Authors/Ockham/Summa Logicae/Book I/Chapter 39

Latin	English
[CAP. 39. DE ISTO TERMINO 'UNUM']	[Chapter 39. On the term ‘one’]
'Unum' autem est passio entis, quia est praedicabile de ente per se secundo modo, et hoc quia significat aliquid quod non eodem modo significatur per ens, quamvis alio modo significatur per ens. Nam 'ens' quidquid significat positive et affirmative significat; 'unum' vero significat quodlibet significatum per 'ens' tam positive et affirmative quam negative et remotive. Quod patet per definitionem exprimentem quid nominis ipsius. 'Unum' tamen multipliciter dicitur, quia secundum Philosophum, V Metaphysicae': "Unum dicitur aliud secundum accidens, aliud secundum se". Quod sic est intelligendum quod hoc nomen 'unum' de aliquibus praedicatur per accidens, ita quod propositio illa est per accidens, sicut haec est per accidens 'Coriscus et musicus sunt unum', similiter ista est per accidens 'iustum et musicum sunt unum'. Cum hoc tamen stat quod tales sunt verae 'musicum et iustum sunt per se unum' et 'musicus et Coriscus sunt per se unum'. Et si inveniantur in auctoribus tales propositiones 'musicum et album sunt unum per accidens', 'musicus per accidens est unum cum Corisco', debent exponi, ut per istas intelligantur tales 'haec est per accidens: musicum et album sunt unum', 'haec est per accidens: musicus et Coriscus sunt unum'.	Now ‘one’ is an attribute of a being, because it is predicable of a being per se in the second mode, and this is because it signifies something that is not signified in the same way by ‘a being’. For whatever ‘being’ signifies, it signifies positively and affirmatively. But ‘one’ signifies whatever is signified by ‘being’, both positively and affirmatively, and negatively and remotely. Which is clear through its nominal definition. But ‘one’ is predicated in many ways, according to the Philosopher in V Metaphysics. ‘ ‘One’ is predicated per accidens in one way, per se in another’. Which is to be understood as meaning that the name ‘one’ is predicated per accidens, so that the proposition is per accidens, just as ‘Coriscus and a musician are one’ is per accidens. Similarly ‘a just person and a musician are one’ is per accidens. But this is consistent with the fact that ‘a musician and a just person are one per se’ and ‘a musician and Coriscus are one per se’. And if you find in some authorities propositions like ‘a musician and a white person are one per accidens’, or ‘a musician is per accidens one with Coriscus’, they ought to be expounded in such a way that ‘this is per accidens: a musician and a white person are one’, and ‘this is per accidens: a musician and Coriscus are one’ are understood by them.
Qualiter autem istae propositiones distinguuntur et non aequipollent, ostendetur inferius. Unum secundum se dicitur illud de quo vel de quibus dicitur unum non per accidens sed per se. Et quamvis Philosophus, V Metaphysicae, ponat multos modos unius per se, tamen ad praesens sufficiat ponere tres modos unius quibus logici frequenter utuntur. 'Unde quaedam dicuntur unum numero, hoc est de quibusdam terminis supponentibus pro eodem verificatur hoc praedicabile 'unum numero', sic dicendo 'iste homo et Socrates sunt unum numero', 'Marcus et Tullius sunt unum numero'.	But how those propositions have distinct senses, and are not equivalent, will be shown below. One per se is predicated of a thing or things of which ‘one’ is predicated not per accidens but per se. And although the Philosopher (Metaphysics V) gives many modes of ‘one’ per se, still for the moment it is sufficient to give three modes of ‘one’, which logicians frequently use. ‘Hence some things are called ‘one’ in number, i.e. of certain terms suppositing for the same thing, the predicable ‘one in number’ is verified, such as in saying ‘that man and Socrates are one in number’, ‘Marcus and Tully’ are one in number’.
Et ideo quod dicit Aristoteles, V Metaphysicae, quod "unum numero sunt quorum materia est una", intelligendum est quod tunc dicuntur unum numero quando non sunt distincta nec secundum materiam nec secundum formam. Quaedam autem dicuntur unum specie, quorum scilicet est eadem species, ita quod semper quaecumque sunt unum specie sunt simpliciter plura vel unum numero, dicente Aristotele, I Topicorum "Idem specie sunt quae cum sint plura", ita, supple, si non sint unum numero, "sub eadem specie continentur".	And so what Aristotle says (Metaphysics V) that ‘what is one in number is whose material is one’ should be understood as saying that things are called ‘one in number’ when they are not distinct either according to material or form. Now certain things are called ‘one in species’, namely, of which there is the same species, so that whatever are one in species are either absolutely several, or one in number. Aristotle says (Topics I) that ‘the same in species are those which are several’, to which you need to add, if they are not one in number, that ‘they are contained under the same species’.
Genere autem sunt illa unum quae sub eodem genere continentur, ita quod quaecumque sunt unum genere sunt simpliciter plura specie et numero, vel sunt unum specie, dicente Aristotele: "Quaecumque numero, specie unum; sed quaecumque specie, non omnia numero, sed genere omnia sunt unum, quaecumque et specie; quaecumque vero genere, non omnia specie". Ex istis verbis sequitur quod nihil est unum specie nisi sit unum numero vel plura numero. Et ideo impossibile est quod sit aliqua natura quae sit una specie et non sit una numero nec plures res numero.	Now things are ‘one in genus’ when they are contained under the same genus, so that whatever are one in genus are absolutely several in species and in number, or are one in species. Aristotle says ‘whatever are one in number are one in species, but not all that are one in species are one in number. Whatever are all one in species are one in genus, but not all that are one in genus are one in species’. From these words it follows that nothing is one in species unless it is one in number or several in number. And therefore it is impossible that there is some nature which is one in species and is not one in number or several things in number.
Similiter impossibile est quod sit aliqua natura una genere nisi illa sit una specie vel plura specie. Et ideo dicendum est quod plura individua sunt unum specie, et quod unum individuum est unum specie cum alio individuo. Similiter plura individua diversarum specierum sunt unum genere, et unum individuum unius speciei est unum genere cum alio individuo alterius speciei, sicut Socrates et iste asinus sunt unum genere, hoc est de Sorte et isto asino natum est unum genus praedicari. Similiter Socrates et Plato sunt unum specie, hoc est Socrates et Plato sub una specie continentur, vel Socrates et Plato sunt illa a quibus potest abstrahi una species communis eis.	Similarly, it is impossible that there is some nature that is one in genus unless it is one in species or several in species. And therefore it should be said that several individuals are one in species, and that one individual is one in species with another individual. Similarly, several individuals of diverse species are one in genus, and one individual of one species is one in genus with another individual of another species, just as Socrates and this donkey are one in genus, i.e. one genus is suited to be predicated of Socrates and this donkey. Similarly, Socrates and Plato are one in species, i.e. Socrates and Plato are contained under one species, or Socrates and Plato are things from which one species common to them can be abstracted.
Et si dicatur quod tunc non essent unum realiter, dicendum est quod sunt unum realiter, accipiendo 'unum' secundum quod dicitur de illis quae sunt unum specie; quia Socrates et Plato sunt realiter illa a quibus potest abstrahi una species. Et ita concedendum est quod est aliqua unitas minor unitate numerali, sed ipsamet individua sunt unum realiter, illo modo accipiendo unum, ita quod nihil imaginabile distinctum ab individuo vel individuis est unum, illo modo accipiendo unum.	And if it is said that then they would not be one in reality, it should be said that they are one in reality, taking ‘one’ according as it is predicated of things that are one in species. For Socrates and Plato are really those things from which one species can be abstracted. And so it should be conceded that there is some unity less than a numerical unity. But those very individuals are really one, by that mode of taking ‘one’. Thus nothing imaginable distinct from an individual or individuals is one, by that mode of taking ‘one’.