Authors/Ockham/Summa Logicae/Book I/Chapter 45

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Latin English
[CAP. 45. DE OBIECTIONIBUS CONTRA PRAEDICTAM OPINIONEM] [Chapter 45.  On objections to the previous opinion]
Ut autem magis pateat intentio sic opinantium, ponendae sunt aliquae obiectiones propter quas videtur quod praedicta opinio sit contra mentem Aristotelis et suorum sequacium. Now in order that the intention of those holding this opinion should be more clear, we should provide some objections, on account of which it seems that the previous opinion[1] is against the thinking of Aristotle, and of his followers.
Et primo videtur dicere oppositum in libro Praedicamentorum, ubi dicit quod multum album non est quantum nisi per accidens. Si tamen quantitas esset qualitas, album esset per se quantum, immo esset per se quantitas. And first, he seems to say the opposite in the Categories, where he says that a large white thing is not quantified, except per accidens. But if quantity were a quality, a white thing would be per se quantified. Indeed, it would be per se a quantity.
Item, dicit idem V Metaphysicae: “Secundum accidens vero dictorum quantorum hoc quidem sic dicitur sicut dictum est, quod musicum quantum et album, per esse quantum quidem cui insunt”. Ex quo sequitur quod album inest alicui quod est quantum per se, et album est tantum quantum per illud; et ita albedo non est quantitas. Likewise, he says in Metaphysics V[2] that ‘Of things that are quantified incidentally, some are so-called in the sense in which it was said that the musical is quantified, and the white, viz. because that to which musicalness and whiteness belong is quantified”. From which it follows that white inheres in something that is quantified per se, and white is only quantified because of that, and so whiteness is not a quantity.
Item, ibidem : “Alia dicuntur secundum se quanta, alia secundum accidens: ut linea quantum aliquid secundum se, musicum vero secundum accidens”. Likewise, in the same place: “Some things are called quantified according to themselves, others incidentally, e.g. the line is quantified according to itself, but the musical incidentally”.
Item, Aristoteles in Praedicamentis ponit quod aliquae sunt quantitates habentes positionem quarum partes copulantur ad aliquem terminum communem, sicut partes lineae ad punctum, partes superficiei ad lineam et partes corporis ad superficiem. Sed partes alicuius non copulantur ad aliquam partem eiusdem totius; igitur punctus distinguitur a linea et linea a superficie et superficies a corpore. Likewise, in the Categories[3] Aristotle supposes that some things are quantities having position, of which parts are joined to some common terminus, such as the parts of a line to a point, the parts of a surface to a line, and the parts of a body to a surface. But the parts of something are not joined to some part of the same whole, therefore a point is distinguished from a line, and a line from a surface, and a surface from a body.
Item, in libro Posteriorum dicit quod punctus est indivisibilis; quod non competit lineae neque superficiei. Likewise, in the Posterior Analytics[4] he says that a point is indivisible, which does not belong to a line or a surface.
Item, vult quod unitas est indivisibilis; et per consequens non est corpus nec linea nec superficies, nec est punctus; igitur est aliquid praeter ista et praeter numerum, quia unitas non est numerus; cuius oppositum asserit praedicta opinio. Likewise, he wishes that unity is indivisible, and as a consequence is not a body nor a line nor a surface, nor is it a point; therefore it is something beyond those and beyond number, for unity is not a number, which is the opposite of what the previous opinion asserts.
Item, I Physicorum contra Parmenidem et Melissum probat plura esse si substantia et quantum sunt; quod non valeret si substantia esset quantitas. Sed istis non obstantibus mihi videtur quod praedicta opinio sequitur ex principiis Aristotelis, sive sit vera sive falsa. Likewise, in Physics I [5] he establishes, against Parmenides and Melissus, that more than one thing exists if substance and the quantified exist, which would not be valid if substance were a quantity. But these things notwithstanding, it seems to me that the previous opinion follows from the principles of Aristotle, whether it is true or false.
Est autem intelligendum primo quod Philosophus in diversis locis aequivoce utitur istis vocabulis 'per se' et 'per accidens'. Quantum autem ad praesens sufficit: Aristoteles in locis allegatis non accipit 'per se' et 'per accidens' ita generaliter sicut in I Posteriorum. Sed illam propositionem dicit esse 'per se' quae vera est, et simul cum hoc praedicatum nihil connotat quin aliquid tale consimili modo significandi connotetur per subiectum, ita quod evidentem contradictionem includit illam propositionem esse falsam simul cum veritate propositionis enuntiantis esse de subiecto. Vel propositionem 'per se' praecise vocat illam in qua praedicatur pars definitionis de definito, vel definitio de definito, vel idem de se, vel synonymum de synonymo; aliam autem propositionem vocat propositionem per accidens. But it should be understood first that the Philosopher uses the words per se and per accidens equivocally in various places. But for the present it is sufficient [to say that] Aristotle in the places mentioned does not understood per se and per accidens so generally as in Posterior Analytics I. But he says a proposition is per se when it is is true, and when at the same time the predicate does not connote anything unless some such thing is connoted by the subject in a similar mode of signifying, so that it involves an evident contradiction for a proposition to be false at the same time as the truth of a proposition asserting being of the subject. Or he calls a proposition per se precisely that in which part of the definition is predicated of the defined, or a definition of the defined, or the same thing of itself, or synonym of synonym. The other [sort of] proposition he calls per accidens.
Et per istud patet ad primas instantias. Quando enim dicitur quod 'multum album non est quantum nisi per accidens', intendit Philosophus dicere quod haec est per accidens 'album est quantum', propter hoc quod hoc praedicatum 'quantum' connotat vel significat partem distare a parte, hoc autem subiectum 'album' nihil tale connotat; propter quod hoc praedicatum 'quantum' non debet poni in definitione albi nec e converso. Cum hoc tamen stat quod album vere et realiter sit quantum et similiter quod sit vere quantitas. Unde Philosophus non plus concedit quod album est quantum quam quod album est quantitas: sicut igitur vere et realiter album est quantum, quamvis per accidens, ita vere et realiter, secundum intentionem Philosophi, album est quantitas, quamvis per accidens. And from this [the reply] to the counter-examples is clear. For when it is said that a large white thing is not quantified except per accidens, the Philosopher means to say that ‘a white thing is quantified’ is per accidens because the predicate ‘quantified’ connotes or signifies part to be distant from part, but the subject ‘white’ connotes nothing of the sort, because the predicate ‘quantified’ ought not to be given in the definition of ‘white’ nor conversely. This is consistent with white being truly and really quantified, and similarly that it is a true quantity. Hence the Philosopher no more concedes that white is quantified than that white is a quantity. Therefore, just as white is truly and really quantified, although per accidens, so truly and really according to the intention of the Philosopher, white is a quantity, although per accidens.
Quod autem haec sit intentio Philosophi patet per eundem, ubi prius. Unde postquam enumeravit species quantitatis et differentias earum dicit sic: “Proprie autem quantitates hae solae sunt quas diximus, alia vero omnia secundum accidens; ad hoc autem aspicientes et alias dicimus quantitates esse, ut multum album dicitur eo quod superficies multa sit”. But that this is the intention of the Philosopher is clear from the same place as before. Hence, after he has enumerated the species of quantity and their differences, he says as follows: “Strictly speaking, only the things which I have mentioned are quantities: all others are quantities only incidentally. But, mindful of this, we call other things ‘quantities’, e.g. what is white is called large because a white surface is large”
Ex quo colligi potest quod intendit quod de aliis ab illis ibi enumeratis vere dicitur hoc praedicabile 'quantitas', ut album vere dicatur quantitas, quamvis non proprie sed per accidens. Unde dicit: “Ad hoc autem aspicientes et alias dicimus quantitates esse”, [id est] et de aliis dicitur hoc nomen 'quantitas', quamvis non per se sed per accidens, de illis autem dicitur per se et proprie, et hoc quia hoc praedicabile 'quantitas' ponitur in definitione eorum. Non sic autem ponitur in definitione albi, nec musici nec hominis nec lapidis. From this it can be gathered that he means that the predicable ‘quantity’ is truly predicated of other things than the things enumerated there, such as when a white thing is truly called a quantity, although not strictly speaking but per accidens. Hence he says “mindful of this, we call other things ‘quantities’”, i.e. the name ‘quantity’ is also predicated of other things, although not per se but per accidens, although of the original things it is predicated per se and strictly, and this is because the predicable ‘quantity’ is given in their definition. But it is not thus given in the definition of ‘white’, nor of ‘musical’ nor ‘man’ nor ‘stone’.
Unde sciendum est quod numquam Philosophus facit distinctionem quantum ad significationem inter ista duo nomina, quorum unum est abstractum et alterum concretum, 'quantum' et 'quantitas', sed quidquid concedit de uno concedit et de reliquo et indifferenter ponit unum vel aliud. Unde apud eum synonyma sunt, nisi forte abstractum includat aliquod syncategorema vel aliam dictionem aequivalentem quantum ad significationem. Hence it should be known that the Philosopher makes a distinction in signification between the two names ‘quantified’ and ‘quantity’, of which one is abstract and the other concrete[6], but whatever he allows of one he allows of the other, and he gives one or the other indifferently. Hence in his works they are synonymous, except perhaps the abstract name includes some syncategorema or another expression equivalent in signification.
Per idem ad secundam auctoritatem, quod album et musicum dicuntur quanta per accidens, quia istae propositiones 'album est quantum', 'musicum est quantum' et consimiles non sunt per se ita quod in eis praedicetur pars definitionis de definito. Et quando dicitur quod sunt quanta per illud cui insunt, non accipit 'inesse' per realem inexsistentiam sed per praedicationem. Unde haec non est vera 'album est quantum' nisi quia superficies, quae praedicatur de albo, est quanta. Haec enim est primo vera 'superficies est quanta'. Et propterea quia album praedicatur de superficie et e converso, ideo haec est vera ‘album est quantum’. [I reply] by the same [argument] to the second authority, that a white and a musical thing are called quantified per accidens, because the propositions ‘a white thing is quantified’ and ‘a musical thing is quantified’ and similar are not per se in the sense that, in them, the part of a definition is predicated of the thing defined. And when it is said that they are quantified by what they inhere in, he does not understand ‘inhere in’ by real existence, but by predication. Hence ‘a white thing is quantified’ is only true because a surface, which is predicated of a white thing, is quantified. For ‘a surface is quantified’ is primarily true. And because of that, because ‘white’ is predicated of a surface, and conversely, ‘a white thing is quantified’ is true.
Per idem ad aliam auctoritatem: quod ideo dicit alia esse quanta per se, puta lineam, corpus et huiusmodi, quia tales propositiones sunt per se 'linea est quantitas', 'corpus est quantitas' et huiusmodi. Alia autem sunt per accidens, quia tales propositiones sunt per accidens 'album est quantitas', 'musicum est quantitas'. [I reply] by the same [argument] to the other authority. He says that other things are quantified per se, e.g. line, body and so on, because propositions such as ‘a line is a quantity’, ‘a body is a quantity’ and so on are per se. But others are per accidens, because propositions such as ‘a white thing is a quantity’, ‘a musical thing is a quantity’ are per se.
Ad aliud de Praedicamentis dicendum est quod non est intentio Philosophi dicere quod quantitates habentes positionem habeant partes copulatas ad aliquam rem distinctam totaliter ab illis partibus, quia tali rei, secundum eum, nullum posset subiectum assignari. Oporteret etiam quod esset per se in genere, cum non possit poni pars alicuius exsistentis in genere; et ita esset quantitas vel substantia vel qualitas etc., quorum quodlibet est falsum. Sed intendit Philosophus quod una pars extenditur ad aliam partem, ita quod nihil est penitus medium inter illas partes; et quod hoc est de ratione continui permanentis quod partes sint ad se protensae mutuo, ita quod si una non sit protensa usque ad aliam non erit ex eis unum continuum. To the other argument about the Categories, it should be said that it is not the intention of the Philosopher to say that quantities having position have parts joined to some thing that is totally distinct from those parts, because to such a thing, according to him, there could be no subject assigned. For it would also have to be that it would be per se in genus, since there could not be given a part of something existing per se in a genus, and so there would be quantity or substance or quality etc., of which all are false. Rather, the Philosopher meant that one part is extended to another part, so that nothing is entirely a medium between those parts, and that it is part of the nature of the permanent continuum that [its] parts are mutually protuding onto one another, so that if one is not protuding onto another, a single continuum will not be made from them.
Et ista est differentia inter quantitatem continuam et discretam, secundum Aristotelem, quia ad quantitatem discretam nihil refert an illa quae constituunt quantitatem discretam sint distincta loco et situ vel non, an etiam inter ea sit medium vel non sit medium. Unde ad hoc quod duo homines sint duo nihil refert an inter illos duos homines sit medium vel non sit medium. Ita enim sunt duo quando nihil est medium inter eos sicut quando distant ab invicem per centum leucas, nec in aliquo propter propinquitatem vel distantiam variatur ista praedicatio istius praedicati 'duo' de istis hominibus, immo si simul essent in eodem loco ita essent duo sicut si non essent in eodem loco. And this, according to Aristotle, is the difference between continuous and discrete quantity, because in the case of discrete quantity it does not matter whether or not the items which constitute the discrete quantity are distinct in place and situation or not, or whether there is a medium between them. Hence, for two men to be 'two', it does not matter whether there is a medium between those two men or not. For they are two when there is no medium between them, just as when they are distant from each other by a hundred leagues, nor does the predication 'two' of those men vary because of anything to do with nearness or distance. On the contrary, if they were in the same place at the same time they would be two, just as if they were not in the same place.
Non sic autem est de partibus continui, quia ad hoc quod sint continuae oportet quod nihil sit medium inter eas, sed oportet quod una sit protensa usque ad aliam, et tamen quod distent situ, et quod faciant unam rem numero, quia aliter non sunt continuae. Si enim non constituant unam rem numero, vel non sint usque ad se protensae mutuo, vel non sint distantes loco vel situ non sunt continuae. Nullum autem praedictorum requiritur ad quantitatem discretam. Et propter hoc dicit Aristoteles quod partes copulantur ad terminum communem, hoc est sunt ad se protensae, simul cum hoc quod non sunt in eodem loco, in tantum quod si esset aliquod indivisibile, illud terminaret utrumque. But it is not so concerning the parts of the continuum, because for them to be continuous it has to be that nothing is a medium between them, but rather it has to be that one is protuding onto another, and yet they are distant in situation, and that they make numerically one thing, because otherwise they would not be continuous. For if they did not constitute a numerically single thing, or if they were not mutually protuded, either they would not be distant, or they would not be continuous. None of these things are required for discrete quantity. And because of this, Aristotle says that the parts are joined to a common terminus, i.e. they protude on each other, while not being in the same place, insomuch as there were something indivisible, it would terminate both.
Non sic autem est de quantitate discreta, quia partes non sunt necessario ad se protensae, immo ita possunt constituere quantitatem si aliquid sit medium sicut si nihil sit medium. Et propter idem dicit quod partes quantitatis continuae habent positionem, quia ad hoc quod sint partes quantitatis continuae oportet quod situaliter distet una ab alia, ita quod contingat dicere quod una pars est ibi et alia hic et alia alibi. Ad quantitatem autem discretam non requiritur talis distantia situalis, sicut dictum est. Unde materia et forma vere sunt duae res, et tamen situaliter non distant. But it is not this way with discrete quantity, for the parts are not necessarily protuding on each other. On the contrary, they would constitute a quantity if something were a medium between them or not. And for the same reason he says that the parts of continuous quantity have a position, for in order to be parts of continuous quantity it has to be that one is distant from the other in situation, so that it is possible [contingat] to say that one part is there, another here, another elsewhere. But for discrete quantity, such distance in situation is not required, as we said. Hence material and form are two things, and yet they are not distant in situation.
Ad aliud dicendum est quod quando Philosophus dicit punctum esse indivisibilem, vel loquitur secundum opinionem famosam, vel loquitur condicionaliter: quod punctus esset indivisibilis si esset alia res a quantitate. Vel per illam propositionem 'punctus est indivisibilis' intelligit istam 'una pars continui extenditur ad aliam sine aliquo divisibili medio inter illas partes', sicut per istam 'partes lineae copulantur ad terminum communem' intelligit istam 'partes lineae protenduntur ad se sine aliquo medio intercepto'. To the other argument, it must be said that when the Philosopher says that a point is indivisible, he either speaks according to common opinion, or he speaks conditionally, that a point would be indivisible if it were something apart from quantity. Or that, by the proposition 'a point is indivisible', he means 'one part of the continuum is extended onto another without any divisible medium between the two parts', just as by 'the parts of a line are joined by a common terminus' he means 'the parts of a line protude on each another without any intervening medium'.
Ad aliud dicendum est quod Philosophus non intendit quod unitas sit quaedam res omni parte carens, quia talis res nulla potest esse in istis inferioribus secundum eum, sed per istam propositionem 'unitas est indivisibilis' intelligit istam 'illud quod est unum non est plura'. Et quod haec sit intentio sua declaravi per eundem II Physicorum, ideo hic causa brevitatis omitto. To the other, it should be said that the Philosopher does not mean that unity is a sort of thing lacking any part, because no such thing can be in this world below according to him, but by the proposition ‘unity is indivisible’, he means ‘that which is one is not several’. And that this is his meaning I have made clear in my commentary on the Physics II, therefore for the sake of brevity I will leave it out here.
Ad ultimum dicendum est quod Philosophus non intendit probare multa esse si substantia et quantum sint, per hoc quod substantia non est quantitas, sed per hoc quod impossibile est quod aliquid sit quantum nisi contineat partium pluralitatem. Et ita necessario si substantia et quantum sunt, multa sunt, quia scilicet partes illius quantitatis sunt. Et hoc sufficit Philosopho contra illos antiquos. To the final argument it should be said that the Philosopher does not mean to prove that many things exist if substance and the quantified exist, because substance is not a quantity, but rather from its being impossible that anything be quantified unless it contains a plurality of parts. And so necessarily if substance and the quantified exist, many things exist, namely because the parts of the quantity exist. And this is sufficient for the Philosopher against the ancients.
Sic igitur dico quod intentio Aristotelis fuit negare omne indivisibile in istis inferioribus, nisi forte ponat animam intellectivam indivisibilem. Voluit etiam ponere quod omnis res vel est substantia vel qualitas. Et si inveniatur aliquando dicere substantiam non esse quantitatem, vel qualitatem non esse quantitatem, intelligit quod haec propositio non est per se 'substantia est quantitas' nec etiam ista 'qualitas est quantitas'. Et hoc quia hoc nomen 'quantitas' si accipiatur pro quantitate continua permanente connotat unam partem ab alia distare situaliter, non sic autem hoc nomen 'substantia' vel 'qualitas'. Thus, I say that Aristotle’s intention was to deny anything indivisible in this world below, unless perhaps he means the indivisible intellective soul. And he also wanted to propose that everything is either a substance or a quality. And if he is sometimes found to say that that substance is not a quantity, or that quality is not a quantity, he means that the proposition 'substance is a quantity' is not per se, nor 'quality is a quantity'. And this is because the name 'quantity', if it is understood as meaning 'continuous permanent quantity', connotes that one part is distant in situation from another, but the name 'substance' or 'quality' [does not connote this].
Dico igitur quod intentio Aristotelis et multorum aliorum fuit quod omnis quantitas non est aliqua res totaliter distincta a substantia et qualitate, nec punctus, linea, superficies et corpus sunt res inter se secundum se totas distinctae. I say therefore that the intention of Aristotle and of many others ws that any quantity is not some thing totally distinct from substance and quality, and point, line, surface and body are not of themselves things wholly distinct from each othe.
Tenentes autem communem opinionem modernorum dicerent quod punctus est alia res a linea, copulans et continuans partes lineae ad invicem; linea autem est alia res a superficie, continuans et copulans partes superficiei; superficies autem est alia res a corpore, continuans et copulans partes corporis ad invicem; numerus quoque est alia res a rebus numeratis, et accidens exsistens in eis; et similiter oratio est alia res a voce prolata et quantitas eius. Idem etiam dicerent de loco et tempore quod sunt distinctae res inter se et ab omnibus supra dictis. But those holding the common opinion of the moderns would say that a point is something different from a line, joining and continuing the parts of the line to one another. And a line is something different from a surface, continuing and joining the parts of the surface. And that a surface is something different from a body, continuing and joining the parts of the body to one another. Number is also something different from the things numbered, and is an accident existing in them, and similarly a sentence is something different from an uttered utterance and its quantity. They would say the same also of place and time, that they are things distinct from one another, and from all the things said above.

Notes

  1. i.e. the opinion given in part 3 of chapter 44 above: that no quantity is really distinct from substance and quality, and that continuous quantity is nothing other than a single thing having one part at a distance from another part, and discrete quantity (number) is nothing other than the numbered things themselves
  2. [1]
  3. Chapter 6
  4. 95b1
  5. 185a20
  6. the reverse order is clearly intended here, as ‘quantified’ (quantum) is the concrete or adjectival form, and ‘quantity’ (quantitas) the abstract or substantival form. See chapter 6 above.
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