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Which clippings match 'Quadrivium' keyword pg.1 of 1
01 JANUARY 2011

New Directions in Interdisciplinarity: Broad, Deep, and Critical

"Before interdisciplinarity in either the disciplinary producing or disciplinary–circumscribing senses could manifest itself, disciplinarity itself had to take on its peculiarly modern form. Any assessment of interdisciplinarity – multi – and trans–, noncritical and critical– will benefit from an appreciation of this background.

Prior to the modern period, learning exhibited a kind of unity that might be called predisciplinary. Aristotle, it is true, introduced distinctions between logic, physics, and ethics, but these were never of a kind to raise the possibility of cross–disciplinary formations such as 'physical ethics.' During the Middle Ages, the division of the artes liberales into grammar, rhetoric, dialectic (the trivium), arithmetic, geometry, astronomy, and music (the quadrivium) ensured that the education of 'free men' included all the knowledge and skills needed to exercise their social roles. Insofar as it existed, disciplinary specialization was present more in the 'servile arts' of artisans and tradesmen. Not even teachers of the liberal arts became specialists in their different branches, because the idea of, for example, possessing arithmetic without grammar would have been considered a deformation of the mind. In the monastery schools, the unfettered pursuit of knowledge was viewed skeptically, criticized as curiositas, and therefore subject to disciplinization in a premodern behavioral sense. Only at the end of the Middle Ages, as the infinite pursuit of disciplinary knowledge took on the character of a spiritual activity, would Renaissance men become necessary to cross boundaries and synthesize diverse areas of learning."

(Robert Frodeman and Carl Mitcham, 2007, p.508)

[1][2] Frodeman, R. and C. Mitcham (2007). "New Directions in Interdisciplinarity: Broad, Deep, and Critical." Bulletin of Science, Technology & Society 27(6).


Aristotlearithmetic • artes liberales • artisanastronomy • cross boundaries • cross-disciplinary • curiositas • dialecticdisciplinary knowledgedisciplinary specialisationdisciplinesdiscursive fielddivisionethicsEuropean Renaissance • free men • geometrygrammarinterdisciplinarityknowledgeknowledge integrationlearningliberal artslogicmiddle agesModern • modern period • monastery schools • multidisciplinaritymusicorderingphysics • predisciplinary • premodernpursuit of knowledgeQuadriviumrhetoricservile artsskillsocial construction of knowledgesocial rolesspecialisation • spiritual activity • synthesis • tradesmen • transdisciplinarityTrivium • unity


Simon Perkins
25 NOVEMBER 2007

The Discourse Of Engineering Needs To Be Expanded

"The discourse of engineering needs to be expanded. The iterative methods, the insistence on quality control, the inherent pragmatism, as well as the responsiveness to expressed needs and articulated problems, all make the practice of engineering the optimal rationalisation of human action. This is to say that engineering is the exemplary human art, the art that allows us to be effective and to achieve desired outcomes. What is crucially missing from engineering is the critical means to evaluate and place into a calculus of human good the many desires that present themselves to us."
(Harold P. Sjursen)



CLAEE • crisis philosophy • engineering • human disciplines • liberal artsNAEQuadrivium • Sjursen • Trivium • UICEE • UNESCO • value added • weltanschauung
20 NOVEMBER 2007

The Seven Liberal Arts: The Trivium & The Quadrivium

"Originally the liberal arts were seven in number. They were divided into the three–fold Trivium of Grammar, Logic, and Rhetoric, and the four–fold Quadrivium of Arithmetic, Geometry, Music, and Astronomy. These words mean, respectively, a three–way and a four–way crossroads, implying that these paths of knowledge are fundamentally interconnected –– and, by extension, that all other paths can be found to intersect here, as well. The T[rivium]. was the basis of elementary education (whence we probably get the word 'trivial'): Grammar taught the craft of reading and writing; Logic, of careful reasoning; and Rhetoric, of effective communication. The Q[uadrivium]. was the basis of advanced education: Arithmetic taught the science of number; Geometry, of form; Music, of sound (and of 'harmony' in the most general sense of the word –– 'number in motion', as it was often put); Astronomy, of time (of 'form in motion'). Moreover, from the very beginning, whether openly acknowledged or carefully alluded to, each of the Quadrivial sciences was accompanied by its complementary metaphysical art. Each dealt not only with the outer structures, but also with the inner meanings of its discipline. Thus, Arithmetic included Arithmology, the understanding that numbers were not merely quantities, but also qualities (that 'two', for instance, is also 'duality, polarity'); Geometry included what is nowadays called Geomancy, the understanding (in, for example, the design of temples or cathedrals, or in the graphic arts) that the spirit and the emotions can be affected in particular ways by particular forms; Astronomy included Astrology, the divination of the meanings of cycles of time; and Music included not only the study of 'practical theory', of nomenclature and technique (e.g. 'this is a minor third', 'this is the Mixolydian mode'), but also the study of 'speculative theory', of the meanings and influences of tones and intervals and scales.

Traditionally the seven liberal arts have been positioned in opposition to the 'servile arts'. In this sense while the liberal arts generally refer to knowledge 'appropriate for free men' (social and political elites) the servile arts have been associated with specialised tradesman skills and knowledge e.g. engineering and design."
(Steven C. Rasmussen 28 March 1996)




arithmeticastronomycathedralcraftcurriculumcycledesigneducationeducational modelemploymentengineeringEuropeangeometrygrammar • high middle ages • interconnectedliberal arts • liberalis arts • logic • medieval university • musicpremodernprofessionalismQuadriviumqualityrhetoric • scholastic guild • scienceservile arts • seven liberal arts • skills • studia generalia • studium • trade • tradesmanship • Trivium • universitas magistrorum • universitas magistrorum et scholarium • universitas scholarium • universityvocationvocational training

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