Rudolf Carnap (1891–1970)

1. Brief Vita

Rudolf Carnap was born on May 18, 1891, in Ronsdorf, which is at present a part of the German city Wuppertal (North Rhine-Westphalia). After the death of his farther, the family moved to the neighbouring Barmen, where he attended the Gymnasium, and in 1909 further to Jena. From 1910 to 1914 he studied philosophy, mathematics and physics at the universities of Jena and Freiburg. A major philosophical influence on his early thought was his teacher Bruno Bauch, a prominent neo-Kantian. In 1913, he was one of the three people that followed Frege’s advanced course “Begriffsschrift II.” In the same year, he started experimental research in physics on thermionic electron emission, which was to lead to a doctoral dissertation. But then World War I broke out. His supervisor was killed early on; he himself served a few years on the front, and the project ended.

After the war, Carnap became interested in more theoretical issues. He wrote a Ph.D. thesis Der Raum (1921), in which he tried to rescue the Kantian conception of space from problems related to Einstein’s relativity theory, at the University of Jena. In the subsequent years, he became more involved in logic, and wrote a first version of his later introduction to logic Abriss der Logistik (1929), mainly inspired by Principia Mathematica, and worked on axiomatic systems for geometry and physics. This work would eventually lead to Carnap’s influential work Der logische Aufbau der Welt (1928).

Carnap became acquainted with other philosophers with a similar interest in a rigorous and clear philosophy, first Hans Reichenbach and later Moritz Schlick. Schlick invited him to Vienna, where he became instructor at the University of Vienna (1926-1931). He joined Schlick’s Philosophical Circle, better known as the Vienna Circle, comprising also Hans Hahn, Otto Neurath, Victor Kraft, Friedrich Waismann, Herbert Feigl, and later Karl Menger, Kurt Gödel, Gustav Bergmann, and Philipp Frank. The Circle had close contacts with the Warsaw logic school (Tarski, Leśniewski, Kotarbiński) and with Reichenbach’s group in Berlin. Carnap and other members of the Vienna Circle had several discussions with Wittgenstein, whose Tractatus Logico-Philosophicus was read and discussed in the Vienna Circle. To Carnap’s regret, Wittgenstein cut off the relation with Feigl and him in the beginning of 1929. Carnap became one of the central figures of the Circle, and together with Schlick and Neurath he wrote the mission statement Wissenschaftliche Weltauffassung: Der Wiener Kreis. To promote the scientific worldview, he and Reichenbach founded the journal Erkenntnis (1930), and with Otto Neurath and Charles Morris, he later started the series International Encyclopedia of Unified Science (1938). In 1931, he was appointed professor in natural philosophy in Prague. Because of the political atmosphere in Europe, and especially the dangerous situation concerning the Sudeten region in Czechoslovakia, he moved to the United States in December 1935.

In the winter of 1936, the University of Chicago offered him a position, which he held until 1952. In 1941, he became an American citizen. He had close contact with W.V. Quine, and was on several occasions in Harvard. In September 1936, he received an honorary degree on Harvard’s Tercentenary Celebration; in August 1939, he attended the Fifth International Congress for the Unity of Science; in 1940-1941, he was visiting professor in Harvard, where he formed a logic discussion group with Quine, Russell and Tarski, both of whom were staying in Harvard at the time. It would seem unavoidable that Carnap and Whitehead would have met, at least at Harvard’s Tercentenary Celebration, where both gave a lecture; but there are no actual reports of such a meeting. In 1952, he left Chicago, and went to the Institute for Advanced Studies in Princeton, and from 1954 until his retirement in 1961 he occupied the chair Reichenbach had occupied in UCLA. He died in Santa Monica on September 14, 1970.

Carnap’s philosophical work did not end with the Logische Aufbau der Welt and the Vienna Circle discussions on verification. But gradually, his interest shifted to linguistics, and especially the use of formal methods in grammar and semantics. Already in The Logical Syntax of Language (1937), metaphysical and epistemological issues had disappeared, and were replaced by a pragmatic comparison of various syntactical systems. Meaning and Necessity (1947) is a major contribution to semantics, and was one of the first elaborate systems in modal logic. The latter work became also famous in another respect, as it was the major target of Quine’s critique on the analytic-synthetic distinction. In the fifties, he set on a programme of clarifying induction by means of statistical methods. His later work formed the basis of the Bayesian confirmation theory in the philosophy of science.

2. The Logical Structure of the World

Carnap is known as the major protagonist of logical positivism or logical empiricism. The Vienna Circle was indeed one of the first places were the new logic was applied to philosophical issues. In the Circle, Frank was inspired by PM, but Carnap had learnt logic directly from Frege. As a matter of fact, he had difficulty in finding a copy of PM (he could not buy one because of the inflation in Germany), and finally asked Russell for one, who sent him a long list of written theorems of PM. He reworked the notes to a German introduction in logic, which became his Abriss der Logistik. In logical empiricism, logic became the language of science. Philosophical problems were to formulated in a logical framework, so that they could be treated in a precise way. Philosophical problems that were not soluble within the logical framework were said to be pseudo-problems. As a result, the language of logic became a means of unification within science; it provided the general framework in which all of science was to be integrated.

The logic of PM would even play a bigger role in Carnap’s major work, Der logische Aufbau der Welt. In this work, he develops a “constitution system” of concepts (and relations). He aimed at a system in which the concepts all have a definite place, and moreover, in which each can be derived from a few basic concepts (eventually he used one single relation). In brief, he tried to give a complete reconstruction of all (scientific) knowledge from a small set of basic concepts. The framework was the theory of relations and the simple type theory of PM. Thus concepts at higher levels in the constitution system were constructed as logical complexes of objects lower in the system. Carnap’s system is based on an autopsychological (i.e. solipsistic) basis; the “given” must be thought of as a stream of experience. The basic building blocks are unanalyzable “elementary experiences;” they are the total experience a person has at some moment in time. Thus Carnap aligns himself with the Gestalt theorists in psychology, rather than the atomists. In addition to these building blocks, Carnap’s constitution system employs one single relation between the elementary experiences, namely the recollection of partial similarity (Rs). Two elementary experiences x and y stand in the asymmetrical relation Rs, if the memory image of the earlier of the two, x, is partially similar to y. On this slender basis, Carnap managed to give a complete constitution system; he was able to (re-)construct the whole of science by using a so-called quasi-analysis procedure. By means of an intricate series of constructions such as similarity circles, quality classes, sense classes, visual field places, colors, the color solid for the lower levels of autopsychological objects; the space-time world, visual things, “my body,” tactile-visual things, the world of physics, and biological objects at the intermediate levels of physical objects; and the production of signs, reports of other people, the world of the other, the intersubjective world, the primary and higher cultural objects, and finally the domain of values at the higher levels of cultural objects—all this Carnap grounded in the constitution system of Der logische Aufbau der Welt.

The logical system of PM is not only an essential component of Carnap’s “logical structure of the world,” but it is also clearly the source of inspiration. His work is meant as an extension of the method of PM. Whereas PM meant to present a reconstruction of the whole of mathematics on the basis of a few primitive logical concepts, the Logische Aufbau seeks to give a reconstruction of all scientific knowledge on the same logical basis and one extra-logical given relation, Rs. It is already clear from the first illustration of the procedure of reduction, namely the reduction of statements about fractions to statements about natural numbers (Carnap 1928, 6), that the ideal of reduction is inspired by PM. Moreover, in the fourth part, in which the formal reduction is presented, Carnap starts with the reduction of logical and mathematical objects as the most basic level in his system, and refers to PM for the further details (1928, §107). PM is thus fully integrated into the Logische Aufbau. It is noteworthy that for the reduction of pure abstract or mathematical geometry he also refers to the unpublished Volume IV of PM, which was to be written mainly by Whitehead.

Whitehead had an important, direct influence on Carnap’s Aufbau, not only as co-author of PM, but also indirectly through Russell’s Our Knowledge of the External World. Carnap’s procedure of quasi-analysis is mainly inspired by Whitehead’s method of extensive abstraction. In the references at the end of the paragraph on quasi-analysis (1928, §73), Carnap mentions the work of Whitehead and Russell, and especially Russell’s Our Knowledge of the External World as the inspiration for the extra-mathematical applicability of the abstraction principle. However, the relevant idea in Russell’s work, namely the abstraction of points and instants from sensory events, was actually Whitehead’s. Russell clearly acknowledged that this procedure, which became known as the method of extensive abstraction, was conceived by Whitehead. As Russell writes in his Autobiography, his use of Whitehead’s idea, five years before Whitehead himself published his ideas, put a severe strain on their relation.

On closer scrutiny, there are flaws in Carnap’s constitutional system. Quine, for instance, pointed out forcefully that there is no smooth transition from the autopsychological to the physical level. Carnap dropped the project, and later worked on other projects. However, Carnap’s constitutional programme, the enlargement of PM’s reduction of mathematics to a reduction of all knowledge, has remained attractive. The work had a large impact on Quine’s naturalism, and thus remained influential in a weakened form. Later, the project has been revisited, most famously by Nelson Goodman in The Structure of Appearance, and most recently by Hannes Leitgeb in The Logical Structure of Empirical Content.

3. Opposite Directions

In the received view, Carnap and Whitehead are very different philosophers; even though both were interested in logic, from a metaphysical perspective, they were outright antagonists. Whitehead was the founding father of process metaphysics, while Carnap became the spokesman of the anti-metaphysical movement in mainstream American philosophy, which turned to philosophy of science. This view is certainly justified, if one considers the philosophical positions Whitehead and Carnap defended in the later stages of their career. But if one looks at the philosophical development of both philosophers, the picture becomes more complex. Carnap was heavily influenced by the thoroughly metaphysical neo-Kantian tradition in which he was immersed in his study years, and later became a staunch formalist. Whitehead, on the other hand, started as an algebraist in mathematics, and gradually enlarged his philosophical position with ever more metaphysical themes.

 At one stage in their philosophical development, their work was closely related. Soon after Einstein’s work on the theory of relativity, both Whitehead and Carnap did investigate the philosophical repercussions for the philosophy of space and time. In his doctoral work Der Raum, Carnap tried to save (neo-)Kantian space and time intuitions as much as possible; and to this end restricted the Euclidean spatial intuition to infinitesimal regions. His major philosophical concern was to retain the bond between the formal geometrical structure and phenomenal space and time experience. Whitehead dealt with the same issue nearly at the same time. Whitehead’s work would result in the method of extensive abstraction, which became a bridgehead from the mathematical to more metaphysical realms. Carnap, however, lost faith in his initial solution, and would gradually expel the remnants of the Kantian tradition from his work. To this end, he cut the bond between experience and geometry altogether, relegating the first to the scientific realm of psychology, the other to the study of formal systems. The epistemological questions relating to space, time and experience were thus eliminated, to be replaced by empirical questions and by questions relating to formal frameworks. It is quite remarkable that nearly the same issue, namely the relation between formal and experienced space, would drive Whitehead and Carnap in entirely different directions.

Works Cited and Further Readings

Books by Rudolf Carnap

Physikalische Begriffsbildung. 1926. Karlsruhe, Verlag G. Braun.

Der Logische Aufbau der Welt. 1928. Berlin, Weltkreis-Verlag.

Abriss der Logistik. 1929. Vienna, Springer.

Wissenschaftliche Weltauffassung: Der Wiener Kreis (H. Hahn, O. Neurath and R. Carnap). 1929. Vienna, Artur Wolf Verlag.

The Unity of Science. 1934. London, Kegan Paul.

The Logical Syntax of Language. 1937. London, Kegan Paul.

Foundations of Logic and Mathematics. 1939. Chicago, University of Chicago Press.

Introduction to Semantics. 1942. Cambridge MA, Harvard.

Formalisation of Logic. 1943. Cambridge MA, Harvard.

Meaning and Necessity. 1947. Chicago, University of Chicago Press.

Logical Foundations of Probability. 1950. Chicago, University of Chicago Press.

The Continuum of Inductive Methods. 1952. Chicago, University of Chicago Press.

Introduction to Symbolic Logic and its Applications. 1958. New York, Dover.

Philosophical Foundations of Physics, edited by M. Gardner. 1966. New York, Basic Books.

The Logical Structure of the World/Pseudoproblems in Philosophy, translated by R. George. 1967. Berkeley, University of California Press.

Selected Articles and Chapters by Rudolf Carnap

“Der Raum,” Kant-Studien, Vol. 56 (1922).

“Über die Aufgabe der Physik und die Anwendung des Grundsatzes der Einfachsheit,” Kant-Studien, Vol. 28 (1923), 90-107.

“Driedimensionalität des Raumes und Kausalität,” Annalen der Philosophie und philosophischen Kritik, Vol. 4 (1924), 105-130.

“Über die Abhängigkeit der Eigenschaften des Raumes von denen der Zeit,” Kant-Studien, Vol. 30 (1925), 331-45.

[Review] “A.N. Whitehead and B. Russell, Principia Mathematica, 2nd ed.,” Erkenntnis, Vol. 2 (1931), 73-75.

[Review] “B. Russell u. A.N. Whitehead, Einführung in die mathematische Logik,Erkenntnis, Vol. 3 (1933), 436-37.

“Testability and meaning,” Philosophy of Science, Vol. 3 (1936), 419-71.

“Logical foundations of the unity of science,” in O. Neurath et al., International Encyclopedia of Unified Science, Vol. 1, No.1 (Chicago, Chicago University Press, 1938).

“On inductive logic,” Philosophy of Science, Vol. 12 (1945), 72-97.

“Modalities and quantification,” Journal of Symbolic Logic, Vol. 11 (1946), 33-64.

“Empiricism, semantics, and ontology,” Revue Internationale de Philosophie, Vol. 4 (1950), 20-40.

“The elimination of metaphysics through logical analysis of language,” in A.J. Ayer, Logical Positivism (Glencoe, Free Press, 1959), 60-81.

“The old and the new logic,” in A.J. Ayer, Logical Positivism (Glencoe, Free Press, 1959), 133-46.

Readings on Carnap

Creath, R. 1991. Dear Carnap, Dear Van: The Quine-Carnap Correspondence and Related Work (Berkeley, University of California Press).

Bonk, T. (ed.). 2003. Language, Truth and Knowledge (Dordrecht, Kluwer).

Friedman, M. 2000. A Parting of the Ways. Carnap, Cassirer and Heidegger (La Salle, Open Court).

Hintikka, J. 1975. Rudolf Carnap, Logical Empiricist (Dordrecht, Reidel).

Kazemier, B.H. et al. (eds.). 1962. Logic and Language (Dordrecht, Reidel).

Kraft, V. 1950. Der Wiener Kreis (Vienna, Springer).

Leitgeb, H. (forthcoming). The Logical Structure of Empirical Content. Lessons from Carnap’s Aufbau (CSLI, Stanford).

Mayhall, C.W. 2001. On Carnap (Belmont, Wadsworth).

Mormann, T. 2000. Rudolf Carnap (Munich, Beck).

Richardson, A. 1997. Carnap’s Construction of the World (Cambridge, Cambridge University Press).

Schilpp, P. A. 1963. The Philosophy of Rudolf Carnap (La Salle, Open Court).

Spohn, W. (ed.). 1991. Erkenntnis Orientated: A Centennial Volume for Rudolf Carnap and Hans Reichenbach (Dordrecht, Kluwer).

Author Information

Lieven Decock
Faculty of Philosophy
Free University Amsterdam
De Boelelaan 1105, 1081 HV Amsterdam, The Netherlands

How to Cite this Article

Decock, Lieven, “Rudolf Carnap (1891–1970)”, last modified 2008, The Whitehead Encyclopedia, Brian G. Henning and Joseph Petek (eds.), originally edited by Michel Weber and Will Desmond, URL = <>.