Second Distinction. Second Part. On the Place of Angels

Question One. Whether an Angel is in Place

189. As to the second part of this distinction, in which the Master [Lombard] treats of ‘where the angels were created’, what remains for inquiry is the place of an angel [n.1], and first whether an angel is in place.

190. It seems that he is not:

Boethius On the Seven Days, “It is the mind’s common conception that incorporeal things do not exist in place.”

191. Further, Augustine 83 Questions q.20 seems expressly to prove that God does not exist in place using this middle term, “because he is not a body;” but this premise is true of an angel;     therefore the conclusion is true of an angel too.

192. Augustine also says about God in Literal Commentary on Genesis 8.26 n.48 that “he moves the corporeal creature through place and time but the spiritual creature through time only;” therefore he denies local motion of the spiritual creature, and so he denies that the spiritual creature exists in place.

193. Further, Aristotle Physics 4.4.212a20-21 says that “place is the ultimate limit of the containing body, etc     .” [n.219]; but no body contains an angel, because the container is more actual than the contained and no body is more actual than an angel;     therefore etc     .

194. Further, everything that is in place has a location; but location only belongs to something extended, a quantum. The point is plain because ‘position’ is in one way a difference of quantity, and in this way it only belongs to quantity; in another way it is taken as a category, and in this way it is a property founded on quantity; therefore in neither way does it belong to an angel; therefore place does not belong to an angel either.

195. Against this there is:

The Master [Lombard] in the text, d.2 ch.4 n.14, and in d.37 chs.6-8 nn.345-49, and he adduces authorities as well.

196. Damascene chs.13, 16, 20; see him in those places [nn.199, 215].

Question Two. Whether an Angel requires a Determinate Place

197. Next I ask - without arguments - whether an angel requires a determinate place such that he can be neither in a greater nor a lesser space but precisely in a space of so much; and this question includes whether he can be at a spatial point, and whether he can be in a place ever so small or ever so large.

I. To the First Question

A. The Opinion of Others

198. [First way of speaking] - As to the first question [n.189], one assertion [from Thomas Aquinas] is that an angel is in place precisely through his operation.

199. For proof of this Damascene ch.13 is adduced, who says, “Incorporeal nature operates where it is; and it is not corporeally contained but spiritually;” and later in the same chapter, “it is said to be intelligibly circumscribed where it also operates;” and in ch.16, “they [sc. incorporeal things] are intellectually present and operate where at least they have been commanded to be.” Thus it seems that ‘an angel’s being in place’ is always conjoined with his ‘operating’ - as if being in place were for an angel the fact that ‘he operates in place’.

200. Against this [sc. an angel is in place by his operation] is that the opinion has been condemned as a certain condemned and excommunicated article by the bishop of Paris.Vatican Editors: by Bishop Stephen Tempier on March 7, 1277. To the extent the articles condemned by Bishop Tempier touched on the teachings of St. Thomas Aquinas, the condemnation was revoked by Stephen de Bourret, Bishop of Paris, in 1325, so that Thomas’ doctrine could be left to free discussion in the schools. ²⁶

201. But if it be said that ‘an excommunication does not pass beyond the sea or beyond the diocese’Vatican Editors: William of Ockham tells of a certain Dominican doctor who claimed there was no problem his holding an opinion condemned by Bishop Tempier because the condemnation did not pass beyond the seas. ²⁷ - yet, if it was condemned as an heretical article, it seems to have been condemned as heretical not only by the authority of the diocese but also by the authority of the lord Pope [Gregory IX],Decretals 5.7 ch.9, “In order to abolish the depravity of the diverse heresies that have begun to burgeon in many modern parts of the world, the vigor of the Church should be stirred up... Therefore do we rise up...against the heretics. by the general sanction of the present decree, and we condemn by apostolic authority every heresy (under whatever name it is held) one by one in this decree. And in general all those who have been judged heretics by the Roman Church, or by individual bishops in their dioceses, we bind with equal bond of perpetual anathema.” ²⁸ in his Extra ‘On Heretics’ ch. ‘In order to abolish’.a Or at least the opinion is suspect, because it has been solemnly condemned in a university.

a.a [Interpolation from Appendix A] and in canon law, d.15 last chapter, in the paragraph ‘Montanus’ [Gratian, p.1 d.15 ch.3 n.81] where it is said that “all heresies that bishops and their disciples have taught or written down we confess to be not only things repudiated but also things eliminated by the whole Roman Church and to be, along with their authors and these authors’ followers, eternally condemned under bond of anathema.”

202. [The second way of speaking] - Others [Henry of Ghent, Richard of Middleton], not wishing to use a suspect statement (namely that an angel is in place through operation) say that an angel is in place through an application of himself to place.

203. But these thinkers seem to hide the same opinion under different words. For ‘application’ does not seem it can be understood as anything other than first act [sc. act of essence] or second act [sc. act of power]. Not first act, as is plain. Nor second act, because if second act is understood, it is operation; and not an immanent operation (as understanding or volition), because the immanent operation of an angel abstracts from place just as does the essence of an angel; therefore ‘application’ is a transitive operation on a body, and so an angel will be in place through his operating on a body in place.

B. Against the Conclusion of the Opinion

204. Argument against the conclusion of this opinion [n.198]:

First thus: that he who posits this conclusion contradicts himself, because in the question ‘whether God is everywhere’ [Aquinas SG 3.68] he proves that God is everywhere through the fact that, according to the Philosopher Physics 7.2.243a3-4, ‘the mover is together with the moved’, and God is the first efficient cause and therefore able to move every movable; and from this he concludes that God is in everything and present to everything. I ask what he means hereby to conclude. Either that God is present, that is, is ‘mover’, and then there is a begging of the question because the premises and the conclusion are the same [sc. ‘because God moves everything, therefore he is present by motion to everything’]; and is nothing to the purpose, because he intends there to infer the immensity of God from the presence of God to everything. Or he means to infer the presence that belongs to God insofar as he is immense, and in that case from God’s presence anywhere is inferred - according to him - the presence that pertains to the divine immensity (which belongs to God insofar as he is God), such that God will as he is immense naturally be present before he is as operating present; and this is inferred from the fact that he is present by operation, the way the prior is inferred from the posterior [sc. as cause is inferred from effect, or ‘God is somewhere by operation, therefore he is first there by essence’]. Therefore by likeness as to the issue at hand, an angel will naturally be present in some place by essence before he is present there by his operation [sc. contrary to the opinion in question here, which says an angel is only present in place by operation and not first by essence].

205. A confirmation of this reason [n.204] is that it seems less true of God that he must by his essence be present in the place where he operates than of an angel, because what is of unlimited power seems able to act on a thing however distant it is, but what is of determinate and limited power requires a determinate nearness to what it acts on so that it may act on it; for there is no agent of limited and determinate power whose action cannot be impeded by too much distance from what is acted on, and so it seems more necessary to posit that an angel is present so as to act [sc. than that God is].

206. Another confirmation is that if there is any action from an angel on a body, how is this action disposed to the power from which it proceeds? Mediately or immediately? If it is disposed immediately to the power from which it proceeds, then the angel is in such body or next to it immediately. If it is mediately disposed, then it is from the power through some medium, and there will be the same question about this medium.

And then one will have to stop at the fact that what is first from such power is immediate to such power (and consequently to him whose power it is), and thus that it will be present in that place.

207. Further and second, there follows [sc. from this opinion, n.198] that an angel may sometimes (nay frequently) be nowhere; for an angel does nothing in the empyrean heaven (because it is neither changeable nor movable, [Aquinas Sentences 2 d.2 q.2 a.2]), so he is never in the empyrean heaven. But he is there most of all.

208. Again, if an angel passes from heaven to earth, he can act on the extreme places while doing nothing in any of the intervening places - because there can be an angel who is not the mover of any intermediate sphere; so he is then [sc. in his passing] neither in heaven, nor on earth, nor in between.

209. Further: for an angel is not there first where he first operates. For the whole of something is first proportioned to the power of an angel, such that he moves the whole of it first (and proportioned such that, according to the Philosopher On the Heavens 2.12.293a9-10 [or rather in the Arabic version], if one star were added, the angel would move it painfully and laboriously), and yet he is not first in the whole heaven;     therefore etc     . [sc. an angel’s place is not just where he operates].

210. And if you say that he first moves some one part [Aquinas ST Ia q.52 a.2] and that part is where he is, and by the motion of that part he moves another part (as by pushing or pulling) - against this:

Although the Philosopher [Averroes On the Heavens 2 com.13] supposes the rustic he imagines to have his head and feet at the poles and his arms stretched or extended to East and West - yet in truth, if the first heaven is posited as movable and not resting, no point in the heaven is more East than another but each point is East successively. Also no point there is in truth more capable of motion than another - and so there is no right or left in the heaven from the nature of the thing as there is in an animal (for the right part in an animal is more capable of the virtue of the soul than the left part). So in no part of the heaven can an angel be placed first from the fact that he first moves that part.

211. There is also a confirmation of this, in that if in some part there were an angel resting as it were but moved per accidens (like a sailor in a ship), such that he was always being carried around by the motion, it would seem unacceptable to attribute such motion to the angel moving the sphere. Nor even can this angel be posited as per se resting and that next to him there is part after part of the heaven as it were flowing by, and that he is always moving first the part of it more present to him; for it is impossible to assign where the angel is resting, since he is continually moving the part present to him -and to exist in something insofar as it is moved is not to be resting in it, as it seems.

212. Further, that which for an angel is the reason for his existing or being in a place is in him formally - otherwise an angel would never be formally in a place; but a transitive operation on a body is not formally in him;     therefore etc     .

213. Further, the action is commensurately in a place, per accidens; therefore if the angel were by this in a place (and in no other way), he would be there commensurately.

214. Further, Damascene - on whom they most of all rely [n.199] - is not in their favor:

Both because all the authorities quoted from him commonly always combine operating with being - and this would be superfluous unless ‘an angel’s being in place’ were formally different from ‘an angel’s operating in a place’ (for Damascene says in the first authority that ‘he operates where he is’, in the second he says that an angel ‘is said to be in a place because of his being intelligibly there and operating there’, and in the third that angels ‘are intellectually present and operate where they are at least commanded to be’ [n.199]).

215. Likewise, the same Damascene says in ch.20 that “the heaven is the container of the forms of visible and invisible creatures, and below it are included the intellectual virtues of angels.” In this way then (according to him), the angels are now in the heaven, because they are included ‘below the heaven’. But they would not be thus included at the beginning of their creation, because Damascene himself in ch.17 seems to agree with Gregory the Theologian that they were made before the corporeal creature was; so they were not then in place as they are now, because now they are contained in place but then they were not; and yet then they were able to understand creatures in place, according to Augustine Literal Commentary on Genesis 4.32 n.39, because they had morning knowledge before they had evening knowledge, and they were able to understand the object ‘on the part of the object’ under the same idea under which they now understand it. Therefore Damascene does not posit that they are present to the object by intellection alone.

C. Scotus’ own Solution

1. How Body is in a Place

216. To solve this question, then, we must first consider the place of body.

For any body, beside the ultimate one (which has nothing outside it containing it), possesses five features: to be in an actual place, to be in a determinate because equal place, to be in a place commensurately, to be determinately in this place or in that, and to be naturally or violently in a place.

217. The first four belong to body insofar as it is extended, a quantum, or a body; the last one belong to it insofar as it is a natural body. For although no extended thing exists unless it also has qualities, yet it is naturally an existent with extension before it is an existent with qualities - and in this regard it is an object of mathematics before it possesses quality, that is, it is first such as is considered per se and first by a mathematician.

218. This is what the Philosopher means in Physics 4.8.216a27-b8 ‘On the Vacuum’, because he maintains that “if a cube is put in air or water, even if it have no natural qualities, yet it causes as much displacement as an inserted body,” so that it causes a distance as great as the body; and this does not belong to it insofar as it is natural only, but insofar as it is precisely an extension, a quantum, and so a mathematical object.

a. On the First Article

219. Now I say, expounding each of these five points in turn [n.216], that every such body (other than the body of the first sphere) is first in place, that is, in that which precisely contains it and is immovable; for this is what is understood by the definition of the Philosopher Physics 4 ‘On Place’ [n.193], namely that “place is the ultimate, immovable, first limit of the containing body.”

220. For the divisible, according to the dimension by which it is divisible, cannot be immediately applied to anything nor can immediately contain it; and that which precisely contains something is an indivisible in the genus of quantity and is per se and extrinsic (for nothing indivisible in the genus of quantity exists per se but exists in something divisible); and so the consequence is that what precisely contains something is the ultimate limit of some divisible container. But this ultimacy does not belong to the idea of place, just as it does not belong to the idea precisely of quantity either - because if an indivisible could per se exist and not be the ultimate limit of anything divisible, it could be what precisely contains a thing.

221. Now place, over and above having this ultimate containing, has immobility in addition (whereby it is distinguished from a vessel, according to Aristotle Physics 4.4.212a14-16), which immobility diverse people have in diverse ways tried to save by reference to the poles and to the center.

222. But briefly I say that if the subject does not remain the same, no relative accident stays the same, according to the Philosopher [Categories 5.2b4-6]. And therefore, since it is manifest that every substance that precisely contains this body precisely can be moved locally and not remain numerically the same, it is plain that any accident (absolute and relative) that is in what contains the body is able not to remain numerically the same; and so neither will place remain numerically the same, whether place is posited to be something absolute in such containing body or something relative.

223. And if it be said [Aquinas, Giles of Rome] that place is the ultimate limit of the whole universe and that, although it varies as it is the ultimate limit of the container, yet it does not vary as it is the ultimate limit of the whole universe - this too is not a solution, because place is only the ultimate limit of the whole universe because it is the ultimate limit of part of it; and therefore, if it is different for one part and for another, it is not the same for the whole universe. For although there are many parts in some whole, yet what belongs to the whole through one part first and precisely and afterwards through another part precisely - this is not numerically the same.

224. I say therefore that place has an immobility opposed altogether to local motion, and an incorruptibility by equivalence when compared to local motion.

225. The first point is plain because, if a place were in some way locally movable, however much this is taken to be per accidens [e.g. as a sailor at rest on a ship is moved per accidens], one could say that it is in a place and a different place can be assigned to it one after another; in the same way that a likeness, although it is moved per accidens quasi-accidentally, namely at four or five degrees removed (because first the body moves, and thereby the surface of the body, and thereby the whiteness of the surface, and thereby the likeness [sc. of this whiteness with another whiteness]), yet likeness and surface are truly in different places one after the other.

226. In like manner, then, something at rest could be moved locally; for, because it has one place after another successively, it is locally moved; but something fixed could have different places containing it if the place were moved per accidens.

227. I prove the second point [n.224] by the fact that, although a place is corrupted by the local motion of its subject, such that, when air is moved locally, the same idea of place does not remain in it as before (as is plain from what has already been proved [n.222]), nor can the same idea of place remain in the water that succeeds to the air, because the same accident numerically cannot remain in two different subjects [n.222], yet the succeeding idea of place (which is different in idea from the preceding one) is truly the same as the preceding one by equivalence as to local motion, for that local motion should be from the preceding place to the succeeding one is as incompossible as if the place were altogether the same numerically. But no local motion can be from one ‘where’ to another ‘where’ unless these two ‘wheres’ correspond to two places different in species - relative to the whole universe; hereby these respects, which are only different numerically, seem to be numerically one, because they are as non-distinct with respect to local motion as if they were only one respect.

228. An example of this is in some way plain in the case of significant names, because this word ‘man’, however often it is spoken, is called numerically one word, and it differs numerically from this word ‘stone’; but since the same word numerically cannot be spoken twice (so that there are as many words distinct in number as there are speakings), and since this word ‘man’ and this word ‘stone’ are distinct not only numerically but also specifically - yet because with respect to expressing the goal of a word (namely the concept signified) the word ‘man’ and the word ‘stone’, however often each is spoken, are by equivalence numerically the same, therefore they are said to be numerically one word with respect to this goal.

229. So I say in the issue at hand that place is immovable locally per se and per accidens - yet it is corruptible when the subject is moved locally, because there does not then remain in it the same idea of place; and yet it is not corruptible in itself and by equivalence, because necessarily there succeeds to the body, in which that idea of place was, some other body, in which there is an idea of place numerically different from the preceding one yet the same as the preceding one equivalently by comparison with the local motion.

230. But is it not the case that any body - different from the first body or sphere -is necessarily in a place because it is an extension, a quantum?

Aristotle would say so, because he would say there cannot be ‘a body different from the celestial body’ in the sphere of the active and passive elements [sc. the sublunary sphere where are the elements of earth, air, fire, and water] unless he said it was necessarily contained under something precisely containing it.

231. But the opposite seems to be true according to Catholics, because God could make a stone without any other body existing that was the place of it - or he could make a stone existing apart from every other body, because he could make it outside the universe; and in both ways it would not be in place and yet it would be the same [sc. as other stones] with respect to everything absolute in itself. By nothing absolute in another thing, therefore, must it necessarily be in place, but it has only a passive potency whereby it can be in place; and this would be when a place has been posited in actual existence and when the presence of the stone with respect to some other body as its place has been posited.

b. On the Other Articles

232. About the second article [n.216] I say that - on the supposition of the first article - an extended body is actually in a place, because it is in what actually precisely contains it; for it cannot be in place without the ultimate limit (which is what proximately contains it) making it actual, because it makes the sides of the containing body to be spatially distant. But it is otherwise about a part in the whole, which does not make a surface potentially in the containing body to be actual; and so a part is not in a whole as a placed thing is in a place (Physics 4.5.212b3-6).

233. About the third article [n.216] I say - because of sameness of quantity - that a body necessarily requires a place equal to it.

And for this reason a body is in place commensurately, such that a part of the contained surface corresponds to a part of the containing surface, and the whole of it to the whole.

234. The fifth article [n.216] belongs to a body from the determinate place that places it.

235. The sixth article belongs to a body insofar as it is a natural body, namely from the fact that - insofar as it has a determinate substantial form and determinate qualities - it is of a nature to be preserved and saved by some place that contains it and to be corrupted by another; and when it is contained by the ultimate surface of that which is of a nature to save it, it is said to be in its natural place, even though that naturalness is in many respects accidental to the idea of place; therefore it is to this extent in its natural place because it is in what naturally places it, that is, in the ultimate of the thing containing it which is of a nature to save what is contained in it.

2. How an Angel is in Place

236. Applying these points to the issue at hand about the angel, I say that an angel is not necessarily in place, because an angel could much more be made without the creation of the corporeal creature or could, after the corporeal creature was made, also be made to be beyond every corporeal creature. And yet there is a passive potency in an angel by which he can be in a place; and this potency is founded either in his substance immediately, or in his substance as it is a limited nature actually existent, or in something extrinsic to the angel (whatever that is). And so there is no need to ask for any intrinsic reason for an angel’s being necessarily in place, because there is none in him, but there is only in him a passive potentiality by which he can be in a place, because this is not repugnant to him.

237. So, on the supposition of this first point [n.236], there is no need for an angel to be in a place actually, because there is no need for him to be in some indivisible container actually existing; for he does not make the sides of the container to be spatially distant, and so he does not make the containing surface to be actual.

238. But about the third article [n.216] there is a doubt, and about this article the second question has been moved [n.197]. However, it can be conceded that an angel cannot be in a place ever so large, because this is proper to God. And from this it seems that he cannot be in a place ever so small, from Euclid 1.35, for Euclid maintains there -look at him there [“parallelograms on the same base and on the same parallel lines are equal to each other”].

239. From this I argue as follows: whatever can be in one of two equals can also be in the other, provided no shape by which one of the equals is distinguished from the other is repugnant to it; but in an angel no shape of the place which he is in is repugnant to him; therefore if he can be in one of the equals, he can be in the other - and consequently if he can be in a little square and there is no repugnance in his being in a quadrilateral ever so narrow (which is something one must say in saying there is no repugnance in his being in any size of place), it seems that there is no repugnance in his being in a place ever so long, because the quadrangle is equal to the little square in which he is able to be.

240. This fact is made clear by the opposite in natural bodies. For water, which can be in a square, can for this reason not be in a quadrangle ever so long, because it cannot be in a place ever so narrow; and so it cannot be extended ever so much in length; for it cannot be extended in length without being narrowed in width, and if it cannot be narrowed to infinity in width, it cannot be extended to infinity in length. The opposite holds in the issue at hand; for if an angel does not determine a place ever so small (because then he will be able to be in however narrow and narrower a place), then etc.

241. Further, if there is some quantity of virtue in an angel according to which he can be in some place in proportion to the utmost of his power (namely, this angel so much and that angel so much), yet if he could, in accord with the utmost of his power, make himself to be in a place ever so much smaller than this one, which is adequate to him (and this ‘could’ belongs to some active power in him, because it is in his power to be able to use it for an effect adequate to him or not) - then ability rather to have this [lesser] quantity is more perfectly in his power, because he has an active power that is greater; and so he is able to use this active virtue ad infinitum so as to cause or be in a smaller and smaller place than is the place adequate to him; therefore he has an infinite power. The consequent is unacceptable, so the antecedent is too; just as, then, an infinity of power in him would be inferred if he could be in a larger and larger place ad infinitum, so an infinity of power in him is inferred if he could be always in a smaller and smaller place ad infinitum.

242. But as to whether he could be in a point or not [n.197] there seems no necessary reason for one side or the other; because although he is indivisible yet he does not have a limited indivisibility as a point does, and so he need not be in a point as in a place; nor perhaps is there any repugnance for him to be in a point as in a place, because nothing unacceptable seems to follow from this - because if from this is inferred that he could not be moved locally unless space were made of points, the inference does not hold (for he could immediately from a point in space put himself into a continuum, of which continuum the point is the term).

243. About this article [sc. the third, n.233] it seems one should concede that an angel has a determinate place, but indeterminately. In this way there is both some place which he cannot have a greater than, and some place which he cannot have a smaller than (speaking of continuous place), although perhaps he could be in a point.

244. Now whether an angel requires a determinate place and in a determinate way, such that an angel having so much power is, if he is present to a place, of necessity present to so much place, and it is not in his power to be present to a larger or smaller place (just as is true of bodies, because each body is necessarily in a place equal to it; the intellective soul too is necessarily in the place of the whole animate body, such that it is not in its power to be in a place larger or smaller than the whole body) - this is doubtful, because it does not seem one can easily prove necessarily either one side of the question or the other. For what is unacceptable if an angel’s quantity of power (by which he can be present to some place) is the natural reason for his being in so much place in his own way, just as the quantity of a natural body is the reason for the body’s being in a place in its own way - such that, although it is in my power to be in this place or in that, yet it is not in my power to be in this much place or in that much, because this effect is naturally consequent to a quantity that is not subject to my power, and just as the quantity in itself is not subject to my power so neither is it subject to my power as to its effect, namely to being in this much place or in that much? So nothing unacceptable seems to follow if this supposition is made about angels. Or if the supposition is made that the quantity of the power of angels has some place adequate to it, than which it cannot have a greater, although however this quantity may be subject to an angel’s will so that he is able not to have this place always but sometimes a larger or a smaller one, nothing unacceptable follows.

245. About the fourth article [sc. being in a place commensurately, n.233], it is plain that an angel is not in place commensurately, because he does not have one part after another side by side with different parts of the place.

246. About the fifth article [sc. being determinately in this place or some other, n.234] I say that an angel is in this place or in that, because he is not everywhere. And the reason for this needs investigating.

I say that although something could in itself be in passive potency to some physical genus and not determinately in potency to some species of this genus, yet the same thing reduces it to the act of the genus and of the species; just as a surface (qua surface), although it is of itself determined to a color and is not of itself determined to whiteness and blackness, yet is reduced by the same agent to the act of color and to the act of a color of this sort, because a surface is not colored save because it is colored thus - so I say here that although an angel is in potency to a ‘where’ in general and is not of himself determined to this ‘where’ or to that, yet he is reduced by the same agent to his actually being in a place and to his being in this place or in that in which first he is in place, when this agent produces him above the containing corporeal creature; but from then on he can reduce himself to the act of place, as will be plain in the question about the motion of an angel [n.444].

247. About the sixth article [sc. being in place naturally or violently, n.235], I say that an angel is not in any place naturally, because then he would be in some other place violently; then too some body would have a natural disposition to conserving him in a place, and some other body to corrupting him.

248. And there is a confirmation of this reason from Avicenna, Metaphysics 9.2 f.102va, when he maintains that the motion of the heaven is not natural (“because then it would reach an end in natural rest, and motion away from that rest would be violent” -and so would it be in the issue at hand), and this when taking naturalness properly, in the way that that is said to be moved naturally which is naturally inclined to motion.

249. And from this sixth article [n.247] it is plain that this passive potency (which is in an angel for being in place) is not natural or violent but neither - because what has this passive potency is not inclined naturally of itself to this form or to the opposite, but is disposed in neither way toward them, just as a surface is indifferently disposed to whiteness and blackness.

D. To the Principal Arguments

250. To the arguments [nn.190-194].

All the authorities that deny an angel is in place [nn.190-192] one must expound to be stating the truth by saying that they mean an angel is not in place circumscriptively. Now circumscription involves being in place ‘actually’ and ‘in a place equal to it’ and ‘commensurately’ (namely, according to the second, third, and fourth conditions of place [nn.237, 243, 245]), and these do not belong to an angel.

251. To the quote from the Philosopher [n.193] one can concede that some surface of a body contains an angel, but from this does not follow that the surface acts or has influence on or contains the angel, because the containing of place is of a different idea from the containing of form or the containing of species. For the containing of place means nothing other than that what is contained in place is under the containing surface and that nothing is outside the surface - and this is true in the case of anything definitively contained in place, because nothing of it is outside the surrounding place.

252. As to the point about location or position [n.194], whether it is taken for a difference of quantity or for a category - if the category presupposes quantity then in neither way is the major [sc. ‘everything in place has a location’] true, because there is no need for ‘every being that is in place’ to have a location in one or other of the ways mentioned, unless it is in place circumscriptively.

II. To the Second Question

253. As to the second question [n.197] the answer is plain from what was said in the case of the third article, namely about determinate place [nn.238-244].

Question Three. Whether an Angel can be in Two Places at Once

254. Seventh [sc. seventh from the beginning of d.2, but third from the second part of d.2] I ask whether an angel could be in two places at once.

255. That he could not.

Because then he would be spatially separate from himself as place is spatially separate from place. The proof of the consequence is from the opposite of the consequent [sc. ‘if an angel was not thus spatially separate from himself, then place would not be spatially separate from place’], because things that exist together with some third thing exist together with each other.

256. Secondly as follows: an angel is a nature limited in every respect, therefore limited as to whatever can be present in him - therefore limited in place too; therefore he cannot be in several places at once.

257. Thirdly as follows: two ‘wheres’ are formally contraries, because there can be a distance of place between them, and because motion is between two contraries or from a contrary to what is in between; and in the preceding question it was said that all distinct ‘wheres’ differ in species [n.227] - and things that differ in species within the same genus are contraries, and contraries cannot be present together in the same thing (because contraries are maximally distant from each other), just as neither can contradictories be;     therefore etc     .

258. Fourthly as follows: because if an angel is in two places at once, then he could be at rest and in motion at once, because he could be at rest as to one ‘where’ and in motion as to the other ‘where’; but to be at rest and to be in motion imply being at rest and not being at rest, which are contradictories and cannot be in the same thing at once;     therefore etc     .

259. Fifthly as follows: because then either he could be in motion toward those two ‘wheres’, or he could be moving from one ‘where’ to the other and yet be remaining in the first ‘where’ and acquiring the second along with it. But not in the first way, because two motions of the same species cannot be present in the same thing (Physics 3.3.202a34-36), and even less two contrary motions. Nor in the second way, because the terms of the motions are incompossible together; and that is why a movable thing necessarily loses the term ‘from which’ when acquiring the term ‘to which’.     Therefore etc     .

260. To the contrary:

An angel can be in some whole place, for example the area of a foot; so let him put himself in the end points of this place without making himself present in the middle (because he is not there as a form is, nor in any way in which he would seem required to make himself present to the whole);     therefore he will be in two non-continuous places.

261. Further: a body can be in two places at once, therefore a spirit can much more be so; the antecedent is made clear in 4 d.10 p.1 q.2 nn.11-24, in the material about the Eucharist; therefore etc     .

I. To the Question

262. On this question Damascene ch.13 says that in fact an angel is not in two places at once, because - in his view - “when they are in heaven, they are not on earth,” and conversely. And this as to the fact.

263. But as to the natural possibility of angels, it seems probable that one angel cannot be at once in two places each of which is adequate to him according to the utmost of his power; to wit, if he could, as to the utmost of his power, be in a place of one mile, he could not, by his own power, be in two such places, because then this place of one mile does not seem to be adequate to him according to his natural power.

264. But whether he could be in two discontinuous places, neither one nor the other of which is adequate to him, is a matter of doubt, and there seems no necessary reason either for it or against.

But that he could be in two places (whether adequate to him or not) by divine power I think to be certain, because this involves no contradiction, as will be said in 4 d.10 p.1 q.2 nn.11-24 in the matter about the Eucharist.

II. To the Principal Arguments

265. And therefore to the arguments for the first part [nn.255-59], which seem to prove not only an impossibility as to the natural power of an angel but also an impossibility simply (because they seem to prove a contradiction), a reply must be made:

And first to the first argument [n.255], that it is a non sequitur; and the converse too is a non sequitur, when the third thing (to which the extremes are compared) is unlimited in the respect in which the extremes are compared to it - as is plain about the soul in the right hand and the left hand, which soul is not spatially separate from itself and yet hand is spatially separate from hand; thus God is not spatially separate from himself and yet the things that exist with him here and in Rome are spatially separate from each other. But whatever is posited as the same in two ‘wheres’, whatever the power be by which it exists in them, is in some way thus unlimited with respect to them, and so neither consequence is valid.

266. To the second [n.256] I say that an angel is of himself limited both in nature and in natural properties; but as to an accidental property or respect (of the sort that ‘where’ states, or at any rate ‘where’ is not without a respect), there is no need that an angel be limited altogether (such that it is incompossible for him to have two such respects), although perhaps he is limited by natural power to one of them as to adequacy.

267. As to the third argument [n.257] see 4 d.10 p.1 q.2 n.25.

268. As to the fourth argument [n.258] I say that just as ‘to be moved’ means to be disposed differently now than before, so ‘to be at rest’ is to be disposed now as before; but it is not unacceptable that something is with respect to one ‘where’ disposed now as before and is with respect to a second disposed differently than before - and so it is not unacceptable that it could be at rest here and in motion there. And hereby I concede absolutely that it is at once at rest and in motion - because affirmative predicates simply taken follow of themselves, being taken with a non-diminishing determination.

269. And when the inference is further drawn that ‘therefore it is at rest and not at rest’ [n.258], there is here a mistaking of the question and a fallacy of simply and in a certain respect; for ‘to be at rest’ does not entail ‘not to be in motion’ absolutely but entails only ‘not to be in motion’ with that determination with which ‘to be at rest’ was taken insofar as it preceded being at rest simply; and therefore all that follows is that the thing is in motion in this ‘where’ and is not in motion in that ‘where’, which are not contradictories.

Here is an example: this is double a and half b, therefore it is double and half. But the further inference ‘therefore it is double and not double’ does not follow; for this inference only follows from the first antecedents together with the determination that the thing is double a and not double b - and from these the further inference does not follow that ‘therefore it is double and not double’, but there is here a mistaking of the question. So, in all such cases where the predicates are taken with a qualification, affirmative conclusions are entailed in which the same predicates are included simply; but negative conclusions are not entailed in which the predicates are involved simply in belonging to the subjects, for the reasons stated.

270. To the final argument [n.259] I say that both ways are possible.

271. And when the first way is criticized, I say that there is no incompossibility of motions unless there is an incompossibility of the forms according to which they are motions; and therefore, if two ‘wheres’ are not formally incompossible (either as to being in motion or as to being in flux), then neither will two motions at once to two ‘wheres’ be incompossible. Now the statement of the Philosopher in Physics 3 [n.259] is true of motions according to incompossible forms, of which sort perhaps are absolute forms (but not of the same species), and of this matter elsewhere [4 d.10 p.1 q.2 nn.13-17, 19].

272. And when the second way is criticized, I say that just as generation and corruption are two distinct motions and have their own distinct terms, even though they frequently coincide (and then there are four terms, namely two terms ‘from which’ - one privation and one form - and two terms ‘to which’ - similarly one privation and one form), so there is in the case of motions a departure from the term ‘from which’ and an approaching to the term ‘to which’; and yet, just as generation can, without contradiction, be without corruption and conversely, because they are not the same change, so there can be motion or change insofar as there is an approaching to the term ‘to which’ without any motion which is a departure from a term ‘from which’. And then the statement ‘the terms of the motions are incompossible’ [n.259] is true of the proximate terms of the same motion, but it is not true of terms that can be those of any different motions whatever.

Question Four. Whether two Angels can be in the Same Place at Once

273. Eighth I ask whether two angels can be in the same place at once.

274. That they cannot be:

Because [Aquinas] two total causes cannot be together in respect of the same effect; but an angel, when existing in a place, is a total cause with respect to an operation in such place that he is said to be there by; so another angel, cannot, because of another operation exercised there, be there along with him.

275. Another reason is given by others: that things that have the same mode of existing ‘in’ cannot be together. The point is made clear about two glorious bodies, which cannot naturally be together in the same place, although a glorious body could be together with a non-glorious body. So about two Gods: if they were equal, neither could be with the other (according to Damascene ch.5), and yet God can be together with a creature because of their different way of being in a place. Since therefore angels have the same way of being in a place, they cannot be together in the same place.

II. To the Question

276. In this question the truth is not as certain and clear as it is in the preceding one [n.262], because Richard of Saint Victor On the Trinity 4.25 seems to prove that demons do not have bodies by the fact that a legion of them was in the body of one possessed man (Mark 5.1-17); but a legion could not have been in someone if they had bodies. Therefore he seems to prove that, if they had bodies with them, their bodies would have been in the same place together; therefore now, when they do not have bodies, it seems one should say that they were together without bodies.

277. Also if one angel, who is moving the heaven, is in the south and another good angel, sent by God from heaven to earth, has to pass through that place, there seems no necessity for him not to pass through in a straight line, as it were, or for the other to yield to him.

278. Also, if all the angels had been created before the corporeal creation (as seems true according to Damascene ch.17 [n.215]), it does not seem easy to assign any way that they were then together - and if they were then not together, then not together now either.

279. Whatever be true of their natural power as to fact and possibility, yet as to possibility in respect of divine power there seems no impossibility in angels’ being able by that power to be together.

II. To the Principal Arguments

280. And so one must reply to the arguments, when they seem to prove the opposite.

To the first [n.274] I say that it presupposes something false, namely that an angel is in a place only by operation - which was rejected in the first question on this topic [nn.204-215]. Also, if that supposition be admitted, one angel could operate about the place with one operation and the other with another operation, and each could, in their view [sc. those holding this opinion], be put by its operation in the place where he was operating (namely the place of the one body) and thus both could be together, which is the opposite of the conclusion of the argument.

281. And if you say that they could not operate without moving bodily - neither does this help, because just as an angel moves freely, so he can move according to the utmost, or below the utmost, of his power; and if he moves something below the utmost of his power, another angel could move the movable thing along with him (as is clear about a man, who while able, according to the utmost of his power, to carry ten stones, can, below the utmost of his power, carry five, so that his active power has an act only about five stones - and then he could have another man, cooperating with him, carrying the same), for an angel is a substance that acts freely.

282. To the second [n.275] I say that the major [sc. ‘things that have the same mode of existing ‘in’ cannot be together’], which is famous in many topics, is not reasonable. For ‘to exist in’ states no essential relation to that in which it is, but ‘to exist by (or from)’ does state an essential relation to that by which it is. What is the reasonableness, then, in saying that several things can be by the same and be so in the same way and that several things cannot be in the same and be so in the same way of being in? For why is an accidental respect more repugnant to the species of one idea than the dependence of an essential respect? Likewise, temporal things have the same respect to time as things in place have to place; so it hereby seems to follow that several temporal things cannot be in the same time, which is absurd.

283. Now as to what is said about two glorious bodies, and about two Gods, if they were together [n.275] - if this is true, it must be proved otherwise than by the term ‘being in a place in the same way of being in’, for no repugnance seems to arise from this for things that are together.

Question Five. Whether an Angel can be moved from Place to Place by Continuous Motion

284. Ninth I ask whether an angel can be moved from place to place by continuous motion.

285. Proof that he cannot:

Because “motion is the act of a being in potency insofar as it is in potency,” from Physics 3.1.201a9-11; but a ‘where’ or place is not an act or perfection of an angel, because every perfection seems to be nobler in some way than the perfectible thing; but a ‘where’ is not such with respect to angelic nature.

286. Secondly, there is argument that an angel cannot move with continuous motion:

And first I prove it in general [the proof in particular at nn.301-308], that nothing successive is continuous, and this I do in two ways: I prove it first from the fact that everything successive is composed of indivisibles, and second because everything successive is composed of minima.

287. The first consequence [sc. everything successive is composed of indivisibles, therefore nothing successive is continuous] is proved from Aristotle Physics 6.1.231a24-28, because “an indivisible cannot be continuous with an indivisible since it does not have a last point.”

288. The antecedent here, namely that ‘everything successive is composed of indivisibles’, I prove in two ways:

First because the successive is divided into indivisibles; therefore it is composed of them. - Proof of this antecedent: it is possible for the successive to be divided into all the things it is divisible into (the subject of this proposition seems to include the predicate), and from this seems to follow further that it can exist divided into all the things it can be divided into (this consequence is proved by the statement of Physics 6.6.237b19-20 that “what cannot come to be cannot have been made to be;” and Aristotle says the same in Metaphysics 3.4.999b11 and On Generation 2.11.337b14-25); further, let this possibility be posited as being actual, and the inference follows ‘therefore it exists actually divided into all the things that it can be divided into’, and from this follows that it exists divided into indivisibles (because if not, then it would not exist divided into everything it can be divided into, since it could be divided still further into the parts of the divisibles).

289. Second I prove the same [sc. the successive is composed of indivisibles] because nothing successive is actual save as indivisible - because if something of it were divisible it would at the same time be successive and not successive, or successive and permanent. When     therefore it is not actually existing but passing by instantaneously, I ask what succeeds to it. If something indivisible in the continuous succeeds to it, the proposed conclusion is reached, namely that an indivisible is immediate to an indivisible, and thus the continuous will be composed of indivisibles. If there is no other indivisible succeeding to it, therefore it will then not be, for the indivisible of it is not; and as was argued, ‘it does not exist unless some indivisible of it exists’, therefore etc     .

290. The second way [n.286] is that the successive is composed of minima; therefore it is not continuous.

291. The proof of the consequence is that what is simply smallest (namely what has nothing smaller than it) does not have any part from which it is composed, because then that part would be smaller than it; therefore it is altogether non-extended, a nonquantum, because everything extended has a part smaller than itself. But something nonextended cannot be continuous with something extended; therefore the smallest thing, the minimum, cannot be continuous.

292. The antecedent [sc. the successive is composed of minima] is proved both by authorities and by reason:

First by the authority of the Philosopher Physics 1.4.187b35-188a2, where his reasonings seem meant - against Anaxagoras - to rest on this principle, that it is possible to take a smallest in nature, as a smallest part of flesh or a smallest part of fire; but according to the Philosopher Physics 6.1.231b18-29, “the fact motion and magnitude and time are composed or exist of indivisibles and the fact they are divided into indivisibles mean the same;” therefore it will be necessary to posit a smallest motion and a smallest time, just as also a smallest permanent thing.

293. The same appears from the Philosopher On the Soul 2.4.416a16-17, where he maintains that “for everything that exists by nature there is a determinate principle of magnitude and increase;” now not only permanent things but also successive ones are natural things; therefore they have a determinate smallness and magnitude.

294. The same is also plain from Aristotle On Sense and Sensibles 6.445b3-11 in his first puzzle, where he seems to maintain that ‘natural properties are not divisible infinitely’; and he seems to prove this from the fact that ‘then the sense would be intensified infinitely’, because, in order to perceive an indivisible minimum, a sense is required that is ad infinitum sharper.

295. A reason for proving this [n.292, that the successive is composed of minima] is from the fact that there can be a first part of motion; therefore also a smallest part of motion.

296. The consequence here is plain, because if anything whatever has a part smaller than itself, it would also have a part of itself prior to a part of itself and so on ad infinitum.

297. The antecedent about firstness (namely that ‘there can be a first part of motion’ [n.295]) is plain from two authorities from Aristotle, Physics 1.3.186a10-16, 8.3.253b23-26: “if what undergoes alteration is divisible ad infinitum, not for this reason is alteration divisible ad infinitum as well, but many times it is swift,” where the Commentator [Averroes, Physics 8 com.23] has “sudden” and gives this exposition, “that is, it happens in an instant and not in time.” And Averroes objects as it were against him [sc. Aristotle] that “this seems to conflict with what is said in Physics 6.6.236b32-7b22, that before any moving there is a having moved, and before any having moved a moving;” and he gives a solution in reply that “the latter statement is understood about motion insofar as it is continuous and divisible, but the former one is understood about motion insofar as it is generated or produced in act.”

298. On behalf of his intention there [sc. in Physics 8] Aristotle seems to have premised an example about drops of water, that “if many drops take away a part of a stone by penetrating the stone, it is not necessary that any drop at all should also take away something of it, but sometimes the whole part is taken away at once.” So when he says that “many drops take away from the stone a certain amount in a certain time, but a part of these many drops takes away that amount in no time” (and he gives an example, “just as many men pull a ship,” but none will per se pull the ship also in no time), he seems to indicate that eventually, after a number of drops, the whole part of the stone is taken away. And so it is in the case of alteration, that not always does this happen part by part, but sometimes the whole alteration happens at once.

299. The point seems more express in the second puzzle of On Sense and Sensibles 6.446b28-7a6, where Aristotle maintains that “there is no need for things to be similar in the case of alteration and of transporting; for alteration of a thing happens at once as a whole and not first a part of it, as when water freezes at once as a whole -however, if there is lot of water that is getting hot or freezing, a part receives or becomes so from a part already so; but the first part must be changed and altered by the causer suddenly and all at once.”

300. Again, the point [n.297] is proved by reason - because between contradictories there is no middle; therefore between the non-being of the form that is to be introduced through motion and the being of it there is no middle (but its non-being was in the ultimate instant of the preceding form, therefore between that instant and the instant that measures the being of the succeeding form there is no middle). But if there is no first between the being of the form that is to be introduced through motion and the non-being of it, the ‘first’ [sc. of the being of the form] would be indivisible. And from this proved firstness there follows that the ‘first’ is a minimal part; for the ‘first’ cannot be indivisible, since the Philosopher in Physics 6.5.236a7-b18 shows that one cannot take a first change in motion [n.297].

301. Third principally [n.286] I argue as follows, that an angel cannot be moved [sc. with continuous local motion] because he is indivisible.

302. For Aristotle proves in Physics 6.4.234b10-20, 10.140b8-31, that nothing indivisible can be in moved (and this is intentional - the proof he gives in ch.4 he repeats in ch.10), because everything that is moved is partly in the term ‘from which’ and partly in the term ‘to which’; for when it is totally in the term ‘from which’ it is not moving but at rest, and when it is totally in the term ‘to which’ then it has been totally moved.     Therefore when an indivisible [sc. an angel] is moved it cannot be partly in the term ‘from which’ and partly in the term ‘to which’, because it does not have part after part; therefore etc     .

303. Aristotle’s second reason [in ch.10] is that everything that is moved passes first through a space equal to itself or less than itself before it passes through a space greater than itself; but an indivisible cannot pass first through a space less than itself; therefore it passes first through a space equal to itself before passing through one greater than itself. But it will, by passing always through a space equal to itself, pass through the whole continuous space over which it moves; therefore that space would be composed of indivisibles equal to the moved indivisible. The consequent seems false, therefore the antecedent too.

304. Aristotle’s third reason seems to be that every motion is in time (as he proved before in Physics 6.10.241a15-23); and for any time it is possible to take a lesser time, in which lesser time a lesser movable can be moved; so for any movable it is possible to take a lesser movable ad infinitum; and thus to take an indivisible movable.

305. Fourth, that an angel cannot be continuously moved through place because he has no resistance.

306. Because, as the Commentator [Averroes] says in Physics 4 com.71 about the vacuum, successiveness in motion comes from the resistance of the movable to the mover, or of the medium to the movable, or of the medium to the mover; but none of these occasions of resistance exists in the issue at hand, for an angel does not resist the medium, nor himself as mover. And there is a confirmation of the reason, because according to him a heavy object would be moved in a vacuum in no time, because there would be no resistance there that could cause successiveness in the motion; but an angel does not resist himself or the medium more than a heavy object resists a vacuum (or than a vacuum resists a heavy object), if a vacuum be posited;     therefore etc     .

307. Again, from the reason of the Philosopher. For he argues there [Physics 4.8.215a24-b21] as follows: what the proportion of medium to medium is in rareness and density, so the proportion of motion to motion is in quickness and slowness; but there is no proportion of vacuum to plenum in rareness and density; therefore neither of motion to motion in quickness and slowness. But there can be a proportion in quickness of any possible motion to any possible motion;     therefore no motion is possible in a vacuum, but a motion is possible in a plenum. - In the way that Aristotle argues on the part of the medium, so can one argue in the issue at hand; for (ceteris paribus) what the proportion of movable to movable is in quickness, so is the proportion of angel to body in rareness; but there is no proportion of angel to body in rareness; therefore etc     . (as in the case of Aristotle’s reason [sc. therefore no motion is possible for an angel but motion is possible for a body]).

308. There is another reason of Aristotle’s there: because if motion were to happen in a vacuum, some other body could be taken that would be rarer than a rare plenum in as great a proportion as the time of motion in a vacuum would be quicker than the time of motion in a plenum; the motion through the medium of that rarer plenum will be in an equal time with the motion in a vacuum - which Aristotle holds to be impossible.

- So can one argue in the issue at hand on the part of movables; for if an angel is moved ever so much quicker than a body, then some other body may be taken that would be rarer than the given body in as great a proportion as the time of motion of an angel would be less than the time of motion of the given body - that body, being rarer in such proportion, will be moved in an equal time with the angel.

309. Damascene chs.13, 17 seems to be to the opposite side, when he maintains that angels are not at once in heaven and on earth [n.262]; and angels are frequently sent to earth, as is apparent from Scripture [nn.312-313].

I. To the Question

310. To the question [n.284] I answer yes - because everything that is receptive of the forms of some genus, and that is not of itself determined to any one of them, nor is unlimited, can be moved or changed from one of these forms toward another (this proposition is plain of itself, because the subject includes the predicate); but an angel is receptive of some ‘where’ definitively and not circumscriptively (as is plain above, in the first question on the place of an angel [nn.245-246]), nor is he unlimited as to all of them, because he is not immense; therefore he can be moved continuously from one ‘where’ to another ‘where’. And that he can do so continuously is plain, because between two ‘wheres’ there are infinite intermediate ‘wheres’ (which is proved by the continuous movement of a body through all those ‘wheres’); now an angel can pass through all those ‘wheres’ such that he is not in any of them save indivisibly - and consequently he cannot pass through them all unless he is moved continuously.

311. There is also a confirmation of this, that the blessed soul will be equal to an angel, according to the promise of the Savior in Matthew 22.30; but the blessed soul -rather the most blessed soul - that is Christ’s was moved locally, because it descended into hell, as an article of faith says [sc. in the Creeds].

312. From the Scriptures too it is plain that angels are sometimes sent in an assumed body [Genesis 19.1-22, Numbers 22.22-35, Judges 6.11-22, 13.3-21, Tobit 5.512, 22, Matthew 18.2-7, Luke 1.11-20, 26-38, 2.9-15, Acts 12.7-10]; and if they were then moved along with the body, it seems that there was some passive motion in them different formally from the passive motion of the body itself, because they were not formally anything of the body itself.

313. Likewise it is credible that they are frequently sent without a body, as in the case of the angel sent to Joseph about the conception of the Blessed Virgin [Matthew 1.20-21, also 2.12-13, 19-20].

II. To the Principal Arguments

A. To the First Argument

314. To the arguments of the question [nn.285-308].

To the first [n.285] I say it is not unacceptable that every creature, however perfect it be (provided however it not have in essence all perfection), is capable of or has a potential with respect to some perfection, although the perfection is lesser than the creature’s nature - just as an angel has intellection, which is a perfection of his intellective power, and yet intellection is less noble simply than angelic nature; and so can one concede about ‘where’ or corporeal presence with an angel [sc. that ‘where’ or corporeal presence is some perfection or act of an angel], just as the angelic nature is said to be an ‘act’ (though in a far different way) for the angel in whom it is.

B. To the Second Argument

315. As to the second argument [n.286], I deny the assumption it makes, namely that ‘nothing successive is continuous’.

1. Rejection of the First Antecedent

316. The antecedent of the assumption (which antecedent is itself assumed for the proof of the assumption), namely that ‘the successive is composed of indivisibles’, I deny. And I prove the falsity of the antecedent from the Philosopher in Physics 6.2.233b19-32 about sesquialterate proportion [the proportion of one and a half to one] (which is more convincing for the adversary, although perhaps some of Aristotle’s reasons are taken more ‘from the cause’), because he supposes that a motion can be taken quicker than every given motion in any proportion whatever - and consequently, when some motion is given that is measured by three instants [sc. on the assumption that motion is composed of such indivisible instants], one will be able to take a motion twice as quick that will be measured by only an instant and a half [sc. which is impossible, because an instant is indivisible].

317. This point about the successive [sc. that it is not composed of indivisibles, n.316] I prove by the continuity of something persisting; because a persisting thing is continuous, so a successive thing is too.

318. The proof of the consequence is that if there are indivisibles in motion [= a successive thing] which are immediate to each other, I raise a question about the movable [= a persisting thing] and about the ‘wheres’ that the movable has in those immediate instants; if there is nothing in the middle between the ultimate of one ‘where’ and the ultimate of another, then the ultimate of one ‘where’ is immediate with the ultimate of the other ‘where’ [sc. and so the ‘wheres’ are continuous like the movable that persists through them]; but if there is some middle between these two ‘wheres’, I raise a question about the ultimate of the movable when it is in the middle (and not in the second indivisible instant); because when it is in the two indivisibles it is in the ‘wheres’ between which the middle was posited, so when it is in the middle it is in some middle between the two instants; therefore the two instants were not immediate [sc. and so the motion of the movable between these instants is no more made up of instants immediate to each other than the movable itself is]. - And this consequence is made clear by Aristotle in Physics 6 [n.292], namely that “the fact motion and magnitude and time are composed or exist of indivisibles and the fact they are divided into indivisibles mean the same.”

319. The antecedent [sc. ‘a persisting thing is continuous’, n.317] can be proved by Aristotle’s reasons, Physics 6.1.231a21-b18, more manifestly about permanent than successive things, because it is more evident and manifest that permanent indivisibles do not make something larger than that indivisibles succeeding each other do.

320. However the antecedent is more efficaciously proved by two geometrical reasons or propositions, of which the first is as follows:

‘About any center a circle can be drawn, occupying any space’, according to the second postulate of Euclid [Elements 1 postul.3]. So about a give center, which may be called a, let two circles be drawn: a smaller circle, which may be called D, and a larger B. If the circumference of the larger circle is composed of points, let two points immediate to each other be marked, and let them be marked as b and c; and let a straight line be drawn from a to b and a straight line from a to c, according to the postulate of Euclid [Elements 1 postul.1], ‘from a point to a point a straight line may be drawn’.

321. These straight lines, so drawn, will pass straight through the circumference of the smaller circle. I ask then whether they will cut the circumference at the same point or at a different point.

If at a different point, then there are as many points in the smaller circle as in the larger; but it is impossible for two unequal things to be composed of parts equal in size and number; for a point does not exceed a point in size, and the points in the circumference of the smaller circle are as many as the points in the larger circle; so the smaller circumference is equal to the larger, and consequently a part is equal to the whole.

But if the two straight lines ab and ac cut the smaller circumference at the same point (let that point be d), then on the line ab let a straight line be erected cutting it at the point d, and let this line be de, so that this line is also tangent to the smaller circle, from Euclid [Elements 3 prop.17, ‘from a given point draw a straight line tangent to a given circle’]. This line de forms with the line ab two right angles or angles equal to two right angles, from Euclid Elements 1 prop.13 [‘if a straight line erected on a straight line makes angles, it will make two right angles or angles equal to two right angles’]; also from the same prop.13, the line de will make two right angles or angles equal to two right angles with the line ac (which is posited as a straight line); therefore the angle ade and the angle bde will equal two right angles; and by parity of reason, the angle ade and the angle cde will equal two right angles. But any two right angles are equal to any two right angles, from Euclid Elements 1 postul.3 [‘all right angles are equal to each other’]; so take away the common angle (namely ade), and the remaining angles will be equal; so the angle bde will be equal to the angle cde, and so a part will equal the whole.Tr. Since points b and c are, by hypothesis, not the same, the lines from b to d and from c to d must form an angle when they meet at d. Hence, since b is, by hypothesis, to one side of c, the angle bde will be smaller than, or a partial amount of, the angle cde; but by the argument from Euclid, bde must equal cde, so a part will equal the whole. ²⁹

322. But to this conclusion the adversary will say that the lines db and dc do not make an angle, because then on that angle a base could be subtended from point b to point c, which is contrary to what was laid down, that the points b and c are immediate. When therefore the supposition is taken that the angle cde is the whole with respect to the angle bde, the supposition is denied, because nothing is added to the angle bde from the angle cde, for between b and c in their coming together at point d there is no angle.

323. This response may seem at first absurd, because it denies an angle where two lines that cover a surface and are not coincident come together, and in this respect it contradicts the definition of an angle in Euclid Elements 1 [def.8, ‘A plane angle is the inclining of one line to another when two lines touch and do not lie in the same direction’] - and also because, by denying that a line can be drawn between b and c, it denies the first postulate of Euclid [n.320, ‘from a point to a point a straight line may be drawn’] -however because these results may not be reckoned unacceptable (because they follow the opponent’s assumption [n.322]), I argue against the response in a different way:

The angle cde includes the whole angle bde and adds to it at least a point (although you perversely say it does not add an angle), and a point for you is a part; therefore the angle cde adds to angle bde some part; therefore the former is a whole in relation to the latter.

324. The assumption [sc. ‘cde adds to bde at least a point’] is plain because, if an angle is called the space between intercepting lines not including the lines, then the first point of the line db outside the smaller circumference will be nothing of the angle bde and will be something of the angle cde [sc. because the angle bde and the line db are, ex hypothesi, included within the angle cde]; but if an angle include, over and above the included space, also the including lines, then the first point of the line dc outside the smaller circumference will be nothing of the angle bde and will be something of the angle cde [sc. because the line dc is, ex hypothesi, not part of the line db but outside it]. And so in either way the angle cde adds a point to the angle bde.

325. Nor can one in any way oppose the principal demonstration [sc. that the lines begin to diverge at point d on the smaller circumference] by supposing the two lines do not begin to diverge from each other at the circumference of the smaller circle but somewhere else, closer to or further from the center, because wherever you put this I will describe there a smaller circumference [sc. than that of the larger circle, though a circumference larger than that of the original smaller circle].

326. This second part, namely that the smaller circumference is not cut at one point if it is cut by two lines, needs to be proved only because of the perversity of the opponent, because it is sufficiently manifest that the same line, if it is continuously extended straight on, will never, from the same point, end at two points, and if this ‘manifest’ truth is conceded, the intended conclusion is plain from the deduction in the first part [n.325].

327. The second proof [n.320] is from Euclid Elements 10 prop.5, 9. For he says in prop.5 that “the proportion of all commensurable quantities with each other is as that of one number to another number,” and consequently, as he maintains in prop.9, “if certain lines are commensurable, the squares on them will be to each other as some square number is to some square number;” but the square on the diagonal is not related to the square on the side as some square number to some square number; therefore neither is the line, which was the diagonal of the square, commensurable with the side of the square.

328. The minor of this syllogism is plain from Euclid Elements 1 prop.47 [“the squares on straight lines commensurable in length have a proportion to each other that is a square number to a square number”], because the square on the diagonal is double the square on the side, because it is equal to the squares on two sides; but no square number is double some other square number, as is plain from running through all the squares, whatever the roots they are drawn from.

329. Hereby is the following conclusion plain, that the diagonal is asymmetrical, that is incommensurate, with the side. But if these lines were composed of points, they would not be incommensurable (for the points of one would be in some numerical proportion to the points of the other); and not only would it follow that they were commensurable lines, but also that they were equal lines, which is plainly nonsensical.

330. Proof of this consequence [sc. ‘if diagonal and side were composed of points they would be equal’].

Let two points in a side be taken that are immediate to each other, and let another two be taken opposite them in the other side, and let two straight lines, equidistant from the base, be drawn joining the opposite points. These lines will cut the diagonal.

I ask therefore whether they will cut it at immediate points or mediate points.

If at immediate points, then there are no more points in the diagonal than in the side; so the diagonal is not larger than the side.

If at mediate points, I take the point between the two mediate points on the diagonal (this in-between point falls on neither line, from the givens). From this point I draw a line equidistant from each line (from Euclid Elements I prop.31, “Through a given point draw a straight line parallel to a given straight line”); let this line be drawn straight on continuously (from the second part of Euclid Elements 1 postul.2, “A terminated straight line may be drawn straight on continuously”); it will cut the side, and at neither of its given points but between both (otherwise it would coincide with one of the other lines from which it was posited to be equidistant - and this is contrary to the definition of equidistance, which is the definition in Elements 1 def.23, “Parallel lines are those that, drawn in the same plane and produced to infinity in either direction, meet on neither side”).     Therefore between the two points, which were posited as immediate in the side, there is an intermediate point; this follows from the fact that it was said [just above] there was a middle point between the points on the diagonal; so from the opposite of the consequent follows the opposite of the antecedent [sc. ‘if there is no intermediate point in the side, there is none in the diagonal; but there is an intermediate in the diagonal, therefore there is one in the side’], therefore etc     . [‘therefore since, ex hypothesi, there is no intermediate point in the side, there is none in the diagonal, and side and diagonal are equal’].

331. Nay, in general, the whole of Euclid Elements 10 destroys the composition of lines out of points, because then there would be altogether no irrational lines or surds, although however Euclid there treats principally of irrationals, as is plain about the many species of irrational lines there that he assigns.

2. Rejection of the Second Antecedent

332. From the same discussion [nn.316-331], the rejection of the second antecedent [about minima, nn.286, 290] is also apparent - for either the minimum could precisely end a simply indivisible line, or it could be taken between the ends of two lines.

If in the first way, a minimum is posited as simply an indivisible point; and then it is the same, in this way, as positing a minimum and a simply indivisible as a part.

If in the second way, let two lines then be drawn - extended from the center - to the end points of such a minimum in the larger circumference, such that the lines precisely enclose in the circumference such a minimum. I then ask: do they enclose some minimum in the smaller circumference, or do they precisely include nothing but have altogether the same connecting indivisible? If in the first way, then there are as many minima in the smaller circle as in the larger; so the two circles are equal. If in the second way, it follows that the smaller circumference will be cut at one point by two straight lines (proceeding from the same point), which was rejected in the first member [sc. when arguing against the first antecedent, nn.316-331, esp. 321]. Rather, there follows something more absurd, namely: let these lines in the larger circumference enclose the minimum; and let a straight line be drawn from the end of one these lines to the end of the other, according to the first postulate in Euclid Elements 1 [‘From any point to any point a straight line may be drawn’]; and then this line will be the basis of a triangle of two equal sides, and consequently it will be able to be divided into two equal parts (from Elements 1 prop.10, ‘to divide a given terminated straight line into two equal parts’); and so what was given as a minimum will not be a minimum. Nay further: let some other line be drawn [within the triangle] parallel to the base of the triangle; it will be shorter than the base, and so there will be something less than the minimum.

333. Likewise, this position [sc. about minima] (provided a sort of thing be understood as does not have a part in a whole), involves, whether in one way or the other [n.332], the commensurability of the diagonal with the side (nay, its equality), as was proved before against the first opinion [sc. the first antecedent, n.330].

334. [Instance about minima as to form] - To these arguments [nn.332-333] a response is made that they do not conclude against a minimum as to form, and thus a minimum as to form is posited and not a minimum as to matter.

335. And this distinction is got from the Philosopher On Generation 1.5.321b22-24, ‘On Growth’, where he maintains that “any part as to kind increases but not as to matter.”

336. However this statement can be understood in three ways:

First that ‘a part as to kind’ is called a part as to form, but ‘a part as to matter’ is called a part of an extension insofar as it is an extension, a quantum, because quantity follows matter. And then the statement returns to an old saying, namely that ‘extensions are divisible ad infinitum as they are extensions, but not as they are natural entities’.

337. Or, second, ‘a part as to kind’ can be understood to be what can per se be in act, while ‘a part as to matter’ is called a part as to potency, namely the way a part exists in a whole. And then the statement returns to another old saying, that ‘there exists a minimum that can per se exist, but there is in a whole no minimum than which there is not, existing in it potentially, a lesser’.

338. Or, in a third way (not in harmony with the two old sayings), ‘a part as to kind’ can be understood as what is in something as a minimal part of the form, or of the whole thing as it has the form, and is not any minimal part as to matter, or as to the whole thing in respect of matter. And then it seems manifestly false, because no part of matter in the whole is without form in act, or even without a form of the same nature in the case of homogeneous wholes; rather, just as in this case the whole is divided into homogeneous parts, so the matter and form are per accidens divided into their homogeneous parts - and there is a minimum of each part in the way that there is a minimum of the whole, and conversely.

339. [Response to the instance] - Dismissing, then, this third way of understanding [n.338], I show, by excluding the other two understandings [nn.336-337], that they do not stop the preceding proofs [nn.332-333].

So first I argue against the first way [n.336] using the authority of the Commentator ad loc. on Physics 3.6.206b27-29, on the remark “And we saw Plato etc.;” look there.Aristotle in the Arabic-Latin translation: “And we saw Plato for this reason posit two infinites, because he thought that a thing can pass through and proceed to infinity both by increase and by decrease.” Averroes: “When Aristotle declared that an infinite is found in decrease simply and in addition non-simply (but in that which is converse to division), he began to accuse Plato because Plato equated infinity in one way with infinity in the other (namely both in addition and in decrease), and Aristotle said ‘And we saw Plato etc.’; that is, and Plato, because he thought an infinite proceeds to infinity both by increase and by decrease, posited two species of infinite, by addition and by decrease; and Aristotle introduced the term ‘increase’ in place of the term ‘addition’, so as to distinguish between a proposition of nature and one of geometry.” ³⁰

340. Second using the authority of Aristotle On Sense and Sensibles 6.445b20-27, in the first puzzle when he alleges something to the contrary [n.294]. For although he solves the puzzle obscurely there, yet he does definitely say that ‘sensible qualities are determinate in species’ (which he proves by the fact that ‘when extremes are posited, the intermediates must be finite; but in every kind of sensible quality extremes are posited, because contraries are’). But as to whether any one individual quality is able to have a term in itself, he seems to say no, ‘because they exist along with continuity, and so they have something in act and something in potentiality’, as a continuous thing does; that is, as a continuous thing is one per se actually and many potentially (the many it is per se divisible into), so a sensible quality as it exists in a continuous thing is one actually and many potentially, although per accidens. And then, when the potentiality of the extension or of the quantum is per se reduced to act, the potentiality of the quality is per accidens reduced to act, such that the quantity [sc. of the quality] is by division never divided into mathematical extensions; because, just as he himself argued in response to the puzzle [sc. here above] that ‘a natural thing is not composed of mathematical parts but of natural parts’, so too it [sc. the sensible quality] is divided into such parts, namely natural ones.

But as to how the first way does not make for its intended conclusion, this will be plain from the response [n.344].

341. That for which the authorities of the Commentator and Aristotle have been adduced is also proved by reasons:

Because when some property belongs to something precisely according to some idea, then whatever it belongs to equally according to that idea it belongs to simply equally (just as if ‘to see’ is of a nature to belong to an animal precisely according to its eyes and not according to its hands, then whatever it belongs to equally according to its eyes it will belong to equally simply, even though it does not belong to it according to its hands); but to be divided into such integral and extended parts of the same idea belongs formally to something only through quantity, and to a largest natural thing no more than to a smallest one; therefore since being divided belongs to the smallest according to the idea of quantity, so it will belong to the smallest simply, just as it does to the greatest.

342. But if it be said that the form of a minimum prevents it from coming together from a quantity (as far as concerns itself, on the part of quantity) - on the contrary: if certain consequents are per se incompossible, then what those consequents follow on are also incompossible; and, much more, if what are of the essential idea of certain things are incompossible, then the things too are incompossible; but divisibility into such parts either essentially follows quantity or belongs to the per se idea of it (the sort of idea that the Philosopher assigns to it, Metaphysics 5.13.1020a7-8); therefore, any natural form that divisibility is posited to be incompossible with, quantity is incompossible with too; and so it will not be simply divisible insofar as it is an extension, a quantum, because it is not simply an extension.

343. A proof also of this is that it is not intelligible for something to be an extension without its being made of parts, or for something to be made of parts without a part being less than the whole; and so it is not intelligible for something to be an indivisible extension such that there is not anything in it, less than it, present in it. Nor too can any simply indivisible flesh be posited in a whole of flesh [n.292], because, just as a separate point would not make a separate extension, so neither would a separate point of flesh (if it existed) make any greater thing, either continuous or contiguous, along with another separate point of flesh; hence the reasons of the Philosopher in Physics 6 [n.319] refute the indivisibility of any natural thing just as they refute the indivisibility of any part of an extension insofar as it is an extension.

344. I say therefore that if the response [n.366] about a natural thing insofar as it is an extension and insofar as it is natural can possess any truth, this response should be understood by affirmation and denial of the formal idea of divisibility, such that the formal idea which says that a natural thing is divided insofar as it is an extension says that it is divided insofar as it is a natural extension, and that the formal idea which says that it is not divided insofar as it is natural denies that naturalness is the idea of this division - as if one were to say that an animal sees insofar as it has eyes and not insofar as it has hands; and this understanding is true. But from this it does not follow that that does not belong simply to a natural thing which belongs to it according to quantity; for the concurrent naturalness of the natural thing does not impede that which naturally belongs to quantity, just as neither do the concurrent hands in an animal take away that which simply belongs to the animal according to its eyes. So therefore, absolutely, every natural thing is divisible into divisibles ad infinitum, just as if the quantity, which exists along with the natural form, were to exist by itself, without any natural form. And so all the reasons that proceed of quantity absolutely (according to the idea of quantity) are conclusive about it as it exists in natural things, because divisibility is a natural property of quantity - and so as a result the reasons are conclusive about the natural thing to which this property belongs.

345. The second response [n.337] does not seem to exclude the aforesaid reasons that a whole is not composed of indivisibles or of smallest parts within the whole [nn.332-333]. Nevertheless, it does seem possible to posit a minimum in motion because of the fact that a part of motion per se exists before it is part of something else, of some whole; and thus a part of a form, according to which there is motion, precedes all the parts of that form (not only in nature but also in duration), and so it seems to exist per se and not in the whole. If therefore there may be a minimum in natural things that could exist per se, then this seems to be the smallest part of a form that could be introduced by motion, and so to be a smallest motion [response in nn.350-352].

346. But against this response [nn.337, 345] I argue that just as it is essential to an extension that it can be divided into parts, so it is essential to it that each individual part of the parts it is divided into can be a ‘this something’; therefore existing per se is repugnant to none of them.

347. There is confirmation of this reason and of this consequence:

First because these parts are, as to both matter and form, of the same idea as the whole; therefore they can have per se existence just as the whole also can.

Second because if these parts existed per se, they would be individuals of the species of which the whole is also an individual; but it seems absurd that something has in itself the nature whereby it is, or could be, an individual of some species in such a way that its being able to be an individual of that species is not repugnant to it while yet its being able to exist simply is repugnant to it, and this at any rate as to things that are not accidents (we are speaking now of homogeneous substances which are not essentially inherent in something).

Third too because parts are naturally prior to the whole; so their being able to exist naturally prior to that whole is not repugnant by contradiction to them, because their being prior in time to the whole itself is not naturally repugnant to them (in this way, that it is not repugnant by contradiction to them - on their part - to be prior in duration).

348. It seems, as far as this fact is concerned [nn.346-347], that one should say that, just as a natural form does not take away from a natural whole its being in this way a whole that is always quantitatively divisible, in the way a quantity would be if it existed by itself [n.344], so too it does not take away from it the possibility of any division of it existing per se (as far as concerns it on its own part), in the way that any quantitative part that an extension might be divided into could exist per se.

349. And if you say that it would at once be changed into what is containing it [sc. as water would be changed into air when divided, as per below], the response is that this does not seem to relate to the meaning of the question. For we are looking for a minimum able to exist per se by its intrinsic idea, that is, a minimum that, by nothing intrinsic to it, has any contradictory repugnance to the per se existence of something smaller than it; but, if the whole is corrupted, no intrinsic idea of this sort of incompossibility is imputed. For let us set aside everything containing it or corruptive of it, and let us suppose that water alone exists in the universe; let any given amount of water be divided, because this is possible, as is proved above against the first response [nn.341-344]. The parts into which the division is made will not be nothings, because this is against the idea of division - nor will they, from the idea alone of division, be non-waters, because then water would be composed of non-waters; nor is this smallness, which is now actual, repugnant to the form of water, because this ‘small’ water was there before (although within the whole); nor is the water corrupted through the division, because everything corruptive of it was set aside. So there seems to be no intrinsic reason that the possibility of something less of it per se existing should be repugnant to any per se existing natural thing, although perhaps an extrinsic reason preventive of such per se existence could be assigned in the opposition of some corrupting agent to it [nn.341-344].

350. I also argue against both responses together [nn.336-337], because neither saves a minimum in motion (although it was to reject this charge that the preceding deduction [n.345] was to some extent touched on); for although a medium for local motion cannot be ground for a movable thing unless the medium is natural, yet if per impossibile a mathematical medium could be ground for a mathematical movable, there would truly be succession in such motion, because of the divisibility of the medium; for the movable would pass through a prior part of the space before it passed through a later part. And even now, just as it is per accidens for a thing in place (on the part of the thing as it is in place) that it has natural qualities (as is plain from the Philosopher about a cube in Physics 4.8.216a27-b8 [n.218]), and just as it is per accidens for place (on the part of place as it is place) that it has a natural quality (from q.1 n.235 about place, because although naturalness belongs to what gives a thing place, yet it belongs per accidens to place) - so too it belongs, albeit necessarily in a way that is altogether per accidens, to motion in place or to motion as to ‘where’ (which is per se in a thing in place insofar as it per se regards place) that a natural quality is in the motion, or that it is in it according as it is motion or is in a magnitude over which there is motion. Therefore quantity is per se the reason for succession, whether in a magnitude or in a movable thing or in both.

351. Hereby is the first response [n.336] destroyed, because it does not make for a minimum in motion; because from the fact that - according to this response - one cannot take a minimum in motion according as it is a quantum [n.336], and that succession is per se in local motion by reason of something insofar as it is a quantum, the result follows that in local motion there can in no way be a minimum. And so not in other motions either, because although this may not be as immediately conceded about alteration (if motion or succession be posited according to form), yet it follows by the argument ‘a maiore’ [a fortiori] negatively; for no motion is quicker than passage in place, and thus no motion can have indivisible parts if passage in place necessarily has divisible parts.

352. By the same fact is the second response [n.337] also destroyed, that it does not make for a minimum in motion [n.345]; because in a magnitude over which there is motion one cannot take a minimal part existing in it; therefore neither can one take a minimal passage over the magnitude, because in that minimal passage one should be able to pass through a minimal part of the magnitude.

353. In addition, the second response - as to a minimal motion - is also destroyed by other facts:

First because when a mover is present and is overcoming the movable, one cannot posit the extrinsic reason because of which such a minimum is denied to be capable of existing per se, namely the presence of something corruptive of it [n.349]—because the presence of the cause moving it and producing such a minimum is then overcoming every corruptive contrary.

Likewise [second], ‘for a minimum in successive things to be able to exist in flux is for a minimum there simply to exist in the whole’, because the part of something successive does not have any being in the whole other than that one part flows by before another, and these flowing by parts integrally make up the whole; so just as, in the case of a permanent whole, ‘for a part to be in the whole is for a permanent part to be in the whole’ so, in the case of successive things, ‘for a part to be in the whole is for a flowing by part to be continuous with another part’.

So therefore, now that the two antecedents [nn.286, 290] have been rejected, reply must be made to the proofs of them adduced on their behalf [nn.288-289, 292-300].

3. To the Proofs of the First Antecedent

a. To the First Proof

354. [On the division of the continuous at every mark in it] - To the first argument [n.288] the response is that ‘although it is possible for the continuous to be divided at every point, yet it is not possible for it to exist as so divided, because this division exists in potency and in becoming and can never be complete in a having come to be’. And then as to the proofs adduced for the opposite [n.288], they are conceded as to any single potency for a single making to be, but not as to infinite makings to be, since when one potency has been reduced to act there necessarily remains another not reduced to act; so it is in the issue at hand, that there are infinite potencies for being divided into infinites (since when one potency has been reduced to act, necessarily another remains not reduced to act), and so, although a possibility for being divided is conceded, yet a possibility for having been divided is not.

355. This response is confirmed by the Commentator on Physics 3.7.207b15-18 where he gives the reason for the Philosopher’s proposition that “an [extensive] magnitude happens to be in potency as much as it happens to be in actuality (it is not so in the case of numbers),” namely: “For the reason that all the potencies that there are for parts of a magnitude are potencies of the same potentiality and of the same nature - not so in the case of numbers.”

356. Against this: it follows for you [from the concession made in n.354] that ‘a continuum can be divided at a, therefore it can exist divided at a’ - and so on for b and c and for any individual point (whether determinate or indeterminate), because there cannot be any single division that cannot be carried out. Therefore all the individuals in the antecedent entail all the individuals in the consequent. The antecedent     therefore entails the consequent: if a continuum can be divided to infinity, then it will be possible for this division to have been actually done to infinity.

357. But if you say that the singulars in the consequent are repugnant but not the singulars in the antecedent - on the contrary: from something possible no incompossibles follow; but from the singulars of the antecedent the singulars of the consequent follow (as is plain by induction); therefore etc     .

358. [On the division of the continuous according to any mark in it] - However, the proposition ‘it is possible for the continuous to be divided at any point whatever’ can be distinguished according to composition and division - so that the sense of composition would be that this proposition ‘it is possible for the continuous to be divided etc.’ is possible, and the sense of division would be that in something continuous there is a potency for it to be at any point divided. The first sense is true and the second false.

359. Or the proposition can be distinguished like this, that it can distribute point divisively or collectively [sc. ‘it is possible for the continuous to be divided at any point singly’ and ‘it is possible for the continuous to be divided at any point together’].

360. It can also be distinguished according as ‘possible’ can precede point or follow it; and if it precedes then the proposition is false, because it would indicate that there is one potency for the attribution of the predicate; if it follows then it is true, because it would indicate that the potency is multiplied on the multiplication of the subject [sc. ‘the continuous is possible to be divided at any point’ and ‘the continuous at any point is possible to be divided’].

361. These responses do not seem very logical; not the third because the mode of putting the proposition together - namely possibility - does not seem it can be distributed to several possibilities (or one possibility to several possible instants), and it would not indicate that the predicate is united to the subject for some one instant; nor is the second response valid, because its distinction has place only when taking ‘any point’ in the plural, as in the proposition ‘all the apostles of God are twelve’; nor is the first response valid, because it still must be that, taking the extremes for the same time (or for a different time), possibility state the mode of composition uniting the extremes [sc. regardless of the distinction between ‘composition’ and ‘division’, ‘possible’ remains the mode by which the proposition combines subject and predicate; see n.362].

362. So passing over long and prolix evasions for these refutations [n.361], I say that this proposition [sc. ‘it is possible for the continuous to be divided at any point whatever’] indicates the union, possibly, of predicate with subject for some one ‘now’ (although the ‘now’ be indeterminate), provided such ampliation of composition can be done by virtue of possibility; for no ampliation can be made for several ‘nows’ such that the possibility of composition for some one ‘now’ not be indicated, whether the extremes are taken for the same ‘now’ or for a different one (to wit, if ‘sitting’ is taken for one instant and ‘standing’ for another). In every sense ‘possibility’ must modify the composition uniting the extremes for some one ‘now’, however indeterminate.

363. So it is in the issue at hand, that the ‘to be divided’ is indicated as being joined to the continuous at a point and at any point of it you like - and this for some indeterminate now. But this is impossible, because whenever the predicate [sc. ‘divided’] is united to it for some singular or singulars [sc. ‘at point a or b’], this predicate is repugnant to it for other singulars; for it is necessary - as the first response says [n.354] -that along with the reduction of a potency (not only to having become but also to becoming) there stands another potency not reduced either to act of having become or even to becoming, because it is necessary that, when division exists ‘in becoming or having become’ at a, something continuous be terminated by a - and thus necessary that the potency which is in that part of the continuous is not reduced to act.

364. But if you argue that any singular is true, therefore the universal is too, one can say that the singulars are true but not compossible, and both are needed for the possibility of a universal.

365. On the contrary: this proposition is true at once ‘a continuum can be divided at a and at b and at c’, and so on about any other singular at once.

366. I reply. I say that singular propositions of possibility, taken absolutely, do not entail formally a universal proposition of possibility, but there is a fallacy of figure of speech ‘from many determinates to one determinate’. For singulars can, from the force of their signification, unite a predicate with a subject for some ‘now’, but a universal unites a predicate with a subject for any now of it universally; and so, by the form of signifying, there is a process ‘from many determinates to one determinate’.Vatican Editors quote from Peter of Spain Logical Summaries tr.7 n.37: “The third mode of fallacy of figure of speech comes from diverse mode of supposition, as ‘an animal is Socrates, an animal is Plato, and so on about each one; therefore an animal is every man’; for a process is made from many determinate suppositions to one determinate supposition... Hence since ‘animal’ supposits in each premise for one supposit and in the conclusion for diverse supposits, its supposition varies.” ³¹ This is the reason why there does not follow from a premise possible for some ‘now’ and a premise possible for another ‘now’ a conclusion about a universal possible as now, because the premises do not - from their form - signify that the extremes are combined with the middle term; and so the union of the extremes to each other does not follow, nor is it even possible for some one and the same now.Tr. That this division is possible at this now and that division possible at that now does not entail that all divisions are possible now, because the particulars do not combine the same now with each division, nor can they. ³²

367. And if you say that the singulars are compossible when taking the potency (but not the act terminating the potency) for the same now, to wit ‘it is at once possible for the continuous to be divided at a and at b etc.’ (but not ‘it is possible for the continuous to be divided at a and at b etc. at once’) - I argue that there is no need for possibility to be divided to the same now in order for the universal to be true, because singular propositions that absolutely assert the predicate of singular subjects, these subjects being sufficiently asserted, entail a universal that absolutely asserts the predicate; if such singular propositions are true, all of them, in themselves, absolutely - then the universal is true as well.

368. And if you ask how singular propositions of possibility are to be taken as sufficiently asserted - I say that they must be taken with specific composition, for the same indeterminate now; to wit, ‘it is possible for the continuous to be divided at a for some now, and possible for it to be divided at c and at b for the same now’, and so on about each of them; and then the universal follows, but otherwise not.

369. And if you argue that these are singulars of a different universal, namely of this universal ‘it is possible for the continuous to be divided at any point whatever according to a single now’, and this universal differs formally from the other [sc. ‘it is possible for the continuous to be divided at any point whatever for the same indeterminate now’ nn.358, 362] - I reply that they differ in words, because that which the former expresses the other by the co-signification of the verb denotes, namely that the extremes are united.

370. And if you say that even in this way, by specification of the predicate to some determinate or indeterminate ‘now’, no singular proposition is repugnant to another, because, just as it is possible for the continuous to be divided at a for some ‘now’, so it is possible for it to be divided at b for the same ‘now’, and so on about c and about any other singular (because if any singular were repugnant, it would be one that took up a point either immediate [sc. to point a] or a point mediate to it; but not one that takes a mediate point, because division at one point does not impede division at another point, even an immediate one; nor one that takes division at an immediate point, because no point is immediate [sc. to point a]; therefore the singular propositions, as they introduce the universal, are true and compossible) - I reply and say that to no singular proposition taken or take-able is any singular proposition repugnant that is determinately taken or take-able with indeterminate composition for the same now, nor are these repugnant among themselves; yet infinite indeterminate propositions are repugnant to any taken singular - and the reason for this repugnance was assigned before, a real one, namely from the incompossibility of the reduction to act of all potentials at once [n.363].

371. An example similar to this in other cases is not easy to get. For one can well posit an example where any singular is possible and yet the universal is not possible, because any one singular is incompossible with any one singular, in the way that the proposition ‘it is possible for every color to be in you’ is impossible, because any determinate singular is repugnant to another determinate singular, as ‘you are white’ is repugnant to ‘you are black’. However, let us posit an example of a man who cannot carry ten stones but only nine (and let the stones be equal), then this proposition ‘it is possible for every stone to be carried by him’ is false; and not because any singular is in itself false, nor because any determinate singular is incompossible with any other determinate singular - but because with some determinate singulars some indeterminate singular is incompossible; for any nine singulars are compossible and the indeterminate tenth is incompossible with them.

372. And in this way must the response of the Commentator at On Generation 1 com.9 be understood where he says that “when a division has been made at one point, a division at another point is prevented from being made,”Averroes: “And it would be possible for a magnitude to be divided at every point at once if the points were in contact with each other, which however is impossible... And so we see that when we divide a magnitude at some point, it is impossible for a division to be made at the point following on that point, although this was possible before the division was made at that point.; but when a division was made at the first point, the possibility of division at the second point was immediately destroyed. When therefore we have taken some point, at any place we wish, it will be possible for the magnitude to be divided at that point; but when the magnitude has been divided at a point and at some place, then it will be impossible for it to be divided at a second point in any place we wish, since it is impossible for it to be divided at a point following on the first point.” ³³ namely not indeed at any indeterminate point (marked or mark-able), but at some determinate one.

373. And then I reply to the argument made above against me, about mediate and immediate points [n.370], namely that it is against the objector. I say therefore that one should not allow a division to be made at some point immediate to another point, but at some mediate one; not however at a determinate mediate one (whether marked or markable), but at an indeterminate one - because let any determinate mediate point be taken, then a division at the initial point could still stand together with a division at this mediate point; yet to the division at the initial point there will be repugnant a division at another mediate point, namely at one that is not an indivisible any longer in the determinate continuum.

374. [On the division of the continuous at any and every mark in it] - If however you ask about this proposition, ‘it is possible for a continuum to be divided at any point whatever’ - this proposition can be conceded, because ‘any whatever’ is not only a distributive particle but also a partitive one, such that for the truth of the universal, whose subject is distributed through the term ‘any whatever’, there suffices a single attribution of the predicate to any singular whatever; so not to every singular at once, but to any singular whatever indifferently (there is no need for it to be attributed to others). But ‘all’ does not signify in this way, but signifies that the subject is taken at once for any respect of the predicate.

375. However about the term ‘any you like’ there is doubt whether it signifies the same as ‘all’ does or the same as ‘any whatever’ does; but whichever of these is posited, one should say the same about it as about what it is equivalent to; for when the meaning is clear, one should not use force about the word.

b. To the Second Proof

376. To the second proof of the antecedent [n.289] it is said that ‘the indivisible is nothing other than lack of the continuous, so that nothing save lack of continuous succession is formally an instant- and so a point is lack of length and states nothing positive’. And in that case the proposition that ‘the successive has precisely being because its indivisible exists’ [n.289] needs to be denied; rather it has precisely successive being because a part of it flows by, and never because an indivisible of it is something positive.

377. Many things seem to make for this opinion:

First, that, when the idea alone of the continuous is posited and everything absolute is removed, the continuous seems to have a term, provided it is not absolute; and it does not seem that God can separate finiteness from line nor - as a consequence - a point from it either, which does not seem likely were a point ‘an absolute essence’ different from line.

378. Likewise, if point and line were two absolute essences, it does not seem possible that some one thing would be made from them unless one of them were an accident of the other; for they are not one by perfect identity since they are posited as two absolute essences; nor possible that a single third thing would be made composed of them, because neither is act or potency with respect to the other. The indivisible then has being and not-being without generation and corruption, because if it is only in the middle of a continuous line it is only one point, but when the line is divided there are two points actually; so there is there some point that was not there before, and there without generation, because it does not seem probable that a generator has generated there some absolute essence.

379. Likewise, it seems, from the author of Six Principles about the figure of an incision,Book of Six Principles 1.4, “In the case of certain things there is doubt whether their beginning is from nature or from act, as in the figure of an incision; for no addition is made but a certain separation of parts.” ³⁴ that this is not something said positively, and yet there is a surface there in actuality that was not in actuality before.

380. But against this [nn.376-379]:

Then the result is that the generation of a substance that is not per se the term of a continuum will be nothing (or at any rate in nothing), because there is no positive measure of it; and so it is in the case of illumination and all sudden changes that are not the per se terms of motion. And although this result could be avoided in the case of changes that are terms of motion and come to be in an instant (as nothing in the case of nothing or privation of continuity in the case of privation of continuity), yet it seems absurd about the former cases, for they are not the per se terms of the continuity of any continuous thing, because they are nothing of anything continuous, whether positively or privatively.

381. Further, according to the Philosopher Posterior Analytics 1.4.7334-37, the idea of line comes from points, that is, point falls into the essential idea of line and is said of line in the first mode of saying per se [sc. the mode of per se when the predicate falls into the definition of the subject]; but no privation pertains per se to the idea of something positive;     therefore etc     . [sc. point must state something positive, contra n.376].

382. From the same [sc. statement of the Philosopher, n.381] the result also follows that, if a point is only a privation, line too will be only a privation, as well as surface and solid; for a termed thing is defined by what terminates it and something positive does not essentially include a privation.

383. Likewise the same result [n.382] follows (for another reason [sc. from what is said in n.376 and not from Aristotle’s statement in n.381]) that, if a point is only a lack of length, a line will be only a lack of width and a surface only a lack of depth; and then there will only be a single dimension, which solid would be posited to be, although however the dimension which is called ‘depth’ could in another respect be called ‘width’ (for the three dimensions are distinguished by imagining three lines intersecting each other at the same point).

384. And from this further is inferred something unacceptable, that if a surface is only the privation of depth, how will a point be the privation of a privation? For nothing seems to deprive a privation unless it is something formally positive.

385. In addition, there are on a surface many corporeal or sensible qualities, as it seems; therefore a surface is not merely a privation.

The antecedent is proved about colors and figures, each of which is per se visible and consequently something positive. The figure too [sc. of a surface] seems most properly to follow the kind or species, and so seems to be an accident manifestive of the species; but it does not seem probable that there is no positive entity to something that is such as to follow a species naturally and to manifest it.

386. If it be said differently [sc. to the proof, nn.289, 376] that ‘the indivisible by which the successive has being exists only in potency’ - this is no help, because, when the indivisible is gone, what succeeds to it in the way it has being in the whole? If another indivisible does, the argument [n.289] stands; if not, then the successive will not exist.

387. My response to the argument [n.289] is that, when the indivisible is gone, a continuous part flows by and not an indivisible; nor does anything succeed immediately, save as the continuous is immediate to the indivisible.

388. And if it be objected ‘therefore time does not always have being uniformly and equally (because, when the indivisible instant is posited, time exists, for its indivisible exists, but when the indivisible has gone, time immediately does not exist, because another indivisible of it does not exist)’ - I reply that, just as a line does not have being uniformly everywhere insofar as ‘everywhere’ distributes over the parts of a line and the indivisibles of a line (because a line has being in the former as it is in the parts and in the latter as it is in the ultimates), and yet a line exists everywhere uniformly to the extent that ‘everywhere’ distributes precisely over the latter or precisely over the former, so it is in the issue at hand of time; if the ‘always’ [at the beginning here, n.388] distributes precisely for the indivisibles or precisely for the parts, then time does have being uniformly; but if for both at once then it does not have being uniformly.

4. To the Proofs of the Second Antecedent

389. To the proofs of the second antecedent, about minimal parts [nn.292-300], I reply:

To the first [n.292] that the Philosopher has enough against Anaxagoras if the whole is diminished by a taking away from the whole such that an equal amount cannot go on being taken from it forever; for Anaxagoras had to say (as Aristotle imputed to him [Averroes Physics 1 com.37]) that, after separation of anything generable out of flesh has been made from the flesh, there would still remain as much flesh as could have anything generable further separated off from it; and this is impossible, because however much the flesh can be divided and diminished ad infinitum, not as much flesh at any rate would remain as could have anything generable generated from it, because anything generable requires a determinate quantity of that from which it is generated (especially if, as is imputed to Anaxagoras, generation is only separation or local motion, and the flesh is diminished, by continual separation of other parts from it, beyond the total quantity that generation might come from). So one is not required by Aristotle’s intention there [n.292] to posit also a separate minimum in natural things which exists per se and not in the whole.

390. To the statement of the Philosopher On Sense and Sensibles [n.294] I say that properties are divisible as much as may be, so that a quantum cannot be divided without dividing the property; and yet the property is not divided ad infinitum as it is sensible (that is, insofar as it is perceptible by sense), just as Aristotle maintains there that ‘a part, however minimal, can be sensible virtually although not in act’; that is, that such a part can cooperate along with other parts so as to affect the senses - and yet, although division could also be made in it as it is a per se existent, it would not however affect the senses.

And then the response to the argument of Aristotle adduced for the opposite [n.294 ‘the senses could be intensified infinitely’] is plain, that ‘the senses grow ad infinitum in intensity if a property divisible ad infinitum is presented to them’; and this is true if the sensible, insofar as it is actually perceptible by the senses, could be divided ad infinitum - but the same does not follow if the thing that is sensible can be divided ad infinitum.

391. As to the statement from On the Soul [n.293], it is plain that Aristotle is speaking of the quantity of something capable of increase and decrease; and this I concede, because the quantity that is a perfect quantity for any natural thing is determinate as to being greater or smaller, speaking of the quantity in which the natural thing is naturally produced; or at any rate it is determinate as to being smaller in the case of animate things, speaking of the quantity which diminution leads to. However, the Philosopher is only speaking there [sc. in the passage from On the Soul] of the limit of size and increase; and so he is precisely in this place understanding the perfect quantity of any natural thing to be determinate as to being greater - and from this he gets his conclusion, which he intended to prove, namely that ‘fire is not the principle of increase in any generation or in any species’; for the principal agent in any species must be determinate to the perfect quantity of that species, so that it may produce that quantity and not more than it; but fire is not determinate as to determinate quantity in any species, because - as for as concerns itself - it would go on producing a greater amount, for it grows ad infinitum if combustible material is added to it ad infinitum.

392. And when the antecedent about the minimum [n.290] is proved through the premise [n.295] that ‘it is possible to take a first part of motion’, the consequence can be denied [n.295, ‘therefore it is possible to take a smallest part of motion’], because those who asserted a first part in motion asserted that change is this first part of motion; however I deny a first in both ways (both a first motion and a first change), because the

Philosopher in Physics 6.6.236b32-7b22 of express intention shows the opposite, namely that every moving is preceded by a having moved ad infinitum, and conversely [n.297].

393. And he gives proof of this as follows: that if fire were to cause some first in motion, by parity of reason it would cause something equal to that first, simultaneous with it, and immediate. And so one would need to imagine that between the first simultaneous caused thing and the second one - equal to it - the agent would either have to be at rest, and so motion would be composed of motions and intermediate rests, or the agent would, after having introduced the first, need to introduce the attained successive whole, which seems thoroughly irrational, because, since the agent is of equal virtue for, and equally near to, the passive subject, then just as the agent can simultaneously introduce any (first) degree simultaneously caused, so it can, simultaneous with that introduced degree, introduce the whole thing, and so the whole motion would be caused immediately of immediate changes, or composed of changes - whether motions or rests -that are intermediate.

394. So here is the following process. Let there be a form subject to change needing to be corrupted by motion, for instance, in the case of an alteration, under a heat that is at rest. Of this motion, I say, it is possible to take a last, namely the terminating change, because a movable thing is now disposed indivisibly as previously it was disposed divisibly, and this ‘being affected’ - just like ‘being changed’ - is a being now indivisibly disposed otherwise than it was disposed divisibly before [n.181]. Now for this reason it is under the same form - under which it was at rest - in the instant of change, because then the agent that ought to be moving it did nothing before, and is not now doing anything in respect of it. From this instant the movable begins to move, and that successively - either because of the parts of the movable, for no parts of the movable are equally close to the agent but one part is nearer ad infinitum than another (only a point of the movable is with all of itself immediate to the agent, and a point is not movable), or because of the parts of the form according to which there must be motion, each of which parts can be introduced before another by the present mover, since the extrinsic reason why a minimum cannot exist per se in natural things is the presence of a corrupter - but this is removed by the presence of the agent, which corrupts everything corruptive of its own effect [nn.349-353].

395. Therefore, from this instant of change, the heat that was present is continually diminished and coldness takes over. For it is not likely that there is only a movement of diminishing up to some instant and then first some coldness is introduced; for in that case either the heat to be diminished would have an ultimate of its being (which the Philosopher denies in Physics 8.8.263b20-26), or, if not, at least the coldness immediately following it would have a first of its being, and then there would be a first change of the motion of cooling, which is as unacceptable as that there is a first diminishing of the motion of the heat. It also seems unacceptable that an agent should diminish heat save by causing in it something according to some degree incompossible with it, and, as it causes that incompossible something in greater or lesser degree, it corrupts degree after degree of the existing heat; now Aristotle manifestly maintains this in Physics 6 [n.302], that everything moved has something of both extremes - and it seems manifest to sense that there is something of heat in water being successively heated, while the coldness still remains and is not yet wholly corrupted.

396. So, from the instant of change, the motion of remission of heat and the motion of intensifying of coldness run together - and of neither of these is anything first and in some instant in which, by a sudden change, some degree of coldness is introduced that is altogether incompossible with the heat; in the first there is no heat and up to it there was heat - such that heat has no ultimate of its being but did have an ultimate in its being at rest; and coldness has no first simply of its being, although it have a first in being of rest (namely what it receives through the change, although this is not rest).

397. When therefore the proof is given by the Philosopher in Physics 8 [n.297], I say that the intention of the Philosopher is this, namely to prove that not everything is always in motion. And against those who say that ‘everything is always in motion’ he says that they are manifestly refuted if we consider the motions by which they were moved; for the motions - for their positing of this view - were taken from the increase and decrease of animate things, which they saw coming about in some great length of time (as in a year), and yet from this fact they concluded for no reason that these motions were coming about throughout the whole time but not perceptibly in any part of the time. To them Aristotle objects that such a movable can very well be at rest for a certain time and be moved in some small period of time, so that there is no need that it be always moving with that motion; and he proves this with an example about drops of water wearing away a stone, which drops fall in some certain number and take nothing away from the stone - eventually, however, one falling drop (let it be the hundredth) takes away, by virtue of all the drops, some part of the stone, and this part is taken away whole at once and not part before part.The Vatican Editors point out that, in his interpretation of Aristotle here, Scotus is in agreement with the like interpretation of Aquinas in his commentary, ad loc., on the Physics. ³⁵

398. Hereby the Philosopher does not intend that this taking away of a part of the stone happen in an instant and be in this way whole at once, for this taking away belongs to local motion (and so the motion is local), which cannot at all happen unless a part of the movable pass over the space before the whole movable does; but although this one part of the stone - which is taken away by the last drop in virtue of all the preceding drops - is taken away successively, yet the taking away of it is not successive corresponding to the whole succession of the falling of the drops; for it is not the case that there were as many parts of this taking away of a part from the stone as there were falling drops, but this whole small part is taken away by the last drop, albeit successively. The Philosopher, therefore, is denying a succession corresponding to this succession, namely to the whole falling of the succession of drops - and for this reason the moving of the stone was not always being moved, although when it was being moved by the last drop it was then being successively moved.

399. And, in accord with this intention, he subjoins afterwards about alteration that “there is no need, for this reason, that the whole alteration be infinite, for frequently it is swift” [n.297], where the translation of the Commentator has “sudden” for the “swift” in our translation; now the Commentator expounds ‘sudden’ thus, “that is, in an instant,” and infers “not in time.” But this exposition is contrary to Aristotle’s text, as is plain from our translation ‘frequently it is swift’, and from his own translation which has ‘suddenly’ - because in Physics 4.13.222b14-15, where our translation has “at once,” his translation has “suddenly,” and he has a note there, “that is said to happen suddenly which happens in an imperceptible time” - and thus does he himself there expound it. So to expound ‘swiftly’ or ‘suddenly’ as an instant is to expound time as an instant.

400. However, the intention of the Philosopher [sc. in Physics 8, nn.297, 399] is as follows: there is no need that, as the alterable is divisible ad infinitum, so a time ad infinitum should correspond to the alteration of the alterable - or that always, while the alterable exists, part after part of it should alter continuously, the way alteration could be a succession by reason of the parts of the alterable; but ‘frequently alteration is swift or sudden’, that is, when the alterable is at rest, and then the parts are not simultaneous (either according to the first change or according to the first part of motion) but in succession.

401. And this is what is immediately added by the reason that the Philosopher appends for the same conclusion, namely that when someone is healed the healing is in time “and not at the limit of time;” and yet the movable is not always in motion with this motion, because this motion is finite between two contraries. How then would Aristotle, for the purpose of proving that ‘not everything is in motion’, be taking in the preceding reason [n.400] that ‘alteration happens in an instant’ [sc. as Averroes interprets Aristotle, n.399], and in this second reason he is taking the opposite, namely that ‘healing is not at the limit of time but in time’, and still healing is, on this account, ‘not always’ because it is between contraries, and so, when the contrary is acquired, the motion ceases?

402. Therefore the Philosopher subjoins that “to say ‘everything is continually in motion’ is extravagant quibbling” (where ‘continually’ is taken for ‘always’, because he rejects, for all these reasons [nn.397, 399, 401, 402], the second member of the five membered divisionAristotle gives in the passage at Physics 8 five arguments against the thesis that everything is always in motion: from increase and decrease, from the wearing away of a stone, from the freezing of water, from health, and from stones remaining hard. ³⁶). And yet too a further exposition is there posited, because ‘stones remain hard’; so they do not undergo alteration.

403. Aristotle does not then deny his whole opinion in Physics 6 because of anything he says here, in Physics 8 [nn.297, 392]; and granted that here there were some term that seems expressly to carry this meaning (although there is not but only one taken from a false interpretation), yet it would seem to need being expounded according to what is said in Physics 6 rather than to retract somewhere else [sc. Physics 8] the whole of what is chief in Physics 6 because of certain things that somewhere else are not said as chiefly or of as express intention as in Physics 6.

404. To the passage from On Sense and Sensibles [n.299] response will be made in the last argument of this distinction [nn.519-520].

405. To the argument about contradictories [n.300] a response is made that statements are contradictories that are taken to hold for the same time (and according to the other required conditions), and statements are not contradictories that are not taken to hold for the same time - as is proved by the definition of contradiction set down in Sophistical Refutations 1.5.167a23-27 [‘A refutation is a contradiction of a same and single thing in the same respect and in relation to the same thing and in like manner and at the same time’]; and so the non-being of heat as it went before in the last instant of change, and the being of heat taken up in the completed time, are not contradictories with respect to heat.

406. On the contrary: the being and non-being of color, taken absolutely (not as they understood to be in the same instant), are incompossible simply, so that because they are incompossible simply they cannot be in the same instant - not conversely; and the reason for this incompossibility ‘for the same instant’ is not other than that they are formally opposed with no other opposition formally than contradictory opposition.

407. This is confirmed by a likeness in other things, that a contrary succeeding to a contrary is truly contrary to it, although the two are not together in the same instant; likewise, a form as the term ‘to which’ of privation is truly opposed to it privatively - and this motion is formally between opposites. Hence the Philosopher in Physics 1.5.188a30-b26, 5.5.229a7-b22 maintains that every motion is between opposites that are contrary or privative or some intermediate of the two, and yet they are, as terms of change, never simultaneous.

408. It could also be argued that the terms of creation were not contraries, because the non-being that preceded the being of the created thing cannot be a contrary or a privative or an intermediate between them because it is not in any susceptive subject -and thus it would not be contradictory to being. Creation therefore would not be between contradictories or contraries, which seems absurd.

409. But as to what is adduced about the definition of a contradiction [n.405], there is an equivocation because contradiction exists in one way in propositions and in another way in terms. Propositions are not contradictory unless they are taken to be for the same instant, and for this instant both must assert the predicate of the subject; but terms absolutely taken, without determination to any being, are contradictories. About the first contradiction the Philosopher speaks in On Interpretation 6.17b16-26, and about the second in Categories 10.13b27-35.

410. I reply in another way to the argument [n.300], because ‘immediate’ can be taken in two ways: in one way that there is no middle between what is a whole in itself and something else, and in another way that what is a whole in itself is at once with something else or after something else. In the first way the continuous is immediate with its term, because nothing falls in the middle between the indivisible point that terminates and the divisible continuum that is terminated. In the second way there is nothing immediate to the indivisible point terminating a continuum; for nothing that is a whole in itself immediately follows the indivisible but a part of the whole does; and what is an immediate whole in the first way follows an indivisible according to a part before a part ad infinitum.

411. To the issue at hand therefore I say that as the measures are disposed to each other so are the things measured, namely that when one contradictory is measured by an indivisible the other is measured by an indivisible as well. And then the minor is false [sc. in n.300, ‘if there is no first between the being of the form that is to be introduced through motion and the non-being of it, the ‘first’ would be indivisible’]; for there is no middle between a contradictory ‘as it is in its whole measure’ and the other contradictory, just as neither between its whole measure and the measure of the other; a contradictory, however, that is measured by an indivisible is not immediate to anything, such that according to some of its being (namely as it is in its measure) it immediately follow the other contradictory. So I say as to the issue at hand that the non-being was in an indivisible, but the being of the form introduced by motion is in the whole completed time - and so nothing is intermediate between them; and yet what follows in time is not immediate - in the second way [n.410] - to what pre-exists in an instant.

C. To the Third Argument

412. As to the third principal argument of the question, when the argument is made that ‘an angel cannot be moved [continuously] because he is indisivible’ [n.301] -although one could easily reply that an angel occupies a divisible place and so, in respect of place, he is disposed as if he were divisible - or that, if he occupies existing as a point a point-place, he cannot be moved continuously so as always to have point-existence -yet, because there seems no reason to deny that an indivisible is moved (even if it were a per se existing indivisible of quantity), then one can concede that an angel, occupying a ‘where’-point, can, as always existing in a point, be continuously moved.

413. And what is here assumed about an indivisible can be proved in many ways: First that a sphere moved over a plane describes a line on the plane and yet only touches the plane at a point; therefore the point passes through the whole line, and yet not for this reason is the line that the point thus passes through composed of points. Therefore, by similarity, neither would this result follow if the point existed per se.

414. Multiple responses are made here:

That there is no spherical thing in nature but only in the intellect or imagination. -But this reply is nothing, because the heaven is simply spherical; and anyway, given that there were no simply spherical thing in nature, there would still be no contradiction on the part of sphere and plane that this thing move over that thing as a sphere over a plane (but there would be a contradiction if, from an indivisible moved over something, the result was that the thing moved over was indivisible).

415. A response in another way is that a natural sphere touches a plane at a line and not at a point. - But this seems impossible, because what is applied to a circular line (so as to touch the whole of it) is necessarily circular, because any circular part is circular in any part; but of a straight line no part is circular or curved.

416. Another response is that, because the point of the sphere [n.413] is moved per accidens, therefore there is no need that the space over which it moves be commensurate with it; but the sphere itself is moved per se, and it is divisible. - But against this is that, although a part in a whole is moved per accidens, yet it is always in a space equal to it, and it describes - in its passage - the whole space; indeed, if a whiteness (which is moved, when the extension is moved, more per accidens than any part or term of the extension) is compared to space according to the quantity it has per accidens , its accidental quantity would still be measured by space. Hence - as far as commensuration is concerned - it does not seem that ‘being moved per accidens’ takes away anything other than ‘being moved per se’.

417. Second [n.413], the line laid down by the sphere is not commensurate with the sphere (because then it would be a solid), and it is commensurate with something moved over it; therefore only with the point that is moved over it. If too the sphere is posited to be in a vacuum and only the line to be a plenum, and if per impossibile the sphere could be moved in a vacuum and the point could be moved over the line-plenum, the line-plenum would only be precisely described by the point. And so the conclusion intended follows from these considerations.

418. Further, take a solid cube and let it be moved. Its primary surface is always on something equal to it, and so always on a surface; or something corresponds to it in the magnitude placed underneath [sc. the magnitude over which the cube is moving], to wit a line - and thus, by always passing over something of the magnitude before something else of it, the cube passes over the whole magnitude; therefore the whole magnitude underneath is composed of a line, if their reasoning be valid [sc. those who say an indivisible cannot be moved continuously, n.412].The idea seems to be that if a cube is moved over a magnitude not continuously but indivisible by indivisible, then the surface of the cube in contact with the magnitude beneath will move over one line of the magnitude before another. So if we focus on just one line in the magnitude, we can consider the whole surface moving over that one line, which will thus be the magnitude the surface moves over. The magnitude moved over will then be composed of that one line. We can repeat this process for every subsequent line of the magnitude, and consequently the surface will always be moving over a magnitude composed of a line. Since this result is unacceptable, we must suppose that the cube moves continuously and not indivisible by indivisible. ³⁷

419. Further, let a first point be marked on a line over which another line is moving. This point on the line placed underneath describes the whole of the moved line, because just as any point of the moved line is always continuously at different points of the line underneath, so conversely any point of the line underneath is underneath different points of the moved line; and yet along with all of these points there stands a continuity of motion.

420. It can therefore be conceded (since the statement about motion per accidens [n.416] seems nothing but a subterfuge) that an indivisible could be per se moved if it existed per se, and still be moved continuously; nor from this does it follow that the magnitude passed over is composed of indivisibles.

421. However, because of what Aristotle means in the passages quoted [nn.302-304], one needs to understand that in local motion there is succession for two reasons, namely the divisibility of the movable and the divisibility of the space, and each of these causes, if it existed per se and precisely, would be a sufficient reason for succession; for any movable first passes over one part of the space before it passes over another, and so there would be succession on the part of the space when comparing the movable to the diverse parts of space; further any same part of the space goes by a first part of the movable before a second, and so there would be succession on the part of the movable when comparing it to any same part of the space. In like way too can it be said of the motion of alteration and perhaps of the motion of increase.

422. The philosopher denies therefore, and well denies, that an indivisible ‘as far as concerns itself’ can be moved or can move such that a continuity of motion on its part can be taken such that it is a movable possessing in itself the complete idea of continuous movable, because being continuously moved is not something it has in itself; yet moving or being continuously moved is not repugnant to an indivisible when taking the continuity of motion from something else [n.421].

423. And such, and nothing more, is what Aristotle’s reasons prove, as is plain by running through all of them:

For when Aristotle takes the principle that ‘everything that is moved is partly in the term from which and partly in the term to which’ [n.302], this principle is true if the movable is of the sort that, from its own idea, there is succession of motion; for such a movable is in both terms according to different parts of itself. However things are not so here [sc. in the case of an indivisible], but an indivisible is partly in one term and partly in the other according to the same part of itself - that is, it is in some intermediate stage, not by being at rest, but insofar as this intermediate stage is something of both terms, that is, insofar as it is that through which the indivisible tends from one term to the other; this is to say that it is under change and under something lying under change, and in this way the parts of motion are continuous. - But when the principle is taken that ‘the indivisible cannot be partly in one term and partly in the other because it does not have parts’ [n.302], this principle is true of the first sense of partly (and so I conclude and concede that the indivisible is not thus a movable), but it is false of the second sense of partly [sc. first and second in this paragraph: the first is that of a movable from whose own idea there is succession, and the second is that of an indivisible].

424. To the other argument [n.303], when it is said that ‘a movable passes through a space equal or less than itself before it passes through a greater space’, I reply by saying that ‘to pass through’ can be understood of a divisible passage or of an indivisible passage.

If for an indivisible one, the proposition is false if the understanding is that before passing through any greater space the movable universally passes indivisibly through some equal space; for then one would have to concede that there would be a first change in local motion; and not even those perverters (and not expositors), who say that Aristotle retracts [in Physics 8] what he said in Physics 6 [n.297], can reasonably say that he contradicts himself within Physics 6 itself. There is no need, then, that any successive passage, which is greater than the movable, be preceded by an indivisible passage.

But if ‘to pass through’ be understood of a divisible passage, then it can be understood of the whole, not by reason of the whole, but by reason of the part; and this not by comparing the part to a ‘where’ equal to it and the whole to a ‘where’ equal to it, because the continuous is that ‘whose motion is one and indivisible’, Metaphysics 5.6.1016a5-6; and in this way the part passes through a space corresponding to it at the same time as the whole movable passes through a whole space corresponding to it. But when understanding ‘to pass through’ with respect to some definite and determinate point in the space, the whole passes first through that point by reason of some part (and, in having passed through it, the whole has passed through something less than itself, speaking of a ‘where’ different from its own first total ‘where’), before it thus passes through a space equal or greater than itself; and this it does per accidens, insofar as the movable can have a ‘where’ less than its total ‘where’.

425. But if we speak of greater or lesser or equal ‘wheres’, according to which continuity of motion is immediately expected (and an infinite number of which ‘wheres’ are something in the first ‘where’), then simply the whole passes through a space greater than itself before it passes through one equal to itself. As such is the response to the issue at hand, saving what belongs to the per se idea of continuous motion and not what does not belong to the per se idea of it.

426. And if you object that, however it may be with Aristotle’s argument in itself [n.303], this point is always in a space equal to itself and so passes through the whole (so it is commensurate with the whole line underneath, and so this line underneath will be composed of points) - I say that it is ‘always’ in the sense that, in any indivisible, it is in a space equal to itself; but it is not ‘always’ in the sense of any part of time.

The same could be argued about the first surface of the cube solid [n.418], that although in any ‘now’ of time it is lying precisely on the line over which it is moved, yet in the intermediate time between two instants it is flowing over the continuous intermediate between the two extremes.

427. As to the last reason [n.304], I well concede that it is possible to take a time less than any given time, but from this does not follow that in that lesser time a lesser movable can be moved, save when speaking of a continuous movable that was, on its own part, the cause of the continuity of the motion.

D. To the Fourth Argument

428. To the fourth principal argument [nn.305-306], about the cause of succession in motion, I say that, although there can be contention and dispute about Averroes’ intention and about what he contradicts Avempace in (the way it appears in Physics 4 com.71, ‘On the Vacuum’), yet I say briefly that the cause of succession in any motion is the resistance of the movable to the mover; not indeed such that the mover cannot overcome the movable (for then it would not move it), nor indeed such that the movable is inclined back toward the opposite (for then precisely it is in violent motion) - but resistance such that the movable is always under something to which the term intended by the mover cannot immediately succeed. And this resistance of the movable to the mover is because of a defect in the virtue of the mover and thereby because of the resistance of the medium to the mover and the movable, and by the ‘medium’ can be understood all that necessarily precedes the introduction of the term to be introduced. But such a medium is not necessarily a medium save to a limited virtue; for if there were an infinite virtue, it could put the movable at once in the term ‘to which’ - such that neither because of the opposed form in the term ‘from which’ (the form that the movable would already have), nor because of the mediums naturally ordered between the form that the movable has and the term ‘to which’, would there be a necessity that such a mover should move through such mediums before it introduced the term.

429. The possibility, then, of succession comes from the resistance of the movable to the mover, which is from the resistance of the medium to the movable and the mover, such that this is one resistance. For the movable, insofar as it has a form of the sort that between it and the term such mediums are of a nature to exist, can be continuously moved through the mediums to the term - and by these mediums, which resist the movable so that it cannot at once be in the term, can be understood the divisibility of the parts of the movable, or the divisibility of the parts of the form according to which there is motion, or both these two together. However the necessity of succession is never from this resistance, but is precisely by comparing this resistance to the agent, which the movable resists because of the resistance of the medium to the agent - such that, just as the possibility was from the resistance alone of the medium to the movable, so the limited virtue cannot take away this resistance; and therefore this resistance resists the agent so that it does not at once introduce the term.

430. Then to the arguments introduced for the opposite [n.306], namely that ‘there is no resistance of an angel to himself’ - I say that, as an angel does not act from the infinity of active virtue when he is in heaven, between which ‘where’ and his own ‘where’ on earth many mediums are of a nature to exist, which are also mediums for his own motive virtue - so neither can his own motive virtue make all those mediums and the term, nor even can he at once make the term save by first making those mediums; and for this reason there is here the whole resistance that is required for succession in motion.

431. And when argument is made about the saying of Averroes, about a heavy object, that ‘if it were put in a vacuum it would descend immediately because of a defect of resistance on the part of the medium’ [n.306] - I say that if a vacuum is posited then the heavy object would not move (according to the Philosopher, Physics 4.8.214b12-215a24), because a vacuum cannot give way to a heavy object and because separate dimensions cannot be together. However, if it were posited that a vacuum could give way and that there was space in it, and not that the sides of the plenum were together (because then there would not be a vacuum) - I say then that there would be motion successively of the heavy object in the vacuum, because a prior part of the vacuum would be prior and also because the whole heavy object would pass through this part of space before that part; and, as was said before in the second argument [n.350], per se succession is only in local motion and in space insofar as space is a quantum.

432. To the arguments of Aristotle as far as they are adduced for the issue at hand [nn.307-308]:

I say that the proposition ‘what the proportion of medium to medium is in rareness and density, so the proportion of motion to motion is in quickness and slowness’ is true (ceteris paribus), and so it follows that there is no motion in a vacuum - or at least this is true against those [sc. the ancient atomists, Democritus and Leucippus] who posited the vacuum to be the whole cause of motion or of succession in motion; but as to the issue at hand, by arguing similarly here about movables as there about spaces, this proposition ‘what the proportion of movable to movable is in rareness, so the proportion of motion to motion is in quickness’ can be denied. And if you take the proposition ‘what the proportion is of this movable under the idea by which it is movable and of that movable under the idea by which it is movable’, I concede it but then the minor is false [sc. that ‘there is no proportion of angel to body in rareness’, n.307]; for an angel is capable of moving continuously insofar as he has a virtual quantity according to which he can coexist in an extended place, just as a body can, according to its quantity, stand in an extended place.

433. Likewise, as to what the Philosopher infers from his second reason, that ‘motion is in an equal time through a vacuum and a plenum’ [n.308] - if something similar to this is inferred, namely that angel and body would be moved in an equal time, it is not impossible; but there is an impossibility there from the idea of mediums, according to which this sort of reason seems to proceed.

434. But although Aristotle’s reasons would not prove much to the purpose (because movables here are not disposed as spaces are there), yet his reasons are simply valid, such that his major is probative and the other argument leads to an impossibility [sc. the major of the reason in n.307 is probative and is allowed to be true in n.432, and the second reason in n.308 leads to an impossibility by reason of the mediums, n.433].

435. I reply, therefore, that if a vacuum could yield and motion were possible in it, then I say that from the divisibility of the space the motion would have divisibility and succession, just as now from the divisibility of the space of a plenum motion would have per se an essential succession; but over and above this succession can be superadded speed or slowness, by reason of the accidental condition of the medium itself (insofar as it promotes or impedes the motion), or by reason of its rareness (whereby it promotes or at least does not impede motion), or by reason of its opposed density. So in that case there would be motion in a vacuum, and proportionality to the motion in a plenum, and this when speaking of essential succession, but not of the superadded speed or slowness, because a movable in a vacuum would altogether have no superadded speed or slowness

(but it would have some in a plenum, but there is no proportion between ‘nothing’ and something).

436. Therefore Aristotle [n.307] has precisely from this fact [n.435] - against the adversary who says there is motion in a vacuum [n.432] - that there can in a vacuum be no motion having any speed or slowness superadded to essential succession. And this would not be unacceptable if one posited precisely that there was motion in a vacuum -but it would be unacceptable if along with this one were to posit a vacuum as a promotive medium in motion (or a necessary medium in motion), on whose part speed or slowness of motion could be taken.

437. In the same way, what is inferred in the second reason [n.308] is not impossible for an adversary who says precisely that there is motion in a vacuum, because a medium that is a plenum can be equated with a medium that is a vacuum insofar as there is reason or cause for essential succession in the motion; and if some plenum were taken in the sort of proportion to a given motion that Aristotle takes it in, it would be altogether neutral (bestowing no accidental quality), being neither a plenum medium nor a vacuum medium.

438. What then does the Philosopher get against the adversary from this reason [n.308]? - I say that he gets only that a vacuum has no accidental quality over and above essential succession; because if it did, some equal medium could be given and then through the plenum medium and the vacuum medium there would be a motion in as much time as corresponds to the accidental condition of the motion, which is impossible - because if so the mediums would be proportional.

Question Six. Whether an Angel can move himself

439. Whether an angel can move himself [d.1 interpolation to n.296].

440. That he cannot:

Because nothing can be in act and in potency at the same time in the same respect; but the mover, insofar as it is mover, is in act, and, according as it is moved, it is in potency; therefore it does not move itself.

441. The reason is confirmed by the fact that some of the divisions of being - as quantity and substance - are incompossible in some one and the same thing; therefore, by parity of reason, act and potency are incompossible in any one thing.a

a.a [Interpolation from Appendix A]. The consequence is plain, because if divisions of being more remote from being are incompossible, much more are also the immediate divisions.

442. Again, everything that moves itself is divided into two parts, one of which is mover first and the other moved first, from Physics 8.5.257b12-13. There is also proof from the first conclusion in Physics 7.1.241b33-242a15, that ‘nothing moves itself first, because then it would rest on the resting of a part and would not rest on the resting of it’, which proof holds about a moved body; and from this there follows that in any selfmoving body such a distinction exists, and from this there seems to follow universally that in any self-mover such a distinction exists (for there seems to be the same incompossibility in the same non-body moving itself first as in the same body moving itself first). But an angel is not divided into two parts, one of which is mover first and the other moved first;     therefore etc     .

443. On the contrary:

An angel can be moved locally (from the preceding question, n.310), and not by a body as efficient cause (as it seems), nor only miraculously by God; therefore he is moved by himself.

I. To the Question

A. Scotus’ own Response

444. I concede that an angel can be moved locally by himself, because in the case of anything that has a passive potency for acquiring or possessing something through motion, it is not a mark of imperfection but of perfection in it that it has an active potency whereby to acquire it. - The point is apparent from animate things, that they have been given an active power with respect to the perfect size that they are, when generated, in potency to; it is also plain in heavy and light things, which have an active potency for the ‘where’ of which they are naturally receptive; likewise, animals have an active potency with respect to the sensation to which they are in passive potency (however, as was made clear in 1 d.3 n.547, they cannot have it in its totality, because a power cannot have all the objects that, namely, are consubstantial with it). Therefore, since there is in an angel a potency for a ‘where’ that he can acquire by motion, it is not a mark of imperfection in him that he have an active power with respect to the same ‘where’; rather it seems to be an imperfection in him if he not have such active power, because there is no repugnance in other less perfect beings having such an active power.

B. Instance

445. And if it be said that this belongs to more imperfect things (as animals) only according to a part of them, because they can be divided into two (namely into mover and moved), but if it be said that what is assumed about heavy and light things [sc. that they have an active power, n.444] is false and against the Philosopher’s intention (as it seems) in Physics 8.4.255a4-18, where he seems to give four reasons specifically against it (first by the fact that a heavy thing is not an animal, second by the fact that it cannot stop itself, third that it cannot move itself with diverse motions, fourth that it is continuous, that is, of the same kind in a part and in the whole, and such a thing cannot move itself), and in solving the question he says that ‘natural things have only a principle of undergoing with respect to motion and not a principle of acting’ - I show the opposite, first from authorities and second through reasons.

C. Rejection of the Instance

446. [From authorities] - The first authority is Aristotle Physics 8.4.255b19-31, where, in solving the doubt about heavy and light things, he says that ‘potency is said in many ways, hence it is not evident what a heavy thing is moved by’. Now he distinguishes ‘potency’ into potency for first act and potency for second act (as is plain about potency for knowledge and potency for actual consideration of knowledge), and when applying it to the issue at hand he says that ‘fire is in essential potency to becoming cold, namely insofar as water is generated from it - but when water has been generated, it is in accidental potency to making something cold, unless it be impeded’.

447. Thus too does he himself say about the heavy and light [Physics 8.4.255b8-12]: “For the light comes from the heavy, as water from air; but when it is already light it will at once operate, unless it is prohibited; now the act of a light thing is to be somewhere and to be upwards, but it is prevented when the contrary is present in it.”

Here there is no validity to the exposition that, since it is actually light, it is actually light such that going upwards is the feature of light, because then to say that ‘it is actually light’ is the same as to say ‘because it is actually light, it goes upwards’, which is nothing other than a causal statement. For he says that ‘it will at once operate, unless it is prohibited’, which cannot be understood of the actually light in first act, because the act of a light thing in this way cannot be prohibited or prevented while it is actually such. Likewise, he says that ‘it is prohibited when it is in the contrary place’; but a light thing is not non-light ‘because it is in a contrary place’. Therefore he means this of second act, namely that ‘its act is to be somewhere’ - that is, that its act, which is upwardness, is its operation. Therefore, just as fire when it has heat as first act is truly and effectively disposed toward heating (which is second operation), so also fire actually existing light is effectively disposed to being upwards, or to the second operation whereby it exists upwards.

448. The same in Physics 4.9.217b16-18 about the vacuum, for he says that ‘two contraries accompany the dense and the rare, namely the heavy and light and the hard and soft’ - and when speaking of the contrariety of the heavy and light he says that “according to this contrariety they will be active in motion, but according to hard and soft they will be passive.”     Therefore etc     .

449. And if you say that that is not his intention (although the words sound that way), because when, in On Generation 2.2.329b18-22, he enumerates the active qualities, he excludes the heavy and light from qualities that are truly active and passive - I reply:

I say that by what he says in On Generation 2 he would contradict himself in Physics 8 [n.445] if he did not understand the matter there differently from here; for in Physics 8 he says, the way it is cited on their behalf, that ‘natural things have a principle not of acting but of undergoing’ - but in On Generation 2 he says that “heavy and light are neither active nor passive,” and his proof there is plain.

450. Therefore he is speaking in one way about action and passion in Physics 8 and where discussion about action and passion occurs, and in another way in On Generation 2 and where discussion about generation occurs; for just as in the Physics he is speaking in general and universally about motion while in On Generation he is speaking about motion toward form, so too in Physics 3 he is speaking of action and passion in general and universally - and thus what he says in Physics 8 is true, that ‘they have a principle of undergoing’, namely with respect to local motion; but in the book On Generation he is speaking of action toward form where agent and patient are contraries (which indeed is true of univocal actiona), and these are equivocal at the beginning, and at the end are alike with univocal likeness (in equivocal action the agent is alike in form to the produced thing with equivocal likeness, as he himself concedes in On Generation 1.7.324a34-b1, that some agent does not communicate with the thing that undergoes, as neither does medicine with the healed body).

a.a [Interpolation] wherein agent and patient are dissimilar and contrary at the beginning and similar at the end.

451. Now in this way [sc. by understanding action as motion toward form] he denies in On Generation 2 that heavy and light things are principles of acting or doing and also of undergoing - and this is what the wording of his reason expressly says, that they are ‘not principles of acting on other things nor of suffering from other things’; and therefore they are not principles of producing something according to some substantial form (and of this producing he is there speaking), nor are they principles of suffering from some agent correspondent to such action. But they are passive principles in some way with respect to local motion to a ‘where’, and in some way active principles with respect to the same - both of which he himself expressly says in Physics 8, that they are passive in that ‘natural things have in themselves a principle of undergoing’ [n.445], and that they are active in that he said the operation of a light thing is ‘to be somewhere’ [n.447], as the operation of a knower is to consider [n.446].

452. The authority of the Commentator, On the Heaven 3 Com.28, could also be adduced for this purpose: “In the case of simples,” he says, “mover and moved are the same in idea but different in manner; for a stone moves itself insofar as it is actually heavy, and it is moved insofar as it is potentially in a lower place; for it is found in one way to be actual and in another way to be potential - and the cause of this is that it is composed of matter and form.” But he seems to speak of this variously, for in the same place he seems to mean that a stone ‘moves itself per accidens, by pushing the medium in which it is, as a sailor moves himself by moving the ship on which he is’ - and for this reason his authorities are not much to be relied on.

453. [From reasons] - There are reasons for this conclusion.

The first is of the following sort: every effect has, when it is actually caused, an actual cause (this is plain from Aristotle Physics 2.3.195b17-20 and Metaphysics 5.2.1014a21-23, the chapter on cause: ‘The efficient cause in act and the caused in act are and are not at the same time’; it is also plain - if there were no authority - from manifest reason, because what is not, when it is not, does not bring anything into being); therefore when the descent of a heavy thing is actual, then there is something actually causing it.

454. But this descent is not actual from something that removes an impediment. Nor consequently is it the heavy thing’s relation downwards, ‘because what impels it moves it per se downwards’, for in this respect the heavy thing is as it were the remover of an impediment - and such a mover, according to the Philosopher in Physics 8.4.255b24-27, is as it were a per accidens mover; and there must, in addition to a per accidens mover, be a per se efficient cause, because everything per accidens has to be reduced to something per se.

455. Nor can this per se cause be the center pulling it, because if per impossibile there were nothing heavy in the center but the whole earth were removed from it (and the center remained, as before, under the relation of being the center), the heavy thing would still tend naturally to the center. - What then is pulling it? Is it the ‘where’? Manifestly not because the ‘where’ is not an active form.

456. Nor too is it the influence of the heaven, because to have recourse to a universal cause seems a subterfuge - it is to deny particular effects and particular causes; also the influence of the heaven (as far as concerns itself) is uniform in the whole medium, so there is no reason for it to move one part upwards in the whole medium and another part downwards unless a particular determining agent is posited.

457. Nor can the ‘actual mover’ (when it is actually moving) be posited to be the actual moved heavy thing, because nothing univocally moves itself toward what it possesses - and for this reason motion is something extrinsic to the heavy thing; nor can what generates the heavy thing be the actual mover, because it can at that point not be.Tr. The generator of a heavy thing need no longer exist when the heavy thing is actually in motion downwards, so that the generator cannot be the actual mover of it at that time. ³⁸ Therefore it must be something intrinsic.a

a.a [Interpolation] to the heavy thing, or it must be the heavy thing through something intrinsic to it.

458. It is said that the generator [of the heavy thing] remains virtually in the heavy thing, and that in this way it moves the heavy thing [cf. 1 d.17 n.89]. - On the contrary: it does not remain virtually save as a cause remains in its effect, and what remains thus does not remain in itself but only because it remains in its effect - and then its virtue in respect of the motion pertains to the genus of efficient causality. For if the generator is said to bring something about, and if it does not bring anything about save as it is in act, it must needs bring something about because it brings about what is virtually the efficient cause, and in this way the proposed conclusion still follows.a

a.a [Interpolation from Appendix A] Again, if the generator remains virtually in the heavy thing, then either in its own virtue and or in that of its effect, because acting presupposes being. If it remains only by virtue of its effect, namely the heavy thing, and it is thereby cause of the motion of the heavy thing, then the heavy thing moves itself.

459. Besides, what does not move another save by being first naturally moved by something else [e.g. as a stick does not move a stone save by being first moved by the hand] gets from the same thing the fact that it moves and that it is moved; but a heavy thing that has a light thing tied to it (and whose lightness is not greater than the heavy thing’s heaviness) moves that same light thing by drawing it with itself toward the center - and it only moves because it is moved; therefore it is moved naturally first before it moves. And it is moved by the same thing as that which is tied to it is moved by; but it moves what is tied to it by something else, namely by its heaviness; therefore it moves itself in the same way.

460. A confirmation can be given for this reasoning because, when something has active power with respect to some form, it can cause that form in any passive thing proportioned and proximate to it; but a heavy thing has active power with respect to a ‘where’ downward, just as it does with respect to what it pulls along with it, and it itself -when it is outside the place downward - is receptive of that form, which it lacks, and it is proportionate and proximate to itself; therefore it can cause that form in itself.

461. This can also be sufficiently plain if one considers that rest requires a cause actually causing it just as motion does; for then one should posit a cause naturally causing coevally with a heavy thing the rest of the heavy thing; but there is no such cause causing rest coevally with the heavy thing save the heavy thing, and so the heavy thing is causing with efficient causality - and so it is causing the motion toward that rest, because these two [sc. motion and rest] are from the same cause.

462. Further, a heavy thing - when prevented from moving - removes what is preventing it if its heaviness is superior to the virtue of the impeding or resisting thing; to wit, if it is placed on something continuous [e.g. a wooden plank] and its heaviness is superior to the nature of the continuity, it breaks it and by thus getting rid of the continuity it gets rid of what impedes its going downward. Now this breaking, since it is a forced motion, must have some existing extrinsic cause for it, and to suppose there is any cause other than the heavy thing itself does not seem rational; but the heavy thing does not break the continuous object save because it aims to put itself in the center; therefore it has the putting of itself in the center from the same principle as that from which it has the removing of the impediment.

463. This could also be made clear in another way, because the heavier object moves more quickly, and yet the same generator could generate something heavier and something less heavy, and these two could be at the same distance from the center and under the same influence of the heaven; therefore the difference of motions in them is from something intrinsic to them.

464. Again “natural motion becomes more intense at the end,” according to the Philosopher On the Heaven 1.8.277b5-7, and it would be difficult to assign a cause for this if the efficient cause of this motion were precisely something extrinsic.

465 [Response to the statements of Aristotle] - I reply then to Aristotle, who is adduced for the contrary view [n.445], that he is in my favor (the way I have adduced him [nn.446-448]) - that the heavy thing does effectively move itself, as a knower moves himself effectively to an act of thinking. And I understand this as follows: just as a thing that has a form, which is of a nature to be the principle of some univocal action, can act by that form on what is receptive of the form and proportioned and proximate to it, so too a thing that has a form, which is of a nature to be the principle of some equivocal action, can by it act on what undergoes and is proximate to it; and if the thing itself is receptive of the equivocal action or equivocal effect and lacks it, then it will, by the fact it is itself most proportioned and proximate to itself, not only be able to cause this effect in itself but will supremely cause it. So also is it in the case of the issue at hand, that a stone which is up above is in potency to a ‘where’ down below, but heaviness with respect to that ‘where’ is an active equivocal principle, just as there is only need universally with respect to a ‘where’ to posit an equivocal principle (for a mover moves a movable to a ‘where’ not because the mover is formally in act with respect to that ‘where’, but merely because it is virtually so). Therefore, because the heavy thing is itself receptive of the equivocal effect and lacks it, so it causes that effect in itself first, and causes it in no other thing save by causing it first in itself, such that its causing it is the operation of the heavy thing - as Aristotle says [Physics 8.5.257b9] - the way heating is the operation of a hot thing. But the fact that it causes the effect in itself is accidental to it insofar as it is active (because it is itself receptive with respect to this causing, or with respect to this causability); this could be understood if the heavy thing - while remaining up above -could propel itself, or something else, to the center; no one in that case would then doubt how a heavy object is the principle of descent in something else; and it is not less an active cause now of its own descent.

466. However, because of what the Philosopher says [n.445, that natural things have, in respect of motion, only a principle of receiving and not of acting], I add further that this motion is ‘natural in itself’ not by the fact that it has an active principle in itself, but only by the fact that the movable thing has an intrinsic passive principle naturally inclining it to motion. - This is plain from the definition of nature in Physics 2.1.192b20-23, that it is “a principle of motion in that in which it is per se and not per accidens” (for nothing is a principle of moving for anything save insofar as it is per se in that which is moved; but it is not per se and first in anything that is moved save insofar as it is passive; therefore it is not anything by nature nor a natural principle of anything save because it is a passive principle in the thing moved). This is plain because something is naturally moved for this reason, that it is moved as it is of a nature to be moved.

467. Thus it is in the case of the issue at hand, so that, although here (as in the case of many other things) an active principle is the principle of moving, yet not because of that active principle of moving is it moved naturally, but because of the passive principle because of which it is thus moved. And this is what the Philosopher subjoins (after he has said that “the act of a light thing is to be somewhere, upwards” [n.447]): “And yet,” he says [Physics 8.4.255b13-15], “the question is raised why they [sc. light and heavy things] are moved to their places.” And he says pointedly ‘to their places’, that is, that they are naturally moved to those places, “because they are of a nature to be there,” that is, they have a natural inclination to that ‘where’. And in this way he adds afterwards that “they have only a principle of undergoing and not of doing” [n.445], namely in respect of motion insofar as it is natural - and so, in this solution of this doubt about the motion of heavy things, he says there by the by of the natural principle of this motion, and of the efficient principle of it, that it is only passive.

468. Now Aristotle’s reasons [n.445] do not conclude against me, for the first three (which have the same force) show that the heavy object does not move itself the way what acts by thought moves itself; for an animal could not move itself short of the intended ultimate end - nor even could it direct itself or stop itself - unless it acted by knowledge. And from this is got the Philosopher’s proposed conclusion, that these things [sc. heavy and light things] are not movers first [sc. do not move themselves] - for a first mover moves by knowledge (because “to guide is the mark of the wise man” [Metaphysics 1.2.982a17-18]), as was shown in the third distinction of the first book about the knowledge of God, and in the second distinction of the same book about the being of God [1 d.3 nn.261-268, d.2 nn.76-78].

469. Also, his fourth reason [n. 445] does not draw its conclusion about the continuous precisely as the continuous is some quantum. But it proves it relative to the continuous - namely because the continuous has the same disposition in every part of itself - that a heavy object does not move itself effectively, because there is not one part of it in act able to make another part of it to be in act according to the same quality, in the way he himself states in On Sense and the Sensed Thing [6.447a3-4; n.299 above]. And I concede that in this way an actually existing part of the heavy object does not cause motion to be in another part; but the whole heavy object is in act according to first act, and it causes in itself second act.

470. But if you object, ‘how will Aristotle, if he concede that a heavy object is thus moved effectively by itself (although not by knowledge, nor even because its naturalness is from it insofar as it has an active principle) - how will he get his principal conclusion, that these things [heavy and light things] are necessarily moved by another -which is something he intends principally to prove [n.445]?’ - I say that he gets this conclusion sufficiently from a distinction of power [n.446]. For these things [sc. heavy and light things] do not reduce themselves from second potency [sc. accidental potency, n.446] to act unless they have first been reduced from first potency [sc. essential potency, n.446] to first act, or at least could be reduced to first act; and I assert this of all the elements, which are all - according to him - ungenerable and incorruptible, and yet, because they are of the same nature as their parts are, it is not repugnant for them to be reduced from first potency to first act in just the way their parts are reduced. So it follows that, although the heavy and light thing move themselves from second potency to second act, yet a movable thing is, or is moved, from first potency to first act by something else outside it; for it is not necessary that ‘if everything that is moved is moved by another’, that it is moved by another in the case of every motion - and the first point [sc. everything that is moved is moved by another] is enough for the Philosopher, because thereby deduction is made to something ‘other than all these things’, which something other cannot be moved by another either in one motion or in any motion but it is altogether ‘an unmovable mover’ [Physics 8.5.256a13-258b9].

471. It can also similarly be said that even if heavy and light things are - in the case of this motion - moved effectively by themselves, yet they are not moved as they are by first movers; from the fact too that they do not move by knowledge, the consequence follows that they presuppose something that does move thus by knowledge - and so, although they do effectively move themselves yet they do not do so without being moved by another, although not as they are by a proximate cause.

II. To the Principal Arguments

472. As to the first principal argument [n.440], it was stated in distinction 3 of the first book [1 d.3 nn.513-517] how something can act on itself, and response was made there to this first principal argument.

473. But as to what is added in confirmation, that ‘some of the divisions of being are not compossible in anything, so these divisions are not compossible either’ [n.441] - I concede the point about these divisions [sc. act and potency] as they are opposites. But they are opposites insofar as they state modes of any being, namely insofar as ‘one and the same thing’ is in potency before it is actually a being (or a being in act) when it already is; and in this way these divisions do not belong to any one and the same being, either formally or denominatively, namely that ‘one and the same thing’ should be said to be denominated by something in some act and at the same time by the same thing in potency. However, as act is taken for active principle and potency for passive principle, which principles fall under the essence of any definable or defined thing, then they are in this way neither opposites nor divisions of being nor repugnant to any one and the same thing.

474. As to the second argument [n.442], I say first to the authority from Physics 8, namely that everything ‘that moves by knowledge’ is divided into two, one of which is mover first and the other moved first - and the reason is of this sort, that the motive power of such a mover is an organic power so that it requires not only a distinction between body and soul as between mover and moved, but requires perhaps in the body itself - where the organic power is - a moving part of the body distinct from the moved part. But it need not be like this in the case of something non-organically moving itself, because here the whole is uniform as to first act, and the whole is in potency as to second act.

475. But as to the proof of this proposition, which is taken from the beginning of Physics 7 [n.442], where is proved that ‘nothing moves itself first’ - I say that what ‘first’ means here can be understood in two ways:

In one way it is taken as it means the same as ‘according to the whole’ and is opposed to what ‘according to a part’ means. And Aristotle takes it this way in Physics 5.1.224a21-29, where he distinguishes what it is for a thing to be moved per accidens, or as a whole, and what it is for it to be moved as to a part; Aristotle also takes ‘to be moved first’ in this way in Physics 6.6.236b19-23, where he says that ‘whatever is moved first in some time is moved in any part of that time’ - and he says it frequently elsewhere.

476. In another way what I mean by ‘first’ means precise causality, in the way it is taken in Posterior Analytics 1.4.73b26-33 in the definition of the universal.

477. I say therefore that the reasoning of Aristotle at the beginning of Physics7 [n.442] does well prove that no body is moved by itself first at the same time in this double firstness:

Because if it is moved by itself first, that is, according to the whole of itself, then the motion is present in any part of it. This consequence holds from the fact that a whole, insofar as it is a mover, is homogeneous, and that ‘to be moved’ is a homogeneous passion; but a homogeneous passion is only present first in a whole by this firstness if it is present in any part of it. So the result is that if a whole is moved first in this way, then if a part of it is at rest then the whole of it is at rest.

478. But when taking the other firstness, the firstness of precise causality, if a whole is moved by itself first, then this predicate ‘to be moved’ is not removed from the whole because it is removed from something that is not the whole, nor is it removed from the whole because it is removed from something that is not any part of the whole; for if a triangle has three angles first by this firstness, not only is the predicate ‘having three angles’ not removed from it if it is removed from a quadrilateral, but it is also not removed from it because of its being removed from a part of the triangle, as from this or that angle. Therefore ‘to be moved’ is not removed from a whole in which it is first by this firstness, even if it be removed from a part of it, which part is not it; and therefore if a whole is moved first by this firstness, it does not rest on the resting of a part.

479. But the prior inference was that it is moved first by the other firstness [sc. the firstness of ‘according to the whole’, nn.477, 475]; so it is impossible for a whole to be moved first by both firstnesses at the same time [nn.477-478], because this involves a contradiction, in that a contradiction follows [sc. the contradiction that the whole would both rest and not rest on the resting of a part]. However, some whole can precisely by the one firstness [sc. the firstness of ‘according to the whole’ n.475] be moved by itself first.

480. Now in the issue at hand, I say that a heavy thing is moved by itself first in the prior way of ‘firstness’ [n.475], because it moves and is moved according to any part whatever, and moving and being moved belong to any part whatever - although not first but insofar as any part is in the whole.

481. But does it ever belong to a heavy thing ‘to be moved first downwards’ by the firstness stated in the second way [n.476]?

I say that we can in general speak of the heavy thing’s being moved downwards either as to the being moved that belongs to the whole heavy thing or as to a part of the being moved that belongs to a part of the heavy thing. And I say that just as the whole heavy thing and a part of the heavy thing are homogeneous in heaviness, so the total being moved (which is a total passion of the whole) and the partial being moved (which is a passion of a part) are ‘being moveds’ of the same nature; and just as being moved downwards is naturally - and in general - present first by the firstness of precise causality in a heavy thing generally, so the total being moved is present in the whole heavy thing by a like firstness, and the partial being moved (which is a part of the total being moved) is present in a part of the heavy thing by a like firstness.

482. Therefore the whole homogeneous heavy thing is not moved by itself first such that the ‘being moved’, as being moved is common to the whole and to any part of the whole, is present in it first according to this firstness [sc. the firstness of precise causality], because then being moved would not be removed from the whole even if it were removed from a part; however this is false because of the other firstness [sc. the firstness of ‘according to the whole’], which is necessarily going along with it, if this other firstness is posited in a homogeneous subject with respect to a homogeneous passion.

483. However, the heavy thing is also moved with this motion by the firstness of causality, namely of precise causality - and it is true that this total motion is not removed from the whole heavy thing because it is removed from anything that is not this whole heavy thing; but it is true that a part of this whole heavy thing is not moved by this total motion, and yet not for this reason is this total motion removed from the whole heavy thing.

484. If you object that at least the total motion is removed from the whole heavy thing if partial motion is removed from a part of the heavy thing - so the total motion is not present in the whole by the firstness of precise causality (for if it were thus present, in no way would it be removed from the whole because of the removal of any other predicate from the whole that is not the whole) - I reply:

I say that the whole heavy thing, insofar as it is homogeneous, is made up of like parts (and these parts are prior in some way to the whole itself), so that when these are destroyed in idea of parts the whole does not remain; thus I say that it is not unacceptable for the parts to have their own partial properties and partial motions (and to have them somehow before the whole motion belongs to the whole itself), because even the whole motion is composed of the partial motions of the parts just as the whole heavy thing is composed of parts of the heavy thing. And then I deny the assumed proposition that ‘what belongs to something first (that is, according to precise causality) is not removed from it’ because something which is not the very predicate is removed from something which is not the very subject. For this assumed proposition is universally false when the subject has a prior subject and the property a prior property; for then on the removal of the prior property from the prior subject there follows the removal of the posterior property from the posterior subject.

485. The reasoning of Aristotle, therefore [nn.477, 442], proves precisely that the whole is not moved by itself first, that is, his reasoning proves that ‘to be moved’, which is a homogeneous property, is not present in the homogeneous whole first (that is, first according to precise causality), insofar as the property is taken as homogeneous (that is, as of the same nature) in the whole quantity and in a part of the quantity - because thus it would not be removed from the whole although it were removed from a part; and this is false, because of the firstness of the whole that is entailed here by reason of precise causality. Yet Aristotle’s reasoning does not prove that, speaking about that total motion whose parts are motions of parts and about the firstness of precise causality, the whole cannot be moved by itself first; and compatible with this stands that it is moved first by another firstness (namely the firstness of the whole), taking ‘to be moved’ generally (namely as it belongs to the whole and to any part of the whole), so that in some way one needs to assume a predicate that must be present in the whole with both the latter firstness and the former.

Question Seven. Whether an Angel can Move in an Instant

486. Eleventh I ask whether an angel can move in an instant.

487. That he cannot:

Because then a greater power could move in less than an instant. Proof of the consequence: for thus does the Philosopher argue in Physics 6.3.234a22-31, that if a greater power were to move something in time, the greatest power would move it in an instant.

488. On the contrary:

Some movings by some moving bodies exist in an instant, as the illumination of a medium; therefore too the much stronger moving of an angel can exist in an instant, because the power of the mover is greater and the resistance of the medium smaller.

I. To the Question

A. The Opinions of Thomas Aquinas and Henry of Ghent

489. Here the statement is made that an angel can move in an instant, not indeed of continuous time but of discrete time; for the proof see Thomas.ST la q.53 a.3 ad 3: “Now the time of motion of an angel can be non-continuous, and thus an angel can be in one place at one instant and in another place at another instant, without any time existing in between. But if the time of motion of angel is continuous, the angel goes through an infinity of places during the whole time preceding the ultimate ‘now’.” Ibid. in corp.: “And thus it is clear that to rest for a whole time in something, as in a whiteness, is to be in that something at any instant of the time; hence it is not possible for something to rest for the whole preceding time in one term and afterwards, in the last instant of the time, to be in another term... But in the local motion of an angel there is no term of any other continuous motion.; hence it is impossible to say that he is for the whole time in some place and is, in the ultimate ‘now’, in some other place, but one must assign an ultimate ‘now’ in which he was in the preceding place.” ³⁹

490. Another doctor speaks about this time; see Henry.Quodlibet 13 q.7: “And the time measuring these sudden changes of an angel is a discrete quantity., but its parts have no permanence but exist only in passing through, and the individual parts coexist with the individual instants of our time; nor do these parts have any continuity among themselves, because between any two instants and the aforesaid changes [of the angel] one must posit a stopping of the angel at the moment at which the preceding change ends, where the angel does not change but rests through some interval and part of our time.” ⁴⁰

B. Rejection of the Opinions

491. Against the first position [n.489] I argue thus:

For he seems to contradict himself. For he seems to posit that an angel exists in place through operation; and if he is understanding the operation of an angel that passes over into a body, then that operation will exist in time or in an instant of common time; but if he is understanding an angel’s immanent operation, namely intellection or volition, then (from what was said earlier in the discussion of aeviternity [nn.153-67]) that operation is neither in our common time nor in any other time but is, according to him, in aeviternity.     Therefore etc     .

492. Besides, his reasoning does not seem conclusive, because then it follows that, in the ultimate instant of pronouncing the words of consecration [sc. in the eucharist], the true form of bread would be there that was there before during the whole time of the pronouncing.

493. Likewise it follows that, when air has remained in darkness for the whole of a time, the air would be in darkness in the ultimate instant of the illumining of this dark air, and thus it follows that illumination does not take place in an instant.ST Ia q.53 a.3: “But sometimes the term ‘to which’ is immediate to the term ‘from which’, as in the case of those changes where the change is from privation to form..., as with illumination; and in these changes too there must be a time annexed to them, since it is clear...that the air is not illumined and in darkness at the same time. But not in such a way that the departure or passage from one extreme to the other takes place in time, but one of the extremes is conjoined to the local motion of the sun (as with illumination), and in the term of that motion there is also a term of the change. Hence all such instantaneous changes are terms of the same motion.” ⁴¹

494. And if you say that this illumining is ‘the term of a local motion’ whereby the sun is made present to the medium - on the contrary:

Let the sun be posited as created de novo and the medium as pre-existing. Then too, although the illumining of the medium (done by the sun made present in this way) goes along with the ‘where’ terminating the local motion, yet the illumining is not per se the term of the local motion but is some ‘where’ acquired by the sun itself; nor even can this happen without the air having remained in darkness up to that instant.

495. Further, if an angel - whatever time he is resting at - has to have moved in the ultimate moment of that time at the same ‘where’, then he never move, either in continuous time or in discrete time.

496. Proof of the consequence:

I take some part of the time at which the angel is at rest and at which, consequently, he changes in the ultimate moment of it.

Even if he should change in some instant of discrete time, I ask: is that instant immediate or mediate with our instant that terminates the time of his resting? If mediate then between our instant (at which the angel has moved) and that instant there is a time in between, at which too the angel would be resting; therefore in and at the ultimate instant of that time he will have changed, and so in that mediate instant (at which he was posited as changing) he does not change. But if the instant is immediate, I ask what within our time corresponds to it? If an instant, then an instant in our time is immediate to an instant [sc. of the angel’s time] (so our time is discrete [sc. as the angel’s time is posited to be discrete]); if time corresponds to it, then the angel does not in that instant instantaneously change, because - according to you - that instant coexists with a part of our time, in which or at which he can continuously change or be at rest.

497. It is because of this argument perhaps [sc. the last argument in the previous paragraph] that the second position [sc. of Henry, n.490] posits that between two instants of discrete time a quasi-intermediate rest of the angel occurs along with an intermediate part of our time.

498. But it was proved above [nn.161-62] against this second position that there is no need for the operation of an angel to have duration along with an instant of our time; so neither will that operation be the reason for the resting of the angel at the term of a sudden local motion. To say ‘therefore it will also be necessary to posit that the angel rests after the sudden local motion’ does not seem to be an argument but merely a subterfuge, to prevent our time being posited to be discrete from the fact that such local moving of an angel is posited to be a discrete time.

499. Further, as to what it [sc. the second position] posits that in such a ‘now’ an angel can locally move, so that he has several equal ‘wheres’ all at once between which there will only be an order of nature, or an order in imagination and not in duration - it seems to be impossible that an angel should, by his own power, have several equal ‘wheres’ “in one instant of his time and of ours”. And this is made clear by the example of the heavy object (which they [sc. Henry and his supporters] adduce for the opposite): for if a vacuum could give way to a body placed in it (and thus if there were motion in a vacuum), there would be no intelligibility in a heavy object’s being in several ‘wheres’ equal to it, but it would be first in one ‘where’ before it was in another ‘where’, and first in a prior ‘where’ before it was in a later ‘where’ [n.431]; and one part of the heavy object would be in a place first in duration before another part of it was.

500. And what he himself [sc. Henry] adduces about a body that passes through an infinity of ‘wheres’ in a finite time, because of the fact that it is only in those ‘wheres’ potentially - this does well prove that the time of an angel can be made of infinite parts of the same quantity and that yet in that time he can pass through an infinite space; but it does not prove that he can pass through so much space in a single instant; rather it proves the opposite; for a body passes through a whole space thus in some period of time, because in different parts of the time it passes through different parts of the space.

C. Scotus’ own Response

501. I say therefore to the question [n.486] that a plurality is not to be posited without necessity,A version of Ockham’s famous razor, which at least in this form is not original to Ockham. ⁴² and there is no necessity why one should posit a discrete time that measures the motion of an angel - for whatever is secured by that discrete time is also secured by continuous time in general; for just as they [sc. those who posit such a discrete time] must say that, if an angel passes through something in an instant, he cannot immediately have another instantaneous passing through, so one can, if an angel instantaneously passes through something in an instant of common time, posit that, although he can immediately have after that instant a continuous motion in actual time, yet he cannot immediately have an instantaneous passing through. There is nothing unacceptable, then, in positing that an angel, to the extent he participates in bodily condition (that is, a condition which is in some way of the same nature in himself as in a body), also participates in some way in the measure of body; but to the extent he moves locally, he participates in a ‘where’ (which is a bodily property that is in some way of the same nature in himself as in a body); therefore he can also be measured by the measure of the first moved body.

502. And if you object that an angel could move while the heaven is stationary, so there is no need for his motion to be in time - I reply:

Peter after the resurrection will be able to walk about when the heaven is thus stationary, and yet this walking about is not imagined to be in any time other than our common continuous time, even though it takes place when there is no first motion of the heaven. The resting of the heaven itself, indeed, is (as was said before [n.178]) measured potentially by the time by which the first motion - if it existed - would be positively and actually measured; and by that potential time can another motion be measured which is then actually existing, such that there is no need for what is measured by the first heaven to depend in its essence (or in its being) on that motion (as was the case with the motion when the heaven was standing still in the time of Joshua [Joshua 10.12-14]), because this measuring of a quantity by quantity and quality is not by something on which the measured thing essentially depends (as is true in the case of quidditative measures), but it is sufficient only for that motion - when it exists - to be able to be distinctly known, according to its quantity, by a distinct knowledge of time, whether actual or potential time. And thus I say that, when this motion of the heaven does not exist, yet another motion will be able to be measured by the time of that motion of the first heaven, namely insofar as the other motion could take place simultaneously with some amount of the former motion, if the former motion existed, and takes place now with as great an amount of rest as there could be of the motion.

503. On this supposition then, that there is no need to posit for the motion of an angel a measure other than common time [n.501] - when it is asked ‘whether an angel could change or move in an instant’ [n.486], I say that change can be understood in two ways and can be said in two ways: one way includes the whole reality of motion, and the other includes the reality precisely of the term of motion.

An example. That this thing is changed from ‘where’ a to ‘where’ b can be understood in two ways: either that it possesses at once all the intermediate ‘wheres’ (in the way it would if it precisely moved successively), or that it would possess by that change exactly the ultimate ‘where’ (the way it would if the change were the ultimate term of motion).

504. In the first way - in contradiction to the second opinion [n.490] - I do not see in what way an angel could by natural power move or change in an instant, because it does not seem that he could by his natural power have several ‘wheres’ equal to himself [n.499]; in the second way [n.503] it does not seem he could not move in an instant, because the fact that the term of a motion is not immediately introduced comes from the imperfection of the power of the mover - and this imperfection is not to be attributed to an angel unless some necessity appears, because a nature should be granted as much worth as appearances allow.

II. To the Principal Arguments

505. To the argument for the opposite [n.487] I say that the consequence of the Philosopher [sc. if a greater power moves in time, a greatest would move in an instant] holds from the fact that in the antecedent is included that the measure is divisible, because of what is posited in it [sc. time, for time is divisible]; but in whatever divisible measure some power can do something, a greater power can do it in a lesser measure. But in the antecedent ‘an angel changes in an instant’ is not included that the measure is divisible.

506. This consequence, then, that ‘it moves in an instant, therefore something can move in less than an instant’, does not so much hold from true propositions and the nature of the thing, but it holds from something false that is included in the antecedent [sc. the antecedent ‘it moves in an instant’]; for this premise, that ‘whatever some power causes in a divisible measure, a greater power can cause in a lesser measure’, is true from the nature of the thing, but the minor premise - which will have to subsumed there under this true major [sc. the minor ‘an angel moves in an instant’] - is not true from the nature of the thing, but only by hypothesis, namely that ‘there is motion in an instant’. But if it be said that ‘an angel changes in an instant’, and if from this one is to infer that ‘some power should change him in less than an instant’ - then the minor thus to be assumed will not be true from the nature of the thing, nor by hypothesis, and so the consequence will not be valid. And from this it is plain that many enthymematic consequences [sc. consequences where one premise is left unexpressed] do not hold precisely by virtue of some understood truth, but sometimes by virtue of some understood falsehood, provided however a falsehood is included in the antecedent.

Question Eight. Whether an Angel could Move from Extreme to Extreme without Passing through the Middle

507. Twelfth and finally I ask whether an angel could move from extreme to extreme without passing through the middle.

508. That he could:

Because either an angel is in place by his operation (according to some), and it seems plain that he can operate on an extreme without operating on the middle [Aquinas Sent. 1 d.37 q.3 a.1, q.4 a.2]; or he does at least move himself by command of will (although through some executive power), and he can wish to be in an extreme without wishing to be in the middle, just as he can understand an extreme without understanding the middle [Aquinas Quodlibet 1 q.3 a.2].

509. Second as follows: the body of Christ, being in the empyrean heaven, is now on the altar, and it does not pass through the middle; therefore an angel will be able to do this, since a body seems more to follow the laws of place than a spirit does [William of Ware, Sent. 2 d.2 q.11 arg.1].

510. On the contrary:

No part of time can pass from the future to the past save through the present; but the essential order between the parts of place seems to be just like that between the parts of time; therefore a transit from extreme to extreme will not be possible save through the middle [William of Ware, Sent. 2 q.11 arg.2 to the opposite].

I. To the Question

511. It is said here by some that extremes can be understood either as two distant ‘wheres’ between which there is some middle that is not part of the extremes, or as two immediate ‘wheres’ between which there are middles yet any one of them is some part of the extremes.

512. Speaking of middles in the second way and of the continuous motion of an angel, I say that he cannot pass from extreme to extreme (speaking in this second way about extremes) save by passing through such a middle as is part of each extreme, because such a middle is the idea of continuity between the extremes passed through, as is plain from the definition of a middle in Metaphysics 10.5.1057a21-26.“We call those middles into which that which changes must change first, as...in the case of colors where, if a thing goes from white to black, it will go to red and to grey before it goes to black.” ⁴³

513. It seems to be similar when speaking of continuous motion and of a middle said in the other way [sc. the first, n.511], because, if an angel moves continuously, he is not completely in either extreme; therefore he is partly in one and partly in the other, or he is in the middle between both; for it cannot be said - as it seems - that he is in part of one extreme and in part of the other and yet that he is altogether not in such a middle between such extremes, because then he would be in two discontinuous places and in not in any way in the middle place, which does not seem to belong to him by natural power [nn.262-64].

514. But if we are speaking of indivisible motion, I say that in such a motion an angel can pass from extreme to immediate extreme without passing through a middle that is some part of either extreme; rather this must be the case, because if he were to pass through such a middle he would pass continuously and not instantaneously [n.512].

515. However as to distant extremes there is doubt. It is plain indeed from the preceding question [nn.503-504] that an angel cannot put himself in a distant extreme with a change that involves the whole reality of motion. - But can he really put himself in a distant extreme that involves precisely the reality of the term of motion, so that in some whole time he is in ‘where’ a and in part of that time he is precisely in ‘where’ b (such that ‘where’ b is distant from ‘where’ a by some middle, and the angel was never in this middle, whether in time or in an instant)? It seems probably that he cannot, because an order pre-established by a superior agent seems to be necessary for any inferior agent when the inferior agent does an action precisely about things in that order (an example: the order of natural forms that succeed each other in natural generation is determined by the institutor of nature, and so this order is necessary in respect of any natural agent, such that no natural agent can make vinegar immediately save from wine); therefore, since the order of the principal parts of the universe has been imposed by God on every created agent and created power, this order seems to be a necessary one when a natural agent moves itself through bodies to which such an order belongs. So when an angel moves himself through bodies to which such an order belongs, he cannot put himself in any ‘where’ whatever and follow no order about any ‘where’ whatever; for then no distance would seem to impede his action.

516. And if you object that this argument [n.515] is conclusive against the second member, ‘about middles that are part of the extremes’ [n.514], I deny it, because in that case, when an angel passes in an instant immediately from one ‘where’ to another ‘where’, he has all the ‘wheres’ in some order of nature (and between these ‘wheres’ there is, from the nature of the thing, a potential order), but he need not have them in an order of duration; and if he passes from a distant ‘where’ to a distant ‘where’ without any order in any way, then he would, without any order at all whether of nature or of duration, possess things to which a natural order belongs even though his acting about them necessarily presupposes the order of them.

II. To the Principal Arguments

517. To the first argument [n.508] I say that a bad angel can will disorderedly; and a good angel, just because he only wills orderedly, need not will with his own power - and so, if a good angel wills to be at once in some ‘where’, still he does not will to be there by his own power, because this would be to will disorderedly. If however such power does not belong to the good angel but he wills to be there at once by the power of God, it is likely that God would accede to his will (if such it be), so as to put the angel in such ‘where’; but an angel can never by his own power be anywhere save in the way in which it belongs to his power.

518. To the second [n.509] I say that the body of Christ is by his infinite power made to be present on the altar, on which point see 4 d.10 p.1 q.3 n.5. But that infinite power can hold any middle between extremes to be no middle, and can hold order for no order, because he is above that order, being the one who prefixes it and not having it prefixed for him; but the limited power of an angel is not of this sort.

519. From this is apparent the response to the passage from On Sense and Sensibles 6.446b28-7a6 [n.404, 299], which was passed over in question 5 about the place of an angel. For it is not unacceptable that some alteration is complete all at once, namely when the agent has regard to the whole passive subject as an indivisible term and to the form in its ultimate degree (according to which degree it introduces the whole form as an indivisible); in that case a perfect form is introduced by an indivisible change in a divisible subject. But according to such form there is no motion, but only a single change - or perhaps several changes are had (in the order either of duration or of nature), as

Aristotle himself there says, that “if it was large, it undergoes one complete change after another” [n.299]; which can be understood in two ways: in one way that a later part is naturally perfected later by a prior part - the prior part naturally perfect before -, so that there is only an order of nature between the change of the prior and of the later part; in another way that there is an order of duration, namely that a later part is moved in succession by a prior part and yet the prior part was changed precisely by the extrinsic agent itself (this second way seems less probable, unless one posits that the prior part -already changed - is more imperfect than what changes it, and thus that it cannot change the later part at once in the way it was itself changed by the extrinsic agent).

520. So the Philosopher says there that “things in change of sound are not as they are in light,” because the multiplication in quantity of a sound, which takes place along with local motion, is necessarily successive - but not so the multiplication of light; and so simultaneity is not repugnant to the idea of alteration as it is to the idea of change of place, and this when making reference to natural power. Yet, however, there is never simultaneity in alterations that are a first change of motion, just as neither in changes of place, because where change is instantaneous, there the change is not a change initiating motion; nor even does simultaneity follow universally where motion follows, if there is a change that is the term of the preceding rest (but where rest, because of the perfection of the power of the agent, is followed immediately by a change, there no change terminating the preceding rest exists).