Semantic Revolution Rudolf Carnap, Kurt Gödel, Alfred Tarski

Author(s):  
Jan Woleński
Author(s):  
Eva-Maria Engelen

ZusammenfassungGegenstandes des Aufsatzes ist die gegenseitige Beeinflussung und Bezugnahme von Rudolf Carnap und Kurt Gödel in ihren jeweiligen Selbstzeugnissen während der 20er- bis 40er-Jahre des 20. Jahrhunderts. Der Vergleicht bestätigt die bisherige Forschung, der zufolge Carnap auf Gödels Arbeiten der Jahre 1930 und 1931 einigen Einfluss hatte. Er zeigt darüber hinaus, dass die beiden sich größtenteils als mathematische Logiker wahrgenommen und rezipiert haben. Nach allem, was wir bisher wissen, bleibt das so hinsichtlich Carnaps Wertschätzung für Gödels Denken. Gödel wendet sich hingegen Carnap ab 1934 auch als einem philosophischen Denker zu, dessen Philosophie eine gewisse Nähe zu der von Gottfried Wilhelm Leibniz aufweist, aber anders als letztere, von Gödel kritisch gesehen wird.


Author(s):  
Anna Brożek

AbstractIn March 1930, Alfred Tarski visited Vienna and delivered few lectures which presented the achievements of the logical branch of the Lvov-Warsaw School. Rudolf Carnap was one of the most careful listeners of these lectures. The same year, in November, Carnap, invited by the Warsaw Philosophical Society, visited Warsaw where he gave three lectures. This was an opportunity for him to meet such members the Lvov-Warsaw School as Jan Łukasiewicz, Stanisław Leśniewski, Tadeusz Kotarbiński, and others. Many years later, Carnap reminisced that he left Warsaw “grateful for many stimulating suggestions and the fruitful exchange of ideas”.In the paper, I reconstruct the details of Carnap’s visit in Warsaw based on Carnap’s diaries, reports published in the Polish Journal Ruch Filozoficzny [Philosophical Movement] and some correspondence. I also discuss some problems presented by Carnap in Warsaw lectures and compare his views to the positons of members of the Lvov-Warsaw School. These problems are: the foundations of psychology, the status of metaphysical sentences, and the character of reasoning.


Author(s):  
Peter Murray

In 1922 Moritz Schlick (1882–1936) transformed the Verein Ernst Mach (Ernst Mach Society), a weekly reading group concerned with logical positivism, into an international assembly of academics known as der Weiner Kreis, or the Vienna Circle, which responded to recent developments within analytic philosophy by leading thinkers Bertrand Russell (1872–1970), Gottlob Frege (1848–1925) and Ludwig Wittgenstein (1889–1951). Early members included Rudolf Carnap (1891–1970), Kurt Gödel (1906–1978) and Otto Neurath (1882–1945). In 1929, Neurath published Wissenschaftliche Weltauffassung. Der Wiener Kreis (The Scientific Conception of the World: The Vienna Circle), a pamphlet delineating the group’s rejection of metaphysics in favour of a scientific worldview predicated upon empirical phenomena.


Author(s):  
Jan von Plato

This chapter discusses how Kurt Gödel found his theorem. He started to study physics at the University of Vienna in 1924, then changed to mathematics in 1926. That same year, he started attending the meetings of the Vienna Circle. These were weekly gatherings on philosophical topics that were headed by the philosopher Moritz Schlick. The philosophy of the circle came to be known as logical empiricism and had an enormous effect on the world of philosophy. Gödel later wanted to emphasize that he by no means shared all of the philosophical ideas of the circle. In the meetings, Gödel came to know the philosopher Rudolf Carnap and the mathematician Karl Menger, in whose mathematical colloquium he later presented many of his results.


Author(s):  
Friedrich Stadler

The Vienna Circle was a group of about three dozen thinkers drawn from the natural and social sciences, logic and mathematics who met regularly in Vienna between the wars to discuss philosophy. The work of this group constitutes one of the most important and most influential philosophical achievements of the twentieth century, especially in the development of analytic philosophy and philosophy of science. The Vienna Circle made its first public appearance in 1929 with the publication of its manifesto, The Scientific Conception of the World: The Vienna Circle (Carnap, Hahn and Neurath 1929). At the centre of this modernist movement was the so-called ‘Schlick Circle’, a discussion group organized in 1924 by the physics professor Moritz Schlick. Friedrich Waismann, Herbert Feigl, Rudolf Carnap, Hans Hahn, Philipp Frank, Otto Neurath, Viktor Kraft, Karl Menger, Kurt Gödel and Edgar Zilsel belonged to this inner circle. Their meetings in the Boltzmanngasse were also attended by Olga Taussky-Todd, Olga Hahn-Neurath, Felix Kaufmann, Rose Rand, Gustav Bergmann and Richard von Mises, and on some occasions by visitors from abroad such as Hans Reichenbach, Alfred Ayer, Ernest Nagel, Willard Van Orman Quine and Alfred Tarski. This discussion circle was pluralistic and committed to the ideals of the Enlightenment. It was unified by the aim of making philosophy scientific with the help of modern logic on the basis of scientific and everyday experience. At the periphery of the Schlick Circle, and in a more or less strong osmotic contact with it, there were loose discussion groups around Ludwig Wittgenstein, Heinrich Gomperz, Richard von Mises and Karl Popper. In addition the mathematician Karl Menger established in the years 1926–36 an international mathematical colloquium, which was attended by Kurt Gödel, John von Neumann and Alfred Tarski among others. Thus the years 1924–36 saw the development of an interdisciplinary movement whose purpose was to transform philosophy. Its public profile was provided by the Ernst Mach Society through which members of the Vienna Circle sought to popularize their ideas in the context of programmes for national education in Vienna. The general programme of the movement was reflected in its publications, such as the journal Erkenntnis (‘Knowledge’, later called The Journal for Unified Science), and the International Encyclopedia of Unified Science. Given this story of intellectual success, the fate of the Vienna Circle was tragic. The Ernst Mach Society was suspended in 1934 for political reasons, Moritz Schlick was murdered in 1936, and around this time many members of the Vienna Circle left Austria for racial and political reasons; thus soon after Schlick’s death the Circle disintegrated. As a result of the emigration of so many of its members, however, the characteristic ideas of the Vienna Circle became more and more widely known, especially in Scandinavia, Britain and North America where they contributed to the emergence of modern philosophy of science. In Germany and Austria, however, the philosophical and mathematical scene was characterized by a prolongation of the break that was caused by the emigration of the members of the Vienna Circle.


2005 ◽  
Vol 11 (2) ◽  
pp. 185-193 ◽  
Author(s):  
Warren Goldfarb

The philosopher Rudolf Carnap (1891–1970), although not himself an originator of mathematical advances in logic, was much involved in the development of the subject. He was the most important and deepest philosopher of the Vienna Circle of logical positivists, or, to use the label Carnap later preferred, logical empiricists. It was Carnap who gave the most fully developed and sophisticated form to the linguistic doctrine of logical and mathematical truth: the view that the truths of mathematics and logic do not describe some Platonistic realm, but rather are artifacts of the way we establish a language in which to speak of the factual, empirical world, fallouts of the representational capacity of language. (This view has its roots in Wittgenstein's Tractatus, but Wittgenstein's remarks on mathematics beyond first-order logic are notoriously sparse and cryptic.) Carnap was also the thinker who, after Russell, most emphasized the importance of modern logic, and the distinctive advances it enables in the foundations of mathematics, to contemporary philosophy. It was through Carnap's urgings, abetted by Hans Hahn, once Carnap arrived in Vienna as Privatdozent in philosophy in 1926, that the Vienna Circle began to take logic seriously and that positivist philosophy began to grapple with the question of how an account of mathematics compatible with empiricism can be given (see Goldfarb 1996).A particular facet of Carnap's influence is not widely appreciated: it was Carnap who introduced Kurt Gödel to logic, in the serious sense. Although Gödel seems to have attended a course of Schlick's on philosophy of mathematics in 1925–26, his second year at the University, he did not at that time pursue logic further, nor did the seminar leave much of a trace on him. In the early summer of 1928, however, Carnap gave two lectures to the Circle which Gödel attended, or so I surmise. At these occasions, Carnap presented material from his manuscript treatise, Untersuchungen zur allgemeinen Axiomatik, that is, “Investigations into general axiomatics”, which dealt with questions of consistency, completeness and categoricity. Carnap later circulated this material to various people including Gödel.


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