In 1543, Nicolaus Copernicus publicly defended his hypothesis that the earth is a planet and the sun a body resting near the center of a finite universe. But why did Copernicus make this bold proposal? And why did it matter? The Copernican Question reframes this pivotal moment in the history of science, centering the story on a conflict over the credibility of astrology that erupted in Italy just as Copernicus arrived in 1496. Copernicus engendered enormous resistance when he sought to protect astrology by reconstituting its astronomical foundations. Robert S. Westman shows that efforts to answer the astrological skeptics became a crucial unifying theme of the early modern scientific movement. His interpretation of this "long sixteenth century," from the 1490s to the 1610s, offers a new framework for understanding the great transformations in natural philosophy in the century that followed.
The Copernican Question Prognostication, Skepticism, and Celestial Order
The pandemic has created major supply chain challenges for publishers, manufacturers, warehousing facilities and shipping companies. Please allow for a minimum of 15 business days to receive your order. If you need your order sooner, consider purchasing from one of our retail partner links in the buying options. Thank you!
The Literature of the Heavens and the Science of the Stars
Printing, Planetary Theory, and the Genres of Forecast
In the fifteenth century, a vast and complex literature described, explained, and invoked the motions of the heavens and their influences on the Earth. From the 1470s onward, the learning of the heavens, much of it inherited from the ancient and medieval worlds, began to acquire a new sort of accessibility as it was reproduced in the medium of print. This chapter describes the broad contours of that literature and its various classifications. It shows how those categories evolved, how it worked as a body of knowledge, and the peculiar forms that it took in the sixteenth century. This corpus of writings-rather than an exclusive and autonomous stream of planetary theory-constituted the foundational categories of the intellectual world in which Copernicus was educated at Krakow and Bologna in the 1490s and in which his work took form and was later evaluated.
Interest in astrological prognosticating had begun to catch on in the Latin West as far back as the twelfth century, with the arrival of sophisticated Arabic astrological writings. Among the most influential of such works was the Great Introduction to Astrology of Albumasar (AbuʼMashar), which emphasized the preeminent effects of great planetary conjunctions. Soon, a good many medieval practitioners were attracted by the prospect of using the heavens in medical prognosis as well as retrospective diagnosis. The popular "zodiac man," representations of which abounded by the fourteenth century, mapped signs of the zodiac onto the body parts that they ruled: it assisted surgeons in deciding when to bleed the patient and guided physicians in prescribing a diet that would counteract a specific disease. The Black Death (or bubonic plague) of 1347-51, which killed one-quarter to one-third of Europe's inhabitants, greatly accelerated a sense of loss of social control and, with it, augmented the special credibility of Albumasarian causal explanations grounded in the power of planetary conjunctions. In the last decade of the fifteenth century, another new and frightening disease entity appeared, accompanying the massive movement of French armies into Italy. It too killed, but first by attacking the genitals. Was this "French disease," as many non-Frenchmen called it, caused by a conjunction of Saturn and Jupiter on 25 November 1484? Was it, soon afterward, augmented by a "horrible" solar eclipse on 25 March 1485? Or did God act directly, without need of celestial influence, to punish men for their sins? Whatever the preferred explanation, "astrology had come to stay," as Olaf Pedersen has aptly observed, "and many scholars came to regard astronomy principally as a theoretical introduction to astrological practice."
It is difficult to generalize with confidence about the full range of astrological works that were composed before the era of print. The extant remains of the considerable library of Simon de Phares, astrologer to the French king Charles VIII, may be a useful indicator; it was principally a collection devoted to the destinies of individuals. Insofar as medical astrology concerned individual patients, that would partly account for such a focus. However, the arrival of syphilis with Charles's marauding armies spawned a genre of writing about the new plague that applied not just to individuals but to groups. Ptolemy had already classified prognostications into two kinds-those concerning "whole races, countries and cities" (general) and those relating to individuals (specific). Print technology made possible the first kind in a way that had not previously existed. Just over twenty years after Gutenberg published the first book in the West, an almanac for the year 1448, the urban or regional forecast became a standard part of the literature of the heavens and soon dwarfed all other types. Although these annual prognostications occasionally circulated in manuscript, by the 1470s they appeared regularly in print and gradually began to displace hand-produced predictions.
Annual astrological prognostications were part of a larger pattern. Overwhelmingly, the celestial productions that the early printers chose to put on their trade lists were short works intended for practical use: single-leaf wall calendars, almanacs, ephemerides (tables of daily planetary positions), lunar tables, and eclipse forecasts. Ernst Zinner's bibliography of "astronomical literature" published in "Deutschland" over the period 1448-1630, comprising more than five thousand items, illustrates this contention by enabling a gross count of different sorts of writings produced by publishers in the domains of the Holy Roman Empire. One can only guess at bibliometric patterns for the rest of Europe, and it is impossible to determine absolute numbers of copies.
Gradually the emerging culture of print dressed up its products. It used a variety of new techniques to encode already existing literatures of heavenly representation, such as visually compelling title pages; epistolary dedications to a patron or general dedications to the general reader; and didactic woodcuts displaying spheres, circles, angles, and movable planetary discs, or volvelles. Regiomontanus, the earliest printer of celestial works, pioneered techniques of setting type for astronomical woodcuts, including those that he used to illustrate the models for Peurbach's New Theorics of the Planets. Print technology also had undeniable consequences for the conditions of prognostication that expanded the limited possibilities previously open to the hand copyists. First, it made possible the rapid replication and distribution of forecasts. Second, as the annual prognostication became a unique feature of print, it helped to make the astrologer into a more public figure. It also fostered demand for astrology's theoretical foundational texts and further promoted the authority of the works of theoretical astronomy on which they depended. And third, because such works were public rather than private, it changed the possibilities for offering advice to rulers and hence the conditions of prognosticatory authorship. How this shift in the social and literary conditions of forecast and advice occurred and how it was implicated in Copernicus's astronomical project is an important concern of this and the two following chapters.
Some preliminary chronological parameters will assist. Between roughly the 1480s and the 1550s, the fundamental texts of Greek and Arabic astrology were published in one edition after another. By 1524, the date for which an enormous quantity of prognostications predicted a flood of biblical proportions, the forecasting literature itself reached a scale unimaginable prior to the invention of printing. This surge in heavenly writings issued from those regions where printing had initially taken hold in various cities of the Holy Roman Empire-notably Nuremberg, Leipzig, Augsburg, and Wittenberg-and the great northern Italian city-states (particularly Venice): soon these sites were joined by another great port, Antwerp, and its neighboring university town, Louvain.
Zinner's bibliography need not be regarded as a definitive count of editions of the literature of the heavens so much as a heuristic for questioning the meaning that planetary theory held for contemporaries. Much of the received historiography makes planetary theory the core of a narrative that leads, willy-nilly, to the undeniably major achievements of Newton. Such narratives generally take their endpoints as justification for the inquiry into what precedes. What they do not explain is the vast quantity of prognosticatory literature that contemporaries viewed as significant and the relation of the genre of planetary theory to it. The primary reason that the calculation of planetary positions held such great importance was that it was necessary for the production of quantitatively based knowledge of the future of the human realm. This book, while also ending with Newton, arrives there by a route that makes prognostication central rather than peripheral.
Why should this matter of prediction be of any concern to a study about Copernicus and the subsequent meanings that contemporaries ascribed to his achievements? Copernicus's formidable position in the history of astronomy and in the historiography of the Scientific Revolution is hardly open to dispute. Yet both among his biographers and among many historiographers of the Scientific Revolution, Copernicus appears as something of a pristine figure in relation to astrology, let alone the bibliometrics to which I have referred. Despite some suspicion that this view is not quite viable, no one has yet seriously challenged the strong position articulated by Edward Rosen. "Did Copernicus believe in astrology?" asked Rosen, and he answered his own question as follows: "This is an extraordinary aspect of Copernicus's mentality. He lived in an age when many of those in power as well as of those on the lower rungs of the social ladder believed in astrology. [Copernicus] did not." And, in his comments on the single instance of the term astrology in Copernicus's extant writings, he stated forcefully: "Fortune-telling astrology received absolutely no support from Copernicus. In this respect he differed markedly from Brahe, Galileo, and Kepler, to mention only a few of the celebrated astronomers who believed in astrology and practiced it for one reason or another. In particular, the contrast between Copernicus and his disciple Rheticus in this regard is complete. Nowhere in the Revolutions nor anywhere else in the unquestionably authentic writings of Copernicus can the slightest trace of belief in astrology be found. On the other hand, Rheticus's addiction to astrology is notorious."
Even authors quite willing to admit into account considerations rejected by Rosen have not found Copernicus easy to integrate into their narratives. "The Copernican Revolution provides the blueprint for the Scientific Revolution as a whole," Charles Webster declared in his influential 1980 Eddington Memorial Lectures. But Webster began with Paracelsus because he could find no evidence to link Copernicus himself with prophecy and eschatology, let alone astrology. And in one of an excellent collection of essays devoted to assessing astrology in early modern science, Keith Hutchison presented a great quantity of convincing illustrations from churches, town halls, instruments, and frontispieces showing that the sun was frequently placed symbolically at the center or associated with the figure of the king, but he did not find any direct evidence linking Copernicus to astrology.
The closest that anyone has come to drawing a plausible connection was J.L.E. Dreyer in his 1905 classic History of Astronomy from Thales to Kepler. Dreyer called attention to a political prophecy inserted near the middle of Rheticus's Narratio Prima (1540), the first work to describe Copernicus's claims in print. This cyclical prophecy predicted that as the Earth's eccentricity slowly changed, different kingdoms would rise and fall. Dreyer admitted that "nothing of this theory of monarchies is mentioned by Copernicus himself" but then suggested that Rheticus would not have inserted such a prophecy without Copernicus's permission. Rosen effectively dismissed Dreyer's speculation. He wrote off the forecast as superstitious nonsense, ascribing it to Rheticus's exuberance and youth while absolving Copernicus of any association with it whatsoever.
The Rosen-Dreyer disagreement still divides scholars. Yet in my opinion Dreyer was on the right track: indeed, his observation can be taken a good deal further. Here I briefly anticipate a preliminary argument against Copernicus's supposed immunity from astrological concerns. Planetary order became problematic for Copernicus within a shared structure of literary and epistemic possibilities that included both the domains of planetary theory and the prognostication of earthly effects. One reason that the link to astrological prognostication is not so obvious is that Copernicus, like other authors of his time, followed conventions of compositional form that included and excluded certain subjects. The prevailing view, widespread among the humanists, held that ancient works represented the ideal stylistic models for the organization and presentation of knowledge. Stylistic models, however, were not merely the subject of high literary theory; stylized conventions were communicated by repetition through the curriculum of Renaissance grammar schools. This practice is well documented for Italy, where students were given Cicero's writings-especially his letters-as examples to be closely emulated for vocabulary, content, and form. Early modern authors thus had a well-schooled sense of rhetorical boundaries and decorum. Copernicus's major work was thus not exceptional in closely following the organization of Ptolemy's treatise of theoretical astronomy, the Mathematical Syntaxis (commonly latinized as the Almagest, after the Arabic). The Almagest provided the models and parameters from which one could make specific predictions for the planets' angular positions but said nothing about its effects on particular persons or geographical regions. For Ptolemy, the prediction of specific effects fell into the separate domain of astrology, and to that subject he devoted a separate work, the Tetrabiblos (or Quadripartitum). Later I will show that, for sixteenth-century readers, the Tetrabiblos was effectively more than a single work.
Practices of Classifying Heavenly Knowledge and Knowledge Makers
The question of Copernicus's exceptionalism is entangled in a dense thicket of knowledge categories and forms of presentation that are anything but obvious. If we want to make sense of his stated intentions as well as his silences (which are many), our account should try to mirror the thickness of these representational resources. To begin, however, it is useful to remind ourselves of what they were not. Copernicus did not present his work in a culture of emerging specialization and professionalization like that of, say, nineteenth-century Germany or England. There were no self-conscious specialty groups with their own journals, no characteristic research techniques and professional ideals of academic advancement, let alone a concern with common standards of measurement. The late-fifteenth- or early-sixteenth-century academic practitioner of Copernicus's time had little resemblance to his counterpart in the bureaucratic university of the late twentieth century, which one historian has called a "factory system"-"the student ... a 'pair of hands' working for the greater glory of his supervisor, the department as a conveyor belt for the production of Ph.D.s, the publication of papers as a sort of dividend."
The sixteenth-century sense of the learned professions and disciplines was hierarchical. Some writers imagined the organization of the professions as a mirror of the aristocratic hierarchy of social ranks or the order of the natural world. But a variety of different criteria were employed for organizing the ranks of knowledge. They might include the subject matter's moral dignity, nobility, historical ancestry, or degree of abstraction; its degree of certitude; its practical value; and the order in which the disciplines were best taught-or some combination thereof. The Renaissance rhetorical fashion for praising or satirizing the professions depended on which of these criteria were favored and in which combination. Regiomontanus, for example, praised Euclid's theorems for possessing the same certitude as they had a thousand years earlier, while opposing them to the uncertainties betokened by the many branches of scholastic philosophy. Copernicus praised the heavenly art ("which is labeled astronomy by some, astrology by others") for the perfection of its subject matter and for its pleasures in contemplation prior to describing the disagreements of its practitioners about principles and assumptions. For Francesco Capuano de Manfredonia, a prolific commentator on John of Sacrobosco's Sphere-the standard, elementary introduction-astronomy's subject matter was physical in its concern for bodies in motion, celestial spheres, and influences, and, in that sense, it fell under natural philosophy; but its methods were also mathematical and, in that sense, were capable of secure demonstrations. Yet, ultimately, Capuano decided that astronomy's demonstrations were "more physical than mathematical." A century after Regiomontanus, Tommaso Garzoni imagined a "universal piazza of all the professions in the world," a survey that ranged from university professors and theologians to cooks, chimney sweeps, prostitutes, and latrine cleaners. Even as Garzoni used comic inversion to rebuke and undermine, he assumed the hierarchical pretensions of the higher professions. Yet pedagogically, the early modern academic could have competences in quite different subjects and was capable of teaching in quite different disciplines while respecting and never challenging the boundaries separating them. Although some prominent early seventeenth-century voices favored the discovery of new knowledge, research as an ideal that embodied originality did not emerge until at least the German philology seminars of the late eighteenth century.
Consequently, not much can-or should-be taken for granted, not even epistemic categories as crucial as science, theory, practice, or truth; disciplinary designators as seemingly apparent as astronomy, astrology, and cosmology; or genres of writing, authors' print identities, and titles assigned to works. None of these notions carried quite the meanings that we would now ascribe to them. But why assume that they should? At best we can try to work out some stable points of signification. Consider, for example, the exchangeable Latin terms scientia stellarum, scientia astrorum, and syderalis scientiae, which may all be translated as "the science of the stars." Whatever their earlier medieval usages, in the sixteenth century these words-rather than astronomy or mathematical astronomy-actually covered the entire subject matter of the study of the heavens. Although arguably the term scientia can be rendered as "knowledge," that translation has the disadvantage of being too vague and general; it fails, for example, to target distinctions that historical agents sometimes made between explanation and description, cause and effect. On the other hand, scientia clearly did not carry the later connotation of science as a special type of method for gaining knowledge (e.g., a specialized or singularly rigorous form of self-correcting knowledge) or vocational training in highly specialized skill sets. Thus we can admit the term science into our descriptive tool kit as long as we are careful not to conflate earlier with later usages. Further along, we shall see that for contemporaries, the phrase "science of the stars" actually encompassed the subject matters of both astronomy and astrology, and each might be further subdivided into theoretical and practical parts.
Terms denoting social roles or identities are another matter. The word scientist, as is now well known, did not exist before the 1830s. It was not an operative category in preindustrial Europe. Its appearance coincided with the emergence of a professionalizing impulse in the scientific movement that evolved in early Victorian Britain. Historians of twentieth-century science do not worry about the strangeness of this term; but historians of our period of concern are now more comfortable designating Newton as a natural philosopher or a physico-mathematician than a scientist. The diversity of early modern usages-especially in those areas of knowledge that mixed together mathematical and physical elements-is a question of empirical investigation.
One approach to sustaining the historical integrity of past social agency is to make a virtue of our limited knowledge and to focus on how authors represented their identities or those of others in the works that they published. Copernicus, for example, wrote that "mathematics is written for mathematicians." Edward Rosen chose to translate this famous passage as "Astronomy is written for astronomers," straining to get the text's language into agreement with his own assumptions about how Copernicus conceived his role. But neither my rendering nor Rosen's is quite satisfactory without further qualification. For the historian to call Copernicus a mathematician evokes confusing associations with the current domain of meaning, in which mathematicians may or may not test hypotheses against the physical world; and to call him an astronomer overrides the meaning that mathematicus had in the sixteenth century, that is, someone skilled in any subject that involved mathematics-for example, optics, music, statics, or astrology. An author's self-representation or print identity-the way he presented himself on the title page and within his writings-thus carries considerable methodological utility. The title-page identity is how that author was often known to readers. Similarly, the language that one author used to characterize another can often provide clues to the larger field of representation-how, for example, he understood (or misunderstood) the authors he had read and how he classified their aims and historical circumstances.
Authorial self-designations were at least as strangely varied as the often-interchangeable singulars astronomus, astrologus, and mathematicus or the conjunctions medicus et astronomus, iatromathematicus, medicus et mathematicus, preferred by academics who held more than one chair in those subjects; the pompous theologastrosophus (wise theologian of the stars); the nonacademic prognosticator who likened himself to a cosmographus (cosmographer or geographer) by the designation astrographus (astrographer); the late fifteenth-century author of an astrological judgment who said that "not for nothing" was he called phisicus et astrologus; the slightly ambiguous "lovers-of-wisdom" forms that may have been used to conceal the absence of other credentials, such as astrophilus, philomathus, Mathematik Liebhaber, or simply astronomiae studens; and the quite specific identity of an author as the "student of" someone famous (discipulo del).
Apart from what authors called themselves on their title pages, it is also useful to note how authors coded others of their kind. Such contemporary practices of authorial classification were anything but standardized. A useful example is that of the Florentine Francesco Giuntini (Junctinus, 1523-90), who, at the end of a massive two-tome work on astrology, included a "Catalogue of Learned Men whose notes and productions benefited us in completing the Mirror of Astrology." Effectively, it was an index of names distributed throughout the work's more than 2,500 pages. The censors who granted permission for the work to be published described Giuntini himself as a "Doctor of Sacred Theology" ("sacrae Theologiae Doctoris") and the royal privilege ("Extraict du Priuilege du Roy") described him with the title "Doctor of Theology and Chaplain to Our Very Dear and Much-Loved Brother, the Duke of Anjou." Never mind that the work of this "theologian" was a massive portable library for defending "good astrology" that contained an edition of Ptolemy's Tetrabiblos, spherics and theorics, lengthy treatises on all aspects of theoretical astrology, and an abundance of horoscopes of famous men.
The ninety-nine names in Giuntini's catalogue illustrate-although they do not exhaust-some typical features of the language and assumptions that he and others used in constructing authorial classifications. The overall structure does not lack coherence, but its anachronisms, inconsistencies, and omissions, easily spotted with hindsight, provide clues for illuminating the unregulated and arbitrary space of authorial representation. Anaximander and Thales, for example, have been readily assigned sixteenth-century professions ("astrologus"; "astronomus"). Likewise, Hipparchus is an "astrologus" but notably not an "astronomus." In addition, the list reflects the contingencies of what Giuntini himself took from his own reading-especially authors' print identities. Marsilio Ficino is an "astrologus" associated with a school ("Platonicus") but is not called a philosopher, whereas Pico della Mirandola is a "poet, orator and philosopher" but is not associated with a school. Vitelo, who wrote on optics in the thirteenth century, is called a "mathematicus," whereas Ptolemy was an "Egyptian astrologer" but not a "mathematicus," and Hermes was an "Egyptian" but not an "astrologus." Messahala (Mashaʼallah ibn Athari), a Jew who wrote about astrology, is an "Arab," while al-Battani, an Arab, is an "Egyptian astrologer."
Coming closer to Giuntini's own time, Regiomontanus is "a man famous in all kinds of mathematics" but is not presented as having any relation to astrology. Leovitius and Stadius are both represented as "astrologers," but although both were well known at the time for their ephemerides, the former is called an "astronomus," whereas the latter is designated a "mathematicus." In much the same way, Christopher Clavius, author of a highly regarded commentary on Sacrobosco's Sphere, is called a "mathematicus" but not an "astronomus" or a "Jesuit." By contrast, the thirteenth-century Spanish king Alfonso X, who lent his name to the important planetary tables still being used in Giuntini's time, curiously merits the title "astronomus." The list excludes Protestant authors and is unusually attentive to authors' membership in different orders of the Catholic Church; but Giuntini does not hesitate to analyze (negatively) the horoscopes of numerous Protestant authorities, such as Osiander and Melanchthon.
Finally, Giuntini used the adjectives famous (insignis) and excellent (eximius) to designate authors of whom he was especially approving: his own teacher, Brother Giuliano Ristori, the "Famous Carmelite Mathematician"; Lucio Bellanti, "Famous Astrologer and Physician of Siena"; Georg Peurbach, "Famous Astronomer"; and Roger Bacon, "Astrologer and Excellent Philosopher." These examples suffice to illustrate the great variability in attributions of authorial identities and the dangers of too hastily imposing our own role designators and categories. Thus we cannot be altogether surprised by an entry in Giuntini's astrological calendar: "Nicolaus Copernicus of Torun, Varmian Canon, born 19 February 1472, 4h 48m P.M." More interesting than Giuntini's error on the year of Copernicus's birth is his decision to call him a canon rather than a famous astronomer.
Besides authorial representation, the language and syntax of a book's title were important means by which an author signaled the category to which the work belonged-a quick guide to a book's rhetorical location. The sixteenth and seventeenth centuries were a period of great innovation, warfare, and religious polemic. Heavenly works announcing controversy or difference sometimes borrowed or echoed such rhetoric in their titles with terms like new, great, defense, against, mystery, and reformed. Conversely, works announcing new entities like comets often resorted to the more neutral-sounding observation, description, or method. By far the most common terms were the plethora of designations learned in the schools: commentaries, principles, elements, rudiments, questions, disputations, doctrines, dissertations, assertions, propositions, problems, demonstrations, epitomes, instructions, uses and exercises, introductions (isagoge), forerunners (prodromus), and visual sketches (hypotyposes). And finally, there were works following ancient models that simply named their subject with the prepositions of, on, or about. De Revolutionibus was such a work, a general exposition of a subject.
Other, more general epistemic criteria could also be deployed as resources for organizing one kind of knowledge with respect to another by rank or precedence. This practice is apparent where an author defines one work as the necessary prelude to another. Ptolemy, for example, defined the Tetrabiblos in relation to astronomy, and sixteenth-century readers took "astronomy" to refer to the Almagest, his major work on the planets. In contrast, the original relationship of the Almagest to the Planetary Hypotheses, the work that contained Ptolemy's physicalized representations of the Almagest's models, was unknown because no Latin work explicitly attributed the latter work to Ptolemy's authorship.
The criteria of precedence underlying the relationships of such works were ultimately beholden to Aristotle's own disciplinary classifications. In the Physics, Aristotle classified astronomy, optics, and harmonics as sciences that combined mathematics and physics. These mixed subjects were to be regarded as in some sense "rather more physical than mathematical" or "the more physical part of mathematics." The difficulty of establishing the meaning of Aristotle's imprecise language reflects, in turn, his own struggle with Plato's view that unchanging reality resided not in matter but in universal Forms. For Aristotle, the student of optics as well as the physicist would be interested in the object's mathematical form-say, the apparent diameter of the Moon-as mentally abstracted and hence separable in thought from matter, but then adding to that form a reality that was physical. Richard McKirahan discusses an example of this kind of subordination from Euclid's Optics, a treatise on illusions of linear perspective: as different angles are formed with the eye E at the vertex (AEB, BEC, CED), the segments representing the Moon's diameter (AB = BC = CD) appear to change, such that AB will appear greater than BC and BC greater than CD. One inferred physical content effectively by invoking the translation rule that straight lines represent light rays. The geometer is only concerned with the lines and angles as a matter of reasoning and mental abstraction, whereas the optician is interested in the apparent changes in the Moon's size and apparent brightness as produced by the angles and the physical substrate of light rays entering the eye.
In this example, geometry treats properties of lines, angles and their relative magnitudes; but physics concerns the nature of the ray itself. They consider and describe different aspects of the same phenomena. In his work on logic, the Posterior Analytics, Aristotle says mathematics is the subject that provides the "cause" or "the reasons why." Yet the geometer need not know the subject matter of optics (the "fact" about the nature of light rays) in order to demonstrate various properties of lines, angles, and triangles; the geometer "explains" or "demonstrates" that abstracted visual lines trace out straight lines that form angles with the eye. This did not mean, however, that mathematics had epistemic precedence over physics, as Aristotle maintained that the forms with which mathematics are concerned are "not said of any underlying subject." Although mathematics could account for the shape of a physical object, it did not thereby determine the object's nature. This ontological tension between form and matter in Aristotle's diverse writings reflects his encounter with Plato's doctrine of forms, a position toward which Aristotle may have moved over his lifetime. In any case, Aristotle's scattered statements left plenty of work for his later commentators and thereby allowed differential uses of his authority.
Ptolemy is an example. He was explicitly indebted to Aristotle's divisions of knowledge, but he leaned toward Plato in granting to mathematics a secure capacity for knowing, rather than to physics, whose subject was sensory and variable, or to theology, whose subject was eternal and could only be guessed at. For if matter is ever-changing and corruptible, the mathematician can still determine whether motion "from place to place" is circular, or whether a body moves in straight lines toward or away from the center. As for the main physical propositions needed to ground the astronomy of the Almagest-the finite sphere and the Earth's immobility at its center-Ptolemy used a counterfactual argument based on what we would observe about falling (or flying) bodies were the Earth to rotate daily on its axis, but he made no reference to the Pythagoreans' annual motion. Thus essentially he endorsed the same conclusion about the Earth's immobility that Aristotle had reached when he appealed for explanation to the physical natures of the things moved. But Ptolemy reserved for the Planetary Hypotheses an account of the unobservable ether's parts as fine, small, rarefied, and also "more homoeomerous," that is, more similar in shape than elemental bodies. And the solid orbs in which he wrapped his geometrical models were essentially built to fit; one could simply translate the geometry of the motions into a geometry of solid, convex, and concave shapes which the perfectly similar aetherial bodies could be said to constitute. By thus carefully segregating his discussion of the eternal aether from the Almagest, Ptolemy reinforced the separation of the specific mathematical techniques and routines of calculation from considerations of celestial physics.
In the sixteenth century, an important instance of how the geometrical models were wedded to the physical spheres occurs in the case of Peurbach's "theoric of orbs." Interpreting Peurbach's diagrams for his readers, the Wittenberg astronomer Erasmus Reinhold wrote: "The eccentric orb having been set up, they [astronomers] then gather together physical reasons whereby they attach to it two other orbs of unequal thickness-one above, the other below-so that the total sphere is made concentric with the center of the world, lest it be necessary to assume a vacuum or that celestial bodies are mutually torn apart." On Reinhold's reading-which not all commentators shared--the astronomer first constructed the geometrical model and then added (or subalternated) the physical substrate, thereby filling up the gaps to preserve a plenum. The off-center "partial orb" (white region), the epicycle diameter of which defined its width, was surrounded by a composite of two, dark-shaded, lunule-like shapes-one concave, the other convex. Reinhold had nothing further to say about the precise physical status of this inner, shaded region.
Reinhold's contemporary Andreas Osiander provides another important instance of how these uncertain relations could be managed. He took it upon himself to defend Copernicus in his famous, unsolicited "Ad Lectorem" ("Letter to the Reader"), which he added without the author's permission to the front matter of De Revolutionibus. Osiander emphasized that the mathematical part of astronomy can produce hypotheses but that these hypotheses can never be known to be true or even probably true. Because the premises of the mathematical part could never be known with certainty, this part could never be a demonstrative science. However, the physical part could be demonstrative in the sense that its premises are "divinely revealed." Thus, without specifying any such divinely revealed physical premises, Osiander implied that natural philosophy must be the superior science within the disciplinary couple constituting astronomy, thereby providing it with whatever secure proofs it possesses. To think otherwise would "throw the liberal arts into confusion"-a charge from which Osiander thought to protect Copernicus.