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This volume is a translation of the book Gödel, written in Japanese by Gaisi Takeuti, a distinguished proof theorist. The core of the book comprises a memoir of K Gödel, Takeuti's personal recollections, and his interpretation of Gödel's attitudes towards mathematical logic. It also contains Takeuti's recollection of association with some other famous logicians. Everything in the book is original, as the author adheres to his own experiences and interpretations. There is also an article on Hilbert's second problem as well as on the author's fundamental conjecture about second order log

Proof theory. --- Logic, Symbolic and mathematical --- Gödel, Kurt. --- Gkentel, Kourt --- גדל --- Godel, Kurt.

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Hao Wang (1921-1995) was one of the few confidants of the great mathematician and logician Kurt Godel. A Logical Journey is a continuation of Wang's Reflections on Kurt Godel and also elaborates on discussions contained in From Mathematics to Philosophy. A decade in preparation, it contains important and unfamiliar insights into Godel's views on a wide range of issues, from Platonism and the nature of logic, to minds and machines, the existence of God, and positivism and phenomenology. The impact of Godel's theorem on twentieth-century thought is on a par with that of Einstein's theory of relativity, Heisenberg's uncertainty principle, or Keynesian economics. These previously unpublished intimate and informal conversations, however, bring to light and amplify Godel's other major contributions to logic and philosophy. They reveal that there is much more in Godel's philosophy of mathematics than is commonly realized, and more in his philosophy than merely a philosophy of mathematics.

Logicians --- Biography. --- Mathematics - General --- Mathematics --- Physical Sciences & Mathematics --- Biography --- Philosophers --- Gödel, Kurt. --- Gkentel, Kourt --- גדל --- PHILOSOPHY/General --- Logicians - United States - Biography. --- Logicians - Austria - Biography.

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Logicians --- Philosophers --- Biography --- Gödel, Kurt. --- Gkentel, Kourt --- גדל --- Gödel, Kurt --- Philosophy of science --- Gödel, Kurt, --- Godel, Kurt --- Biography. --- Logique --- Histoire --- Logicians - United States - Biography --- Logicians - Austria - Biography --- Histoire des mathematiques --- 20e siecle

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This volume tackles Gödel's two-stage project of first using Husserl's transcendental phenomenology to reconstruct and develop Leibniz' monadology, and then founding classical mathematics on the metaphysics thus obtained. The author analyses the historical and systematic aspects of that project, and then evaluates it, with an emphasis on the second stage. The book is organised around Gödel's use of Leibniz, Husserl and Brouwer. Far from considering past philosophers irrelevant to actual systematic concerns, Gödel embraced the use of historical authors to frame his own philosophical perspective. The philosophies of Leibniz and Husserl define his project, while Brouwer's intuitionism is its principal foil: the close affinities between phenomenology and intuitionism set the bar for Gödel's attempt to go far beyond intuitionism. The four central essays are `Monads and sets', `On the philosophical development of Kurt Gödel', `Gödel and intuitionism', and `Construction and constitution in mathematics'. The first analyses and criticises Gödel's attempt to justify, by an argument from analogy with the monadology, the reflection principle in set theory. It also provides further support for Gödel's idea that the monadology needs to be reconstructed phenomenologically, by showing that the unsupplemented monadology is not able to found mathematics directly. The second studies Gödel's reading of Husserl, its relation to Leibniz' monadology, and its influence on his publishe d writings. The third discusses how on various occasions Brouwer's intuitionism actually inspired Gödel's work, in particular the Dialectica Interpretation. The fourth addresses the question whether classical mathematics admits of the phenomenological foundation that Gödel envisaged, and concludes that it does not. The remaining essays provide further context.  The essays collected here were written and published over the last decade. Notes have been added to record further thoughts, changes of mind, connections between the essays, and updates of references.

Philosophy. --- Phenomenology. --- Mathematical Logic and Foundations. --- Philosophy of Science. --- Philosophy (General). --- Science --- Logic, Symbolic and mathematical. --- Phénoménologie --- Sciences --- Logique symbolique et mathématique --- Philosophie --- Science_xPhilosophy. --- Philosophy & Religion --- Philosophy --- Mathematics --- Gödel, Kurt --- Logic of mathematics --- Mathematics, Logic of --- Gkentel, Kourt --- גדל --- Philosophy and science. --- Mathematical logic. --- Phenomenology . --- Normal science --- Philosophy of science --- Algebra of logic --- Logic, Universal --- Mathematical logic --- Symbolic and mathematical logic --- Symbolic logic --- Algebra, Abstract --- Metamathematics --- Set theory --- Syllogism --- Philosophy, Modern --- Science and philosophy

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"This volume commemorates the life, work, and foundational views of Kurt Godel (1906-1978), most famous for his hallmark works on the completeness of first-order logic, the incompleteness of number theory, and the consistency - with the other widely accepted axioms of set theory - of the axiom of choice and of the generalized continuum hypothesis. It explores current research, advances, and ideas for future directions not only in the foundations of mathematics and logic, but also in the fields of computer science, artificial intelligence, physics, cosmology, philosophy, theology, and the history of science. The discussion is supplemented by personal reflections from several scholars who knew Godel personally, providing some interesting insights into his life. By putting his ideas and life's work into the context of current thinking and perceptions, this book will extend the impact of Godel's fundamental work in mathematics, logic, philosophy, and other disciplines for future generations of researchers"--

Gödel, Théorème de --- Gödel, Kurt --- Godel's theorem --- Mathematics/ Logic --- Godel, Kurt --- Gödel's theorem. --- Gödel's incompleteness theorem --- Undecidable theories --- Incompleteness theorems --- Decidability (Mathematical logic) --- Gödel's theorem --- Gödel, Théorème de --- Gödel, Kurt --- Mathematics --- 510.2 --- 510.6 --- 510.6 Mathematical logic --- Mathematical logic --- 510.2 Foundations of mathematics --- Foundations of mathematics --- Logic of mathematics --- Mathematics, Logic of --- Arithmetic --- Completeness theorem --- Logic, Symbolic and mathematical --- Number theory --- Philosophy --- Foundations --- Gödel, Kurt. --- Gkentel, Kourt --- גדל --- Mathématiques --- Philosophie --- Gödel's theorem. --- Philosophy. --- Mathematical Sciences --- General and Others --- Mathematics - Philosophy --- Gödel, Kurt (1906-1978) --- Mathématiques --- Godel's theorem. --- Godel, Kurt.