The beginning of the classical Greek history-as-a-cultural-unit is marked by Homerus’ composition of the ‘Iliad‘ and ‘Odyssey‘ (eighth century BC) and the works of the poet Hesiod (c. 750 BC), ‘Opera et dies’ (Works and Days) and the ‘Theogony‘. These literary masterpieces coincided more or less with the beginning of the Greek calendar, calculated from the first Olympiad in 776 BC. The games were held every four years (up to its discontinuity in 394 AD).
Just like any major cultural appearance, the first visible presence (or ‘beginning’) is not an absolute event, but it is interpreted from the present point of observation. In the case of the Greek antiquity the matter of (first) cultural appearance is further complicated by the topic of geographic definition: are the Minoan (Cretean) and Cycladic cultures part of the greater Greek civilization or not?
There is an extensive literature on the early-Greek heroic poems. One particular aspect is highlighted here: the so-called ‘epic circle’ (WHITMAN, 1958/1965). The ‘epic circle’ is a symmetric pattern in the way stories were told. In the composition is a precise repetition of certain motifs. Epic events have a clear sequence and order, which cannot be attributed to coincidence (FENIK, 1968). The ‘epic circle’ is, more likely, developed in a natural way as a mind-trajectory, used by the reciter to remember the events.
OOSTENBROEK (1977) indicated that the ‘Theogony‘ of Hesiod was a philosophical rather than a mythological work. Some distinct thought-directions are given in the poem. Eris (strife) and Eros (love) are complementary. In a cyclic process (described in the ‘Works and Days’) there is a strife with nature and eventually a victory of the good of nature. The basic (two-fold) concept of unity (love) and separation (strife), in a constant cycle of transformation, was elaborated in the ‘Theogony’ and therefore, earlier than Heraclites and Empedocles, who followed the same line of thought.
Pythagoras (c. 570 – 500 BC)
The first, major philosophical system based on division thinking was founded by Pythagoras (and his school), centred on Croton in Southern Italy. The system provided the intellectual base for a model, which visualized the human mind as an entity, which could be divided in parts. The parts were associated with numbers and communication.
The primary sources of Pythagorean thoughts are fourfold (HENINGER, 1974): 1. In the ‘De vitis, dogmatibus… libri X’ of Diogenes Laertius; 2. From the ‘Pythagorae vita’ of Porphyry (234 – c. 305 AD.); 3. A book with the same title with additions by Jamblichus (c. 250 – c. 330); and 4. From the ‘Myriobiblon‘ of Photius (c. 820 – 891), a patriarch in Constantinople.
These sources were also mentioned by JOOST-GAUGIER (2006), but she added a much wider range of Pythagoras’ influences in her excellent book. The list includes Xenophanes of Colophon, Alcmaeon, Pherecydes of Syros, Heraclitus of Ephesus, Ion of Chios, Empedocles and others in the Greek world. The memory of Pythagoras lingered on in the Roman world by representatives like Cicero (‘who uses the historical Pythagoras as an emblem of a holistic mode of thought’), Livy, Varro, Ovid (Metamorphoses, fifteenth book, Pythagoras was not mentioned by name), Pompeius Trogus, Nicomachus, Plutarch, Apuleius, Theon of Smyrna and others.
The role of numbers is crucial in the Pythagorean world view: ‘Numbers are the ultimate constituents of reality. Number is pure form.’ Every communication was, in Pythagoras’ view, constituted of accountable parts that interact with each other. It is the emphasis on the analogical element of thought, which makes his approach so fruitful for the (modern) fourfold-way of thinking.
Unfortunately, the intellectual inheritance of Pythagoras was, in later ages, handled with incomprehension and simplification. For instance, the so-called ‘Sphere of Pythagoras’ was a device to predict the outcome of an illness by means of comparing certain symptoms with particular days in a month (fig. 90). The outcome – Vita (alive) or Mors (death) – points to a straightforward use of oppositional thinking.
Fig. 90 – The ‘Sphere of Pythagoras’ – Vita and Mors. Wenen, MS 67, fol. 174. Fig. 9 in: CAVINESS (1983).
An upsurge of Pythagoreanism in later ages did not coincide with broadminded thinking. The original message was, more often then not, wrongly understood. The emphasis on numerology, associated with mystical elements, drifted away from the functionality of numbers as indicators in a dynamic analogy (communication). Many sixteenth and seventeenth century authors paid their tribute to Pythagoras, like Gregor Reisch in the encyclopedic ‘Margarita philosophica‘ (Freiburg, 1503) (fig. 91), Cornelius Gemma in ‘De arte cyclognomica‘ (Antwerp, 1569), Johannes Kepler in ‘Harmonices mundi’ (Linz, 1619) and Athanasius Kirchner in his ‘Arithmologia‘ (Rome, 1665), to mention only a few. The interest in the number-symbolism was waning at the end of the eighteenth century and at that time one could make a mockery of the ‘somnia Pythagoraeorum‘ (BOLL & BEZOLD, 1931).
Fig. 91 – ‘Margarita Philosophica Nova’ with the seven liberal arts. To the left the trivium (Logica, Rhetorica and Grammatica), in the middle and to the right the quadrivium (Arithmetica, Musica, Geometrica and Astronomica). Under the watchful eyes of the four Church fathers Augustine, Gregorius, Hieronymus and Ambrosius. In: WOLFF (1971).
Fig. 92 – Pythagoras with arithmetica, as depicted in: Thomasin von Zerclaere – Der Welsche Gast (1408). Munchen, Staatsbibl. Cgm 571, fol. 71r. Fig. 15 in: TEZMEN-SIEGEL, 1985. This didactic poem – translated as ‘A Visitor from Italy‘ – was written by a young cleric from Friaul (Italy) in 1215 (TESKE, 1933). Thomasin distributed such one-liners as ‘Hie sprich ich, daz dehein dinch ist guot, daz unmazze ist‘ (Here I say that no thing is good which is immoderate; Part 8).
The philosopher Ralf Cudworth (1617 – 1680), in his book ‘The true intellectual system of the universe‘ (London, 1678) presented Pythagoras as ‘the most eminent of all ancient Philosophers’, but his appreciation of the philosopher was probably fed by completely the wrong arguments.
The English theologian and writer Thomas Burnet (c. 1635 – 1715) was – in his ‘Archaeologiae philosophicae’ (1692/1728) – a staunch enthusiast of the numerical procedure attributed to Pythagoras. Chapter XI of Burnet’s ‘Archaeologiae‘ was dedicated to ‘De Pythagora & secta Pythagorica‘, with subjects like the Systema Pythagoricum, the Tetractys (fig. 93) and the Numerus Quaternarius, Pythagoricus.
Fig. 93 – Tetractys was an ordering principle of the first ten numbers attributed to Pythagoras and described by Theon of Smyrna (2nd cent AD). The first four numbers/ rows symbolize the harmony of the the spheres: the unity (1) is divided in a dyad (2), related to the peras/apeiron (limit/unlimited). The third number (3) stands for harmony, while the number four (4) represents the kosmos. (GUTHRIE, 1987). The musical intervals, which can be measured on a string, have an affinity with the ‘tetractys‘ as a division principle: 4 : 3 (the fourth), 3 : 2 (the fifth) and 2 : 1 (the octave).
Thomas Burnet gave a four-fold description of the Cabala and the ‘Quatuor Mundi Cabalistici’ (in Ch. VII of the ‘Archaeologiae‘ ) corresponded in his objectives:
————————- 1. Aziluth Mundus Emanationis
————————- 2. Briah Mundus Creationis
————————- 3. Jetzira Mundus Formationis
————————- 4. Ashiah Mundum Fabricae vel Factionis
Burnet mentioned further as contemporary supporters of Pythagoras: ‘Joh. Meursium’ (Johannes van Meurs, 1579 – 1639; Denarius Pythagoricus ,1631), ‘Fab. Paulinum’ (Fabius Paulinus, c. 1535 – 1605) and ‘Petrum Bongum’ (Pietro Bongo (d. 1601), the writer of the ‘Numerorum Mysteria’, 1584).
Thomas Taylor (1758 – 1835) and Fabre d’Oliver (1767 – 1825) are other scholars caught by the (numerological) ideas of Pythagoras (GUTHRIE, 1987). Thomas Taylor translated the ‘Mysteries‘ of Jamblichus’ (TAYLOR, 1895). Jamblichus – called by CLARK (1989) ‘a notoriously unclear writer’ – wrote in a spirit of theurgy: ‘a ritual invocation of divine presence, dangerously close to magic’.
Pythagoras’ ideas should be treated in their own right. It might well be that Pythagoras’ system of thoughts – initially based on numbers as the representations of a communication – contained similarities with the present four-fold approach. ‘Visibility’ in terms of a particular number are an integrated part of modern quadralectic thinking, which is directly indebted to Pythagoras.
Empedocles (c. 450 BC)
Whereas Pythagoras provided the base, it was the Greek Empedocles, with his theory of the four elements, who actually shaped a philosophy of the fourfold way of thinking. The philosopher lived from c. 494 to 434 BC. and was banished from Acragas (Agrigentum), on the south coast of Sicily. He traveled extensively and was ‘the mixture of philosopher, prophet, man of science, and charlatan’ (RUSSELL, 1945). Parts of his epic didactic poem ‘Peri physeos’ (About Nature/The Physics, in two books, concerning the formation of things), and the ‘Katharmoi‘ (Purifications, about four hundred-and-fifty lines) are preserved.
Empedocles joined the number-based-thinking of Pythagoras (with the emphasis on the ‘accountable’ world) and the philosophical ideas of Parmenides about being (of the invisible One; AUSTIN, 1986) into a new doctrine. CORNFORD (1912) pointed to the concurrence of a mystical/theological origin, which he called ‘Italiotic‘ (Pythagoras) and a ‘scientific’ source (Anaximander, atomism), provided by the Ionian (Western Turkey) tradition. Empedocles’ ideas are a compromise between the balance of (opposite) forces, put forward in the medical theory of Alcmaeon, and the more extreme approaches of the early Ionian physicists (VLASTOS, 1947).
Empedocles carried the idea of equilibrium from the physical (medical) to the philosophical world and promoted the ‘isomoiria‘ (equal division) of the basic principles. Strife (Neikos) is the equivalent of illness and indicates a wrong mixture of the basic ingredients. Love (Philia) means the right mixture (harmonia) of constituents.
The four basic components (of all being), which remain unaltered in the process of observation, are: the sun, the air, the earth and the sea. Empedocles defined his basic elements therefore as fire, air, earth and water. These elements are, in the classical view, considered to be indivisible, unchangeable and for ever. Their combination offers a theory of nature, which is originated in the fourfold-way of thinking and applicable on different levels of human endeavor and physical investigation (fig. 92).
Fig. 92 – The Creation. This illustration from a German Bible, printed by Heinrich Quentell in Cologne around 1479, shows the four elements in a cyclic fashion. Central is the earth, where the act of creation is visualized: God the Father sends the Holy Spirit to the World and, through Christ, creates Eve from the rib of Adam. Around the world is the sea (water), with fish and a mermaid. The air is portrayed as a fringe with stars and sun and moon. The outer circle (fire) is crowded with angels and at the top sits God. Four winds blow to different directions. In: PILTZ (1981).
CORNFORD (1912) called Empedocles ‘a candid dualist’ and determined that ‘Platonism (theory of Forms or ‘Ideas’) was another offshoot of Pythagoranism, another attempt in relating the one God, who is good, to a manifold and imperfect world’. This statement does not justice to the width of Empedocles’ world and emphasized the two-fold aspect.
A more plausible postulate was put forward by MONDOLFO (1958, p. 77): ‘Empedocles cosmic cycle, abstractly reduced by Plato to two opposite phases, unfolds itself in reality in four; two extremes, the total mixture of the elements and their complete separation, and two intermediate phases, or phases of partial mixture and distinction’ (fig. 93).
Fig. 93 – The fourfold way of thinking according to Empedocles. The four phases are divided in two kinds: two of unity and two of plurality. The first is symbolized by Love and rest and the second is characterized by Strife and movement.
The cyclic system of Empedocles was thoroughly studied by O’BRIEN (1969). Four elements are governed by two forces: love aims at unity and happiness, while strife leads to pluriformity, division and misery. The sphere is the symbol of unity, where everything is at rest. In pluriformity (of parts) the interaction is caused by displacement. Therefore, a cyclic movement is, according to Aristotle in his ‘Physics‘, an alternation between rest and movement. Most scientists are now of the opinion, that the system consists of four periods (O’BRIEN, 1969; Ch. 8).
Clara Elizabeth MILLERD (1908/1980) presented an excellent PhD. -thesis on the subject in 1901 to the University of Chicago. She described the ‘cycles of transformation’ between the poles of Love (Philia), which unites and Strife (Neikos), which separates. In a later development Empedocles’ cycles were translated in a Neo-Platonic antithesis and the influence of the tetradic nature of the interaction between the elements was diminished. Much of the occasional misunderstanding about the original intentions of Empedocles can be traced back to the inability to visualize a tetradic system.
The thoughts of the Greek philosopher Aristotle offer the most comprehensive summary of the four-fold way of thinking. In many ways, he reaped the philosophical fruits of his predecessors and presented them in a logical framework (fig. 94).
Fig. 94 – The square of opposition. This demonstration of the different types of categorical propositions is put forward in the logic of Aristotle (in his ‘Perihermeneias‘/On propositions). Top left (type A) is universal affirmative. Top right (type E) is universal negative, bottom left (type I) is particular-affirmative and bottom right (type O) is particular negative. The relationship of A to O and E to I is contradictory. From the ‘Tractatus duodecim’ of Petrus Hispanus, printed by Johannes Knob in Strassburg in 1514.
Aristotle provided, in his ‘Categories‘ (Praedicamenta) and the ‘Perihermeneias‘, a theory of interactions in a communication. It is the rediscovery of Boëthius’ translations of these works and of the ‘Isagoge‘ of Porphyrius, which set the spark – in the eleventh century – for a new level of thinking in Europe (PILTZ, 1981).
The (tetradic) thoughts of Aristotle have, in a wider historical sense, close links with the development of practical ideas, initiated by the physicists. Philistion, head of the medical school in Sicily, a contemporary of Plato and a follower of Empedocles extended the concept of a medical, two-fold equilibrium theory of Alcmeaon to a fourfold equilibrium. According to HAHM (1977, p. 99) ‘he took the easiest course of all and simply identified fire with the hot, air with the cold, water with the wet, and earth with the dry.’
………………………………………….. fire – hot
……………………………………………. air – cold
……………………………………………. earth – dry
……………………………………………. water – wet
The theoretical-philosophical division was, in this way, connected with human qualities and became an empirical tool (LONIE, 1981). Illness had to do with a surplus or deficiency of a certain quality. There might be a contact between Philistion of Locri and Plato, by means of Timaeus (originated from Southern Italy). Plato staged Timaeus – in a book with the same name – as a person, who explains his theory of nature.
Hippocrates (c. 400 BC) had earlier postulated the actual theory of the four ‘humores’ as the essential parts of a human body. ‘The humours are nothing but the original elements relabeled for use in the medical laboratory’ said ROSS (1987) in his discussion of the ‘Georgica‘ of Vergil. The Hippocratic treatise ‘Over air, waters and places‘ favors a holistic approach to the medical profession: ‘He who studied the medical science has to know all there is about seasons, the winds, the water, the use of the land and the way of living of its inhabitants.’ Climate and the time of the year are of direct influence of the ‘crasis‘, the balance of the opposing elements.
Hippocrates and his followers placed the human humours and qualities in a cosmic context:
This scheme got a further ‘update’ in the second century AD. by the Greek physician Galen (129 – 199). He originated from Pergamum and was educated in Smyrna, Corinth and Alexandria in Egypt. It might be in this last city that he got more acquainted with the four-fold approach, and applied them on the elements in relation with seasons, humours and temperaments. After his return to Pergamum, he practiced as a physician, but due to political troubles he was forced to leave and went in 164 to Rome. He became the personal physician of Emperor Commodus (161 – 192 AD) and was particular involved in the care for the gladiators. He wrote (in Greek) many books of which the majority got lost, but about eighty medical books survived. His ‘Methodi medendi libri XIV’ is concerned with the medical methodology in general. More anatomical and physiological treatises, like ‘De anatomicis administrationibus’, and works on the causes of illnesses, as ‘De causis momborum’ and ‘De morborum differentiis’ are some of the books, which delineates his ideas. This corpus of works, added with many commentaries by others, provided the fertile grounds for the medical practice in the European Middle Ages.
The classical fourfold-scheme (or ‘Viererscheme‘, SCHÖNER, 1964), often attributed to Aristotle, but ‘we may be sure that the qualities of the four elements had been fixed long before Aristotle’ (ROSS, 1987) can be given as follows (modified after JACQUART & THOMASSET, 1985) (fig. 95):
Fig. 95 – The classical four-fold scheme. Many of the numerological expressions of the four-fold find there origin here.
This general scheme has been presented in many different forms. The topological setting and the sequence of the four elements depends on the depth of understanding of the pluriform way of thinking. In many cases, it was only used in a dualistic or numerological way, or – like Paracelsus – fitted into a three-fold representation, in which a corpus consists of three elements (salt, sulphur and mercurius).
LLOYD (1964) pointed, in a clarifying essay on ‘The Hot and the Cold, the Dry and the Wet in Greek Philosophy‘, to the abstract meaning of the pairs of opposites in the original – teleological – meaning of Aristotle. His book ‘Polarity and Analogy‘ (LLOYD, 1966/1992; p. 60) was a further elaboration of this theme. The opposites must be seen in a symbolic association. In Aristotle’s view, expressed in his ‘On Generation and Corruption‘, ‘hot’ means a capacity to combine things of the same kind.
‘Cold’ brings together homogeneous and heterogeneous things alike. ‘Wet’ is readily delimited (i.e. by something else), but is not determined by its own boundary. ‘Dry’ is not readily delimited (i.e. by something else), but is determined by its own boundaries.
Aristotle’s dynamic interpretation (of limitations) and his ingenious explanation for the transformation of elements – matured in ‘On Generation and Corruption‘ – fits into a general appreciation of the tetradic way of thinking. A quadralectic representation could be as follows:
Quadrant I Quadrant II Quadrant III Quadrant IV —————————————————————————————————————————————— hot dry cold wet
fire air earth water
joining same kind not readily delimited joining different readily delimited
Aristotle discussed the principles (or ‘archai’) in a dynamic environment. He thoroughly investigated the relation of Empedocles’ four elements with the four powers (hot, dry, cold, wet) and knew that the discussion of ‘archai’ was of prime importance, because it provides the cornerstone of a cosmological philosophy. The element water was the ‘arche‘ in the philosophy of Thales. Air was crucial in Anaximenes’ thoughts. Fire was the leading principle to Heraclitus (and later the Stoics).
Aristotle was a seeker after truth and not so much concerned with the development of a ‘system’ – like the Stoics, where Zeno aimed to produce a unified system based on Aristotle’s legacy (HAHM, 1977; p. 102). Therefore, Aristotle did not care to stray of the four-fold path in order to reach his aims. In his description of the cosmos (in a book called ‘On the Heavens‘) he introduced a fifth element at the periphery, distinct from the familiar four elements. He did not give this element a name, but indicated that the ancients were calling it ‘aether’.
The element ‘fire’ and ‘the hot’ (situated in a quadralectic ‘First Quadrant’) caused most of the problems in relation to matter (a ‘Third Quadrant’ commodity). In addition, the status of ‘air’, being either warm (in ‘On Generation and Corruption’) or cold (as a refrigerant, in ‘On the Parts of Animals‘) was not consistent in a comparison with the visible matter. Theophrastus of Eresus (372 – 287 BC) – who took over the position of Aristotle in the Peripatetic School – was also unable to solve the position of fire in relation to air, water, and earth (in his treatise ‘On Fire’). The latter elements could change into each other, but fire changes into no other.
‘Aristotle’s influence, which was very great in many different fields, was greatest of all in logic’ according to RUSSELL (1945; p. 195). Even so, his doctrine of the syllogism, which was the outcome of his logic and described in his book ‘The Prior Analytics’, was essentially a step back towards a three-fold system, because this logic instrument is an argument composed of three parts: a major premise, a minor premise and a conclusion.
Aristotle was, in his metaphysics and the treatment of ‘causes’ (the so-called ‘entelecheia‘), as much a four-fold thinker as one can be. An act of creation (or a cause of change) consisted in his view of four phases: final, formal, material and efficient (fig. 96).
Fig. 96 – The four causes (Entelecheia) of change in Aristotle’s metaphysics corresponds with the various types of interaction in a quadralectic communication.
These stages corresponded with the various positions of an observer in a communication:
1. The final cause is the realm of the invisible invisibility or ultimate communication (where boundaries are not yet drawn);
2. The formal cause is on the borderline of visible and invisible communication, where boundaries are proposed, established and/or rejected;
3. The material cause is the area of visible visibility, where boundaries are accepted for the sake of interaction, in short the physical world around us and,
4. The efficient cause is again on the boundaries of visibility, where communication is searching for (lost) frontiers in the multitude.
Aristotle regarded the craftsman as a model of the way nature operated (MANSION, 1913/1946). He used this example in his books ‘Physics II‘ (a discussion of the concept of ‘physis‘), and ‘On the Parts of Animals I’ (an introduction to the study of biology). His teleological view of nature – in which all actions have some purpose – is related to the two-fold way of thinking and can be demonstrated in this model: material and efficient causes are instrumental to formal and final causes.
Epicurus (c. 342 – 270 BC)
The philosopher Epicurus is the fourth and last in the chain of tetradic thinkers in classical Greek history, following Pythagoras, Empedocles and Aristotle. He was born around 342 BC on the isle of Samos. He journeyed to Athens when he was eighteen. Later he started a school in Mitylene (on the isle of Lesbos) and in Lampsacus and resided from 307 in Athens, where he died around 270 BC.
The philosophy of Epicurus was centered on the finding of a happy and useful life. He aimed at a state of ‘ataraxia‘ (freedom from disturbance and negative influences) and the absence of pain: ‘Absence of pain is in itself pleasure, indeed in his ultimate analysis the truest pleasure’ (BAILEY, 1928). This search for happiness was, essentially, the reaction of a pessimistic mind to the uncertainties of life and, in later ages, often misinterpreted as hedonic and egocentrical. The word ‘epicuric‘ is still synonymous with gluttony.
HICKS (1910) described Epicurus as ‘no man was ever more vilely slandered or more cruelly misunderstood’. The ‘pleasure principle’ was, wrongly, placed in a world of opposites, leading to false conclusions. The idea that Epicurus thoughts were the last stage in a tetradic philosophy, was even less understood. Epicurus’ scientific method (ASMIS, 1984) has all the characteristics of a pluriform system. His book ‘Rules‘ was lost, but excerpts from Diogenes Laertius and Sextus Empiricus, enable a reconstruction. Two basic rules were central in the method of inquiry:
1. There are certain ideas (concepts) visible before they are formulated;
2. Empirical observations point to an invisible world.
These rules refer to the position of an observer in a dynamic environment. The first rule pointed to various stages of (visible) invisibility, looking backwards. The Austrian physicist Wolfgang Pauli (1900 – 1958) said the same thing in a different way (quoted by Heisenberg): ‘All understanding is a protracted affair, inaugurated by processes in the unconscious long before the content of consciousness can be rationally formulated’. The second rule noted a world behind the (visible) visibility, aiming at the future.
The ‘Epicurean way of seeing’ is the apotheosis of the Greek tetradic philosophy (fig. 97).
Fig. 97 – A schematic survey of the ‘Epicurean way of seeing‘ or the major constituencies of a tetradic communication. The similarities with Empedocles’ theory of attraction and separation are evident.
The Epicureans – or ‘those from the gardens‘ – renounced worldly ambition and the pursuit of wealth, power and fame, because they surpassed these material obsessions. Instead, there should be the joy of friendship and a dedication to the principle of ‘isonomia‘ or balance. The rules of Epicurus provide the continuity of thoughts in any communication. They read in a quadralectic interpretation:
An observer uses information of a partly known (II) and fully unknown (I) past, to construct an empirical observation (III), which can be transposed to a partly known (IV) and a fully unknown (I) future.
This statement is, in a nutshell, the essence and dynamics of the four-fold way of thinking: an interplay of several positions taken by an observer, based on a distance, which expresses itself in a degree of visibility.
The ideas of Epicurus are summarized into a remedy for a happy life. This recipe is called the ‘tetrapharmacon’ (fig. 98). The principles are described in his ‘Letter to Menoeceus‘ (WALLIS, 1972/1995)(fig. 98):
Fig. 98 – The ‘Tetrapharmacon’ of Epicurus as a recipe for moral health.
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