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Kurt Gödel
Paris of the year 1900 left two landmarks: the Tour Eiffel, and David Hilbert's celebrated list of twenty-four mathematical problems presented at a conference opening the new century. Kurt Gödel, a logical icon of that time, showed Hilbert's ideal of complete axiomatization of mathematics to be unattainable. The result, of 1931, is called Gödel's incompleteness theorem. Gödel then went on to attack Hilbert's first and second Paris problems, namely Cantor's continuum problem about the type of infinity of the real numbers, and the freedom from contradiction of the theory of real numbers. By 1963, it became clear that Hilbert's first question could not be answered by any known means, half of...
Kurt Gödel: Results on Foundations
Kurt Gödel (1906-1978) gained world-wide fame by his incompleteness theorem of 1931. Later, he set as his aim to solve what are known as Hilbert's first and second problems, namely Cantor's continuum hypothesis about the cardinality of real numbers, and secondly the consistency of the theory of real numbers and functions. By 1940, he was halfway through the first problem, in what was his last published result in logic and foundations. His intense attempts thereafter at solving these two problems have remained behind the veil of a forgotten German shorthand he used in all of his writing. Results on Foundations is a set of four shorthand notebooks written in 1940-42 that collect results Göde...
Kurt Gödel
Paris of the year 1900 left two landmarks: the Tour Eiffel, and David Hilbert's celebrated list of twenty-four mathematical problems presented at a conference opening the new century. Kurt Gödel, a logical icon of that time, showed Hilbert's ideal of complete axiomatization of mathematics to be unattainable. The result, of 1931, is called Gödel's incompleteness theorem. Gödel then went on to attack Hilbert's first and second Paris problems, namely Cantor's continuum problem about the type of infinity of the real numbers, and the freedom from contradiction of the theory of real numbers. By 1963, it became clear that Hilbert's first question could not be answered by any known means, half of...
Chapters from Gödel’s Unfinished Book on Foundational Research in Mathematics
This volume contains English translations of Gödel's chapters on logicism and the antinomies and on the calculi of pure logic, as well as outlines for a chapter on metamathematics. It also comprises most of his reading notes. This book is a testimony to Gödel's understanding of the situation of foundational research in mathematics after his great discovery, the incompleteness theorem of 1931. It is also a source for his views on his logical predecessors, from Leibniz, Frege, and Russell to his own times. Gödel's "own book on foundations," as he called it, is essential reading for logicians and philosophers interested in foundations. Furthermore, it opens a new chapter to the life and achievement of one of the icons of 20th century science and philosophy.
Selected Reflections in Language, Logic, and Information
The European Summer School in Logic, Language and Information (ESSLLI) is organized every year by the Association for Logic, Language and Information (FoLLI) in different sites around Europe. The papers cover vastly dierent topics, but each fall in the intersection of the three primary topics of ESSLLI: Logic, Language and Computation. The 13 papers presented in this volume have been selected among 81 submitted papers over the years 2019, 2020 and 2021. The ESSLLI Student Session is an excellent venue for students to present their work and receive valuable feedback from renowned experts in their respective fields. The Student Session accepts submissions for three different tracks: Language and Computation (LaCo), Logic and Computation (LoCo), and Logic and Language (LoLa).
Gödel, Tarski and the Lure of Natural Language
Introduces an original approach to foundations of mathematics, departing from Gödel and Tarski and spanning many different areas of logic.
The Vienna Circle and Religion
This book is the first systematic and historical account of the Vienna Circle that deals with the relation of logical empiricists with religion as well as theology. Given the standard image of the Vienna Circle as a strong anti-metaphysical group and non-religious philosophical and intellectual movement, this book draws a surprising conclusion, namely, that several members of the famous Moritz Schlick-Circle - e.g., the left wing with Rudolf Carnap, Otto Neurath, Philipp Frank, Edgar Zilsel, but also Schlick himself - dealt with the dualisms of faith/ belief and knowledge, religion and science despite, or because of their non-cognitivist commitment to the values of Enlightenment. One remarka...
Ways of the Scientific World-Conception. Rudolf Carnap and Otto Neurath
Rudolf Carnap (1891-1970) and Otto Neurath (1882-1945) had a decisive influence on the development of the scientific world view of logical empiricism. Their relationship was marked by mutual intellectual stimulation, close collaboration, and personal friendship, but also by controversies that were as heated as they were rarely fought out in public. Carnap and Neurath were, in the words of Olga Hahn-Neurath, "like-minded opponents". The essays in this volume deal with these key thinkers of logical empiricism from different perspectives, shedding light on the complex development of one of the most influential philosophical currents of the twentieth century in the midst of dark times.
Maximen IV / Maxims IV
Over a period of 22 years (1934-1955), the mathematician Kurt Gödel wrote down philosophical remarks, the so-called Maximen Philosophie (Max Phil). They are preserved in 15 notebooks in Gabelsberger shorthand. The first booklet contains general philosophical considerations, booklets two and three consist of Gödel's individual ethics. The following volumes show that Gödel developed a philosophy of science in which he places his discussions on physics, psychology, biology, mathematics, language, theology and history in the context of a metaphysics. A complete, historical-critical edition of Gödel's Philosophical Notebooks is now being prepared for the first time at the Kurt Gödel Research Centre of the Berlin-Brandenburg Academy of Sciences and Humanities. One volume will be published each year as part of this edition. In volume 4, Gödel deals with fundamental questions of mathematics and logic as well as the philosophy of mathematics. In addition, the relationship between different scientific disciplines and their specific questions are at the centre of his considerations. These include, in particular, philosophy, psychology and theology.
