Authors/Ockham/Summa Logicae/Book I/Chapter 47

Latin	English
[CAP. 47. DE PROPRIETATIBUS QUANTITATIS]	[Chapter 47. On the properties of quantity]
Iuxta praedictam opinionem videndum est de proprietatibus quantitatis. Ponit autem Aristoteles tria esse propria quantitati. Quorum primum est quod quantitati nihil est contrarium, sicut linea non est contraria superficiei nec bicubitum contrariatur tricubito. Sed ex ista proprietate evidenter videtur haberi quod quantitas non est substantia neque qualitas, quia si quantitas esset qualitas, cum qualitati aliquid sit contrarium, quantitati etiam aliquid esset contrarium:	In connection with the previous opinion, we should look at the properties of quantity. Now Aristotle gives three properties of quantity, of which the first is that there is not contrary to quantity, just as a line is not contrary to a surface, nor that two cubits long is contrary to three cubits long. But from that property evidently it seems to be held that quantity is neither a substance nor nor a quality, for if quantity were a quality, since something is contrary to quality, something would also be contrary to quantity.
Ad hoc dicendum est - quod dictum est prius – istum terminum 'contraria' multipliciter accipi posse. Verumtamen Philosophus in negando quantitati aliquid esse contrarium accipit 'contrarium' pro termino aliquo importante res contrarias aliis praecise, quae scilicet ideo dicuntur contrariae quia non possunt simul in eodem exsistere sed successive, et simul cum hoc partibiliter adquiri possunt.	To this it should be said that – as was said before – the term 'contrary' can be understood in many ways. Nevertheless, in denying that something is a contrary to quantity, the Philosopher understands 'contrary' for some term conveying things precisely contrary to others, which are therefore called contrary because they cannot exist at the same time in the same thing, but only successively, and together with this can be acquired divisibly.
Sic autem accipiendo 'contraria' manifestum est quod nulla per se contenta in genere quantitatis tamquam de aliis praedicabilia contrariantur, nam nullum est per [se] contentum in illo genere cuius quodlibet significatum vel consignificatum contrariatur et repugnat significato vel consignificato alterius. Patet inductive. Et ita concederent sic opinantes quod haec est vera 'alicui quantitati aliquid contrariatur', accipiendo 'contrariari' pro 'repugnare realiter inesse eidem simul, quamvis non successive'. Haec tamen est vera 'nulla contenta in genere quantitatis per se contrariantur', accipiendo 'contrariari' illo modo quo dictum est.	And understanding 'contrary' in this way it is manifest that no predicables contained per se in the genus of quantity are contraries in the sense of being contraries of other ones, for nothing contained per se in that genus is such that any of its significates or co-significates is a contrary of or repugnant to any significate or co-significate of another. This is clear inductively, and so it would be conceded by those who think that 'something is contrary to some quantity', understanding 'contrary' as 'repugnant in reality to being in the same thing at the same time, although not successively'. But 'no items in the genus of quantity are per se contrary, in the way that was said.
Unde quamvis albedo et nigredo contrarientur, tamen isti termini 'bicubitum', 'tricubitum' non contrariantur, nec isti 'duo', 'tria', nec isti 'linea' et 'superficies', et sic de aliis. Et ita albedo tricubita contrariatur nigredini bicubitae, et ita quantitas una realiter contrariatur quantitati alteri. Et tamen isti termini 'bicubitum', 'tricubitum' non contrariantur, quia 'bicubitum' significat albedinem eodem modo quo significat nigredinem, quae tamen albedo contrariatur nigredini.	Hence, although whiteness and blackness are contraries, nevertheless the terms 'two cubits long', 'three cubits long' are not contraries, nor 'two', 'three', nor 'line', 'surface', and so on. And so 'a three cubit long whiteness' is contrary to 'a two foot long blackness', and so one quantity is really contrary to the other quantity. And yet the terms 'two cubits long', 'three cubits long' are not contraries, for 'two cubits long' signifies a whiteness in the same way that it signifies a blackness, which whiteness is nevertheless contrary to the blackness.
Breviter igitur dicendum est quod intentio Aristotelis est quod haec est vera 'quantitas contrariatur quantitati' si termini supponant personaliter pro re extra. Haec tamen vera est 'nulli termini per se contenti in genere quantitatis contrariantur sic quod semper important res contrarias'. Et istam propositionem intelligit Aristoteles quando dicit quod quantitati nihil est contrarium.	Briefly therefore, it should be said that the intention of Aristotle is that 'quantity is contrary to quantity' is true if the terms supposit personally for something outside [the soul]. But nevertheless 'no terms contained per se in the genus of quantity are contraries in such a way that they always convey contrary things'. And Aristotle means that proposition when he says that nothing is a contrary to quantity.
Secunda proprietas est quod quantitas non suscipit magis et minus, hoc est nullum contentum sub genere quantitatis praedicatur de aliquo aliquando cum hoc adverbio 'magis', aliquando cum hoc adverbio 'minus'. Sicut non dicitur quod ista res est aliquando magis bicubita, aliquando minus bicubita, ad modum quo dicimus quod hoc corpus aliquando est magis album, aliquando minus album; nec etiam dicimus quod ista tria sunt magis tria quam illa, sicut dicimus quod hoc est magis album quam illud.	The second property is that quantity is not susceptible of greater or less. That is, nothing contained in the genus of quantity is sometimes predicated of something with the adverb 'more', sometimes with the adverb 'less'. Just as it is not said that this thing is sometimes 'more two cubits', sometimes 'less two cubits', in the manner in which we say that this body is sometimes more white, sometimes less white, nor also do we say that these three are sometimes more three than those three, in the way that we say that this thing is 'more white' than that thing.
Tertia proprietas est quod quantitas dicitur aequalis vel inaequalis alteri quantitati, sicut unum corpus dicitur aequale vel inaequale alteri. Similiter est de aliis. Ex ista proprietate patet quod non est intentio Philosophi negare qualitatem esse quantitatem, nec substantiam esse quantitatem, nam secundum Philosophum haec proprietas est maxime propria quantitati, et per consequens est convertibilis cum quantitate. Igitur de quocumque dicitur haec proprietas, de eodem dicitur quantitas. Sed haec est vera simpliciter, quamvis non sit per se vera 'unum lignum est aequale alteri' et 'unum album est aequale alteri' et 'una nigredo est aequalis alteri nigredini vel albedini'. Igitur haec est simpliciter vera 'substantia est quantitas' et similiter ista 'qualitas est quantitas', quamvis sit per accidens.	The third property is that quantity is called equal or unequal to another quantity, just as one body is said to be equal or unequal to another. Similarly with the others. From this property it is clear that it is not the intention of the Philosopher to deny that quality is a quantity, nor that substance is a quantity, for according to the Philosopher this property is particularly a property of quantity, and as a consequence it is convertible with quantity. Therefore, of whatever this property is predicated, of the same thing quantity is predicated. But this is absolutely true, although 'one [block of] wood is equal to the other' and 'one white thing is equal to another' and 'one blackness is equal to another blackness or whiteness' are not per se true. Therefore 'substance is a quantity' is absolutely true, and similarly 'quality is a quantity', although it is per accidens'.
Nec valet dicere quod non omne aequale vel inaequale est quantitas, quia non est proprie proprium quantitati esse aequale vel inaequale, sed est sibi proprie proprium quod secundum eam aliquid dicitur aequale vel inaequale. Quia non dicit Philosophus quod secundum quantitatem aliquid dicitur aequale vel inaequale, sed dicit quod hoc est proprie proprium quantitati quod quantitas est aequalis vel inaequalis.	Nor is it valid to say that everything which is equal or unequal is a quantity, for it is not strictly a property of quantity that it is equal or unequal, but it is strictly a property of it that in terms of quantity something is called equal or unequal. For the Philosopher does not say that something is called equal or unequal in terms of quantity, but he does say that it is strictly a property of quantity that quantity is equal or unequal.
Unde dicit sic: 'Proprium autem quantitatis maxime est quod aequale vel inaequale dicitur. Singulum enim earum quae dictae sunt quantitatum aequale dicitur et inaequale, ut corpus aequale vel inaequale dicitur, et numerus aequalis vel inaequalis dicitur, dicitur tempus aequale vel inaequale; similiter et in aliis singulis quae dicta sunt aequale vel inaequale dicitur'. Ex istis verbis apparet quod dicit ipsas quantitates esse aequales vel inaequales, et non aliud secundum eas esse aequale vel inaequale. Et ideo dicendum est quod sicut albedo et substantia est aequalis vel inaequalis alteri, quamvis per accidens, ita substantia, secundum opinionem Aristotelis; et similiter qualitas est quantitas, quamvis per accidens.	Hence he says "a particular property of quantity is that it is called equal or unequal. For a singular of those things that were mentioned is called equal or unequal, e.g. a body is called equal or unequal [to another], and one number equal or unequal [to another], and one time equal or unequal [to another]. Similarly in other singulars which have been mentioned, the singular is said to be equal or unequal". From these words it is apparent that he says those quantities are equal or unequal, and not that something else is equal or unequal according to quantity. And therefore it should be said that just as a whiteness or a substance is equal or unequal to another, although per accidens, so also substance according to the opinion of Aristotle, and similarly a quality is a quantity, although per accidens.
Nec istis obstat illud quod postea dicit Philosophus quod in aliis praedicamentis non dicitur aliquid aequale vel inaequale, quia non intendit negare quin de contentis in aliis praedicamentis praedicetur 'aequale' vel 'inaequale', sed intendit dicere quod in aliis non dicitur per se aequale vel inaequale sed per accidens tantum. Et hoc insinuat cum dicit: 'In ceteris vero quae quantitates non sunt', supple, per se, 'non multum videtur aequale vel inaequale dici', quia de illis non per se, sed solum per accidens aequale vel inaequale dicitur. Cum hoc tamen stat quod vere de aliis dicitur aequale vel inaequale, et eodem modo quantitas praedicatur de eisdem.	Nor is what the Philosopher says afterwards an objection to these claims, that in other categories something is not called equal or unequal. For he does not deny that equal or unequal is predicated of things on other categories, but rather he means to say that equal or unequal is not predicated per se in other categories, but only per accidens. And he implies this when he says "In other categories which are not quantities" (add: per se), "it by no means seems that equal or unequal can be predicated". For of those items the predication of equal or unequal is not per se, but per accidens. But it is consistent with this that being equal or unequal is truly predicated of those items, and in the same way quantity is predicated of those same items.