RUDOLF CARNAP ON SEMANTICAL SYSTEMS AND
W.V.O. QUINE'S PRAGMATIST CRITIQUE
BOOK III - Page 1
This book examines the linguistic philosophies of the positivist Rudolf Carnap and the contemporary pragmatist Willard van Quine. Carnap took Mach’s positivism as his point of departure, and Quine took Duhem’s philosophy of mathematical physical theory.
Rudolf Carnap (1891-1970) was a leading member of a group of philosophers and scientists in Vienna, Austria, during the interwar years, which called itself the “Vienna Circle.” A statement of the group’s manifesto, “The Scientific Conception of the World”, written by Otto Neurath (1882-1945) with Carnap’s collaboration can be found in Neurath’s Empiricism and Sociology. The group was scattered when the National Socialists came to power in Germany, and he and several other members of the group migrated to the United States. With the aid of Willard Van Quine of Harvard University, Carnap received an appointment to the faculty of philosophy at the University of Chicago in 1935, which he retained until 1952, when he spent two years at the Institute for Advanced Study at Princeton. In 1954 he filled the vacancy created by the death of Hans Reichenbach at the University of California at Los Angeles, and held the position until his retirement from teaching in 1961. However, he continued to write for the ten years of his intellectually active retirement. Carnap died in 1970 and is memorialized in Boston Studies in the Philosophy of Science (1971).
In his “Intellectual Autobiography” published in The Philosophy of Rudolf Carnap (ed. Schilpp, 1963) Carnap reports that while he was studying at the University of Jena during the years just before the First World War, he was greatly influenced by one of his teachers, Gottlob Frege, who maintained that logic should be the foundation for mathematics. Shortly after the war Carnap read Bertrand Russell’s Principia Mathematica, the seminal document establishing the Russellian symbolic logic, and was greatly impressed by Russell’s theory of relations. But Carnap was even more impressed by Russell’s philosophical outlook expressed in Our Knowledge of the External World. This book states that the logical-analytical method can provide a method of research in philosophy, just as mathematics supplies the method of research in physics. Carnap reports that upon reading this text he felt that its words had been directed to him personally. As a result of these influences, the construction of logical systems would characterize all of Carnap’s philosophical work during his long career. There would be many other influences, but they would only produce variations on his basic agenda of logical constructionalism.
Carnap’s philosophy of science was positivist, and he and the other members of the Vienna Circle were favorably disposed to the philosophies of Mach, Poincare, and Duhem. The antimetaphysical and scientistic character of Mach’s philosophy was reinforced by the early writings of Ludwig Wittgenstein. Wittgenstein maintained that all philosophical sentences including most notably all of metaphysics are meaningless pseudo sentences, and that in spite of their grammaticalness and common usage, these pseudo sentences are really devoid of any cognitive content. Later Wittgenstein departed from this view and moved away from the constructionalist approach in philosophy. But the earlier views of Wittgenstein expressed in his Tractatus Logico-Philosophicus had a lasting influence on the Vienna Circle positivists. One of the central philosophical tasks that the Vienna Circle members set for themselves was the use of logical constructionalist methods to implement the positivist philosophy, and especially the symbolic logic in the >Principia Mathematica of Russell and Whitehead. For this reason they are known as the “logical” positivists.
Einstein and Mathematical vs. Physical Geometry
Like many philosophers of his generation, Carnap was impressed by Einstein’s revolutionary theory of relativity. Philosophers such as Popper found the significance of this successful overthrow of the three-hundred-year reign of Newtonian physics in its implications for scientific criticism. But Carnap found its significance in the distinction between mathematical and physical geometry, or more generally in the rôle of mathematics as the logic for the physical theory. The central rôle in the relationship between the formal and the empirical in the development of modern physics became the axis for Carnap’s whole philosophical career. He made it the subject of a distinctive type of metatheory for science, which evolved into his metatheory of semantical systems.
Carnap had started his studies in experimental physics at the University of Jena before the First World War, and then later turned to philosophy after the war. In 1921 he wrote a Ph.D. dissertation titled >Der Raum, in which he attempted to demonstrate that the contradictory theories about the nature of space maintained by the mathematicians, philosophers and physicists, are entirely different subjects. He distinguished three meanings of the term “space” corresponding to the three disciplines that treat it. These are the formal meaning used by mathematicians, the intuitive meaning used by philosophers, and the physical meaning used by physicists. The intuitive meaning used by philosophers is based on the Kantian idea of “pure intuition”; Carnap later rejected this idea and retained only the formal and empirical meanings.
A later development in Carnap’s thinking on these matters occurred when he read Wittgenstein’s Tractatus. Wittgenstein had defined formal meaning in terms of tautologies or logical truth. This was the origin of Carnap’s use of analyticity, and he believed that the concept of logical truth supplied the key to the problem of formal systems such as mathematical geometry, which had enabled Einstein to make his revolutionary relativity physics. In his autobiography Carnap says that due to the doctrine of logical truth, Wittgenstein had the greatest influence on his thinking besides Russell and Frege.
After many years of silence on the subject of geometry, Carnap returned to it in his >Philosophical Foundations of Physics (1966). There he says that he views the Euclidian, the Lobachevskian, and the Riemannian geometries as different languages in the sense of theories of logical structure, which as such are concerned only with the logical implications of axioms. In this work he references Einstein’s Sidelights on Relativity (1921) where Einstein says that the theorems of mathematics are certain in so far as they are not about reality, and that in so far as they are about reality they are uncertain. Carnap states that the philosophical significance of Einstein’s theory of relativity is that it made clear that if geometry is taken in an a priori or analytic sense, then like all logical truths it tells us nothing about reality, while physical geometry is a posteriori and empirical, and describes physical space and time.
Carnap notes that in relativity theory Einstein used the Riemannian mathematical geometry as the axiomatic system for his physical geometry, but the reason for the choice of which mathematical geometry to use for a physical theory is not obvious. Several years before Einstein developed his relativity theory the mathematician Poincare postulated a non-Euclidian physical space, and said that physicists have two choices. They can either accept non-Euclidian geometry as a description of physical space, or they can preserve Euclidian geometry for the description of physical space by adopting new physical laws stating that all solid bodies undergo certain contractions and expansions, and that light does not travel in straight lines. Poincare believed that physicists would always choose to preserve the Euclidian description of physical space, and would claim that any observed non-Euclidian deviations are due to the expansion or contraction of measurement rods and to the deflection of light rays used for measurement. Einstein’s choice of the Riemannian geometry and physical laws for measurement was based on the resulting simplicity of the total system of physics. Relativity theory using Riemannian geometry greatly simplifies physical laws by means of geodesics, such that gravitation as a force is replaced by gravitation as a geometrical structure.
The Aufbau and “Rational Reconstruction”
In 1928 Carnap published his Der Logische Aufbau der Welt. The book was translated in 1967 with the title The Logical Construction of the World, which in the literature is always referred to merely as the Aufbau. This work exhibits a detailed design for an ambitious investigation. In the first three of the book’s five parts Carnap sets forth the objective, plan, and essentials of this investigation. His objective is the “rational reconstruction” of the concepts of all fields of knowledge on the basis of certain elementary concepts that describe the immediately given in experience. His phrase “rational reconstruction” means the development of explicit definitions for concepts that originate in the more or less unreflected and spontaneous psychological processes of cognition.
But the task is not a work in psychology; it is a work in logic. It yields a constructional system, which Carnap states is more than merely a division of concepts into various kinds and an integration of the relations among them. It is furthermore a step-by-step logical development or “construction” of all concepts from certain fundamental concepts. The result is a genealogy of concepts, in which each concept has a definite place, because at each level concepts are constructed from others at a lower level, until one reaches the basis of the system consisting of basic concepts. And the logical construction is implemented by means of the theory of relations in Whitehead and Russell’s symbolic logic, or “logistic.” The selected basic elements are “elementary experiences”, which are unanalyzable, and there is one basic relation, which takes the elementary experiences as arguments. The basic relation is “recollection of similarity”, which in the logic is symbolized as x Rs y. This symbolism means: x and y are elementary experiences, which are recognized as partly similar through the comparison of a memory image of x with y. Carnap illustrates his system in the fourth part of the Aufbau, and develops various constructions for concepts such as quality classes, sensations, the visual field, colors, color solids, the space-time world, tactile-visual things, and “my body.”
In the fifth and concluding section of the book Carnap sets forth his explicit statement of the aim of science, which he views in terms of his rational-reconstruction and the Vienna Circle’s unity-of-science agendas. He says that the formulation of the constructional system is logically the first aim of science. From a purely logical point of view statements made about an object become statements in the strictest scientific sense only after the object has been constructed from the basic concepts. Only the constructional formula in the Russellian logistic – as a rule of translation of statements about an object into statements about the basic objects consisting of the relations between elementary experiences – gives a verifiable meaning to such statements, because verification means testing on the basis of experience.
The second aim in turn is the investigation of the nonconstructional properties and relations of the objects. The first aim is reached by convention; the second aim is reached through experience. Carnap adds that in the actual process of science these two aims are almost always connected, and that it is seldom possible to make a selection of those properties that are most useful for the constructional definition of an object, until a large number of properties of the object are known. Carnap illustrates the relation between the two aims of science with an analogy: the construction of an object is analogous to the indication of the geographical coordinates for a place on the surface of the earth. The place is uniquely determined through the coordinates, so that any other questions about the nature of the place have definite meaning. The first aim of science locates experience, as does the coordinate system; the second aim addresses all other questions through experience, and is a process that can never be completed. Carnap says that there is no limit to science, because there is no question that is unanswerable in principle. Every question consists of putting forth a statement whose truth or falsity is to be ascertained. However, each statement can in principle be translated into a statement about the basic relation and the elementary experiences, and such a statement can in principle be verified by confrontation with the given.
Fifty years later Quine also uses the coordinate system analogy to express his thesis of ontological relativity. But instead of developing an absolute ontology consisting ultimately of the immediately given in terms of elementary experiences and a basic relation, Quine relativizes ontology to one’s “web of belief” including science, and ultimately by nonreductionist connection to one’s own “home” or native language. The Vienna Circle’s unity-of-science agenda is integral to Carnap’s view of the aim of science. He sees the task of unified science as the formulation of the constructional system as a whole. By placing the objects of science in one united constructional system, the different “sciences” are thereby recognized as branches of one science.
Logical Syntax of Language
When Carnap discovered Gestalt psychology, he reconsidered the phenomenalist constructionalism that he had undertaken in his Aufbau, and concluded that a physicalist language, a “thing language” describing things in ordinary experience, is more suitable as a basis of all scientific concepts. At about the same time he also learned of Hilbert’s metamathematics program. The influence of Russell had led the Vienna Circle to prefer the logistic approach in foundations of mathematics to Hilbert’s formalist approach. But Carnap was attracted to Hilbert’s idea of a metalanguage, not just for mathematics but as the logic of all science. This was his idea of a “metalogic”, which he developed in his Logical Syntax of Language (1934). The metalogic is the logical syntax of language viewed as a purely analytic theory of the structure of its expressions. In his autobiography Carnap reports that the theory of language structure and its possible applications in philosophy came to him like a vision during a sleepless night in January 1931 when he was ill, and that on the following day he wrote down the idea in a manuscript of forty pages titled Attempt at a Metalogic, which was the first draft of his Logical Syntax.
One of the central ideas in Logical Syntax is Carnap’s distinction between metalanguage and object language. On his definition the former contains no reference to the meanings of linguistic signs occurring in the object language; it refers only to the logical structure of the expressions in the object language. Carnap says that his chief motivation for developing this syntactical method was to formulate more precisely philosophical problems that have evaded resolution when expressed in traditional manner. In 1934 he published “On the Character of Philosophical Problems” in the American journal Philosophy of Science, which expounded his treatment of metaphysical issues in the German edition of Logical Syntax published in the same year. In this work he distinguishes the formal or syntactical perspective from the connotative or material perspective.
He identifies logic as a set of metalinguistic transformation rules, and he identifies the logic of the language of science as an object language in which logical entailment is a formal transformation rule. Then Carnap defines the “content” of a proposition in science as a class of entailments from a synthetic proposition in the science. Content is thus a purely formal concept, and the difference between the formal and material perspectives is merely a difference between modes of expression. Accordingly philosophical analysis consists of translating statements into the formal mode. Meaningful statements in science can be translated into the formal mode of speech, but he says that meaningless metaphysical statements cannot be translated into the formal mode. For this reason he maintained that differences between positivists and realists disappear, when their respective positions are translated into the formal mode. Similarly problems in the foundation of physics are also problems in syntax. For example verification of physical laws is the syntactic deductive coherence between the general law-like propositions and singular propositions called protocol sentences, and the problem of induction is a question of how transformation rules lead from protocol sentences to laws.
In 1937 Carnap published his English edition of Logical Syntax. This latter edition contains additional material not in the earlier German edition, and its bibliography includes reference to Quine’s “Truth by Convention” published in 1936, in which Quine rejected the idea of analytic truth. Quine viewed the thesis of analytical truth as the Achilles-heel of Carnap’s philosophy of science, i.e., its parallel postulate to be replaced with the new pragmatist philosophy of language.
Logical Syntax is divided into five parts. The first three set forth two artificial object languages. Language I is designed to be acceptable to philosophers persuaded of the intuitionist philosophy of mathematics that includes no infinities. Language II is adequate to all classical mathematics including what the intuitionists would not accept, and it includes Language I as a sublanguage.
The fourth part sets forth the general procedures for constructing any artificial language, and is titled “General Syntax.” Carnap defines general syntax as a system of definitions of syntactical terms. In general a language is any sort of calculus in the sense of a system of formation and transformation rules concerning expressions, which in turn are defined as finite, ordered series of elements called symbols. Formation rules determine concatenations of symbolic elements to form expressions, and transformation rules determine what transformations produce valid deductions and proofs. The “interpretation” of a language is the method of learning by explicit statements that are translations from an already interpreted language that can be represented formally and thus is syntax. Firstly a system of axioms in a calculus is given, and then it is interpreted in various ways by translations that establish correlations between the expressions of the language being interpreted and those already interpreted.
The fifth and concluding part of the book pertains to philosophy and syntax, where philosophy is identified with the logic of science. The material for the 1934 article in Philosophy of Science was taken from Section A of this part. In Section B Carnap considers the logic of science as syntax, stating that the logical analysis of physics is the syntax of the physical language. The language must have formation rules both for the protocol sentences, which express observations, and for postulated or “P-primitive” laws, which have the form of universal sentences of implication and equivalence. The transformation rules of the physical language consist either of only “L-rules”, which are logical rules, or of the L-rules together with “P-rules”, which are empirical rules.
Deriving consequences using the transformation rules tests a sentence in physics, until finally sentences in the form of protocol sentences are generated. These derived protocol sentences are then compared with the protocol sentences that are observation reports and the former are either confirmed or refuted by the latter. If a sentence that is an L-consequence of certain P-primitive sentences contradicts a sentence which has been stated as a protocol sentence, then some change must be made in the system. But there are no established rules for the kind of change that must be made, nor is it possible to set down any sort of rules as to how new primitive laws are to be established on the basis of actually stated protocol sentences. There are no rules for induction due to the universality of laws; the laws are created hypotheses in relation to protocol sentences. Furthermore not only general laws, but also singular sentences are postulated hypotheses, i.e., P-primitive sentences, which are sentences about unobserved processes from which certain observed processes can be obtained.
Carnap also treats the topic of scientific criticism, and maintains that there is no final falsification or confirmation of any hypothesis. When an increasing number of L-consequences of the hypothesis agree with previously acknowledged protocol sentences, then the hypothesis is increasingly confirmed, but it is never finally confirmed. He states that it is impossible to test even a single hypothetical sentence, because the test applies not to a single hypothesis but also to a whole system of physics as a system of hypotheses. In this context Carnap references Duhem and Poincare. He also says that both P-rules and L-rules including those of mathematics are laid down with the reservation that they may be altered as expediency dictates, and that in this respect P-rules and L-rules differ only in degree with some more difficult to renounce than others.
Carnap’s thesis that logical and descriptive language differs only in degree was proposed by Alfred Tarski. Carnap explains that if every new protocol sentence introduced into a language is synthetic, then L-valid (i.e., analytic) sentences differ from synthetic sentences, because such a new protocol sentence can be incompatible only with the P-valid synthetic sentence. It cannot be incompatible with the logical L-valid or analytic sentence. But then he further goes on to say that in spite of the above fact, it may come about that under the inducement of new protocol sentences the language may be altered to such an extent that the L-valid or analytic sentence is no longer analytic. He emphasizes in italics that the construction of the physical system is not effected in accordance with fixed rules, but is a product of convention. These conventions are not arbitrary; they must be tested. The choice of convention is influenced firstly by practical considerations such as simplicity, expediency, and fruitfulness, and secondly by their compatibility with the total system of hypotheses to which the already recognized protocol sentences belong. Thus in spite of the subordination of hypotheses to empirical control by means of protocol sentences, hypotheses contain a conventional element, because the system of hypotheses is never uniquely determined by empirical material however rich it may be. Carnap never developed this thesis of the empirical underdetermination of a system of hypotheses, and the artifactual theory of language it implies, which was extensively developed by Quine in the 1950’s and afterward. Later Carnap rejected Tarski’s thesis that logic and descriptive language differ only in degree, but he always maintained that definitions of L-true sentences are relative to the specific language system under construction.