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Dist. 24, Art. 1, Q. 1

Book I: On the Mystery of the Trinity · Distinction 24

Textus Latinus
p. 420

ARTICULUS I. De termino numerali et partitivo unus.

QUAESTIO I. Utrum hoc nomen unus positive, vel privative dicatur in divinis.

Quod autem1 dicatur privative, videtur:

1. Per eius rationem. Nam Philosophus2 dicit, quod unum est quod non dividitur; sed ista ratio data est per privationem: ergo unum dicitur privative.

2. Item, Commentator dicit super Metaphysicam3, quod unum et multa opponuntur sicut privatio et habitus, quia unum dicit privationem, multitudo dicit habitum; quod si verum est, unum non tantum in Deo, sed etiam in omnibus dicitur privative.

3. Item, hoc ipsum videtur ratione, quia unum opponitur ei quod est multa: aut ergo contradictorie, aut contrarie, aut privative, aut relative.4 Non contradictorie; hoc patet. Iterum nec relative, quia relativa sunt simul5, et unum dependet ab alio mutuo; sed unum non dependet a multis. Non contrarie, quia unum contrariorum non est alterius principium: sed unum est principium multorum6: ergo per locum a divisione opponitur privative. Sed constat, quod multa dicit positionem: ergo unum non dicit nisi privationem.

4. Item, quod in Deo specialiter dicatur privative, videtur, quia unum, secundum quod dicitur positive, est principium multitudinis et quantitatis7: sed in Deo nulla est quantitas: ergo nec unum positive dicitur.

5. Item, hoc ipsum videtur, quia, si Deus est positive unus et lapis unus, ergo Deus et lapis sunt duo: ergo Deus et creatura constituunt numerum, et si hoc, Deus est pars numeri, quod supra improbatum est8. Si dicas, quod non sequitur, quia unum non dicitur univoce; illud enim9 nihil est, ut videtur; quia, si aliquid ponit, cum istud etiam possit convenire creaturae, ad minus analogice, et secundum analogiam attendatur numeratio, ut cum dicitur: humanitas et albedo sunt duae essentiae: ergo hoc non solvit.

Contra:

1. Ab eodem habet aliquid esse et unum10, quoniam forma, quae dat esse, dat esse distinctum; si ergo ens non dicitur privative, sed positive, pari ratione nec unum de aliquo dicitur privative.

2. Item, quod sonat in complementum sonat in habitum, non in privationem; sed unum sonat in complementum, quia quanto aliquid perfectius, tanto magis accedit ad unitatem11: ergo unum non dicitur privative.

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3. Item, si unum est privativum, constat quod non nisi12 multitudinis. Sed contra: nulla privatio antecedit habitum naturaliter13; sed unum naturaliter antecedit multa: ergo unum non est privatio.

4. Item, nulla privatio constituit suum habitum nec salvatur in illo; sed unum salvatur in multis et illa constituit14: ergo non opponitur ut privatio: non ergo accipitur privative.

Conclusio. Unum in Deo dicitur solummodo positive, et non privative; in creaturis vero aliquando positive, aliquando privative etiam secundum rem.

Respondeo: Dicendum, quod quorundam opinio fuit, et Magistri principaliter, quod quidquid sit de hoc nomine unum in creaturis, in Deo non dicitur positive, sed privative, ut dicit in littera et assumit auctoritatem ab Hilario; quamvis Hilarius non dicat expresse, nisi quod horum nominum usus in Deo inventus est magis causa privandi quam aliquid ponendi. Et ratio sua fuit, quia unum, positive dictum, est principium quantitatis et numeri; Deus autem non habet in se quantitatem nec in se est numerabilis nec alii connumerabilis.

Sed quamvis haec positio probabilis videatur15, tamen communiter non tenetur. Et ratio huius est, quia, cum unum multo completius sit in Deo quam in creaturis, multo fortius ibi dicitur positive. Et rursus, cum omnis unitas ad primam unitatem reducatur, et non est reductio habitus ad privationem, necesse est, quod unus16 in Deo aliquid ponat.

Et propterea dicendum, quod est loqui de hoc nomine unus in creaturis quantum ad rem intellectam, vel quantum ad rationem intelligendi. Si loquamur quantum ad rationem intelligendi, sic dico, quod dicitur privative; unde et ratio eius assignatur per privationem divisionis sive multitudinis. Et hoc est, quia unum est primum, et prima non habent intelligi a nobis neque notificari nisi per posteriora; et inde est, quod privative dicitur17. Unde unitas in substantia, vel quantitate, vel qualitate, quia habet aliquid prius, per quod possit intelligi, dicitur positive, ut identitas, aequalitas, similitudo, et eorum opposita privative18.

Si autem loquamur quantum ad rem intellectam, sic unum habet respectum ad materiam, et habet respectum ad formam. Ratione respectus ad materiam est in se indivisum, tamen potentia divisibile est; et quia potentia materialis se habet per modum privationis, similiter et unum. Ratione respectus ad formam, quae dat esse distinctum et limitatum, sic dicit positionem19. Quoniam igitur in Deo unum est omnino secundum formam, in creaturis attenditur et secundum formam et secundum materiam, hinc est, quod in Deo solum positive, in creaturis aliquando accipitur positive, aliquando privative etiam20 secundum rem.

Ad 1. Ad illud ergo quod obiicitur primo, quod definitur sive notificatur privative; patet responsio, quia secundum rationem sui nominis, eo quod primum, sic debet notificari.

Ad 2. Ad illud quod obiicitur secundo, quod opponitur ut privatio; dicendum, quod unum per respectum ad materiam accipitur privative, et sic accipit Commentator; per respectum ad formam, accipitur contrarie, secundum quod multitudo formaliter accipitur; per respectum ad actum consequentem, qui est mensurare, accipitur relative et secundum genus relativorum in quo unum non dependet ab altero, sicut patet in scientia et scibili21; et sic diversae super hoc opiniones sunt verae.

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Ad 3. Ad illud quod obiicitur, quod in Deo non est principium numerandi etc.; dicendum, quod unum dicit privationem multitudinis secundum generalem nominis rationem; sed illa privatio, etsi nomine tenus sit privatio, tamen realiter est positio; quia quanto magis est privatio divisionis in aliquo, tanto illud est completius et perfectius. Cum igitur in Deo sit perfectissima unitas, ibi accipitur secundum omnimodam privationem multitudinis. Hoc autem modo dicitur unum, quod non habet in se22 actu multitudinem, nec est in potentia ad multitudinem, neque per divisionem neque per aggregationem. Hoc autem unum est perfectissimum et summum et infinitum, et illud23 non est in potentia ad numerum, et hoc non est alii connumerabile; et hoc modo est in solo Deo. Et sic patet, quod dicitur Deus unus positive et quomodo differat unitas eius a creatura.

Ad 4. Quod ergo obiicitur, quod unum est principium multitudinis; dicendum, quod verum est in unitate creata, sed non est verum in unitate perfecta et increata — dico principium intra, sicut pars24.

Ad 5. Unde si dicatur: Deus et creatura sunt duo, aut hoc improprie dictum est, et duo cadit a ratione numeri secundum rem; aut si dicit numerum, hoc est solum a parte intelligentis; quia, cum intelligit diversa et distincta, accipit sub ratione numeri, sicut, cum intelligit intellectus noster, concernit tempus25.

Scholion

I. Pro intelligentia huius quaestionis haec praenotamus.

1. Unum dupliciter accipitur: vel quatenus convertitur cum ente, vel quatenus est formaliter principium numeri. Primum est transcendens omne genus, sicut ens, verum, bonum, et haec unitas essentialis invenitur in omnibus rebus; secundum est in praedicamento quantitatis et dicitur unitas accidentalis. Unitatem accidentalem non esse in Deo, una omnium est sententia. Unde tota quaestio est de unitate essentiali.

2. Controversia est inter philosophos et theologos, quid hoc unum, secundum rationem addat super ens. Differentia sententiarum principalium doctorum a multis auctoribus determinatur, ut sequitur. S. Thom. (S. I. q. 11. a. 1.), Henr. Gand. (Quodl. I. q. 1.) aliique, Aristotelem et eius commentatorem Averroem secuti, resolvunt: « quod unum non addit super ens rem aliquam, sed tantum negationem divisionis ». Et (S. I. q. 11. a. 1. ad 3.) dicit S. Thom.: « Unum addit aliquid secundum rationem super ens ». — Omnino oppositum docuit Avicenna, teste S. Thoma (loc. cit.), asserendo, quod unum addat rem aliquam positivam super substantiam entis, ut albus super hominem. Ipse enim tenuit falsam opinionem, non dari nisi accidentalem unitatem, quae est principium numeri. — Mediam viam inter opinionem Avicennae et Averrois tenent S. Bonav. (hic), Alex. Hal. (S. p. I. q. 13. m. 1. 2, et q. 65. m. 2. a. 1.), B. Albert. (hic. a. 3.), Petr. a Tar. (qui hic q. I. a. 2. doctrinam Seraphici dilucide contrahit), Richard. a Med. (hic q. 1. a. 1. praesertim ad 1.). Hi docent, unum importare aliquid positivum, sed tantum virtualiter ab ente distinctum. Scot. (IV. Metaph. c. 2, et II. Sent. d. 3. q. 2.) cum suis putat, unum esse quid positivum et ex natura rei formaliter distinctum ab ente.

II. S. Bonaventura praeter duplicem speciem unitatis distinguit duplicem modum loquendi de unitate, scilicet quoad rem intellectam, id est secundum rationem essendi, et quoad rationem intelligendi, id est secundum modum, quo intellectui nostro ratio unitatis innotescit. Intellectus enim humanus simplicissima, quae sensui minus sunt obvia, semper a posteriori intelligit et notificat, unde etiam unum vel punctum per negationem divisionis explicat. Itaque sanctus Doctor concedit, quod unitas secundum rationem innotescendi dicat privationem divisionis. — Secundum rationem vero essendi iterum ipse unum dupliciter distinguit: primo, quatenus habet respectum ad materiam, quae tum est potentia divisibilis, tum ad formam se habet per modum privationis; et sic iterum concedit, quod unum non dicat quid positivum. Secundo, quatenus unum respicit formam; sub hoc respectu unum iuxta eius sententiam importat aliquid positivum, identificatum tamen cum eius subiecto, ut aliquis actus formae; et sic unum addit super ens rationem positivae perfectionis. De hac controversia cfr. Caietanus (ad S. I. q. 11. a. 1.) et Forestus (de Trinitatis Mysterio q. 5. pag. 235 seqq.), qui nititur sententiam S. Thomae praesertim ex q. 1. de Verit. a. 1. ita interpretari, ut in re parum vel nihil a Seraphico discedat.

III. Solutiones ad 2. 3. 4. fundantur in hoc, quod unum et multa sub diversa ratione opponuntur vel privative, vel contrarie, vel relative. Respectu ad materiam unum privat divisionem et multitudinem actualem, ad quam ratione materiae est in potentia; respectu ad formam, quae tum esse tum unum esse confert, unum sumitur positive et contrarie ad multa; respectu « ad actum consequentem qui est mensurare », cum unum sit mensura multorum, accipitur relative; nam sic est pars multitudinis et non privatio. Haec oppositio relativa ad multitudinem pertinet ad genus imperfecte relativorum, quae nec semper sunt simul, nec unum ab alio dependet; cuius exemplum est in scientia et scibili. — De hac specie relationis cf. infra d. 30. q. 3. et Scholion.

Haec doctrina Seraphici amplius explicatur a B. Alberto M. (hic a. 3.) his verbis: « Dicendum, quod est unum indivisibile reductum ad materiam vel dispositionem materiae, et unum reductum ad naturam formae, sicut dicimus continuitate unum; et cum dicimus continuitate unum, dicimus materia unum et forma unum, quia continuitas dispositio materiae est. Quidquid autem continuitate est unum, potentia est multa; omnis autem potentia in genere privationis est, praecipue potentia materiae, quae est potentia continui; quod patet, quia continuum potentia passiva multum est, et non potentia activa. Unum ergo reductum ad materiae unitatem oppositionem habet ad multum, sicut privatio ad habitum; quia talis unitas susceptibilis est multitudinis; et haec est intentio Philosophi et commenti (commentatoris) hoc dicentis. Unum autem, quod reductum est ad formam, habet tres considerationes, scil. secundum formalem rationem unius, et secundum id quod est, et secundum id quod est proximum et consequens ipsum. Primo modo consideratum habet rationem contrarietatis ad multum, quia utrumque ponitur in specie, et mutuo se expellunt ab eodem susceptibili... Si autem accipiatur unum secundum id quod est, ipsum nullam habet oppositionem ad multum, sed potius est principium multi et salvatur substantialiter in ipso multo. Et hoc attendit Avicenna dicens, quod non habet oppositionem, quia nec privatio facit habitum nec salvatur in ipso... Si accipiatur unum secundum rationem proximo se consequentem, quae est ratio mensurae; tunc unum, quod est certum, est mensurans multum, quod est incertum; et sic opponuntur ut mensura et mensuratum. Et hoc intendit Aristoteles in X. Primae philosophiae et Commentator ibidem et Avicenna in sua Metaphysica dicentes, quod opponuntur relative unum et multum. Sed distinguitur ibidem in relativis, quod quaedam sunt, quorum utrumque dependet ad alterum, et illorum utrumque ponit reliquum, ut pater et filius, et dominus et servus; quaedam autem sunt, quorum unum dependet ad alterum, et non e converso, et ideo ibi unum ponit alterum et non e converso, ut scientia et scibile; et sic opponuntur relative unum et multum, quia multum ponit unum et non convertitur ».

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English Translation

ARTICLE I. On the numeral and partitive term "one."

Question I. Whether this name "one" is said positively or privatively in divine matters.

That1 [it is said] privatively, however, is shown:

1. By its account. For the Philosopher2 says that one is that which is not divided; but this account is given through privation: therefore "one" is said privatively.

2. Likewise, the Commentator says on the Metaphysics3 that "one" and "many" are opposed as privation and habit, since "one" expresses privation, "many" expresses habit; and if this is true, "one" is said privatively not only in God but also in all things.

3. Likewise, this same thing seems [to follow] by reason, since "one" is opposed to that which is "many": either then contradictorily, or contrarily, or privatively, or relatively.4 Not contradictorily; this is plain. Again, neither relatively, since relatives are simultaneous5, and one depends on the other mutually; but "one" does not depend on "many." Not contrarily, since one of contraries is not the principle of the other: but "one" is the principle of many6: therefore by the topic from division it is opposed privatively. But it is established that "many" expresses position: therefore "one" expresses nothing but privation.

4. Likewise, that in God it is said privatively in a special way is plain, since "one," insofar as it is said positively, is the principle of multitude and quantity7: but in God there is no quantity: therefore neither is "one" said positively.

5. Likewise, this same thing is plain, since, if God is positively one and a stone is one, therefore God and a stone are two: therefore God and a creature constitute a number, and if so, God is part of a number, which has been disproved above8. If you say that this does not follow, since "one" is not said univocally; this9 is nothing, as it seems; for if it posits something — since this could also belong to a creature, at least analogically, and numbering be reckoned according to analogy, as when one says: humanity and whiteness are two essences — therefore this does not solve [the difficulty].

On the contrary:

1. From the same source a thing has being and being-one10, since the form, which gives being, gives distinct being; if therefore "being" is not said privatively but positively, by parity of reason neither is "one" said privatively of anything.

2. Likewise, what sounds in the direction of completion sounds in the direction of habit, not of privation; but "one" sounds in the direction of completion, since the more perfect a thing is, the more it approaches unity11: therefore "one" is not said privatively.

3. Likewise, if "one" is privative, it is established that it is so only12 of multitude. But on the contrary: no privation precedes habit naturally13; but "one" naturally precedes "many": therefore "one" is not a privation.

4. Likewise, no privation constitutes its own habit nor is preserved in it; but "one" is preserved in many [things] and constitutes them14: therefore it is not opposed as a privation: therefore it is not received privatively.

Conclusion. "One" in God is said only positively, and not privatively; in creatures, however, sometimes positively, sometimes privatively even according to the thing itself.

I respond: It must be said that the opinion of certain ones, and of the Master principally, was that whatever may be the case about this name one in creatures, in God it is not said positively but privatively, as he says in the littera and takes up an authority from Hilary; although Hilary does not say it expressly, except that the use of these names in [reference to] God is found rather for the sake of denying [something] than of positing something. And his reason was that "one," said positively, is the principle of quantity and of number; but God does not have quantity in himself, nor is he in himself numerable, nor numerable along with another.

But although this position seems probable15, nevertheless it is not commonly held. And the reason for this is that, since "one" is much more completely in God than in creatures, much more strongly is it there said positively. And again, since every unity is reduced to the first unity, and there is no reduction of habit to privation, it is necessary that "one"16 in God posit something.

And therefore it must be said that one [way] is to speak of this name one in creatures with respect to the thing understood, [another] with respect to the account by which [it is] understood. If we speak with respect to the account by which [it is] understood, thus I say that it is said privatively; whence its account is also assigned through privation of division or multitude. And this is because "one" is first, and first things cannot be understood by us nor made known except through posterior things; and hence it is that it is said privatively17. Whence unity in substance, or quantity, or quality, since it has something prior through which it can be understood, is said positively, as identity, equality, likeness, and their opposites privatively18.

If, however, we speak with respect to the thing understood, then "one" has a relation to matter, and has a relation to form. By reason of the relation to matter, it is in itself undivided, yet it is potentially divisible; and since material potency stands by way of privation, so likewise does "one." By reason of the relation to form, which gives distinct and limited being, thus it expresses position19. Since therefore in God "one" is wholly according to form, [whereas] in creatures it is considered both according to form and according to matter, hence it is that in God it is taken only positively, [but] in creatures sometimes positively, sometimes privatively even20 according to the thing itself.

To 1. To that, then, which is objected first, that it is defined or made known privatively; the response is plain, since according to the account of its name, in that it is first, it must be made known thus.

To 2. To that which is objected secondly, that it is opposed as a privation; it must be said that "one" by relation to matter is taken privatively, and so the Commentator takes it; by relation to form, it is taken contrarily, according as multitude is taken formally; by relation to the consequent act, which is to measure, it is taken relatively and according to the genus of relatives in which one [member] does not depend on the other, as is plain in knowledge and the knowable21; and so the various opinions on this are true.

To 3. To that which is objected, that in God there is no principle of numbering etc.; it must be said that "one" expresses privation of multitude according to the general account of the name; but that privation, although in name it is a privation, nevertheless really is a position; since the more there is privation of division in something, the more complete and perfect that thing is. Since therefore in God there is the most perfect unity, there it is taken according to every-way privation of multitude. In this way, however, that is called "one" which does not have in itself22 multitude in act, nor is it in potency to multitude, neither through division nor through aggregation. Now this "one" is most perfect and supreme and infinite, and that23 is not in potency to number, and this is not numerable along with another; and in this way it is in God alone. And so it is plain that God is called "one" positively, and how his unity differs from [that of] a creature.

To 4. What then is objected, that "one" is the principle of multitude; it must be said that this is true in created unity, but is not true in perfect and uncreated unity — I mean a principle within, as a part24.

To 5. Hence if it be said: God and a creature are two, either this is said improperly, and "two" falls away from the account of number according to the thing itself; or if it expresses a number, this is only on the part of the one understanding; since, when [the intellect] understands diverse and distinct [things], it takes [them] under the account of number, just as, when our intellect understands, it concerns time25.

Scholion

I. For an understanding of this question we note these [things] beforehand.

1. "One" is taken in two ways: either insofar as it is converted with being, or insofar as it is formally a principle of number. The first is transcendent of every genus, like being, true, good, and this essential unity is found in all things; the second is in the predicament of quantity and is called accidental unity. That accidental unity is not in God is the one [common] judgement of all. Hence the whole question is about essential unity.

2. There is a controversy among philosophers and theologians [as to] what this one, according to its account, adds over being. The difference of the principal opinions of the doctors is determined by many authors as follows. St. Thomas (Summa I, q. 11, a. 1), Henry of Ghent (Quodl. I, q. 1), and others, following Aristotle and his commentator Averroes, resolve: « that "one" does not add over being any thing, but only the negation of division ». And (Summa I, q. 11, a. 1, ad 3) St. Thomas says: « "One" adds something according to reason over being ». — Quite the opposite Avicenna taught, on the testimony of St. Thomas (loc. cit.), asserting that "one" adds some positive thing over the substance of being, as "white" over "man." For he himself held the false opinion that there is given only an accidental unity, which is the principle of number. — A middle way between the opinion of Avicenna and Averroes is held by St. Bonaventure (here), Alexander of Hales (Summa p. I, q. 13, m. 1, 2, and q. 65, m. 2, a. 1), Bl. Albert (here, a. 3), Petrus a Tarantasia (who here, q. I, a. 2, lucidly summarizes the Seraphic Doctor's teaching), Richard of Mediavilla (here, q. 1, a. 1, especially ad 1). These [doctors] teach that "one" imports something positive, but only virtually distinct from being. Scotus (IV Metaph. c. 2, and II Sent. d. 3, q. 2) with his [followers] thinks that "one" is something positive and from the nature of the thing formally distinct from being.

II. Beyond the twofold species of unity, St. Bonaventure distinguishes a twofold mode of speaking about unity, namely with respect to the thing understood, that is, according to the account of being, and with respect to the account of understanding, that is, according to the mode by which the account of unity becomes known to our intellect. For the human intellect always understands and makes known the most simple things, which are less obvious to sense, a posteriori; whence also it explains "one" or "point" through negation of division. And so the holy Doctor concedes that unity, according to the account of being made known, expresses privation of division. — But according to the account of being, again he himself distinguishes "one" in two ways: first, insofar as it has a relation to matter, which both is potentially divisible, and stands toward form by way of privation; and so again he concedes that "one" does not express anything positive. Second, insofar as "one" looks to form; under this respect "one," according to his judgement, imports something positive, identified however with its subject, as some act of form; and so "one" adds over being the account of positive perfection. On this controversy, cf. Cajetan (on Summa I, q. 11, a. 1) and Forestus (On the Mystery of the Trinity, q. 5, pp. 235 ff.), who endeavors so to interpret the judgement of St. Thomas, especially from q. 1 de Verit. a. 1, that he departs little or nothing in fact from the Seraphic Doctor.

III. The solutions to [objections] 2, 3, 4 are founded on this, that "one" and "many" under diverse accounts are opposed either privatively, or contrarily, or relatively. With respect to matter, "one" denies division and actual multitude, to which by reason of matter it is in potency; with respect to form, which confers both being and being-one, "one" is taken positively and contrarily to "many"; with respect « to the consequent act which is to measure », since "one" is the measure of many, it is taken relatively; for so it is part of multitude and not a privation. This relative opposition to multitude pertains to the genus of imperfectly relative [things], which neither are always simultaneous, nor does one depend on the other; an example of which is in knowledge and the knowable. — On this species of relation cf. below d. 30, q. 3, and the Scholion.

This doctrine of the Seraphic [Doctor] is more amply explained by Bl. Albert the Great (here, a. 3) in these words: « It must be said that there is one indivisible reduced to matter or to a disposition of matter, and one reduced to the nature of form, as we say "one by continuity"; and when we say "one by continuity," we say "one in matter" and "one in form," because continuity is a disposition of matter. But whatever is one by continuity is many in potency; and every potency is in the genus of privation, especially the potency of matter, which is the potency of the continuum; which is plain, since the continuum in passive potency is many, and not in active potency. Therefore "one" reduced to the unity of matter has opposition to "many," as privation to habit; since such unity is susceptible of multitude; and this is the intention of the Philosopher and the commentary (the Commentator) saying this. But "one" which is reduced to form has three considerations, namely according to the formal account of "one," and according to that which it is, and according to that which is proximate and consequent to it. Considered in the first way it has the account of contrariety to "many," since both are placed in a species, and they mutually expel each other from the same recipient... If, however, "one" is taken according to that which it is, it itself has no opposition to "many," but rather is the principle of "many" and is preserved substantially in the "many" itself. And this Avicenna attends to, saying that it does not have opposition, since neither does privation produce habit, nor is it preserved in it... If "one" is taken according to the account proximately consequent to it, which is the account of measure; then "one," which is certain, is what measures the "many," which is uncertain; and so they are opposed as measure and measured. And this Aristotle intends in book X of the First Philosophy and the Commentator at the same place and Avicenna in his Metaphysics, saying that "one" and "many" are opposed relatively. But it is distinguished there in relatives, that some there are of which both [members] depend on the other, and of those each posits the other, as father and son, and master and servant; but some there are of which one depends on the other and not conversely, and therefore there one [member] posits the other and not conversely, as knowledge and the knowable; and so "one" and "many" are opposed relatively, since "many" posits "one" and is not converted ».

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Apparatus Criticus
  1. Supple cum ed. 4 mss. Mox ex mss. et ed. 1 adiecimus hoc et eius.
    Supply with ed. 4 [and the] mss. Soon afterwards, from the mss. and ed. 1 we have added hoc et eius ("this and its").
  2. Verba Aristotelis invenies supra pag. 408, nota 1 transcripta. — In fine argumenti cod. Y per privationem pro privative.
    You will find the words of Aristotle transcribed above on p. 408, note 1. — At the end of the argument, cod. Y [reads] per privationem ("through privation") in place of privative ("privatively").
  3. Libr. X. text. 9: Multum igitur et unum sunt contraria ea contrarietate, secundum quam sunt contraria privatio et habitus... quia indivisibilitas est privatio divisibilitatis, et divisibilitas est quasi habitus. — In fine argumenti, fere omnibus mss. et ed. 1 obnitentibus, Vat., omisso etiam, exhibet dicit privationem pro dicitur privative.
    Book X, text 9: "Many" therefore and "one" are contraries by that contrariety according to which privation and habit are contraries... since indivisibility is privation of divisibility, and divisibility is as it were habit. — At the end of the argument, with nearly all the mss. and ed. 1 resisting, the Vatican [edition], with etiam also omitted, exhibits dicit privationem in place of dicitur privative.
  4. Vat. cum pluribus codd. Item; cod. Y quamlibet particulam omittit. Mox post simul cod. X addit natura, quod et ab Aristotele, de Praedicam. c. de Ad aliquid sive de Relatione, additur.
    The Vatican [edition] with several codices [reads] Item ("likewise"); cod. Y omits any particle. Soon afterwards, after simul, cod. X adds natura ("by nature"), which is also added by Aristotle in Categories, c. on Ad aliquid or on Relation.
  5. Cfr. Dionys., de Div. Nom. c. 5. et 13. Vide etiam argum. immediate subsequens. — Locum a divisione, de quo mox est sermo, Petrus Hispanus in Summula super librum Topicorum, circa finem, sic definit: Est habitudo unius condividentium ad reliquum, ut: si Socrates est animal, aut est animal rationale aut irrationale; sed non est irrationale: ergo rationale. Maxima: Posito uno membrorum dividentium in aliquo subiecto, removetur reliquum (et remoto uno, ponitur reliquum).
    Cf. Dionysius, On the Divine Names, c. 5 and 13. See also the argument immediately following. — The "topic from division," about which there is presently discussion, Peter of Spain in his Summula on the book of Topics, near the end, defines thus: It is the relation of one of the co-dividing [members] to the remainder, e.g.: if Socrates is an animal, [he] is either a rational animal or an irrational; but he is not irrational: therefore rational. Maxim: When one of the dividing members is posited in a subject, the remainder is removed (and when one is removed, the remainder is posited).
  6. Plura de hac quadruplici oppositione eiusque principiis invenies in Aristot., de Praedicam. c. de Oppositis.
    You will find more on this fourfold opposition and its principles in Aristotle, Categories, c. on Opposites.
  7. Cfr. Aristot., V. Metaph. text. 12, et X. text 21. (IV. c. 6, et IX. c. 6). Boeth., I. Arithmeticae, c. 7. dicit: Quare constat, primam esse unitatem cunctorum, qui sunt in naturali dispositione numerorum, et etiam rite totius, quamvis prolixae, genitricem pluralitatis agnosci. — Paulo ante Vat. absque ulla auctoritate mss. et ed. 1 omittit secundum. Mox post nulla est Vat. cum aliquibus mss. addit omnino.
    Cf. Aristotle, V Metaph., text 12, and X, text 21 (IV, c. 6, and IX, c. 6). Boethius, I Arithmetic, c. 7, says: Whence it is established that unity is the first of all [the things] which are in the natural arrangement of numbers, and also rightly that it is to be acknowledged as the begetter of the entire — though prolix — totality of plurality. — A little before, the Vatican [edition], without any authority of mss. or ed. 1, omits secundum. Soon after nulla est, the Vatican [edition] with some mss. adds omnino ("at all").
  8. Dist. 19. p. II. q. 4. — In principio huius argumenti in pluribus codd. et ed. 1 deest ipsum. Dein Vat. contra antiquiores mss. et ed. 1 videtur igitur, quod lapis et Deus pro ergo Deus et lapis. Mox nonnulli codd. ut SZ bb Deus cum creatura pro Deus et creatura.
    Distinction 19, p. II, q. 4. — At the beginning of this argument, in several codices and ed. 1 ipsum is missing. Then the Vatican [edition], against the older mss. and ed. 1, [reads] videtur igitur, quod lapis et Deus in place of ergo Deus et lapis. Soon, several codices such as SZ bb [read] Deus cum creatura in place of Deus et creatura.
  9. Ex plurimis mss. et edd. 1, 2, 3, 6 restauravimus enim, pro quo Vat. certe.
    From very many mss. and editions 1, 2, 3, 6 we have restored enim ("for"), in place of which the Vatican [edition reads] certe ("certainly").
  10. Cfr. Dionys., de Div. Nom. c. 8. et 13; Boeth., de Unitate et Uno. De ratione addita vide supra pag. 84, nota 7. — Vat. cum cod. cc, aliis codd. et ed. 1 refragantibus, omittit esse secundo loco positum.
    Cf. Dionysius, On the Divine Names, c. 8 and 13; Boethius, On Unity and the One. On the added account see above p. 84, note 7. — The Vatican [edition] with cod. cc, other codices and ed. 1 resisting, omits esse placed in the second position.
  11. In libr. de Causis, prop. 17: « Omnis virtus unita plus est infinita quam virtus multiplicata ». Vide etiam Dionys., loc. paulo ante cit.
    In the Book of Causes, proposition 17: « Every united power is more infinite than a multiplied power ». See also Dionysius, the place cited a little before.
  12. Supple: privativum, vel cum Vat. et aliquibus codd. respectu.
    Supply: privativum, or with the Vatican [edition] and some codices respectu ("with respect to").
  13. Aristot., II. de Caelo et Mundo, text. 18. (c. 3.): καὶ τῆς στερήσεως πρότερον ἡ κατάφασις (affirmatio), iuxta translationem Arabico-latinam: Habitus est ante privationem, ut calidum et frigidum. Et text. 22. (c. 4.) reperitur propositio subsequens: Quoniam autem prius natura in unoquoque genere unum multis et simplex compositis etc.
    Aristotle, II On the Heavens and the World, text 18 (c. 3): καὶ τῆς στερήσεως πρότερον ἡ κατάφασις (affirmation), according to the Arabic-Latin translation: Habit is before privation, as hot and cold. And in text 22 (c. 4) the following proposition is found: But since in each genus "one" is by nature prior to many, and simple to composites etc.
  14. Sub hoc respectu Dionys., de Div. Nom. c. 13. § 1. ait: « Non enim est multitudo non participans uno ». Vide etiam supra d. 19. p. II. q. 4. definitionem numeri ex Aristotele et Boethio allatam. — Plura similia argumenta invenies apud Avicennam, III. Metaph. c. 6.
    Under this respect Dionysius, On the Divine Names, c. 13, § 1, says: « For there is no multitude not participating in one ». See also above d. 19, p. II, q. 4, the definition of number adduced from Aristotle and Boethius. — You will find many similar arguments in Avicenna, III Metaph. c. 6.
  15. Vat. cum solo recentiore codd. cc habeatur, et inferius multo formalius pro multo fortius.
    The Vatican [edition], with only the more recent cod. cc, [reads] habeatur, and below multo formalius ("much more formally") in place of multo fortius ("much more strongly").
  16. Vat. cum cod. cc unum.
    The Vatican [edition] with cod. cc [reads] unum [in place of unus].
  17. Aristot., X. Metaph. text. 9. (IX. c. 3.) Dicitur autem ex contrario ipsum unum, et significatur ex divisibili indivisibile, eo quod multitudinem esse et divisibile magis est sensibile quam esse indivisibile. Quare multitudo ratione prior quam indivisibile propter sensum est. — Paulo ante, antiquioribus mss. et ed. 1 refragantibus, Vat. et pro neque; hic vero contra fere omnes codd. et ed. 1 mutata interpunctione, legit dicitur unum. Unitas autem in substantia etc. Cod.: dicitur unum simpliciter; sed unum et unitas in etc.
    Aristotle, X Metaph., text 9 (IX, c. 3): "One" itself is said from the contrary, and the indivisible is signified from the divisible, since to be a multitude and to be divisible is more sensible than to be indivisible. Whence multitude is by reason prior to the indivisible because of sense. — A little before, with the older mss. and ed. 1 resisting, the Vatican [edition reads] et in place of neque; here, however, against nearly all the codices and ed. 1, with the punctuation changed, it reads dicitur unum. Unitas autem in substantia etc. Cod.: dicitur unum simpliciter; sed unum et unitas in etc.
  18. Aristot., loc. cit. text. 1: Item unius quidem est... idem, simile et aequale; multitudinis vero diversum, dissimile et inaequale est. Cfr. etiam V. Metaph. text. 27. (IV. c. 22.).
    Aristotle, loc. cit. text 1: Likewise of one indeed... is the same, the like, and the equal; but of multitude, the diverse, the unlike, and the unequal. Cf. also V Metaph., text 27 (IV, c. 22).
  19. August., de Genesi ad Lit., libr. imperfect. c. 10. n. 32: « Vis ipsa formae commendatur nomine unitatis. Hoc est enim vere formari, in unum aliquid redigi; quoniam summe unum est omnis formae principium ». Cfr. etiam libr. de Vera Religione, c. 36. n. 66. — B. Albert., hic a. 1. ait: Sunt enim tres actus formae sive eius, quo res est id quod est: primus est dare esse, secundus autem dare rationem naturae, et tertius est terminare; et ab isto ultimo actu formae est ratio unius, quia per hoc efficitur in se indivisa et ab aliis divisa; et haec est eius definitio, et hoc intendit Philosophus, quando dixit, quod id quod non dividitur, dicitur unum, secundum quod non dividitur; hoc modo bene dicimus, quod haec res una, haec res et illa sunt duae, et hoc modo bene dicimus, quod Deus est unus.
    Augustine, On Genesis according to the Letter, unfinished book, c. 10, n. 32: « The very power of form is commended by the name of unity. For this is truly to be formed, to be brought back into something one; since the supremely one is the principle of every form ». Cf. also the book On True Religion, c. 36, n. 66. — Bl. Albert, here a. 1, says: For there are three acts of form, or of that by which a thing is what it is: the first is to give being, the second is to give the account of [its] nature, and the third is to terminate; and from this last act of form is the account of "one," since through this it is made undivided in itself and divided from others; and this is its definition, and this is what the Philosopher intends when he said that "what is not divided is called one according as it is not divided"; in this way we rightly say that this thing [is] one, [that] this thing and that are two, and in this way we rightly say that God is one.
  20. In Vat. desideratur etiam, quod exhibetur a mss. et ed. 1.
    In the Vatican [edition] etiam is missing, which is exhibited by the mss. and ed. 1.
  21. Cfr. de hoc Aristot., X. Metaph. text 2-22. (IX. c. 1-6.).
    Cf. on this Aristotle, X Metaph., text 2–22 (IX, c. 1–6).
  22. Antiquiores codd. cum ed. 1 exhibent in se, quod Vat. cum cod. cc minus apte omittit.
    The older codices with ed. 1 exhibit in se ("in itself"), which the Vatican [edition] with cod. cc less suitably omits.
  23. Codd. GZ et ed. 1 addunt unum. Mox codd. V X ideo pro illud.
    Codices GZ and ed. 1 add unum ("one"). Soon, codices V X [read] ideo ("therefore") in place of illud ("that").
  24. Id est: Unum tunc est principium multitudinis, quando ipsum sicut pars intrat multitudinem. — Vat. contra fere omnes mss. et ed. 1 post intra perperam adiungit se, et mox post Unde addit non est verum.
    That is: "One" is then the principle of multitude, when it itself as a part enters into the multitude. — The Vatican [edition], against nearly all the mss. and ed. 1, after intra wrongly adds se, and soon after Unde adds non est verum.
  25. Aristot., de Memoria et Reminiscentia, c. 1: Non contingit intelligere aliquid sine continuo, neque sine tempore quae non in tempore sunt etc.
    Aristotle, On Memory and Reminiscence, c. 1: It is not possible to understand anything without the continuous, nor without time those things which are not in time etc.
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