MENTAL vs. Universal Scientific Language, by Carnap
MENTAL vs. Carnap's Universal Scientific Language
MENTAL vs. CARNAP'S UNIVERSAL SCIENTIFIC LANGUAGE
"If we have in science a unified language, then the separation disappears: science itself becomes unified" (Rudolf Carnap).
"Philosophy is to be replaced by the logic of science" (Rudolf Carnap).
"The meaning of a proposition is its method of verification" (Neopositivist Thesis).
Neopositivism
Neopositivism −also called logical positivism, logical empiricism, radical empiricism and neoempiricism− was a current in the philosophy of science that arose around a group of scientists and philosophers who formed the so-called "Vienna Circle". It was founded by the philosopher and physicist Moritz Schlick in Vienna in 1922. Rudolf Carnap was one of its most prominent members and Schlick's successor.
The aims and principles of the Vienna Circle were as follows:
Scientific vision.
An exclusively scientific view, interpretation, formalization and explanation of the world. In fact, its original name was "Vienna Circle for the Scientific Explanation of the World". In 1929, the Vienna Circle published a programmatic manifesto entitled "The Scientific Conception of the World" in which it argued that the only legitimate interpretation of the world is the scientific one.
Verificationism.
Defense of the empiricism of David Hume, John Locke and Ernst Mach. For a statement to be meaningful it must be verifiable by physical experience. The limits of the knowable are the empirical and verifiable. The empirical sciences constitute a continuous whole, ranging from physics to sociology.
Auguste Comte's 19th century positivism defended the scientific method as the only valid form of knowledge. Neopositivism went further, limiting scientific knowledge to the empirical and verifiable. The thesis of neopositivism is "Knowledge is meaning and meaning is verification". Truth is the correspondence between propositions and facts, between theory and practice, between meaning and verification.
Scientific statements that provide knowledge were called "protocols" because they contained in themselves a method of verification.
Anti-metaphysics.
Complete rejection of all idealistic, metaphysical, theological or speculative tendencies, because they are based on ambiguous concepts that are not verifiable by experience. Any non-empirical question is meaningless. Discarding metaphysical discourse is the only way to get rid of traditional philosophical polemics that have proven to be useless and irresolvable. Metaphysical hypotheses are not false, because if they were, then they would no longer be metaphysical, but meaningless. Any attempt to transcend the limits of scientific knowledge leads to absurdity.
Analytical statements.
According to Kant, there are two kinds of statements: analytic and synthetic, and there are also a priori (prior to experience) and a posteriori (after experience) statements.
A priori statements are necessary (they always have to happen). A posteriori statements are contingent (they may or may not happen).
The meaning of an analytic statement depends only on the meaning of its terms, it yields no information, it is a tautology. Analytic statements are cognizable by pure reason, they are a priori and necessary. For example, "All bachelors are unmarried" and "Food is edible".
Synthetic statements provide information about the world, and are a posteriori and contingent. For example, "It is raining."
According to Kant, there are a priori synthetic statements, such as mathematics and logic. Neopositivists denied their existence because mathematical statements are abstract and do not speak of the real world. But they admitted as true statements (besides those verifiable by physical experience) the analytical statements, because it is possible to know the world by means of the pure logical-deductive (a priori and necessary) reasoning (a priori and necessary) used in mathematics and logic. For example, "2+2 =4" and "If a then b, and a, then it follows b".
Truths.
There are only two legitimate strategies for testing the truth of a proposition:
Empirical justification for properties that refer to the real world.
The purely formal justification, valid in the formal sciences (logic and mathematics). To prove a logical or mathematical proposition it is not necessary to resort to experience, it is sufficient that it conforms to the laws of logic or mathematics.
According to Leibniz, there are two kinds of truths: truths of reason and truths of fact. Neopositivists, under the influence of Kant and Leibniz, divided meaningful statements into analytic and factual.
Logic and mathematics.
Following the logicist tradition of Frege and Russell, mathematics is considered to be part of logic. And they hold that mathematics is totally meaningless because it does not refer to the real world. Mathematics is simply syntactic forms. Wittgenstein −inspirer of the Vienna Circle with his famous Tractatus− said that mathematics is syntax and that all mathematical statements are analytic and are tautologies.
Philosophy.
No foundation of the sciences should be sought in philosophy. Philosophy should play an auxiliary role, charged only with distinguishing between what is scientific and what is not. Philosophy should not be a theory, but an activity: the logical classification of the concepts and propositions of the proposed theories of empirical science: how concepts and statements are related, how some concepts are included in others, how some statements can be inferred from others, and so on. Philosophy must deal with the means of representation and not with the nature of representation. "Philosophy is to be replaced by the logic of science" (Carnap).
Physicalism.
Any science that aspires to qualify itself as scientific must be posed in exclusively physical terms. For example, psychology must be formulated in physicalistic terms, considering only behavioral phenomena. Psychology must be separated from the theory of knowledge. The theory of knowledge is the logic of science, the logical analysis of scientific statements.
Principle of induction.
Rejection of any a priori or dogmatic element or concept in the constitution of knowledge. Knowledge must be constructed from the bottom up, from the particular to the general, from facts to laws by means of generalizations, using the principle of induction, which must be interpreted as probability: the degree of confirmation of a general law. All inductive reasoning is reasoning in terms of probability.
Universal scientific language.
Elaboration of a universal scientific language, a common language for all sciences based on the language of physics, since physics is the most objective, the most intersubjective and the most experimentally verifiable scientific discipline. This physicalist language should be formal, rigorous, logical and unequivocal to describe physical reality based on the analysis of the language in which scientific statements are expressed. In fact, the adjective "logical" was added to "positivism" to indicate that mechanisms of rigor and precision should be included in knowledge, thus excluding meaningless propositions.
Physicalist language is not the same as phenomenalist language. The statements of phenomenalist language deal with sense data. Physicalist language statements deal with physical objects to which are ascribed properties or qualities that are inferred from intersubjective observations.
In this language, the meaning of a proposition was to be the method of verification. There must be correspondence between language, knowledge and reality, as Wittgenstein claimed in the Tractatus, a work that inspired the Vienna Circle.
Unified science.
All factual or empirical sciences are subject to the same criteria; there are no basic methodological differences between them, so it must be possible to create a unified science founded on the universal scientific language so that every scientific concept can be formally expressed in that language.
The main goal is the unity of science, a goal justified by faith in the potential of logical analysis of scientific statements and in empirical research. This unity of science must be realized by reducing everything observable to a language of a physicalist type, seeking the nucleus common to all the positive sciences.
The Vienna Circle set itself the goal of creating a unified encyclopedia of science based on the universal language of science.
Carnap's universal language of science
The universal scientific language postulated by Carnap to express empirical facts had to fulfill the following requirements:
Formal physicalist language.
It had to be a formal language, with a rational and logical structure so that all scientific knowledge could be expressed. This formal language was to be based on the mathematical logic of Russell and Whitehead's Principia Mathematica (PM), for its value as an epistemological tool, in order to formalize the underlying logical structure of scientific language. In the same way that formal logic grounds mathematics, it must also ground scientific knowledge.
To carry out this project of universal scientific language, Carnap proposed to carry out a logical analysis of the statements of the factual sciences, an analysis centered on the logical aspects of syntax, logical syntax. He thus followed an idea proposed by Wittgenstein in the Tractatus: in the analysis of language lies the key to the structure of reality and knowledge. According to Wittgenstein, the only way to do philosophy is the logical analysis of language, all philosophy is linguistic criticism and every proposition is a representation of reality.
Form and content.
We must distinguish between form (syntax) and content (meaning) of the expressions of language. When such a distinction is forgotten, one falls back into metaphysics and, therefore, between propositions and pseudo-propositions. The latter are metaphysical propositions that have no objective referents.
The old logic is based on predicative forms (a predicate applied to a subject). Carnap's new logic contemplates two levels:
Pure formal logic, where neither content nor meaning is considered. It has a tautological character and is true by virtue of its form. At this level the truths are purely formal (e.g. "It rains or it doesn't rain"). Logical calculations can be performed with this type of logic. The corresponding language is syntactic: it refers to the logical structures of the object language, i.e. the structure of the physicalist language.
Applied logic or theory of knowledge, where content, meaning, is considered. Truths depend on the meaning of the terms used. The corresponding language is the language of the empirical sciences.
Logic.
Scientific language must be formulated in syntactic, purely formal terms, for all epistemological problems are syntactic problems.
Carnap sought a methodological universalism based on a general formal logical theory that would underlie all scientific theory. This methodological universalism is concretized in logical syntax, a theory of linguistic forms that should allow the construction of different languages and particular logics. He thus renounced a single language and a single logic.
Carnap conceived a general axiomatics as the foundation of a general logical theory, a metalogic or a metalogical language capable of expressing logical and empirical statements. The ultimate purpose was to achieve a general theory of scientific languages as formal languages having a physicalist interpretation. The metalogic would be "the logic of science".
Primitive elements.
Every scientific statement must be able to be expressed and grounded in a set of elementary statements with the help of a formal logic.
On this subject there was a great debate on two aspects: 1) On the meaning of those elementary statements, that is, on their epistemological status; 2) The means to establish the truth or falsity of those elementary statements, that is, their empirical evidence.
Accessibility.
This universal scientific language should be able to be accessible so that everyone could have a broader knowledge of scientific truth.
The evolution of Carnap's thought
Carnap passionately defended scientific rationality, but he frequently corrected theoretical details of his general position.
Carnap's first major work, "The Logical Structure of the World" (Der Logische Aufbander Welt, known in short as "Aufbau"), published in 1928, was for years the official doctrine of the Circle. This work is considered one of the most important books in the history of analytic philosophy. In it he aims to apply the new logic developed by Frege, Russell and Whitehouse, developing a formal and rigorous theory of empiricism, defining all scientific terms in phenomenological terms.
The main aim of the Aufbau was to introduce a new discipline called "theory of constitution." For Carnap, "constitution" meant "reduction." In effect, he set out to construct a logical system, such that all scientific concepts would be derived from a fundamental core based on elementary sensible experiences and a reduced set of logical principles, as in Principia Mathematica by Russell and Whitehead. Carnap intended to construct a logically based ontology, where all scientific objects would be defined by structural or relational properties.
Initially, Carnap favored phenomenalist language, a language based on sense data (of a subjective kind). Later he changed his mind and decided to go for the physicalist language, because it is intersubjective: one can only speak of the unity of the language of science if all scientific terms refer to observable physical objects, properties or relations. The idea was to reduce all science to a set of basic, elementary or primitive protocol statements, from which scientific statements could be expressed by means of a logical formalism.
In 1934 he published the influential book "Logical Syntax of Language". His main ideas were as follows:
Logical syntax is the foundation of the language of science. The logical syntax of a language is the formal theory of that language. Logical syntax is the study of the relations of signs to each other, without reference to the meaning of the symbols. The logical syntax of a language is an artificial system of relations. "The purpose of logical syntax is to provide a system of concepts, a language, by means of which the results of logical analysis will be accurately formulable."
He intended to refute the thesis of the first Wittgenstein (the one in the Tractatus) that "there are things that cannot be said but only shown," such as the semantics of language, the logical structure of sentences, or the relation between language and the world.
He defended the "principle of tolerance", according to which there is no language that can be qualified as absolute and true, since everyone is free to adopt the language that best suits his purposes. The choice of language is conventional and justified by practical considerations. In this respect he agreed with the second Wittgenstein (that of Philosophical Investigations).
From 1938 onwards, Carnap changed: the analysis of scientific statements could not be only syntactic. The concepts of meaning and truth should be included. He also softened his earlier anti-metaphysical stance.
Popper criticized the verificationist principle of neopositism and proposed to change it to the falsification principle: every scientific statement must be falsifiable. Carnap accepted Popper's proposal and changed the verificationist method (correspondence between the theoretical and the empirical) for the principle of confirmation of hypotheses by observational data.
Carnap distinguished between confirmable and experimental propositions. Confirmable propositions are those that have records of observations that confirm them. Experiential propositions are confirmable propositions susceptible to experimentation.
Carnap initially argued that scientific knowledge is unlimited, in the sense that there is no question whose answer is unattainable by science. Later (circa 1954), Carnap assimilated the result of Gödel's incompleteness theorem −Gödel was an associate member of the Vienna Circle who never came to share the neopositivist theses−, recognizing that mathematics and physics have in common the impossibility of absolute certainty.
Carnap was a central figure in the development of analytic philosophy. He was an advocate of the introduction of formalism in philosophy. He made great contributions to logic, philosophy of science, philosophy of language and mathematics, which he reflected in several works: "Introduction to Semantics" (1941), "The Formalization of Logic" (1942), "Meaning and Necessity" (1947), "The Logical Foundations of Probability" (1959), "Studies in Inductive Logic and Probability" (1971). In short, Carnap helped to create modern science.
MENTAL vs. Carnap's Universal Scientific Language
There are certain analogies and differences between MENTAL and the universal language advocated by Carnap:
Ideal language.
With MENTAL the expectation of the ideal or perfect language pursued by neopositivists to represent scientific knowledge is fulfilled. But it is not a physicalist language, but an abstract one, since it is impossible to make physicalism and universality compatible. Universality necessarily implies supreme abstraction.
Representation in MENTAL is based on primary archetypes, common to the internal and external world. The semantics of language is the semantics of possible worlds, a semantics that is inexpressible but which constitutes the foundation of everything.
Universal language.
Carnap aspired to create a universal language capable of expressing all kinds of languages and logics. This is precisely MENTAL. What Carnap called "logical syntax" or metalogic we can consider as the universal semantic primitives, capable of defining or expressing all kinds of particular languages and logics.
Top-down (top-down) approach.
MENTAL follows a strategy contrary to neopositivism. Neopositivism starts from the particular to reach the general. MENTAL starts from the deep, abstract and universal to express the superficial. It applies the principle of descending causality.
Completeness.
It is impossible to express all scientific propositions in a physicalist language because the physicalist language is superficial and cannot be grounded in itself (in also physicalist statements). Science is the superficial, the phenomenal. It only considers the "how", not the "what", the cause of phenomena. The "scientific explanation of the world" proposed by the neopositivists is not such, it is only "description".
According to the first Wittgenstein, there are things that cannot be said. The inexpressible are the primary archetypes, which are at the root of everything. We can only see their manifestations in language and in the real world.
According to the early Wittgenstein, in the structure of language we are shown the structure of the world. According to Carnap, "Linguistic phenomena are events within the world, not something that refers to the world from outside" [Carnap, 1992]. According to the philosophy of MENTAL, the structure of language shows the structure of possible worlds, including the physical world.
Truth.
Truth always lies in the profound, never in the superficial and phenomenological. Simplicity, consciousness and truth converge in MENTAL. Truth is inexpressible because, if it were expressible, truth would be limited. "The first law of science is that truth cannot be discovered. The laws of science are mere working hypotheses" (Joseph Campbell).
Metaphysics.
Metaphysics cannot be dispensed with because the profound, the metaphysical, although inexpressible, underlies the superficial, including scientific knowledge.
Logic.
Logic is only one dimension of mathematics, it is part of mathematics. Mathematics cannot be grounded in logic because logic is a part of mathematics. This statement goes against logicism.
Influenced by the logic of Principia Mathematica, Carnap emphasized the role of logic and tried to ground the language of science beyond logic, in metalogic, so that there could be different languages and different logics. But there is no metalogic that founds all possible logics. All possible logics derive from universal semantic primitives.
Carnap sought a higher, meta level, and identified it with metalogic. But the true meta level, the most fundamental level, is that of universal semantic primitives.
For Carnap, universal language must be grounded in syntactic terms. It is clear and evident that semantics must come first and then its representation, syntax.
Analytic and synthetic sentences.
When mathematics refers to itself, at the abstract level, all its sentences are analytic. For example, when we define a function, an operation, an algebraic structure or an arithmetic law. But when they refer to the world, to concrete objects, the sentences are synthetic. For example, when we assign a predicate to an object or when we establish a mathematical relation of a physical phenomenon. In this case, we are establishing a connection between the abstract and the concrete world, and producing knowledge. In all knowledge, consciousness is implied as the connector or relational of the opposites or duals (the abstract and the concrete).
The great power of mathematics is its ability to formalize the external world from the internal world.
Gödel's Theorem.
Gödel's incompleteness theorem reflects the unsolvable problem of grounding mathematics from mathematics itself. This theorem does not apply in MENTAL because it is a constructive-descriptive language of a metamathematical type that grounds mathematics and the formal sciences in general.
Accessibility.
MENTAL shares with Carnap's hypothetical universal language in its claim to be a language accessible to all because of its simplicity.
Foundation.
The defining phrase of logical positivism is: "A statement is cognitively meaningful only if it possesses a method of empirical verification or is analytic." According to physicist David Deutsch, this sentence is not a cognitively meaningful statement because it cannot be empirically verified nor is it analytic. Logical positivism cannot ground itself. Science cannot ground itself. It makes no sense to speak of "the science of science."
The foundation of everything is based on the primary archetypes, which manifest themselves in all orders, including science.
It is simpler to base everything on the universal than on the particular, because in the universal is the supreme simplicity, in consciousness.
Encyclopedia.
The Vienna Circle tried to create an International Encyclopedia of Unified Science. With MENTAL an encyclopedia is also promoted, but not of all sciences, but only of the formal sciences (mathematics, computer science, artificial intelligence, etc.). This encyclopedia begins precisely with this work.
There are several reasons that justify the elaboration of this encyclopedia:
To demonstrate that MENTAL is truly a universal formal language.
To demonstrate that a single language allows to formalize all formal sciences, thus favoring the connection between them. However, it is also falsifiable: if a subject within the formal sciences is found to be inapplicable, it will cease to be universal.
Show that this formalization is the simplest possible, of maximum expressive possibilities, where problems are clarified, simplified or solved.
Carnap's theory is complex, ambiguous, generic and speculative. It did not come to fruition in any proposal for a universal scientific language. Because of this ambiguity, his theories have had different interpretations, and also require a lot of time to understand them.
The reduction of scientific statements to the physicalist language never came to fruition and the projects of universal scientific language and unified science were relegated to the realm of utopias. On the contrary, MENTAL is a simple, theoretical and practical universal formal language, with its precise semantics and syntax, valid for all formal sciences, including scientific knowledge.
Carnap tried to connect in the field of science the disciplines of philosophy, logic, mathematics and linguistics. MENTAL connects, incredibly simply, philosophy (philosophical categories), depth psychology (primal archetypes), linguistics (universal semantic primitives) and their application to all the formal sciences. As always, the solution to problems lies in simplicity.
Addenda
Neurath's role
Otto Neurath −another leading figure of the Vienna Circle− was an extraordinarily prolific writer on a wide variety of subjects. He spoke out against metaphysics and in favor of the unity of science. He was a disseminator of the encyclopedic ideas that were the driving force behind the ambitious program of the creation of a unified science. In 1936, he founded the "Unity of Science Institute".
For Neurath, the universal physicalist scientific language was simply an ordinary, informal language, but enriched with terms common to all sciences to facilitate communication between different scientific fields. He believed that a formal universal scientific language would imply an absolute, finished and static view of reality.
Neurath was in favor of an exclusively protocol-like language, a record of personal scientific experiences. For Carnap this was unsatisfactory, because descriptions of particular physical events cannot be generalized, so they could not serve to construct universal language. The protocol language is of a subjective type. Physicalist language is intersubjective.
The Universal Encyclopedia of Unified Science
In 1939, Rudolf Carnap, Otto Neurath and Charles Morris began publishing the "International Encyclopedia of Unified Science". Its main promoter was Neurath. The encyclopedia was based on Carnap's physicalist theory, which advocated that all sciences should be based on physics. The function of the encyclopedia was: 1) to bring together the collective scientific knowledge; 2) to highlight interdisciplinary connections; 3) to serve as a dissemination to the entire scientific community. Neurath's death and the Second Great War interrupted the publication of the work. Twenty-six volumes were planned, of which only two were published [Neurath, 1937].
Popper and the Vienna Circle
Karl Popper was neither a member nor an associate of the Vienna Circle, and he was a great critic of the theses of this group of philosophers. In his 1934 work "The Logic of Scientific Inquiry", −which generated a great controversy in the Circle− he presented his conception of science and the logic of scientific inquiry:
On science and the scientific method.
There is no certain science or infallible scientific method. The ancient Greeks distinguished between epistéme (sure and definitive knowledge) and dóxa (mere opinion). For Popper, everything is dóxa, there is no epistéme. There are only conjectures, which are always provisional. Mistakes are always made. It is not a matter of avoiding them, but of detecting them, overcoming them and learning from them. Mistakes make us advance when we overcome them. Progress in science requires freedom, imagination and creativity. We must not be afraid to make mistakes, because fear restricts our freedom, imagination and creativity.
General laws.
No theory or general law can be verified, justified, validated or confirmed absolutely and definitively. What is possible is the refutation of the theory, since it is enough that some of its predictions or consequences are not fulfilled for the theory to be invalidated. And no matter how many predictions are fulfilled, the theory can never be confirmed. That is why the scientist should not focus on the cases in which the theory is fulfilled, but the other way around, in the cases in which it is not fulfilled.
Criterion of demarcation between science and non-science.
For the neopositivists of the Vienna Circle, the criterion of demarcation lies between the verifiable (the scientific) and the unverifiable (the pseudoscientific). Popper opposed this conception: the criterion of demarcation lies between the falsifiable (the scientific) and the non-falsifiable (the pseudoscientific). In science all theses must be refutable.
Law of induction.
Traditional science starts from the observation of empirical facts in order, by means of induction, to establish theories or general laws. These laws become more and more abstract to cover more scientific domains, in a bottom-up process, from the particular to the general.
Hume had already denounced that induction is not a logically justifiable procedure. On the other hand, Francis Bacon and John Stuart Mill saw in induction the infallible method of empirical science.
For Popper, the inductive method is incorrect and inconclusive, and furthermore has nothing to do with scientific practice. Induction does not even serve to establish the probability of scientific laws. The method of science is hypothetico-deductive.
Popper was a great advocate of freedom. He opposed dogmatism (a theory can never be definitely confirmed), subjectivism (objective reality often contradicts the subjects' conception) and determinism (not everything is predetermined in nature or in society).
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