Wehmeyer’s research focuses on defining self-determination and how it can be studied and promoted for people with developmental handicaps. Building upon Angyal (1941) and Deci et al. (1985), Wehmeyer et al. (2001) construct a model of the components of self-determined behaviour, so that these skills can be trained and taught in schools. They define four essential functions that produce self-determined behaviour.


P – Behavioral Autonomy: Individuated behaviour guided by personal preferences, not requiring much guidance or support from others, free from undue external influence or interference.


A – Self-Regulation: The capacity to manage events by monitoring self and world, making plans and decisions on how to act, evaluating outcomes and revising/improving plans, self-instruction, self-reinforcement and self-governance.


E – Self-Realization: Most generally the “tendency to shape one’s life into a meaningful whole” ((Angyal, 1941), p. 165) self-realization involves using a strong and syncretic (and largely accurate) knowledge of one’s preferences, strengths and limitations to produce better outcomes. This sense of self forms with experience, and is influenced by learning, self-analysis and interactions with others.


I – Psychological Empowerment: Belief in oneself and in the value of one’s goals. “Learned hopefulness.” Derived from community psychology, it arises from experiences of success reaching personal goals and enables people to achieve socially positive outcomes in the community.


Weiner’s work in attribution theory evolved over time. At its root lay a concern structure model. For example, in the domain of academic achievement, he hypothesized that students explained their own academic outcomes in terms of four categories that varied along two dimensions: locus of control (their outcome was due to an internal or external cause), and stability over time (temporary or permanent (Weiner et al., 1971).


In PAEI order, the four categories are:


P – Effort (Internal, Unstable)

A – Task difficulty (External, Stable)

E – Ability (Internal, Stable)

I – Luck (External, Unstable)


P – Effort (Internal, Unstable)

The mindset of someone who thinks that goals may fall out of reach unless aggressively and immediately pursued. “Nothing comes for free in this world. You have to go out there and take it.” Attributing effort to effort is self-serving.


A – Task difficulty (External, Stable)

Consistent with uncertainty about one’s own ability, a focus on the task and the procedure required to complete it is preferred. Proven and successful procedures then become highly prized. Attributing success to task difficulty is self-effacing.


E – Ability (Internal, Stable)

Confidence in one’s own ability makes it possible to approach unknown and unstructured problems without anxiety. Doubts about one’s own ability can motivate a large effort to prove ability, or easy abandonment of the task as too difficult. Attributing success to ability is highly self-serving.


I – Luck (External, Unstable)

Attributing outcomes to luck is self-effacing, and avoids any implication of social comparison. It also represents the surrender of personal control to the shifting context. Accountability, responsibility and both blame and praise are thwarted. This attribution dilutes the social ramifications of success or failure.


Wiener’s Attribution scheme is very similar to Michael Lewis’ typology of self-conscious evaluative emotions.

The Thematic Aptitude Test was developed by Christina Morgan in the 1930's and 40's, together with Harry Morgan, a physician and biochemist whose interest in psychology bloomed after meetings with Freud and especially Jung. Harry Morgan co-founded and later directed the Harvard Psychological Clinic (Teglasi, 2001).


The TAT was a novel psychological projection technique based on the fact that when individuals interpret a social situation, they are saying more about themselves than about what they are observing. In a TAT session, subjects are presented with a series of pictures, each of which depicts a different social situation or event. Their instructions are to interpret the action in each picture and give an imaginary reconstruction of the preceding events and the final outcome. It was thought that the performance of this task would force people to project some of their own fantasies into the material and so reveal their more pressing psychological needs.


The test was quite popular in the postwar period. Clinicians found it useful in eliciting information from patients, but there remained widespread uncertainty about the interpretation and scoring of the stories patients told. In response to this uncertainty, Magda Arnold, then Director of Research and Training, Psychological Services with the Canadian Department of Veterans' Affairs, developed a technique of abstracting the universal situational-behavioural ‘maxim’ or ‘moral’ embedded in each story a client might create. This abstraction of story maxims or imports proceeded according to definite rules, and the sequence of imports was thought to reveal "the development of the storyteller's thought from story to story" in a way that revealed important facts about motivations, values and attitudes (Arnold, 1962). Arnold later accepted a chair at Loyola University, where this TAT story analysis technique was refined and further codified as a psychological assessment instrument.


Interestingly, after seven years of empirical studies, with the elicitation and coding of a vast number of stories, Arnold discovered that all TAT story imports could be roughly divided into four categories, listed below in PAEI order:


P - Reactions to adversity

A - Issues of right and wrong

E - Achievement, success, happiness, active effort (or the lack of it)

I - Human relationships


Each of these clusters was further subdivided into themes and facets of themes, but the highest level of analysis specified these four categories.


P - Reaction to adversity - includes response to any kind of adverse situation except personal failure, which is an E-category.


A - Right and wrong - stories of human action where success and failure is not the theme, but rather the ethical significance of an action or its personal consequences.


E - Achievement, success, happiness, active effort (or lack of it) - includes success or failure in its widest sense, not only success in tasks, but happy outcomes of any kind. Similarly, category one includes failures of every kind; unhappiness, disappointment and every kind of unfavourable outcome. (Mood-relevant: expectation of mood outcome - inherently future oriented. Anticipated mood=anticipated situation for emotional release.)


I - Human relationships - influence of other characters on story hero, or influence of hero on them, independent of concerns from the other categories.


Cloninger is a major personality theorist, who during the mid-1980’s produced a model of personality dimensions with three core personality characteristics which he argued were heritable and biologically based (Cloninger 1986a; 1986b). He later added a fourth element to this set. (Cloninger, 1994; Stallings et al., 1996). The fourth element had been a facet of one of the previous three factors that did not prove to be correlated to the other facets of that factor. This four-factor model gave a satisfactory account of the heritable cognitive, perceptual and affective differences underlying temperamental differences.


However, Cloninger felt that this four-factor model ignored the developmental aspect of personality. It obscured the differences between two people of similar temperaments, one of whom was self-actualized and one of whom was not. This reduced its clinical value. He thus later combined his four factors with three additional factors based partly on concepts of self-actualization from humanistic psychology (Cloninger, 1994; Cloninger et al., 1993). These three new factors measured “character” rather than temperament. I leave them aside to focus on Cloninger’s four temperamental dimensions, listed below:


P – Persistence (or Happiness Seeking): Determination and tenacity to achieve a goal, industrious, stable and resolute in the face of frustration or fatigue. Low persistence leads to underachievement.


A – Harm Avoidance: Intense response to signs of impending aversive stimuli, resulting in learned tactics for minimize behaviors that may expose them to punishment, loss or novelty. Cautious, tense, inhibited, easily fatigued, shy and apprehensive. Low harm avoidance implies people who are optimistic, open to experience, outgoing, trusting and energetic. Associated with the 5-HT system.


E – Novelty Seeking: Excited and exhilarated responses to stimuli that are novel or that signal potential reward or escape from punishment. Frequent exploration to obtain rewards and avoid structure and monotony. Bases decisions on vague impressions. Low novelty-seeking implies preference for routine, order, details, frugality and social stability. This behavioral trait is related to the DA system.


I - Reward Dependence (or Security-Seeking): Responds to stimuli that suggest a reward is forthcoming, particularly verbal indications of social succour, approval or sympathy. More able to maintain behaviors that have been socially acknowledged and reinforced in the past. Low reward dependence implies introversion, self-reliance and self-directedness. Associated with the noradrenergic system.


Kiesler’s interpersonal circumplex model has roots in Timothy Leary’s work, introducing developmental consideration in the development of interpersonal style, interactive role identities and other aspects of self-definitions (Kiesler, 1983). Early in life, we situate ourselves on an interpersonal field bounded by an affliative dimension (love-hate, friendliness-hostility) and a control dimension (dominance-submission, high status-low status). Our interactions with others continually broadcast our claims of how close or intimate we wish to be with others, and how much dominance and control we are willing to assert. By pushing this self-presentation towards others over repeated interactions, we pull reinforcing and validating responses from interactants. This constant push-pull interplay is described be Kiesler as an interpersonal force field.


Like Leary’s model, sixteen ‘interpersonal claims’ are defined, within the two dimensions of affiliation and control. Each claim has a normal and a pathological expression. They are listed below by dimensional quadrant in PAEI order:

Alan Miller has undertaken a systematic and comprehensive review of personality typologies and cognitive style typologies, developing a synthetic typology to capture the essence of most of them while avoiding the failings of some (Miller, 1991). He selects three dimensions for the analysis of these frameworks: cognitive, affective and conative (motivational).


The cognitive dimension is structured between an analytic pole and a holistic one. The analytic style clusters together perceptual analysis, field independence, verbal and analytic representation, conceptual differentiation, convergent memory retrieval, serial mental classification, tight associations and an actuarial judgment style. Holistic processes are more synthetic, field-dependent, visually structured, with divergent memory access, loose associations and an intuitive judgment style.


Along the conative/motivational dimension, Miller reviews various models of motivation and goal-directedness, including drive theories, volitional theories and intrapsychic conflict theories in the tradition of Angyal and Bakan. Favouring the latter, he reviews Maddi’s ‘autonomy/agency – surrender/communion’ conflict paradigm (Maddi, 1999) among others, and suggests an objectivity-subjectivity distinction to summarize them all. Objective intentions are instrumental, externally grounded and geared towards seeking advantage or power. Subjective purposes are more affiliative, internally grounded and empathic.


Miller’s affective dimension covers psychological research into Negative Emotionality, Positive Emotionality and Affect Intensity. He isolates the distinction between emotional stability and instability as the most relevant for personality typing, and he places this dimension orthogonal to the other two. This creates a structure of concern model that recognizes varying degrees of emotional stability in each quadrant. I set aside this dimension, since it does not change the structure that concerns me.


An interesting aspect of Miller’s work is that his original research goal was to understand professional behaviours and interactions among scientists and academics. Thus his typology, while serving to describe general personality dynamics, is labelled with terms that describe academic theoretical preferences or investigative biases. Crossing his cognitive (analytic-holistic) and conative/motivational (objective-subjective) dimensions thus gives us the following four type descriptions in PAEI order:


P – Reductionist (Objective, Analytic): Focused on agency, achievement and control over self, others and environment. Emotionally detached and externally focused with a mechanistic worldview. Intellectualizes and rationalizes problems, seeking detailed factual knowledge.


A – Schematist (Objective, Holistic): Objective and impersonal, achieves an illusion of control by developing schemes, theories and systems of thought. When these are threatened, global defences such as denial or repression are used to suppress awareness of the discrepancies. Emotionally detached and externally oriented, judgmental.


E – Gnostic (Subjective, Analytic): Seeks communion with the world through understanding and knowledge. Rejects objective, impersonal outlook in favour of cognitive empathy and introspection. Can become lost within a reflective, narrowly preoccupied world, but has few defences against intrusions by objective obstacles. Absent-minded prisoner of psychological honesty.


I – Romantic (Subjective, Holistic): Seeks communion through intimate, nurturing relationships. Aims to empower others and improve their surroundings. Empathic and grounded in the inner experiences of self and others, but not probingly introspective or self-analysing. Impressionistic, subjective, evaluative and imaginative, touched by personal anecdote and raw accounts of experiences.


On Nash’s account, personality “evolved specifically to make human culture possible by managing the flow of information within the culture, especially by mediating teaching and learning, competition and cooperation, and leading and following.” (Nash, 1998) All of these transactions are predicated upon a basic function of information gating that directs attention and determines openness for the bidirectional flow of information and interaction between internal self and external social systems, as the situation demands. In this model, personality disorders are maladaptive gating rhythms that chronically admit and release too much or too little social information and interaction.


Crossing the dimensions of relative openness to incoming information and relative openness for outgoing information gives us the follow expression of the structure of concern.


P – Influence (Closed to incoming, Open for outgoing): Leading, teaching, selling

A – Isolation (Closed to incoming, Closed for outgoing): Waiting, exercising, meditating

E – Incorporation (Open to incoming, Closed for outgoing): Following, learning, empathizing

I – Intimacy (Open to incoming, Open for outgoing): Love relationships, friendships, psychotherapy


It may be worth mentioning that Nash is a US Navy psychiatrist, in a stronger command-and-control culture than civilian or free-enterprise contexts. His PAEI roles thus take their shape in a P-dominant environment. In entrepreneurial business contexts, E is more typically associated with leadership, and P with followership.


All four gating styles are functional in the right situations, and dysfunctional outside of them. Nash speculates that the movement of self information out into the cultural environment, along with the movement of cultural information into the self, “has the effect of bringing the inner and outer worlds into closer approximation.” The goal of personality may thus be a sort of equilibrium, deploying information gating as a way of monitoring the gap between inner and outer worlds. Motivation to establish a new inner-outer equilibrium by enabling information and interaction to flow between them would be proportional to the severity of mismatch detected.


Nash lines up information gating with DSM-IV personality disorder clusters as follows: P – Antisocial, A – Schizoid, E – Dependent, I – Borderline. In many civilian-based accounts the E and I roles would be reversed. However on the timescale of military functions, E would constantly need to be told what to do (dependent), and the I profile of preferred interaction values would be continuously disrupted (distressed).


The XFL was a professional American football league which played one season in 2001. It was operated as a joint venture between the World Wrestling Federation (WWF, now known as WWE) and NBC. The XFL was conceived as an outdoor football league that would take place during the NFL off-season, and promoted as having fewer rules and encouraging rougher play than other major leagues. The league had eight teams in two divisions, including major markets and those not directly served by the NFL, including Birmingham, Las Vegas, Memphis, and Orlando. The XFL operated as a single entity, with all teams centrally owned by the league.


AFL Team Owners held a meeting nine days later and adopted the third place winning team name, the Oakland Raiders. The initial color scheme for the Oakland Raiders was black and gold. That’s correct Raider Nation, Pittsburgh Steelers colors. The first team logo was a pirate face with a black helmet atop a yellow football and two crossing swords.


Thankfully, in 1964 the team colors were changed by General Manager/Head Coach Al Davis to the beloved silver and black. Davis also changed the team logo. The face is the likeness of Actor Randolph Scott, with a patch over his right eye. Davis changed the color of the helmet from black to silver, and this sat atop two crossed swords. The shield background changed from silver to black, and just the team name “Raiders” was added above the head. With only slight modifications, this has stood as the Raiders logo and team colors for nearly 50 years.


Stephen Pepper identified four basic worldviews - formism, mechanism, contextualism and organicism, each with its own distinctive 'root metaphor' - respectively, similarity, simple machine, historic event and organism (Pepper 1942, 84ff). Meyer Abrams has identified Pepper's scheme as an application of synecdoche, since each worldview presents the whole of reality in terms of one of its parts (Abrams 1971, 31).


Giambattista Vico (1668-1744) is usually credited with being the first to identify metaphor, metonymy, synecdoche and irony as the four basic tropes (to which all others are reducible), although this distinction can be seen as having its roots in the Rhetorica of Peter Ramus (1515-1572) (Vico 1968, 129-131). This reduction was popularized in the twentieth century by the American rhetorician Kenneth Burke (1897-1993), who referred to the four 'master tropes' (Burke 1969, 503-17). Each of these four tropes represents a different relationship between the signifier and the signified; Hayden White suggests that these relationships consist of: resemblance (metaphor), adjacency (metonymy), essentiality (synecdoche) and 'doubling' (irony) (White 1979, 97). These tropes seem to be so ubiquitous that Jonathan Culler (following Hans Kellner) suggests that they may constitute 'a system, indeed the system, by which the mind comes to grasp the world conceptually in language' (Culler 1981, 65). Fredric Jameson's use of the semiotic square provides a useful mapping of these tropes (Jameson in Greimas 1987, xix). Note that such frameworks depend on a distinction being made between metonymy and synecdoche, but that such terms are often either defined variously or not defined at all. In his book Metahistory, White saw the four 'master tropes' as part of the 'deep structure' underlying different historiographical styles (White 1973, ix). In what is, of course, a rhetorical act of analogy itself, White also linked metaphor, metonymy, synecdoche and irony with four literary genres, Pepper's worldviews and four basic ideologies. In Lévi-Straussian rhetoric, he saw these various systems of classification as 'structurally homologous with one another' (White 1978, 70).

Hayden White has suggested a tropological sequence in Western discourse (originally based on historical writing), whereby the dominant trope changed from one period to the next - from metaphor to metonymy to synecdoche to irony (White 1973). He interprets Vico as the originator of this particular sequence, although Vico's hypothetical historical sequence for the development of the four key tropes seems to be open to the interpretation that it was from metonymy to synecdoche to metaphor to irony (White 1978, 5ff, 197ff; Vico 1968, 129-31). White suggests an ontogenetic parallel to his proposed sequence of tropes in Piaget's four stages of cognitive development. However, he denies any implication that earlier modes within such developmental schemes are in any way 'inferior' (White 1978, 9). This speculative analogy should not to be taken as suggesting that children's acquisition of these tropes is related to the age-ranges which are included here.

Michel Foucault undertook an 'archeological' study of three loosely defined historical periods: the 'Renaissance' period, the 'Classical' period and the 'Modern' period. He argued that each period had an underlying epistemology. White suggests that each of these periods, together with the Postmodern period in which Foucault wrote, reflects one of the four master tropes in White's suggested sequence (White 1978, 230-60). Elsewhere he argues that in Foucault, 'every "discursive formation" undergoes a finite number of... shifts before reaching the limits of the épistème that sanctions its operations. This number corresponds to the fundamental modes of figuration identified by the theory of tropology: metaphor, metonymy, synecdoche and irony (which is here understood as self-conscious catechresis)' (White 1979, 95). Cathachresis is variously defined, but it is based on the notion of an abusive comparison.


Foucault himself speculated about a sequence of tropes, although this is not the same sequence as that proposed by White. He related this to the development of writing and language in a three-part sequence from synecdoche to metonymy to catachresis or metaphor. This is reminiscent of the speculations of Peirce about the evolution of language from the indexical and iconic towards the symbolic (Peirce 1931-58, 2.299, 2.92, 2.90, 2.280, 2.302).


True writing began when the attempt was made to represent, no longer the thing itself, but one of its constituent elements, or one of the circumstances that habitually attend it, or again some other thing that it resembles... These three methods produced three techniques: the curiological writing of the Egyptians... which employs 'the principal circumstance of a subject in lieu of the whole' (a bow for a battle, a ladder for a siege); then the 'tropal' hieroglyphics... which employ some notable circumstance (since God is all-powerful he knows everything and sees all that men do: he is therefore represented by an eye); finally symbolic writing, which makes use of more or less concealed resemblances (the rising sun is expressed by the head of a crocodile whose round eyes are just level with the surface of the water). We can recognize here the three great figures of rhetoric: synecdoche, metonymy, catachresis. And it is by following the nervature laid down by these figures that those languages paralleled with a symbolic form of writing will be able to evolve...

In any representation, the mind can attach itself, and attach a verbal sign, to one element of that representation, to a circumstance attending it, to some other, absent, thing that is similar to it and is recalled to memory on account of it. There is no doubt that this is how language developed and gradually drifted away from primary designations. Originally everything had a name - a proper or peculiar name. Then the name became attached to a single element of the thing, and became applicable to all the other individual things that also contained that element: it is no longer a particular oak that is called tree, but anything that includes at least a trunk and branches. The name also became attached to a conspicuous circumstance: night came to designate, not the end of this particular day, but the period of darkness separating all sunsets from all dawns. Finally, it attached itself to analogies: everything was called a leaf that was as thin and flexible as the leaf of a tree. The progressive analysis and more advanced articulation of language, which enable us to give a single name to several things, were developed along the lines of these three fundamental figures so well known to rhetoric: synecdoche, metonymy, and catachresis (or metaphor, if the analogy is less immediately perceptible)... At the base of spoken language, as with writing, what we discover is the rhetorical dimension of words: that freedom of the sign to align, according to the analysis of representation, upon some internal element, upon some adjacent point, upon some analogous figure. (Foucault 1970, 110-11; 113-4)


Hayden White's four-part tropological system is widely cited and applied beyond the historiographical context in which he originally used it, and the application of such frameworks can often be enlightening. However, some caution is necessary in their use. Catachresis may be involved in applying any tropological framework. White himself notes that the 'affinities' suggested by his alignment of tropes with genres, worldviews and ideologies 'are not to be taken as necessary combinations of the modes in a given historian. On the contrary, the dialectical tension which characterizes the work of every master historian usually arises from an effort to wed a mode of emplotment with a mode of argument or of ideological implication which is inconsonant with it' (White 1973, 29). There is a danger of over-systematization when three- or four-fold distinctions are multiplied and correlated by analogy. Taken to relativistic extremes, everything can be taken as resembling everything else. Phenomena are seldom as tidy as our systems of classification. Systems always leak (and it's no good replacing the plumbing with poetry). Even Francis Bacon, who sought scientific dominion over nature, observed that 'the subtlety of nature is greater many times over than the subtlety of argument' (Bacon 1620, 261-2). It is for the individual reader to assess how interpretatively useful the application of such schemes may be on any particular occasion of use - and what the limitations of such analogies may be. Since they can be extraordinarily compelling, we need to ensure that they do not become 'more real' than what they purport to describe.


White argued that 'the fourfold analysis of figurative language has the added advantage of resisting the fall into an essentially dualistic conception of styles'. Roman Jakobson adopted two tropes rather than four as fundamental - metaphor and metonymy. White felt that Jakobson's approach produced a reductive dichotomy dividing nineteenth century literature into 'a romantic-poetic-Metaphorical tradition' and 'a realistic-prosaic-Metonymical tradition' (White 1973, 33n). However, Jakobson's notion of two basic poles has proved massively influential. He found evidence in the pathology of speech for metaphor and metonymy being basic in language and thinking. In a paper entitled 'Two Aspects of Language and Two Types of Aphasic Disturbances', he drew on existing data on two types of aphasia, interpreting these as 'similarity disorder' and 'contiguity disorder' (Jakobson & Halle 1956, 67-96). Aphasics with similarity disorder had difficulty selecting the word they want and fell back on contiguity and contexture, making metonymic (or synecdochic) mistakes - such as saying 'pencil-sharpener' when they meant 'knife', or 'knife' when they meant 'fork' (Jakobson & Halle 1956, 79, 83). Aphasics with contiguity disorder had difficulty combining words correctly and used quasi-metaphorical expressions - such as calling a microscope a 'spy-glass' (ibid., 86).


Jakobson argued that metaphor and metonymy, or selection and combination, are the two basic axes of language and communication. Metaphor is a paradigmatic dimension (vertical, based on selection, substitution and similarity) and metonymy a syntagmatic dimension (horizontal, based on combination, contexture and contiguity) (Jakobson & Halle 1956, 90-96). Many theorists have adopted and adapted Jakobson's framework, such as Lévi-Strauss (Lévi-Strauss 1974). Jakobson related the tropes to Freud's dreamwork processes, regarding Freud's 'condensation' as synecdochic and his 'displacement' as metonymic (Jakobson & Halle 1956, 95). Jacques Lacan linked metaphor with condensation and metonymy with displacement (Lacan 1977, 160). Hayden White made the same links as Lacan whilst suggesting that synecdoche was linked to representation and irony to secondary revision (White 1978, 13-14). The film theorist Christian Metz posited discursive and referential axes, both involving relationships of similarity and contiguity. Whilst the discursive function acts at the level of the signifier in the form of paradigms and syntagms, the referential function operates at the level of the signified in the form of metaphor and metonymy (Metz 1982; Silverman 1983, 288).


In a more lighthearted vein, there is an amusing discussion of metaphor and metonymy in David Lodge's novel, Nice Work (Lodge 1988).

The four stages theory[edit]

The term "conjectural history" was not generally accepted in Stewart's time.[26] There was an orthodox four stages theoryof society, the stages being:

  1. hunting;

  2. pasturage;

  3. agriculture; and

  4. commerce.

This ladder-like ordering was taken to be a strict, linear progression, or unilineal evolution. Some economic determinismapplied, in the sense that the baseline of subsistence was assumed to have a serious effect on social matters. The stages were supposed to represent progress on a moral level, as well as that of economic complexity. French as well as Scottish Enlightenment writers subscribed to such a pattern.[27]

The invention of this type of theory (three or four stages) is attributed to a number of European writers from the 1750s onwards, such as Adam Smith, Turgot and Vico.[28] In the Scottish context it appears in works from 1758 by David Dalrymple and Lord Kames; it has been argued that their source was the Edinburgh lectures of Smith on jurisprudence.[29]In France it was published at much the same time, also, by Claude Pierre GoujetClaude Adrien Helvétius, and François Quesnay.[16] Smith's "natural progress of opulence" is a closely related theory.[30]

Representative works[edit]

Besides Adam Smith, prominent Scottish authors in the field of conjectural history included Adam Ferguson, David Hume, Lord Kames, John Millar, and Lord Monboddo, writing from the later 1750s to later 1770s.[31] Smith, Kames and Millar were content to adhere to the four stage theory.[32] Monboddo's stadial history was more complex, and very much more controversial. He included primates and feral children as material.[33] Robertson in his History of America moves between narrative and conjectural history.[34]

John Millar, Observations concerning the Distinction of Ranks in Society (1771)[edit]

Millar argued in terms of a "system of manners" associated with each of the four stages.[37] He also discussed the advance of freedom, and denounced slavery.[38] As property became more complex, it followed that government did so also.[39]Poovey states that this work makes apparent the relationship of conjectural history with the experimental moral philosophyof Thomas Reid and George Turnbull.[40]


There are few paradigms more tightly connected with the Scottish Enlightenment than the four stages theory. Yet it arguably remains one of the least understood.


John Millar

James Tassie, Medallion of John Millar (1767). Courtesy of the University of Glasgow Archive Services, University collection, GB 248 UP3/26/1.


In the second half of the eighteenth century, a whole host of famous Scottish thinkers – Adam Smith, Adam Ferguson, William Robertson, Henry Home (Lord Kames) and John Millar – attempted to explain a range of social phenomena according to a single, universal narrative of the history of progress. The spirit of the paradigm was that the fundamental distinguishing components of societies lay not in accidents of climate, religion or race, but rather in the social, psychological, legal and cultural effects of the history of property and sustenance relations. While French thinkers such as Anne Robert Jacques Turgot used three stages to achieve similar analyses, the Scots preferred four:


Hunting, where property only extended to what one could carry on one person (savagery),

Pastoralism, where shepherding witnessed the development of animal property (barbarism),

Agriculture, where society became settled and landed property became pivotal in the production of sustenance (civilisation),

Commercial society, defined by contemporary Europe.

The paradigm has, for good reason, been widely identified as a pioneering step in the development of various disciplines of the modern social sciences. At the same time, in taking the commercial society of eighteenth-century Britain as the pinnacle of the history of liberty, postcolonial scholars have, with validity, critiqued it as a blatant example of Eurocentric world historical narration.


John Millar, the protégé of Adam Smith and Regius professor of civil law at the University of Glasgow for nearly four decades at the end of the eighteenth century, is often cited as the most systematic articulator of the four stages theory. Attention has been paid particularly to his reflections on the history of family and gender, which constitute the great bulk of his stadial theory-infused magnus opus, the Origin of the Distinction of Ranks.




I began research for my book John Millar and the Scottish Enlightenment: family life and world history with the intention of revealing how Millar managed his oft-celebrated cohesion. In fact, I was quickly confronted with lacunae, gaps and contradictions with Millar’s stadial analysis. Digging deeper, I realised that these arose from his difficulties in overcoming a complex intellectual web of competing analytical frameworks using evidence and existing scholarship that defied any easy organisation. Moreover, it became clear that his intention was much less to innovate any coherent science of stage-based analysis than to set out his convictions about politics, the family and the nature of authority.


Too often, Millar’s lack of full coherence in his use of stadial analysis has been attributed to intellectual underperformance. In my book, I take a different approach, viewing Millar as a guide to the history of knowledge underpinning the pursuit of stadial history, with a particular focus on gender and the family. Millar used the stadial model as only one of several intersecting paradigms. His deployment and innovation of classic natural law structures, such as the history of household authority relations and the tripartite division of marriage struggle, reveals the importance of his professional setting as a professor of law in Glasgow. Additionally, in his retention of religion as a critical means for explaining differences in marriage practices, we see that even Millar had doubts about stadial analysis as a fully convincing alternative to paradigms such as sacred history.


In Historical Law Tracts and later in Sketches on the History of Man he described human history as having four distinct stages. The first was as a hunter-gatherer where people avoided each other out of competition. The second stage he described was a herder of domestic animals which required forming larger societies. No laws were needed at these stages except those given by the head of the family or society. Agriculture was the third stage requiring greater cooperation and new relationships to allow for trade or employment (or slavery). He argued that 'the intimate union among a multitude of individuals, occasioned by agriculture' required a new set of rights and obligations in society. This requires laws and law enforcers. A fourth stage moves from villages and farms to seaports and market towns requiring yet more laws and complexity but also much to benefit from. Kames could see these stages within Scotland itself,[2] with the pastoral/agricultural highlands, the agricultural/industrial lowlands and the growing commercial ("polite") towns of Glasgow and Edinburgh.



Hjelmslev's sign model is a development of Saussure's bilateral sign model.[5] Saussure considered a sign as having two sides, signifier and signified. Hjelmslev's famously renamed signifier and signified as respectively expression plane and content plane, and also distinguished between form and substance.[5][6][7][8] The combinations of the four would distinguish between form of content, form of expression, substance of content, and substance of expression.[5] In Hjelmslev's analysis, a sign is a function between two forms, the content form and the expression form, and this is the starting point of linguistic analysis. However, every sign function is also manifested by two substances: the content substance and the expression substance. The content substance is the psychical and conceptual manifestation of the sign. The expression substance is the physical substance wherein a sign is manifested. This substance can be sound, as is the case for most known languages, but it can be any material support whatsoever, for instance, hand movements, as is the case for sign languages, or distinctive marks on a suitable medium as in the many different writing systems of the world.


The Grand Slam tournaments, also called majors, are the four most important annual tennis events. They offer the most ranking points,[1] prize money, public and media attention, the greatest strength and size of field, and greater number of "best of" sets for men. The Grand Slam itinerary consists of the Australian Open in mid January, the French Open in May and June, Wimbledon in July, and the US Open in August and September. Each tournament is played over a period of two weeks. The Australian and United States tournaments are played on hard courts,[a] the French on clay, and Wimbledon on grass. Wimbledon is the oldest, founded in 1877, followed by the US in 1881, the French in 1891, and the Australian in 1905. However, of these four, only Wimbledon was a major before 1924–25, when all four became designated Grand Slam tournaments. Skipping Grand Slam tournaments—especially the Australian Open because of the remoteness, the inconvenient dates (around Christmas and New Year's Day) and the low prize money—was not unusual before 1982, which was the start of the norm of counting Grand Slam titles.


In 1981, the tiered system of competition in use today was created, in which the 16 best national teams compete in the World Group and all other national teams compete in one of four groups in one of three regional zones. In 1989, the tiebreak was introduced into Davis Cup competition, and from 2016 it is used in all five sets.[5]


The 16 best national teams are assigned to the World Group and compete annually for the Davis Cup. Nations which are not in the World Group compete in one of three regional zones (Americas, Asia/Oceania, and Europe/Africa). The competition is spread over four weekends during the year. Each elimination round between competing nations is held in one of the countries, and is played as the best of five matches (4 singles, 1 doubles). The ITF determines the host countries for all possible matchups before each year's tournament.


The World Group is the top group and includes the world's best 16 national teams. Teams in the World Group play a four-round elimination tournament. Teams are seeded based on a ranking system released by the ITF, taking into account previous years' results. The defending champion and runner-up are always the top two seeds in the tournament. The losers of the first-round matches are sent to the World Group playoff round, where they play along with winners from Group I of the regional zones. The playoff round winners play in the World Group for the next year's tournament, while the losers play in Group I of their respective regional zone.


Each of the three regional zones is divided into four groups. Groups I and II play elimination rounds, with the losing teams facing relegation to the next-lower group. The teams in Groups III and those in Group IV play a round-robin tournament with promotion and relegation.

I'm a paragraph. Click here to add your own text and edit me. It's easy.


While many nations enter the Fed Cup each year, only 16 countries qualify for the elite World Group and World Group II each year (eight in World Group and eight in World Group II).[4]


They reach World Group and World Group II as follows:


(a) World Group - the four nations that win their World Group first round tie remain in the World Group for the following year. First round losers contest the World Group Play-offs against the four winning nations from World Group II to determine relegation/promotion for the following year's competition. (The four nations that win World Group Play-offs will be in the World Group the following year, while the four losers will start the following year in World Group II.)

(b) World Group II - the four nations that win their World Group II ties will compete in the World Group I Play-Offs to determine relegation/promotion for the following year, as described above. Similarly the four nations that lose their World Group II ties will face winning nations from Group I Zonal competitions, in the World Group II Play-offs, to determine relegation/promotion. (The four nations that win their World Group II Play-offs will be in World Group II the following year, while the four losers will begin the next year in Group I Zonal events.)

Once in the World Group or World Group II, four nations will be seeded in each. The decision as to which nations will be seeded is made by the Fed Cup Committee, according to the ITF Fed Cup Nations Ranking.


At the levels below the World Group and World Group II, the Fed Cup nations compete in Zonal Competition events, which are split into three zones: The Americas Zone, the Asia/Oceania Zone and the Europe/Africa Zone. In each zone there are two groups, Group I being the higher and Group II the lower, except for the Europe/Africa Zone, which also has a Group III.


Within the Group zonal regions, teams are split into pools and play against each other in a round robin format. The exact format of each Group event, and promotion and relegation between them, varies according to the number of participating teams. Two teams are always promoted from Europe/Africa Group I to that year's World Group II Play-Offs, while one team each go to the World Group II Play-Offs from Americas Group I and Asia/Oceania Zone Group I.


Four New Years[edit]

The Torah itself does not use any term like "new year" in reference to Rosh Hashanah. The Mishnah in Rosh Hashanah[23] specifies four different "New Year's Days" for different purposes:


1 Tishrei (conventional "Rosh Hashanah"): "new year" for calculating calendar years, sabbatical-year (shmita) and jubilee cycles, and the age of trees for purposes of Jewish law; and for separating grain tithes.

15 Shevat (Tu Bishvat): "new year" for trees–i.e., their current agricultural cycle and related tithes.

1 Nisan: "new year" for counting months and major festivals and for calculating the years of the reign of a Jewish king

In biblical times, the day following 29 Adar, Year 1 of the reign of ___, would be followed by 1 Nisan, Year 2 of the reign of ___.

In modern times, although the Jewish calendar year number changes on Rosh Hashanah, the months are still numbered from Nisan.

The three pilgrimage festivals are always reckoned as coming in the order Passover-Shavuot-Sukkot. This can have religious law consequences even in modern times.

1 Elul (Rosh Hashanah LaBehema): "new year" for animal tithes.


There are four major extant shrines of the Sixty-four Yogini (Chausathi jogan), among other spellings) in India (named for 64 legendary yogini), two in Odisha and two in Madhya Pradesh.

The Kumaras are four sages (rishis) who roam the universe as children from the Puranic texts of Hinduism,[1][2] generally named Sanaka, Sanatana, Sanandana and Sanatkumara. They are described as the first mind-born creations and sons of the creator-god Brahma. Born from Brahma's mind, the four Kumaras undertook lifelong vows of celibacy (brahmacharya) against the wishes of their father. They are said to wander throughout the materialistic and spiritualistic universe without any desire but with purpose to teach.[1] All four brothers studied Vedas from their childhood, and always travelled together.[3]


The four sages Sanak,Sanandan,Sanatan,Sanat were learned Brahmins. They were the sons of Lord Brahma. They were very proud of their father, Brahma because he was the creator of the holy books, Vedas. They were aware of three Vedas,- Rigved, Yajurved, and Samveda and considered that the whole knowledge is complete in these three books.On the other hand, Sage Atharva approached Lord Shiva to get approval of his knowledge which he gathered from the universe using his divine powers. Lord Shiva, impressed by his creation and blessed Sage Atharva that his book of knowledge would constitute the list of Vedas and will be called as ‘Atharvaveda’. When this news reached the sons of Lord Brahma, they protested as according to them the other three Vedas was a complete set of knowledge and there was no need of fourth Veda. They argued with Lord Shiva and challenged his authority to certify a fourth Veda. Finally, in all humbled fairness and peaceful reverence for not blemishing the value of the wealth of knowledge, the decision whether to certify a fourth Veda or not, was mutually agreed to be purely depend upon the results of a Knowledge-debate (Jyan-Vivad) amongst them (i.e. 4 Kumaras' & Lord Shiva). Goddess Saraswati was appointed as judge. The four Sages fired too much and too complicated questions to Lord Shiva and they were very confident of their victory as they underestimated Lord Shiva. But Shiva, who is the Lord of all the Supreme Knowledge, answered each and every question. The Sages accept their defeat gracefully and ask for forgiveness. Since then Artharva Veda was added to the list of Vedas, making the total four. The Sages went to their brother Prajapati Daksha who was bitter rival of Lord Shiva. On listening about the defeat of his four brothers, he cursed them to be small children. After that the four sages turned into small children. Since the sages were very learned, they thanked their brother for the curse because after becoming children their urge for learning would be greater.


Vaishnavism (the sect that worships Vishnu as the Supreme) is divided into four sampradayas or traditions. Each of them traces its lineage to a heavenly being. The Nimbarka Sampradaya, also known as the Kumara Sampradaya, Catuḥ Sana Sampradaya and Sanakadi Sampradaya, and its philosophy Dvaitadvaita ("duality in unity") is believed to be propagated in humanity by the four Kumaras. The swan avatar of Vishnu Hamsa was the origin of this philosophy and taught it to the four Kumaras, who in turn taught Narada, who finally passed it to the earthy Nimbarka, the main exponent of the sampradaya.[20]


The origin of Sama is credited to Rumi, Sufi master and in whose name the Mevlevi Order was founded.

The Sama was practised in the samahane (ritual hall) according to a precisely prescribed symbolic ritual with the dervishes whirling in a circle around their sheikh, who is the only one whirling around his axis. The Sama is performed by spinning on the Left foot.[5] The dervishes wear a white gown (tennure) (symbol of death), a wide black cloak (hırka) (symbol of the grave) and a tall brown hat (kûlah or sikke), symbol of the tombstone.


Sama ceremonies are broken up into four parts which all have their own meanings.


Naat and Taksim – Naat is the beginning of the ceremony where a solo singer offers praise for the Islamic prophet Muhammad. The first part is finished with taksim (improvisation in free rhythm) of the ney reed flute which symbolises our separation from God.


Devr-i Veled – During the following Devr-i Veled, the dervishes bow to each other and make a stately procession in single file around the hall. The bow is said to represent the acknowledgement of the Divine breath which has been breathed into all of us. After all the dervishes have done this they kneel and remove their black cloaks.


The Four Salams – The Four Salams are the central part of Sama. The samazens or whirling dervishes are representative of the moon and they spin on the outside (sufi whirling) of the Sheikh who is representative of the sun. They, as previously mentioned, spin on their left foot and additionally, they have their right palm facing upwards towards Heaven and their left hand pointing at the ground. The four salams themselves are representative of the spiritual journey that every believer goes through. The first one is representative of recognition of God, the second one is recognition of the existence in his unity, the third one represents the ecstasy one experiences with total surrender and the fourth one, where the Sheikh joins in the dance, is symbolic of peace of the heart due to Divine unity. After the four salams, this part of the ceremony is concluded with another solo Taksim.


Concluding Prayer – The fourth part of the ceremony is a recitation from the Qu'ran and a prayer by the Sheikh and then the Sama is complete.[6][7]



Hunnenschlacht (The Battle of the Huns), S.105, is a symphonic poem by Franz Liszt, written in 1857 after a painting of the same name by Wilhelm von Kaulbach. Liszt conducted the premiere himself in Weimar on 29 December 1857.[1]

The second section, Più mosso, begins with a "Schlachtruf" (battle cry) in the horns, which is then taken up by the strings. The main battle theme is then stated, a fully formed version of material from the very opening. This entire section makes use of the so-called gypsy scale, which Liszt frequently used in his Hungarian-themed compositions. In this section Liszt introduces an unusual effect: against the current of the raucous battle music in the rest of the orchestra, the trombones play the ancient plainchant melody "Crux fidelis". Liszt's own description of this section was of "two opposing streams of light in which the Huns and the Cross are moving." [3]

The "Crux fidelis" theme is later taken up by the strings in a quiet, peaceful contrasting section. The music grows in intensity, eventually including an organ and offstage brass section, and it ends triumphantly.

Die Hunnenschlacht, as painted by Wilhelm von Kaulbach- CROSS TOP LE


In the preface to Legende von der Heiligen Elisabeth (Legend of St. Elizabeth), Liszt identifies a "cross motive" that may have motivated him to change the key in movement four (which had been movement three), "Hirtengesang an der Krippe." Otherwise it is difficult to understand why he would make such a decision.


The original key scheme would have been:


G major–G major–G major–C minor/major


After the transposition and rearrangement of movements three and four, it becomes:


G major–G major–A major–C minor/major


It is impossible to know if LIszt made those transpositions to conform to the cross motive, but there is hardly any other reason to do so. Changing the key of "Hirtengesang an der Krippe" serves no real purpose. Certainly G major is a better key for woodwinds and brass than A major.


No one would be able to identify the cross motive by listening to Part I; it can only be seen on paper. Nevertheless, it is there and Liszt must have made the changes for a reason. And in my mind this one is as good as any.


St. Matthew Passion No. 23 (mm. 1-20)

Bach's association of the cross with the Greek letter Chi (, first letter in , the Greek spelling of Christos), can be established in the several instances where he substituted one for the other. In No. 23 of the St. Matthew Passion (left), not only did Bach substitute for Kreuz he coupled both symbols with the melody associated with his name -- his musical symbol for the cross. Here is the context.

During the vigil at Gethsemane, Christ prays, "My Father, if it be possible, let this cup pass from me; nevertheless, not as I will, but as Thou wilt." Bach investigates this propositio (reading of scripture) with tractatio, a recitative wherein the Evangelist sings: "The Savior falls down before His Father [falling strings] thereby he raises me and all men [rising strings] from our fall upward to God's grace again. Because it pleases God, he is ready to drink the cup of death's bitterness, wherein the sins of this world are poured and stink odiously." Next, Bach proposes an applicatio, but not directed as one might expect toward his congregation. Instead, the composer weaves his own name into the subsequent bass aria (N.B.A. 23), focusing the application inward, thereby making it a conclusio, a resolve to carry Christ's cross himself: "Gladly, whatever the cost, I welcome the cross and cup, in the same manner as it was offered the Savior to drink." On the words "cross and cup" (Kreuz und Becher) Bach substitutes for the word Kreuz. This phrase is set to the melody for Bach's name (in retrograde or inversion). All told, Bach's name is heard six times, the last of which (mm. 65-66) is un transposed.



But how can one justify the linkage of with the Well-Tempered Clavier, a work that has no words? Well, if Bach himself connected with Kreuz and his name in the St. Matthew Passion, it is plausible to make the same association in reverse. The WTC contains many instances of Bach's name in tones, which we can safely associate with Kreuz and .


Measure 75 of the St. Matthew Kommt ihr Töchter represents another instance where Bach substituted for Kreuz. Although I've not seen it, I've heard that he does the same thing in the Kreuzstab cantata. In the Christmas Oratorio (title pages of the 2nd & 3rd parts) Bach employs sti in place of "Christi."


Why Did Bach Sign His Name Backwards in the St. Matthew Passion?

Tim Smith

Nearly a third of the way through the St. Matthew Passion, Bach signed his name in tones. Curiously, he spelled it backwards. In tones, Bachʼs name is b♭-a-c-b♮ (or you might recognize it as ♭-a-c-♮). But here he begins with ♮-c-a-♭.

For reasons that we'll explore, Bach retrograded his signature motif in the midst of this sentence: “Gladly I will submit myself to accept the cross and cup, and even drink of it after the Savior does.” I am drawn to the word “submit,” for the cross and cup require discipline, sacrifice, and turning one's life around. In the present aria, the words “cross and cup” are sung three times. Bach associated the first two with his name backwards, then he crowned the aria by stating his name forward, with emphasis on “I will.”

In the Garden of Gethsemane, Jesus fell with his face to the ground and asked the Father to let the cup of bitterness pass from him. “Yet,” he prayed, “not as I will, but rather as you will.” Here is the paradox of will forsaking will. Desire is redirected for the sake of a higher goal. This is the crux of Luther's theology of the cross, and the paradox of Picander's poem. In this essay we'll explore how Bach revealed that paradox by invoking retrograde motion in the fifth aria of the St. Matthew Passion: “Gerne will ich mich bequemen.”

After the biblical narrative, and before the aria is sung, we hear a recitative. It explains what weʼve just heard from Scripture. Here, under Bachʼs supervision, the poet Picander contrasted the low point, of Jesus falling, with his high resolve to do Godʼs will: “The Savior fell down before his father; thereby lifting me and all people from our snare up to Godʼs grace once more.” Characteristically, Bach accompanied the idea of lowness with falling triads until that moment when “grace again” is sung. Now rising triads! The poet continued by explaining that Jesus faced the “bitter cup of death.” Here Bach used the dissonant diminished seventh chord to paint the sins of the world that have been poured into that cup, and which “putridly stink.”

Next we hear the present aria where Bach signed his name backwards. As weʼve noted, the retrograde of his melody is associated with “Kreuz und Becher” (cross and cup), a phrase of fourteen letters. The sum of B+A+C+H (with A=1, B=2, etc) is 14. Again we detect the composerʼs personal attachment to the aria.


Bachʼs name is heard backwards four times – twice to the words “cross and cup,” and twice in the violin alone.1 But he also wrote his name once in its correct orientation. Here it is sung to the words “I will gladly.” This is the only time that these words are heard in that order, with three prior instances having been “gladly I will.” Thus in the same phrase that he turned his name around, Bach also reversed the words, giving emphasis to “I will.”

Listen to the phrase in its approach. How unusual it is; how different from anything so far! Toward its end, Bach vaulted into his name via the difficult interval of a diminished seventh, culminating on E♭, the highest pitch. This is the powerful athlete who ramps up his energy and will to break a personal best. The Olympian E♭ is the high point of the aria! Now study Picanderʼs poem so that you can recognize its phrase order, reversed, at the peak.

(1) Gladly I will submit myself

(2) to accept the cross and cup

(3) and even drink of it after the Savior does.

Having stated the above twice, Bach re-composed its phrases in reverse. This is the high point of the aria.

(3) To drink of it after the Savior does, [segment 1] (2) and to accept the cross and cup, [segment 2] (1) I will gladly submit myself! [segment 3]

Segment 1 is in canon between the voice and violin. It is the only canonic episode of the aria. In a canon, one voice “takes up” the tones of another. Here the violin “drinks” of the same melody “after” the bass, but in the dissonant interval of a seventh. In this way Bach implies the Christianʼs obligation to imitate Christ, but the suffering falls short of the octave – only nearly the same.

Segment 2 is a false sequence, where repetition is disrupted by a false element. That element is an ascending augmented fourth (+4) in the word “anzunehmen,” which means “to accept.” In baroque counterpoint, the +4 is difficult and unpleasant. Thus Bach has submitted himself to accept the difficulty of the cross. The violin, having sunk to the bottom of its register, sustains a very long note. Elsewhere in Bachʼs music, long and low pitches represent eternity and the sleep of death. So in segment 4 Bach affirmed the cross as requiring that one die to self.

1 This number does not account for the repeat of part 1, with all instances of Bachʼs signature motif being heard there. With the repeat, his name is heard fourteen times. Four of these are in the violin alone, including the first and last hearings of Bachʼs name. Four are heard with the bass singing “Kreuz und Becher” (cross and cup), accompanied by violin statements of the motif, in parallel, a sixth higher. The foregoing account for twelve iterations of Bachʼs name, all in retrograde, and all to “cross and cup.” The one forward rendition is sung by the bass, without violin, to the words “will I gladly.” Bachʼs name motif commences with “I” and includes the first syllable of “gladly” (“gerne”). This one statement, being repeated, brings the total to fourteen.


In segment 3, Bach retrograded his name, ironically restoring its rightful order. Note well the high E♭ on the word “ich” (“I”). This pitch is painfully out of range for a bass. If you didn't hear Bach's name, that is because he transposed the second pair of notes down an octave. To have maintained the abnormal tessitura would have required an even higher note, an impossible F (for most basses). Listen to this sequence with the high F, and you will clearly hear Bach's name. By transposing the second pair of notes down an octave, Bach demoted their word “gerne” (“gladly”), and promoted the words “will I”, with the personal pronoun “I” landing on the difficult E♭. This is the Olympian moment of the aria – Bach's personal best.

So why did Bach sign his name backwards? It was to provide the ariaʼs high point by re-signing it forward. This resignation is supported by retrograding not just the order of phrases in Picanderʼs poem, but also key words in them. The vital phrase is “I will,” and the aria culminates in returning ♭-a-c-♮ to the right. This mirrors Jesusʼ words: “Yet not as I will, but rather as you will.” Musically, the correction displays absolute purposefulness and energy – a forcing of form to the height and to the right.

The term for music like this is “chiastic,” meaning in the shape of a cross. Chi (χ) is the first letter in the Greek spelling of “Christ,” and a sign that early

Christians used to identify themselves. In this aria, Bach substituted χ for the word “Kreuz” (cross), thereby indicating his approach to both words and music. His name in tones is a chiastic melody. By stating it in both directions, he personified the words: “I will gladly carry the cross and drink of the cup after my Savior.”


Eight of Shakespeare's history plays are divided into two tetralogies. 1 Henry VI, 2 Henry VI, 3 Henry VI, and Richard III are the plays in the minor tetralogy. The major tetralogy consists of: Richard II, 1 Henry IV, 2 Henry IV, and Henry V. King John and Henry VIII stand alone.


Philo’s Exegesis of the Fourth Day of Creation in Genesis

While we again do not have direct sources of the underlying meaning and explanation of this geometric symbol according to the Pythagoreans themselves, we do have later interpretations of the symbol and its underlying meaning from later Hellenic philosophers. One of the best sources of this material is Philo Judaeus (c. 25 BCE – c. 50 CE), or Philo of Alexandria, who lived and wrote in the first century CE in Ptolemaic Egypt. Philo was first and foremost a Jewish scholar, but he was trained in the Hellenic philosophical tradition and read and wrote in ancient Greek, the lingua franca from the Mediterranean in antiquity prior to the prevalence of Latin as advanced by the Roman Empire.


Embedded in Philo’s extensive analysis and “allegorical” interpretations of the five books of Moses from Hebrew Bible, or Pentateuch (πεντάτευχος in Greek or literally “five scrolls”) , specifically in perhaps his most influential work which was a commentary on the beginning of Genesis entitled De Opificio Mundi, or On the Creation of the World, we find a fairly extensive description of the symbolic figure in his explanation of the establishment of the heavenly bodies on the fourth day, the text of which is quoted below :


14 And God said, Let there be lights in the firmament of the heaven to divide the day from the night; and let them be for signs, and for seasons, and for days, and years:

15 And let them be for lights in the firmament of the heaven to give light upon the earth: and it was so.

16 And God made two great lights; the greater light to rule the day, and the lesser light to rule the night: he made the stars also.

17 And God set them in the firmament of the heaven to give light upon the earth,

18 And to rule over the day and over the night, and to divide the light from the darkness: and God saw that it was good.

19 And the evening and the morning were the fourth day.


This passage, which describes the creation of the Sun, Moon and Stars by God (Yahweh) on the fourth day of creation is interpreted by Philo from an intrinsically Hellenic philosophical perspective, and in particular Pythagorean, as he interprets these heavenly bodies and their importance in the theo-philosophical traditions of antiquity as representing the establishment, and ultimate representation, of time and order underlying the universe.


In his explanation of this part of Genesis, in particular on day Four of creation, Philo lays out the understanding of the importance of the number 4 within the context of the Hellenic philosophical tradition, a tradition marked quite clearly – at least from a numerological and arithmetic standpoint – by Pythagorean philosophy as embedded in the tetractys even though he does not specifically allude to the tetractys.


But the heaven was afterwards duly decked in a perfect number, namely four. This number it would be no error to call the base and source of 10, the complete number; for what 10 is actually, this, as is evident, 4 is potentially; that is to say that, if the numbers from 1 to 4 be added together, they will produce 10, and this is the limit set to the otherwise unlimited succession of numbers; round this as a turning-point they wheel and retrace their steps.


Philo describes the underlying perfection, or completeness, implied by the number Four as viewed within the context of the number Ten which he calls the most “complete” or “perfect” number (the sum of the four layers of the tetractys – 1 + 2 + 3 + 4) within classically Aristotelian terms of potentiality (4) and actuality (10). He also describes the sense of motion, or cyclical nature implied by this number 4, which actuates to the number 10, as a “turning point” and “wheel”, alluding to the base 10 that was used by the Greeks for counting and within which after the number 10 one begins to “count again”, starting with 11, 12 and so on.


He also describes the number Four as embedding within it three dimensional space, making it the perfect day (symbolically speaking of course) within which God should establish the foundations of the Heavens within which the world of man was thought to be governed in antiquity, and speaking to the importance the field of geometry held to the ancients, a tradition that became the hallmark of the West.


There is also another property of the number 4 very marvelous to state and to contemplate with the mind. For this number was the first to show the nature of the solid, the numbers before it referring to things without actual substance. For under the head of 1 what is called in geometry a point falls, under that of 2 a line. For if 1 extend itself, 2 is formed, and if a point extend itself, a line is formed: and a line is length without breadth; if breadth be added, there results a surface, which comes under the category of 3: to bring it to a solid surface needs one thing, depth, and the addition of this to 3 produces 4. The result of all this is that this number is a thing of vast importance. It was this number that has led us out of the realm of incorporeal existence patent only to the intellect, and has introduced us to the conception of a body of three dimensions, which by its nature first comes within the range of our senses.


And lastly, in reference to the four elements, and four seasons upon which the ground and order of human existence ultimately rests, Philo concludes with the following summation:


There are several other powers of which 4 has the command, which we shall have to point out in fuller detail in the special treatise devoted to it. Suffice it to add just this, that 4 was made the starting-point of the creation of heaven and the world; for the four elements, out of which this universe was fashioned, issued, as it were from a fountain, from the numeral 4; and, beside this, so also did the four seasons of the year, which are responsible for the coming into being of animals and plants, the year having a fourfold division into winter and spring and summer and autumn.



Porphyry: On the Life of Pythagoras

Another source of Pythagorean philosophy in antiquity is through the works of Porphyry (c. 234 – c. 305) and Iamblichus (c. 245 – c. 325 CE) who were contemporaries in 3rd century CE antiquity and who both wrote biographies of Pythagoras, who by that time had become a pseudo mythical figure. It is from Porphyry that we find the reference that it was Pythagoras who created and “would swear by” the Tetractys, what Porphyry referred to as the “eternal Nature’s fountain spring”.


Within Porphyry’s biography, he describes the fascination of the Pythagoreans with numbers, arithmology, and ultimately geometry thus:


49. As the geometricians cannot express incorporeal forms in words, and have recourse to the descriptions of figures, as that is a triangle, and yet do not mean that the actually seen lines are the triangle, but only what they represent, the knowledge in the mind, so the Pythagoreans used the same objective method in respect to first reasons and forms. As these incorporeal forms and first principles could not be expressed in words, they had recourse to demonstration by numbers. Number one [Monad] denoted to them the reason of Unity, Identity, Equality, the purpose of friendship, sympathy, and conservation of the Universe, which results from persistence in Sameness. For unity in the details harmonizes all the parts of a whole, as by the participation of the First Cause.

50. Number two, or Duad [Dyad], signifies the two-fold reason of diversity and inequality, of everything that is divisible, or mutable, existing at one time in one way, and at another time in another way. After all these methods were not confined to the Pythagoreans, being used by other philosophers to denote unitive powers, which contain all things in the universe, among which are certain reasons of equality, dissimilitude and diversity. These reasons are what they meant by the terms Monad and Duad, or by the words uniform, biform, or diversiform.


Here we see not only an explanation of the underlying geometrical formation of the Tetractys in terms of Platonic Forms, reflecting the underlying sentiment of the period that geometry and numbers are the best and most profound way to describe elemental reality, but also an explanation of the principles of the Monad (the One) and the Dyad (the Two) as the basic archaic elements of the universe from which all numbers, all of reality really, ultimately originates and emanates from.


Porphyry goes on to describe the meaning of the Triad, and in turn the Decad (Ten), which is formed from 1 + 2 + 3 + 4, the four layers of the Tetractys, and underpins the Pythagorean philosophical system which reflected in the Tetractys thus:


51. The same reasons apply to their use of other numbers, which were ranked according to certain powers. Things that had a beginning, middle and end, they denoted by the number Three, saying that anything that has a middle is triform, which was applied to every perfect thing. They said that if anything was perfect it would make use of this principle and be adorned, according to it; and as they had no other name for it, they invented the form Triad; and whenever they tried to bring us to the knowledge of what is perfect they led us to that by the form of this Triad. So also with the other numbers, which were ranked according to the same reasons.

52. All other things were comprehended under a single form and power which they called Decad [10], explaining it by a pun as decad, meaning comprehension. That is why they called Ten a perfect number, the most perfect of all as comprehending all difference of numbers, reasons, species and proportions. For if the nature of the universe be defined according to the reasons and proportions of members, and if that which is produced, increased and perfected, proceed according to the reason of numbers; and since the Decad comprehends every reason of numbers, every proportion, and every species, why should Nature herself not be denoted by the most perfect number, Ten? Such was the use of numbers among the Pythagoreans.


Here we see the direct metaphysical link drawn between Nature and Number, Ten being the reflection of the most perfect of numbers, upon which – to use Philo’s analogy – the (metaphysical) world turns. We also here can see the source of the Trinity, not in terms of the language and words that are used to describe it as defined by the early Church Fathers, but the underlying potency and perfection of the Triad as a symbolic representation of that which is most holy.




So with Philo and Porphyry, both of whom undoubtedly had access to knowledge regarding the Pythagorean philosophical school and their obsession with the tetractys that has subsequently been lost (even though later scholars indicate that his teachings were incorporated into those of the Hellenic philosophical tradition that followed), we find a full and complete explanation of the numerology and arithmology embedded in the Pythagorean philosophical system as manifest in the tetractys, a system which ultimately bounds the spatial dimensions of the material universe within it and from it, as well as enclosing it as it were with a beginning and an end as represented by the underlying numerology, arithmology, and geometry of the figure itself which represented to the ancient philosophers the best possible representation of the inherent cosmological world order.