptolemaic astronomy, Copernicus discovered the reasons why the Ptolemaic planetary models link the planetary motions to the position of the Sun. He discovered the ordering of the planets, and how their ordering uniquely explains the phenomena of bounded elongation and retrograde motions as a natural and necessary consequence of the planets’ order and of the Earth’s annual motion. Convinced that he was right and convinced that Aristotelian principles were generally correct, he used Aristotelian principles and the views of Aristotle’s critics to criticize the theory of geocentrism. He pounced on the assumption that all observed natural motions are simple. That was the fatal flaw in Aristotelian cosmology. To correct that mistake he tried to adapt Aristotelian principles to the heliocentric system. He took advantage of centuries of combinations of Aristotelian principles with other beliefs, with empirical discoveries, with other philosophical schools, and he took advantage of humanists who harmonized Plato with Aristotle to suggest his own quasi-Aristotelian system.
84 Markowski, 173–179. For Stoic sources and the medieval background, see Grant, Much Ado About Nothing. See chapter four for details. On Asclepius and Hermes Trismegistus, referred to by Copernicus in I, 10, see Grant, Much Ado, 114–115. See also Rosen, Commentary to Revolutions, 359. Marsilio Ficino translated Asclepius into Latin in the fifteenth century.
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The place of natural philosophy in Copernicus’s reflections became clear. On the structure of the universe, natural philosophy is subordinate to astronomy and mathematics. The subordination, which he did not make general, depends on the following considerations: the requirements of geometry or geometrical models, ordering of parts according to a mathematical rule or relation (siderial periods), and mathematical results such as the ratios of planetary orbital radii. For all of these reasons he concluded that natural philosophers should yield to astronomers on the problem of the position and motion of Earth. An epistemological feature of his natural philosophy was his reluctance to draw conclusions of an empirical nature without compelling astronomical reasons or empirical evidence as, for example, in his reluctance to speculate about the axial rotation of the Sun, Moon, and planets other than Earth. He was suspicious of speculation based only on dialectical considerations, which he characterized pejoratively as logical exercises or merely acts of reason.85 The role of natural philosophy in his reflections also became clear— he knew he had to persuade the Aristotelians to reconsider their assumptions. As we all know, his efforts to persuade Aristotelians have to be counted in the short term among the most miserable failures in the history of philosophy. Some sixteenth and seventeenth-century Aristotelians displayed flexibility on the question of the Earth’s motion, but most sixteenth-century Aristotelians rejected the theory out of hand, just as Copernicus had feared. Even the Aristotelians who attributed an axial rotation to Earth explained it, however, as the result of an extrinsic force, not a natural motion. Also, some Aristotelians who adopted this view remained geocentrists. None followed the revisions of Aristotle that Copernicus had recommended. Without Copernicus’s aesthetic vision and mathematical intuition that the planets were ordered in one, and only one, way, late scholastic revisions of Aristotle lacked the coherence of Copernicus’s proposals. Aristotelians continued to maintain that the motion of heavy bodies downwards is simple; that was the assumption that Copernicus rejected.86 In the sixteenth century some Renaissance humanists questioned Aristotle’s
85 De revolutionibus I, 8: 16, 17–20: “Nempe et hoc, quod Aristoteles in tria genera distribuit motum simplicem, a medio, ad medium, et circa medium, rationis solummodo actus putabitur, quemadmodum lineam, punctum et superficiem secernimus quidem, cum tamen unum sine alio subsistere nequeat, et nullum eorum sine corpore.” 86 For the exceptions, see Grant, Defense.
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allegedly infallible authority, but it would take another thirty years after 1543 before explicitly anti-Aristotelian arguments in support of heliocentrism appear and yet another ten years or so before some of those attacks become vicious. We cannot fairly count Copernicus among those critics and certainly not among the vicious calumniators of Aristotle. One could say that sixteenth-century Aristotelians themselves provoked those kinds of reactions as their credibility waned. The discovery of cometary parallax in the 1570s destroyed the theory of celestial spheres of ancient cosmology.87 Although it would take another eighty years to become obvious, the discovery of cometary parallax also doomed Copernicus’s effort to revise Aristotelian natural philosophy.88 In this chapter I have tried to provide the likeliest answers to questions that scholars have posed about Copernicus’s natural philosophy. I have based the answers in part on an acquaintance with Copernicus’s intellectual milieu, that is, sources that we either know or reasonably assume were available to him,89 and in part on a systematic approach to his major works. In the next chapter I turn to questions about Copernicus’s beliefs about hypotheses, spheres, celestial matter, and mathematical models.
87 Swerdlow’s analysis, “PSEUDODOXIA,” 147–148, is persuasive. See Jervis, Cometary Theory. 88 It goes almost without saying that the effort to revise Aristotelian natural philosophy continued. Indeed, scholars continue to revise Aristotelian natural philosophy. The mysteries of quantum mechanics inspire some to return to Aristotelian holism as an alternative to mechanistic principles of natural philosophy. 89 Although I have examined many of the better-known works, I have relied on Dilwyn Knox’s extensive acquaintance with and persuasive interpretation of the sources.
CHAPTER TEN
COPERNICUS AS MATHEMATICAL COSMOLOGIST 1. Introduction By the time Copernicus began writing the substantial parts of De revolutionibus in the 1520s, he had his most intensive years as administrator and defender of Varmian canonical rights against the Teutonic Order behind him.1 In 1517 he wrote his work on the reform of the currency, and in 1525 the Treaty of Cracow dissolved the Knights of the Teutonic Order, thus ending the war with Varmia but at the cost of the greater dependence of Varmia on the Kingdom of Poland.2 We have concluded that Copernicus formed his fundamental philosophical views by 1510. It is likely, however, that he sharpened his focus on some issues, especially those regarding hypotheses and mathematical models. In this chapter we undertake a systematic analysis of Copernicus’s ideas about hypotheses and models, especially as revealed in De revolutionibus. In chapter seven I showed how his reading of sources persuaded him to adopt ancient assumptions concerning the perfection of spheres and circles. In this chapter I explicate the consequences of that decision. The chapter explains features of Copernicus’s mathematical cosmology that reflect a less robustly realist portrayal of Copernicus’s philosophy than one often encounters in surveys of his contribution to early modern science.3 Above all, the chapter presents some new insights explaining why Copernicus
1 This is not to say that he no longer had obligations, but they were not as intense as the years of struggle with the Teutonic Knights. See Biskup, Regesta copernicana. Many of the documents for the period 1525–1543 testify to Copernicus’s responsibilities, but many of the documents include personal correspondence relating to medical advice and matters concerning the preparation and publication of De revolutionibus. Cf. Prowe, Coppernicus, I, II, covering the years 1512–1543. On the period 1512–1537, see also Biskup, Nowe materiały. See also Rosen, “Biography,” 348–386. 2 According to Biskup, Regesta, 133, No. 284, Copernicus prepared the final version of the treatise on the reform of the Prussian currency in 1528. 3 One of the classic expressions of that view is found, of course, in Duhem, SOZEIN, esp. 71–109.
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conceived his heliocentric cosmology in a way that was so indissolubly and intimately linked with ancient spherical cosmology. Copernicus was not a philosophically systematic thinker. As a consequence, his reticence about both the physical attributes and mechanical details of his models have left scholars to speculate about his views. Although he provides clues and even makes explicit statements sometimes, they are often puzzling. The contexts of the remarks are often ambiguous. These circumstances have misled many to supply global solutions to problems that are driven by the internal logic of their reconstructions rather than by Copernicus’s texts in their different contexts. 2. Hypotheses My proposal, however basic it may appear, is to begin with a typology of Copernicus’s use of the term “hypotheses” and terms that he often uses in conjunction with hypotheses, namely, “principles,” “assumptions,” and “axioms.” The indexes of the modern editions are incomplete, but the Octavo Edition of the 1543 edition with commentary by Owen Gingerich provides a searchable option.4 I begin with a simple count. In De revolutionibus Copernicus uses the word hypothesis or a variant of it forty-five times. He uses the word principia or a derivative fifteen times, usually in conjunction with hypothesis or axioma or in the sense of axiom. The word assumptio or a derivative such as assumptus or assumere in conjunction with hypothesis, principle, or axiom appears eight times. On one occasion in the holograph in conjunction with principles, hypotheses, and assumptions, he uses the expression “cornerstone,” primarius lapis (Gesamtausgabe 2: 490, line 10). Axioma appears three times, usually in reference to a principle of natural philosophy. What does Copernicus mean by hypothesis? In some cases he clearly means one or more motions of the Earth (along with the implication that the stars and Sun are stationary). I will first discuss the cases
4
Copernicus, De revolutionibus, CD-ROM. To my knowledge, Copernicus never uses the word “theoria” in the sense of “hypothesis.” Compare with Schmeidler, Kommentar, 47, and his claim, 179, that Copernicus uses the word “hypothesis” only in the sense of “axiom.”
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where Copernicus refers to his own hypotheses and, second, to the hypotheses of the ancients. Of the forty-five times he uses hypothesis, twelve of them can be taken as referring to his fundamental cosmological assumption or about one or more of the Earth’s motions (De revolutionibus I, 11; (I, 12 in the Warsaw edition; Gesamtausgabe 2: 490, line 6); II, 1; III, 3; III, 7; V, 10; V, 15; V, 20; V, 22; V, 35; VI, 2, and VI, 8). Eight of these twelve refer explicitly and exclusively to the Earth’s motion as the hypothesis in question (I, 11; II, 1; III, 3; V, 10; V, 15; V, 20; V, 35; and VI, 8). There are three occasions where he refers to geometrical models in conjunction with the motion of Earth (III, 7; V, 22; and VI, 2). On one occasion in the holograph, Copernicus uses hypothesis to refer explicitly to principles of natural philosophy (Gesamtausgabe 2: 490, 3–10). He specifies the following: that the universe is spherical, immense, and similar to the infinite; and that the sphere of the fixed stars as the container of everything is stationary. It is in this same context that he refers to the “assumption” that the Earth moves in certain revolutions as the “cornerstone,” on which he depends to erect the entire science of the stars. Hypothesis here includes the assumption of Earth’s motion as well as propositions of natural philosophy. In VI, 2, Copernicus refers to the approach and withdrawal of a planet as commensurable with the motion in parallax “by hypothesis.” The hypothesis is the Earth’s annual motion, but it appears in the context of “hypotheses of circles.” In VI, 8, Copernicus refers to the Earth’s annual motion as well as to the librations of Mercury and Venus that follow as a result. The expression, “hypotheses of circles” (hypotheses circulorum) in VI, 2, however, brings me to the second way in which Copernicus talks about his own hypotheses, namely, as a reference to geometrical models. There are nineteen examples, of which I select only three as representative (IV, 3; V, 25; and VI, 2).5 In IV, 3, after he has pointed out the defect in the assumptions of the ancient lunar models, he concludes that the lunar epicycle appears bigger and smaller not on account of an eccentric but rather another arrangement or system of circles (alium modum circulorum). After describing his double-epicycle model, he claims that all of the other phenomena related to the Moon’s motion will be as observed.
5 The complete list includes I, 13; I, 14; II, 12; IV, 3; IV, 16; V, 5; V, 9; V, 11; V, 16; V, 19; V, 25 (twice); V, 28; V, 29 (twice); V, 30; VI, 2; VI, 7; and VI, 8.
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He says that he will demonstrate the agreement later by means of his “hypothesis,” although, he adds, he can produce the same phenomena by eccentrics just as he did with regard to the Sun (in III, 15). Now, this is a remarkable passage for three reasons. First, the hypothesis in question is the geometrical model for the motion of the Moon, that is, the double-epicycle model—it has nothing explicitly to do with Earth’s motion. Second, he makes it clear that the same phenomena can be demonstrated by assuming eccentrics. Third, in III, 15, Copernicus referred to the equivalence of epicycle and eccentric solutions for demonstrating the non-uniformity of the Sun’s apparent motion. In that context Copernicus comments:6 From all these analyses it is clear that the same apparent non-uniformity always occurs either through an epicycle on a concentric or through an eccentric equal to the concentric. There is no difference between them provided that the distance between their centers is equal to the epicycle’s radius. Hence it is not easy to decide which of them exists in the heavens.
On the basis of this quotation, it is hard for me to see why we should suppose that Copernicus always believed in the reality of his models. True, Ptolemy preferred the eccentric model here and Copernicus implies that one of them is true, but he does not seem to be completely certain about which is true. He proposes and uses them as mathematical solutions that he regards as superior to the models and solutions of his predecessors, but he is not always confident that he has found the uniquely true solution to the problem. He abandoned most of the double-epicycle models of the Commentariolus because when he realized that the apsidal lines shifted, he found it awkward to continue with the double-epicycle models. He replaced them with eccentricepicycle models for the superior planets, and eccentreccentric models for Venus and Mercury. Furthermore, in III, 20, Copernicus provides three solutions to account for the non-uniformity in the motion of the Earth’s apsidal line and a periodic variation in its eccentricity. He says that one of them must be true, and does eventually settle for the third, but in III, 6 Revolutions III, 15, 156, ll. 41–45, tr. Rosen. Notice here that Copernicus is indirectly referring to Regiomontanus’s Epitome XII, 1–2. On this point, see chapter seven, section eight. When I say that the lunar model has nothing explicitly to do with Earth’s motion, I mean except for the distance between the centers of an equivalent eccentric model, which refers to Earth’s orbital radius.
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25, he proposes yet another alternative and so leaves the matter as something that he could not completely resolve but, as he says, “only to the best of his ability.”7 In V, 25, Copernicus constructs a very complicated model for Mercury. In the context of remarks about the planet’s motion up and down along its diameter, a motion that can be the result of uniform circular motions, Copernicus then goes on to describe his accompanying figure for the purpose of making the “hypothesis” clear. Which hypothesis? He is clearly referring to the devices of his geometrical model by means of which Mercury’s appearances will be demonstrated. To be sure, the purpose of the model is to show how the planet’s motion is linked with the Earth’s motion, but there is little in this passage to suggest that he regarded the geometrical model as anything more than a mathematical solution to a problem. On the assumption of the Earth’s annual motion, geometrical models can be devised by means of which Mercury’s appearances can be demonstrated. Finally among Copernicus’s references to his own hypotheses, I come to VI, 2, the hypothesis of circles by which the motions of the planets in latitude are carried or moved. Some commentators make much of the verb ferre here, concluding that Copernicus is referring to spheres or orbs by which the planets are moved, but in this case Copernicus uses the word circulus, not orbis. The hypotheses refer primarily to the devices of the geometrical model by which he tries to demonstrate the appearances. However, in this case he encounters a problem that cannot be explained by variations in the Earth’s distance, leading him to conclude that the tilt of the planets’ orbits must also oscillate. Near the end of the chapter he indicates that the models proposed are intended to solve one problem at a time. First, (in V, 25) he considered Mercury’s longitude apart from its latitude and, second, (in VI, 2) its latitude apart from its longitude. Therefore, he announces, a single motion and the same oscillation, at once eccentric and oblique, could produce both variations. He adds that there is no other arrangement than the one just described. While the principal connotation here is the geometrical model by which the appearances can be demonstrated, the introduction to
7 Swerdlow and Neugebauer, Mathematical Astronomy, 1: 157–161, and note their comment that one of his statements is “very much in the spirit of poor, abused Osiander.” Cf. Schmeidler, Kommentar, 47.
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Book VI makes it clear that the Earth’s annual motion affects not only the planets’ motions in longitude but also in latitude. Here too, then, he must show how the Earth’s motion controls their deviations in latitude. In this context he does not use the word “hypothesis” but rather “assumption” (assumpta reuolutio terrae and terrae . . . assumptam eius mobilitatem). In VI, 8, he uses the word “hypothesis,” referring to the Earth’s annual motion and the librations of Mercury and Venus that follow as a result. In referring to the demonstrations contained in VI, 7, however, Copernicus makes the following comments. He says that he has recorded the latitudes of Mercury’s and Venus’s declinations at four critical points, adding that what occurs between these points can be derived by the subtlety of the mathematical art from the proposed system or arrangement of circles, but not without effort. Here again, Copernicus is referring to geometrical models by means of which the appearances can be demonstrated on the assumption of Earth’s motion. To sum up the results to this point, the primary sense in which Copernicus uses “hypothesis” refers to the motion of Earth and the stability of the fixed stars and the Sun. But it seems equally clear that Copernicus does use the word to refer to geometrical models, the devices of which are mathematical means by which the appearances can be demonstrated. In other words, in this secondary sense the hypotheses or models are mathematical solutions to a problem, although he does indicate that the combination in some cases is a unique solution. Before we turn to Copernicus’s references to the hypotheses of the ancients, we should address Osiander’s comments about hypotheses.8 In speaking of the “novel hypotheses” of this work, Osiander refers explicitly to the Earth in motion and the Sun at rest. Where Osiander departs from Copernicus, however, is in conflating these hypotheses with mathematical models as all imaginary and fictitious. Although he regards the geometrical hypotheses of the ancients as equally fictitious, Osiander is silent about the geocentric hypothesis, which he seems to take for granted not on philosophical grounds but on scriptural grounds, for only in revelation, he asserts, do we find anything certain.
8 In my count of Copernicus’s use of hypothesis or a variant (45), I did not include the appearance of the word on the title page or in Osiander’s “Letter.”
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Copernicus understood that the ancients distinguished hypotheses that they believed to be true from ones they assumed for the purpose of demonstrating the appearances. The ancient principles and hypotheses that they regarded as fundamental and true include the principles of uniform and circular motion, geocentrism, geostability, and the circular motion of the fixed stars. Copernicus accepts the principles of uniform, circular motion (expressed as the hypothesis of uniform motion in V, 15), but rejects the others as false because from those assumptions they have failed to deduce the structure of the universe. Other hypotheses, however, clearly refer to the devices of the geometrical models. In geometrical contexts, Copernicus refers consistently to the hypotheses of circles by means of which the ancients demonstrated the appearances. In their demonstrations they have omitted something necessary or essential and admitted something extraneous and wholly irrelevant. The necessary or essential that has been omitted refers to one or more of the fundamental propositions of natural philosophy (Praefatio, 4 and V, 35). The extraneous and irrelevant refer most likely to the mathematical models that violate a fundamental hypothesis. The word translated as “extraneous” is alienum, exactly the word he uses to criticize the models that have the epicycle center moving uniformly on an extraneous circle (in circulo alieno). Copernicus says and repeats on several occasions that the defect in the ancients’ assumptions was that their hypothesis of combinations of circles was neither suitable enough nor adequate (IV, 2).9 The principal example that he provides is always of the same sort, namely, while they claim that the motion of the epicycle’s center is uniform around the center of Earth or some other point, it is non-uniform on its own eccentric. Copernicus says:10 Therefore, the epicycle’s motion on the eccentric described by it is nonuniform. But if this is so, what shall we say about the axiom that the heavenly bodies’ motion is uniform and only apparently seems nonuniform, if the epicycle’s apparently uniform motion is really nonuniform and its occurrence absolutely contradicts an established principle and assumption? But suppose you say that is enough to safeguard uniformity. Then what sort of uniformity will that be on an extraneous circle
9
There is another example in IV, 2, and in several other places he refers exclusively to ancient hypotheses, for example, IV, 16; IV, 22; and V, 25 (twice, an ancient mathematical device that Copernicus adopted). 10 Revolutions IV, 2, 176, ll. 1–9.
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So here he refers explicitly to the violation of an axiom, an established principle and assumption.11 His solution is to propose another arrangement or system of circles that he claims does not violate the axiom. I will return to this problem below and a discussion of Copernicus’s “hidden” equant, but here I continue with the recitation of Copernicus’s comments. One of the principal achievements of Book V is to show how the motion of Earth and the motions of the planets account for retrograde motion better than the assumption of motion on an epicycle around a stationary Earth. Here again in recounting the ancients’ theory, he complains that the motion of the epicycle is not uniform around the deferent center but around an extraneous and non-proper center (V, 2: circa centrum alienum et non proprium). He refers explicitly to the case of Mercury, and adds the comment:12 I have already adequately refuted this result in my account of the moon. These and similar consequences furnished the occasion to consider the mobility of the earth and other ways by means of which to preserve uniform motion and the principle of the science and to render the account of apparent non-uniformity more constant.
This is, to be sure, another cryptic comment, but I will return to it later as well. In sum, then, Copernicus uses hypotheses, whether referring to his own or those of the ancients, in two ways. Some hypotheses are fundamental and established propositions, principles, assumptions, or axioms of natural philosophy that are taken to be true (14). Some hypotheses are geometrical models, combinations of circles, or other devices that are assumed for the sake of constructing demonstrations that show how the appearances follow from the models in conformity with the fundamental principles (34).13 From a violation of the fundamental principle about uniform, circular motion, Copernicus
11 It is one thing to conclude that the resultant motion is non-circular and nonuniform but altogether another matter to conclude that the circular motions out of which it is composed are themselves non-uniform! See V, 4. 12 My translation. 13 The total here of 48 includes three cases that fit in both categories, that is, examples where a mathematical hypothesis is used in conjunction with a fundamental hypothesis.
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infers not only that there is something wrong with the models but that some, perhaps all, of the other fundamental principles or assumptions are false. In short, natural-philosophical hypotheses are either true or false. Geometrical hypotheses, by contrast, are sufficient or adequate, and when he criticizes the geometrical hypotheses, it is because they are extraneous or irrelevant. He seems to imply that judging the geometrical hypotheses as true or false would be a category mistake. It is unlikely, however, that Copernicus was that indifferent about his geometrical models. The demonstration of appearances follows from hypotheses of circles. The hypotheses of circles follow from and are subsidiary to the overarching natural-philosophical or cosmological hypotheses. Copernicus believed that the hypotheses of circles must also be true, and so it follows that he regarded the assumption of uniform, circular motion as a fundamental cosmological hypothesis. With respect to strictly geometrical models, however, he is sometimes uncertain about which alternative hypothesis or model is true. In other words, he does not always propose a uniquely true hypothesis but rather suggests alternative ways of demonstrating the same appearances. It would be an exaggeration to say that he regarded these hypotheses as imaginary and as fictions, but his uncertainty about some of them suggests that these hypotheses have a more provisional character than the fundamental propositions do.14 With the results of the typology now in place, I turn to spheres. 14 This is not to say that Copernicus was an instrumentalist. The distinction here has to do with demonstrations in natural philosophy that are propter quid and those in astronomy that are quia. See McMenomy, “Discipline of Astronomy,” 303. See also Barker and Goldstein, “Realism and Instrumentalism,” 232–258. Barker and Goldstein suggest that because astronomers were not fictionalists, then they were realists. Their qualification, 253, that sixteenth-century astronomers were perpetually frustrated realists is a little closer to my meaning. Copernicus believed that true natural-philosophical hypotheses could explain the non-uniformities enumerated in I, 4, but the task of geometrical devices was to deduce adequate demonstrations of the appearances from them in conformity with the natural-philosophical hypotheses. Of course, Copernicus’s justifications for the truth of his natural-philosophical hypotheses appeal to the structure of the universe and the explanations of the non-uniformities. In other words, he has to appeal to the results, the logic of which involves reasoning from whole to part. See Lerner and Verdet, “Copernicus,” 147–173, at 170–171, for the emphasis on the architectonic element in the appraisal of planetary systems. Although the hypotheses are natural-philosophical, their justification rests on properly astronomical reasons. On the logic of this reasoning, see chapter eight. With the benefit of his meticulous analysis of Tycho Brahe’s data and physical assumptions about the motions of the planets, Kepler was able to identify the problem with false hypotheses.
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chapter ten 3. Spheres and the Nature of Celestial Matter
Copernicus was very familiar with the natural-philosophical tradition. Aside from his study of technical astronomy, he knew and had access to the qualitative introductions to astronomy (John of Sacrobosco’s De sphaera and its various commentaries) and the Theorica planetarum literature. He probably received some instruction from Albert of Brudzewo and almost certainly knew of Albert’s commentary on Georg Peurbach’s Theoricae novae planetarum.15 The gaps in Copernicus’s training, whatever they may have been, were likely filled during his years in Bologna where he served as a kind of apprentice to Domenico Maria Novara while presumably attending classes on law. By now there is consensus that Copernicus believed in the existence and reality of the total spheres that move the planets. Aware as he was of the different opinions among natural philosophers, however, he did not take sides on questions that they did not settle. This is not only true of differences about the extent of the universe, whether it is finite or infinite, but on all questions that natural philosophers resolve by means of dialectical argumentation from speculative principles.16 On the reality of spheres and on celestial and earthly matter, Copernicus was less radical than most textbook summaries allege. If Earth is a planet, then it is very likely that the Sun, Moon, and the other planets possess the same impulse implanted by God that causes them to come together in the form of a sphere. With that move he appeared to break with the traditional division between the supralunar and sublunar regions. This similarity among celestial bodies seems to make celestial and earthly matter homogeneous, but the conclusion is hasty. Here we can see that he adapted principles of Aristotelian philosophy, modified and transformed by his reading of other ancient traditions, to the motion of the Earth.17 First, Copernicus attributed a unique position and unique attributes to the Sun. He did not attribute any motion, not even axial rotation, to the Sun. It does not appear that he attributed an axial rotation to the In my view Kepler articulated the distinction that Copernicus left implicit. I return to the issue in the conclusion of this study. 15 Albertus de Brudzewo, Commentariolum. In my opinion, there is no evidence that Copernicus knew this text directly, but he very likely received instruction on astronomy and astrology from Albert’s students. See chapter five for details. 16 See chapter four, sections 3.2 and 3.3; and chapter nine, section five. 17 Grant, “Celestial Matter,” 157–186.
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Moon either.18 Second, the sphere of stars is also unique in position and attributes, so we cannot say without qualification that he made celestial and earthly matter homogeneous or that he simply broke the division between the supralunar and sublunar regions. In fact, he replaced that division with another, which delineates the sphere of the motionless stars from everything from that last sphere down to the sphere of the Sun. Because the Sun’s light penetrates the entire universe, perhaps even to the sphere of the stars, it unites the entire cosmos into one whole. The matter of the stars, however, is either heterogeneous with the matter of the planets or if homogeneous, then of another species, for the properties of stars are clearly different from those of the planets. Copernicus believed moreover that spheres move the planets. He entitled chapter 10 of Book I “The Order of the Celestial Spheres,” and referred several times to motions and revolutions of the celestial spheres in the dedication. The terms “sphere” and “orb” almost always refer to the spheres of ancient cosmology.19 Why did he retain these spheres in his cosmology? First, he believed that the heavenly bodies are moved uniformly in circles. They could not move uniformly unless a single sphere moved them uniformly.20 Some have maintained that his proclaimed rejection of the equant was motivated by mechanical considerations, and others claim that the rejection was motivated by cosmological concerns deriving from real spheres whose axis must rotate uniformly on a diameter.21 I have addressed that issue in chapter seven but take it up again separately in section four below. Second, his models of planetary motions required him to construct epicycles, and for centuries astronomers had combined this scheme with the homocentric spheres of early Greek astronomy. For Copernicus, the spheres could explain the motions of planets on epicycles around the Sun. The planets are either embedded in the spheres, and they rotate with the rotation of the spheres, or planets are attached somehow to the spheres that carry
18
De revolutionibus I, 10; III; and IV. Rosen’s commentary to his translation, 333–334. Cf. Hugonnard-Roche, Rosen, and Verdet, Introductions, 39–42. 20 De revolutionibus I, 4: 10, 11–12: “Quoniam fieri nequit, ut caeleste corpus simplex uno orbe inaequaliter moveatur.” 21 Copernicus never explicitly addressed the anomalies resulting from his own models. On the equant and spheres, see Swerdlow and Neugebauer, Mathematical Astronomy, 1: 289–297. Cf. Barker, “Copernicus, the Orbs, and the Equant,” 317–323. 19
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the planets as they rotate. In other words, the spheres provide the substance by means of which the planets can move on epicycles. Third, he knew that as Earth orbited the Sun, the Earth’s axis is not perpendicular to the plane of the Earth’s orbit around the Sun. The axis is inclined to the plane of its orbit and the axis points towards the polar star. Why did he have to attribute a third motion to the Earth whereby its axis describes a conical motion unless he believed that a sphere moves the Earth around the Sun? In other words, he attributed a third motion to the Earth to compensate for the annual motion of the sphere that moves the Earth around the Sun.22 Fourth, the Moon orbits Earth as Earth orbits the Sun. If the Moon is similar in nature to Earth, what keeps it from falling to Earth? Or, alternatively, what keeps it from flying off, the sort of objection Copernicus made to the circular motion of the starry vault?23 Now this is not a question that he posed directly, but the objection is imminent. How is it possible for the Moon to retain its orbit unless the MoonEarth system is as a whole moved by the sphere in which they are contained with the Earth at the center of this sphere?24 In other words, the fact that he saw no problem here is another indication that he was not thinking in terms of mechanical forces operating across space. All of these considerations leave no doubt that he adopted the celestial spheres of ancient Greek cosmology.25 Once he accepted the existence of spheres, the real problem for Copernicus was in deciding about the nature of these spheres. They cannot be bodies like planetary bodies. On the other hand, if they are not like planetary bodies, then how do they move the planets? He did not have an answer to this question, or one, at least, that was based on a consensus among natural philosophers and astronomers. He knew of the debates about celestial and earthly matter among scholastic Aristotelians at the University of Cracow in the 1490s. None of them
22
Moraux, “Copernic et Aristote,” 229–230. Cf. Smith, “Galileo’s Proof,” 543–551. De revolutionibus I, 8: 14, 24–32. 24 Copernicus’s sketch of the system places Earth and the Moon together in the same sphere. See De revolutionibus I, 10, and Rosen, commentary, 359. 25 De revolutionibus I, 4: 10, 11–12; I, 10: 19, 20–25. Compare Rosen, commentary, 333–334 and 348–349; Copernicus, Commentariolus, tr. Rosen, Complete Works, 3: 122–126; Rosen, “Copernicus’s Spheres,” 82–92; Lerner, Le monde, 1: 131–164, and 315–335; 2: 67–73 and 238–241; Westman, “Astronomer’s Role,” 112–116; Jardine, “Significance,” 174–178; Swerdlow, “Derivation,” 466–478; and Swerdlow, “PSEUDODOXIA,” 108–158, with Rosen’s reply, 301–304. 23
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followed Averroes in denying matter altogether of the heavens. A few followed Thomas Aquinas in regarding celestial and earthly matter as heterogeneous. Some argued that celestial matter and earthly matter were homogeneous, but of a different species. Some affirmed the incorruptibility of the heavens, while others adopting a Christian modification of Aristotelian theory concluded by invoking God’s absolute power that the heavens are generable and corruptible and thus not naturally corruptible. By maintaining the specific difference between celestial and earthly matter they preserved a distinction between the supralunar and sublunar regions. As we saw in chapter four, the teaching of natural philosophy in the 1490s was highly eclectic.26 Cracow natural philosophers accepted the materiality of the celestial spheres, but they disagreed among themselves about whether celestial matter is heterogeneous from earthly matter or homogeneous with, but specifically different from, earthly matter. Their indecision is reflected in Copernicus’s comments—he remained neutral, apparently leaning towards the view that the spheres are material, probably homogeneous with planetary matter, but of a species different from the matter of the planets. Without a consensus among natural philosophers on the issue, however, he left the question open. One idea is clear, though. He did not conclude that the matter of bodies in the entire system of the universe is homogeneous without specific differences, nor did he think that the laws governing all bodies in the universe could be reduced to a single set of laws governing the entire system. He retained a division between the stars and the planets, and he attributed unique properties to the Sun. The word impetus appears four times in one chapter of De revolutionibus, but Copernicus used it as a synonym either for “force” or for “weight.” He did not apply the concept to explain the motions of the planets or spheres, as Buridan suggested.27 In fact, Copernicus used the
26 In addition to chapter four, see Markowski, Filozofia przyrody, 140–172; Włodek, “Note sur le problème,” 730–734; and Grant, “Celestial Matter.” In overreacting to Pierre Duhem, some have adopted a radical discontinuity. See, for example, Ingarden, “Buridan et Copernic,” 120–129. 27 De revolutionibus I, 8. Buridan’s theory is mentioned in Quaestiones Cracovienses, ed. Palacz, q. 141, 251; and in the commentary by Johannes de Glogovia, “Quaestiones in octo libros Physicorum Aristotelis,” f. 240v.
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expression virtus movens only to reject the inconstancy of such a force as unsuited to the constant motion of a sphere.28 The question about how a sphere moves or influences a planet remains. Is the planet affixed or attached to the sphere somehow? Is it just embedded in the sphere and so moves with it as the sphere rotates? How does the sphere transmit its natural circular motion to the planet? Does its motion follow somehow from the principle of like-to-like? To answer these questions we must focus on the nature of the spheres themselves insofar as Copernicus addressed their nature. Created by God and moved initially by God, the spheres that were so moved continue to move in circles by nature. What spherical bodies of heterogeneous matter, or of homogeneous but specifically different matter, share is sphericity, the form of a sphere. The connection is formal. As we saw in chapter nine, even Aristotle maintained that the motions of the celestial sphere influence the motions of terrestrial elements and bodies. The higher can influence the lower, and the relation was often expressed in scholastic sources as a relation between actuality and potentiality, or formal and material, or essential and accidental. Copernicus relied without doubt on Stoic sources such as Pliny and Cicero, but his explanation of the circular and rotational motions of Earth is that as a sphere Earth possesses a capacity for circular motion. The celestial sphere that carries Earth around in a circle actualizes Earth’s capacity to move in a circle. Near the beginning of this section I posed the question, why Copernicus retained spheres at all in his cosmology? His decision is a startling example of how little he anticipated the physical cosmology of seventeenth-century astronomy. His decision also verifies his acceptance of Aristotelian principles, though drastically modified by his reading of other sources, which he also fitted to his own purposes. In other words, his revisions of all ancient and scholastic authorities were motivated by the principles of his own theory. On the material nature
28 De revolutionibus I, 4: 10, 11–15. Let me hasten to explain that my speculative reconstruction here does not require us to suppose that Copernicus would have remembered details about university teaching and debates. It is sufficient to maintain that he left the university with an impression of flexible and diverse interpretations of Aristotle that would have encouraged his own revisions. We can reasonably suppose that he would have remembered differences of opinion on the nature of celestial spheres because we know that his interest in astronomy was awakened during his years of study at Cracow. See Part I for details, and see Swerdlow and Neugebauer, 4.
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of the spheres, his departures from Aristotle had Christian, scholastic, and other ancient precedents. Finally on the spheres, I cannot ignore the problem of “solid” spheres. Copernicus never added the adjective “solid” to his descriptions of spheres.29 He knew that the word “solid” was used of spheres in three senses. First, “sphere” is the same as “hard,” the sense in which Earth is called “solid.” Second, “solid” is the same as “continuous,” the sense in which celestial bodies like the planets are called “solid.” Third, “solid” is the same as three-dimensional, the sense in which any body is said to be “solid.”30 Copernicus sometimes used the words sphaera and orbis interchangeably, but he also used orbis at times to refer to “circle,” and at times to refer to a spherical figure distinct from a sphere in the strict sense. Strictly speaking, some scholars regarded spheres as the most regular of solid bodies bounded by a single surface having only one center.31 Orbs are also solid spherical figures, but they have two surfaces, an interior concave surface and an exterior convex surface. If the surfaces of an orb have the same center, the orb is regular and the part between the exterior and interior surfaces has a uniformly equal thickness throughout. If the surfaces of the orb have different centers, however, then the thickness of the part between the surfaces is non-uniform and irregular. Copernicus maintained that celestial orbs or spheres do not share a common center,32 and because celestial spheres are non-concentric, we conclude that he regarded them as irregular orbs. Are orbs solid throughout or are they hollow in part? Sometimes an orb is described as excavata, meaning “hollow,” but this cannot mean “empty” in the sense of “void,” because natural philosophers rejected the existence of void as a contradiction in terms.33 Spheres and orbs are constituted of aether, or, in alternative theories, of some kind of fire or air, and in these contexts some natural philosophers 29
Rosen, Copernicus and his Successors, 62–63. Thorndike, Sphere,” 76–77; also the commentary by Robertus Anglicus, 145. These distinct uses and hence ambiguity of the term “solid” are rarely reflected in the scholarly literature thus adding to the confusion. Brudzewo, Commentariolum, 5–9, makes similar distinctions. 31 Grant, Planets, chapters 13 and 14, esp. 284–286, where he describes the compromise three-orb system. 32 Commentariolus, Postulate 1; De revolutionibus I, 9. 33 Litt, Corps célestes, 25, 29, and 40. See also Westman’s reference, 113, to Erasmus Reinhold’s commentary on Peurbach’s Theoricae, where he uses the expression sphaera excavata in referring to the sphere of the Sun. 30
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resorted to descriptions that suggest that the area inside a sphere is airlike or fluid.34 Copernicus says nothing about their constitution. Both “sphere” and “orb” are described as solid figures or bodies. The differences between them are their surfaces. An orb has two surfaces that produce another sphere in the interior of the orb, but presumably that sphere is also solid. Earth is a hard solid. No two bodies can occupy the same place at the same time, nor can celestial spheres have terrestrial qualities.35 Hence, Copernicus could not have regarded orbs as solid in the sense of “hard.”36 Celestial bodies are said to be “continuous,” but are celestial orbs solid in this sense? This is harder to decide. Continuous things have nothing of the same kind in between and constitute one thing.37 An orb has an interior surface with another sphere embedded inside the orb, and irregular orbs do not have a common center. Hence, it is unlikely that Copernicus regarded his celestial spheres as solid in the sense of “continuous.” This sense of solid fits the description of the celestial bodies such as the Sun, Moon, and planets. Celestial orbs and
34
Lerner, 1: 115–138; Litt, 56–59 and 340–341; Aiton, “Celestial Spheres,” 75–114; Grant, Planets, chs. 13 and 14; and McMenomy, “Discipline,” 185–303. Copernicus’s conception seems to correspond to the notion of a fluid heaven, but he does not say so. His later sixteenth and seventeenth-century interpreters attributed to him all of the above notions, namely, that the spheres are solid, airlike, or fluid. See Jardine, 174–183. Note Grant’s caution, esp. 345–348, in distinguishing medieval scholastic from late-sixteenth and seventeenth-century scholastic views. 35 Although some authors describe spheres in terms of earth-like elemental qualities, they do not seem to mean that the qualities are homogeneous, suggesting that the attributes are to be understood analogously. I am not referring here to bodies like the Sun, Moon, and planets, which do share properties like gravity with Earth, but that does not tell us explicitly what elements they possess. Copernicus keeps any inclination to speculate about such matters under control. See De revolutionibus I, 9, for one possible exception. 36 Jardine, “Significance,” 174–180. Grant, Planets, ch. 14, esp. 345–348, leans to the view that it was first with Tycho Brahe that “solid orb” became synonomous with “hard orb.” As for Copernicus, Grant, 346, says: “Nothing that Copernicus said or implied in De revolutionibus enables us to decide with any confidence whether he assumed hard or fluid spheres. Copernicus fits the pattern of the Middle Ages, when explicit opinions about the rigidity or fluidity of the orbs were rarely presented.” Aiton, “Peurbach’s Theoricae,” 5–44, esp. 8, suggests that Peurbach settled the issue by his belief in the reality of spheres, but even some commentators on his text (Albert of Brudzewo, for example) rejected the reality of epicycle spheres. The fact is that Aiton nowhere explains how geocentrists could have attributed terrestrial qualities to the celestial realm without rejecting or drastically modifying Aristotelian cosmological principles. The attribution of terrestrial qualities to the heavens seems often to work in contexts where they are best described as analogous. 37 Aristotle, Physics IV, 3.
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spheres were normally regarded as contiguous for there cannot be any gaps or void spaces below the last or eighth sphere, yet there are gaps between Copernicus’s spheres or orbs, so they are also not contiguous.38 That leaves “three-dimensional” as the only appropriate sense in which to describe Copernicus’s orbs. Why, then, did he sometimes use the word “sphaera”? He used the word to refer specifically to the total sphere in which a planet is embedded or to the sphere of the fixed stars or Earth and the other celestial bodies. In sum, Copernicus’s celestial orbs, or what he understood by celestial “spheres,” are “solid” only in the abstract sense of “three-dimensional.” They are not hard, not continuous, nor even contiguous. The Moon-Earth “system” appears to be a regular orb,39 although its center (the mean Sun) is certainly not the common center of the remaining orbs and hence they are all irregular. Distinct spheres or orbs cannot interpenetrate, but they can contain other bodies. Because of the ambiguity of the term “solid,” Copernicus did not call the celestial orbs or spheres “solid” at all. Perhaps he took it for granted that the orbs containing the epicycles that describe the motions of all planets other than Earth are resistant at their surfaces but non-resistant in their interiors. Even Earth is surrounded by an orb that contains the two epicycles that describe the motion of the Moon. It would follow again that orbs are “solid” only in the third sense. The third sense alone would be sufficient to explain his rejection of the equant supposing that he was concerned with cosmological issues such as the interpenetration of real spheres. Yet his concern is strictly with uniform motions on circles around their proper centers, and Copernicus never explained how the spheres move the planets.40
38 Lerner, Monde, 2, 3: 69–70 and 240, n. 16, contrary to Swerdlow and Neugebauer, 58, 160, and 474. There are also some gaps between orbs in medieval models, but they “filled” these gaps with aether. Perhaps Copernicus took the view for granted, or he may have overlooked it. 39 Swerdlow, “PSEUDODOXIA,” 115: “[T]he sphere carrying the earth and moon [has] two concentric surfaces,” a description that fits the definition of a regular orb. 40 Aiton, “Celestial Spheres,” also concludes that if Copernicus followed the view that derived from Sosigenes, “then it was not necessary for him [Copernicus] to commit himself to solid (material) spheres. It was sufficient that the celestial bodies, whatever their precise nature, were moved in accordance with the axiom of Aristotle, as modified by Sosigenes; that is, in accordance with an accepted principle of physics.” See also Goldstein, “Copernicus and the Origin,” 219–235. See my reconstruction in chapter seven. More on the equant below.
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There are several other troubling questions that Copernicus does not answer. Even if we concede that he accepted the existence of orbs, that is, partial orbs, that would presumably commit him to the reality of eccentric or deferent orbs, but not necessarily epicycle orbs. There are a number of reasons for emphasizing agnosticism about their existence. There were several astronomers who explicitly regarded eccentrics and epicycles as imaginary and fictitious. When one considers the devices that Copernicus used in his demonstrations, he seems to have regarded them as primarily mathematical. The traditional accounts of orbs never make it clear how the orbs are consistent with the mathematical models.41 In most illustrations, the epicycle is embedded in the eccentric orb, yet the epicycle center describes the deferent circle, which suggests that the deferent circle is not an orb. And what are we to make of double-epicycle models? Either both are orbs, in which case one orb does interpenetrate another, or they are not orbs at all. These are typical difficulties with the treatises that try to combine physical representations of the spheres with mathematical models. Copernicus was aware of these problems and says nothing to clarify them, although some of his remarks about eccentrics and deferents suggest that these too are spheres. His reticence holds also, in my view, for De revolutionibus I, 4, the text that has been used to justify Copernicus’s supposed belief in real eccentric and epicycle orbs.42 I conclude this section with an exposition of that chapter.43 The motion of the heavenly bodies is uniform, eternal, and circular or composed of circles (or circular motions). The motion of heavenly bodies is circular because the motion appropriate to a sphere is rotation in a circle. A sphere expresses its form as the simplest body by moving in a circle.44 In subsequent sentences, however, Copernicus proceeds to enumerate difficulties with these general principles. The numerous celestial spheres have many motions with the daily motion of the entire universe the most conspicuous. Second are the proper motions of the Sun, Moon, and five planets, which motions differ from the daily motion in many ways. They move west to east 41
Lerner, 1: 136. Jardine, 182–183. There is a summary in chapter seven, but here the focus is on the reality and nature of spheres. 43 The discussion here supplements the analysis in chapter seven, the section on Commentariolus. 44 I resort here and below to a paraphrase of Rosen’s translation and the original by way of summary. 42
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through the zodiac obliquely to the equator; they appear to move non-uniformly in their orbits (first anomaly); the planets retrograde at times (second anomaly) and vary in latitude, sometimes nearer to Earth and at other times farther away. In spite of these difficulties Copernicus says that it is necessary to grant that the motions are circular or composed of circles because their non-uniformities recur regularly according to a certain law, which could not happen if their motions were not circular. By a composite motion of circles the Sun displays a regularity in which several motions are discerned because a single orb cannot move a simple heavenly body non-uniformly. If a single orb were the cause of nonuniformity, then it would have to be caused either by an inconstancy in the moving power (virtus movens) or by some difference or change in the revolving body. In other words, if an object moves in a circle, what could cause it to move non-uniformly? Such defects cannot be attributed to bodies that are constituted in the best order. It follows, then, that their motions are uniform but appear nonuniform to us. There are two possible causes. Either their circles have poles different from Earth’s or the Earth is not at the center of the circles on which they revolve. The planets seem to vary in distance, and their motions appear non-uniform in equal times because of their varying distances. Because of these observations Copernicus advises us to consider diligently the relation of Earth to the heavens so that we may not make the error of attributing to the celestial bodies what belongs to the Earth, and so ends Chapter 4. It is reasonable to infer from these passages that Copernicus believed in real eccentric spheres, but it is difficult to understand how some commentators have extracted from this passage the conclusion that Copernicus believed in epicycle orbs as well. The celestial spheres move in circles and move the bodies in them. A single orb cannot cause the observed non-uniformities. Far from concluding that several distinct orbs must cause these non-uniformities, however, Copernicus is clearly trying to prepare the reader for the conclusions announced in I, 5 and I, 9–11. The motions of Earth cause the regular non-uniformities and variations in distance, thus eliminating or explaining some of the most peculiar non-uniformities. As for his belief that the motions of heavenly bodies are circular or composed of circles, he is anticipating Earth’s motions. Earth’s rotation on its axis eliminates the diurnal rotation of the entire universe. Earth’s annual motion around the Sun explains the regularity of the seasons, and the direct motions of all of
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the planets and their varying distances from Earth. In short, just as in Commentariolus, he is far from mentioning the complications of the geometrical models but is rather content here to insinuate the Earth’s motions as providing an initial approximation of the solutions and explanations of the observed non-uniformities. As for his comment implying that sphericity is the cause of motion in a circle, as in I, 5 where he appeals to the Earth’s sphericity as entailing rotation on its axis, once again some commentators have drawn conclusions that are too global.45 Copernicus’s own theory requires the sphere of the stars and the Sun to be stationary. Aside from the spheres that move the planets, he does not attribute axial rotation to any continuous body other than Earth. No such rotations have been observed and rather than let a general principle settle a question a priori, Copernicus says nothing. As for Earth’s annual revolution with its Moon through the great orb, Copernicus offers no explanation as to how Earth with its bulk is carried by the orb, nor does he speculate about what the stuff or matter of the orbs is.46 Even when he does speculate about the Sun, Moon, and planets forming into spheres by virtue of having parts endowed by their creator with a tendency or desire to gather into a whole, he does not explicitly conclude that they must be constituted of the same elements as Earth is. He leaves that question open as well. In sum, then, we have no reason to assert that Copernicus believed in the existence of real epicycle orbs, only in the large orbs or spheres and the eccentric or deferent orb in which the planets are embedded. Furthermore, his celestial orbs are not hard, continuous, or even contiguous. They are three-dimensional, the only sense in which we may call them “solid.” And we have no idea about their constitution or attributes other than their capacity for uniform, circular motion, their function as containers of the planets, and their ability to cause the planets to move in circles uniformly or in ways that are composed of circular motions. I turn now to equants, Copernicus’s dissatisfaction with them, and the “hidden” equants in his models.
45 46
In this regard I agree with Jardine. Westman, 112–115.
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4. Equants There are some who maintain that Copernicus’s dissatisfaction with equants can be explained only by supposing that the problem is contrary to simple mechanical sense, and others see it as a cosmological objection to spheres rotating about an axis that is not a diameter.47 As Copernicus discusses the problem, his objection is expressed in purely geometrical terms referring to circles, not orbs. In Commentariolus, Copernicus expresses the objection to the equant as involving a uniform motion neither on its deferent sphere nor its own epicycle center, so here he does refer to a deferent sphere. But he characterizes his own solution as an arrangement of circles (modus circulorum) not spheres. What is more, the double-epicycle devices in Commentariolus raise more doubts about epicycle spheres. In his reconstruction of Copernicus’s derivation of the heliocentric theory, Noel Swerdlow found evidence of a Capellan or Tychonic transitional stage to complete heliocentrism. The reconstruction is attractive except for one dull thud, the speculation that Copernicus would have anticipated the intersection of the solar and Martian spheres. On the assumption that this is not permissible, he would have switched the positions of Earth and Sun as a way of avoiding the intersection of the spheres.48 Because Copernicus is not forthcoming about the nature of 47 Swerdlow, “Aristotelian Planetary Theory,” 36–48, at 36; Swerdlow and Neugebauer, 41, 44, and 50; and Barker, “Copernicus, the Orbs,” 319. In my view, Copernicus’s concern reveals a detail about his understanding of mechanics that departs from Ptolemy’s understanding. Because this point requires another line of argument not strictly relevant to this discussion, I have relegated it to Appendix IX. 48 As I argued in chapter seven, Copernicus considered the Capellan arrangement, which orders those two planets around the Sun and the Earth, and hence orders them according to two different principles, already sufficient reason for Copernicus to reject a geo-heliocentric compromise. In other words, any speculation in that direction was already checked. See Swerdlow, “Derivation,” 477–478. See also Swerdlow and Neugebauer, 54–64. See Goldstein, “Origin,” 221–222, who agrees that Copernicus was unconcerned with the intersection of orbs. But that question is, in my view, independent of whether Copernicus considered a Capellan arrangement as an intermediate step. See chapter seven for my analysis of Commentariolus and the origin of the heliocentric theory. On the “Uppsala Notes” and their dating, see Swerdlow, 426–431; Dobrzycki, “Uppsala Notes,” 161–167. See also Copernicus, Commentariolus, tr. Rosen, 107, n. 69, and 111–113, n. 200. See also Grażyna Rosińska, “Kwestia,” 71–94. His use of the numbers does not help us to date the folio. Also the recto side of the folio (f. 284r or 15r) was written no earlier than 1532, and the next folio was probably written about 1505–1506, according to Dobrzycki, 167. Dobrzycki later withdrew his analysis, but it is not clear what effect the revision has on the proposed dating of the folio. See Dobrzycki, “One Copernican Table,” 36–39.
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celestial spheres, we cannot evaluate this objection. It is likely that he regarded the spheres as impenetrable, but Copernicus nowhere says so. He was aware of the Capellan arrangement, so we may suppose that it played a role. But perhaps his reasoning started from the traditional arrangement of Mars, Jupiter, and Saturn according to sidereal periods and the realization that a switch between Sun and Earth would determine the order of Mercury and Venus according to the same principle. The only explanation that Copernicus provides about the path to his discovery is in a context related to the equant, and those comments, three of them (De revolutionibus, Preface and V, 2; and Commentariolus) are cryptic and ambiguous. The comment in the 1542 Preface is a critique of Ptolemaic method. He says in V, 2 that the uniform motion of an epicycle center around an extraneous center and similar situations or consequences gave him occasion to consider the Earth’s motion and other ways of preserving uniform motion. Earlier, in the Commentariolus, he says that the inadequacy of the equalizing circles, that is, equants, led him to look for “a more reasonable arrangement of circles from which every apparent irregularity would be derived while everything in itself would move uniformly, as is required by the rule of perfect motion.”49 Copernicus does not specifically mention the motions of Earth here although he immediately follows this comment by saying that at length he hit upon a solution, and proceeds to enumerate his seven postulates, among which are the Earth’s diurnal and annual motions. It is not possible that Copernicus meant that it was the inadequacy of the equant that led him directly to consider Earth’s motion. Although this is what Edward Rosen implied in his comment on V, 2, it was also Rosen who pointed out that Ibn al-Haytham rejected the equant without being led to geokineticism.50 That fact along with Copernicus’s “hidden” equants forces us to look more closely at Copernicus’s statement in V, 2. Copernicus says that similar situations or consequences, that is, situations or consequences similar to the problem of uniform motion around an extraneous center gave him occasion to consider Earth’s
49
Rosen tr., 81. Citing Pines in his commentary on De revolutionibus, 417. See also Swerdlow and Neugebauer, 43–45. 50
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motions and other ways of preserving uniform motion. Among the other ways are Copernicus’s geometrical models that he thought worked better than the equant. But what were the problems of uniform motion solved by the Earth’s motions? Surely he means the problems he associates with the diurnal rotation of the starry vault, the regular but apparently non-uniform motions of the Sun and Moon through the zodiac oblique to the celestial equator, the retrograde motions of the planets, and the varying distances between the planets and Earth. In short, Copernicus did not mean to imply that it was the inadequacy of the equant that led him directly to geokineticism, but rather the other problems of uniform and circular motion that he enumerated in I, 4, and that are also included among the postulates in the Commentariolus. He conceived of Earth’s motions as a superior way of explaining apparent deviations from uniform circularity more generally conceived than the equant problem. In discussing the varying distances between the planets and Earth, Copernicus concludes in I, 8, that motion around the middle must be interpreted in a more general way; it is sufficient that each such motion encircle its own center.51 Then why does he refer to the equant problem at all in this context? The inadequacy of the model led him to focus his attention on other problems of apparent non-uniformity. These problems led him, in turn, to question the other fundamental propositions about geocentricity and geostability. He might have considered the Capellan arrangement at this point as a transitional stage, which finally led him to consider Earth’s motion. By means of Earth’s motion, he could transfer many of the appearances to the relevant motions of Earth, distinguish them from the regular and direct motions of the other celestial bodies, and then construct models that would demonstrate the appearances in conformity with his fundamental assumptions. In a very indirect way, or, as he says, “at length,” the equant problem led him to a solution. Did Copernicus overlook “hidden” equants? The answer is yes.52 James Evans speculates that Copernicus did not fully understand how
51 Aiton, 96–98, cites Fritz Krafft, who concludes that the traditional distinction between hypothetical astronomy and real physics became largely irrelevant because his axioms annulled the distinction. But this interpretation still does not tell us which geometrical solution is the uniquely correct one. One might still conclude that Copernicus could be satisfied with general solutions to the problems without committing himself to the existence of solid, material spheres. 52 To my knowledge, Michael Mästlin was the first to comment on the fact in a discussion of Copernicus’s general model for the motion of a superior planet in V,
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nearly perfectly his model duplicated Ptolemy’s because of a change he had to make in the eccentricity of the Martian model to make the motion most rapid at perihelion, as required.53 In the Martian model he departed from a bisection of the total eccentricity. The solution, Evans says, was the mechanism proposed by Ibn al-Shatir nearly two hundred years earlier. Evans adds that Copernicus probably did not perceive that the angular motion of the planet was uniform with respect to a point that corresponds to Ptolemy’s equant point. But by the uniform angular motion, Evans means the uniform motion of the planet on its effective or resultant oblong path relative to the equant, not the center of the epicycle relative to its center.54 Copernicus maintains that the motions must be circular or composed of circles. He acknowledges that the path is not perfectly circular, but it must be composed of uniformly moving circles. Is it not likely that Copernicus thought that he had solved the problem without the equant because in his model the planet moves uniformly on its epicycle and the center of the epicycle moves uniformly around its proper center? The departure from bisected eccentricity in the Martian model would also have obscured the equivalence with Ptolemy’s equant model.55 5. Summary Copernicus rejected the equant as a mathematical hypothesis. He proposed a number of devices that result in motions that are not circular and uniform but that he believed could be composed from circles 4. He says that Copernicus omitted the equant in his figure, suggesting that it was an error. See Mästlin’s letter to Kepler dated 9 March 1597 in Kepler, Gesammelte Werke, 13, No. 63: 108–112, at 110, lines 98–102: “Vidi mox, cum relegerem tuum scriptum (vtinam te praesente id factum esset) erroris causam ex schemate Copernici lib. 5. cap. 4, pag. 142. oriri, quo Copernicus centrum aequantis omisit, id ego in appendice post Narrationem Rhetici pag. 170. addidi. Etenim tam in copernici hypothesibus (licet non exprimat ipse) quam apud Ptolemaeum, aequantis centrum est D.” He then goes on to explain how point D corresponds to Ptolemy’s equant point (lines 107–109): “Quod si autem assumatur D eiusque circulus IKLM (quem Copernicus loco allegato omittit) manifestum fit, eum esse verum aequantem, aequanti Ptolemaei absolutissimè correspondentem.” 53 Evans, “Division,” 1012–1014 and 1021–1022. See Swerdlow and Neugebauer, 289–299. 54 Evans, 1023, n. 9. See also Swerdlow, “Copernicus,” 166–167. 55 Evans, 1013. The fact that the “major” axis of the Copernican orbit coincides with the “minor” axis of the Keplerian ellipse means as well that Copernicus’s model represents a step backwards from Ptolemy’s.
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provided the circular motion is uniform around its proper center.56 Whether he actually succeeded is another matter, but he evidently believed that he had. Spheres are not irrelevant. They remain among Copernicus’s natural-philosophical hypotheses, but their nature, function, and precise influence are left vague. Not all spheres move. His tacit rejection of Aristotelian intelligences indicates that he conceived of them as a simple mechanism. If they move, then they move in circles, but a spherical form is not the direct cause of every circular motion and not all spheres move in circles. Copernicus apparently overlooked equants in his models because he thought that he had solved the problem. The circular motions that the spheres generate must be perfectly uniform and circular or composed of circles that move uniformly around their proper centers. We further conclude that, perhaps by way of a Capellan intermediary stage, he recognized that the Earth’s motions eliminated or clarified some of the non-uniformities that he describes in I, 4, by which means he tried to preserve the traditional belief that the heavenly bodies are moved by spheres. My final conclusion is about Copernicus’s method. His fundamental assumptions are natural-philosophical hypotheses, but their justification depends on the relation of the whole to the part. This means that his reasoning depends on architectonic principles that subordinate natural-philosophical hypotheses to astronomical considerations. His argument from whole to part retains a dialectical character for it depends on the greater probability of his architectonic principles.57 His reluctance to answer numerous questions about the nature of the spheres reveals a methodological principle that guided him. He was suspicious of speculation based only on dialectical considerations,
56 Schmeidler, 148–149, comments that the discovery of an effective equant in Copernicus’s model is trivial. We may add that if there are equants in fact, then it means that not all spheres in Copernicus’s models turn on an axis that is a diameter through the center. Or Copernicus noticed the equivalence but ignored it because the equant has nothing to do with spheres. In other words, if there are “hidden” or “effective” equants in Copernicus’s models, then there must in fact be an intersection of spheres or orbs. This means that Copernicus either did not assume the existence of all orbs, or they are mutually penetrable. One might conclude, then, that either because of a lack of consensus or a lack of detail about the nature of orbs, Copernicus left this question, like so many others, unresolved. 57 I agree with Lerner’s reluctance to follow Swerdlow’s and Barker’s robust realism about spheres, and with his criticism that they tend to neglect or oversimplify the effect of the traditions in logic, natural philosophy, metaphysics, and theology on Copernicus.
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which he characterized pejoratively as logical exercises or merely acts of reason.58 He was reluctant to draw conclusions of an empirical nature without compelling astronomical reasons or empirical evidence. Anticipating rejection by Aristotelians, he knew that he had to persuade Aristotelians to reconsider some of their assumptions and suggest how to adapt their principles to heliocentrism. He avoided taking sides on questions about which natural philosophers continued to dispute. The most important conclusion from the analysis is related to Copernicus’s criticism of Ptolemaic astronomers for the flaw in their method. The false hypotheses from which they started out cannot refer to mathematical or strictly astronomical hypotheses. Copernicus accepted the hypothesis of uniform, circular motion as well as the geometrical devices used to save uniform, circular motion. He rejected the equant because it violates a fundamental proposition, not because the proposition is false. The false hypotheses, then, must refer to cosmological or natural philosophical propositions. These include the position and motions of the Sun, the stability and position of Earth, the assumption of a unique center for all celestial motions, the motion of the fixed stars, and that the motions of the celestial bodies can explain the observed irregularities or non-uniformities. As supporting evidence he refers to the disagreements over the ordering of the spheres and planets, and the failure of his predecessors to provide a genuine explanation of bounded elongation and retrograde motion. When Copernicus claimed that his meaning would be clear, he was referring to his own fundamental hypotheses about the Sun, Earth, ordering of the planets, and “natural explanations” of bounded elongation and retrograde motion. This is a promise fulfilled qualitatively in Book I, chapters 4, 8, 9, and 10, and quantitatively in Books II through VI.
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CONCLUSION AND EPILOG 1. Summary This study of Copernicus and the Aristotelian tradition has examined astronomy in relation to philosophical cosmology. Throughout the first two parts I tried to place Copernicus’s work on astronomy in context, providing a concrete sense of his socio-political environment, education, and reading. In focusing on Aristotelian schools, I have accepted them as a community of scholars who modified Aristotle’s doctrines and who represented themselves as Aristotelians.1 Copernicus, I have argued, learned from his university education above all to adapt Aristotelian principles to his own interests and conclusions. There was no question of rejecting Aristotelian metaphysics, natural philosophy, or logic, or of replacing Aristotle completely by adopting the views and criticisms of other ancient philosophers. As Copernicus read the works of other authors, they informed his approach to astronomical issues, his understanding of Aristotle, and his revision of Aristotelian and scholastic traditions. The most important influence that Aristotle exercised on Copernicus was on the highly controversial question of the truth of cosmological hypotheses, Copernicus’s belief that astronomical phenomena (the observational facts, data) can follow only from true hypotheses. Aristotle had affirmed such a view in three different texts, all of which indicate, however, that he was referring to causal connections and to demonstrations propter quid. Relying on the well-developed area of philosophical dialectic, Copernicus expanded Aristotle’s doctrine to stipulate relevance as a condition of validity, and irrelevance and omission as criteria of invalidity in evaluating the connection between the antecedent and consequent of a hypothetical proposition. The arguments supporting such an expansion relied on dialectical topics, and they resulted in conclusions that were probable and even more probable, Copernicus maintained, than their alternatives. Such was his
1 H. Kuhn, “Aristotelianism”; Jordan, “Aquinas.” For the many editions of Aristotle’s works in the sixteenth century, see Cranz, Bibliography. Similarly, on the survival and influence of Aristotelian principles, see Leijenhorst et al., eds. Dynamics.
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debt to Aristotle in logic and to those scholastic Aristotelians who had argued in a similar fashion.2 How Copernicus arrived at this way of interpreting Aristotle is also controversial. There were precedents in Cracow and Bologna, but an annotation that is in Copernicus’s hand indicates that Plato’s views on the thorough evaluation of hypotheses or suppositions provide clues on how Copernicus applied Plato’s advice in astronomy.3 This advice led him to formulate the questions that focused attention on the principal weaknesses of geocentric astronomy. These were initially questions having to do with the principles of uniform, circular motion, the puzzles about the ordering of celestial spheres and the multiple centers of heavenly motions, and the variations in the distances of planets from Earth. This is why I had to address astronomical and mathematical details in chapter seven, and reconstruct his path to the first heliostatic, heliocentric theory.4 Other philosophical questions required discussion of other details about his models. The summaries of the books that he used and read helped to answer other relevant questions about the origin of the heliocentric theory. Much of this is admittedly material intended to persuade readers that I have not ignored the most important literature on Copernicus and his sources. In my view, these summaries strengthen the story of how Copernicus arrived at his theory, and why his arguments take the form that they have.
2
For similar arguments that emphasize Copernicus’s rhetorical strategies, see Westman, “La préface,” 365–384, and idem, “Proof,” 167–205. 3 The evidence that the annotation is genuine is summarized in chapter seven. For the complete analysis see Goddu, “Copernicus’s Annotations,” 202–226. 4 The detailed evidence is presented in Goddu, “Reflections,” 37–53. I have modified and strengthened the argument presented there in chapter seven. On variations in distance, the ratios in Ptolemy and Copernicus are in agreement. In De revolutionibus I, 4, 9, and 10, Copernicus suggests that the large spaces or gaps required by the large epicycles of Mars and Venus, though presumably filled with some substance, seemed to trouble him. He rejected the explanation for placing the Sun between the superior and inferior planets with the Moon. The superior planets show every elongation from the Sun, but so does the Moon, hence, to be consistent they should have placed the Moon beyond the Sun. Even in the Commentariolus, where he adopted doubleepicycle models, he made them as small as possible as if their sizes troubled him and because his theory no longer required epicycles to account for retrograde motion. By placing the Earth in motion, of course, Copernicus explained the variations in distance as a result of the motions of both Earth and the planets, not just the planets. But see chapter seven where I acknowledge the difficulty in distinguishing between a clue and an afterthought.
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In as few words as possible, then, the Aristotelian tradition exercised its most important influence on Copernicus in the areas of logic, dialectic, and argumentation. Neoplatonism as represented by Renaissance scholars and Plato influenced his exercise of dialectical inquiry, and his view on the relation between mathematics and natural philosophy. It was by means of Aristotelian texts and scholastic commentaries or handbooks, however, that he learned how to construct and support arguments. I have examined natural philosophy and cosmology to resolve a number of puzzles, but only to the extent that Copernicus’s texts permit us to arrive at solutions. He left many questions unanswered, and where the texts fail to lead us to a resolution, I have left them undecided. In some instances I believe that Copernicus was simply in doubt. In others, I suspect that he had a preferred answer but judiciously avoided discussing questions that he knew divided natural philosophers. What I have yet to do is document completely his acquaintance with Aristotelian texts. Here I bring together all of the references and contexts that suggest acquaintance with Aristotle’s texts and with the tradition. In section three, I turn to a consideration of his reception, but in keeping with the character of this study, my focus is on the reception of his understanding of hypotheses, their truth, and of his adaptation of Aristotelian natural philosophy to the heliocentric theory. 2. Copernicus’s Interpretation of Aristotle Scholars for the most part have focused on Copernicus’s acquaintance with Aristotelian texts on natural philosophy, especially De caelo, Metaphysics, and Meteorology. In fact, only Aleksander Birkenmajer and Edward Rosen, to my knowledge, made even a single reference to a work of Aristotelian logic. From the point of view of Copernicus’s innovative cosmological ideas, the emphasis on natural philosophy and metaphysics is understandable. From the point of view of his arguments and likely university education in the arts and law, I have tried to reconstruct Copernicus’s training in logic. From a methodological point of view and in light of Copernicus’s criticisms of Ptolemaic astronomers for omissions and irrelevant intrusions in their method, I have constructed an account linking his training in logic to his evaluation of hypotheses.
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Copernicus was familiar with Aristotelian views on demonstration and dialectical arguments. His arguments demonstrate that he was trained in these techniques, and I have emphasized the role that dialectical topics played in the presentation of his arguments. The most important texts by far are those that help us to understand his apparently strong assertions about the truth agreeing with the truth along with the implicit corollary relevant to astronomy, the exact sciences, and natural science in general that false hypotheses will generate results that reveal inconsistencies, irregularities, and striking unexplained facts. This, I suggest, is what Copernicus meant by his promise that his obscure remarks would become clearer in the proper place. I have identified these passages in chapters three and eight, but I gather them here together with comments on the role of dialectic in Copernicus’s arguments. Although not a text on logic, the idea expressed in Nicomachean Ethics I, 8, 1098b11–12 (“with a true view all the data harmonize, but with a false one the facts soon clash”) is reasonably close to Copernicus’s belief that false hypotheses will generate results that are unsatisfactory. In Prior Analytics II, 2–4, Aristotle makes it clear that in cases where demonstration is the aim or where we assert a causal connection between premises and a conclusion, then the premises must be true for the conclusion to follow. Some readers think that Copernicus also believed that he had demonstrated the truth of the heliocentric theory, but I have argued that none of his arguments satisfies the conditions for a genuine demonstration in the Aristotelian sense. Similarly, the text from Metaphysics I minor, 993b26–27 (“that which causes derivative truths to be true is most true”), the text that Copernicus very likely knew, suggests that Aristotle had demonstration in mind.5 I have concluded in light of the dialectical and probable nature of his arguments and conclusions that Copernicus expanded Aristotle’s criterion from causal connections entailed in propter quid demonstrations to the somewhat weaker criterion of relevance. Medieval and later scholastic commentators applying Aristotelian principles to astronomy concluded that astronomical hypotheses could not be certified by observational data because the data can be derived from or made to fit several alternative hypotheses. To put it in the 5
The text is cited by Rheticus, Narratio prima, but in Bessarion’s translation. See Rosen tr. 142, n. 133. Compare the edition by Hugonnard-Roche, Verdet, Lerner, and Segonds with French translation, with that in Rc. For the quotation, see Sc, 71, lines 118–123; Rc, 37, lines 16–20.
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technical terms of Aristotelian terminology, the data and the principles assumed to account for them are not convertible. To assert that they are convertible, as Copernicus seems to imply, is to commit the fallacy of affirming the consequent. The commentators adopted or preferred those hypotheses that agreed with the more fundamental principles of cosmology and natural philosophy.6 That move was already implicit in Ptolemy’s Almagest I, 7, where he took the trouble to recite the Aristotelian objections to the motion of Earth, even adding his own objection based on Aristotle’s ratio of weight to resistance. This was the impasse that Copernicus confronted. In Commentariolus, De revolutionibus I, 4 and in the Preface, he outlined a strategy for breaking through the impasse. He emphasized the failures of his predecessors, explained the alternatives, refuted the Aristotelian assumptions and conclusions related to simple, natural elemental motions, and proposed the motions of Earth as the only way to resolve the problems and produce a coherent system. In the next section on reception, I will return to Copernicus’s insistence on discovering or asserting true hypotheses. The only other citation from a logical text known to me is from Posterior Analytics I, 4, 73b4–5.7 Aristotle says that predicates that belong to a thing as an element of its essence or as included in its definition belong to the thing per se. Predicates that belong to a thing in neither of these ways are said to be accidents. Also in Metaphysics VI, 7, 1033a7–13, Aristotle compares a sick and healthy man. Aleksander Birkenmajer speculated that Copernicus conflated these two passages in his comments in De revolutionibus I, 8, where he compares circular motion with “being alive” and rectilinear motion with “being sick.” Copernicus maintains that rectilinear motion occurs only to things that are not in their proper condition and not in complete accord with their nature, suggesting that he regards rectilinear motion as an accident.8
6 As Crombie, Styles, 1: 530–537, so neatly summarizes in citing Averroes, Thomas Aquinas, Agostino Nifo, Alessandro Piccolomini, Peter Ramus, Christopher Clavius, and Michel de Montaigne. 7 Incorrectly cited by A. Birkenmajer as I, 3 in his commentary to the Latin edition, De revolutionibus, Opera omnia, 2: 369. 8 A. Birkenmajer, 369.
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But it also seems plausible that in this context Copernicus had the following passage in mind from De caelo II, 12, 292b1–25, where Aristotle says the following: That which is in the best possible state has no need of action. That which is nearest to its best possible state should achieve it by little and simple action, and that which is farther removed by a complexity of actions. Just as with men’s bodies one is in good condition without exercise at all, another after a short walk, while another requires running and wrestling and hard training, and there are yet others who however hard they worked themselves could never secure this good, but only some substitute for it.
As I indicated, scholars have been more thorough in identifying Copernicus’s acquaintance with Aristotle’s texts in natural philosophy. Copernicus knew or referred to De caelo I, 1, and especially the following passage (268b7–10):9 Now bodies that are classed as parts of a whole are each complete according to our formula, because each possesses every dimension. But each part is limited by contact with that part which is next to it by contact, for which reason each of them is in a sense many bodies. But the whole of which they are parts must necessarily be complete, and thus, in accordance with the meaning of the word, have being, not in some respect only, but in every respect.
In several passages of De revolutionibus but principally in I, 1–2, Copernicus asserts the completeness of the universe, and implies its finiteness and the relation of the parts of the universe to the whole. In De caelo I, 2, I, 8, and II, 14, where Aristotle argues for the finite extent of the universe, he makes the assumption, implicitly regarded by Copernicus as fatal, that simple elements have simple motions.10 In De revolutionibus I, 7, where Copernicus repeats the ancients’ arguments
9
I have combined the translations by Stocks and by Guthrie, On the Heavens. I have modified all of the translations slightly. To avoid misunderstanding, I repeat here my conviction that Knox, though expressing caution about his discoveries, has correctly identified texts from Pliny, Cicero, and the Suidae lexicon as the sources on which Copernicus relied to re-interpret Aristotle. See Knox, “Copernicus’s Doctrine of Gravity,” 189–208. Knox does not reject the idea that Copernicus was familiar with Aristotelian and scholastic interpretations, but emphasizes the extent to which Copernicus’s account relies on other sources. I am in wholehearted agreement with his view, although I am more inclined than he to understand Copernicus’s modifications as re-interpretations of Aristotle’s principles or of the Aristotelian tradition. 10 These texts are also cited by Rheticus, Narratio, Sc, 58; Rc, 22; Encomium Prussiae, Sc, 85; Rc, 54; and De terrae motu et Scriptura Sacra, Rc, 65 and 69–70.
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supporting the conclusion that Earth is the center of the universe, he refers explicitly to Aristotle without specifying a text. Copernicus implies in I, 7 and explicitly argues in I, 8 that if Earth rotates on its axis, then a falling body would have a compound motion, and, therefore, simple elements would not have simple motions. If Earth rotates and does not exhibit all of the dire consequences predicted by Aristotle and Ptolemy, then its rotational motion would be natural, not violent. It is in this context that he asserts the principle of the relativity of motion and the equivalence between the observations that we make whether Earth rotates or is stationary. There is some disagreement among interpreters whether Copernicus considered the motions of falling bodies unnatural or violent, but Copernicus’s language suggests that he relativized the concepts “natural” and “violent.” He says that bodies that move with rectilinear motion are not in their proper condition and not in complete accord with their nature. He does not say that the motions themselves are violent, but rather implies that the removal of bodies from their natural place or condition involves violence. As we saw in chapter nine, rectilinear motion is natural insofar as it is caused by gravity (a natural appetite), but its acceleration requires a cause, the impetus of its weight. Indeed, Aristotle himself, in the very complicated analysis of self-moving bodies in De caelo III, 2, makes a similar point about natural elemental motions. Aware that bodies accelerate as they fall, he apparently concludes that the cause of acceleration must be partly violent. The passage (301b18–30) is obscure. Aristotle distinguishes between nature as a cause of motion in the thing itself, and force as a cause in something else or in the thing itself regarded as something else. Force accelerates natural motion, as in a stone downwards, and is the sole cause of unnatural. Now, as Aristotle explains, he regards air as an instrumental cause because its nature is to be both light and heavy. Why does it aid upward movement in one case, and downward in another? The answer is because it is pushed and receives an impulse from the original force. The original force transmits the motion by impressing it on the air. Now, what is the original force in the case of a falling body? Aristotle does not say, but what other causes are there for its motion downwards other than the weight of the body and the removal of obstacles to its motion? The original force that causes acceleration must be the body’s weight (the thing itself regarded as something else), and its actual rate of acceleration in a given case is partly the result of the instrumentality of air and of the resistance of
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the medium. Little wonder that some scholastics found the notion of the transfer of motion directly to the body (impetus) compatible with Aristotle’s account.11 It would follow that bodies that fall (or generally move, as fire upwards) or move in a rectilinear fashion are, as it were, striving to return to their most natural condition. Furthermore, Copernicus argues that natural motions are uniform and eternal whereas rectilinear motions undergo variation in the form of acceleration and sudden stops.12 As we noted in chapter nine, Copernicus’s account of fire is ambiguous. Copernicus combines Aristotelian conceptions with non-Aristotelian accounts. Aristotle’s account in Meteorology I, 3 is not consistent with the account in De caelo, and he also seems to make a distinction between some sort of celestial fire and what we call fire. On the one hand, Copernicus appears to adapt Aristotle’s account, but in doing so he suggests that fire is not a terrestrial element and that its motion upwards, which he claims decelerates as it approaches the periphery, is violent. His reference to the expansion of fire as in explosions suggests that the force diminishes with distance from its source.13
11 Even the Latin version of Aristotle’s text in the Leonine version of the works of Thomas Aquinas combines nature and force as causes of motion and acceleration respectively. See Aquinas, Opera omnia, Lectio 7, 249 (Text 28): “Quoniam autem natura est in ipso existens motus principium, virtus autem in alio secundum quod aliud; motus autem hic quidem secundum naturam, hic autem violentus, omnis. Eum quidem qui secundum naturam, puta lapidi eum qui deorsum, velociorem faciet quod secundum virtutem: eum autem qui praeter naturam, totaliter ipsa. Ad ambo autem tanquam organo utitur aere. Natus est enim hic et levis esse et gravis. Eam quidem igitur quae sursum faciet lationum secundum quod levis, cum feratur et sumat principium a virtute; quod deorsum iterum secundum quod gravis: velut enim imprimens tradit utrique. Propter quod et non assequente eo quod movit, fertur vi motum. Si enim non tale aliquod corpus existeret, non utique esset qui vi motus. Et eum autem qui secundum naturam uniuscuiusque motum promovet eodem modo. Quod quidem igitur omne aut leve aut grave, et qualiter praeter naturam habent se motus, ex his manifestum.” 12 This appears to be a case where he uses an Aristotelian principle against Aristotle, for in De caelo II, 3, Aristotle asserts that “the circular movement is natural, because otherwise it could not be eternal for nothing unnatural is eternal.” But, as Dilwyn Knox, pointed out to me, it does not follow from Aristotle’s assertion that everything natural is eternal. 13 Rosen, Commentary, Revolutions, 345, 347–348, 350–351, 353–355. Cf. Moraux, 229–233; A. Birkenmajer, “Commentary,” 363, 370–371, and 387. See also Knox, “Ficino and Copernicus,” 413–414, where he points out that the association of natural places with the wholes to which God has consigned them became a standard Neoplatonic doctrine, and some commentators thought it was Platonic. See also Knox, “Copernicus’s Doctrine.” Rheticus, De motu terrae, Rc, 70, in referring to De caelo II, 14, 296b21–25, shows no indication that he rejected fire as an element.
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Also in this context Copernicus makes the controversial reference to impetus, suggesting that weight generates impetus in the falling body and that bodies cease to be heavy or light when in their natural place. Circular motion, by contrast, continues forever in a uniform manner because it has an unfailing cause. He does not specify the cause. Some have suggested that he is referring here to impetus again, or alternatively, to the form of a sphere, but he may rather have meant the original moving cause, namely, God. Copernicus regarded impetus as resulting from a quality that weakens, as in the case of a falling body. As for the suggestion that the form of a sphere is a cause, not all spheres rotate. For example, he does not attribute rotation to the Sun. The argument about an unfailing cause and the resulting uniform and eternal motion appears to be an adaptation of an Aristotelian passage from De caelo II, 6, 288a28–35: Because everything that is moved is moved by something, the cause of the irregularity of movement must lie either in the mover or in the moved or both. For if the mover does not act with a constant force, or if the moved were altered and did not remain the same, or if both were to change, the result might well be an irregular movement in the moved. But none of these possibilities can be applied to the heavens.
If Copernicus intended to apply the theory of impetus here, then we would have to conclude that in the case of heavenly motions, he regarded impetus as indefatigable. But, as we have just seen, the principle is Aristotelian and has nothing transparently to do with the theory of impetus.14 With Earth itself a sphere with a natural capacity for circular motion and embedded in or attached to a celestial sphere, Copernicus seems to imply that the rotation of the celestial sphere actualizes the capacity of Earth for circular motion and rotation. We have already cited the passage from De caelo II, 12, as a possible source for Copernicus’s comparison of circular with “being alive” and rectilinear with “being sick.” Copernicus does not provide a thorough account here, leaving us to construe his comments in a way that seems the most consistent with his theory. In the next chapter he would also have seen Aristotle’s comments about the Pythagoreans and their view about the motion of Earth around a central fire, although he gives Plutarch as his source in the Preface. He cites it there as evidence that
14 Rosen, 348–349; A. Birkenmajer, 369; and Moraux, 230–233. Compare Schmeidler’s virtual silence, Kommentar, 81–82.
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some ancients proposed the motion of Earth. He does suggest that he derived his hypothesis from such comments, yet the context rather indicates that his intention was rhetorical, namely, as support for the legitimacy of his own speculation.15 Consequently, Copernicus dismisses Aristotle’s analysis in De caelo I, 3–4 (on heaviness and lightness, and the motion of a body as due to a simple quality), as a logical exercise.16 But Copernicus also commits himself to the “Platonic axiom” and Aristotle’s application of it to the uniform circular motions of the heavenly bodies, insisting significantly that each motion encircle its own proper center. In De caelo II, 13; III, 2; IV, 3; and in Meteorology IV, 9, Aristotle argued for the center of Earth as the center of gravity, citing the principle that the motion of the whole is the same as the motion of the part. In De revolutionibus I, 7, Copernicus recites the Aristotelian arguments, which he proceeds to refute in I, 8. In I, 9, he also argues that there is no one center of the celestial circles, which he uses to relativize the notion of center of gravity. Copernicus then adapts the Aristotelian principle about the relation between part and whole to argue for the natural circular motion of earth, leaving the rectilinear component of a falling body as the result of the body’s inclination to be joined with the whole.17 In De caelo I, 5–9, Aristotle goes on to argue for the finiteness of the universe based on the principles and conclusions established in the previous chapters. It seems clear from his insistence on heliocentrism and on the stability of the stars that Copernicus too accepted the finiteness of the universe, yet in De revolutionibus I, 8 he leaves the question of whether the universe is finite or infinite to natural philosophers. Earlier I argued that he adopted this tactic because natural philosophers were divided on the question, but I ended section five of chapter nine with the comment that the conclusion was provisional. Copernicus read Aristotle’s arguments in De caelo closely enough to recognize a problem. Aristotle’s conclusion and that of all Aristotelians followed from their analysis of the motion of the stars in a circle, which has to
15 Moraux, 227, also cites the passage from Aristotle here, but also thinks that Copernicus had only a secondary interest in the ancient theories. Rheticus, Narratio, Sc, 61; Rc, 26–27, also refers to Plato, Timaeus 40 B-C, and Aristotle, De caelo II, 13. But see Knox, “Copernicus’s Doctrine,” for a thorough review of ancient sources and their availability to Copernicus. 16 Rheticus echoes the criticism in De terrae motu, Rc, 65. 17 Rosen, Commentary, 348 and 350–351. Compare A. Birkenmajer, 365–366, 368, and 382; and Moraux, 227 and 231.
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be finite because it is completed within a day, and from the rectilinear motions of sublunar bodies. Because he had placed the Sun and stars at rest, there was now no compelling reason that would generate a logical contradiction for asserting apodictically that the universe is finite. Copernicus may have regarded the question as an empirical one or as one that perhaps cannot be settled at all with certainty.18 In I, Introduction and I, 1, however, Copernicus asserts that the universe is spherical and a complete whole, but his reasons have an a priori and aesthetic character about them. Where Aristotle supports his conclusion about the sphericity of the universe and the heavens as a complete whole as a consequence of its circular motion (De caelo II, 4), Copernicus asserts that spheres are the most beautiful, perfect, and complete objects. Hence, it is fitting that the universe be one complete whole. Where he expressed doubt about its finiteness is also illuminated, I believe, by reference to Aristotle’s remarks in De caelo I, 9. There Aristotle distinguishes three different senses in which the word “heaven” is used. All of them support his belief in the finiteness of the universe, but in De revolutionibus I, 8, there are indications that Copernicus also had in mind scholastic discussions about void space beyond the visible heavens and about even more senses in which Christians talk about the heavens, including the empyrean. Here is an excellent example where the reading of Copernicus’s works benefits from comparison with Aristotle’s texts and their scholastic commentaries.19 These are the sorts of puzzles that motivate discussions about the compatibility of concepts such as “whole,” “infinite,” and “center.” Likewise, Copernicus adapts Aristotle’s argument in De caelo II, 8 that the stars are attached to the spheres that move them in circles, rejecting the idea that each of the stars has its own proper circular motion. Of course, in adopting the Earth’s rotation on its axis, Copernicus eliminates the daily rotation of the stars, but he retains the idea that the planets are attached to spheres, explaining why their motions are circular or compounded of circular motions (De revolutionibus I, 4).20
18 Compare the comments of Birkenmajer, 362 and 366; Rosen, 351–353; Moraux, 231–232; and Schmeidler, 82. 19 Moraux, 229. 20 The idea is also supported by De caelo II, 6–7. See Rosen, Commentary, 348–349; and Moraux, 229. Compare Rheticus, De terrae motu, Rc, 65.
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In De caelo II, 10 Aristotle explained the order of the spheres as a consequence of their distance from the periphery or the most rapid daily motion of the starry vault. As we saw, however, some scholastic commentators known at Cracow interpreted this principle as a causal explanation of their varying motions while describing them as ordered according to periods as measured from Earth.21 Contrary to Aristotle in De caelo II, 11, where he argues that the planets, Moon, and Sun are spherical and yet do not move themselves because a sphere has no inherent capacity for motion, Copernicus argues that a sphere is particularly suited to rotation. Yet nowhere, to my knowledge, does Copernicus conclude that the planets, Moon, and Sun have an axial rotation. To that extent, then, he seems to have been following Aristotle’s reasoning here as well, for Aristotle keeps the spherical Earth at rest.22 Copernicus agreed with Aristotle (De caelo II, 14) about the shape of Earth, and that bodies falling towards its surface strike the surface at an angle perpendicular to the tangent of the curved surface, and tend towards the center of Earth. He rejected Aristotle’s objections to the motions of Earth based on astronomical observations. Aristotle could not understand how the observations of the stars would remain the same if Earth moved. Ptolemy, we know, considered Earth’s rotation on its axis, and realized that the observations would be exactly the same. Ptolemy did not object on astronomical or mathematical grounds, but on strictly physical ones, that is, what we would observe of the motions of bodies here on Earth. As for the motion of Earth from one place to another, Ptolemy did not consider orbital motion. Following Aristotle and influenced by Stoic ideas, Ptolemy assumed that if Earth moved from its place at the center, it would have a rectilinear motion. He objected again on physical grounds. Here we might also suppose an astronomical objection, for if Earth moved in a straight line, then it would presumably approach stars in one direction and recede from the stars in the opposite direction, a motion that should produce a visible difference in the distances between the stars. This would be another version of the problem of stellar parallax, but Ptolemy did not in fact raise this objection. Aristotle seemed
21 This, of course, was the opinion advanced by Johannes Versoris. See chapters four, seven, and nine for the details. Compare Birkenmajer, 373; and Rosen, 350 and 355. 22 As Rosen, 347, emphasizes.
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to think that if Earth moved from place to place that it would have a motion along the ecliptic. But he evidently failed to recognize that its axis would be tilted to the plane of the ecliptic, and thus he mistakenly concluded that our observations of the stars would be different. Aside from the fact that Aristotle’s assumption was wrong, Copernicus’s only anticipation of such objections led him to suppose that the stars are farther than imagined, and he argued that God put them at such a great distance so that we might detect the motions of the planets more easily. At the end of De revolutionibus I, 10, he says: From Saturn, the highest of the planets, to the sphere of the fixed stars there is an additional gap of the largest size. This is shown by the twinkling lights of the stars. By this token in particular they are distinguished from the planets, for there had to be a very great difference between what moves and what does not move. So vast, without any question is the divine handiwork of the most excellent Almighty.
Copernicus was no doubt familiar with one of Aristotle’s favorite examples, namely, the relation between the observation of the nontwinkling of the planets and the nearness of the planets in Posterior Analytics I, 13, 78a30–78b3 and in De caelo II, 8.23 Physics II, 2 represents the view about the relation between mathematics and natural philosophy. Copernicus modified Aristotle’s account here at least with respect to determination of the order of the cosmos. He also implicitly rejected the Aristotelian doctrine of natural place and its relation to motion as supported in Physics III, 1 and IV, 1–9. Copernicus tended to attribute motions to bodies on the basis of their formal characteristics and their inclination to be united with other like bodies in their most perfect condition. This inclination was implanted in things by God.24 Copernicus went further than Aristotle in Physics IV, 11, where Aristotle relates time to motion, and measures time by distance. By measuring the order of the spheres according to their periods, Copernicus discovered a principle by means of which he could determine the relative linear distances of the planetary spheres from the Sun.25
23
Rosen, 360; A. Birkenmajer, 385; and Schmeidler, 88. A. Birkenmajer, 366 and 382; and Rosen, 359. See also Rheticus, De terrae motu, Rc, 70. 25 Rosen, 367. 24
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Aristotle’s analysis of motion in terms of actuality and potentiality (Physics VIII, 4), and the argument leading to the existence of an unmoved mover (Physics VIII, 6–10) involved consideration of natural elemental motions and projectiles. Natural things have a capacity or potentiality that generates motion towards their actuality, which Aristotle views as their most perfect state. The ambiguity in his account generates some confusion for elemental bodies achieve actualization when they are perfectly at rest in their natural places.26 The proper motion of the heavenly spheres is uniform, circular motion (Physics VIII, 6). Copernicus upset the relation between the unmoved mover and the prime mover of the starry vault. In Copernicus’s natural theology, if you will, God as creator endowed the stars, planets, Moon, and Sun with properties, and God endowed the planets and Moon with their uniform motions. Perhaps the topsy-turvy consequence of his ordering led him in De revolutionibus I, 10 to cite the references to the Sun as the “lantern of the universe, its mind, and its ruler,” “a visible god, . . . the all-seeing.” “Thus indeed, as though seated on a royal throne, the Sun governs the family of planets revolving around it.”27 Copernicus also finds an opportunity to cite Aristotle here in referring to the relation of Earth and Moon: “The Moon has the closest kinship with the Earth.”28 In addition to Metaphysics I, 1, I minor 1, and II, 4–5, Copernicus was evidently familiar with other passages. Metaphysics III, 2 repeats Aristotle’s view about primary beings and his rejection of mathematical entities as belonging to primary being. VI, 7 contains the text in which he characterizes health as the best state and sickness as its privation. Health as product comes out of the privation (1033a11).29 26
Rosen, 348, 351, and 353; and Moraux, 231. Rosen’s translation, 22. See also Rheticus, De terrae motu, Rc, 60, where he refers to Aristotle, Physics VIII, 1, and to Plato, Timaeus 38 B-C. 28 De generatione animalium, IV, 10, 77b18–19. The reference does not fit perfectly, and so commentators have pointed to Averroes as the source. Compare Rosen, 360; and A. Birkenmajer, 383–384. 29 A. Birkenmajer, 369. On Metaphysics I, minor, 1, 993b11–13, see Copernicus, Letter Against Werner, tr. Rosen, Complete Works, 3: 146 and 151, n. 11. As mentioned before, I checked Tiedemann Giese’s copy of the Metaphysics at Uppsala to see if this was Copernicus’s source, and I repeat it here for the sake of convenience. Catalogued at Uppsala as Inc. 31:164, the text on fol. 13v reads: “Non solum autem his dicere gratiam iustum est quorum aliquis opinionibus communicaverit. Sed his qui adhuc superficialiter enunciaverunt; etenim conservunt aliquid.” Giese’s gloss does not correspond with Copernicus’s comment on the passage, hence this version was not Copernicus’s source. 27
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Copernicus implicitly rejected Aristotle’s dialectical argument (Metaphysics XI, 10) that refutes the actual infinite extent of the universe based on the daily motion of the starry vault and the centrality of Earth. The motionless stars and the motions of Earth remove the basis for Aristotle’s conclusion, leaving Copernicus with no observational basis for affirming the finiteness of the universe. Still, Copernicus seems to have preferred that view, but he evidently realized that his only justification was a metaphysical preference for sphericity, wholeness, and completeness, principles that Aristotle also preferred.30 Aristotle’s description of the universe as perfect, complete, beautiful, and good, and thus worthy of admiration (Metaphysics XII, 7) accords with Copernicus’s praise of astronomy in De revolutionibus I, Introduction. Aristotle’s acceptance of the spherical astronomy of his predecessors followed from his assertion that the numbering and ordering of the spheres and their motions depend on that mathematical science which is most like philosophy, astronomy. This is so because astronomy studies not just sensible being, but the kind of sensible being that is primary and eternal (1073b1–10).31 I have argued that questions about the ordering of the spheres and their varying distances from Earth led Copernicus to the heliostatic, heliocentric theory. Although he rejected the details of Aristotle’s analysis (Metaphysics XII, 8), Copernicus, I contend, revealed his Aristotelianism most conspicuously in his acceptance of the axiom of uniform circularity and in his belief that we can discover the true order of the spheres, the principal task of mathematical astronomy.32 Guided as they were by a vision of an ordered cosmos, both Aristotle and Copernicus sought a principle of order. Focusing as he did on causal principles, Aristotle emphasized the relation between the unmoved mover and the prime mover. As we saw, scholastic
30
A. Birkenmajer, 366; also 370, where he suggests that Copernicus may also have relied on Metaphysics XII, 6 (1071b20–25) about potentiality and actuality to support his view that the natural capacity for a sphere to move does not entail that all spheres move. As Dilwyn Knox pointed out to me, the reference seems forced because Aristotle does not address the problem of spherical motion explicitly here. 31 Rosen, 348; A. Birkenmajer, 370; and Moraux, 229. 32 Rosen, 348; A. Birkenmajer, 370; and Moraux, 229. See also Rheticus, Narratio, Sc, 57 and 71; Rc, 21 and 37. Of course, the origin of concentric spheres is attributable to Eudoxus, and the axiom of uniform circular motion was attributed to Plato, but Aristotle transformed it unambiguously into a physical, not just a mathematical, computational device. Copernicus adopted Aristotle’s physical interpretation of celestial spheres.
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commentators like Johannes Versoris adopted Aristotle’s dynamic analysis, and combined it with astronomical models that ordered the spheres from the center. Copernicus adopted the astronomical ordering from the center. Even Aristotle, however, in Metaphysics XII, 10, emphasized the unity of the universe. Everything in the world is connected for all things are ordered to one end. In some translations, the idea is expressed from the point of view of the relation of all things to a common center. The Greek text reads pròs hén “ad unum” in Latin, but Aristotle uses the analogy of a household, suggesting order around a central reference such as a hearth. Copernicus rejected the idea that all circular motions have a unique center, but he retained the principle of ordering the spheres from the center.33 In Meteorology, Aristotle addressed more specific questions about the elements and comets. How are they ordered? How is Earth heated? Again, Aristotle’s analysis proceeds from consideration of causal relationships and the nature of the celestial spheres. Fire is a sublunar element, hence the heat generated by the Sun is the result of its motion. The fire that surrounds the terrestrial sphere is driven downwards by the motions of the celestial sphere. Celestial rotation also causes the circular motion of air (I, 3 and 7). Copernicus’s comments in De revolutionibus I, 8 (about the air moving with the rotating Earth) represent another example where he adapts an Aristotelian explanation, even referring to the Aristotelian account of comets.34 Copernicus does not explicitly adopt the Pythagorean notion of a central fire (De caelo II, 13), but he does refer to the Sun as a lamp that lights up the entire universe (De revolutionibus I, 10). He thereby suggests that heat is generated by light.35 Aristotle (Meteorology I, 14) emphasized the smallness of Earth in comparison to the whole universe, a view that Copernicus (De revolutionibus I, 6) shared, but to argue to the contrary that Earth’s distance from the center is as a point to the immensity of the universe.36
33 See the translation of Metaphysics XII, 10, 1275a18–25 by Hope, 336, 24a. Compare Schmeidler, 83. Ordering around a hearth presumably did not inspire Copernicus to order the cosmos around the Sun, yet the metaphor is consistent with his vision. 34 Although Pliny, Natural History II, 22, 89, is the likely direct source. See A. Birkenmajer, 367; and Rosen, 352. Compare Schmeidler, 82. See also Knox, “Copernicus’s Doctrine,” 167, n. 48. 35 Rosen, Commentary, 352, and A. Birkenmajer, 367. 36 Moraux, 229.
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Meteorology IV, 9 and De generatione et corruptione II, 3–4 discuss the relation between the elements, especially water and earth. As commentators have pointed out, Copernicus’s citation of the definition of fire as “blazing smoke” is from these passages in Aristotle. Copernicus evidently relied on some Aristotelian source, for he rejected what he calls the Peripatetic view on the proportion of water to earth. Earth and water form that which moves towards the center—on that Aristotle and Copernicus agree.37 As we have noted, Aristotle attributed a centripetal impulse (De caelo II, 14) to the motions of the heavenly spheres, that is, that their circular motions generate an inward pressure towards the center.38 With the exceptions noted, this study tends to confirm Aleksander Birkenmajer’s judgment that Copernicus conserved those features of Aristotelian natural philosophy that he could reconcile with heliocentrism.39 In addition to Birkenmajer and other such interpretations, however, I accept Knox’s exhaustive examination of other sources on which Copernicus relied to accomplish his transformation of Aristotelian doctrine.40 Copernicus achieved a drastic adaptation of Aristotelianism to heliocentrism by reliance on other ancient sources made available by printed editions of texts, summaries, encyclopedias, and dictionaries. 3. Epilog: Reception of Copernicus’s Interpretation Originally, I had intended to end this study with a general summary of the reception of the Copernican theory down to 1600. That overly ambitious idea I put aside as soon as I began to assemble bibliography on reception. Such a summary would be premature, for ever more specialized studies are appearing, all making it clear that the story of the reception of the Copernican theory will require a very long book.41
37 De revolutionibus I, 2–3. See also Pliny, Natural History II, 65, 164–165; Rosen, Commentary, 345. 38 A. Birkenmajer, 368; and Rosen, 353. 39 A. Birkenmajer, “Éléments,” 37–48, and approved by Moraux, 233 and note 53. 40 Knox, “Copernicus’s Doctrine,” above all. See Tatarkiewicz, “Mikołaj Kopernik,” 7–18, for parallels between Copernicus’s texts and ancient/medieval sources on cosmic symmetry. 41 Foundational remains the work of Zinner, Entstehung. Compare Westman, “Essay Review,” 259–270. See also Costabel, “État,” on methodological problems with the whole notion of reception. For more recent sources and studies, see Rc, and also
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My study is about Copernicus’s appropriation and adaptation of Aristotelianism to the heliocentric theory. The epilog constitutes a modest contribution to the evolution of ideas on the nature of astronomical and cosmological hypotheses by tracing the reactions to Copernicus’s interpretation of Aristotelian logic and natural philosophy. Despite my narrowing of its goals, even this survey is not exhaustive. My aim is rather to try to illuminate the reception of Copernicus’s claims about the truth of astronomical hypotheses and the extraordinary transformation that Kepler achieved in how we should understand hypotheses and models in astronomy.42 The parties to these discussions interpreted Aristotle’s comments about truth and consequences in ways that we can distinguish into five types recognizable by the different nuances in their interpretations. The first I call the genuinely Copernican view, according to which we can conclude that some cosmological hypotheses are more probable than other alternatives because the results are consistent with the fundamental assumptions of astronomy and account for otherwise inexplicable facts. Of alternative mathematical models, one must be true on the assumption that we have exhausted the alternatives, but we may not be able to decide which alternative is true because there is no compelling reason or consensus. The second I ascribe to Rheticus, who adopted a more robust view of the truth of cosmological hypotheses, and who was more optimistic about the demonstrability of the conclusions. He may have been equally realist about the truth of astronomical hypotheses, and his recognition that the Sun is somehow the cause of planetary motions surpassed Copernicus’s view, which was compromised by having the
on the reception as treated in several international meetings and collected as proceedings in Reception, Colloquia copernicana, 1, Studia copernicana, 5. See also the papers on the reception in Colloquia copernicana, 2, Studia copernicana, 6; Colloquia copernicana, 4, Studia copernicana, 14; The Copernican Achievement; and Das 500 Jährige Jubiläum. For an excellent brief summary of the 16th-century reception with extensive bibliography, see Pantin, “New Philosophy,” 237–262. As Pantin turns to the seventeenth century, however, her analysis becomes curiously reductionistic. In addition, see Diffusione; Vermij, Calvinist Copernicans; de Bustos Tovar, “Introducción,” 235–252; Dobrzycki and Szczucki, “On the Transmission,” 25–28; Donahue, “Solid Planetary Spheres,” 244–275, followed by Heilbron, “Commentary” 276–284; and Juznic, “Copernicus in Ljubljana,” 231–232. 42 Crombie, Styles, 530–543, provides a selective but illuminating summary of the logical and methodological issues regarding hypotheses. See Jardine, “Significance,” 168–194; idem, “Many Significances,” 133–137.
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center of Earth’s orbit, not the true Sun, as the center of planetary motions. The third is the standard Lutheran interpretation sometimes referred to as the Wittenberg Interpretation.43 Astronomical hypotheses are fictions devised for the purpose of calculation not for the purpose of ascertaining the truth. Cosmological conclusions are true because derived from the more certain principles of natural philosophy and metaphysics. Even false cosmological hypotheses, however, may yield models that predict the positions of celestial bodies accurately. Aristotle’s pronouncements about truth agreeing with truth refer only to those cases where genuine demonstrations are possible and where the true causes of phenomena have been discovered. The fourth view is Michael Mästlin’s. Mästlin accepted the heliostatic theory, and while judging it as true from a cosmological perspective, he otherwise adopted a thoroughly mathematical interpretation of the theory.44 The fifth and final view we will find in Kepler’s assertions, the details of which I leave for later, but suffice it here to say that Kepler seizes on Aristotle’s assertion that a false hypothesis will sooner or later lead to false results and reveal itself as false. As is by now well known, the first known reactions to Copernicus’s theory were highly critical, accusing him of ignorance of logic and the principles of natural philosophy, of threatening to throw the liberal arts into confusion, and of contradicting the plain meaning of some biblical passages interpreted literally. Roman authorities may have intended to condemn the theory on scriptural grounds, but the criticisms suggest that they were developing a broadly based attack that would refute Copernicus’s understanding of logic, method, natural philosophy, and cosmology. As far as I know, there is no document explaining why that project did not go ahead. We know that its instigators, Bartolomeo Spina and Johannes Tolosani, died, but we do not know why no one else took it up after their deaths. A rehearsal of the circumstances may provide an explanation, after which we may turn
43 Westman, “Melanchthon Circle,” 165–193, and idem, “Three Responses,” 285– 345. I agree with Jardine, Birth, 225–257, that the Wittenberg Interpretation did not constitute an endorsement of skepticism. See also Pantin, 241, n. 19. 44 When Mästlin adopted the theory is unclear, but certainly by 1596. See Methuen, “Maestlin’s Teaching.”
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to Luther’s reaction, Rheticus’s portrayal of Copernicus’s achievement, and the arguments that Tolosani constructed. In 1545, Pope Paul III convened the Council of Trent, a council that met on and off for seventeen years. When it completed its task in 1562, the Church had virtually recreated Roman Catholicism, the Roman Catholic Church that anyone above the age of reason in 1958 would have easily recognized. Aside from reforming its entire bureaucratic structure, establishing a seminary system for the training of its priests, solidifying the authority of the papacy, responding to Lutheran challenges (on the doctrines of faith and works, the priesthood of all believers, and the authority of Sacred Scripture), the Council established the Roman Inquisition under the control of the Holy Office, and, under the jurisdiction of the Inquisition, the Congregation of the Index of Forbidden Books. With respect to Sacred Scripture, the Council decreed that there could be no new interpretation of the Bible that was contrary to the common consensus of the Church Fathers and of modern approved interpretations. Although the interpretation of this decree would take a surprising turn in 1616 by being confused with the doctrine of divine inspiration, there is no evidence that the decree was used against the heliocentric theory until 1616. In spite of the claims of some who ought to know better that the principal objections to the Copernican theory were religious or biblical, nearly everyone rejected the theory on physical, observational, or methodological grounds.45 That is to say, no one, not even the Holy Office in 1616, based restrictions of the theory on exclusively biblical grounds without support from philosophical and the then scientific consensus. The rotation of Earth on its axis and its orbit around the Sun raised numerous physical objections. As we now know, without a physical explanation of how Earth’s atmosphere “sticks” to Earth and insulates us from all of the predicted sensible effects, common-sense objections persuaded the majority of astronomers even to the middle of the seventeenth century that geokineticism was physically impossible. The orbit of the Moon around Earth as Earth orbits the Sun was also physically implausible, and became even more so, not less, after
45 Westman, “Copernicans and the Churches,” 76–113, places theological controversies usefully in the context of standards of textual interpretation.
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Tycho Brahe concluded that the spheres of ancient astronomy were non-existent. The major observational problem, of course, was the failure to observe stellar parallax. That problem also took a while to dissipate. People needed time to adjust to a universe that is much larger than most imagined. Galileo’s telescopic observations and those of more powerful telescopes later in the seventeenth century eventually persuaded most intellectuals that the stars are indeed farther than most had imagined. There was still no observation of stellar parallax, but the excuse that the stars are too far to observe it became entirely plausible. Galileo’s observation of the moons of Jupiter also contributed to acceptance of the plausibility of the Moon’s orbit around Earth as Earth orbits the Sun. From a methodological perspective, we may recognize that there were several major problems, and some of them remain the subject of controversy even to this day. Copernicus adopted the axiom of uniform motions in circles as suited to the heavenly bodies. With all of the resulting epicycles and eccentrics, his mathematical models were as complicated as Ptolemy’s models. Even the supposed elimination of the equant was a dubious achievement, and merely confirms the extent to which Copernicus was obsessed with the axiom of uniform circular motion. Ptolemy’s planetary epicycles were necessary not only to fit the data but also to account for the observation of planetary retrograde motions. Of course, as the epicycle models for the Moon demonstrate, an object can be moved on an epicycle without generating a retrograde motion. Still, the fact that Copernicus proposed a natural explanation for the observation of retrograde motion emphasizes the extent to which he needed epicyclets to regulate the motions of the planets and to account for the latitude of the planets. His planetary epicyclets are very small, but the resulting orbits of the models for the superior planets are not perfectly circular. Copernicus tried to minimize the departure from perfect circularity, but the admission is startling nonetheless. Of course, modern readers who have never looked closely at his book or read more than superficial accounts are surprised to discover that he retained epicycles.46 46
Even Cardinal Bellarmine thought that Copernicus dispensed with epicycles and eccentrics. See his “Letter to Foscarini,” in Finochiarro, Galileo Affair, 67–69. In the document evidently preparatory to the “Letter to the Grand Duchess Christina,” Galileo did not resist the opportunity to correct Bellarmine on this point. See Finocchiaro, 83.
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Beyond that, Copernicus’s eccentreccentric models for Mercury and Venus are complicated and cumbersome. The lunar model is observationally superior to Ptolemy’s, but he achieved it by putting the Moon on a double-epicycle model. And, of course, his latitude theory is another remnant of Ptolemaic geocentrism and his retention of spheres as the carriers of celestial bodies is a remnant of Aristotle’s physical interpretation of concentric spheres. As I have argued, Copernicus distinguished cosmological hypotheses from geometrical ones. The former he held as true, but he adopted a more pragmatic and tentative view on the truth of geometrical hypotheses and models. Only after he thought that he had exhausted all of the mathematical alternatives, did he adopt one, and even then he would commit himself to no more than the assertion that one of them must be true. We have also shown that, like almost all of his contemporaries, he admired both Plato and Aristotle, and he evidently believed that he could adapt ancient and scholastic principles of natural philosophy (Aristotelian and non-Aristotelian) to geokinetic heliocentrism. Unless we appeal optimistically to the survival of Aristotelian conceptions and notions in the ideas of major thinkers down to Leibniz, I concluded that his effort to persuade Aristotelians to adapt their principles to heliocentrism has to be counted among the most abject failures in the history of philosophy.47 That judgment holds at least for the short term. Copernicus understood perfectly well that scholastic Aristotelians would attack him mercilessly. In Book I of De revolutionibus he tried his best to ease them from their dogmatic stance. The first stage was to urge the plausibility of Earth’s motions by means of reinterpreting and adapting Aristotle’s principles accompanied by a brief recitation of the results and advantages of heliocentrism. He probably wrote that effort already in the 1520s. Over the course of the next fifteen years or so he tried to work out the details. Aside from fear over the reception of his theory, numerous calculatory and observational problems that he encountered convinced him by the late 1530s that something was terribly wrong.48 When
47 I take no account of modern neo-scholastic Aristotelians who now find the principles of gravitation, special relativity, and general relativity in Aristotle’s works. 48 Moesgaard, “Hunting,” 93–100, provides an intriguing analysis based on his belief that Copernicus aimed at making the true Sun the center, but found Mars and Venus to be recalcitrant. That failure, Moesgaard thinks, persuaded Copernicus that following Ptolemy had reached its limit. Rheticus reminded Copernicus of what he
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Georg Joachim Rheticus came to visit him in 1539, he stirred Copernicus from his slumber and perhaps even depression. This was a period in which Copernicus experienced several personal problems. Bishop Dantiscus pressured him to end his relationship with Anna Schilling. Copernicus’s legal dispute with a fellow canon, and suspicions of heresy for his support of Alexander Scultetus also troubled him. In addition, there were already indications by 1538 that his health was beginning to decline.49 As Rheticus became familiar with the details of Copernicus’s theory, he became enthusiastic and reminded Copernicus of the advantages of his major results. Perhaps Rheticus’s reaction persuaded Copernicus that there was hope after all that his arguments and results could persuade others. We do not know precisely what happened, but my speculation is supported by several striking facts. Suddenly, Copernicus got back to work. Rheticus did not understand everything perfectly, but he was the first to recognize the true dimensions of Copernicus’s achievement. The change in tone between Book I and the Preface to Pope Paul III (1542) is striking. Still indebted to and respectful of Ptolemy, Copernicus returned to the tone adopted at the beginning of Commentariolus and laid out in more detail than he had ever expressed all of the failures of his predecessors. The most striking are the failures of method and the failure to arrive at the unique structure of the universe. Without much further preparation he explained that he thought that he could find better explanations for the revolutions of the celestial spheres by assuming some motion of Earth, already announced within the first fifteen lines of the Preface and cited in the previous letter from Nicholas Schönberg. By then, of course, word of Copernicus’s theory had spread; there was hardly any reason to hold it back. Still, he explained the circumstances behind the delay, his hesitation, and appealed to the authority of ancient predecessors. Even taking all of those comments into account, we must conclude that his tone is nonetheless startling, more abrupt, and more aggressive. His disdain for objections based on Sacred Scripture takes one by surprise even today. Copernicus had regained his confidence. How else can we account for it except as a result of Rheticus’s intervention? Before we turn to Rheticus’s Narratio prima, however, here
had accomplished, and his enthusiasm persuaded Copernicus to finish the work. On Copernicus’s troubles, see Gingerich, Eye of Heaven, 37. 49 Biskup, Regesta, 171–185; Rosen, “Biography,” 366–372, 382–386, and 394–400.
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is the appropriate place to discuss Luther’s reaction and its very likely effect on Andreas Osiander. The historicity of Luther’s remark in 1541 remains an open question, but supposing that he expressed himself negatively about the heliocentric theory, we can interpret his remark in a plausible way.50 Luther makes two criticisms. Copernicus will turn the whole art of astronomy upside down, another example of innovation for its own sake. Surely what Luther meant is that the relation between natural philosophy and astronomy is clear with respect to questions about the order of the universe. If he did refer to the text from Joshua, the citation has rather the character of a clinching argument than the main reason for rejecting the theory. As we all know, Luther set great store in the biblical text as providing the only legitimate source for Christian doctrine. It is doubtful that he regarded geocentrism as a Christian doctrine, but he probably did see the Bible as supporting the common-sense view about Earth. It is striking that Osiander also warns against the subversion of the liberal arts and appeals to revelation as the only source of certain truth. Whatever Osiander’s motives may have been, he echoed Luther’s reaction. Rheticus seems to have been unimpressed. From correspondence, some of which has disappeared, we know that Osiander was in contact with Rheticus and Copernicus.51 He tried to persuade them to adopt his doubts about astronomical hypotheses. In the “Letter to the Reader,” however, Osiander expressed doubt about all astronomical hypotheses, geocentric as well as heliocentric, but his advice left geocentrism in effect as the standard view in cosmology. Did he mean to imply that geocentrism is divinely revealed? The correspondence makes it clear that he advocated caution and doubt as a strategy to avoid disagreements. But that implies that there were some who would defend geocentrism on biblical grounds, committing themselves to a narrow view of literal interpretation. Perhaps Osiander concluded that this would be a debate without any winners, and so recommended evasion. As we know from Robert Westman’s studies in particular, most Lutherans interpreted astronomical hypotheses in the pragmatic way advocated by Osiander while professing geocentrism
50 Norlind, “Copernicus and Luther,” 273–276. Norlind cites two versions, one by Johann Aurifaber (the one that refers to Copernicus as a fool) and one by Anton Lauterbach, which Norlind considers to be more accurate. 51 For the Narratio prima, see Sc and Rc. For the comment about the correspondence, see the French translation, in Sc, Appendix II, 208.
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on philosophical and cosmological grounds.52 Even Michael Mästlin, who accepted heliocentrism as true, rejected Kepler’s physical interpretation of the theory and his search for a physical explanation of the motions of celestial bodies. I turn now to Rheticus, after whom we may trace the known comments of readers of De revolutionibus. Although the Narratio prima appeared in print three years before De revolutionibus, I include Rheticus in the category of reception. That said, I cannot overlook the fact that the Narratio was written before the Preface to Pope Paul III. Although the ideas in the Preface are, I believe, Copernicus’s, we must consider the possibility that Rheticus influenced Copernicus’s choice of words and the specific formulation of his thoughts. In that respect, we cannot completely ignore Rheticus’s priority.53 In the Narratio, Rheticus cites Aristotle explicitly on several occasions, often in the Greek. We do not know how familiar Copernicus was with the Narratio. It is hard to believe that he did not have his own copy, but if so, then it has disappeared. Its publication in 1540 at Gdańsk and second edition in 1541 at Basel settle some issues, but they also provoke further questions. Rheticus confirms Copernicus’s work with Domenico Maria Novara, yet other remarks are the stuff of legends, as, for example, the report that Copernicus lectured on his theory before a large audience in Rome. Where Copernicus says virtually nothing about astrology, Rheticus cannot resist making predictions and relating them to Copernicus’s efforts to determine the mean motion of the solar apogee. Rheticus expresses Copernicus’s relation to his predecessors ambiguously. Time reveals the errors of astronomy. An imperceptible error at the foundation of astronomy is revealed by the passage of time.54 Rheticus here makes the claim that Copernicus could not just restore astronomy but had to build it anew, for Copernicus’s aim was to arrange the order of all of the motions and appearances in a certain and consistent structure or harmony. On the other hand, immediately after that comment, Rheticus portrays Copernicus’s work as a restoration of Ptolemaic astronomy, arguing forcefully that Copernicus’s 52
Westman, “Melanchthon Circle”; idem, “Michael Mästlin’s Adoption,” 53–63; idem, “Comet and the Cosmos,” 7–30; and idem, “Three Responses,” 285–345. 53 Burmeister, I: 44–62. 54 Sc, 52–53.
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achievement can be understood only as a completion and fulfillment of the chief task of astronomy. Ptolemy had failed to establish the perpetual and consistent connection and harmony of celestial phenomena. By proposing new hypotheses, Copernicus solved the problems, says Rheticus, who proceeds to explain a number of the inconsistencies and observed irregularities and how Copernicus’s hypotheses achieve what Ptolemy’s failed to achieve. In the enumeration of the new hypotheses [IX], Rheticus emphasizes the inconsistencies between natural philosophy and the astronomical observations, soliciting Aristotle’s own authority in support of new discoveries.55 As he turns to the section on the arrangement of the universe [X], Rheticus quotes Aristotle in Bessarion’s Latin translation of the Metaphysics I, minor, 1, 993b26–27: “That which causes derivative truths to be true is most true.”56 Rheticus understands this to mean that Copernicus sought hypotheses that would contain causes capable of confirming past true observations and predicting future true ones. Rheticus understands the connection to be a causal one, but he also seems to be aware of the hypothetical character of the assumptions that we are justified in taking as true provided they include causes from which true results follow. Again a little later, near the end of the section on the motions of the five planets [XIII], Rheticus refers to Aristotle’s dictum that humans by nature desire to know.57 Rheticus immediately relates this desire to our search for causes, and repeats Copernicus’s frustration over ignorance of the causes of the heavenly motions. Near the conclusion of the Narratio, Rheticus again comments on the relation between hypotheses and phenomena [XIV]: “When the observations of scholars have been set forth, the hypotheses of my teacher agree so well with the phenomena that they can be mutually interchanged, like a good definition by the thing defined.”58 Such a characterization is not just Aristotelian, but it is consistent with scholastic accounts of real definitions that express the essence of a thing, that is, the convertibility of the definiens with the definiendum. 55 Sc, 57–58 and 109–110; Rc, 21–22, and the references to Aristotle, De caelo II, 5, and Metaphysics XII, 8. 56 Rosen tr. 142; Sc, 58; Rc, 22. See Blake, “Theory of Hypothesis,” 22–49, esp. 27. In addition, Blake provides a useful summary, and I subscribe to his conclusions on the fallible and probable nature of physical and astronomical hypotheses. 57 Rosen tr. 167; Sc, 71, citing Metaphysics I, 1, 980a21; Rc, 37. 58 Rosen tr. 186; Sc., 80; Rc, 47.
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In the Encomium Prussiae, Rheticus repeats Averroes’s complaint against Ptolemaic astronomy that its models are adapted to calculation, not to reality.59 It is clear that Rheticus thought that Aristotle’s assertions were the justification and perhaps even the source for Copernicus’s critique of Ptolemaic method, especially his strong claim that the whole truth can follow only from true assumptions. Rheticus evidently believed that Copernicus meant knowledge of the causes. Any results that are false must be due to assumptions that are false. Conversely, if the causes are true, then only true results can follow from them. Worth noting is Rheticus’s emphasis on variations in the distance of Mars from Earth, an issue that I have argued constituted a motive for Copernicus’s formulation of Earth’s orbital motion.60 Rheticus’s most important contribution to the development of the heliocentric theory is his belief that the Sun is the source of movement, namely, that it is a cause of motion.61 Rheticus does not provide any explanation of how the Sun moves the planets, but he seems to have derived this conclusion from the ordering of the spheres and from Copernicus’s explanation of why Ptolemy’s planetary models linked the planetary motions to the motion of the Sun. Rheticus’s emphasis on “common measure” and the ordering of the spheres indicates that he understood Copernicus’s use of the topic from an integral whole, yet he does not say so explicitly. His assertions are also stronger, that is, more demonstrative and less dialectical in tone than we find in Copernicus. Perhaps convinced by Copernicus’s arguments, Rheticus tended to present them as more apodictic and more in agreement with “true” principles of natural philosophy than they in fact are.62 He was also the first to introduce the word systema to refer to both the explanatory hypothesis of the celestial motions and the real ordering of the parts.63 We know from Giese’s letter to Rheticus (July 1543) thanking him for the copy of De revolutionibus that Giese approved of Rheticus’s argument that the motion of Earth does not contradict the Bible. Giese 59
Sc, 193, note 278 for the source. Sc, 162, n. 85. 61 Sc, section [X], 60: “Adde, quod orbes maioris ambitus tardius, et propiores Soli, a quo quis principium motus et lucis esse dixerit, velocius, ut conveniebat, suos circuitus perficiunt.” Cf. 23, 113, and 169, n. 129. 62 Compare especially the texts in Narratio, Sc, 52–53, 58, 60, and 80. 63 Lerner, “Origins,” 410–413. 60
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also refers to Rheticus’s biography of Copernicus, which unfortunately has been lost. Giese offers no correction of the biography, adding only a few details about Copernicus’s death. Although Giese was an expert on Aristotle and apparently approved of Copernicus’s theory, he offers no explicit comments in its defense or about its relation to Aristotelian natural philosophy.64 In a letter to Dantiscus, perhaps the first known reaction to Rheticus’s Narratio, Gemma Frisius expresses a view similar to Osiander’s in adopting a purely hypothetical interpretation of heliocentric hypotheses. The question of their truth is of no importance; all that matters is whether the observations follow the models.65 The next known reaction is contained in the now famous treatise by Johannes Maria Tolosani, discovered and partly edited by Eugenio Garin.66 Tolosani wrote his critique around 1546 to 1548. Tolosani was a Dominican friar, an astronomer, and the friend of Bartolomeo Spina, Master of the Sacred Palace during the pontificate of Paul III. Spina had intended to write a refutation of Copernicus’s De revolutionibus, perhaps with the intention of condemning it as contrary to Sacred Scripture, but he died in 1546. Tolosani included in one of his treatises a series of appendixes divided into four chapters intended to fulfill the intention of his friend.67 Tolosani died in 1549, which seems to have ended the matter insofar as official Catholic reactions are concerned, but Garin notes as well that the Dominican Thomas Caccini later held public readings of Tolosani’s work in Florence. This is the same Caccini who accused Galileo of heresy at Santa Maria Novella in 1614.
64 Perhaps this particular argument on the motion of Earth and the Bible may have been lost as well, but a treatise by Rheticus, De motu terrae, was published anonymously in 1551. See Sc, 217–218, n. 11; cf. Rc, 37–73. I have referred in the previous section to the relevant pages that support Copernicus’s interpretation of Aristotle. 65 Sc, 248–249. See Danielson, “Achilles Gasser,” 459. 66 Garin, “Alle origini,” pp. 31–42. See Lerner, “Aux origins,” 681–721. See Granada, “Giovanni Maria Tolosani,” 11–35; and Kempfi, “Tolosani Versus Copernicus,” 239–254. 67 Garin, 41–42: “Unde conqueri non debet de ipsis cum quibus Romae disputavit, a quibus plurimum reprehensus fuit, sed magis eis gratias agere convenit, a quibus didicit quae ignoraverat. Sed illa disceptatio tarde contigit, vel post libri sui publicatam impressionem. Et ideo necesse fuit, ut ea quae ipse falsa conscripsit huius opusculi nostri veritate retundantur, ne legentes eius librum praedictis eius erroribus seducantur. Cogitaverat magister sacri et apostoloci palatii eius improbare librum, sed prius infirmitate, deinde morte praeventus, hoc implere non potuit. Quod ego postea in hoc opusculo perficere curavi pro veritate tuenda in communem ecclesiae sanctae utilitatem.”
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Tolosani begins his critique with a chapter that relies almost exclusively on passages of the Bible interpreted according to the standard medieval view of the universe. It is striking that he neglects the text from Joshua. Such interpretations of Scripture tend to confirm the extent to which scholars read the Bible as a text that supported Aristotelian natural philosophy and even corrected it in those cases where the views of ancient pagan authors could be excused for their ignorance of Scripture. Tolosani cites five passages of Aristotle, supported by the commentary of Thomas Aquinas, emphasizing the agreement between Scripture and natural philosophy. He also cites other ancient authors, even the so-called Pythagorean view, which Aristotle refuted.68 As he begins the second chapter on heaven and the elements, Tolosani comments that the assertions in the first chapter would have sufficed if not for Copernicus’s effort to revive the Pythagorean doctrine. No one but Copernicus really holds the doctrine as true, says Tolosani, but advance it to display ingenuity rather than teach the truth.69 After praising Copernicus’s command of Latin and Greek and his expertise in mathematics and astronomy, Tolosani accuses Copernicus of being very deficient in his knowledge of physical science and logic. Furthermore, adds Tolosani, he appears to be incompetent in Sacred Scripture because some of his principles contradict the Bible thus constituting a danger to the faith and to his readers.70 Here Tolosani makes some astronishing claims in comparison with what Thomas Aquinas maintained, namely, that the observational data can be derived from several assumptions, adding that some other theory might explain them.71 Tolosani, instead, relates natural philosophy to astronomy as a
68
Garin, 33–35. Garin, 35: “Et nullus eam [opinionem quorundam pictagoricorum de mobilitate terrae] sequitur, nisi iste Copernicus, qui ut putamus eam opinionem veram esse non censet, sed in hoc libro suo potius voluit aliis ostendere acutiem ingenii sui, quam rei veritatem docere.” Compare Lerner edition, 701. Later in this section, Tolosani will refer to what we now know as Osiander’s “Letter,” indicating that the author is unknown. 70 Garin, 35: “Peritus est etiam in scientiis mathematicis et astronomicis, sed plurimum deficit in scientiis physicis ac dialecticis, nec non [in] sacrarum literarum imperitus apparet, cum nonnullis earum principiis contradicat, non absque infidelitatis periculo et sibi et lectoribus libri sui.” See Lerner, 701–703. Bracketed words indicate places where I have adopted Lerner’s reading. Although he uses the word dialectica, Tolosani means this in the broad sense to include all of logic, not just probable arguments. For a partial English translation, see Goddu, “Logic,” 32. 71 See Thomas Aquinas, Summa theologiae Ia, q. 32, art. 1, reply to objection 2, No. 47, 18. 69
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superior to an inferior science, the conclusions of which follow deductively from the superior science.72 No astronomers can be perfect in their discipline unless they first learn the physical sciences, because astronomy presupposes natural celestial bodies and their natural motions. Perfect astronomers and philosophers learn logic by means of which they can distinguish between the true and false in disputations, and have the knowledge of arguments that are required in medicine, philosophy, theology, and other sciences.73 Because Copernicus does not know physical science and logic, is it any wonder that he is deceived in his opinion, and takes as true what is false as a result of his ignorance of those sciences? Tolosani asserts that Copernicus’s arguments in Book I on behalf of Earth’s motion and the immobility of the starry vault have no strength and can be easily refuted. It is, he says, foolish to contradict long-standing received opinions supported by the strongest reasons without stronger and irrefutable demonstrations, refuting the contrary reasons fully, something that Copernicus never does. The above argument does suggest that Tolosani’s genuine view is less demonstrative than the passage about subalternation indicates. Yet, it seems that Tolosani is trying to have it both ways, a symptom of what I have elsewhere characterized as “creeping demonstrability.” There is no genuine demonstration of geocentrism, yet we must accept it until there is a genuine demonstration of the contradictory opinion. To accommodate this ambiguity (to put it kindly) in Tolosani’s argument, I conclude that we should distinguish between strong and weak versions. Tolosani proceeds in chapter two to repeat all of the relevant Aristotelian, Ptolemaic, and Thomistic arguments against the Copernican hypotheses, rejecting Copernicus’s claims that those arguments prove nothing, and in effect relying on authority to refute Copernicus. He 72 Garin, 35–36: “Contra negantem autem prima scientiarum principia non est disserendum quoniam ex primis principiis conclusiones rationis discursus deducuntur. Scientia quoque inferior a superiore principia comprobata recipit. Itaque omnes scientiae sibi invicem connectuntur, ita ut inferior superior indigeat, et se invicem adiuvant.” Cf. Lerner, 703. 73 Garin, 36: “Non potest enim esse perfectus astronomus, nisi prius didicerit scientias physicas, cum astrologia presupponat naturalia corpora coelestia et naturales eorum motus. Nec homo potest esse perfectus astronomus et philosophus nisi per dialecticam sciat discernere inter verum et falsum in disputationibus, et habeat argumentoram notitiam: quod requiritur in medicinali arte, in philosophia, theologia et ceteris scientiis.” Cf. Lerner, 703.
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concludes this section by quoting the “Letter to the Reader on the Hypotheses of this Work.” He quotes the remark specifically and approvingly about the foolishness of expecting anything certain from astronomy.74 Tolosani seems puzzled that Copernicus would ignore the advice, for “by those words the foolishness of the author of this book is censured.”75 Worse yet, because the Pythagorean opinion is expressly contrary to human reason and opposite to sacred texts, it could have pernicious results. To avoid such scandal, he concludes chapter two, he wrote this little work.76 In its concluding two chapters, Tolosani quotes Thomas Aquinas’s comments on Aristotle and Ptolemy at length in support of Earth’s stability and centrality. Thomas’s first argument against the natural motion of Earth emphasizes the principle of part and whole. Because the natural motion of the whole and part must be the same, if Earth moved in a circle, then its parts would have to move in a circle. But we see that this is false; the parts of earth move in a straight line towards the center of Earth. It follows that if Earth moved in a circle, then its motion would be violent. But if the motion of Earth were circular and violent, it could not be sempiternal, because no violent motion lasts forever. Yet those who hold this opinion maintain that the order of the universe is sempiternal. Because the motion and rest of the principal
74 Garin, 38: “Unde author ille, cuius nomen ibi non annotatur, qui ante libri eius exordium loquitur ‘ad lectorem de hypothesibus eiusdem operis’, licet in priori parte Copernico blandiatur, in calce tamen verborum, recte considerata rei veritate absque assentatione sic inquit: ‘Neque quisquam (quod ad hypotheses attinet) quicquam certi ab astronomia expectet, cum ipsa nihil tale praestare queat, ne si in alium usum confictam pro veris arripiat, stultior ab hac disciplina discedat quam accesserit.’ Haec ille ignotus author.” Cf. Lerner, 708–709. 75 Garin, 38: “Ex quibus verbis authoris eiusdem libri taxatur insipientia, quod stulto labore conatus fuerit Pictagoricam confictam opinionem iam diu merito extinctam denuo suscitare, cum expresse contraria sit rationi humanae atque sacris adversa literis, ex qua facile possent oriri dissensiones inter divinae scripturae catholicos expositores et eos qui huic falsae opinioni pertinaci animo adhaerere vellent.” Tolosani was evidently not the source of the belief that Copernicus himself had written the letter, an unfortunate mistake that would occasion much confusion in the official Catholic response to De revolutionibus. In spite of Tolosani’s caution, Catholic authorities in the early seventeenth century perpetuated the confusion. For the details, consult the relevant documents in Finocchiaro, Galileo Affair. See especially Bellarmine’s letter to Foscarini (67–69), the Inquisition documents of 1616 (146–153), and the assertions and actions of the committee of the Index in 1620 that was charged with the responsibility for censoring Copernicus’s text (200–202). 76 Garin, 38: “Ad cuius vitandum scandalum, hoc nostrum opusculum scripsimus.”
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parts of the universe belong to the order of the universe, it follows that Earth does not move in a circle.77 With the above comment I conclude the summary of Tolosani’s effort to refute the Copernican theory. His approval of what we now know as Osiander’s view suggests that he understood the comments to support his claim about the deductive relation between natural philosophy and astronomy. According to the strong version of Tolosani’s argument, natural philosophy provides the principles and conclusions, from which the hypotheses of astronomy should be derived. Astronomers should construct their mathematical models in conformity with those hypotheses. Among the critics and supporters of the heliocentric theory, those who insisted on the causally explanatory relation between principles of natural philosophy (physics) and the astronomical hypotheses from which mathematical models should be derived advanced the strongest views.78 The next important reaction brings us back to Rheticus. In the preface to Ephemerides novae (Leipzig, 1550), Rheticus points out the discrepancies in the position of the stars between existing tables and observation. Copernicus, we know, devoted a great deal of time to correcting errors or confusions in the texts available to him, but his models reproduce virtually the same predictive results that we find in Ptolemy. Within a few years of the publication of his book, however, Rheticus emphasizes the discrepancies and points out the efforts of predecessors going back to the Middle Ages to correct the Alfonsine Tables. Again, he repeats the story that Copernicus lived
77 Garin, 38: “Quatuor enim ponit rationes physicas et exponit divus Thomas ibidem. ‘In quarum prima, hoc pro suo principio accipit, quod si terra moveretur circulariter, sive existens in medio mundi, sive extra mundi medium, necesse esset quod talis motus sit ei violentus. Manifestum est enim quod motus circularis non est proprius et naturalis motus terrae, quia si esset ei hic motus naturalis, oporteret quod quaelibet particula ipsius hunc motum haberet, cum idem sit motus naturalis totius et partis. Hoc autem videmus esse falsum. Nam omnes terrae partes moventur motu recto usque ad medium mundi. Si vero motus terrae circularis sit violentus, [praeter] naturam, sempiternus esse non potest; quia nullum violentum perpetuum. Sed si terra movetur circulariter, necesse esset quod talis motus sit sempiternus iuxta ipsius opinionem, quia secundum ipsum oportet quod ordo mundi sit sempiternus. Motus autem vel quies partium principalium mundi pertinent ad ordinem ipsius. Sic ergo sequitur terram non moveri circulariter.’ ” Cf. Lerner, 711. 78 Whether Tolosani was familiar with Thomas’s more cautious view of the relation between astronomical hypotheses and observations is not known, but he may have neglected to see a distinction between a cosmological system and an astronomical theory that follows from it.
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with Domenico Maria Novara and aided him in his observations. He reports that he quarreled with Copernicus over the imprecision, and that Copernicus confessed that he rejoiced when his results came to within10 minutes of arc, pointing out several difficulties. The first was that the ancients often accommodated their observations to the models. Second, the ancients did not achieve a precision of the positions of the fixed stars that was superior to 10 minutes of arc. Little wonder, then, that the planetary positions were no more accurate. Finally, he pointed out what in effect was a complaint about a corrupted tradition. Ptolemy had the advantage of the great many observations of his predecessors, but Copernicus had to make do with what was available and what he himself was able to observe often with great difficulty. It was the task now for Rheticus to establish the data as precisely as possible.79 In effect, Rheticus has drawn the conclusion that follows from Copernicus’s belief that astronomers must postulate true hypotheses, for from false hypotheses false results will follow sooner or later. Thus does Rheticus characterize Copernicus’s achievement, not as a complete success but as a spur to the improvement and perfection of astronomy. He repeats Copernicus’s charge to him in his preface to two works by Johannes Werner (Cracow, 1557).80 Six years later (1563) Peter Ramus wrote the famous letter to Rheticus, in which Ramus complains about the complications and obscurities deriving from astronomical hypotheses. He calls on Rheticus to produce an astronomy that is completely free of hypotheses, an astronomy as simple as that produced by nature itself. Whatever his limitations in mathematical astronomy, Ramus provides a short history of those astronomers who proposed fictional hypotheses to meet Plato’s challenge to astronomers in the Republic to save the phenomena. Ramus considers eccentrics and epicycles to be false and absurd, whether proposed as simple fictions or as real. He pointedly argues that demonstrating the truth from false causes is the highest absurdity. If Rheticus will construct an astronomy that suppresses hypotheses, Rheticus will be regarded as the king of astronomy.81
79 80 81
Sc, 221–223. See Kremer, “Use,” 126. Sc, 227–235, esp. 233. Sc, 238–242 and 244, n. 39.
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Rheticus was evidently not in any great hurry to reply, for his letter has been dated 1568. After explaining what he had done in the meantime, basically a report of his efforts in mathematics and in improving observational accuracy, his response is that by improving observations precisely we may free astronomy from hypotheses.82 I turn now to the annotations reported by Owen Gingerich in his census of the first two editions of De revolutionibus.83 Gingerich estimates that he has located a little over half of the copies. Of the seventy astronomers who might have owned the book, thirty copies have been found. Gingerich further estimates that by 1620 thirty to forty scholars read the book carefully and worked on it. I have focused my attention on annotations in the Preface that Gingerich reported. In many copies there are no annotations at all, according to Gingerich, but I cannot independently verify the completeness of his comments; Gingerich took note of all annotations, he was not just focused on the ones of interest to me. Although we have only a selection that has survived to some degree by chance, the annotations to Copernicus’s comment on method fall into patterns that are consistent with the known views up to about 1600. There are generally three types of reactions, two of which can be distinguised into more subtle versions, thus amounting to a total of five, as I enumerated earlier. The vast majority adopted the pragmatic view advocated by Osiander. A few accepted the heliocentric theory as true or probably true, but they too tended to accept the view that the principal task of astronomy was to generate models from which future positions could be accurately predicted, and which the observations would confirm. At least one astronomer expanded that goal to include the physical causes that with the data would lead to both the correct models and as perfect a match between models, predictions, and data as the data permitted. I will discuss the more subtle versions later. One of the early readers of De revolutionibus was Jofrancus Offusius, a Rhenish astronomer in Paris who annotated his copy around 1550. Other scholars worked from his notes; sometimes they copied or paraphrased his notes. One such copy of the 1543 edition clearly shows a preference for Osiander’s reading of hypotheses, and the comment 82
Sc, 245–246. Gingerich, Annotated Census. See also Gingerich, “Supplement,” 232, who announces that Brill will issue a corrected reprint that will update some entries and add a total of twenty-two copies. 83
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shows that the author believed that Copernicus himself did not believe in the truth of his own hypotheses.84 The copy of De revolutionibus annotated by Erasmus Reinhold Salveldensis, one of the members of the Melanchthon Circle of interpretation contains, unfortunately, no comments on the preface.85 Another copy that apparently belongs to this circle has a quotation from Aristotle on the first flyleaf, a passage that Rheticus also quoted in the Narratio prima:86 Aristot. Verissimum est id, quod posterioribus ut vera sint, causa est. “That is most true which is the cause of something true that follows from it.” On the verso of the flyleaf is a lengthy comment, only part of which I quote here: Anyone can rightly wonder how from such absurd hypotheses of Copernicus, which conflict with universal agreement and reason, such an accurate calculation can be produced and why he did not undertake the correcting of the Ptolemaic hypotheses, which agree with Sacred Scripture and experience, rather than producing such a paradox. Nevertheless, if you at the least will recognize some of the causes and reasons for his admirable discovery, by which he was moved to fashion new [hypotheses], you will stop wondering. Even if those of Ptolemy seem at first glance to be more plausible, nevertheless they commit more absurdities in conflict with geometry, with first principles, and the nature of celestial bodies than those of Copernicus do.
If it seems that the author of these comments is about to adopt heliocentrism, he continues by emphasizing the first axiom of astronomy and Ptolemy’s violation of it, concluding thus: For what comes first ought to agree always with what follows, as Galen teaches in his treatise, On the Best Sect, for Thrasyboulos. Therefore, Copernicus did not invent new hypotheses out of a desire to dissent from Ptolemy, whose hypotheses he everywhere followed to the extent allowed by the demonstrations, but rather that he might restore Ptolemy’s astronomy to its rightful place and dignity.
As these authors see it, astronomical hypotheses do not trump the common sense assumptions of natural philosophy.
84
Gingerich, I, 47: 62. See also Gingerich, I, 218: 278–283. Gingerich, I, 217: 268–278. Typical of members of this circle, Reinhold focuses entirely on the technical, mathematical details, and their relation to the observations. In addition to the reference in Gingerich, see Westman, “Melanchthon Circle.” 86 Gingerich, I, 220: 284–288. The translations have been very slightly modified. 85
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Jerome Schreiber received a copy of De revolutionibus in 1543. Schreiber studied mathematics under Johannes Schöner, and then matriculated in the same class with Rheticus (1532) at Wittenberg. This copy is important because Kepler later owned it, and his remarks in it suggest that Schreiber’s questions and comments may have alerted Kepler to problems with the centering of planetary orbits, not on the Sun, but on the center of Earth’s orbit.87 I will comment on the significance of this issue later. In an anonymous comment possibly from a later period, a copy of the 1566 edition in Venice contains a reference to Michael Mästlin in which Kepler’s teacher makes the curious observation that the comet of 1577 made the superiority of Copernicus’s hypotheses evident.88 Mästlin’s most interesting comments by far appear in a copy that he annotated over several years. To my knowledge, here is the first direct comment on the logic of Copernicus’s view about hypotheses:89 The true agrees with the true, and from what is true nothing follows unless it is true. In the process [of demonstration] if something false and impossible follows from a doctrine or the hypotheses, then it is necessary that the defect be hidden in a hypothesis. If, therefore, the hypothesis of the immobility of Earth were true, then what follows from it would also be true. But in [Ptolemaic] astronomy many inelegant and absurd consequents both in the arrangement of the orbs as in the understanding of their motions follow. Therefore the defect is in the hypothesis itself. The minor proposition is evident from the motion of the Sun, from the length of the tropical year, also from the motion of the three superior planets, but most of all from Venus and the stellar orb.
As we have pointed out, the expression “Verum vero consonant” is of Aristotelian origin, which Mästlin probably took from the Latin edition of Averroes with the analytical index prepared by Marcantonio Zimara. The most proper context involves demonstration from causes
87
Gingerich, I, 68: 76–80. Gingerich, II, 131: 134. For analysis of Mästlin’s reaction to the comet of 1577 and its relation to the heliocentric theory, see Westman, “Mästlin’s Adoption,” esp. 63. See also Jarrell, “Contemporaries,” esp. 26, for an explanation of Mästlin’s mistake. 89 Gingerich, I, 178: 219–227, esp. 222 [translations modified]. For analysis of Maestlin’s interpretation and acceptance of Copernicus’s hypotheses, see Westman, “Mästlin’s Adoption.” Mästlin explains his emphasis on Venus as follows. The demonstration of the epicycle for Venus cannot be constructed from the assumption of an immobile Earth at the center without penetration of orbs. Westman discovered the most important texts on which I have relied for my account. See Gingerich, 223–225. 88
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to effects, but Mästlin understands that Copernicus was concerned with astronomical demonstration of the phenomena:90 This is certainly the main argument, how all of the phenomena as well as the order and sizes of the orbs act in concert with the mobility of Earth.
On the same folio, he added: Such an ordering of the machine of the whole universe, which permits surer demonstrations, is altogether more rational. By means of that ordering, the whole universe moves in such a way that nothing can be interchanged without confusing everything, from which all of the phenomena can be demonstrated very exactly, and in which nothing discordant occurs in the process (for, as far as astronomy is concerned, Copernicus wrote this whole book, not as a natural philosopher, but as an astronomer).
As we will see below, Mästlin preserves the distinction between the task of the astronomer and that of the natural philosopher. Even as he accepts the mobility of Earth, he is careful to limit astronomy to the formulation of hypotheses, the construction of models in accordance with the hypotheses, and the demonstration of the phenomena from the models.91 Mästlin’s principal objections to Ptolemaic hypotheses and models include inconvenient consequences, absurdities, demonstrations that entail penetration of spheres, violations of the foundations of astronomy, disagreements with the observations, and other like catastrophes. From his perspective, the motions of Earth are the causes of the phenomena; the astronomer should not propose explanations for the causes of the motions. In a similar vein, an anonymous early annotator on the 1566 edition commented:92 “In what way are we to understand hypotheses? It is necessary to believe them, for our senses cannot reach farther than
90 Gingerich, 223. On Zimara, see Lohr, Latin Aristotle Commentaries, 507, No. 3, Tabula dilucidationum in dictis Aristotelis et Averrois. The earliest edition is from Venice, 1537, which means that Copernicus could have consulted it prior to writing the Preface in 1542. Lohr lists at least ten editions, two colophons, and one reprint, all published between 1537 and 1576. 91 Gingerich, 227. 92 Gingerich, II, 212: 227–228, esp. 228 [translation modified]. On the title page the same annotator comments that astronomers should be allowed to set forth what hypotheses they please as long as they have a true relation to the motion of celestial bodies.
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our eyes can discern or our hands touch.” Kepler, much to Mästlin’s consternation, would change all of that.93 A Cracow copy of the 1543 edition containing also the 1617 edition is important for the comments in it by Jan Brożek on Osiander’s interpretation of hypotheses:94 Actually [Osiander’s] opinion that ‘it is not necessary for astronomical hypotheses to be true, nor indeed probable, so long as they agree with the phenomena’ is completely absurd. Ptolemy’s hypothesis is that Earth is at rest; Copernicus’s that Earth moves. Is therefore neither true? It is necessary for one of two contradictory hypotheses to be true. If Earth rests, then it does not move. If it moves, then it does not rest. In his preface to the reader, Osiander has deceived many about the hypotheses of Copernicus’s work. . . . But someone will ask how one can know which of the two is truer, Ptolemy’s or Copernicus’s? To answer this question I wish for a judge who knows all of astronomy well, Ptolemaic and Copernican. Only those ignorant of astronomy will base a judgment on sense appearances alone.
In a copy of the 1566 edition that was used at Paris in the early 1600s, probably by David Sinclair, we find comments that display support for Copernicus’s hypotheses:95 The wonderfully respected and learned Copernicus paints for us in this first book the admirable construction of the entire machinery of the world, and supported by using his hypothesis as a very certain foundation, attempts to represent and begins to demonstrate most credibly all the observations of all ages and the appearances of the motions of the stars; to which he attaches as much as the doctrine of triangles as is necessary for his work.
93 On Mästlin’s rejection of Kepler’s program for a dynamical astronomy, in Westman’s phrase (“Mästlin’s Adoption,” 59), see Mästlin’s letter to Kepler, 9 March 1597, Johannes Kepler, Gesammelte Werke, 13: 111: “Veruntamen huic capiti istud adjicio. Non aspernor hanc de anima et virtute motrice speculationem. Verum metuo ne nimis subtilis sit, si nimium extendatur. Qualis illa ipsa est, quam de Luna moues. Vereor profectò, si vltra modum nimis specialis fiat, ne iacturam vel certe ruinam totius Astronomiae post se trahat. Existimo omnino parcè et valde moderatè hac speculatione vtendum. Et vt verè dicam quod sentio: Non aspernor, et profectò languidus est meus assensus, plurima enim contraria mihi obstant. Sed de his alias.” The passage contains several puns, but despite his claim not to reject Kepler’s speculation about a moving soul and force, Mästlin was obviously worried that such speculation would drag along with it the overthrow and ruin of astronomy. See Voelkel, Composition, 67–69. 94 Gingerich, I, 133: 153–155, esp. 154 [translation slightly modified]. 95 Gingerich, II, 260: 294–295.
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These remarks give no indication that the author finds any problem with Copernicus’s models, and so would suggest a lack of familiarity with Kepler’s corrections. Owen Gingerich’s census provides a basis for studying the ways in which subsequent authors used De revolutionibus through the early seventeenth century. Because not all copies have survived, there is a possibility that the surviving copies are not representative. That possibility to the contrary notwithstanding, the surviving copies tend to show that annotators focused on the technical, mathematical parts of the treatise. Only relatively few contain comments on the nature of hypotheses, and many of those relate to the identification of Osiander’s letter. This fact leads us to conclude that we have identified all of the types of interpretation of hypotheses. In order, they are the physical and geocentric (Tolosani, strong version), the mathematical and still geocentric (Osiander, Tolosani’s weak version, Ursus, and the Melanchton Circle), the mathematical and heliocentric (Mästlin), the natural philosophical and heliocentric (Rheticus), and the explicitly physical and heliocentric (Kepler). Kepler’s interpretation is more nuanced than Tolosani’s strong version, but they are superficially contrary. Suffice it to say that my hypothesis warrants closer examination of those copies with annotations on the early material that Gingerich has not quoted in his census.96 Before turning exclusively to Kepler, I include here an additional noteworthy reaction. Erasmus Reinhold’s extensive commentary begins with Book III, and completely ignores the issues on which this study focuses.97 We know from other studies that Reinhold was an important member of the Melanchton Circle.98 In a later reaction by Mästlin we find confirmation of both his reservations about Kepler’s physical interpretation and also of the
96
Gingerich, 378–380. Rc, 191 and 570. See Gingerich, “Role of Erasmus Reinhold,” 43–62 and 123–125; idem, “Early Copernican Ephemerides,” 403–417. 98 Westman, “Melanchthon Circle,” 174–177. See Moesgaard, “How Copernicanism Took Root in Denmark and Norway,” 117–151, esp. 124–126, where he summarizes Caspar Bartholin’s critique of Copernicus (1619). Bartholin follows the pragmatic strategy but also criticizes Copernicus for logical and physical absurdities. Moesgaard concludes his summary, 126, with the comment that “apart from easily discernible sophisms it must be admitted that he has with merciless acuteness unveiled the weakness of Copernicus’ embodying his new cosmology in an Aristotelian vocabulary.” 97
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principal logical or dialectical warrant in Copernicus’s arguments.99 Mästlin criticizes in the strongest terms claims made by Aristotelians that the observation of bodies falling to Earth provides evidence that Earth is the center of the universe. Such observations confirm at best that the observed bodies have a tendency to fall towards the center of Earth. What is the justification for inferring the whole from the part? Copernicus was right to argue from the whole to the parts. Mästlin follows that claim immediately with Copernicus’s hypotheses by means of which he enumerates, arranges, connects, and measures the order and magnitude of all orbs and spheres, such that no change can be admitted without throwing the entire universe into confusion.100 As we argued earlier and throughout, Copernicus relied on the dialectical topic from an integral whole, among other topics, as the warrant for his conclusions. Mästlin implicitly recognizes that the topic from [integral] part to whole can be used only destructively, and that it is a fallacy to use it constructively. The topic from [integral] whole to part, 99 For the complete preface written by Mästlin in 1596 in an edition of Rheticus’s Narratio that was included with Kepler’s Mysterium Cosmographicum, see Rc, 447– 452. See 449 in particular. On his rejection of Kepler’s physical hypotheses, see 451. To my knowledge, Westman was the first to comment on this text. See Westman, “Mästlin’s Adoption,” 59–62. For a translation, see Goddu, “Mereological Vision,” 336–337. 100 Rc, 449–450: “An non omnis sedes et totum domicilium omnium eorum, quae nobis gravia sunt aut levia, Terra, et circa terram Aer est? Sed quid Terra, quid eam ambiens Aer, respectu immensae totius Mundi vastitatis? Punctum sunt, sive punctuli, et si quid minus dici posset, rationem habent. Quod cum sit, an non Philosophum dicturum putas, quod infirma argumentatio a particula sive hoc punctulo ad totum Mundum extruatur? Non ergo ex iis, quae ad hoc punctulum appetunt vel ab eo refugiunt, de spaciosissimi huius Mundi centro certi esse possumus. Locum quidem suum proprium, qui Philosopho teste est perfectio rei, haec nostra gravia et levia a Natura sibi tributum appetunt, quam affectionem, ut Copernicus lib. I cap 9 erudite disserit, credibile est etiam Soli, Lunae caeterisque errantium fulgoribus inesse, ut eius efficacia in ea, qua se repraesentant, rotunditate permaneant: Quod si is locus alicubi simul sit Mundi centrum, id non nisi per accidens contingit. Verum Copernici rationes Astronomicae non a particula, eaque minutissima, ad totum: sed contra, a toto ad partes procedunt. “Sed et ex ipso hypothesium usitatarum et Copernici processu facile agnoscitur, utrae plus fidei mereantur. Etenim Copernici hypotheses omnium Orbium et Sphaerarum ordinem et magnitudinem sic numerant, disponunt, connectunt et metiuntur, ut nihil quicquam in eis mutari aut transponi sine totius Universi confusione possit; quin etiam omnis dubitatio de situ et serie procul exclusa manet.” He goes on to emphasize how predecessors disagreed about the number of spheres, their arrangement, connection, and magnitude, and concludes his argument by contrasting the orbital motion of Earth with the ineffable velocity of the sphere of fixed stars. This is support, of course, for Copernicus’s argument from simplicity, an argument that is dubious from the point of view of the Aristotelian hypothesis about celestial matter.
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conversely, can be used constructively. As far as I am aware, Mästlin is the only commentator to make explicit mention of this feature of Copernicus’s argumentation, although it is virtually certain that all scholars educated in dialectic were familiar with the principle. At the very least, Mästlin confirms my analysis of Copernicus’s logic, and that at least one author of the sixteenth century recognized explicitly the most important logical move in Copernicus’s argument.101 On one point, however, Mästlin made a mistake. His comments fail to notice that Copernicus’s inference about gravity depends on a constructive application of the topic from an integral part. Because all of the observable heavenly bodies appear to be spheres, the rectilinear component of falling bodies led Copernicus to speculate that gravity is a tendency or desire that God implanted in all of the observable celestial bodies that have the form of a sphere (Sun, Moon, and planets). Copernicus’s cosmos, however, is finite, and the spheres of the fixed stars and the Sun are stationary, hence Copernicus did not conclude that all spheres rotate on their axes. Valid inferences from part to whole, then, rely on observation and depend on a critique of existing accounts, eliminating those that do not fit in the already established structure. The same kind of argument would lead Kepler to conclude that the physical principles discovered on Earth must be the principles of all motion.102 In Astronomia nova, Kepler devotes an entire chapter to the issue of hypotheses. Even more so than the important Apologia pro Tychone contra Ursum, this chapter from his war with Mars reveals Kepler’s grasp of the issues and his understanding of the limits.103 At the same time, the chapter suggests his self-consciousness about achieving the complete transformation of astronomy, a suggestion that he confirms
101
See chapter eight for the details. Mästlin, like Copernicus, does not elaborate on the logical technicalities, suggesting that he too relied on a simplified version like that of Peter of Spain. This would also suggest that he shared Copernicus’s view about the universe as a heterogeneous integral and essential quantitative whole. 102 Goddu, “Mereological Vision,” 336–337, also explains the relation between the topic from an integral part and Newton’s Rule 3 of reasoning in natural philosophy. 103 Jardine, Birth. On 41–57, Jardine provides a free translation of a part of the treatise by Nicolaus Ursus defending the interpretation of hypotheses as represented in the “Letter to the Reader.” In the Apologia (1600), Kepler’s response is prolix, although in some places he makes his motivation clear. See Jardine’s translation, 134–207. See also Jardine, “Many Significances,” for criticism of anachronistic interpretations of Kepler’s Apologia.
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later in Astronomia nova. It is a signal moment in the history that I have traced in this study. In Part II, chapter 21, Kepler asks “Why, and to what extent, may a false hypothesis yield the truth?”104 Part II is on Mars’s first inequality, “in imitation of the ancients.” At the beginning of Part II, that is, chapter 7, Kepler explained the circumstances under which he “happened upon the theory of Mars.”105 After referring to Mästlin’s encouragement and support in his preface to Rheticus’s Narratio prima that Mästlin had appended to Kepler’s Mysterium cosmographicum, he says that he “began to think seriously of comparing observations.” He wrote to Tycho Brahe in 1597, who mentioned his own observations in reply, which “ignited” in Kepler “an overwhelming desire to see them.” In 1600 Kepler travelled to Bohemia “in hopes of learning the correct eccentricities of the planets.” He continues: But when I found out during the first week that, like Ptolemy and Copernicus, he made use of the sun’s mean motion, while the apparent motion would be more in accord with my little book [Mysterium cosmographicum] (as is clear from the book itself), I begged the master to allow me to make use of the observations in my manner.106
As he goes on to explain, Tycho’s aide was working on the theory of Mars. If he had been working on a different planet, Kepler would have started on it. I therefore once again think it to have happened by divine arrangement, that I arrived at the same time in which he was intent upon Mars, whose motions provide the only possible access to the hidden secrets of astronomy, without which we would remain forever ignorant of those secrets.
Tycho’s aide had worked out a table of mean oppositions starting with 1580, and he invented a hypothesis, which, he claimed, represented all these oppositions within a distance of two minutes in longitude.
104 I rely primarily on Kepler, New Astronomy, tr. Donahue, 294–300, based on Astronomia nova, ed. Caspar, See Westman, “Kepler’s Theory,” 233–264. Cf. Evans, “Division,” 1009–1024. 105 Donahue tr. 184–187. 106 In some instances I provide the Latin to reinforce the dramatic feature of Kepler’s discovery. See Caspar ed. 3: 109: “Eo igitur veni sum initium anni MDC spe Planetarum correctas eccentricitates addiscendi. Cum autem primo octiduo didicissem ipsum adhibere cum Ptolemaeo et Copernico medium motum Solis, esset vero apparens motus meo libello accommodiator (quod ex ipso libro patet), ab authore impetravi ut mihi liceret observationibus meo modo uti.”
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“The mean motions, apogees, and nodes were extended over a period of forty years.” He got stuck “in the latitude at acronychal positions and also the parallax of the annual orb.”107 There was a hypothesis and table for the latitudes, “but it failed to elicit the observed latitude.” A similar problem would emerge in the lunar theory. Kepler continues: Now since I suspected what proved to be true, that the hypothesis was inadequate, I entered upon the work girded with the preconceived opinions expressed in my Mysterium cosmographicum. At the beginning there was great controversy between us as to whether it were possible to set up another sort of hypothesis which would express to a hair’s breadth so many positions of the planet, and whether it were possible for the former hypothesis to be false despite its having accomplished this so far over the entire circuit of the zodiac. I consequently showed, using the arguments presented already in Part I, that an eccentric can be false, yet answer for the appearances within five minutes or better, provided that the centre of the equant be correctly known. As for the parallax of the annual orb, and the latitudes, that prize is not yet won, and besides, was not attained by their hypothesis. What remains, then, is to find out whether they with their means of computation, might not somewhere differ from the observations by five minutes. I therefore began to investigate the certitude of their operation. What success came of that labour, it would be boring and pointless to recount. I shall describe only so much of that labour of four years as will pertain to our methodical enquiry.
In fact, in a little more than seventy-one pages of Max Caspar’s edition, Kepler describes how he found a hypothesis to account for the first inequality, showing in chapters 19 and 20 how he refuted the hypothesis, thus bringing us to the conclusion of Part II. I particularly abhor that axiom of the logicians, that the true follows from the false, because people have used it to go for Copernicus’s jugular, while I am his disciple in the more general hypothesis concerning the system of the world. I therefore considered it particularly worthwhile
107 The clearest explanation is in Stephenson, Kepler’s Physical Astronomy, 209: “Acronychal observations: observations of a planet made at the moment when its second anomaly has vanished. In heliocentric theories, an acronychal observation is one made when the earth is directly on a line between the sun and the body being observed, so that the observed direction to the body is also the direction from the sun to that body.”
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conclusion and epilog now to show the reader how it does happen here that the true follows from the false.108
First, you have already seen that what has followed is not exactly the truth. Kepler goes on to explain that his false supposition does not give the planet the right latitude. “So it is not exactly the truth that follows from this false hypothesis.” Even with respect to longitude, “the lack of perceptible difference in effects between the as yet unknown true hypothesis and the false one assumed by us does not make the effect identical.” For there can be a small discrepancy which the senses do not perceive. There are, however, occasions upon which a false hypothesis can simulate truth, within the limits of observational precision, with respect to the longitude.
By means of a sequence of false hypotheses, Kepler goes on to show how each succeeding hypothesis corrects the error in the preceding one, reducing the amount of error at the sixteenths of the period to the point where the results are within the limits of observational accuracy.109 He continues: It is at least now clear to what extent and in what manner the truth may follow from false principles: whatever is false in these hypotheses is peculiar to them and can be absent, while whatever endows truth with necessity is in general aspect wholly true and nothing else. Further, as these false principles are fitted only to certain positions throughout the whole circle, it follows that they will not be entirely correct outside those positions, except to the extent (as shown in this example) that the difference can no longer be appraised by the acuteness of the senses. Also, this same dullness of the senses hides the following additional small error which remains at the eighths of the period.
108 Caspar ed. 183: “CAVSA, CVR FALSA HYPOTHESIS VERVM PRODAT ET QUATENUS? Porro quia ego axioma hoc dialecticorum, ex falso verum sequi, vehementer odi, propterea quod eo Copernici (quem sequor magistrum in hypothesibus universalioribus systematis mundani) jugulum petatur: operae precium putavi lectori ostendere, quomodo his ex falso verum sequatur.” 109 This argument supersedes refutation 9 of chapter 1 of the Apologia, 148–150. By 1602 Kepler had become aware of how more difficult the problems were. See the detailed account of Kepler’s approach after Tycho’s death in Voelkel, Composition, 130–141.
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Kepler shows that the result would place the planet three minutes higher than it should be. “The equation therefore will be seen to be too large, and thus the eccentricity [of the equant] is too large.”110 He concludes chapter 21 thus: This mutual tempering of various influences causes one error to compensate for another, brings the calculation within the limits of observational precision, and makes it impossible to perceive the falsity of this particular hypothesis. And so this sly Jezebel cannot gloat over the dragging of truth (a most chaste maiden) into her bordello. Any honest woman following this false predecessor would stay closely in her tracks owing to the narrowness of the streets and the press of the crowd, and the stupid, bleary-eyed professors of the subtleties of logic, who cannot tell a candid appearance from a shameless one, judge her to be the liar’s maidservant. This is without doubt the reason for the remaining discrepancies of one or two minutes in chapter 18, in Cancer, Leo, Scorpio, and several other places. But the error cannot easily be seen, since the observations used do not fall at the apsides and at the quarters and eighths of the period.
We may take this conclusion as Kepler’s response to both Tolosani and Ramus.111 Kepler immediately concludes Part II: Up to the present, the hypothesis accounting for the first inequality (in which Brahe and Copernicus are in agreement, both different somewhat in form from Ptolemy) has been presented using the sun’s mean motion, which all three authors had substituted for the sun’s apparent motion. Thereafter, it was shown that whether we follow the sun’s apparent motion and the hypothesis found in chapter 16, or the sun’s mean motion and the hypothesis proposed in chapter 8 according to Brahe’s rendition, in both instances there result false distances of the planet from the centre, whether of the sun (for Copernicus or Brahe) or of the world (for Ptolemy). Consequently, what we had previously constructed from the Brahean observations we have later in turn destroyed using other observations of his. This was the necessary consequence of our having
110 Caspar ed. 186: “Ita vel jam patet, quatenus et quomodo verum sequatur ex falsis principiis: nempe id, quod in hisce falsum, speciale est et abesse potest, quod vero necessitatem affert veritati, sub generali ratione verum omnino et ipsum est. . . . Atque utrinque Planeta 3 scrupulis fiet altior justo. Aequatio ergo nimis videbitur magna. Quare eccentricitas nimis magna.” 111 In Apologia, 154, Kepler distinguishes geometrical hypotheses from astronomical hypotheses. The latter describe paths that can be derived from geometrical hypotheses. Later, 156, he distinguishes the practical and mechanical part of astronomy from contemplative astronomy.
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conclusion and epilog observed (in imitation of previous theorists) several things that were plausible but really false. And this much of the work is dedicated to this imitation of previous theorists, with which I am concluding this second part of the Commentaries.
It would take us far afield to follow Kepler to his final results, but we must comment on the meaning of his procedure and its significance for our thesis about Copernicus and the Aristotelian tradition. Although he does not cite Aristotle here and, indeed, expresses contempt for academic logicians, Kepler was in fact following Aristotle’s injunction that a false assumption will sooner or later be exposed by the consequences that follow from it. That was why he found it necessary to test every relevant alternative hypothesis. By contrast, from what is true only the true will follow. Indeed, as Westman has found, Kepler evidently quoted Mästlin’s comment:112 If one considers how easily falsehood is inconsistent with itself and, on the contrary, how the truth is always consonant with the truth [verum vero consonet], then one may perhaps begin from the [argument] alone to understand the most important argument for the arrangement of the Copernican orbs.113
We may find it arguable whether or not we can ever be certain about possession of the truth. Copernicus contented himself with greater probability and the somewhat weaker criterion of relevance between hypotheses and results, but Kepler tried to meet the challenge of an astronomy without hypotheses. In Part IV of Astronomia nova, Kepler treats the inequality in the heliocentric longitudes (the first inequality) from physical causes and his own ideas. As William Donahue has commented, Kepler consid-
112
Westman, “Mästlin’s Adoption,” 60, n. 25, citing Kepler, Gesammelte Werke,
1: 17. 113 The full quotation in context is from Kepler, Mysterium cosmographicum, ed. Caspar, 1: 16–17: “Neque tamen temerè, et sine grauissima Praeceptoris mei Maestlini clarissimi Mathematice authoritate, hanc sectam amplexum sum. Nam is, etsi primus mihi dux et praemonstratur fuit, cùm ad alia, tum praecipuè ad haec philosophemata, atque ideo iure primo loco recenseri debuisset: Tamen alia quadam peculiari ratione tertiam mihi causam praebuit ita sentiendi: dum Cometam anni 77 deprehendit, constantissimè ad motum Veneris à Copernico proditum moueri, et capta ex altitudine superlunari coniectura, in ipso orbe Venerio Copernicano curriculum suum absoluere. Quòd si quis secum perpendat, quàm facilè falsum à seipso dissentiat, et econtrà, quàm constanter verum vero consonet: non iniuria maximum argumentum dispositionis orbium Copernicanae vel ex hoc solo coeperit.”
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ered it nonsense to separate the geometry from the physics on which it is based.114 We need not accept Kepler’s strong causal thesis here, but his reasons for seeking a physically causal explanation of planetary motions are compelling. Kepler concluded that Tycho Brahe’s determination of cometary parallax (along with the interpenetration of spheres required by Tycho’s own geo-heliocentric system) required jettisoning this remnant of Aristotelian cosmology. If there were no spheres, then “epicycles no longer made sense, because they were no longer supported by any substance.”115 And he objected to the idea that bodies could move through space around empty points. Without spheres to support, contain, and move them, Kepler had to try to discover what really moves the planets. In short, the geometry had to work, to be sure, but the actual paths described accurately by the geometry had to be explained by physical principles.116 As we now know, however, it was not necessary for Kepler to have the correct physical principles or causes.117 Simply postulating physical causes that required using the true Sun as a focus along with Tycho’s data led to the correct orbit.118 In chapter 19 of Part II, on which I briefly focused above, Kepler makes one of his most startling and most quoted statements about the “hypothesis constructed according to the opinion of the authorities”:119
114
Donahue, 4. Donahue, 7. On Tycho Brahe, the historiography has become very complicated. See Thoren, “Tycho Brahe,” 3–21; Jarrell, “Contemporaries,” 22–32; and Schofield, “Tychonic,” 33–44. Compare Gingerich and Westman, Wittich Connection; and Granada, “Did Tycho Eliminate the Celestial Spheres Before 1586?” 125–145. 116 In Apologia, 146, Kepler alludes to William Gilbert, suggesting that he had already concluded in 1600 that magnetism could account in part for the Sun’s moving power. 117 Later, in Epitome (1618), Kepler appeals to causas probabiles. See Jardine, Birth, 250. As we know, the term “probabilis” is ambiguous, sometimes meaning “provable,” sometimes “plausible.” It seems likely that Kepler means it in the dialectical sense as supported by the evidence and hence as worthy of approval, as Jardine also concludes. 118 I must leave it to the reader to ponder the apparently ironic consequence that Kepler derived true results from an incorrect physical theory. See Stephenson, Kepler’s Physical Astronomy, 136–137 and 202–205, for his insightful distinction between an unsound theory and the right kind of a theory, and his emphasis on the essential purpose that physical investigations served for Kepler in discovering the relations that we know as “Kepler’s laws.” 119 Donahue, 281. Caspar ed. 3: 174: “Fieri quis posse putaret? Haec hypothesis observationibus acronúchioi tam prope consentiens falsa tamen est, sive observationes ad medium Solis locum sive ad apparentem examinentur.” 115
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conclusion and epilog Who would have thought it possible? This hypothesis, so closely in agreement with the acronychal observations, is nonetheless false whether the observations be considered in relation to the sun’s mean position or to its apparent position.120 Ptolemy indicated this to us when he taught that the eccentricity of the equalizing point is to be bisected by the centre of the eccentric bearing the planet. For here neither Tycho Brahe nor I have bisected the eccentricity of the equalizing point. Now for Copernicus it was a matter of religion not to neglect this anywhere.121 For he made very little use of observations, perhaps thinking that Ptolemy used no more than are referred to in his Great Work. Tycho Brahe balked at this. For in imitating Copernicus, he set up this ratio of the eccentricities, which the acronychal observations require. But when this was gainsaid not only by the acronychal latitudes (for these still underwent some increase arising from the second inequality) but also, and much more forcefully, by observations of other positions with respect to the sun which are affected by the second inequality, he stopped here and turned to the lunar theory, and I meanwhile stepped in. Now the method by which the whole theory of Mars could easily be absolved of error, if the premises were correct, and by which it is demonstrated to be incorrect is this.
After several pages of geometrical demonstration Kepler shows that the result is an error of eight minutes, and concludes:122 Since the divine benevolence has vouchsafed us Tycho Brahe, a most diligent observer, from whose observations the 8´ error in this Ptolemaic computation is shown, it is fitting that we with thankful mind both acknowledge and honour this benefit of God. For it is in this that we shall carry on, to find at length the true form of the celestial motions,
120 Or, in Owen Gingerich’s more colorful translation in his Foreword to Donahue, xii: “Who would believe it! The hypothesis . . . goes up in smoke.” 121 In a marginal comment, Kepler himself explains his point: “In Saturn and Jupiter he bisected it simply; that is, the Copernican form attributes the quadrant to the semidiameter of the epicycle. In Mars, however, since he had attributed to the epicycle the quadrant of the Ptolemaic eccentricity, he argued that in our time the whole Ptolemaic eccentricity must be diminished, but left to the epicycle its original quantity. And so he moved the centre of the eccentric (to speak Ptolemaically) 40 units closer to the centre of the annual orb than to the centre of the circle of the equant. Book 5 ch. 16. See also ch. 16 of this book.” 122 Donahue, 286. Caspar ed. 178: “Nobis cum divina benignitas Tychonem Brahe observatorem diligentissimum concesserit, cujus ex observatis error hujus calculi Ptolemaici VIII minutorum in Marte arguitur; aequum est, ut grata mente hoc Dei beneficium et agnoscamus et excolamus. . . . Nam si contemnenda censuissem 8 minuta longitudinis, jam satis correxissem (bisecta scilicet eccentricitate) hypothesin cap. XVI inventam. Nunc quia contemni non potuerunt, sola igitur haec octo minuta viam praeiverunt ad totam Astronomiam reformandam, suntque materia magnae parti huius operis facta.”
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supported as we are by these arguments showing our suppositions to be fallacious. In what follows, I shall myself, to the best of my ability, lead the way for others on this road. For if I had thought I could ignore eight minutes of longitude, in bisecting the eccentricity I would already have made enough of a correction in the hypothesis found in ch. 16. Now, because they could not have been ignored, these eight minutes alone will have led the way to the reformation of all astronomy, and have constituted the material for a great part of the present work.
Nevertheless, Kepler was never able to free himself completely of Aristotelian physical principles.123 Copernicus had thought that Aristotle’s spheres supported, contained, and moved the planets on their epicycles or eccentrics with uniform circular motion. However much he departed from Aristotelian accounts of the elements and gravity, he remained firmly in the Aristotelian tradition of celestial spheres and their uniform, circular motions. * * * I have now brought this study of Copernicus’s relation to the Aristotelian tradition to a conclusion that contains no little irony. Copernicus had concluded that Earth moves and the Sun is the center of the universe by subordinating natural philosophy to astronomy. Kepler certainly did not abandon metaphysical and architectonic principles, but he restored the traditional relation between natural philosophy and astronomy, yet he did so in part by assuming that the laws that govern motions of bodies on Earth must be the same as the laws governing the motions of bodies throughout the universe. In chapter eight, as I shifted the study from the more biographical approach of the first two parts to concentrate on Copernicus’s philosophy, I constructed an account that traces the application of dialectical topics down to Kepler, and showed how Kepler initiated a transformation of the arguments of his era that contributed to the solutions that he achieved. Copernicus, for his part, relied on mostly printed sources of ancient works to support his departures from Aristotelian and scholastic traditions. He made his bold innovation by overturning the traditional relation of the liberal arts in an effort to break the impasse that had blocked the progress of astronomy. Perhaps no one would have been as surprised as Copernicus to see the outcome within a few generations of his death. 123
Cohen, Birth, 142–148 and 210–211; and Martens, Kepler’s Philosophy, 99–111.
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As it turns out, recent investigations by Polish scholars have also shed light on his death (24 May 1543) and burial. As was already well known, he died in Frombork, and was buried in its cathedral. Earlier scholars concluded that he was buried near an epitaph commemorating him. According to custom, however, Copernicus should have been buried near the altar for which he was responsible among his duties as a canon. Based on the statutes of the chapter and other records, Jerzy Sikorski concluded that Copernicus was indeed buried near his altar (dedicated to Saint Vaclav, later dedicated to the Holy Cross).124 Based on Sikorski’s critique of previous scholarship and research on the statutes and documents of burials at the cathedral, scientists from the Baltic Research Center in Frombork undertook investigations of the site around Copernicus’s altar, discovered a corpse whose age is consistent with Copernicus’s at the time of his death,125 and by means of forensic reconstruction have generated an image of Copernicus’s head and face at the time of his death.126 More recently, DNA analysis comparing hair found in one of Copernicus’s books in Uppsala University Library reportedly matches the remains, so it seems that Copernicus’s remains have indeed been found.127 After the study of Copernicus’s philosophical views I turned to subsequent interpretations of Copernicus’s achievement in the epilog to put Copernicus’s effort and its limitations in relief. As supporters and 124
Sikorski, “Grób Mikołaja Kopernika,” 85–177. Gąssowki and Jurkiewicz, “Poszukiwanie,” 1–26; Pacanowski and Musiatewicz, “Zastosowanie metody,” 45–58; and Czajkowski and Morysiński, “Zastosowanie nowoczesnych,” 75–83. The authors of the archeological and forensic research have expressed their results in appropriately cautious terms as highly probable and not certain. The convergence of historical, archaeological, and forensic evidence tends to support their conclusions. Readers may find a summary of the research with photographs of Copernicus’s self-portrait and reconstruction of his head at the following website: http://archeologia.ah.edu.pl/Frombork_eng.html. For a review, see Goddu, “Copernicus in Person.” The comparison was based on what I called a “probable selfportrait.” The surviving portrait in Toruń may be an original but painted by a professional artist. If not a self-portrait or not copied from a self-portrait, then one of the comparisons between the forensic reconstruction and the portrait may be based on a false inference. See Westman, “Proof,” 201, n. 73. See also Metze et al. “Wandel,” for a review of the literature on portraits of Copernicus. 126 Piasecki and Zajdel, “Badania,“ 27–44. 127 The book is Copernicus’s copy of Calendarium Romanum magnum. The most complete accounts known to me are available at the following websites: http://www .tagesspiegel.de/weltspiegel/Kopernikus;art1117,2673205; and http://www.france24. com/en/20081120–dna-finally-gives-exact-localization-copernicus-remains-geneticshistory. I am grateful to Veronika Wündisch for sending me the article “Ein Geniestreich” by Knut Krohn in Berliner Tagesspiegel. 125
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opponents appealed to Aristotle, they extended the tradition. Opponents clung to principles of natural philosophy, such as the simplicity of natural motions. Copernicus and his supporters cited deeper metaphysical and logical principles while relying on dialectical arguments to generate a revision of Aristotle’s natural philosophy. Even with that revision, however, Copernicus inaugurated a revolution in cosmology. In logic, natural philosophy, and astronomy, Copernicus thought that he could adapt details of the Aristotelian and other ancient-medieval traditions to a heliocentric cosmology. He accomplished much of this cosmological revolution in northeastern Poland in Frombork on the lagoon fed by the delta estuary of the Vistula River. Along its banks he spent his entire childhood and received his early education in Toruń. Later and farther upstream in Cracow, where his father was born and raised, he attended the university. While still an undergraduate in 1493, he purchased astronomical and trigonometrical tables, our first concrete evidence of his interest in astronomy. The codex containing those tables remained his almost constant companion for the next fifty years, and through them we gain an entry into the mind that ordered the spheres of Aristotelian cosmology and ancient astronomy uniquely, by imagining the Earth with its Moon in motion around the Sun.
APPENDICES
APPENDIX I A SUMMARY OF PETER OF SPAIN’S DIVISION AND ENUMERATION OF TOPICS Intrinsic From substance From definition, for example, “A mortal rational animal is running; therefore, a man is running.”1 From the thing defined, for example, “A man is running; therefore, a mortal rational animal is running.” From description, for example, “A risible animal is running; therefore, a man is running.” From explanation of a name, for example, “A lover of wisdom is running; therefore, a philosopher is running.” From concomitants of substance From the whole From a universal whole or from a genus, for example, “A stone is not an animal; therefore, a stone is not a man.” From a species or from a subjective part, for example, “A man is running; therefore, an animal is running.” From an integral whole, for example, “A house exists; therefore, a wall exists.” and From an integral part, for example, “A wall does not exist; therefore, a house does not exist.” From a quantitative whole, for example, “Every man is running; therefore, Socrates is running.” and From a quantitative part, for example, “Socrates is running, Plato is running, etc.; therefore, every man is running.” From a modal whole, [no example provided; formed in the same way as genus and species]. From a locational whole, for example, “God is everywhere; therefore, God is here.”
1 After each example, Peter states the maxim. For example, in the case of from definition, the maxim is “Whatever is predicated of the definition is also predicated of the thing defined.” In the case of from authority, the maxim is “Any expert should be believed in his own field of knowledge.” In the case of from division, the maxim is “If something is exhaustively divided by two things, when one is posited, the other is removed; or, when one is removed, the other is posited.”
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appendices and From a locational part, for example, “Caesar is not here; therefore, Caesar is not everywhere.” From a temporal whole, [no example provided; formed in the same way as locational whole]. From a cause From an efficient cause, for example, “The house is good; therefore, the builder is good.” and From an effect [converse of from an efficient cause; no example provided]. From a material cause, for example, “Iron exists; therefore, there can be iron weapons.” From the effect of a material cause, for example, “Iron weapons exists; therefore, iron exists.” From a formal cause, for example, “Whiteness exists; therefore, a white thing exists.” From the effect of a formal cause [converse, no example provided]. From a final cause, for example, “Happiness is good; therefore, virtue is good.” From the effect of a final cause [converse, no example provided]. From generation, for example, “The generation of the house is good; therefore, the house is good.” and From the thing generated [converse, no example provided]. From destruction, for example, “The destruction of the house is bad; therefore, the house is good.” and From the thing destroyed [converse, no example provided]. From uses, for example, “The riding is good; therefore, the horse is good.” From associated accidents, for example, “He is repentant, therefore, he has done something wrong.”
Extrinsic From opposites From relative opposites, for example, “A father is; therefore, a child is.” From contraries, for example, “The animal is healthy; therefore, it is not sick.” From privative opposites, for example, “He has sight; therefore, he is not blind.” From contradictory opposites, for example, “That Socrates is seated is true; therefore, that Socrates is not seated is false.” From a greater, for example, “The king cannot capture the fortress; therefore, neither can a knight.”
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and From a lesser, for example, “A knight can capture the fortress; therefore, the king can also.” From a similar, for example, “As capable of laughing inheres in a man, so capable of neighing inheres in a horse, but capable of laughing is a proprium of man; therefore, capable of neighing is a proprium of horse.” From proportion, for example, “As the governor of a ship is related to the ship, so is the governor of a school related to the school; and as the governor of a ship should be chosen by art and not by lot; therefore, the governor of a school should be chosen by art and not by lot.” From transumption, for example, “A wise man is not envious; therefore, a philosopher is not envious.” From authority, for example, “An astronomer says that the heaven is revolvable; therefore, the heaven is revolvable.” Intermediate From conjugates, for example, “Justice is good; therefore, what is just is good.” From cases, for example, “What is just is good; therefore, what is done justly is done well.” From division, for example, “If Socrates is an animal, he is either rational or irrational; but he is not irrational; therefore, he is rational.”
APPENDIX II Text 1 [To Chapter 4.3.1]: Quaestiones cracovienses, ed. Palacz, Q. 34, pp. 65–67: “Circa secundum Physicorum primo quaeritur, utrum definitio naturae sit bene posita, in qua dicitur: ‘Natura est principium et causa movendi et quiescendi eius, in quo est primum per se et non secundum accidens.’ . . . “Istis notatis ponitur ista conclusio: Definitio naturae posita ab Aristotele est sufficiens. Probatur conclusio, quia illud est natura, quo naturalia differunt ab artificialibus; sed naturalia differunt ab artificialibus penes primum et per se principium movendi et quiescendi etc.: quia entia naturalia habent in seipsis non secundum accidens; ergo natura est principium movendi et quiescendi. Maior et minor patent ex sequenti quaestione. . . . “Sed diceres, quod natura caeli non est principium movendi et quiescendi; propter hoc dicit Avicenna in Summa sua, quod ‘et’ debet poni pro ‘vel.’ “Sed dicendum est, ut tactum est: non oportet naturam esse principium movendi et quiescendi semper, sed in his, quibus convenit motus, est principium movendi; sed in his, quibus convenit, quies, quies est principium quiescendi. Vel posset dici secundum Aegidium, quod caelum quodammodo quiescit et quodammodo movetur. Movetur videlicet secundum partes, quia partes caeli mutant situm, sed totum caelum secundum substantiam stat et non mutat situm.” Q. 35, pp. 67–69: “Utrum entia naturalia different ab artificialibus, quia naturalia habent in seipsis principium motus et status, sed artificialia neque unum habent impetum mutationis innatum. . . . “Secundo arguitur contra quaesitum, quia motus caeli est naturalis et caelum est res naturalis, et tamen non habet in seipso principium motus, quia intelligentia movet caelum, quae non inhaeret ipsi caelo. Et confirmatur, quia corruptio est mutatio naturalis et non fit a principio intrinseco. . . . “Secunda conclusio: Aliqua est res naturalis, quae non habet in se principium motus et status. Patet de corpore caelesti, hoc enim non stat. “Tertia conclusio: Omnis res naturalis in se habet principium motus vel quietis. Unde omnia, quae sub concavo orbis lunae moventur, aliquando quiescunt et aliquando moventur. Sed corpora caelestia, quae moventur, circulariter moventur sine quiete. “Sed diceres: “Quid tunc dicitur ad Aristotelem, qui dicit: ‘sub copulatione motus et status’? “Dicitur, quod Aristoteles, ponit, quod entia naturalia, quae quiescunt, habent in se principium quietis, et entia naturalia, quae moventur, habent in se principium motus. “Pro sequenti conclusione sciendum, quod duplex est principium motus: quoddam est activum, ut anima, quae est principium activum motus animalis, passivum vero est materia.
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“Est ergo quarta conclusio: Omnis res naturalis habent in se principium activum sui motus. Patet de corpore caelesti, ut argutum est ante oppositum, hoc enim moventur ab intelligentia ei assistente. “Ultima conclusio: In omnibus rebus naturalibus eo modo est principium motus, quo modo convenit eis principium motus; quibus enim convenit movere, eis inest principium activum, quibus vero convenit moveri, eis inest principium passivum motus, scilicet materia. Ex quo patet, quod motus caeli est naturalis tantum a principio passivo, licet a principio activo sit intellectualis. “Per hoc ad rationes: . . . “Ad secundam dicitur, quod, licet caelum in se non habeat principium activum, habet tamen in se principium passivum. Unde intelligentia non inhaeret caelo, sed assistit ei sicut nauta navi. Similiter dicitur de corruptione, quae habet principium passivum intrinsecum, et hoc est pro ultima conclusione.” Text 2 [To Chapter 4.3.1]: Quaestiones cracovienses, Q. 74 pp. 127–128: “Circa initium quarti Physicorum quaeritur, utrum ad physicum pertineat considerare de loco. “Arguitur, quod non, quia quantitas consideratur a mathematico et non a physico; sed locus est quantitas; ergo etc. Minor patet, quia locus est superficies, ut patebit; etiam patet in Praedicamentis, quod locus est species quantitatis. . . . “In oppositum est Aristoteles in textu. . . . “Per hoc ad rationes: Ad primam dicitur, quod quantitas etiam consideratur a physico sub esse naturali. In loco autem est virtus naturalis immobilis salvativa sui locati. Unde, quia posteriora non abstrahunt a prioribus, licet econverso, physicus, qui est posterior artifex, etiam considerat entia mathematicalia, minus tamen abstracte. . . .” Q. 75, pp. 128–129: “Utrum locus sit aliquid distinctum a locato. . . . “Arguitur primo, . . . “Ultimo: Si esset, vel esset mobilis, vel immobilis. Non mobilis, ut patebit, nec immobilis, quia quando locatum augeretur, oportet locum augeri, quia locus est aequalis locato. “In oppositum est Aristoteles. “Pro responsione sciendum, quod duplex est motus: quidam motus est ad ubi et alius est motus ad formam. In motu ad formam per transmutationem cognoscitur materia, quae est commune receptaculum utriusque termini motus. “Est ergo prima conclusio: Locus est. Probatur sic: quia aliquid movetur localiter et, ubi unum corpus fugit, aliud intrat; quare locus est commune receptaculum corporum locatorum. Ex quo patet, quod sicut transmutatio naturalis secundum formam facit scire materiam esse, ita transmutatio localis facit scire locum esse. Secundo probatur conclusio: quia partes et differentiae loci sunt, scilicet sursum et deorsum etc., igitur locus est. “Secunda conclusio: Locus est quid distinctum a locato. Patet, quia manet in mutatione locali tamquam commune receptaculum sub utroque termino. “Tertia conclusio: Locus habet quandam naturalem virtutem, quae salvat locatum ex naturali appetitu corporum simplicium, quae naturaliter omnia
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tendunt in locum et appetunt locum sicut eorum esse, quod non esset etc. Probatur conclusio ex naturali appetitu corporum simplicium, quae naturaliter omnia tendunt in locum et appetunt locum sicut eorum esse; quod non esset, nisi esset quaedam mirabilis virtus loci. . . . “Ad ultimam, cum dicitur: ‘vel est mobilis, vel immobilis,’ dicendum quod in loco duo sunt, scilicet materiale et formale. Materiale est ultima superficies, quae se habet ut vas et continens. Sed formale loci est distantia vel ordo ad totum caelum; talis autem distantia sive ordo non est mobilis, sed materiale loci bene movetur, ut patebit postea.” Text 3 [To Chapter 4.3.1]: Johannes de Glogovia, Quaestiones in octo libros Physicorum Aristotelis, BJ, MS 2017, [Q. 43]: ff. 149r-v: “. . . motus ipsius gravis deorsum in fine est intensior non tamen trahitur a loco effective, sed hoc fit ideo, quia quando grave descendit tunc fortatur grave et fit motus fortificatus non tamen est intelligendum, quod aliquid addatur ad gravitatem corporis descendentis et per remotionem a contrario confortatur gravitas quo ad actum secundum ex quo enim grave circa proprium locum existens ut coniungitur sue perfectioni, scilicet loco deorsum et elongatur a contrario, scilicet a loco sursum imperfectius habet suum actum gravitatis quam prius.” [Q. 47]: f. 161v: “Dubitatur primo unde proveniat successio in motu celesti. Dicendum quod tenendo, quod intelligencia moveat celum naturaliter, tunc successio provenit ex resistentia mobilis, quia ut corpus celeste est in uno situ quodam modo resistit moventi, ut est in alio situ. Sed tenendo, quod intelligencia celum movet intellectualiter et libere, ut dicit Albertus. Dicendum quod successio provenit ex parte finis, intelligencia enim movet celum tanta velocitate quanta exigit finis motus celestis, qui est generacio istorum inferiorum, que requirit successionem.” [Q. 81], f. 228r concludes thus: “Dubitatur tamen Aristoteles in septimo sufficienter ostendit quod omne quod movetur ab alio movetur. Dicendum quod aliter probat Aristoteles ibi et aliter hic quia ibi probat in generali hic autem in speciali applicando diversitatem speciei motus et ad diversa mobilia tam ad mobilia que moventur violenter quam esse ad ea que movetur per se ut dictum est in nostro libro secundo et sic non est superfluitas.” Text 4 [To Chapter 4.3.2]: Quaestiones cracovienses, Q. 16, pp. 31–32: “Utrum infinitum secundum quod infinitum sit ignotum. “Arguitur, quod non, quia hoc implicat contradictiionem, quia ly “secundum quod” explicat rationem infiniti, omne autem, quod habet rationem, est notum, implicat igitur infinitum secundum quod infinitum esse ignotum. “Secundo sic: quia Aristoteles dat hic scientiam de infinito, quod est notum. “Tertio: Infinitum, si esset, esset notum primae causae. “Quarto: Primus motor notificatur octavo huius et tamen ipse est infinitum, ut probatur ibidem. “In oppositum est Aristoteles.
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“Pro responsione sciendum, quod genus entis dividitur penes actum et penes potentiam, infinitum ergo aliquando attribuitur actui, aliquando potentiae. Et sic intelligitur quoddam infinitum in actu, quoddam vero in potentia. Unde infinitum in actu habet se ex parte actus, sed infinitum in potentia tenet se ex parte materiae, quia materia quodammodo infinita est ante formam susceptam, sed forma finit materiam sive claudit potentiam materiae et materia claudit communicabilitatem formae. Ex quo sequitur, quod non potest esse aliquod corpus naturale infinitum, quia in eo sunt materia et forma terminata, quia materia finit formam et forma materiam. “Secundo patet: ex quo ratio infiniti primo reperitur in quantitate, aliquando potest attribui magnitudini, aliquando multitudini. “Tertio sciendum, quod duplex est ratio: quaedam quid nominis alia quid rei. “Istis praemisis est prima conclusio: Quid [nominis]* infiniti est nobis notum. Probatur: quia alias non uteremur nomine infiniti. Et hoc arguit prima ratio ante oppositum. “Secunda conclusio: Quid rei ipsius infiniti, etiam si infinitum esset, esset nobis ignotum. Patet, quia noster intellectus inter terminos suae apprehensionis est finitus, ergo non est apprehendere infinitum. “Tertia conclusio: Infinitum, si esset, bene esset nobis notum in ente, sive sub ratione entis. Patet, quia cognoscimus ens et per consequens omnia ea, quae comprehenduntur sub ente. “Quarta conclusio: Infinitum, si esset, esset ignotum, quantum esset. Patet ex secunda conclusione, quia quid rei infiniti est ignotum, sed quid rei infiniti sumitur in genere quanti, quia ratio infiniti quantitati congruit. “Sed diceres: Utrum illud, quod est dictum, intelligitur de infinito in actu tantum, aut etiam in infinito in potentia? “Pro illo sciendum, quod infinitum in potentia bene est finitum in actu, ut bipedale est in actu et tamen est infinitum in potentia. Secundo sciendum, quod nihil cognoscitur, nisi ut in actu est, quia cognoscibile debet movere potentiam cognoscitivam, nihil autem movet, nisi existat in actu. Dicitur igitur, quod intelligitur de utroque infinito ea parte, qua finitum est. Nam infinitum in potentia bene cognoscitur ea parte, qua est finitum in actu, non autem ea parte, qua infinitum est, quia est in potentia. Ergo de se est ignotum, etiam quia intellectus noster est finitae capacitatis et non capit nisi actu finitum. “Sed diceres: Utrum prima causa cognosceret infinitum, si esset? “Respondetur, quod sic. Quia intellectus eius est infinitus, ergo intellectus eius non finiret ipsum infinitum cognoscendo, sicut intellectus noster, immo magis infinitaret. “Ultimo dubitatur, utrum intellectus noster omnia cognoscat. “Respondetur, quod omnia cognoscit quodammodo, sed non omnia apprehendit. Primum patet, quia obiectum intellectus est ens, ergo cognoscit omne cadens sub ente, quia potentia cognoscit omne illud, quod cadit sub eius obiecto, et hoc mediate vel immediate, quia separata a materia cognoscuntur per suos effectus sensibiles, cum nostra cognitio semper incipiat a sensu. Sed secundum patet, quia intellectus noster finitus est.
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“Ad rationes: Ad primam dicitur, quod habemus quid nominis infiniti, sed non quid rei. Et sic habemus rationem infiniti dicentem quid nominis, et tamen ipsum est ignotum quantum est. “Ad secundam dicitur, quod Aristoteles dat scientiam infiniti per abnegationem, sed de ipso nihil affirmat. “Ad tertiam dicitur concedendo, hoc est contra conclusionem.” *Palacz ed. reads “Quid nobis infiniti . . .,” but BJ, MS 2007, f. 11r reads “Conclusio prima: Quid nominis infiniti est nobis notum.” Text 5 [To Chapter 4.3.2 and 4.3.6]: Quaestiones cracovienses, Q. 81, pp. 138–139: “Utrum ultima sphaera sit in loco. “Arguitur, quod non, quia locus est ultimum corporis continentis; sed ultima sphaera continetur; igitur etc. “Secundo: Caelum omnia continet et est circulare, et ergo a nullo continetur, et per consequens sequitur, quod non est in loco. “In oppositum arguitur: quia caelum movetur localiter, ergo est in loco. “Pro responsione sciendum, quod duo hic faciunt difficultatem. Primum est definitio loci, ex qua sequitur, cum extra caelum nihil sit, continens ipsum in loco non esse. Secundum est motus localis caeli, quia de necessitate corpus, quod movetur localiter, est in loco. “Secundo sciendum, quod tripliciter aliquid est in loco: per se, secundum partes et per accidens. “Est ergo prima conclusio: Caelum non est per se in loco, quia non habet aliquod extrinsecum continens ipsum, eo quod extra caelum non est corpus. “Secunda conclusio: Ultima sphaera est in loco per alterum. Probatur conclusio, quia locus est de necessitate corporis, quod movetur localiter; sed cum ultima sphaera non sit per se in loco, ut prima dicit conclusio, oportet ut per alterum; ex quo necesse est ipsam esse in loco. “Tertia conclusio: Ultima sphaera est in loco per partes eius. Patet per Aristotelem in textu dicentem, quod si ultimum caelum esset aqua, partes eius essent in loco, quia ab invicem continerentur. “Quarta conclusio: Partes ultimae sphaerae non sunt in loco actu, sed solum in potentia. Patet, quia locus actualis debet esse separatus a locato; sed pars continens in ultima sphaera non est actu separata a parte contenta, sed tantum potentia. “Sed diceres: Una pars caeli semper manet sub eodem, ergo non mutat locum. “Dicitur concedendo, quod semper manet et ideo non mutat locum secundum actum, sed secundum potentiam, quia si superadderetur caelum et superior pars quiesceret, inferior pars mutaret locum. “Ex conclusionibus sequitur correlarie, quod caelum per accidens est in loco, quia per partes, in quibus est; partes autem per se sunt in loco in potentia. Secundo ponitur, quod motus caeli est actualissimus, quia tantum variat locum in potentia, et hoc est rationale, quia in primo caelo est minima diversitas, unde plurimum habet de entitate et unitate, et minimum de deformitate.
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“Sed diceres: Totum non est aliud quam suae partes; ideo, si totum non est in loco, nec partes. “Dicitur, quod totum non distinguitur a partibus simul collectis, tamen particularia loca partium in potentia differunt ab actuali loco totius. “Ex istis patet, quod non est dicendum cum Alexandro caelum non esse in loco simpliciter, nec cum Avicenna, qui dicit motum caeli non esse secundum locum, sed secundum situm, nec cum Ioanne grammatico, quod per se sit in loco, nec cum Averroe, Alberto, Aegidio, quod per accidens non sit in loco, sed per centrum; sed dicendum est cum Themistio, Thoma, Aristotele, qui ad hoc expresse sunt, quod caelum sit in loco per accidens et per partes, quae non actu in loco sunt, sed potentia. Dicit enim textus: ‘Alia secundum accidens in loco sunt, ut anima et caelum; per partes enim in loco quodammodo sunt omnes, in eo enim, quod circulariter sunt, continent alia aliam.’ “Ad rationes dicitur, quod sunt pro prima conclusione.” Text 6 [To Chapter 4.3.3]: Quaestiones cracovienses, Q. 25, pp. 48–50: “Utrum omnium corporalium et incorporalium sit eadem materia secundum speciem. “Arguitur, quod sic, quia distinctio est per formam, ergo materiae ante formas acceptae non sunt distinctae specie et per consequens erunt eadem specie. . . . “Secundo: si materiae essent specie distinctae, tunc haberent quo convenirent, videlicet genere, et haberent quo distinguerentur. Omne autem habens quo conveniat et quo distinguatur est compositum et non simplex, quod est contra dicta. “In oppositum tamen arguitur, quia, quorum materia est eadem, illa agunt et patiuntur ad invicem; sed corpora caelestia et inferiora non agunt et patiuntur ad invicem; ergo non habent unam materiam. “Pro responsione sciendum, quod Plato dixit esse caelum de natura elementorum et corruptibile ex se, sed quod non corrumpitur, hoc est voluntate opificis. Unde dicitur in Timaeo: ‘O dii deorum quorum ego opifex sum, natura quidem vos mutabiles estis, mea autem voluntate sic permanentis.’ Et loquitur hic in persona Dei ad corpora caelestia. Et sic Plato dicit unam omnium corporalium materiam. Sed Aristoteles posuit, quod corpora contraria habent contrarios motus. Secundo, quod motui circulari nullus est contrarius. Dixit ergo Aristoteles: ‘Cum caelum movetur circulariter, non habet contrarium et per consequens est incorruptibile’; et per consequens secundum Aristotelem caelum est alterius naturae ab elementis. “Est ergo prima conclusio: Materia caelestium et materia corporum elementata non differunt specie. Probatur conclusio, supponendo materiam extra in potentia ad formam. Secundo supponitur, quod omne habens privationem materiae admixtam est corruptibile. Arguitur igitur sic: Si sic esset eadem materia, esset in potentia ad omnem formam tam caelestium quam inferiorum; ergo materia caeli stans sub forma caeli est in potentia ad formam inferiorum et non habet eam; quare ibi est primatio et per consequens caelum est corruptibile per illam secundam suppositionem, quod est falsum. Ergo sequitur quod materia caelestium et inferiorum differunt specie.
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“Sed diceres: quia forma caeli continet formam inferiorum, ideo materia caeli non appetit formam inferiorum, sed forma caeli perfecte faciat materiam caeli. “Respondetur, quod potentia respicit actum et habet se per differentiam ad actum perfectum et imperfectum; ideo stans sub actu perfecto adhuc appetit actu imperfectum. Licet enim imperfectum sit in perfecto, hoc tamen non est secundum actum proprium imperfecti. Et ergo adhuc materia habens formam perfectam appetit formam imperfectam. Et si replicatio valeret, tunc materia stans sub forma hominis nihil amplius appeteret nec relinqueret privationem. Ex quo sequitur, quod in materia caeli non est potentia ad aliquid esse, loquendo de potentia distante ab actu, est tamen ibi potentia ad ubi. “Secunda conclusio: Eadem est materia superiorum secundum analogiam. Patet, quia convenit in ratione potentiae. Unde sciendum, quod Averroes dicit naturam caeli esse actum et quod caelum non esset compositum ex materia et forma. Utrum autem ista forma sit anima aut non, videbitur in De caelo et mundo. “Pro ultima conclusione sciendum: Omne, quod est in praedicamento, ut genus et species, componitur ex quo est et quod est. Unde quod est habet se ut materia sive potentia ad ipsum quo est. “Est ergo tertia conclusio: Omnium corporalium et incorporalium habentium materiam est eadem materia in genere. Patet conclusio ex notabili, quia conveniunt in genere. “Sed diceres: ‘Utrum omnium generabilium et corruptibilium sit eadem materia, in numero, loquendo de materia prima?’ “Respondetur, quod aliquid est unum duobus modis: uno modo actuale, alio modo potentionale. Unde unum potentionale dicitur unum per carentiam actus distinguentis. Dicitur ergo, quod omnium generabilium et corruptibilium est eadem materia numero. Secundo modo per indifferentiam, quia una pars illius massae non habet quo distinguatur ab altera; non tamen una est sicut punctus, ut prius dictum est. “Per hoc ad rationes: Ad primam, cum arguitur: ‘distinctio est per formam’, conceditur. Et quando arguitur: ‘ergo materiae ante formas acceptae non distinguuntur specie’, negatur consequentia, quia materia est in potentia ad formam. Ideo ergo, quod potentiae sunt ad diversas formas distinctae, sunt secundum speciem. “Ad secundam dicitur, quod materia non est species, sed principium speciei, et eius convenientia et differentia sumitur pro quanto est ad formam.” Text 7 [To Chapter 4.3.3]: Quaestiones cracovienses, Q. 31, pp. 60–62: “Utrum materia appetit formam. “Arguitur, quod non, quia appetitus est inclinatio consequens formam, qua res intendit in illud, quod est sibi bonum, sicut est declinatio terrae ad centrum mundi. Sed materia non habet formam, ergo non convenit ei appetitus. . . . “In oppositum est Aristoteles in littera dicens: ‘Aliud tamen aptum natum est appetere et desiderare formam secundum sui ipsius naturam.’
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“Pro responsione supponitur, . . . “Secundo supponitur, quod appetens necessario cognoscit id, quod appetit, vel dirigens ipsum, quia omne appetens aut ordinat se in illud, quod appetit, vel tendit in illud, quod appetit, ex ordinatione et directione alicuius cognoscentis, ut sagitta appetit signum non ex ordinatione eius in signum, sed et ordinatione sagittantis ducentis eam in signum. Ex quo sequitur, quid appetitus naturalis non est nisi ordinatio et inclinatio rei secundum propriam eius naturam in suum finem. “Est ergo prima conclusio: Materia appetit formam appetitu naturali. Patet ex correlario, quia appetitus naturalis non est nisi ordinatio alicuius in finem eius; sed forma est finis materiae, eo quod materia est in potentia ad formam sive actum; ergo materia appetit formam. . . . “Sed diceres: Utrum materia appetit formam accidentis? “Respondetur, quod secundario appetit eam, quia primo appetit formam substantialem et postea formam accidentalem. . . . “Ad rationes: Ad primam, cum dicitur: ‘appetitus est inclinatio consequens formam,’ dicitur, quod hoc est verum de appetitu consequente formam, quia sicut materia non intelligitur nisi per formam, ita materiae appetitus non intelligitur nisi per appetitum formae, et sic melius dicitur, quod appetitus naturalis est inclinatio rei secundum propriam naturam in suum finem.” Text 8 [To Chapter 4.3.3]: Quaestiones cracovienses, Q. 132, pp. 235–236: “Utrum ad hoc, quod motus sit unus, continuus et perpetuus, oporteat esse movens aliquod immobile, unum et perpetuum. . . . Ex conclusione sequitur, quod motor primus est incorporalis. Probatur conclusio, quia est immobilis; modo omne corpus est mobile, ut patet primo Caeli, primus autem motus est immobilis; ergo incorporalis . . . “Secunda conclusio: Primus motor immobilis est perpetuus . . . “Probatur ergo conclusio aliter: quia motus est perpetuus et unus, ut patet ex principio huius, ergo oportet movens esse perpetuum et unum. . . . “Ponitur tamen tertia conclusio: Primus motor immobilis est tantum unus. Probatur conclusio, quia, ut dicitur in littera, frustra fit per plura, quod aeque bene fit per pauciora; sed ponendo primum motorem unum, omnia salvari possunt; ergo non sunt ponendi plures, cum nihil frustra sit in natura. Verum tamen est, quod istud argumentum magis videtur esse rhetoricum quam argumentum iam tactum, quod sumitur ab unitate ipsius motus. . . .” Q. 133, pp. 237–239: “Utrum primus motor omnino sit immobilis, ita quod non movetur nec per se nec per accidens. . . . “Pro responsione dicendum, . . . “Istis praemissis est prima conclusio: Primus motor est immobilis omnino, ita quod nec movetur per se nec per accidens. Probatur: Nam quod movetur ex se, patet ex praecedenti quaestione. Quod autem non moveatur per accidens, patet, quia motus primus est incessibilis et immortalis motus, ergo necesse est primum motorem immobilem esse, ita quod non movetur per accidens. Tenet consequentia: si moveatur per accidens, ipse non posset esse causa continui uniformis et incessibilis motus, ut patet ex dictis. Quia autem motus sit
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perpetuus, etiam patet ex dictis. Et quod etiam aliquis motus in specie sit perpetuus, patebit in sequentibus. Secundo probatur conclusio a priori: quia primus motor, tenendo, quod ipse sit Deus benedictus, est tantum actum, ergo nullo modo est mobilis, cum omne mobile est ens in potentia. Ex conclusione sequitur, quod primus est perpetuus et incessibilis. Patet, quia primus motor semper est immobilis, ergo semper uniformiter se habet ad motum. “Sed diceret aliquis iuxta primam rationem ante oppositum: Quare, cum intelligentia sit in primo corpore, ipsa non moveatur motu corporis per accidens? Secundum dubium: quare intelligentiae inferiorum orbium dicuntur moveri per accidens? “Pro responsione notandum, quod duplices sunt formae substantiales. Quaedam sunt in corporibus et non informant corpus, et istae dicuntur formae non ab informando, sed a formis manendo, et istae non subduntur legibus corporis nec esse earum et per consequens nec proprietates earum dependent a corpore. Aliae sunt formae, quae sunt in corporibus et informant corpora, immo esse capiunt a corpore, et istae subduntur legibus corporis tam secundum esse quam secundum proprietates. Ergo intelligentiae motrices orbium sunt de numero primarum formarum, cum non subduntur legibus corporis. “Sed contra istud est secundum dubium. Pro quo sciendum, quod dupliciter aliquid dicitur moveri per accidens, ut vult Philosophus in textu: uno modo a seipso, ut anima movendo corpus movetur ad motum illius etiam localiter et successive; alio modo ab altero. Quemadmodum aliquid est in loco per accidens dupliciter: uno modo per alterum, ut caelum, alio modo secundum se, ut partes per accidens sunt in loco totius. Dicitur igitur, quod intelligentiae motrices orbium moventur per accidens non a se, sed ab altero. Nam sicut centrum est aliquid caeli et ob hoc secundum Averroem caelum est in loco, ita orbis quodammodo est aliquid intelligentiae. Ideo motu orbis intelligentia dicitur moveri per accidens, non omnis intelligentia, sed illa, cuius orbis movetur per accidens, qualis est intelligentia inferioris orbis. . . .” Text 9 [To Chapter 4.3.3]: Quaestiones cracovienses, Q. 136, pp. 241–243: “Utrum in omni motu necesse sit mobile in puncto reflexionis quiescere. “Arguitur, quod non; . . . “In oppositum est Aristoteles in illo capitulo, in quo probat, quod motus rectus non potest esse perpetuus. . . . “Est ergo prima conclusio responsiva, quod per se omne mobile puncto reflexionis quiescit. Probatur: nam motus accessus et motus recessus, qui sunt inter contrarios terminos, ipsi sunt contrarii, ex quinto huius, ubi patuit, quod motus contrarii non possunt esse continui; ergo oportet, quod illi motus dividantur per quietem mediam. Verbi gratia: motus factus ab a in b et ab b in a contrariantur; quare non continuatur. Eodem modo dicitur de reflexione facta in circulo. “Sed contra hoc obiceret aliquis, quia motui circulari non est motus contrarius, primo Caeli.
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“Respondetur, quod motus dupliciter dicuntur contrarii: uno modo a terminis suis, et sic in circulo non est contrarietas motuum; alio modo, quia unus impedit alium, et sic in circulo est contrarietas motuum. “Sed diceres, quod in circulo motus ab oriente non impedit eum, qui est ab occidente, ut patet in sphaeris planetarum, quae duplici motu moventur. Dicendum, quod illi motus non sunt super eosdem polos facti, sed super diversos; omnes enim planetae moventur ab oriente in occidens super polos mundi et omnes moventur ab occidente in oriens super polos zodiaci. “Pro responsione quaestionis sciendum, quod, si motus contrarii continuarentur, tunc idem moveretur contrariis motibus; dum enim esset in termino a quo, ascenderet; ideo, si non sit media quies, etiam descenderet. Secunda ratio Philosophi est ista et supponit, quod esse in instanti est in potentia, ut patuit alias in quinto. Ex isto patet ratio: cum accedere et recedere dicant actus distinctos, qui actus non possunt esse in eodem instanti et in eodem mobili, sequitur, quod impossibile est, quod in puncto reflexionis non est quies media, quia ex quo illi actus conveniunt mobilibus in diversis instantibus et inter quaelibet instantia est tempus medium, ergo in illo tempore medio necessario fit quies; format autem Aristoteles quattuor rationes logicales, quae patent in littera. . . .” Q. 137, pp. 244–245: “Utrum motus circularis possit esse continuus et perpetuus . . . “Pro responsione ponitur ista conclusio: Motus circularis potest esse continuus et perpetuus per reiterationem. Probatur, quia illud est possibile, ad quod non sequitur impossibile. . . . “Secunda conclusio Aristotelis est, quod motus circularis est continuus et perpetuus. Patet, quia motus localis est perpetuus et non rectus, ut iam probatum est in praecedenti quaestione, ergo circularis. Tenet consequentia ex sufficienti divisione. Verum tamen est, quod ista conclusio non est catholica, immo falsa. Dicimus enim et firmiter credimus, quod motus caeli incepit determinato principio temporis; sed hoc non habemus per philosophiam, sed per prophetiam. Prima vero conclusio simpliciter conceditur . . .” Text 10 [To Chapter 4.3.5]: Quaestiones cracovienses, Q. 120, pp. 210–212: “Circa initium septimi Physicorum quaeritur, utrum omne, quod movetur, moveatur ab alio, id est utrum omne mobile, quod movetur, habeat motorem ab eo distinctum. “Et arguitur primo, quod non, quia animalia moventur a seipsis, quia in hoc different a non animalibus; ergo non omne, quod movetur, habet motorem ab ipso distinctum. “Secundo: grave existens sursum movetur deorsum a removente prohibens; sed grave descendens est removens prohibens; ergo movetur a seipso. “Tertio: aliqua sunt indivisibilia, qualis est anima humana, et moventur a seipsis, sicut anima intelligendo movetur a seipsa; quare non omne motum movetur ab alio. “In oppositum est Aristoteles. “Pro responsione supponitur, quod eorum, quae moventur, quaedam moventur a principio intrinseco, ut animal, quaedam vero ab extrinseco, ut proiectum
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a proiciente. Et de illis non est difficultas dubitationis, sed de primis: quia non cognoscimus principium activum intrinsecum distingui a passivo, credimus mota ab principio intrinseco non habere motorem ab ipsis distinctum. “Secundo sciendum, quod aliquod movetur a seipso vel ab alio dupliciter, scilicet per se primo et per accidens. Et accipitur hic ‘per accidens,’ ut extenditur ad moveri per partem, quia pars non est eadem toti; alias enim una pars esset alia, quia quaecumque uni in eodem sunt eadem, inter se sunt eadem; ergo pars est altera a toto. Unde moveri ab aliquo per accidens est moveri ex esse in eo, quod est per accidens. Unde sciendum, quod illud contingit alicui per se, quod non contingit ei per aliud, sed aliis per seipsum. Ex quo sequitur correlarie: Illud, quod movetur a se ipso per se primo, nullo modo quiesceret quiescente altero. Patet, quia motus eius non dependet ab altero, sed a seipso. “Est ergo prima conclusio: Aliquid movetur a seipso per accidens. Probatur: ut anima movet corpus et, quia est in corpore, movetur per accidens motu corporis, et nauta movet navem et movetur per accidens ex esse in navi mota. “Secunda conclusio: Nihil movetur a seipso et primo. Probatur conclusio demonstratione Aristotelis: nihil, quod quiesceret, si aliud ab eo quiesceret, movetur a seipso per se primo; sed omne, quod movetur, quiesceret, si aliud ab eo quiesceret; igitur nullum mobile, quod movetur, movetur a seipso et primo. Tenet consequentia in ‘Celarent.’ Maior patet ex uno correlario sive ex definitione eius, quod est primo a seipso moveri. Minor probatur, quia omne mobile, quod movetur, quiesceret quiescente una parte. Cum igitur omne sit divisibile, ut patet ex dictis, sequitur conclusio. . . . “Ex omnibus igitur istis habetur, quod omne, quod movetur a seipso, dividitur in partem per se moventem et per se motam, ut animal dividitur in animam et corpus. “Per hoc ad rationes: Ad primam dicendam quod hoc est per partem et non primo; primo enim movetur corpus ab anima et per illud totum animal. “Ad secundam dicitur, quod hoc etiam est per accidens; per se enim dividit aerem et movet, et tunc ipsum grave movetur motu aeris. “Ad tertiam dicitur, quod quaestio intelligitur de motu physico; modo talis non est motus physicus.” Q. 129, pp. 229–231: “Utrum gravia et levia per se moveantur a generante et per accidens a removente prohibens. “Et arguitur, quod non, . . . “Secundo: nam dicitur secundo huius, quod natura est principium movendi et quiescendi, ergo gravia et levia moventur a suis naturis et per consequens non a generante. “Tertio arguitur contra secundam particulam. Nam ponatur lapis supra traben et tandem corrumpat trabem: tunc grave per movetur a seipso; cum igitur ipsum est removens prohibens, ideo per se movetur a removente prohibens. “In oppositum est Aristoteles. “Pro responsione sciendum, quod tria sunt in motu, scilicet movens, mobile et potentia mobilis, qua suscipit motum. Unde movens est duplex, scilicet naturale et violentum. Unde movens est duplex, scilicet naturale et violentum. Naturale est, quod confert formam naturalem mobili, ut actu calidum movet
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naturaliter illud, quod est potentia calidum. Sed per oppositum definitur movens violentum. Similiter distinguetur de mobili, quia quoddam movetur naturaliter, aliud violente. Potentia etiam est duplex: una est essentialis, alia est accidentalis . . . Similiter aqua est in potentia essentiali ad fieri sursum, leve detentum a motu sursum est in potentia accidentali. “Secundo sciendum, ut patet ex praecedenti quaestione: ‘per se’ dicit circumstantiam causae; potest ergo dicere vel circumstantiam materiae, vel formae, vel finis, vel efficientis. “Est ergo prima conclusio: Gravia et levia moventur per se ad loca sua naturalia, ut ‘per se’ dicit circumstantiam materiae. Patet, quia habent in seipsis principium patiendi et sustinendi motum. “Secunda conclusio: Gravia et levia moventur per se ad sua loca naturalia, ut ‘per se’ dicit circumstantiam formae. Patet ex secunda ratione ante oppositum, quia forma gravis et materia eius principiant formaliter motum, quo movetur in loco eius. “Tertia conclusio: Illud, quod est grave in potentia essentiali, vel illud, quod est leve in potentia essentiali, per se movetur a generante, ut ‘per se’ dicit circumstantiam causae efficientis. Probatur conclusio, quia ab illo movetur efficienter grave, a quo suscipit formam, qua movetur; sed grave in potentia essentiali suscipit formam suam a generante; ergo per se movetur a generante. Secundo probatur conclusio, quia gravia et levia moventur ab aliquo et non moventur a seipsis, ut patet ex praecedenti quaestione; ergo a generante. Tenet consequentia, quia nihil vicinius est gravi quam generans ipsum. Unde ad istud est exemplum: aliquis enim diceret parietem esse album ab albedine formaliter; sed est albus a pictore efficienter; sic etiam albescit non ab albedine, sed a pictore efficienter; sic grave non movetur a sua gravitate efficienter, sed a dante gravitatem, sicut est generans. “Quarta conclusio: Grave, quod est in potentia accidentali, movetur a removente prohibens per accidens et a generante per se. Patet conclusio ex notabili primo, quia movens per accidens non confert formam, sed movens per se, et ita generans confert formam, non autem removens prohibens; sed removens prohibens tollit impedimentum. Exemplum est de hoc, ut sol de se elevat vaporem, quem generat; sed si vapor ab aliquo detineatur, removens illud prohibens movet vaporem per accidens. “Ex conclusionibus sequitur correlarie, quod grave, quod est potentia essentiali, movetur successive, secundum quod successive sibi datur forma gravitatis a generante. Unde, si simul daretur sibi forma gravis, simul et subito moveretur. Ex quo sequitur ulterius, quod grave aliquando movetur per accidens a seipso. Patet, quia aliquando ipsummet grave est removens prohibens. “Per hoc ad rationes: Ad primum dicitur concendendo [sic]. Et cum dicitur ‘ergo non movetur a generante,’ negatur consequentia. Et cum dicitur: ‘ab illo, quod nihil est, non movetur,’ dicendum, quod aliquid habet esse dupliciter: primo, quia sua substantia est; secundo, quia virtus sua est. Dicitur ergo, quod ab illo, quod non est secundum suam substantiam, sed tamen est secundum suam virtutem, bene aliquid movetur, ut sagitta posset moveri sagittante interfecto. Et ita est in proposito. Nam manente gravi genito maneret virtus generantis ipsum in eo.
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“Ad secundam dicitur, quod illa procedit secundum intentionem secundae conclusionis. “Ad tertiam dicitur, quod ipsa est pro ultimo correlario.” Text 11 [To Chapter 4.3.5]: Johannes de Glogovia, [Q. 88], ff. 239r–240v. The text has been published by Markowski, Burydanizm, 177–181, and I have corrected it against the manuscript. “Utrum proiecta cessante proiciente moveatur a medio, per quod ferunter,ab ipso proiciente? “Pro intellectione questionis mote notandum primo, quod postquam Aristoteles ostendit primum motorem esse infinite virtutis, de quo tamen adhuc latius dicetur in questione ultima. Ideo consequenter ostendit unitatem primi motoris. Et circa hoc Aristoteles presupponit unum, scilicet quod unitas motus dependet ex unitate moventis et occasione illius querit, quo modo proiecta moveantur. Et primo ostendit, quod non movent se ipsa, quia non sunt animata, modo animal movetur a se non animatum, ut probatum est ante. Nec etiam videatur moveri a proiciente, quia movens effective debet esse simul cum moto, sicut probatum est septimo huius. Constat autem, quod proiectum non est simul cum proiciente, immo constat proiciens esse corruptum et proiectum moveri. Non videtur ergo, a quo /f. 239v/ moveantur talia proiecta. “Notandum secundo, Aristoteles in textu ponit solutionem questionis huius. Et primo excludit opinionem Platonis, que fuit, quod proiciens proiciendo movet aerem proximum et ille aer ulterius moveret proiectum usque ad finem absque motu aeris consequenter se habentis. Sed hanc opinionem Aristoteles excludit et vult, quod si ille aer proximus motus a proiciente esset causa proiecti, tunc proiectum moveretur in aere propinquiori tantum et nunc consequenter hoc apparet manifeste falsum. Et ideo Philosophus ponit unam aliam solutionem et est: Proiciens movet aerem proximum circa se et ille aer movet alium aerem proximum circa se et ille aer movet alium aerem et sic ulterius donec cessat virtus proicientis in aere et illa virtute deficiente deficit motus. Et est simile de inclinationibus, quia parte mota ista movet aliam partem et ulterius ista pars movet aliam, donec cessat virtus primi moventis, sic etiam est in aere, quamvis non ita manifeste apparet ad sensum. Sequitur corrolarie, quod positio Platonis, que dixit proiecta moveri per antiparistasim et per partium positionem, scilicet quod cum proiectum dividit aerem quo aere terminato proiectum se veniret impetuose et impelleret sic impetuose proiectum. Sic etiam sequeretur, quod moto lapide celum moveretur. Lapis enim motus movet aerem et aer iterum alium, cui alter cedit et sic uno motu omnia moverentur. Unde et ipse dixit, quod sicut navis mota cum decursu procellarum deferuntur per impetum, qui est in procellis, ita etiam moveretur proiectum ab aere, in quo est virtus proicientis et tertio Celi loquens de hac opinione dixit, quod aer est organum et instrumentum in motu gravium et levium.” [Cf. Aristotle, De caelo III, 2, 301b16–25.] “Notandum tertio, quod Aristoteles in textu ostendit, quod motus proiectorum non est unus. Fit enim a diversis moventibus consequenter se haben-
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tibus et ex hoc concluditur, quod si non esset unus motus primus et ergo a sensu contrario. Si motus primus est unus, quod verum est etiam, quod motor primus est unus, quod Aristoteles hic intendit. Movet autem Aristoteles istam questionem de motu proiectorum, secundum intentionem Johannis de Janduno, non intentione principali sed potius incidentaliter. Intendit enim Aristoteles hic probare, quod unitas motus deficit propter diversitatem moventium et hoc probat ex motu proiectorum, qui non est unus. Si ergo est unus motus primi motoris, tunc concludit, quod necesse est tantum unum esse primum motorem alias non esset unus motus. “Notandum quarto, quod proiecta moventur a pluribus consequenter se habentibus, cuius rationem assignat Aristoteles in textu istam, quia quanto aliqua virtus est fortior, tanto distantius se diffundit in operationem, sic tamen, quod semper proximum movens simul sit cum proximo motu. Cum ergo virtus proiectiva sit, que virtus ergo diffundit se primo in proximo mobili, quod est aer et ille aer movet alium aerem proximum et etiam proiectum. Ille autem aer proximus ultimus movet remotiorem aerem et hoc fit donec cessat virtus proicientis et tunc etiam cessat motus et sic semper proximum movens est simul cum moto, quia ille aer, qui est immediate circa proiectum est proximum movens, ut declaratum est in declarationibus ipsius aque, in quibus una pars aque movet aliam. Sequitur corrolarie, quod in motu proiectorum est tria assignare: Primum quod est motum tantum et hoc est proiectum. Secundum quod est movens et motum simul et hoc est aer medium, quia talis aer movetur a virtute /f. 240r/ proicientis et movet ulterius ipsum proiectum. Tertium est movens tantum et proiciens. Sequitur corrolarie secundo, quod proiecta moventur a pluribus moventibus consequenter se habentibus, quia a partibus aeris consequenter se habentis. Una enim pars aeris movet aliam, donec cessat virtus proicientis. “Istis sic stantibus est hec conclusio responsalis: Motus proiectorum non est unus motus continuus et proiecta post recessum a primo proiciente moventur ab aere. Modo dato et expresso virtus huius conclusionis patet pro ambabus partibus ex dictis. Sequitur corrolarie primo, quod licet motus proiectorum videtur esse unus et continuus propter unitatem mobilis et temporis, tamen, quia ibi non est unitas moventis, talis motus non est unus. Alii tamen ponunt impetum esse in proiecto. Aristoteles autem dixit in aere. Sequitur corrolarie secundo, quod non oportet omnia moveri tenendo positionem Aristotelis, licet enim aer cedat lapidi, hoc tamen est per condensationem. Sequitur corrolarie tertio, quod impetus concurrit in motu proiectorum et est in aere. “Arguitur primo, ex declaratione sequitur, quod motus celi etiam non esset unus. Probatur, quia motus celi fit a diversis motibus. Videtur ergo, quod motus proiectorum est unus. Dico, quod aliquis motus dupliciter potest dependere ex diversis motoribus: uno modo secundum subordinationem moventium, sic quod moventia sunt subordinata et sic unus motus potest esse ex diversis motoribus. Et ratio, quia tunc secundum movens movet in virtute primi. Secundo modo potest motus dependere ex diversis moventibus non subordinatis et sic ex diversitate moventium impeditur unitas motus et sic est de motu proiectorum qui omnino accidentalis est, quod una pars aeris plus movet quam alia. Sic autem non est in causis subordinatis, quia semper
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causa movet universalior, movet essentialiter particularem et non contra, sic quod particulares cause moverent universalem. “Arguitur secundo. Illud, quod impedit motum, non iuvat motum, sed medium impedit motum, igitur proiectum non movetur ab aere. Maior est nota, quia resistentia fit ex parte medii, ut dictum est in quarto huius. Dico, quod medium, ut aer, acciditur dupliciter: uno modo secundum se et sic non iuvat motum, sed potius impedit motum; secundo acciditur secundum quod in se recipit aliquam virtutem movendi et sic iuvat motum et simile est de alteratione, quia aqua secundum se impedit calefactionem, cum sit secundum se frigida, tamen aqua calefacta iuvat ad calefactionem, quia calefacit carnes in illa. “Arguitur tertio: Proiecta moventur ab impetu in tribus horis, igitur non moventur a pluribus motoribus consequenter se habentibus vel moventibus. Probatur, quia si non, tunc non posset salvari, quoniam tam vehementer moveretur navis contra et sagitta a balista. Dico, quod propter ista argumenta aliqui dicunt, quod necesse est proiecta moveri ab aliqua forma sibi impressa a proiciente ex ignorancia, quod lapis proiectus in manu reciperet in se unam formam sibi impressam a proieciente, per quam moveretur alicuius ad ipsum locum et sic non fieret ab aere moto, quod est contra Aristotelem et etiam hec positio est inconveniens, quod proiecta moveantur a forma deimpressa. Patet, quia si sic moverentur, tunc non esset assignare causam cessationis a tali motu occurrente aliquo obstaculo, ex quo enim illa forma est in proiecta, sic ea ratione semper moveretur in tali forma. Non enim apparet, unde posset talis forma corrumpi. Dicendum est ergo, quod ista mobilia, de quibus dictum est, moverentur per formam impressam a movente non proiectum sed in aerem medium et illa impressio faciliter potest fieri in aere, quid est faciliter mobilis et ideo, quando navis velociter movetur contra fluvium, tunc est fortis impressio facta in aqua circa navem et aerem, /f. 240v/ ideo illa aqua et aer moveret navem absque attractione in ea signum. Aqua habet tumorem ante navim et ideo apparet, quod aqua mota fuit et quod aer motus fuit, quia si quis poneret unam plumam etiam navim deberet moveri, quod est signum et ille aer motus est circa navim. Et similiter dicendum est de arcu et balista, quia talis impressio citius recipitur in arcum quam in navim vel in lapidem. “Arguitur quarto, veritas conclusionis videtur esse contra rationem. Igitur probatur, quia mirum videtur, quo modo aer posset ita pellere lapides magnos machinarum, non esset tempus impressus in machinam. Dico, quod non est verum agnoscente naturas rerum. Declaretur enim in libris Metheororum, quod subtilis aer grandia edificia subvertit immo movens elevant terram, facit tremorem. Sequitur corrolarie, quod impetus in motu proiectorum est in aere et non in proiecto. Patet veritas ex duobus signis. Primum, quia sagitta in certa distantia ab arcu velocius movetur et hoc non fieret, si impetus esset in arcu, sed hoc fit ab aere. In principio enim, cum sagitta emittitur ab arcu medius aer motus est et ergo non valde vehementer movetur sagitta, sed postea movetur maior quantitas aeris, unde et maior apparet motus insagitta et vehementer secundum signum, quia videmus tempore tonitrui aerem depulsum grandia edificia subvertere aut arbores dividere. Non ergo mirum,
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si aer motus sufficit lapidem proiectum moveri. Aer enim, quia aliquid levis, aliquid gravis est faciliter, suscipit impetum et postea movet proiectum. “Dubitatur, cuius nature sit virtus proiecta. Dicendum, quod in movente est naturalis potentia, que oritur ex principiis subiecti, sed in aere moto ista virtus non est in aliquo predicamento, quia non potest esse in aere moto actualiter, quia tunc in aere moto esset actualis potentia motiva et sic aer semper moveret proiectum absque extrinseco movente sic nunc facit proieciens. Oportet ergo dicere, quod ista virtus est in aere moto potentialiter et virtualiter et illa virtus solvatur in motu talis aeris, qui motus est de predicamento ubi. Unde potest dici, quod virtus proiectiva in aere acciditur dupliciter: uno modo quo ad eius fundamentum et sic est de predicamento ubi, quia est motus localis aeris; alio modo quo ad actum et sic non est in aliquo predicamento, quia non est ens reale actuale, sed solum virtuale.” Text 12 [To Chapter 4.3.6]: Quaestiones cracovienses, Q. 97, pp. 165–166: “Circa initium huius quintiutrum ab eo, quod inest parti, totum habeat denominari. “Et videtur, quod non, quia si sic, Socrates diceretur eius manus, quia pars eius dicitur manus, et sic Socrates diceretur minor Socrate. Patet, quia pars eius dicitur minor Socrate. “Secundo: quia a parte ad totum non valet argumentum, quia multa praedicantur de parte, quae non praedicantur de toto. “Tertio: Illud, quod inest alicui secundum partem, inest ei secundum quid, igitur etc. “In oppositum est Aristoteles in littera, qui dicit: ‘ex hoc, quod pars mutatur, dicitur totum simpliciter mutari.’ “Pro quo sciendum, quod ad ostendendum species motus Aristoteles declarat mobile tribus modis posse moveri. Primo per accidens, scilicet ex esse in eo, quod per se movetur. Secundo aliquid movetur secundum partem, quia aliquid eius movetur. Tertio aliquid movetur primo, quia movetur, et non secundum accidens neque secundum partem. “Secundo sciendum, quod denominationes convenientes parti sunt in multiplici differentia. Quaedam enim est partis, et est extranea toti, sicut esse simplex convenit animae et tamen non convenit toti homini, immo est extraneum toti homini. Alia sunt accidentia non extranea toti, et illa subdividuntur. Quaedam parti conveniunt ab accidentibus partium, quae per partem afficiunt totum, ut dolor capitis afficit totum hominem. Alia denominatio sumitur ab accidente, quod non afficit totum per partem, et illa subdividuntur. Quaedam determinant sibi certas partes in toto, ut simitas determinat sibi nasum et crispitudo crines. Alia vero non determinant sibi certas partes, sicut albedo. “Est ergo prima conclusio: Accidentia partium, quorum denominatio est extranea toti, non denominant totum per partem. Patet per primam rationem ante oppositum. “Secunda conclusio: Accidentia partium, quae non sunt extranea toti et per partem efficiunt totum, denominant totum, ut quia caput dolet, totus homo dicitur dolere.
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“Tertia conclusio: Accidentia, quae insunt parti et non afficiunt totum, sed determinant sibi certam partem in toto, denominant totum. Patet, quia a naso totus homo dicitur simus et a crinibus totus homo dicitur crispus. “Ultima conclusio: Accidentia, quae insunt parti et non determinant sibi certam partem in toto, illa non denominant totum simpliciter, ut albedo in digito non denominat totum, quia denominatio sumitur ab esse perfecto; quando ergo accidens est in parte et potest esse in toto, tunc exspectat esse perfectius et per consequens non denominat in eo, quod non habet esse perfectum. “Ad rationes: Ad primam dicitur, quod est pro prima conclusione. “Ad secundam et tertiam dicitur, quod sunt pro ultima conclusione.”
APPENDIX III [To Chapter 4.5]: BJ, Inc. 597 is bound with Inc. 596: Lambertus de Monte, Questio de salvatione Aristotelis (Köln, Henricus Quentell, ca. 1498), 2–0. BJ: Inc. 596; Nr. inw. 16528 fol. sig. Aiir: “De salvatione Arestotelis. Questio incidentaliter mota diffuse tamen ac amplissime per venerabilem magistrem nostrum Lambertus de Monte . . .” fol. sig. Bivv: “Idcirco venerandus eximius magister noster Lambertus de Monte sacrarum litterarum interpres et scrutator profundissimus in praehabita questione ostendit et concludit probabiliter per auctoritates scripture divine et iuxta saniorem doctorum sententiam Arestotelem summum et philosophorum principem esse de numero salvandorum.” Inc. 596 is not annotated. Versor Ioannes, Quaestiones De coelo et mundo, De generatione et corruptione, Metheororum, Parva naturalia, Aristotelis (Köln, Conradus Welker, 1488), 2–0. Inc. 597; Nr. inw. 16529 See Inkunabuły Biblioteki Jagiellońskiej, ed. A. Lewicka-Kamińska (Kraków: Jagiellonian University, 1962), p. 23, 364*: 5 III 1488 Versor Joannes. Quaestiones super libros De coelo, Meteora, Parva naturalia, De generatione Aristotelis. 20. HC* 16046; VK 1227 and 1234; Birk. 129; W 544.—Inc. 597. HC = Hain Copinger. VK = Voullième E.: Der Buchdruck Kölns bis zum Ende des fünfzehnten Jahrhunderts. Bonn 1903. Publikationen der Gesellschaft für rheinische Geschichtskunde 24. Birk. = Birkenmajer A.: Die Wiegendrucke der physischen Werke Johannes Versors. Uppsala 1925. Odb.: Bok-och bibliotekshistoriska Studier tillägnade Isak Collijn. W = Wisłocki W.: Incunabula typographica Bibliothecae Universitatis Jagellonicae Cracoviensis inde ab inventa arte imprimendi usque ad a. 1500. Cracovia 1900. Munera saecularia Universitatis Cracoviensis vol. 3. Inc. 597 is annotated is more than one hand, and some annotations appear to date from the late fifteenth or early sixteenth century. fol. sig Aii: “Primus de celo et mundo. Folio i.” fol. sig. Dviv (= f. 27v): “Et hec de questionibus magistri Johannis Versoris super libros de celo et mundo Arestotilis dicta sufficiant.” fol. sig. Eir: “Primus metheororum Folio i.” fol. sig. Gviv (= f. 18v): “Questiones magistri Johannis Versoris supra libros metheororum Arestotilis hic feliciter finem habent.” fol. sig. dir: “Tabula. Incipit remissorium librorum de generatione et corruptione in quo questionum dubitationumque effectus assignantur cum foliorum numero.”
462
appendices
fol. sig. diiir: “De generatione et corruptione. fo. i. Circa initium librorum de generatione et corruptione. Nota textum . . .” fol. sig. fviv (= f. 21v): “Et sic est finis questionum Versoris super duos libros Arestotilis de generatione scilicet et corruptione secundum processum burse montis Anno incarnationis domini nostri M. cccc. lxxx. viii. tertio nonas Martii.” fol. sig. gir: “Recapitulatio secundi libri de generatione.” fol. sig. giv: “Auctoritates primi libri de generatione et corruptione.” The text is lightly annotated in what appears to be a single hand from perhaps the early sixteenth century. In fact, the only annotations appear on fol. sig. civv (= f. 11v)–cvv (= f. 12v), qq. 17–18 on “mixtio.” Here I list the tables of questions from Johannes Versoris, Questiones de celo et mundo and Questiones metheororum. Questiones primi de celo et mundo Tabula [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11]
[12] [13] [14] [15] [16] [17] [18] [19]
Utrum scientia naturalis versetur circa corpora et magnitudines? Quid est subiectum attributionis libri de celo et mundo? Quare dicitur in textu fere ubi habetur de natura autem (artem?) scientia fere? Quid Aristoteles intelligit per passiones et motus? Utrum mundus sit perfectus? Que sunt principales partes universi corporei? Utrum probatio ista ternarius est numerus omnis et sufficiens? Utrum sint tantum tres motus simplices? Utrum unius corporis simplicis sit tantum unus motus simplex secundum naturam? Utrum propter motum circularem praeter quattuor elementa sit ponendum unum corpus quintum circulariter motum scilicet caelum? Utrum celum sit grave et leve? Vide ibidem diffinitiones gravis, levis, sursum, et deorsum in tertio notabili. In tertio notabili vide diffinitiones gravissimi et levissimi. Utrum celum sit ingenerabile et incorruptibile, inaugmentabile et inalterabili? Qualiter differunt philosophi a theologiis de productione celi? Utrum in celo sit materia? Utrum omne alterabile sit augmentabili? Utrum motui circulari sit aliquis motus contrarius? Utrum motus planetarum ab occidente in orientem contrarietur motui diurno primi mobilis quae sit ab oriente in occidentem? Utrum corpus circulariter motum possit esse actu infinitum? Utrum in corpore infinito possit dari centrum?
fo. i fo. i fo. i fo. i fo. i fo. ii fo. ii fo. ii fo. iii fo. iii fo. iii fo. iiii fo. iiii fo. iiii fo. iiii fo. v fo. v fo. v fo. v fo. v fo. vi
appendix iii [20] Utrum in tali corpore possit dari medium quaerere ibidem? [21] Utrum in aliquod corpus simplex recte motum possit esse infinitum? Ibidem vide pulcras rationes et propositiones in mathematica. [22] Utrum possibile sit aliquod corpus sensibile esse actu infinitum? Ibidem vide tres conclusiones de tali corpore infinito. [23] Utrum possibile sit finitum pati ab infinito? [24] Utrum si essent plures mundi terra unius mundi moveretur ad terram alterius mundi? [25] Utrum possibile sit esse plures mundos? In prima conclusione eiusdem questiones vide quod extra celum non est corpus et quod celum est ex materia sua tota. Ibidem in secunda conclusione vide pulchram autoritatem gentilis philosophi de substantiis separatis et quod extra celum non est locus neque vacuum nec tempus. [26] Utrum totalis mundus sit genitus corruptibilis? De illa materia vide ibidem quattuor conclusiones. [27] Utrum omnis potentia terminetur ad maximum? [28] Utrum ex parte sempiterni possit demonstrari de ingenitum esse incorruptibile et omne incorruptibile esse ingenitum? [29] Utrum genitum et corruptibile convertantur, et econtra dicitur de ingenito et incorruptibili? [30] Utrum omne corruptibile de necessitate corrumpatur? Questiones secundi de celo et mundo.
463 fo. vi fo. vi fo. vii fo. vii fo. vii fo. vii fo. viii fo. viii fo. ix fo. ix fo. ix fo. x fo. x fo. xi fo. xi.
Tabula [1] [2] [3] [4] [5] [6] [7] [8] [9]
Utrum celum sit sempiternum immortale sempiterne motum et sine fatigatione pena seu labore? Utrum in omni corpore reperiantur sex directione positionum ex natura rei distincte? Utrum in corpore celesti sex directione positionum sint ex natura rei distincte? Utrum in celo polus arcticus semper nobis apparens sit deorsum et polus antarticus sursum, oriens dextrum et occidens? Utrum ad salvandum generationem et corruptionem in istis inferioribus sit necesse celum pluribus motibus moveri? Ibidem vide pulcram conclusionem. Utrum necesse sit celum esse spericum. Ibidem vide pulcra conclusione que est tertia. Utrum celum debeat moveri ad unam partem determinatam, scilicet ad ante, et ab una parte determinata scilicet a dextro? Utrum motus celi sit uniformis et regularis. Ibidem vide pulchram conclusionem. Utrum ad salvandum ea que apparent in motibus planetarum sint in celo ponendi circuli eccentrici et epicicli?
fo. xii fo. xii fo. xiii fo. xiiii fo. xiiii fo. xiiii fo. xv fo. xvi fo. xvi fo. xvii
464
appendices
[10] Utrum astra sint de natura ignis? fo. xviii [11] Utrum de astrum aliud a sole lumen suum a sole recipi? fo. xviii Ibidem vide pulcram questionem et conclusionem. [12] Utrum astra moveantur motu proprio distincto [a motu suorum orbium]? fo. xix Ibidem vide pulcrum et prolixam conclusionem de motu astrorum. [13] Utrum astra et orbes quibus infiguntur causat sonos armonios? fo. xx [14] Utrum orbes superiores et propinquiores supremo celo moveantur velocius motu diurno distantioribus etc.? fo. xx [15] Utrum astra sint sperice figure? fo. xxi [16] Utrum motus orbium celestium debeant multiplicari secundum proportionem uniuscuiusque orbis ad supremum celum? fo. xxii Quare in octavo orbe est tanta multitudo astrorum et non in inferioribus? fo. xxiii [17] Utrum terra naturaliter quiescat in medio mundi? fo. xxiii An idem sit medium mundi et terre? fo. xxiiii An motus gravium sit ad medium? fo. xxiiii Que est causa quietis terre in medio mundi? fo. xxiiii Utrum terra secundum se totam sit mobilis ad medium mundi? fo. xxiiii [18] Utrum terra sit sperice figure? fo. xxiiii. [Questiones tertii de celo et mundo. f. xxvrb has an explanation why Book III is neglected. The Tabula lists nothing under Book III but simply passes over it and continues:] Questiones quarti de celo et mundo. Tabula [1]
[2] [3] [4] [5]
Utrum sit aliquod corpus grave simplex et aliquod leve simplex et aliquod grave et leve in respectu? Utrum gravitas sit forma substantialis gravis et levitas forma substantialis levis? Utrum aliquod elementum in suo loco naturali sit grave aut leve? Utrum corpus quod est gravius in aere altero corpore sit gravius eodem in aqua? Utrum plenum et vacuum sint causae gravitatis et levitatis? Utrum ex parte qualitatum motivarum posset concludi quaternarius numerus elementorum? Utrum levitas aeris et ignis speciei differant? Utrum loca naturalia gravium et levium sint cause suorum motuum? Utrum figure gravium et levium sit cause motuum sursum et deorsum?
fo. xxv fo. xxv
fo. xxv fo. xxv fo. xxvi fo. xxvi fo. xxvii fo. xxvii.
appendix iii
465
Tabula “Incipiunt tituli questionum in libros metheororum Arestotilis. Questiones primi libri metheororum. [1] Utrum corpus simplex mobile ad formam mixti imperfecti prout est in via ad taliter mixtionem sit subiectum huius libri? fo. i [2] Utrum necesse sit hunc mundum inferiorem esse continuum lationibus <su>perioribus ut omnis virtus <eius> inde gubernetur? fo. i. [3] Utrum unum elementum sit naturaliter locatum in concavo alterius? fo. ii [4] Utrum motus localis sit calefactivus? fo. ii Utrum ignis et suprema regio aeris naturaliter moveantur motu circulari? fo. iii Utrum lumen sit de se calefactivum? fo. iii [5] Utrum media regio aeris sit semper frigida? fo. iii Utrum in suprema regione aeris possint generari nubes? fo. iii Utrum sub polis generantur nubes? fo. iii Que sit figura medie regionis aeris? fo. iii [6] Utrum unum contrarium sit fortificativum alterius per antiparistasim? fo. iii [7] Utrum omnes impressiones ignite sint eiusdem speciei specialissime? fo. iiii [/ f. 4v–5r /] Utrum sidera volantia moveantur per continuam extrusionem aut per adustionem? fo. v Utrum sidera volantia sint in celo aut in regione elementari? fo. v Quo tempore fiunt huiusmodi impressiones? fo. v Utrum vapor natus sit ascendere altius quam exalatio? fo. v [8] Utrum de nocte existente serenitate aeris debeant apparere hyatus voragines et sanguinei colores? fo. v Quare dicte impressiones non apparent de die sicut apparent de nocte? fo. v Quare talia apparent in celo cum sint tamen in regione aeris? fo. v Quare talia fantasmata apparent magis tempore serenitatis quam alio tempore? fo. v Quare audiuntur aliquando soni parui quando apparent talia fantasmata? fo. v Utrum exalatio et vapor sint eiusdem speciei cum corpore a quo elevantur? fo. v [9] Utrum cometa sit de natura celesti? fo. v [10] Utrum cometa sit de natura elementari? fo. vi Quo tempore magis generatur cometa? fo. vi Quare cometa diu sic permanet in aere? fo. vi
466
appendices
[f. 6:] Que sit causa diversitatis colorum comete? fo. et littera(?) eodem Utrum possunt simile apparere plures comete? fo. eodem Que sint signa comete? fo. eodem [11] Utrum gallaxia sit de natura elementari? [“Galaxia” = circulus lacteus (Milky Way).] fo. vii [12] Utrum pluvia generetur in media regione aeris? fo. eodem Que sunt signa pluvie? fo. vii Que sunt accidentia pluvie? fo. vii [13] Utrum ros et pluvia similiter generantur? fo. viii Que sunt accidentia roris? fo. viii Que sunt accidentia nivis? fo. viii [f. 8: ] [14] Que sunt accidentia pruine? fo. viii Que sunt accidentia grandinis? fo. viii [f. 8: ] [15] Utrum aque fontium et fluviorum generentur in concavitatibus terre ex aere in ipsis incluso? fo. viii [16] Utrum ubi nunc est mare aliquando prius fuerit aut posterius erit terra arida aut econtra? fo. ix Questiones secundi libri metheororum. [1] Utrum terra debeat esse totaliter cooperta aquis? [2] Utrum mare in suo loco naturali sit generabile et corruptibile? [3] Utrum mare debeat fluere et refluere? Quare astrologi magis aspiciunt ad orientem in nativitatibus hominum quam ad punctum meridiei? An luna habeat movere mare per lumen suum an per aliquam aliam influentiam distinctam a lumine? Utrum fluxus et refluxus maris sunt maiores in uno tempore quam in alio? Quare aliqua maria solum fluunt in mense et aliqua numquam? [4] Utrum mare sit salsum? Quare aliqui fontes convertunt corpora terrestria in ipsis posita in lapides? Quare alique aque fontales causant strumam in collo? Quare alique aque faciunt nigras ovex ex illis bibentes et alique econverso faciunt albas? Que aque sunt saniores? [5] Utrum ventus sit exalatio calida et sicca laterialiter mota circa terram? Utrum pluvie quandoque faciant cessare ventos?
fo. x fo. x fo. xi fo. xi fo. xi fo. xi fo. xi fo. xi fo. xi fo. xii fo. xii fo. xii fo. eodem fo. xii
appendix iii
[6]
[7] [8]
[9]
Utrum sol sit causa commotionis ventorum et causa efficiens cessationis eorundem? Utrum tantum duodecim sint venti? Quare venti boreales communiter flant in autumpno post tropicum estivalem, et tamen venti australis non flant in vere post tropicum hyemalem? Utrum venti australes flent a polo antarctico nobis manifesto? Utrum plures venti debeant flare a septentrione quam a meridie? Utrum venti debeant reduci ad quatuor principales? Utrum venti contrarii possunt simul flare? Utrum aliqui venti faciunt alios cessare? Que est causa generationis ventorum? Utrum venti distinguantur secundum calidum et frigidum, humidum et siccum? In qua parte anni debent flare etnephei et venti circulares? [sic] Utrum motus terre sit possibilis? [earthquakes, volcanic eruptions, etc.] Que sunt accidentia motus terre? Utrum tonitruum sit sonus factus in nubibus? Unde causatur diversitas sonorum in tonitruo? Que tonitrua sunt magis timenda? Quomodo causatur cuneus fulminis? Utrum tiphones etnephias incensiones et fulmina sint eiusdem speciei et substantie?
Questiones tertii libri metheororum. [1] Utrum radius visualis refrangatur in occursu medii rarioris vel densioris? [2] Utrum halo habeat apparere circularis figure? [3] Utrum colores apparentes in yride sint veri colores? [4] Utrum yris debeat apparere tricolor? Quare per iuxtapositionem viridis et alurgi non apparet unus color sicut per iuxtapositionem viridis et punicei apparet zandros? [5] Utrum quando apparent due yrides superior sit debilior in coloribus quam inferior? An yris possit causari a luna sicut a sole? An duo homines possint eandem yridem in eadem parte nubis videre? Quare est quod quandoque videmus yridem inter nos et arbores vel montes? Utrum yris appareat semper per modum semicirculi? [6] Utrum parelii et virge debeant apparere per reflecionem vel refractionem?
467 fo. xii fo. xii fo. xiii fo. xiii fo. xiii fo. eodem fo. xiii fo. xiii fo. xiii fo. xiiii fo. xiii fo. xiiii fo. xiiii fo. xiiii fo. xiiii fo. xiiii fo. xv fo. xv
fo. xv fo. xvi fo. xvii fo. xvii fo. xvii fo. xviii fo. xviii fo. xviii fo. xviii fo. xviii fo. xviii
468
appendices Que sunt accidentia virgarum et pareliorum? Utrum ad istrum librum pertineat determinare de mineralibus?
fo. xviii fo. xviii
Finis tabule. BJ, Inc. 597, De generatione et corruptione. fol. sig. dir: Tabula fol. sig. dira: “Incipit remissorium librorum de generatione et corruptione in quo questionum dubitationumque effectus assignantur cum foliorum numero. Questiones primi libri de generatione et corruptione. [1] Utrum de corpore mobili ad formam sit scientia tamquam de subiecto attributionis huius libri? fo. i Utrum corruptio sit naturalis et an de ipsa possit scientia naturalis? fo. i Utrum re corrupta possit manere eius scientia in anima? fo. i [2] Utrum ponentes unum materiale principium et hoc in actu possint salvare generationem distingui ab alteratione et aliis motibus? fo. i Utrum generatio secundum quid et alteratio sive motus accidentalis et proprie dictus sint idem? fo. ii [3] Utrum omnium habentium transmutationem adinvicem sit una materia? fo. ii Utrum materia sit una numbero specie genere aut analogia? fo. ii [4] Utrum Democritus ponens corpora indivisibilia esse principia rerum possit salvare distinctionem generationis simpliciter ab alteratione et aliis motibus? fo. iii Utrum corpus componatur ex indivisibilibus? fo. iii [5] Utrum sit aliqua generatio simpliciter? fo. iii Que sit causa perpetuitatis generationis et corruptionis? fo. iiii Utrum ens in potentia ex quo est generatio sit substantia vel accidens? fo. iiii Utrum quicquid generatur ex aliquo corrupto generetur? fo. iiii [6] Utrum verum sit quod generatio unius sit corruptio alterius que quidem questio habetur tam in questiuncula quam etiam inferius in principali questione? fo. iiii Utrum generatio secundum quid que est in accidentibus presupponat corruptionem? fo. iiii Utrum generatio scientie presupponat corruptionem erroris? fo. iiii [7] Utrum generatio differat ab alteratione et ab aliis motibus? fo. v Utrum generatio differat ab aliis motibus? fo. v Utrum eadem qualitas maneat in generato que prefuit in corrupto? fo. v [8] Utrum in corruptione substantiali ex pate formarum substantialium necesse sit resolutionem fieri usque ad materiam primam? fo. v Utrum plurium agentium idem effectus numero a quolibet produci possit? fo. v
appendix iii
[9]
[10]
[11]
[12] [13] [14] [15] [16]
[17]
Utrum ab eodem agente in quolibet plurium instantium possit idem effectus numero produci? Utrum augmentatio et diminutio sint motus distincti ab aliis motibus? Quomodo differunt augmentatio et rarefactio. Utrum augmentatio et diminutio ab invicem distin/ fol. sig. dirb / guantur? Utrum illud quod augetur sit solum in potentia quantum nullam penitus habens quantitatem? Utrum in augmentatione id quod advenit, scilicet cibus vel corpus vel membrum vel utrumque augeantur: Utrum augmentatio fiat adveniente aliquo extrinseco ibi arguitur pro et contra? Utrum in quantitate sit aliqua mutatio proprie dicta? Que sit causa effectiva augmentationis? Utrum tres conditiones augmentationis sint bene assignata? Utrum ad salvandum augmentationem conveniens sit ponere poros? Utrum calor naturalis continue agat in humidum radicale? Utrum nutrimentum sit simile vel dissimile ei quod nutritur? An augmentatio sit ad quantum in communi? An motus nutrimenti quo transmittitur ad singulas partes viventis sit naturalis? Utrum membrum patiatur mixtionem a nutrimento? Utrum augmentatio sit unus motus et continuus? An vivens quam diu vivit nutriatur? Utrum omne agens agat per contactum? Utrum simile agat in sibi simile? Queritur decimoquinto, utrum omne agens in agendo repatiatur? Queritur decimoquinto [sic], utrum actio et passio habent fieri poros? Ibidem vide quatuor opiniones et quinque conditiones quomodo fiunt actio et passio. Utrum mixtio sit possibilis? Ibidem vide pulcra notata in quatuordecim conclusionibus.
469 fo. vi fo. vi fo. vi fo. v [sic] fo. vi fo. vii fo. vii fo. vii fo. vii fo. vii fo. viii fo. viii fo. viii fo. viii fo. viii fo. viii fo. viii fo. viii fo. ix fo. ix fo. x fo. xi fo. xi fo. xi fo. xi et xii fo. xii
[18] Utrum elementa formaliter maneant in mixto? Ibidem vide opiniones Averrois, Alberti, et Egidii de Roma de illa materia. fo. xii Recapitulatio primi libri de generatione et corruptione. fo. xiii Registrum libri secundi de generatione et corruptione. [1] Utrum qualitates prime sint principium formale elementorum et materia prima sit principium materiale eorundem? fo. xiii [2] Utrum tantum sint quatuor qualitates prime? fo. xiiii Ex quo quodlibet elementum determinat sibi certam
470
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qualitatem in summo quare non sufficiat una qualitas ad constitutionem unius elementi? fo. xv Que sunt loca elementorum? fo. xv An ignis et aqua magis contrarientur quam ignis et terra? fo. xv / fol. sig. div / [4] Utrum cuilibet elementorum primo conveniat una qualitas prima? fo. xv An quodlibet elementum habeat duas qualitates in summo? fo. xv Utrum calor, ignis, et aeris sint eiusdem speciei et similier querendo de aliis qualitatibus? fo. xv [5] Utrum ex quolibet elemento potest immediate generari quodlibet elementum? fo. xvi Ibidem secundo etiam declarat in quibus elementis est facilior transitus et in quibus non, tertio declarat ibidem ex quibus duobus elementis potest fieri tertium. fo. xvi [6] Utrum in genere corporum elementa sint prima? fo. xvii [7] Utrum ad generationem cuiuslibet mixti perfecti existentis circa medium concurrant quatuor elementa? fo. xvii Ibidem agitur de generatione et corruptione elementorum que generantur et corrumpuntur per naturam elementorum. Utrum elementa in equali pondere concurrant ad generationem mixti? fo. xviii Utrum sit possibile qualitates elementorum in mixto equaliter convenire? fo. xviii [8] Utrum tantum sint tria principia generationis et corruptionis mixtorum inferiorum, scilicet, materia, forma, et efficiens? fo. xviii [9] Utrum quatuor elementa per suas virtutes activas et passivas sint agentia sufficientia ad generationem et corruptionem mixtorum? fo. xviii [10] Utrum motus solis sub obliquo circulo factus sit causa perpetuitatis generationis et corruptionis in istis inferioribus? fo. xix Qualiter habet veritatem ista propositio idem inquantum idem et similiter se habens semper natum est facere idem? fo. xix [11] Utrum omne vivens habeat determinatam periodum sue durationis? fo. xx [12] Utrum ex parte finis et ex parte cause moventis possit ostendi perpetuitas generationum et corruptionum? fo. xx Utrum motus capiat suam unitatem a mobili aut a termino? fo. xxi [13] Utrum aliquod corruptum possit idem numero reproduci? fo. xxi Et sic est finis registri questionum et dubitationum huius libri totalis de generatione et corruptione. / f. 21vb / “Et sic est finis questionum Versoris super duos libros Arestotilis de generatione scilicet et corruptione secundum processum burse montis. Anno incarnationis domini nostri M. cccc. lxxx. viii. tertio nonas Martii.”
APPENDIX IV Ficino’s Translation of Parmenides The text in Ficino’s translation (Florence, 1484; Uppsala, Copernicana 31; the Estienne or Stephanus numbers are in brackets) reads, beginning selectively with the context: f. e4va [134b]: “Uerumtamen ipsas species neque nos habere neque circa nos esse posse assenteris. Non profecto. Cognoscuntur ne ipsa scientie specie genera ipsa que singula sunt? Certe. Quam speciem nos haud habemus. Non certe. Nulla igitur species a nobis cognoscitur, cum ipsius scientie particeps minime simus. Non apparet. [134c] Ignotum itaque nobis ipsum pulchrum et ipsum bonus est et omnia denique ut ideas esse supponimus. Uidetur. Consydera et hoc etiam grauius. Quid nam? Num fateris si est ipsum quiddam scientie genus, multo illud prestantius esse hac nostra scientia, et ipsam pulchritudinem ac reliqua eodem pacto. Immo. [134d] Non ne si quid aliud est ipsius scientie particeps, nullum nisi deum dices supremam habere scientiam? Necesse est. . . . [135a] Unde uacillat quisquis hec audit, ac dubitat ne forte idee nihil sint omnino, vel si sint /f. e4vb/ necesse eas esse humane nature ignotos existimat. A deo ut qui ista dicit inferre aliquid uideatur. Et ut paulo ante dixi mirum est quam sit incredibile, et uiri admodum ingeniosi percipere posse quod sit genus quoddam cuiusque, [135b] et ipsa secundum se ipsam essentia, nec non mirabilioris iuri officium est, hoc postquam inuenerit alios docere posse sufficienter omnia discernentem. Assentior. Parmenides inquit Socrates . . . [135d] Ante quam exercitatus sis o Socrates, definire aggrederis, quid pulchrum, iustum, bonum, et aliarum quelibet specierum, hoc enim pridem animaduerti, hic te audiens una cum hoc Aristotele disputantem, pulcher sane atque diuinus mihi crede impetus iste tuus, quo ad rationes aduolas. Ceterum collige te ipsum diligentusque te in eo facultate exerce, que in utilis esse uidetur, et a multis nugatio siue garrulitas nuncupatur dum iuuenis es, alioquin te ueritas fugiet. Quis exercitationis huiusce modus est Parmenides? [135e] Iste inquit quem a Zenone audisti. Sed etiam illud tuum aduersus hunc dictum miratus sum cum diceres non in iis que oculis percipiuntur eorumque errore cogitationem sistere oportere, sed ad ea conscendere quae quis maxime ratione comprehendere ac species esse putaret. Neque in hunc modum arduum esse uidetur, similia utrum atque dissimilia cetera ue quae rebus existentibus competunt explicatur. Et probe quidem disiste. Est autem propter hoc, illud etiam obseruandum, [136a] ut non modo si est aliquid supponas, ac deinde que proueniunt ex suppositione consideres uerum etiam si non sit id ipsum supponas si perfectius exercitari uoleris, quo pacto id ais. Uerbi causa si uelis circa istam suppositionem /f. e5ra/ [Copernicus’s annotation is directly above the following words through ‘euentu’:] quam Zenon inuexit, si multa sunt quid euenturum est ipsis multis ad se ipsa et ad unum, et uni ad se ipsum et ad multa. Ac rursus si non sunt multa, iterum consyderandum
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quid accidat uni atque multis, tum ad se ipsa, tum inuicem. Et rursus si supposuerit esse similitudinem, vel non esse, quid potissimum ex utraque suppositione contingat, tam iis que supposita sunt quam ceteris omnibus, ad se ipsa pariter atque inuicem. [136b] Eadem quoque de dissimilitudine ratio est, de motum statu, generatione, corruptione, esse, atque non esse, et ut uno uerbo completar, de quocunque supponitur, aut esse, aut non esse, siue quamuis aliam passionem suscipere, consyderanda sunt que ex suppositione proueniant ad se ipsum, et ad quodlibet aliorum, quodcunque elegeris, et ad plura et ad uniuersa similiter, [136c] et alia rursus ad se ipsa atque ad aliud, quodcumque adsumpseris siue ut existens siue ut non existens ipsum posueris, si modo absolute exercitatus, ueritatem sis penitus inspecturus. Arduum inquit opus adducis nec te omnino intelligo. Sed cur ipse non supponis aliquid illud eo modo percurrens, ut clarius intelligam? [136d] Grande o Socrates onus seni imponis. Tunc Socrates cur non ipse o Zenon hanc rem discutis? Cui Zeno subridens respondit, ipsum o Socrates oremus Parmenidem neque enim leue quiddam est quod ait. an non uides quantum sit negocium quod iubes? Quod si plures essemus haud sane id postulare deceret. Indecorum nanque huiusmodi quedam in conspectu multorum tractare, atque id seni precipue. Ignorant enim multi quod absque hoc discursu ac peruagatione per omnia impossibile sit mentis ueritati coniuncte compotem fieri. [136e] Ego igitur o Parmenides una cum Socrate precor, ut et mihi etiam liceat tanto tempore transacto hec audire. Cum uero hec intulisset Zenon retulit. Antiphon dixisse Pythodorum, se quoque et Aristotelem ac reliquos omnes obsecrauisse Parmenidem, ut quod dixerat, demonstraret, neque aliter faceret. [137a] Tunc demum Parmenides necesse est inquit obtemperare, et si mihi uideor in id quod passus est ibicius equus incidere. Cui profecto equo athlete seniori curruum subituro certamen et propter experientiam euentum ex /f. e5rb/ timescenti ibycus ipse se conferens inuitas inquit et ipse tam senex ad amores aggredi cogor. Eadem ratione ego mihi admodum trepidare uideor, cum cogito quo pacto possim iam grandis natu tam profundum differendi Pelagus transnatare. Obsequendum tamen cum et Zenon ipse roget, iidem enim sumus. Unde igitur incipiemus? Quid ue primum supponemus? An multis postquam negociosum ludum ingressi sumus a me ipso meaque suppositione in primis exordiar? [137b] De ipso uno supponens, siue unum sit siue non, quid accidat? Prorsus inquit Zenon. Quis igitur mihi respondebit? An iunior est minus enim negocii prebebit, et que ipse sentit maxime respondebit ut eius responsio minus me defatiget paratum sum o Parmenides. [137c] Aristoteles inquit me namque significas dum iuniorem respondere iubes. Sed age ut lumet interroga me, tanquam libentissime responsurum. “Age igitur si unum est, non utique multa erit ipsum unum. At quo modo? Neque igitur partem esse illius aliquam, neque totum esse ipsum oportet. Cur nam? Pars utique totius pars est. Est. Quid vero? Non se totum est, cui nulla pars deest? Prorsus. Utrinque igitur ipsum unum ex partibus esset, totumque existens ac partem habens. Necesse est. Utrinque rursus ipsum unum multa potius quam unum esset. Uerum. [137d] Oportet autem non multa, sed unum ipsum existere. Oportet, sane. . . .”
APPENDIX V Summary of Plutarch’s De facie1 Here I emphasize only those ideas that are the most relevant to Copernicus’s critical evaluation of Aristotelian and Ptolemaic geocentrism. In Plutarch’s dialogue, the narrator, Lamprias, is a supporter of the Platonic Academy who elsewhere is described as an Aristotelian, but one who criticizes him usually by adopting a Platonic doctrine. The issue that the dialogue addresses is how there can be dark spots on the Moon if it is the sort of perfect celestial body maintained by Aristotle. The Platonists had come to the conclusion, supported here, that the Moon must be an Earth-like spherical body possessing weight and solidity. It does not fall towards Earth because its circular motion generates a centrifugal tendency that remains circular and stable because a natural motion preserves itself unless it is diverted.2 In holding the view that Earth is in the middle, Stoics maintained that all weights in their natural inclination press against one another and towards which they move and converge from every direction. In response to objections to the sphericity of Earth, Lamprias argues as follows: If all heavy body converges to the same point and is compressed in all its parts upon its own centre, it is no more as centre of the sum of things than as a whole that the earth would appropriate to herself the heavy bodies that are parts of herself; andof falling bodies proves not that the <earth> is in the centre of the cosmos but that those bodies which when thrust away from the earth fall back to her again have some affinity and cohesion with her. For as the sun attracts to itself the parts of which it consists so the earth too accepts as own the stone that has properly a downward tendency, and consequently every such thing ultimately unites and coheres with her. If there is a body, however, that was not originally allotted to the earth or detached from it but has somewhere independently a constitution and nature of its own, as those men would say of the moon, what is to hinder it from being permanently separate in its own place, compressed and bound together by its own parts? For it has not been proved that the earth is the centre of the sum of things, and the way in which things
1 See Plutarch, Moralia, Vol. 12 (Cambridge: Harvard University, 1957), Concerning the Face Which Appears in the Orb of the Moon, tr. Harold Cherniss, 67–71, 924 D-F. I have quoted the text at length because Copernicus’s later arguments display familiarity with the notions represented here, and his language even echoes some expressions, suggesting that he adopted Neoplatonic doctrines on the elements, motions of elemental bodies, and the like. He believed that Aristotelian views could be adapted, however, to accommodate these Neoplatonic doctrines. 2 The similarity to a “circular” inertia is at hand.
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appendices in our region press together and concentrate upon the earth suggests how in all probability things in that region converge upon the moon and remain there. The man who drives together into a single region all earthy and heavy things and makes them part of a single body—I do not see for what reason he does not apply the same compulsion to light objects in their turn but allows so many separate concentrations of fire and, since he does not think that there must also be a body common to all things that are fiery and have an upward tendency.
In the dialogue Lamprias reports the view of some mathematicians who place all of the planets above the Sun (the Platonic opinion, although not explicitly identified here as Platonic), which Lamprias uses to argue explicitly for the Platonic assimilation of the Moon to Earth. In other words, with the Moon separated from the other planets by the Sun, there is even greater reason to consider the Moon Earth-like.3 Arguments about the size of the universe and Earth in the middle are shown to be fraught with a number of difficulties, all pointing to the dialectical nature of the arguments. So also are the principles “natural” and “unnatural” that, if improperly applied, would rather result in a dissolution of the cosmos thus leading to disorder by insisting on the absolute separation of what is heavy from what is light.4 The relation of part to whole also does not support conclusions about what is natural in any absolute sense but is rather a matter of relative wholes and how as related to one another they constitute the whole ordered cosmos.5 This is clearly an argument directed at the Aristotelian (and Stoic) assumption that is used abruptly to support the conclusion that as a principle of order in nature, Nature established directionality by means of the absolute separation of the light from the heavy. This is why the Platonic Academy placed emphasis on a universe controlled by a rational principle rather than one under the direction of Nature.6 We may comment that scholastic Aristotelians seem not to have realized to what extent they had substituted Platonic principles for Aristotelian ones that they nonetheless continued to call “Aristotelian.” It is little wonder that late medieval scholastics defended Aristotle as they did, for they blended their Platonized Aristotle with what they had come to accept as Aristotle rightly understood.7 The remainder of the genuinely philosophical portion of the dialogue returns to the argument that the Moon is Earth-like. The text appeals to optical phenomena and eclipses, all of which support the conclusion that the
3
De facie, 71–73, 925 A-C. Ibid. 77–83, 925 F-926 E. Compare with Copernicus’s arguments from De revolutionibus I, 4–10, which are examined in chapter nine. 5 De facie, 89–91, 927 D-928 A. 6 Ibid. 91–95, 928 A-D. 7 Di Napoli, 346–347, points out that Ficino too oriented Aristotle to Plato, meaning that he interpreted Aristotle in a Platonic way. See also Monfasani, “Marsilio Ficino,” 195–196. 4
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Moon must have the same consistency as Earth, for the same effects must be produced by similar agents.8 A little later, the possibility of habitation on the Moon is discussed, leading to the speculation that if the Moon moves and rotates, then it would have to be gentle and smooth enough so as not to pose any danger to those on it. The rotation “smooths the air and distributes it in a settled order, so that there is no danger of falling and slipping off for those who stand there.”9
8
De facie, 99–121, 929 A-932 C. Ibid. 157–167, esp. 167, 938 F-939A. Note the implication that if the Moon rotates, then rotation must be natural to it. 9
APPENDIX VI EXCURSUS ON TRANSMISSION This is a difficult subject to discuss in the current environment. There is no doubt that Islamic astronomers and mathematicians of the Middle Ages and well into the fifteenth century were far ahead of their western Latin contemporaries.1 The appearance of several mathematical solutions in the Latin West from the fourteenth to the sixteenth century that seem to descend from Islamic predecessors has inspired a perfectly legitimate hypothesis, namely, that there must have been a connection and that these solutions and models were transmitted by Byzantine or Latin intermediaries that have either disappeared or have not yet been discovered. Some scholars speak of the hypothesis as if it were a certainty. A recent example confirms the extent to which even knowledgeable and highly regarded scholars have adopted the hypothesis as fact: We should not be surprised, then, that Nicolaus Copernicus (1473–1543) gained insight into the mathematical problems concerning the motions of the planets from the work of the astronomers at the Maragha observatory, in particular that of Nasir al-Din al-Tusi (d. 1274).2 All I wish to emphasize is that even a highly likely hypothesis is still just that until the missing link is found, and that in the meantime we ought to entertain other possible hypotheses. What follows is less a fully articulated hypothesis than a series of observations and questions that suggest how certain problems may have inspired solutions that were similar, so similar in fact that it did not seem possible that they could have been discovered independently. Of course, they may not have been constructed independently, but post hoc ergo propter hoc is a fallacy, and the contrary claim that it is impossible for them to have been discovered independently in the absence of the hypothesized source is also fallacious. How, then, would the story go? It is striking to read all of the articles describing the problems and solutions. In mathematics there are probably no unique solutions to a problem, although some are certainly more elegant than others. Still, there is a selection. We have been introduced to solutions that are similar. Now, what is there about these problems that “led to” specific kinds of solutions? These kinds of solutions began to appear in the Latin West in the fourteenth century. Part of the background here includes either rejection or
1 Endress, “Mathematics”; King, In Synchrony; and Sabra, “An Eleventh-Century Refutation” are representative and exemplary. 2 Smith, “Science on the Move,” 370–371.
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neglect of Aristotelian/Averroist prohibitions that restricted the application of mathematics to analyzing problems. Although the applications were mostly in hypothetical, theoretical, or imaginary contexts, they challenged standard philosophical solutions. Because natural philosophy and astronomy were primarily speculative or theoretical sciences, the “practice” of natural philosophy and astronomy meant carrying out thought experiments and evaluating them for their logical consistency and coherence.3 In responding to Averroes’s objections to Ptolemaic models, some astronomers distinguished between the considerations proper to philosophy from those proper to astronomy. Philosophers regard spheres as concentric because they refer all of the motions to the prime mobile or the starry vault, the proper motion of which is diurnal, and it carries or influences all of the motions below it. Astronomers consider this motion, of course, but they also consider the proper motions of lower spheres, and these motions are proper to astronomy. The motions of lower spheres compelled astronomers to develop mathematical models, mechanisms, or devices to account for these motions. These considerations usually generated eccentric, epicycle, and equant models. On the other hand, some philosophers or astronomers who treated the proper motions of the lower spheres attempted to find solutions that minimized the inconsistencies between the models and the philosophical axiom about the uniform, circular motions of the spheres concentric to Earth. Turning now to the history of the transmission of models, we may observe that in several seminal and otherwise important articles on the resonance of Islamic solutions in the Latin West we find the same pattern. Authors recognized problems with the Ptolemaic models or accuracy of predictions, and they proposed solutions that involved generating a variety of devices. These devices are mechanisms that solve the problems by means of circles that generate a harmonic motion. These are the devices that apparently derive from the Islamic sources by way of a supposed Byzantine or Latin intermediary that has yet to be found. We cannot recite all of the details here, but it is the sketch that is suggestive. One version of this story begins with Ibn al-Haytham’s physical interpretation of Ptolemy’s planetary theory.4 Ibn al-Haytham (965–ca. 1040) proposed a physical mechanism of two concentric solid spheres (a Eudoxan device) to account for Ptolemy’s assumptions in the Almagest. In the thirteenth century, Nasir al-Din al-Tusi (1201–1274) criticized and modified Ibn al-Haytham’s solution by proposing his own that used a spherical version of his “couple.” As Mancha summarizes it, al-Tusi proved “that the spherical version of his ‘couple’ may also be applied to three similar problems involving an oscillatory motion of a point along an arc of a sphere: the oscillation of the inclined planes of the eccentrics of Venus and Mercury, the change in the obliquity of the ecliptic between a maximum and minimum value,
3 4
Podkoński, “Charm.” Sabra, “Refutation,” 121; Mancha, “Homocentric Epicycles,” 70–73.
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and trepidation.”5 Three astronomical texts of the fourteenth and fifteenth centuries describe physical arrangements of two concentric spheres describing the epicycle or eccentric similar to that of Ibn al-Haytham. Henry of Hesse, magister Julmann, and Albert of Brudzewo describe arrangements of two concentric spheres. Brudzewo explicated a passage in Peurbach’s Theoricae. Peurbach’s own description is unclear, but Brudzewo attributes the arrangement to some unknown author. Because Hesse’s text also suggests dependence on some unknown source, it seems likely that Hesse, Julmann, Brudzewo, and possibly Peurbach took the Eudoxan device from a source that described Maragha planetary theory. In any case, these three and possibly all four authors used two homocentric spherical devices to provide a physical mechanism to account for “the different oscillatory motions of the Ptolemaic epicycle diameters required by the equant and latitude theory.”6 Now, Brudewo seems to have known Hesse’s argument,7 and Regiomontanus certainly knew it.8 Julmann seems to provide additional evidence that the device circulated, as it were, among late fourteenth-century authors, and, in any case, his elaborations seem to depend on Hesse.9 In short, the intermediary may have been a text on which Hesse drew. And here I suggest that we insert Oresme’s “rolling device.”10 The context of Oresme’s discussion is the question whether any heavenly body moves circularly? After presenting several observational reasons supporting a negative answer, Oresme responds to the Aristotelian and Averroist objections that the heavens move regularly. His first conclusion is that a planet can move naturally with rectilinear motion that is composed from several circular motions. To my knowledge there are only two editions and explications of Oresme’s text, one published and the other an unpublished doctoral dissertation. I quote the principal sections here:11
5
Mancha, 82. See also Sabra, 122–124. Mancha, 81. 7 Mancha, 86–87, n. 20. 8 Mancha, 82, n. 4. 9 Mancha, 78. 10 Droppers, Questiones; and Kren, “Rolling Device.” 11 Oresme, Questiones de spera, ed. Droppers, Q. 13: “Utrum quodlibet corpus celeste moveatur circulariter. Et arguitur quod non primo de luna quia per experientiam videmus lunam moveri tardius motu proprio quando est in oppositione et coniunctione et velocius quando est in quadraturis et e contrario est de motu diurno. Secundo, dies naturales sunt longiores in illo tempore et in alio breviores. Ergo sol movetur irregulariter. Consequentia tenet quia dies naturalis est revolutio solis super terram. Et antecedens patet per auctorem de Spera, et per omnes astrologos. Unde repertum est quod dies naturales sunt longiores in estate quam in yeme et quod una medietas anni est maior quam alia. Tertio, sol aliquando describit minorem circulum in uno tempore quam in alio. Ergo sol movetur irregulariter. Consequentia tenet ex diffinitione irregularitatis. Antecedens patet quia circulus tropici est minor quam circularis equinocialis ut dicit auctor in littera et tamen sol describit tropicum in uno die naturali et in alio describit equinocialem. Quarto, auctor de Spera dicit quod signa 6
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Whether any heavenly body moves in a circle? Some argue that it does not, because we observe in ordinary experience that the moon moves more slowly in its proper motion when it is in opposition and conjunction, and more quickly when at quadrature, and it moves in a contrary manner in its diurnal motion. Second, the natural days are longer at one time of the year and shorter at another; therefore, the Sun moves non-uniformly. The consequence holds because a natural day is the revolution of the Sun around the Earth. The antecedent is evident [because] supported by the author of the Sphere and by all astronomers. Hence, we find that the natural days are longer in the summer than in the winter, and that one-half of the year is greater than the other half. Third, the Sun sometimes describes a smaller circle at one time than at another; therefore, the Sun moves non-uniformly. The consequence holds by virtue of the definition of “non-uniformity.” The antecedent holds because the tropic circle is smaller than the equinoctial circle, as the author says in the text; nevertheless, the Sun describes the tropic circle in one natural day and the equinoctial circle in another. Fourth, the author of the Sphere says that the signs rise non-uniformly, for some rise more quickly and some more slowly. Fifth, astronomers maintain that certain planets are sometimes retrograde and sometimes stationary, for the planets are said to be stationary when they seem to stand still and delay their initial motion because they do not move as quickly as they did before. . . . Aristotle and the Commentator (On the Heavens, Book II, comment 39) hold the opposite, maintaining that heaven does not accelerate at some times or decelerate at other times.12 In answer to this question I propose three elegant conclusions. First, it is possible for a planet to move perpetually according to its own nature with a rectilinear motion composed of several circular motions. This motion can be accomplished by several intelligences, any one of which may endeavor to move with a circular motion without being frustrated in its purpose. To prove this, let us suppose by imagination, as the astronomers do, that A is a deferent circle of some planet, or its center, B is the epicycle circle of the same planet, and C is the planetary body or its center—I take these to be the same.
oriuntur irregulariter. Unde quedam oriuntur velocius, quedam tardius. Quinto, per astrologos qui ponunt quasdam planetas aliquando retrogrades, aliquando stationarios, planete enim dicitur stationarius eo quod videtur stare et cessare a primo motu quia non movetur ita velociter sicut ante. . . . Oppositum patet per Aristotelem et Commentatorem Secundo Celli, commento 39, ubi point quod cellum non vigoratur aliquando in motu nec aliquando tardatur.” The translation is mine. 12 From this point on, the Latin text is available in Kren, “Rolling Device,” 491–492.
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appendices Let us further imagine that the line BC extends from the center of the epicycle to the center of the planet, and that the line CD is a line on the planet on which BC falls perpendicularly. Let circle A move on its center toward the east, and circle B toward the west, while the planet C revolves on its center toward the east. Therefore, because line BC is always equal (for it is a radius), I maintain that the distance that B descends with the motion of the deferent is the distance that point C ascends with the motion of the epicycle. From this it follows evidently that point C will move in a certain time on a straight line. Further, I maintain that as point B ascends on its circumference so will the planet ascend. It is evident that the point D will move continuously on the same line. Therefore the whole planetary body moves with a rectilinear motion to some point and returns again with an entirely similar motion.
Skipping over the responses to objections, I now turn to the four corollaries: First, at least three circles are required for such a rectilinear motion. Second, circular motion never arises from rectilinear motion, nor does rectilinear motion result from rectilinear and circular motions, but a rectilinear motion can result from several circular motions. Third, the conclusion drawn by Aristotle and the Commentator that no rectilinear motion of heaven is possible is false. . . . Fourth, it is possible to imagine a rectilinear motion that is eternal with the exception that at the point of reflection the moving body would not be said to move or rest. None of the manuscripts provides a figure, leaving readers to construct their own. The first explication, by Claudia Kren, does not fit Oresme’s description very well. In her figure 1, she provides a version of al-Tusi’s rolling device, and supposes that Oresme produced a garbled description of the Tusi couple.13 This interpretation is implausible. Even if by “deferent circle” Oresme means a sphere on the inside surface of which an epicycle is rolling, he says explicitly that the solution requires at least three circles, but the rolling device has only two circles, or one circle rolling inside a sphere. Next, Oresme says nothing about having relied on a source. On the contrary, he suggests that the idea that circular motions can be combined to generate a rectilinear motion is obvious. Now, the text does not support that claim, but the idea of constructing a rectilinear motion by combining circular motions is explicit, and Oresme does not suggest an application other than an astronomical one, as his examples and references indicate. In his explication and more detailed illustration, Droppers makes an additional assumption, namely that the radius of the epicycle carrying C must be
13 Kren refers to Droppers’s dissertation, but she does not comment on or criticize his reconstruction.
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A = center of deferent. B = center of epicycle. C = center of planet. C2 and C4 = extremes of straight-line path of center C. CD = line in planet ⊥ to CB.
Figure 5—Droppers’s representation of Oresme’s Reciprocation Device. (From Droppers, p. 287) twice the length of the deferent carrying B. Oresme says nothing about the length of the radii, yet Droppers assumes here that there must be a 2:1 ratio, and supplies the following illustration: The motion of C around its center B is non-uniform because as B sweeps out angle α in some uniform time, C sweeps out angle α + β. Angle β continuously varies, and when angle α = 180o (at B3), angle β = 45o. Perhaps a simpler mathematical solution can be seen in the following illustration, although it is a figure interpreting the Tusi couple. In sum, Oresme describes a reciprocation device, and he employs an epicycle model. The likeliest interpretation is that he hit on a solution similar to the Tusi couple, but there is no indication that Oresme was directly concerned with the physical characteristics of the bodies or the mechanisms. In fact, he takes it for granted that the motion proceeds from several intelligences. He presents it simply as a geometrical solution of a geometrical problem, albeit in the context of a discussion about the circular motions of heavenly bodies. It is very likely that Hesse was familiar with Oresme’s works, a likelihood that extends to Julmann. Almost no one has doubted Oresme’s originality or ingenuity. Still, it may be that Oresme saw some Islamic solution, but his version constitutes hardly more than a hint, which might explain Hesse’s silence. If Hesse and Julmann elaborated on a suggestion in Oresme, then we
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A = center of a deferent circle. B = epicyclic circle revolving on circumference of A to the west. C = center of the planet to east. D = point on circumference of planet such that CD ⊥ BC (not drawn; see Figure 5). B1B2B3B4 = successive positions of B. C1C2C3C4 = successive positions of C corresponding to those of B. R = radius and RB = 2RA. ∠ α = ∠ described by B revolving on A. ∠ β = ∠ described by C around B (and it varies as explained).
Figure 6—Droppers’s Interpretation of Oresme’s Reciprocation Device. (From Droppers, p. 461)
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A combination of uniform circular motion can be devised to produce motion in a straight line. a. First, imagine (above) a circle of diameter d rolling on a flat surface. A planet fixed to the circle moves halfway around the circle as the circle rolls a distance of half its circumference (πd/2), and completes a circuit as the circle rolls a distance πd. b. Next (above), curve the flat surface into a circle of diameter D, with D = 2d. (The new circle is twice the size of the original circle.) Roll the small circle inside the large circle. A point on the small circle will come back into contact with the circumference of the large circle after one complete turn of the small circle. This occurs after the small circle moves a distance πd (its circumference) around the large circle, or halfway around the large circle (πd = πD/2). c. Finally, as the small circle rolls around the inside of the large circle, a point (planet) on the small circle constantly falls along a straight line, which is also a diameter of the large circle (in this case, the vertical diameter). Three positions of the small circle are shown above. Intermediate positions also place the planet on the same straight line. The net result is to convert uniform circular motion into seemingly straight-line motion.
Figure 7—Straight-line motion from circular motion. (From Hetherington, p. 79)
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may suppose that Oresme may be either the Latin intermediary who saw or heard of the Maragha mechanism, or that Oresme himself produced it while contemplating a geometrical problem. As for double-epicycle models, as we saw in chapter five, Sandivogius proposed one as a solution to account for the observations of the Moon; it was adopted by Brudzewo, and Copernicus certainly could have heard about Brudzewo’s double-epicycle model even if he did not know the Commentariolum directly.14 None of this sketchy reconstruction is intended to minimize the originality of Islamic astronomers.15 Copernicus’s use of these devices, however, seems to derive from his critical evaluation of the work of his teachers and Regiomontanus’s Epitome. From the former he may have adopted double-epicycle models, and from the latter his acquaintance with Hesse’s use of two concentric spherical mechanisms. It would follow, then, that Copernicus did not invent or discover these solutions independently, but that he adopted and modified solutions deriving immediately from Brudzewo and Regiomontanus, and indirectly from Oresme and Hesse. Di Bono has offered an alternative reconstruction. I am persuaded by his critique of the usual scenario, but the dependence of his argument on the homocentric astronomy of the Paduan school, while plausible—especially the return to Eudoxus and Callippus—remains as nebulous as the supposed missing textual link. Still, as di Bono pointedly emphasizes,16 when Copernicus took up the demonstration of the harmonic linear motion in De revolutionibus, he elaborated it independently. Why would he have done so if he had just copied it? Di Bono’s second hypothesis seems even likelier, namely, that from critical reflection on problems with the Ptolemaic system, Copernicus followed the same path more or less to results very similar to those obtained by his predecessors. Di Bono’s dismissal of textual or pedagogical precedents at Cracow leaves him without a textual basis for Copernicus’s initial versions in Commentariolus. Copernicus’s recognition of problems with the Ptolemaic system, his likely familiarity with the mechanisms described at Cracow, his reliance on Regiomontanus’s Epitome, and the internal logic of the methods employed by the Islamic astronomers and Copernicus—all together may be sufficient to explain Copernicus’s derivation of the reciprocation device. I conclude this excursus with some consideration of Dobrzycki’s and Kremer’s comment on di Bono’s argument.17 They assert that their reconstruction of Johannes Angelus’s tables weakens di Bono’s claim “that Copernicus rein-
14
Rosińska, “Al-Tusi and al Shatir.” Ragep, “Ali Qushji,” 363, shows that there was also a fifteenth-century Islamic precedent for Regiomontanus’s use of eccentric models to account for the motions of Mercury and Venus, and again there is a striking similarity between the geometrical figures. Ragep finds parallel developments implausible, but if the scenario developed here is correct, then some of the solutions in the West appear already in the fourteenth century and not just “in a fifty-year span in the last part of the fifteenth century.” 16 Di Bono, “Copernicus,” 147. 17 “Peurbach,” 33, n. 55. 15
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vented the Tusi couple rather than borrowing it from Islamic traditions via unknown sources.” The logic of this assertion eludes me. Their reconstruction is ingenious, but, first, even if their claim that Angelus’s parameters for longitudes cannot be reproduced by modifying the geometry of Ptolemy’s models in obvious ways—asserted and not proved with only one alternative actually eliminated—and their further claim that their reconstruction is a unique solution are true, they do not prove that mechanisms of harmonic motion rely on an Islamic source or an intermediary. They simply repeat the usual assumption. Di Bono does not deny that the hypothesis about an Islamic intermediary may be correct; his argument is that the hypothesis remains unconfirmed, and that it does not explain Copernicus’s independent elaboration of some of the mechanisms. Second, how can a hypothetical reconstruction based on a still unconfirmed hypothesis weaken a reconstruction that demonstrates the differences between Copernicus’s versions and the Islamic solutions? It is in such contexts that hypotheses about Maragha have taken on the status of dogma. It remains a hypothesis, and one that may turn out to be based on a ghost. From someone who regards the connection as likely, Emilie Savage-Smith offers an important reminder:18 As for the hypothesis that there was a causal link between the activities of the later Islamic astronomers and the development of Copernican astronomy, it remains only a hypothesis until the mechanism for such borrowing can be found. Yet the evidence is mounting for some form of connection, especially given the sudden appearance in Europe of technical geometric innovations that had a centuries-long tradition in Islam. All of that said, scholars convinced of the hypothesis should continue to search for the intermediary link. It may yet turn out to be correct, and the fact remains that the Maragha hypothesis still provides the most complete version of the models that Copernicus could have adapted both in the Commentariolus and De revolutionibus. I would welcome the discovery for it would finally put all of the speculation, including mine, to rest. In the meantime, however, I urge others to read the literature on Oresme, Hesse, Julmann, Sandivogius of Czechel, Albert of Brudzewo, Peurbach, and Regiomontanus, and consider all of it with the following consideration in mind. Historians have long recognized Oresme’s ingenuity and precociousness as compared with his contemporaries. Scholars, Marshall Clagett in particular, have questioned his influence beyond the early fifteenth century.19 What I am suggesting here is the possibility that Oresme’s cryptic geometrical proposal of a reciprocation device along with an epicycle model in De sphera was the Latin source for some of the later elaborations of these techniques. The path to Copernicus would have proceeded from Oresme to Hesse, Julmann, and Sandivogius, and from them to Peurbach, Brudzewo, and Regiomontanus. On the basis of what we find in both Brudzewo and Regiomontanus, we can try to reconstruct
18 19
“Islamic Influence,” 540. Clagett, Nicole Oresme, 3.
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Copernicus’s elaboration of the models, and in these cases, at least, we have reasonable grounds for believing that Copernicus knew them. The weakest connection is his knowledge of Hesse’s treatise, leaving us to speculate that Copernicus may have been acquainted with the version of it that Regiomontanus had preserved, or that Novara saw the treatise and communicated its solution to Copernicus.
APPENDIX VII EXAMPLES FROM CHAPTER 8, SECTION 7 Example 1: (Ia) If hypotheses (A) should be relevant to the consequent (B), then astronomical hypotheses (A) should be relevant to the structure of the universe (B). (II) Hypotheses should be relevant to the consequent; therefore, (III) Astronomical hypotheses should be relevant to the structure of the universe. Example 2: (Ia) (Ib) (II) (III)
If the efficient cause is good, then what God creates is good. What is good is well ordered. The efficient cause is good; therefore, What God creates is well ordered.
Example 3: (IA) If the whole is well ordered, then the parts are linked together. (IB) If parts are linked together, then the parts cannot be shifted without disruption of the whole. (II) The whole is well ordered; therefore, (III) The parts cannot be shifted without disruption of the whole. Example 4: (IA) (IB) (II) (III)
If a form is spherical, then circular motion is proper to the form. What is proper to the form is proper to the sphere. The form is spherical; therefore, Circular motion is proper to the sphere.
Example 5a: (Ia) If the distances between one part and the whole vary, then either the part moves or the whole moves. (Ib) From the observation of motion alone without a third fixed reference point we cannot tell whether the part moves or the whole moves (the principle of relativity of motion). (II) The distances vary; therefore, (III) We cannot tell whether the part moves or the whole moves. Example 5b: (Ia) If the part does not move, then the whole may or may not move. (Ib) From the non-motion of the part, we cannot infer the motion of the whole (topic from the part).
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(II) The part does not move; therefore, (III) The whole may or may not move. Example 6: (Ia) If Earth is located and enclosed, then its rotation accounts for the observation of daily rotation of the celestial sphere. (Ib) Rotation should be attributed to the located and enclosed rather than to what locates or encloses (a topic proper to metaphysics). (II) Earth is located and enclosed, heaven locating and enclosing; therefore, (III) Earth’s rotation accounts for the observation of the daily rotation of the celestial sphere. Example 7: (Ia) If Earth’s eccentricity and distances in relation to the Sun and planets vary, then Earth approaches to and withdraws from the Sun and other planets. (Ib) The variable eccentricities and distances of a body with respect to other bodies can be explained more naturally and more simply by the motion of the one body relative to the other bodies (topic from the whole and the principle of simplicity). (II) Earth’s eccentricity and distances relative to the Sun and planets vary; therefore, (III) Earth approaches to and withdraws from the Sun and other planets. Example 8: (Ia) If rotation is natural to a sphere, then Earth’s rotation is a natural effect. (Ib) What is natural has natural effects. (II) Rotation is natural to a sphere; therefore, (III) Earth’s rotation is a natural effect. Example 9: (Ia) If planets move away from and towards Earth, then Earth is not the center of their motions. (Ib) Circular motions around the center exclude motions away from and towards the middle. (II) Planets move away from and towards Earth; therefore, (III) Earth is not the center of their motions. Example 10a: (Ia) If Earth orbits the Sun, then the observed retrograde motions of the planets are an optical illusion. (Ib) An optical illusion is caused by the proper motion of one body relative to the proper motions of other bodies (a warrant or topic proper to optics). (II) Earth orbits the Sun; therefore,
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(III) The observed retrograde motions of the other planets are an optical illusion. Example 10b: (Ia) If Earth and the planets orbit the Sun, then the Sun is the body near the center of the planetary motions. (Ib) The body near the center of the planetary orbits is the mean center of their motions. (II) Earth and planets orbit the Sun; therefore, (III) The Sun is the mean center of the planetary motions. Example 11a: (Ia) If Mercury and Venus are arranged around the Sun according to their bounded elongations, then they are arranged according to their distances from the Sun. (Ib) The distances of planets correspond to the duration of their orbits (calculated by Copernicus and the principle was adapted from the standard view of the orbits of Mars, Jupiter, and Saturn). (II) Mercury and Venus are arranged around the Sun according to bounded elongations; therefore, (III) Mercury and Venus are arranged according to the duration of their periods. Example 11b: (Ia) If Mercury and Venus are arranged according to the duration of their orbits, then all of the planets are arranged according to their sidereal periods. (Ib) The position of Earth’s orbit outside the orbits of Mercury and Venus explains the bounded elongations of Mercury and Venus and why we see the remaining planets in opposition (natural explanation of observations). (II) Mercury and Venus are arranged according to the duration of their orbits inside Earth’s orbit; therefore, (III) All of the planets are arranged according to their sidereal periods.
APPENDIX VIII SUIDAE LEXICON, ED. THOMAS GAISFORD AND GOTTFRIED BERNHARD (1853, REPR. OSNABRÜCK: BIBLIO VERLAG, 1986) Kinesis. Motus localis in hominibus causa est mens (ipsa enim animal movet), in brutis vero sensus. Est etiam alia praeter has motus localis causa; nimirum appetitus, qui varius est, et tam facultatibus ratione praeditis quam brutis inest.—Motus etiam existit, cum res alium ex alio locum mutant.—Quae per orbem aguntur interitu vacant.—Aliter de motu. Non est, inquit [Aristoteles,] glebae naturale moveri deorsum, neque igni sursum ferri: neque enim talis motionis principium in se habent, sed extrinsecus ab alio moventur. unumquodque enim elementum in suo toto quiescit: quippe tota vel stare volunt vel in orbem moveri: est autem motio in orbem quies quaedam. Iam secundum naturam suam gleba cum movetur, in suo toto manet immobilis; quemadmodum hic ignis in sua sphaera. cum vero gleba vel aqua vel hic aer extra locum naturalem existit, singula ad totum suum tendunt, et quieti naturali restitui cupiunt. nam ab vi quadam externa ex loco naturali pulsa moventur ea via, quae est secundum naturam. quando quidem sic moventur, ut quae in alieno loco existant, et toto suo contra naturam privata sint. Non igitur motus ille secundum naturam est, quo res ad locum naturalem tendunt (alioquin enim ipsa tota sic moverentur), sed viae ad id quod est secundum naturam. Potest tamen etiam motus ille naturae consentaneus dici: eo nimirum sensu quo dicimus sanitatem esse secundum naturam, morbum vero contra naturam. illa ducit ad id quod est secundum naturam hic vero ad id quod est contra naturam. id enim quod primum movet, si quidem corpus sit, ipsum etiam movetur. movet enim baculum ianuam, et baculum manus, quae non manet immota, sed ipsa movetur. quod si primum movens sit incorporeum, nihil necesse est ipsum quoque moveri, dum alterum movet. nam deus, qui universum movet, ipse est immotus, utpote stabilem habens essentiam et facultatem et actionem. praeterea nihil eorum quae appetuntur, quamvis moveat, ideo movetur: ut neque pulchritudo movetur, quamvis amatorem saepe moveat; neque imago, quae intuentem movet; et id genus alia.—Plato cum animam dicit per se moveri, non intelligit motum localem.—Anima saepe mutationem subit, a potentia ad actum transiens: velut ab ignoratione rei ad eius scientiam. quod si mutationem subit, eadem movetur. huiusmodi autem motus et mutatio generatio quaedam est; sed non simpliciter essentiae generatio.—Differt motio ab actione, nam motio est actio imperfecta, cum actio sit perfecta. quare etiam in deo actio est sine potentia. Quaeritur autem, utrum duae sint motiones in eo qui movet et movetur, an una? et utrius sit motio, moventisne an eius qui movetur? Affirmant autem eius esse qui movetur. is est enim qui ab imperfecto progrediatur ad perfectum, non qui movet: uti se res habet in discipulo et magistro. unus est enim in utroque motus, qui a magistro profectus in discipulo desinat. Ita anima quoque movetur. nam ab imperfecto transit
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ad perfectum, neque habet actionem omnino perfectam, neque caret potentia. accedit ut in quibus prius et posterius, in iis etiam sit tempus; in quibus vero tempus, in iis etiam motio. haec enim inter se reciprocantur. quamobrem in quibus est motio, in iis etiam est tempus. in anima autem est prius et posterius; est igitur motio. esse autem in anima prius et posterius manifestum est. nam a propositione ad conclusionem transit; neque omnia simul cognoscit, sed aliud ante aliud; neque omnia quae novit, simul tractat, sed aliud quidem prius, aliud posterius; et, ut universe dicam, ab virtute ad vitium, ab ignorantia ad scientiam transit. itaque recte Plato eam per se moveri affirmat. accedit etiam Aristoteles, qui cum animam moveri negat, non hanc motionem ab ea abiudicavit, sed qualemcunque motionem naturalem nobisque cognitam. neque enim ea augetur aut imminuitur; neque qualitatis aut quantitatis mutationem subit, sed alias habet motiones, quae intellectuales sunt et maxime vitales. Movetur autem anima, cum mutationem subit: ut cum a dispositione transit ad habitum, ab ignorantia ad scientiam. Aristoteles autem eam moveri negat, ad corporeas motiones respiciens. si enim anima, inquit, non movetur per accidens, natura habebit motum; si hoc, etiam locum. omnes enim motiones corporum in loco fiunt. quicquid est enim in loco, corpus est.
APPENDIX IX COPERNICUS’S UNDERSTANDING OF PTOLEMY Following Kepler’s comment that Copernicus modeled Ptolemy rather than nature, several historians have rightly concluded that no one understood Ptolemy as well as Copernicus did.1 On the whole I agree with this judgment. There is, however, one respect in which Copernicus’s understanding of Ptolemy may have been based on a mistake or on an assumption that Ptolemy did not share. In Copernicus’s interpretation of Ptolemy’s geometrical models he adopted a “mechanical” understanding of the motions of celestial spheres that conditioned his reaction to the so-called equant model. Copernicus did not consider the possibility that Ptolemy adopted Aristotelian-like intelligences as movers of the planets, calculating and adjusting their motions as the models represented them, or simply willing them to move as needed. In his explanation of Ptolemy’s exposition of spherical mechanisms in Planetary Hypotheses, Olaf Pedersen describes a typical mechanism and comments:2 We notice that there is no sphere corresponding to the equant circle, and therefore no body revolving with uniform mean angular velocity. Thus the non-uniform motion of the deferent sphere . . . is not produced by any kinematical device, but is caused directly by the vital force of the whole system. No wonder that this force has to be conceived as an ‘intelligence’. Likewise, Bernard Goldstein emphasizes the point that Ptolemy was more concerned about periodic mean motion than uniform motion, and adds that Ptolemy understood the nature of the gods to be different from what Geminos and others believed.3 If Pedersen and Goldstein are correct, then it would mean that Copernicus misunderstood the relation between the celestial movers and the mathematical models that account for the observed motions, or, at least, that he rejected Ptolemy’s view about the movers of the spheres and planets. Copernicus’s reading of Ptolemy in this way may have been conditioned by Albert of Brudzewo’s interpretation of the equant model. Brudzewo maintained that the model could not refer to the motion of an orb, which led him to interpret the model as a mathematical fiction.4 Of course, neither of them knew the Planetary Hypotheses. Copernicus, however, drew a different conclusion, namely, that if an orb cannot move in the way described, then
1 2 3 4
For example, Swerdlow, “Copernicus,” 167; Evans, History, 425–427. Pedersen, Survey, 397. Goldstein, “Saving,” 6–10. Brudzewo, Commentariolum, 85–92.
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the model violates the fundamental axiom about uniform, circular motion. In both cases, the Averroistic objections to Ptolemy’s models may have influenced them to focus on strictly mechanical issues, thus accounting for their interpretations of the models. The distinction between instrumentalist and realist interpretations of astronomical models was falsely attributed to ancient authors. Later authors did make a distinction, attributed it to earlier authors, and thus fabricated a non-existent problem that many continued to perpetuate. The tradition also created another problem when some authors reduced causal explanation of celestial motions to strictly mechanical principles without the agency of Aristotelian intelligences or vital forces. As a result, Copernicus attributed the axiom about uniform, circular motions to Ptolemy, and then, implausibly, accused him of having violated it because he was content to solve the problem only mathematically. If Copernicus did begin his critique of Ptolemy with a mistake, the result is not as unfortunate as it might seem. The reason is that he did not stop there. The “problem” with the equant merely motivated him to look for other problems, and in most other cases he did find genuine problems with or puzzles in Ptolemy’s models that led him to seek the kind of solution out of which his hypotheses about the motion of Earth around the Sun emerged.
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Abbreviations DSB JHA PSB Rc Sc SPS ZGAE
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INDEX OF NAMES Pre-1800 Achillini, Alessandro viii, 184–188, 219, 238–243 Aelius Donatus 8 Aeneas Sylvius Piccolomini, Pius II, Pope 13, 138 Aëtius Amedinus (see also PseudoPlutarch) viii, 196, 229–230 Agricola, Rudolf 181, 281–284, 304 Albert Caprinus of Buk 18, 49 Albert (also Adalbertus) of Brudzewo viii, xxii, 15, 23, 31–36, 41, 44–49, 135, 141, 144, 148, 150, 153–156, 159–162, 218, 244, 248, 370, 376, 478, 485, 492 Albert of Pnyewy 29–32, 41, 46, 48, 161 Albert of Saxony vii, 42, 47–48, 100–104, 111–112, 128–132, 148 Albert of Szamotuli (also Schamotuli and Szamotuły) 32, 46, 48, 160–161, 191 Albert Piotrokow of Swolszowice 31, 42, 140 Albert the Great 15–16, 36, 42, 47, 54, 72, 74, 95–96, 100, 103, 107, 109, 111, 446, 449, 469, 514 Al-Bitruji 219 Albohazen Haly 191, 211 Albrecht of Prussia, Duke 293 Alciato, Andrea 178 Alessandro Piccolomini 391 Alexander of Aphrodisias 61, 449 Alexander of Hales 10, 47 Alexander of Villa Dei 9, 25 Alfonso de Corduba Hispalensis 250 Alhazen (Ibn al-Haytham) 145, 156, 382, 477–478 Alidosi, Giovanni 179, 181, 183 Ambrosius Regius 211 Amico, Giovanni Battista 262, 267–268 Andrew of Kokorzyna 111 Andrzej Grzymala 150 Antiphon 472 Antonius Andreae 42 Aratus 211 Aretino, Pietro 13
Aristarchus of Samos 202, 234–236 Aristotle ix, 10, 25, 46, 52, 55–60, 69, 72, 75, 80, 90, 92, 98, 107, 110, 112, 116, 118, 122–125, 142, 148, 171–172, 185, 187, 192, 198–199, 216, 220, 223–224, 229–233, 238–239, 242, 262, 277, 284, 289–290, 303–304, 320, 323–325, 328, 334, 336, 338, 343–347, 352, 354, 358–360, 374–375, 408, 411–417, 421, 423, 432, 435, 437, 444–460, 471–474, 480 Categories 26, 30, 53, 63, 102 De anima 26, 35, 43, 115, 350 De caelo vii, 26, 32, 37–38, 49, 95, 100, 111–114, 117, 119, 124, 126, 128, 250, 288, 311, 318, 332, 335, 339–342, 348–353, 357, 389, 392–399, 402–403, 412, 456, 479 De generatione animalium 400 De generatione et corruptione vii, 26, 32, 37–39, 95–96, 100, 114–115, 119, 127, 403 De interpretatione 26 Meteorologica vii, 26, 28, 32, 39, 95, 100, 114, 119–121, 126, 346, 389, 394, 396, 402–403 Metaphysics vii, 26, 28, 35–36, 43, 45, 49, 88, 91, 114, 121, 133–134, 222, 276, 286–287, 318, 321–322, 332–333, 389–391, 400–402, 412 Nicomachean Ethics 86–87, 135, 276, 321, 390 Parva naturalia 26, 28, 32, 37, 40–41, 115, 461 Physics vii, 26–27, 30, 35, 41–42, 45, 49, 77, 89, 91, 94–95, 99–109, 114, 117, 128, 318–319, 332, 337, 356, 376, 399–400 Posterior Analytics 26, 35, 41, 43, 51, 54, 64, 87, 337, 391, 399 Prior Analytics 26, 35, 51, 54, 64, 86–87, 135, 276, 390 Rhetoric 55, 303 Topics 26, 32, 52–55, 58–59, 61–62, 64, 73, 281, 286, 292, 296, 303 Augustine of Hippo 10, 45, 97, 224
526
index of names
Aurifaber, Johann 410 Averroes (also Ibn Rushd) 49, 86–87, 94, 100–105, 124, 134–135, 143, 148, 155, 157, 163–166, 184–186, 239–241, 250, 373, 391, 400, 413, 422, 449–452, 469, 477 Avicenna 100–101, 199, 201, 444, 449 Bacon, Francis 194 Barbaro, Ermolao 140 Bardella, Philippo 203–204 Bartholin, Caspar 425 Bartholomew of Lipnica 29, 40 Bartholomew of Oraczew 46, 160 Beldomandi, Prosdocimo 153, 162 Bellarmine, Robert, Cardinal 407, 417 Bernard of Biskupie 40, 48, 161 Bernard of Verdun 148 Beroaldus, Philip 140, 184 Bessarion, Cardinal viii, xxiii, 167, 188, 196, 208, 211–216, 220–229, 243, 251, 271, 297, 318, 390, 412 Bianchini, Johannes 25, 151, 162, 188 Biondo, Flavius 141 Blasius of Parma 98 Boccaccio 141 Boethius, Anicius 10, 26, 30, 42–44, 52–56, 59–64, 160, 181–182, 281–284, 288–289 Bonaventure, St. 10, 42, 47 Boniface VIII, Pope 177 Boniface IX, Pope 14–15 Bracciolini, Poggio 13, 139 Brahe, Tycho 166, 243, 254–255, 271, 369, 376, 381, 407, 427–434 Brożek, Jan 37, 49, 424 Bruni, Leonardo 139 Bruno, Giordano 356 Caccini, Thomas 414 Caesarius, Johannes 281–284, 304 Cajetan of Thienne 407 Callimachus (also Buonacorsi), Philip 140–142, 225 Callippus 122, 240, 244, 267, 484 Campanus of Novara 143, 147–148, 217–218 Campeggi, Giovanni 183 Capuano da Manfredonia, Giambattista 186–187 Casimir III 14 Casimir IV Jagiellon 7 Caspar Salionis Cervimontani 237 Cato the Elder 9, 102
Celtes, Conrad 26, 37, 43, 140–141, 159–160, 167 Cicero, Marcus Tullius 26, 45, 102, 140, 181–182, 214, 238, 250, 282, 284, 288–289, 345, 347–348, 374, 392 Chalcidius 237 Clavius, Christopher 391 Cleanthes 345 Cleomedes 229 Conrad Gesselen 9–10 Copernicus, Andrew 11, 19 Copernicus, Barbara 6, 19 Copernicus, Nicholas vii–viii, xiii–xiv, xvii, xxi, 1, 5–6, and passim Commentariolus xxiii–xxvi, 16, 29, 154, 157, 187, 212–216, 219, 221, 226–229, 233–243, 251–257, 261, 264, 267–272, 275, 291, 294–295, 307, 364, 375, 378–383, 388, 391, 409, 484–485 De revolutionibus xi, xxiii–xxv, 29, 37, 85, 92, 122, 124, 127, 132, 134, 144–145, 154, 165, 172, 185–188, 190, 192, 202, 206–219, 221–229, 234–235, 237–238, 242–243, 249–260, 264, 266–271, 275, 278, 292–313, 322, 326–330, 333, 336, 339, 341, 351, 355–363, 371–378, 382, 386, 388, 391–392, 396–403, 408, 411–414, 417, 420–422, 425, 474, 484–485 Letter Against Werner 47, 242, 318, 400 Letters of Theophylactus Simocatta 143, 194–196, 206, 211 Uppsala Notes xi, 146, 150–151, 249–250, 257–259, 381 Copernicus, Nicholas Sr. 19 Corvinus, Lawrence 31, 43–44, 48, 140–141, 167 Crastonus, Johannes 195–197, 211, 235 Da Montagnana, Bartholomaeus 199, 201 Da Montagnana, Bartholomaeus Jr. 201 Dantiscus, John, Bishop 213, 409, 414 D’Aquila, Johannes 199 Del Ferro, Scipio 193 Della Mirandola, Pico xxiii, 185–187, 191 Della Torre, Marcus Antonius 199 Democritus 231, 234, 468 De Sala, Antonio 183 D’Estouteville, Cardinal 73
index of names Digges, Thomas 356 Diogenes 232 Epicurus 230–232 Euclid 10, 26, 32, 45, 146, 157, 160, 191, 195, 211, 214 Eudoxus 122, 240, 244, 267, 269, 401, 484 Eugenius IV, Pope 139 Fantuzzi, Giovanni 181, 183 Ficino, Marsilio viii, 141–142, 195–196, 208–215, 221, 224–228, 235, 243, 278, 314, 318, 323, 349, 358, 471–474 Foscarini, Paolo Antonio 407, 417 Fracastoro, Girolamo (also Hieronymus) 186–187, 262, 268, 294 Francis of Meyronnes 47 Frisius, Gemma 414 Gabriel Biel 47 Gabriel Zerbus of Verona 106–107 Galen 199, 421 Galilei, Galileo 58, 166, 199, 318, 325, 407, 414 Gammaro (also Gambari and Gambarinus de Casali), Pietro 181, 183, 284 Ganfredum 29 Geminos 492 George of Trebizond 222 Gerard de Monte 134 Gerard of Cremona 147–148 Gerard of Harderwyck 42 Gerard of Sabionetta 147 Gertner, Bartholomew 19 Giese, Tiedemann xvii, 13, 37, 134, 293–294, 321–322, 400, 413–414 Gilbert, William 189, 433 Giles (Aegidius) of Rome 15–16, 47, 72, 96, 100, 103, 106–107, 241, 444, 449, 469 Gratian 176–177 Gregory of Rimini 47 Gregory of Sanok 138–139 Gregory the Great 13 Gregory IX, Pope 177 Gualterus de Vino Salvo 25 Gustavus Adolphus, King 208 Grynaeus, Simon 228 Haller, Jan 100 Henry of Hesse (also Langenstein) 127, 144, 155–159, 478, 481, 484–486
527
Hermes Trismegistus 223, 358 Hipparchus 211, 222 Hippocrates 199 Horace xvii, 25 Hugh of St. Victor 10 Ibn al-Shatir 157, 384 Ibn Rushd (see Averroes) James of Gostynin 29–30, 35, 38, 47–49, 74, 86 James of Iłzy (also Iszla) 46, 160 James of Szadek 29, 45–46 Jan Długosz 138 Jan of Dąbrówka 138 Jan of Ludzisko 138 Jan of Szamotuły (also Schamotuli and Szamotuli) 160–161 Jan Ostraróg 138, 140 Jerome, St. 13 Johannes Angelus 484 Johannes de Muris 26, 160 Johannes Peckham 26 Johannes Versoris (also John Versor) vii, 47, 72–74, 95–96, 100, 111, 122–128, 134, 322, 333, 345, 398, 402, 461–462, 470 John Argyropulos 44 John Buridan 15–16, 41–42, 47–48, 72–73, 93, 99, 107, 128, 148, 335, 340–341, 348, 373 John Duns Scotus 15, 39, 42, 72, 74, 107 John Gerson 10, 13, 47 John Gromaczky (also Gromaczki) 29–30, 46, 160 John Isner 42 John Magister 39 John of Cracow 29 John of Glogovia vii, xvii, xxii, 27–32, 35–39, 44–53, 57, 73–86, 97, 100, 103–109, 112, 128, 132–133, 150, 158–161, 219, 281–282, 373, 446, 456 John of Jandun 111, 457 John of Lesznica 29 John (also Jan) of Ożwięcimia 44 John of Sacrobosco 26, 32, 35, 41–42, 123, 147, 214, 240, 370 John of Seville 147 John of Slupy (also Słupczy) 29, 46 John of Stobnicy 40 John of Zanau 172 John Philoponus 92, 348 John Premislia 29
528
index of names
John Stöffler 269 John Teschner 11 John Wohlgemuth 10 John XXI, Pope 26 John XXII, Pope 177 Joshua 410, 415 Julmann, Magister 155–156, 478, 481, 485
Michael Falkener of Wrocław) 32, 38–40, 47–49, 73–75, 96, 98, 107, 161 Michael of Oleśnica 140 Michael Parisiensis of Biestrzykowa 29–30, 39, 47–49, 74, 82–84, 142 Michael Stanislaus of Wratislavia 18 Montaigne, Michel de 391
Kepler, Johannes xiii–xiv, xxvii, 166, 235, 277, 291, 323, 369–370, 384, 404–405, 411, 422–425, 435, 492
Nasir al-Din al-Tusi xi, 144, 154–157, 248, 261–267, 476–477, 480–481, 484–485 Newton, Isaac 90, 325–326, 427 Nicholas de Orbellis 39, 42 Nicholas Labischin 160–161 Nicholas of Cracow 45 Nicholas of Lyra 10 Nicholas of Marienwerder 12 Nicholas of Pilcza 29, 43 Nicholas Wodka of Kwidzyn 12 Nicholas V, Pope 73, 224 Nicolaus Cusanus (also Nicholas of Cusa) 341, 348–349, 356 Nicole Oresme xi, 47, 98, 112, 128, 131, 148, 155–156, 299, 334–335, 349, 478–485 Nifo, Agostino 185, 198–199, 391 Novara, Domenico Maria viii, xxiii, 152, 159, 173, 184, 187–193, 197, 202–205, 216, 219–221, 240, 370, 411, 419, 486
Lactantius 297 Laetus, Pomponius 141 Lambert of Auxerre 181 Lambert of Monte 42, 461 Lamprias 473–474 Lauterbach, Anton 410 Lawrence of Lindores 111 Lawrence of Raciborz 152 Leibniz, Gottfried 408 Leo I, Pope 13 Leoniceno, Niccolò 199–200 Leonard Vitreatoris of Dobzyc 44–45 Leutus, Antonio 203–204 Livy 138 Louis XI, King 73 Luther, Martin 276, 279, 299, 302, 406, 410 Lysis 211, 222 Macrobius 159, 238 Mästlin, Michael 291, 295, 383–384, 405, 411, 422–428, 432 Marsilius of Inghen 26, 39, 47 Martianus Capella 144, 159, 238, 250, 253–257, 313, 381–385 Martin (also Marcin) Biem of Olkusz 40–41, 48, 269 Martin Bylica of Olkusz xvii, 15, 153, 161–162 Martin Król of Żurawica 15, 40, 150, 153, 162 Martin Kułab of Tarnowiec 42, 48 Martin of Szamotuli 31 Martin of Zeburk (also Martin Jezioran) 46, 160–161 Matthew of Kobylina 30–31, 41–42, 48 Matthew of Miechów 244 Melanchthon, Philipp 181, 214, 304, 421 Metrodorus 231–232 Michael Falkener de Wratislavia (also
Offusius, Jofrancus 420 Oleśnicki, Zbigniew, Cardinal 138 Osiander, Andreas 277, 279, 315, 365–366, 410, 414–415, 418, 420, 424–425 Ovid 25 Pappus of Alexandria 10 Parmenides 228, 471–472 Paul of Venice 47, 56 Paul of Zakliczew 29, 46, 96 Paul III, Pope 223, 276, 293, 295, 321, 327, 406, 409, 411, 414 Peckau, Catherine 19 Peter Damian 13 Peter John Olivi 98 Peter Lombard 45 Peter of Spain 26, 29–30, 35, 42–46, 53, 56, 58, 62–83, 179, 181, 280–284, 289, 292, 296, 427, 441 Peter of Żnanow 152 Peter Tartaret 39
index of names Petrarch 139 Petrus Roselli 39 Peurbach, Georg 139, 143–144, 148–151, 154–155, 158–167, 172, 188, 215, 217, 220–221, 244, 370, 375–376, 478, 485 Pierre d’Ailly 148 Philolaus 233–234, 308 Plato 97, 101, 113, 119, 132, 135, 141, 144, 172, 208–215, 220–235, 243, 250–253, 256, 271, 275, 278–279, 286, 305, 312, 314, 323, 327–328, 337–338, 345, 347, 351, 357–358, 388–389, 396, 400–401, 408, 419, 449, 456, 474, 490–491 Plautus 25 Pliny the Elder viii, 121, 132, 189, 196, 199–200, 210–215, 237–238, 243, 249–250, 347–348, 355, 374, 392, 402–403 Plotinus 214 Plutarch viii, 196, 212, 227–236, 347, 395, 473–475 Poliziano, Angelo 140, 195 Pomponazzi, Pietro 184 Pontanus, Johannes 211, 271 Proclus 92, 157, 195, 214, 250, 267, 288 Profatius (Jacob ben Nahir) 153 Pseudo-Plutarch (see also Aëtius Amedinus) viii, 196, 212, 227–236, 347 Pseudo-Scotus 185 Ptolemy of Alexandria xi, xvii, 23, 32, 35, 37, 45–49, 124, 133, 143–144, 148, 153–161, 166, 174, 184, 187–188, 191–197, 206, 212–221, 225–238, 242–245, 248, 253, 257, 260, 272, 295, 300, 303–306, 309, 312, 318, 327–328, 341–342, 353, 364, 381, 384, 388, 391, 393, 398, 407–409, 412–413, 417–421, 428, 431, 434, 477, 485, 492–493 Pythagoras 231 Pythodorus 472 Quintilian
xvii, 181
Ramus, Peter 181, 391, 419 Regiomontanus, Johannes xvii, xxiii–xxiv, 15, 26, 41, 107, 127, 139, 144–146, 150, 154, 159–162, 166–167, 172–173, 187–193, 196, 205–208, 211, 214–221, 243, 248, 250, 255, 259, 261, 271, 295, 364, 478, 484–486
529
Reinhold, Erasmus 375, 421, 425 Rheticus, Georg Ioachim xvii, 88, 152, 157, 172–173, 184, 186, 188, 191, 193, 195, 197, 202, 210, 219, 228, 252, 256, 271, 276, 278, 293–294, 300, 302, 311, 314, 318, 321, 355, 390, 392–401, 404, 406–414, 418–422, 425–426, 428 Richard of Mediaevalia 47 Richard of Wallingford 164 Ristoro d’Arezzo 127 Robert Grosseteste 86, 92 Robert Holcot 47 Robertus Anglicus 375 Sabellius, Marcus 140 Sandivogius of Czechel 144, 153–156, 484–485 Schilling, Anna 409 Schönberg, Nicholas, Cardinal 409 Schöner, Johannes 172, 293, 422 Schreiber, Jerome 422 Scultetus, Alexander 409 Seleucus 232 Simon of Sierpc 31, 46, 48, 160–161 Simplicius 124 Sinclair, David 424 Spina, Bartolomeo 405, 414 Socrates 228, 471–472 Sommerfeld, Jan (also John of Sommerfelt) 29–30, 140–141 Sophocles 196 Sosigenes 377 Stanisław Biel 30, 161 Stanisław Bylica (also Stanisław of Ilkusch, Stanislaus Bylica) 30, 32, 41, 48, 160–161 Stanisław Gorky 29 Stanisław (also Stanislaus) Kleparz 32, 46, 160–161 Starowolski, Szymon 18, 36–37, 49, 269 Statius 25 Stobner, John 15, 41, 152–153 Terence 9, 25 Thales 231 Themistius 64, 103, 449 Theon 195, 211, 214 Theophrastus 61, 230 Theophylactus Simocatta 43, 194, 196, 206, 211 Thomas Aquinas 10, 15–16, 35–36, 42–47, 72, 97, 100–107, 110, 114, 116, 125, 127, 134, 241, 276, 319, 373, 387, 391, 394, 415, 417, 449
530
index of names
Thomas Cajetan de Vio 47 Thomas of Strasbourg 47 Thomas of Sutton 127 Tolosani, Johannes (also Giovanni) Maria 405, 414 Trapolini of Padua, Petrus 199 Urceo da Forlì, Antonio (also Codro) 140, 184, 195–196 Ursus, Nicolaus 425, 427 Vaclav, Saint 436 Valla, Giorgio viii, 196, 212, 227–236, 243, 247, 250, 349 Valla, Lorenzo 140, 281–282, 304 Vergil 25, 29, 44 Vitruvius 124, 238, 250 Vitus de Brunna 29
Walter Burley 47 Walther, Bernard 152, 166, 172, 192 Wapowski, Bernard 47 Watzenrode, Barbara 6 Watzenrode, Lucas, Bishop 8, 11–12, 18–19, 22–23, 207–208, 225, 270–271 Werner, John 47, 242, 318, 322, 400, 419 William of Ockham xiii, 47, 97, 185, 319 William of Sherwood (also Shyreswood) 64, 83, 181 Władisław Jagiello 14 Zabarella, Giacomo 58 Zeno 471–472 Zimara, Marcantonio 86–87, 422–423
Post-1800 Achinstein, Peter 277 Aiton, E. J. 149, 376–377, 383 Ameisenova, Zofia 141 Ashworth, E. Jennifer xv, 51, 56–57, 63, 71, 73, 78, 82, 84, 185, 203, 281–282 Aurivillius, P. F. 209 Babicz, Józef 144 Baldner, Stephen 107 Baldwin, Martha xvi Barker, Peter 149, 160, 184, 239, 293–294, 369, 371, 381, 385 Baroncini, Gabriele 297 Barone, F. 239 Barwiński, Eugeniusz 213, 226 Barycz, Henryk 38, 40, 43–44 Bayer, Greg 54 Benjamin, Francis 143, 147, 158, 217 Berger, Harald 128 Berman, Harold 173, 177 Bernhard, Gottfried 490 Bianchi, Luca 90 Biliński, Bronisław 188, 191, 225 Bird, Otto 51–52, 280 Birkenmajer, Aleksander 13, 40, 94, 134, 145, 157, 160–161, 192, 211, 345, 348, 352–353, 384, 391, 394–403 Birkenmajer, Ludwik Antoni xiv, 12, 36, 140, 146, 151, 158–162, 165, 187–193, 196, 201, 206, 208–209, 212–216, 218–219, 222, 225–226, 237–240, 244, 248, 327
Biskup, Marian 5–12, 17, 19, 21, 161, 173–175, 192, 197–200, 202, 204, 244, 248, 269, 271, 361, 409 Blair, Ann 143, 178, 237 Blake, Ralph 412 Boh, Ivan 75–81, 84, 282 Boncompagni, D. 203 Booth, Wayne 292 Bostwick, David 91 Braakhuis, H. A. G. 73 Brachvogel, Eugen 210, 212–214, 226, 236 Brown, Stephen xiv Bulmer-Thomas, Ivor 327 Burkhardt, Hans 84, 285–286, 298 Burmeister, Karl 294, 411 Busard, H. L. L. 155 Buzzetti, Dino xv Carmody, Francis 144 Caspar, Max 428–434 Celano, Anthony xvi Chabás, José 150–151 Charles-Saget, Annick 288 Charlton, William 91 Cherniss, Harold 473 Chojnacki, Piotr 52 Clagett, Marshall 155, 485 Cleary, John xiv Clutton-Brock, Martin 253–254 Cochrane, Eric 199 Cohen, I. B. 326, 435
index of names Collijn, Isak 134, 208–216, 226, 229, 236, 461 Colomb, Gregory 292 Conroy, Kathy xvi Copleston, Frederick 185, 199 Costabel, Pierre 403 Cranz, F. Edward 387 Crombie, A. C. 391, 404 Crowe, Michael xiii, 158, 302 Curtze, Maximilian 151, 195, 302 Czacharowski, Antoni 6 Czajkowski, Karol 436 Czartoryski, Paweł 146, 191, 195–196, 200, 202, 208–212, 226–227, 249 Daiber, Hans 230 Dales, Richard 92, 335 Dallari, Umberto 179, 181, 183, 192–193 Danielson, Dennis 302, 414 De Bustos Tovar, Eugenio 404 De Haas, Franz xiv Denifle, Heinrich 173 De Pace, Anna 228, 279 De Rijk, L. M. 30, 64 Derolez, Albert 146, 209 Desrosiers, Nathaniel xvi, 350 Dianni, Jadwiga 145 Di Bono, Mario xix, 143, 154–157, 184, 239, 261–269, 484–485 Diels, Hermann 230 Dijksterhuis, E. J. 144, 159 Dilg, Peter 201 Di Napoli, Giovanni 222, 224, 474 Dinneen, Francis 63 Dobrzycki, Jerzy 5, 8–12, 24, 146, 150–151, 155, 161, 197, 206, 216, 244, 381, 404, 484 Domenkos, Leslie 162 Donahue, William 404, 428, 432–434 Drake, Stillman 338 Dreyer, John 262 Droppers, Garrett xi, xix, 155, 478, 480–482 Dufour, Carlos 84, 285–286, 298 Duhem, Pierre 327, 361, 373 Dunne, Michael xiv Eastwood, Bruce 159 Ebbesen, Sten 51–52, 61–62, 80 Egan, Regina xvi Eisenstein, Elizabeth 180, 182 El Bouazzati, Bennacer xiv Endress, Gerhard 476
531
Estreicher, Karol 39 Evans, James 130, 206, 260, 327–329, 383–384, 428, 492 Everett, Glenn xvi Farndell, Arthur 228 Favaro, Antonio 199 Finocchiaro, Maurice 407, 417 Freeman, James 292 Friedberg, Helena 45 Funkenstein, Amos xiii, 335 Furley, David 104 Gaisford, Thomas 490 Gardenal, Gianna 230 Gariepy, Thomas xvii Garin, Eugenio 196, 276, 414–418 Gąssowski, Jerzy iv, 436 Genequand, Charles 143 Geyer, Bernhard 100, 159 Ghisalberti, Alessandro 107 Gilbert, Neal 203 Gill, Mary Louise 228 Gilson, Étienne 144 Gingerich, Owen xiii–xv, xxvi, 7, 150–151, 206, 254, 362, 409, 421–425, 433–434 Goddu, André 47, 55, 69, 72, 76, 79–84, 89, 93, 100–101, 107, 110, 122–128, 131, 142, 146, 187, 209–212, 226–227, 238, 244, 248–249, 253, 255, 275, 277–278, 282, 285, 296, 319, 326, 333, 338, 345, 388, 415, 426–427, 436 Golden, John xvi Goldstein, Bernard 124, 149–150, 215, 219, 249–250, 255, 293–294, 327, 369, 377, 381, 492 Golińska-Gierych, M. 201 Górski, Karol 5, 8, 13–14, 18 Grässe, Johann 237 Grafton, Anthony xxvi, 143 Granada, Miguel 143, 187, 239–240, 294–295, 356, 414, 433 Grant, Edward 90, 92, 97–98, 104, 143, 149–150, 358–359, 370, 373–376 Green-Pedersen, Niels 52, 59, 62, 64, 80, 282–283 Grendler, Paul 174–179, 198–200 Grootendorst, Rob 292 Guthrie, W. K. C. 288, 392 Hajdukiewicz, Leszek 24 Halecki, O. 138 Hamel, Jürgen 6, 20, 271
532
index of names
Hamesse, Jacqueline 81, 116 Hankins, James 222 Hartner, Willy 154 Hartwig, Otto 159 Heiberg, J. L 230 Heilbron, John 404 Heninger, Jr., S. K. 159 Henry, Desmond Paul 285, 289 Herbst, Stanisław 9 Hetherington, Norriss xi, xix, 483 Hilfstein, Erna 18, 36–37, 49, 269 Hipler, Franz 5, 8, 10, 20, 36, 152, 187, 195, 208, 210–213, 226, 341 Hooykaas, Reijer 344, 351 Hope, Richard 286–287, 402 Horne, Michael xvi Hoskin, Michael xix Houtlosser, Peter 303, 323 Hugonnard-Roche, Henri 276, 371, 390 Hussey, Edward 94, 320, 337 Ingarden, Roman 373 Ingram, David 351 Jacobi, Klaus xvi, 83 Janik, Allan 292, Jardine, Lisa 280–282 Jardine, Nicholas 158, 372, 376, 378, 380, 404–405, 427, 433 Jarrell, Richard 254, 422, 433 Jarzębowski, Leonard 210 Jervis, Jane 360 Johnson, Monte 93 Jordan, Mark 95, 387 Jung, Elżbieta xiv Jurkiewicz, Beata 436 Juznic, Stanislaw 404 Karliński, Franciszek 11, 25, 28–33, 36, 38–46, 96, 160 Kempfi, Andrzej 414 Kennedy, E. S. xix, 154, 264–265 Kiełczewska-Zaleska, Maria 8 King, David 476 King, Peter 285–286, 288–289 Kirschner, Stefan 200–202 Kiryk, F. 46 Knoll, Paul 137–140, 142, 158 Knorr, Wilbur 243, 327 Knox, Dilwyn xv, 91–92, 97, 102, 107, 117, 132, 195–196, 214, 225–227, 234–238, 250, 256, 288, 330, 333, 335,
339, 342–345, 347–353, 357, 360, 392, 394, 396, 401–403 Koczy, Leon 138 Kokowski, Michał xiv, 95, 300, 333–335, 338–343, 345, 347–348 Kolberg, Anton 213 Kolberg, Joseph 187, 210, 212–213 Korolec, Jerzy 39 Koutras, Demetrios 59, 277 Krafft, Fritz 235–236, 347, 383 Kremer, Richard 152–153, 155, 192, 419, 484 Kren, Claudia 155, 159, 478–480 Kristeller, Paul 209 Krohn, Knut 436 Krókowski, Jerzy 141 Kruiger, Tjark 292 Kubach, Fritz 7 Kuhn, Heinrich 387 Kuhn, Thomas xiii Kühne, Andreas 173, 200–202 Kuksewicz, Zdisław 89 Kurdziałek, Marian 89 Lai, T. 356 Laird, Walter Roy 58 Lakatos, Imre 90 Lang, Helen 89, 93, 101, 111, 335 Lee, H. D. P. 346 Leijenhorst, Cees 387 Lemay, Richard 147, 159, 191 Lerner, Michel-Pierre 143, 149, 218, 276, 369, 372, 376–378, 385, 390, 413–418 Lesnodorski, Bogusław 8 Lewicka-Kamińska, A. 461 Lhotsky, Alphons 141 Lines, David 174–175 Litt, Thomas 375–376 Lloyd, G. E. R. 327 Lohr, Charles 79, 87, 89, 423 Longeway, John Lee 185 Lüthy, Christoph xiv Łoś, Jan 213 Mack, Peter 281–282 Maclean, Ian 203 McMenomy, Christe 32, 149–150, 369, 376 McMullin, Ernan xiv, 94, 300, 319 Madyda, Władysław 138 Magee, John 288 Mahoney, Edward 185
index of names Maier, Anneliese 89, 93, 98, 111 Maierù, Alfonso xv Malagola, Carlo 140, 173–175, 187–188, 192–194, 196 Małłek, Janusz 9 Malmsheimer, Arne 228 Mancha, José Luis 145, 156, 477–478 Mandosio, Jean-Marc 195 Markowski, Mieczysław 12, 15–16, 21–22, 35–42, 46–49, 52–53, 72–75, 80, 82, 86, 89, 94–100, 106, 111–112, 122, 128, 142, 144–145, 149, 153, 158–162, 343, 358, 373, 456 Martens, Rhonda 435 Martin, Craig 120 Matsen, Herbert 185 Methuen, Charlotte 405 Mett, Rudolf 162 Metze, Gudula 436 Meyer, Christoph 177 Mignucci, Mario 54 Mikulski, Krzystof 18, 138 Mincer, Franciszek 207 Moesgaard, Kristian 408, 425 Mohler, Ludwig 221–222, 224 Monfasani, John 224, 474 Mooney, Susan xvi Moraux, Paul 326, 332, 341, 348, 372, 394–397, 400–403 Moraw, Peter 13–18, 22, 49, 138 Morawski, Casimir 17–18, 29, 138, 140 Mortari, Vincenzo 180–183 Morysiński, Tadeusz 436 Moss, Jean Dietz 280, 301 Muczkowski, Jósef 26, 29 Müller, Rainer 173 Murdoch, John xiv Musiatewicz, Mikołaj 436 Naas, Valérie 237 Nardi, Bruno 185 Neugebauer, Otto xxvi, 6, 144, 151, 154–155, 194, 216–219, 260, 269, 302, 328–329, 333, 365, 371, 374, 377, 381–384 Nobis, Heribert 187, 192, 230 Norlind, Wilhelm 299, 302, 410 North, John 150 Nowak, Zenon 5, 8–13 Obrist, Barbara
347
Pacanowski, Grzegorz Pakulski, Jan 36
436
533
Palacz, Ryszard 15–16, 25–26, 36, 38, 73, 75, 89, 100, 111, 159, 373, 444, 448 Pantin, Isabelle 404–405 Papritz, Johannes 18 Patar, Benoît 340 Pawlikowska-Brożek, Zofia 36 Pedersen, Olaf 135, 143, 147, 156, 158, 166, 326–327, 492 Pennington, Kenneth 177 Pepe, Luigi 204 Perlbach, Max 17 Perry, Heather xvi Piasecki, Karol 436 Pihl, Mogens 143, 326–327 Pinborg, Jan 52, 55, 60–61, 65 Pociecha, Władysław 134, 321 Podkoński, Robert xiv, 477 Poschman, Brigitte 7 Poulle, Emmanuel 6, 150, 152, 160 Price, Derek de Sola 150, 153 Prowe, Leopold 5, 8, 10–12, 43–44, 151, 173, 175, 184, 188–198, 203, 208, 211, 244, 361 Pruckner, Hubert 159 Rabin, Sheila 6, 191 Ragep, F. Jamil 154, 262, 484 Randi, Eugenio 90 Rashed, Roshdi xix Read, Stephen 82, 277 Reeds, Karen 201 Rieke, Richard 292 Risse, Wilhelm 280 Roberts, Victor 154 Rose, Paul Lawrence 143, 312, 314 Rosen, Edward xxvi, 5, 8–9, 18, 24, 49, 127, 137, 145, 150, 172–75, 184–197, 200, 202, 211, 215–216, 219, 222–223, 227–229, 234–238, 243–252, 256, 264–270, 276–278, 282, 294, 296–297, 311, 314, 318, 321, 325, 327, 330, 340–341, 345–346, 348, 355, 358, 361, 364, 371–372, 375, 378, 381–382, 389–390, 394–403, 409, 412 Rosenberg, Bernhard-Maria 200–201, 210 Rosińska, Grażyna 15, 25, 89, 144–146, 151–153, 156, 161, 227, 381, 484 Rospond, Stanisław 9 Ross, W. D. 86, 322 Rossmann, F. 244 Rouse, Richard xiii Rupprich, Hans 141, 160 Ryan, Paul 228
534
index of names
Sabra, A. I. 476–478 Saliba, George xix, 154, 262–265 Sarnowsky, Jürgen xvi, 102, 104, 112, 132, 158, 338 Savage-Smith, Emilie 485 Schmauch, Hans 5, 7–9, 11–12, 19, 208 Schmeidler, Felix 172, 189, 191, 215–216, 230, 236, 243–244, 248, 269, 327, 349, 362, 365, 385, 395, 397–399, 402 Schmitt, Charles 90 Schofield, Christine 254 Schupp, Franz 52, 62, 80 Schwinges, Rainer 17 Segel, Harold 139, 141, 194 Segonds, Alain 390 Seńko, Władisław 36, 38, 89, 95, 111, 142 Serene, Eileen 58, 280 Shank, Michael 139, 158, 187, 295 Sharples, R. W. 93 Sikorski, Jerzy 21, 436 Simon, Peter 285 Siorvanes, Lucas 92 Slomkowski, Paul 52, 62, 296 Smith, A. Mark 372 Smith, Pamela 476 Smith, Robin 51, 54–55 Solmsen, Friedrich 89, 338 Sorbelli, Albano 179, 193 Speca, Anthony 52 Spitz, Lewis 141 Spruyt, Joke 26, 63, 68, 72, 280, 292 Steneck, Nicholas 127, 159 Stephenson, Bruce 429, 433 Stocks, J. L. 392 Stravinsky, Igor xvii Strzelecka, Bożena 47 Stump, Eleonore 51–52, 55–56, 59–65, 288 Swerdlow, Noel xiii, xxvi, 6, 151, 154–155, 190, 194, 215–217, 219, 221, 242–245, 248–249, 253–254, 257, 260, 262, 264, 267, 269, 295, 302, 325–326, 328–330, 333, 360, 365, 371–372, 374, 377, 381–382, 384–385, 492 Szczeciniarz, Jean-Jacques 332–333, 355 Szczucki, Lech 244, 404 Szelińska, Wacława 36, 38, 40–42, 44–46, 139–141 Szujski, Józef 73 Świeżawski, Stefan 36, 89, 103, 105, 166, 241
Tarnowska, Irena 40 Tatarkiewicz, Władysław 403 Tessicini, Dario 143, 187, 239–240, 294–295 Thijssen, Hans (also Johannes) xiv, 90 Thimm, W. 21 Thoren, Victor 254, 433 Thorndike, Lynn 375 Tomkowicz, Stanisław 27 Toomer, Gerald xxvi, 143, 147, 158, 217–218 Toulmin, Stephen 280, 292–293 Trifogli, Cecilia 89, 103 Troupe, Bonnie xvi Turnbull, Robert 228 Ueberweg, Friedrich 159 Ulewicz, Tadeusz 137 Usowicz, Aleksander 36 Valentin, H. 191 Van Eemeren, Frans 292 Van Luchene, Stephen 93 Varzi, Achille 285 Vasoli, Cesare 174, 230 Verdet, Jean-Pierre 369, 371, 390 Vermij, Rienk 404 Vickers, Brian 194 Visconti, Alessandro 204 Voelkel, James 424, 430 Voullième, E. 461 Wagner, David 42 Walde, O. 213 Wallace, William 58, 319 Warrington, John 87 Wasiutyński, Jeremi 151 Waters, C. Kenneth 277 Wattenberg, Diedrich 219–220 Weijers, Olga 52 Weisheipl, James 89, 93, 101, 115 Westman, Robert S. xiii, 179, 186, 191, 254, 293, 295, 317, 372, 375, 380, 388, 403, 405–406, 410–411, 421–422, 424–426, 428, 432–433, 436 White, Lynn Jr. xiii Wieacker, Franz 180 Williams, Joseph 292 Windakiewicz, Stanisław 23 Wisłocki, Władisław 80, 461 Wiszniewski, Michał 37 Wittgenstein, Ludwig 90 Włodarczyck, Jarosław 152–153
index of names Włodek, Zofia 35, 37–39, 41–42, 46, 80, 89, 107, 373 Wörner, Marcus xvi Wolff, Michael 333, 338–341, 347–348 Wróblewski, Andrzey 137 Wündisch, Veronika 436
535
Zajdel, Dariusz 436 Zarębski, Ignacy 140 Zathey, Jerzy 41, 43, 161 Zekl, Hans 244–245, 264 Zinner, Ernst 25, 137, 159, 172, 189, 216, 217, 219–220, 230, 403 Zwiercan, Marian xiv, 26–27, 35–39, 48–49, 79, 89
INDEX OF PLACES Baltic 7 Baltic Sea 5, 207 Basel 138, 411 Berkidy 5 Black Sea 7, 222 Bohemia 216, 428 Bologna xxiii, 11–14, 18–19, 22–24, 107, 138, 140, 152, 162, 167, 173–188, 192–193, 195–197, 199, 201, 203–205, 211, 216, 238, 275, 278, 282, 284, 322–323, 370, 388 Bourges 178 Braniewo (Braunsberg) 3, 6, 187, 207, 213
Lidzbark-Warmiński (Heilsberg) 2–3, 187, 200, 204, 207–208, 211–215, 226, 229, 235–236, 269–271, 341 Lublin 89
Chełmno (Kulm) 2–3 Cologne 11, 16, 19, 42, 72–73, 81–82, 93, 96, 282–283, 322 Constance 138 Constantinople 221 Cracow (Kraków) xiii–xiv, xxi–xxvi, Chapters 1–5, 171–172, 179, 184–186, 191–194, 202, 207–208, 211, 214, 216, 219–220, 225, 237–238, 241, 245, 262, 267, 269–271, 275, 277–278, 281, 283, 285, 298, 322–323, 332, 334, 336, 338, 357–358, 361, 327–374, 388, 398, 419, 424, 437, 484 Crete 222
Olmütz 216 Olsztyn (Allenstein) 2–3, 9, 200, 207 Oxford 14, 16
Elbląg (Elbing) 2–3, 6 Erfurt 282–283 Ferrara 171, 173–174, 176, 178, 180, 198–199, 203–204 Florence 141, 224, 414 Frombork (Frauenburg) 2–3, 6, 134, 177, 187, 207–209, 211–215, 226, 229–230, 235–237, 269–271, 293, 321, 341, 436–437 Gdańsk (Danzig) 411 Geismar 9 Hesse 9
2–3, 5–6, 137, 210,
Mantua 238 Mierzeja Wiślana (Vistulan Sandbar) 3, 207 Milan 162, 196, 218 Naples 138, 199 Nicaea 221 Nogat River 3, 207 Nürnberg 172, 207
Padua xxiii, 14, 22, 155, 162, 171, 173, 184, 191, 196, 198–201, 203–204, 268, 278 Paris 13–16, 39, 73, 93, 142, 149, 177, 420, 424 Pieniężno (Mehlsack) 3, 200 Poland xi, xix, 1–2, 5–9, 15, 43–44, 47, 74, 94–95, 138–140, 142, 169, 178, 183, 188, 192, 194–196, 198, 204, 207, 214, 216, 235, 261, 361, 437 Pomerania xi, 3, 5–6, 207 Prague 14–15, 56 Rome 139, 171, 173, 175–177, 180, 197, 205, 411 Royal Prussia 5–9 Stockholm 214 Sweden 208, 212–213, 226, 341 Toruń (Thorn) xxi, 2–3, 5–9, 11–13, 17–19, 43, 137–138, 172, 207–208, 436–437 Trapezunt 222 Ukraine 7 Uppsala 134, 146, 150, 191, 195–196, 202, 208–209, 211–214, 216, 222, 226,
index of places 228–229, 235, 238, 249, 258–259, 321–322, 400, 436, 471 Varmia (Warmia, Ermland) xi, xxiv, 3, 6–7, 9, 11, 19–22, 134, 172, 175, 178, 187, 196–197, 200, 205, 207–208, 210–213, 226, 270–271, 361 Venice 201, 422 Vienna 12, 35, 139, 141, 143, 159, 221
Vistula River (Wiśła, Weichsel) 2–3, 5–6, 11, 207, 437
537 xxi,
Warsaw 2, 5 Wieliczka 139 Wittenberg 405, 422 Wocławik (Leslau) 12 Wrocław 43, 47, 141, 150 Zalew Wiślany (Vistula Lagoon) 207
INDEX OF SUBJECTS Albertism 42, 89, 96 Alfonsine Tables 35, 146, 149–150, 154, 211, 221, 418 Aristotelianism xv, xxii, xxiv–xxv, 90, 93, 95, 99, 134, 172, 225, 325–326, 330, 387 Copernican 171, 401, 403–404, 408, 435 Paduan 58, 198–199, 203, 268–269 Scholastic xxv, 86, 89, 91–93, 98, 110, 127–128, 133–135, 142, 171–172, 181, 184, 209, 230–231, 236, 238, 276, 283, 330–331, 340, 344, 347–353, 359, 372, 387–401, 408, 412, 474 Tradition xxi–xxii, 36, 89–93, 97, 179 astronomy, astronomical xxi–xxiii, xxvii, 9–16, 23–29, 33, 35–41, 43, 45–50, 53, 58, 68, 72, 88–89, 93–94, 96, 105, 107, 114, 120, 123, 134–135, 137–167, 171–174, 180, 182–184, 190, 192–197, 203–205, 208–209, 215, 219, 239–242, 270–271, 275, 278–279, 284, 291, 293–296, 299, 301–306, 311, 317, 320, 322–327, 330–337, 358–359, 369–371, 374, 383, 387–388, 390, 401, 404, 407, 410–424, 427–428, 431–432, 435, 437, 477, 484–485 anomaly 158, 221, 249, 379, 429 astrology 10, 15, 29, 32, 35, 38–41, 45–46, 48, 137, 145–146, 149, 160–161, 186, 190–191, 202–203, 370, 411 bounded elongation 125, 133, 241, 246, 249, 253, 257, 312–314, 329, 358, 386, 489 calendar 25–26, 30, 35, 41, 144–145, 149, 160–161, 295, 299, 436 concentric, homocentric 123, 128–129, 134–135, 143, 145, 148, 155–156, 158–159, 161, 163–164, 184, 239–240, 242, 244–245, 248–251, 264, 267, 294–296, 328, 364, 371, 375, 377, 401, 408, 477–478, 484 cosmos, kósmos 91–92, 94, 99, 101, 115–116, 118, 126, 135, 143,
148–149, 226, 231, 287–288, 290, 298, 328, 337, 347, 355–358, 371, 399, 401–402, 427, 473–474 distances, planetary and stellar, angular and linear 115, 124–126, 130, 144–145, 218, 221, 241, 246, 248, 252–257, 260, 266, 279, 307–308, 311, 314, 318, 321, 329, 355, 364–365, 379–380, 383, 388, 398–399, 401–402, 413, 428, 431, 480, 483, 487–489 ecliptic 118–120, 124–125, 127, 129, 131, 190, 192, 197, 218–219, 264, 267, 311, 399, 477 ephemerides 15, 35, 150, 270 geocentric xxiv, 123, 134–135, 143–145, 147, 158, 174, 242–243, 246–247, 251, 256–257, 272, 315, 321–322, 324, 327, 353, 366, 383, 388, 410, 425 heliocentric xxiv, 16, 24, 44, 93, 173–174, 186, 206–208, 215, 238, 242–243, 249–253, 255, 272, 276, 279, 297, 300, 321, 327–328, 330–331, 339, 353, 358, 362, 381, 388–390, 401, 404, 406, 410, 413–414, 418, 420, 422, 425, 429, 432–433, 437 heliostatic 122, 272, 355, 388, 401, 405 instruments 146, 151–154, 172, 191, 218–219, 241, 271 latitude 25, 151–152, 163, 188–189, 219, 248–250, 254, 264, 266–267, 269, 313, 329, 365–366, 379, 407–408, 429–430, 434, 478 longitude 150, 152, 158, 163, 249–250, 266–267, 269, 365–366, 428, 430, 432, 435, 485 mathematical 15, 16, 26, 38, 40, 45–46, 58, 88, 107, 134–135, 142, 145–149, 154, 157–158, 162, 164, 174, 179, 190, 193–195, 199, 206, 219, 225, 229, 240, 242–243, 246–247, 249–251, 256, 262, 267, 270, 272, 276, 279, 300, 305, 308–309, 314–320, 323, 327, 329, 333, 337, 353, 359–361, 364–368,
index of subjects 378, 384, 386, 388, 398, 401, 404–405, 407–408, 418–419, 421, 425, 476–477, 481, 492–493 observations 23, 40, 45, 144, 146–147, 152–153, 160, 163–164, 166, 172, 184, 188–192, 207, 217, 219, 228, 237, 241–242, 244, 246–247, 269–271, 276, 279, 295, 297–300, 305, 308, 310, 313–314, 318, 327, 334, 345, 379, 393, 398–399, 407, 412, 414, 418–419, 421, 425, 476–477, 481, 492–493 period 124–125, 230, 314, 430–431, 492 sidereal 125, 233, 235, 238, 246–247, 252–253, 255, 257, 260–261, 291, 315, 329 synodic 255, 257, 261 zodiacal 125, 130, 233, 253, 257 physical 147–148, 157, 219–220, 246, 262, 305, 309–310, 319, 326–327, 337, 362, 369, 374, 378, 398, 401, 406, 408, 411–412, 415–416, 420, 425–427, 432–433, 435, 477–478, 481 Planetary Hypotheses 156, 253, 492 Ptolemaic 49, 53, 92, 123, 126, 131, 134, 143–144, 146, 150, 154–159, 163, 172, 174, 183, 191, 215, 219, 221, 228, 238, 241–242, 246, 257, 262, 268, 270, 291, 294, 296, 300–302, 322, 325–327, 358, 382, 386, 389, 408, 411, 413, 421–424, 434, 473, 477–478, 484 retrograde motion 124, 133, 241, 246, 248–249, 253–255, 257, 311, 313–314, 316, 329, 358, 368, 379, 383, 386, 388, 407, 479, 488–489 stellar parallax 246, 314, 355–356, 398, 407 tables 10, 15, 35, 45, 143, 146, 149–154, 160–162, 172, 189–190, 211, 214, 221, 270, 418, 437, 484 Tabula directionum 146, 150, 161–162, 211, 216, 259 Tabula eclipsium 151, 160 Tabulae resolutae 46, 146, 150–151, 160 Theorica 147, 253 trepidation 144, 478 Tychonic 191 year sidereal 125, 192, 233, 248, 251, 261
539
solar 144, 197, 241, 248 tropical 192, 247–248, 252, 422 zodiacal 125, 130, 233, 252, 257 Averroism xxv, 184 Paduan 295 Baltic Research Center 436 Bible, Sacred Scripture 12, 20, 295, 299, 406, 409–410, 413–415, 421 Brethren of the Common Life 11–13 Collegio Romano 58 Council of Trent 178, 406 Earth 94, 97, 109–110, 114, 117–120, 125–133, 143–145, 148–149, 153, 157, 186, 188–192, 218, 220–221, 226, 230–235, 238, 246, 260, 287–288, 290, 305–306, 321, 346, 375–377, 473–475, 477, 479 motion of 230, 234, 246–249, 252–257, 259, 268, 279, 288, 291, 297–299, 307–313, 315–317, 321, 327–342, 345, 347–348, 350–351, 353–359, 362, 368, 370–372, 374, 379–402, 405–409, 413–418, 422–424, 426–427, 435, 488–489, 493 education 1, 5, 8, 11–14, 16–18, 20, 22–24, 31, 33, 37–38, 44, 49, 51, 64, 75, 85, 96, 99, 138–140, 147, 162, 169, 171–174, 177–180, 183, 188, 193, 198, 200, 203, 206, 215, 271, 275, 278–282, 387, 389, 437 astronomy xxi, Chapter 5 curriculum xxii, 8, 15–16, 24–28, 49, 52, 62, 64, 74, 89, 93, 114, 140, 142, 145–154, 173, 175, 198–199, 205 early, elementary 5, 7–8, 12–13, 196 liberal arts (see liberal arts) mathematics 10–11, 15, 18, 23, 25, 28, 40, 46, 48–49, 143, 145, 159, 171, 193, 198, 201, 223–224, 301, 304–305 music 10–13, 26, 28, 32–33, 41, 160 quadrivium (also quadrivium) 12, 26, 32 School of St. John 8–9, 11, 13 teachers xxii, 12–13, 16, 23–25, 28–30, 32–33, 75, 93–95, 99, 101, 114, 124, 131, 133, 140, 151, 159–166, 184, 199, 205, 275, 284, 322, 325, 484 trivium 26
540
index of subjects
elements xxvi, 92, 97, 101–102, 115, 117, 119–121, 127, 132, 150, 184, 223, 230, 232, 235, 255, 287, 325, 332, 336–338, 345, 347–348, 354, 374, 376, 380, 392–393, 402–403, 415, 435, 473 aether (also ether) 116–117, 120, 126, 232–233, 288, 345–346, 348, 354, 375, 377 atom, atomism 122, 345 earth 118, 125, 231, 288, 342–343, 345–346, 350–351, 370–373, 396, 417, 474 fire 233, 345, 395 fictionalism (see hypotheses and instrumentalism) saving the hypotheses 321 saving the phenomena 163, 327 Florentine Academy 142, 224 geocentrism 54, 116, 252, 291, 315, 317, 320, 326, 330–332, 337, 353, 358, 367, 408, 410, 416, 473 geography 9, 35, 43, 47, 120, 142, 212, 238, 306 navigation 149 heliocentrism xv, xxvii, 202, 242–243, 291, 320, 329, 331, 336, 360, 381, 386, 396, 403, 408, 411, 421 humanism xxii, 39, 43–44, 49, 99, Chapter 5, 137–167, 178–179, 182, 194, 199–201 hypotheses xxv, 11, 28, 53, 67, 72, 75, 85, 88, 90, 129, 131, 171, 209–210, 212, 215, 228, 237, 242, 256, 272, 276–280, 291, 296, 299–300, 302, 305, 314–318, 320–324, 328, 360–369, 385–391, 404–405, 408, 410, 412, 414, 416–427, 430–432, 476, 485, 487, 492–493 fictitious, imaginary 147, 157–158, 315, 366, 369, 378, 477 assumption 57, 115, 145, 242–243, 246–247, 250–251, 254, 256, 271–272, 278, 280, 284–286, 305, 312, 315, 320, 324, 326, 330, 354, 359, 361–363, 367–369, 383, 385–386, 391, 404, 412–413, 415, 421, 477 axiom 37, 131, 147, 165, 217, 243, 253, 277, 316, 327, 342, 362, 367–368, 377, 383, 396, 401, 407, 421, 429–430, 477, 493
postulate 228, 240, 243, 245–246, 250–253, 256, 291, 307, 375, 382–383, 419 principle 55, 58–61, 73, 85–86, 92–95, 101–102, 107–108, 110, 113, 117–118, 124, 128, 130–131, 133, 135, 145, 151, 171–172, 176–177, 180–181, 183, 212, 215, 223–224, 229–230, 240, 243–245, 250–255, 257, 275, 277–278, 291–293, 296, 305, 307–308, 310–317, 321–322, 324–328, 330–332, 334–335, 337, 339–340, 344, 348, 351, 353, 357–358, 360, 362–363, 367–370, 374, 376–378, 380–382, 385–388, 390–396, 398–399, 401–402, 405, 408, 413, 415, 417–418, 421, 427, 430, 433, 435, 437, 474, 487–489, 493 instrumentalism xxv Islamic astronomy 145, 476–485 Jagiellonian Library 35, 40, 95–96, 107, 128, 139, 142, 151, 225 languages German xxi, 5, 7, 9, 13–14, 17, 139 Greek xxiii, 43–44, 59, 140, 171, 173, 180, 184–185, 193–197, 204–205, 211, 219, 221, 229, 234–236, 244, 415 Latin xxi, 8–9, 13, 43, 146, 193–196, 210–211, 235, 296, 415 Polish xxi, 5, 7, 9 law xxiii, 10–11, 14–15, 18–24, 42, 45–46, 49, 138, 140, 166–167, 171, 173–183, 192, 198, 203–205, 214, 275, 278, 282, 285, 370, 389 liberal arts xxi–xxii, 8, 11, 18, 23–24, 27, 33, 35–36, 38, 142, 177, 193, 195, 279, 304, 317, 404, 410, 435 logic, logical xxi–xxii, xxiv, 9, 11–13, 16, 24–33, 35–42, 45–49, Chapter 3, Chapter 8, 387–391, 397, 404–405, 415–416, 422, 425–427, 429, 431–432, 437, 477, 484–485 antecedent/consequent 61–62, 68–72, 75–86, 88, 106, 183, 247, 277, 290, 387, 391, 422, 450–451, 453, 455, 478–479, 487 argumentation xxiv–xxv, 53–57, 60, 65, 73, 180, 299, 301, 336, 354, 356–357, 370, 385, 390, 401, 433, 437, 474
index of subjects conditional 52, 61, 68, 71, 76, 80, 183, 275, 334–335 connexivist 69 consequences xv, 26, 51–53, 56–57, 60, 62, 64, 68–69, 72–73, 75–84, 88, 108, 123, 183, 228, 277–278, 281–282, 285–286, 289, 315, 317–318, 324, 404, 423 convertibility 412 demonstration 54–60, 64–65, 72–74, 85, 131, 135, 185, 199, 203, 242, 244, 246, 249, 251, 262, 267, 279–281, 283, 315, 318, 322, 335, 366–369, 378, 390, 405–416, 421–423, 454, 484 dialectic 55–58, 60, 64, 72–88, 93, 119, 127–128, 173–178, 180–184, 205, 214, 218, 220, 230, 242, 275, 278, 290, 295, 323, 329, 336, 338, 359, 387, 389 dialectical method 59, 251–256, 276, 291, 301, 314, 321–326, 330, 389 dialectical topics 52–57, 62, 100, 108, 113–114, 171, 179, 181–182, 203, 279–286, 292–314, 322, 387, 390, 413, 426–427, 435 authority 56–57, 157, 181–182, 284–285, 297–298, 305, 308, 409, 412, 416, 441, 443 extrinsic 64–65, 67, 69, 83, 182, 283–284, 297, 442–443 intermediate 61, 64–65, 67, 69, 283–284, 443–444 intrinsic 64–65, 67, 69, 83–84, 182, 283–284, 441–442 part/whole (see mereology) enthymemes 60, 63–64, 181, 283, 292, 303, 323 example 63, 181 habitudo 80–81, 83 hypothetico-deductive system 59, 277, 323–324 induction 63, 86, 181, 277 inference 51, 56, 58, 60, 63, 65, 68–69, 71, 73, 78, 183, 185, 247, 278, 282, 288–289, 296, 307, 427 metábasis 107, 156, 318 necessary propositions 56, 58, 62, 68–69, 73, 76, 183, 277, 280–281, 315, 367, 422, 424, 431 omission 387, 389 paradoxes xv, 51–53, 57, 62, 72–73, 99, 182, 203, 218, 278, 280, 291–292, 354, 358, 387, 390, 404, 412, 415, 424, 436
541
probable propositions 56–57, 59, 64–65, 72–73, 99, 182, 203, 218, 278, 280, 291–292, 354, 358, 387, 390, 404 regressus 412, 415, 424, 436 relevance 56–57, 62, 66, 68–69, 71–72, 75–76, 81, 84–85, 88, 108, 171, 228, 251, 275, 277–278, 280, 285, 296, 299, 315, 321–322, 324, 367, 369, 387, 389–390, 432, 487 rhetoric 23, 25–30, 33, 44–45, 48, 53–57, 70, 93, 178, 184, 214, 222, 279–282, 286, 293, 295, 297, 299–301, 303–305, 323, 327, 330, 345, 355, 388, 396, 451 semantics 56, 60, 62 simplicity 301, 313, 334, 354, 426, 437, 488 syllogism 30, 51–52, 60–61, 63–65, 73–75, 86–87, 181, 185, 217–218, 220, 281, 283, 286, 293, 296, 323 syncategorematic terms 26, 62, 64, 68, 82 terminism 63, 72 typology 362, 369, 404, 420, 425 validity 60–62, 65, 69, 73, 81, 275, 277–278, 281–282, 285, 323–324, 387 warrants 62–63, 75, 280, 282, 284, 292–293, 296–297, 299, 304–311, 317, 323, 425–426, 488 Lutheranism 13, 44, 177, 405–406, 410 matter (see metaphysics under natural philosophy) medicine 14–15, 20–23, 49, 171, 173–174, 176, 178, 185, 190, 198–204, 230, 416 Melanchthon Circle 405, 411, 421, 425 mereology 83, 285–291 part/whole 66–67, 81, 83, 113–119, 127, 163, 183, 238, 278, 283, 285–291, 296–300, 307–308, 310–312, 314, 317, 343–344, 348, 350–351, 359, 369, 380, 385, 392, 396, 413, 417–418, 426–427, 441–442, 459–460, 462, 472–474, 487–488 models 23, 88, 92, 123, 126, 129–130, 133–135, 143–149, 154–158, 161, 163–164, 166, 174, 191–192, 206, 218–221, 223, 229, 239–242, 244–246, 248, 250–252, 255–256, 261, 268, 270, 272, 294, 302, 313–316, 320, 327–329, 333, 353, 355, 358–369, 371, 377–378, 380, 383, 385, 388, 402, 404–405,
542
index of subjects
407–408, 413–414, 418–420, 423, 425, 476–486, 492–493 Apollonius’s theorem 249 Capellan 159, 254–255, 257, 313, 381–383, 385 crank mechanism 158 device, mechanism 131, 155–158, 262–269, 315, 365–369, 378, 381, 384–386, 401, 477–485, 492 oscillatory, reciprocation, rolling 155, 165, 248–250, 252, 261–262, 264, 266–269, 365, 477–485 double-epicycle 165–166, 248–251, 363–364, 378, 381, 408, 484 eccentreccentric 313, 341, 364, 408 eccentric and epicycle-deferent 85, 123–124, 126, 128–130, 133–135, 143, 145, 147–150, 155–158, 161, 164–166, 221, 239–241, 245–246, 248–255, 257, 259–268, 291, 308, 312–316, 328–329, 341, 355, 363–365, 367–368, 371–372, 376–382, 384, 388, 407–408, 419, 422, 428–429, 431–435, 463, 477–485, 488, 492 Egyptian 159 equant xxvi, 130–131, 133, 135, 145, 149, 154, 156–158, 161, 165, 245, 251, 253, 262, 264, 268–269, 291, 316, 321, 329, 368, 371, 377, 380–386, 407, 429, 431, 434, 477–478, 492–493 Eudoxan, Eudoxian 155–156, 477–478 libration 264, 363, 366 Maragha 154–156, 261, 476, 478, 484–485 oval 158, 232, 313 radius 165, 260, 262, 364, 480, 482 orbital 259 three-orb system 130, 148, 375 Tusi couple/device 155, 157, 248, 261–267, 476–477, 480–481, 485 Tychonic 381–382 Moon 10, 107, 110, 117, 119, 121, 125, 128, 132, 144, 148, 155–158, 165, 193, 217–218, 230, 232–235, 248, 252, 254–255, 260, 262, 291, 311–312, 316, 334, 348, 353, 359, 363–364, 370–372, 376–378, 380, 383, 388, 398, 400, 406–408, 427, 473–475, 479, 484 motion 91, 94, 98, 101–103, 107–108, 111–112, 127, 131, 149–150, 195, 216,
230, 235, Chapter 9, 411, 413–417, 428–431, 435 acceleration 58, 103, 119–122, 129, 343, 393–394 circular xv, 37, 105, 114–118, 120, 122–125, 130, 135, 147, 163–165, 215–218, 232–233, 238–240, 242, 251–253, 255, 266, 268–269, 290, 306–307, 309–311, 315–320, 365, 367–374, 379–380, 395–399, 401–402, 407, 435, 473, 477–485, 487–489, 493 compound 255, 306, 310, 393, 397 cone-shaped 232 conical 372 directionality 126, 290, 348, 474, 490 force, virtus, vis 92, 102, 111–113, 118–119, 132, 135, 158, 240, 306, 372–374, 393–395, 411, 413, 424, 433, 445–446, 455–459, 465, 492–493 gyrational/spiral 240 impetus 48, 89, 92, 98–100, 110–112, 129, 132, 373–374, 393–395, 457–458, 471 inclination 58, 101–102, 113, 132, 271, 376, 396, 399, 456, 473, 490–491 inertia 98, 338, 473 mechanics 58, 90, 97, 338, 360, 381, 492 natural 91, 94, 105, 109, 116, 118, 122–123, 129, 132–133, 255, 286–288, 309, 325, 331, 334, 336–338, 340–344, 351–352, 356, 358–359, 393–394, 416–417, 437, 473 non-uniform 156, 164, 248, 251–252, 255, 262, 287, 306–307, 311, 339, 364, 367–369, 375, 379–380, 383, 385–386, 479, 481, 492 periodic mean 492 planetary 45, 129, 133, 143, 145–146, 158, 163–164, 186–192, 219–220, 230, 244, 246–249, 253–254, 256, 279, 291, 297–300, 313, 316–317, 362–364, 370–373, 380, 391, 404–405, 408, 412, 421–423, 437, 476, 489, 493 projectile, violent 91–92, 110–111, 129, 132–133, 231, 325, 335, 341, 351, 400 rectilinear 115, 117, 123, 131, 155, 165, 217, 252, 255, 262, 266–267,
index of subjects 309–310, 319, 340, 342–344, 349, 351–352, 354, 391, 393–398, 427, 478–481 relativity of 393 resistance 119, 129, 334–335, 342, 344, 391, 393 simple 94, 102, 110, 115–116, 122–123, 126, 157, 163, 165, 287–288, 290, 309–310, 325, 332, 336, 339–340, 343–345, 347–348, 358–359, 371, 378–379, 391–393, 396, 462–463 teleological 238, 287, 347–348 uniform xv, 98, 129, 147, 155–156, 244–246, 251–253, 255, 296, 320, 368, 378, 382–389, 395, 400, 435, 492–493 void 91, 97–100, 104, 110–112, 117, 123, 135, 145, 165, 218, 230–232, 262, 356–358, 375, 377, 397 natural philosophy xxi–xxiii, xxvii, 15–16, 24, 26, 28, 30–33, 35–36, 38, 40–41, 48–49, 53, 75, Chapter 4, 147–149, 163, 171–172, 174, 176, 198, 201, 212, 214–216, 225, 236, 240, 247, 256, 276, 279, 284, 292–293, 299, 307–308, 317–320, 323, Chapter 9, 362–363, 367–369, 373, 385, 387, 389, 391–392, 399, 403–405, 408, 410, 412–415, 418, 421, 427, 435, 437, 477 according to nature 91, 115, 123, 310, 333–334, 341–342, 350–352, 393 body 58, 97–98, 101, 103–104, 107, 109, 111–112, 115–117, 122–123, 126, 129–132, 135, 155, 157–158, 163–164, 218, 231–232, 235, 255, 287–288, 306, 308–310, 313, 325, 333–337, 339–341, 343–345, 348, 350–352, 358, 375, 378–380, 393–396, 429, 473–474, 478–480, 488–489, 492 heavy 103, 109, 111, 114, 116–119, 122, 124, 126, 131, 217, 231–232, 309–310, 325, 343–344, 346, 348, 356, 359, 393, 395, 446, 464, 473–474 light 111, 116, 118–119, 122, 126, 217, 231–233, 310, 312, 342–343, 346, 348, 393, 395–396, 474 shape 108, 110, 118–119, 122, 126, 132, 158, 189, 216–217, 230–232, 305–307, 333, 354, 398
543
cosmology xv, xxiii–xxiv, 53, 88, 93, 96, 134–135, 208, 253, 323, 326, 330–331, 339, 344–345, 353, 358, 360, Chapter 10 architectonic 313, 317, 369, 389, 435 axiom (see hypotheses) commensurability 296, 300–301, 329, 363 cornerstone (primarius lapis) 362–363 enclosed/enclosing 307–308, 310, 331, 488 eternity 91, 116, 223, 230, 239, 290, 310, 332, 378, 394–395, 401, 480 harmony 252, 301–302, 311, 329, 411–412 intelligence, vital force 98, 101, 112, 129–130, 135, 156, 158, 163, 239–240, 290, 335, 340, 385, 479, 481, 491–493 prime mobile, mover 124–125, 224, 340, 400–401, 477 symmetry 128, 301, 403 system, systema 118, 122–123, 129, 148, 173, 245–246, 252–253, 255, 257, 259, 262, 268, 277, 291, 297, 302, 314, 316, 321–322, 325, 328–331, 335, 353–358, 363, 366, 368–369, 372–373, 375, 377, 391, 413, 418, 429–431, 484, 492 gravity 129, 131, 235, 238, 246, 252, 298, 306, 311, 335, 343, 347–348, 353, 376, 393, 396, 427, 435 inclination, appetite, desire 101–102, 113, 129, 132, 238, 325, 340, 343–344, 348, 350, 352, 380, 393, 396, 399, 427, 456, 473 metaphysics, metaphysical principles Chapter 10 accident 55, 59, 66–67, 83, 103, 113, 129, 239, 283, 343, 350, 352, 357, 374, 391, 442, 451, 455, 457, 459–460, 466–468 actuality/potentiality 103, 119–121, 247, 332, 374, 400–401 cause/effect 65–68, 71, 77–78, 81, 84, 88, 91, 98, 101–102, 108, 111–114, 117–133, 158, 185, 230, 242, 246–249, 256, 276, 283–284, 290, 297, 305–309, 318, 321–322, 332–346, 350, 370, 379–380, 385,
544
index of subjects
390, 393–395, 402, 404–405, 412–413, 419–423, 431–433, 442, 458, 464, 470, 487–488, 492 dignity 78, 293, 308, 310, 336, 421 empyrean 357, 397 essence 54, 233, 350, 391, 412 form/matter xxvi, 54, 91–92, 97, 100–103, 105–109, 114–117, 119, 123, 216–217, 223, 230, 238–239, 290, 305–306, 311, 325–333, 337, 339, 342–345, 351, 353–354, 360, 370–374, 378, 380, 385, 388, 395, 426–427, 434, 445, 447, 449–452, 454–455, 458, 464–465, 468, 470, 487 perfection 103, 130, 132, 208, 223, 295, 336, 351, 361, 446 power 101–102, 111, 186, 341, 350, 356, 373, 379, 433 principle, see hypotheses quality 111, 132, 311, 340, 395–396 substance 65–66, 108, 112, 115, 120–121, 125, 283, 287, 289–290, 325, 372, 388, 433, 441 physics 325–326, 337, 342, 353, 377, 383, 418, 433 place 66, 98–105, 113, 116–119, 123–124, 131–132, 216, 218, 230–231, 288, 310, 325, 333, 337–338, 343–351, 357–358, 376, 393–395, 398–400, 473 Neoplatonism xxiv–xxv, 43, 92, 94, 97, 141–142, 172, 220, 222, 224, 229, 275, 288, 318, 327, 349, 389, 394, 473 planets 45, 106–107, 117, 119, 127–133, 143–146, 148–152, 154, 156, 158–159, 162–165, 186, 191–193, 197, 202, 230, 244–245, 250, 252, 256, 262, 264, 291, 298, 300, 308, 310–311, 318, 321, 325, 328, 332, 348, 353–356, 358–359, 369–381, 383–384, 386, 397–400, 404–405, 407, 412, 419, 422, 429–431, 433–435, 453, 462–463, 474, 476–483, 488–489, 492 Mars 125–126, 128, 189, 218, 221, 232–235, 247–248, 253–255, 257, 259–260, 312–313, 382, 388, 408, 413, 427–428, 434, 489 Mercury 125, 128, 130, 133, 144, 159, 161, 165, 172, 186, 207, 217–219, 221, 227, 232–235, 238, 241, 246, 249, 253–255, 257,
259–261, 266–267, 269, 312–314, 316, 329, 363–366, 368, 382, 408, 477, 484, 489 Jupiter 125–126, 128, 218, 232–233, 253, 257, 259–260, 269, 312–313, 382, 407, 434, 489 Saturn 125–126, 128, 133, 218, 232–234, 248, 253, 257, 259–260, 264, 269, 312–313, 355, 382, 399, 434, 489 Venus 125–126, 128, 130, 133, 144, 159, 161, 165, 186, 218–219, 221, 227, 232–234, 238, 241, 246, 249, 252–255, 257, 259–261, 264, 312–314, 329, 363–364, 366, 382, 388, 408, 422, 477, 484, 489 Platonic Academy 224, 473–474 Platonism xxiv, 43, 92, 97–98, 101, 107, 118, 132, 135, 141, 159, 172, 198, 220–221, 223–225, 230, 253, 255, 275, 318–319, 326, 328, 338, 347, 357, 394, 456, 473–474, 477 “Platonic axiom,” uniformity and circularity 147, 396 Pythagoreanism 107, 118, 211, 221–223, 232–234, 247, 395, 402, 415, 417 realism, realist xxv, 74–75, 149, 158, 229, 327, 361, 369, 385, 404, 493 Santa Maria Novella 414 Scotism 39, 42, 142 Sodalitas litteraria Vistulana 43–44, 141 space 11, 91, 98, 104, 135, 145, 217–218, 221, 230, 249, 254–255, 308, 310, 312–314, 353, 355–358, 372, 377, 388, 397, 433 sphere xxvi, 37, 97–98, 100, 103–107, 112, 114, 117–118, 120, 122–135, 143–144, 147–150, 153–159, 161, 163–165, 188, 208, 215, 217–219, 230, 232–233, 242, 244–256, 259, 264, 269, 287–288, 290–291, 297–298, 305–308, 311, 313, 325, 331–336, 338–341, 345, 348–358, Chapter 10, 388, 395, 397–402, 407–409, 413, 423, 426–427, 433, 435, 437, 477–480, 487–488, 492 orb 112, 123–126, 128–131, 133, 143–144, 148, 157–158, 163–165, 224, 234, 239–241, 245, 248–250, 256, 264, 333–334, 339, 349, 365, 371, 375–381, 385, 413, 422–423, 426, 429, 432, 434, 444, 452, 464, 490, 492
index of subjects Stobner chair 15, 41, 152–153 Stoicism xxiv–xxv, 51–52, 56, 94, 97, 102, 229–233, 345, 347, 357–358, 374, 398, 473–474 Suda (also Suidae lexicon) 195–197, 214, 235, 344, 348–349, 351, 353, 392, 490–491 Sun 10, 107, 117, 119–121, 125, 127–130, 132–133, 144–145, 148–149, 155–156, 158–159, 163–165, 186, 219, 221, 227, 230, 232–234, 238, 240–241, 246–247, 252–257, 260, 279, 287, 291, 308, 311–313, 315, 317, 320, 328–329, 333, 338, 345, 348, 353, 355–359, 362, 364, 366, 370–373, 375–383, 386, 388, 395, 397–400, 402, 404–408, 413, 422, 427–429, 431, 433–435, 437, 479, 488–489, 493 as king 219, 240 as visible god 400 Teutonic Knights xvii, 7, 175, 177–178, 201, 271, 361 Thomism 42, 96, 100 universe 91, 99, 103, 113, 115, 117–120, 123–124, 129, 136, 164, 218, 223, 230–232, 234, 246–247, 250, 252, 255–256, 286, 290, 296, 298–299, 302, 305, 308–311, 318, 331, 338, 348, 350, 363, 371, 373, 378–379, 393, 400, 402, 410, 415, 426, 435 finite/infinite xxvi, 115, 136, 202, 237–238, 241, 302, 310, 332, 345,
545
355–358, 370, 392, 396–397, 401, 407, 474 structure 91–92, 250–262 university 8, 13 Bologna 11–14, 18–19, 22–24, 138, 140, 152, 162, 167, 173–193, 195–197, 199, 201, 203–205, 211, 215–216, 238, 275, 278, 282, 284, 322–323, 370, 388 German Nation 173, 196 Bourges 178 Cologne 11, 16, 19, 42, 72–73, 81–82, 93, 96, 282–283, 322 Erfurt 282–283 Ferrara 171, 173–174, 176, 178, 180, 198–199, 203–204 Jagiellonian of Cracow 11, 13–33, Chapters 3–5, 179, 244, 279, 281, 357, 372, 374, 387, 389, 437 Oxford 14, 16 Padua 14, 22, 155, 162, 171, 173, 184, 191, 198–203 Paris 13–16, 39, 73, 93, 142, 177 Prague 14–15, 56 Tübingen 283 Vienna 35, 141, 159 Wittenberg Interpretation 405 world 91, 95, 106–107, 115–117, 131, 136, 163–164, 212, 217–223, 225, 231–233, 238–239, 277, 287–288, 297, 322, 402, 424, 429, 431 world machine (machina mundi) 223, 297, 322, 423–424
History of Science and Medicine Library ISSN 1872-0684 1. Fruton, J.S. Fermentation. Vital or Chemical Process? 2006. ISBN 978 90 04 15268 7 2. Pietikainen, P. Neurosis and Modernity. The Age of Nervousness in Sweden, 2007. ISBN 978 90 04 16075 0 3. Roos, A. The Salt of the Earth. Natural Philosophy, Medicine, and Chymistry in England, 1650-1750. 2007. ISBN 978 90 04 16176 4 4. Eastwood, B.S. Ordering the Heavens. Roman Astronomy and Cosmology in the Carolingian Renaissance. 2007. ISBN 978 90 04 16186 3 (Published as Vol. 8 in the subseries Medieval and Early Modern Science) 5. Leu, U.B., R. Keller & S. Weidmann. Conrad Gessner’s Private Library. 2008. ISBN 978 90 04 16723 0 6. Hogenhuis, L.A.H. Cognition and Recognition: On the Origin of Movement. Rademaker (1887-1957): A Biography. 2009. ISBN 978 90 04 16836 7 7. Davids, C.A. The Rise and Decline of Dutch Technological Leadership. Technology, Economy and Culture in the Netherlands, 1350-1800 (2 vols.). 2008. ISBN 978 90 04 16865 7 (Published as Vol. 1 in the subseries Knowledge Infrastructure and Knowledge Economy) 8. Grellard, C. & A. Robert (Eds.). Atomism in Late Medieval Philosophy and Theology. 2009. ISBN 978 90 04 17217 3 (Published as Vol. 9 in the subseries Medieval and Early Modern Science) 9. Furdell, E.L. Fatal Thirst. Diabetes in Britain until Insulin. 2009. ISBN 978 90 04 17250 0 10. Strano, G., S. Johnston, M. Miniati & A. Morrison-Low (Eds.). European Collections of Scientific Instruments, 1550-1750. 2009. ISBN 978 90 04 17270 8 (Published as Vol. 1 in the subseries Scientific Instruments and Collections) 11. Nowacki, H. & W. Lefèvre (Eds.). Creating Shapes in Civil and Naval Architecture. A Cross-Disciplinary Comparison. 2009. ISBN 978 90 04 17345 3 12. Chabás, J. & B.R. Goldstein (Eds.). The Astronomical Tables of Giovanni Bianchini. 2009. ISBN 978 90 04 17615 7 (Published as Vol. 10 in the subseries Medieval and Early Modern Science) 13. Eagleton, C. Monks, Manuscripts and Sundials: The Navicula in Medieval England. 2010. ISBN 978 90 04 17665 2
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