PEIRCE-L Digest 1292-- February 10, 1998

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   From PEIRCE-L Forum, Jan 5, 1998, [name of author of message],
   "re: Peirce on Teleology"   

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Topics covered in this issue include:

  1) Peirce's 1-2-3 nesses, the Semiotic Square and Number
	by Douglas Moore 


Date: Tue, 10 Feb 1998 22:32:30 +0200
From: Douglas Moore 
To: peirce-l[…]
Subject: Peirce's 1-2-3 nesses, the Semiotic Square and Number
Message-ID: <34E0B95E.8F503F5C[…]>

I'm rather puzzled by the way that many list members have been using
Peirce's triadic notions. Often the trichotomy is used as some kind of
absolute categorization. For example, do numbers have Oneness,
Secondness, or Thirdness, or all three? In an endeavor to help clarify
the concepts involved, I'll sketch out a quick comparison with the
French semiotic equivalent. I'll sprinkle in a few thoughts of my own.

For European semiotics, of course, it is not a trichotomy that counts
but a fourfold division in the form of a "semiotic square." For the good
coverage of the semiotic square, one can refer to the works of the late
Professor Greimas of the Ecole des Hautes Etudes, Paris. Perhaps his
"Dictionnaire de la Semiologie" might be a good place to start.

A fair while back, I quit life as an technical academic (for the first
but not the last time) and went to study independently in Paris. I meant
to stay only for a few years but ended up spending 12 years there. I had
already spent some time reading Peirce and was already imbued with his
"first flash" concerning the trichotomy. Of all the courses I followed
it was the couple given by Greimas that impressed me, possibly because
he had the most tractable approach (always a problem) and was
potentially the closest to my technical inclinations.

If Peirce saw a trichotomy in anything he thought about, Greimas saw a
semiotic square. Thus I was faced with a choice. Was I to remain a
trichomaniac like Peirce or become a Cartesian quadramaniac? I ended up
being both, as I will explain later.

What was interesting about Gremeis's approach was that instead of
attempting to apply his brand of wisdom to logical, philosophical  and
metaphysical questions, as did Peirce, he applied it to more mundane
problems. His particular bent was to apply his semiotic square notions
to the analysis of discourse - mainly literary discourse but he didn't
exclude the scientific.  In addition to lectures, his courses involved
many workshops, each based on a semiotic analysis in a different area.
They included a semiotic analysis of the bible, political speeches, the
dicourse on art, literary criticism, literary texts and so on.

This type of approach is widely applied in France, particularly in the
advertising industry - I still have in my library a report from an
advertising company involving a semiotic analysis of the four
fundamental ways of advertising under arm deodorant, for example. You
can't get more mundane than that.

So, in a few brief words, what is the semiotic square and how is it

For Greimas, the theoretical justification for the semiotic square came
from Aristotle's logical square of oppositions. Although harboring few
pretensions as a philosopher, he was essentially saying that the basic
organizational coherence of any production emanating from a system of
signs (a semiology) was articulated out of basic logical units based on
the semiotic square.

This approach differs somewhat from Peirce's triadic version which he
applied to logic to get what he claimed was the fundamental trichotomy
of logic - abduction, induction and deduction. For Greimas, and possibly
Aristotle in a certain  way, the semiotic square itself, was the
fundamental logical element in its own right. You don't apply it to the
problematic of logic, it _is_ the logical problematic applicable even to

A very simple example of discourse analysis would be a  novel involving
the archetypal villain, the brave hero and the vulnerable but desirable
heroin. A Peircien would possibly pick this out as a basic Oneness,
Secondness and Thirdness of the piece. The Cartesian semiologist would
add a fourth entity into the equation which we could call the People.
There are thus three typed entities in the equation - the villain, the
vulnerable heroine and hero types - and one entity of a different kind -
the People which is an untyped entity but susceptible to these three
types. These four entities could make up a semiotic square.

Greimas was particularly skillful, although sometimes rather opaque, in
interpreting the relationships between such foursomes in terms of the
six oppositions of Semiotic Square. Greimas taught this at the status of
an art. One could possibly say that it could also be an embryonic
science in the making applicable to anything - or at least anything you
could discourse about.

In brief, the semiotic square approach doesn't negate the three type
trichotomy of Peirce, it merely adds a fourth kind of entity into the
equation. In the above example, the fourth element was called the

One could say that the People entity differs in cardinality from the
three typed individual entities. The latter three are all instances of
the People so to speak. It also differs from the three by being
unqualified, except by being situated relative to them within the
implicit logic of the semiotic square.  It certainly is of a different
kind. But the French semioligist would probably say that this is only
the "premier plan." There is always a second plan. In the second plan,
the archetypal individual - any individual - always harbors an element
of the tyrant, the vulnerable and the heroic. Well written, this novel
could become universal literature- the epic story of the villain, the
vulnerable and the heroic in You or Me - another twist of the People
entity.. And that is what really make the a novel different from a
travel documentary. (Good travel documentaries also have good semiotic
structure. French documentaries are square shaped)

Greimas provides an excellent example of his technique in an analysis of
a work by Maupassant.  There he discerns a number of semiotic squares as
the author's discourse moves from one problematic to another. Greimas
explains this in terms of a "debrayage" (changing gears) from one
semiotic square to the next.

In the case of our novel, there is nothing absolutely fixed about the
villains typology, for example. He might start off in a pure villainous
"Firstness" position and later move to other positions and even himself
show heroic and vulnerable qualities, but not, of course, in the same
scene. The villain as temporary hero becomes Firstness as Secondness and
so on.

It's an art and not a science, just as for Peirce's metaphysical
trichotomy approach. Once you start applying the semiotic square
-including Peirce's trichotomy, you become hooked.

My favorite semiotic square is in electromagnetic wave theory. Maxwell
started off with three first order partial differential equations. The
first was for Coulombs' Law for electric fields. The second was for
Ohms' Law applied to potential fields. The third, the Biot-Savart law
for magnetic fields. Maxwell's genius was to first discern this
trichotomy a la Peirce. 1-2-3 => electric, potential and magnetic
fields. He then, more or less,  combined these three single first order
equations, canceled a few things out and came up with a second order
differential equation - the wave equation for the, as yet,  undiscovered
phenomena of electromagnetic wave  propagation. This a marvelous example
of "Fourthness". Without Fourthness, there would be no talk back radio!
No blanket TV coverage of the Clinton scandal either! Thank god for

Another example of lesser interest is the four dimensional vector used
in the space-time of classical relativity theory - three dimensions for
space and a "fourthness" dimension for time. If this was a deeply
fundamental approach then the three dimensions would have to be typed
into firstness, secondness and thirdness. I think that Peirce was very
interested in proving the necessity of  three dimensionality.
Unfortunately all he kept coming up with was the three and not the

To get a reasonable competence of the art of semiotic analysis I
strongly recommend  applying the construct in many areas, over and over
again. It's applicable to anything. If not, its not anything. There is a
tautological twist.

After mastering the art, then one can start to have a stab at turning
this all into some kind of tractable science. Either that or make a
living from the proceeds, which is what I'm doing at the moment -
applying the art to system software design.

Theology and comparative religion is a good stamping ground. Here is a
rough example of a "square of semiotic squares" drawn from a rapid
comparative religion analysis.

In Christian theology the Trinity is God the Father, the Son and the
Holy Spirit. The fourth element is simply god unqualified (almost). The
Islamic trinity is the Koran, Faith and Divine Justice. The fourth is
also an unqualified god, but different to Christianity as it is a
different kind of unqualified god - the three triadic types are

What's interesting is that  Islam itself can be considered as Firstness
and Christianity as Secondness. In the search for Thirdness one finds
Buddhism with its own Trinity (the three jewels) with the Fourthness
being the unqualified state of Nirvana. There is no god in this scenario
but only a totally unqualified entity.  Nirvana is totally unqualified,
except that it isn't a god but a state.

Here we almost have a semiotic square of semiotic squares. To complete
the big square we need "fourthness." In the fourth place we find a
religion of a radically different kind. This is the most seemingly
eclectic religion on earth: Hinduism, the religion of the unqualifiable

It can be explained that each of these religions is based on an overall
prise de position regarding the deep question concerning the explicit
relationship between the One and the Multiple. There are 4 possible
basic variations.
1. Islamic monism  => The Multiple is One
2. Christian psuedo monism/duality => The One is Multiple
3. The Buddhist Doctrine of Non Self  =>There is no One, everything is
           Every individual is qualified by a multiplicity of others.
Nothing is primordial.
The finally we have the 1000 year old problem that frustrated nascent
Hinduism, only definitively resolved by Sankara in the tenth century -
the problem of characterizing the doctrine of the uncharacterizable.
Sankara stated in in terms of:-

4. The Doctrine of Non Duality => There is only the One, all else is
To understand this simple formula, you have to go to the subtle second
plan of Fourthness - Sankara's nuance.

A lot of this stuff I've discussed a bit in my book "The Metaphysics of
the Computer" Edwin Mellon Press 1992. The level of rigor is not much
better than used here. Since then, I've made some considerable advances
due to insights gained from my software work and plan to write another
more rigorous work when I get the free time. The work will be couched in
a Stoic framework but may use Peirce as a continual reference point.

In short, there's absolutely no problems with Peirce's 1-2-3 doctrine.
Peirce argued insistently against a fourth or higher primordial. He was
quite right. There are only three primordial types. That's it. Any
entity whatsoever can be broken up into three qualified type entities -
even protons. However, this any entity whatsoever is not any one of
these types or attributes. It's something different as we can see from
the theological examples, or from Maxwell's wave equation. In the latter
case, there were three force fields. Maxwell's wave equation is not a
force field, but a dynamic synthesis of  three force fields -something
of a different, less qualified, "higher" kind.

In brief, there are only three primordial types. However, integrally
related to them there is a thing of a different kind. The fourth thing
is unqualified in itself. Its three types provide the qualification.
They provide the qualifying "boundary conditions" in some way.

However, it can be that an entity is seen as being one of these types.
Whether something is a type of entity or an entity with a type depends
on context. In the grand theological semiotic square example above, The
Islamic god is the (almost) unqualified god, qualified in a weak way -
as unadulterated Firstness - the most dogmatic and indisputable
qualification. This Firstness is relative to the other three World
religions. In isolation within its own semiotic square, Firstness is the
Koran, an expression of god as Divine knowledge substance.

The Christian god is qualified as Secondness relative to the other
religions. Within its own semiotic square Secondness becomes the Christ
- god living. .


Thus when Cathy Legg talks about number being Firstness, she should
really fill out the rest of the semiotic square, relative to which this
statement would be valid. A similar argument could show number as being
Secondness or Thirdness as other have claimed, but in a different
semiotic square context. Of course, if we take the totally unqualified
number, except being qualified as a number, then it should be
explainable in terms of it's 1-2-3 qualifying constituents. Number as a
Trinity (Fourthness), or number as an element in a Trinity. A  number
Trinity might be something like:

 Firstness -  Number as a name (symbol) for a value
 Secondness - Number as a value
Thirdness - Number as a place holder for a value (a variable)
Fourthness - Any number  capable of being so qualified by this

You mightn't like this trichotomy, but don't worry, there are three
other such number trichotomies.
This leads to the question of whether my number trichotomy above is
itself in a 1, 2, 3 or 4 position in the larger semiotic picture. I
think its Secondness in this case.

All are valid. After all, it all depends on context. The semiotic square
is a fundamental tool for expressing context.

However, its not much good for handling context. For that you need yet
another element - Fifthness. Greimas's "debrayages" from one context to
the next are just too informal to make sense. The quantum mechanics
people have already cottoned on to this fifth "context entity,"
describing it as being "tucked up" and not perceptible. But that is a
longer story. Besides, it has all been done before, a long time ago.

Doug Moore
Dr Douglas J H Moore
For the month of February in Israel
    email: djmoore[…]
Usual Australian address
    email : djhmoore[…]



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