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After serving in WWI, Rudolf attended the University of Jena where he earned his Doctorate. While at Jena, he wrote a dissertation on the concept of space. "He argued that the conflicts between the various theories of space then held by scholars resulted from the fact that those theories actually dealt with quite different subjects; he called them, formal space, physical space, and intuitive space and exhibited their principal characteristics and fundamental differences."(Britannica 2022)
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A small group of scholars who met and discussed philosophical issues, at the University of Vienna, extended an invitation to Rudolf to join their group. The Vienna Circle. While apart of the Vienna Circle, Rudolf became a prominent figure at the university and with his involvement with the Logical Empiricism Movement, Logical Positivism.
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Known to be his first great work, Rudolf created Der logische Aufbau der Welt or, The Logical Structure of the World. "Carnap developed, with unprecedented rigor, a version of the empiricist reducibility thesis according to which all terms suited to describe actual or possible empirical facts are fully definable by terms referring exclusively to aspects of immediate experience, so that all empirical statements are fully translatable into statements about immediate experiences."(Britannica 2022)
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Rudolf eventually moved to Chicago. Soon after his arrival, he joined a Vienna Circle colleague and a pragmatist philosopher in the creation of the International Encyclopedia of Unified Science. It was published "... as a series of monographs on general problems in the philosophy of science and on philosophical issues concerning mathematics or particular branches of empirical science."(Britannica 2022)
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His major works include The Logical Structure of the World (1928), The Logical Syntax of Language (1934), Introduction to Semantics (1942), Meaning and Necessity (1947), and The Logical Foundations of Probability (1950).