MENTAL, THE INTEGRAL UNION OF OPPOSITES

"Nothing exists except in relation to its opposite" (Paul Twitchell).

"There is union between the internal and external world, therefore I am" (Rodolfo Llinás).

"Both myth and science are structured by pairs of logically related opposites" (Lévi-Strauss).

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Opposites, Complementary and Dual
We must differentiate between opposite (or contrary), complementary and dual elements:

• Opposites are different elements of the same level and symmetrical with respect to a third central element. Together they cancel each other out and produce a null, empty or higher element. This element symbolizes or represents consciousness because it is undifferentiated and refers only to itself. Examples:
  
  
  • The numbers +3 and −3 are symmetrical with respect to zero and together (added) give zero.
    
    
  • An electron (negatively charged) and a positron (positively charged) when colliding produce energy in the form of gamma rays, a high-energy electromagnetic radiation.
    
    
  • Future and past. In the "now" resides consciousness, where past and future meet, where there is no time.
  
  
• Complementaries are components of the same entity that when united give rise to that entity. If that entity is of a universal type, it also symbolizes consciousness because it represents totality. Examples:
  
  
  • Internal world and external world.
    
    
  • A set C and its complementary C'. Together they give the universal set: C∪C' = U (universal set).
    
    
  • The empty set ∅ and the universal set U: ∅∪U = U.
  
  
• Duals of horizontal type are two aspects or manifestations of the same entity or concept, or two entities that can be transformed into each other. Example:
  
  
  • In Platonic solids, the cube and the octagon are dual. So are the icosahedron and the dodecahedron. The tetrahedron is dual of itself. A polyhedron can be transformed into its dual. The union of cube and octahedron, as well as the union of icosahedron and dodecahedron are symbols of consciousness. The union of two tetrahedra opposite each other forms a three-dimensional Star of David which is a symbol of pure consciousness, the consciousness that is only aware of itself. It is also a symbol of the soul (Merkaba).
  
  
• Vertical type duals are two concepts, one being superior to the other or one is the particularization or manifestation of the other. Examples:
  
  
  • Semantics and syntax. Semantics is superior to syntax: the same semantics can be manifested or expressed in different ways.
    
    
  • Simplicity and complexity. Simplicity is superior to complexity: from simplicity emerges complexity.
    
    
  • Continuous and discrete. The continuous is superior to the discrete: the continuous manifests itself as discrete.
    
    
  • Theory and practice. Theory is superior to practice: practice is the application of theory.

In general, we can speak only of "opposites," since complementaries and duals are really types of opposites, and because consciousness transcends, connects, and unifies them.


The 12 Pairs of Opposite Primitives of MENTAL
MENTAL's primitives are structured in 12 pairs of opposites or duals:

Nº	Primitive	Opposite
1	Parameterized Generalization	Non-Parameterized Generalization
2	Qualitative Particularization	Quantitative Particularization
3	Parallel Grouping (Set)	Series Grouping (Sequence)
4	Full Distribution	Linear Distribution
5	Potential Substitution	Actual Substitution
6	Equivalence	Opposite Equivalence
7	Evaluation	No Evaluation
8	Adition	Subtraction
9	Condition	Opposite Condition
10	Ascending Hierarchical Access	Descending Hierarchical Access
11	Start Execution	Finish Execution
12	Continue Process	Stop Process

The "Primitive" column can be identified with the consciousness associated with the right hemisphere of the brain (HD), i.e., deep, general or higher. The "Opposite" column can be identified with the consciousness associated with the left hemisphere (HI), i.e., superficial, particular or lower.

• Parameterized Generalization is more general than Non-Parameterized Generalization.
  
  
• Qualitative Particularization is more general than Quantitative Particularization.
  
  
• Parallel Grouping (Set) is profound because it indicates simultaneity. Serial Grouping (Sequence) is shallow because it indicates linearity.
  
  
• The Full Distribution is more general than the Linear Distribution.
  
  
• Potential Substitution is deeper and more general than Actual or Immediate Substitution, which is superficial and particular.
  
  
• Ascending Hierarchical Access is superior to Descending, which is more detailed.
  
  
• The rest of the primitives are pairs of opposite primitives.

The Implied or Derived Pairs of Opposites in MENTAL
MENTAL is the integral union of opposites, starting with the primitives themselves.

MENTAL unites dual disciplines, such as mathematics and computer science, arithmetic and algebra, algebra and geometry (geometric algebra). Geometric algebra is a geometrically inspired algebra. Mathematics is associated with the descriptive, the logic of deduction and theorems. Computer science is associated with the operational, the logic of decision and problem solving.

Pairs of explicit opposites are the primitives of MENTAL. The implicit or language-derived opposites are as follows:


General aspects

• Superficial - Deep. O Manifest - Not manifest. O Expressible - Not expressible.
  These two aspects (and their equivalents) constitute the essence of language. The deep are the primitives, which are inexpressible. Only its particular (superficial) manifestations are expressible.
  
  
• Necessity - Possibility.
  MENTAL is a necessary language; semantic primitives cannot be obviated. MENTAL is the Magna Carta of possible worlds.
  
  In MENTAL, what is necessary is operationally implemented by means of generic expressions. What is not restricted by the necessary is the possible.
  
  
• Maximum - Minimum.
  Language achieves maximum expressiveness with minimum conceptual resources. "Less is more" (Mies van der Rohe).
  
  
• Intensive - Extensive.
  An intensive expression is one that refers to several expressions, and is defined by a parameterized generic expression. An intensive expression can describe several (or infinite) concrete expressions or other intensive expressions of lower order.
  
  
• Absolute - Relative.
  The relative appears in expressions of qualitative and quantitative particularization. What is not relative is absolute.
  
  
• Abstract - Concrete.
  MENTAL is an abstract language that manifests itself in concrete expressions.
  
  
• Abstraction - Reification.
  Reification is the opposite process of abstraction and is the transformation or conversion of an abstract mental content (an idea or a concept) into something concrete that can be represented and manipulated, with the same status as an ordinary object. With MENTAL, concepts such as the imaginary, the diffuse, the shared, the infinite, the infinitesimal, etc. are reified.
  
  
• A priori - A posteriori.
  MENTAL is an a priori language because the primitives are innate. MENTAL can also be considered an a posteriori language because it is the result of abstraction from reality.
  
  
• Natural - Artificial.
  The boundary between the natural and the artificial is blurred because both domains share the same primary archetypes. They are manifestations of the same archetypal language.
  
  
• Invention - Discovery.
  At the semantic level, MENTAL is the discovery of a coherent set of abstract concepts that constitute a formal language. These concepts are the primary archetypes, that is, the archetypes of consciousness present in all things. At the syntactic level it is an invention, since it uses a specific notation.
  
  
• Science - Humanism.
  MENTAL is a language of the so-called "third culture" (according to the denomination of Charles Percy Snow, 1959), a language that is both scientific and humanistic. It is scientific because it is a language that is applicable to the formal sciences (mathematics, computer science, artificial intelligence, cybernetics, systemics, etc.). It is humanistic because the universal semantic primitives are very simple and intuitive, and are philosophical categories and archetypes of consciousness. With MENTAL the cryptic and dehumanized language of traditional mathematics ends and becomes an easily understandable language.
  
  
• Simplicity - Complexity.
  MENTAL is a simple language and the foundation of complexity. Complexity appears when simplicity is applied successively or recursively. The essence of complexity lies in simplicity. In the deep lies simplicity. In the superficial appears the complex. Complexity is only apparent and is the result of the combinations of the simple. The greater the combination, the greater the complexity.
  
  
• Static - Dynamic.
  MENTAL is a language that allows to describe static expressions (that are self-evaluating), and dynamic expressions that are not self-evaluating, that is, they are evaluated as a different expression.
  
  
• Active - Passive.
  MENTAL is a language that contemplates active and passive expressions. A passive expression is one that does not alter other expressions. An active expression is one that alters other expressions.
  
  
• Generic - Specific.
  MENTAL allows you to specify generic (parameterized or not) and specific (non-generic) expressions.
  
  
• Exact - Fuzzy.
  Fuzzy expressions are those with fuzzy or ambiguous semantics, such as: tall, rich, good, fast, etc. Exact expressions are those that have a clear meaning, such as: 34, meter (the unit of measurement), etc. There are also mixed expressions:
  
  
  exact-exact: 3*meter
  exact-fuzzy: 0.3*height
  fuzzy-fuzzy: blue/light
  
  MENTAL goes beyond fuzzy logic, as the concept of fuzziness applies to all kinds of expressions, not just logical ones.
  
  
• Existence - Non-existence.
  These two concepts are represented by the meta-expressions α and θ, respectively. They are also the two branches of the primitive Condition.
  
  
• Qualitative quantities - Quantitative quantities.
  13*Kgr is a quantitative quantity. The factor can be any and is applied to a quantitative unit. 0.6*high is a qualitative quantity. The factor is between 0 and 1 and applies to a quality.
  
  
• Real - Virtual.
  MENTAL contemplates real and virtual expressions. Virtual expressions are those that are defined from real expressions.
  
  
• Reductionism - Holism.
  MENTAL is a reductionist language because it is based on a reduced set of semantic primitives. MENTAL is holistic because these primitives are of a universal type and underlie the totality of what is expressible.
  
  
• Theory - Practice.
  MENTAL is a theoretical language, independent of its possible implementations. At the same time, it is a practical language. Both are linked and are two poles of the same thing. As such a theoretical language, it is not expressible. Only its manifestations, the practice, the concrete expressions, are expressible.
  
  
• Base level - Target level.
  The link between the base level and the target level is made through generic expressions. There may be hierarchical target levels.
  
  
• Sacred language - Profane language.
  MENTAL is a sacred (or initiatory) language because it connects us with the essence of reality, both externally (physical) and internally (mental). It allows us to perceive reality from a holistic point of view, which makes us more aware of the essential unity of all things.
  
  MENTAL is a lay language because it can be used for practical purposes, to encode and process data, information and knowledge. In this task we are connecting or projecting the universal over the particular, the intuitive over the rational. As a sacred language it is inexpressible. It is only expressible in its practical application, as profane language.
  
  
• Abstract space - Abstract time.
  The structure of abstract space is the same as that of abstract time: it is linear (sequence) or parallel (set). Abstract time is associated with the process of evaluation of expressions.
  
  
• Local - Non-local.
  In abstract space, local is between the components of an expression. In unrelated expressions there are no distances, everything is non-local. Non-local means that relationships can be established between any expressions in abstract space. Non-local expressions are related to each other by means of generic expressions, such as, for example, shared expressions (linked, interlinked, etc.).

Matemática

• Formalism - Intuitionism.
  MENTAL integrates and harmonizes the most important approaches to the foundations of mathematics: the intuitionist and the formalist.
  
  
  • It is intuitionist because it makes use of primitive concepts of an intuitive and universal type. These primitive concepts make it possible to construct and describe expressions, thus generalizing and qualifying the assertions of the intuitionist school.
    
    
  • It is formalist because it uses generic axioms and theorems, relative to the relations between primitives, which are not specific to any particular domain. In this sense, MENTAL can be considered a universal axiomatic system.
  
  
• Mathematics - Metamathematics.
  MENTAL is the foundation of mathematics, and that foundation is philosophical, for the primitives are philosophical categories. Therefore, it is no longer necessary to do philosophy of mathematics because the foundation of mathematics is philosophical.
  
  
• Arithmetic - Algebra.
  The same arithmetic operations apply to numbers and variables. They serve, for example, to add numbers and to add variables. For example, 3+4 is an arithmetic operation, and (3*x + 4*x) is an algebraic operation. Arithmetic is a particular case of algebra when the variables are equal to unity.
  
  
• Finite - Infinite.
  All MENTAL expressions represent or describe finite or infinite expressions. For example, {⟨ n ← n>3) ⟩} is a finite expression describing the infinite set {4, 5, 6, ...}. Infinity is defined by recursive potential substitution.
  
  
• Infinitely small - Infinitely large.
  The infinitely small is the infinitesimal (ε). The infinitely large is the numerable infinite (∞). Both are derived concepts.
  
  
• Real - Imaginary.
  There are real and imaginary expressions. Imaginary expressions are linked to substitution expressions, where the left-hand side is not a variable name. For example, the definition of the imaginary unit (i*i = −1) or the definition of infinitesimal (ε*ε = 0).
  
  
• Discrete - Continuous.
  The continuum is inexpressible because it is at a deep level. It can only be expressed through the discrete, the superficial, which are the points and the rational numbers of the real line. The continuous is not formed by points, but manifests itself as points.

Computer Science

• Operating language - Descriptive language.
  There is a long-standing controversy over whether programming languages should be descriptive or operational (or procedural). This controversy has been diluted in favor of mixed languages, that is, languages that have some descriptive and some operational components. But usually both components are separate and distinct and not integrated into a common linguistic structure.
  
  In MENTAL, this distinction is diluted, since it contemplates both aspects with the same linguistic structures. In artificial intelligence, it unifies descriptive (Prolog-like) and operational/functional (Lisp-like) language.
  
  MENTAL also unites operational (or computational) complexity and descriptive complexity.
  
  
• Source code - Object code.
  MENTAL is a compact language because it is a symbolic language that does not use keywords, without losing readability. This feature makes it possible to consider the source code and object code as unified. In virtual machines it can act as pseudo-code or intermediate code between the source language and the real machine code. In this sense, MENTAL can be considered a universal code.
  
  
• Data - Processes.
  In almost all programming languages, data and processes are clearly differentiated. In MENTAL, all expressions are evaluated. Data are self-evaluating expressions.
  
  
• Static semantics - Dynamic semantics.
  MENTAL unites static semantics (the semantics at compile or interpretation time) and dynamic semantics (the semantics at runtime).
  
  
• Data - Metadata.
  A metadata is a data or attribute assigned to a data. In MENTAL this is done by means of a particularization. The result is another data, so the distinction between data and metadata is diluted. For example, blue/dark.
  
  
• Quantitative variables - Qualitative variables.
  A quantitative variable takes a specific numerical value. A qualitative (or linguistic) variable takes qualitative values. For example, the variable "age" can take the values "very young", "young", "middle-aged", "old" and "very old".
  
  
• Databases - Knowledge Bases.
  Database management systems (DBMSs) are evolving into knowledge base management systems (KBMSs), which go beyond mere data repositories to incorporate some associated intelligence. And artificial intelligence systems increasingly have particular knowledge (data or instances) storage and processing needs.
  
  MENTAL allows to specify traditional databases and knowledge bases used in artificial intelligence.
  
  
• Contents - Continent.
  In traditional programming languages a distinction is made between content of a memory location and its address. In MENTAL a name can be considered equivalent to an address (or container) to which its content is associated. For example, in (x° = x+1):
  
  
  x° (which evaluates to x) is equivalent to the address (or continent)
  x is the value (or content)
  
  For reasons of syntactic simplification, it is assumed that this expression is equivalent to (x = x+1)
  
  Content can be associated with shallow, and direction with deep.
  
  
• Direct and inverse evaluation.
  The normal evaluation of an expression is direct evaluation. Inverse evaluation is tied to potential substitution expressions. For example:
  
  
  (x° = 3)
x // ev. 3 (direct evaluation)

(x° =: a) // x stands for "a".

a // ev. x (inverse evaluation)
  
  
• Internal (programmer's) language - External (user's) language.
  In MENTAL, the internal and external language is the same. The user is just another agent of the system that interacts with the environment (the abstract space). It is like another expression that interacts from the outside modifying contents of the environment. The input and output of a program are expressions. This implies great possibilities of interaction with the environment. If the user knows the program's code, he can interact with it, modify it, add new functionalities, etc. This means total flexibility.
  
  MENTAL, being a simple language, is within the reach of both the programmer and the user. The boundary between the two is blurred.
  
  
• Low-level and high-level language. Or programming language and specification language.
  The same language is applied for high-level (general type) and low-level (detail) developments. MENTAL is both a high-level and a low-level programming language.
  
  Programming is the detailed part of a program. Specification is the general. MENTAL unifies specification and programming in such a way that it allows for high-level specification (the "what"), while allowing for low-level specification, the detail (the "how").
  
  
• Internal memory - External memory. Or variables - Files.
  All expressions created by a MENTAL application are kept in abstract space and do not disappear after execution unless explicitly deleted. Where expressions reside (internal or external memory) is an irrelevant implementational aspect. In traditional programming languages, elements that are not explicitly "saved" on an external storage device are lost at the end of program execution or when the computer is turned off. This is the opposite of what happens in the real world, where objects persist. Moreover, persistence has always been associated with data. In MENTAL, persistence applies to all expressions.
  
  The traditional division between variables and files is a reflection of implementer aspects: the existence in computers of two types of storage: primary or main memory (RAM) and secondary (external) memory. Traditionally, the way of managing data in memory (internal data) is different from the way of managing data stored in external devices (external data), for example, with a DBMS (Database Management System). The expression "impedance mismatch" has been coined to reflect this lack of correspondence or analogy between the programming language and the DBMS language, a mismatch that disappears in MENTAL.
  
  
• Interactive processes - Batch processes.
  MENTAL code can be executed as commands in an interactive environment or as batch processes. And to chain processes together you do not need a scripting language, as it is the language itself that acts as a link.
  
  
• Sequential processes - Parallel processes.
  With MENTAL no special instructions are needed to program parallel processes. The Sequence primitive allows you to describe sequential processes, and the Set primitive allows you to describe parallel processes.
  
  
• Programming - Metaprogramming.
  Metaprogramming is programming that generates programs, that is, it is code that when executed produces other code. As in MENTAL the distinction between code and data is diluted, the distinction between programming and metaprogramming is also diluted.
  
  
• Operating System - Applications.
  MENTAL, besides being an application and language development language, can be considered the foundation of every operating system. Actually, MENTAL can be considered the real operating system-descriptive of the internal and external reality.
  
  
• Hardware - Software.
  With MENTAL we are closer to the possibility that hardware and software speak the same language, i.e. that the set of universal semantic primitives is also the hardware instruction set.

Artificial Intelligence (AI)

• Mind - Computer.
  MENTAL is a metamodel of the mind in the sense that it is not a concrete model, but is a set of degrees of freedom, which are the archetypes of consciousness. It is also a generic computer model. The mind is like a computer of 12 pairs of "instructions".
  
  
• Strong AI - Weak AI.
  Strong AI admits that it is possible to construct an artificial mind. Weak AI admits that only simulations of the mind are possible.
  
  By using primary archetypes we are accessing the maximum possible AI, so both types of AI are unified.

Linguistics

• Syntax - Semantics.
  There is a biunivocal correspondence between syntax and semantics. Given the syntax, you get the semantics, and vice versa. They are two sides of the same coin. Syntax is minimized and reduced to the simplest and most essential forms.
  
  
• Syntactic grammar - Semantic grammar.
  A syntactic or formal grammar of a language is a metalanguage that specifies or describes the syntax (the form) of the different elements of that language. It is based on abstract categories that make it possible to define the structure of the language.
  
  A semantic grammar is structured and organized on the basis of combinations of lexical categories, i.e. on concrete concepts or categories relating to a domain.
  
  In MENTAl, syntactic grammar and semantic grammar are united as two sides of the same coin. Given a form (a given expression) its semantics is inferred, and given a semantics its syntax is inferred.
  
  
• Language - Metalanguage.
  MENTAL is a universal language, but it is also a universal metalanguage, since it allows defining particular languages by means of their corresponding grammars. MENTAL is the foundation of all formal languages.
  
  
• Meaning - Denotation.
  Every linguistic expression has two aspects or dimensions: its meaning and its denotation (or reference). The meaning is the idea associated with the expression, its understanding, its epistemological or cognitive content. The denotation (or reference) is the object (or objects) to which the expression refers, which can be itself.
  
  In MENTAL meaning and denotation are closely linked. The meaning of an expression is determined by the semantic primitives used. The denotation is the expression itself. Both are aspects of the same thing. In natural languages denotation refers to the real world. In MENTAL the denotation refers to expressions of abstract space, although they may represent entities of the physical or mental world.
  
  
• Operators - Delimiters.
  MENTAL uses operators and delimiters. Operators are internal: they join arguments. Delimiters are external: they group arguments.
  
  
• Lexical semantics - Structural semantics. The semantics of a language has two main aspects or dimensions:
  
  
  1. Lexical semantics. It refers to the meaning of each of the language primitives.
     
     
  2. Structural semantics. Refers to the meaning of the combinatorial mechanisms that apply to the primitives.
  
  In the case of MENTAL, the structural semantics is the same as the lexical semantics, i.e., the combinatorial patterns of the primitives are the primitives themselves.
  
  
• Signs - Symbols.
  MENTAL is a language that uses a notation that is halfway between symbols (which do not require interpretation) and signs (which do).

Philosophy

• Analytic Philosophy - Synthetic Philosophy.
  Analytic philosophy is a way of doing philosophy based on the analysis of the language in which philosophical problems are formulated. Synthetic philosophy is based on the overcoming of dichotomies or oppositions by means of their union or synthesis, a synthesis that can be ascending (Hegel) or descending (Leibniz). With MENTAL it is possible to make philosophical reflection because it is a language that is both analytical and synthetic.
  
  
• Platonic language - Aristotelian language.
  MENTAL is an ideal or Platonic language because the primitives correspond to the higher world of ideas, that is, they are innate, a priori (prior to experience), transcendental, universal, eternal, intuitive and immanifest. But it is also a realistic or Aristotelian language, in the sense that it is also a real, concrete and practical language.
  
  
• Realism - Idealism.
  Realism is the doctrine which holds that objects perceived by the senses have an existence independent of the perceiving subject. Idealism is the doctrine that holds that reality is fundamentally mental. From MENTAL the inner (mental) world and the outer (physical) world are contemplated as manifestations of the same primary archetypes.
  
  
• Realism - Nominalism of universals.
  A universal is a class or category of objects that share one or more properties. At the philosophical level, the main problem that arises with universals is their ontological status, i.e., whether universals really exist or are just names that are assigned to classes of objects. The semantic primitives of MENTAL are universals are real because the universal is more real than the particular and because everything particular is grounded in the universal.
  
  
• Horizontal Dialectic - Vertical Dialectic.
  The vertical dialectic is that which relates universal semantic primitives (of an intuitive nature) to particular expressions which are manifestations of these primitives. The horizontal dialectic is that which relates expressions to each other.
  
  
• Ontology - Epistemology.
  Ontology is a branch of metaphysics that studies the nature of being, the essence of things. Epistemology is a branch of metaphysics that studies the nature of knowledge. The internal and external worlds are governed by the same primary archetypes. Einstein said: "The most incomprehensible thing about the world is that it is comprehensible". The explanation is simple: because ontology and epistemology share the same primary archetypes. That is why reality is intelligible.

Logic

• Decision logic - Logic of inference (or deduction). Or Material implication - Logical implication.
  In MENTAL, logic is represented by the primitive Condition, which can be either material (or particular) implication or logical (or general) implication. The material (shallow) implication corresponds to the "condition" (if ... then ... else ...) of imperative programs. The logical (deep) implication corresponds to the inference made when the condition is specified by a generic expression.

Psychology

• Outer world - Inner world. U Objective - Subjective.
  The boundaries between the internal (the mental) and the external (nature), as pursued by the ancient alchemists, fade away. The primary archetypes of MENTAL are present on the physical plane and on the mental plane.

Metaphors

• Fox - Hedgehog.
  MENTAL unites the psychology of the fox and the hedgehog in the metaphor expressed by Archilochus: "The fox knows many things, but the hedgehog knows only one great thing". The fox knows many things, many particular details. The hedgehog knows only the most important and fundamental: the global, the general. These metaphors represent the two modes of consciousness. MENTAL unites or connects both aspects: the universal (symbolized by the hedgehog) and the particular (symbolized by the fox).

☆☆☆
In short, MENTAL unites all possible opposites, which justifies its qualification as "language of consciousness". MENTAL is a paradigm and a universal language that unites all opposites and from which the essential unity of all things is contemplated,

Some of the above points are expanded upon in the following chapters of this section.