1 “Eadem tribus aeternitas, eadem incommutabilitas, eadem maiestas, eadem potestas. In patre unitas, in filio aequalitas, in spiritu sancto unitatis aequalitatisque concordia, et tria haec unum omnia propter patrem, aequalia omnia propter filium, conexa omnia propter spiritum sanctum” (Augustine, , De doctrina Christiana , 1.12 [V.5], ed. Green, R. P. H. [Oxford, 1995], 16–17).Google Scholar

2 Moderatus had suggested that Pythagorean philosophers adverted to numbers as a pedagogical device, since the primal forms of things, being invisible and difficult to conceive, are best conveyed by definite numbers. The number three, he states, represents the perfection of things, while the number one denotes “unity [henotês], equality [isotêtos] or sameness, and the cause of harmony [sympnoia] and sympathy” (Porphyry, , Vita Pythagorae 49, ed. Nauck, August, Porphryrii philosophi Platonici opuscula selecta [Leipzig, 1886; Hildesheim, , 1963], 44:8–12; trans. in Guthrie, K. S., The Pythagorean Sourcebook [Rapids, Grand, 1987], 133).Google Scholar

3 “Deus est monos, monadem ex se gignens, in se unum reflectens ardorem…. Sic quidem etiam in multis: unaquaeque unitas proprium habet numerum quia super diversum ab aliis reflectitur” (Hudry, Françoise, Le Livre des XXIV Philosophes: résurgence d'un texte du IVe siècle [Paris, 2009], 150). For details on Victorinus's sources, including Vita Pythagorae 50–51, see ibid., 24–29.Google Scholar

4 Augustine, , De doctrina Christiana , 1.13–14 (VI.6), ed. Green, , 16–19.Google Scholar

5 See Horn, Christoph, “Augustins Philosophic der Zahlen,” Revue des Études Augustiniennes 40 (1994): 389–415.Google Scholar

6 The triad has long been viewed as an invention of Peter Abelard, but new research by Dominique Poirel has raised the possibility of Hugh of St. Victor's priority (Livre de la nature et débat trinitaire au XIIe siècle: Le De tribus diebus de Hugues de Saint-Victor [Turnhout, 2002], 345–420). See further, however, Constant Mews, J., “The World as Text: The Bible and the Book of Nature in Twelfth-Century Theology,” in Scripture and Pluralism: Reading the Bible in the Religiously Plural Worlds of the Middle Ages and Renaissance , ed. Thomas, J. Heffernan, and Thomas, E. Burman, (Leiden, 2005), 95–122; cf. comments by Boyd Taylor Coolman and Hugh Feiss in Trinity and Creation , ed. Coolman, Boyd Taylor and Coulter, Dale M., Victorine Texts in Translation 1 (Turnhout, 2010), 28–35 and 52–58, respectively. On the prehistory of the triad in ancient Greek philosophy, see further Reynolds, P. L., “The Essence, Power and Presence of God: Fragments of the History of an Idea, From Neopythagoreanism to Peter Abelard,” in From Athens to Chartres: Neoplatonism and Medieval Thought: Studies in Honour of Édouard Jeauneau , ed. Westra, Haijo Jan (Leiden, , 1992), 351–80.Google Scholar

7 On Peter Lombard, see below; cf. Summa theologiae I, q. 38, art. 8.Google Scholar

8 Thierry of Chartres, Tractatus de sex dierum operibus 30–47, in Commentaries on Boethius by Thierry of Chartres and His School , ed. Nikolaus, M. Häring, (Toronto, 1971), 568–75.Google Scholar

9 Boethius, Institutio arithmetica 1.1.4, ed. Guillaumin, Jean-Yves, Institution Arithmétique (Paris, 2002), 7. Without being able to explore this further, one should note that in the late eleventh century a new office for the feast of the Trinity was instituted at Cluny that included this antiphon: “In patre manet aeternitas in filio aequalitas in spiritu sancto aeternitatis aequalitatisque connexio.” The office was compiled by Stephen of Liège, who drew from Alcuin's prayers and treatises, which in turn borrowed especially from Marius Victorinus's theology of divine unity. See Feiss, Hugh, “The Office for the Feast of the Trinity at Cluny in the Late Eleventh Century,” Liturgy O. C. S. O. 17.3 (1983): 39–66; cf. Jungmann, Josef Andreas, “Marius Victorinus in der karolingischen Gebetsliteratur und im römischen Dreifaltigkeitsoffizium,” in Kyriakon: Festschrift Johannes Quasten , ed. Granfield, Patrick and Jungmann, Josef A. (Münster, 1970), 691–97 and Hadot, Pierre, “Marius Victorinus et Alcuin,” Archives d'histoire doctrinale et littéraire du moyen âge 29 (1954): 5–19, at 7. I owe thanks to an anonymous reviewer for illuminating this connection.Google Scholar

10 See Thierry of Chartres, Commentum super Boethii librum de Trinitate 2.30–38, in Commentaries , ed. Häring, 77–80; idem, Lectiones in Boethii librum de Trinitate 5.16–19, in Commentaries , ed. Häring, , 218–19; idem, Glosa super Boethii librum de Trinitate 5.17–29, in Commentaries , ed. Häring, , 296–99.Google Scholar

11 “Unitas ergo ex se per semel equalitatem gignit. Unitas enim semel unitas est. Gignit ergo unitas equalitatem unitatis ita tamen ut res eadem sit unitas et unitatis equalitas. Unitas ergo in eo quod gignit Pater est; in eo quod gignitur Filius est. Unum igitur Pater est et Filius…. Amor autem hic et conexio nec gignitur nec gignit sed ab unitate et ab unitatis equalitate procedit: non ab uno scilicet illorum sed ab utroque. Nec enim amor uel conexio unius tantum est. Hie amor igitur et conexio ab unitate et ab unitatis equalite procedens Spiritus sanctus est ut quoniam unitas Pater est, equalitas essendi Filius, a Patre et Filio procedat Spiritus sanctus” (Thierry, , Commentum 30, 38, in Commentaries , ed. Häring, , 78, 80).Google Scholar

12 See Chenu, M.-D., “Une définition pythagoricienne de la vérité au moyen âge,” Archives d'histoire doctrinale et littéraire du moyen âge 28 (1961): 7–13; Jeauneau, Édouard, “Mathématique et Trinité chez Thierry de Chartres,” in Die Metaphysik im Mittelalter , ed. Wilpert, Paul (Berlin, 1963), 289–95; Riesenhuber, Klaus, “Arithmetic and the Metaphysics of Unity in Thierry of Chartres: On the Philosophy of Nature and Theology in the Twelfth Century,” in Nature in Medieval Thought — Some Approaches East and West , ed. Koyama, Chumaru (Leiden, 2000), 43–73; McGinn, Bernard, “Does the Trinity Add Up? Transcendental Mathematics and Trinitarian Speculation in the Twelfth and Thirteenth Centuries,” in Praise No Less Than Charity: Studies in Honor of M. Chrysogonus Waddell , ed. Elder, Rozanne (Kalamazoo, 2002), 237–64.Google Scholar

13 Southern, R. W., Scholastic Humanism and the Unification of Europe, vol. 2: The Heroic Age (Oxford, 2001), 88.Google Scholar

14 Cusanus, Nicolaus, Dies Sanctificatus (Sermo 22), §22, in Nicolai de Cusa opera omnia , vol. 16.4, ed. Haubst, Rudolf and Bodewig, Martin (Hamburg, 1984), 346. Cf. De docta ignorantia 1.7–10, §§18–29, in Nicolai de Cusa opera omnia, vol. 1, ed. Hoffmann, Ernst and Klibansky, Raymond (Leipzig, 1932), 14–21.Google Scholar

15 Cusanus's version of the arithmetic Trinity has been well explained elsewhere. See Santinello, Giovanni, “Mittelalterliche Quellen der ästhetischen Weltanschauung des Nikolaus von Kues,” in Die Metaphysik im Mittelalter , ed. Wilpert, , 679–85; McGinn, Bernard, “Unitrinum Seu Triunum: Nicholas of Cusa's Trinitarian Mysticism,” in Mystics: Presence and Aporia , ed. Kessler, Michael and Sheppard, Christian (Chicago, 2003), 90–117; Elpert, Jan Bernd, “Unitas-Aequalitas-Nexus: Eine textkommentierende Lektüre zu De venatione sapientiae (Kap. XXI–XXVI),” in Nikolaus von Kues: De venatione sapientiae , ed. Euler, Walter Andreas, Mitteilungen und Forschungsbeiträge der Cusanus-Gesellschaft 32 (Trier, 2010), 127–82.Google Scholar

16 Haubst, Rudolf, Das Bild des Einen und Dreieinen Gottes in der Welt nach Nikolaus von Kues (Trier, 1952), 1.Google Scholar

17 See, e.g., Beierwaltes, Werner, “Einheit und Gleichheit: Eine Fragestellung im Platonismus von Chartres und ihre Rezeption durch Nicolaus Cusanus,” in idem, Denken des Einen: Studien zur neuplatonischen Philosophie und ihrer Wirkungsgeschichte (Frankfurt am Main, 1985), 368–84. Cf. Christian Trottmann's comparison of Alan of Lille and Nicholas of Cusa in “Unitas, aequalitas, conexio: Alain de Lille dans la tradition des analogies trinitaires arithmétiques,” in Alain de Lille, Le Docteur Universel: philosophie, théologie et littérature au XIIIe siècle , ed. Solère, Jean-Luc, Vasiliu, Anca, and Galonnier, Alain (Turnhout, 2005), 401–27.Google Scholar

18 Duhem, Pierre, “Thierry de Chartres et Nicolas de Cues,” Revue des sciences philosophiques et théologiques 3 (1909): 525–31; cf. Chenu, , “Une définition Pythagoricienne.”.Google Scholar

19 See McGinn's appendix in “Unitrinum Seu Triunum,” 105–9. Nicholas invents, for example, triads of absolute equality, equality of equality, and their nexus (De aequalitate, 1459); the unity of love, the equality of love, the connection of love (Cribratio Alkorani, 1461); and possibility, equality, and their union (Compendium theologiae, 1464).Google Scholar

20 E.g., Lemoine, Michel, “Le Nombre dans l'École de Chartres,” PRIS-MA 8 (1993): 65–78. This may contribute to Lemoine's misperception that although Thierry's mathematical “speculation” would return again with Meister Eckhart and Nicholas of Cusa, his theology was already in the twelfth century enjoying great success and broad diffusion (ibid., 73–74).Google Scholar

21 Jeauneau, Édouard, “Note sur l'École de Chartres,” in idem, “Lectio philosophorum”: Recherches sur l'Ecole de Chartres (Amsterdam, 1973), 5–36. Jeauneau lists the following sources: two shorter glosses from Thierry's circle, Clarembald of Arras, De septem septenis, Helinand of Froidmont's Christmas sermon, Alan of Lille's Regulae, and Achard of St. Victor's De unitate, as well as a collection of others who cite the Augustinian triad without giving it Thierry's meaning.Google Scholar

22 Ibid., 11.Google Scholar

23 McGinn proposes that Meister Eckhart may have mediated Thierry's arithmetic Trinity to Cusanus. See McGinn, , “Does the Trinity Add Up?” (n. 12 above), 258–64.Google Scholar

24 Colish, Marcia L., Peter Lombard , vol. 1 (Leiden, 1994), 101–5.Google Scholar

25 Life and Works of Clarembald of Arras , ed. Häring, Nikolaus M. (Toronto, 1965), 4. On what we know of Thierry's life and his standing in the schools, see Ward, J. O., “The Date of the Commentary on Cicero's ‘De Inventione’ by Thierry of Chartres (ca. 1095–1160?) and the Cornifician Attack on the Liberal Arts,” Viator 3 (1972): 219–73.Google Scholar

26 Commentaries , ed. Häring, (n. 8 above), 47. Häring first dated Commentum to 1135, but subsequently revised it to 1148. Mews argues for the “early 1120s” (Mews, Constant J., “In Search of a Name and Its Significance: A Twelfth-Century Anecdote about Thierry and Peter Abaelard,” Traditio 44 [1988]: 171–200, at 192). Mews concurs (as do I) with Häring's sequence of Tractatus, Commentum, Lectiones, and Glosa, pace Enzo Maccagnolo (see Maccagnolo, Rerum universitas: Saggio sulla filosofia di Teodorico di Chartres [Florence, 1976], 211–15) and Dronke, Peter (“Thierry of Chartres,” in A History of Twelfth-Century Western Philosophy, ed. idem [Cambridge, 1988], 358–85, at 360).Google Scholar

27 Fredborg, Karen M., Latin Rhetorical Commentaries by Thierry of Chartres (Toronto, 1988), 8–9; Life and Works of Clarembald , ed. Häring, , 23–27.Google Scholar

28 On this tumultuous period in which the cathedral schools developed a new program for theological education, see Ferruolo, Stephen C., The Origins of the University: The Schools of Paris and Their Critics, 1100–1215 (Stanford, 1985); Fichtenau, Heinrich, Heretics and Scholars in the High Middle Ages, 1000–1200 , trans. Kaiser, Denise A. (University Park, PA, 1998); and Stephen Jaeger, C., The Envy of Angels: Cathedral Schools and Social Ideals in Medieval Europe, 950–1200 (Philadelphia, 1994). Two fine surveys are Mews, Constant J., “Philosophy and Theology 1100–1150: The Search for Harmony,” in Le XIIe siècle: Mutations et renouveau en France dans le première moitié du XIIe siècle , ed. Gasparri, François (Paris, 1994), 159–203 and Gemeinhardt, Peter, “Logic, Tradition, and Ecumenics: Developments of Latin Trinitarian Theology between c. 1075 and c. 1160,” in Trinitarian Theology in the Medieval West , ed. Kärkkainen, Pekka (Helsinki, 2007), 10–68.Google Scholar

29 Mews, Constant J., “The Council of Sens (1141): Abelard, Bernard, and the Fear of Social Upheaval,” Speculum 77 (2002): 342–82. On Abelard's possible connections to Thierry and his similar interests in Plato and the Timaeus , see further Luscombe, D. E., The School of Peter Abelard (Cambridge, 1970), 57–58 and Gregory, Tullio, “Abélard et Platon,” Studi Medievali, ser. 3a, 13 (1972): 539–62.Google Scholar

30 For an overview of Gilbert's academic career, see Gross-Diaz, Theresa, The Psalms Commentary of Gilbert of Poitiers (Leiden, 1996), 1–24. A good introduction to his doctrine of God is Williams, Michael E., The Teaching of Gilbert Porreta on the Trinity, Analecta Gregoriana 56 (Rome, 1951); cf. Lauge Olaf Nielsen, Theology and Philosophy in the Twelfth Century (Leiden, 1982), 142–63.Google Scholar

31 Marcia Colish argues that Peter Lombard's engagement with Gilbert's views in the wake of Rheims was both more substantive and more positive than is often assumed; see Colish, , “Gilbert, the Early Porretans, and Peter Lombard: Semantics and Theology,” in Gilbert de Poitiers et ses contemporains , ed. Jolivet, Jean and de Libera, Alain (Naples, 1987), 229–50.Google Scholar

32 For this dating, see Colish, , Peter Lombard , 23–25. On the theologies of unitas and forma in the Porretani and Chartrians, cf. Otto, Stephan, Die Funktion des Bild-begriffes in der Theologie des 12. Jahrhunderts, Beiträge zur Geschichte der Philosophic und Theologie des Mittelalters (= BGPhThM) 40 (Münster, 1963), 176–99, 224–50. Otto notes (ibid., 185) that Gilbert never used the mathematical triad.Google Scholar

33 See, for example, Magnus, Albertus, Commentarii in I Sententiarum, dist. 31, art. 1–2, in Opera omnia , vol. 27, ed. Borgnet, S. C. A. (Paris, 1893), 99–101; Aquinas, Thomas, Commentum in Quatuor Libros Sententiarum, vol. 1, dist. 31, q. 1, art. 2, in Opera omnia, vol. 6 (Parma, 1856, repr. New York, 1948), 250.Google Scholar

34 On the history of the theory of appropriated Trinitarian names, see Ott, Ludwig, Untersuchungen zur theologischen Briefliteratur der Frühscholastik , BGPhThM 34 (Münster, 1937), 254–66 and 581–94 and Hödl, Ludwig, Von der Wirklichkeit und Wirksamkeit des dreieinen Gottes nach der appropriativen Trinitätstheologie des 12. Jahrhunderts, Mitteilungen des Grabmann-Instituts der Universität München (Munich, 1965), 5–14, and in more doctrinal perspective, 28–59. Hödl argues that the divisions of the twelfth century are ultimately the fruit of two responses to Arianism after Nicaea: “Der Unterschied zwischen der Trinitätstheologie Augustins und des Hilarius ist der Unterschied der abendländischen und morgenländischen Theologie, der Unterschied einer an der Proprienspekulation orientierten Trinitätslehre und der appropriativen Trinitätsbetrachtung” (ibid., 50). This situation is then repeated in the twelfth century and exacerbated by the divide between Peter Lombard's almost exclusive use of Augustine and Gilbert of Poitiers's adoption of Boethius and Hilary of Poitiers (cf. ibid., 26, 35, 52).Google Scholar

35 As Théodore de Régnon remarked in 1892, “le système d'Abailard est la théorie des appropriations, mais renversée” (Ott, , Untersuchungen , 256 n. 48). Abelard's deliberations begin when he asks whether diversity in the Trinity is real, nominal, or somehow both; none of the answers is immediately satisfactory. “Aut enim, inquiunt, haec diuersitas personarum in solis uocabulis consistit, non in re, ut uidelicet uocabula tantum diuersa sint et nulla sint in Deo rei diuersitas, aut in re sola et non in uocabulis; aut simul et in re et in uocabulis” (Abelard, Theologia Christiana 3.90, ed. Buytaert, E. M., Petri Abaelardi Opera Theologica, GCM 12 [Turnhout, 1969], 230). Peter of Poitiers begins his account of appropriative names with an allusion to this passage: “Fit autem personarum distinctio bipartito: tum appropriatione nominum et rerum, tum appropriatione nominum, sed non rerum” (Sententiae Petri Pictaviensis, Lib. 1, cap. 22, ed. Moore, Philip S. and Dulong, Marthe, vol. 1 [Notre Dame, 1943], 183, lines 5–7).Google Scholar

36 “Dieser Satz bereitete dem theologischen Denken der Frühscholastik, das sich noch nicht allenthalben zur vollen Klarheit über den Unterschied zwischen Proprietäten und Appropriationen durchgerungen hatte, erhebliche Schwierigkeiten” (Ott, , Untersuchungen , 569).Google Scholar

37 McGinn, , “Does the Trinity Add Up?” (n. 12 above), 256 n. 53. McGinn cites Lectiones 5.16, but in my opinion there are other passages that provide stronger evidence.Google Scholar

38 “Quamuis autem unitas et eius equalitas sint una penitus substantia tamen quoniam nichil se ipsum gignere potest et alia proprietas est genitorem esse que proprietas est unitatis: alia uero proprietas est genitum esse que proprietas est equalitatis idcirco ad designandum has proprietates que sunt unitatis et equalitatis eterna identitate diuini philosophi uocabulum persone apposuerunt ita ut ipsa eterna substania dicatur persona genitoris secundum hoc quod ipsa est unitas: persona uero geniti secundum hoc quod ipsa est equalitas” (Thierry, , Tractatus 41, in Commentaries , ed. Häring, [n. 8 above], 572).Google Scholar

39 “Equalitas uero diuine substantie ascribitur per hoc quod est Filius quia in Uerbo i.e. in Filio genito a Patre cuncta creauit…. Et per talem proprietatem hoc uocabulum filius refertur ad deum” (Thierry, , Lectiones 7.7, in Commentaries , ed. Häring, , 225).Google Scholar

40 “Istud amborum relatiuum est ad proprietates has quas dixi equalitatem et unitatem: non ad res discretas. Non enim est nisi sola unitas: trina tamen in proprietate. Conexio enim unitas est…. Tamen non concedimus quod conexio equalitas sit: propter personales proprietates” (ibid.; cf. ibid., 7.6, in Commentaries , ed. Häring, , 225; idem, Glosa 5.22–29, in Commentaries ed. Häring, , 297–98).Google Scholar

41 Ibid. On the distinction of proportio and proportionalitas and their significance for the broader study of the quadrivium, see Boethius, , Institutio arithmetica 2.40.1–3, ed. Guillaumin, (n. 9 above), 140.Google Scholar

42 In this way I hope to distinguish this limited case of reading Augustine's triad from the larger debate on the logic of universals between “nominalists” and “realists.” For a survey of old and new scholarship on twelfth-century nominalism, see the special issue of Vivarium 30.1 (1992) edited by Courtenay, William J..Google Scholar

43 The Cistercian Helinand of Froidmont (1162–1237), another important witness of Thierry's views, is too late to be considered here. Helinand's Sermon 2 (PL 212:486A–498C) seems to draw on Thierry's Commentum or Tractatus — his most well-circulated texts, particularly among Cistercian monasteries — in its references (sometimes verbatim) to the Son as aequalitas and veritas and to God as forma essendi. At the same time, some passages of the sermon resemble the Johannine exegesis of De septem septenis; see, e.g., PL 212:491C on John 14:6. For background on Helinand's sermons, see Kienzle, Beverly M., “Hélinand de Froidmont et la prédication cistercienne dans le Midi (1145–1229),” in La prédication en Pays d'Oc (XIIe-début XVe siècle), Cahiers de Fanjeaux 32 (Toulouse, 1997), 37–67.Google Scholar

44 Both texts follow the sole exemplar of Thierry's Lectiones in MS Paris BN Lat 14489, fols. 62r–66r (Tractatus de Trinitate) and fols. 67r–95v (Commentarius Victorinus, formerly called In titulo and attributed to Ps.-Bede). On Commentarius Victorinus, see the general account in Ermenegildo Bertola, “Il ‘De Trinitate’ dello Pseudo Beda,” Rivista di Filosofia Neoscolastica 48 (1956): 316–33. Häring, Nikolaus M. (“A Short Treatise on the Trinity from the School of Chartres,” Mediaeval Studies 18 [1956]: 125–34) notes several reasons for dating the two works after Thierry's Glosa, whether they were written by an aging Thierry or by one of his students: “Especially the manner of handling the ‘mathematical’ explanation of the Trinity, based on the Augustinian dictum cited above, offers impressive evidence to the effect that both works belong to the school of Thierry of Chartres” (ibid., 128). Häring would later argue, however, that Commentarius Victorinus could well have been written by Thierry himself, noting “very striking points of contact” with the anonymous Tractatus de Trinitate (Commentaries on Boethius, 40–45); cf. Ott, , Untersuchungen, 571.Google Scholar

45 Thierry, , Lectiones 7.5, in Commentaries , ed. Häring, , 224–25; Glosa 5.17, in Commentaries , ed. Häring, , 296–97.Google Scholar

46 “Procedat igitur Augustinus in medium qui trium personarum distinctionem sub hac forma uerborum diligens ueritatis speculator assignat: In Patre inquit unitas in Filio equalitas in Spiritu sancto unitatis equalitatis conexio. Sancte Trinitatis statum non de facie ad faciem intuens ad mathematicam ut ex forma uerborum datur intelligi disciplinam confugit ut saltern sic aliquam distinctionis personarum insinuaret noticiam. Arimetici namque unitatem primum omnium constituunt numerorum principium” ( Tractatus de Trinitate 12, in Commentaries , ed. Häring, , 306). “Ad hanc enim pro modulo capacitatis nostre declarandam dicit Augustinus: In Patre unitas in Filio equalitas in Spiritu sancto unitatis equalitatisque conexio uel concordia. Sed sicut ex formula uerborum haberi potest uolens Augustinus quoquo modo insinuare quod ineffabile erat et incomprehensibile confugit ad mathematicam. Arithmetici unitatem principium numerorum constituunt” (Commentarius Victorinus 81, in Commentaries , ed. Häring, , 498).Google Scholar

47 This suggestion by the two student treatises — that mathematical symbols can work hand in hand with negative theology — is a striking anticipation of Nicholas of Cusa's entire theological project.Google Scholar

48 Tractatus de Trinitate 12, in Commentaries , ed. Häring, , 306; Commentarius Victorinus 81, in Commentaries , ed. Häring, , 498.Google Scholar

49 Tractatus de Trinitate 12, 13, 17, 18, in Commentaries , ed. Häring, , 306–7. See, for example, Thierry, , Commentum 2.34 and 4.4, in Commentaries , ed. Häring, , 78, 96; Tractatus 30, in Commentaries , ed. Häring, , 568; but cf. Thierry, , Lectiones 3.5, in Commentaries , ed. Häring, , 178.Google Scholar

50 Commentarius Victorinus 87, in Commentaries , ed. Häring, , 499.Google Scholar

51 Tractatus de Trinitate 26, 28, in Commentaries , ed. Häring, , 309–10; citations of both authors in Commentarius Victorinus are numerous.Google Scholar

52 Tractatus de Trinitate 13–18, in Commentaries , ed. Häring, , 306–7.Google Scholar

53 Thierry, , Commentum 2.31–36, 2.46–49, in Commentaries , ed. Häring, , 78–79, 82–84; Commentarius Victorinus 86–88, in Commentaries , ed. Häring, , 499.Google Scholar

54 The texts from MSS Munich (clm) 5254 and 9516 are transcribed as two independent versions in Wilhelm von Giesebrecht, , Geschichte der deutschen Kaiserzeit , vol. 4 (Leipzig, 1877), 502–6. The original sense of the Sibyl concerns German nobles traveling first to Constantinople, where the Greek emperor sits eternally and the nobility stand eternally, and thence toward Jerusalem (Giesebrecht, Geschichte, 502). On the Sibyls generally in medieval literature, see Dronke, Peter, “Hermes and the Sibyls: Continuations and Creations,” in idem, Intellectuals and Poets in Medieval Europe (Rome, 1992), 219–44.Google Scholar

55 “Cum perueneris ad costam Tetragoni sedentis eterni et ad costam tetragonorum stantium eternorum” (Thierry, , Commentum 2.34, in Commentaries ed. Häring, , 79). Thierry cites only a fragment of the Sibyl but must have used the version from MS Munich (clm) 5254, viz. from Otto of Freising's Gesta Friderici Imperatoris, which continues “et ad multiplicationem beati numeri per actualem primum cubum” (Giesebrecht, Geschichte, 505).Google Scholar

56 Thierry, , Commentum 2.34, in Commentaries ed. Häring, , 78–79.Google Scholar

57 “Et quoniam tetragonatura prima generatio Filii est, et Filius tetragonus primus est. Tetragonatio uero figura est. Merito ergo Filium figuram substantie Patris appellat…. Bene autem tetragonus Filio attribuitur quoniam figura hec perfectior ceteris propter laterum equalitatem iudicatur” (Thierry, , Commentum II.34, in Commentaries ed. Häring, , 79). Cf. Thierry, , Tractatus 41, in Commentaries ed. Häring, , 572: “Est igitur ipsa unitatis equalitas eiusdem unitatis quasi quedam figura et splendor. Figura quidem quia est modus secundum quern ipsa unitas operatur in rebus. Splendor uero quia est id per quod omnia discernuntur a se inuicem. Fine enim modoque proprio cuncta inuicem a se discreta sunt.”.Google Scholar

58 Commentarius Victorinus 95, in Commentaries ed. Häring, , 501; cf. Thierry, , Commentum 2.33–34, in Commentaries ed. Häring, , 78–79.Google Scholar

59 On Clarembald's life, see Life and Works of Clarembald , ed. Häring, (n. 25 above), 4–23 and Fortin, John R., Clarembald of Arras as a Boethian Commentator (Kirksville, MO, 1995).Google Scholar

60 Ibid., 17.Google Scholar

61 See Clarembald, , Tractatus super librum Boetii De Trinitate 1.24–28, in Life and Works ed. Häring, , 95–97; 1.52–53, in Life and Works ed. Häring, , 105; 2.48–50, in Life and Works ed. Häring, , 126–27; and 3.36–39, in Life and Works ed. Häring, , 145–46.Google Scholar

62 Clarembald, , Epistola ad Odonem 2–3, 7–8, in Life and Works ed. Häring, , 63–65.Google Scholar

63 Häring discusses Clarembald's critique of Abelard and Gilbert of Poitiers in Life and Works , 38–45; cf. Ott, , Untersuchungen (n. 34 above), 264; Fortin, , Clarembald of Arras, 44–48.Google Scholar

64 Of the nine paragraphs on the arithmetic Trinity in Clarembald's Tractatus, six concern aequalitas. During this discussion of the Son as equality, Clarembald cites verbatim from every paragraph of Thierry's text on the arithmetic Trinity in Commentum : cf. Thierry, , Commentum 2.30–38, in Commentaries ed. Häring, , 77–80; cf. Tractatus 2.34–40, in Commentaries ed. Häring, , 120–23.Google Scholar

65 “Necesse est ut singula membra i.e. consimilia et officialia quae in Abraham et Ysaac fuisse cognovisti in figuris ipsis sub eodem numero et eadem si fieri potest insignire studeas. Alioquin non bene quod volueras per figuras representabis” (Clarembald, , Tractatus 2.36, in Life and Works ed. Häring, , 121).Google Scholar

66 Ibid., 2.38, in Life and Works ed. Häring, , 122.Google Scholar

67 PL 199:945D–964D. The sole known manuscript is in the British Museum, London, MS Harley 3969, fols. 206v–215v. The final page seems to be missing, since the author's conclusion is broken off in midsentence. The treatise was formerly attributed to John of Salisbury, but Peter Dronke rightly refers to “the anonymous twelfth-century author of the De septem septenis, whose precise date and milieu are still uncertain” ( Fabula: Explorations into the Uses of Myth in Medieval Platonism [Leiden, 1974], 35; cf. Schaarschmidt, Carl, Johannes Saresbariensis nach Leben und Studien, Schriften und Philosophic [Leipzig, 1862], 278–81; Daniels, Hans, Die Wissenschaftslehre des Johannes von Salisbury [Kaldenkirchen, 1932], 91–94).Google Scholar

68 “Haec, magistrum nostrum sequentes, pro viribus succincte diximus” (Septem, PL 199:960A).Google Scholar

69 See Lucentini, Paolo, “L'Asclepius Hermetico nel Secolo XII,” in From Athens to Chartres: Neoplatonism and Christian Thought, Studies in Honour of Édouard Jeauneau , ed. Westra, Haijo Jan (Leiden, 1992), 397–420. Lucentini notes that while Asclepius had been known to Christian thought since Lactantius and Augustine, its influence was greatest during the twelfth century, including such anonymous Hermetic texts as Liber de VI rerum principiis, and is discussed in works by Abelard, Hermann of Carinthia, Bernardus Silvestris, Alan of Lille, and Thierry of Chartres (in Tractatus and Commentum). Lucentini mentions De septem septenis only briefly as a “fragment” by John of Salisbury, noting that John mentions “Hermes Trismegistus” once by name in Policraticus. See Policraticus 2.28, ed. ClementWebb, C. J., vol. 1 (Oxford, 1909), 163.Google Scholar

70 Septem, PL 199:960BC, 962D; cf. Asclepius 8, in Hermetica , ed. and trans. Scott, Walter, vol. 1 (London, 1968), 301–3.Google Scholar

71 The citations from Hermes, the Sibyl, the Gospel of John, and Ps.-Augustine in Septem, PL 199:960D–961B stem from Quodvultdeus, Adversus quinque haereses, PL 42:1102–3 (“Ex Hermete et Sibylla adversus Paganos”).Google Scholar

72 “Parmenides quoque dicit: Deus est cui esse quidlibet quod est esse omne id quod est. Item idem: Deus est unitas: ab unitate gignitur unitatis aequalitas. Connexio vero ab unitate et unitatis aequalitate procedit. Hinc igitur Augustinus: Omni recte intuenti perspicuum est, quare a sanctae Scripturae doctoribus Patri assignatur unitas, Filio aequalitas, Spiritui sancto connexio; et licet ab unitate gignitur aequalitas, ab utroque connexio procedat: unum tamen et idem sunt. Haec est illa trium unitas: quam solam adorandam esse docuit Pythagoras…. Opinor ideo cum qui illam veram unitatem considerare desiderat, mathematica consideratione praetermissa, necesse est ad intelligentiae simplicitatem animus sese erigat” (Septem, PL 199:961B–C). It is difficult to determine the precise relationship between this passage and known texts of Thierry's circle. One good conjecture for a mediating source is the Commentarius Victorinus, which includes the first sentence quoted by Parmenides but does not attribute the triad to him: “Et secundum theologicam affirmationis data est illa descriptio de deo a Parmenide philosopho quam utinam dedisset aliquis sanctorum: deus inquit est cui quodlibet esse quod est est esse omne id quod est” ( Commentarius Victorinus 99, in Commentaries ed. Häring, , 502). Septem's summary of Thierry's arithmetic Trinity resembles the account at Commentarius Victorinus 83–85, in Commentaries ed. Häring, , 498–99, in the pages preceding the Parmenides passage; but cf. also Thierry, Commentum 2.38, in Commentaries ed. Häring, , 80.Google Scholar

73 Glorieux, P., “La Somme ‘Quoniam Homines’ d'Alain de Lille,” Archives d'histoire doctrinale et littéraire du moyen âge 20 (1953): 116.Google Scholar

74 For a general comparison, see Lemoine, Michel, “Alain de Lille et l'école de Chartres,” in Alain de Lille , ed. Solère, Vasiliu, and Galonnier, (n. 17 above), 47–58. For further evidence of Alan's Chartrian influences and his mediation of Thierry's ideas beyond France, see Pick, Lucy, Conflict and Coexistence: Archbishop Rodrigo and the Muslims and Jews of Medieval Spain (Ann Arbor, 2004), 88–90 and 122–25.Google Scholar

75 On Alan's biography generally, see Evans, G. R., Alan of Lille: The Frontiers of Theology in the Later Twelfth Century (Cambridge, 1983); Hudry, Françoise, Règles de théologie (Paris, 1995), 7–47; eadem, “Mais qui était donc Alain de Lille?” in Alain de Lille , ed. Solère, Vasiliu, and Galonnier, , 107–24.Google Scholar

76 Glorieux, , “La Somme,” 114. For an overview of the contents and the method, respectively, of the Summa “Quoniam Homines“ (hereafter SQH), see Glorieux, P., “L'auteur de la Somme ‘Quoniam homines,”’ Recherches de théologie ancienne et médiévale 17 (1950): 29–45 and de Libera, Alain, “Logique et théologie dans la Summa ‘Quoniam Homines’ d'Alain de Lille,” in Gilbert de Poitiers , ed. Jolivet, and de Libera, (n. 31 above), 437–69.Google Scholar

77 The second part begins at SQH 1.31, ed. Glorieux, , “La Somme,” 167.Google Scholar

78 Alan distinguishes the first two kinds of names summarily at SQH 1.55 (ed. Glorieux, , “La Somme,” 198–99), but the third at 1.80 (ed. Glorieux, “La Somme,” 226): “Pertractatis hiis que de nominibus personalibus dicenda erant que personis appropriantur nomine et re; agendum est de illis que appropriantur nomine et non re, ut hoc nomen potentia, sapientia, bonitas.”.Google Scholar

79 Trottmann, Christian (“Unitas, aequalitas, conexio: Alain de Lille dans la tradition des analogies trinitaires arithmétiques,” in Alain de Lille , ed. Solère, Vasiliu, and Galonnier, , 401–27) considers this first instance of the triad in SQH 1.31 as well as the Regula, but not the second instance in SQH 1.114 nor De fide catholica .Google Scholar

80 “Unde videntes unitatem esse principium et origo omnium numerorum, simile coniectaverunt in creatione rerum ut unum esset creator a quo, tamquam a principali et suprema unitate procederet omnis alteritas, id est omne mutabile” (SQH 1.31, ed. Glorieux, , “La Somme,” 167). See further Niederberger, Andreas, “Naturphilosophische Prinzipienlehre und Theologie in der Summa ‘Quoniam Homines’ des Alain von Lille,” in Metaphysics in the Twelfth Century: On the Relationship among Philosophy, Science and Theology , ed. Lutz-Bachmann, Matthias, Fidora, Alexander, and Niederberger, Andreas (Turnhout, 2004), 185–99.Google Scholar

81 “Tamen multa dixerunt de Deo et mente eius et anima mundi, que ad tres personas referri possunt. Et ideo dicuntur habuisse noticiam [sic] de Trinitate…. Nonne et plura dixerunt de anima mundi que possunt ad Spiritum Sanctum referri?” ( SQH 1.31, ed. Glorieux, , “La Somme,” 168).Google Scholar

82 See further McGinn, Bernard, “The Role of the Anima Mundi as Mediator between the Divine and Created Realms in the Twelfth Century,” in Death, Ecstasy, and Other Worldly Journeys , ed. Collins, John J. and Fishbane, Michael (Albany, 1995), 289–319.Google Scholar

83 “Et ita videntur invenisse quedam vestigia Trinitatis; sed quasi per sompnium; nec ita distincte ut catholici” ( SQH 1.31, ed. Glorieux, , “La Somme,” 168).Google Scholar

84 “Sed quasi quedam in divinitate considerabant quorum nominibus persone solent distingui, ut potentia, sapientia, benignitas…. Sed non habuerunt notitiam de tribus personis ut scirent eas distinguere suis notionibus” (ibid., 1.31, ed. Glorieux, “La Somme,” 168).Google Scholar

85 “Quamvis enim una sit potentia trium personarum, una sapientia, una bonitas, tamen nomen potentie appropriatur Patri et non res nominis; similiter nomen sapientie Filio, nomen bonitatis Spiritui Sancto” ( SQH 1.80, ed. Glorieux, , “La Somme,” 226).Google Scholar

86 Ibid., 1.122, ed. Glorieux, , “La Somme,” 255.Google Scholar

87 On the broad range of possible terms for appropriation, see Ott, , Untersuchungen (n. 34 above), 580.Google Scholar

88 “Unitas ideo potius dicitur esse in Patre quam in Filio quia sicut unitas a nullo est et omnis numerus ab unitate, sic Pater a nullo et omnia a Patre” ( SQH 1.114, ed. Glorieux, , “La Somme,” 248).Google Scholar

89 “In Filio autem dicitur equalitas non alteritas esse; quia si diceretur alteritas esse in Filio videretur esse minor Patre” (ibid., 1.114, ed. Glorieux, , “La Somme,” 248).Google Scholar

90 “Spiritus autem Sanctus ideo communitas dicitur unitatis et equalitatis sive connexio” (ibid.).Google Scholar

91 “Nec nos numerum theologicum quantitatem dicimus, sed potius pluralitatem personarum quam faciunt distinctiones que attenduntur secundum paternitatem, filiationem, spirationem…. Non concedimus ergo quod ibi predicatur numerus sed numerus sui generis, scilicet numerus theologicus. Nec inde sequitur quod quantitas predicatur, quid de numero theologico non potest inferri numerus logicus, id est numerus qualis apud logicum consideratur” (ibid., 1.115, ed. Glorieux, , “La Somme,” 250). Cf. Boethius, , De sancta trinitate 3, in Boethius: De Consolatione Philosophiae, Opuscula Theologica , ed. Moreschini, Claudio (Munich, 2005), 171:132–34: “Numerus enim duplex est, unus quidem quo numeramus, alter vero qui in rebus numerabilibus constat.”Google Scholar

92 John of Damascus's De fide orthodoxa was translated around 1150 and cited frequently by Peter Lombard. See Chenu, M.-D., La théologie au douzième siècle (Paris, 1957), 283–84. Although he does not discuss the case of Alan in particular, see further Häring, Nikolaus M., “The Porretans and the Greek Fathers,” Mediaeval Studies 24 (1962): 181–209.Google Scholar

93 Glorieux rightly notes that the Summa (for Glorieux, , as yet anonymous) closely resembles passages in Alan's Regulae and Contra haereticos ; but he assumes that the arithmetic Trinity has the same meaning in each text regardless of context; see Glorieux, “L'auteur” (n. 76 above), 33–34, 37–38.Google Scholar

94 The work is also known as Regulae caelestis iuris or De maximis theologicis. Comparing these two texts on the mathematical triad encourages one to suppose that Alan wrote the Summa first and then adapted portions of it within his ongoing project of the Regulae .Google Scholar

95 Häring, Nikolaus, “Magister Alanus de Insulis: Regulae Caelestis Iuris,” Archives d'histoire doctrinale et littéraire du moyen âge 48 (1981): 97–226, at 99, 118.Google Scholar

96 Hudry dates the Summa to 1155–67, the Regulae to 1192–94, and De fide catholica (see below) to 1190–1200; see Règles de théologie (n. 75 above), 85–89.Google Scholar

97 “Vnitas de se gignit unitatem, de se profert equalitatem” ( Regulae 1.5 ed. Häring, , “Magister Alanus,” 125).Google Scholar

98 Ibid., 2.3 ed. Häring, , “Magister Alanus,” 126.Google Scholar

99 Ibid., 3.1–4 ed. Häring, , “Magister Alanus,” 127–28. Cf. SQH 1.31, ed. Glorieux, , “La Somme,” 168.Google Scholar

100 “In Patre unitas, in Filio equalitas, in Spiritu Sancto unitatis equalitatisque connexio” ( Regulae 4 [regula] ed. Häring, , “Magister Alanus,” 128).Google Scholar

101 “In Patre specialiter dicitur esse unitas, in Filio equalitas” (ibid., 4.2, ed. Häring, “Magister Alanus,” 128). Cf. SQH 1.114, ed. Glorieux, , “La Somme,” 248.Google Scholar

102 Dreyer, Mechthild ( More mathematicorum: Rezeption und Transformation der antiken Gestalten wissenschaftlichen Wissens im 12. Jahrhundert , BGPhThM 47 [Münster, 1996], 106–61) notes that the most important context for Alan's axiomatic method in the Regulae are the commentaries on Boethius's De hebdomadibus by Gilbert of Poitiers, Thierry of Chartres, and Clarembald of Arras. See further Evans, G. R., “Boethian and Euclidean Axiomatic Method in the Theology of the Later Twelfth Century,” Archives internationale d'histoire des sciences 30 (1980): 36–52; Lohr, Charles H., “The Pseudo-Aristotelian Liber de causis and Latin Theories of Science in the Twelfth and Thirteenth Centuries,” in Pseudo-Aristotle in the Middle Ages: The Theology and Other Texts , ed. Kraye, Jill, Schmitt, Charles B., and Ryan, W. F. (London, 1986), 53–62; Hudry, Françoise, “Métaphysique et Théologie dans les Regulae Theologiae d'Alain de Lille ^†1202),” in Metaphysics in the Twelfth Century , ed. Lutz-Bachmann, , Fidora, , and Niederberger, (n. 80 above), 201–15.Google Scholar

103 “Communis animi conceptio est enuntiatio quam quisque intelligens probat auditam. Hec omnes maximas, cuiuscumque sint facultatis, sua generalitate conplectitur…. Vnde indemonstrabilis, per se nota et maxima nuncupatur” (Regulae, Prologus, 10, ed. Häring, , “Magister Alanus,” 123). Cf. Boethius, , Quomodo substantiae [De hebdomadibus] 1, ed. Moreschini, , Opuscula (n. 91 above), 187:17–18.Google Scholar

104 De fide catholica contra haereticos sui temporis, PL 210:306–430. See Häring, Nikolaus M., “Alain of Lille's De fide catholica or Contra haereticos,” Analecta Cisterciensia 32 (1976): 216–327.Google Scholar

105 De fide catholica 3.3, PL 210:404B–405A; cf. SQH 1.31, ed. Glorieux, , “La Somme,” 168.Google Scholar

106 “Idem rationibus potest probari” ( De fide catholica 3.4, PL 210:405B–C).Google Scholar

107 “Quia sicut ab unitate indivisibili omnis procedit pluralitas quae divisibilis est, ita a Creatore invariabili omne procedit variabile, quia ‘Ipse manens stabilis dat cuncta moveri.’ Et sicut in unitate et numero resultant Creatoris et creaturae imago, ita et Trinitatis similitudo: in proprietate enim unitatis quodam modo resultat vestigium Trinitatis, quia, ut apud arithmeticum legitur, unitas gignit se ipsam. Inter unitatem autem genitam et gignentem quaedam invenitur aequalitas. In quo ergo subsistente autem hoc poterimus invenire, nisi in Deo? Deus autem gignit Deum, et non alium Deum a Deo gignente, imo genuit illum qui est idem Deus cum gignente; et est ibi perfecta aequalitas gignentis et geniti, sive convenientia, seu connexus, qui dicitur Spiritus sanctus, in quo Pater et Filius conveniunt. Unde et philosophus ait: ‘Monas gignit monadem, et in se suum reflexit ardorem.’ Ergo aut in nullo subsistente invenies quod de unitate dicitur, aut in unitate et trinitate divina reperitur” (ibid., 3.4, PL 210:405C). Alan quotes from Boethius's hymn “0 qui perpetua” (De consolatione philosophiae 3.9, ed. Moreschini, , Opuscula 79:103) and from Liber XXIV philosophorum 1 (ed. Hudry, Françoise, Liber Viginti Quattuor Philosophorum , Hermes Latinus III/1, CCM 143A [Turnhout, 1997], 5).Google Scholar

108 Achard is named as present with Robert of Melun at a disputation over Peter Lombard's theology. Unfortunately this event is difficult to date, but must have occurred after Robert succeeded Abelard around 1137 and before Achard's abbacy beginning in 1155. See Châtillon, Jean, Théologie, spiritualité et métaphysique dans l'oeuvre oratoire d'Achard de Saint Victor (Paris, 1969), 74–75.Google Scholar

109 Feiss, Hugh, Achard of Saint Victor: Works (Kalamazoo, 2001), 20–24.Google Scholar

110 Achard's other known treatise, De discretione animae, spiritus et mentis, is concerned with ideas associated with Gilbert of Poitiers rather than Thierry of Chartres. In fact Häring attributes the treatise to Gilbert, but Châtillon follows Germain Morin's attribution to Achard; see Châtillon, , Théologie , 131–33.Google Scholar

111 As Châtillon aptly writes: “Cet important traité, dont l'existence est pourtant plus assurée, n'a pas été beaucoup mieux préservé de l'oubli ni défendu contre les rigeurs du temps que les Quaestiones de théologie” ( Théologie , 119). Achard's treatise is cited by John of Cornwall in the late twelfth century and alluded to by John Leland again in the early sixteenth, but had been considered lost until recently. In 1944, André Combes (Un inédit de saint Anselme? Le traité De unitate divinae essentiae et pluralitate creaturarum d'après Jean de Ripa, Études de Philosophic Médiévale 34 [Paris, 1944]) showed that Jean de Ripa cited long extracts from treatise De unitate in his Sentence commentary and attributed them to Anselm of Canterbury; this has since proved to be Achard's work. Ten years later, Marie-Thérèse d'Alverny discovered a manuscript at the Monastery of St. Anthony in Padua (Scaf fale V, 89, fols. 177–88) that she believed to be Achard's book, but only published extracts sufficient to prove its authenticity (d'Alverny, M.-T., “Achard de Saint-Victor, De Trinitate — De unitate et pluralitate creaturarum,” Recherches de théologie ancienne et médiévale 21 [1954]: 299–306). Emmanuel Martineau finally transcribed the manuscript in its entirety along with a French translation and analysis in L'Unité de Dieu et la pluralité de créatures (Saint-Lambert des Bois, 1987). Châtillon points out (Théologie, 121 n. 33) that strictly speaking, the two parts of the treatise have different names: De unitate et Trinitate (Treatise I) and De unitate et pluralitate creaturarum (the partially preserved Treatise II). For this reason I will refer to the work as De unitate for short. I will use Hugh Feiss's translation of De unitate and the sermons, noting any modifications that I find necessary.Google Scholar

112 Châtillon, ( Théologie , 277) notes Achard's unusual, idiosyncratic philosophical vocabulary. Mohammad Ilkhani (La philosophic de la création chez Achard de Saint-Victor [Brussels, 1999]) likewise contends that once De unitate is understood in context — something he finds lacking in Martineau's analysis — the book will be judged as “sans doute l'une des plus importantes [oeuvres] du XII^e siècle” (26; cf. discussion 22–23). “Une telle démarche était trés audacieuse, parce qu'elle s'accordait mal avec l'orthodoxie de l'époque. À l'époque où la tendance generale de la théologie essayait de prouver l'unité et la simplicité en Dieu, — n'oublions pas les difficultés encourues par Abélard et Gilbert de la Porrée —, Achard a voulu montrer qu'il y a non seulement une pluralité en Dieu, mais en plus que cette pluralité est la vraie pluralité et qu'elle est le fondement de la pluralité des créatures” (ibid., 107).Google Scholar

113 See the discussion in Châtillon, , Théologie , 123–26. As Ilkhani puts it, Achard's method may be Anselmian, but his results are a “syncrétisme audacieux” of Seneca, Augustine, Boethius, Chalcidius, Eriugena, and Thierry of Chartres (Philosophic, 357).Google Scholar

114 See Ilkhani's fine analysis in Philosophic, 101–8, 116–17. D'Alverny compares Achard's discussion of the Trinity to those of Thierry of Chartres and Clarembald of Arras, as well as to the Regulae of Alan of Lille (d'Alverny, , “Achard de Saint-Victor,” 303–4).Google Scholar

115 But he is capable of comparing the Holy Spirit to conexio: see De unitate 2.3, ed. Martineau, , 144–46; trans. Feiss, , Achard, 439. Achard also uses conexio in a more philosophical context at 2.10 (ed. Martineau, , 166; trans. Feiss, , Achard, 455–56). On Achard's independence from Thierry, see Ribaillier, Jean, Richard de Saint-Victor: Opuscules théologiques (Paris, 1967), 178.Google Scholar

116 Achard, , De unitate 1.36, ed. Martineau, , 104.Google Scholar

117 On the image of the desert in Sermon 15, see Châtillon, , Théologie , 233–52 and McGinn, Bernard, The Growth of Mysticism (New York, 1994), 395–98. Châtillon (Théologie, 142–47) dates Sermons 13–15 together to the post-abbatial period from 1155 to 1161.Google Scholar

118 As Feiss notes (Achard, 202–3), Achard's triad resembles the Abelardian triad of potentia, sapientia, and benignitas that Robert of Melun and Richard of St. Victor, despite Bernard's attacks, would finally embrace.Google Scholar

119 On this passage see Chatîllon, , Théologie , 218–21.Google Scholar

120 Sermon 13, para. 11–14, ed. Châtillon, Jean, Achard de Saint-Victor: Sermons inédits , Textes philosophiques du moyen âge 17 (Paris, 1970), 145–49; trans. Feiss, , Achard, 221.Google Scholar

121 Sermon 13, para. 15–16, ed. Châtillon, , Achard , 149–50.Google Scholar

122 “Forma tarn formosa ex pietate sola se univit materie tarn informi, nec modo informi sed et deformi” (Sermon 13, para. 16, ed. Châtillon, , Achard , 150; trans. Feiss, , Achard, 228).Google Scholar

123 “Forma autem ista et Dei est et nostra: Dei est quia a Deo est, nostra est quia in nobis est; a Deo est expressa, et ab ipso nobis est impressa” (Sermon 13, para. 16, ed. Châtillon, , Achard , 150; trans. Feiss, , Achard, 229).Google Scholar

124 “Quadratura quedam est hec forma, quia stabilis est et firma…. Christus forma nostra est, qui, ut ostendit Apostolus ab eo formatus, spiritualis quadratura nobis est factus: Christus namque, juxta verbum Apostoli, factus est sapientia nobis a Deo, et justitia, et sanctificatio, et redemptio. Ecce quadratura vitalis atque celestis. Accedite et earn suscipite, lapides vivi, immo sine ea mortui atque terreni; in ea quadramini, et sic ex mortuis vere vivi et ex terrenis celestes efficiemini” (Sermon 13, para. 17, ed. Châtillon, , Achard , 150–51; trans. Feiss, , Achard, 229 [trans. modified]). On the image of the square, see Châtillon, , Théologie, 219. In viewing Christ as form and in his preference for architectural metaphors, Achard no doubt follows his master Hugh of St. Victor: see Coolman, Boyd Taylor, The Theology of Hugh of St. Victor (Cambridge, 2010), 83–102.Google Scholar

125 “In sola etiam dilectione dei quadratura proponitur et suscipienda nobis imponitur” (Sermon 13, para. 21, ed. Châtillon, , Achard , 153; trans. Feiss, , Achard, 232).Google Scholar

126 “Qui quadraturas hujusmodi acceperit, per eas ad superiorem quamdam perveniet quadraturam” (Sermon 13, para. 22, ed. Châtillon, , Achard , 154; trans. Feiss, , Achard, 234).Google Scholar

127 See Feiss, , Achard , 22.Google Scholar

128 On Achard's rigorist conception of the abbot's role, see Châtillon, , Théologie , 76–78.Google Scholar

129 Furthermore, Ribaillier (Richard [n. 115 above], 177–78) contends that Richard of St. Victor knew Achard's De unitate when he wrote his letter De tribus personis, and the terminus a quo of that letter is 1160–62.Google Scholar

130 On the organization of De unitate, see Martineau's astute discussion (L'Unité [n. 111 above], 52–61), which, however, lacks a comprehensive outline. Ilkhani (Philosophie [n. 112 above], 12–13) construes the texts's organization in terms of philosophical topoi: (1) unity and plurality, 1.1–36; (2) creation and eternal reasons, 1.37–42; (3) intellectual forms, 1.43–50; (4) formal reasons, 2.1–17; (5) causal-final reasons, 2.17–21. While helpful, this outline ignores the author's evident Trinitarian concerns.Google Scholar

131 Achard, , De unitate 1.5–6, ed. Martineau, , L'Unité, 72–74.Google Scholar

132 “Nunc enim personae discernendae sunt proprietatibus et secundum proprietates distinguendae nominibus; cujus tamen distinctionis sive in proprietatibus sive in nominibus postea, Dei largiente gratia, manifestior exponetur ratio” (De unitate 1.24, ed. Martineau, , L'Unité , 96). Châtillon (Théologie, 224–27) notes that Achard would be familiar with the technical terms surrounding the controversies over Abelard and Gilbert.Google Scholar

133 When I refer to the “first part” or “second part,” I intend to designate the major division of Achard's argument outlined here (i.e., before and after 1.37), not books 1 and 2 of De unitate. On Achard's ratio explicatrix and its resemblance to Thierry of Chartres's explicatio , see Ilkhani, , Philosophie , 295–96.Google Scholar

134 Achard, , De unitate 1.39, ed. Martineau, , L'Unité, 108. Achard repeats the triad in similar terms at De unitate 1.42 (ed. Martineau, , L'Unité, 112) and 2.19 (ed. Martineau, , L'Unité, 192). Martineau (L'Unité, 109 n. 2) contends that the third term should be translated cause déployante, in contrast to Feiss's “explanatory cause,” and proposes that it refers to efficient causality. Châtillon (Théologie, 282–87) speculates that William of Conches's Glosae on Boethius's Consolatio and on the Timaeus may have been the source of Achard's exemplar doctrine.Google Scholar

135 This difficult section, which exceeds the purview of this essay, merits much greater attention than it has received. See the excellent analysis in the second half of Ilkhani's Philosophie, as well as Massie, Pascal, “The Metaphysics of Primary Plurality in Achard of Saint Victor,” Saint Anselm Journal 5.2 (2008): 1–18, at 15–18.Google Scholar

136 “Si namque et opera Trinitatis, licet sint indivisa, quaedam tamen specialiter solent Patri attribui, quedam specialiter Filio, quedam specialiter Spiritui sancto” (Sermon 13, para. 3, ed. Châtillon, , Achard , 136). Châtillon notes (136 n. 14): “Les positions d'Achard, sur ce point, sont donc beaucoup moin affirmatives que elles de son illustre confrère [viz. Richard of Saint Victor]. L'intention de l'abbé de Saint-Victor n'est d'ailleurs pas de prendre parti dans ce débat, mais seulement d'invoquer la théorie des appropriations trinitaires pour montrer qu'il est légitime d'établir une certaine distinction entre les attributs divins.” Ilkhani similarly reads Achard as making a conciliatory effort to “bridge” the methods of Gilbert and Thierry: “Avec sa science des nombres Achard rejoint Boèce et, par lui, les néopythagoriciens. Gilbert de la Porrée n'avait pas appliqué les mathématiques à la Trinité, il avait essayé de résoudre le problème de l'unité et de la pluralité divine par le raissonement, autrement dit par les sciences physique et théologique. C'est surtout chez Thierry de Chartres que les mathématiques dominent car c'est par elles qu'il essaie de concevoir la pluralité divine. Achard établit en fait un pont entre les deux et applique le raissonement et les lois de mathématiques à la Trinité” (Philosophie, 361–62).Google Scholar

137 Achard, , De unitate 1.24, ed. Martineau, , L'Unité , 96.Google Scholar

138 “Rationibus omnibus praetermissis Trinitatis ostensa videtur distinctio in Patre et Filio et Spiritu sancto, quorum proprietatum et nominum causae in unitate, et eo quod unitati est aequale, et in aequalitate ipsa sunt inventae” (ibid., 1.37, ed. Martineau, , L'Unité , 106; trans. Feiss, , Achard [n. 109 above], 406).Google Scholar

139 “Unde et quod unitati est aequale, persona necessitate dicetur alia, constat ergo ex superioribus, quia nec ipsum potest non esse persona[m]. Eadem etiam ratione et in ipsa earum aequalitate persona reperietur tertia” (Achard, , De unitate 1.16, ed. Martineau, , L'Unité , 90).Google Scholar

140 Ibid., 1.36, ed. Martineau, , L'Unité , 104.Google Scholar

141 Ibid., 1.12, ed. Martineau, , L'Unité , 80; trans. Feiss, , Achard, 387.Google Scholar

142 Achard, , De unitate 1.5, ed. Martineau, , L'Unité , 74. On the diverse meanings of ratio in Anselm of Canterbury, none of which accord well with the Aristotelian or Boethian senses, see Gersh, Stephen, “Anselm of Canterbury,” in A History of Twelfth-Century Western Philosophy , ed. Dronke, Peter (Cambridge, 1988), 255–78, here 260–61.Google Scholar

143 Achard, , De unitate 1.5, ed. Martineau, , L'Unité , 72.Google Scholar

144 “Utriusque enim pulchritudo secundum se totam in unitatem illam alterius concurrit et quodammodo confluit pulchritudini…. Liquet igitur quia pulchritudine unitatis praefatae et summae illius convenientiae pulchrius nihil vel majus esse, sed nec excogitari potest. Ipsam itaque in Deo esse, sed et Deum esse est necesse” (ibid., 1.5, ed. Martineau, , L'Unité , 74; trans. Feiss, , Achard, 382).Google Scholar

145 Achard, , De unitate 1.11, ed. Martineau, , L'Unité , 80.Google Scholar

146 Ibid., 1.10, ed. Martineau, , L'Unité , 78.Google Scholar

147 “Hac igitur ibi variis jam et necessariis inventa assertionibus, sequitur quod nunc propositum est, cujusmodi natura scilicet ipsa sit, et an personalis esse monstrari possit” (ibid., 1.12, ed. Martineau, , L'Unité , 80; trans. Feiss, , Achard, 387).Google Scholar

148 Achard, , De unitate 1.18–19, ed. Martineau, , L'Unité, 90–92.Google Scholar

149 See respectively Thierry, Commentum 4.4, in Commentaries , ed. Häring, (n. 8 above), 96; Commentum 2.32–35, in Commentaries ed. Häring, , 78–79.Google Scholar

150 “Numerus quoque penes quern vis et forma consistit omnium rerum ab unitate aequalitatis: ab aequalitate species omnes docetur procedere inaequalitatis…. Sed ratio monstrat, cum aequalitas non possit nisi inter plura consistere, primam illam aequalitatem esse omnium quae inter duo constiterat, praesertim si et illa omnium fuerit prima, ut sit et aequalitas ipsa ab eis tertia et cum eis erit tria” (Achard, , De unitate 1.20, ed. Martineau, , L'Unité, 92; trans. Feiss, , Achard, 395).Google Scholar

151 Boethius, , Institutio arithmetica 1.32.1–2, ed. Guillaumin, (n. 9 above), 66–67. This is also a major principle of Boethian harmonics: see Boethius, , De institutions musica 2.7, ed. Friedlein, Gottfried (Leipzig, 1867, repr. Frankfurt am Main, 1966), 232. Thierry repeats the doctrine in the same passage of Commentum, but also in his Tractatus on Genesis; the author of Commentarius Victorinus follows closely. Cf. Commentum 2.36, in Commentaries ed. Häring, , 79; Tractatus 39, 43, and 44, in Commentaries ed. Häring, , 571–74; Commentarius Victorinus 87–88, in Commentaries ed. Häring, , 499.Google Scholar

152 Achard, , De unitate 2.5, ed. Martineau, , L'Unité, 150.Google Scholar

153 Ibid., ed. Martineau, , L'Unité , 152; cf. ibid., 2.12, ed. Martineau, , L'Unité, 170.Google Scholar

154 Achard turns to conexio only in the second part of De unitate, where it serves epistemological rather than theological ends. See De unitate 2.3, 2.4, and 2.10, ed. Martineau, , L'Unité , 144–49, 166–67.Google Scholar

155 PL 175:431–634. On the question of attribution, compare Ott, Untersuchungen (n. 34 above), 576; Châtillon, , Théologie (n. 108 above), 115–18; and especially Glorieux, P., “Essai sur les Quaestiones in epistolas Pauli du Ps.-Hugues de Saint-Victor,” Recherches de théologie ancienne et médiévale 19 (1952): 48–59. This text could represent one of two lost quaestiones linked to Achard; another candidate treatise has since been attributed to Odo of Ourscamp, the correspondent of Clarembald of Arras. As to dating, the Quaestiones have been shown to rely on Robert of Melun. See Landgraf, Artur M., Introduction à l'histoire de la littérature théologique de la scholastique naissante , trans. Geiger, Louis B., Publications de l'lnstitut d'études médiévales 22 (Montreal, 1973), 92.Google Scholar

156 “Quod a magistro Acardo accepimus” ( Quaestiones in epistolas Pauli , q. 93, PL 175:531).Google Scholar

157 Ibid., qq. 280–87, PL 175:500–502.Google Scholar

158 Ibid., q. 282, PL 175:500–501.Google Scholar

159 Ibid., q. 283, PL 175:501.Google Scholar

160 “Salva secretorum reverentia dicimus, quod in Patre ideo dicitur unitas … hoc dico salva fide catholica, quorum verborum occultam intelligentiam mallem ab alio audire, quam aliquid de tenuitate mea super his dicere” (ibid.).Google Scholar

161 “In patre unitas, in filio aequalitas, in spiritu sancto unitatis aequalitatisque concordia, et tria haec unum omnia propter patrem, aequalia omnia propter filium, conexa omnia propter spiritum sanctum” (Augustine, , De doctrina Christiana , 1.12 [V.5], ed. Green, [n. 1 above], 16–17). This immediately recalls Thierry of Chartres's doctrine of a “trinity of perpetuals” (materia, forma, spiritus) that reflect the arithmetic Trinity within the natural order. See Thierry, , Commentum 2.39–42, in Commentaries, ed. Häring (n. 8 above), 80–82.Google Scholar

162 “In creaturis praelucet vestigium Trinitatis, quia ostendunt in se unitatem, et speciem, et ordinem tenere, quia unumquodque et unum aliquid est, et aliqua specie formatur, et aliquem ordinem tenet, unde dictum est: Omnia fecit in numero, et pondere, et mensura. Numerus enim ad unitatem, pondus ad ordinem, mensura ad speciem pertinet. De quolibet enim verum est, quod ex quo incipit esse, statim cadit sub numerum quia vel unum est, vel plura. Pondus ad ordinem ideo dicitur pertinere; quia singula ordinem tenent secundum naturam ponderis…. species vero rerum, quod quidam modus est earum, et mensura” ( Quaestiones in epistolas Pauli , q. 284, PL 175:501–2).Google Scholar

163 On the latter point, see Ilkhani, , Philosophie (n. 112 above), 252–54.Google Scholar

164 My account here draws on Colish's survey in Peter Lombard (n. 24 above), 245–63.Google Scholar

165 Lombard, Peter, Sententiae in IV Libris Distinctae , lib. 1, dist. 31, ed. Brady, Ignatius C. (Grottaferrata, 1971), 223–32. “Es zeigt sich keinerlei Berührung mit der Erklärung der Schule von Chartres. In der Hilflosigkeit, mit der der Lombarde der Augustinussentenz gegenübersteht, macht sich der Mangel einer Vorlage deutlich bemerkbar…. Am unsichersten fühlt sich der Lombarde in der Appropriation der Gleichheit an den Sohn” (Ott, , Untersuchungen, 571–72).Google Scholar

166 Lombard, Peter, Sententiae , dist. 31, cap. 1.1, ed. Brady, , 223–24.Google Scholar

167 Ibid., dist. 31, cap. 1.2, 1.4, ed. Brady, , 224–25.Google Scholar

168 Ibid., dist. 31, cap. 3, ed. Brady, , 229.Google Scholar

169 Hödl, , Von der Wirklichkeit (n. 34 above), 19–24; cf. Häring, Nicholas M., “Simon of Tournai and Gilbert of Poitiers,” Mediaeval Studies 27 (1965): 325–30.Google Scholar

170 Simon of Tournai, Glossa Sententiarum , dist. 8, cap. 5, ed. Hödl, , Von der Wirklichkeit, 15–19, at 18 (§o).Google Scholar

171 The point of appropriation theory, he reasons, is to maintain that the sharp distinction of “unity” and “equality” and is ultimately arbitrary and reversible, since both are common attributes of the one divine essence. But this very nominal opposition introduces potential discord that must be overcome: hence concordia is the true, unique name of the third person (et nomine et re appropriata), unlike unitas and aequalitas, which are merely appropriated in relative terms (non res nominis appropriata). “Spiritui sancto vero et nomine et re appropriata dicitur unitatis aequalitatisque concordia…. Cum enim nomen unitatis Patri approprietur contra Filium, aequalitatis nomen Filio contra Patrem, sic appropriationum causa in eis sunt unitas et aequalitas discorditer. Sed cum Spiritus sanctus et unum dicatur cum eis et aequalis eis nec dictio unitas et aequalitas contra aliquem eorum” (ibid., ed. Hödl, , Von der Wirklichkeit , 19 [§o]).Google Scholar

172 Peter of Poitiers's account of appropriation theory, more systematic than original, was particularly influential in later scholastic tradition. See Ott, , Untersuchungen , 593–94.Google Scholar

173 Gandulph of Bologna, Sententiarum libri quatuor 1.47, ed. von Walter, Johannes (Vienna, 1924), 35; cf. Peter of Poitiers, Sententiae 1.21, ed. Moore, and Dulong, (n. 35 above), 179:82–99. On Gandulph, see Ott, , Untersuchungen, 572–73.Google Scholar

174 Peter of Poitiers, Sententiae 1.22, ed. Moore, and Dulong, , 183:5–7.Google Scholar

175 Ibid., ed. Moore, and Dulong, , 184:23–43.Google Scholar

176 As Peter explains ( ibid. , ed. Moore, and Dulong, , 189:149–72), Simon provided three reasons for the Spirit being named concordia. His point is that the second reason yields an appropriation by name alone, but the first and third yield an appropriation by name and thing: “Ecce alia iterum personarum distinctio appropriatione nominum non rerum partim, ut cum de Patre dicitur unitas, de Filio equalitas, partim appropriatione nominis et rei, ut cum de Spiritu dicitur concordia primo et tertio modo” (ibid., ed. Moore and Dulong, 190:173–76).Google Scholar

177 Richard of St. Victor, De tribus personis appropriatis in Trinitate, in Ribaillier, Richard (n. 115 above), 169–87. For commentary see Ott, , Untersuchungen, 573–80.Google Scholar

178 Ribaillier, , Richard , 173. “L'exposé de Richard se situe à un moment où se produit dans l'Ecole une réaction en faveur d'Abélard” (ibid., 179).Google Scholar

179 Richard, , De tribus personis, fol. 153c–153d, ed. Ribaillier, , Richard , 182–83.Google Scholar

180 Ibid., fol. 154a, ed. Ribaillier, , Richard , 183.Google Scholar

181 “Sicut equalitas nulla est sine consistentium pluralitate, sic nec quid tertium ponitur concordia duorum sine consistentium Trinitate. In Patre origo unitatis, in Filio inchoatio pluralitatis, in Spiritu sancto completio Trinitatis” (ibid., fol. 154a, ed. Ribaillier, , Richard , 183–84).Google Scholar

182 Ribaillier, , Richard , 179.Google Scholar

183 Albert and Thomas explore the triad in some detail; see, respectively, Commentarii, dist. 31, art. 9–11, 111–14; Commentum, dist. 31, q. 3, art. 1–2, 252–53. Bonaventure mentions it only in passing with the comment that while the “appropriation of Hilary” explicates the origin of the Trinity, the “appropriation of Augustine” explicates its order. See Commentaria in quatuor libros Sententiarum, dist. 31, para. 2, art. 2, q. 3 in Opera omnia, vol. I/2 ( Quaracchi , 1883), 548–59. Duns Scotus does not discuss the triad per se but rather the question of whether identity, similitude, and equality are “real relations” in God. See Quaestiones in primum librum Sententiarum, dist. 31, q. 1, in Opera omnia, vol. 10 (Paris, 1893), 489–99.Google Scholar