medieval and seventeenth-century conceptions of an infinite void space beyond the cosmos

Medieval and Seventeenth-Century Conceptions of an Infinite Void Space beyond the CosmosAuthor(s): Edward GrantSource: Isis, Vol. 60, No. 1 (Spring, 1969), pp. 39-60Published by: The University of Chicago Press on behalf of The History of Science SocietyStable URL: http://www.jstor.org/stable/229021 .

Accessed: 23/11/2013 18:03

Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at .http://www.jstor.org/page/info/about/policies/terms.jsp

.JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range ofcontent in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new formsof scholarship. For more information about JSTOR, please contact [email protected].

.

The University of Chicago Press and The History of Science Society are collaborating with JSTOR to digitize,preserve and extend access to Isis.

http://www.jstor.org

This content downloaded from 130.194.20.173 on Sat, 23 Nov 2013 18:03:38 PMAll use subject to JSTOR Terms and Conditions

http://www.jstor.org/action/showPublisher?publisherCode=ucpress

http://www.jstor.org/action/showPublisher?publisherCode=hss

http://www.jstor.org/stable/229021?origin=JSTOR-pdf

http://www.jstor.org/page/info/about/policies/terms.jsp


Medieval and Seventeenth-

Century Conceptions of an

Infinite Void Space

b ond the Cosmos

By Edward Grant'

I N THE LATIN WEST medieval discussions of the vacuum are separable into three quite distinct subtopics, all arising from Aristotle's intense attacks against

the possible existence of void in any manner or place. These are (1) the separate void,1 (2) the interparticulate void,2 and (3) the extracosmic void. In this paper only the third topic will be considered.'

In the process of rejecting the existence of a plurality of worlds in De caelo, Book I, Chapter 9, Aristotle sought to strengthen his position by declaring that there can be "neither place, nor void, nor time, outside the heaven."4 He had earlier argued that no bodily mass could come into being beyond the heavens, or outermost circumference of the universe, and from this inferred that neither place nor vacuum could exist there, since "in every place a body can be present"5 (no body, therefore no place) and since "void is said to be that in which the presence of body, though not actual is possible"6 (no possible body, therefore no vacuum). And so it was that Aristotle set the stage in antiquity and the Middle Ages for a question that would be frequently posed: If it were possible to push a lance, or an arm, through the outermost celestial sphere, what would be the disposition of such a body?7 What lies beyond the cosmos? For Aristotle the

*Indiana University. I wish to acknowledge my gratitude to the National Science Founda- tion, Division of Social Sciences, Program in History and Philosophy of Science, for its support of my researches into the role and concept of void in medieval physics, of which this paper forms a part. An abridged version was first presented 28 Dec. 1967, in Toronto, at the annual meeting of the History of Sci- ence Society.

I Aristotle's major assault against the separate void appears in Physics IV, Chs. 6-8, esp. 8.

2 Among other places, see Physics IV, Ch. 9.

3 Topics (1) and (2), which are the focal points of my current research, will be ex- amined in future articles.

4De caelo I.9.279a.12-13, 17-18. 5 Ibid., 13-14. 6 This definition occurs at least twice in

substantially the same form; see De caelo I.9.279a.14-15 and Physics IV.7.214a.18-19.

7 According to Simplicius (Commentary on the Physics 108a), this question had al- ready been raised by Archytas of Tarentum (first half of the 4th century B.C.). See Max Jammer, Concepts of Space (Cambridge, Mass.: Harvard Univ. Press, 1954), pp. 7,

39



40 EDWARD GRANT

only intelligible response was-absolutely nothing, or mere privation; for many others, including many later Aristotelians, the question would not resolve itself so easily. It is the purpose of this paper to describe, summarize, and analyze some of these responses and arguments. For convenience I have subdivided it into two parts and a conclusion. Part I will be devoted primarily to medieval discussions; Part II will include one major discussion from the sixteenth century and the rest from the seventeenth century.

Perhaps the most important ancient response to this problem came from the Stoics, who, while in agreement with Aristotle that (1) the cosmos itself was a finite sphere without any vacua whatever (it was filled with pneuma) and that (2) all existent matter and reality were contained within it, nevertheless insisted that beyond our finite world there exists an infinite three-dimensional void capable of receiving matter and serving as its receptacle.8 If an account by Cleomedes is typical, their conception of vacuum was substantially the same as Aristotle's most considered definition of it. Where Aristotle says that "void is said to be that in which the presence of body, though not actual is possible,"9 Cleomedes asserts that "since this vacuum [or emptiness] receives bodies, so it is also something that is capable of receiving bodies. Therefore this something which is capable of being filled by a body or to be abandoned by a body is a vacuum."10 It follows that the infinite void serves as the receptacle of the finite cosmos. In- deed, that seems to be its only function, since interaction between cosmos and void is denied on grounds that the void has no properties of its own and can in no way affect the material world, which constitutes a closed system that cannot be dissipated into the void.1" But granting that the world is surrounded by void,

10-11. In the discussions of this paper Aris- totle's cosmology would most frequently pro- voke the question.

8 Aristotle himself seems to have suggested that proponents of void might perhaps assume a full cosmos surrounded by void. Thus he says (Physics IV.6.213b.2-3) that "it might perhaps be maintained that, though material existence is continuous throughout the cosmos, the void is something existing outside it." The translation is that of P. H. Wicksteed and F. M. Cornford in the Loeb Classical Library.

9 See above, n. 6. 10 On the Circular Motion of the Heavenly

Bodies (De motu circulari corporum caelestium), Bk. I, Ch. 1. The Greek text was published by H. Ziegler, Cleomedes De motu circulari corporum caelestium (Leipzig: Teubner, 1891) and translated into German by Arthur Czwalina in Kleomedes Die Kreis- bewegung der Gestirne in Ostwald's Klassiker der exakten Wissenschaften (Leipzig: Engel- mann, 1927). The passage above appears on p. 8 of the former and p. 3 of the latter vol-

ume. Cleomedes, who may have lived during the 1st century A.D., wrote the above treatise in defense of the Stoics.

11 "But, they argue, if a vacuum existed outside the world, the world would move away through this vacuum, while, on the other hand, nothing would exist to keep it together and support it. To this we answer that it is impossible for the world to move away through the void. The world strives toward its own mid-point [or center] and what lies under us has the same mid-point toward which it strives" (Ziegler, p. 10; Czwalina, p. 4). In the next paragraph Cleo- medes responds to those who declare that the world would be destroyed by moving through this void. "To this we answer that the world cannot experience such a fate, for it possesses a force which keeps it together and preserves it. And the vacuum surrounding the world exercises no influence on the world" (Ziegler, pp. 10, 12; Czwalina, p. 4). A few paragraphs earlier (Ziegler, p. 8; Czwalina, p. 3) Cleo- medes said of this void: "it is incorporeal



CONCEPTIONS OF THE EXTRACOSMIC VOID 41

why, it was asked, must it be assumed infinite? In response it was argued that because no body could exist beyond the physical world, no material substance could limit the void; and since it was absurd to suppose that void could limit void or that void should terminate at one point rather than another-a clear violation of the principle of sufficient reason-the infinity of void space seemed an irresistible conclusion.12

No comprehensive account of the Stoic conception of vacuum was available in the Latin Middle Ages. The little that was known was probably derived from Simplicius, who, in his Commentary on Aristotle's De caelo, had occasion to discuss Aristotle's celebrated statement that there can exist "neither place, nor void, nor time, outside the heaven." He informs us that:

. .the Stoics, however, thinking that there is a vacuum beyond the sky, prove it by this kind of assumption: let it be assumed that someone standing motionless at the extremity [of the world] extends his hand upward. Now if his hand does extend, they take it that there is something beyond the sky to which the hand extends. But if the arm could not be extended, then something will exist outside that prevents the extension of the hand; but if he then stands at the extremity of this [obstacle that prevents the extension of his hand] and extends his hand, the same question as before [is asked], since something could be shown to exist beyond that being.13

However meager this report of Stoic doctrine on the void, there is little doubt that it came to be widely known, for hardly had William Moerbeke made it available in Latin translation when Thomas Aquinas saw fit to discuss it in his Expositio on De caelo,14 to be followed by a number of fourteenth-century

and ungraspable; it has no form and is not formable; it undergoes [i.e., endures or suffers] nothing and it concerns nothing ; but it is only capable of receiving a body." (Unless stated otherwise, the translations in this article are my own.)

12 Ziegler, pp. 14, 16; Czwalina, pp. 5-6. For further discussion of the Stoic doctrine of void see E. Brehier, La The'orie des incorpo- rels dans l'ancien Stoicisme (2nd ed., Paris: J. Vrin, 1928), pp. 46-52, and S. Sambursky, Physics of the Stoics (London: Routledge & Kegan Paul, 1959), pp. 110-114, 128, 143- 144.

13 Simplicii . . . commentaria in quatuor libros de celo Aristotelis Guillermo Morbeto in- terprete (Venice, 1540), fol. 44v, c.2. William Moerbeke translated Simplicius' Commentary on De caelo in 1271. For John Buridan's interesting discussion of this very same problem, see his Questiones super octo phisicorum libros Aristotelis diligenter recognite et revise a ma- gistro Johanne Dullaert de Gandavo (Paris, 1509), fol. 77v, c.1 and my analysis of it in "Jean Buridan: A Fourteenth Century Carte- sian," Archives internationales d'histoire des sciences, 1963, 16 : 251-255. The dilemma posed by the Stoics was probably directed

against Aristotelians who, it was hoped, would be compelled either to concede the existence of void or concede that the plenistic world is indefinitely extended. The remainder of Sim- plicius' discussion centers on this argument and the absurdities arising from attempts to consider an extramundane void as either finite or infinite.

14 In Aristotelis libros De caelo et mundo; De generatione et corrtuptione; Meteorologi- corum Expositio cum textu et recensione leonina, ed. Raymundi M. Spiazzi, O.P. (Marietti: Taurini, 1952), pp. 102-103. In considering Simplicius' report, Thomas insists that it would not do to reject the Stoic belief in an extramundane void by arguing- as had Alexander of Aphrodisias-that no hand or body could be extended beyond the outermost celestial sphere because of the latter's impenetrability. Since no bodies could penetrate beyond, then by Aristotle's definition no void could exist ("void is said to be that in which the presence of body, though not actual is possible"). The proper response, says Thomas, is to insist with Aristotle that "it is the nature of all natural bodies to be contained within the extreme circumference of the heaven." Hence a body could not



42 EDWARD GRANT

authors.'5 But the Stoic conception of an infinite void had little appeal in the Middle Ages perhaps because, lacking purpose or justification, it seemed a mere privation made three dimensional.

Much more congenial to medieval Christian theology, as well as anti-Stoic in conception, was a brief passage in the Latin Hermetic treatise called Asclepius.16 Speaking to Asclepius, Hermes Trismegistus says:

But as to void, which most people think to be a great thing of great importance, I hold that no such thing as void exists, or can have existed in the past, or ever will exist. For all the several parts of the Kosmos are wholly filled with bodies of various qualities and forms, each having its own shape and magnitude; and thus the Kosmos as a whole is full and complete.... And the like holds good of what is called 'the extramundane', if indeed any such thing exists; for I hold that not even the region outside the Kosmos is void, seeing that it is filled with things apprehensible by thought alone, that is, with things of like nature with its own divine being. . 17

And so, Asclepius, you must not call anything void, without saying what the thing in question is void of, as when you say that a thing is void of fire or water or the like. For it is possible for a thing to be void of such things as these, and it may consequently come to seem void; but the thing that seems void, however small it be, cannot possibly be empty of spirit and of air.18

Although I am ignorant of the subsequent influence of this brief passage, its potential impact in light of later medieval developments described below could have been significant, for we have here an idea in harmony with Christian

possibly exist beyond the world and (Thomas implies) void would be impossible. Only im- mutable beings such as God and separate substances could exist beyond the heavens and even these are not in any sense locatable in places (". . . they are separated from all magnitude and motion. Furthermore, such substances are said to be there (ibi), that is, outside the sky [or world] not as in a place, but as things that are not contained or in- cluded within containers of corporeal things.; but these things exceed all corporeal natures." Ibid., p. 103).

15 For example, John Buridan's discussion mentioned above in n. 13 was probably occa- sioned by knowledge of Simplicius' account, as was a similar discussion by Nicole Oresme in Bk. I, Ques. 19 of his Questiones super de celo (p. 281, lines 13-18 of Claudia Kren's edition cited below in n. 40), and Richard of Middleton in his Questions on the Four Books of the Sentences (see Jammer, Concepts of Space, p. 73).

16 The profound impact of the Hermetic literature on Renaissance thinkers and Gior- dano Bruno in particular is described by Frances A. Yates, Giordano Bruno and the Hermetic Tr-adition (Chicago: Univ. Chicago Press, 1964).

17 For although "Bruno would not have found in the Hermetic writings the conception of an infinite universe and innumerable worlds, the spirit in which he formulates such a conception is to be found in them" (ibid., p. 245). Along with a brief passage from the Corpus Hermeticum, Miss Yates singles out and quotes (ibid.) the last few lines of this paragraph as potentially significant, for "Bruno had but to add to this that there is an infinite space outside the world and it is full of divine beings and he would have his extended Hermetic gnosis of the infinite and the innumerable worlds." In similar fashion, I shall claim below that this passage-and one from St. Augustine-may have influenced Thomas Bradwardine to arrive at his concept of a God-filled infinite extramundane void.

18 Walter Scott, ed. and trans., Hermetica, the Ancient Greek and Latin Writings which Contain Religious or Philosophic Teachings Ascribed to Hermes Trismegistus, 4 vols. (Ox- ford: Clarendon Press, 1924-1936), Vol. I, pp. 319-321. While the edition of As- clepius by A. D. Nock and A.-J. Festugiere in Vol. II of their Corpus Hermeticum (Paris: Societe d'1Rdition "Les Belles Lettres," 1945) is better than Scott's, the latter's translation seems to agree well even with their text.




theology, and one which by its implications was also subversive of Aristotelian physics and cosmology (this despite an initial apparent consonance when Hermes emphatically denies the actual existence of void both inside and outside the cosmos). For Hermes declares that if void did exist beyond the cosmos, it would be void of physical bodies only but never of spiritual substances "apprehensible by thought alone." The concept of an extramundane space filled with spirit but empty of matter would become a significant element in later discussions of what, if anything, lay beyond the cosmos.

Indeed, this concept may have directly influenced St. Augustine, who, in The City of God, quotes from a few chapters in the Latin Asclepius'9 and leaves little doubt that he knew firsthand the Latin version which was to be quite influential in the Middle Ages and Renaissance. In Book XI, Chapter 5,20 he takes issue, it seems, with non-Christians who in agreement with Christians accepted God as a spiritual being and the creator of all things. In the course of the discussion he remarks approvingly that these men rightly hold that God, the divine substance, cannot be limited but is "spiritually present everywhere." Hence, if there existed infinite spaces beyond this world, they would be committed to a belief in the omnipresence of the divine substance in these infinite spaces, since no reason would remain for confining God to our relatively small finite world. Fortunately, says Augustine, they were not compelled to extend the presence of the Creator beyond the cosmos, since "they maintain that there is but one world, of vast material bulk, indeed, yet finite and in its own determinate position" and would probably argue "that tlhe thoughts of men are idle when they conceive infinite places, since there is no place beside the world, . . ."

Thus Augustine agrees with the author of the Asclepius that the world is finite with nothing existing beyond, neither space nor void; but if something did exist beyond, the divine spiritual substance would of necessity be omnipresent in it. In the later Middle Ages a number of authors would conclude that something did indeed exist beyond the cosmos. But while they might disagree with Asclepius and Augustine on this point, they would accept their hypothetical conditions about God's necessary omnipresence.

In the fourteenth century Thomas Bradwardine, whose arguments for the existence of an infinite extramundane void we shall now consider, was familiar not only with The City of God, but also with Asclepius, the Hermetic text just mentioned (he cites it under the title De aeterno verbo ),21 and the influential

19 See Nock and Festugiere, Corpus Her- meticum, pp. 264-266.

20 The title of this chapter is: "We ought not to think of infinite extents of times (de infinitis temporum spatiis) before the world, nor of infinite extents of places (de infinitis locorum spatiis) beyond [or outside] the world, since just as there are no times before the [creation of the] world so there are no places beyond it." My translation is from Corpus Scriptorum Ecclesiasticorum Latino- rum, Vol. 40 (Vienna, 1889), p. 517. The

translations from this chapter in the remainder of this paragraph are by Marcus Dods, The City of God by Saint Augustine, 2 vols. (New York: Hafner, 1948; first pubhlished Edin- burgh: T. & T. Clark, 1872), pp. 441-442.

21 See Nock and Festugiere, Corpus Her- meticum, pp. 273-274. Bradwardine cites the De aeterno verbo in his De causa Dei contra Pelagium, which we shall discuss below. For a list of other medieval authors who cited or used Asclepius, see ibid., pp. 267-273; to their list may be added Nicole Oresme, De



44 EDWARD GRANT

pseudo-Hermetic treatise The Book of the XXIV Philosophers (Liber XXIV philosophorum) composed around 1200 A.D.22

Bradwardine's lengthy discussion appears in Book I, Chapter 5 of his De causa Dei contra Pelagiunl,23 a chapter bearing the title "That God is not mutable in any way" and from which Bradwardine immediately elicits five corollaries, three of which (1, 2, and 5) seem to reflect the earlier discussions of Hermes Tris- megistus and Augustine cited above:

1. First, that, essentially and in presence, God is necessarily everywhere in the world and all its parts;

2. And also beyond the real world in a place or imaginary infinite void.24 3. And so truly can he be called immense and unlimited. 4. And so a reply seems to emerge to the old question of the gentiles and heretics

-"where is your God? And where was God before the [creation of the] world?" 5. And it also seems obvious that a void can exist without body, but in no

manner can it exist without God.25

Following a demonstration of the first corollary that God is necessarily everywhere inside the world,26 Bradwardine presents a demonstration of the second corollary that God is everywhere outside the finite cosmos. Let A be the imaginary place of this world and B an imaginary, and quite distinct, place outside the world; assume, furthermore, that God moves the world from A to B-or re-creates it in

commensurabilitate vel incommensurabilitate motuum celi, who, in Part III of that treatise, cites from the Asclepius three times. See my forthcoming edition and translation of this treatise (in press, Univ. Wisconsin Press).

22 The modem Latin edition of this treatise is cited below in n. 35. As part of the neo- Platonic and neo-Pythagorean-and therefore non-Aristotelian-tradition, Hermetic and pseudo-Hermetic literature played a significant role in the history of medieval and Renais- sance thought, exerting a profound influence on such figures as Nicholas of Cusa, Marsilio Ficino, Pico della Mirandola, Giordano Bruno, and numerous others who found attractive and compelling their mystical and cryptic utterances about God, spirit, and cosmos.

23 Written perhaps in 1344, it was published by Henry Savile in London, 1618, under the title: Thomae Bradwardini Archi- episcopi olim Cantuariensis De causa Dei Contra Pelagium et de virtute causarum libri tres ... opera et studio Henrici Savilii.... In a manner similar to Spinoza's Ethics, Brad- wardine uses a quasi-mathematical form an- nouncing propositions and deriving numerous corollaries therefrom. Except where it seems especially desirable, I shall conserve space by giving only my English translations. The interested reader may consult a recent reprint of this edition, or read A. Koyre's important article "Le vide et l'espace infini au XIVe siecle," Archives d'histoire doctrinale et lit-

te'raire du moyen-age, 1949, 24: 45-91, which includes the relevant Latin text with French translation.

24 This, of course, marks a radical departure from Asclepius and Augustine, for here Bradwardine declares the existence of an imaginary infinite extramundane void.

25 It is in this fifth corollary that we can detect the possible direct influence of Ascle- pius, for, as we recall, its author insisted that if void existed, it would of necessity be filled with spirit. Here is the Latin text for these corollaries (De causa Dei, p. 177):

1. Prima, quod Deus essentialiter et prae- sentialiter necessario est ubique in mundo, et in eius partibus universis; 2. Verum etiam extra mundum in situ seu vacuo imaginario infinito. 3. Unde et immensus et incircumscriptus veraciter dici potest. 4. Unde et videtur patere responsio ad Gentilium et Haereticorum veteres quaes- tiones. Ubi est Deus tuus? et ubi Deus fuerat ante mundum? 5. Unde et similiter clare patet, quod vacuum a corpore potest esse, vacuum vero a Deo nequaquam. 26 This argument (De causa Dei, p. 177)

is far from obvious and will be omitted since its substantive content is not relevant to what follows. It is sufficient to know that Brad- wardine assumed that God's omnipresence within the world was demonstrated.




B-and the world is now in place B.27 Consequently, God must be in B, since it was earlier shown that God is everywhere inside the cosmos. Therefore when the world was moved to place B either God was there before or not. If He was in B before, and assuming that B represents any place beyond the world, it would follow that God is everywhere beyond the cosmos and Bradwardine would have made his point. If He was not in B, then we must ask what was there before the creation of the world? The answer, says Bradwardine, is the place of the world, a place whose size and location were freely determined by God and of which God could have made as many as He pleased.28 But what properties or characteristics would such a place have? It could have "no positive nature, for

27 In arguing that God could move the world from A to B or re-create it in B, Brad- wardine attacks the Aristotelians who denied that the world could be moved and who thereby placed limits upon God's absolute power. As I shall argue below, it is significant that in his attack Bradwardine appeals to one of 219 articles condemned in 1277 by Etienne (Stephen) Tempier, the Bishop of Paris. (This was article 49 ; later in the same section he re- fers to another, probably 52; see below, n. 29. The complete list of condemned articles was published by H. Denifle and A. Chatelain, Chartularium Universitatis Parisiensis, Vol. I, 1889, pp. 543-555.) Many of these articles were condemned solely because they represented attempts by Aristotelian philosophers to limit the absolute power of God to do as He pleased-e.g., to make as many worlds as He pleased, as many voids as He pleased, and to place or create the world where He pleased. It is obvious, in the passage cited below and throughout his discussion, that Bradwardine believed that God possesses absolute power to do as He pleases notwithstanding efforts to limit that power in accordance with Aristotle's metaphysical and scientific "demonstrations."

Some of those who follow the Philosopher [i.e., Aristotle] in Bk. I of On the Heavens reply to this. They assume that every local motion is necessarily upward, downward, or circular-i.e., away from the center [of the world], toward the center, or around the center. But they say that if this motion [from A to B] were assumed, it could not be any one of the ways just mentioned. For this reason, they say that it is impossible for the world to be moved. But these [followers of Aristotle] seriously diminish and mutilate the divine-indeed omnipotent- power. For, in the beginning, God could have created this world in B. Why, then, is He unable to put it in B now? Further- more, He can now create another world in B. Why, then, is He unable to put this world in B? This reply [that the world can-

not be moved] is condemned by Stephen, bishop of Paris, in these words: "That God cannot move the heavens with rectilinear motion. The reason is that a void would remain." But this response does not avoid the difficulty. For it could be assumed that without [resort to] local motion, God could create another world in B and annihilate the world in A. [On this assumption], the difficulty returns. (De causa Dei, p. 177.)

Bradwardine's point is that whether the world is moved by God from place A to place B by local motion-and this is denied by Aristote- lians-or by its annihilation in A and re-creation in B, the same problem arises: Was God in place B before the creation of the world?

28 In establishing this, Bradwardine attacks Christian Aristotelians who, while admitting that the world was created in a place (Aris- totle denied that the world was in a place) nevertheless sought, under the influence of Aristotle, to place limits upon God's power. For they say that

God, for all his omnipotence could not have made the world greater or smaller in anything, which would very much restrict and confine his omnipotence. For they must say that God necessarily makes the world in place A, and that place A, and no other, existed before there was a world. But why this place, and no other? Why was the world just this size and no greater or smaller? For, indeed, either this [i.e., the size of the world] was fixed by God, or by itself and not by God. If by God, then, in virtue of his infinite power, He could make a place greater and greater; and [He could] make another place, and yet another place, without end. If, however, the size is determined by the world itself-and not by God-what power determines this? What is the reason for it? What nature has fixed the world at this [particular size], and inviolately determined the limit beyond which it cannot pass? (De causa Dei, p. 177.)



46 EDWARD GRANT

otherwise there would be some positive nature which is not God, nor from God, . .. Such a nature would be coeternal with God, something no Christian can accept."29

Nor could Bradwardine accept an alternative argument that "prior to the creation of the world, there was an imaginary void place unoccupied by any body."30 For without qualification such a void place would also be coeternal with God if interpreted as mere emptiness devoid of matter and God. Bradwardine concludes that God Himself occupied this void place which in and of itself could have had no positive nature. But God is not confined to the place where he created the world, since "it is more perfect to be everywhere in some place, and simultaneously in many places, than in a unique place only; . ."31 From all this, Bradwardine concludes that "God is, therefore, necessarily, eternally, infinitely everywhere in an imaginary infinite place, and so truly omnipresent, "32 But although God is infinitely everywhere, He can be called an infinite magnitude only in a metaphysical and improper sense,

For He is infinitely extended without extension and dimension. For truly, the whole of an infinite magnitude and imaginary extension, and any part of it, coexist fully and simultaneously, for which reason He can be called immense, since He is unmeasured; nor is He measurable by any measure; and He is unlimited because nothing surrounds Him fully as a limit; nor, indeed, can He be limited by any. thing, but [rather] He limits, contains and surrounds all things.33

29 Ibid. Bradwardine goes on to cite another article condemned in 1277 (probably article 52), one held by Aristotelians, which declared that there are many eternal things and not even God could destroy them. If this were so, Bradwardine observes, God would be deprived of omnipotence. But "the argument of these [Aristotelians] tells against them. For if, according to the assumption of the Philosopher and his followers, there could be no void, nor any imaginary place not filled with body, [then] the world is eternal, which is heretical, and which these people [themselves] deny" (ibid., p. 178)-no doubt because they were themselves Christian Aristotelians.

30". . . ante creationem ipsius [i.e., the world] erat situs eius imaginarius vacuus nec corpore occupatus" (ibid., p. 178). This asser- tion follows immediately after the Aristotelian argument quoted in n. 29.

31 Ibid. 32 "Est ergo Deus necessario, aeternaliter

infinite ubique in situ imaginario infinito, unde et veraciter omnipraesens . . ." (ibid., pp. 178-179).

A brief summary of Bradwardine's approach may be useful at this point. Since the world is not eternal, Bradwardine assumes that a place for it must have existed prior to its creationi. Indeed, an infinite number of such places must have existed, since God could have created the

world anywhere He pleased. Now presumably Bradwardine did not wish to adopt the theologically troublesome position that God created the place of the world prior to the creation of the world itself, for this would somehow detract from the uniqueness of the creation of our cosmos and make it seem a second effort. Nor, indeed, would he wish to fall victim to the charge that this infinity of places was coetemal with and independent of God. To avoid these major difficulties, Brad- wardine argued that God himself had always occupied the infinite number of possible empty places in which He could have created the world. And so it was unnecessary to in- voke a special creation for these places in which the world could have been created, as it was also unnecessary to confer upon them a separate and coetemal existence with God.

33 Ibid., p. 179: Est enim inextensibiliter et indimensionaliter infinite extensus. Infinitae namque magni- tudini et extensioni imaginariae et cuilibet parti eius totus simul plenarie coexistit, quare et similiter dici potest immensus, enim non mensus; nec mensurabilis ulla mensura; et incircumscriptus quia non cir- cumscribitur ab aliquo ipsum plenarie cir- cundante, nec sic potest ab aliquo circum- scribe sed ipse omnia circumscribit, continet, et circundat.




In support of these remarks, Bradwardine cites definitions 2, 18, and 10 (in this order ) 34 from The Book of the XXIV Philosophers,35 which I render as follows:

2. God is an infinite sphere whose center is everywhere and circumference nowhere.36

18. God is a sphere that has as many circumferences as points. 10. God is that whose power is not numbered, whose being is not enclosed, [and]

whose goodness is not limited.

And so it was that by uniting Christian and Hermetic (including pseudo- Hermetic) elements-the doctrine of the world's creation in time and God's absolute power37 from the former, and the notion that places devoid of matter must necessarily be filled with spirit38 and the conception of God's infinite ubiquity in the form of an infinite sphere from the latter-Bradwardine con- structed and formulated a Christian response to Aristotle's denial of void beyond the cosmos and concluded that "by means of His absolute power God could make a void anywhere He wishes inside or outside of the world. Truly even now there is in fact an imaginary void place outside of the world, which I say is void of any body and of everything other than God..

To supplement Bradwardine's lengthy treatment, let us now summarize the views of another major fourteenth-century figure, Nicole Oresme, whose brief discussions appear in two commentaries on Aristotle's De caelo, the first in Latin40 probably written early in his career, say in the late 1340's or early 1350's, the second in French (Le Livre du ciel et du monde )41 and completed in 1377, as far as is known his last extant work.

4'4 Ibid. 35 The Latin text was published by Clemens

Baeumker, "Das pseudo-hermetische 'Buch der vierundzwanzig Meister' (Liber XXIV philosophorum )" in Beitrdge zur Geschichte der Philosophie des Mittelalters, 1927, Band XXV, Heft 1/2, pp. 194-214. The definitions appear on pp. 208, 210, and 212.

36 Bradwardine's version agrees with Baeumker's text. This famous definition was apparently formulated by the anonymous author of this treatise. It also influenced Cusa, Ficino, Bruno, and Fludd (see Yates, Gior- dano Bruno, p. 247 and n. 2) and an anonymous Coimbra commentator (see col. 515 of the edition cited below in n. 55).

37 The role of God's absolute power will be discussed at the conclusion of Part I.

38 It should be emphasized that although Bradwardine did not cite Asclepius (or De aeterno verbo, as he called it) in this chapter, he does cite it a number of times elsewhere in the De causa Dei, and it seems likely that this idea was derived from that treatise or from Augustine's City of God, Bk. XI, Ch. 5 (see above)-and perhaps, as seems plausible, from both.

quin Deus posset de omni potentia

sua absoluta facere vacuum ubi vellet in mundo vel extra; quin etiam nunc de facto sit situs imaginarius vacuus extra mundum, vacuus in quam a corpore et a quolibet alio praeter Deum...." De causa Dei, p. 180.

40 This has been edited and translated by Claudia Kren, The Questiones super De celo of Nicole Oresme (Ph.D. Dissertation, Univer- sity of Wisconsin, 1965) and will be cited as Oresme, De caelo. My quotations from this work are from Kren's translation.

41 My translations below were made origi- nally from the edition by A. D. Menut and A. J. Denomy, Maistre Nicole Oresme: Le Livre du ciel et du monde in Mediaeval Studies (New York), 1941-1943, Vols. 3-5. Recently, a revised edition with English translation has appeared: Nicole Oresme Le Livre du ciel et du monde edited by Menut and Denomy, translated with an introduction by Menut (Madison: Univ. Wisconsin Press, 1968). Al- though I have retained my own translations, textual references will be made to the new edition in which the passages quoted here are unaltered. To my knowledge, only Pierre Duhem has quoted and discussed the passages on infinite void space in Oresme's Du ciel et du monde. See Duhem's Le Systeme du



48 EDWARD GRANT

In the Latin Questions on De caelo, Book I, Question 19, Oresme inquires "whether there may be or could be something outside the heaven."42 In the course of a lengthy response, Oresme remarks that in one sense a vacuum re- quires the notion of a space into which a body can potentially move. "But," he says, "according to faith there is no space outside the heaven but one can concede that outside the heaven there may be a vacuum because God can create a body or a place there. Therefore, if it is asked what is that vacuum outside the heaven, one should reply that it is nothing but God Himself, Who is His own indivisible immensity and His own eternity as a whole and all at once."43 If now God were to place another world in this infinite void, Oresme emphasizes that "He [God] would be in that [world] and He would not need to acquire a new place nor would He be changed. Thus more properly one may say that the world is in Him than the contrary."44

Years later, when considering the possibility of a plurality of worlds in his French commentary, Oresme declared that the "human understanding consents naturally that beyond the heavens and world, which is not infinite, there is some space, whatever it may be; and one could not readily conceive the contrary."45 He repeated the substance of his earlier discussion, declaring that this void space "is infinite and indivisible, and is the immensity of God, and is God Himself, just as the duration of God, called eternity, is infinite and indivisible, and is God Himself, . . ."46 Moreover, this space is incorporeal and without extension.47 It is

monde, 10 vols. (Paris: Hermann, 1913-1959), Vol. V, p. 232; Vol. VII, pp. 297-302; and Vol. VIII, pp. 58-59.

42 Oresme, De caelo, p. 280. 43 Ibid., p. 288. 44 Ibid., p. 294. I have added the bracketed

words. Like Bradwardiine, Oresme insists that God "is everywhere in the world and outside" (ibid).

45 "Je respon, et me semble premierement, que entendement humain aussi comme na- turelment se consent que hors le ciel et hors le monde qui n'est pas infiny est aucune espace quelle que elle soit, et ne puet bonnement concevoir le contraire." Oresme: Du ciel et du monde, Bk. I, Ch. 24, p. 176.

46 "Item ceste espasse dessus dicte est infinie et indivisible et est le immensite de Dieu et est Dieu meismes, aussi comme la duracion de Dieu appellee eternite est infinie et indivisible et Dieu meisme...." Ibid. Oresme here identifies the infinite extramundane void with God Himself. In this he differs from Brad- wardine.

47 Despite a lack of explicitness, and even some ambiguity, it seems that Oresme would have denied physical extension to the extramundane void. He explains that "God by His infinite magnitude (without quantity and absolutely indivisible), called immensity is necessarily wholly in every extension or space

or place which is or which could be imagined" (". . . semblablement Dieu par sa grandeur infinie sanz quantite et simplement indivisible appellee immensite est de necessite tout en toute extension ou espace ou lieu qui est ou qui peut estre ymagine." Ibid., p. 278). Thus it would seem that God, though dimensionless, would be in every physically extended space. From this it might be supposed that Oresme would have argued that the infinite void beyond the cosmos, which is also occupied by God, would also be a physically extended space, differing not all in this regard from any finite physical space occupied by God. This seems unlikely, however, for, as we have seen, Oresme identified the extramundane void with God Himself, who is without extension (". . . His eternity is without succession and His immensity without extension . . ." [". . . son eternite est sanz succession et son immensite sanz extension. . . . Ibid., p. 272]; hence this particular space would also be extensionless. Nowhere does Oresme identify "God Himself" with actual physical or dimensional spaces, but rests content to say only that God is in them because He is everywhere. It would appear that Oresme's identification of God with an infinite void beyond the cosmos conferred upon the latter a transcendent and nondimensional character. It should be mentioned, however, that in Bk. IV, Ch. 11 (ibid., p.




therefore imperceptible and not properly comprehensible except by reason. And perhaps-though he makes no mention of this-it is "imaginary"; for since it is imperceptible, whatever little understanding of it we may have results from our reason alone.

Although Oresme readily conceded that by virtue of His absolute power, God could, if He wished, create a plurality of worlds in this infinite void, he concurred with Aristotle that there is only one world which contains all the matter in existence. But despite its lack of extension and matter, this infinite extramundane void was invoked by Oresme as a hypothetical backdrop for an absolute motion bearing no relationship to any other. Such an absolute motion would result if God chose to move our finite cosmos with a rectilinear motion through this infinite void,48 an illustration that Samuel Clarke found useful in countering Leibniz's relational concept of space.49

The seemingly novel and unusual arguments advanced by Bradwardine and Oresme may have served as the source and basis of similar discussions of this

725), Oresme declares that one of three ways bodies might exist in the final resurrection is in a space that is now absolutely void so that they would not be contained or surrounded by anything since "it is a place imagined void and infinite-i.e. the immensity of God and God Himself, as we declared at the end of the twenty-fourth chapter of the first book. And perhaps this is what job understood when he said of God: 'He stretcheth out the north over the empty place.'" (". . . une est que l'espace ou il seront soit maintenant simplement wide, et quant il y seront que il n'i ait autre corps que les contienne, mais est un lieu ymagine vieu et infini-ce est le immensite de Dieu et Dieu meisme, si comme il fu declare en la fin du xxiiiie chapitre du premier. Et peust estre que ce entendoit Job quant il dist de Dieu: Qui extendit aquilonein super vacuum." Ibid., p. 724). How this example and that of the motion of the cosmos through the same infinite void (see the next paragraph) bear on the question of its dimensionality is a puzzle. Despite these difficulties, I feel some degree of confidence that if pressed Oresme would have declared it without extension or dimension.

48 Ibid., pp. 368-370 (Duhem quotes the French text in Le Systeme, Vol. VII, p. 300):

But perhaps someone will say that to move with respect to place is to change one's position in relation to some other body which may, or may not, be in motion itself. Yet, I say that this is not valid, primarily because there is an imagined infinite and immobile space outside the world, as was stated at the end of the twenty-fourth chapter of the first book, and it is possible without contra-

diction, that the whole world could be moved in that space with a rectilinear motion. To say the contrary is an article condemned at Paris. Now assuming such a motion, there would be no other body to which the world could be related with respect to place, and the description given above would be invalid.

The article condemned at Paris in 1277, and converted here into an illustration of absolute motion, is number 49 (see above, n. 27). In his Questions on the Physics, Bk. III, Ques. 7, Marsilius of Inghen, a 14th-century nominal- ist, also employs this illustration and mentions an infinite space beyond the heavens. See M. Clagett, The Science of Mechanics in the Middle Ages (Madison: Univ. Wisconsin Press, 1959), p. 623.

49 In par. 4 of his Third Reply to Leibniz in 1716, Clarke argued for Newtonian absolute space by noting that "if space was nothing but the order of things coexisting [as Leibniz maintained] ; it would follow, that if God should remove the whole material world entire, with any swiftness whatsoever; yet it would still always continue in the same place" (The Leibniz-Clarke Correspondence, ed. H. G. Alexander, New York: Philosophical Library, 1956, p. 32 ; the bracketed qualification is mine). Thus if space is merely a relationship between coexistent things-as Leibniz held-and God moved the world taken as a single thing, the world could not be said to have undergone any motion, since there would be no other existent thing to which it could be related. For Clarke, as for Oresme, the hypothetical conditions described above would indeed produce a motion-an absolute motion.



50 EDWARD GRANT

problem in the Middle Ages and Renaissance.50 Rather then elaborate more of these, however, I propose to examine a significant question. Why did Brad- wardine, Oresme, and perhaps others see fit to adopt a position that had been rejected by Augustine and Aquinas, and, to my knowledge, all others prior to the fourteenth century? In the absence of direct and obvious evidence, my response must be tentative and suggestive. But it would appear that a reasonable ex- planation could be formulated in terms of the tremendous consequences that flowed from the condemnation of 219 articles by the Bishop of Paris in 1277.51

Almost all are agreed that this massive condemnation must be interpreted as a major assault upon Christian Aristotelians at the University of Paris who, in employing Aristotelian metaphysical principles and determinism in their many physical and theological demonstrations, had placed serious limitations on God's absolute power.52 They had argued, for example, that God could not create more than one world, that He could not move the world and leave behind a void, that He was unable to create an accident without a subject, that He could not perform the absolutely impossible in nature,53 and so on. The Condemnations of 1277 represent the theological reaction against the deterministic Christian Aris- totelianism that had developed soon after the reception of Aristotle's natural books in the late twelfth and the thirteenth centuries. Not long arter 1277 theo- logians used philosophical argument to restrict the domain of certain and demon- strable knowledge and came to emphasize God's absolute power to act as He pleased in a manner that was largely unfathomable and utterly unpredictable.

50 For example, the discussions of John Buridan (see above, n. 15), Marsilius of Inghen (n. 48), John Major (Le Traite' 'De L'Infini' de Jean Mair, ed. and trans. Hubert Elie, Paris: J. Vrin, 1938, p. 94), and Christo- pher Clavius (In Sphaeram Joannis de Sacro Bosco Commentarius, Rome, 1570, Bk. I, at the very end of the section De ordine sphaera- rum caelestium). According to Duhem (Le Systeme, Vol. V, pp. 231-232), I-Iasdai Crescas (1340-1410), a Spanish Jew, also identified an infinite extramundane void with God's immensity, thereby influencing Spinoza, who ascribed to God the attribute of extension. In this, says Duhem, he was but echoing Oresme. But Harry Wolfson (Crescas' Critique of Aristotle, Cambridge, Mass.: Harvard Univ. Press, 1929, p. 123) denies such an identification, claiming that Crescas' God is transcendent. In arguing against Aristotle, however, Crescas did propose the existence of an infinite extramundane void. The issue is not unambig- uous, and it hardly seems farfetched to suppose that perhaps Crescas and Spinoza were influenced ultimately by the medieval views formulated in the 14th century and thus far best represented by Bradwardine and Oresme.

There were also theological arguments denying an extramundane infinite void in which

God is omnipresent. Thus Duns Scotus and his followers insisted that God's presence in a place was not a necessary prerequisite for His acting in that place. God's will, not His omnipresence, was taken as the basis of His actions, so that it was assumed that He could act on and in a place remote from His presence. With "action at a distance" as God's modus operandi, Scotus denied the necessity of God's presence in the empty place where He came to create the world and, a fortiori, denied the necessity of God's omnipresence in an infinite void space. For Scotus' argument see the Questio Unica in Bk. I, Distinction 37 in his Questions on the Sentences in Joannis Duns Scoti ... opera omnia editio nova juxta editionem Waddingi XII tomos continentem

. . ., Vol. X (Paris Vivies edition, 1893), p. 597, col. 2.

51 They are conveniently published in the Chartularium (see n. 27).

52 See Julius Weinberg, A Short History of Medieval Philosophy (Princeton: Princeton Univ. Press, 1964), pp. 171-172, 238; also my article "Late Medieval Thought, Copernicus, and the Scientific Revolution,"' Journal of the History of Ideas, 1962, 23: 199-207.

53 Articles 34, 49, 141, and 147 of the Con- demnations.




The outcome was fourteenth-century nominalism and the concept of a God free to act independently of and even contrarily to Aristotelian metaphysics and natural philosophy.

It is against this intellectual background that our question can be quite plausibly answered. After the Condemnations it would have seemed absurd to some that the omnipresence of an infinite and all powerful God should extend no further than the finite cosmos of His own making simply because Aristotle had denied that anything at all could exist beyond the world. But Aristotle's demonstration of this had involved just the sort of appeal that had fallen under a theological and philosophical cloud in the fourteenth century. To the extent that it had theological application or impact, it was truly suspect. The spirit of 1277 is embodied in article 49 of the Condemnations, which reads: "That God could not move the heavens [i.e., the world] with rectilinear motion; and the reason is that a vacuum would remain." Thus to deny that God could move the world with a rectilinear motion, despite the vacuum left behind, was to risk excom- munication. It is significant, therefore, that both Bradwardine and Oresme cited this very article in their arguments in behalf of an infinite extramundane void.54 Perhaps as they considered the full implication of that article they were led to the conclusion that if God did move the world in a straight line, not only would the place left behind be void, but so also would the successive places occupied by the world, all of which must necessarily exist outside of the world. If, then, void exists beyond the cosmos, would it not be reasonable to suppose, as St. Augustine had argued in The City of God, that if God is omnipresent inside the world, He would also be present in anything existing outside the world? But if it is to contain an infinite God, would it not be appropriate and even necessary that this extramundane void be infinite? Indeed, what arguments could be pro- posed for assuming it finite? Where could it terminate? With the breakthrough made, Bradwardine, or perhaps others before him, could then have formulated the more elaborate and detailed justification which we find in De causa Dei.

Only further research can determine the soundness of this interpretation. But it seems true to say that by the fourteenth century the God of Latin Christianity had filtered through the outermost celestial sphere of the Aristotelian universe to wholly occupy and constitute an infinite surrounding void.

II

The peculiarly medieval and anti-Aristotelian cosmological views just described were destined to exert a significant impact on sixteenth- and seventeenth- century authors, including Isaac Newton, who assigned to his absolute space properties and attributes that bear the unmistakable influence of this extraordinary and near-incomprehensible medieval doctrine. In what follows, a few major problems will be kept at the forefront: (1) how the term "imaginary"

54 See above, notes 27 and 48. Thus even if prior to the Condemnations of 1277 views similar to Bradwardine's had been enunciated, it is nevertheless obvious that article 49 played

a role in justifying the acceptance of an infinite extramundane void by Bradwardine and Oresme.



52 EDWARD GRANT

was understood in the expression "imaginary infinite void space," (2) whether or not it was three dimensional, and (3) how God was conceived to exist in this infinite void.

In medieval discussions about an imaginary infinite extramundane void there seems to have been little direct and explicit concern about the meaning of the term "imaginary." Thus, as we described above, only indirectly did Oresme suggest that infinite incorporeal space might be "imaginary" because it is not perceptible to the senses and insofar as it is comprehended at all, it is by reason alone. But in a sixteenth-century Jesuit scholastic commentary on Aristotle's Physics, written in Coimbra, Portugal, the question is raised explicitly and a very different interpretation given. The medieval problem of imaginary infinite void space is considered at length in Book VIII, Chapter 10, Question II, where it is asked "whether or not God exists beyond the sky [or celestial heavens]."55 In the course of formulating an affirmative response the anonymous commentator asks in Article IV "What is Imaginary Space?"56 At the outset he insists that this imaginary space, both inside and outside the world, is not a true three- dimensional entity.57 Nor is it a mere object of the reason or intellect alone, "since by means of this thing itself bodies are received within the world without the action of the intellect; and they can [also] be received outside [or beyond] the world if they were created there by God."58 Since actual bodies are potentially receivable into this space, its dimensions are surely not imaginary because "they are fictions (fictitiae) or depend solely on a mental conception, or are thought to be beyond the understanding...."59 It is rather because we imagine the dimensions of this space "in a certain relationship corresponding to the real and positive dimensions of bodies."60 That is, although it is itself devoid of quantitative dimension, its capacity to receive real three-dimensional bodies confers upon it a correspondence to those three-dimensional bodies. Neverthe- less, despite its correspondence "to the real and positive dimensions of bodies," it is not itself a "real and positive being since besides God, no such thing could exist from eternity."6' In earlier articles of this same question our author argued

55 Commentariorum Collegii Conimbricensis Societatis Iesu in octo libros Physicorum Aris- totelis Stagiritae. Prima Pars qui nunc primum Graeco Aristotelis contextu Latino e regione respondenti aucti ob studiosorum Philosophiae usum in Germania sunt editi . . . (Cologne, 1602), col. 514.

56 "Quidnam sit imaginarium spatium?" Ibid., col. 518.

57 "Primum sit: hoc spatium non esse veram quantitatem trina dimensione praeditam" (ibid.). Perhaps of influence here was Aris- totle's insistence in Physics IV, Ch. 8 (216a.26-216b.11) that if void were a three- dimensional entity and received a three- dimensional material body, it would follow that two equal dimensions would occupy the same place.

58 "Secundum est: spatium hoc non est ens

rationis cum ab eo re ipsa absque opera in- tellectus intra mundum corpora recipiantur; et extra mundum recipi queant si illic a Deo creantur." Ibid., col. 519. Although Oresme had argued that it was known by the reason, he also believed that it had objective reality.

59"Quare eius dimensiones non iccirco imaginariae dici consueverunt quod fictitiae sint, aut a sola mentis notione pendeant, nec extra intellectum dentur; . . ." Ibid.

60 This quotation follows immediately after the passage in n. 59 :"sed quia imaginamur illas in spatio proportione quadam respon- dentes realibus ac positivis corporum dimen- sionibus." Ibid. The italics are my own.

61 "Item nec esse ullum aliud reale ac positivum ens cum nihil tale praeter Deum ab aeterno fuit." Ibid., col. 518. This is the position which Bradwardine had adopted earlier.




that the world was created in a place that formed part of a preexistent uncreated space.62 And yet if this space were a positive thing it would have existed co- eternally with God, a consequence repugnant to Christians. The dilemma is resolved by denying reality and positiveness to this preexistent space, thus allow- ing our commentator to conclude that "this space always existed and always ought to be."63

Moreover, he declares that "God is actually in this imaginary space, not as in some real being but through his immensity, which, because the whole uni- versality of the world cannot [accommodate it], must of necessity, also exist in infinite spaces beyond the sky."64 But how can God exist in something that is not a real and positive being-that is, how can God be in nothing? The response to this query is made by appeal to God's absolute power. Since by divine power God could, if He wished, create a stone in this nothingness, it follows that He Himself could also exist in this imaginary void space.65 Indeed, God must exist "beyond the sky because He cannot be excluded from any place, whether true or imaginary."66

Although a number of seventeenth-century authors would be concerned with the very same problem, it is likely that few, if any, presented so detailed an account as Otto von Guericke in his justly celebrated New Magdeburg Experi- ments on Void Space.67 Because of his familiarity with the Coimbra Scholastic commentaries on Aristotle's Physics and De caelo and his acceptance of important elements in their discussions on infinite void,68 von Guericke can rightly be said to have been influenced by the medieval tradition, even to the extent of pursuing one aspect of the earlier views to startling extremes.69 But he also departed sig- nificantly from his predecessors and, as we shall see, despite a statement to the contrary in which he seems to associate himself with the medieval tradition of a dimensionless space, he conceived of extramundane void as a three-dimensional entity.

As with his medieval predecessors, it is Aristotle's denial of void and any kind of existence beyond the cosmos that provides the point of departure for von

62 As will be seen below, Otto von Guericke shared this opinion.

63". . . hoc vero spatium semper extiterit semperque esse debeat." Conimbricensis, cols. 518-519.

64 "In hoc igitur imaginario spatio asseri- mus actu esse Deum, non ut in aliquo ente reali sed per suam immensitatem quam quia tota mundi universitas capere non potest necesse est etiam extra coelum in infinitis spatiis existere." Ibid., col. 519.

65". . ., we deny that God cannot be in nothing-i.e. in a space which is not a real and positive being; otherwise no stone could exist beyond the world by [an act of] the divine power." (". . . inficiamur non posse Deum esse in nihilo, id est, in spatio quod ens reale et positivum non est alioqui nec lapis

divina virtute extra coelum esse posset.") Ibid.

66"Est extra coelum quia a nullo seu vero seu imaginario loco excludi potest." Ibid.

67 Experimenta nova [ut vocantur] Magde- burgica de vacuo spatio (Amsterdam, 1672; reprinted, Aalen: Otto Zeller, 1962).

68 At the end of Bk. II, Ch. 8 (p. 65, col. 2), following a lengthy presentation of his own views on infinite imaginary space, von Guericke remarks that "the Coimbra (Conim- bricenses) discussions confirm all these things, as can be seen [above] in [Bk. I], chapter 35.,,

69 Little or no attention has been paid to this extraordinary aspect of von Guericke's in- terest in void space. As will be seen, he had a good grasp of the different historical interpretations of this unusual problem.



54 EDWARD GRANT

Guericke's lengthy discussion.70 After observing that the Coimbra commentators on Aristotle's Physics and De caelo assumed an imaginary space or receptacle beyond the cosmos that was capable of receiving bodies,7' he distinguishes a number of different interpretations that were held about the nature of imaginary space. Some insist that it is nothing; others that it is empty of all reality; still others that it is the negation of all being; and there are those who consider it a mere fiction. There were also those who interpreted it as a possible location for an infinite corporeal mass, while others understood it as God Himself.72 Finally, and perhaps surprisingly, the views of Descartes are quoted from the Principles of Philosophy, Part 2, Number 21, in which, according to von Guericke, Descartes argues that imaginary space is something real, namely an indefinitely extended corporeal substance.73

Launching into a presentation of his own opinions, von Guericke assumes a finite world and raises the popular question of what lies beyond, offering substantially the same Stoic argument reported by Simplicius and cited frequently in the Middle Ages.74 He concludes that beyond the cosmos there exists a

70 Experimenta nova, Bk. I, Ch. 35, p. 51, col. 1.

71 Ibid., p. 51, col. 1-p. 52, col. 1. He quotes at some length from the commentary on the Physics, repeating much of what has been cited here in notes 57-66.

72 Here is von Guericke's report of descriptions of and hostile reactions to a number of different conceptions of "imaginary space" (ibid., p. 52, cols. 1-2):

Others say that imaginary space is nothing other than nothing.

Others hold that it is empty of all reality. Others proclaim that it is the negation of

all being. Others respond [to these last three

descriptions as follows]: (1) as for its being "nothing," if it were nothing, space could not be conceived, for "nothing" could have neither extent, nor width, nor length, nor depth. With respect to [description] (2), they infer that if imaginary space is space that is empty of all reality and being, and since the same thing is said of vacuum, therefore vacuum or imaginary space are one and the same thing. As for [description] (3), they reply that if imaginary space is the negation of every being, then it cannot be called space.

Furthermore, some desire that imaginary space be merely something fictitious. From this they conclude that before the creation of the world there was no thinking [or con- ceiving] intellect [and] therefore no imaginary space. And since God cannot be in that which does not exist (as in chimeras), but only in that which does exist, imaginary

space does not exist, according to their view. Therefore, God is not in imaginary spaces.

Others understand imaginary space as some merely possible, immense, corporeal mass that is diffused everywhere into infinity; or [imaginary space is] a possible location of such a corporeal mass [or quantity].

Some say (as does Lessius in Bk. 2 of De perfectione divino) :"imaginary space is God himself, who, in accordance with His immensity is necessarily everywhere, or infinitely, diffused." For if someone could transcend all the [celestial] heavens and seek what is in the space which he forms in his imagination, he would surely find God.

Some wholly reject imaginary space for this reason: because what is conceived only by our imagination or mind is not something about a real thing. For example, someone could conceive or imagine that he has 1000 gold pieces, when, indeed, he does not have a single one. Therefore, there is no imaginary space. In order to conserve space and include the

interesting and relevant portions of von Guericke's arguments, I shall often present only my own translation and omit the Latin text.

73 Ibid., p. 52, col. 2. 74 Ibid., Bk. II, Ch. 6, p. 61, col. 2:

Assuming, according to the more common opinion, that there is "nothing" (nihil) beyond the world (taking "nothing" in the Aristotelian sense), then if someone should reach the last confines of the world, he either could, or could not, extend his arm beyond the last surface of the last heaven




special kind of infinite nothing filled with God and in which, barring obstructions, inertial motions would ordinarily occur.75

Adopting a position contrary to the anonymous Coimbra commentator, von Guericke characterizes imaginary infinite space as a positive and real thing, nothing less than true space.76 Anticipating an objection that something imaginary cannot also be a positive and real entity, he replies that

it is necessary that at least we imagine everything we never see and which is beyond our grasp, as, for example, it is necessary that one who never sees Rome, or a spirit, or an exotic animal, or some other thing, must imagine them; and because no one can comprehend the infinite, it is grasped at least in some way, by the imagination. Meanwhile, it does not follow that Rome, or spirit, or the infinite, are not real (verum) or positive things.77

But is this real and positive God-filled imaginary space extensionless and dimensionless, as conceived by medieval authors, or is it dimensional? Initially, in Book II, Chapter 4, von Guericke seems to adopt the medieval position when he declares that he is not considering space in the usual and common three-dimensional manner, but rather as a universal container of all things "which is not to be conceived according to quantity, or length, width, and depth."78 This space is a

or hurl a spear and a stone into this nothingness.

In the first case, if one could [do this], there would be nothing to obstruct it and so it would be true that "nothing" is there; but nevertheless space is there (for if no space were there, a stone could not be projected beyond, nor an arm be extended because it cannot be in something into which it cannot be sent; nor could anything be in it because what is not has neither extent nor width, but is absolutely incapable of receiving anything) and, consequently, there would be something [out there].

In the second case, if one could not [do this], something must necessarily im- pede [or obstruct] it, [since] one [body] could not occupy the place of another. Now what obstructs it will be, necessarily, something hard or corporeal. Therefore, something will exist outside the last bound- ary [or terminus] of the world, since [mere] "nothing" cannot obstruct. Nor can what obstructs be called "non-being." 75 Ibid., p. 61, col. 2-p. 62, col. 1 Indeed, since it cannot be denied that the Divine Essence, infinite [and] immense, is beyond the world, then all the more reason it is appropriate that it [i.e., the space beyond the world] is immense in extent, width, depth, i.e., according to space or expanse; but it is not to be considered an absolutely infinite nothing (indeed according to what will be said in the following

chapters, we know that it is not [an infinite nothing] ).

It follows, moreover, that unless the spear or stone were impeded by another body, it could be projected beyond and such a projection (jactus) could be continued into infinity. 76 He tells us "that the nothing (nihil) be-

yond the world and space (spatium) are one and the same; and so-called imaginary space is true space, for imaginary space (in the common opinion of philosophers) is nothing and nothing is space, and the space which they call imaginary is true space (spatium verum). Nor can it be objected that whatever is imaginary is not a positive and real thing even if it is not always efficacious." Ibid., p. 62, cols. 1-2. Also see the quotation a few lines below. As we have seen (n. 61), the Coimbra commentator denied that imaginary space had a real and positive being.

77 Ibid., p. 62, col. 2. This passage follows immediately after the quotation in n. 76.

78 I include the full relevant quotation here (ibid., p. 57, col. 1):

Non tractamus hoc loco de Spatio secundum trinam dimensionem, vel ut vulgus Spatium concipere solet, de Magnitudine, Amplitud- ine, aut Capacitate, huius vel illius Rei, vel Loci, vel Aedificii, vel Palatii, Agri, Re- gionis, Distantiae, etc. Sed de Universali omnium rerum Vase aut Continente; quod non est aestimandum secundum quantitatem, seu longitudinem latitudinem atque profunditatem: neque considerandum re-



56 EDWARD GRANT

permanent, immobile, indivisible entity permeating everything corporeal and incorporeal. But in Book II, Chapter 6, von Guericke describes this God-filled space as three dimensional when he says that it is "immense in extent, width, depth, i.e., according to space or expanse" (see above, n. 75). A bit later, tri- dimensionality is clearly implied when he argues that "if the projection of a spear or stone could be continued into infinity and no terminus for resting is revealed, it follows that this space beyond the world is extended or expanded without end toward all parts and thus is infinite and immense."79 It is again implied when we are told that "in relation to the immensity of this space" the finite world "does not have the likeness of a point or atom."80 Such descriptions and comparisons make it reasonable to conclude that Otto von Guericke conceived imaginary infinite void space as a three-dimensional entity.

But how did he relate this space to God and the creation? As for the first part of this question, he contends that space is eternal, arguing that "the infinite essence of God is not contained in space, or vacuum, since God, who is present everywhere, is not contained in space or vacuum but the space and vacuum of the whole creation are in Him, by Him, and for Him."81 A response to the second part emerges in his answer to the question raised by Bradwardine and other medieval scholastics as to what existed before the creation of the world. Here von Guericke replies that two responses are correct and equivalent, namely Nothing (nihil) and the Uncreated (increatus), which are in fact identical with

spectu ullius substantiae, vel punctim, vel sectim, vel divisim vel ex parte, aut super- ficialiter aut interne aut exteme, etc. Nec per aliquam diffusionem, dilatationem vel expansionem sui ipsius; sed ita quod infini- tum et omnium rerum continens est, in quo omnia sunt vivunt, et moventur, nullam inde sustinens variationem, alterationem aut mutationemn.

This kind of absolute nondimensional space is contrasted with the spaces which all bodies occupy within the finite cosmos and the spaces between those bodies:

Moreover the space which a mundane body occupies, namely according to its quantity or three dimensions, is its internal space; its external space is the sky or expanse [extending] from its surface to the farthest [visible?] determination. ("Spatium itaque, quod Corpus Mundanum occupat, secundum scilicet cujusvis quantitatem seu trinam dimensionem, est Spatium ejus intrinsecum: Extrinsecum autem est Coelum vel Expan- sum a superficie ad extimam determina- tionem." Ibid., Bk. II, Ch. 5, p. 59, col. 2. 79 Ibid., Bk. II, Ch. 6, p. 62, col. 2. Earlier,

in Bk. I, Ch. 35, after describing various interpretations of imaginary space von Guericke seems to present a preview of his own understanding of imaginary space when he says (p. 52, col. 2):

. . .finally, if imaginary space is conceded,

it follows that it is infinite and immense or infinitely expanded in all its parts, i.e. in length, width, and depth; it also follows that it is incorruptible, sempitemal, immobile, fixed, and permanent, so that by no force or reason could it be destroyed; and thus it could be the receptacle [or container] of any body whether great or small. On this matter, see several places in Bk. 2, following. 8 044 ..quia Mundus hic, in illo Infinito

Spatio (et quidem respectu immensitatis Spatii non puncti vel Atomi instar) contentus est

..." Ibid., Bk. II, Ch. 8, p. 65, col. 1. 81 Ibid., p. 64, col. 2. This remark follows

shortly after a lengthy quotation from Athana- sius Kircher's Itinerarium ecstaticum (1656), in which Kircher argued that God necessarily fills an infinite imaginary void because outside of God "it is necessary that neither Noth- ing, nor emptiness, nor vacuum be left." Von Guericke criticizes Kircher for seeming to deny the existence of void and imaginary space because he (Kircher) supposed that God fills these entities and thereby actually prevents their existence. For von Guericke these are real entities contained in God and existing for God. On this issue von Guericke seems to agree with Oresme that space is in God, whereas Bradwardine and the Coimbra commentator held that God is in (i.e., contained in) an eternal infinite space.




infinite void space: "For where created things subsist and are now, Nothing was there before and they were received in Nothing, that is, in the Uncreated, for they could not be received in any created thing both because it was not and because if it was it was not a Nothing but a created something."82 By virtue of his conception of infinite void space as a positive, real, and uncreated thing contained in God, von Guericke was led to almost lyrical heights in characterizing the enormous power and efficacy of this empty space. Indeed his description is nothing less than an Ode to Nothing:

For the "Uncreated" is that whose beginning does not pre-exist; and Nothing, we say, is that whose beginning does not pre-exist. Nothing contains all things. It is more precious than gold, free of origin and distinction, more joyous than the appearance of beautiful light, more noble than the blood of kings, comparable to the heavens, higher than the stars, more powerful than a stroke of lightning, perfect and blessed in every part. Nothing always inspires. Where Nothing is there ceases the jurisdiction of all kings. Nothing is without any mischief. Accord- ing to Job, the earth is suspended over Nothing. Nothing is outside the world. Nothing is everywhere. They say the vacuum is Nothing; and they say that imaginary space-and space itself-is Nothing.83

We are here far removed from atomist and Stoic conceptions of infinite void space. No longer is the infinitely extended void an inefficacious, impotent, and completely empty three-dimensional space. For von Guericke, who was extending and elaborating a strong medieval Christian theological tradition founded upon an omnipresent God, infinite imaginary void space has become a three-dimensional, positive, real, all-powerful, and divine force.

If I have emphasized von Guericke's interpretation, it is only because he reveals so clearly his debt to the medieval tradition. But the same tradition was available in England, if not through the Coimbra commentaries then through the 1618 edition of Thomas Bradwardine's De causa Dei contra Pelagium edited by no less a figure than Henry Savile. In England men like Henry More, Joseph Raphson, Samuel Clarke, and even Newton himself also conferred upon this space an extended dimensionality which it never possessed in the medieval tradition, and in so doing made of their God a dimensionally extended being.

Thus Henry More conceives of a finite world located in an infinite space filled with God, but an infinite space that is "by immense spaces larger and more

82 "Ubi enim nunc sunt Creata et subsistunt, Nihil erat prius, et in Nihilo recepta sunt, id est in Increato, quia in aliquo Creato non recipi potuerunt, tum quia non erat, tum quia si fuisset, non fuisset Nihil, sed Creatum aliquid." Ibid., Bk. II, Ch. 7, p. 63, col. 2.

83 Ibid.: Nam Increatum est, cujus nullum praeexistit initium: et Nihil, dicimus esse, cujus nullum praeexistit initium. Nihil continet omnia; est pretiosius auro, expers originis et interi- tus, jucundius conspectu almae lucis, nobi- lius Regum sanguine, aequiparabile Coelo, altius Astris, potentius fulmineo ictu, perfec-

tum et ab omni parte beatum. Nihil semper sapit: Ubi Nihil est, ibi omnium Regum cessat jurisdictio: Nihil est sine ulla calami- tate: Super Nihil, secundum Hiob, suspensa est Terra; Nihil est extra Mundum, Nihil est ubique; Vacuum dicunt esse Nihil, et Spat- ium Imaginarium ut et Spatium ipsum, dicunt esse Nihil.

The italics were supplied by von Guericke himself. The reference to Job is 26,7, where it is said of God: "He stretched out the north over the empty space." Interestingly, in his discussion of imaginary space, Oresme also cited this line.



58 EDWARD GRANT

ample" than the world it contains.84 Thus we have an apparent physically extended space converting God to a physically extended being. And Joseph Raphson, in his De spatio reali of 1702, argues that God's true omnipresence is a necessary prerequisite for the existence of all things. But only if God is actually extended can he be omnipresent. "Indeed to be present in places diverse and distant from each other, for instance in the globe of the Moon and in that of the earth, and also in the intermediate space, what else is it but, precisely to extend oneself?"85 For Raphson "this extension is truly real, indivisible, immaterial (or, if you wish, spatial, ) "86 for he was convinced that every positive and primary attribute "such as extension in matter, etc. must necessarily be really and truly present in the First Cause and be in it in a degree of infinite excellence in the manner most perfect of its kind."87 Indeed Raphson, indicating an acquaintance with medieval arguments, says that the Schoolmen had conceived of the extension of God as transcendent. But, in seeming disagreement, he asks how extended beings can come from something that is only transcendently, not actually, extended.88 Hence Raphson does not hesitate to think of God as actually extended in space. Newton too seems to think of God as actually extended through an infinite dimensional space. This is borne out by the General Scholium in the second edition of the Principia in 1713, where Newton says of God that

He is omnipresent not virtually only, but also substantially; for virtue cannot subsist without substance. In him are all things contained and moved; yet neither affects the other: God suffers nothing from the motion of bodies; bodies find no resistance from the omnipresence of God. It is allowed by all that the Supreme God exists necessarily; and by the same necessity he exists always and everywhere.89

To bother to explain, as Newton does, that bodies in motion through space- undoubtedly a three-dimensional space-are not affected or otherwise resisted by the omnipresent God is to say that God is actually in every part of that space. In his defense of Newton against Leibniz, Samuel Clarke would call infinite

84 Enchiridium metaphysicum (1672), Ch. 8, as quoted in A. Koyre, From the Closed World to the Infinite Universe (Baltimore: Johns Hopkins Press, 1957), p. 154. Koyre observes that More made infinite space an attribute of God (p. 155) and "by a strange irony of history, the x%vov of the godless atomists became for Henry More God's own extension, . . ." (p. 154). Koyre has brilliantly described, analyzed, and quoted the opinions of those few authors who will be mentioned here. Since it is merely our purpose to indicate very briefly how these few "spatialized" God, to use Koyre's term, it will be convenient to cite some of the quotations from his book.

85 Koyre, From the Closed World, pp. 197- 198.

86 Ibid., p. 198. 87 Ibid., p. 199. 88 Ibid. In Pt. VII of the eighth of his Di-

alogues on Metaphysics and on Religion, Nicolas Malebranch seems to adopt the very

transcendent medieval sense which Raphson criticizes. His spokesman, Theodore, says: "God, then, is extended, no less than bodies are; since God possesses all absolute realities or all perfections. But God is not extended in the way in which bodies are, .... there are no parts in His substance" (trans. Morris Ginsberg, Library of Philosophy, London, 1923, p. 211). In Pt. VIII of the same dialogue (pp. 212-213), Theodore insists that "The immensity of God is His substance itself spread out everywhere, filling all places without local extension, and this I submit is quite incomprehensible . . . . Assuredly, Theotimus, if you judge of the immensity of God by means of the idea of extension, you are giving God a corporeal extension."

89 Sir Isaac Newton's Mathematical Princi- ples of Natural Philosophy, translated into English by Andrew Motte in 1729. The translation revised . . . by Florian Cajori (Berke- ley: Univ. California Press, 1947), p. 545.




space an attribute of God90 and insist that "space and duration are not hors de Dieu but are caused by, and are immediate and necessary consequences of his existence. And without them, his eternity and ubiquity (or omnipresence) would be taken away."91 Thus for Clarke space is eternal because it is a necessary consequence of God's existence, and it must be conceived as dimensionally extended because it is the instrumentality through which God makes himself actually omnipresent.

It is evident that in England and elsewhere the position developed in the Middle Ages was widely adopted-that God in virtue of His infinite power and immensity must necessarily occupy and fill an infinite void space. But whereas in the Middle Ages God's nondimensionality was deemed paramount so that He was held to occupy an imaginary nondimensional extramundane infinite void, in the seventeenth century He is thought to fill a three-dimensional void and thereby has become a physically extended three-dimensional incorporeal being. How did this happen? If I may be allowed to conjecture and speculate-for there is little that would at present pass for solid evidence in tracing this transition- it seems to me bound up with the Aristotelian cosmos and its collapse in the seventeenth century.

CONCLUSION

It is no exaggeration to say that the medieval Scholastics who accepted and argued for the reality of an imaginary infinite void space beyond the finite and spherical Aristotelian cosmos did so on purely theological grounds. Perhaps in the aftermath of the Condemnations of 1277 it was inconceivable to them that a God possessed of infinite and absolute power should be confined to an abode at the empyrean heaven or be otherwise restricted to the universe He created. Rather, it was necessary that He be omnipresent both inside and outside the world and therefore infinitely everywhere. But it was an equally indispensable condition that He be nondimensional and unextended, for otherwise He would be a divisible being; hence His spatial omnipresence was to be taken only in a transcendent sense. Incomprehensible as all this may seem, it provoked no intense debate and had almost no impact on medieval Aristotelian physics, which was concerned exclusively with motion and change within-not without-the finite world. To be sure, God could, if He wished, create bodies beyond the cosmos. But most were content to side with Aristotle and believe that all existent matter lay within our finite world, wholly filling it to the exclusion of all vacua. And so it was that apart from a few extremely interesting hypothetical arguments the existence of an imaginary extramundane infinite void required no adjustments in medieval physics and cosmology.

By the seventeenth century, however, an enormous change had occurred.

90 The paragraph containing this declaration is worthy of full citation because it reflects the medieval position described above. "Void space, is not an attribute without a subject; because, by void space, we never mean space void of everything, but void of body only. In all void space, God is certainly present, and

possibly many other substances which are not matter; being neither tangible nor objects of any of our senses." Clarke's Fourth Reply, par. 9, in The Leibniz-Clarke Correspondence, p. 47.

91 Ibid., par. 10.



60 EDWARD GRANT

Aristotelian physics and cosmology were barely alive, except in Scholastic cir- cles. The significant advances in astronomy and physics were being made outside of and in opposition to the Aristotelian science of the Schoolmen. Moreover, opinions and viewpoints about the actual existence of void spaces had undergone some transformation in the course of the seventeenth century. Experiments and discoveries about atmospheric pressure-especially those by Pascal, von Guericke, and Robert Boyle-had shown that nature did not abhor a vacuum and that atmospheric pressure decreased as the height of the air above the earth's surface increased. By means of pumps, artificial vacua were produced in enclosed vol- umes, and while many still denied the interpretations placed upon such experiments, others eagerly accepted the actual existence of both artificial and natural vacua. Finally, ancient atomism with its three-dimensional void space extending to infinity also had its adherents, as did Stoic cosmology in which a sealed finite world was surrounded by a real infinite three-dimensional extramundane void.

Despite continued opposition to the existence of any kind of void by Aristote- lians, Cartesians, and others, the cumulative impact of the events just described may have led proponents of void to accept it as three dimensional-especially since it could be artificially produced upon the evacuation of an enclosed volume. Three-dimensional vacua had become part of a new physics. But for those who also accepted the medieval view that God occupied all void space, there was now a genuine dilemma. If God fills a three-dimensional space, He becomes physically extended; but if God is nondimensional, then in what sense can He be said to fill a three-dimensional space? The Scholastics, for whom the issue of infinite extramundane void space was divorced from their physics, were content to assume the reality of extramundane void space-after all, God could create a body there-but deny it dimensionality, choosing to take refuge in transcendent meanings of terms such as "extension" and "dimension" when applied to God. Authors in the seventeenth century had no such options and devices. Convinced that void space was three dimensional and that God was omnipresent in it, those whose views we have briefly described here were driven, however reluctantly, to extend God into their three-dimensional void space. The demands of a new physics compelled the proponents of infinite void space, in whatever form they accepted it, to make God an extended three-dimensional being. And so, despite a near identity in language and substantive description of an omnipresent God extended through infinite void space, there was yet a gulf that separated medieval and seventeenth-century viewpoints. Whereas in the Middle Ages God's nondimensionality determined the characteristics of an imaginary infinite extramundane void, in the seventeenth century it was the three-dimensional infinite void space of a new physics that conferred upon God a new property-three-dimensionality. And yet this important difference must not be allowed to obscure an important contribution. Whether conceived dimensionally or not, the belief in God's omnipresence in an infinite void made that overpowering and difficult concept more readily acceptable to a number of significant and theologically oriented philosophic and scientific figures in the seventeenth and early eighteenth centuries. This belief and the arguments justifying it were a legacy from the late Middle Ages.



medieval and seventeenth-century conceptions of an infinite void space beyond the cosmos

Documents