Authors/Duns Scotus/Ordinatio/Ordinatio II/D2/P2Q5
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- I. To the Question
- II. To the Principal Arguments A. To the First Argument
- B. To the Second Argument
- 1. Rejection of the First Antecedent
- 2. Rejection of the Second Antecedent
- 3. To the Proofs of the First Antecedent a. To the First Proof
- b. To the Second Proof
- 4. To the Proofs of the Second Antecedent
- C. To the Third Argument
- D. To the Fourth Argument
| Latin | English |
|---|---|
| Question Five: Whether an Angel can be moved from Place to Place by Continuous Motion | |
| 284 Nono quaero utrum angelus possit moveri de loco ad locum motu continuo. | 284. Ninth I ask whether an angel can be moved from place to place by continuous motion. |
| 285 Quod non, probo: Quia ((motus est actus entis in potentia, secundum quod huiusmodi)), ex III Physicorum; 'ubi' autem, vel locus, non est actus angeli ƿvel perfectio, quia omnis perfectio videtur esse nobilior perfectibili, aliquo modo; non sic autem 'ubi' respectu naturae angelicae. | 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 Secundo, quod non possit moveri motu continuo, arguitur: Et primo probo in communi, quod nullum successivum sit continuum, et hoc duplici via: primo probo ex hoc quod omne tale componitur ex indivisibilibus, - secundo, quia componitur ex minimis. | 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 Primam consequentiam probat Aristoteles VI Physicorum, quia 'indivisibile non potest continuari indivisibili, cum non habeat ultimum'. | 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 Antecedens, illud scilicet quod 'successivum componitur ex indivisibilibus', probo dupliciter: Primo, quia dividitur in indivisibilia; igitur componitur ex eis. - Probatio antecedentis huius: possibile est ipsum dividi in omnia illa in quae est divisibile (subiectum huius propositionis videtur includere praedicatum), et ex hoc videtur ulterius ipsum posse esse divisum in omnibus in quibus possibile est ipsum dividi (ista consequentia probatur per illud VI Physicorum 'quod imposƿsibile est fieri, impossibile est factum esse'; et III Metaphysicae et II De generatione dicit Aristoteles idem); ulterius, ista de possibili ponatur in esse, et sequitur 'igitur est actu divisum in omnia in quae possibile est ipsum dividi', et ex hoc sequitur quod est divisum in indivisibilia (quia si non, non esset divisum in omnibus in quibus posset dividi, quia adhuc ulterius posset dividi in partes illorum divisibilium). | 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 Secundo probo idem, quia successivum nihil est actu nisi indivisibile, - quia si aliquid eius esset divisibile, simul esset successivum et non successivum, vel successivum et permanens. Illo igitur non exsistente actu, sed raptim transeunte, quaero quid succedit sibi? Si aliquod indivisibile succedit sibi in continuo, habetur propositum, quod indivisibile sit immediatum indivisibili, et sic 'continuum' erit compositum ex indivisibilibus. Si non aliud indivisibile, igitur tunc non erit, nam indivisibile eius non est; et sicut argutum est 'non est, nisi quia aliquod indivisibile eius est', igitur etc. | 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 Secunda via est, quia componitur ex minimis; igitur non est continuum. | 290. The second way [n.286] is that the successive is composed of minima; therefore it is not continuous. |
| 291 Consequentia probatur, quia minimum simpliciter (quo scilicet non est aliquid minus ipso) non habet partem ex qua sit, quia tunc ƿilla esset minor eo; ergo est omnino non quantum, quia omne quantum habet partem minorem se. Sed non quantum non potest continuari quanto; igitur minimum non potest continuari. | 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 non-quantum, because everything extended has a part smaller than itself. But something non¬ extended cannot be continuous with something extended; therefore the smallest thing, the minimum, cannot be continuous. |
| 292 Antecedens probatur et auctoritatibus et ratione: Primo, auctoritate Philosophi I Physicorum, ubi videntur rationes suae velle - contra Anaxagoram - inniti isti principio, quod est accipere minimum naturale, ut minimam carnem vel minimum ignem; sed secundum ipsum VI Physicorum, ((eiusdem rationis est, ipsum motum et magnitudinem et tempus componi vel esse ex indivisibilibus, et dividi in eis)); igitur oportebit ponere minimum motum et minimum tempus, sicut permanens minimum. | 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 Idem videtur a Philosopho II De anima, ubi vult quod ((omnium natura constantium determinata est ratio magnitudinis et augmenti)); non autem 'permanentia' naturalia sunt tantum, sed etiam successiva; igitur habent determinatam parvitatem et magnitudinem. | 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 Patet etiam idem per Aristotelem De sensu et sensato,in illa ƿprima dubitatione, ubi videtur velle quod 'passiones naturales non sunt divisibiles in infinitum'; et hoc probare videtur, quia 'tunc sensus posset intendi in infinitum', quia ad percipiendum minimum indivisibile requiritur acutior sensus in infinitum. | 294. The same is also plain from Aristotle On Sense andSensibles 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 Ratio ad hoc probandum est ex hoc quod est dare primam partem motus; igitur et minimam. | 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 Ista consequentia patet, quia si quaelibet haberet minorem partem se, haberet etiam 'aliquid sui' prius aliquo sui in infinitum. | 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 Antecedens istud de primitate (scilicet quod 'contingat dare primam partem motus') duabus auctoritatibus Aristotelis patet: I Physicorum, - et VIII, ubi dicit Philosophus quod ((non, si partibile - quod alteratur - in infinitum, quod propter hoc et ƿalteratio, sed velox est multoties)); ubi habet Commentator ((subito)), et exponit ((hoc est in instanti, non in tempore)). Et quasi obicit contra se, quia 'videtur hoc repugnare illi quod dicitur in VI Physicorum, quod ante omne moveri praecedit mutatum esse et ante mutatum esse moveri'; et respondet, solvendo, quod 'illud intelligitur ibi de motu in quantum est continuus et divisibilis, istud autem intelligitur hic de motu in quantum est generatus sive productus ad actum'. | 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 Ad istam intentionem videtur ibi Aristoteles praemisisse quoddam exemplum de guttis, quod 'non est necesse, si multae guttae aliquam partem de lapide auferant, penetrando lapidem, quod etiam gutta quaelibet aliquid amoveat et quod semper pars amoveatur ante partem, sed aliquando simul totum amovetur'. Quando igitur dicit 'tot guttae amovent de lapide tantum, in aliquo tempore, pars autem illarum in nullo tempore tantum amovet' (et exemplificat 'sicut multi trahunt navem', nullus autem per se etiam in nullo tempore trahet navem), videtur innuere quod post aliquas guttas tandem tota pars lapidis simul amovetur. Et ita est in alteƿratione, quod non semper pars sequitur partem, sed quandoque alteratio tota simul. | 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 Hoc expressius in secunda dubitatione De sensu et sensato videtur, ubi vult quod ((non oportet quod similiter sit in alteratione et latione: contingit enim aliquid simul totum alterari et non dimidium prius, velut aquam simul totam coagulari, - attamen si fuerit multum quod calefit et coagulatur, habitum ab habito fit vel patitur; primum autem ab ipso faciente transmutari et simul alterari et subito, necesse est)). | 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 Item, probatur per rationem, - quia inter contradictoria non est medium; igitur inter non esse formae inducendae per motum et esse ipsius non est medium (non esse autem ipsius fuit in ultimo instanti formae praecedentis, ergo inter illud instans et illud quod mensurat esse formae succedentis non est medium). Sed si nullum esset primum inter esse formae inducendae per motum et non esse ipsius, illud 'primum' esset indivisibile. Ex ista primitate probata concluditur quod illud 'primum' sit minima pars; non enim potest illud 'primum' esse indivisibile, quia Philosophus in VI ostendit quod non contingit accipere primam mutationem in motu. | 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 Tertio principaliter arguo sic, quod angelus non possit moveri, quia est indivisibilis. ƿ | 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 Probat enim Aristoteles VI Physicorum, cap. 3 et ultimo, quod nullum indivisibile potest moveri (et hoc ex intentione, - et illam rationem quam facit cap. 3, replicat cap. ultimo), quia omne quod movetur, partim est in termino 'a quo' et partim in termino 'ad quem': quando enim est totaliter in termino 'a quo', non movetur sed quiescit, - quando est totaliter in termino 'ad quem', tunc totaliter motum est. Igitur quando movetur indivisibile, non potest partim esse in termino 'a quo' et partim in termino 'ad quem', quia non habet partem et partem; quare etc. | 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 Secunda ratio sua est (cap. ultimo), quia omne quod movetur, prius pertransit spatium sibi aequale vel minus, quam maius; sed indivisibile non potest prius pertransire minus se; igitur prius pertransit aequale quam maius se. Sed in pertranseundo semper spatium sibi aequale, pertransibit totum continuum super quod movetur; igitur illud componeretur ex indivisibilibus aequalibus indivisibili moto. Consequens videtur falsum, igitur et antecedens. ƿ | 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 Tertia ratio sua videtur esse, quia omnis motus est in tempore (sicut prius probavit VI Physicorum); et omni tempore contingit accipere minus tempus, in quo minore potest minus mobile moveri; igitur omni mobili potest accipi minus mobile in infinitum, et ita indivisibile mobile! | 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 Quarto, quod non possit moveri continue localiter, quia non habet resistentiam. | 305. Fourth, that an angel cannot be continuously moved through place because he has no resistance. |
| 306 Quia, sicut dicit Commentator super IV Physicorum cap. 'De vacuo', successio in motu est ex resistentia mobilis ad motorem, vel medii ad mobile, vel medii ad motorem; sed nulla istarum resistentiarum est in proposito: non enim angelus resistit medio, nec sibi ipsi ut motori. Et confirmatur ratio, quia secundum ipsum grave in vacuo moveretur in non tempore, quia ibi nulla esset resistentia quae posset causare successionem in motu; non ƿmagis autem resistit angelus sibi vel medio, quam grave vacuo (vel vacuum gravi), si ponatur; igitur etc. | 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 Item, per rationem Philosophi. Ibi enim arguit sic: quae est proportio medii ad medium in subtilitate et densitate, eadem est proportio motus ad motum in velocitate et tarditate; sed nulla est proportio vacui ad plenum in subtilitate et densitate; ergo nec motus ad motum in velocitate et tarditate. Sed omnis motus possibilis, ad omnem motum possibilem, potest esse aliqua proportio in velocitate; igitur nullus motus est possibilis in vacuo, sed aliquis possibilis est in pleno. - Sicut ipse arguit ex parte medii, ita potest argui in proposito: nam (ceteris paribus) quae est proportio mobilis ad mobile in velocitate, eadem est proportio angeli ad corpus in subtilitate; sed nulla est proportio angeli ad corpus in subtilitate; igitur etc. (sicut in ratione sua). | 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 Alia ratio sua est ibi: quia si in vacuo fiat motus, accipiatur aliquod aliud corpus 'plenum subtile' in tanta proportione excedere in quanta tempus motus vacui velocius est quam tempus motus pleni; per illud medium 'plenum subtilius' erit motus in aequali tempore cum tempore motus in vacuo, - quod habet pro ƿimpossibili. - Ita potest in proposito argui ex parte mobilium: si enim angelus quantumcumque velocius movetur quam corpus, accipiatur aliquod aliud corpus subtilius ad corpus illud datum in tanta proportione in quanta tempus motus angeli minus est tempore motus corporis dati, - illud corpus, in tali proportione subtilius, in aequali tempore movebitur cum angelo. | 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 Ad oppositum videtur esse Damascenus cap. 13 et 16, ubi vult quod non sunt simul in caelo et in terra; et frequenter mittuntur in terram, quod apparet per Scripturam. | 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 Ad quaestionem dico quod sic, - quia omne receptivum formarum alicuius generis, quod non est ex se determinatum ad aliquam unam illarum nec est illimitatum, potest moveri vel mutari ab una illarum formarum ad aliam (ista propositio patet per se, quia subiectum includit praedicatum); sed angelus est receptivus alicuius 'ubi' definitive et non circumscriptive (sicut patet prius, in prima quaestione de locatione angeli), - nec est illimitatus ad omnia, quia non est immensus; igitur potest continue moveri ab uno 'ubi' ad aliud 'ubi'. Et quod continue, patet, - quia inter duo ƿ'ubi', infinita sunt 'ubi' media (quod probatur ex continuo motu corporis per omnia illa 'ubi'); per omnia autem illa potest angelus transire, ita quod in nullo illorum 'ubi' sit nisi indivisibiliter, - et per consequens, non potest omnia illa pertransire nisi continue moveatur. | 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 Hoc etiam confirmatur, quia anima beata aequabitur angelo, iuxta promissum Salvatoris in Matth.; anima autem beata - immo beatissima - quae est Christi, localiter movebatur, quia descendebat ad inferos, sicut dicit articulus fidei. | 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 Patet etiam ex Scriptura quod angeli mittuntur quandoque in corpore assumpto; et si tunc cum corpore movebantur, videtur quod tunc fuit aliqua motio passiva ipsorum, alia formaliter a motione passiva ipsius corporis, quia non erant formaliter aliquid ipsius corporis. | 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 5.5-12, 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 Similiter, credibile est quod frequenter missi sunt sine corpore, sicut de illo misso ad Ioseph de conceptu beatae Virginis. ƿ | 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 Ad argumenta quaestionis. Ad primum dico quod non est inconveniens omne creatum, quantumcumque perfectum sit (dummodo tamen in essentia omnem perfectionem non habeat), esse capax vel potentiale respectu alicuius perfectionis, licet illa absolute minor sit natura sua, - sicut angelus habet intellectionem, quae est perfectio potentiae suae intellectivae, et tamen intellectio est simpliciter ignobilior natura angelica; et ita potest concedi de 'ubi' vel praesentia corporali cum angelo, sicut aliquis 'actus' dicitur (sed longe aliter) illa natura cui inest. | 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 Ad secundum nego illud quod assumitur, scilicet 'nullum successivum esse continuum'. | 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 Antecedens eius (quod assumitur ad eius probationem), scilicet quod 'componitur ex indivisibilibus', - nego. Et eius falƿsitatem probo per illam rationem Philosophi VI Physicorum de proportione sesquialtera (quae plus convincit adversarium, licet forte aliquae rationes eius magis sint 'a causa'), quia supponit quod in quacumque proportione possit motus accipi velocior omni motu dato, - et per consequens motu aliquo dato, mensurato tribus instantibus, erit accipere motum duplo velociorem, qui mensurabitur instanti cum dimidio tantum. | 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 Istud etiam de successivo, probo per continuitatem permanentis: quia permanens est continuum, igitur et successivum. | 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 Consequentiam probo, quia si in motu sunt indivisibilia sibi invicem immediata, quaero de mobili, et de ipsis 'ubi' quae habet in ipsis instantibus immediatis: si inter ultimum unius 'ubi' et alterius, nihil sit medium, igitur ultimum unius immediatum est ultimo alterius; Si autem inter ista duo 'ubi' sit aliquod medium, quaero de ultimo ipsius mobilis quando est in ipso medio (et non in altero instanti): quia in illis duobus indivisibilibus est in ipsis 'ubi' inter quae ponitur istud medium, - est igitur in medio illo, in medio aliquo inter ista duo instantia; ergo ista duo instantia non erant immediata! - Et istam consequentiam declarat Aristoteles VI Physicorum, quod scilicet ((eiusdem rationis est, motum, magnitudinem et tempus componi ex indivisibilibus)). ƿ | 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 Antecedens probari potest, manifestius de permanentibus quam de successivis, per rationes Aristotelis in VI Physicorum, quia magis est evidens et manifestum quod indivisibilia permanentia non faciunt maius, quam de indivisibilibus sibi invicem succedentibus. | 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 Efficacius tamen probatur illud antecedens per duas rationes sive propositiones geometricas, quarum prima est ista. 'Super centrum quodlibet, quantumlibet occupando spatium, contingit circulum designare', secundum illam petitionem 2 I Euclidis. Super igitur centrum aliquod datum, quod dicatur a, describantur duo circuli: minor, qui dicatur D, - et maior B. Si circumferentia maioris componitur ex punctis, duo puncta sibi immediata signentur, quae sint b c, - et ducatur linea recta ab a ad b et linea recta ab a ad c, secundum illam petitionem I Euclidis ((a puncto in punctum lineam rectam ducere)) etc. | 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 Istae rectae lineae, sic ductae, transibunt recte per circumferenƿtiam minoris circuli. Quaero ergo aut secabunt eam in eodem puncto, aut in alio? Si in alio, igitur tot puncta in minore circulo, sicut in maiore; sed impossibile est duo inaequalia componi ex partibus aequalibus in magnitudine et multitudine: punctus enim non excedit punctum in magnitudine, et puncti in circumferentia minore sunt tot quot in circumferentia circuli maioris; ergo minor circumferentia est aequalis maiori, et per consequens pars est aequalis toti! Si autem duae rectae lineae ab et ac secent minorem circumferentiam in eodem puncto (sit ille d), super lineam a b erigatur linea recta secans eam in puncto d, quae sit d e, - quae sit etiam contingens respectu minoris circuli, ex 17 III Euclidis. Ista, ex 13 I Euclidis, cum linea a b constituit duos angulos rectos vel aequales duobus rectis, - ex eadem etiam 13, cum linea a c (quae ponitur recta) constituet de angulos duos rectos vel aequales duobus rectis; igitur angulus ade et etiam angulus bde valent duos rectos, pari ratione angulus ade et angulus cde, valent duos rectos. Sed quicumque duo anguli recti sunt aequales quibuscumque duobus ƿrectis, ex 3 petitione I Euclidis; igitur dempto communi (scilicet ade), residua erunt aequalia: igitur angulus bde erit aequalis angulo cde, et ita pars erit aequalis toti! | 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.[1] |
| 322 Sed ad istud diceret adversarius quod db et dc non includunt aliquem angulum, quia tunc posset illi angulo basis subtendi a puncto b ad punctum c, quod est oppositum positi, quia b et c ponuntur puncta immediata. Quando igitur accipitur quod angulus cde est totalis ad angulum bde, negatur, quia angulo bde nihil additur ex angulo cde, - quia inter b et c, in concursu eorum in d, non est angulus. | 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 Ista responsio licet primo videatur absurda, negando angulum ubi duae lineae concurrunt quae expanduntur super superficiem et applicantur non directe, et in hoc contradicat definitioni anguli I Euclidis, - negando etiam a b in c lineam posse duci, neget primam petitionem I Euclidis, - tamen quia haec non reputarentur inconvenientia (quia sequuntur ad propositum), arguo contra responsionem aliter: Angulus cde includit totum angulum bde, et addit saltem punctum (licet protervias quod non addit angulum), et punctus per te ƿest pars; ergo angulus cde addit super angulum bde partem aliquam; ergo est 'totum' ad illud. | 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 Assumptum patet, quia si angulus dicatur spatium interceptum inter lineas, non includendo lineas, - tunc punctus primus lineae db extra circumferentiam minorem, nihil erit anguli bde, et est aliquid anguli cde; si angulus, ultra spatium inclusum, includat lineas includentes, - tunc primus punctus lineae dc extra circumferentiam minorem, nihil erit anguli bde, et erit aliquid anguli cde. Et ita utroque modo angulus cde addit punctum super angulum b d e. | 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 Nec potest aliquo modo obviari demonstrationi principali, quasi in ista circumferentia non incipiant lineae dividi a se, sed alibi, propinquius centro vel remotius, - quia ubicumque hoc posueris, ibi describam circumferentiam minorem. | 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 Istam secundam partem, scilicet quod minor circumferentia non secetur in uno puncto si secetur a duabus lineis, non oporteret probare nisi propter proterviam adversarii, - quia satis est manifestum quod eadem linea, si protrahatur in continuum et directum, numquam terminabitur ex eadem parte ad duo puncta; et si istud 'manifestum' verum conceditur, statim ex deductione in prima parte patet propositum. ƿ | 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 Secunda probatio est ex 5 sive ex 9 X Euclidis. Dicit enim illa 5 quod 'omnium quantitatum commensurabilium proportio est ad invicem sicut alicuius numeri ad aliquem numerum', et per consequens - sicut vult 9 - 'si lineae aliquae sint commensurabiles, quadrata illarum se habebunt ad invicem sicut aliquis numerus quadratus ad aliquem numerum quadratum'; quadratum autem diametri non se habet ad quadratum costae sicut numerus aliquis quadratus ad aliquem numerum quadratum; igitur nec linea illa, quae erat diametri quadrati, commensurabilis erit costae illius quadrati. | 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 Minor huius patet ex paenultima I, quia quadratum diametri est duplum ad quadratum costae, pro eo quod est aequale quadratis duarum costarum; nullus autem numerus quadratus est duplus ad alium numerum quadratum, sicut patet discurrendo per omnes quadratos, ex quibuscumque radicibus in se ductis. | 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 Ex hoc patet ista conclusio, quod diameter est asymmeter costae, id est incommensurabilis. Si autem lineae istae componerentur ex punctis, non essent incommensurabiles (se haberent enim ƿpuncta unius ad puncta alterius in aliqua proportione numerali); nec solum sequeretur quod essent commensurabiles lineae, sed etiam quod essent aequales, - quod est plane contra sensum. | 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 Probatio huius consequentiae. Accipiantur duo puncta immediata in costa, et alia duo opposita in alia costa, - et ab istis et ab illis ducantur duae lineae rectae, aequidistantes ipsi basi. Istae secabunt diametrum. Quaero ergo aut in punctis immediatis, aut mediatis? Si in immediatis, ergo non plura puncta in diametro quam in costa; ergo non est diameter maior costa. Si in punctis mediatis, accipio punctum medium inter illa duo puncta mediata diametri (illud cadit extra utramque lineam, ex datis). Ab illo puncto duco aequidistantem utrique lineae (ex 31 I); ista aequidistans ducatur in continuum et directum (ex secunda parte primae petitionis I): secabit costam, et in neutro puncto eius dato, sed inter utrumque (alioquin concurreret cum alia, cum qua ponitur aequidistans, - quod est contra definitionem aequidistantis, quae est ultima definitio posita in I). Igitur inter illa duo puncta, quae ponebantur immediata in costa, est punctus medius: ƿhoc sequitur ex hoc quod dicebatur inter diametri puncta esse punctus medius; igitur ex opposito consequentis sequitur oppositum antecedentis, - igitur etc. | 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 Immo, generaliter, totus X Euclidis destruit istam compositionem lineae ex punctis, quia nulla esset omnino linea irrationalis sive surda, cum tamen ibi principaliter tractet de irrationalibus, sicut patet ibi de multis speciebus lineae irrationalis quas assignat. | 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 Ex eodem etiam apparet improbatio alterius antecedentis, de partibus minimis, - quia aut illud minimum posset praecise terminare lineam indivisibilem simpliciter, aut posset intercipi inter terminos duarum linearum? Si primo modo, minimum ponitur simpliciter punctus indivisibilis; et tunc idem est ponere, illo modo, minimum et simpliciter indivisibile pro parte. Si secundo modo, ducantur igitur duae lineae - protractae a centro - ad terminos talis minimi in circumferentia maiore, ita quod ƿincludant praecise tale minimum in illa circumferentia. Tunc quaero: aut includunt aliquid minimum in circumferentia minore, aut praecise nihil includunt, sed omnino habent idem indivisibile continuans? Si primo modo, igitur tot minima in minore circulo quot sunt in maiore; igitur erunt aequales. Si secundo modo, sequitur quod circumferentia minor secabitur in uno puncto a duabus lineis rectis (exeuntibus ab eodem puncto), quod est improbatum in primo membro. - Immo sequitur absurdius, quod scilicet lineae istae in circumferentia maiore includant illud minimum: et ducatur a termino unius ad terminum alterius linea recta, secundum primam petitionem I; et tunc illa erit basis trianguli duorum laterum, et per consequens poterit dividi in duo aequalia (ex 10 I); et ita non erit minimum, quod datum est minimum. Immo ulterius: ducatur aliqua alia, aequidistans illi basi trianguli, illa erit minor illa base (ex 21 I), et ita erit aliquid minus minimo. | 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 Similiter, illa positio, sive uno modo sive alio (Si tamen intelƿligatur tale quod non habet partem in toto), concludit commensurabilitatem diametri ad costam (immo aequalitatem), sicut deductum est prius, contra primam opinionem. | 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 Ad ista argumenta respondetur quod non concludunt contra minimum secundum formam, - et sic ponitur minimum secundum formam, non autem secundum materiam. | 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 Et habetur haec distinctio a Philosopho I De generatione cap. 'De augmentatione', ubi vult quod 'pars secundum speciem quaelibet augeatur, et non secundum materiam'. | 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 Potest tamen istud dictum tripliciter intelligi: Vel quod 'pars secundum speciem' dicatur pars secundum formam, - 'pars autem secundum materiam' dicatur pars quanti in quantum 'quantum' est, quia quantitas consequitur materiam. Et tunc redit in quoddam antiquum dictum, scilicet quod 'quanƿta, secundum quod quanta, sunt divisibilia in infinitum, - non autem secundum quod naturalia'. | 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 Vel potest intelligi 'pars secundum speciem' quae potest per se esse in actu, - et 'pars secundum materiam' dicatur pars secundum potentiam, videlicet pars ut exsistit in toto. Et tunc redit in idem cum alio dicto antiquo, quod 'est dare minimum, quod posset per se exsistere, - non autem est minimum in toto, quo non est minus, exsistens in eo in potentia'. | 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 Aut potest intelligi tertio modo (discordando ab istis duobus dictis antiquis), quod sit in aliquo ut minima pars formae sive totius in quantum habet formam, et non minima pars aliqua respectu materiae sive totius illius secundum materiam. Et tunc videtur manifeste falsum, quia nulla pars materiae in toto, est sine forma in actu, - nec etiam sine forma eiusdem rationis, in totis homogeneis; immo sicut ibi 'totum' dividitur in partes homogeneas, ita materia per accidens et forma per accidens dividitur in partes suas homogeƿneas, - et eo modo quo minimum totius, est minimum utriusque partis, et e converso. | 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 Dimittendo ergo istum tertium intellectum, alios duos intellectus excludendo ostendo quod non impediunt probationes praecedentes. Primo quidem arguo contra primam viam, auctoritate Commentatoris super III Physicorum, super illud ((Et vidimus Platonem)) etc.; quaere ibi. | 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 adloc. on Physics 3.6.206b27-29, on the remark "And we saw Plato etc.;" look there.[2] |
| 340 Secundo, auctoritate Aristotelis De sensu et sensato, in dubitatione illa prima ubi allegatur in oppositum. Ibi enim licet dubitationem illam obscure solvat, hoc tamen certum dicit quod 'qualitates sensibiles sunt determinatae secundum species' (quod probat, quia 'ubi extrema sunt posita, necesse est media esse finita; in omni autem genere qualitatum sensibilium extrema sunt poƿsita, quia contraria'). Sed de quacumque una qualitate singulari, utrum ipsa habeat terminabilitatem in se, - videtur dicere quod non: 'quia exsistunt cum continuitate, ideo habent aliud in actu, aliud in potentia', sicut continuum; hoc est: sicut 'continuum' unum est per se in actu et plura in potentia (in quae est per se divisibile), ita qualitas sensibilis ut exsistens in continuo, est una in actu et plura in potentia, licet per accidens. Et tunc reducta potentialitate quanti per se ad actum, reducitur potentialitas passionis ad actum per accidens, ita quod numquam quantitas per divisionem dividitur in quanta mathematica; quia sicut ipse arguebat ad quaestionem quod 'naturale non componitur ex partibus mathematicis, sed naturalibus', ita etiam in tales partes - scilicet naturales - dividitur. Qualiter autem non facit ad propositum, patebit respondendo. | 340. Second using the authority of Aristotle On Sense andSensibles 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 Istud etiam ad quod adductae sunt auctoritates Commentatoris et Aristotelis, probatur per rationes: Quia quando aliqua passio convenit alicui praecise secundum aliquam rationem, - cuicumque convenit aequaliter secundum illam rationem, eidem convenit simpliciter aequaliter (sicut, si 'videre' natum est praecise convenire animali secundum oculos, et non secundum manus, - cuicumque aequaliter convenit secundum ocuƿlos, ei simpliciter conveniet aequaliter, licet non conveniat ei secundum manus); sed dividi in partes integrales tales, eiusdem rationis, extensas, nulli convenit nisi per quantitatem formaliter, nec maximo naturali magis quam minimo; igitur cum minimo conveniat secundum rationem istam, ita simpliciter conveniet sibi sicut maximo. | 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 Quod si dicatur quod forma minimi prohibet istud quod competeret ex quantitate (quantum est de se, ex parte quantitatis), contra: si per se 'aliqua consequentia' sunt incompossibilia, et illa ad quae sequuntur sunt incompossibilia, - et multo magis, si illa quae sunt de essentiali ratione aliquorum sunt incompossibilia, et ipsa erunt; sed divisibilitas in tales partes vel essentialiter consequitur quantitatem vel est de per se ratione eius (sicut Philosophus assignat rationem eius, talem qualem, IV Metaphysicae); ergo cuicumque formae naturali ponitur istud incompossibile, ei quantitas est incompossibilis, et ita non erit simpliciter divisibile in quantum 'quantum', quia simpliciter non est quantum. | 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 Hoc etiam probatur, quia non est intelligibile aliquid esse 'quantum' quin sit ex partibus, nec quod sit ex partibus quin pars sit ƿminor toto; et ita non est intelligibile quod aliquid sit quantum indivisibile, ita quod non sit aliquid in eo, minus eo, inexsistens sibi. Nec etiam potest poni aliqua caro simpliciter indivisibilis in tota carne, quia sicut punctus separatus non faceret quantum separatum, ita nec caro separata punctalis (Si esset) cum alia faceret aliquid maius, nec continuum nec contiguum; unde ita improbant rationes Philosophi VI Physicorum indivisibilitatem alicuius rei naturalis, sicut alicuius partis quanti in quantum 'quantum'. | 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 Dico igitur quod ista responsio de naturali in quantum 'quantum' et in quantum 'naturale', Si potest habere aliquam veritatem, debet intelligi affirmando et negando rationem formalem divisibilitatis, ita quod illa quae dicit quod dividitur in quantum 'quantum', dicit quod dividitur in quantum 'naturale', et quae dicit quod non dividitur in quantum 'naturale', negat naturalitatem esse rationem huius divisionis, - sicut si diceretur quod animal in quantum habet oculos videt, non in quantum habet manus; et iste intellectus verus est. Sed ex hoc non sequitur quod non simpliciter ei conveniat quod convenit ei secundum quantitatem: non enim per naturalitatem concurrentem impeditur illud quod convenit naturaliter quantitati, sicut nec per manus concurrentes in animali tollitur illud quod simpliciter convenit ei secundum oculos. Ita igitur, absolute, ƿest omne 'naturale' divisibile in semper divisibilia (in infinitum), sicut si illa quantitas quae est cum forma naturali esset per se, sine omni forma naturali. Et ita omnes rationes quae procedunt de quantitate absolute (secundum rationem quantitatis), concludunt de ea ut est in naturalibus, quia divisibilitas est passio naturalis eius, et ex consequente concludunt de naturali, cuius est haec passio. | 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 Secunda responsio non videtur excludere rationes praedictas, quin 'totum' non esset compositum ex indivisibilibus, nec ex minimis partibus in toto. Tamen videtur posse ponere minimum in motu, pro eo quod pars motus per se est, antequam sit aliquid alterius, totius; et ita pars formae secundum quam est motus, praecedit omnes alias partes illius formae (non tantum natura, sed etiam duratione), et ita tunc videtur esse per se, et non in toto. Si ergo sit minimum in naturalibus, quod possit per se esse, - videtur esse minima pars formae quae posset induci per motum, et ita minimus motus. | 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 Sed contra istam responsionem arguo: quia sicut essentiale est 'quanto' posse dividi in partes, ita est ei essentiale quod singulum eorum in quae dividitur, posset esse hoc aliquid; igitur nulli eorum repugnat per se esse. | 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 Confirmatur ista ratio et consequentia ista: Tum quia partes istae sunt eiusdem rationis, quantum ad materiam et formam, cum toto; igitur possunt habere per se exsistentiam, sicut et totum potest. ƿTum quia si essent per se, essent individua illius speciei cuius 'totum' est individuum; absurdum autem videtur quod aliquid habeat in se naturam illam unde sit individuum (vel possit esse individuum) alicuius speciei, ita quod sibi non repugnat posse esse individuum illius et repugnat sibi posse esse simpliciter, et hoc saltem de illis quae non sunt accidentia (loquimur modo de substantiis homogeneis, quae non inhaerent essentialiter). Tum etiam quia partes sunt naturaliter priores toto; igitur non repugnat eis, contradictorie, posse esse priores toto ipso naturaliter, quia naturaliter non repugnat ipsi toti esse prius tempore (hoc modo, quia non repugnat sibi contradictorie - ex parte sui - esse prius duratione). | 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 Videtur ergo quoad hoc dicendum quod sicut forma naturalis non tollit a toto naturali quin ita sit 'totum' semper divisibile per quantitatem, sicut quantitas esset si sola esset, - ita etiam non tollit quin quodlibet divisum posset per se esse (quantum est ex se et ex parte sui), sicut posset quaelibet pars quantitativa in quam divideretur 'quantum'. ƿ | 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 Et si dicas quod statim converteretur in continens, - responsio ista non videtur esse ad intellectum quaestionis. Quaerimus enim minimum, potens per se esse ex ratione intrinseca, hoc est, cui per 'aliquid sibi intrinsecum' contradictorie non repugnat minus eo esse per se; nulla autem ratio intrinseca huiusmodi incompossibilitatis assignatur, si totum corrumpatur. Circumscribamus enim omne continens et omne corruptivum, et quod sola aqua sit in universo; quaecumque aqua data dividatur, quia hoc est possibile, ut probatur supra contra primam responsionem. Illa in quae fit divisio, non erunt nihila, quia hoc est contra rationem divisionis, - nec erunt non aqua, ex sola ratione divisionis, quia tunc aqua componeretur ex non aquis; nec etiam repugnat formae aquae ista parvitas quae iam est in actu, quia ista 'parva' praefuit (licet in toto), - nec per ipsam divisionem corrumpetur aqua, quia circumscriptum est omne corruptivum. Non igitur videtur aliqua ratio intrinseca quare naturali repugnet quin semper, quocumque per se exsistente, posset aliquod minus esse per se exsistens, licet forte ratio extrinseca impeditiva talis 'per se exsistentiae' assignetur contrarietas corrumpentis. ƿ | 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 Arguo etiam contra utramque responsionem simul, quia neutra salvat minimum in motu (propter quod improbandum tacta est aliqualiter praecedens deductio) licet enim medium in motu locali non posset cedere mobili nisi esset naturale, tamen si per impossibile medium mathematicum posset cedere mobili mathematico, vere esset successio in motu tali, propter divisibilitatem medii; prius enim pertransiret mobile priorem partem spatii, quam posteriorem. Et etiam modo, sicut per accidens est in locato (ex parte locati in quantum locatum est) quod habeat qualitates naturales (sicut patet per Philosopum IV Physicorum, de cubo), et per accidens in loco (ex parte loci in quantum locus est) quod habeat qualitatem naturalem (ex quaestione 1 'De loco', quia licet naturalitas conveniat locanti, tamen per accidens convenit loco), - ita etiam, licet necessario tamen per accidens omnino, convenit motui secundum locum sive motui secundum 'ubi' (quod est in locato, per se, in quantum respicit per se locum) quod qualitas naturalis sit in ipso motu, vel quod sit in illo secundum quod est motus sive in magnitudine super quam fit motus. Per se ergo ratio successionis est quantitas: vel in magnitudine vel in mobili vel in utroque. | 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 Ex hoc destruitur prima responsio, quia non facit pro minimo ƿin motu: quia ex quo - secundum eam - non est accipere in eo minimum secundum quod quantum, et successio est in motu locali per se ex ratione alicuius in quantum 'quantum', sequitur quod in motu locali nullo modo posset esse minimum. Et ita nec in aliis motibus, quia licet non ita immediate concedatur de alteratione (si ponatur motus vel successio secundum formam), tamen sequitur per 'locum a maiore' negative: nullus enim motus est velocior latione, et ita nullus potest habere partes indivisibiles, si iste necessario habeat partes divisibiles. | 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 Ex eodem etiam destruitur secunda responsio, quod non faciat pro minimo in motu: quia in magnitudine super quam est motus, non est accipere minimam partem inexsistentem; igitur nec minimum transitum super illam magnitudinem, quia in illo minimo transitu oporteret transire minimam partem magnitudinis. | 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 Secunda etiam responsio - quantum ad minimum motum - destruitur etiam per alia: Primo, quia quando movens est praesens et vincens super motum, non potest poni illa ratio extrinseca propter quam negatur tale minimum posse per se esse, scilicet praesentia corruptivi, quia praesentia causae moventis et producentis tale minimum, tunc vincit contrarium omne corruptivum. ƿSimiliter: minimum in successivis posse esse in fluendo, hoc est minimum ibi simpliciter esse in toto, quia pars successivi non habet aliud esse in toto quam fluere unam partem ante aliam, quae partes fluentes integrant totum; sicut igitur in toto permanente 'hoc est partem esse in toto, quod est partem permanentem esse in toto', ita in successivis 'hoc est partem esse in toto, quod est partem fluentem continuari alii parti'. Sic igitur improbatis illis duobus antecedentibus, respondendum est ad probationes eorum adductas pro eis. | 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 Ad primum dicitur quod 'licet possibile sit continuum dividi secundum omne signum, non tamen possibile est divisum esse, quia ista divisio est in potentia et in fieri, et numquam potest esse tota in facto esse'. Et tunc ad illas probationes adductas in oppositum, conceditur de quacumque una potentia ad unam factionem, non tamen de ƿinfinitis factionibus, cum quarum una reducta ad actum, necessario stat alia non reducta ad actum; sic est in proposito, quia sunt infinitae potentiae ad infinita dividi (cum quarum una reducta ad actum, necessario stat alia non reducta ad actum), et ideo licet concedatur possibilitas ad dividi, non tamen ad divisum esse. | 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 Confirmatur responsio ista per Commentatorem super illud III Physicorum, ubi assignat rationem illius propositionis Philosophi 'quantam magnitudinem contingit esse in potentia, tantam contingit esse in actu (non sic in numeris)': 'Propter hoc quod omnes istae potentiae, quae sunt ad partes magnitudinis, sunt potentiae eiusdem potentialitatis et eiusdem rationis, - non sic in numeris'. | 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 Contra istud: sequitur per te 'continuum posse dividi secundum a, igitur possibile est ipsum esse divisum secundum a', - et ita de b et c et quocumque alio singulari (et hoc determinato vel indeterminato), quia nulla una divisio potest esse quae non potest esse completa. Ergo omnes singulares antecedentis inferunt omnes ƿsingulares consequentis; antecedens ergo infert consequens: si potest in infinitum dividi, igitur possibile erit divisionem istam esse factam in actu in infinita. | 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 Quod si dicas singularia consequentis repugnare, non autem singularia antecedentis, - contra: ex possibili non sequuntur incompossibilia; sed ex singularibus istis sequuntur illa (patet inductive); igitur etc. | 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 Sed ista propositio 'possibile est continuum dividi secundum quodlibet signum', posset distingui secundum compositionem et divisionem, ut esset sensus compositionis iste, quod haec propositio est possibilis 'possibile est continuum dividi' etc.; sensus divisionis est iste, quod in continuo est potentia ad 'dividi' ad quodcumque signum. Primus sensus est verus, et secundus est falsus. | 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 Vel posset distingui sic, secundum quod signum posset distribuere divisive vel collective. ƿ | 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 Posset etiam distingui secundum quod 'possibile' posset praecedere signum, vel subsequi: et si praecederet, esset propositio falsa, quia notaretur esse una potentia ad attributionem praedicati; si sequeretur, vera, quia notaretur potentiam multiplicari ad multiplicationem subiecti. | 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 Istae responsiones non videntur multum logicae: tertia non, quia modus compositionis - puta possibilitas - non videtur posse distribui ad plures possibilitates (sive una possibilitas pro pluribus possibilibus instantibus), et non notaretur praedicatum uniri subiecto pro aliquo uno instanti; neque responsio secunda valet, quia illa non habet locum nisi accipiendo hic signum in plurali, sicut ibi 'omnes apostoli Dei sunt duodecim'; neque responsio prima valet, quia necesse est quod accipiendo extrema pro eodem tempore (vel pro alio), quod possibilitas dicat modum compositionis unientis extrema. | 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 Omittendo igitur longas et prolixas evasiones istarum improbationum, dico quod ista propositio signat unionem praedicati ƿcum subiecto, possibiliter, pro aliquo uno 'nunc' (licet illud 'nunc' sit indeterminatum), si talis ampliatio compositionis posset fieri virtute possibilitatis; non enim potest fieri ampliatio ad plura 'nunc' ut non notetur possibilitas compositionis pro aliquo uno 'nunc', sive extrema accipiantur pro eodem 'nunc' sive pro alio (puta, si 'sedens' accipiatur pro uno instanti, et 'stans' pro alio). In omni sensu, oportet quod possibilitas modificet ipsam compositionem unientem extrema pro aliquo uno 'nunc', tamen indeterminato. | 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 Ita in proposito est, quod notatur 'dividi' uniri continuo secundum signum, et pro quolibet eius, - et hoc pro aliquo 'nunc' indeterminato. Hoc autem est impossibile, quia quandocumque unitur sibi praedicatum pro aliquo vel aliquibus singularibus, necessario repugnat sibi pro aliis; necesse est enim - sicut dicit prima responsio - quod cum reductione potentiae (non tantum ad factum esse, sed ad fieri) stet alia potentia, non reducta nec ad actum facti esse nec etiam ad fieri, quia necesse est divisione exsistente 'in fieri vel facto esse' secundum a, aliquod continuum terminari per a, - et ita potentiam quae est in illa parte continui, non reduci ad actum. | 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 Sed si arguas quod quaelibet singularis est vera, ergo et universalis, - posset dici quod singulares sunt verae, non tamen ƿcompossibiles, et utrumque ad possibilitatem universalis requiritur. | 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 Contra: simul est haec vera 'continuum potest dividi secundum a et secundum b et c', et sic de quolibet alio singulari simul. | 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 Respondeo. Dico quod singulares propositiones de possibili, absolute sumptae, non inferunt formaliter universalem de possibili, sed est fallacia figurae dictionis 'a pluribus determinatis, ad unum'. Possunt enim singulares ex vi significationis unire praedicatum subiecto pro aliquo 'nunc', universalis autem unit praedicatum subiecto pro quolibet eius universaliter; et ideo proceditur ex forma significandi 'a pluribus determinatis, ad unum'. Ista est ratio quare de praemissa possibili pro aliquo 'nunc' et possibili pro alio 'nunc', non sequitur conclusio de universali possibili ut ƿnunc, quia praemissae illae non significant - ex forma sua - extrema uniri medio; et ideo non sequitur unio extremorum inter se, nec etiam possibilis est pro aliquo eodem. | 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'.[3] 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.[4] |
| 367 Et si dicas quod singulares sunt compossibiles accipiendo potentiam (sed non actum terminantem potentiam) pro eodem, puta 'simul est possibile dividi secundum a et secundum b' etc. (non tamen 'est possibile simul dividi secundum a et b' etc.), - arguo quod non oporteat possibilitatem dividi pro eodem, ad hoc quod universalis sit vera, quia singulares absolute enuntiantes praedicatum de singularibus sufficienter enuntiatis, inferunt universale absolute enuntians illud praedicatum; si tales singulares sunt verae, omnes, in se et absolute, - igitur et universalis. | 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 Et si quaeras qualiter accipiendae sunt singulares de possibili, ut sufficienter, - dico quod oportet eas accipi compositione specifica, pro eodem 'nunc' indeterminato: puta 'possibile est dividi secundum a pro aliquo nunc, et possibile est dividi secundum c et b pro eodem nunc', et sic de singulis; et tunc sequitur universalis, alias non. | 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 Et si arguas quod istae singulares sunt alterius universalis, puta istius 'possibile est continuum dividi secundum quodlibet signum, ƿsecundum unum nunc', quae formaliter differt ab alia, - respondeo quod differunt secundum vocem, quia hoc quod ista exprimit, hoc alia ex consignificatione verbi denotat, extrema uniri. | 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 Et si dicas quod etiam hoc modo, specificando praedicatum pro aliquo 'nunc' determinato vel indeterminato, nulla singularis repugnat alii, quia sicut possibile est dividi secundum a pro aliquo 'nunc', ita possibile est dividi secundum b pro eodem 'nunc', et ita de c, et ita de quolibet alio singulari (quia si aliqua repugnaret, aut esset illa quae reciperet punctum immediatum, aut mediatum: non illa quae accipit punctum mediatum, quia divisio secundum unum signum non impedit divisionem secundum aliud signum, etiam immediatum; nec secundum punctum immediatum, quia nullum est immediatum; igitur singulares, ut inducunt universalem istam ut nunc, sunt verae et compossibiles), - respondeo: dico quod cuilibet singulari acceptae vel acceptabili, nulla singularis determinate accepta vel acceptabilis repugnat indeterminata compositione pro eodem 'nunc', nec repugnant; tamen cuicumque acceptae repugnant infinitae indeterminatae, - et huius ratio repugnantiae assignata est prius, realis, ex incompossibilitate reductionis omnium potentiarum simul ad actum. ƿ | 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 Simile huius non habetur faciliter in aliis. Bene enim potest poni exemplum ubi quaelibet singularis est possibilis, et tamen universalis non est possibilis, quia aliqua una singularis alicui uni singulari est incompossibilis: sicut 'possibile est omnem colorem tibi inesse', hoc est impossibile, quia aliqua una singularis determinata alteri determinatae repugnat, sicut 'te esse album' repugnat huic 'te esse nigrum'. Tamen ponamus quod iste non possit portare lapides decem sed novem tantum (et sint illi lapides aequales), ista propositio 'possibile est omnem lapidem portari ab isto' est falsa; et non quia aliqua singularis sit in se falsa, nec quia aliqua singularis determinata sit alicui alteri determinatae incompossibilis, - sed aliquibus determinatis est aliqua indeterminata incompossibilis: quaecumque enim novem singularia sunt compossibilia, et decimum indeterminate est eis incompossibile. | 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 Et isto modo debet intelligi responsio Commentatoris suƿper I De generatione, qui dicit quod 'facta divisione in uno puncto, prohibetur fieri divisio in alio puncto': non quidem in aliquo determinato (signato vel signabili), sed in aliquo indeterminato. | 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,"[5] namely not indeed at any indeterminate point (marked or mark-able), but at some determinate one. |
| 373 Et tunc respondeo ad argumentum prius factum contra me, de mediato et immediato, quod scilicet sit contra eum. Dico igitur quod non est dandum divisionem fieri in aliquo immediato, sed in aliquo mediato: non tamen determinato (sive signato vel signabili), sed indeterminato, - quia quodcumque determinatum mediatum accipiatur, etiam posset divisio stare secundum illud signum simul cum divisione secundum istud signum; repugnabit tamen divisioni isti divisio secundum aliud signum mediatum, secundum aliquod scilicet quod non est in continuo determinato adhuc indivisibile. | 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 mark-able), 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 Si tamen quaeras de ista propositione 'possibile est continuum dividi secundum quodcumque signum', - ista potest concedi, quia 'quodcumque' non tantum est distributivum, sed etiam partitivum, ita quod ad veritatem universalis, cuius subiectum distribuitur per 'quodcumque', sufficit singillata attributio praedicati cuicumque singulari: ita quod non omni singulari simul, sed cuicumque indifferenter (non oportet quod aliis). 'Omnis' autem non sic significat, ƿsed significat subiectum simul accipi pro quolibet respectu praedicati. | 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 De hoc autem signo 'quilibet', est dubium utrum significet idem cum eo quod est 'omnis' vel cum eo quod est 'quicumque': utrum horum ponatur, dicendum est de isto sicut de illo cui aequivalet; cum enim de intellectu constat, non est vis facienda in nomine. | 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 Ad secundam probationem illius antecedentis dicitur quod 'indivisibile nihil est nisi carentia continui, ita quod nihil formaliter est instans nisi carentia successionis continuae, - et ita punctus est carentia longitudinis et nihil positivum dicit'. Et tunc neganda esset illa propositio quod 'successivum praecise habet esse, quia suum indivisibile sit'; immo praecise habet esse successivum, quia pars eius fluit, et numquam quia indivisibile eius sit aliquid positivum. | 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 Pro ista opinione videntur facere multa: Primo, quia posita sola ratione continui, circumscripto omni absoluto, - videtur esse terminatum, si non sit absolutum; nec videtur quod Deus possit separare finitatem a linea, nec - per consequens - punctum, quod non videtur esse probabile si punctus esset alia 'essentia absoluta' a linea. ƿ | 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 Similiter, si essent duae essentiae absolutae, non videtur possibile quod fieret unum aliquid ex istis, nisi unum accideret alteri: non enim sunt unum per identitatem perfectam, quia ponuntur duae essentiae absolutae; nec unum tertium, compositum ex se, quia neutrum respectu alterius est actus vel potentia. Indivisibile igitur habet esse et non esse absque generatione et corruptione, quia si est tantum in medio lineae continuae, est tantum unus punctus, - divisa autem ipsa, sunt duo puncta in actu; igitur est ibi aliquis punctus qui prius non fuit, - et sine generatione, quia non videtur probabile quod generans generaverit ibi aliquam essentiam absolutam. | 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 Similiter, de figura incisionis videtur - per auctorem Sex principiorum - quod non sit aliquid positive dictum, et tamen est ibi superficies in actu, quae prius non fuit in actu. | 379. Likewise, it seems, from the author of Six Principles about the figure of an incision,[6] that this is not something said positively, and yet there is a surface there in actuality that was not in actuality before. |
| 380 Sed contra istud: Tunc sequitur quod generatio substantiae quae non est per se terminus continui, nihil erit (vel saltem in nihilo), quia non est eius aliqua mensura positiva; et ita est de illuminatione, et de omnibus mutationibus subitis quae non sunt per se termini motus. Et licet possit evadi de mutationibus quae sunt termini motuum et fiunt in instanti (sicut nihil in nihilo vel privatio continuitatis in privatione continuitatis), tamen de istis videtur absurdum, quia non sunt per ƿse termini continuitatis alicuius continui, quia nihil sunt alicuius continui, nec positive nec privative. | 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 Praeterea, secundum Philosophum I Posteriorum ratio lineae est ex punctis, - hoc est, in ratione essentiali lineae cadit punctus, qui dicitur de linea primo modo dicendi per se; nulla autem privatio pertinet per se ad rationem alicuius positivi; ergo etc. | 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 Ex eodem etiam sequitur quod si punctus tantum est privatio, quod etiam linea tantum erit privatio, - et superficies et corpus; semper enim terminatum definitur per terminans, et positivum non includit essentialiter privationem. | 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 Similiter, sequitur idem (propter aliud), quod linea tantum erit carentia latitudinis et superficies tantum erit carentia profunditatis; et tunc non erit nisi unica dimensio quae poneretur corpus, cum tamen illa dimensio quae dicitur 'profunditas' posset alio respectu dici 'latitudo' (istae enim tres dimensiones distinguuntur per imaginationem trium linearum, intersecantium se in eodem puncto). | 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 Et ex hoc ulterius infertur inconveniens, quod si superficies est tantum privatio profunditatis, quomodo punctus erit privatio priƿvationis? Nihil enim videtur privare privationem nisi sit formaliterpositivum. | 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 Praeterea, secundum superficiem insunt multae qualitates corporales vel sensibiles, ut videtur; igitur non tantum est privatio. Antecedens probatur de coloribus et figuris, quorum utrumque est per se visibile, et per consequens 'positivum'. Figura etiam propriissime sequitur speciem, et ideo videtur 'accidens manifestativum' esse speciei; non autem videtur probabile non esse entitatem positivam talis consequentis speciem naturaliter et manifestantis eam. | 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 Si aliter dicatur quod 'indivisibile, per quod successivum habet esse, tantum est in potentia', - hoc non iuvat: quia eo modo quo habet esse in toto, quando cedit, quaero quid succedit sibi? Si aliud indivisibile, stat argumentum; si non, tunc successivum non erit. | 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 Respondeo ad argumentum, quod eo cedente succedit pars continua fluens, et non indivisibile; nec aliquid immediate, nisi sicut continuum est immediatum indivisibili. | 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 Et si obiciatur 'ergo non semper habet tempus esse uniformiter et aequaliter (quia quando illud instans positum est, tempus est, quia suum indivisibile est, - transacto illo, immediate non est, quia aliud eius indivisibile non est)', - respondeo: sicut linea non habet ƿuniformiter esse ubique prout 'ubique' distribuit pro partibus lineae et indivisibilibus lineae (quia in istis habet esse ut in partibus et in illis ut in ultimis), et tamen ubique est uniformiter secundum quod 'ubique' distribuit praecise pro istis vel praecise pro illis, ita est in proposito: si 'semper' distribuit praecise pro indivisibilibus vel praecise pro partibus, tunc uniformiter habet esse, sed si pro utrisque simul, non habet esse uniformiter. | 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 Ad probationes alterius antecedentis, de partibus minimis, respondeo. Ad primam, quod Philosophus contra Anaxagoram habet satis si, per ablationem a toto, minoretur totum, ita quod non semper possit de eo aequale subtrahi; oportebat enim Anaxagoram dicere (sicut imponebat ei Aristoteles) quod facta segregatione a carne cuiuslibet generabilis de carne, quod adhuc remaneret caro tanta ut ex ea posset ulterius segregari quodcumque generabile: et hoc est impossibile, quia quantumcumque caro posset in infinitum dividi et minorari, saltem non maneret tanta ut posset ex ea quodcumque generabile generari, quia generabile quodcumque requirit determinatam quantitatem illius ex quo generatur (maxime ƿsi generatio sit tantum segregatio vel motus localis, quod imponitur Anaxagorae, et ultra omnem quantitatem illam ex qua generatur, minoretur caro per continuam segregationem aliorum ex ipsa). Non igitur propter intentionem Aristotelis ibi, oportet ponere minimum in naturalibus etiam separatum, per se exsistens, nec in toto. | 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 Ad illud Philosophi De sensu et sensato dico quod passiones sunt divisibiles quantumcumque, ita quod non posset 'quantum' dividi nisi divisa passione; et tamen non dividitur in infinitum in quantum sensibilis (id est, in quantum est perceptibilis a sensu), sicut ipse vult ibi quod 'pars quantumcumque minima potest esse sensibilis virtute, licet non actione': hoc est quod ipsa in toto potest cooperari aliis partibus ad immutandum sensum, - et tamen licet posset fieri divisio in eam etiam per se exsistentem, non tamen immutaret sensum. Et tunc patet ad argumentum eius - quod adducitur in oppositum - quod 'sensus crescit in infinitum, si apponatur' etc.: verum est, si sensibile, in quantum actu perceptibile a sensu, posset dividi in infinitum, - non autem sequitur si illud quod est sensibile, potest dividi in infinitum. ƿ | 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 Ad illud de II De anima patet quod loquitur de quantitate augmentabilis et deminuibilis; quod concedo, quia illa quantitas quae est quantitas cuilibet naturali perfecta, est determinata in maius et minus, loquendo de illa quantitate in qua naturaliter producitur, aut saltem in minus, in animatis, loquendo de illa quantitate ad quam procedit deminutio. Tamen Philosophus non loquitur ibi nisi de termino magnitudinis et augmenti; et ideo praecise in loco illo intelligit Philosophus quod quantitas perfecta cuiuslibet naturalis est determinata in maius, - ex quo habet propositum suum quod intendit probare, scilicet quod ' ignis non est principium augmentationis in aliqua generatione vel in aliqua specie': oportet enim principale agens in aliqua specie, esse determinatum ad quantitatem perfectam illius speciei, ut illam solam producat et non ultra; ignis autem non est determinatus ad quantitatem determinatam in aliqua specie, quia - quantum est ex se - produceret maius quantum, quia crescit in infinitum si apponantur combustibilia in 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 Et cum probatur illud antecedens de minimo per hoc quod 'conƿtingit accipere primum in motu', - posset negari consequentia, quia illi qui dixerunt 'primum' in motu, dixerunt mutationem esse istam partem motus; tamen nego 'primum' utroque modo (et primum motum et primam mutationem), quia Philosophus VI Physicorum ex intentione ostendit oppositum, scilicet quod omne moveri praecedit mutatum esse, in infinitum, et e converso. | 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 Et persuadetur hoc sic: quia si ignis causaret aliquid primum in motu, pari ratione posset causare aequale illi, simul cum eo, immediatum. Et ita aut necesse esset fingere quod inter primum 'simul causatum' et secundum - illi aequale - causatum, oporteret agens quiescere, et ita motus componeretur ex motibus et quietibus intermediis; aut oporteret agens, post primum inductum, inducere totum habitum successivum, - quod videtur valde irrationabile, quia cum sit aequalis virtutis et aeque approximatum passo, sicut potest aliquem gradum simul causatum (primum) simul inducere, ita illo inducto potest simul inducere ipsum totum, et ita componeretur totus motus immediate ex mutationibus immediatis, vel ex mutationibus - sive motibus et quietibus - intermediis. | 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 Est ergo iste processus. Sit forma sub aliqua mutatione corrumpenda per motum, puta in alteratione, sub calore in esse quieto. ƿHuius - inquam - mutationis est accipere ultimum, scilicet immutationem terminative, quia mobile se habet nunc indivisibiliter ut prius divisibiliter, et hoc 'immutari' - sicut 'mutari' - est aliter se habere nunc indivisibiliter quam prius divisibiliter. Ideo autem est sub forma eadem - sub qua quievit - in instanti mutationis, quia tunc agens quod debet ipsum movere, nihil egit prius, nec nunc agit circa ipsum. Ab isto instanti incipit movere illud mobile, et hoc successive: vel propter partes mobilis, quia nulla pars 'mobilis' est aeque propinqua agenti, sed pars propinquior alteri parti, in infinitum (solus punctus 'mobilis' est se toto immediatus agenti, et ille non est mobilis); sive propter partes formae secundum quas debet esse motus, quarum quaelibet ante aliam est inducibilis a movente praesente, quia ratio extrinseca propter quam minimum non posset esse per se in naturalibus, est praesentia corrumpentis, - haec autem tollitur propter praesentiam agentis, corrumpentis omne corruptivum sui effectus. | 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 Ab illo ergo instanti mutationis continue remittitur calor qui infuit, et acquiritur frigus. Non enim est verisimile quod sit solus motus remissionis usque ad aliquod instans, et tunc primo inducatur aliquid frigoris: vel enim calor remittendus haberet ultimum sui in esse (quod negat Philosophus VIII Physicorum), - vel si non, saltem frigus immediate sequens ipsum haberet primum sui, ƿet tunc esset prima mutatio motus infrigidationis, quod est ita inconveniens sicut de prima remissione motus caloris. Inconveniens etiam videtur quod agens remittat calorem nisi causando in ipso aliquod incompossibile secundum aliquem gradum, et secundum quod causat illud in maiore vel minore gradu, corrumpit gradum et gradum ipsius exsistentis; hoc autem vult Aristoteles manifeste VI Physicorum, quod omne quod movetur, habet aliquid utriusque extremi, - et videtur manifestum ad sensum quod aquae successive calefaciendae aliquid caloris inest, manente adhuc frigiditate et non adhuc totaliter corrupta. | 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 Currunt igitur simul, ab instanti mutationis, motus remissionis caloris et motus intensionis frigoris, - quorum neutrius est aliquid primo et in aliquo instanti in quo per mutationem subitam inducitur aliquis gradus frigoris omnino incompossibilis calori: in illo primo, calor non est, et usque ad illum calor fuit, - ita quod calor nullum ultimum sui esse habet, sed habuit ultimum in esse quieto; et frigus nullum primum habet simpliciter sui esse, licet habeat in esse quieto (scilicet quod accipit per mutationem, licet illud non sit quies). | 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 Cum ergo probatur per Philosophum VIII Physicorum, dico quod intentio Philosophi est ista, scilicet probare quod non omnia semper moventur. Et contra eos qui dicunt 'omnia semper ƿmoveri', dicit quod manifeste convincuntur si consideremus illos motus ex quibus movebantur: moti enim erant - ad hoc ponendum - ex augmentatione et deminutione animatorum, quam viderunt fieri in aliquo magno tempore (puta in anno), et tamen ex illo in nullo concludebant quod illa fiebant in toto tempore et in nulla parte temporis perceptibiliter. Quibus Aristoteles obviat quod bene potest tale mobile quiescere per aliquod tempus et in parvo tempore aliquo moveri, ita quod non oportet semper moveri illo motu; et probat hoc per exemplum de guttis cavantibus lapidem, quae in aliquo certo numero cadunt et nihil auferunt de lapide, - tandem tamen una cadens (sit centesima), aufert in virtute omnium aliquam partem lapidis, quae tota simul aufertur et non pars ante partem. ƿ | 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.[7] |
| 398 Per hoc non intendit Philosophus quod ista ablatio partis sit in instanti et ita tota simul, nam ista ablatio est motus localis (et ita motus est localis), quod nullo modo potest fieri nisi pars mobilis prius pertranseat spatium quam totum mobile; sed ista una pars lapidis - quae aufertur per ultimam guttam in virtute omnium praecedentium - licet successive auferatur, tamen ablatio eius non est successiva, correspondens toti successioni casus guttarum: non enim quot erant guttae cadentes, tot erant partes huius ablationis partis a lapide, sed tota ista parva pars per ultimam guttam aufertur, licet successive. Negat igitur Philosophus successionem huic correspondentem, scilicet toti casui successionis guttarum, ac per hoc ille lapis motus non semper movebatur, licet quando movebatur per ultimam guttam, tunc successive movebatur. | 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 Et secundum istam intentionem subdit postea de alteratione quod 'non est necesse quod propter hoc sit tota alteratio infinita, frequenter enim velox'. Ubi habet translatio Commentatoris ((subito)), pro ((velox)) in nostra translatione; exponit autem 'subito': ((id est in instanti)), - et ((non in tempore)), inferendo. Quae expositio est litterae contraria: quod patet ex translatione ƿnostra 'frequenter enim velox', et ex translatione sua quae habet 'subito', - quia in IV Physicorum, ubi translatio nostra habet ((repente)), sua translatio habet ((subito)); et notificatur ibi quod 'illud dicitur fieri subito, quod fit in tempore imperceptibili', - et ita exponit ipse ibi. Ergo exponere 'velox' vel 'subito' per instans, est exponere tempus per instans. | 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 Sed intentio Philosophi est ista, quod non oportet quod sicut alterabile est divisibile in infinitum, quod ita tempus in infinitum correspondeat alterationi alterabilis, - sive semper, dum alterabile est, quod pars eius post partem continue alteretur, sicut posset esse successio ex ratione partium alterabilis; sed 'frequenter alteratio est velox sive subito', id est quiescente illo alterabili, - et tunc non sunt simul (neque secundum primam mutationem, neque secundum primam partem motus), sed successive. | 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 Et hoc est quod subdit statim ratio apposita a Philosopho ad eandem conclusionem, quod scilicet quando quis sanatur, sanatio est in tempore, ((et non in termino temporis)); et tamen mobile non semper movetur isto motu, quia iste motus finitus est, ƿinter duo contraria. - Quomodo ergo acciperet ipse in praecedente ratione 'alterationem fieri in instanti', ad hoc ut probaret 'non omnia esse in motu'? Et in ista secunda ratione accipit oppositum, scilicet quod sanatio 'non est in termino temporis, sed in tempore', et tamen ideo 'non semper', quia est inter contraria! Et ideo, acquisito illo contrario, cessat motus. | 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 Subdit igitur Philosophus quod ((dicere 'omnia continue moveri', multum ambigere est)) (ubi 'continue' accipitur pro 'semper', quia illud membrum secundum divisionis quinquimembris improbat per omnia ista). Et adhuc etiam ponitur expositio ulterior ibi, quia 'lapis manet durus'; igitur non alteratus. | 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 division[8]). And yet too a further exposition is there posited, because 'stones remain hard'; so they do not undergo alteration. |
| 403 Non igitur ex aliquo quod hic dicit, negat totam sententiam suam in VI Physicorum; et dato quod hic esset aliquod verbum quod expresse hoc videtur sonare (licet nullum sit nisi ex falso intellectu sumptum), magis tamen esset exponendum secundum illud quod hic dicitur, quam totum istud quod est principale hic, ƿalibi retractare, propter aliqua quae dicuntur alibi non ita principaliter nec ex intentione sicut hic. | 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 Ad aliud, De sensu et sensato, dicetur in argumento ultimo huius distinctionis. | 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 Ad rationem de contradictoriis dicitur quod illa sunt contradictoria quae sunt accepta pro eodem tempore (et secundum alias condiciones requisitas), et illa non sunt contradictoria quae non sunt accepta pro eodem tempore, - quod probatur per definitionem contradictionis, positam I Elenchorum; et ideo non esse caloris ut praecessit in ultimo instanti mutationis, et esse caloris susceptum in tempore habito, non sunt contradictoria respectu caloris. | 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 Contra: esse caloris et non esse, absolute sumpta (non prout sunt intellecta in eodem instanti), sunt incompossibilia simpliciter, ita quod quia sunt incompossibilia simpliciter, non possunt esse in eodem instanti, - non e converso; et ratio huius incompossibilitatis 'pro eodem instanti' non est alia nisi quia formaliter sunt opposita, nulla alia oppositione formaliter quam oppositione contradictoria. | 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 Confirmatur hoc per simile in aliis, quia contrarium succedens ƿcontrario, vere est ei contrarium, licet non sint simul in eodem instanti; similiter, forma ut terminus 'ad quem' privationis, vere opponitur sibi privative, - et est iste motus inter opposita formaliter. Unde Philosophus I Physicorum et V vult quod omnis motus sit inter opposita contraria vel privativa vel media inter haec, et tamen ista ut sunt termini transmutationum, numquam simul sunt. | 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 Posset etiam argui quod creationis termini non essent contrarii, quia non esse quod praecedit esse creati, non potest esse contrarium nec privativum nec medium inter haec, quia in nullo susceptivo est, - et sic non esset contradictorium ei. Creatio igitur non esset inter contradictoria vel contraria, quod videtur absurdum. | 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 Quod autem adducitur de definitione contradictionis, aequivocatio est, quia alio modo est contradictio in complexis et alio modo in incomplexis. Complexa non sunt contradictoria nisi accipiantur pro eodem instanti, pro quo oportet illa ambo enuntiare praedicatum de subiecto, - incomplexa autem absolute sumpta, non determinando ad aliquod esse, sunt contradictoria. De contradictione prima loquitur Philosophus in Perihermeneias, de secunda in Praedicamentis. ƿ | 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 Aliter respondeo ad argumentum quod 'immediatum' potest accipi dupliciter: uno modo inter quod 'secundum se totum' et aliud non est medium, alio modo quod 'secundum se totum' est statim cum altero vel post alterum. Primo modo, 'continuum' est immediatum suo termino, quia inter indivisibile terminans et divisibile terminatum nihil cadit medium. Secundo modo, indivisibili terminanti continuum nihil est immediatum: nihil enim 'secundum se totum' statim sequitur illud indivisibile, sed pars illius totius; quod est immediatum totum primo modo, sequitur indivisibile secundum partem ante partem, in infinitum. | 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 Ad propositum igitur dico quod sicut mensurae istae se habent, ita et mensurata, scilicet quod quando unum contradictorium mensuratur indivisibili et aliud mensuratur divisibili. Et tunc minor est falsa: nullum enim est medium inter contradictorium 'secundum quod est in tota sua mensura' et contradictorium aliud, sicut nec inter mensuram suam totam et mensuram illius alterius; contradictorium tamen quod mensuratur indivisibili, non est alicui immediatum, ita quod secundum aliquod esse sui (secundum quod videlicet est in mensura sua) statim reliquum contradictorium sequatur. Ita dico in proposito quod non esse fuit in indivisibili, esse ƿautem formae inductae per motum est in toto tempore habito, - et ideo nullum est medium inter illa; et tamen quod sequitur in tempore, non est immediatum - secundo modo - praeexsistenti in instanti. | 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 Ad tertium argumentum principale quaestionis, quando arguitur quod 'angelus non posset moveri, quia est indivisibilis': Quamvis posset faciliter responderi quod angelus occupat locum divisibilem, et ideo respectu loci se habet ac si esset divisibilis, - aut si occupat locum punctalem ut punctaliter exsistens, non potest moveri continue ut semper habeat esse punctale, - tamen quia non videtur ratio quare negatur indivisibile moveri (etiam si esset indivisibile quantitatis, per se exsistens), ideo potest concedi quod angelus, habens 'ubi' punctale, potest continue moveri ut in puncto semper exsistens. | 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 Et istud quod assumptum est de indivisibili, probatur multipliciter: Primo, quia sphaera mota super planum, describit lineam in plano, et tamen non tangit nisi in puncto; igitur illud punctum pertransit totam lineam, et tamen non propter hoc linea quae sic petransitur a puncto, componitur ex punctis. Ergo a simili, nec hoc sequeretur si punctus esset per se. | 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 Hic respondetur multipliciter: Quod non est 'sphaericum' in natura, sed tantum in intellectu ƿvel imaginatione. - Sed hoc nihil est, quia caelum est simpliciter sphaericum; et tamen dato quod non esset aliquid simpliciter sphaericum in natura, adhuc non est contradictio ex parte sphaerae et plani quod hoc super illud moveatur ut sphaera super planum (esset autem contradictio, si ex motu indivisibili super aliquid, sequeretur ipsum esse indivisibile). | 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 Aliter dicitur quod naturalis sphaera tangit planum in linea, non in puncto. - Sed hoc videtur impossibile, quia quod applicatur lineae circulari (ita quod eam totam contingit), necessario est circulare, quia quaelibet pars 'circularis' est in qualibet parte circularis; rectae autem lineae nulla pars est circularis vel curva. | 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 Aliter dicitur quod, quia punctus ille per accidens movetur, ideo non oportet quod commensuret sibi spatium super quod movetur; sphaera autem ipsa per se movetur, et est divisibilis. - Sed contra istud, quia quamvis pars in toto moveatur per accidens, tamen semper est in spatio sibi aequali, et - pertranseundo - illa describit totum spatium; immo si albedo (quae magis movetur per accidens, moto quanto, quam aliquid quod est pars vel terminus quanti) secundum quantitatem suam quam habet per accidens, comparetur ad spatium, adhuc quantitas eius accidentalis commensuraretur spatio. Unde non videtur quod - quantum ad comƿmensurationem - aliquid auferat 'moveri per accidens' aliter quam 'per se moveri'. | 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 Item, ista linea supposita non commensuratur sphaerae (quia tunc esset corpus), et commensuratur alicui moto super ipsam; igitur tantum puncto moto super eam. Si etiam ponatur sphaeram esse in vacuo et solam lineam esse plenam, et per impossibile sphaera posset moveri in vacuo et iste punctus super lineam plenam, ista linea plena non describeretur praecise nisi ex puncto illo. Et ideo sequitur propositum ex istis. | 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 Praeterea, accipiatur corpus cubum, et moveatur. Superficies prima eius semper est in aliquo sibi aequali, et ita in superficie. Vel correspondet sibi aliquid in magnitudine supposita, puta linea, - et sic, pertranseundo semper prius aliquid magnitudinis quam aliud, pertransit totam magnitudinem; igitur tota magnitudo supposita componitur ex linea, si ratio illorum valeat. | 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].[9] |
| 419 Praeterea, signetur primus punctus in linea, super quam alia linea movetur. Iste punctus in linea supposita describit totam lineam motam, quia sicut semper quicumque punctus lineae motae est continue in alio et alio puncto lineae suppositae, - ita et e converso quicumque punctus lineae suppositae supponitur alii et alii lineae motae; et tamen, cum omnibus istis, stat continuitas motus. ƿ | 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 Potest ergo concedi (cum non videatur nisi fuga dictum illud de moveri per accidens) quod indivisibile posset per se moveri si per se esset, et tamen continue; nec ex hoc sequitur magnitudinem pertransitam esse compositam ex indivisibilibus. | 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 Propter tamen intentionem Aristotelis qui allegatur, oportet intelligere quod in motu locali est successio ex duplici causa, videlicet ex divisibilitate mobilis et ex divisibilitate spatii, - quarum utraque causa, si esset per se et praecisa, esset sufficiens ratio successionis: nam quodlibet mobile prius pertransit unam partem spatii quam aliam, et ita esset successio ex parte spatii, comparando idem ad diversas partes eius; quodcumque etiam idem in spatio, prius pertransit primam partem in mobili quam secundam, et ita esset successio ex parte mobilis, comparando ad quodcumque idem in spatio. Ita etiam posset assignari in motu alterationis, et forte in motu augmentationis. | 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 Negat igitur Philosophus, et bene, quod indivisibile 'quantum est ex se' non potest moveri vel movere, ita quod ex parte eius possit accipi continuitas motus, ita quod sit 'mobile' habens in se completam rationem mobilis continui, quia non habet in se quod continue moveatur; non tamen est illud cui repugnat continue moveri vel movere, accipiendo ab alio continuitatem motus. | 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 Et istud concludunt rationes suae, et non plus, sicut patet discurrendo per omnes: ƿCum enim primo accipit quod 'omne quod movetur, partim est in termino a quo et partim in termino ad quem', verum est quidem, si sit tale mobile ex cuius ratione sit successio motus; tale enim 'mobile' est secundum partem et partem sui in termino et termino. Et tamen hic non est ita, sed secundum idem sui est partim in termino uno et partim in termino alio, - hoc est in aliquo medio, non quiescendo sed in quantum est aliquid utriusque, hoc est in quantum est per quod tendit ab uno ad alterum: hoc est dictu, quod est sub mutatione et sub aliquo subiacente mutationi, et sic continuat partes motus. - Cum autem accipitur quod 'indivisibile non potest esse partim in uno termino et partim in alio termino, quia non habet partes', verum est de prima partibilitate (et ideo concludo quod sic non est mobile, et concedo), falsum autem est de secunda partibilitate. | 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 Ad aliud, cum dicitur quod 'prius pertransit - mobile - aequale vel minus, quam pertranseat maius', respondeo et dico quod 'pertransiri' potest accipi pro pertransitione divisibili, vel pro indivisibili. Si pro indivisibili, propositio est falsa si intelligitur quod ante omne pertransire maius, universaliter pertranseat indivisibiliter aequale; tunc enim oporteret concedere quod esset dare primam ƿmutationem in motu locali, quod etiam nec ipsi perversores (non expositores!), dicentes ipsum retractare quod dixit in VI Physicorum, possunt rationabiliter dicere quod in ipso VI contradicat sibi ipsi. Non igitur oportet quod omnem pertransitionem successivam, quae est maior ipso mobili, praecedat pertransitio indivisibilis. Si autem intelligat de pertransitione divisibili, tunc posset intelligi non de toto ratione totius, sed ratione partis: et hoc, non comparando partem ad 'ubi' sibi aequale et totum ad 'ubi' sibi aequale, quia continuum est 'cuius motus est unus et indivisibilis', ex V Metaphysicae; et ita simul pertransit pars spatium sibi correspondens, et totum mobile totum spatium sibi correspondens. Sed intelligendo respectu alicuius certi et determinati puncti in spatio, prius pertransit - totum - ratione partis alicuius illud punctum (et in hoc quod pertransivit illud, pertransivit aliquid minus se, loquendo de 'ubi' alio a suo primo 'ubi' totali) quam sic pertranseat aequale vel maius; et hoc est per accidens, in quantum mobile potest habere 'ubi' minus suo totali 'ubi'. | 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 Sed si loquamur de 'ubi' maiore et minore et aequali secundum quae attenditur immediate continuitas motus (quorum infinita sunt aliquid primi 'ubi'), simpliciter prius pertransit maius se quam aequale sibi. Ad propositum igitur, salvando illud quod est de per ƿse ratione motus continui, non illud quod non est de per se ratione eius! | 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 Et si obicias quod quidquid sit de ratione Aristotelis in se, semper iste punctus est in spatio sibi aequali, et sic pertransit totum (igitur commensurat totam lineam suppositam, et ita illa linea supposita erit composita ex punctis), - dico quod 'semper', id est in quolibet indivisibili, est in spatio sibi aequali; non autem 'semper', id est in qualibet parte temporis. Idem posset argui de superficie prima corporis cubi, quod licet in quolibet 'nunc' temporis superponatur praecise lineae super quam movetur, tamen in tempore medio inter duo instantia, fluit super continuum medium inter illa extrema. | 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 Ad ultimam rationem bene concedo quod omni tempore dato contingit accipere minus tempus, sed ex hoc non sequitur in illo minore tempore posse moveri minus mobile, nisi loquendo de mobili continuo, quod erat ex parte sui causa continuitatis motus. | 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 Ad quartum argumentum principale, de causa successionis in motu, dico quod licet posset fieri contentio et altercatio de intentione Averrois et in quo contradicit Avempace (sicut apparet IV Physicorum cap. 'De vacuo'), breviter tamen dico quod causa successionis in quocumque motu est resistentia mobilis ad motoƿrem; non quidem talis quod movens non possit vincere mobile (tunc enim non moveret ipsum), sed nec etiam talis quod mobile reinclinetur ad oppositum (quia sic est praecise in motu violento), sed talis resistentia, quod mobile semper est sub aliquo cui non potest immediate succedere terminus intentus a movente. Et ista resistentia 'mobilis ad motorem' est propter defectum virtutis moventis, - et cum hoc, propter resistentiam medii ad movens et mobile, per quod 'medium' potest intelligi omne illud quod necessario praecedit inductionem termini inducendi. Sed tale medium non est necessario 'medium' nisi virtuti limitatae; si enim esset virtus infinita, posset ponere mobile statim in termino 'ad quem', - ita quod nec propter formam oppositam termino 'a quo' (quam mobile iam haberet), nec propter media naturaliter ordinata inter illam formam quam habet mobile et terminum 'ad quem', esset necessitas quod tale movens prius moveret per talia media, quam induceret terminum. | 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 Possibilitas igitur successionis est ex resistentia mobilis ad motorem, quae est ex resistentia medii ad mobile et ad motorem, ita quod haec est una resistentia. Mobile enim in quantum habet talem formam, inter quam et terminum nata sunt esse talia media, potest continue moveri per illa ad terminum, - et per ista media, quae resistunt mobili ut possit non statim esse in termino, potest intelligi divisibilitas partium mobilis vel divisibilitas partium formae secundum quam est motus, vel utraque simul. Necessitas taƿmen successionis numquam est ex ista resistentia, sed praecise comparando illam ad agens, cui mobile resistit propter istam resistentiam medii ad ipsum, - ita quod, sicut erat possibilitas ex sola resistentia medii ad mobile, ita virtus illa limitata non possit tollere istam resistentiam; et ideo resistit ista resistentia agenti, ne statim inducat terminum. | 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 Tunc ad illa quae adducuntur ad oppositum, scilicet quod 'angeli ad se nulla est resistentia', - dico quod ex quo agit non ex infinitate virtutis activae quando est in caelo, inter quod 'ubi' et suum 'ubi' in terra nata sunt esse multa media, quae etiam virtuti suae motivae sunt media, - ita nec virtus sua motiva potest omnia illa media facere et terminum, nec etiam potest statim terminum facere nisi prius faciendo illa media; et ideo est hic resistentia tota quae requiritur ad successionem in motu. | 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 Et cum arguitur de dicto illius Averrois, de gravi 'si ponatur in vacuo, quod descenderet subito, propter defectum resistentiae a parte medii', - dico quod si vacuum ponitur, grave non moveretur (secundum Philosophum), quia vacuum non posset cedere gravi et dimensiones separatae non possent esse simul. Tamen si poneretur vacuum posse cedere et esse spatium, et non quod latera pleni essent simul (quia tunc non esset vacuum), - dico tunc ƿquod motus gravis esset successive in vacuo, quia prior pars vacui prius esset et etiam totum grave prius pertransiret hanc partem spatii quam illam; et, sicut dictum fuit prius in secundo argumento, modo 'per se successio' est in motu locali et in spatio in quantum quanto. | 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 Ad argumenta Aristotelis, in quantum adducuntur ad propositum: Dico quod illa propositio 'quae est proportio medii ad medium' etc., vera est (ceteris paribus), et ideo sequitur motum non esse in vacuo, - aut saltem vera est contra illos qui posuerunt vacuum esse totam causam motus vel successionis in motu; sed ad propositum, arguendo similiter hic de mobilibus sicut ibi de spatiis, ista propositio potest negari 'quae est proportio mobilis ad mobile in subtilitate, eadem est proportio motus ad motum in velocitate'. Et si accipias 'quae est proportio huius sub ratione qua mobile, et illius sub ratione qua mobile', concedo, sed tunc est minor falsa; angelus enim mobilis est continue in quantum habet virtualem quantitatem, secundum quam potest coexsistere loco quanto, sicut corpus secundum quantitatem suam potest consistere in loco quanto. ƿ | 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 Similiter, quod Philosophus infert ex secunda ratione sua, quod 'motus sit in aequali tempore per vacuum et plenum', - si inferatur aliquid illi simile, scilicet quod in aequali tempore moveretur angelus et corpus, non est impossibile; ibi autem est impossibilitas ex ratione mediorum, secundum quod videtur ratio huiusmodi procedere. | 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 Sed dato quod rationes Aristotelis non multum concluderent ad propositum (quia non ita se habent hic mobilia sicut ibi spatia), valent tamen rationes suae simpliciter, ita quod maior sua ostensiva et reliqua ducens ad impossibile3. | 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 Respondeo igitur quod si vacuum posset cedere et motus posset esse in eo, dico quod ex divisibilitate spatii motus haberet divisibilitatem et successionem, sicut modo ex divisibilitate spatii pleni motus habet per se successionem essentialem; sed ultra istam successionem potest addi velocitas vel tarditas, ratione condicionis accidentalis ipsius medii (in quantum est promotivum vel impeditivum ipsius motus), sive ratione subtilitatis (per quam promovet, aut saltem non impedit), aut densitatis oppositae. Tunc igitur fieret motus successionis in vacuo, et esset proportionabilis motui in pleno, - et hoc, loquendo de successione essentiali; non de velocitate et tarditate superaddita, quia omnino nullam velocitatem ƿaut tarditatem superadditam haberet mobile in vacuo (haberet autem aliquam in pleno, sed 'nihil' ad aliquid non est proportio). | 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 Praecise ergo habet Aristoteles ex hoc - contra adversarium dicentem motum esse in vacuo - quod nullus motus, habens aliquam velocitatem vel tarditatem superadditam successioni essentiali, posset esse in vacuo. Et hoc non esset inconveniens, si poneret praecise motum esse in vacuo, - sed esset, si cum hoc poneret 'vacuum' medium promotivum in motu (vel medium necessarium in motu), ex parte cuius sumeretur velocitas vel tarditas motus. | 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 Eodem modo, illud quod infert in secunda ratione, non est impossibile adversario dicenti praecise motum esse in vacuo, quia medium plenum potest aequari medio vacuo in quantum est ratio vel causa successionis in motu essentialis; et si aliquod plenum acciperetur in tali proportione in quali accipit Aristoteles ad motum datum, illud esset omnino neutrum (nullam qualitatem accidentalem dans), nec medium plenum, nec medium vacuum. | 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 Quid igitur habet Philosophus contra adversarium ex illa ratione? - Dico quod habet tantum quod vacuum nullam qualitatem accidentalem habet ultra successionem essentialem; quia si sic, posset dari aliquod medium aequale, et tunc per medium plenum ƿet vacuum fieret motus in tanto tempore quantum correspondet illi condicioni accidentali motus, quod est impossibile, - quia si hoc, media essent proportionalia. | 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. |
Notes
- ↑ 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.
- ↑ 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."
- ↑ 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."
- ↑ 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.
- ↑ 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."
- ↑ 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."
- ↑ 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.
- ↑ Aristotle 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.
- ↑ 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.
