motion in the void and the principle of inertia in the middle ages

Motion in the Void and the Principle of Inertia in the Middle AgesAuthor(s): Edward GrantSource: Isis, Vol. 55, No. 3 (Sep., 1964), pp. 265-292Published by: The University of Chicago Press on behalf of The History of Science SocietyStable URL: http://www.jstor.org/stable/228571 .

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Motion in the Void and the

Principle of Inertia in the

Middle Ages

By Edward Grant *

A AN INTEGRAL part of his repudiation of an actually existent void space, Aristotle in his Physics describes the properties which motions

would possess in void space (Bk. IV, Chs. 6-9). Two of these properties will be of particular interest here in the course of summarizing significant reactions of a few important scholastics to the possibility of motion in the void. Intimately associated with this problem is the nature of a resistant medium, and of resistance to motion in general. Hence some discussion of this is indispensable in dealing with the major theme.

The fundamental notion of void as formulated by Aristotle is a " place deprived of body . . . either unseparated or separated " (IV. 7. 214a. 17-20) . Among the absurdities which would follow from the existence of a void, two are especially relevant to the objectives of this paper. The first, paradoxically, is an enunciation of inertial motion deriving from an application of the principle of sufficient reason to conditions obtaining in a void. Since a material medium and natural places are lacking in a void, " no one could say why a thing once set in motion should stop anywhere; for why should it stop here rather than here? So that a thing will either be at rest or must be moved ad infinitum, unless something more powerful get in its way" (IV. 8. 215a. 19-21).2 This important statement evoked almost no critical

* Indiana University. 1 Quoted from The Works of Aristotle trans-

lated into English under the editorship of W. D. Ross (Oxford: Clarendon Press, 1908- 1931). Vol. II contains the Physics translated by R. P. Hardie and R. K. Gaye (1930). Aris- totle, who associated void with place, at- tributed this novel view to partisans of the void who seem not to have interpreted it in this sense. See Friedrich Solmsen, Aristotle's System of the Physical World; A Comparison with His Predecessors (Ithaca: Cornell Uni- versity Press, 1960), pp. 140-142.

2 In the medieval subdivision of the text of the Physics this passage was numbered as Text 69 of Bk. IV. Referring to this passage, I. E. Drabkin remarks that Aristotle enunciated a principle of inertia " only to reject it; from

ISIS. 1964, VOL. 55. 3, No. 181.

this a sound deductive science of dynamics would not have been a far step. But Aristotle would not approach the problem by way of a hypothetical limiting case; . . . ," " Notes on the Laws of Motion in Aristotle," American Journal of Philology, 1938, 59: 61.

Although Aristotle does not specify the sort of motion this would be, it seems reasonable to assume that he conceived it as uniform rectilinear motion, for why should it increase or decrease its speed, or change direction? Furthermore, such a motion could only occur in an infinite void space. That Aristotle was discussing infinite void space is borne out by IV. 8. 215a. 6-9 where, in referring to the void, he says: " for in so far as it is infinite, there will be no up or down or middle, and in so far as it is void, up differs no whit from

265



266 EDWARD GRANT

comment or discussion in the Middle Ages 3 but will receive a great deal of belated consideration in this paper.

In the second absurdity Aristotle says that motion would be instantaneous in the void since " there is no ratio in which the void is exceeded by body, as there is no ratio of 0 to a number " (IV. 8. 215b. 12-13) for which reason " the void can bear no ratio to the full, and therefore neither can movement through the one to movement through the other, but if a thing moves through the thickest medium such and such a distance in such and such a time, it moves through the void with a speed beyond any ratio" (IV. 8. 215b. 20-23) .4

Opposition to Aristotle's position came in late antiquity from John Philoponus who, in a commentary on Aristotle's Physics, insisted that motion in a void was possible because speed is proportional to weight where the function of a resistant medium is only to retard the body's motion thereby increasing its original time of fall over a given distance in the void.5 Al- though Philoponus' Commentary on the Physics remained unknown in the Latin West during the Middle Ages, Philoponus may have exerted an influence through the Spanish Arab Avempace (Ibn Bajja) who expressed similar objections subsequently reported by Averroes in his commentary on Text 71 of Aristotle's Physics. Averroes says: 6

Avempace, however, here raises a good question. For he says that it does not follow that the proportion of motion of one and the same stone in water to its motion in air is as the proportion of the density of water to the density of air, except on the assumption that the motion of the stone takes time only because it is moved in a medium. And if this assumption were true, it would then be the case that no motion would require time except because of something resisting it - for the medium seems to impede the thing moved. And if this were so, then the heavenly bodies, which encounter no resistant medium, would be moved instantaneously. And he says that the proportion of the rarity of water to the rarity of air is as the proportion of the retardation occurring to the moved body in water, to the retardation occurring to it in air.

And these are his own words, in the seventh book of his work, where he says: " And this resistance which is between the plenum and the body which

down...." Medieval discussions of Aristotle's sections on the void are almost always in terms of a void space conceived as lying somewhere between the heavens and earth in a finite universe.

3 This important consequence failed to emerge as a specific problem in the Questiones literature on Aristotle's Physics. Indeed, it is not even mentioned in the treatises which I have examined. In Commentaries on the Physics it is mentioned or recapitulated only because the text is itself included.

4 This passage forms the concluding portion of Text 71 and the introduction to Text 72 of Bk. IV of the medieval text of the Physics.

5 A translation of the relevant section is

given in Morris R. Cohen and I. Drabkin, A Source Book in Greek Science (Cambridge: Harvard University Press, 1958), pp. 217-221.

6 The translation is that of E. A. Moody, "Galileo and Avempace," Journal of the His- tory of Ideas, 1951, 12: 184-186. The views of Avempace are thoroughly discussed by Moody. For an earlier consideration of Avempace and a detailed treatment of certain topics connected with the notion of void space see Pierre Du- hem, " Le vide et le mouvement dans le vide," in Le Systeme du monde; histoire des doctrines cosmologiques de Platon a Copernic (10 vols.) (Paris: A. Hermann, 1913-1959), Vol. 8, pp. 7-120. Avempace is treated on pp. 10-16.



MOTION IN THE VOID AND THE PRINCIPLE OF INERTIA 267

is moved in it, is that between which, and the potency of the void, Aristotle made the proportion in his fourth book; and what is believed to be his opinion, is not so. For the proportion of water to air in density is not the proportion of the motion of the stone in water to its motion in air; but the proportion of the cohesive power of water to that of air is as the proportion of the retardation occurring to the moved body by reason of the medium in which it is moved, namely water, to the retardation occurring to it when it is moved in air.

" For, if what some people have believed were true, then natural motion would be violent; therefore, if there were no resistance present, how could there be any motion? For it would necessarily be instantaneous. What then shall be said concerning the circular motion? There is no resistance there, because there is no cleavage of a medium involved; the place of the circle is always the same, so that it does not leave one place and enter another; it is therefore necessary that the circular motion should be instantaneous. Yet we observe in it the greatest slowness, as in the case of the fixed stars, and also the greatest speed, as in the case of the diurnal rotation. And this is caused only by the difference in perfection between the mover and the moved. When therefore the mover is of greater perfection, that which is moved by it will be more rapid; and when the mover is of lesser perfection, it will be nearer (in perfection) to that which is moved, and the motion will be slower."

And these are his words. And if this which he has said be conceded, then Aristotle's demonstration will be false; because, if the proportion of the rarity of one medium to the rarity of the other is as the proportion of accidental retardation of the movement in one of them to the retardation occurring to it in the other, and is not the proportion of motion itself, it will not follow that what is moved in a void would be moved in an instant; because in that case there would be subtracted from the motion only the retardation affecting it by reason of the medium, and its natural motion would remain. And every motion involves time; therefore what is moved in a void is necessarily moved in time and with a divisible motion; and nothing impossible will follow. This, then, is Avempace's question.

Here was available to all scholastics a passage in which, contrary to Aris- totle, motion in a void is held to be " natural " and the role of the medium merely one of retardation and quite unessential to motion itself. The analogy between the lack of resistance to celestial motion - the consequence of a resistanceless aetherial medium - and that between motion in a void which wholly lacks a medium was to be oft-repeated in the literature on the void. Avempace's account of differences in finite velocities in the void is vague, depending as it does on " the difference in perfection between the mover and the moved." Speed is a function of the " perfection" of the motive power which, as Moody explains, " is conceived as an absolute indwelling power of self-motion animating the body like a soul." 7 Although quite different accounts were to be given in the Middle Ages, the opinions of Avempace were central to most of the discussions on Text 71 of Book IV of the Physics. There were to be many supporters of some version of Avempace's theory

7 Moody, " Galileo and Avempace," p. 186.



268 EDWARD GRANT

of motion in the void, but, curiously, they failed to take cognizance of Aristotle's inertial consequence as set forth unequivocally in what was designated in the Middle Ages as Text 69. Averroes had also commented on this text, accepting Aristotle's position while adding further trivial elaborations. It was incumbent upon those who accepted the possibility of motion in a void to either deny that the motion they deemed possible would be of an inertial character, or accept it with appropriate justification. In fact, the inertial argument did not become part of the traditional literature on that question, and in order to ascertain the positions to which partisans of voidal motion would have been committed, it is necessary to resort to indirect evidence. We shall now consider the arguments of four scholastics who coped with the problem of motion in a hypothetical void.

ST. THOMAS AQUINAS (1225-1274)

In his Commentary on the Physics Thomas explains Text 69 as follows: 8

If there were motion in a void that which is moved would remain [at rest] anywhere because no cause can be assigned to account for its motion. Neither in natural or violent motion is there any reason why that which is moved should rest more in one part rather than in another since there is no difference in the parts of a void, as was said above. Now according to the two causes assigned above,9 we say that a violent motion ceases where there is lacking either antiperistasis of the air or impulsion of the air. Therefore, [in a void] it is necessary that every body either rests and nothing is moved, or, if something should be moved, it would be moved into infinity unless some greater body obstructed its violent motion.

In support of this latter consequence, Thomas, in the very next paragraph, says that Aristotle asserted that some believed in motion in a void because a void yields and offers no resistance to bodies. But in an apparent allusion to Text 70 10 Thomas replies that " since a void yields similarly in every part, a body would be carried into infinity from any direction." In general, Thomas is in agreement with Aristotle that motion in a void would be ad infinitum if no bodies obstructed the motion. It seems, then, that in

8 My translation has been made from the Commentaria in octo libros Physicorum Aris- totelis, which is Vol. 2 of Sancti Thomnae Aquinatis . . . opera omnia iussu impensaque Leonis XIII.P.M. edita (Rome, 1884), p. 182, c. 2. The ready availability of this edition makes it unnecessary to cite the Latin text.

9 The two causes are given by Thomas as follows (ibid.):

Some say that things which are projected are moved after they are no longer touched by the projector because of antiperistasis, that is by rebounding or counter-resistance, for air which is moved strikes another [portion] of air, and the latter [strikes] another [portion] of air, and so on successively. A

stone is moved by such repercussions of [successive portions] of air. Others say that this happens because air, which is continuous and impelled by that which projects it, moves the projected body quicker than it would be carried naturally to its proper place. 10 In The Works of Aristotle, Vol. II, Text

70 reads: " Further, things are now thought to move into the void because it yields; but in a void this quality is present equally everywhere, so that things should move in all directions" (IV. 8. 215a- 22-23) . This translation renders very well the Latin text given by Thomas, op. cit., p. 180, c. 2.




the context of this question, void space is conceived as infinite, undiffer- entiated space.

In his commentary on Text 71, Thomas, fully aware of the essential conflict between Averroes and Avempace, surprisingly sides with Avempace, though never mentioning his name. Despite his disbelief in the existence of a void, Thomas finds unacceptable Aristotle's contention that no ratio could obtain between motions in void and in full space: 11

But several difficulties arise against the opinion of Aristotle. The first of these is that it does not seem to follow that if a motion occurs in a void it would bear no ratio in speed to a motion made in a plenum. Indeed, any motion has a definite velocity [arising] from a ratio of motive power to mobile - even if there should be no resistance. This is obvious by example and reason. An example is that of the celestial bodies whose motions are not impeded by anything, and yet they have a definite speed in a definite time. An appeal to reason is this: just as there is a prior and posterior part in a magnitude traversed by a motion, so also we understand that in the motion [itself] there is prior and posterior. From this it follows that motion takes place in a definite time. But it is true that in virtue of some impedi- ment [or resisting medium] something could be subtracted from this speed. It is not necessary, therefore, that a ratio of speeds be related as a ratio of resistance to resistance, for then, if there were no resistance, motion would occur instantaneously. But it is necessary that the ratio of retardation to retardation be as the ratio of resistant medium to resistant medium. Thus if motion in a void were assumed, it follows that no retardation would occur beyond the natural velocity; and it does not follow that motion in a void would bear no ratio to motion in a plenum.

Thomas' justification of Avempace's argument was destined to form one of the major defenses for adherents of motion in a void and " came to be designated in the later scholastic discussions as incompossibilitas terminorum or distantia terminorum." 12 Many were to follow this line of argument. Indeed, the assigning of distinct parts to the void was later characterized as a form of resistance, since motion in the void would of necessity be successive and of finite duration.

But even conceding that the void has distinct parts which must be traversed, if at all, with a successive motion over a finite time, Thomas felt compelled to explain how such motion could occur. His account reveals that just as in a plenum, motion in a void is dependent on the conjoint action of a motive force and resistance. His explanation comes by way of reply to Averroes who, in his comment on Text 71, had insisted that motion arises from a conjoint action between two forces or powers - namely, between a motive force and the body which is moved. Now in the motion of

11 Thomas, op. cit., Bk. IV, lect. 12, p. 186, c. 1. Although I have used my own translation, Ernest Moody has previously translated a large portion of this passage in his " Ockham and Aegidius of Rome," Franciscan Studies, 1949, 9: 424.

12 Moody, " Ockham and Aegidius . . . "

pp. 424-425. Moody adds (p. 425) that "St. Thomas was the recognized advocate, or even originator, of the thesis that distantia terminorum is the essential and sufficient cause of the temporal character of motion; ...."



270 EDWARD GRANT

animals and celestial bodies, which are self-moved beings, an actual motive force can be distinguished from the body in motion, the latter being taken as a resistance. Elemental bodies, however, cannot be so distinguished, and the body in motion is not a resistance, so that an external resistant medium is essential for motion to occur.13 Earlier, in the same discussion, Averroes had remarked 14 that heavy and light bodies are composed of prime matter and simple forms where motive power is a form and the body in motion is matter. Despite the application of these terms, Averroes insists that in elemental bodies such entities are not distinct and an external resistant medium is necessary, for otherwise motion would be instantaneous.

After briefly summarizing these arguments,15 Thomas replies that even if a body in the void lacked motive power, or form, one could conceive of it as a magnitude or dimension, which he calls corpus quantum. This corpus quantum will of itself constitute a resistance if it is opposed to a motive power. Thus it appears that for Aquinas resistance in a void is proportional to magnitude or corpus quantum."'

The position taken by Thomas Aquinas is of great significance for medieval discussions on the void. By treating the void as something which has parts that are, of necessity, traversable in time and not instantaneously, he has made the void serve the most vital function of a resistant medium as conceived by Aristotle - namely to produce motions measurable in time. The next step was also taken with Aristotle in mind. Motion can only arise by the conjoint action of a motive force and resistance. This problem is solved by introducing the corpus quantum as resistance which awaits only

13 Aristotelis De Physico Auditu libri octo cum Averrois . . commentariis in Aristotelis opera cum Averrois commentariis, Vol. IV (Venetiis apud Junctas, 1562; reproduced by Minerva, Frankfurt am Main, 1962), fol. 162r., c. 1:

Et omnis motus erit secundum excessum po- tentiae motoris super rem motam et diver- sitas motuum in velocitate et tarditate est secundum hanc proportionem quae est inter duas potentias. Et ista resistentia aut erit ex ipso moto quando illud quod movetur ex se voluntate dividitur in motorem in actu et rem motam in actu sicut est dispositio in animalibus et in corporibus coelestibus; aut erit ex ipso medio in quo movetur et hoc erit quando res mota non dividitur in motorem et rem motam in actu, sicut est dispositio etiam in corporibus simplicibus.

All abbreviations have been expanded and punctuation supplied or altered wherever necessary. This has been done for all Latin quotations from early printed editions.

14Ibid., fol. 161v., c. 2. In elementis vero res mota est in potentia

et motor in actu cum sint composita ex prima materia et formis simplicibus. Et motor est forma et res mota est materia. Et

quia hec corpora non distinguuntur in rem motam et motorem in actu impossibile est ea moveri sine medio. Et Aristoteles declara- vit quod propter hoc fuit necesse illa non moveri ex se in octavo istius libri. Si igitur haec corpora simplicia moverentur sine medio non esset hic resistentia inter motoremn et rem motam; immo non esset haec res mota omnino essentialiter. Et, si hoc, con- tingeret ut moverentur in non tempore et in quolibet moto. 15 Thomas, op. cit., p. 186, c. 2. 16The passage in question reads as follows

(ibid., p. 187, c. 1): " Next, when the form, which is given by that producing the motion, has been removed from heavy and light bodies there [yet] remains the concept of a quantified body. From the very fact that this is a magnitude existing in an opposed position, it offers resistance to a motive force." This passage is also translated by Moody, " Ockham and Aegidius . . . ," p. 424. Duhem (Le Systeme . . ., Vol. 8, p. 19) equates the corpus quantum with mass and believes that Thomas was the first to introduce this notion into mechanics. He sees it as " equivalente a ce qui reste dans un corps quand on en a supprime toute forme pour n'y laisser que la matiere premiere quan- tifiee pas des dimensions determinees."




the action of an external motive force to be set in motion in the void. Al- though arriving at anti-Aristotelian conclusions, Thomas has remained faithful to the primary Aristotelian conditions for the production of temporal motion.

A crucial question now emerges. If a corpus quantum were set in motion in the void, would it continue in uniform motion ad infinitum? 17 We have already seen that Thomas agreed with Aristotle that this was a legitimate consequence of the existence of a void and provided grounds for denying the possibility of a separate void space. Nevertheless, motion ad infinitum seems a consequence of Thomas' explanation. For if a corpus quantum is a resistance, what will change its motion in the void after some motive power sets it in motion? In Aristotle's words " why should it stop here rather than here? So that a thing will either be at rest or must be moved ad infinitum, unless something more powerful get in its way." Paradoxically, the argument which Thomas accepted from Aristotle in Text 69 as demonstrating the impossibility of void space is, in his commentary on Text 71, derivable as a consequence from his very acceptance of the possibility of motion in a hypothetical void.

The views of Avempace and the further elaborations and additions by Thomas Aquinas played an instrumental role in the subsequent scholastic literature on the subject. But another current flowing from the massive condemnation of 219 articles by the Bishop of Paris in 1277 was also of some importance. The forty-ninth article, which asserted " that God could not move the heavens with rectilinear motion. The reason is that a void would remain," 18 was effective in reinforcing the position of those who believed motion possible in a void space. After 1277, and especially during the fourteenth century, it became quite respectable to argue that even if void space was not naturally possible according to traditionally accepted physical principles, it was certainly possible supernaturally.'9 Of the remaining

17 More precisely, we must ask whether both the motive force and resistance, or corpus quantum, will move off ad infinitum. The corpus quantum will continue in motion only so long as an external mover remains in direct contact. In Thomas' account, then, any motion in the void involves, at the very least, two separate, but touching, bodies: one a motive force, the other a resistance.

18 H. Denifle and A. Chatelain, Chartularium Universitatis Parisiensis (Paris, 1889) , Vol. I, p. 546: " 49. Quod Deus non possit movere celum motu recto. Et ratio est, quia tunc relinqueret vacuum."

19 Duhem, in Le Systeme . . . , traces the impact of this condemned article on subsequent discussions of the void. In his eagerness to see momentous positive consequences following upon the condemnations of 1277, Duhem ignores the role of Avempace and attributes to the forty-ninth article the major influence in stimulating discussion on the

topic of motion in the void (Vol. 8, p. 117): La dynamique peripateticienne voulait que la notion meme de mouvement impliquat non seulement une puissance motrice, mais encore une resistance; que cette resistance soit simplement accidentelle, mais non pas essentielle, cela r6sulte de la possibilit6 du mouvement dans le vide; et ce qui demontre la possibilit6 du mouvement dans le vide, c'est une des condemnations portees en 1277.

There is little doubt that the forty-ninth article was frequently cited in later discussions. Whereas earlier the void was purely hypothetical, it became after 1277 supernaturally possible. While this added new dimensions to other questions, it did not alter the basic problems raised by Avempace and transmitted to the Latin West by Averroe6s. The broad lines of argument justifying motion in the void and the mechanisms producing such motion had already been established and were not sub- stantially affected by the condemnations.



272 EDWARD GRANT

authors to be considered here, all wrote after the condemnations and two reveal its influence.

NICHOLAS BONETUS (d. 1343?)

Nicholas Bonetus was a follower of Duns Scotus and agreed with the latter that motion in a void was certainly possible.20 He argues that 21

... it does not seem impossible that motion could occur in a void. Indeed, there could be in the void both a local motion and another which is quicker or slower. You should realize that succession in motion [depends on] division of space and a positive or privative medium. But essential speed or slowness [of motions] depends on the divisibility and differences between motive forces, whereas accidental speed in a motion arises from the resistance of a full medium - rare or dense, subtle or gross - which hinders or aids the

20 Duns Scotus admits the possibility of motion in the void in the following passage, in P. Marianus F. Garcia, 0. F. M. (ed.) , B. Ioannis Duns Scoti Commentaria Oxoniensia ad IV. Libros Magistri Sententiarum, Vol. II (Quaracchi, 1914), Lib. II. Dist. II. Quaest. IX. Art. III, pp. 193-194:

. . .; tamen si poneretur vacuum posse cedere, et esse spatium, et non quod latera pleni essent simul, quia tunc non esset vacuum, dico tunc quod motus gravis esset successiva in vacuo, quia prior pars vacui prius cederet, et totum grave prius transiret hanc partem spatii quam illam, et sicut dictum fuit prius in precedenti argumento et modo, per se successio est in motu locali

.ex spatio in quantum quanto. See also Duhem, Le Systeme . Vol. 8,

pp. 78-83, and A. Maier, An der Grenze von Scholastik und Naturwissenschaft (Rome, 1956), pp. 229-231.

21 The italics and brackets are mine. Habes Nicholai Bonetti . . . quattuor volumina: Meta- physicam videlicet, Naturalem Phylosophiam, Predicamenta, necnon Theologiam Naturalem (Venice, 1505), fol. 62v., c. 2:

Dicamus autem quod non videtur aliquod impossibile quod motus possit fieri in vacuo. Adhuc autem et motus localis et unus alius velocior vel tardior potest esse in vacuo. Diligenter autem debes attendere quod successio possibiliter (?) in motu ex divisione spacii et medii positivi seu privativi. Sed velocitas vel tarditas essentialis ex divisibilitate vel diversitate motorum. V7elocitas autem accidentalis inest motui ex resistentia medii pleni rarioris vel densioris subtilioris vel grossioris impedientis vel promotivi motus. Dicamus igitur quod successio erit in vacuo cum sit ibi spacium et medium privativum et distantia privativa quoniam latera continentia vacuum non se tangunt. Velocitas etiam essentialis motus que oritur ex divisibilitate vel ex diversitate motoris po-

test etiam esse in vacuo. V7elocitas autem acci- dentialis que inest motui ex resistentia medii pleni rarioris vel densioris impedientis vel promotivi motus nullus est in vacuo. Bonetus, in company with a number of other

scholastics who accepted motion in a void, tries to explain that Aristotle and Averroes did not actually deny the possibility of all motion in the void but only denied that in the void there could be (fol. 63r., c. 1)

. . .motion whose accidental speed or slowness depends on the resistance of a full medium - denser, rarer, or grosser - which assists or impedes the motion. But they do not conclude that in a void there could not be motion receiving its speed and slowness directly from some other thing, just as in the motion of celestial bodies there is speed or slowness resulting from the diversity of the motive forces but not because of the resistance of the medium. (Dicimus autem in ultimi quod si omnes Aristotelis et Com- mentatoris rationes aliquid concludunt, concludunt quod in vacuo non potest esse motus cuius velocitas vel tarditas accidentalis insit motui ex resistentia medii pleni vel densioris vel rarioris vel grossioris promotivi vel im- pedimentivi motus. Non tamen concludunt quod in vacuo non possit esse motus simpliciter habens velocitatem et tarditatem aliunde sicut in motu corporum celestium est velocitas vel tarditas propter diversitatem motorum in vigore, non autem propter resistentiam medii.) Bonetus here follows a rather common prac-

tice of softening and distorting Aristotle's strong stand against the possibility of motion in a void. His technique is to pretend that Aristotle's arguments repudiated only accidental speed in the void which, of course, lacked a resistant medium. It then follows, for Bonetus, that Aristotle did not condemn motion in the void resulting from some cause other than the resistance.




motion. We say, therefore, that there will be succession in a void, for we find there space, a privative medium, and a privative distance since the surfaces containing the void do not touch. Indeed, the essential speed of a motion, which depends on divisibility or differences in motive power, could occur in a void. However, accidental speed, which pertains to a motion as a result of the resistance of a full, rare, or dense medium hindering or aiding the motion, does not occur in a void.

Bonetus now raises, by implication, a fundamental question: once it is initiated, how are we to account for the cessation of motion in the void? His pertinent remarks are embodied in a section where he inquires about the possibility of natural and violent motion in the void.22 Natural motion is possible in general.23 He considers briefly the flight of birds in a hypothetical vacuum extending from the earth to the concave surface of the lunar sphere.24 Although reluctant to express an opinion, Bonetus believes that such flights might be possible for short periods of time.

It is in dealing with violent motion that Bonetus faces the basic question. Violent motion, he insists,

can occur in a void as long as the moving force is conjoined to the mobile, whether this [connection] be real, or causal or virtual. Let us give an example: when some light body is conjoined to a heavy body which draws [the light body] to the center of the world.25 Another example is that of a man moving in a void and carrying a stone in his hand. Here, [now,] is an example of the second kind [involving causal or virtual conjunction]. If an abstract intelligence were in a void it could move a heavy body upward violently without really being connected to it except virtually and causally. For even if it were assumed that between the intelligence and the heavy body there is a positive intermediate distance as in a plenum, or a privative distance as in a void, it could still move a heavy body violently.26

22 This section introduces the fifth book of his Questions on the Physics. The question reads (fol. 62v., c. 1): " An in vacuo sit motus naturalis et violentus et talium motuum con- ditiones." The passage in the previous note is also from this question.

23 Fol. 63r., c. 1: De motu autem naturali patet manifeste

quod ibi possibilis est: et motus progressivus animalium, et motus a medio, ad medium, et motus circa medium. Et si queras an sit possibilis motus animalium volatilium et volatus eorum, ut si a terra usque ad concavum orbis lune esset intermedium omnino vacuum, numquid aves possent in illo spacio vel vacuo volare? De hoc taceo. Volatum tamen ibi esse pro modico tempore non videtur impossibile. 24 Discussions on the existence of void space

were made relevant to two separate regions: (1) a finite void space extending over all or

part of the region between the earth and lunar orb, or even the outermost celestial sphere, and (2) an infinite void beyond the outermost sphere. The problem of motion in void space

seems to have been largely confined to the first of these regions. See A. Maier, An der Grenze * * ., p. 219, n. 1.

25 The heavy body, which moves naturally toward the center, pulls the light body with it, thus producing a violent motion for the light body contrary to its natural inclination for movement away from the center.

26 Fol. 63r., c. 1-2: De motu autem violento quod dicendum

numquid possit esse in vacuo? Dico quod sic, dum tamen movens coniugatur mobili vel realiter, vel causaliter vel virtualiter. Exemp- lum ponitur: si alicui gravi esset colligatum aliquid leve virtute cuius traheretur ad cen- trum; exemplum de homine moto in vacuo portante lapide[m] in manu sua. Exemplum secundi: intelligentia abstracta si esset in vacuo posset movere grave sursum violenter absque hoc quod sibi coniungeretur realiter, sed tantum virtualiter et causaliter. Quoniam dato quod inter intelligentiam et grave esset spacium intermedium positivum, sicut in pleno, vel privativum, sicut in vacuo, adhuc posset movere grave violenter.



274 EDWARD GRANT

Bonetus now raises some doubts. If an external motor conjunctus (he does not use this expression) is necessary to produce violent motion in a void, then such motions would be impossible, for " they would occur without a motive force since the air does not move for there is no air in a void, nor, indeed, anything else. Moreover, it does not seem that anything could project [bodies] in the void because the projector would cease projecting immediately after [the initial] projection." 27 In answering this objection, Bonetus says that " some hold that a violent motion can occur in a void without a real or virtual conjunction of a prime moving or projecting force with a mobile. The reason given for this is that in a violent motion some non-permanent and transient form is impressed in the mobile so that motion in a void is possible as long as this form endures, but when it disappears the motion ceases." 28 Thus Bonetus accounts for motion in the void by a self-expending impetus, and, without mention of Aristotle's inertial consequence in Text 69, has avoided indefinite motion by invoking a self- corrupting motive force upon the disappearance of which motion in the void ceases immediately. That this was Bonetus' view is borne out by his argument 29 that violent motion in the void is slower in the end than in the beginning, since " that force or impressed form continually fails and diminishes in moving the mobiles, and, as a consequence, moves slower. Thus violent motion made in the void has to be slower in the end than in the beginning, just as [violent motion] in the plenum."

What is the significance of Bonetus' comments? They reveal an awareness of the need to explain the cessation of violent motion in the void, for otherwise Aristotle's inertial consequence would obtain - a consequence which had to be avoided if motion in the void was to be at all intelligible. In terms of force and resistance, the cessation of motion in the void was best accounted for by invoking a self-expending impressed force.

JEAN BURIDAN (c. 1300-c. 1358)

It may have been an implicit desire to avoid the inertial consequence of

27 Although I have translated only the concluding portion, it seems worthwhile to include the few lines preceding the translated material (fol. 63r., c. 2):

Palam autem quoniam si movens non con- iungitur mobili nec realiter nec virtualiter non posset movere in vacuo aliquid violen- tum. Et hinc est quod fertur quod motus proiectorum non posset fieri in vacuo, ut quod lapis sursum ab homine proiciatur. Et ratio huius dicti est ista: quia tunc esset motus sine motore, quoniam aer non movet, cum non sit ibi, nec aliquid aliud. Nec videtur quod proiiciens aliquid faciat ibi, posset enim proiiciens desinere statim esse postquam proiicit. 28 Ibid.:

Fertur autem ab aliquibus quod motus

violentus posset esse in vacuo absque hoc quod movens primum (?) sive proiiciens con- iungatur mobili vel realiter vel virtualiter Et ratio huius dicti est ista: quia in motu violento mobili imprimitur aliqua forma non diu permanens sed quasi transiens, et quamdiu illa forma durat posset esse motus in vacuo; illa autem deficiente cessat motus. 29 Fol. 63v., c. 1:

De motu etiam violento semper est dicendum quod esset debilior in fine quam in principio. Intelligo autem de motu proiectorum, si sit possibilis. Ratio huius dicti est ista: quoniam virtus illa seu forma im- pressa mobilia a movente continue deficit et debilitatur, et per consequens tardius movet. Motus itaque violentus factus in vacuo habet esse tardior in fine quam in principio, sicut et in pleno.




his own impetus theory which drove Jean Buridan to oppose the concept of motion in the void. A long discussion on the void in Buridan's Questions on the Physics 30 is, however, quite disappointing. Almost nothing is said about violent motion - usually the most interesting and relevant case. The Aristotelian inertial argument is, as usual, neither mentioned nor alluded to. Indeed, one gets the impression that for Buridan the topic was a frustrating and unprofitable one thrust upon him by events beyond his control. More than most authors, he reveals how strong could be the influence of the condemnations of 1277. A number of his arguments involve an appeal to the absolute power of God.

As is well known, Buridan was the greatest of the medieval impetus theoreticians. He described impetus as a 31

. thing of permanent nature, distinct from the local motion in which the projectile is moved. . . . And it is probable that that impetus is a quality naturally present and predisposed for moving a body in which it is impressed, just as it is said that a quality impressed in iron by a magnet moves the iron to the magnet. And it also is probable that just as that quality (the impetus) is impressed in the moving body along with the motion by the mover; so with the motion it is remitted, corrupted, or impeded by resistance or a contrary inclination.

Buridan emphasizes that impetus would last forever if it were not destroyed - as it always is - by opposing resistances, or the tendency of bodies to seek their natural places and come to a state of rest.32

We have already stated that Buridan omits any proper consideration of violent motion in the void and we must, therefore, improvise an illustration in hope of acquiring a deeper insight into his attitude toward the possibility of motion in the void. If a body were put into motion in the void and in the process acquired impetus, then the body would function as a resistance and the impetus as motive force, thereby fulfilling the Aris- totelian requirements - to which Buridan subscribed - that every motion arises from the conjoint action of a force and a resistance. But in contrast

30 Johannis Buridani subtilissime questiones super octo phisicorum libros Aristotelis diligenter recognite et revise a magistro Johanne Dullaert de Gandavo (Paris, 1509), fols. 72v., c. 2-78r., c. 2.

31 Translated by Marshall Clagett, The Sci- ence of Mechanics in the Middle Ages (Madi- son: University of Wisconsin Press, 1959), p. 537. This passage appears in Buridan's Ques- tions on the Physics, Bk. VIII, Question 12.

32 In his Questions on the Metaphysics, Bk. XII, Question 9, Buridan states explicitly that many people, including himself,

. . . posit that after a projectile has lost contact with the motive force it is moved by an impetus given to it by the motive force, and is moved as long as the impetus remains stronger than the resistance. And the impetus would last into infinity except that

it is diminished and corrupted by a contrary resistance, or by an inclination to a contrary motion. (. . . multi ponunt quod proiectum post exitum a proiciente movetur ab impetu dato a proiciente et movetur quamdiu durat impetus fortior quam resistentia: et in infinitum duraret impetus, nisi diminueretur et corrumperetur a resistente contrario vel ab inclinante ad contrarium motum.

This is quoted from A. Maier, Zwei Grund- probleme der scholastischen Naturphilosophie (Rome: Edizioni di Storia e Letteratura, 1951),

p. 223. Miss Maier insists (p. 233) that Buri- dan applied the concept of indefinite motion exclusively to celestial motion. However, the passage just quoted is clearly applicable to violent motion which is strictly a terrestrial phenomenon. The impetus would last forever were it not corrupted by resistances.



276 EDWARD GRANT

to Bonetus, Buridan's impetus is permanent and the body would have acting upon it an impressed force which remains constant. Such a motion would be inertial in the sense that it would move ad infinitum unless something obstructed it.33 Thus where Bonetus could avoid Aristotle's inertial consequence by utilizing a self-corruptive impressed force, Buridan could properly do so only by denying the possibility of motion in the void; and this is, in effect, what he did, although confining himself to a discussion of natural motion.

Successiveness in motion, says Buridan, is dependent on resistance. But what does he mean by resistance?

It must be noted that a resistance is called an inclination of a mobile to a disposition which is opposite that intended by the motive force. And if the resisting force in resisting exceeds the motive force in moving, then there is no motion from that motive force. . . . And if there were no resistance there would be an instantaneous change - if the motive force were applied instantly, and not successively, to the mobile... . And I wish it understood that what I have said is true about natural motive forces.34

33 In her Zwei Grundprobleme , Miss Maier would emphatically deny my inference. She poses the following question (p. 224):

Wenn man also die Frage stellt: wie wiurde nach Buridans Impetustheorie die Bewegung des proiectum separatum erfolgen, wenn wir von den Widerstanden absehen, die einer- seits die Schwerhaft, anderseits die Reibung des Mediums ausiiben? so lautet die Ant- wort nicht etwa: dann wiirde der impetus und mit ihm die Bewegung des proiectum in alle Ewigheit weiterdauern, sondern: dann hatte der impetus immer noch den Trag- heitswiderstand, d. h. die inclinatio ad quietem, im proiectum zu uiberwinden und wiirde von diesem allmiihlich zerstort werden.

Thus even ignoring all resistances, the impetus would be destroyed by the body's inclination to come to rest, and inertial motion would be impossible. Since these very conditions would obtain in a void, my hypothetical discussion seems wholly misleading. But concerning violent motion in a void we may ask at what point would the body's " inclination to rest" (inclinatio ad quietem) become operative? Why at this point in space, rather than at another point? Would it be gradual or instantaneous? The very fact that such legitimate questions arise indicates that Miss Maier has simplified, to the point of distortion, the issues which emerge when we attempt to anticipate the manner in which Burdian might have conceived the action of impetus in a void. Further- more, bodies have an inclination to seek their natural places and come to rest therein. But in an infinite void, natural places are non- existent and, consequently, no inclinatio ad

quietem would be operative and no reason for the motion to cease - provided, as we have assumed, that the body in motion functions as a resistance, and the impetus acts as a constant motive force. Should the void be finite, the questions just raised would become para- mount.

But leaving all this aside, it is a fact that Buridan believed impetus would be of infinite duration-and thus produce eternal motion- if uncorrupted by opposing resistances or ten- dencies (see note 32). Thus under certain hypothetical, albeit unrealizable, conditions, there could be an eternal inertial-like motion. This constitutes a significant step forward. For should we deny some measure of credit to Buridan on grounds that his conditions are impossible, then we could also show that Des- cartes never enunciated the principle of inertia. For is it not true that in Descartes' full space every motion must cease and the inertial ten- dencies of bodies become unrealizable and impossible? It would then seem improper to attribute to him the honor of having formulated that fundamental principle.

34 Fols. 74r., c. 2-74 v., c. 1: Deinde notandum quod resistentia vocatur

inclinatio mobilis ad oppositam dispositionem ei quam motor intendit. Et si potentia resistens superet in resistendo potentiam motoris in movendo tunc ab illo motore non fit motus.... Et si nulla esset resistentia tunc fieret mutatio instantanea, si movens instanter applicaretur mobili et non successive. . . . Et ideo quicquid ego dicam . . ego volo quod intelligatur de motibus qui fiunt a potentiis naturalibus....




Resistance, then, is the tendency of a body to move in a direction opposite that in which the motive force is moving it.

We note that Buridan does not resort to the Thomistic argument of the incompossibilitas or distantia terminorum, which provided the basic justification for assuming the possibility of motion in a void. In fact, Buridan discusses this mode of resistance in connection with his own asser- tion that there are neither internal nor external resistances in celestial motion.35 Apparently, some had maintained that the " incompossibility of the termini" was a type of resistance applicable to celestial motion. In summarizing the " incompossibility " thesis, Buridan mentions Thomas Aquinas by name and cites the latter's interpretation as it was commonly understood.36 But Buridan denies the applicability of this concept of resistance to celestial motion, noting, among other things, that " the incompossibility of the termini is inadequate to explain that a mutation [or instantaneous change] might be successive because there could be an incompossibility of termini in an instantaneous change [mutatio] even as God could make a body in the heavens reach the earth instantaneously." 37

Although this entire discussion occurs in the context of the general question " whether in motions of heavy and light bodies to their natural places the entire succession arises from the resistance of the medium," 38

there is a connection with the problem -of motion in the void. The argument against the " incompossibility of the termini " shows that Buridan would not have accepted it as demonstrating the hypothetical possibility of motion in a void. If God could make a body in the heavens move to the earth instantaneously, then we have an instance of an intervening distance -

which is, of course, a magnitude consisting of prior and posterior parts -

traversed instantaneously. Now if, as Aristotle insists, a body would traverse

35 Fol. 75 v., c. 1-2: Tertia conclusio est difficilis, scilicet quod

nulla spera celestis in motu suo vel in motibus suis habet aliquam resistentiam. Proba- tur quia non habet resistentiam intrinsecam ut dictum est nec extrinsecam quia non ex parte debet (?) intelligentiarum quia ille secundum Aristotelem nullo modo adver- santur adinvicem; nec aliquid potest resistere potentie divine propter eius infinitatem; nec ex parte celorum et motuum potest esse quod unum alteri resistat quia non invicem continua sunt nec colligata propter quod unus orbis debeat alteri resistere vel alterum trahere aut pellere. 36 Fol. 75v., c. 2:

Item beatus Thomas adhuc in omni motu locali imaginatur aliam resistentiam, scilicet incompossibilitatem terminorum. Non enim est possibile naturaliter quod idem lapis sit simul sursum in spera ignis et in terra et in locis intermediis, scilicet in aqua et aere quia oporteret ipsum distare a se ipso quod est impossibile. Ido necesse est si sit in spera ignis et post in loco terre quod hoc sit suc-

cessive prius in aere et post in aqua, et, tandem, in terra. Et ad hoc vadit auctoritas Aristotelis quarto huius dicentis quod prius et posterius in motu provenit ex priori et posteriori in magnitudine, scilicet in spacio in quo est motus; unde in sexto huius dicitur quod oportet motum tempus et spacium dividi proportionaliter in partes priores et posteriores et quod in nullo eorum est dare primum hoc enim totum provenit ex incom- possibiltate essendi simul terminos magni- tudinis ita. Ergo impossibile est quod simul sol sit in oriente et in occidente oportet quod sit successio licet non esset aliunde resistentia. 37 Fol. 76v., c. 2: "Et iterum incompossi-

bilitas terminorum non sufficit ad hoc quod mutatio sit successiva quia in mutatione instantanea esset incompossibilitas terminorum immo etiam corpus quod est in celo Deus posset facere instanter esse in terra."

38 Fol. 74r., c. 2: " Queritur consequenter nono utrum in motibus gravium et levium ad sua loca naturalia tota successio proveniat ex resistentia medii."



278 EDWARD GRANT

a void space instantaneously, this may also be construed as a case where the intervening void space, consisting of prior and posterior parts, is likewise traversed instantaneously for lack of a resisting medium. Hence a distance, consisting of prior and posterior parts and, therefore, incompossible termini, might yet be traversed instantaneously and the " incompossibility of the termini " does not guarantee - nor is it the cause of - temporal, finite motion.

In striking at Aquinas' " incompossibility" argument, Buridan has in- voked God's absolute power to produce instantaneous motion. This bit of irony must not be overlooked. We have already mentioned that the forty-ninth article, of those condemned in 1277, compelled all to admit that God could produce a vacuum by moving the world rectilinearly, and, in general, that God could produce motion in a vacuum. Buridan, to whom motion in the void was a distasteful possibility, had to concede that God could move a heavy body in the void " for this is no less possible than moving the whole world in a straight line." 39 But in his counterargument against the " incompossibilty" doctrine Buridan invokes the absolute power of God to undermine the most fundamental argument justifying motion in a void. But he did not stop there. For if God could produce motion in a void, he could also prevent it. Thus in the proposition " there is a void, therefore a heavy body must be moved in it," it is obvious, says Buridan, that the consequent does not follow, because (1) there might be no heavy body in the- void, or (2) if there were a heavy body, it might be kept at rest by the divine power or some other cause.40 It appears that Buridan has deliberately attempted to neutralize arguments appealing to divine power by offering trivial counterarguments designed to show that just as God could produce motion in a void, so also could he prevent it.

But where Buridan was content to cloud the issue involving motion produced supernaturally in the void, he leaves no doubt that in terms of natural causes such motion is impossible. If a void existed in the spheres of air, water, and earth, a stone in contact with the concave surface of the sphere of air would not descend, " because there would be nothing lighter under the stone so that it would have no inclination to be under something other than the concave surface of the sphere of air." 4' Appealing

39 Fol. 77r., c. 1: " Quarta conclusio est quod possibile est grave moveri in vacuo scilicet per potentiam divinam hoc enim non minus est possibile quam totum mundum moveri motu recto.

40 Here is the text of this brief passage (ibid.): "Ideo dico pro secunda conclusione quod ista non est bona consequentia: vacuum est, ergo grave movetur in eo. Quia posito quod vacuum esset cum hoc sit possibile tamen forte nullum grave esset in eo, vel licet esset grave in eo tamen forte quiesceret aut per potentiam divinam aut aliter."

41 This is part of the sixth proposition within the general question (fol. 76v., c. 2) "' whether if there were a void, a heavy body

would be moved in it." (" Queritur consequenter utrum si vacuum esset grave moveretur in eo.") Earlier, Buridan had defined two ways in which a stone could be situated in the sphere of air after all the air had been removed leaving a void (fol. 77r., c. 1): ". . . dupliciter potest imaginari quod lapis esset' positus in illo aere: uno modo quod esset infra latera concavitatis illius aeris sicut sunt nunc terra et aqua." The translation above is from the sixth proposition which takes up the first mode. Fol. 77r., c. 2:

Sexta conclusio est quod de priori modo. Concludo quod lapis sit in vacuo, scilicet quod si ille lapis esset omnino sub illo aere tangens ex uno latere superficiem concavam




next to Aristotle's principle of sufficient reason, Buridan insists that " there is no reason why it ought to tend above or below, to one side or another. " 42

It appears then that Buridan was definitely hostile to the concept of motion in the void. But somewhat later in the eighth proposition of the same question he seems to waver. Some preliminary remarks are con- sonant with his previous position, for he asserts that " if a simple heavy body were moved in a void by its gravity, it would be moved instantaneously and fall with an equal speed in void and plenum because there is no resistance." 43 Upon supporting these orthodox Aristotelian positions, Buri- dan introduces, without elaboration, the viewpoint of Avempace. He remarks that 44

. . . this eighth proposition and the reasons in support of it are based on the supposition that Avempace's opinion -cited earlier - is not true. However, I do not know how to disprove it, and, indeed, agree more with it than with the opposite opinion. Now if this opinion of Avempace were conceded then this eighth proposition ought not to be conceded and Aristotle's supporting reasons are invalid.

Later, in the same paragraph, we read that 45

Aristotle did not intend to say that motion in a void would be instantaneous etc., but rather intended to assert it as a conditional [proposition], namely that if a heavy body were moved in a void by its own gravity, then [it would be moved] in an instant, etc. This can be conceded -provided that Avem- pace's opinion is not conceded - because the consequent is impossible absolutely (simpliciter). Thus Aristotle wished to conclude from this that it would be impossible for a heavy body to be moved by its own gravity in a void and this has been conceded, although, as was said, it could be moved by a divine power.

Are we to understand that Buridan has shifted his position and adopted the view that motion in the void is naturally possible? Pierre Duhem,

illius aeris ille lapis non moveretur nec amplius descenderet per suam gravitatem. HIec conclusio probatur quia ille lapis nichil haberet sub se levius. Ideo nullam inclina- tionem haberet ad esse sub aliquo alio quam sub illo sub quo iam erat. 42 The complete passage is as follows (fol.

77r., c. 2): " Ideo sicut bene dicit Aristotelis non esset ratio quare magis deberet inclinari ad superius vel inferius, ad unum latus vel ad alterum."

43 This passage appears in the eighth proposition of the general question cited in note 41 (ibid.): " Octava conclusio quod si grave simplex moveretur per suam gravitatem in vacuo ipsum moveretur in instanti et eque velociter in pleno sicut in vacuo propter nullam esse resistentiam."

44 Fol. 77v., c. 1: " Notandum tamen quod hec octava conclusio et eius rationes posite sunt

ex suppositione quod non sit vera opinio Avempeche posita prius quam tamen nescirem improbare et cui magis consentio quam opinioni opposite. Et que opinio Avempeche si concederetur illa octava conclusio non esset concedenda, nec valerent rationes Aristotelis."

45 The italics and brackets are mine. Ibid.: . . . Aristoteles non intendebat dicere quod in vacuo fieret motus in instanti etc. sed intendebat istam conditionalem, scilicet quod si in vacuo grave esset ipsum moveretur per suam gravitatem in instanti etc. Et hoc est concessum, - si non conceditur opinio Avem- peche - quia consequens est impossibile simpliciter. Ideo volebat ex hoc Aristoteles con- cludere quod impossibile esset grave per suam gravitatem moveri in vacuo, et hoc etiam concessum est, licet dictum sit quod posset in eo moveri per potentiam divinam, etc.



280 EDWARD GRANT

after citing certain passages in the immediately preceding question 46 which show that Buridan was fully aware of the incompatibility of the views of Aristotle and Avempace, assumes from Buridan's admission in that section and the passage quoted above that Buridan threw in his lot with Avempace, despite the former's own realization that this required a rejection of Aris- totelian dynamic rules.47 But this is a misinterpretation of Buridan's entire position. In the passage quoted in the preceding paragraph, the assumption is made that a heavy body could move in a void - an assumption contrary to Buridan's own firm conviction.48 Arguing from this assumption, however, Buridan admits that he is uncertain as to what would follow, but leans toward Avempace's view. That is, if a heavy body fell in a void - which Buridan had previously shown to be impossible - then it is, perhaps, more likely that it would fall with a determinate velocity rather than instantaneously. But this by no means entails any rejection of Aristotelian dynamic rules, since Buridan believes such motion is impossible and he could, without prejudice to his own position, concede that motion might be finite in the void if one accepted as a premise that motion in the void is possible.

ALBERT OF SAXONY (1316?-1390)

The inclusion of Albert of Saxony is justified by the unusually thorough manner in which he summarizes the various modes of resistance, and by the fact that some of his arguments do not appear in the other authors treated here. Furthermore, Albert formulates an interesting inertial argument of his own which is compatible with the sort of impetus he appears to accept, but incompatible with the given dimensions of his void space.

In Book IV, Question 8, of his Questions on the Physics,49 Albert considers " whether the existence of a vacuum might be possible." 50 He dis- tinguishes two types of void space.51 One is wholly separate from any connection with body, while the second is conceived as a body which is devoid of matter between its inner surfaces. He subsequently denies that either of these modes is " naturally possible," 52 but God could supernaturally

46 See Le Systeme . . . , Vol. 8, pp. 100-102.

47 Duhem says (ibid., p. 102) that " Buridan a fort bien vu qu'admettre l'opinion qu'Ibn Badja avait empruntee a Jean Philopon, c'est rejeter toutes les r&gles fondamentales de la Dynamique peripateticienne; . La gravit6 de cette consequence n'effraye pas Butidan. Son consentement va plus volontiers 'a la theorie d'Ibn B'adj'a qu'a celle d'Aristote."

48 Duhem, in his quotation from this passage, does not actually include the argument itself but quotes only that portion of it where Buridan says he agrees more with Avempace than with Aristotle. See specifically ibid., pp. 101-102.

49 All quotations will be taken from the edition of Albert's Questions on the Physics which appears in Questiones et decisiones physicales insignium virorum: Alberti de Saxonia in Octo

libros physicorum Thimonis in Quatuor libros Meteororum . Buridani in lib. de sensu et sensato . . . Aristotelis . . . recognitae rursus et emendatae summa accuratione . . . Magistri Georgii Lokert. ... (Paris, 1518).

50 Fol. 48r., c. 2: "Queritur octavo: utrum vacuum esse sit possibilis."

51 Fol. 48r., c. 1: ". . . dupliciter imaginan- dum est de vacuo: uno modo quod sit spatium separatum cui non est coniunctum aliud corpus; secundo modo quod vacuum sit unum corpus inter cuius latera non tamen proxima adinvicem sit nihil."

52 In arguing against the first view, Albert insists that a separately existent void would itself be a body since it has length, width, and depth. But if it is a body, it follows that when it receives another body there would be two interpenetrating bodies, which is absurd




produce a void of the second kind.53 For example, God could annihilate all matter which lies between the surfaces of the outermost celestial sphere, in which event there would be a body containing void space and moving with a circular motion.

In the following ninth question,5 Albert produces an elaborate analysis of the concept of resistance. In the most general sense resistance is a tendency to resist being moved in an opposite direction, or a tendency to resist coming to rest.55 Resistances are then divided into external and internal kinds. Under external resistance seven types are differentiated.

1. Two heavy bodies in equilibrium on the arms of a balance mu- tually resist and consequently prevent each other from descending.56

2. When a light body is fastened or connected to a heavy body, the natural tendency of the light body to rise would act as a resistance to the natural downward tendency of the heavy body.57

3. When a body joined to another body resists by virtue of its shape or figure. To illustrate this Albert assumes that a sheet of extended or flattened paper is joined to a heavy body. He then explains that the heavy body would descend more slowly than it would were the paper not linked with it.58 This is merely a variation of the second mode of external resistance.

(fol. 48v., c. 1): ". . . si est ponendum tale spatium separatum, tunc cum ipsum sit corpus -quia longum, latum, et profundum [habet] -

sequitur quod cum ipsum reciperet locatum quod corpora se penetrarent, quod est impossibile." (I have added the bracketed word.) The second kind of void is dismissed by appeal to certain widely known experiments. If the apertures of a bellows were blocked, the sides of the bellows would be inseparable; however, should a hole be made in the bellows, the sides could easily be parted after air had en- tered. This, says Albert, shows that " nature abhors a vacuum." Ibid.:

Secunda conclusio. Per nullam potentiam naturalem possibile est esse vacuum lo- quendo de vacuo secundo modo. Probatur quibusdam experientiis. Primo, si omnia foramina alicuius follis obstruerentur nulla potentia posset elevare unum asserem ab alio, nisi fieret alicubi ruptura per quam sub- intraret aer. Quo facto, faciliter unus is- torum asserum levaretur ab alio. Nam tunc esset aliquid quod posset recipi inter latera ipsius follis. Hoc videtur esse signum na- turam abhorrere vacuum. Secundo, potest probari hoc idem de clepsydra.

Many of the experiments and observations in support of the concept that "nature abhors a vacuum" were derived from a treatise of Greek or Arabic origin called in Latin Trac- tatus de inani et vacuo. This work, and the belief that " nature abhors a vacuum," are discussed in detail by Pierre Duhem in a chap-

ter called " L'Horreur du vide " in his Le Syst6ne du monde, Vol. 8, Ch. 9, pp. 121-168. Essentially the same material, with the title " Roger Bacon et l'horreur de vide," appears in Roger Bacon Essays, collected and edited by A. G. Little (Oxford: Clarendon Press, 1914), pp. 241-284.

53 Fol. 48v., c. 1: " Tertia conclusio. Tamen per potentiam supernaturalem possibile est esse vacuum secundo modo. Patet hoc quia Deus posset annihilare totum quod est infra latera celi. Quo facto, celum esset vacuum et in isto casu tunc vacuum esset una bona res circulariter mobilis."

54 The question reads (fol. 48v., c. 2): "Con- sequenter queritur utrum grave simplex habeat resistentiam intrinsecam quantum ad motum eius deorsum et consimili modo leve ad motum eius sursum."

55 Fol. 49r., c. 1: " Sciendum est quod resistentia dicitur inclinatio ad non moveri vel ad motum oppositum vel ad quietem."

56 Ibid.: " Extrinseca potest imaginari multi- pliciter. Primo sicut in equilibria. Unde posito quod A, terra pura, moveretur ad unum brachium equilibre et B, pura terra, ad aliud, tunc nullum eorum descenderet propter hoc quod unum alteri resisteret, et hoc extrinsice."

57 Ibid.: " Secundo potest imaginari de resistentia extrinseca sicut si uni gravi alligaretur unum leve, tunc in descensu illius gravis illud leve resisteret illi gravi extrinsice."

58 Fol. 49r., c. 1-2: "Tertio illud alligatum quandoque resistit ratione sue figure. Ut si



282 EDWARD GRANT

4. Resistance which arises when an opposite pull is exerted on a body. An instance of this would be a magnet suspended above a very large piece of iron moving downward. In this case the magnet serves to retard the downward motion, although it cannot stop or reverse it.59

5. Resistance offered by an external medium where the velocity of a given mobile is inversely proportional to the density of the medium. Thus the same mobile will fall more slowly in water than in air.60 This is the traditional Aristotelian sense of resistance.

6. The moving body itself can serve as a resistance when it does not, for some reason, move with the speed of which it is capable.61

7. The final mode of external resistance is the incompossibilitas terminorum 62 which, as already noted, is traceable to Thomas Aquinas. The fact that a body cannot be simultaneously in its terminus a quo and its terminus ad quem makes it necessary that it move from the former to the latter in a finite time and, therefore, with a finite velocity. Since the function of a resistance is to produce finite velocities enduring through a finite time, it became customary to designate the incompossibilitas terminorum as a mode of resistance.

Having elaborated seven modes of external resistance, Albert offers only one type of internal resistance, which is actually based upon Avempace's opinion, although the latter is not mentioned by name.

As for internal resistance, some say that any natural agent is of finite power, namely that it is limited to a certain degree of speed which it cannot exceed however much the external resistance may be removed so that they designate such a limitation as an internal resistance. Thus they say that if pure earth were assumed to be in a void, it would descend with a finite velocity. ... Furthermore, they say that a heavier body would be limited to a more intense degree of speed than a smaller heavy body. They also say that a heavy simple body63 posited in a void would not be moved instantaneously but successively because of the limitation and finitude of the force moving it.64

alicui alligaret unum folium papyri extensum, tunc illud grave tardius descenderet quam si illud non esset sic alligatum."

59 Fol. 49r., c. 2: " Quarto aliquando trahens ad oppositum resistit extrinsece. Verbi gratia, si teneretur magnes sursum, et sub eo esset positum unum ferrum ita magnum quod ille magnes non sufficeret illud ferrum desinere descenderet tardius quam si supra non esset magnes positus propter hec quod ille magnes aliqualiter trahit ferrum et per talem trac- tionem impeditur velocitas [the text has "velocitatis "] ferri descendentis. Ergo ille magnes in tali casu potest dici resistentia extrinseca."

60 Ibid.: " Quinto resistentia extrinseca potest dici medium per quod sit motus. Hoc enim propter eius grossitiem resistit mobili et propter hoc idem mobile tardius movetur per aquam quam per aerem."

61 Ibid.: " Sexto movens potest tenere locum resistentie extrinsice sicut si movens non velit velociter movere, nec ita velociter sicut posset."

62 Ibid.: " Septimo incompossibilitas terminorum, scilicet termini a quo et termini ad quem potest dici resistentia extrinseca, quare etc." Albert rejects this mode on fol. 49v., c. 2.

63 Earlier (fol. 49r., c. 1), Albert distinguished between a "heavy simple body " (grave simplex) and an "absolutely heavy body" (grave simpliciter). The former is a heavy body, say a piece of earth, which moves through some lighter element, say fire, which serves to lighten it somewhat. This must be distinguished from a grave mixtum (see below), which is a body compounded of a light and heavy element. The " absolutely heavy body" is one which is uncontaminated by any degree of lightness and, although Albert does not specify this, it would have to be in its




The notion of a "natural velocity " is here associated with an inherent limitation on the motive force, which is conceived not only as internal but also, curiously, as a resistance. Thus by virtue of its limited finite capacity, the internal motive force is treated as a resistance.

Albert has little sympathy for this opinion and musters a series of counterarguments, one of which emphasizes that 65

. . . the limitation and finitude of the power of the agent is not the cause of succession in the motion of a heavy simple body; nor is it an adequate substitute for resistance. This is proved [as follows]: if any natural agent acted successively because it is a finite power, it would follow that a luminous body should transmit its light successively into a medium. Now this is false because the illumination of a medium is, instantaneous....

Albert simply dismisses the notion of internal resistance as a factor in the motion of light and heavy simple bodies.66

But what of external resistances? Here Albert insists that an external resistance is essential for motion "since every motion varies as a ratio of motive force to resistance." This would seem to eliminate the " incompossibility of the termini" argument and certainly seems to imply that Albert is committed to the position that motion in a void is impossible since there is no external medium which would provide the necessary resistance. That this is not Albert's opinion is revealed in the very next question - the eleventh - where he asks " whether, if there were a vacuum, a heavy body could be moved in it." 67 Assuming the existence of a void, he argues that a " heavy mixed body " (grave mixtum) could move in a separate void space with a successive motion because unlike a " heavy simple body" it does have an internal resistance. For example, if a heavy mixed body has a " heaviness " of two degrees, and a " lightness " of one degree, the latter will incline upwards and the former downwards. In this way the one degree of lightness resists the downward motion of the two degrees of heaviness so that the body moves downward with a successive motion in the void.68

own natural place. That is, pure earth would be absolutely heavy only in the natural place of earth.

64 Fol. 49r., c. 2: ... de resistentia intrinseca quidam dixerunt quod quodlibet agens naturale est potentie finite, id est quod ipsum est limitatum ad aliquem certum gradum velocitatis quem non transiret quantumcumque resistentia extrinseca amoveretur ita quod illi talem limitationem ponunt pro resistentia intrinseca. Unde tales dicerent quod si terra pura poneretur in vacuo descenderet finita velocitate.... Ulterius illi dicerent quod graviora essent limitata ad intensiorem gradum velocitatis quam minus gravia. Ulterius dicerent quod grave simplex positum in vacuo si esset non moveretur in ipso subito sed successive propter limitationem et finitatem

potentie moventis ipsum. 65 Ibid.: " Limitatio et finitas potentie

agentis non est causa successionis motus gravis simplicis, nec sufficit loco resistentie. Probatur quia (?) si (?) quodlibet agens naturale ageret successive propter hoc quod esset finite potentie, sequeretur quod corpus luminosum ageret lumen suum successive in medium. Modo hoc est falsum quia illuminatio medii sit subito. The instantaneous transmission of light is opted for by Aristotle and accepted by most, but by no means all, scholastics.

66 Fol. 50r., c. 1: ". . . sit prima conclusio. Gravia et levia simplicia non habent resistentiam intrinsecam quo ad eorum motum...."

67 Fol. 50r., c. 2: " Quaeritur nunc unde- cime: utrum si vacuum esset, grave moveretur in ipso."

O8Fol. 50v., c. 1:



284 EDWARD GRANT

Indeed, under the proper conditions, a heavy mixed body (grave mixtum) could move more slowly in a void than in a plenum.69 Assume the existence of a heavy mixed body consisting of three degrees of earth and two of air, and suppose, furthermore, that everything below the sphere of fire is annihilated, leaving a vacuum. If, now, this compound body is in the sphere of fire and the latter resists it with a degree of one, the ratio of force to resistance will be as five to one since, in fire, both earth and air descend, requiring that the degrees of heaviness and lightness be added. But when it falls to the sphere of air, which is now void space, the air in the compound body serves as internal resistance and the earth as motive force. Hence the ratio of force to resistance in the void is as three to two. It follows that the body falls more slowly in the void than in the plenum, which completely overturns the Aristotelian position. Albert offers other arguments to show that even a heavy simple body could fall with a successive motion in the void.70

In Question 12, 1 Albert proposes his most interesting example.72 He postulates that a vacuum exists between the heavens and earth. Located somewhere in this void is a plane surface on which are two heavy spherical

Secunda conclusio. Accipiendo vacuum primo modo sicut solet communiter accipi in isto proposito, grave mixtum bene moveretur in ipso successive. Patet hoc nam sit unum grave mixtum cuius gravitas sit sicut duo, et levitas sicut unum. Et attingat concavum aeris ipsum descendet successive donec in isto vacuo medium gravitatis eius sit medium mundi propter hoc quod habet resistentiam intrinsecam. Habet enim unum gradum levitatis inclinantern sursum, et duos gravitatis inclinantes deorsum. 69 Ibid.:

Tertia conclusio. In aliquo casu grave mixtum velocius movetur in pleno quam in vacuo. Probatur, nam sit unum mixtum ex terra sicut tria et aere sicut duo. Et sit totum annihilatum quod est infra spheram ignis; tunc ponatur illud grave ad spheram ignis, que resistat illi gravi, sicut unum. Tunc quia tam ex parte terre quam ex parte aeris est extra locum sibi naturalem, et tam ex parte terre quam ex parte aeris appetit descendere per ignem et sic tota potentia motiva est sicut quinque quia terre tria et duo aeris. Et solum resistentia medii est sicut unum, sicut positum est in casu. Ergo hoc movetur per ignem seu per plenum a proportione quintupla. Deinde cum venit ubi est locus naturalis aeris, si [vero] [the text has "non "] esset vacuum, ille aer, ut duo, incipit resistere terre, ut tria, propter hoc quod aer appeteret ibi manere. Sed quia in illo mixto dominatur terra, illud mixtum ulterius descendet ita quod tunc solum terra movet et aer resistit ibi ubi prius in medio pleno ambo movebant. Et

sic illud mixtum ulterius descendet in vacuo a proportione trium ad duo, que est multo minor quam proportio quintupla et per consequens motus qui illam proportionem consequitur. Et sic in vacuo est multo tardior motus eiusdem mixti quam erat in pleno, scilicet per ignem. 70 See ibid. 7' The question reads (fol. 51r., c. 1):

"' whether if there is a vacuum something could be moved in it with a finite velocity, or local motion, or motion of alteration." (" Utrum si vacuum esset, aliquid posset moveri in ipso velocitate finita, seu motu locali, seu motu alterationis.")

72 Fol. 51r., c. 1-2: Secundo conclusio. Si esset vacuum inter

celum et terram, et esset aliqua superficies plana eque distans a centro super quam essent due sphere graves, una A alia B et -A esset gravior quam B, tunc quecunque virtus parva quantumcumque posset in infinitum faciliter movere quamlibet istarum spherarum super ista superficie. Probatur, nam quelibet istarum spherarum tangeret illam superficiem in puncto, et sic quielibet medie- tas ponderaret contra aliam equaliter sicut duo pondera in equilibria. Et cum quilibet excessus sufficiat ad motum, sequitur quamlibet virtutem quamlibet istarum spherarum in infinitum faciliter posse movere. Verum est tamen quod hoc non esset in pleno quia tunc pellenti non solum resisteret una spherarum sed etiam aer. Et sic in aere non quantuncunque parva virtus posset pellere et movere istas spheras.




bodies equidistant from the center of the earth C (see Fig. 1). Let us call these bodies A and B, with A heavier than B. Albert seems now to say that by however little A may exceed sphere B in heaviness, this difference is sufficient to move B ad infinitum beyond the plane surface. That is, A

,,~~~~~~~Z

\ / C~~M C

FIGURE 1. Representation of Albert of Saxony's example showing that a heavy body can move ad infinitum in a void.73

pushes the plane surface downward and overcomes the resistance of B,74 thereby moving it in the opposite direction ad infinitum. If this interpretation is correct, it follows that B will move forever unless obstructed by some other body. Although Albert makes no reference whatever to Aristotle's inertial consequence, his own example may ultimately derive from it. He concludes this section by noting that in air, in contrast to void space, a very small force would be unable to move sphere B because the resistance of the air would be added to that of B, acting as a resistance.

How can we plausibly explain Albert's silence concerning Aristotle's inertial consequence? Having proposed an indefinite motion, Albert might have been expected to mention Aristotle's comparable pronouncement. The answer to this question is bound up with an entire tradition in which Aris- totle's statement was ignored. A possible explanation, admittedly tenuous, will be offered in the conclusion.

But a more fundamental question now emerges. What would keep the body in motion? It is necessary to raise this question because the motion described in Albert's example is a violent one requiring for its continuation a constantly acting force. Earlier, indeed, Albert had insisted that every motion requires a force and resistance. If the body is taken as resistance in the void, then the only candidate for the motive power is an impressed force,

73 Since no figure accompanies the text, I have supplied one.

74 This appears to be an instance of the

first mode of external resistance, except that the bodies are not in equilibrium.



286 EDWARD GRANT

or impetus which would have been transmitted to body B when it was projected from the plane surface. Now Albert accepted the impetus theory in very much the same form as Buridan; i. e., it was a permanent entity of indefinite duration corruptible only by a resistant medium or by the tendency of a body to come to rest in its natural place.75 Thus Albert had available a motive force which could impel the body ad infinitum through the void. But he fails to link impetus theory with this indefinite motion, and indeed, offers no explanation to account for such a motion. Compli- cating matters further, his void space is itself finite, situated as it is between earth and heaven.

It is painfully apparent that Albert of Saxony was utterly unaware of the enormous problems attaching to his example. Motion ad infinitum in the void is proclaimed without explanation or justification, and without mention of Aristotle. The vaguest realization of the problems associated with this example might have convinced Albert to confine this one to his private thoughts.

CONCLUSION

Any attempt to evaluate the impact of Aristotle's inertial consequence on medieval conceptions of motion in the void must, of necessity, be highly conjectural and tentative since, as we have seen, it never become a standard part of discussions concerning the void in the Questiones literature on the Physics. Nevertheless, some reflections are in order.

In arguing against the existence of void space, Aristotle's tactic is to say, in effect, that if a void space were assumed, certain absurd consequences would follow which would compel us to deny its existence. Thus, motion is impossible in a void because there are no natural places - no up, down, or middle - and motion requires a differentiated space. " Either, then, nothing has a natural locomotion, or else there is no void " (IV. 8. 215a. 12). Furthermore, there is no medium in a void and no means to continue the motion of a projectile when it is out of contact with the moving force (IV. 215a. 13-19). Again, there can be no locomotion and a void is impossible.

But if motion were possible in the void,

(1) it would be instantaneous (IV. 8. 215b. 12-23); or if not instantaneous,

75 This interpretation of the nature of Al- bert's impetus theory is based on an example in which he cites a millstone as an illustration of what perpetual motion might be like. If the impetus which causes the millstone to turn could be free from debilitating external resistances, the wheel would be moved forever by that impetus. "Et forte si ista mola sic mota seinper duraret sine aliqua diminutione vel alteratione et non esset aliqua resistentia corrumpens impetum talem ibi generatum, mola ab illo impetu perpetuo moveretur."

This is quoted from Maier, Zwei Grundprob- leme . . . , p. 268, who appears to have taken this passage from Albert's Questions on the De Caelo (Venice, 1492), Bk. II, Question 14. Like Buridan, Albert explains the unceasing motion of the celestial spheres in terms of a permanent impetus which is never corrupted in the resistanceless ether of the supra-lunar region. Albert also discusses impetus in his Questions on the Physics, Bk. VIII, Question 13, which is fully cited by Maier in the Zwei Grundprobleme . . . , pp. 260-263.




(2) it would be inertial in the sense that a body would move off ad infinitum unless obstructed by some other body (IV. 8. 215a. 19-21);

(3) a body would also move off in any direction because there is no resistant medium (IV. 8. 215a. 23-24); and finally,

(4) all bodies would move with equal velocities since a greater body does not divide a void more easily than a smaller one, as would happen in a resistant medium (IV. 8. 216a. 12-20).

Since all these consequences are, for Aristotle, obvious absurdities, any one of them would be sufficient grounds for repudiating the existence of void space.

Al dramatic departure from Aristotle's attitude occurred in the Middle Ages. While agreeing with Aristotle that a void is not naturally possible, many insisted - contrary to Aristotle - that if there were void space, motion wvould not only be possible but its character would be essentially the same as in a plenum since it would be successive and finite. Those scholastics who adopted this position were clearly obligated to deny those properties of motion assigned by Aristotle to bodies conceived as moving in a void. Indeed, this was done for arguments (1), (3), and (4) listed above, but significantly not for (2), the inertial consequence.

Even Galileo's discussion in his De motu is squarely in the medieval tradition. In his tenth chapter he argues " in opposition to Aristotle . . . that if there were a void, motion in it would not take place instantaneously, but in time." 76 Galileo insists that in the void bodies have a natural weight, and speed is a function of natural weight. He says 77

... to put it briefly, my whole point is this. Suppose there is a heavy body a, whose proper and natural weight is 1000. Its weight in any plenum whatever will be less than 1000, and therefore the speed of its motion in any plenum will be less than 1000. Thus if we assume a medium such that the weight of a volume of it equal to the volume of a is only 1, then the weight of a in this medium will be 999. Therefore its speed too will be 999. And the speed of a will be 1000 only in a medium in which its weight is 1000, and that will be nowhere except in a void.

Upon refuting the argument we have listed above as (1), Galileo says that "from this refutation it can readily be seen that motion in a void does not have to be instantaneous. The other arguments of Aristotle are without force or cogency." 78 He then proceeds to repudiate Aristotle's " other arguments " which include only (3) 79 and (4) 80 listed above. There is no men-

76 Galileo Galilei On Motion and On Me- chanics comprising De motu (c. 1590) translated with introduction and notes by I. E. Drabkin, and Le Meccaniche (c. 1600) translated with introduction and notes by Stillman Drake (Madison: University of Wisconsin Press, 1960), p. 41.

77 Galileo, ibid., p. 47. Galileo does not use the incompossibilitas terminorum argu-

ment as justification for successive and finite motion in the void. His position is an elaboration and extension of that given by Philoponus, and much less clearly by Avempace, namely that " natural speed " is a function of " natural weight." Galileo's use of the concept of specific gravity is not found in either Philoponus or Avempace.

78 Ibid.



288 EDWARD GRANT

tion whatever of Aristotle's inertial consequence. Had Galileo considered it, however, he almost certainly would have rejected it, for in refuting Aris- totle's argument that it is the air which moves a projectile after it has lost contact with the motive force, Galileo opts for a self-expending impetus.,, He offers a reductio ad absurdum demonstration to show that this impressed force must continuously diminish. For on the assumption that the impressed motive force is the same at two different points of time, " it will be shown that the forced motion is never diminished, but continues always and without end at the same speed, with the motive force always remaining the same. But this is surely most absurd." 82 Thus, following in the footsteps of his medieval predecessors, Galileo discusses all of Aristotle's arguments concerning motion in the void except the inertial consequence.

Why was this argument not also repudiated, or at least discussed, by those who insisted that motion in the void was not absurd. Perhaps this will remain an insoluble problem, but it is conceivable that those authors who were favorably disposed to the thesis of motion in the void focused all of their attention on the primary problem of convincing their opponents

79 Ibid., pp. 47-48: To say, for example, that in a void the

body will not move in one direction rather than another, or up rather than down, because the void does not give way upward or downward but equally in all directions, is childish. For I could say the same thing about air. That is, when a stone is in air, how does the air give way downward rather than upward, or to the left rather than to the right, if the rareness of the air is everywhere the same? At this point someone, quoting Aristotle, might say that air has weight in its own place and therefore helps downward motion more. We shall examine these fantasies in the next chapter, where we shall investigate whether elements have weight in their own proper places. And similarly, when they say that in a void there is neither up nor down, who dreamt this up? If the air were a void, would not the void near the earth be nearer the center than the void which is near [the region of] fire?

Galileo's insistence that there would be up and down in the void is based on the fact that his void is conceived as lying somewhere between the heavens and the earth. This was almost always the medieval view. However, as we have seen in an earlier note, when Aristotle denied the directions of up and down in the -void he was definitely thinking of an infinite void where such absolute directions are meaningless.

8OAfter quoting Aristotle to the effect that .projectiles cannot move in a void because there is no corporeal medium to move them along, Galileo, after calling this false, says (ibid., -p. 48):

And what he adds to his argument, about different bodies moving in the same medium, is also false. For he assumes that in a plenum heavier bodies move more swiftly because they cleave the medium more forcibly, and that this is the only reason for their speed; but since that resistance is not present in a void, he supposes that all motions in a void will take place in the same time and with the same speed-and this he asserts, is impossible.

Since, for Galileo, speed is a function of natural weight in the void, he denies this. A longer refutation is given in Ch. 13, pp. 61-63. In Ch. 10 (p. 49), Galileo acknowledges that Duns Scotus, Thomas Aquinas, and Philoponus had disagreed with Aristotle on the possibility of motion in the void, and then remarks that they did not refute his basic view " that the speed in one medium is to the speed in the other, as the rareness of the first medium is to the rareness of the second. And no one up to now has ventured to deny this relation." Drab- kin, in a note, observes that both Philoponus and Benedetti had, indeed, denied this relation. We may add that St. Thomas also rejects it in commenting on Text 71 (this is quoted above) .

Galileo also rejects the notion, which he attributes to the above-mentioned trio of authors, of a twofold resistance, " one external, resulting from the density of the medium, the other internal, by reason of the determinate weight of the body" (ibid.).

81 Ibid., p. 84. See also Moody, " Galileo and Avempace," pp. 181-182.

82 Galileo, op. cit., p. 85.




that such motions would be neither instantaneous nor of equal velocity, and never advanced to the next stage of determining whether or not such motions were to be inertial in character. Indeed, it may even be argued that such a consequence was of little import in the context of the discussion considered in this paper since the vacua imagined in all of these cases are, in one form or another, located within the confines of a spherical, finite universe. Motion ad infinitum is obviously impossible in such a universe, even when all matter has been annihilated, and the question of indefinite motion does not even arise. But, on the contrary, even if a body moved only to the circumference of the universe, the same fundamental problem posed by Aristotle remains: how does a body moving with a violent motion cease its motion? Or, indeed, is it necessary that it cease moving? If not, then surely some justification for this novel state of affairs should have been forthcoming. Albert of Saxony reveals better than any of the authors discussed here how little attention was paid to such crucial questions. He assumed motion ad infinitum in a void postulated between the earth and heavens, but felt no compulsion to explain this peculiar situation.

There was clearly a problem to be faced. And if it had been confronted directly, it seems almost certain that Aristotle's consequence would have been denied, for, otherwise, every violent motion in the void would have been of an inertial character. It seems a reasonable conjecture that if this problem had arisen - as it should have - mechanisms would have been devised for bringing about the cessation of such motions, as had been done by Bonetus and Galileo, though not addressing themselves directly to Aris- totle's statement. If this is plausible, then we may infer that enunciation of a principle of inertia by one who accepted the possibility of void space would have been highly improbable, for Aristotle's inertial consequence would have had to be denied in order to render motion in that void space intelligible.

It is perhaps no mere coincidence that the first complete formulation of the principle of inertia was made by one who was a plenist and deemed void space, and a fortiori motion in void space, as absurd. Descartes, who made this momentous contribution to the development of physics,83 returned to

83 Descartes' contribution is thoroughly treated by A. Koyre in his Atudes GaliWenes (3 fascicules; Paris: Hermann & Cie, 1939), fasc. III, pp. 158-181.

Miss Anneliese Maier insists that as early as 1397, Blasius of Parma had clearly expressed the inertial principle in his Questions on the Physics, Bk. III, Question 3. In the seventh conclusion of that question, he asserts that

local motion is a gradual intensible and re- missible quality inhering subjectively in a mobile . . . because when a mobile is moved sometimes quicker and sometimes slower and slower to zero, it is reasonable to believe that this disposition can be intended or remitted to zero. And this is evident because -when some heavy body meets a hard body

it rebounds in a contrary direction since a quality such as motion cannot be destroyed instantaneously. It is true that some say [the body rebounds] because of the impetus acquired in [the course ofl the motion; but it is not helpful to speak this way in the present [context]. (Septima conclusio, quod motus localis est qualitas gradualis inten- sibilis et remissibilis, mobili inhaerens sub- iective .. . quia cum mobile aliquando move- atur velocius, aliquando tardius et tardius usque ad non quantum, rationabile est ex- istimare hanc dispositionem intendi vel re- mitti posse usque ad non quantum. Et per hoc patet, quod cum grave aliquod occurrit duro resilit in contrarium, eo quod talis qualitas, quae est motus, non potest subito



290 EDWARD GRANT

the Aristotelian position that void space was an absurdity, and certainly did not entertain the popular medieval view that motion in a hypothetical void was possible. In referring to his principle of inertia,84 Descartes pro- vides a most illuminating clue which helps explain why the inertial principle was more likely to have been formulated for a full, rather than void, space. By postulating the principle of inertia, Descartes says, " we avoid the difficulty which the Doctors met when they wished to explain why a stone continues to be moved [for] some time after leaving the hand of the one who has thrown it, because we must ask, rather, why it does not

deperdi. Verum quod hic dicunt aliqui hoc esse propter impetum acquisitum in motu. Sed non expedit sic loqui in praesenti.) Quoted from Maier, Zwischen Philosophie und Mechanik (Rome: Edizioni di Storia e Letteratura, 1958), p. 142.

Rejecting the impetus theory as an explanation of the phenomenon of rebound, Blasius, according to Maier, would hold that the quality motion does not disappear even when the force which produced it is no longer operative. In- deed, Maier says that for Blasius motion ceases only when destroyed by external counter forces (. . .wenn der motus localis eine Qualitat ist, so ist es ganz selbstverstandlich, dass diese Qualitat nicht sofort vergehen kann, sondern dass sie weiter dauert - auch wenn die Ur- sache, die sie erzeugt hat, nicht mehr wirkt -

bis sie von ausseren Faktoren zerstbrt wird. Denn Qualitaten vergehen nicht von selbst, sondern werden von entgegengesetzten Kraften vernicht" [p. 143]).

Miss Maier is justified in emphasizing the importance of Blasius' conception of motion continuing without the action of an internal or external motive force. Although William Ockham had also-on quite different grounds -characterized motion from this kinematic point of view, we must recognize that Blasius has taken an important preliminary step toward an inertial concept. But Miss Maier's sweeping claim of a fully expressed inertial principle finds no support in the passage quoted above from Blasius (" Aber jedenfalls konnen wir ohne Ubertreibung sagen, dass Blasius von Parma im vollen und eigentlichen Sinn das Triigheitsprinzip ausgesprochen hat, . . ." [p. 143]). Indeed, apart from the preliminary step mentioned above, Blasius' meager passage has no relevance for the issues fundamental to the principle of inertia.

The purpose of the passage is to convince the reader that motion is a quality inhering in a mobile and capable of intension and remission. Since it is capable of remission, it can decrease continuously to zero degree. Now when we see body A strike a hard body B why is it that A rebounds? Because motion is a

quality and, like any quality capable of successive and continuous remission to zero degree, it does not cease instantaneously. The fact that body A rebounds is evidence that the quality of motion in body A has not yet diminished to zero degree, as it will eventually. Rather than invoke the impetus theory to explain the phenomenon of rebound, Blasius treats motion as a quality inhering in a body, and because that quality is not destroyed instantaneously on impact, it follows that it must rebound (how would Blasius account for the lack of rebound when a lump of clay falls to the ground?)

But on the most crucial point, Blasius does not say (as Maier would have it) or even imply that motion ceases because it is destroyed by external forces. It is quite possible that Blasius thought of motion as a quality which naturally diminishes continuously to zero even if unhindered by external resistances, in which event his concept of motion as a quality inhering in a body would be analogous to a self-expending impetus, and it becomes meaningless to speak of an inertial concept. In the absence of any discussion by Blasius of this vital issue, it is improper to credit him with an awareness of the inertial principle.

84 The text of that principle appears in Le Monde ou Traite de la Lumiere (Oeuvres de Descartes publiees par Charles Adam et Paul Tannery, 12 vols. [Paris, 1897-1913], Vol. 11, p. 38) as follows:

Que chaque partie de la matiere, en particu- lier, continue toujours d'estre en un mesme estat, pendant que la rencontre des autres ne la contraint point de la changer. C'est a dire que: si elle a quelque grosseur, elle ne deviendra jamais plus petite, sinon que les autres la divisent; si elle est ronde ou quairee, elle ne changera jamais cette figure, sans que les autres l'y contraignent; si elle est arrestee en quelque lieu, elle n'en partira jamais, que les autres ne 1'en chassent; et si elle a une fois commence a se mouvoir, elle continuera toujours avec une egale force, jusques i ce que les autres l'arrestent ou la retardent.



MOTION IN THE VOID AND THE PRINCIPLE OF INERTLU 291

continue to be moved forever. But the reason is easy to give, because who could deny that the air in which it is moved offers some resistance to it? " 85

The implication of this profound remark is clear. Knowing, obviously, that all but celestial motions eventually cease, the scholastics focused their attention on explaining how, in violent motion, a body continues its motion after losing contact with the motive force. But, says Descartes, they ought to have asked why such motions do not continue forever and then they would have understood the role of the resistant medium.86 Although he denies the possibility of void space, Descartes makes use of the concept as a limiting case. Bodies would move forever with a uniform rectilinear motion if there were no resistant media - i. e., if there were void space. But void space is an absurdity and all bodies do cease their motions.7

The major theme of this article has been to show that those scholastics who argued that motion in a void was successive and finite did not raise the question posed by Descartes -i. e., why do bodies not move forever -

because, for some reason, they ignored Aristotle's inertial consequence which would have compelled them to raise Descartes' question. But if they had asked that momentous question, a reasonably consistent answer would have required them to deny motion ad infinitum just as they had to deny the other Aristotelian consequences concerning the nature of motion in void space. The mechanism for avoiding indefinite, uniform, violent motion was ready at hand in the form of a self-expending impetus. Ironically, then,: had Aristotle's inertial consequence been properly considered, it would have been destined for an unfruitful history in the framework of ideas erected by partisans of motion in the void; but the same consequence enunciated

85 Ibid., p. 41: . . . nous sommes exempts de la peine oii se trouvent les Doctes, quand ils veulent rendre raison de ce qu'une pierre continue de se mouvoir quelque temps apres estre hors de la main de celuy qui l'a jett6e: car on nous doit plutost demander, pourquoy elle ne continue pas toujours de se mouvoir? Mais la raison est facile a rendre. Car qui est-ce qui peut nier que l'air, dans lequel elle se remue, ne luy fasse quelque resistance? 86 It is significant that Buridan, a plenist

who did not accept the arguments for motion in a hypothetical void, advocated a permanent impetus and also raised the sort of question posed by Descartes. In answering the question - why does a body not continue in motion indefinitely? - Buridan replies that " it is moved as long as the impetus is stronger than the resistance." It is noteworthy that Buridan's permanent impetus is a step in the inertial direction. In a real sense Aristotle also raises this question, for otherwise why should he have seen inertial motion as characteristic of motion in a void space.

87 When Descartes came to write Le Monde he denied the existence and even the possibility of void space. Koyre reflects that, paradoxically, Descartes enunciated the principle of inertia when the foundations of his new physics made the realization of that principle utterly impossible (Atudes Galildenes, III, p. 167):

Or, a l'epoque du Monde, Descartes n'admet plus l'existence, ni meme la possibilite, du vide - seul milieu ou le mouvement rectiligne est possible -; et pourtant, c'est au mouvement rectiligne qu'il limite desormais la loi de la conservation. Ainsi, chose curi- euse, Descartes formule le principe d'inertie au moment meme ofu les fondements nou- vellement acquis de sa physique en rendent la realisation rigoureusement impossible.

A less dramatic paradox, perhaps, is that, for reasons outlined in this paper, it was almost certain that such a principle would not have been enunciated for a void space simply because it was realizable in such a space unless one devised means of preventing it - which some did.



292 EDWARD GRANT

by Descartes, a confirmed plenist, as a fully developed principle of inertia was to become the cornerstone of Newtonian physics.88

88 I am fully aware, as Professor Koyre has taught us, that the full conception of the principle of inertia presupposes a number of significant developments such as an infinite space, motion as a state rather than a process, and so on. But it has seemed to me that Aristotle's insistence that motion in a void would be inertial is significantly, if negatively, related to the flow of ideas which eventually produced

the principle of inertia. We may even properly ask if Descartes, unlike his medieval predecessors, gave careful consideration to this most important but brief statement. In any event, Aristotle's remark forms an early and relevant part of the history of the development of the principle of inertia, and the fate of this statement through the centuries prior to Descartes seems worthy of still further investigation.



motion in the void and the principle of inertia in the middle ages

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