"Meaning is a pre-scientific concept" (Hilary Putnam).
"No consistent language can contain the necessary means to define its own semantics" (Tarski).
"Linguistics is a branch of cognitive psychology" (Noam Chomsky).
Semantics
Semantics is a branch of linguistics that deals with meaning in language. Its origin dates back to the writings of Plato and Aristotle. Since then it has constituted one of the permanent topics of reflection by, not only linguists, but also philosophers, psychologists and logicians.
The term "semantics" was introduced in 1897 by the French linguist Michel Jules Alfred Bréal with the publication "Essay on Semantics". In this work he defines semantics as "the science of meaning". Bréal is considered the founder of modern semantics.
"Meaning" is something more general than "semantics." Semantics is the meaning of linguistic expressions. Semantics is a kind of meaning. But according to Bréal's definition, semantics is the science of meaning, so the term "semantics" is often identified with meaning in general.
According to the traditional conception, semantics establishes the relationship between language and reality, that is, between the linguistic and ontological levels. The meaning of a linguistic expression is the reality to which it refers. This meaning can be true or false, depending on whether or not it corresponds to reality.
Semantics is a young science that was born late compared to syntax, another branch of linguistics. But since the second half of the 20th century the situation has changed and semantics has evolved greatly, becoming the branch of linguistics that has attracted the most interest. "The very essence of linguistics is the search for meaning" (Benjamin Lee Whorf). The process, however, remains slow because of its apparent complexity. There is a wide variety of proposals, methods and points of view, which has led to talk of "the linguistic semantics".
Lexical and structural semantics
Natural language semantics deals with the meaning of words and how they combine to form meaningful sentences. Generalizing to all kinds of languages, semantics studies the meaning of linguistic signs and their combinations. In this sense, a distinction must be made between:
Lexical semantics. This is the semantics associated with the words of the language or with linguistic signs in general.
Structural semantics. This is the semantics associated with the combination of words (or linguistic signs) to form sentences (or linguistic expressions in general).
An important concept −that was first studied by Frege− is the so-called "compositional semantics" (or compositional principle): the meaning of a linguistic expression is a function of its components (lexical semantics) and their relations (structural semantics).
Meaning and reference
Frege is considered the pioneer in modern thinking about language by distinguishing between sense and reference. Sense is the form of a linguistic sentence or expression. The reference (or referent) is the object to which the sense refers.
There are expressions that have both sense and reference. For example: "Madrid" and "the natural number that follows 3".
There can be expressions with different senses and the same reference. For example, "Cervantes" and "The author of Don Quixote".
There are expressions that have sense but no reference. For example: "the greatest even number", "Don Quixote", prepositions (with, since, from, towards, on, etc.), conjunctions (and, or, or, nor, etc.), etc.
There are expressions with the same meaning and different referents. For example, pronouns (I, you, you, we, etc.).
Aspects of semantics
Since semantics is tied to language and there are many types of languages, there are different semantics. Additionally, if we interpret semantics as meaning in general, there are different interpretations according to the field to be considered: natural semantics (linked to natural language), mathematical, functional, procedural, operational, descriptive, algebraic, axiomatic, relational, computational, logical, denotational, representational, intensional, extensional, extensional, combinatorial, generative, dynamic, conceptual, interpretative, psychologistic, cognitive, fractal, etc.
There are semantics that are easier to understand by observing their effects at a superficial level. For example, semantics linked to operations and their results.
In the face of these particular semantics, the question arises as to the possible existence of a general or universal semantics, from which particular semantics can be derived.
The syntax-semantics duality
Every language (natural or artificial) has two essential components: syntax and semantics. The syntax of a language is the external, superficial, visible part. Semantics is the internal, deep, hidden part, the meaning.
Syntax has been approached by linguistics because it is the easiest and most accessible part. Semantics, on the other hand, has been considered as something unapproachable, because it belongs to the inner world, to the world of the mind and consciousness. Because of its intrinsic difficulty, semantics has been practically ignored. The problem of meaning is, together with consciousness, one of the Gordian knots of the philosophy of mind.
The behaviorism-mentalism duality
The problem of syntax-semantics duality is reflected in the behaviorist and mentalist streams of psychology.
According to the behaviorist psychology of John B. Watson and Burrhus Skinner, any psychological study must be based exclusively on observable human behavior. At the linguistic level, behaviorism takes the form of empiricism, the mere observation of verbal behaviors, rejecting all postulates about internal mental states and mechanisms governing such behaviors.
The empiricist linguist refuses to deal with meanings or mental entities. Meaning is something unclear, too diffuse, so it cannot be included in a rigorous science of language. Meanings are only patterns of behavior determined by stimulus-responses.
Mentalism is the opposite position to behaviorism. For mentalism, what is important are mental states and processes, the internal, with external behavior being the reflection of the internal. It is the naturalistic approach to language: the study of the mind as a component of the natural world.
For many years, the only model of the mind was behaviorism, a model based exclusively on externally observable, superficial behavior. The mind as a "black box" that cannot be accessed. Only the inputs (the stimuli) and the outputs (the responses) can be studied.
The modern conception of linguistics is to consider it as a branch of cognitive psychology. Cognitive psychology (or cognitivism) claims the mind as the object of study of psychology. According to cognitive psychology, thought is prior to spoken language. The external is the manifestation of the internal. Language is the manifestation of thought.
Structuralism
Ferdinand de Saussure is the originator of structural linguistics, a scientific model of language. Saussure is considered the founder of modern linguistics:
A distinction must be made between "speech" and "language", i.e. between language as a particular activity and language as a general structure.
"Linguistics has as its only true object language, considered in itself and by itself" (Curso de Lingüística General). Language is a theoretical entity to be studied as an immanent structure.
The essential dichotomy is that of substance and form. Substance is the concept, the internal aspect. Form is the external aspect. Only the formal aspects can be studied. Substance is not linguistics. Language is a form and not a substance.
Every language is a structure or system of interrelated signs. Signs have a dual nature: the signifier (the form, the external representation) and the signified (the internal representation, the concept, the interpretation or mental reality). The signifier is arbitrary. What is important is the signified, the semantics. There is no intrinsic relationship between form and meaning, as can be proven by the existence of the different languages.
The value of a sign (that which confers identity or specificity on it) resides in its relations with other signs. The properties of a language cannot be explained or described from its isolated elements (linguistic signs).
To study a language is to go beyond appearances and try to discover the hidden relationships, the structures of meaning.
The set of signs is governed by a set of syntactic, phonemic and grammatical rules.
Concepts are mental products (constructs) and not entities of the mind. Language is a social construct. Signs acquire their function through social interaction.
Language is only one among several sign systems, although it is the most important of these systems.
Saussure traced the general lines of the science that studies signs: semiology (or semiotics). With his theory of signs, he attempted to unite syntax and semantics, considering that every sign has two inseparable aspects.
The structuralist movement
The structuralist movement began with Saussure's linguistics and subsequently spread to other fields, mainly anthropology and philosophy. Structuralism is a method of understanding reality, a universal paradigm, whose general principles are as follows:
Every object is part of an interrelated whole (or structure) that must be known as a whole and not fragmented.
All surface structures (society, human behavior, language, myths, etc.) are based on the same deep structures.
Meaning is found in the relationships between things, rather than in isolated or independent things. That is, primacy is given to pattern, to structure, rather than to substance.
It is necessary to describe this deep reality by means of a language based on universal structures. These deep structures are assimilable to universal archetypes. They are universal because they manifest in all domains.
All systems that constitute a structure are linguistic systems. Every structure is linguistic.
Syntaxcentrism
This term refers to the historical priority given to syntax over semantics, whose main referents were Leonard Bloomfield and Noam Chomsky. Both promoted a meaningless linguistics by giving priority to syntax to the detriment of semantics, of "absolutizing" syntax.
Bloomfield is the forerunner of syntaxcentrism and the leading representative of the empiricist tradition of linguistics. He argued that only direct observation of linguistic events could provide knowledge about language. Bloomfield worked on morphology and syntax, ignoring semantics. He defined himself as an anti-mentalist. In his work "Language" (1933) he adopts the psychological framework of Watson's behaviorist school and rejected what was not "directly observable" for linguistic analysis. For Bloomfield, the mentalist position on linguistic meaning is "unscientific." He considered the word "mentalism" as something close to esotericism and "meaning" as something outside the scientific realm.
Noam Chomsky claimed the autonomy of syntax in linguistic studies, which gave a decisive boost to syntaxcentrism in linguistics. Semantics took a back seat. Chomsky, with his generative grammar, was the driving force behind formal syntax, without any reference to meaning. His work "Syntactic Structures" (1957), based on his doctoral thesis "Logical Structure of Linguistic Theory", revolutionized theoretical linguistics by introducing the concept of "generative grammar", a system that makes it possible to describe infinite sentences by means of a finite set of formal syntactic rules. This revolution paralleled in time the revolution in analytic philosophy with the "linguistic turn" in philosophy.
Prior to the publication of Chomsky's 1957 work, most linguists followed structural linguistics, based on the analysis, classification and description of the different elements of human languages (phonemes, morphemes, etc.), using objective methods. With Chomsky came the revolution, a paradigm shift based on the synthesis of language.
Today, the formalization of the syntax of languages is a task that is considered to be completed.
Chomsky applied in his syntactic theory certain structuralist intuitions by understanding language as a closed system formed by a finite number of rules that allowed to formally describe the infinite possible sentences of a language. Although Chomsky initially ignored semantics with his generative grammar, he has subsequently tried to formalize it, but his results and conclusions have been of a general type. Chomsky's current position is that linguistics should be considered a branch of cognitive psychology.
Cognitive Science
Cognitive psychology is a science that studies cognition, that is, the mental processes or mechanisms involved in the elaboration of knowledge. This science is integrated within the so-called "Cognitive Science", together with artificial intelligence, linguistics, philosophy, neuroscience and anthropology. It is the so-called "cognitive hexagon".
From this new point of view, one can hypothesize about the underlying patterns responsible for behavior, make inferences, and so on. But the openness involved in including cognitive psychology also allowed mentalism to infiltrate, where internal processes were subject to all sorts of particular subjective interpretations.
Within Cognitive Science, different models of the mind or cognitive theories have been proposed, but among them two stand out: the symbolic model and the connectionist model.
The symbolic model of the mind
For the symbolist model, the mind is a system made up of symbols, and thoughts consist of the manipulation of those symbols, as in a computer. It is a computationalist model.
The best known symbolic model of the mind is the cognitive theory of the "language of thought" (mentalés), proposed by Jerry Fodor in 1975 [Fodor, 1985]: the mind is a system of symbols, and cognition is the manipulation of those symbols.
In favor of the symbolic model of the mind are:
The fact that many of our behaviors appear to be symbolic in nature, the most prominent being linguistic ability, along with logical and mathematical reasoning ability.
The development of artificial intelligence applications, which have proved successful through mere symbolic manipulation.
However, the symbolic model requires that all behavior be established explicitly, externally, superficially, in the form of rules, processes, event management, and so on. But mental phenomena there are no such explicit forms, but hidden and unknown internal mechanisms. The fact that a system behaves apparently as governed by a rule does not imply, nor can it be interpreted, that such a rule actually exists internally.
Cognitive Science has relied on the computationalist model of the mind. Our brain is like the hardware of machines. The mind is the software that processes information, encodes it and stores it inside the hardware that is the brain.
With this model, we have moved from "semantics" to "information" and from "semantic expressions" to "information processing". It all started with Boole with his "laws of thought", where language was based on binary logic and ignored meaning.
The connectionist model
A rival to the symbolic model of the mind appeared with Frank Rosenblatt [1962]: the connectionist model. It is based on a network of interconnected units with "weights" (numerical values), which represent the strengths of the connections between the units in the network:
Each unit is regulated by inputs and outputs. Each unit can be activated or inhibited.
The process is carried out in parallel, not in series, as in the symbolic model.
The information (or memory) is distributed over the different unit weights.
There is no central control unit. The process is performed in each of the units.
It is an input/output model. There is a global signal input to the network and a global signal output.
Computation is not governed by explicit rules.
Computation is purely quantitative. In the symbolic model the computation is qualitative.
The network is dynamic, it changes over time. The system moves from one state to another based on the modification of the weights and the activation or inhibition of each unit.
The system is adaptive. It is able to adjust its processing units to produce the required output. Learning consists of modifying the weights of the connections between the units.
This model of the mind provides at the same time a simplified model of the brain: cognition consists not in the manipulation of symbols, but in dynamic patterns of neural activity.
Connectionist systems are basically pattern-recognition learning models of data. They lack formal language and are limited to restricted categories of problems, so they do not constitute a generic or universal system applicable to all types of problems.
Furthermore, a connectionist system can be implemented by a symbolic system, so it is really a particular type of symbolic system. The symbolic model is more general than the connectionist model.
The formalization of semantics
Attempts to formalize the semantics of natural language began with Tarski, who tried to construct a logical structure of language that would allow the definition of concepts such as truth, meaning, synonymy, implicature, etc. He reached several conclusions:
It is impossible to formalize semantics. Trying to describe the semantics of a language in that same language is impossible. A higher-order language, a metalanguage, is needed.
It makes no sense to raise the problem of the coherence or incoherence of linguistic expressions.
The concept of truth (and other philosophical concepts) possesses a character relative to language. Truth is not absolute.
It is possible to develop a general semantics that could be applied to a wide class of particular languages.
Other authors:
Wittgenstein, in Philosophical Investigations, says that it is not possible to use language to teach language. It is not the same as using language to teach piano playing. To teach language you have to go outside language. Language cannot be studied with language itself, it has to be studied from a higher level: metalanguage. "It is impossible to describe the fact that corresponds to a sentence without repeating the sentence."
Haskell Curry introduced the idea of "U-language", as the language of underlying human communication that is mutually understood by the speaker and the hearer [Curry, 1950]. This language serves as a metalanguage, a language from which it is not possible to transcend and which cannot be described, defined or explained.
According to Hilary Putnam, meaning is not accessible to science because it is a pre-scientific concept. "The pre-scientific concept on which semantics is based the pre-scientific concept of meaning is much worse outlined than the pre-scientific concept of syntax" [Putnam, in "The Meaning of Meaning"]. Indeed, if science studies observable natural phenomena and their laws, semantics belongs to an internal realm (the mental), which is not observable.
For Jaakko Hintikka, the universalist conception of language implies the ineffability of semantics.
For Willard von Orman Quine, traditional semantics is mentalistic, since it claims to explain observable facts (linguistic behavior) by means of mysterious unobservable internal mechanisms (abstract entities, ideas, possible entities, etc.) whose existence cannot be experimentally verified. Semantics must abandon these unscientific explanations and focus on the observable: the behavior of speakers.
According to conceptual semantics, by Ray Jackendoff [1998], there is a correspondence between conceptual structure and syntactic structure: the structures that govern the construction of sentences and those that govern the construction of concepts are the same.
The problem of semantics in machines
A computer is a symbolic system, a machine that processes only symbols. The machine is a superficial, syntactic, formal device and, therefore, does not possess semantics. A machine, when it is performing a process, "does not know" what it is doing. Machines do not possess semantics, nor do they have consciousness.
A symbolic system has the following characteristics:
It is constituted by a set of elementary symbols, from which, by means of a series of syntactic rules, the different possible sentences of a language can be expressed.
A symbolic system can perform the processes linked to the set of rules provided. These processes manipulate strings of symbols that correspond to data. In the most advanced case, the rules can manipulate themselves.
The way a symbolic system is implemented is irrelevant. It can be done manually (with pencil and paper), with a digital computer or any other physical device. What is important is the functionality.
The symbols and the sentences that can be formed with the symbols, can be interpreted extrinsically (by humans), but have no intrinsic interpretation. Extrinsic interpretation is open; they can be objects, properties, situations, etc.
The problem of grounding semantics by means of symbols (symbol grounding problem), is the problem of connecting the symbols (the syntax, the superficial, the external) of a symbolic system with their meaning (the semantics, the deep, the internal) in a univocal way: every symbol must have a unique meaning.
The Chinese box
The problem of the impossibility of semantics in machines is nicely illustrated by John Searle's "Chinese box" (or "Chinese room") metaphor. It is a closed box with two windows for communication with the outside: one for entry and one for exit. Inside the box there is a person who does not know Chinese, but who has been given a set of formal instructions or rules so that when he is shown a Chinese text in the input window, he answers in the output window with another Chinese text that has a coherent relationship with the input text. The entire Chinese box system thus becomes a device that apparently "knows" Chinese. But it really does not. The person inside the box is performing a formal function, analogous to that performed by a computer, a mere symbolic manipulation, with no semantics at the linguistic level, although semantics of a functional kind.
The Chinese box clearly highlights the gap in linguistics between syntax and semantics, and the limitations of symbolic systems.
"The reason that no computer program can ever have a mind is simply that a computer program is only syntactic, and minds are more than syntactic. Minds are semantic, in the sense that they have more than formal structure, they have content" (John Searle).
Searle published his famous Chinese box metaphor in an article entitled "Minds, Brains, and Programs" [Searle, 1980], accompanied by several commentaries by philosophers, computer scientists, cognitive psychologists, and neurophysiologists. In 1990 he again included the Chinese box metaphor in an article in Scientific American entitled "Is the Brain Mind a Computer Program?", along with a reflection by Paul and Patricia Churchland entitled "Can a Machine Think?".
John Searle proposed the Chinese box metaphor as a rejoinder to the so-called "Turing test." This test was proposed by Turing in his 1950 paper "Computing machinery and intelligence" to assess the intelligence of a machine. It is based on the idea that verbal interaction is the medium in which intelligence is most apparent. It involves a machine answering the questions of a human interrogator and the human interrogator not knowing whether he is interrogating a person or a machine. Turing predicted that machines could eventually reach a level of intelligence comparable to human intelligence.
According to Searle, if a machine passes the Turing test, it does not mean that the machine thinks, that it has semantics and consciousness.
According to Searle, there are two types of artificial intelligence ( AI): "weak" AI (which claims only the simulation of the human mind by computer programs) and "strong" AI (which claims that the mind is a computer that processes symbols). Searle is a proponent only of weak AI. The Chinese box argument goes against strong AI, i.e., the possibility of achieving a machine that actually thinks.
MENTAL and Semantics
Semantics and consciousness
The mind is semantic in nature. By this I mean that the mind categorizes, looking for previously known patterns. Faced with a new phenomenon, we try to pigeonhole it into an already known category or pattern. When this objective is achieved, it produces mental stability. If it is not achieved, it produces restlessness, even panic.
According to the traditional conception, semantics is the relationship between language and reality. But the semantic nature of the mind transcends the real world. The interpretation of the real world is a constraint of semantics, which is of a universal kind. The mind is not simply a reflection of external reality. Mind is something higher that transcends the physical world.
Semantics is not necessarily linked to language, but it appears distinctly in language (natural or artificial).
Everything superficial (whether linguistic or not) has a meaning, and this meaning does not reside at the superficial level, but is found at the deep level. To understand something is to establish that vertical relationship between the superficial and the deep.
Semantics is a mental activity. But to understand the mind and semantics we have to place ourselves at a higher level: the level of consciousness, which is a faculty of the soul, where there is no duality. Semantics, as the mental activity that it is, is inexpressible because the mind cannot describe itself.
Meaning is a pre-scientific concept because science is circumscribed only to the superficial. Meaning is beyond science. Meaning is supported or grounded in consciousness. Independent meaning does not exist. It is consciousness that makes the connection between opposites in general, and the deep-superficial connection in particular. Consciousness always goes from the general to the particular. Consciousness is clothed in imagination and meaning arises from the vertical relation between superficial and deep contents. Meaning is mental.
The formalization of semantics
Meaning is something that is very familiar to us, but it is shocking that we cannot explain what it consists of. It is the same as with consciousness. Since it is in both cases something deep, we cannot explain it, that is, bring it to the surface. Therefore, semantics is not formalizable.
Numerous attempts have been made to formalize the semantics of languages in different senses, without conclusive results. All this is due to the fact that the mental contents of languages are more difficult to grasp and study than the concrete, visible and superficial aspects.
These failures are justified because semantics cannot be formalized, for a very simple reason: semantics is associated with the deep mental aspect, with cognition, and cannot be brought to the surface because it would be a contradiction: a thing cannot be both superficial and deep. This is the generalized interpretation of Gödel's theorem: the deep cannot be formalized.
The semantics (the deep) of language manifests itself in particular (superficial) expressions, but the semantics itself cannot manifest itself, since it is of an internal type.
Semantics, like consciousness, cannot be captured, cannot be "explained", cannot be formalized into something objective. At a deep level, semantics refers to the fundamental structures of the human mind that are activated when emitting (speaking or writing) and receiving (listening or reading).
But it is possible to formalize semantics at a basic level by means of the primary archetypes, the archetypes of consciousness, which are the first categories of reality, manifesting at the internal (mental) and external (physical) level.
Primary archetypes make it possible to connect the deep and the superficial, the internal and the external world. Primary archetypes are present in all things, including natural and artificial language. Primary archetypes are neither accessible nor describable, they are ineffable, but we can intuit them through their concrete manifestations.
The solution to the problem of formalization of semantics is therefore based on the union of syntax and semantics by means of the primary archetypes, for consciousness is based precisely on the union of opposites, and syntax and semantics are opposites, they are two sides of the same coin.
The primary archetypes are universal semantic primitives: a set of generic concepts or general categories, domain-independent, structured as a language, that underlie by combinatorics all possible semantics. Each primitive is a concept that is both simple and generic, with a simple syntax that allows its corresponding semantics to be easily associated to a syntactic expression. In this way, the formal and direct connection between syntax and semantics and the formalization of semantics is achieved.
Meaning has its foundation in the primary archetypes, which connect mind and consciousness. The meeting point between the deep and the superficial are the archetypes of consciousness.
Meanings are mental patterns or categories based on relationships. The primitives of MENTAL are the primary categories of reality, the philosophical categories.
This is the only foundation on which to build a theory (or model) of mind and semantics.
Semantics pertains to the deep. Syntax (form) belongs to the superficial. But in MENTAL both aspects are united. From syntax the semantics is inferred and vice versa. This is one of the multiple unions of opposites. That is why MENTAL is the language of consciousness.
Everything has a three-level foundation:
Consciousness.
Semantics (mental patterns or categories).
Linguistic expressions.
Linguistic expressions are supported by semantics. Semantics is supported by consciousness. Consciousness and semantics are connected by primary archetypes. Linguistic expressions are manifestations of the primary archetypes. There can be no linguistic expressions without semantics, and there can be no semantics without consciousness.
This solution bears some parallelism with Chomsky's generative grammar:
With Chomsky, a few syntactic mechanisms make it possible to describe all possible languages and all possible sentences that can be constructed with each language. Similarly, a few mechanisms (the semantic primitives) are sufficient to cover all the semantics of all possible languages.
Chomsky claims that those abstract general principles used to syntactically describe languages are universal in the human species; there is a universal grammar. Analogously, with the solution proposed here what is claimed is that, at a deep level, syntax and semantics are united in such a way as to constitute a universal grammar and language.
MENTAL is a synthesis of language, like Chomsky's syntactic revolution, only at a level where syntax and semantics are united.
MENTAL and semantics
Regarding semantics, we can distinguish in MENTAL the following aspects:
Sense and reference.
Sense and reference (the two concepts proposed by Frege) are superficial, horizontal. It is better to consider two vertical concepts: one deep (the primary archetypes) and the other superficial (the concrete expressions). In MENTAL it makes no sense to speak of reference because the expressions are of a mental type and it is secondary that they can be interpreted as references on the physical plane.
Lexical and structural semantics.
Lexical semantics is the same as structural semantics. The primitives are combined by the primitives themselves. Compositional semantics is always fulfilled.
Universality.
MENTAL is a universal or general semantics because it integrates all the semantic aspects mentioned above.
In the deep, the boundaries between all domains are diluted, because all semantics have the same foundation, they are all manifestations of universal semantics. In the deep there is only one language (the language of the primary archetypes), the universal language, which coincides with the universal grammar.
Symbol grounding problem.
MENTAL solves the symbolic grounding problem because it associates symbols with meanings in a biunivocal manner.
Model of the mind.
MENTAl is a meta-model of the mind. It is also a semantic computer, where the instructions are the semantic primitives. It goes beyond the Turing machine, which is purely computational.
Fractal language.
A geometric fractal has a pattern that repeats at all levels. It follows the principles of self-similarity and scale invariance. In the case of MENTAL, the patterns that repeat at all levels are the universal semantic primitives.
Ineffability of semantics and truth.
Semantics is ineffable. We can only speak of its manifestations. If semantics is ineffable, it is impossible to define the concept of truth and to define the concept of true statement. Truth is also ineffable. From the point of view of MENTAL, absolute truth is the set of semantic primitives, because they have an absolute character. Truth cannot depend on the superficial. Truth resides in the deep and sustains itself.
Interpretations.
Primary semantics has only one interpretation, it is fixed, it is universal. What is interpretable are the concrete contents, which are only the names, because numbers have a fixed meaning, not so the magnitudes in which quantities (numbers and units) are integrated.
The union of mentalism and behaviorism.
In MENTAL it is possible to deduce semantics by observing how expressions behave externally when evaluated. In this sense, MENTAL unites mentalism and behaviorism (another pair of opposites). For example,
{a b b c} // ev. {a b c}
{a b c}/(b=3) // ev. {a 3 c}
{a b c}↓ // ev. a b c
a+a // ev. 2*a
The structuralist movement.
MENTAL is the true structuralist movement. Everything is based on the same deep structures: the primary archetypes. Meaning is found in the relationships between things, and those relationships are structured in primary or fundamental patterns. Deep reality is based on universal structures.
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