Rudolf Carnap
Rudolf Carnap
Born (1891-05-18)May 18, 1891
Ronsdorf, Lennep, Düsseldorf, Rhine, Prussia, German Empire
Santa Monica, California U.S.
Alma mater University of Jena (PhD, 1921)
Era 20th-century philosophy
Region Western philosophy
School Analytic philosophy
Logical atomism[1]
Main interests
Logic · Epistemology
Philosophy of science
Notable ideas
Phenomenalism in linguistic terms
Analytic-synthetic distinction (revised)
Semantics for modal logic
Constructed systems
Conceptual schemes
Beobachtungssatz (observational statement)
Carnap's categoricity (Monomorphie)[3] problem
Forkability theorem (Gabelbarkeitssatz): "every complete axiom system is also categorical (monomorph)"[4][5]
Logical positivism
Epistemic structural realism[6]
Ramsey sentences

Rudolf Carnap (;[7]German: ['ka??na:p]; May 18, 1891 - September 14, 1970) was a German-born philosopher who was active in Europe before 1935 and in the United States thereafter. He was a major member of the Vienna Circle and an advocate of logical positivism. He is considered "one of the giants among twentieth-century philosophers."[8]

Life and work

Carnap's birthplace in Wuppertal

Carnap's father had risen from the status of a poor ribbon-weaver to become the owner of a ribbon-making factory. His mother came from academic stock; her father was an educational reformer and her oldest brother was the archaeologist Wilhelm Dörpfeld. As a ten-year-old, Carnap accompanied his uncle on an expedition to Greece.[9] Carnap was raised in a religious family, but later became an atheist.[10]

He began his formal education at the Barmen Gymnasium. From 1910 to 1914, he attended the University of Jena, intending to write a thesis in physics. But he also studied carefully Kant's Critique of Pure Reason during a course taught by Bruno Bauch, and was one of very few students to attend Gottlob Frege's courses in mathematical logic. While Carnap held moral and political opposition to World War I, he felt obligated to serve in the German army. After three years of service, he was given permission to study physics at the University of Berlin, 1917-18, where Albert Einstein was a newly appointed professor. Carnap then attended the University of Jena, where he wrote a thesis defining an axiomatic theory of space and time. The physics department said it was too philosophical, and Bruno Bauch of the philosophy department said it was pure physics. Carnap then wrote another thesis in 1921, with Bauch's supervision, on the theory of space in a more orthodox Kantian style, and published as Der Raum ("Space") in a supplemental issue of Kant-Studien (1922). In it he makes the clear distinction between formal, physical and perceptual (e.g., visual) spaces.

Frege's course exposed him to Bertrand Russell's work on logic and philosophy, which put a sense of the aims to his studies. He accepted the effort to surpass traditional philosophy with logical innovations that inform the sciences. He wrote a letter to Russell, who responded by copying by hand long passages from his Principia Mathematica for Carnap's benefit, as neither Carnap nor his university could afford a copy of this epochal work. In 1924 and 1925, he attended seminars led by Edmund Husserl,[11] the founder of phenomenology, and continued to write on physics from a logical positivist perspective.

Carnap discovered a kindred spirit when he met Hans Reichenbach at a 1923 conference. Reichenbach introduced Carnap to Moritz Schlick, a professor at the University of Vienna who offered Carnap a position in his department, which Carnap accepted in 1926. Carnap thereupon joined an informal group of Viennese intellectuals that came to be known as the Vienna Circle, directed largely by Moritz Schlick and including Hans Hahn, Friedrich Waismann, Otto Neurath, and Herbert Feigl, with occasional visits by Hahn's student Kurt Gödel. When Wittgenstein visited Vienna, Carnap would meet with him. He (with Hahn and Neurath) wrote the 1929 manifesto of the Circle, and (with Hans Reichenbach) initiated the philosophy journal Erkenntnis.

In 1928, Carnap published two important books:

  • The Logical Structure of the World (German: "Der logische Aufbau der Welt"), in which he developed a rigorous formal version of empiricism, defining all scientific terms in phenomenalistic terms. The formal system of the Aufbau (as the work is commonly termed) was grounded in a single primitive dyadic predicate, which is satisfied if "two" individuals "resemble" each other. The Aufbau was greatly influenced by Principia Mathematica, and warrants comparison with the mereotopological metaphysics A. N. Whitehead developed over 1916-29. It appears, however, that Carnap soon became somewhat disenchanted with this book. In particular, he did not authorize an English translation until 1967.
  • Pseudoproblems in Philosophy asserted that many philosophical questions were meaningless, i.e., the way they were posed amounted to an abuse of language. An operational implication of this opinion was taken to be the elimination of metaphysics from responsible human discourse. This is the statement for which Carnap was best known for many years. (See also: Ramsey sentence.)

In February 1930 Tarski lectured in Vienna, and during November 1930 Carnap visited Warsaw. On these occasions he learned much about Tarski's model theoretic method of semantics. Rose Rand, another philosopher in the Vienna Circle, noted, "Carnap's conception of semantics starts from the basis given in Tarski's work but a distinction is made between logical and non-logical constants and between logical and factual truth... At the same time he worked with the concepts of intension and extension and took these two concepts as a basis of a new method of semantics."[12]

In 1931, Carnap was appointed Professor at the German language University of Prague. There he wrote the book that was to make him the most famous logical positivist and member of the Vienna Circle, his Logical Syntax of Language (Carnap 1934). In this work, Carnap advanced his Principle of Tolerance, according to which there is not any such thing as a "true" or "correct" logic or language. One is free to adopt whatever form of language is useful for one's purposes. In 1933, W. V. Quine met Carnap in Prague and discussed the latter's work at some length. Thus began the lifelong mutual respect these two men shared, one that survived Quine's eventual forceful disagreements with a number of Carnap's philosophical conclusions.

Carnap, whose socialist and pacifist beliefs put him at risk in Nazi Germany, emigrated to the United States in 1935 and became a naturalized citizen in 1941. Meanwhile, back in Vienna, Moritz Schlick was murdered in 1936. From 1936 to 1952, Carnap was a professor of philosophy at the University of Chicago. During the late 1930s, Carnap offered an assistant position in philosophy to Carl Gustav Hempel, who accepted. The two conducted research including Logical Syntax.[13] Thanks partly to Quine's help, Carnap spent the years 1939-41 at Harvard, where he was reunited with Tarski. Carnap (1963) later expressed some irritation about his time at Chicago, where he and Charles W. Morris were the only members of the department committed to the primacy of science and logic. (Their Chicago colleagues included Richard McKeon, Mortimer Adler, Charles Hartshorne, and Manley Thompson.) Carnap's years at Chicago were nonetheless very productive ones. He wrote books on semantics (Carnap 1942, 1943, 1956), modal logic, being very similar in Carnap (1956) to the now-standard possible worlds semantics for that logic Saul Kripke proposed starting in 1959, and on the philosophical foundations of probability and induction (Carnap 1950, 1952).

After a stint at the Institute for Advanced Study in Princeton, he joined the philosophy department at UCLA in 1954, Hans Reichenbach having died the previous year. He had earlier refused an offer of a similar job at the University of California, because accepting that position required that he sign a loyalty oath, a practice to which he was opposed on principle. While at UCLA, he wrote on scientific knowledge, the analytic - synthetic dichotomy, and the verification principle. His writings on thermodynamics and on the foundations of probability and induction, were published posthumously as Carnap (1971, 1977, 1980).

Carnap taught himself Esperanto when he was 14 years of age, and remained sympathetic to it (Carnap 1963). He later attended the World Congress of Esperanto in 1908 and 1922, and employed the language while traveling.

Carnap had four children by his first marriage to Elizabeth Schöndube, which ended in divorce in 1929. He married his second wife, Elizabeth Ina Stöger, in 1933.[9] Ina committed suicide in 1964.

Logical syntax

Carnap's Logical Syntax of Language can be regarded as a response to Wittgenstein's Tractatus.

Carnap elaborated and extended the concept of logical syntax proposed by Wittgenstein in the Tractatus (Section 3.325).

3.325. In order to avoid such errors we must make use of a sign-language that excludes them by not using the same sign for different symbols and by not using in a superficially similar way signs that have different modes of signification: that is to say, a sign-language that is governed by logical grammar--by logical syntax.

-- Wittgenstein, Section 3.325, Tractatus

However, Wittgenstein stated that propositions cannot represent logical form.

4.121. Propositions cannot represent logical form: it is mirrored in them. What finds its reflection in language, language cannot represent. What expresses itself in language, we cannot express by means of language. Propositions show the logical form of reality. They display it.

-- Wittgenstein, Section 4.121, Tractatus

Carnap disagreed. Wittgenstein proposed the idea of logical syntax. It is Carnap who designed, formulated and implemented the details of logical syntax in philosophical analysis. Carnap defined logical syntax as:

By the logical syntax of a language, we mean the formal theory of the linguistic forms of that language - the systematic statement of the formal rules which govern it together with the development of the consequences which follow from these rules. A theory, a rule, a definition, or the like is to be called formal when no reference is made in it either to the meaning of the symbols (for examples, the words) or to the sense of the expressions (e.g. the sentences), but simply and solely to the kinds and order of the symbols from which the expressions are constructed.

-- Carnap, Page 1, Logical Syntax of Language

In the U.S, the concept of logical syntax helped the development of natural language processing and compiler design.[]

The purpose of logical syntax

The purpose of logical syntax is to provide a system of concepts, a language, by the help of which the results of logical analysis will be exactly formulable.

Carnap stated:

Philosophy is to be replaced by the logic of science - that is to say, by the logical analysis of the concepts and sentences of the sciences, for the logic of science is nothing other than the logical syntax of the language of science.

-- Carnap, Foreword, Logical Syntax of Language

According to this view, the sentences of metaphysics are pseudo-sentences which on logical analysis are proved to be either empty phrases or phrases which violate the rules of syntax. Of the so-called philosophical problems, the only questions which have any meaning are those of the logic of science. To share this view is to substitute logical syntax for philosophy.

-- Carnap, Page 8, Logical Syntax of Language

Carnap wanted only to end metaphysics but not philosophy.

Rejection of metaphysics

Carnap, in his book Philosophy and Logical Syntax, used the concept of verifiability to reject metaphysics.

The function of logical analysis

Carnap used the method of logical analysis to reject metaphysics.

The function of logical analysis is to analyse all knowledge, all assertions of science and of everyday life, in order to make clear the sense of each such assertion and the connections between them. One of the principal tasks of the logical analysis of a given proposition is to find out the method of verification for that proposition.

-- Carnap , Page. 9-10, Philosophy and Logical Syntax

Primary source materials

The Carnap Papers consist of approximately 10,000 personal letters of correspondence. The papers were donated by his daughter, Hanna Carnap-Thost in 1974. Documents that contain financial, medical, and personal information are restricted.[14] These were written over his entire life and career. Carnap used the mail regularly to discuss philosophical problems with hundreds of others. The most notable were: Herbert Feigl, Carl Gustav Hempel, Felix Kaufmann, Otto Neurath, and Moritz Schlick. Photographs are also part of the collection and were taken throughout his life. Family pictures and photographs of his peers and colleagues are also stored in the collection. Some of the correspondence is considered notable and consist of his student notes, his seminars with Frege, (describing the Begriffsschrift and the logic in mathematics). Carnap's notes from Russell's seminar in Chicago, and notes he took from discussions with Tarski, Heisenberg, Quine, Hempel, Gödel, Jeffrey are part of the University of Pittsburgh's Archives and Collections. Digitized contents include:

  • Notes (old), 1958-1966[15]

More than 1,000 pages of lecture outlines are preserved that cover the courses that Carnap taught in the United States, Prague, and Vienna, Prague. Drafts of his published works and unpublished works are part of the collection. includes manuscript drafts and typescripts both for his published works and for many unpublished papers and books. A partial listing include his first formulations of his "Aufbau". "Quasizerlegung"(1932), and "Vom Chaos zur Wirklichkeit"(1922) "Topologie der Raum-Zeit-Welt" (Topology of the Space-Time World, 1924) is his later 104-page piece about a logical reconstruction of the space-time framework without the use of mathematics. The holdings include a large number of unpublished papers. Much material is written in an older German shorthand, the Stolze-Schrey system. He employed this writing system extensively beginning in his student days.[14] Much of the content has been digitized. The University of California also maintains a collection of Rudolf Carnap Papers. Microfilm copies of his papers are maintaind by the Philosophical Archives at the University of Konstanz in Germany.[16]

Selected publications

For links to Carnap's publications and discussions of his work, see ""Carnap" in All Fields of Study". Microsoft Academic Search. Retrieved . 

  • 1922. Der Raum: Ein Beitrag zur Wissenschaftslehre, Kant-Studien, Ergänzungshefte, no. 56. His Ph.D. thesis.
  • 1926. Physikalische Begriffsbildung. Karlsruhe: Braun.
  • 1928. Scheinprobleme in der Philosophie (Pseudoproblems of Philosophy). Berlin: Weltkreis-Verlag.
  • 1928. Der Logische Aufbau der Welt. Leipzig: Felix Meiner Verlag. English translation by Rolf A. George, 1967. The Logical Structure of the World. Pseudoproblems in Philosophy. University of California Press. ISBN 0-812-69523-2
  • 1929. Abriss der Logistik, mit besonderer Berücksichtigung der Relationstheorie und ihrer Anwendungen. Springer.[17]
  • 1934. Logische Syntax der Sprache. English translation 1937, The Logical Syntax of Language. Kegan Paul.[18]
  • 1996 (1935). Philosophy and Logical Syntax. Bristol UK: Thoemmes. Excerpt.
  • 1939, Foundations of Logic and Mathematics in International Encyclopedia of Unified Science, Vol. I, no. 3. University of Chicago Press.[19]
  • 1942. Introduction to Semantics. Harvard Uni. Press.
  • 1943. Formalization of Logic. Harvard Uni. Press.
  • 1945. On Inductive Logic in Philosophy of Science, Vol.12, p. 72-97.
  • 1945. The Two Concepts of Probability in Philosophy and Phenomenological Research, Vol.5, No.4 (Jun), p. 513-532.
  • 1947. On the Application of Inductive Logic in Philosophy and Phenomenological Research, Vol. 8, p. 133-148.
  • 1956 (1947). Meaning and Necessity: a Study in Semantics and Modal Logic. University of Chicago Press.
  • 1950. Logical Foundations of Probability. University of Chicago Press. Pp. 3-15 online.
  • 1950. "Empiricism, Semantics, Ontology", Revue Internationale de Philosophie 4: 20-40.
  • 1952. The Continuum of Inductive Methods. University of Chicago Press.
  • 1958. Introduction to Symbolic Logic and its Applications. Dover publications, New York. ISBN 9780486604534
  • 1963, "Intellectual Autobiography" in Schilpp (1963: 1-84).
  • 1966. Philosophical Foundations of Physics. Martin Gardner, ed. Basic Books. Online excerpt.
  • 1971. Studies in inductive logic and probability, Vol. 1. University of California Press.
  • 1977. Two essays on entropy. Shimony, Abner, ed. University of California Press.
  • 1980. Studies in inductive logic and probability, Vol. 2. Jeffrey, R. C., ed. University of California Press.
  • 2000. Untersuchungen zur Allgemeinen Axiomatik. Edited from unpublished manuscript by T. Bonk and J. Mosterín. Darmstadt: Wissenschaftliche Buchgesellschaft. 167 pp. ISBN 3-534-14298-5.

Online bibliography. Under construction, with no entries dated later than 1937.


  • Interview with Rudolf Carnap, German TV, 1964.

See also


  1. ^ Carnap, R. (1934), "On the Character of Philosophic Problems (Über den Charakter der philosophischen Probleme)," translation by W. M. Malisoff, Philosophy of Science, 1, pp. 5-19.
  2. ^ Rudolf Carnap, The Logical Syntax of Language, Routledge & Kegan Paul, 1937, pp. 13-14.
  3. ^ A. W. Carus, Carnap and Twentieth-Century Thought: Explication as Enlightenment, Cambridge University Press, 2007, p. 222.
  4. ^ A. W. Carus, Carnap and Twentieth-Century Thought: Explication as Enlightenment, Cambridge University Press, 2007, pp. 223 and 227; Thomas Uebel, Empiricism at the Crossroads: The Vienna Circle's Protocol-Sentence Debate Revisited, Open Court, 2015, p. 142.
  5. ^ Steve Awodey pronounces Carnap's Gabelbarkeitssatz-related pursuits "ill-fated" (Steve Awodey, "Structuralism, Invariance, and Univalence" (March 4, 2014)).
  6. ^ "Structural Realism": entry by James Ladyman in the Stanford Encyclopedia of Philosophy
  7. ^ "Carnap". Random House Webster's Unabridged Dictionary.
  8. ^ California Digital Library
  9. ^ a b Quine, W.V. and Rudolf Carnap (1990). Dear Carnap, Dear Van: The Quine-Carnap Correspondence and Related Work. Berkeley, CA: University of California Press. p. 23. 
  10. ^ "Carnap had a modest but deeply religious family background, which might explain why, although he later became an atheist, he maintained a respectful and tolerant attitude in matters of faith throughout his life." Buldt, Bernd: "Carnap, Paul Rudolf", Complete Dictionary of Scientific Biography Vol. 20 p.43. Detroit: Charles Scribner's Sons, 2008.
  11. ^ Smith, D. W., and Thomasson, Amie L. (eds.), 2005, Phenomenology and Philosophy of Mind. Oxford and New York: Oxford University Press, p. 8 n. 18.
  12. ^ Rand, Rose. "Reading Notes and Summaries on Works by Rudolph Carnap, 1932 and Undated" (PDF). Rose Rand Papers. Special Collections Department, University of Pittsburgh. Retrieved 2013. 
  13. ^ Carnap, Rudolf. "Rudolf Carnap Papers". Special Collections Department, University of Pittsburgh. Retrieved 2013. 
  14. ^ a b "Guides to Archives and Manuscript Collections at the University of Pittsburgh Library System". 
  15. ^ "AS Notes (old), 1958-1966 Box 19, Folder 7 Rudolf Carnap Papers, 1905-1970, ASP.1974.01, Special Collections Department, University of Pittsburgh" (PDF). Retrieved . 
  16. ^ "Finding Aid for the Rudolf Carnap papers, 1920-1968". Retrieved . 
  17. ^ Weiss, Paul (1929). "Review: Abriss der Logistik by Rudolf Carnap" (PDF). Bull. Amer. Math. Soc. 35 (6): 880-881. doi:10.1090/s0002-9904-1929-04818-3. 
  18. ^ Mac Lane, Saunders (1938). "Review: The Logical Syntax of Language by Rudolf Carnap, translated from the German by Amethe Smeaton" (PDF). Bull. Amer. Math. Soc. 44 (3): 171-176. doi:10.1090/S0002-9904-1938-06694-3. 
  19. ^ Church, Alonzo (1939). "Review: Foundations of Logic and Mathematics by Rudolf Carnap" (PDF). Bull. Amer. Math. Soc. 45 (11): 821-822. doi:10.1090/s0002-9904-1939-07085-7. 


  • Richard Creath, Michael Friedman, ed. (2007). The Cambridge companion to Carnap. Cambridge University Press. ISBN 0521840155. 
  • Roger F Gibson, ed. (2004). The Cambridge companion to Quine. Cambridge University Press. ISBN 0521639492. 
  • Ivor Grattan-Guinness, 2000. In Search of Mathematical Roots. Princeton Uni. Press.
  • Thomas Mormann, 2000. "Rudolf Carnap" (book). München, Beck.
  • Willard Quine
    • 1951, Two Dogmas of Empiricism. The Philosophical Review 60: 20-43. Reprinted in his 1953 From a Logical Point of View. Harvard University Press.
    • 1985, The Time of My Life: An Autobiography. MIT Press.
  • Richardson, Alan W., 1998. Carnap's construction of the world : the Aufbau and the emergence of logical empiricism. Cambridge Uni. Press.
  • Schilpp, P. A., ed., 1963. The Philosophy of Rudolf Carnap. LaSalle IL: Open Court.
  • Spohn, Wolfgang, ed., 1991. Erkenntnis Orientated: A Centennial Volume for Rudolf Carnap and Hans Reichenbach. Kluwer Academic Publishers.
  • 1991. Logic, Language, and the Structure of Scientific Theories: Proceedings of the Carnap-Reichenbach Centennial, University of Konstanz, May 21-24, 1991. University of Pittsburgh Press.
  • Wagner, Pierre, ed., 2009. Carnap's Logical Syntax of Language. Palgrave Macmillan.
  • Wagner, Pierre, ed., 2012. Carnap's Ideal of Explication and Naturalism. Palgrave Macmillan.

External links

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