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Studia Lulliana 2015 STUDIA LULLIANA olim Estudios Lulianos ÍNDEX A. BONNER i A. SOLER, Les figures lul·lianes: la seva naturalesa i la seva funció com a raonament diagramàtic 3-30 V. TENGE-WOLF, Ramon Llull’s Disputatio quinque hominum sapientium: some remarks on the Latin version edited in ROL XXXV (2014) 31-54 T.LV T.LV C. PLAZA, Jacques de Molay i els templers catalans. L'actitud de Llull davant l'afer del Temple i les propostes de croada 55-81 S. CAMpaNINI, Una fonte trascurata sul rapporto tra qabbalah e combinatoria lulliana in Pico della Mirandola: il commento alle preghiere di Yehudah Ibn Malka 83-127 Bibliografia lul·lística 129-142 Ressenyes 143-208 Crònica 209-217 Índex d’obres lul·lianes citades 219-222 Procediments de publicació de Studia lulliana 223-230 STUDIA LULLIANA LULLIANA STUDIA MAIORICENSIS SCHOLA LULLISTICA VOL. LV 2015 Núm. 110 Studia Lulliana (des de 1991) és la continuació d’Estudios Lulianos (1957-1990). Anuari d’es- ABREVIATURES UTILITZADES A STUDIA LULLIANA tudis sobre Ramon Llull i el lul·lisme Abreviatures de revistes Consell editor: ATCA = Arxiu de Textos Catalans Antics (Barcelona) BSAL = Bolletí de la Societat Arqueològica Lul·liana (Palma) Anthony Bonner (director), Maria Isabel Ripoll (secretària), Lola Badia, Jordi Gayà, Pere EL = Estudios Lulianos (Palma) (1957-1990. Vegeu SL) Rosselló, Albert Soler (vocals) SL = Studia Lulliana (a partir del 1991. Abans EL) SMR = Studia Monographica et Recensiones (Palma) Consell assessor: Abreviatures de col·leccions Fernando Domínguez (Raimundus-Lullus-Institut, Emeritus), Kurt Flasch (Ruhr-Universität ENC = Els Nostres Clàssics (Barcelona) Bochum, Emeritus), Harvey Hames (Ben Gurion University of the Negev), J.N. Hillgarth MOG = Raymundi Lulli Opera omnia, ed. I. Salzinger, 8 vols. (Magúncia, 1721- (Pontifical Institute of Mediaeval Studies, Toronto, Emeritus), Ruedi Imbach (Université Paris 42; reimpr. Frankfurt, 1965)1 Sorbonne – Paris IV), Michela Pereira (Università degli Studi di Siena Emerita), Josep M. NEORL = Nova Edició de les obres de Ramon Llull (Palma, 1991 i ss.) Ruiz Simon OE = Ramon Llull, Obres Essencials, 2 vols. (Barcelona, 1957-60) (Universitat de Girona) ORL = Obres de Ramon Lull, edició original, 21 vols. (Palma, 1906-50) OS = Obres selectes de Ramon Llull (1232-1316), ed. A. Bonner, 2 vols. Redacció i gestió: (Palma, 1989) ROL = Raimundi Lulli Opera Latina (Palma i Turnhout, dins el Corpus Maioricensis Schola Lullistica Centre de Documentació Ramon Llull Christianorum, Continuatio Mediaevalis, 1959 i ss.) Apartat de Correus, 17 Universitat de Barcelona Palma (Espanya) Granvia 585 Abreviatures de fonts bibliogràfiques www.msl.cat 08007 Barcelona (Espanya) [email protected] http://centrellull.ub.edu/ Llull DB = Anthony Bonner (dir.), Base de Dades Ramon Llull, Centre de Docu- [email protected] mentació Ramon Llull (Universitat de Barcelona), <http://orbita.bib.ub.es/ llull>. Amb els suport de: RD = Estanislau Rogent i Elies Duran, Bibliografia de les impressions lul·lianes (Barcelona, 1927; reimpr., 3 vols., Palma, 1989-1991); se cita segons el Servei de Biblioteca i Documentació Departament de Filologia Catalana i Língüística número d’edició (no segons pàgina). de la Universitat de les Illes Balears General de la Universitat de les Illes Balears Universitat de les Illes Balears Universitat de les Illes Balears Catàlegs d’obres de Ramon Llull Cra. de Valldemossa, km. 7’5 Cra. de Valldemossa, km. 7’5 07122 Palma (Espanya) 07122 Palma (Espanya) http://biblioteca.uib.cat/ http://dfc.uib.cat/ Se citen els catàlegs d’obres de Bonner o de la ROL acompanyant les sigles Bo i ROL de la referència que correspongui a l’obra en qüestió. Hom pot trobar aquests catàlegs a la següent adreça de la Llull DB: <http://orbita.bib.ub.edu/llull/cioarl.asp>. © Studia Lulliana Maioricensis Schola Lullistica —————— 1 Apartat, 17. Palma de Mallorca Se cita «MOG I, vii, 23: 455», donant primer la paginació de l’edició original, és a dir, la p. 23 de la setena numeració interna, i llavors, després dels dos punts, el número corresponent ISSN 1132 - 130X de la paginació contínua de la reimpressió (ed. Stegmüller, Frankfurt, 1965). Aquest sistema ISSN digital 2340-4752 permet la consulta tant a aquells lectors que utilitzen la versió original com a aquells que fan DL: PM-268-1961 servir la reimpressió. STUDIA LULLIANA Maioricensis Schola Lullistica Vol. LV MALLORCA 2015 SL 55 (2015), 3-30 A. Bonner i A. Soler Les figures lul·lianes: la seva naturalesa i la seva funció com a raonament diagramàtic* Anthony Bonner i Albert Soler Maioricensis Schola Lullistica Centre de Documentació Ramon Llull [email protected] [email protected] En la història del pensament, els recursos gràfics –figures, diagrames, es- quemes, arbres, taules, etc.– han tingut una acceptació canviant. A l’època grega, el descobriment o, millor dit, la prova tradicionalment atribuïda a Pità- gores que hi havia quantitats, com per exemple √2, no expressables en nom- bres racionals (és a dir, ni en nombres enters ni en fraccions) però perfectament expressables en geometria (la longitud de la hipotenusa d’un triangle rectangle de costats de llargària d’1) va deixar l’aritmètica en un pla inferior (una eina de comptables, recaptadors d’impostos, etc.) i la geometria, tal com la va de- senvolupar Euclides, com a camp paradigmàtic del rigor científic. La física va ser articulada a través de la geometria fins a Galileu. La cosa va començar a canviar amb la invenció cartesiana de la geometria analítica, que permetia la unificació de la geometria amb l’àlgebra i mostrava com, per exemple, una Rebut el 29 de maig de 2015. Acceptat el 14 de juny de 2015. doi: 10.3306/STUDIALULLIANA.110.03 *Aquest treball és el primer d’una sèrie que té com a centre d’interès els recursos visuals en l’obra de Ramon Llull, i sobretot en el seu aspecte funcional o diagramàtic. Hi ha nombrosos estudis sobre les figures lul·lianes, generalment centrats en el seu desenvolupament dintre de l’Art. Un dels pocs treballs que s’aparten d’aquest camí ha estat l’article d’Anna Serra (2013), que és una primera visió d’algunes de les figures lul·lianes des d’un punt de vista diagramàtic, i que ens ha servit com a punt de partida. L’estudi forma part del projecte FFI 2014-53050-C5-1-P del Ministerio de Educación i del SGR119 2014-2016de la Generalitat de Catalunya. 4 ANTHONY BONNER I ALBERT SOLER paràbola es podia representar igualment amb una equació. Amb la invenció del càlcul infinitesimal i integral per part de Newton (i Leibniz), la física va prendre volada gràcies a la seva expressió algebraica. El descobriment d’al- guns defectes en el rigor lògic del sistema euclidià va esperonar la separació entre la ciència i les representacions visuals. En les matemàtiques, aquesta tendència va arribar fins al punt que, ara fa cinquanta anys, una figura desta- cada del grup Bourbaki va escriure una introducció a la geometria en la qual es vantava d’haver-la pogut escriure sense mostrar cap figura geomètrica.1 Si en la lògica, les matemàtiques o la física s’empraven algunes figures era pura- ment com a ajuts heurístics, com a recursos mnemònics o com a il·lustracions; no tenien cap funció en l’estructura lògica del discurs verbal o algebraic. La situació es resumeix en dos passatges d’un volum de 1996: Despite the obvious importance of visual images in human cognitive activities, visual representation remains a second-class citizen in both the theory and practice of mathematics. In particular, we are all taught to look askance at proofs that make curial use of diagrams, graphs, or other nonlinguistic forms of representation, and we pass on this disdain to our students.2 Mathematical discoveries often have been made using visual reasoning, but those very same discoveries were not justified by the visual reasoning. Diagrams are associ- ated with intuitions and illustrations, not with rigorous proofs. Visual representations are allowed in the context of discovery, not in the context of justification.3 Hi ha una actitud similar en els estudis lul·lians, en què les figures són considerades d’importància secundària, simples ajuts mnemònics o heurístics. La història de la filosofia ha ensenyat que només un text és capaç de produir arguments rellevants i que les representacions gràfiques són més aviat il·lus- tracions, mitjans visuals que poden ajudar a la comprensió del text.4 1 Dieudonné (1964) ho va dur a terme gràcies a una mena de descendent de la geometria analítica que és l’àlgebra lineal. El grup Bourbaki, fundat els anys trenta del segle passat, va intentar unificar sobre un fonament rigorós tots els camps de la matemàtica en una obra col·lectiva que s’anomenava Éléments de mathématiques. 2 John Barwise i John Etchemendy, «Visual Informationand Valid Reasoning», dins Allwein i Bar- wise (1996), p. 3. 3 Isabel Luengo, «A Diagrammatic Substystem of Hilbert’s Geometry», dins Allwein i Barwise (1996, 149). Val la pena subratllar la frase «in the context of discovery», que en llatí medieval era la «inventio», tan important per a Llull (només cal tenir en compte els títols d’obres com Ars compendiosa inveniendi veritatem, Ars inventiva veritatis, etc.). Vegeu el passatge corresponent a la n. 66 més avall. 4 L’ús de recursos visuals de caràcter diagramàtic i simbòlic ateny probablement el seu punt de màxim desenvolupament al segle XII, amb la tradició victorina, en Hildegarda de Bingen i Joaquim de Fiore. Se- gons Meier (2003, 510), la centralitat d’aquest segle en la història de la diagramàtica ve d’una superació de l’ús purament didàctic o mnemònic dels diagrames que desemboca en noves construccions simbòliques. Prové d’un encreuament d’interessos simbòlics i científics, d’exegesi al·legòrica del cosmos, que desenvo- LES FIGURES LUL·LIANES 5 Tanmateix, en el camp de la ciència, observacions crítiques com les de les dues citacions anteriors són símptomes d’un canvi, de la reivindicació de l’ús de les representacions visuals.5 És un canvi que potser caldria prendre com a exemple en el camp dels estudis sobre Ramon Llull.
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