"I don't believe in things, I believe in their relationships" (Georges Braque).
"Structuralism is that awakened and restless consciousness of modern knowledge" (Michel Foucault).
"Structuralism deals with the relations between the parts and the whole" (Amir D. Aczel).
Structuralism
Structuralism is an intellectual current, a scientific method and a general theory that provides a way of understanding meaning and knowledge. It emerged in the early 20th century with Saussure's structural linguistics, and its success caused it to spread to other fields, both formal disciplines (philosophy, anthropology, sociology, psychology, economics, biology, etc.) and to culture and human activities in general.
According to Amir D. Aczel [2009], "Structuralism is a method of intellectual analysis that provides a framework for understanding and organizing areas of study related to the production and perception of meaning."
Structuralism is based on the concept of structure, a concept of a general kind that is common to all fields. There is no formal consensus definition of structure. However, there is some consensus regarding its essential characteristics:
Relationships.
A structure is a set of relationships between the elements of a system. Relationships are more important than the entities that link them. Meaning is found in the relationships between things, rather than in isolated or independent things.
According to structural realism, things exist only in relations to other things. Things in themselves do not have or do not produce meaning.
Totality.
A structure is conceived as a totality, with a global meaning that is constituted through all the relations of the elements that conform it and that make the system intelligible. For example, a person's face cannot be recognized by analyzing each of its parts (eyes, nose, mouth, etc.), since they do not have meaning in isolation. Meaning emerges when the relationships between its parts produce a recognizable pattern.
System.
A structure is a system. It consists of interrelated elements, such that a change in any element or relationship implies a change in the entire system.
Model.
A structure does not refer to an empirical reality but to a model that represents it.
With Lévi-Strauss the modern conception of structuralism was established:
Universality.
All realms of reality, including scientific and humanistic disciplines (mathematics, physics, biology, psychology, literature, and philosophy), and human activities (language, culture, society, customs, myths, etc.) are surface manifestations of the same deep structures, structures that are amenable to scientific investigation. The deep structure is more important than the superficial, because the superficial is a manifestation of the deep.
Deep structures are universal because they are manifested in all domains. They are based on intuitive, innate, a priori, pre-reflective and collective principles that constitute the foundation of reality.
Language.
It is necessary to search for or establish the universal language based on the deep structures. Through that universal language it is necessary to discover the general or universal laws common to all areas of reality.
Transcendentality.
Universal structures can be considered transcendental. They are beyond superficial phenomena to constitute themselves as deep and meaningful phenomena.
Structuralism was a universal idea, theory and method, a metatheory or universal paradigm that transformed the way we contemplate and understand all areas of reality. It was a highly productive idea, as is the case with any universalist idea. Its vocation was interdisciplinary, multidisciplinary or transdisciplinary.
Origins
Although the term "structure" does not appear in his "Course in General Linguistics" (1916), Ferdinand de Saussure is considered the creator of the principles that gave rise to the structuralist current. Saussure considered language as a structure of signs. He created semiology: "A science that studies the life of signs within social life". Semiology later became with Pierce semiotics, the general theory of meaning and representation.
Given its success, structuralism soon spread to other disciplines beyond linguistics: philosophy, mathematics, anthropology, psychology, systems theory, etc. Since the 1950's it became a true social phenomenon. Every discipline aspired to the qualification of "structural".
Prominent authors were: Claude Lévi-Strauss in anthropology, Jean Piaget in psychology, Nicolas Bourbaki in mathematics, Jacques Lacan in psychoanalysis and Roland Barthes in literary criticism.
Linguistic structuralism
Linguistic structuralism starts at the beginning of the 20th century with Ferdinand de Saussure, and constitutes the beginning of modern linguistics. In essence, it is based on the following:
A language is a structure of interrelated signs.
The properties of a language cannot be explained or described from its elements (the linguistic signs) in isolation.
The formal structure of language is what makes the transmission of meaning possible.
To study a language is to go beyond appearances and try to discover its hidden relationships, the structures of meaning.
Linguistics is only a part of the general science of semiology, since semiology also encompasses the study of non-linguistic sign systems. Language is semiology, but not all semiology is language.
Saussure devoted special attention to the study of dichotomies (or dualities):
Language has two aspects: language and speech. Language is the sign system of a society. Speech is the individual performance of a language.
The sign has two aspects: signifier and signified. The signifier is the external, superficial or material aspect of the sign, which points to the signified. The signifier is the internal, deep aspect, the mental content associated with the signified, the concept.
The signifier is arbitrary. What is important is the meaning, the semantics. There is no intrinsic relationship between form and meaning, between syntax and semantics.
There are two approaches to language: the diachronic and the synchronic. The first is concerned with the history of language. The second is interested in the language at a given moment in history.
Structuralism succeeded functionalism in which each element of language has a given function. On the other hand, according to structuralism, no element of language can be valued if it is not considered in relation to the other elements.
Jakobson's linguistic structuralism
Roman Jakobson −phonologist, cultural theorist and author of considerable work− was a theoretical rather than an empirical researcher. He had a great influence on Lévi-Strauss and Roland Barthes, among others. He was a key figure in the adaptation of the structural analysis of language to other disciplines. He attached great importance to forms, from the simplest to the most complex.
He defined a model of the theory of linguistic communication in which he included 6 factors: sender, receiver, message, linguistic code and communication channel. For Jakobson, metaphor and metonymy are the structural axes of all linguistic communication. [Metonymy is to designate one thing or idea with the name of another, using some semantic relation existing between the two].
A pioneer of the structural analysis of language, Jakobson helped form the influential Prague Linguistic Circle, founded in 1926, which created the most coherent structurally oriented linguistic discipline: phonology:
His is the first modern definition of phoneme: "Mental impression of a sound, minimal distinctive unit or minimal semantic vehicle."
Phonetics and phonology are not synonymous terms. Phonetics is concerned with the physical and physiological description of sounds. Phonology is the branch of linguistics that deals with phonemes.
A phoneme is an abstraction of language. It is not a sound, but a category of sound defined by the way it is distinguished from other categories.
The sound structure is a language that can be generated by a relatively small number of rules.
The phonologists of the Prague Circle came to the conclusion that the phonemes of a language form a system, that is, they are as perfectly structured as words or grammatical forms. This discovery came to corroborate Saussure's theories.
Bourbaki and mathematical structuralism
In the 1930s, mathematics was an absolute mess, a junk drawer in which a multitude of scattered tools had accumulated. It was paradoxical that a science that had become fundamental in scientific activity and that had imposed Galileo's idea that "the book of nature is written in mathematical characters", had no formal structure of its own.
Faced with this situation, André Weil succeeded in 1934 in bringing together a group of mathematicians (mainly French) to reorganize and reform mathematics around the concept of structure, using set theory as a foundation. Under the fictitious name of Nicolas Bourbaki, born in a fictitious country (Moldova), the group began publishing books under the general title of "Elements of Mathematics" (it published a total of 10 volumes, each in a different field). In a few decades the Bourbaki group reworked mathematics from that structuralist perspective and its result was called "modern mathematics". Mathematics thus made an enormous qualitative leap.
Bourbaki intended to transform mathematics (plural) by mathematics (singular), a unified mathematics. For this purpose they chose three species of structures or "mother structures" to found and hierarchize the whole mathematical edifice: the topological, the order and the algebraic [Bourbaki, 1986].
Characteristics of mathematical structuralism:
Mathematical entities do not possess intrinsic properties, but are defined by relations with other mathematical entities. For example, the natural number 1 is defined as the successor of 0 in the linear structure of the natural numbers. In general, a natural number is defined by its relationship to other natural numbers.
Mathematical propositions do not have an objective truth value. They only assert what type of entity it is and not its type of existence. Its type of existence depends on the structure in which it is embedded.
All mathematics is a hierarchy of structures. All mathematical research boils down to the investigation of structures.
The main breakthrough achieved by Bourbaki was the issue of emphasis on logical rigor. This rigor has since permeated all new mathematical developments. This emphasis on rigor has been seen as a reaction to Poincaré's emphasis on intuition in mathematics. They also made innovations in nomenclature and symbolism that soon became commonplace. For example, they invented the symbol for the empty set.
The structuralism of the Bourbaki group was thrown into crisis by the appearance of category theory, a theory more general than set theory and which aspired to unify and ground all of mathematics. Despite the successes achieved with structuralism, the group discovered that structuralist philosophy was incomplete and decided not to continue with its initial purpose and to abandon the labyrinth into which they had gotten themselves (that "hell", in their own words).
Bourbaki's mistakes were:
Relying on set theory and three "mother structures" (topological, order and algebraic), which are structures derived from simpler, universal structures.
Not based on simple intuitive concepts. They only considered the concept of set (axiomatized) and the concept of structure (not formalized). The concept of structure is intuitive but was not formalized, so it remained an ambiguous concept. In any case, it cannot be defined because it is too generic. It is necessary to define the concrete types of relationships.
Not to harmonize intuition and formalization. However, Bourbaki, in his work "The Architecture of Mathematics" (1946) stressed the need for this harmonization, but the intuitive concepts did not become concrete.
Their formal extremism, with the use of a hierarchical conglomerate of axioms to formalize structures, which curtailed freedom and creativity. Nor did they consider the practical aspect.
Not contemplating categories, but not in the sense of modern (and complex) category theory, but categories defined simply as classes of mathematical expressions or expressions sharing a certain structure. Bourbaki came close to tackling something similar to the concept of category but they did not, perhaps because they were repelled by an excessively complex and unclear subject at the time.
Not to create a formal language for all mathematics, despite innovations in nomenclature and symbolism.
Structuralism in philosophy of science
In philosophy of science, structuralism is based on the concept of scientific theory as structure. Since theories are not presented in isolation but interrelated, structures of theories also appear: the relationships between different theories.
Structuralism in philosophy of science is based on:
Constructing a metatheory (a theory of theories), which requires a different type of formalization, more general, than those employed in particular theories.
The structuralist program provides a general framework for metatheory building, for formalizing and interrelating particular theories.
The formalization of metatheory is based on Bourbaki's concept of "species of structures" or "mother structures" (the topological, the order and the algebraic).
Despite the multiple theories that may coexist to explain the same facts, the unity of science must be based on a single theory. This unity of science is sought by physicists with a "theory of everything". In reality, structuralism in philosophy of science tries to construct a metascience (a science of sciences) or a universal science.
Structuralist philosophy of science was born with the publication in 1971 of the book "The Logical Structure of Mathematical Physics" by Joseph D. Sneed, as a synthesis of classical physics with logical positivism. It was reworked and disseminated by Wolfgang Stegmüller and Carlos Ulises Moulines.
The structural anthropology of Lévi-Strauss
The anthropologist Claude Lévi-Strauss is the founder of the so-called "structural anthropology", a vision or explanation of cultural and social diversity based on the application of the structural method to the human sciences. His conception of structuralism was deeper and more universal than Saussure's structural linguistics. Its characteristics are as follows:
Universal vs. particular.
The universal in man is something that belongs to nature, it does not depend on any particular culture. Cultural, on the other hand, is synonymous with relative, with belonging to a particular community. Universal and cultural seem to be contrary concepts, but there are common deep structures.
Deep structures.
The various cultural and human manifestations are manifestations of unchanging categories or deep, unconscious structures. Everything manifest and visible is explained by the hidden and invisible.
The human spirit is not free. It is not free because other structures (such as those of language) condition its activity from the deep, from an unconscious depth.
There is no fundamental difference between primitive and so-called "civilized" cultures, for they are manifestations of the same deep mechanisms.
Language.
The deep structures constitute a hidden, implicit and universal language, which is reflected in the external or explicit language.
A language is a system of relations. All phenomena are communication phenomena and, consequently, are linguistic phenomena that obey an unconscious structure. Language is not only a social phenomenon, but constitutes the foundation of every society because it reflects its deep structures.
The various human cultural manifestations (behaviors, customs, thoughts, spoken language, non-verbal communication, etc.) have a superficial structure that is a cultural language, which is a reflection of a deep structural language, since there are unconscious, underlying and structural aspects in all human behaviors. These deep structures (or infrastructures) are constituted by a set of invariable and universal forms, but they appear in the superficial cultural language with very different contents.
The anthropological-cultural study is the study of cultural language. Since a language is a system of interrelated signs, to study cultural language is to study the relationships between those signs in order to discover the underlying universal forms. A sign is the association between a superficial external aspect (signifier) and a concept (signified). The signifier is arbitrary. What is important is the meaning, the semantics.
Linguistic elements (signs) have no independent reality. Their reality (value) depends on the relations with the other elements. The relationships between the elements are more important than the elements themselves.
The importance of language.
"Saussure represents the great Copernican revolution in the field of human studies, for having taught us that language is not so much a thing of man as man is a thing of language" [Caruso, 2003].
The union of science and humanism. The dissolution of man.
The human mind is a natural object. The products of the mind are natural facts. There need be no distinction between nature and culture. Man and culture are objects of science. Reality (natural and cultural) must be conceived globally.
"The ultimate aim of science is not to constitute man, but to dissolve him", that is, to consider him as one more manifestation of the profound. It is necessary to reintegrate human culture into nature, the dissolution of human subjectivity in the objectivity of structures.
Lévi-Strauss considered it possible that the various sciences would in the future be unified by the same deep structures, and that one day anthropology would "awaken" among the natural sciences, forming part of a single unified science.
Myths.
The explanation of the similarities between the various human cultures is explained by the existence of common internal structures, in some universal and innate principles or structures, which are manifested in myths, symbols, religions, rituals, art, spoken language, non-verbal communication, human relationships, narratives, customs, human behaviors and thoughts, etc., but mainly in myths. These manifestations are very diverse, but structurally identical in all human societies. Myths are the common heritage of a culture or society.
These universal or deep structures must be analyzed as the grammar of a universal language or universal rules that constitute a system of relationships. In "The Elementary Structures of Kinship" (1949), Lévi-Strauss reveals the relationship between myth and language.
Deep structural language are universal laws, principles, or patterns that are mythical structures or categories.
Myth is the deep, underlying language. Myth is a system of interpretation of the world, of nature and of man. Myth provides meaning to the world, its true meaning. Myth is a symbolic linguistic system, a language whose purpose is to organize experience, to give meaning to the world. Myth has the function of providing social order, giving structural and functional unity to the group.
All myths of different cultures are manifestations of the same underlying symbolic language. Every culture is a system of symbolic communication based on the same mythical categories. Mythic thought is governed by universal laws. The myths of a culture are reflected in language. Myths can be deduced by analyzing the language. Mythical thought constitutes the purest expression of human thought.
Myths deal with opposites by means of opposites. A myth is a system of binary oppositions or dualities (thesis and antithesis) and their unification or resolution (synthesis). It is this structure that makes meaning possible. The object of myth is to provide a logical model that makes it possible to resolve and harmonize a contradiction. Myth is beyond dualism, it transcends opposites.
Myths are universal and beyond time. "Myths, like music, are machines for the suppression of time" (Mythological I). Myths are timeless, they are beyond time.
A myth should not be interpreted in a single way, for it is a linking of many levels of explanation. A myth is multidimensional.
Myths should be interpreted only in relation to other myths. A myth is defined by the set of its versions.
All myths are distinct, but they have a common structure of which each myth offers an aspect. Ultimately, that common structure is the structure of the human spirit. To investigate this was the aim of Lévi-Strauss's research. The structure of the spirit already basically carries an image of the world. The structure of the world and of the mind are homologous.
Mythemes.
The fundamental units of myth he calls "mythèmes". A mythème is the smallest possible unit of meaning in mythical language. It is a constant element that appears connected with other mythèmes. Mythèmes combine at different levels to constitute a mythical system. They consist essentially in the assignment of a predicate to a subject.
Mythemes are analyzed in the 4 volumes of "Mythologiques" (1964-1971), one of the most important works of anthropology.
The science of signs.
Society is a structure formed by a set of signs. The structure is a system governed by an internal cohesion. This cohesion is revealed in the study of transformations. Each system is a language that can be translated into the language of another system. Anthropology could be considered a branch of linguistics, i.e. as a part of the general science of signs.
Simplicity.
Scientific analysis must be explanatory and simplifying. Structuralist explanation consists of organizing data in the simplest possible way. All science must be structuralist and reductionist.
The human mind.
From the structural analysis of myths, which have an algebraic structure, Lévi-Strauss deduced that also the human mind and cognition have an algebraic structure.
Myth is dynamic, operative, and is a general model of specific human thought processes. Myths are only constrained by the nature of the human mind.
Lévi-Strauss sought to identify the universal laws of human mind and cognition or their logical-mathematical structure. His purpose was to discover the intellectual unity of mankind. In this sense, Lévi-Strauss is part of the intellectual movement known as "the cognitive revolution".
Gestalt Psychology
The Gestalt psychology, born in Germany at the beginning of the 20th century, is the most prominent form of the structuralist current in the field of psychology.
The German word "Gestalt" translates into English as "form", "structure" or "configuration". It refers to the psychological mechanism of perception (stimulus-response) as a meaningful whole of relationships in which the overall pattern or configuration prevails over the component elements. This is summarized in the phrase "The whole is greater than its parts".
Initially, Gestalt psychology was born with the mechanism of perception, but was later applied to all domains of human behavior.
Rubin's Glass (Gestalt image)
The psychoanalytic structuralism of Jacques Lacan
Lacan was a structuralist in the field of psychoanalysis. He drew mainly on structural linguistics, philosophy, and mathematics (topology, graph theory, knot theory, set theory, game theory, number theory, and combinatorics), although he also drew on phenomenology, anthropology, and existentialism.
Lacan attempted to formalize the unconscious as a language: "The unconscious is structured as a language and operates combinatorially by the same processes that generate metonymy and metaphor." Lacan considered himself a Freudian and tried to return to the conception of the unconscious proposed by Freud.
To formalize the psychoanalytic contents, Lacan introduced the concept of "mathema" (from the Greek mathema, knowledge), an algebraic expression or formula that symbolically represents the relationships between various elements. For Lacan, the mathema is the expression "of what is not said, but can be transmitted". Lacan was trying to wrest knowledge from the ineffable and give it form so that it can be transmitted. In this sense, Lacan adopts a position opposite to that of Wittgenstein ("What cannot be spoken about must be kept silent").
The real is what cannot be expressed by language. The real is always present but always mediated by metonymy, the symbolic and the imaginary. Metaphor is a condensation of metonymies.
The real, the imaginary and the symbolic are intertwined as in the Borromean rings. The unbinding of one of the rings causes the unbinding of the other two.
Borromeo rings
Lacan was an innovator of the structuralist current and provoked great controversy among other professionals. He was accused of being cryptic, diffuse, and not very rigorous, even asystematic and pseudoscientific.
Jean Piaget's genetic structuralism
For Piaget, "A structure is a system of transformations involving laws as a system, and which is preserved or enriched by the very play of its transformations, without these reaching beyond its borders or drawing on external elements. In a word, a structure implies the three characters of totality, transformation and self-regulation" [Piaget, 1968].
Piaget was the originator of genetic psychology, the science that investigates the construction of knowledge in the child, and in which a parallel is drawn with the construction of scientific knowledge. Piaget was more interested in discovering the mechanisms of creation and complexification of knowledge, the construction of cognitive categories, rather than their contents.
Knowledge is an active process of interaction between the knowing subject and the known object. In this process, subject and object change.
Scientific knowledge is a dialectical process between observation/experimentation and the formulation of theories.
Logical thinking in the child has a long process of construction, linked to the development of cognitive structures, which precedes linguistic behavior.
The literary structuralism of Roland Barthes
Critical literary structuralism examines the structure of a narrative rather than the content, so as to establish links with similar structures in works from other periods and different cultures.
Barthes philosopher, writer, essayist and semiotician is considered the main representative of structuralism in the field of literary criticism. His main interest was the mechanisms of signification in literary works. His structural semiology is heir to Saussurian linguistics.
For Barthes, structuralism is an activity: "The aim of all structuralist activity is to reconstruct an 'object', so that in this reconstruction the rules of functioning (the 'functions') of this object become manifest" [Barthes, 1973].
His main ideas are:
Since the author of a literary work does not provide the meaning, the reader must create it, interpret it actively through the process of analysis of the text. In his work "The Death of the Author" (1967) he states that the reader is the authentic source of meaning in a text. It is the "birth of the reader".
This interpretation of the text of the literary work must be contemplated from different points of view: from different sources of meaning and relevance. However, the plurality of meanings is limited by the linear structure of writing.
The ideal text should be open to a variety of different interpretations. This is the concept of the "open work", a dialectic between the work and the interpreter.
A univocal language is a language whose meaning is unique, literal. A denotative language is one that has several possible meanings. Literature is based on the latter.
Structuralist literary criticism dispenses with all external reference. It does not look for meaning. It looks for the structure, not the message.
Each text must be considered as a significant entity whose immanent structures the literary critic must discover.
The "structural man" is not defined by his ideas or his languages but by his imagination (or imaginary), that is, the way he mentally lives the structure.
A metalanguage (a second order language) is necessary, to transcend and overcome the limitations of traditional languages and in which symbols were to be used instead of words and phrases ("Elements of Semiology [1971]).
Post-structuralism
Post-structuralism emerged in the late 1960s with the questioning of the primacy of structuralism in the human sciences. This questioning was motivated by several reasons:
The awareness of the limitations of structuralism, even by the structuralists themselves. Among these limitations is that structuralism is only descriptive and needs the operational aspect.
The complexity and instability of the human sciences defeat the purpose of establishing structures. This is interpreted by poststructuralists as a freedom of interpretation.
Human systems do not follow a strict and immutable logic.
The study of underlying structures is conditioned by biases and assumptions from history and culture.
The questioning of the theme of structuralism's binary oppositions.
Because the relations between power and knowledge had not been taken into account.
Post-structuralists advocated the search for a metalanguage capable of describing the configurations of the human sciences.
However, the boundary between structuralism and post-structuralism is blurred. For example, Barthes and Lacan can be considered structuralists or post-structuralists, depending on which aspect is considered. Prominent post-structuralists were Michel Faucault, Jaques Derrida and Gilles Deleuze. Derrida's 1966 John Hopkins University lecture "Structure, Sign, and Play in the Discourse of the Human Sciences" is considered the manifesto of poststructuralism.
Foucault
Michel Foucault (1926-1984) −historian of ideas, psychologist, social theorist, and philosopher− is known for his analyses of power structures and their relationship to knowledge, as well as for his critiques of social institutions, especially psychiatry, courts, and prisons. He dissected social norms and searched for truth in the human being.
In the 1960s he became interested in structuralism, from which he later distanced himself as too rigid. His 1965 book "The Order of Things" [1999] was published during the height of his interest in structuralism. In this work Foucault searches for the origins of the human sciences (especially psychology and sociology), an epistemological archeology of the human sciences, coming to the conclusion that the sciences are explained by certain archetypes, that all periods of history have maintained different underlying truths. Jean Piaget compared Foucault's position with Kuhn's concept of paradigm.
Derrida
Jacques Derrida (1930-2004) was a controversial thinker because of his iconoclasm and radical critical stance. He investigated the structures of language, but tried to go beyond them to look for their foundation. This "looking at the structure underneath the structure" and finding no foundation he calls "deconstruction". He came to the following conclusions:
Philosophy is incapable of establishing a solid and stable foundation.
Language structures are the foundation of our understanding of reality and science. Concepts are formed through language.
Language is the human creative vehicle, but language is artificial and subjective.
There are no predetermined and external structures to human creation.
There is no transcendental meaning, so the field of signification extends to infinity.
In every word of language there is room for every possible signification.
Delauze
Gilles Delauze (1925-1995) was a French heterodox philosopher, author of numerous philosophical works. His ideas are as follows:
In the beginning was Chaos, but not a chronological but a logical anteriority. Chaos is the infinite, the indiscernible, the indeterminate. Only from Chaos can we dialectically understand thought.
Philosophy is the art of inventing concepts. Philosophy is a knowledge of the first degree that acts directly on Chaos. Philosophy must construct a plane of immanence on Chaos, a self-sufficient reality, closed in itself. The function of philosophy is to save Chaos by giving it consistency.
Identity is the result of difference. Traditionally, difference is considered to derive from identity. Difference is a system of differential relations.
Concepts are characterized by internal and external consistency. Internal consistency refers to the relationships between the components of a concept. The external consistency refers to the relations of some concepts with others. A concept is situated on a higher plane than its components. Concepts are self-referential. Concepts are attributive totalities. The meaning of a component of a concept is only understood in relation to the other components.
MENTAL and Structuralism
MENTAL is the paradigm, the most illustrative and complete example, of structuralist philosophy:
Because of its linguistic character based on symbols and signs. Among the symbols are those associated with primitives. Other symbols are: ∅ (empty set) and the triad θ (null expression), α (existential expression) and Ω (universal expression).
MENTAL is a universal language and a metalanguage with which particular languages can be defined.
MENTAL is situated at the deepest level, which is necessarily abstract. Any structure that can define structuralism must rest on that abstract level.
Because of its emphasis on the concept of relation. In MENTAL everything is relations. Every manifestation of a primitive is a relation, as is every combination of primitives.
The concept of relation on which structuralism is based is ambiguous or fuzzy. In MENTAL many types of relations can be specified: causal, functional, logical, property or attribute, sharing, recursive, etc. The possible relationships are determined by the language. Thanks to the relational mechanisms, with MENTAL there are formally all possible structures.
Because of its universality, since it provides a universal structuralism: philosophical, psychological, linguistic, mathematical, etc. It is the "theory of everything" sought by structuralist philosophy.
MENTAL follows the modern structuralist conception (that of Lévi-Strauss), i.e., the belief that all surface manifestations are manifestations of the same deep structures. And that there is a universal, deep language that allows to formalize all these superficial manifestations. These deep structures are the universal semantic primitives which are the primary archetypes or philosophical categories.
There is no distinction between mind and nature, between internal and external, between ontology and epistemology, for all things share the same primary archetypes.
MENTAL provides the formal structure that enables the transmission of meaning.
By relying on dualities, which are the two aspects of each semantic primitive. It also unites the opposites of: structural and functional, quantitative and qualitative, precise and diffuse, analytical and synthetic, descriptive and operational, etc.
By the establishment of general laws.
For its philosophical character, profound, the foundation of everything superficial.
MENTAL expressions have a unique interpretation at the deep or abstract level, and different interpretations at the mental or conceptual level. For example, the expressions {x y z} or a/b have a unique meaning at the abstract level, but no concrete meaning because they are only symbols (x, y, z, a, b).
But MENTAL goes beyond the structuralist paradigm to rise to a universal paradigm:
Traditionally, the structural (or static) has been considered as opposed to the functional (or dynamic). In MENTAL all expressions are both structural and functional, since every expression is evaluated.
MENTAL provides a universal language. A simple language from which complexity is derived.
MENTAL allows higher order relationships.
MENTAL is intuitive as well as formalistic. It is intuitive because the semantic primitives are intuitive in nature. It is formalistic because there are mechanisms for combining the primitives, which are the primitives themselves. Its structural semantics is equal to the lexical semantics.
MENTAL contemplates categories. Category theory, as it is in mathematics, is too complex. The true categories, the simplest ones, are the universal semantic primitives. From them one can construct categories of expressions: open groups defined by means of parameterized generic expressions.
MENTAL is a language of consciousness for several reasons: 1) because it is based on primary archetypes; 2) because it unites opposites; 3) because its essence is the relation, present in every primitive and in the combinatorics of primitives.
At bottom, what underlies structuralism is the search for some universal mechanisms, some relational primitives or "mother" relations that are the foundation of all relations to describe all kinds of systems. In MENTAL, these relations are the primary archetypes, the archetypes of consciousness. It also underlies the principle of descending causality, where the general and universal prevails over the particular.
In short, we can say that structuralism is based on primary archetypes, the foundation of all that exists, including scientific and humanistic thought.
Structuralism had its origin in linguistics. With MENTAL we return to the origins but clothed in universality. MENTAL is:
The "language of the spirit" sought by Lévi-Strauss, in which the myths are the universal semantic primitives, the units of meaning, but not "minimal" (as Lévi-Strauss affirmed) but the simplest and, therefore, universal. It is the deep mythical language common to the world and to the mind. Mythemes are subject-predicate type with content. In MENTAL the primitive of particularization is abstract (has no content) and includes the subject-predicate aspect.
The metalanguage advocated by post-structuralists.
The language, not of the unconscious proposed by Lacan, but the language of archetypes that connects the conscious with the unconscious.
The foundation of meta-science or universal science.
Contrary to Derrida's skepticism of lack of foundations, MENTAL is a solid foundation, for it provides deep and fundamental structures (innate, abstract, predetermined and transcendent) from which to understand physical and mental reality, i.e., the real and the possible. These structures are in all manifestations. The foundation of everything is necessarily abstract.
MENTAL is the "immanent plane" postulated by Deleuze's philosophy: a self-sufficient reality closed in itself.
A universal structuralist method
The structural linguistic method used in MENTAL is universal. It is based on two principles:
All phenomena (natural, mental, social, cultural, etc.) must be reduced to the smallest possible number of elements that provide maximum intelligibility.
It is necessary to discover the structural relationships between these elements in order to understand their overall meaning.
Actually these two principles correspond in linguistics to lexical semantics and structural semantics, respectively.
Addenda
Umberto Eco's structuralist view
Umberto Eco's book "Open Work" (1962) is described by some authors as the first post-structuralist book. According to Eco, a reader "rewrites" the text of a literary work and becomes an author. This creates a particular relationship between author and reader. "Open work" does not mean that there is a lack of structure, but that there is a general structure that supports other interpretative structures. In this sense, a work is symbolic, for a symbol admits a plurality of meanings.
Eco's book was published at the same time that Barthes was proposing that the literary work must be open in order to remain always alive.
In 1967, Eco published "The Absent Structure", another book that caused a great impact in the field of structuralism (or post-structuralism). According to the Italian author, structures are not existing entities, but only formal tools to aid the representation of ideas or concepts.
The mathematics of Lévi-Strauss's structural anthropology
Lévi-Strauss made use of mathematical formalism in his works. The following are worth noting:
Lévi-Strauss's thesis "The Elementary Structures of Kinship" (1943) is one of the most important classics of all times in anthropology, and is considered as the foundational act of structuralism in its most modern and complete version. The thesis was originally a study of kinship systems in Australian Aboriginal tribes. But its author realized that the study was superficial, merely descriptive, and that there must be a deep underlying structure, which required advanced mathematics to formalize it.
Lévi-Strauss's thesis includes an appendix prepared by André Weil in which the algebraic structure of Klein's group was applied. With this collaboration between Lévi-Strauss and Weil a link between anthropology and mathematics was established.
A Klein group is a commutative group of 4 elements where each element is the inverse of itself: G = {e, α, β, γ} and α−1 = α , β−1 = β , γ−1 = γ. The element e is the neutral element. The table of the Klein group is:
·
e
α
β
γ
e
e
α
β
γ
α
α
e
γ
β
β
β
γ
e
α
γ
γ
β
α
e
The elements of the group represent transformations. They are governed by the following laws:
We start initially from three transformations: e (identity or neutral transformation), α and β.
Two equal transformations applied successively produce the transformation identity (e): αα = e, ββ = e.
Therefore, α and β are inverses of themselves: α−1 = α and β−1 = β.
The commutative property is satisfied: αβ = βα = γ.
From these properties it follows: γα = αγ = β , γβ = βγ = α , γγ = e
Therefore, γ is inverse of itself: γ−1 = γ.
An example of Klein's group is that of two arithmetic transformations:
α : x → −x (opposite element)
β : x → x−1 (inverse element)
e = 1 (neutral element)
γ : x → −x−1 (inverse of inverse)
Another example of a Klein group is 4-element permutations (a, b, c, d) in which two pairs of elements are inverted at the same time:
α : (a, b, c, d) → (b, a, d, c)
β : (a, b, c, d) → (c, d, a, b)
e : (a, b, c, d) → (a, b, c, d)
γ : (a, b, c, d) → (d, c, b, a)
This Klein group theory was applied to the subject of the kinship of Kariera, an Aboriginal tribe of Western Australia. In this tribe there are 4 types of individuals: A) Banaka; B) Karimea; C) Burung; D) Palyeri.
The marriage rules are A-C and B-D. If we call f the conjugate function, one has:
f(A) = Cf(C) = A f(B) = Df(D) = B
The rules for the children are:
(A, C) → D (C, A) → B
(B, D) → C (D, B) → A
Calling p the "parent" function and m the "mother" function, we have:
p(A) = Dp(B) = C p(C) = Bp(D) = A
m(A) = Bm(B) = A m(C) = Dm(D) = C
The set K = {e, f, m, p} is then a Klein group.
The Klein group harmonizes two dichotomies. The 4 transformations constitute a tetralemma of Greek, Taoist and Buddhist logics. A tetralemma is a double dialectic, a logic beyond dualism.
Lévi-Strauss created, in an intuitive-symbolic way, a "canonical formula" to describe the common structure of all myths:
Fx(a) : Fy(b) ∼ Fx(b) : Fa−1(y)
where there are two elements (a and b) and two functions (x and y). This formula is somewhat cryptic and has had many interpretations [Miranda, 2001].
The symbol "∼" does not indicate an equivalence relation. An equivalence relation fulfills the properties of identity, symmetry and transitivity. In the case of the canonical formula relation it is not symmetric because the symmetry of the right expression does not produce the left expression but Fx(y) : Fb−1(a−1). Therefore it is not an equivalence relation.
The canonical formula is then interpreted as a transformation, so mathematically it should be written like this:
Fx(a) : Fy(b) → Fx(b) : Fa−1(y)
Where the transformations are a → b, b → y, y→ a−1, and x remains unchanged.
The canonical formula is also called "double twist" because there is a double transformation:
Fx(a) : Fy(b) → Fx(b) : Fy(a) → Fx(b) : Fa−1(y)
In the first transformation, the two functions exchange their arguments. In the second transformation, the function y becomes an argument of the inverse function of a (a−1).
Lévi-Strauss used the topological structure of the Moebius strip (a single-sided, single-edged figure) in "The Jealous Potter" (1985) to explain and symbolize the dynamic transformation of the structure of myth.
Given the relationship between myth and mental structure, the canonical formula can also be interpreted as a certain structure of mental processes or a cognitive (or geometric-symbolic) pattern shared by all mankind.
The canonical formula was proposed by Lévi-Strauss in 1955 in the chapter entitled "The Structural Study of Myth" of his book "Structural Anthropology" [2000]. Since that date, its author used it sporadically in other works, especially in the Mythological.
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