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 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 although Carnap was a native German citizen, he and several other members of the group migrated to the U.S.  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.  He died in 1970 and is memorialized in Boston Studies in the Philosophy of Science (1971).

Logical Constructionalism

          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, 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 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 they 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, and 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 role of mathematics as the logic for the physical theory.  The central role 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 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 thesis 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; English, 1923) 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 maintained 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, but in the literature the book is always referred to 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.  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 derivation 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 the basis contains 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.”
          The fifth and concluding section of the book Carnap sets forth his explicit statement of the aim of science.  He views the aim of science in terms of his rational-reconstruction and 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 beliefs” 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.
          Carnap’s idea of rational reconstruction is different from the views of some contemporary information scientists, who propose that their procedural reconstructions of historic scientific discoveries with computerized artificial-intelligence discovery systems are hypotheses in "cognitive psychology", also known as “cognitive science.”  However, such efforts can be recast into a linguistic analysis that is more familiar to philosophers and also more like Carnap’s procedural approach than a psychological investigation.