Yesterday's entry Deep Structures discussed the "semiotic square," a device that exemplifies the saying "If you can't dazzle 'em with brilliance, then baffle 'em with bullshit."

A search today for what the Marxist critic Fredric Jameson might have meant by saying that the square "is capable of generating at least ten conceivable positions out of a rudimentary binary opposition" leads to two documents of interest.

1. "Theory Pictures as Trails: Diagrams and the Navigation of Theoretical Narratives" (pdf), by J.R. Osborn, Department of Communication, University of California, San Diego (Cognitive Science Online, Vol.3.2, pp.15-44, 2005)

2. "The Semiotic Square" (html), by Louis Hébert (2006), professor, Université du Québec à Rimouski, in Signo (http://www.signosemio.com).

Shown below is Osborn's picture of the semiotic square:

Osborn's discussion of the square, though more clear than, say, that of Rosalind Krauss (who reverses the bottom two parts of the square-- see Deep Structures), fails. His Appendix A is miserably obscure.

On the brighter side, we have, as a sign that Gallic clarity still exists, the work of Hébert.

Here is how he approaches Jameson's oft-quoted, but seemingly confused, remark about "ten conceivable positions"--

"The Semiotic Square,”   by Louis Hébert 1. ABSTRACT The semiotic square, developed by Greimas and Rastier, is a means of refining oppositional analyses by increasing the number of analytical classes stemming from a given opposition from two (life/death, for instance) to four (for example, life, death, life and death (the living dead), and neither life nor death (angels)) to eight or even ten. 2. THEORY The actantial model, isotopy and the semiotic square are undoubtedly the best-known theoretical propositions that have emerged from the Paris School of semiotics, with Greimas as its central figure. Like the actantial model and the veridictory square, the semiotic square is designed to be both a conceptual network and a visual representation of this network, usually depicted in the form of a "square" (which actually looks like a rectangle!). Courtés defines it as the visual representation of the logical structure of an opposition (cf. Courtés, 1991, 152). The semiotic square is a means of refining oppositional analyses by increasing the number of analytical classes stemming from a given opposition from two (for instance, life/death) to four (for example, life, death, life and death (the living dead), and neither life nor death (angels)) to eight or even ten. Here is an empty semiotic square. Structure of the semiotic square     5. (=1+2) COMPLEX TERM       1. TERM A   2. TERM B   9. (=1+4) 10. (=2+3)   3. TERM NOT-B   4. TERM NOT-A   7. (=1+3) POSITIVE DEIXIS 8. (=2+4) NEGATIVE DEIXIS         6. (=3+4) NEUTRAL TERM     LEGEND: The + sign links the terms that are combined to make up a metaterm (a compound term); for example, 5 is the result of combining 1 and 2. 2.1 CONSTITUENT ELEMENTS The semiotic square entails primarily the following elements (we are steering clear of the constituent relationships of the square: contrariety, contradiction, and complementarity or implication): 1. terms 2. metaterms (compound terms) 3. object(s) (classified on the square) 4. observing subject(s) (who do the classifying) 5. time (of the observation) 2.1.1 TERMS The semiotic square is composed of four terms: Position 1 (term A) Position 2 (term B) Position 3 (term not-B) Position 4 (term not-A) The first two terms form the opposition (the contrary relationship) that is the basis of the square, and the other two are obtained by negating each term of the opposition. 2.1.2 METATERMS The semiotic square includes six metaterms. The metaterms are terms created from the four simple terms. Some of the metaterms have been named. (The complex term and the neutral term, despite their names, are indeed metaterms). Position 5 (term 1 + term 2): complex term Position 6 (term 3 + term 4): neutral term Position 7 (term 1 + term 3): positive deixis Position 8 (term 2 + term 4): negative deixis Position 9 = term 1 + term 4: unnamed Position 10 = term 2 + term 3: unnamed

These ten "positions" are apparently meant to explain Jameson's remark.

Hébert's treatment has considerably greater entertainment value than Osborn's. Besides "the living dead" and angels, Hébert's examples and exercises include vampires, transvestites, the Passion of Christ, and the following very relevant quotation:

"Simply let your 'Yes' be 'Yes,' and your 'No,' 'No'; anything beyond this comes from the evil one." (Matthew 5:37)

"The diagram above is from a ninth century manuscript of Apuleius' commentary on Aristotle's Perihermaneias, probably one of the oldest surviving pictures of the square."

-- Edward Buckner at The Logic Museum

From the webpage "Semiotics for Beginners: Paradigmatic Analysis," by Daniel Chandler:

The Semiotic Square

"The structuralist semiotician Algirdas Greimas introduced the semiotic square (which he adapted from the 'logical square' of scholastic philosophy) as a means of analysing paired concepts more fully (Greimas 1987,* xiv, 49). The semiotic square is intended to map the logical conjunctions and disjunctions relating key semantic features in a text. Fredric Jameson notes that 'the entire mechanism... is capable of generating at least ten conceivable positions out of a rudimentary binary opposition' (in Greimas 1987,* xiv). Whilst this suggests that the possibilities for signification in a semiotic system are richer than the either/or of binary logic, but that [sic] they are nevertheless subject to 'semiotic constraints' - 'deep structures' providing basic axes of signification."

* Greimas, Algirdas (1987): On Meaning: Selected Writings in Semiotic Theory (trans. Paul J Perron & Frank H Collins). London: Frances Pinter

Another version of the semiotic square:

Krauss says that her figure "is, of course, a Klein Group."

Here is a more explicit figure representing the Klein group:

There is also the logical
    diamond of opposition --

A semiotic (as opposed to logical)
diamond has been used to illustrate
remarks by Fredric Jameson,
 a Marxist literary theorist:

"Introduction to Algirdas Greimas, Module on the Semiotic Square," by Dino Felluga at Purdue University-- The semiotic square has proven to be an influential concept not only in narrative theory but in the ideological criticism of Fredric Jameson, who uses the square as "a virtual map of conceptual closure, or better still, of the closure of ideology itself" ("Foreword"* xv). (For more on Jameson, see the [Purdue University] Jameson module on ideology.) Greimas' schema is useful since it illustrates the full complexity of any given semantic term (seme). Greimas points out that any given seme entails its opposite or "contrary." "Life" (s1) for example is understood in relation to its contrary, "death" (s2). Rather than rest at this simple binary opposition (S), however, Greimas points out that the opposition, "life" and "death," suggests what Greimas terms a contradictory pair (-S), i.e., "not-life" (-s1) and "not-death" (-s2). We would therefore be left with the following semiotic square (Fig. 1): As Jameson explains in the Foreword to Greimas' On Meaning, "-s1 and -s2"—which in this example are taken up by "not-death" and "not-life"—"are the simple negatives of the two dominant terms, but include far more than either: thus 'nonwhite' includes more than 'black,' 'nonmale' more than 'female'" (xiv); in our example, not-life would include more than merely death and not-death more than life. * Jameson, Fredric. "Foreword." On Meaning: Selected Writings in Semiotic Theory. By Algirdas Greimas. Trans. Paul J. Perron and Frank H. Collins. Minneapolis: U of Minnesota P, 1976.

"The Game in the Ship cannot be approached as a job, a vocation, a career, or a recreation. To the contrary, it is Life and Death itself at work there. In the Inner Game, we call the Game Dhum Welur, the Mind of God."

-- The Gameplayers of Zan, by M.A. Foster

"For every kind of vampire,
there is a kind of cross."
-- Thomas Pynchon,
 Gravity's Rainbow

Crosses used by semioticians
to baffle their opponents
are illustrated above.

Some other kinds of crosses,
and another kind of opponent:

Monday, July 11, 2005 Logos for St. Benedict's Day Click on either of the logos below for religious meditations-- on the left, a Jewish meditation from the Conference of Catholic Bishops; on the right, an Aryan meditation from Stormfront.org.       Both logos represent different embodiments of the "story theory" of truth, as opposed to the "diamond theory" of truth.  Both logos claim, in their own ways, to represent the eternal Logos of the Christian religion.  I personally prefer the "diamond theory" of truth, represented by the logo below. See also the previous entry (below) and the entries   of 7/11, 2003. Sunday, July 10, 2005 Mathematics and Narrative   Click on the title for a narrative about Nikolaos K. Artemiadis,  (co-) author of From Artemiadis's website: 1986: Elected Regular Member of the Academy of Athens 1999: Vice President of the Academy of Athens 2000: President of the Academy of Athens "First of all, I'd like to    thank the Academy..." -- Remark attributed to Plato

"Preserving a strict unity of time and place, this stark tale of a young woman's decline into insanity is set in a summer home on a holiday island. It is the first part of the trilogy

that comprises Winter Light and The Silence, films which are generally seen as addressing Bergman's increasing disillusionment with the emotional coldness of his inherited Lutheran religion. In particular here, Bergman focuses on the absence of familial love which might perhaps have pulled Karin (Andersson) back from the brink; while Karin's mental disintegration manifests itself in the belief that God is a spider. As she slips inexorably into madness, she is observed with terrifying objectivity by her emotionally paralyzed father (Björnstrand) and seemingly helpless husband (von Sydow)."

-- Nigel Floyd, Time Out, quoted at Bergmanorama

Related material:

1. The "spider" symbol of Fritz Leiber's short story "Damnation Morning"--

2. The Illuminati Diamond of Hollywood's "Angels & Demons" (to open May 15), and

3. The following diagram by one "John Opsopaus"--

(Cf. Sinatra's birthday, 2004)

One for his baby:

Ron Silver as
Alan Dershowitz in
"Reversal of Fortune"
suggests the epigraph of
The Particulars of Rapture:
Reflections on Exodus --
two stanzas from attorney
Wallace Stevens
quoted here yesterday afternoon.

One more for the road:

A link that appeared in a
different form in Saturday's
"Flowers for Barry"--

Speed the Plow.

This leads to
A Hanukkah Tale
containing the following:

This is, in turn, related to
Harvard's Barry Mazur's recent
essay on time in mathematics
and literature (pdf).

L'Chaim.

The Origin of Change

A note on the figure
from this morning's sermon:

"Two things of opposite natures seem to depend
On one another, as a man depends
On a woman, day on night, the imagined

On the real. This is the origin of change.
Winter and spring, cold copulars, embrace
And forth the particulars of rapture come."

-- Wallace Stevens,
  "Notes Toward a Supreme Fiction,"
   Canto IV of "It Must Change"

Lawrence Summers, former president of Harvard, home of the rat psychology of Skinner and Quine, today offered a lesson in behavioral economics.

From a transcript of Summers's remarks (for a video, see the previous entry)--

"An abundance of greed and an absence of fear on Wall Street led some to make purchases - not based on the real value of assets, but on the faith that there would be another who would pay more for those assets. At the same time, the government turned a blind eye to these practices and their potential consequences for the economy as a whole. This is how a bubble is born. And in these moments, greed begets greed. The bubble grows.

Eventually, however, this process stops - and reverses. Prices fall. People sell. Instead of an expectation of new buyers, there is an expectation of new sellers. Greed gives way to fear. And this fear begets fear.

This is the paradox at the heart of the financial crisis. In the past few years, we've seen too much greed and too little fear; too much spending and not enough saving; too much borrowing and not enough worrying. Today, however, our problem is exactly the opposite.

It is this transition from an excess of greed to an excess of fear that President Roosevelt had in mind when he famously observed that the only thing we had to fear was fear itself. It is this transition that has happened in the United States today."

Related material

Spatial Practice,
Paris-Style:

"Voids, a Retrospective,"
an exhibit of empty rooms
that runs through March 23
at the Centre Pompidou

See also "Art Humor"
 and "Conceptual Art."