Quadrívium: diferència entre les revisions
mCap resum de modificació |
m →Orígens |
||
| Línia 9: | Línia 9: | ||
==Orígens== |
==Orígens== |
||
Aquests quatre estudis componen la part secundària del [[Currículum educatiu|currículum]] descrit per [[Plató]] a ''[[La República (Plató)|La República]],'' i es descriuen en el setè llibre d'aquest treball (en l'ordre aritmètica, geometria, astronomia i música).<ref name="nie"/> |
|||
El quadrivi està implícit en els primers escrits [[pitagòrics]] i en els ''De nuptiis'' de [[Marcià Mineu Fèlix Capel·la|Martianus Capella]], encara que el terme «quadrivi» no va ser utilitzat fins a [[Boeci]], a principis del segle VI.<ref>Marrou, Henri-Irénée (1969). "Les Arts Libéraux dans l'Antiquité Classique". pp. 6–27 in ''Arts Libéraux et Philosophie au Moyen Âge''. Paris: Vrin; Montréal: Institut d'Études Médiévales. pp. 18–19.</ref> Com [[Procle]] va escriure: |
|||
<blockquote> |
|||
The Pythagoreans considered all mathematical science to be divided into four parts: one half they marked off as concerned with quantity, the other half with magnitude; and each of these they posited as twofold. A quantity can be considered in regard to its character by itself or in its relation to another quantity, magnitudes as either stationary or in motion. Arithmetic, then, studies quantities as such, music the relations between quantities, geometry magnitude at rest, spherics [astronomy] magnitude inherently moving.<ref>Proclus. ''A Commentary on the First Book of Euclid's Elements'', xii. trans. Glenn Raymond Morrow. Princeton: Princeton University Press, 1992. pp. 29–30. {{ISBN|0-691-02090-6}}.</ref> |
The Pythagoreans considered all mathematical science to be divided into four parts: one half they marked off as concerned with quantity, the other half with magnitude; and each of these they posited as twofold. A quantity can be considered in regard to its character by itself or in its relation to another quantity, magnitudes as either stationary or in motion. Arithmetic, then, studies quantities as such, music the relations between quantities, geometry magnitude at rest, spherics [astronomy] magnitude inherently moving.<ref>Proclus. ''A Commentary on the First Book of Euclid's Elements'', xii. trans. Glenn Raymond Morrow. Princeton: Princeton University Press, 1992. pp. 29–30. {{ISBN|0-691-02090-6}}.</ref> |
||
</blockquote> |
|||
==Ús medieval== |
==Ús medieval== |
||
Revisió del 21:11, 19 ago 2018
El quadrivi o quadrivium (del llatí quadrivium, «quatre vies»; plural: quadrivia[1]) tracta dels quatre temes, o arts, ensenyats després d'ensenyar el trivi.
La paraula és llatina, que significa «quatre vies», i s'utilitza als quatre temes que han estat atribuït a Boeci o Cassiodor al segle VI.[2][3] Junts, el trivi i el quadrivi comprenien les set arts liberals (basades en les habilitats del pensament),[4] tan distingides de les arts pràctiques (com la medicina i l'arquitectura).
El quadrivi consistia en aritmètica, geometria, música i astronomia. Aquest va seguir el treball preparatori del trivi, que consistia en gramàtica, lògica i retòrica. Al seu torn, el quadrivi va ser considerat el treball preparatori per a l'estudi de la filosofia (de vegades anomenat «art liberal per excel·lència»)[5] i la teologia.
Va ésser especialment aquesta branca de coneixement la que va rebre més impuls amb els múltiples contactes dels monestirs catalans amb l'Islam; un clar exemple es troba en els avançats estudis matemàtics que Gerbert d'Orlhac va portar a terme amb el bisbe Ató de Vic durant la seva estada a Catalunya. A través de l'Islam es van conèixer els treballs de Maslama sobre l'astrolabi, l'establiment de les taules astronòmiques, l'ús de les xifres àrabs i del zero i es van ampliar els coneixements sobre àlgebra en el món cristià. Els nous coneixements van facilitar i millorar l'estudi de la geometria, l'aritmètica i l'astronomia en els diferents centres d'ensenyament.[6]
Orígens
Aquests quatre estudis componen la part secundària del currículum descrit per Plató a La República, i es descriuen en el setè llibre d'aquest treball (en l'ordre aritmètica, geometria, astronomia i música).[4]
El quadrivi està implícit en els primers escrits pitagòrics i en els De nuptiis de Martianus Capella, encara que el terme «quadrivi» no va ser utilitzat fins a Boeci, a principis del segle VI.[7] Com Procle va escriure:
The Pythagoreans considered all mathematical science to be divided into four parts: one half they marked off as concerned with quantity, the other half with magnitude; and each of these they posited as twofold. A quantity can be considered in regard to its character by itself or in its relation to another quantity, magnitudes as either stationary or in motion. Arithmetic, then, studies quantities as such, music the relations between quantities, geometry magnitude at rest, spherics [astronomy] magnitude inherently moving.[8]
Ús medieval
At many medieval universities, this would have been the course leading to the degree of Master of Arts (after the BA). After the MA, the student could enter for bachelor's degrees of the higher faculties (Theology, Medicine or Law). To this day, some of the postgraduate degree courses lead to the degree of Bachelor (the B.Phil and B.Litt. degrees are examples in the field of philosophy).
The study was eclectic, approaching the philosophical objectives sought by considering it from each aspect of the quadrivium within the general structure demonstrated by Proclus (AD 412–485), namely arithmetic and music on the one hand[9] and geometry and cosmology on the other.[10]
The subject of music within the quadrivium was originally the classical subject of harmonics, in particular the study of the proportions between the musical intervals created by the division of a monochord. A relationship to music as actually practised was not part of this study, but the framework of classical harmonics would substantially influence the content and structure of music theory as practised in both European and Islamic cultures.
Ús modern
In modern applications of the liberal arts as curriculum in colleges or universities, the quadrivium may be considered to be the study of number and its relationship to space or time: arithmetic was pure number, geometry was number in space, music was number in time, and astronomy was number in space and time. Morris Kline classified the four elements of the quadrivium as pure (arithmetic), stationary (geometry), moving (astronomy), and applied (music) number.[11]
This schema is sometimes referred to as "classical education", but it is more accurately a development of the 12th- and 13th-century Renaissance with recovered classical elements, rather than an organic growth from the educational systems of antiquity. The term continues to be used by the Classical education movement and at the independent Oundle School, in the United Kingdom.[12]
Referències
- ↑ Kohler, Kaufmann. «Wisdom». Jewish Encyclopedia. [Consulta: 7 novembre 2015].
- ↑ "Part I: The Age of Augustine". ND.edu. 2010. ND205.
- ↑ "Quadrivium (education)". Britannica Online. 2011. EB.
- ↑ 4,0 4,1
«Quadrivium». A: D. C. Gilman. New International Encyclopedia. 1st. New York: Dodd, Mead, 1905.
- ↑ Gilman, Daniel Coit, et al. (1905). New International Encyclopedia. Lemma "Arts, Liberal".
- ↑ Diccionario de Arte II (en castellà). Barcelona: Biblioteca de Consulta Larousse. Spes Editorial SL (RBA), 2003, p.197. DL M-50.522-2002. ISBN 84-8332-391-5 [Consulta: 7 desembre 2014].
- ↑ Marrou, Henri-Irénée (1969). "Les Arts Libéraux dans l'Antiquité Classique". pp. 6–27 in Arts Libéraux et Philosophie au Moyen Âge. Paris: Vrin; Montréal: Institut d'Études Médiévales. pp. 18–19.
- ↑ Proclus. A Commentary on the First Book of Euclid's Elements, xii. trans. Glenn Raymond Morrow. Princeton: Princeton University Press, 1992. pp. 29–30. ISBN 0-691-02090-6.
- ↑ Wright, Craig (2001). The Maze and the Warrior: Symbols in Architecture, Theology, and Music. Cambridge, Massachusetts: Harvard University Press.
- ↑ Smoller, Laura Ackerman (1994). History, Prophecy and the Stars: Christian Astrology of Pierre D'Ailly, 1350–1420. Princeton: Princeton University Press.
- ↑ Kline, Morris (1953). "The Sine of G Major". In Mathematics in Western Culture. Oxford University Press.
- ↑ «Oundle School – Improving Intellectual Challenge». The Boarding Schools' Association, 27-10-2014.
Each of these iterations was discussed in a conference at King's College London on "The Future of Liberal Arts" at schools and universities.
Vegeu també
Bibliografia
- Sadurní i Puigbò, Núria: Diccionari de l'any 1000 a Catalunya. Edicions 62, Col·lecció El Cangur / Diccionaris, núm. 280. Barcelona, octubre del 1999. ISBN 84-297-4607-2, plana 106.