Dist. 24, Art. 2, Q. 1
Book I: On the Mystery of the Trinity · Distinction 24
ARTICULUS II. De nominibus pure numeralibus.
Secundo principaliter quaeritur de secundo articulo, scilicet de nominibus pure numeralibus, ut sunt duo et tres etc. Et circa hoc similiter quaeruntur duo. Primo quaeritur, utrum dicantur positive, aut privative. Secundo, utrum dicantur secundum substantiam, aut secundum relationem.
QUAESTIO I. Utrum nomina pure numeralia in divinis positive, an privative dicantur.
Et quod dicantur privative solum, videtur:
1. Per auctoritatem Magistri in littera1, qui dicit, quod « horum usus magis inductus est causa privandi quam ponendi »; et videtur per auctoritates aliorum firmari auctoritas Magistri. Dicit enim Boethius in libro de Trinitate2: « Illud vere unum est, in quo nullus est numerus»; sed in divinis unum est verissime: ergo in divinis non est numerus: ergo isti termini in divinis aut falso dicuntur, aut non praedicant numerum. Sed non dicunt aliud quam numerum, si aliquid ponunt: ergo etc.
2. Item, Isidorus3 dicit, quod numerus est virtus[?] memoris, id est divisionis, secundum etymologiam; sed in Deo non cadit divisio, ergo nec numerus: ergo idem quod prius.
3. Item, Philosophus4 dicit, quod « numerus est multitudo mensurata per unum »; sed in Deo non cadit mensuratio, cum ipse sit immensus: ergo etc.
4. Item, hoc videtur per rationem: quia a quocumque removetur genus, et species; sed genus quantitatis removetur a Deo: ergo etc.
5. Item, in quocumque est genus, necesse est ponere aliquam specierum5: ergo si numerus est in Deo, vel est ibi binarius, vel ternarius, vel aliquis aliorum. Sed Sancti omnes species negant, ergo et genus: ergo idem quod prius.
Contra:
1. Si tantum privative dicerentur, quia non sunt unus vel duo, tunc ergo pari ratione posset dici: chimaerae sunt tres, quia non sunt una vel duae; sed illud non dicitur: ergo etc.
2. Item, quod dicat numerum, videtur. Eusebius6 dicit: « In divinis est numerus, sed non ordo »; sed si est ibi numerus: ergo contingit illum significare esse. Et si hoc: ergo positive tenentur dictiones, quae illum significant.
3. Item, Bernardus7: « Si una est essentia, tres quis numerum neget»? quasi dicat, nullus: ergo etc.
4. Item, hoc ipsum videtur ratione, quia discreta quantitas est maioris abstractionis quam continua: ergo et discretio magis quam duratio. Sed nomen dicens durationem in divinis dicitur positive, ut aeternus: ergo et nomen dicens discretionem.
5. Item, in quocumque est ponere speciem positive, est ponere genus; sed in Deo est ponere trinitatem: ergo et pluralitatem.
Conclusio. In divinis numerus dicitur quidem positive, sed non est ibi simpliciter, sed numerus personarum.
Respondeo: Ad praedictorum intelligentiam dicendum8, quod positio Magistri fuit, quod huiusmodi nomina numeralia in divinis non ponerent aliquid, sed privarent, sicut patet in littera. Et ratio huius positionis fuit, quia huiusmodi nomina, si aliquid ponunt, numerum utique ponunt; sed numerum non esse in divinis ponendum, et ratio dicit et auctoritas Sanctorum confirmat. Cum enim in divinis non sit divisio et separatio, non sit etiam aggregatio, non sit etiam mensuratio; numerus separationem importet antecedenter, et aggregationem et mensurationem consequenter: numerus in divinis non videtur esse9 ponendus. Et ideo dictiones numerales in divinis non dicunt aliquid, sed magis privant, maiorem scilicet numerum et minorem.
Sed nec positio nec ratio positionis est10 conveniens, si interius attendatur. Positio enim destruit
se ipsam. Ponit enim, quod nomina designantia pluralitatem dicantur privative, similiter et nomina designantia unitatem. Et si hoc, si sic invicem opponuntur, ut utrumque sit privatio alterius, erit ibi circulatio in notificando; et si utrumque alterius privatio est — cum privatio non sit privationis, sed habitus — utrumque aliquid ponit; et ita, si dicuntur privative, dicuntur positive; et propterea[?] positio non est conveniens.
Ratio similiter positionis non est convenienter sumpta. Nam numerus importat distinctionem et super hoc compositionem aggregationis; et quamvis in divinis non sit aggregatio, nihilominus est distinctio; et ideo numerus non est simpliciter removendus a divinis, sed numerus talis. Et Magister omnino removet; ideo positione sua defecit. Et in isto articulo non sustinetur[?] communiter a magistris Parisiensibus.
Concedendum ergo, quod huiusmodi nomina dicuntur positive, sicut probant rationes ad hoc inductae. Et concedendum, quod in divinis aliquo modo est numerus, aliquo modo non. Nam secundum quod dicit distinctionem personarum secundum originem, sic dicendum est esse in divinis; secundum autem quod aggregationem et divisionem substantialem dicit, non est ponendus numerus in divinis.
Ex his patent obiecta. Nam rationes ad primam partem procedunt de numero secundum eam acceptionem, qua sumitur in his inferioribus quantum ad conditiones praedictas. Unde in sensu suo verum concludunt, quod ibi non est numerus.
Similiter rationes ad partem oppositam procedunt, secundum quod numerus distinctionem certam importat, et hoc quidem est ponere in divinis; et ideo verum concludunt in suo sensu. Unde in divinis negandum est esse numerum simpliciter, sed concedendum est esse numerum personarum.
Ad 4. 5. Ad illud tamen quod obiicitur de quantitate continua, et de specie numeri, dicendum, quod nec quantitas continua est in Deo, quia aeternitas non est quantitas, nec Trinitas est species numeri.
I. Circa quaestionem, quid numeri in divinis formaliter significent, eadem redit differentia opinionum, quam supra (a. 1. q. 1.) circa rationem unius observavimus. Sententiam Petri Lombardi, quam S. Bonav. minus sufficientem esse censet, S. Thom. tum in Comment. (hic q. 1. a. 1.), tum in Sum. (1. q. 30. a. 3.) approbat eamque in hoc sensu explicat, quod numerus in divinis sit transcendentalis, qui numeratis personis addat duplicem negationem, scil. negationem divisionis in se et indivisionis ab alio, et quod praeter hanc negationem nihil aliud significet. Quod autem contra hanc sententiam obiicitur, scilicet eam incidere « in circulationem », id est circulum vitiosum, Angelicus (S. loc. cit. ad 3.) solvere nititur hac assertione, quod non unum et multum, sed unum et divisum sint formaliter opposita. Ad quod contrariae sententiae assertores respondent, divisum et multum esse idem. — Ceterum duae sententiae in hac assertione conveniunt, numerum addere entitatibus illam duplicem negationem; differunt vero circa hoc, quid unum et plura formaliter significent in Deo. Hic iterum asserit S. Bonav., unum, sicut alii termini rerum simplicium, cognosci quidem et definiri per negationem tanquam quid notius, ipsam vero negationem esse potius aliquid consequens ad constitutionem unius et plurium; sicut etiam incommunicabilitas personam iam constitutam consequitur, ut in distinctione sequenti docetur. S. Thomas convenit cum Magistro in conclusione, sed aliquatenus differt ab ipso, procedendo ab alio fundamento, de quo videri potest Caietanus (ad S. I. q. 30. a. 3.).
II. Cfr. praeter iam laudatos Alex. Hal., S. p. I. q. 65. m. 2. a. 1. — Petr. a Tar., hic. q. 2. a. 1. 2. — Richard. a Med., hic a. 2. q. 2. — Aegid. R., hic 1. princ. q. 2. — Henr. Gand., S. a. 73. q. 11. n. 8. et seq.; a. 74. q. 5[?]. n. 11; a. 75. q. 1. n. 9. — Dionys. Carth., hic q. 2. 3.
---
ARTICLE II. On the purely numeral names.
Secondly, the principal inquiry concerns the second article, namely on the purely numeral names, such as two and three etc. And concerning this, two [questions] are likewise asked. First, it is asked whether they are said positively or privatively. Second, whether they are said according to substance or according to relation.
Question I. Whether the purely numeral names in God are said positively or privatively.
And that they are said only privatively is shown:
1. By the authority of the Master in the littera1, who says that « the use of these is rather brought in for the sake of denying than of positing »; and the Master's authority seems to be confirmed by the authorities of others. For Boethius says in his book On the Trinity2: « That is truly one in which there is no number »; but in God "one" is most truly: therefore in God there is no number: therefore these terms in God are either said falsely, or they do not predicate number. But they say nothing other than number, if they posit anything: therefore etc.
2. Likewise, Isidore3 says that number is the power[?] of the memorial-mark, that is, of division, according to the etymology; but in God division does not occur, therefore neither does number: therefore the same as before.
3. Likewise, the Philosopher4 says that « number is a multitude measured by one »; but in God measuring does not occur, since he himself is immeasurable: therefore etc.
4. Likewise, this seems [to follow] by reason: since from whatever the genus is removed, the species also [is removed]; but the genus of quantity is removed from God: therefore etc.
5. Likewise, in whatever the genus is, it is necessary to posit some one of the species5: therefore if number is in God, either there is there the binary, or the ternary, or some [one] of the others. But all the saints deny the species, therefore also the genus: therefore the same as before.
On the contrary:
1. If they were said only privatively, since they are not one or two, then by parity of reason it could be said: chimaeras are three, since they are not one or two; but that is not said: therefore etc.
2. Likewise, that it expresses number, is plain. Eusebius6 says: « In God there is number, but not order »; but if there is number there: therefore it happens that it signifies being. And if so: therefore the words which signify it are taken positively.
3. Likewise, Bernard7: « If one is the essence, [and] three [are the persons], who would deny the number »? as if to say, no one: therefore etc.
4. Likewise, this same thing is plain by reason, since discrete quantity is of greater abstraction than continuous: therefore also discreteness more than duration. But a name expressing duration in God is said positively, as eternal: therefore also a name expressing discreteness.
5. Likewise, in whatever the species is to be posited positively, the genus is to be posited; but in God trinity is to be posited: therefore also plurality.
Conclusion. In God number is indeed said positively, but it is not there simply, but [rather] number of persons.
I respond: For an understanding of the foregoing it must be said8 that the position of the Master was that such numeral names in God did not posit anything, but were privative, as is plain in the littera. And the reason for this position was that such names, if they posit anything, posit number absolutely; but that number is not to be posited in God, both reason says and the authority of the saints confirms. For since in God there is no division and separation, neither is there aggregation, nor is there measuring; and number imports separation antecedently, and aggregation and measuring consequently: number in God does not seem9 to be posited. And therefore the numeral words in God do not say anything, but rather privatively deny, namely a greater number and a lesser.
But neither the position nor the reason of the position is10 suitable, if attention be turned inwardly. For the position destroys
itself. For it posits that names designating plurality are said privatively, and similarly the names designating unity. And if so, [and] if they are thus mutually opposed, so that each is the privation of the other, there will be there a circle in making known; and if each is the privation of the other — since privation is not of privation, but of habit — each posits something; and so, if they are said privatively, they are said positively; and on this account[?] the position is not suitable.
The reason of the position is likewise not suitably taken. For number imports distinction and beyond this composition of aggregation; and although in God there is no aggregation, nevertheless there is distinction; and therefore number is not simply to be removed from God, but [only] such-and-such number. And the Master removes [it] altogether; therefore by his position he failed. And in this article he is not commonly upheld[?] by the masters of Paris.
It must therefore be conceded that such names are said positively, as the reasons adduced for this prove. And it must be conceded that in God in some way there is number, in some way not. For according as it expresses the distinction of persons according to origin, so it must be said to be in God; but according as it expresses aggregation and substantial division, number is not to be posited in God.
From these things the objections are plain. For the reasons for the first part proceed concerning number according to that acceptation in which it is taken in these lower things with respect to the aforesaid conditions. Whence in their own sense they conclude truly, that there is no number there.
Likewise the reasons for the opposite part proceed according as number imports a certain distinction, and this indeed is to posit [it] in God; and therefore they conclude truly in their own sense. Whence in God it must be denied that there is number simply, but it must be conceded that there is number of persons.
To 4 and 5. To that, however, which is objected concerning continuous quantity, and concerning the species of number, it must be said that neither is continuous quantity in God, since eternity is not a quantity, nor is the Trinity a species of number.
I. Concerning the question, what the numbers in God formally signify, the same difference of opinions returns which we observed above (a. 1, q. 1) concerning the account of one. The judgement of Peter Lombard, which St. Bonaventure judges to be less sufficient, St. Thomas both in his Commentary (here, q. 1, a. 1), and in the Summa (I, q. 30, a. 3), approves and explains in this sense, that number in God is transcendental, which adds to the persons numbered a twofold negation, namely the negation of division in itself and of indivision from another, and that beyond this negation it signifies nothing else. As to what is objected against this judgement, namely that it falls « into circulation », that is, into a vicious circle, the Angelic Doctor (Summa loc. cit. ad 3) endeavors to solve by this assertion, that not one and many, but one and divided are formally opposed. To which the assertors of the contrary judgement reply, that divided and many are the same. — For the rest, the two judgements agree in this assertion, that number adds to entities that twofold negation; but they differ on this, what one and many formally signify in God. Here again St. Bonaventure asserts that one, like the other terms of simple things, is indeed known and defined through negation as something more known [to us], but the negation itself is rather something consequent to the constitution of the one and the many; just as also incommunicability follows upon the person already constituted, as is taught in the following distinction. St. Thomas agrees with the Master in the conclusion, but differs from him in some measure, proceeding from another foundation, on which Cajetan (on Summa I, q. 30, a. 3) may be consulted.
II. Cf., besides those already cited, Alexander of Hales, Summa p. I, q. 65, m. 2, a. 1. — Petrus a Tarantasia, here, q. 2, a. 1, 2. — Richard of Mediavilla, here a. 2, q. 2. — Aegidius Romanus, here 1 princ., q. 2. — Henry of Ghent, Summa a. 73, q. 11, n. 8 ff.; a. 74, q. 5[?], n. 11; a. 75, q. 1, n. 9. — Dionysius the Carthusian, here q. 2, 3.
---
- Circa principium. — In Vat. et cod. cc, omissis verbis in littera, legitur auctoritate pro per auctoritatem. Paulo infra nonnulli codd. ut A T U X cum ed. 1 auctoritatem loco auctoritates.Near the beginning. — In the Vatican [edition] and cod. cc, with the words in littera omitted, auctoritate is read in place of per auctoritatem. A little below, several codices such as A T U X with ed. 1 [read] auctoritatem in place of auctoritates.
- Cap. 2.Chapter 2.
- Locus citatus ex Isidoro nec inveniri nec a corruptione emendari potuit; maxima pars codicum habet virtus vel nutus memoris, pauci nutus memoriae. Idem locus apud B. Albertum hic a. 1. occurrit: nutus memoris; et in Comment. 1. Poster. tract. 2. c. 1. ait: « Numerus enim fit ex iteratione unitatis secundum mentem acceptae, propter quod et numerus dicatur nutus mentis vel memoris, hoc est divisionis »; et in antiquis edd. Commentarii S. Thomae, hic a. 2: unicus merus scilicet divisionis, quam lectionem per coniecturam parum feliciter P. Nicolai mutavit in unius meros vel unius merismos, scilicet divisio, adiungens: quod subiungitur ex Isidoro, nullibi apud illum occurrit. — In III. Etymolog. c. 3. Isidorus ait: « Numerus est multitudo ex unitatibus constituta; nam unum semen numeri esse (volunt), non numerum. Numero nummus nomen dedit et a sui frequentatione vocabulum indidit ». — In fine argumenti ante numerus Vat. perperam et praeter fidem mss. et edd. 1, 2, 3 omittit nec.The passage cited from Isidore could neither be found nor emended from corruption; the greater part of the codices has virtus vel nutus memoris, a few nutus memoriae. The same passage in Bl. Albert here a. 1 occurs as: nutus memoris; and in Commentary on I Posterior [Analytics], tract. 2, c. 1, he says: « For number arises from the iteration of unity received according to the mind, on account of which number is also called the nod (nutus) of the mind or of the memorial-mark, that is, of division »; and in the old editions of the Commentary of St. Thomas, here a. 2: unicus merus scilicet divisionis ("a single 'merus' namely of division"), which reading P. Nicolai by conjecture not very felicitously changed into unius meros vel unius merismos, namely divisio, adding: that which is appended from Isidore, nowhere in him occurs. — In III Etymologies c. 3 Isidore says: « Number is a multitude constituted of units; for they hold that the one is the seed of number, not [itself] a number. To "numerus" the "nummus" (coin) gave its name, and from its frequent use bestowed the term ». — At the end of the argument, before numerus, the Vatican [edition], wrongly and against the trust of the mss. and editions 1, 2, 3, omits nec.
- Libr. X. Metaph. text. 21. (IX. c. 6.).Book X Metaphysics, text 21 (IX, c. 6).
- Aristot., II. Topic. c. 2. (c. 4.): Necessarium, de quibus genus praedicatur, et specierum aliquam praedicari.Aristotle, II Topics, c. 2 (c. 4): It is necessary that, of those things of which the genus is predicated, some one of the species also is predicated.
- Cfr. De Trin. Confessio S. Eusebii Vercellensis, n. 8. Paulo post ex plurimis mss. et ed. 1 adiecimus esse.Cf. On the Trinity, Confession of St. Eusebius of Vercelli, n. 8. A little later, from very many mss. and ed. 1 we have added esse.
- Libr. V. de Consid. c. 7. n. 17: Cum tres illae personae illa substantia sint, et illa una substantia tres illae personae, quis numerum neget?Book V On Consideration, c. 7, n. 17: Since those three persons are that substance, and that one substance is those three persons, who would deny the number?
- Vat. notandum.The Vatican [edition reads] notandum ("it is to be noted") [in place of dicendum].
- Vat. cum paucis codd. est pro videtur esse, et deinde ideo etiam pro Et ideo; post dictiones adiungit vel rationes.The Vatican [edition] with a few codices [reads] est in place of videtur esse, and then ideo etiam in place of Et ideo; after dictiones it adds vel rationes ("or accounts").
- Vat. cum cod. cc videtur esse. Cod. W continens veritatem pro [...][?]The Vatican [edition] with cod. cc [reads] videtur esse. Cod. W [reads] continens veritatem in place of [...][?] (end of note truncated in the IA djvu OCR; see ambiguities log).