Foundations of Logic and Mathematics.

1953. Chicago, The University of Chicago Press, (1953). 8vo. In the original blue printed wrappers. Light miscolouring and wear to extremities. Paper label pasted on to verso of back wrapper. Otherwise a fine and clean copy. VIII, 71 pp. Seventh impression of Carnap's seminal publication of his semantical period. Here Carnap presents a clear and detailed account of the application of logic and mathematics in empirical science and the central importance of the analytic/synthetic distinction herein.Carnap thought that the logic of science could be fruitfully applied to the problems of quantum theory as well. In particular, the final sections of Foundations of Logic and Mathematics (1939, §§24, 25) suggest that the vexed question of the "interpretation" of the wave-function can be resolved by appreciating that theories of modern mathematical physics operate with "abstract" terms which are implicitly defined, in the manner of Hilbert, in an axiomatic system (and thus require no "intuitive" or "visualizable" meaning) but which still relate to empirical phenomena (experimental measurements) indirectly. (Cambridge Companion to Carnap).These thoughts anticipate Carnap's later conception of the "partial interpretation" of theoretical terms.Rudolf Carnap (born 1891 in Ronsdorf, Germany, died 1970 in Santa Monica, California) was an immensely influential analytic philosopher, who has contributed decisively to the fields of logic, epistemology, semantics, philosophy of science, and philosophy of language. He was one of the leading figures of the Vienna Circle, and a prominent logical positivist. He studied philosophy, physics and mathematics at the universities of Berlin and Freiburg, and worked at the universities of Jena, Vienna and Prague until 1935, when he, due to the war, emigrated to the U.S., where he became an American citizen in 1941. In America he became professor of the University of Chicago.