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MENTAL. General Summary of the Work
 GENERAL SUMMARY
OF THE WORK

"Doubt everything. Find your own light." (Buda)

"Believe nothing merely because many believe it or pretend to believe it; believe it after submitting it to the dictates of reason and the voice of conscience." (Buda)


A Universalist Thesis

The thesis put forward in this work is that all reality, both internal (mental) and external (physical), is founded and governed by a set of semantic primitives that constitute a universal formal language. These primitives are configured as 12 pairs of opposite or dual concepts of supreme level of abstraction, simple, intuitive and independent of each other, which are degrees of freedom, mental dimensions or dimensions of consciousness; hence the name assigned to this language: MENTAL.

This language is especially applicable to the formal sciences. Formal sciences are disciplines that deal with general, abstract, rational and coherent concepts. Their results can be applied to physical-natural reality. Among the formal sciences are mathematics, computer science, artificial intelligence and systemics.

As we have indicated in the Prologue, MENTAL has its origin in the search for a universal language for computer science, a search that led to the identification of universal semantic primitives and their combinatorics, and which, due to its supreme level of abstraction, was progressively extended to mathematics and the formal sciences in general, as well as to psychology (the universal semantic primitives are primary archetypes or archetypes of consciousness) and philosophy (the universal semantic primitives are philosophical categories).

MENTAL is a universal thesis based on a reduced set of simple semantic primitives that constitute the foundation of reality. It is the simplest thesis and, therefore, − according to the principle of Occam's razor− the one most likely to be true. It goes beyond the Church-Turing thesis, since the latter is only computational (operational), while MENTAL is an operational and descriptive language. The MENTAL thesis is that everything that can be expressed is what can be expressed with MENTAL. Like any thesis, it is not provable.

MENTAL is the Magna Carta of possible worlds, the common essence of all that exists: of internal (mental) and external (physical) reality. In short, it is a "theory of everything".


MENTAL Applications

Mathematics

✲ Nature of mathematics.
There is currently no consensus on what the true nature of mathematics is. MENTAL clarifies this issue: mathematics is the abstract science that studies the particular and general relationships between universal semantic primitives, regardless of whether they can be interpreted in concrete domains such as geometry or physics.

✲ Foundation of mathematics.
Mathematics has no foundation since the appearance of the famous Gödel theorem (of incompleteness or undecidability) in 1931. Gödel proved that in every formal axiomatic system that includes the natural numbers there are undecidable truths, i.e., it is not possible to prove their truth or falsity. But the deep meaning of Gödel's theorem is that mathematics cannot ground itself. Mathematics must be grounded in something higher or deeper, which Hilbert called "metamathematics". It is not possible to access the deep from the superficial, from the formal. But it is possible to access the superficial from the deep, because everything superficial is a manifestation of the deep.

From the point of view of MENTAL, Gódel's theorem is irrelevant because MENTAL provides a foundation from the deep or universal, not from the superficial or particular. It does not use restricted formal axioms, but semantic axioms (the universal semantic primitives), which are degrees of freedom.

✲ A mathematical language.
There is general talk of a "mathematical language", but mathematics lacks a formal language. MENTAL provides a formal mathematical language:
  • The language is theoretical-practical, with a clear, logical and consistent notation. It is linear and, therefore, computer-processable.

  • It unites mathematics with metamathematics.

  • It restores the original purity of Cantorian set theory, the misnamed "naive theory", as opposed to the complexity of the axiomatic theory of Zermelo-Fraenkel (ZF). It breaks the mold that traditional mathematics has imposed on our thinking. It is time to abandon the old axiomatic theory and adopt what is evidently simpler, more expressive and creative.

  • It allows the creation of more generic, more compact, conceptually clearer and more efficient algorithms.
✲ Expressiveness.
MENTAL, due to its supreme level of abstraction, allows expressing all kinds of mathematical entities: numbers, vectors, matrices, tensors, sets, sequences, functions, categories, rules, algebraic structures, etc., as well as all kinds of imaginable combinations: categories of vectors, sets of functions, sequences of rules, etc.

✲ Foundationalist schools of mathematics.
MENTAL unites and harmonizes the intuitionist and formalist schools of mathematics:
  • It is aligned with the intuitionist school because it is based on primitive intuitive concepts and because it is based on the philosophy that only that which can be constructed or formally described by means of language exists. Language defines the limits of what can be expressed.

  • It is aligned with the formalist school because MENTAL can be considered a universal formal axiomatic system, in three aspects:

    1. Primitives can be considered as "semantic axioms".

    2. Axioms are used that relate primitives to each other by means of formal axioms, which are universal in nature. For example, the expression that establishes the commutative property of addition (x+y ≡ y+x) relates addition to equivalence.

    3. Theorems can be derived.

    MENTAL also allows to define particular formal axiomatic systems. Formulas are the expressions of language. Axioms are generic expressions that establish relations between primitives. Rules of inference are conditional generic expressions. Theorems are expressions that are obtained from the axioms or theorems and the rules of inference.
✲ Hilbert's dream.
MENTAL is the culmination of Hilbert's dream of creating a unified mathematics by means of a metamathematics. But not in the exclusively formalistic sense (intended by Hilbert), but essentially semantic. And it goes further, for MENTAL transcends mathematics itself.

Hilbert erred in pretending to do so in an exclusively formal and superficial way, disregarding semantics, by means of a universal formal axiomatic system that would allow the derivation of all mathematics. Hilbert did not manage to propose a concrete set of universal formal axioms, due to the irruption of Gödel's incompleteness theorem, which revealed the limitations of formal axiomatic systems and, therefore, that his dream was impossible.

MENTAL, on the other hand, is based on a reduced set of universal semantic primitives. This does not imply that mathematics is closed to freedom and creativity. On the contrary, MENTAL provides and makes explicit the universal resources available (the degrees of freedom) from which creativity is favored. MENTAL is the metamathematics conceived by Hilbert.

✲ Imaginary expressions.
MENTAL generalizes the concept of imaginary numbers to imaginary expressions and higher order imaginary expressions. The imaginary unit and the infinitesimal are defined by imaginary expressions. Non-diophantine arithmetic are particular cases of imaginary arithmetic expressions.

✲ Lambda calculus.
MENTAL puede utilizarse como un lenguaje funcional y emular el cálculo lambda de Alonzo Church, un sistema basado en expresiones funcionales (funciones definidas a partir de otras funciones).

MENTAL is the realization of the old dream of Church, who wanted to invent a language for mathematics and which in the end was reduced to a functional language: the lambda calculus. MENTAL is a universal formal language for modeling all mathematics.

✲ The P. vs. NP problem.
P-type problems are those that are solved in polynomial time. NP problems are those that are not solved in polynomial time but when a solution is provided it can be verified in polynomial time. The P vs. NP problem is: can problems that are verified in polynomial time also be solved in polynomial time?

The resolution of this problem is considered very important for understanding the true nature of computation. But the essential nature of computation lies in the identification of the deep computational resources, which are the universal semantic primitives. Both kinds of complexity share the same computational essence, the same universal semantic primitives. The true nature of computation is not clarified by the resolution of the P vs. NP problem, but by the identification of the abstract and deep conceptual resources, which are the universal semantic primitives.

✲ Platonism.
MENTAL is the realization of Gödel's dream of a mathematics based on Platonic ideas.

In short, MENTAL is a reinvention of mathematics. From a universalist point of view, it leaves behind particular theories. In practice one can forget about formal disciplines such as category theory, universal algebra, lambda calculus, geometric algebra, etc. It is enough to make free use of the primitive semantic resources most appropriate at any given moment.


Logic

Logic is integrated into MENTAL, just as logic is currently integrated into mathematics. Historically, logic was born as a philosophical discipline, later "mathematical logic" was created, and finally it was incorporated into mathematics itself, of which it is considered an inseparable part. But in MENTAL, logic (essentially represented by the primitive "Condition") is one of its dimensions or degrees of freedom.
Computer Science

✲ Foundation.
Computer science was born by borrowing theories and concepts from mathematics (arithmetic, Boolean algebra, set theory, mathematical logic, etc.), but lacks solid foundations, as is the case with mathematics. An attempt has been made to base it on the concept of "information", but this is an indefinable concept, like consciousness.

The semantic primitives of MENTAL provide a common foundation for mathematics and computer science. This implies that MENTAL is the foundation of all operating systems; indeed, it can be said that universal semantic primitives constitute the true operating system, the web (in particular, the semantic web), programming languages, generalized markup languages (such as SGML and XML), database management languages, ontology languages, and so on. A single language is sufficient to formalize the different domains of computer science.

Since mathematics had no standard algorithmic or operational language, computer science had to invent it, but the result has been a veritable linguistic tower of Babel.

✲ Multiparadigm programming language.
At the computer science level, MENTAL is mainly a programming language that is beyond the languages considered "high-level" (such as Apl, Setl, Snobol, Icon, Lisp or Prolog), so it can be called "a very high-level language" or a "supreme-level language", since MENTAL is the language of the highest possible conceptual abstraction.

With MENTAL, the restrictions and limitations of most programming languages are definitively eliminated. It is, therefore, an important qualitative leap, allowing a freedom and flexibility unknown until now:
  • By having semantic resources of supreme abstraction level, the software development process is greatly simplified.

  • It allows the use of different programming paradigms (imperative, functional, logical, etc.).

  • Developments tend to be generic and reusable.

  • The code is compact because it does not use keywords.

  • Encourages creativity.

  • It allows the creation of particular specialized languages.
MENTAL is a multi-paradigm programming language, capable of expressing any traditional paradigm (procedural or imperative, functional, logical, relational, object-oriented) and modern paradigms (evolutionary, intensional, multi-dimensional, generic, multi-phase, genetic, event-driven, agent-driven, constraint-driven, aspect-driven, etc.).

There are many languages considered "multi-paradigm", but they are merely an integration of paradigms. MENTAL, on the other hand, could be called "uniparadigm", because all the particular paradigms arise from the same linguistic structure. A monoparadigm language contemplates only one paradigm. A uniparadigm language contemplates all paradigms from a unified linguistic structure.

✲ Database Management System (DBMS).
MENTAL is a DBMS. Different models such as relational, object, multidimensional, etc. can be specified.

✲ Computational model.
MENTAL is a new computational model and a new computational paradigm. It provides a new meaning to the term "computation". Computation is the evaluation of an expression that produces a result. Computation is equivalent to evaluation.

It replaces the old Turing machine model. MENTAL offers a model in which the computational principles are the universal semantic primitives themselves, which are of supreme level of abstraction. The Turing machine, on the other hand, is a superficial model, of low level of abstraction, of detail.

It replaces the Church-Turing thesis (the maximum computational power is represented by the Turing machine or by recursive functions). The primitives of MENTAL are the computational (operational) and descriptive principles themselves, which establish the limits of what is expressible, computable and describable.

✲ Generalized marking language.
MENTAL is a generalized markup language. It is a simpler alternative to SGML and its simplified version for the Internet, which is XML.

The concept of "markup" refers to the assignment of attributes to data. This concept, which was born to specify the structure of the content of text documents, is used today to define the structure of all types of information structures.

✲ Ontology language.
MENTAL is a language for defining ontologies, based on the entity-attribute-value model. It is a simple alternative to the complex RDF standard, a language for describing resources, properties and relationships with other resources through metadata encoded with XML syntax. RDF is the language used on the semantic web to define ontologies at a basic level. It uses a model called "triple", because it is a ternary relationship between subject, predicate and object.

The semantic web has not yet become a reality due to the rigidity of XML, the complexity of RDF and the lack of a universal language that relates all the elements. MENTAL is the simple alternative to the semantic web.

✲ Graphic language.
MENTAL is a graphical language. Traditional graphical languages are independent languages, disconnected at the semantic and syntactic level from alphanumeric languages. MENTAL primitives allow "drawing" on an abstract space. The drawings created could be represented on a physical device by means of a communication system between the abstract (internal) space and the external world.


Artificial Intelligence (AI)

✲ AI language.
Traditionally, the languages used in AI have been Lisp (a functional language) and Prolog (a logical, rule-oriented language). MENTAL is an AI language that includes the features of both in a much simpler and more efficient way, making the development of AI applications much easier. Paradoxically, MENTAL is more powerful and flexible than Lisp and Prolog combined, despite its greater simplicity.

✲ Knowledge representation.
MENTAL is a system and a language for knowledge representation.

✲ Common sense.
MENTAL is a language of common sense that also allows to formalize and represent common sense. Common sense is a concept close to consciousness.

✲ Frame problem.
MENTAL solves the frame problem in a simple way. The frame problem consists of the difficulty of expressing with first-order logic that which does not change (the "frame") in a dynamic environment. In MENTAL, the frame is simply the abstract space.


Linguistics

✲ Formalization of semantics.
With MENTAL the old problem of the formalization of semantics is clarified. Semantics is inexpressible, and its limit is when a biunivocal relation between syntax and semantics of universal primitives is established.

✲ Natural language.
The universal semantic primitives are also reflected in natural languages. They are included in the semantic primitives (semantic primes), the primitives common to all languages, proposed by Anna Wierzbicka, the most prominent linguist in this area of linguistic research.

✲ Metalanguage.
MENTAL is a language and also a metalanguage with which specific languages can be defined by means of the corresponding grammars.

MENTAL is not just another particular language, but the mother language from which all formal languages derive. For this reason, it can serve as an intermediate or bridging language in machine translation processes by representing the sentence structure of natural language.

✲ Universal grammar.
MENTAL is the universal grammar postulated and sought by Chomsky, the innate grammar possessed by all human beings, the common deep structure of all languages. But in MENTAL universal language and universal grammar are the same thing because lexical semantics is the same as structural semantics.

MENTAL does not have a concrete grammar, because if it did, the language would not be universal because it would be restricted by imposing combinatorial restrictions. The grammar of MENTAL is semantic and universal, but grammars of particular languages can be defined.

✲ Universal scientific language.
MENTAL is the universal scientific language sought by Carnap, but not on a physicalist basis but on an abstract basis, on a supreme level of conceptual abstraction.

✲ Universal language.
MENTAL is a universal language along the lines of the language sought by Leibniz: the Lingua Characteristica Universalis. It is also a Calculus Ratiocinator, with the difference that it is a language capable of automatic inferences.

✲ Transdisciplinary language.
MENTAL is a transdisciplinary language along the same lines as the language sought by Basarab Nicolescu, UNESCO and CIRET (Centre de Recherches et d'Etudes Transdisciplinaires).


Physics

Physical phenomena are expressed formally by means of mathematics. But traditional mathematics has limitations, mainly because it is not a formal language with precise syntax and semantics and because it does not establish the degrees of freedom.

✲ Operational and descriptive language.
MENTAL provides a unified operational and descriptive language for physics. Equations describe physical phenomena, but computation is playing an increasingly important role in physics. The idea that computation and computer programs may be the foundation of the universe originated with pioneers Konrad Zuse and Edward Fredkin and, more recently, with Stephen Wolfram. The result has been the development of a science called "computational physics" or "digital physics", a bridging field between physics and computer science. In this context, the concept of the cellular automaton has emerged strongly as a standard model, comparable to the concept of a field.

✲ Quantum physics.
MENTAL allows formalizing quantum phenomena such as superposition and entanglement. With MENTAL it is simpler to formalize the theories of quantum physics because abstract space does not have the limitations of ordinary physical space. And quantum phenomena take place at a deep physical level close to or analogous to abstract space. Interestingly, string theory, in its F version (from father, father) also establishes 12 dimensions or degrees of freedom, the same number as that of universal semantic primitives. String theory is a very complex mathematical theory, perhaps because the mathematics it uses is not the most adequate. A deep physical theory needs a deep mathematics, which must necessarily be simple.

✲ The Wiegner question.
MENTAL provides the answer to the question posed by Eugene Wiegner in his famous 1959 lecture, "Why is mathematics so useful for describing physical phenomena?" The answer is simple: because the physical world and the mathematical world are both manifestations of the same primary archetypes.

The relationship between MENTAL, mathematics and physics is hierarchically descending:

MENTAL ⇒ Mathematics ⇒ Physics

Mathematics is a manifestation of MENTAL, and physics is a manifestation of mathematics.


Philosophy

✲ A philosophical language.
The primitive universal semantics are also philosophical categories. Philosophical categories are the most generic, the most abstract, the most essential and profound concepts, the supreme genera of things, the ontological and epistemological roots of reality, the foundation of our understanding of the world. And their grammar is philosophical, because it is built from philosophical principles.

From this point of view, it makes no sense to speak of philosophy of mathematics, computer science, linguistics, etc. as a philosophy that applies from "outside" to these disciplines, but philosophy itself grounds them through philosophical categories.

MENTAL is the formalization of the idea of the first Wittgenstein (the one of the Tractatus) of the existence of an isomorphism between language, internal (mental) reality and external (physical) reality. This isomorphism exists but at a deep level, at the level of primary archetypes. It is also the deep grammar sought by the second Wittgenstein (that of Philosophical Investigations).

MENTAL is also the universal paradigm sought by Ervin Laszlo: a set of principles underpinning science and philosophy.

In short, MENTAL is a universal linguistic turn of phrase, since everything has a linguistic foundation.

✲ Ideal language.
MENTAL is the ideal language sought by analytic philosophers, especially Wittgenstein and Russell. But MENTAL is not a language based exclusively on logic, but on a set of primary concepts, logic being one of these concepts. There are not the logical atoms that Russell was looking for; they are really the universal semantic primitives, which we can call "semantic atoms".

MENTAL follows Hegel's philosophy of absolute idealism: everything is a manifestation of a profound, indivisible and absolute reality.

For idealist philosophers, ordinary language is not suitable for philosophical analysis, because of its ambiguity, so an ideal language is necessary. MENTAL is a language based on philosophical categories and, therefore, ideal for philosophical analysis.

✲ Structuralist language.
MENTAL is a structural language because it deals only with structures. A structure is a set of relationships between the elements of a system, a set that is conceived as a whole.

MENTAL is also a structuralist realist language, in the sense that we cannot know the nature of things; only the structure of the world is knowable.

Structuralism was born with Saussure's structural linguistics and is based on the concept of structure as a set of relations. Meaning resides in relationships, as in MENTAL. The modern conception of structuralism was born with Lévi-Strauss: there are deep structures that give rise to all superficial manifestations, and we must look for the universal language that is based on these deep structures.

✲ General semantics.
MENTAL is the "general semantics" postulated by Korzybski and that he did not formalize. And where map (mental world) and territory (physical world) share the same primary archetypes.

✲ It is a global ontology-epistemology.
MENTAL, with its semantic primitives of supreme level of abstraction, provides a global ontology. It is an ontology because it deals with the common essence of concepts and their relations. It is global because it is applicable to all domains, providing them:
  • A common semantic basis.
  • A way of integration, relationship and communication, which dilutes its borders.
  • A generic conceptual framework of reference.
  • A semantic standardization.
MENTAL is also a global epistemology because the primitives constitute a model of the human mind.


Psychology

✲ Neutral language.
MENTAL is the "neutral language" postulated by Jung and Pauli, a language based on primary archetypes, valid for the external (physical) world and the internal (psychic) world.

The universal (the universal paradigm and the universal language) is not to be sought in the physical world, nor in the psychological world, nor in mathematics, nor in logic. The universal is to be sought in the archetypes of consciousness. Jung and Pauli were right in orienting their search in this direction.

At a deep level everything is connected and everything converges in the same conceptual framework: the archetypes of consciousness.

✲ Model of the mind.
MENTAL is a model of the mind. As with grammar, it is really a metamodel of the mind, for it is not a concrete model of the mind, but degrees of freedom.

MENTAL is the realization of David Hume's dream of discovering mathematical laws for the mental world, following the line traced by Newton for the physical world. Indeed, MENTAL is the platform for discovering the abstract laws of the mental plane.


Systemics

✲ It is a universal language of science, the language that von Bertalanffy sought for General Systems Theory.


Mythology

✲ It is the "language of the spirit" sought by Lévi-Strauss, in which the mythemes (the minimal units of meaning) 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 physical and mental world. Mythemes are restricted structures, for they are of the subject-predicate type. In MENTAL the primitive of particularization includes the general subject-predicate scheme.


Properties of MENTAL

✲ It is a language of consciousness.
Consciousness is not definable but manifests itself as:
  1. Simplicity. The true essence of everything is simple. In simplicity is truth and consciousness. Consciousness is supreme simplicity and supreme abstraction.

  2. Union or connection in general, and the union of opposites or duals in particular. Consciousness connects the internal and the external, the superficial and the deep, the generic and the specific.

  3. The principle of descending causality, which is a type of union. Everything goes from the universal or general to the particular.
MENTAL follows these principles. It is a language of supreme conceptual simplicity and integrates, unites or harmonizes the opposites or duals in the primitives themselves and in the characteristics of language: syntax and semantics, ontology and epistemology, theory and practice, analysis and synthesis, the operative and the descriptive, the intensive and the extensive, etc.

MENTAL is not mentalese, the hypothetical language of thought postulated by Fodor, but the language of consciousness, the foundation of mental language.

✲ It is a creative language.
MENTAL is a language of supreme creativity. Creativity is the ability to generate new and unsuspected relationships. Creativity is produced by combining concepts to produce new concepts. The more generic, deep, abstract and different the concepts to be combined, the greater the creativity. As the semantic primitives are all different from each other and are of supreme level of abstraction, creativity is also supreme.

✲ It is a bootstrapp language.
The term "boostrapp" has two, but closely related, meanings:
  1. Self-sustaining, sustaining oneself solely through one's own efforts and resources.

  2. Creation of a system from a few essential elements and evolution or development by itself, without external help. The image that best symbolizes this process is the spiral.
In the case of MENTAL, the primitives are independent (they are degrees of freedom) but they support each other; each one depends on the others. And they have the potential capacity to expand, to develop to create new expressions, applications and derivative operations. It is a big bang that allows to generate potentially the whole universe of possible expressions.

✲ It is a falsifiable language.
It is falsifiable in the sense established by Karl Popper. According to Popper, a theory, in order to be scientific, must be falsifiable, that is, it must be possible to find a case that can invalidate the theory. MENTAL is a thesis that can be falsified when a domain of a formal science that cannot be formalized is detected. Therefore, in this sense, MENTAL can be considered a scientific theory.

✲ It is the universal science or meta-science.
MENTAL is the universal science or meta-science that underlies the formal sciences. It is the foundation of the unity of knowledge.

✲ It is a metaphorical language.
It is the return to the fundamental or primordial metaphors that we had forgotten and that constitute the foundation of every concept and of all knowledge.

✲ It is a multidimensional language.
The dimensions are the universal semantic primitives, which are orthogonal (independent of each other).

✲ It is a universal synchronistic language.
Synchronicity is a concept proposed by Jung and refers to the meaningful connections between mind and matter produced by the Unus Mundus, the deepest realm where space and time are transcended and from which all manifestations emanate. MENTAL is the language of primal archetypes, where space and time are abstract, from which all manifestations emanate and which constitutes the boundary between the manifest and unmanifest realms. There is a universal synchronicity, where everything is a manifestation of the primary archetypes.

✲ It is a fullerian synergistic language.
Synergy is the effect produced by the elements of a system that is greater than the sum of the effects of the individual elements. Richard Buckminster Fuller also called "synergetics" a universalistic system based on "the geometry of thought", a philosophy of creating systems through a hierarchical top-down process: from the universal to the particular, and from the simple to the complex. MENTAL also follows this philosophy, as the structures that are created can be considered an essential geometry (or pre-geometry) of mind and consciousness.

✲ It is a pattern language.
Universal semantic primitives are universal patterns, the patterns of internal and external reality. It also allows to create particular patterns by means of generic expressions.

✲ It is a "naive" language.
The naive attitude is innocent, simple, direct, without a priori conceptions, seeking the essence of things, the simplest, most natural and intuitive explanation or foundation.

✲ It is a limit language.
The universal semantic primitives are of supreme level of abstraction and establish the boundary between pairs of opposites or duals. It is not possible to go further.

✲ It is a philosophical computer model.
It is a theoretical computer model based on a reduced set of "instructions" which are philosophical principles.

✲ It is a universal categorical closure.
The concept of "categorial closure" is due to the philosopher Gustavo Bueno. It refers to the fact that all sciences are closed in their respective categories. In each science there are interrelated elements and operations that define or form a closed domain. Each science is defined by its categorial closure. MENTAL is a universal categorical closure where all disciplines are interrelated from the deep level because they all share the same primary archetypes.

✲ It is the "Magna Carta" of the Possible Worlds.
MENTAL offers an extremely simple universal model of possible worlds. The possible worlds are based on the degrees of freedom, which are the universal semantic primitives, where all possibilities reside.

Wittgenstein said: "The limits of my language mean the limits of my world" (Tractatus 5.6). Here we say that the limits of universal formal language are the limits of the possible, of internal and external reality.

✲ It is a fractal language.
MENTAL is a fractal language because the same semantic-syntactic resources are always applied at all levels.
  • Fractals always use the same simple generating laws at all scales.

  • The complexity of the result is a consequence of applying the simple laws recursively or iteratively. But the complexity is only apparent, because behind the complexity hides the simplicity.

  • Fractals are self-reflexive, they contain themselves. The fractal paradigm is closely related to consciousness, for fractals unite opposites: the internal and the external, the finite and the infinite.
MENTAL is also a holographic language because it recognizes the general maxim that "everything is isomorphic".

✲ It is a dialectical language.
Dialectics studies the confrontation, struggle or contradiction between opposites and how to overcome them, harmonize them, transcend them from a higher perspective. This confrontation and its overcoming is usually presented as the triad "thesis-antithesis-synthesis". In this sense, the number 3 is the number of consciousness, since it symbolizes the transcendence of opposites.

In MENTAL there are two types of dialectics:
  • Vertical, between abstract primitive concepts and their concrete instances or expressions, that is, between the universal and the particular.

  • Horizontal, between the primitives themselves (multilectics), including pure dialectics (between contrary or opposite primitives) and autolectics (the combination of a primitive with itself).
MENTAL represents the overcoming of all opposites through the universal synthesis realized by language.

✲ It is a universal language of representation.
Representation is a phenomenon in which the mind and consciousness organizes or "collapses" into certain simple, essential and direct forms, which are the invariants of consciousness. These invariants are precisely the primary archetypes.

✲ It is an ontology of language.
The ontology of language is based on the fact that language is the key to everything. We live in language. Language generates being. With language, human beings evolve and shape their identity and that of the world. MENTAL, not only unites ontology and epistemology, but it is also a reality that is the object of study. To study MENTAL is to study the universal.

✲ It is an abstract imaginal language.
The imaginal realm is a realm superior to the mental realm. One cannot think without imagining. When MENTAL is used, imagination also comes into play, an imagination that we can call "abstract". According to James Hillman and Patrick Harpur, the imaginal is the true reality.

✲ It is an alchemical language because:
  • It is the result of the total conjunction of opposites or duals. This is precisely the central idea of alchemy.

  • It is present, like the philosopher's stone, in all manifested things. It is the essence, the unity and simplicity that is hidden behind the diversity and apparent complexity of reality.

  • It is the "Great Work", the discovery of the common essence of oneself and of creation, the unified consciousness where the unity of all things is perceived.
✲ It is a language of the new gnosis.
The new gnosis is transcendental knowledge and also self-knowledge, a total union of opposites and a mother or universal language.

✲ It is a para-spiritual language.
MENTAL is not a spiritual language, but it presents many analogies with the spiritual world, since it refers to the ineffable, to truth, to the transcendent, to freedom and to conscience.

✲ It is an initiatic language.
To know MENTAL is to make an inner journey to the universal center, where everything is connected and where consciousness, truth, simplicity, freedom, power, abstraction, creativity, wisdom and transcendence reside. One achieves an awareness that allows one to contemplate all of reality as a manifestation of the same thing.

✲ It is a language of the New Age.
Because the New Age movement, like MENTAL, advocates a new unifying consciousness, a global and holistic vision of reality based on the search for the ultimate essence that connects all things.

✲ It is a language of the third culture.
Computer science has been considered the paradigm of the third culture, as it has its roots in both scientific (mathematics, logic, linguistics, etc.) and humanistic (psychology, philosophy of mind, etc.) disciplines. But today computer science has been replaced by Cognitive Science, a science (or meta-science) composed of 6 sciences (the so-called "cognitive hexagon"): linguistics, psychology, neurology, philosophy, anthropology and artificial intelligence. Its objective is the study of the human mind. However, it is an integration of different sciences. MENTAL brings, on the other hand, a unification. MENTAL is the foundation of Cognitive Science.

✲ It is a transdisciplinary language.
MENTAL is a language that blurs the boundaries between different disciplines:
  • It transcends formal sciences: mathematics, computer science, logic, linguistics, artificial intelligence, systemic, etc.

  • It transcends the humanities: philosophy (philosophical categories, global ontology, possible worlds, dialectics, Platonism, etc.), psychology (archetypes of consciousness, models of the mind, etc.).
✲ He is a "general problem solver".
With MENTAL problems are clarified, solved or simplified. All problems are of mental origin and from the deep level of consciousness all problems are seen as the same problem. "Look deep into nature and then you will understand everything better" (Einstein).

✲ It is a "theory of everything".
The progress of science has always been along the lines of further generalization and universalization. Its main current manifestation is the search in physics for a final theory, a "theory of everything", whose greatest exponent is "string theory", in which the concept of dimension plays a major role. But it is not really about "everything", since it only tries to explain physical phenomena. MENTAL transcends the physical to contemplate the essence of everything, including possible worlds.

✲ The Tao of MENTAL.
There are analogies between MENTAL and the Tao. The Tao cannot be expressed, as MENTAL; it can only manifest itself as particular expressions.


Comparisons

From their respective points of view, scientists, philosophers, linguists, psychologists and mathematicians have speculated about the possibility of the existence of a universal paradigm and a universal formal language for science and even for philosophy. Numerous proposals have been made throughout history, but none have been consistent and complete.

MENTAL is the answer to this search, a simple, open, flexible, creative and profound language of consciousness from which to contemplate the unity of all things. MENTAL participates, to a greater or lesser extent, in all the universalist ideas that have existed throughout history:
Conclusions

As a consequence of all the above-mentioned properties of MENTAL, we can draw the following conclusions:


Dissolution of borders

With MENTAL the boundaries of the different formal sciences and thus their corresponding "egos" dissolve. In this sense, for example, there is no essential difference between applications, new language specification, operating system, Semantic Web, databases, artificial intelligence, etc. With MENTAL everything is the same thing because everything shares the same essence.


Universal convergence

In the deep resides consciousness, truth, simplicity, freedom, power, abstraction, creativity, wisdom and transcendence. The deep is the world of all possibilities and where everything is connected.

In MENTAL all universals converge. It is a universal language, a universal paradigm, a universal grammar, a universal science, a universal model of the mind, a universal computational model, etc. It is a universal "linguistic turn".

MENTAL is the answer to the problem of the hypothetical universal formal language based on consciousness, where everything converges: In short, MENTAL is a universal paradigm, an essential and unified way of contemplating reality.

We have contemplated reality from different paradigms. From the essential unity there are no particular paradigms, but only one way of seeing the world: the universal or absolute paradigm from which all particular paradigms are derived.

Kant, with his "Copernican revolution", postulated that the universal and the foundation of everything was based on the mind. The universal principle of economy demands that the internal world and the external world have the same foundation.


A universal standard

MENTAL opens the door to the standardization of the semantics of formal languages, as a semantic grammar, in the same way that formal grammars have made it possible to standardize syntax. Its simplicity of use makes it an ideal candidate to be a "popular" semantics.

There are powerful reasons why MENTAL should be declared a standard language. We highlight mainly:
  1. Because it is the language of consciousness.
  2. For its universality.
  3. For its simplicity.
  4. By the union of opposites or duals.
Decimal numerical notation (Indo-Arabic) is currently the only language that can be considered a universal standard. MENTAL can extend this standard and be the new universal language for science.

The digital revolution has allowed the implementation of all types of content (text, images, graphics, sound, video, etc.). MENTAL represents a conceptual revolution as it allows to represent all types of contents through its semantic-syntactic structure, which represents a "semantic ascent" with respect to the simple linear structure of the digital, which requires an interpretation.


Troubleshooting

From the level of supreme simplicity and abstraction, from the language of consciousness, problems are clarified, solved or simplified. The problems not only of the formal sciences, but also the philosophical and psychological ones. The problems that were not solved were not solved because they had been approached from the same level as the problem. To solve a problem, you have to look at it from a higher point of view. "No problem can be solved from the same level of consciousness that created it" (Einstein).

In fact, we can say that there is only one problem: finding the archetypes of the consciousness and their language. Once identified, everything becomes simpler. This strategy has led to clarify, simplify or solve many problems.

From the privileged (deep) point of view of MENTAL, problems of all kinds are clarified, simplified or solved, among themselves: In short, MENTAL is a Copernican cognitive revolution, basing everything on the archetypes of consciousness. MENTAL is the "master key" that opens all doors.