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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.
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).
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...
Can Mathematics Be Proved Consistent?
Kurt Gödel (1906–1978) shook the mathematical world in 1931 by a result that has become an icon of 20th century science: The search for rigour in proving mathematical theorems had led to the formalization of mathematical proofs, to the extent that such proving could be reduced to the application of a few mechanical rules. Gödel showed that whenever the part of mathematics under formalization contains elementary arithmetic, there will be arithmetical statements that should be formally provable but aren’t. The result is known as Gödel’s first incompleteness theorem, so called because there is a second incompleteness result, embodied in his answer to the question "Can mathematics be pr...
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.
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...
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.
Husserl and Mathematics
Husserl and Mathematics explains the development of Husserl's phenomenological method in the context of his engagement in modern mathematics and its foundations. Drawing on his correspondence and other written sources, Mirja Hartimo details Husserl's knowledge of a wide range of perspectives on the foundations of mathematics, including those of Hilbert, Brouwer and Weyl, as well as his awareness of the new developments in the subject during the 1930s. Hartimo examines how Husserl's philosophical views responded to these changes, and offers a pluralistic and open-ended picture of Husserl's phenomenology of mathematics. Her study shows Husserl's phenomenology to be a method capable of both shedding light on and internally criticizing scientific practices and concepts.
Proceedings Of The International Congress Of Mathematicians 2018 (Icm 2018) (In 4 Volumes)
The Proceedings of the ICM publishes the talks, by invited speakers, at the conference organized by the International Mathematical Union every 4 years. It covers several areas of Mathematics and it includes the Fields Medal and Nevanlinna, Gauss and Leelavati Prizes and the Chern Medal laudatios.
