Edward Ockham: /* Chapter 10 */

2015-02-21T23:08:39Z

Chapter 10

Edward Ockham: Created page with "==Chapter 10== {| border=1 cellpadding=10 !valign = top width=45%|Latin !valign = top width=55%|English |- valign = top |{{ln|bk1066a35}} ''Infinitum autem''..."

2014-03-13T20:14:40Z

Created page with "==Chapter 10== {| border=1 cellpadding=10 !valign = top width=45%|Latin !valign = top width=55%|English |- valign = top |{{ln|bk1066a35}} ''Infinitum autem''..."

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==Chapter 10==
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|{{ln|bk1066a35}} ''Infinitum autem'' aut quod impossibije pertransire eo quod non sit natum pertransiri, quemadmodum vox invisibilis, aut pertransitionem habens imperfectam aut quod vix, aut quod {{ln|bk1066b1}} natum est habere non habet pertransitionem aut terminum;

|'''Chapter 10'''. The infinite is either that which is incapable of being traversed because it is not its nature to be traversed (this corresponds to the sense in which the voice is ''invisible'' ), or that which admits only of incomplete traverse or scarcely admits of traverse, or that which, though it naturally admits of traverse, is not traversed or limited;

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|adhuc appositione aut ablatione aut ambo.

|further, a thing may be infinite in respect of addition or of subtrac['''66b''']tion, or both.

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|''Separabile quidem'' itaque ipsum aliquid ens non possibile esse. Si enim neque magnitudo est neque multitudo, substantia autem ipsum infinitum et non accidens, indivisibile erit; quod enim {{ln|bk1066b5}} divisibile aut magnitudo aut multitudo. Si autem indivisibile, non infinitum, nisi sicut vox inuisibilis; sed non sic dicunt neque nos quaerimus, sed tamquam impertransibile.

|The infinite cannot be a separate, independent thing. For if it is neither a spatial magnitude nor a plurality, but infinity itself is its substance and not an accident of it, it will be indivisible; for the divisible is either magnitude or plurality. But if indivisible, it is not infinite, except as the voice is invisible; but people do not mean this, nor are we examining this sort of infinite, but the infinite as untraversable.

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|Adhuc quomodo contingit per se esse infinitum, si non et numerus et magnitudo, quorum passio infinitum?

|Further, how can an infinite exist by itself, unless number and magnitude also exist by themselvess-since infinity is an attribute of these?

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|''Adhuc si'' secundum acci{{ln|bk1066b10}}dens, non utique erit elementum entium in quantum infinitum, quemadmodum neque inuisibile loquele, quamvis vox inuisibilis. Et quod non est actu esse infinitum, palam; erit enim quaecumque ipsius infinita pars accepta. Infinito enim esse et infinitum idem, siquidem substantia infinitum et non de subiecto. {{ln|bk1066b15}} quare aut indivisibile, aut in infinita divisibile, si partibile. Multa autem esse idem impossibile infinita; quemadmodum enim pars aer aeris, sic infinitum infiniti, si est substantia et principium. Impartibile igitur et indivisibile. Sed impossibile actu ens infinitum; quantum enim esse necesse. Secundum acci{{ln|bk1066b20}}dens igitur existit. Sed si sic, dictum est quod non contingit {{p|239}} esse principium, sed illud cui accidit, aerem aut parem. Haec quidem igitur inquisitio universalis.

|Further, if the infinite is an accident of something else, it cannot be qua infinite an element in things, as the invisible is not an element in speech, though the voice is invisible. And evidently the infinite cannot exist actually. For then any part of it that might be taken would be infinite (for ''to be infinite'' and ''the infinite'' are the same, if the infinite is substance and not predicated of a subject). Therefore it is either indivisible, or if it is partible, it is divisible into infinites; but the same thing cannot be many infinites (as a part of air is air, so a part of the infinite would be infinite, if the infinite is substance and a principle). Therefore it must be impartible and indivisible. But the actually infinite cannot be indivisible; for it must be of a certain quantity. Therefore infinity belongs to its subject incidentally. But if so, then (as we have said) it cannot be it that is a principle, but that of which it is an accident-the air or the even number. This inquiry is universal;

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|''Quod autem in sensibilibus'' non est, hinc palam. Si enim corporis ratio ‘superficiebus determinatum\ non erit utique infinitum corpus neque sensibile neque intellectuale,

|but that the infinite is not among sensible things, is evident from the following argument. If the definition of a body is ''that which is bounded by planes'' , there cannot be an infinite body either sensible or intelligible;

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|''neque numerus'' ut separatus et infinitus, numerabile enim numerus aut {{ln|bk1066b25}} habens numerum.

|nor a separate and infinite number, for number or that which has a number is numerable.

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|''Naturaliter autem'' ex hiis palam. Neque enim compositum possibile esse neque simplex. Compositum quidem enim non erit corpus, si finita sunt multitudine elementa. Oportet enim equari contraria et non esse unum ipsorum infinitum; si enim cuicumque deficit alterius corporis virtus, corrumpetur ab infi{{ln|bk1066b30}}nito finitum. Unumquodque autem infinitum esse impossibile. Corpus enim quod omnino habet distentionem, infinitum autem quod infinite distat; quare infinitum corpus omnino erit infinitum.

|Concretely, the truth is evident from the following argument. The infinite can neither be composite nor simple. For (a) it cannot be a composite body, since the elements are limited in multitude. For the contraries must be equal and no one of them must be infinite; for if one of the two bodies falls at all short of the other in potency, the finite will be destroyed by the infinite. And that each should be infinite is impossible. For body is that which has extension in all directions, and the infinite is the boundlessly extended, so that if the infinite is a body it will be infinite in every direction.

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|Neque unum autem simplex contingit infinitum esse corpus, {{ln|bk1066b35}} neque ut dicunt quidam praeter elementa ex quo generant haec (non enim est tale corpus praeter elementa; omne enim ex quo est et dissolvitur in hoc, non videtur autem hoc circa simplicia {{ln|bk1067a1}} corpora), neque ignis neque aliud aliquod elementorum nullum. Sine enim eo quod est infinitum esse aliquid ipsorum, impossibile omne, et si sit finitum, aut esse aut fieri unum aliquod ipsorum, quemadmodum Eraclitus ait omnia fieri aliquando {{ln|bk1067a5}} ignem. Eadem autem ratio et in uno quod faciunt praeter elementa phisici; omne enim permutat ex contrario, puta ex calido in frigidum.

|Nor (b) can the infinite body be one and simple-neither, as some say, something apart from the elements, from which they generate these (for there is no such body apart from the elements; for everything can be resolved into that of which it consists, but no such product of ['''67a'''] analysis is observed except the simple bodies), nor fire nor any other of the elements. For apart from the question how any of them could be infinite, the All, even if it is finite, cannot either be or become any one of them, as Heraclitus says all things sometime become fire. The same argument applies to this as to the One which the natural philosophers posit besides the elements. For everything changes from contrary to contrary, e.g. from hot to cold.

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|{{p|240}}''Adhuc sensibile'' corpus alicubi, et idem locus totius et partis, puta terre.

|Further, a sensible body is somewhere, and whole and part have the same proper place, e.g. the whole earth and part of the earth.

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|Quare si quidem eiusdem speciei, immobile erit aut {{ln|bk1067a10}} semper feretur; hoc autem impossibile. Quid enim magis deorsum quam sursum aut ubicumque? Puta si bolus fuerit, ubi hic movebitur aut manebit? Locus enim ipsius connaturalis corporis infinitus. Optinebit igitur totum locum. Et quomodo? Quae igitur mansio et motus? Aut ubique manet, non movebitur {{ln|bk1067a15}} igitur, aut ubique, non igitur stabit.

|Therefore if (a) the infinite body is homogeneous, it will be unmovable or it will be always moving. But this is impossible; for why should it rather rest, or move, down, up, or anywhere, rather than anywhere else? E.g. if there were a clod which were part of an infinite body, where will this move or rest? The proper place of the body which is homogeneous with it is infinite. Will the clod occupy the whole place, then? And how? (This is impossible.) What then is its rest or its movement? It will either rest everywhere, and then it cannot move; or it will move everywhere, and then it cannot be still.

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|''Si autem'' dissimile totum, dissimilia et loca, et primo quidem non unum corpus omnis nisi tactu. Deinde aut finita haec erunt aut infinita specie. Finita quidem igitur non possibile; erunt enim haec quidem infinita {{ln|bk1067a20}} haec autem non, si omne infinitum, puta ignis aut aqua; corruptio autem quod tale contrariis. Si autem infinita et simplicia, et loca infinita et erunt infinita elementa. Si autem hoc impossibile et loca finita, et omne necesse finitum esse.

|But (b) if the All has unlike parts, the proper places of the parts are unlike also, and, firstly, the body of the All is not one except by contact, and, secondly, the parts will be either finite or infinite in variety of kind. Finite they cannot be; for then those of one kind will be infinite in quantity and those of another will not (if the All is infinite), e.g. fire or water would be infinite, but such an infinite element would be destruction to the contrary elements. But if the parts are infinite and simple, their places also are infinite and there will be an infinite number of elements; and if this is impossible, and the places are finite, the All also must be limited.

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|Totaliter autem impossibile infinitum esse corpus et locum {{ln|bk1067a25}} corporibus, si omne corpus sensibile aut gravitatem aut levitatem habet; aut enim ad medium aut sursum feretur. Impossibile autem infinitum, aut omne aut dimidium, quodcumque passum esse. Quomodo enim divides, aut qualiter infiniti erit hoc quidem deorsum hoc autem sursum, aut extremum et medium?

|In general, there cannot be an infinite body and also a proper place for bodies, if every sensible body has either weight or lightness. For it must move either towards the middle or upwards, and the infinite either the whole or the half of it-cannot do either; for how will you divide it? Or how will part of the infinite be down and part up, or part extreme and part middle?

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|''Adhuc omne'' sensibile corpus in loco, loci autem species sex, {{ln|bk1067a30}} impossibile autem in infinito corpore haec esse.

|Further, every sensible body is in a place, and there are six kinds of place, but these cannot exist in an infinite body.

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|Totaliter autem si impossibile locum infinitum esse, et corpus impossibile. Quod {{p|241}} enim in loco alicubi, hoc autem significat aut sursum aut deorsum aut reliquorum aliquod, horum autem unumquodque terminus aliquis.

|In general, if there cannot be an infinite place, there cannot be an infinite body; (and there cannot be an infinite place,) for that which is in a place is somewhere, and this means either up or down or in one of the other directions, and each of these is a limit.

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|Infinitum autem non idem in magnitudine et motu et tempore, ut una quaedam natura, sed quod posterius dicitur secun{{ln|bk1067a35}}dum prius, puta motus secundum magnitudinem in qua movetur aut alteratur aut augetur, tempus autem propter motum.

|The infinite is not the same in the sense that it is a single thing whether exhibited in distance or in movement or in time, but the posterior among these is called infinite in virtue of its relation to the prior; i.e. a movement is called infinite in virtue of the distance covered by the spatial movement or alteration or growth, and a time is called infinite because of the movement which occupies it.

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==Notes==
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Authors/Aristotle/metaphysics/l11/c10 - Revision history

Edward Ockham: /* Chapter 10 */

Edward Ockham: Created page with "==Chapter 10== {| border=1 cellpadding=10 !valign = top width=45%|Latin !valign = top width=55%|English |- valign = top |{{ln|bk1066a35}} ''Infinitum autem''..."