Gödel’s Theorem: An End and a Beginning

2017 ◽  
Author(s):  
Jan von Plato
Keyword(s):  
Vienna Circle ◽  
Logical Empiricism ◽  
Rudolf Carnap ◽  
University Of Vienna ◽  
Kurt Gödel ◽  
The World ◽  
The University ◽  
Gödel’S Theorem

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.

The Vienna Circle

2018 ◽  
Author(s):  
Peter Murray
Keyword(s):  
Vienna Circle ◽  
Logical Positivism ◽  
Bertrand Russell ◽  
Gottlob Frege ◽  
Rudolf Carnap ◽  
Ernst Mach ◽  
Kurt Gödel ◽  
The World ◽  
Recent Developments ◽  
Scientific Worldview

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.

scholarly journals On Gödel's Way In: The Influence of Rudolf Carnap

2005 ◽  
Vol 11 (2) ◽  
pp. 185-193 ◽  
Author(s):  
Warren Goldfarb
Keyword(s):  
Philosophy Of Mathematics ◽  
Vienna Circle ◽  
Early Summer ◽  
Mathematical Truth ◽  
Rudolf Carnap ◽  
Modern Logic ◽  
Kurt Gödel ◽  
Representational Capacity ◽  
The Subject ◽  
The University

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.

scholarly journals We praise our heroes : Notes, translation of "The School of Vienna at Prague” by Jean Cavailles. – and the limits of our world.

2019 ◽  
Author(s):  
Camille Akmut
Keyword(s):  
Social Sciences ◽  
Vienna Circle ◽  
Diverse Group ◽  
Far Right ◽  
University Of Vienna ◽  
The University

In this highly influential 1935 text, Jean Cavailles, after describingthe historical sociological characteristics of the so-called “Vienna Circle”,turns to an analysis of Wittgenstein’s Tractatus Logico-Philosophicus, andthree of its thesis specifically which he considers to be central to the under-standing of their ideas. Vienna Circle : a diverse group of philosophers andscientists, and philosopher-scientists, and scientists-turned-philosophers,from the whole array of disciplines, mathematics to social sciences, thatmet regularly at the University of Vienna in the 1920s and 1930s untilthe rise of far-right politics forced them into exile, or killed them. BeforeNazism, they organized meetings and talks to make sense of important ad-vances and works of the sciences of their times; discussions out of whichemerged theirs, which Cavailles renders here for us.

„Bilder zukünftiger Vollendung“ – Der freistudentische Serakreis 1913 in den Tagebüchern und Briefen von und an Wilhelm Flitner

2013 ◽  
Vol 38 (2) ◽  
Author(s):  
Meike G. Werner
Keyword(s):  
Vienna Circle ◽  
Rudolf Carnap ◽  
The University

Conceived as a collage, this essay presents annotated excerpts from diaries and correspondences from the year 1913. It recreates a plethora of voices, especially of young intellectuals, progressive students and artists, focusing on the Sera Circle around the publisher Eugen Diederichs in Jena. Among the voices included are Wilhelm Flitner, who became a professor of education at the University of Hamburg, Rudolf Carnap, who later joined the Vienna Circle, Helene Czapski-Holzman, an artist and student of Max Beckmann, as well as Franz Roh, an art critic, photographer and collage-artist.

Wolfgang Ernst Pauli, 1900-1958

1960 ◽  
Vol 5 ◽  
pp. 174-192 ◽  
Keyword(s):  
Fairy Tales ◽  
Theoretical Physics ◽  
Wolfgang Pauli ◽  
University Of Vienna ◽  
Jules Verne ◽  
University Of Munich ◽  
The Press ◽  
The World ◽  
High Standards ◽  
The University

Wolfgang Pauli was born on 25 April 1900 in Vienna. His father, Wolfgang Joseph Pauli, was distinguished as a biochemist and was a Professor in the University of Vienna; previously he had practised as a doctor, and his patients included many prominent figures in Vienna society. The mother, Bertha, née Schütz, was a writer and had many contacts in the world of the theatre and the press. It is probable that this background and the acquaintance with the leading authorities in many fields had a profound effect in creating the high standards and the impatience with anything but the best of its kind, which became later an important characteristic of the young Pauli. The young Wolfgang showed early signs of exceptional ability. He was outstanding at school in scientific subjects and particularly in mathematics, and first-rate in all other subjects, except in languages in which his performance was good but not exceptional. He was probably a ‘bookish’ child and was not interested in games, though he was, and remained throughout his life, fond of walking, particularly in the mountains, and of swimming. As a small child he disliked fairy tales, which seemed to worry him. As a growing boy he was fascinated by books like those of Jules Verne, and he later developed a special interest in astronomy. His younger sister, Hertha (now Mrs Ashton), had to serve as an audience for his current discoveries in astronomy, and he was most impatient when the audience did not respond adequately to the instruction. In 1918 he became a student in the University of Munich under A. Sommerfeld, and he obtained his Ph.D. there after three years, the shortest period allowed by the University regulations, and exceptionally short for a subject like theoretical physics.

Logical positivism

2018 ◽  
Author(s):  
Michael Friedman
Keyword(s):  
Philosophy Of Science ◽  
National Socialism ◽  
Vienna Circle ◽  
Logical Empiricism ◽  
Logical Positivism ◽  
Scientific Philosophy ◽  
The Usa ◽  
Mathematical Techniques ◽  
English Speaking World ◽  
The University

Logical positivism (logical empiricism, neo-positivism) originated in Austria and Germany in the 1920s. Inspired by late nineteenth- and early twentieth-century revolutions in logic, mathematics and mathematical physics, it aimed to create a similarly revolutionary scientific philosophy purged of the endless controversies of traditional metaphysics. Its most important representatives were members of the Vienna Circle who gathered around Moritz Schlick at the University of Vienna (including Rudolf Carnap, Herbert Feigl, Kurt Gödel, Hans Hahn, Karl Menger, Otto Neurath and Friedrich Waismann) and those of the Society for Empirical Philosophy who gathered around Hans Reichenbach at the University of Berlin (including Walter Dubislav, Kurt Grelling and Carl Hempel). Although not officially members of either group, the Austrian philosophers Ludwig Wittgenstein and Karl Popper were, at least for a time, closely associated with logical positivism. The logical positivist movement reached its apogee in Europe in the years 1928–34, but the rise of National Socialism in 1933 marked the effective end of this phase. Thereafter, however, many of its most important representatives emigrated to the USA. Here logical positivism found a receptive audience among such pragmatically, empirically and logically minded American philosophers as Charles Morris, Ernest Nagel and W.V. Quine. Thus transplanted to the English-speaking world of ‘analytic’ philosophy it exerted a tremendous influence – particularly in philosophy of science and the application of logical and mathematical techniques to philosophical problems more generally. This influence began to wane around 1960, with the rise of a pragmatic form of naturalism due to Quine and a historical-sociological approach to the philosophy of science due mainly to Thomas Kuhn. Both of these later trends, however, developed in explicit reaction to the philosophy of logical positivism and thereby attest to its enduring significance.

Editorial: The Migration Conference and 13 years of Migration Letters

2016 ◽  
Vol 13 (3) ◽  
pp. 329-332
Author(s):  
Ibrahim Sirkeci ◽  
Philip L. Martin
Keyword(s):  
Presidential Campaign ◽  
Migration Studies ◽  
Economic Crises ◽  
Donald Trump ◽  
University Of Vienna ◽  
The Us ◽  
The World ◽  
And Migration ◽  
The University ◽  
The Eu

Questions concerning migration and refugees made the headlines around the world in recent years amid wars in many locations coinciding with economic crises and slow down. Migration as a subject and migration studies as a field are ever more popular, and Migration Letters supported the 4th Turkish Migration Conference (http://turkishmigration.com), which attracted about 400 participants to the University of Vienna. Some 350 papers were presented in plenary and parallel sessions over four days from 12 to 15 July 2016. In summer 2016, Europeans debated how to reduce the influx of unwanted foreigners and integrate those who are settling, the US presidential campaign featured candidate Donald Trump calling for a wall on the Mexico-US border and the deportation of 11 million unauthorized foreigners, and the British voted 52-48 percent to leave the EU because of “too much” intra-EU migration.

scholarly journals Profesor Marian Smoluchowski (1872–1917) – zapomniany rektor Uniwersytetu Jagiellońskiego

2020 ◽  
pp. 87-110
Author(s):  
Grzegorz P. Słowik
Keyword(s):  
World Wide ◽  
Albert Einstein ◽  
Scientific Activity ◽  
Experimental Physics ◽  
Natural Laws ◽  
Childhood Education ◽  
University Of Vienna ◽  
Inaugural Lecture ◽  
The World ◽  
The University

Professor Marian Smoluchowski (1872–1917): The Forgotten Rector of the Jagiellonian University The article presents the figure of the great Polish physicist Professor Marian Smoluchowski who lived at the turn of the 19th and 20th centuries. It presents his most important achievements as a scientist, a physicist of the Nobel Prize dimension, and in other fields:: didactic, organizational, as well as personal (related to his greatest passion – mountaineering). The study specifies the three most important periods of Smoluchowski’s life and scientific activity: the Vienna, Lviv and Krakow periods, and describes his cooperation with other scholars, mostly of the world-wide renown, such as Albert Einstein. The Viennese period included childhood, education at the Collegium Theresianum, physical studies at the University of Vienna, PhD and habilitation. In Lviv, Smoluchowski spent fourteen years employed at Jan Kazimierz University. There, he developed, among others, the theory of Brownian motion. He spent the last four years of his life in Krakow as a professor at the Jagiellonian University, where he mainly dealt with experimental physics. In 1917 he was elected rector of the University, but in the same year, at the age of 45, he died prematurely of dysentery before taking over this office. He managed to prepare the inaugural lecture “On the uniformity of natural laws.”

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