The Construction of Elements

This page is about the regular construction of elements from a syntactic point of view. Explanations about the meaning of the primitive symbols and the IEML alphabet can be found in this page (the six primitives) and this one (the 25 lower-case letters)

IEML contains about 3,000 elements forming the basic semantic building blocks, or elementary concepts, from which all the expressions of the language are composed. The elements are generated in a regular way from six primitive symbols which form the layer 0 of the language. The generative operation being recursive, the elements are stratified on six layers above the layer 0.

The primitive symbols are: E (emptiness), U (virtual), A (actual), S (sign), B (being), and T (thing).

The meanings of the elements are not attributed by some arbitrary translations into another language, but is defined through a network of explicit semantic relations inside the IEML dictionary.

An element is a ternary concatenation (recursive on 6 layers) of primitive symbols, by using emptiness elision processes at the end of the expression and by representing certain chains of three primitives by a lowercase letter. The three syntactic roles of the ternary concatenation are : 

the substance (role 1), the attribute (role 2) and the mode (role 3) 

In practice, the elements appear as sequences of letters of a 35-character alphabet (10 capitals and 25 lowercase letters) interspersed with punctuation marks without spaces. The final punctuation mark of an element indicates the syntactic layer of the element, while the internal punctuation marks are traces of the recursive concatenations of which the element is the product. The meaning of the letters (below) is only indicative: each letter essentially designates a place in a system of symmetry.

10 capital letters 

  • E = emptiness
  • U = virtual
  • A = actual
  • S = sign
  • B = being
  • T = thing

Learn more about the semantic primitives.

  • Virtual/actual binary symmetry
    • O = U⊕A = process, 
  • Ternary symmetry sign/interpreter/referent
    • M = S ⊕B⊕T = entity or representation, 
  • 2/3 symmetry: process/entity 
    • F = O⊕M = fullness
  • 5/1 Symmetry fullness/emptiness
    • I = F⊕E = information

25 lowercase letters

In the ternary concatenations represented below, the final E is elided. For instance U:U:E:. becomes U:U:.

25 lowercase letters

The above table shows an example of an IEML paradigm at the most basic level of the elements. Codes with punctuation marks are IEML expressions and their English translation is shown below. IEML codes have two components, selected from the semantic primitives U: (virtual), A: ( actual), S: (sign), B: (being), and T: (thing). The first component corresponds to the syntactic role « substance » and the second to the syntactic role « attribute ». Codes with the same substance are on the same row and codes with the same attribute are on the same column. The punctuation mark « : » means « layer 0 » and the punctuation mark « : » means « layer 1 ». In order to reduce space and complexity, the pairs (substance, attribute) of the primitives (U: A: S: B: T:) are represented by 25 lowercase letters. For example, T:T:. is represented by « l ».

The meaning of the 25 lower-case letters is explained further here.

Quaternary symmetry

O:O:.

  • wo. = U:U:. = exist
  • wa. = U:A:. = act
  • we. = A:A:. = appear
  • wu. = A:U:. = perceive

Hexagonal symmetry 1

O:M:.

  • y. = U:S:. = know
  • o. = U:B:. = want
  • e. = U:T:. = can
  • u. = A:S:. = say
  • a. = A:B:. = commit
  • i.  = A:T:. = do

Hexagonal symmetry 2

M:O:.

  • j. =  S:U:. = idea
  • g. = S:A:. = message
  • h. = B:U:. = subject
  • c. = B:A:. = individual
  • p. = T:U:. = object
  • x. = T:A:. = body

Nonagonal symmetry

M:M:.

  • s. = S:S:. = reflection
  • l. = S:B:. = language
  • t. = S:T:. = memory
  • k. = B:S = society
  • m. = B:B:. = emotion
  • n. = B:T:. = world
  • d. = T:S:. = truth
  • f. = T:B:. = life
  • l. = T:T:. = space

Learn more about the 25 lower case letters which are the basic IEML concepts.

Punctuation marks

  • Layer 0 :
  • Layer 1 .
  • Layer 2
  • Layer 3
  • Layer 4 ,
  • Layer 5 _
  • Layer 6 ;

k.i.- means « gift » because gifts weave the social bond (k. in substance) through a material « doing » (i. in attribute). The emptiness in mode is elided.

k.i.-k.i-‘ means « economic good » by suggesting a relationship between the increasing complexity of the exchange of gifts and counter-gifts and the development of the economy. Here the gift k.i.- is repeated in substance and in attribute and the vacuum in mode is elided.

Example of a Paradigm at layer 2

Human Development Paradigm

In the Table above, the 54 IEML expressions in the matrix cells have two lowercase characters, the first corresponding to the syntactic role « substance » and the second corresponding to the syntactic role « attribute ». These characters are chosen from the upper right (O:M:.) and lower right (M:M:.) quadrants of Table « 25 lowercase letters ».

The table is called « human development » as it declines the kinds of knowledge, values, skills, signs, social roles and techniques (columns) according to the nine interdependent dimensions of human experience: reflection, language, memory, society, emotion, world, truth, life and space (rows).

Again, expressions with the same substance are in the same row and expressions with the same attribute are all in the same column. The punctuation mark « – » means « third layer ». The reader can easily see that a row or a column contains concepts that have some meaning in common, and that the common semantic feature is represented in IEML by the same character.

Learn more about IEML paradigms.

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