![Sample our Humanities journals, sign in here to start your FREE access for 14 days]({"type":"image" , "src" : "/sda/5939/TOC-Subject-Sample-2021-Humanities.jpg"})
Acknowledgements
This paper was written during a fellowship at the Notre Dame Institute for Advanced Study, 2012–2013. I am grateful to Robert Goulding and James Hirstein for their thoughtful comments and corrections.
Notes
1. Ramus, Dialecticae institutiones, 6v. On this passage and Ramus' belief that mathematics mirrored the real structure of nature see Goulding, Defending Hypatia, 21–24.
2. Nauta, In Defense of Common Sense.
3. Cicero, Rhetorica ad herennium, 1.2.3; Quintilian, Institutiones oratoriae, 3.3.1. This view of “invention” was standard through the middle ages: Carruthers, Craft of Thought, 10–14.
4. Ong, Ramus, Method, and the Decay of Dialogue, 182–183. On Ramus' failure to provide an experimental basis for his method, see 268–269.
5. For an overview of the literature, see Olmos, “Pedro Simón Abril's Conception of Logic,” 481–485.
6. Meerhoff, “Agricola et Ramus,” 273. See also the important paper of Heath, “Logical Grammar.”
7. Ong, Ramus, Method, 74–79.
8. Rossi, Logic and the Art of Memory, 29 and 38.
9. Vasoli, La dialettica e la retorica, 187 and 201–203.
10. For Paris at this time, see Renaudet, Préréforme et humanisme. Beatus' studies in Paris are described by Faye, “Beatus Rhenanus.” The relation of Lefèvre's program to monastic reform is explored in Legall, Les moines, 125–140.
11. On Clichtove, see Massaut, Josse Clichtove; Farge, Biographical Register, no. 101. For Bovelles, see the biographical material in Margolin, Lettres et poèmes; specifically on his role as Beatus' teacher, see Faye, “Beatus Rhenanus.”
12. Victor, “Revival of Lullism”; Emery, “Mysticism.”
13. Edited in Rice, Prefatory Epistles, ep. 45. “En pius egreditur latum Raemundus in orbem [ … ] Iam bene tricenos Raemundus vixerat annos | Pomposus, vecors, desidiosus, iners [ … ] Noxia praeteritae redimens ubi crimina vitae [ … ] Grammaticen libans primum, infus arte reliquit | innumeros nuda simplicitate libros.” Beatus' copy is Bibliothèque humaniste de Sélestat [hereafter BHS] K 1134a.
14. The common translation of idiota as “layman” is inaccurate; the term laicus was a perfectly good Latin word with that meaning. Moreover, the notion of “layman” presumes an opposition between clericus and idiota; a common grammar commentary by Synthen (and Hegius) of Deventer, which Beatus owned, clarified that a clericus might not know grammar, and so be an idiota, while there were many examples of laici who commanded excellent Latin. Synthen, Dicta Sinthis, sig. a2r. Lull's lay character is examined by Johnston, Evangelical Rhetoric.
15. Rice, Prefatory Epistles, ep. 45, 141.
16. Rice, Prefatory Epistles, ep. 22, 77. “Neque vos quicquam deterreat quod vir ille idiota fuerit et illiteratus, horridae rupis et vastae solitudinis assiduus accola; nam et creditur quadam superna infusione dignatus, qua sapientes huius saeculi longe pracelleret.”
17. Ibid., where Lefèvre quotes 2 Tim. 4:3–4.
18. On the Lullian art, see Yates, “Art of Ramon Lull”; Lohr, “Mathematics and the Divine”; Rossi, Logic and the Art of Memory, passim.
19. Llull, Contenta. For the repeated use of “inventio” as the basic activity of the art, see fol. 2v. The section on “qualiter deus scit quantitatem et numerum omnium rerum” is at fols. 17v–18v. See also Rossi, Logic and the Art of Memory, 46.
20. Sabundus, Theologia naturalis sive liber creaturarum. “Liber naturae, sive creaturarum” was the original title; theologia naturalis appears to be the addition of the first printer.
21. Sabundus, Theologia naturalis; Sive, liber creaturarum, ed. Friedrich Stegmüller (1966), 27*. “ista scientia docet omnem hominem cognoscere realiter, infallibiter, sine difficultate et labore omnem veritatem necessariam [...]”
22. Ibid., 30*–31*. “Ista scientia nulla alia indiget scientia nec aliqua arte. Non enim praesupponit grammaticam nec logicam nec aliquam de septem liberalibus artibus, nec physicam, nec metaphysicam, quia ista est prima, et est homini necessaria.” As Emmanuel Faye points out, Sebonde goes on to say that the liber naturae is open to all sorts of people, “est communis clericis et laecis, et omni conditioni hominum.” Faye, Philosophie et perfection, 52.
23. Ibid., Titulus 97, 122. “Hic declaratur experimentaliter, quod omnia serviunt homini, et sunt ad bonum hominis.” Famously, Montaigne responded to Lull with something akin to fideism; Voltaire lampooned the Lullian tradition of natural theology (vis-à-vis Leibniz) in the figure of Pangloss, in his Candide.
24. Bovelles, In artem oppositorum introductio, sig. a1r.
25. Reinhardt, “Die Lullus-Handschriften.”
26. Nicholas of Cusa, Operum clariss. P. Nicolai Cusae, fol. 77v. “sic infinita sapientia est simplicitas omnes formas complicans et omnium adaequatissima mensura, quasi in perfectissima omnipotentis artis idea, omne per artem formabile simplicissima forma ars ipsa existat.”
27. Ibid., fol. 81v. “mentem quidem a mensurando dici coniicio.” Translations, with modifications, from Hopkins, ed., Cusa's Complete Treatises, 535–536. In this second dialogue, the orator is replaced by a philosopher.
28. Nicholas of Cusa, Operum clariss. P. Nicolai Cusae, fol. 82r; Hopkins, Cusa's Complete Treatises, 538. “Symbolica paradigmata.” “IDIOTA. Omnis ergo ars finita ab arte infinita [ … ].”
29. Nicholas of Cusa, Operum clariss. P. Nicolai Cusae, fols, 81r, 83r, 83v, 84r, 86r, 91v, 92r, et alia.
30. Shank, “Unless You Believe.”
31. Hobbins, “Gerson on Lay Devotion.” On Gerson's success at shifting the academic culture from “nominalism” to the “realism” of Albert the Great, see Kaluza, Les querelles doctrinales à Paris.
32. The lay origins and investment in the cults of the saints has become a commonplace, thanks to Vauchez, Sainthood in the Later Middle Ages. See also perceptive comments by Kieckhefer, Unquiet Souls, 87–88.
33. Van Engen, “Multiple Options,” 277.
34. For a typology of these traditions, see Emery, “Benet of Canfield,” 147–248. Nicholas of Cusa chose intellect over affections quite deliberately in a debate with Johann Wenck, recounted in McGinn, Harvest of Mysticism, 445–456.
35. Lefèvre d’Étaples, Clichtove, and Bovelles, Epitome, fol. 97r. “Et haud secus quam rerum sapientissimus optimusque opifex veros caelos et veros motus divinae mentis opificio producit, mens nostra sui semper aemula parentis (cum ignorantiae labes pluscum detergitur) effictos caelos effictosque motus intra se profert, verorumque motuum simulacra quadam, in quibus ut in vestigiis divinae mentis opificii deprehendit veritatem. Est igitur astronomi mens, cum caelos caelorumque motus gnaviter effingit, similis rerum opifici caelos caelorumque motus creanti [ … ] Id enim quis dubitat ex immortalis naturae cognatione illi obtingere?”
36. Perusinus, Tractatus, sig. 5r. BHS K 981d. “Unde utile est locum considerare in quo dicta ut facta sunt illa, quorum volumus reminisci. Unde Cicero pro memoria artificiali habenda docet stabiliri quedam loca, et illis cogitatis facile venimus in oblitum.”
37. Foeniseca, Opera. BHS K 825m.
38. Lefèvre d’Étaples, Introductiones logicales, sig. d6v. “Nemo item brevitatem damnet, nam quicquid ars praecipit breve esse debet [ … ] adde quod intellectus brevitate gaudet [ … ] ita quoque et vobis iter philosophiae ingressis summopere gratum esse debet, hac methodo etiam quam brevissima ad disciplinarum portus ocissime appelere, quasi aura flante secunda et quasi transtris remigibusque iuti.”
39. de Bovelles, Libellus, fol. 4v–5r. “Visus est materialis sensus inventionis proprietatum rerum atque ideo et scientiarum realium, que rerum proprietates determinant [ … ] Idem quoque et realium et sermocinalium eruditionis sensus est. Enimvero sub vocibus, eruditio fit omnis inventorum prius aut visu aut auditu.”
40. The doctrine of internal senses was most influentially stated by Albert the Great, based on Avicenna. For more detail, see Park, “Organic Soul.” Lefèvre gave his own version of this psychology in his Totius philosophiae naturalis paraphrases, sig. D2v–D6r.
41. For an orientation to these debates, see Park, “Albert's Influence on Late Medieval Psychology”; Tachau, Vision and Certitude in the Age of Ockham; Spruit, Species Intelligibilis.
42. Liber de sensibus in Bovelles, Liber de intellectu, 22r et seq.
43. Ibid., 22v.
44. On this hierarchy, see Frangenberg, “Comparisons of Hearing and Vision.”
45. Vasoli, La dialettica e la retorica, 206–209.
46. Lefèvre described this third section on its separate title page (1503) as about invention.
47. My object here is not to comment on the vexed distinction between nominalists and realists in the fifteenth century (which often makes assumptions based on fourteenth-century polemical stances). Practically, I take the categories still to be useful, following Hoenen, “Via Antiqua and Via Moderna.”
48. Renaudet, Préréforme et humanisme, 131, 473. Vasoli quoted this at La dialettica e la retorica, 187.
49. Aristotle, De anima, 3.7, 431b12–16; Physica, 2, 193b22–35, 194a4–7; Metaphysica, 6.1, 1026a13–17, 11.7, 1064a31–35; 13.2, 1076b12–13, 1076b40–1077a19, 1077a31–b18.
50. BHS K 1047, 27r. “Unde sunt numerantia, sunt numerata, sunt numeri. Numerantia sunt anime numeros suos rebus applicantis. Numerata sunt ea quibus anima numeros apte accommodeque applicat. Numeri sunt discrete ille rationes numerandi.”
51. In fact, Lefèvre never produced an introduction to last part of the Metaphysica, where Aristotle chiefly argued for his abstractionist account of numbers; he only ever addressed the first six books: Lefèvre d’Étaples, Introductio in metaphysicorum libros Aristotelis. Such a distinction of numbers can be traced to Boethius, De trinitate 3.10–22; the notion of formal numbers was also important for Pico: Mandosio, “Beyond Pico Della Mirandola.”
52. See, for example, Jardine, “Epistemology of the Sciences.”
53. Meno 80e.
54. Lefèvre d’Étaples, Libri logicorum, fol. 177v. “Omnis doctrina et omnis disciplina intellectiva ex preexistente fit cognitione. Manifestum autem hoc speculantibus in omnibus mathematice enim scientie per hunc modum fiunt, et aliarum unaqueque artium. Similiter autem et circa orationes que per syllogismos et que per inductionem, utreque enim per prius nota faciunt doctrinam [ … ] similiter autem et rhetorice persuadent, aut enim per exempla quod est inductio, aut per enthymemata quod quidem est syllogismus.”
55. Ibid. “enim mathematice scientie et alie liberales artes propriis certisque ratiociniis instituunt; dialectice, communibus disceptationibus; oratorie autem et rhetorice, verisimilibus.”
56. See Ben-Zaken, Reading Hayy Ibn-Yaqzan, chap. 3. Ben-Zaken argues that Pico had found an autodidactic example in the twelfth-century Arabic tale Hayy Ibn-Yaqzan, about a boy who grew up alone on an island, prodigiously making philosophy out of his isolated experience of the world. Lefèvre could have encountered Pico's account of autodidacticism in his Heptaplus or Disputationes adversus astrologicam divinatricem.
57. Lefèvre d’Étaples, Libri logicorum, fol 178r. “in mathematicis scientiis ex antecedente cognitione scientiam nasci, nunc principiorum, nunc eorum que ex principio sunt cognita, quam manifestum est.”
58. The oratorical faculty “deals with civil affairs” (oratoria facultas circa civilia versatur, ibid.).
59. Ibid., fol. 178v, “Verum quedam talia sunt, que cognitis terminis (attentione mentis adhibita) statim cognoscimus, perinde ac apertis fenestris, et revelatis ciliis. Statim lumen cognoscimus. Est intellectus oculus.” It should be noted that Lefèvre uses Plato's account in part to provide authority for innate knowledge, in part because he wants to support the immortality of the soul. At the end of this passage, referring to Augustine's Retractationes, he warns readers off from incautiously reading Plato, notably for supposing the human soul to be uncreated.
60. Long, Artisan/Practitioners. The term “trading zones” comes from Galison, Image and Logic. The question, if not the term, has long history: Olschki, Geschichte.
61. Lefèvre d’Étaples, Arithmetica elementa, sig. a1v (=Prefatory Epistles, ep. 5, 18), sig. f1v (=Prefatory Epistles, ep 10, 32).
62. See Mandosio, “Le De magia naturali”, graciously shared with me in manuscript. On Lefèvre's turn from magic, see especially Rice, “The De magia naturali”; Veenstra, “Jacques Lefèvre d’Étaples.”
63. Jacques Lefèvre d’Étaples, Arithmetica elementa. On music theory and mathematics in the sixteenth century, see Pesic, “Hearing the Irrational.”
64. Lefèvre, Libri logicorum, fol. 77r; de Nolhac, “Recherches sur Fra Giocondo de Vérone.”
65. Juřen, “Fra Giovanni Giocondo.”
66. Lefèvre, Libri logicorum, fol. 176r.
67. On this fascinating figure, see Margolin, “Bonet de Lattès.”
68. Margolin, Lettres et poèmes, 66.
69. Bovelles recounts the meeting as a dialogue between himself and Bonetus: de Bovelles, Quaestionum theologicarum libri septem, fol. 53r.
70. Besides the references to Ong and Vasoli mentioned above, see Janssen, “Rise of the Typographical Paragraph.”
71. Lefèvre, Textus de Sphera Johannis de Sacrobosco, sig. a4r.
72. de Bovelles, Géométrie en françoys.
73. de Bovelles, Livre singulier et utile. See now Brioist, “Les singularités.” My thanks to the author for sharing this work before publication.
74. Renouard, Documents, 128–130.
75. Schreiber and Veyrin-Forrer, Simon de Colines. On these frontispieces, see Pantin, “L'inspiration du cosmographe.”
76. Pantin, “Oronce Fine's Role as Royal Lecturer.”
77. Fine and Savetier, Aequatorium planetarum, fol. A2r. “Cuiusmodi est insigne illud theoricarum instrumentum in formam libri digestum et tam mediis quam veris planetarum motibus ornatum, quod inter philosophicam suppellectilem mei patris Francisci Finei, medici ac philosophi praestantissimi primum animadverti, propria eius manu ac industria aliquando fabrefactum.”
78. A. Mizauld, Vita Orontii, fol. 6r; quoted and translated by A. Marr, Worlds of Oronce Fine, 8.
79. This poem, first published in 1531, cited in the edition in Fine, Le sphere du monde, fol. 59r–64v.
80. Axworthy, “Epistemological Foundations.”
81. Fine, Protomathesis, sig. AA2v. “Quique in locum bonarum artium frivolas quasdam terminorum altercationes [ … ]”
82. On this theme, see Axworthy, “Le Statut des mathématiques,” 76ff.
83. On the timing and enduring significance of mathematics in Ramus' pedagogical program, see Goulding, “Method and Mathematics.”
84. Reiss, Knowledge, Discovery and Imagination, 33–37; Reiss, “From Trivium to Quadrivium.”
85. On this “hunger for reality” see Oberman, Dawn of the Reformation, 55; Schreiner, Are You Alone Wise? 210–259; and Bynum, Christian Materiality.
86. On “experience” see Dear, Discipline and Experience.
87. Dee, Mathematicall Praeface, sig. A3v.
88. Nagel, Nicolaus Cusanus, 142–148.
89. Schmitt, “Rise of the Philosophical Textbook.” For Ong, see introductory comments above.
90. Rice, Renaissance Idea of Wisdom.