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The Decline of Space: Euclid between the Ancient and Medieval Worlds

Michael J. Sauter División de Historia Centro de Investigación y Docencia Económicas, A.C. Carretera México-Toluca 3655 Colonia Lomas de Santa Fe 01210 México, Distrito Federal Tel: (+52) 55-5727-9800 x2150 Table of Contents List of Illustrations ...... iv Acknowledgments ...... v Preface ...... vi Introduction: The divine and the decline of space ...... 1 Chapter 1: Divinus absconditus ...... 2 Chapter 2: The problem of continuity ...... 19 Chapter 3: The space of ...... 21 Chapter 4: Euclid in ...... 40 Chapter 5: The ladder of ...... 63 Chapter 6: The harvest of homogeneity ...... 98 Conclusion: The deracinated ...... 125 Bibliography ...... 128

iii

For tribal man space was the uncontrollable mystery. For technological man it is that occupies the same role. --Marshall McLuhan (1951) 1

1Marshall McLuhan, : Folklore of Industrial Man (New York: Vanguard Press, 1951), 85.

vii Chapter 3: The space of hierarchy

The Christian should beware of Mathematicians and all those who make empty prophesies. The danger already exists that the Mathematicians have made a covenant with the Devil to darken the and to confine man in the bonds of . --Augustine of (354)1

Western thought between 350 and 900 was tinctured by an overlooked intellectual phenomenon, the absence of Euclid’s Elements. This absence is odd, since unlike many classical texts the Elements did not disappear with post-Antiquity’s arrival. When the

Roman Empire broke apart in the fifth century AD, both its -speaking western half and Greek-speaking eastern halves maintained contact with Euclid’s work, with the former clinging to incomplete copies of the Elements and the latter complete ones.

Despite this accessibility, however, Euclid’s thought entered isolation, as late Antique

Christian thinkers were more interested in understanding humanity’s relationship to God and Creation, than in contemplating idealized points, lines, planes, and spheres. Indeed,

Christian thought between the fourth century and the end of the twelfth was decidedly post-Euclidian, in so far as its preoccupations were not amenable to the Elements’ space.

It was only in the early fourteenth century (and then only in the former Empire’s western half) that Euclid touched religious issues anew.

In this chapter and the succeeding one, the world from which Euclid and homogeneous space were conspicuously absent. In this chapter I examine Euclid’s slow departure from Western thought, between the years 350 and 900, and emphasize how the

1Augustine of Hippo, "De Genesi Ad Litteram," in Opera Omnia, ed. A.B. Caillau and M.N.S. Guillon (Parisiis: APud Parent-Debarres, 1835), 218-19.

21 Mediterranean’s growing preoccupation with hierarchy—whether with respect to the theological or philosophical status of —made medieval European thought impervious to Euclid’s influence. In the next chapter I pick up the story after the year

1000 and will explain how in the course of the eleventh and twelfth centuries, in spite of profound changes in multiple areas of medieval thought, the resistance to homogeneous space intensified. It was only when the early fourteenth century wrought a theological transformation that the application of homogeneity to every part of Europe’s mental cosmos became possible.

Euclid’s medieval absence was foretold by the Mediterranean’s religious ferment of the fourth and fifth centuries. Some of this was Christian, although much of it was not.

With respect to early ’s Fathers, most of whom were born before 400, none mixed the Elements into their amalgams of Christian and pagan —and this was regardless of whether they wrote in Greek or Latin, the former being Euclid’s native tongue.2 Basil the Great, a Greek speaker from Anatolia who was born around 330, paid little attention to Euclid, and , a Latin-speaking

North African who was born in 354, did much the same. Although Augustine dabbled initially in , he turned away from further study and also chided his co- religionists in On the of the not to discuss pagan disciplines that they did not understand.3 It was best, so he thought, for Christians to stick to what they knew, i.e., their sacred texts. Given the ’ influence, it is not surprising

2In general, see Etienne Gilson, of in the , The Lifetime (New York: Random House, 1955); John Marenbon, Early (480-1150) : An Introduction (London: & K. Paul, 1983); Colish, Medieval Foundations; Jorge J. E. Gracia and Timothy B. Noone, eds., A Companion to Philosophy in the Middle Ages, Blackwell Companions to Philosophy (Malden: Blackwell Publishers, 2003). 3John Hammond Taylor, ed. The Literal Meaning of Genesis, 2 vols., vol. 1, Ancient Christian Writers (New York: Newman Press, 1982), 39.

22 that for a millennium no one on either side of the Latin-Greek divide applied Euclid to

God. Substanceless points, breadthless lines, depthless planes and locationless spheres were afterthoughts for a that confronted profound mysteries, such as the ,

Creation, and why God became man.

Christian disregard of Euclid was, however, only one factor in the Elements’ withdrawal. The ancient Roman world was dissolving in ways that had powerful effects across the Mediterranean basin. In 313, Constantinople was consecrated as a new capital in the east, inaugurating a process that left the empire divided in into two linguistic halves, with Greek dominating in the east and Latin in the west.4 Moreover, even on the

Italian peninsula itself, Rome’s as an imperial capital was fading. In the fourth century, the western empire’s capital became , followed in the fifth century by

Ravenna—both of which in the Italian boot’s north.5 Finally, one byproduct of

Rome’s general decay was the western zone’s retreat into monolinguality, as a once cosmopolitan limited itself to mere Latin. Since the Elements was composed in

(and remained in) Greek, the potential audience in the west for Euclidian space, which had always been small, became even smaller.

There was one attempt to swim against these powerful currents. In the mid-sixth century, the Roman Christian Anicius , who served the Ostrogothic king

Theodoric, made the only known late-Antique of the Elements into Latin.6

4Ralph-Johannes Lilie, Byzanz: Das Zweite Rom, 1. Aufl. ed. (Berlin: Siedler, 2003). 5A. K. Bowman, "Diocletian and the First , A.D. 284-305," in The Cambridge Ancient History: Volume Xii, the Crisis of Empire, A.D. 193-337, ed. Stanley Arthur Cook, et al. (London: Cambridge University Press, 1966), 74-78. 6On this history see, Menso Folkerts, Boethius Geometrie Ii: Ein Mathematisches Lehrbuch Des Mittelalters (Wiesbaden: Steiner, 1970); John Murdoch, "Euclid: Transmission of the Elements," in Dictionary of Scientific Biography, ed. Charles Coulston Gillispie (New York, NY: Charles Scribner's Sons, 1971); Menso Folkerts, "Euclid in Medieval Europe," in The Development of Mathematics in

23 This version did not, however, circulate widely.7 Equally important, it was incomplete, as it included only the first five of the original thirteen books.8 (The five in question cover plane geometry, whereas discussions of three-dimensional geometric objects appear only in the final three books.9) Boethius’ Elements dealt purely with two-dimensional geometry (triangles, circles and such) and, thus, presented the reader with a distinctly

“flat” Euclid. Even more telling, perhaps, is that Boethius’ translation disappeared, as mere fragments (at best) were preserved in other medieval works on geometry, many of which were informed by Roman-era works on agricultural measurement.10 Although have celebrated the medieval echoes of Euclid, the contents of the various only underscore three-dimensional space’s absence, since none of them goes beyond the Elements’ fifth book either.

The fate of Boethius’ translation epitomizes the slow withdrawal of geometric space from . Euclid’s Elements was part of an ancient tradition of projecting space onto the physical world that dated back, at least, to in the sixth century BC. As a result, many famous ancient thinkers, such as , and

Democritus not only had access to Greek geometric traditions but also pondered space’s

Medieval Europe: The Arabs, Euclid, Regiomontanus ed. Menso Folkerts, Variorum Collected Studies Series; 811 (Aldershot: Ashgate, 2006), 2. 7John Marenbon, Boethius, Great Medieval Thinkers (Oxford: Oxford University Press, 2003), 15. 8There is disagreement about exactly how much of Euclid survived. But no one has suggested that anything but the earliest pat of the text made its way into Latin. Menso Folkerts, Euclid in Medieval Europe (Benjamin Catalogue for , 1989); The Development of Mathematics in Medieval Europe: The Arabs, Euclid, Regiomontanus, Variorum Collected Studies Series; 811 (Aldershot: Ashgate, 2006); "The Importance of the Pseudo-Boethian Geometria During the Middle Ages," in Boethius and the Liberal Arts : A Collection of Essays, ed. Masi, Utah Studies in Literature and (Berne Peter Lang, 1981); H. L. L. Busard, Menso Folkerts, and J. P. Hogendijk, eds., Vestigia Mathematica: Studies in Medieval and Early Modern Mathematics in Honour of H.L.L. Busard (Amsterdam: Rodopi, 1993); Kurt Vogel and Menso Folkerts, eds., Kleinere Schriften Zur Geschichte Der Mathematik, 2 vols., Boethius (Stuttgart: Franz Steiner Verlag, 1988). 9I have used the following modern edition: Euclid, Euclid's Elements: All Thirteen Books Complete in One Volume, trans. Thomas L. Heath (Santa Fe: Green Lion Press, 2002). 10Folkerts, Mathematics in Medieval Europe; O. A. W. Dilke, The Roman Land Surveyors: An Introduction to the Agrimensores (Newton : and Charles, 1971), 26.

24 most basic philosophical implications. Aristotle and , for instance, rejected geometry’s homogeneous space, if for different , while Plato accepted geometry but emphasized the symbolic use of forms over the of space itself. As I will explain the next chapter, medieval thinkers avoided these philosophical resonances by concentrating on practical things, such as measuring fields of grass. However important land measurement was for a that was clearing Europe’s forests, the restriction of geometry to the practical realm exemplified the discipline’s isolation from bigger theological issues. Boethius’ translation disappeared, in part, because no one needed access to a of space—and as the tide of indifference rose, the Elements became completely submerged.

Euclid’s decline was, nevertheless, not a purely Christian phenomenon, but was also product of other Mediterranean that had contributed to the new religion’s rise.

In the west the crumbling empire’s Germanic overlords showed no more interest in

Euclidian geometry than had Basil or Augustine. Indeed, Theodoric had Boethius executed, although for reasons that were quite separate from his translation of the

Elements.11 And as the barbarian interlopers converted to Christianity, they joined a contemplative culture that paired reflections on God with disregard of the Elements. In the burgeoning east, meanwhile, the political situation was different, but the intellectual result the same. Beginning with Constantine’s reign in the fourth century AD, the emperors in Constantinople were no more likely than their barbarian counterparts to support geometry, but concentrated instead on the elaboration of Christian .12 In

11Marenbon, Boethius, 9-10. 12Frances M. Young, From Nicaea to Chalcedon: A Guide to Literature and Its Background (London: SCM Press, 1983).

25 the year 325, for instance, Constantine oversaw a conference in Nicea that produced the

Nicene .13 Still recited in contemporary churches, it begins:

We believe in one God,

the Father, the Almighty,

maker of heaven and earth,

of all that is, seen and unseen.

We believe in one Lord, Jesus ,

the only Son of God,

eternally begotten of the Father,

God from God, Light from Light,

true God from true God,

begotten, not made,

of one Being with the Father.

Through him all things were made.14

This text exemplifies the Christian interest in hierarchical being. In eleven lines

Constantine’s theologians established God’s primordial unity, his in Creation, and his sojourn in human form. And the text contains but eleven lines more, which collectively elaborate the of the , which is the Trinity’s third component. This is quite a journey for all of three paragraphs.

13Ibid., 43; Richard Price, "Fathers and the Church Councils," in The Wiley Blackwell Companion to , ed. Kenneth Parry, Wiley Blackwell Companions to Religion (Malden: Wiley Blackwell). 14Episcopal Church, The Book of Common Prayer and Administration of the and Other Rites and Ceremonies of the Church : Together with the Psalter or of David According to the Use of the Episcopal Church (New York: Church Hymnal , 1979), 326.

26 The incorporated two then-rising currents that long sustained

Euclid’s absence. First, early Christians inherited a hierarchy of being, in which God was qualitatively “above,” while everything else was “below.” Second, they associated this spiritual hierarchy with a physical one that was rooted in a geocentric . (This cosmos is outlined for ancient Christians in the Book of Genesis, on which Augustine, not coincidentally, wrote his commentary, On the Meaning of Genesis. Pagans, for their part, cultivated the same cosmology, but emphasized different texts.)15 Thus, within late

Antiquity’s mental cosmos human looked up to the heavens and to God, simultaneously. The mixture of spiritual hierarchy within an inherently terrestrial was, nevertheless, fundamentally incompatible with the Elements’ notion of uniform space. Euclidian geometry understands geometric points both as nothing and as equal, with no point having greater positional than any another. (The Elements’ first line is, after all, “A point is that which has no part.”16) As a result, a rising

Christianity’s most profound assumptions about God and the cosmos necessarily marginalized Euclid.

The call of the divine

Although I have concentrated on the early Christian disregard for Euclidian geometry and its attending of space, it is important to note that the pagan realm turned away from space, too. Some of the resistance came from an unexpected source,

15For the Christian view, see Genesis 1: 1-31. I have used the following edition: New American Standard , 1st ed. (Carol Stream, IL: Creation House, 1971), 1-2. For key ancient texts on the cosmos to which I return in chapter two, see Aristotle, The Complete Works of Aristotle: The Revised Oxford Translation, 2 vols., vol. 1, Bollingen Series Lxxi (Princeton: Princeton University Press, 1984); Claudius Ptolemy, Ptolemy's Almagest, trans. G. J. Toomer (Princeton: Princeton University Press, 1998). 16Euclid, Euclid's Elements. I will return to this issue in the next chapter.

27 Chapter 5: The ladder of reason

God is an intelligible sphere, whose center is everywhere, and whose circumference is nowhere. --Alan of Lille (ca. 1170)146

Ancient geometry was long overshadowed by philosophical and theological developments that, from a contemporary perspective, had little to do with the discipline.

As I argued in the previous two chapters, between 350 and 1050 both late antique and early medieval Christians absorbed ’s penchant for using geometry to illustrate the relationship between the mundane and the divine, rather than to project and manipulate idealized space. This trend increased in intensity between 1050 and 1300, particularly prominent around 1200, in the wake of Aristotle’s return to

Europe. This latter development was crucial, because Aristotle cultivated a fractured space that denied geometry’s general applicability to the cosmos. On the one hand, he held that space was not diffused in a geometric sense, but that spaces were defined by whatever contained them. On the other hand, he transferred this idea to the cosmos, arguing that the concentric crystalline spheres that surrounded the Earth contained their own spaces. For Aristotle the cosmos did not exist within a space, but comprised multiple spaces. This approach had powerful implications for how medieval thinkers envisioned the cosmos, as well as for how they understood its relationship to both God and Man.

The high medieval appropriation of Aristotelian space yielded a cosmovision that was riven by a fundamental spatial .147 Heaven, where God resided, was

146J. P. Migne, Patrologiae Cursus Completus ... Series Latina, 221 vols., vol. 210 (Parisiis: Apud Garnieri Fratres, editores et J.-P. Migne successores, 1841), 627. Also available in Alan of Lille, Liber Viginti Quattuor Philosophorum (Turnholti [Turnhout, Belgium]: Brepols, 1997), 7.

63 understood to be not only above but also perfect, while the Earth, on which humanity dwelled, was both below and imperfect. The boundary between the two realms was demarcated by the Moon’s crystalline sphere, with those planets higher up being borne by other spheres. Along these lines, it is critical that Aristotle also held that heaven was qualitatively different from what lay below, because this paralleled Christianity’s view that the God was “above.” Moreover, since medieval Christians also believed their God to be omnipresent, it was easy to pair Aristotle’s emphasis on the cosmos’ basic with their own view of the divine. Thus, to the extent that the Christian

Aristotelian cosmos comprised a whole, it was not rooted in spatial homogeneity’s pervasiveness, but in divine rationality’s ubiquity.

The medieval philosophical-theological bulwarks against homogeneous space were eroded, however, when late medieval thinkers began to question “rationalist” approaches to God.148 It will not come as a surprise that this volte-face was a complicated process that comprised many critics who dotted the continent. I concentrate in this chapter on one group of critics that was located at the . Between

1300 and 1350, there arose at Oxford a corrosive tradition that is called —not altogether correctly—and that undermined older notions of the divine’s relationship to

147On the medieval cosmos’ physical structures, see: Edward Grant, Planets, Stars, and Orbs: The Medieval Cosmos, 1200-1687 (Cambridge Cambridge University Press, 1996); "The Medieval Cosmos: Its Structure and Operation," Journal for the History of 28 (1997); Science and Religion, 400 B.C. To A.D. 1550 : From Aristotle to Copernicus, Greenwood Guides to Science and Religion (Westport: Greenwood Press, 2004). 148I am borrowing heavily from the following works, although their collective tendency is to emphasize the rise of science, rather than of space: James Hannam, God's : How the Medieval World Laid the Foundations of Modern Science (London: , 2010); Edith Wilks Dolnikowski, : A View of Time and a Vision of in Fourteenth-Century Thought, Studies in the History of Christian Thought (Leiden ; New York: E.J. Brill, 1995); George Molland, Mathematics and the Medieval Ancestry of , vol. 481 (Variorum Publishing, 1995); John Freely, Before Galileo: The Birth of Modern Science in Medieval Europe (New York: Overlook Duckworth, 2012).

64 the cosmos.149 Nominalists such as the Oxford-trained undermined the confidence in reason’s divine ubiquity and emphasized, instead the contemplation of the divine will, which they believed to be inscrutable.150 This Voluntarist Turn enabled homogeneous space’s rise, because it extricated God from the cosmos’ physical whole and made Creation contingent on His will alone.151 Nominalists held that we know not why God constructed the cosmos as he did, but only that he willed it to be so. Moreover, once the cosmos became a product of divine will, God’s own place within Creation could no longer be justified along “rational” lines.152 Thus, did the ancient spatial hierarchy begin to dissolve in the face of a largely theological transformation.

The late medieval shift toward discourses of will legitimized the broader application of geometric homogeneity to the cosmos—and this had profound implications for European thought.153 Consider that the Nominalist-inspired imposition of homogeneity onto the “below” no longer threatened God’s position “above”—and this new arrangement opened multiple intellectual avenues. In particular, the theologically authorized application of space to every physical thing had two effects. First, it stoked a profound anthropological change. As I suggested in this book’s introduction with my

149This issue is too complex to be explicated fully. For discussions of what nominalism was, how uniform it was (or not), and whether the term should be used, see the following works by Gordon Leff, the great critic of the term: Gordon Leff, Medieval Thought: St. Augustine to Ockham (Harmondsworth: Penguin Books, 1958); William of Ockham: The Metamorphosis of Scholastic Discourse (Manchester: Manchester University Press, 1975); The Dissolution of the Medieval Outlook: An on Intellectual and Spiritual Change in the Fourteenth Century, Harper Torchbooks (New York: Harper & Row, 1976), 12-13. 150I have found the following to be especially helpful: William of Ockham, 561-66; Marenbon, Medieval Philosophy, 296-304; Colish, Medieval Foundations, 311-18. 151André Goddu, The Physics of William of Ockham (Leiden: E.J. Brill, 1984), 218. 152This shift also changed the sense that some had of the church’s mission, as it became more about the cultivation of moral lessons than understanding of the divine. See Heiko Augustinus Oberman, The Harvest of Medieval Theology: Biel and Late Medieval Nominalism, The Robert Troup Paine Prize Treatise (Cambridge: Harvard University Press, 1963), 164-66. 153See, along these lines, André Goddu, "The Impact of Ockham's of the Physics on the Mertonians and Parisian Terminists," Early Science and 6, no. 3 (2001).

65 précis on , by assuming that humanity could use geometry to understand both heaven and earth, late medieval thought foregrounded Man’s powers as an intellective and creative being.154 Second, by swaddling everything within space,

European thinkers resituated the Earth so thoroughly that it swapped positions with the

Sun. After having been renovated by the thoroughgoing application of space the Western triad was ready to host new visions of Man, the cosmos and God.

This illustrates exactly the issue: Ockham was not a Euclidian. That thought had to come into the continent from expressly non-theological sources.

In this chapter I will frame the extent of the resulting shifts in European thought and culture by juxtaposing one thinker from the late twelfth century with another from the early sixteenth century. With respect to the former, I return to this chapter’s epigraph:

“God is an intelligible sphere, whose center is everywhere, and whose circumference is nowhere.” The words come from Alan of Lille, a theologian at the who (significantly) was more of a Platonist, than an Aristotelian.155 (I have discussed

Platonism’s approach to geometry in the previous chapter.) Lille probably did not read much, if any, of the Elements, although copies may have been available to him. It is, therefore, not coincidental that Lille’s written illustration of God’s majesty was spaceless. As I have already explained, kept homogeneity from touching the boundary between real and and concentrated, instead, on the cultivation of geometric forms. By following the same path, Lille also dodged a conflict between God

154For a discussion of the anthropological currents that ran from late medieval thought into visions of God, see Charles Edward Trinkaus, In Our Image and Likeness: Humanity and Divinity in Italian Humanist Thought, 2 vols. (Notre Dame: University of Notre Dame Press, 1995), 1: 3-4, 65-71. 155Gillian R. Evans, Alan of Lille : The Frontiers of Theology in the Later Twelfth Century (Cambridge: Cambridge University Press, 1983), vii.

66 and the physical realm, in so far as space’s marginalization meant that the Biblical version of the cosmos’ passage from nothing to something remained uncontested.

When we view Lille with Platonist approaches to space in mind, we see that his application of geometry to God glorified the latter, while enervating the former. He deployed a sphere, the most perfect of forms, not only to highlight God’s , but also to underscore how limited was humanity’s ability to contemplate the divine. Thus, he put God into an ideal “world,” while also justifying tenuous access to Him via geometry’s forms. However, in emphasizing the cultivation of forms over the projection of space Lille marginalized geometry’s theoretical underpinnings. Consider that the notion of a sphere whose center is everywhere and circumference nowhere is not only logically contradictory but also devoid of the space that was Euclidian geometry’s sine qua non. In the Elements, for instance, a sphere’s center and circumference form a logical pair that makes sense only inside a homogeneous, three-dimensional realm. As a result, if center and circumference lack a logical relationship, no underlying uniformity in space exists. Lille revealed (unwittingly, perhaps) that Christianity’s pairing of the spiritual with the physical could not function inside a fully realized geometric homogeneity.

As we look ahead to the sixteenth century, we get a sense for the threat that

Euclidian space posed to medieval Christianity. Here, I turn to the second figure, the sixteenth-century Reformer Philipp Melanchthon. Unlike his mentor ,

Melanchthon was interested in geometry, even going so far as to write a celebratory preface for a 1536 Latin edition of Euclid’s Elements.156 He also touched on geometry’s

156Euclid, Elementa Geometriae Ex Evclide Singulari Prudentia Collecta a Ioanne Vogelin ... Arithmeticae Practicae Per Georgium Peurbachium Mathematicum. Cum Praefatione Philippi Melanthonis (Vitebergae1536). In general, see Wilhelm Maurer, Der Junge Melanchthon Zwischen Humanismus Und , 2 vols. (Göttingen: Vandenhoeck & Ruprecht, 1967).

67 in another text that was published that same year, in which he concluded that,

“Arithmetic and Geometry are, therefore, the wings of the human mind.”157

Melanchthon’s calls attention not only to geometry’s increasing cultural significance, but also to the theological problems that its spatial homogeneity caused. On matters pertaining to natural science Melanchthon was an Aristotelian, as he accepted both geocentricity and fractured space.158 Within the Aristotelian cosmos, however, the human mind should not have been able to rise “above” its location, i.e., to cross the boundary between earth and heaven. Yet, Melanchthon happily imagined his way

“upward.” And it is hardly coincidental that his mind spread its wings just as Renaissance cartographers, cosmographers, and astronomers were learning to illustrate Heaven and

Earth within a uniform space.159 (I deal with this issue in chapter four.) Something would have to give—and it turned out to be traditional views of God’s relationship to the other parts of the triad.

Against the medieval Christian Aristotelian backdrop, it is important to underscore that both the Spatial Reformation and the more famous Protestant one share a common origin. It has long been established that borrowed from

157Philip Melanchthon, "Praefatio in Arithmeticen (1536)," in Corpus Reformatorum Philippi Melanthonis Operae Quae Supersunt Omnia, ed. Carolus Gottlieb Bretschneider and Henricus Ernestus Bindseil (Halle: 1834-1860), 288. 158For the best general discussion, see Sachiko Kusukawa, The Transformation of : The Case of , Ideas in Context (Cambridge: Cambridge University Press, 1995). More specific to astronomy, see Charlotte Methuen, "The Role of the Heavens in the Thought of Philip Melanchthon " Journal of the History of Ideas 57, no. 3 (1996); Robert S. Westman, "The Melanchthon Circle, Rheticus, and the Wittenberg Interpretation of the Copernican Theory," Isis 66, no. 2 (1975). 159Uta Lindgren, "Die Bedeutung Philipp Melanchthons (1497-1560) Für Die Entwicklung Einer Naturwissenschaftlichen Geographie," in Gerhard Mercator Und Seine Zeit : Vorträge Und Berichte, ed. Wolfgang Scharfe, Duisburger Forschungen (Duisburg: Walter Braun Verlag, 1996).

68 Nominalism, as the early Reformers heavily emphasized God’s will over His reason.160

Moreover, early Protestants also read Euclid carefully. Melanchthon’s embrace of Euclid throws into relief, thus, the theological processes that encouraged homogeneity’s rise, as well as spatial homogeneity’s corrosive anthropological and cosmological effects. After medieval thinkers renovated Man, the cosmos and God’s relationship to reason (or, reason’s relationship to Man, the cosmos and God) space became a dominant in

European thought.

Reason and the return of emptiness

Medieval thought consistently marginalized spatial homogeneity—regardless of the many changes that were ongoing in its and society, including as I noted in the previous chapter, the rise of universities. Indeed, universities guaranteed that the trend against space only became more intense. After the turn of the millennium, a yearning developed for the application of logical tools to both God and the cosmos—and the resulting of thought was inherently hostile to homogeneous space. An example that allows us to track the effect of the shift toward comes with Anselm of

Canterbury, whom I mentioned in the previous chapter. He was born in southern in 1033 and entered the monastery at Bec in Normandy, before becoming its abbot and transforming it into one of the Continent’s premier centers of learning.161 Later, he became of Canterbury at William of Normandy’s invitation, after the

160For (still) the finest discussions of this issue, see Oberman, Harvest of Medieval Theology; Spätscholastik Und Reformation (Zürich: EVZ-Verlag, 1965). See also Steven E. Ozment, The Age of Reform, 1250-1550: An Intellectual and Religious History of Late Medieval and Reformation Europe (New Haven: Yale University Press, 1980), 16-21. 161G. R. Evans, "Anselm's Life, Works, and Immediate Influence," in The Cambridge Companion to Anselm ed. Brian Davies and Brian Leftow, Cambridge Companions to Philosophy (Cambridge: Cambridge University Press, 2004).

69 Chapter 6: The harvest of homogeneity

There is an immense usefulness in the consideration of lines, angles and figures, because without them natural philosophy cannot be understood. They are applicable in the universe as a whole and in its parts, without restriction, and their validity extends to related , such as circular and rectilinear motion, nor does it stop at action and passion, whether as applied to or sense... -- (ca. 1230)

Both intellectually and culturally the thirteenth century was a remarkably fruitful period, as its most prominent remnants attest. Among these are, of course, the great chain of whose profiles still Europe’s city skylines, and the theological- philosophical whose daring attempts to summarize all about Man, the cosmos and God can still be appreciated.220 Yet, the vertiginous heights that the era reached also engendered reactions that would shape much of fourteenth-century thought.

The initial recoil against logic was both generally diffused and, at , brutally specific.

In 1277, for example, Étienne Tempier, the of Paris, Rector of the Sorbonne and trained theologian, condemned as heretical 219 from various theologians who, in his view, had applied logic to God too enthusiastically.221 The sweep of the condemnation was impressive, as Tempier attacked not only radicals, such as Siger of

220The classic expression of the relationship between these phenomena remains: , Gothic Architecture and (Latrobe: Archabbey Press, 1951). See also, Duby, The Age of the Cathedrals. 221For a brief academic overview, see Takashi Shigomen, "Academic Controversies," in The Medieval Theologians: An Introduction to Theology in the Medieval Period, ed. G. R. Evans (Oxford: Blackwell Publishers, 2001), 233-35. See also Gilson, History of Christian Philosophy, 403-10. For the possible relationship to the history of science, see Pierre M. Duhem, Medieval Cosmology: Theories of , Place, Time, Void, and the Plurality of Worlds (Chicago: University of Chicago Press, 1985), xxii- xxiii.

98 Brabant and , but also , the thinker who had only a few years before defined Christian Aristotelian moderation.222 (This vindictive act prompted

Albert the Great to rush to Paris, in order to defend his deceased student’s honor.) In , Tempier felt that logic’s creeping expansion had threatened the Christian God’s . He was not wrong in this; nevertheless, he also failed to identify a still bigger threat to God.

There is a tradition among contemporary historians of seeing in Tempier’s intervention early of mental traits that are characteristic of —and especially of modern science. Early in the twentieth century, for example, the great of science identified the Condemnation of 1277 as sparking modern science’s rise.223 In Duhem’s view Tempier’s attack on reason liberated

European thought from an increasingly ossified . Aristotle did not disappear from European science, of course. Nevertheless, Duhem held that the cracks in the medieval edifice enabled an era speculation that was already fully underway with the

French Nominalist (c. 1295-1363) and then ran up through Newton.224

Contemporary views are more differentiated. Historians of science reject the notion that science began with Tempier’s intervention, while medievalists view this moment as having been interesting theologically and philosophically, but without immediate

222On the first two thinkers, see Colish, Medieval Foundations, 291; 338; Gilson, History of Christian Philosophy, 389-99; 422-23. On conservative dislike for both Aquinas and Siger, see Leff, Paris and Oxford Universities, 228. 223See especially Duhem, Medieval Cosmology, 179-268. This is a condensed, selective translation of the original massive work, which was published under the following title: Pierre Duhem, Le Système Du Monde; Histoire Des Cosmologiques De Platon À Copernic (Paris: A. Hermann, 1913). 224On Buridan and his relationship to Nominalism, see Gyula Klima, John Buridan, Great Medieval Thinkers (Oxford: Oxford University Press, 2009).

99 effects.225 No one has, however, discarded Duhem’s basic insight, namely that changes in medieval Europe’s vision of God initiated processes that would, one day, characterize modern thought.226

Against this historiographical backdrop, I emphasize the significance for the history of space of two fourteenth-century currents, the emphasis on God’s will and the increasing interest in mathematics. The former became manifest especially after 1300, while the latter was an important theme before then, but grew dramatically in significance as the fourteenth century progressed. The respective rises of and mathematics are hardly unrelated phenomena; indeed, they could not be independent, given medieval thought’s lack of specialization. It is, therefore, a difficult task to separate these themes. For analytical purposes, however, I must keep them apart—although it is important to understand that a profound relationship connected the two. Keeping this point in mind will be made easier, by how the examples in this section come from one medieval place, the University of Oxford. Medieval philosophical-theological debates were always continental in scope and reach. Nevertheless, for historical reasons, Oxford formed late medieval thought’s cutting edge on spatial matters.

The University of Oxford played a central—although by no means solitary role— in impelling the Spatial Reformation’s rise. This is for two reasons. First, it was

225Kent Emery and Andreas Speer, "After the Condemnation of 1277: New Evidence, New Perspectives, and Grounds for New Interpretations," in Nach Der Verurteilung Von 1277 : Philosophie Und Theologie an Der Universität Von Paris Im Letzten Viertel Des 13. Jahrhunderts : Studien Und Texte = after the Condemnation of 1277 : Philosophy and Theology at the University of Paris in the Last Quarter of the Thirteenth Century : Studies and Texts, ed. Jan Aertsen, Kent Emery, and Andreas Speer, Miscellanea Mediaevalia (Berlin: W. de Gruyter, 2001). For a view of the condemnation that sees it as part of the rise of a new form of at the University of Paris, see Étienne Gilson, La Philosophie Au Moyen Âge, 2 vols., vol. 1 (Paris: Payot & Cie, 1922), 559. 226Still the finest expression of this interpretation is: Funkenstein, Theology and the Scientific Imagination from the Middle Ages to the Seventeenth Century (Princeton: Princeton University Press, 1986).

100 physically situated on the margins of an intellectual system whose center lay in Paris, i.e., on the other side of the English Channel. Thus, neither the Bishop of Paris nor the in Rome could influence Oxford’s affairs as directly as the Condemnation of 1277 affected intellectual life at the University of Paris.227 Indeed, in Oxford the Condemnation seems to have been proclaimed only mildly, with some thinkers agreeing with some parts, while mostly ignoring other parts.228 Second, along similar lines, the university itself was under the Bishop of Lincoln’s administrative control. Given, however, that the city of Lincoln was relatively far away, practical control of the institution’s daily affairs usually remained with the local administration.229 All of this translated into more freedom for Oxford’s campus thinkers, relative to their counterparts in Continental universities.

Oxford was well positioned to bring an independent voice to medieval Europe’s orthodoxies. With respect to the theological changes that shaped subsequent discussions about space, two Oxford-trained figures are significant, (c. 1266-1308) and

William of Ockham (1287-1347). The former was probably of Scottish origin and entered a Franciscan school (Studium) in Oxford that was located near the university.230 In this school he studied a standard curriculum that included the works of Aristotle. Scotus’ educational mark an extension of my earlier point about the fruitful interaction between religious orders and universities. Here, however, the rivalry between the two greatest orders offered an additional impulse toward change, since the

Franciscans saw the critical reaction to Aristotle as also offering opportunity to challenge

227L. W. B. Brockliss, The University of Oxford: A History (Oxford: Oxford University Press, 2016), 95-96; Leff, Paris and Oxford Universities, 238-41. 228Paris and Oxford Universities. See also, Trevor H. Aston, J. I. Catto, and Ralph Evans, The History of the University of Oxford, 8 vols., vol. 2 (Oxford Oxford University Press, 1984), 112, 56; Brockliss, The University of Oxford: A History, 85-87. 229Leff, Paris and Oxford Universities, 271-72. 230C. K. Brampton, "Duns Scotus at Oxford," Franciscan Studies 24 (1964).

101 the Dominicans. Although Scotus probably did not register at the university itself, he did lecture there and, later, lectured at the University of Paris.231 Thanks to this career trajectory, Scotus’ critical (and highly corrosive) ideas moved rapidly from medieval thought’s margins to its bustling center.

Scotus had probably the finest philosophical mind of any thirteenth-century thinker, including both Albert the Great and Thomas Aquinas. Although his works are dense—the contemporary pejorative “” is a corruption of his name—Scotus routinely identified fundamental philosophical problems within the Christian Aristotelian synthesis. For my purposes here, the most important among his innovations was the doctrine of the “,” which held that there is no between the essence and the of a thing.232 The modern mind will likely find nothing objectionable in this, since existence now officially precedes essence. The Aristotelian mind begged to differ, however, since with this idea Scotus broke with both Aristotle and

Thomas Aquinas.

Against the backdrop of Scotus’ thought, let us return to the relationship between

Aristotelianism and . In his Aristotle held, first, that the discipline of metaphysics constituted the study of being and, second, that being could be subdivided into infinite and finite kinds. Aquinas, meanwhile, built on Aristotle’s distinctions and added that finite being is itself divided into essence and existence, while reserving absolute unity only to infinite being. (He needed these distinctions to justify both God’s

231Brockliss, The University of Oxford: A History, 88-90. 232For an overview of Scotus’ very complex thought, see Thomas Williams, ed. The Cambridge Companion to Duns Scotus, Cambridge Companions to Philosophy (Cambridge: Cambridge University Press, 2003). Very informative on the subject of the divine is: Willilam E. Mann, "Duns Scotus on Natural and Knowledge of God," in The Cambridge Companion to Duns Scotus, ed. Thomas Williams (Cambridge: Cambridge University Press, 2003). On metaphysics and the “univocity of being,” see Peter King, "Scotus on Metaphysics," ibid., 18-22; Leff, Dissolution of the Medieval Outlook, 44-48.

102 hierarchical superiority and the human ’s immortality.) Scotus crushed all of this under his heel.233 On the one hand, he held that being is a transcendental , which meant that it unites in thought finite being with infinite being. On the other hand, he also held that being unified essence with existence, because humans cannot think of a thing’s essence without first postulating that it actually exists. Scotus argued, thus, that the thorough application of reason to God, which had been in full bloom since Anselm’s time, undermined ’s omnipotence.234

Although Scotus died relatively young, his doctrine of the univocity of being went on to undercut key aspects of Christian Aristotelianism’s worldview.235 The idea that higher spaces hosted higher beings could not, for instance, withstand the Scotist vision of unity. If being was univocal, as Scotus claimed, then no part of the cosmos could be reserved to an array of beings, with the additional result that the ancient hierarchy of the divine was called into question. If God needed on philosophical grounds to be kept separate from the physical cosmos, then—as I will explain in my discussion of melancholy in chapter five— would be the first casualties. (Scotus himself argued that angels were merely contingent beings. It is a short step from this idea to the dismissal of angels entirely.)236

There were, however, compensatory advantages to Scotus’ destruction of a hierarchical metaphysics. First, with God’s stumbling egress from the cosmos, the physical realm could now be studied purely as a product of God’s will, which afforded

233See, for example, John Duns Scotus, God and Creatures: The Quodlibetal Questions, trans. Felix Alluntis and Allan B. Wolter (Princeton: Princeton University Press, 1975), 128-29. 234A very useful English translation of selected theological works by Scotus is available in: Philosophical Writings, trans. Allan B. Wolter, The Library of Liberal Arts (Indianapolis: Bobbs-Merrill, 1964). 235On , see Gilson, History of Christian Philosophy, 465-71. 236King, "Scotus on Metaphysics," 57 (n. 4). For Scotus’ own view of angels and their connection to intellect, see Duns Scotus, God and Creatures, 315.

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