DOC33/4496a - Grammatica

Martianus Capella, Mailand. Ambr. F. 119 Sup Ital., fol. 18v (detail); 14th cent. Abb. 1 in: TEZMEN-SIEGEL, Jutta (1985). Die Darstellung der 'septem artes liberales' in der Bildenden Kunst als Rezeption der Lehrplangeschichte. tuduv-Verlagsgesellschaft, Munchen. ISBN 3-88073-167-5

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FOUR - Marten Kuilman (p.390):

The 'quadrivium' is the name for a part of the mediaeval curriculum, as it was derived from the seven 'artes liberales'. The 'artes liberales' were distinguished by bishop and philosopher Augustine (354 - 430 AD) in an effort to give (Latin) education a theoretical framework. The 'artes' were, later, divided in two parts, reflecting the 'human' and the 'natural' sciences:

 

the 'trivium'

 

grammatica

rhetorica

dialectica

 

the 'quadrivium'

 

arithmetica

geometrica

astronomica

harmonia (music)

 

 

FOUR - Marten Kuilman p. 392ff

The division of knowledge found its roots in classical times. The Greek oral tradition (the 'epic cycles') and Roman rhetorical rules (expressed by Cicero) used divisions in the art of memory. This art was, according to legend, invented by the poet Simonides of Ceos, who realized that orderly arrangement was essential for a good memory. Cicero tells the story of the named poet, who established the identity of mutilated bodies after the roof of the banqueting hall collapsed. He remembered the seating of the guests at a banquet, which he had left just minutes before.

 

Four operations can be used to improve memory (PILTZ, 1981; p. 223):

 

1. Use pictures, which resemble what you are trying to remember. These pictures should be slightly out of the ordinary and stand out against a certain background;

 

2. A systematic attention is necessary and a certain order must be introduced;

 

3. A selection of the things to remember is of prime importance because the more firmly something is etched in our senses, the more difficult it is to escape our memory;

 

4. Meditation about the choice is necessary all the time: 'it is meditation that saves the memory'.

 

A logical result of the systematic attention (of the second step) is the introduction of a division. The choice of a division introduces, in a philosophical environment, a cognitive environment: the elementary dual, tri- or quadripartitions reveal the frame of mind in which decisions are taken.

'The actual grouping of the four branches went back to Plato, as well as to Archytas, in the fourth century before Christ', stated Pearl KIBRE (in: MASI, 1981; p. 69). Their common nominator and purpose were a definition of quantity, expressed in a language of 'mathematica' (or 'quadriviales'): 'And this quantity was either discontinuous or continuous, that is discontinuous either per se as in arithmetic, or in relation to another, as in music or harmony; and continuous either without motion as in geometry, or in motion as in astronomy. Thus the quadripartition was specifically that of quantity' (MERLAN, 1960; pp. 94 - 95).

An important contribution to structural thinking came from the Roman orator and man of letters Marcus Tullius Cicero (Tully), born in 106 BC. Cicero's teacher was Posidonius of Apamea, a man who calculated the earth diameter and had his teachings recorded in the 'Tusculanae Disputationes'. Cicero's keen interest in cosmological matters led to the translation of Plato's 'Timaeus' into Latin (and handed to the West in the Middle Ages an important lead to their 'Greek-Pythagorean' past). He was also the first to mention Euclid, although it is unlikely that a Latin translation of this work existed at the time (no record of any Latin translation of Euclid is known before Boethius, c. AD 480; RUSSELL, 1945; p. 212).

One of Cicero's earlier works was the 'De inventione' (or 'Rhetorici libri duo') written in 84 BC. He defined the basic four virtues. The book was concerned with the first part (of five) of the rhetoric, the 'inventio': the composing of the subject matter of a speech and the collection of 'things' to deal with. The work was often associated with an anonymous work called 'Ad Herennium' (Rhetorica nova), and together they were known in the Middle Ages as the ‘First and Second Rhetorics’ of Tullius (YATES, 1966; p. 36). Cicero personalized the theme with four individuals (Crassus, Marcus Antonius, Quintus Scaevola and Caesar Strabo) in a later work called 'De Oratore' (in three books). The book was written in 55 BC and described the positions in a communication:

 

1. Crassus pointed to knowledge of law and philosophy as a prerequisite for a good communication; Antonius reckoned that natural ability and experience was sufficient;

 

2. Antonius expounded his ideas (in Book 2) with the 'inventio' (the deliberate choice of items to draw the attention of the audience); Caesar highlighted the importance of humour;

 

3. Antonius was in favor of order and a clear structure of the material discussed; and

 

4. Crassus (in Book 3) summarized the preconditions of a competent conversation and considered elegance in style and rhythm as the highest objective.

 

Cicero's thoughts were fully developed in his book 'De Officiis' ('On Moral Duties'; MILLER, 1921), written in his 'days of distraction' towards the end of his life (46 - 43 BC). The four virtues were presented in three books: 1. Moral goodness; 2. Expediency; and 3. The conflict between the right and the expedient. The book was about duty and morality, and gave practical rules to achieve those goals.

The four cardinal virtues were in the centre of attention: wisdom, justice, fortitude (courage) and temperance represented the four stages of communication, aiming at equilibrium in a dynamic environment: 'the rule of the golden mean is best' and 'the whole glory of virtue is in activity'. He also realized that the position taken by an observer in a communication (either voluntary or involuntary) was of prime importance: 'tanta vis est et loci et temporis' (Great is the significance of place and circumstance; Book I, XL, 144). VAN DER ZANDE (1998) vividly described the triumphal reception of Christian Garve's German translation of Cicero's work in 1783.

Varro (116 - 27 BC) presented, in his 'De Novem Disciplinis libri novem' (Nine Books of the Nine Disciplines; 33 - 31 BC), a general view of the curriculum in ancient times. Unfortunately, only fragments of this work remain. 'The most learned man of his times', as Varro was called by Quintilian, added medicine and architecture to the list of primary subjects (KNOWLES, 1962), bringing the total to nine.

The actual (theoretical) division into trivium and quadrivium dated from later than the seventh century (COBBAN, 1975). RAJNA (1928) put the effective introduction of the division during the life of Alcuin (730 - 804; articulated in the 'Horatius'-commentary of Pseudo-Alcuin). RASHDALL (1895/1936, p. 36) insisted that 'the real education of the Dark Ages was the trivium'. The quadrivium was, with retrospective effect, 'filled up by discoveries or rediscoveries of the twelfth-century Renaissance'.

Calvin BOWER (in MASI, 1981; p. 163) stated that 'recent studies have shown that the liberal arts played a rather minor educational role in most of Europe between 500 and 850'. A five-fold division prevailed at that time. The actual duties of the monks in their educational quest were formulated in Charlemagne's 'Capitular 72':

 

psalmi (or liturgy),

notae (writing),

cantus (singing),

computus (calendric studies) and

grammatica (reading).

 

Two writers had a direct influence on the European scholars of the Middle Ages: Martianus Capella and Boethius, both living around 500 AD, at the time when the Roman Empire disappeared from the stage of European cultural history. Both can be seen as vital links between the classical knowledge (and imagery) and the young European culture.

Martianus Capella lived in Cartage and used the classical division of knowledge in his 'De Nuptiis Philologiae et Mercurii' (On the Marriage of Philology and Mercury). The book is an encyclopedia in a popular form and became the leading canon of the 'septem artes liberales' from the sixth to the fourteenth century (STAHL, 1971). The tractate was often attributed to 'Tullius', for instance, by Hieronymus Stridonensis in his letter (#53) to Paulinus of Nola, and associated with Cicero's 'De Inventione'.

The book of Martianus Capella was a tribute to division-thinking in general. Firstly, the marriage, as a unity of two: the allegorical marriage between Mercury and scholarship (Book I-II), the unity of words is three-fold (Philology: Book III - V: Grammatica, Dialectica, Rhetorica) and the unity of things is four-fold (Mercury: Book VII - IX: Geometrica, Arithmetica, Astronomia and Harmonia). Two-hundred-and-forty-one manuscripts of 'De Nuptiis' are known to exist. Eight are illustrated (TEZMEN-SIEGEL, 1985).

The Roman philosopher Boethius was born c. 480 AD in Rome and executed in 524 AD at Pavia. He used division-thinking as a guideline in his thoughts (MASI, 1974, 1981; WHITE, 1981). The term 'tessares methodoi' (four methods) was rendered as 'quadrivium', or a place where four roads join (STAHL, 1971; HÜBNER, 1989) in Boethius' translation of Nicomachus of Gerasa's book 'De Arithmetica' (second century AD).

These crossroads marked the four areas of knowledge: 'it is impossible to achieve the summit of perfection in the disciplines of philosophy, unless one approached this noble wisdom by a kind of fourfold way' ('De Arithmetica'; PL. LXIII, 1079D). The following cerebral processes (De Cons. Phil., Book V; in the translation of WATTS (1969), p. 157) were noted to guide a human communication:

 

1. sense-perception

2. imagination

3. reason

4. intelligence (understanding)

 

The transmission of the quadripartite image into the European Middle Ages was intensified by Boethius' 'De Consolatione Philosophiae' (The Consolations of Philosophy), written in jail before his execution on October 23, 524, when he was forty-four years old. In this 'consolatio', or manual for mental health, the goddess 'Philosophia' sings of the power of love in the natural world preserving peace and keeping chaos at bay (in the last poem of Book II). Philosophy moves on (in Book IV, poem 6) to the concord of the elements, of the seasons, and of birth and death's finality.

UHLFELDER (in: MASI, 1981; p. 31) noticed thematic bonds in the thirty-nine poems, which intermingle with the same number of passages in prose: 'Boethius' explicit identification of divisions of the argument proves that there were two coexistent structural principles, one based on the fivefold division into books, and the other on the fourfold stages of the 'plot', with special emphasis on the threefold division of the philosophical argument.'

The world view of Boethius was manifestly put forward in the first poem of Book IV, describing the ascent of the soul to God, the centre of light, and its return.

The human mind travels from the earth through the sky to the sphere of the moon. The lightest element (fire) reaches to the moon. Beyond the moon is the fifth element, the quintessence or ether. The soul succeeds through the sphere of the stars to its ultimate destination: God, the source of light. The (cyclic) movement of the (human) invisibility continues, descending from God, back through the ether, to reach the earth and emanate (again) in a human soul.

At birth the soul emanates or descends to the earth from God, and its ascent is an account of its return. The emanation is described as follows (verses 15 - 26; translated by WATTS, 1969; p. 117/118):

 

And when the orbit's path is done

The furthest heaven it forsakes.

It treads beneath the ether swift

Possessing now the holy light,

For here the King of kings holds sway,

The reins of all things holding tight,

Unmoving moves the chariot fast,

The lord of all things shining bright.

If there the pathway brings you back -

The path you lost and seek anew -

Then, 'I remember,' you will say,

'My home, my source, my ending too.'

 

A 'descriptio' (visual explanation) of Boethius' cosmic consciousness was given in an eleventh-century copy of the book 'De Arithmetica' (Arithmetike eisagoge) by Nicomachus of Gerasa (Jerash, Jordan). This important mathematician lived in the Roman province of Syria from c 60 - 120 AD. Boethius’ ‘De institutione arithmetica’ was a Latin translation of this book (MURDOCH, 1984; p. 102, fig. 97).

Cassiodorus and Isidore of Seville ('Etymologiae') jointed Boethius crucial position in the continuation of classical knowledge into the Middle Ages. They also contributed to the formal use of the system of division of knowledge. Cassiodorus, living towards the end of the sixth century and founder of the monastery of Vivarium in Calabria, wrote a handbook on the liberal arts (the 'Institutiones' or 'Introduction to Divine and Human Readings').

The 'quadrivium' could be seen as a path to abstract knowledge (WHITE, 1981). In terms of a Pythagorean number-symbolism it means, that arithmetic deals with the numbers itself, geometry with the numbers in space, harmony with the numbers in time and astronomy with numbers in space and time (GUTHRIE, 1987). This division reflected the cognitive 'visio', as it was experienced during the apex of medieaval thinking.

A clarifying article on the possible origin of the term 'quadrivium', was written by HÜBNER (1989). He pointed to the difference in age: the term 'quadrivium' was older than the 'trivium'. Boethius never knew the term 'trivium' (MASI, 1981; p. 11). The associated subjects (of the quadrivium) reached prominence only when tetradic thinking itself became visible in a wider sense (from the middle of the eighth century). The general use of the terms 'trivium' and 'quadrivium' dated from the eleventh century (LESNE, 1940; WOLTER, 1959).

The symbolism of the cross-roads was, according to Hübner, more often seen as a metaphor (sometimes in connection with a 'bridge') of the opposition between body and soul: 'this was the way the metaphorical 'quadrivium' was understood in the Middle Ages'. A reference to Alcuin had to support his view. To draw the symbolism (of the quadrivium) in such a dualistic environment is, in my view, a simplification. It is true that Alcuin was - in his 'Retorica' - a faithful follower of Augustine (HOWELL, 1941), who felt attracted to lower division-thinking. However, Alcuin - the 'educator of Europe', originating from York and a teacher of Charlemagne - distinguished himself from Augustine and brought a 'Celtic' flavor to his teaching.

Augustine - who had earlier crossed the Channel to England (in 596 AD) - was a representative of the 'Roman' interpretation of Christianity, with its emphasis on opposition. Now (some two hundred years later) Alcuin returned the tetradic mood back to the Continent and brought with it a reintroduction of the liberal arts. He referred to the arts in his 'Grammatica' as seven gifts of the Holy Spirit and as the seven steps to the study of philosophy (PL 101, col. 853).

Rhabanus Maurus (c. 784 - 856) showed interest (but little knowledge) in the liberal arts in his 'De Clericorum Institutione'. Book III is a reworking of Isidore's description of the arts with slight additions. A 'Grammatica' attributed to Clemens Scotus, of Irish origin and composed around 800 AD, divided philosophy in three genera (physics, ethics and logic) and divided physics in turn in four principal parts, the four mathematical arts or 'quadrivium philosophiae' (quoting Boethius' mathematical work for the first time). John Scotus Erigena quoted an even more extended passage from the 'Proemium' of Boethius' arithmetical treatise in Book I of his 'De Divisione Naturae'.

'It is no coincidence', according to BOWER (in : MASI, 1981; p. 167), 'that both names citing Boethius contain the term 'scottus', for the revival of the liberal arts and of speculative philosophical thought in the ninth century was largely the result of the work of 'scotti peregrinantes'. They brought to the continent, along with their love of learning and speculative thinking, many books that had been basically unknown for several centuries.'

The education at the Carolingian monastery schools was given at three levels (PILTZ, 1981; p. 15), inspired by a practical approach:

 

1. The first step consisted in the learning of the elementary principles of writing, reading and singing, some grammar and an explanation of the calendar.

 

2. The next step was a study of the seven liberal arts ('septem artes liberales'), divided into the 'trivium', i.e. grammar, rhetoric and dialectic, and the 'quadrivium', consisting of arithmetic, geometry, astronomy and music (fig. 252). The seven liberal arts were mentioned by Plato in his 'De Republica' (The Republic, book VII; LARSON, 1979) and are part of the Platonian system of 'planned education' (COBBAN, 1975).

 

3. The final step in the Carolingian cathedral and monastery schools was the actual preparation to the task as a priest and the practical familiarity with the skills of priesthood, like the reading and interpreting the Scriptures and teaching the catechism.

 

The cathedral school of Chartres became in the early twelfth century, under the guidance of Thierry of Chartres, a centre of the 'exact' sciences of the quadrivium (STODDARD, 1966; MASI, 1983). Plato's 'Timaeus' (in the adaptation of Chalcidius, living in the fourth century) was the major point of departure. It was thought possible to learn more about God within the structural setting of nature. The study of nature was therefore regarded as a devotion to the almighty God.

'For three centuries, from the thirteenth century until the revolutionary changes that took place at the beginning of the sixteenth century, all people in Europe with any claim to education at all could make themselves understood to each other. This was not only because they shared a common language in Latin. What is more remarkable is that they shared a common world picture and uniform terminology for describing it', said Anders PILTZ (1981) in the preface of his book on 'The World of Medieval Learning'. This unity was mainly due to the Roman Catholic Church and its schools associated with churches and cloisters.

The ever-present current of Neo-Platonism in the European cultural history favored the reciprocity between the Idea and Nature and showed therefore an interest in the quadrivium. The scholar Gemistus (Plethon), for instance, living in Mistra (southern Greece), some two hundred years later, was educated in the trivium and quadrivium (FUCHS, 1926; MASAI, 1956; p. 55)

The transfer of knowledge in the Middle Ages followed an established, trodden path. VERGER (1973, p. 13) noted in his expose of teaching at the universities in the Middle Ages: 'The method was always the same; the master reads the text which had to be learned (lectio) and interrupts his reading by commentaries, which explain the literal sense (sensus) and reveal the deeper meaning of the excerpt (sententia). VERGER (1973) divided the different universities in their way of origin:

 

1. spontaneous (from cloister schools), like Paris, Bologna, Oxford and Montpellier;

 

2. by migration, like Cambridge (1208), Orleans, Padua (1222);

 

3. planned, like Naples (by Frederick II, 1224), Toulouse (1229), and the Spanish universities Palencia, Salamanca and Valladolid.

 

The quadrivium remained favorite in the faculties of arts in Padua, Bologna and particularly Oxford. Furthermore, Toledo, in Spain, was the 'famed city for the teaching of the arts of the quadrivium' (GIMPEL, 1979/1988).

 

Done