Authors/Ockham/Summa Logicae/Book I/Chapter 46

Latin	English
[CAP. 46. DE ILLIS QUAE PONUNTUR IN GENERE QUANTITATIS]	[Chapter 46. About things which are supposed to be in the genus of quantity]
Visa varietate opinionum circa distinctionem et identitatem quantitatis cum substantia et qualitate secundum utramque opinionem, videndum est de illis quae ponuntur in genere quantitatis. Et primo secundum opinionem primam, quae mihi videtur esse Philosophi.	Having seen the variety of opinion about distinction and identity of quantity with substance and with quality according to both opinions, we must look at those things which are supposed to be in the genus of quantity. And first according to the first opinion, which seems to me to be that of the Philosopher.
Unde secundum illam opinionem dico quod omne illud per quod responderi potest ad quaestionem factam per 'quantum' reponendum est in genere quantitatis. Et accipio hic hoc interrogativum 'quantum' secundum quod est commune et quasi generale ad 'quantum' stricte sumptum et ad 'quot'. Potest autem per tale interrogativum quaeri de pluribus, ita quod interrogativum est expressivum plurium, sicut si quaeram 'quot sunt hic intus', 'quot homines sunt hic'. Et tunc illud per quod respondetur ad talem quaestionem est inter quantitates discretas connumerandum, quando scilicet exprimit pluralitatem.	Hence, according to that opinion, I say everything which can be a reply to the question 'how much' should be replaced in the genus of 'quantity'. And I accept here the interrogative 'how much' [quantum] according as it is common and quasi-general to 'how much', stricly understood, and to 'how many'. Now by such an interrogative one can be ask about several things, so that the interrogative is expressive of several. For example, if I ask 'how many are here within', 'how many are here'. And then the reply to such a question should be numbered among discrete quantities, namely when it expresses plurality.
Et isto modo numerus est quantitas discreta, quia si quaeratur 'quot sunt isti homines' et respondeam 'tres', illud per quod respondeo exprimit plura. Isto etiam modo oratio est quantitas discreta, quia quaerendo de oratione 'quanta est', intelligitur quaestio de pluralitate syllabarum et quantitate earum. Aliter enim contingeret uniformiter quaerere de una littera et de una syllaba, cum possit esse longa et brevis, et ideo illud per quod respondetur debet esse expressivum plurium, et propter hoc inter quantitates discretas connumeratur.	And in this way number is a discrete quantity, for if you ask 'how many are these men?' and I reply 'three', my reply expresses plurality. And in this way a sentence is also discrete quantity, for in asking of a sentence 'how long is it?', a question about the plurality of syllables and their quantity is understood. For otherwise one could uniformly ask [this] of one letter and one syllable, since it could be long or short, and therefore the reply ought to be expressive of several things, and because of that it is numbered among discrete quantities.
Si autem interrogativum quantitatis non sit expressivum plurium, oportet quod sit expressivum unius, habentis plures partes distantes situaliter ab invicem. Et tunc vel exprimit distantiam secundum longitudinem et sic est linea; vel secundum latitudinem, et sic est superficies; vel secundum profunditatem, et sic est corpus. Vel quaerit de loco vel de tempore, et sic ista duo 'locus' et 'tempus' reponuntur in genere quantitatis.	But if an interrogative of quantity is not expressive of several things, it must be expressive of one thing, having several parts distant in situation from one another. And it either expresses distance according to length, and so is a line, or according to breadth, and so is a surface, or according to depth, and so is a body. Or it asks about place or time, and so 'place' and 'time' are replaced in the genus of quantity.
Ad cuius evidentiam sciendum est quod ista duo 'locus' et 'tempus' non ita per se pertinent ad genus quantitatis sicut alia, sed de loco et tempore diversa ratio quaerenda est. Unde tempus ideo non ponitur ita per se de genere quantitatis sicut alia, quia tempus non significat praecise rem exsistentem in rerum natura sicut alia.	For evidence of this, you should know that 'place' and 'time' do not pertain to the genus of quantity as the other [terms] do, but rather a different nature for space and time should be sought. Therefore, time is not given in this way per se in the genus of quantity as the others are, for 'time' does not signify precisely a thing existing in the state of nature as the others do.
Unde linea, superficies, corpus et numerus significant res praecise exsistentes, non significando nec connotando aliquid nisi rem exsistentem. Tempus autem, sicut motus, connotat vel significat rem non exsistentem vel in actu vel in potentia. Unde secundum istam opinionem tempus non est aliqua res distincta realiter a motu, nec motus est aliqua res distincta realiter a rebus permanentibus. Immo motus non importat nisi quod una res habet aliam partem post aliam, vel quod una coniungitur uni post aliam, vel quod coniungeretur sibi si aliqua res quiescens esset sibi approximata. Et ita motus non est aliqua res distincta realiter a rebus permanentibus, et eodem modo nec tempus.	Hence 'line', 'surface', 'body' and 'number' signify things precisely existing, not by signifying nor by connoting anything except an existing thing. But time, like motion, connotes or signifies a thing that does not exist either in actuality or potentiality. Hence, according to that opinion, time is not anything distinct from motion, nor is motion anything distinct in reality from permanent things. On the contrary, motion only conveys that one thing has one part after another, or that one thing is joined to one thing after another, or that it would be joined to it if some thing at rest were brought near to it. And so motion is not some thing distinct in reality from permanent things, and in the same way neither is time.
Et propter hoc non ponitur tempus nisi quasi per accidens vel quasi passio rerum permanentium exsistentium in genere quantitatis. Et consimiliter motus potest poni in genere quantitatis, sicut ponit Aristoteles V Metaphysicae.	And because of this, time is not given except as if per accidens, or as if an affection of things permanently existing in the genus of quantity. And similarly, motion can be put in the genus of quantity, just as Aristotle puts it in Metaphysics V.
De loco autem alia ratio danda est. Unde locus non dicitur esse per se in genere quantitatis, quia locus non est aliquid distinctum a superficie. Et simul cum hoc, cum veritate propositionis enuntiantis locum de subiecto aliquo non potest locus variis modis et cum variis determinationibus connotantibus quantitatem successive verificari de eodem absque consimili variatione consimilis praedicationis superficiei vel lineae vel corporis de eodem.	But concerning place, another reason should be given. Hence place is not said to be in the genus of quantity, for place is not anything distinct from a surface. And together with this, with the truth of a proposition asserting place of some subject, place cannot be given in various ways and with various determinations connoting that quantity is successively verified of the same thing without a similar variation of a similar predication of surface, or of line, or of body, concerning the same thing.
Verbi gratia sit haec modo vera 'a est locus' stante ista propositione 'a est locus' non possunt tales verificari successive 'a est maior locus', 'a est minor locus', 'a est longior', 'a est brevior' et sic de consimilibus, nisi tales etiam successive verificentur 'a est maior superficies', 'a est minor superficies'; vel tales 'a est maior linea', 'a est minor linea'; vel tales 'a est longius corpus vel brevius corpus'. Et universaliter nullae tales determinationes repugnantes additae huic praedicabili 'loco' possunt successive verificari de loco nisi simul verificentur si addantur alicui istorum trium 'linea', 'superficies', 'corpus'.	For example, let 'a is a place' now be true. With the proposition 'a is a place' remaining [true], such propositions as 'a is a greater place', 'a is a lesser place', 'a is longer', 'a is shorter', and similar ones cannot be verified unless such propositions as 'a is a greater surface', 'a is a lesser surface', or 'a is a greater line' or 'a is a lesser line' are verified – or 'a is a longer body or a shorter body'. And generally no such repugnant determinations added to the predicable 'place' can be successively verified of a place, unless at the same time they are verified if they are added to one of the three terms 'line', 'surface', 'body'.
Et ex isto patet ratio quare non obstante quod ista opinio ponat quod linea, corpus et superficies non sunt distinctae res, sicut nec locus distinguitur ab eis, tamen magis per se pertinent ad genus quantitatis quam locus, quia scilicet non obstante quod significent eandem rem, tamen possunt tales successive verificari 'a est longior', 'a est brevior', quamvis nullae tales verificentur 'a est latius', 'a est minus latum', 'a est profundius', 'a est minus profundum'.	And from this the reason is clear why (notwithstanding that the opinion posits that line, body and surface are not distinct things, just as place is not distinct from them) nevertheless they pertain more per se to the genus of quantity than place, namely, because notwithstanding that they signify the same thing, still such propositions as 'a is longer', 'a is shorter' can be successively verified of them, although no such propositions as 'a is wider', 'a is less wide', 'a is deeper', 'a is less deep' are verified.
Ex praedictis patet quod locus non est ita distinctum praedicabile a linea, superficie et corpore sicut ipsa sunt distincta inter se. Ex praedictis etiam colligi potest quod prima et essentialior divisio et distinctio illorum quae sunt in genere quantitatis sumitur per hoc quod illud per quod respondetur ad interrogativum factum per 'quantum', large accipiendo 'quantum', vel est expressivum plurium, et sic est numerus, vel est expressivum unius compositi ex pluribus, et sic sumitur magnitudo, quae dividitur aliquo modo in lineam, superficiem et corpus. Et ita nec oratio nec locus nec tempus continentur ibi in ista divisione, sed magis sunt passiones vel accidentia eorum.	From the previous [remarks] it is clear that place is not a distinct predicable from line, surface and body, in the way that they are distinct from each other. From the previous remarks it can also be gathered that the first and more essential division, and distinction, of those things which are in the genus of quantity is taken from the fact that the reply to the interrogative 'how much' [quantum], broadly understanding 'how much', is either expressive of several things, and so is a number, or is expressive of one thing composed of several, and thus 'magnitude' is understood, which is divided in some way into line, surface and body. And so neither speech nor place nor time are contained there in that division, but rather they are more affections or accidents of those things.
Et isto modo dividendi utitur Philosophus, V Metaphysicae, ubi enumerando illa quae sunt quanta per se et primo, non ponit nisi numerum, lineam, superficiem et corpus. Unde primo describens 'quantum' dicit sic: 'Quantum vero dicitur quod est divisibile in ea quae insunt, quorum utrumque aut singulum, unum aliquid et hoc aliquid natum est esse'. Per primam particulam scilicet 'divisibile in ea quae insunt' excluduntur tempus et oratio et motus, quia quodlibet istorum importat aliquid quod non est vel importat aliquid quod est negative, et hoc saltem vel respectu alicuius vel simpliciter. Iste est modus loquendi Anselmi, De casu diaboli, qui est multum necessarius in diversis difficultatibus. Et propter hoc ista non ponuntur primo quanta.	And the Philosopher in Metaphysics 5, where in enumerating things which are quantified [quanta] per se and primarily, only gives number, line, surface and body. Hence, when he first describes 'how much', he says "Quantum means that which is divisible into two or more constituent parts of which each is by nature a one and a this". By the first part, namely " divisible into two or more constituent parts", time and motion and speech are excluded, because each of those conveys something that does not exist, or conveys something which exists negatively, and this is at least either in respect of something, or simpliciter. This is the manner of speaking of Anselm, in On the Fall of the Devil, which is greatly necessary in the case of various difficulties.
Per secundam particulam possunt excludi omnia accidentia et omnes formae et materiae, quia talia non sunt nata esse 'hoc aliquid'. Sed tunc accipitur 'quantum' stricte, pro illo scilicet quod est per se exsistens, non innitens alteri nec tamquam pars nec tamquam accidens alterius.	And because of this, these are not primarily given as quanta.By the second part can be excluded all accidents and all forms and materials, because such things are not by nature a 'this'. But then quantum is understood strictly, namely for that which is per se existent, not depending the another thing nor a kind of part or accident of the other.
Et sic, secundum istam opinionem, sumendo 'quantum' stricte, sola substantia composita ex materia et forma - vel, secundum opinionem Aristotelis, corpus caeleste - est quantum. Et ideo Philosophis postea enumerando illa quae sic dicuntur quanta, dicit sic: 'Multitudo igitur quantum aliquid si numerabilis fuerit; magnitudo autem si mensurabilis fuerit. Dicitur autem multitudo quoddam divisibile potestate in non continua; magnitudo autem quod in continua. Magnitudinis autem, quae quidem ad unum continua, longitudo; quae autem ad duo, latitudo; quae autem ad tria, profunditas. Horum autem pluralitas finita, numerus; sed longitudo, linea; latitudo, superficies; profunditas, corpus'.	And so, according to that opinion, taking quantum strictly, only substance consisting of material and form (or, according to the opinion of Aristotle, a heavenly body) is a quantum. And therefore, after enumerating the things which are called quanta, says "A quantum is a plurality if it is numerable, a magnitude if it is a measurable. 'Plurality' means that which is divisible potentially into non-continuous parts, 'magnitude' that which is divisible into continuous parts. Of magnitude, that which is continuous in one dimension is length; in two breadth, in three depth. Of these, limited plurality is number, limited length is a line, breadth a surface, depth a solid".
Ex quo patet quod ista quatuor, lineam, superficiem, corpus et numerum praecise enumerat, et ita nec tempus nec orationem nec locum, propter rationes prius positas.	From this it is clear that he precisely enumerates the four things – line, surface, body and number – and so [he does not enumerate] either time nor speech or place, for the reasons given above.
Post praedicta sciendum est quod aliqua quae ponuntur in genere quantitatis sunt illa per quae respondetur ad quaestionem factam per 'quantum', et sic 'bicubitum', 'tricubitum', 'duo', 'tria', et sic de consimilibus, sunt in genere quantitatis. Alia dicuntur in genere quantitatis quia sunt communia per se primo modo ad talia, et sic linea, superficies, corpus, numerus sunt in genere quantitatis.	After what has been said, it should be known that some things which are put in the genus of quantity are those which are a reply to the question 'how much' (quantum), and so 'two cubits long', 'three cubits long', 'two', 'three', and so on, [and] they are in the genus of quanity. Others are predicated in the genus of quantity because they common in the first mode of per se, and so line, surface, body, number are in the genus of quantity.