A Logical Journey
MIT Press (Verlag)
978-0-262-23189-3 (ISBN)
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Hao Wang (1921-1995) was one of the few confidants of the great mathematician and logician Kurt Gdel. A Logical Journey is a continuation of Wang's Reflections on Gdel and also elaborates on discussions contained in From Mathematics to Philosophy. A decade in preparation, it contains important and unfamiliar insights into Gdel'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 Gdel's theorem on twentieth-century thought is on 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 These previously unpublished intimate and informal conversations, however, bring to light and amplify Gdel's other major contributions to logic and philosophy. They reveal that there is much more in Gdel's philosophy of mathematics than is commonly believed, and more in his philosophy than his philosophy of mathematics.
Wang writes that "it is even possible that his quite informal and loosely structured conversations with me, which I am freely using in this book, will turn out to be the fullest existing expression of the diverse components of his inadequately articulated general philosophy." The first two chapters are devoted to Gdel's life and mental development. In the chapters that follow, Wang illustrates the quest for overarching solutions and grand unifications of knowledge and action in Gdel's written speculations on God and an afterlife. He gives the background and a chronological summary of the conversations, considers Gdel's comments on philosophies and philosophers (his support of Husserl's phenomenology and his digressions on Kant and Wittgenstein), and his attempt to demonstrate the superiority of the mind's power over brains and machines. Three chapters are tied together by what Wang perceives to be Gdel's governing ideal of philosophy: an exact theory in which mathematics and Newtonian physics serve as a model for philosophy or metaphysics. Finally, in an epilog Wang sketches his own approach to philosophy in contrast to his interpretation of Gdel's outlook.
Introduction: the logician and his theorem; Godel's philosophy - program and execution; relation of philosophy to mathematics and logic; from Godel to logic and metaphilosophy. Gode's life: a sketch; health and daily life; some of his general observations; marriage; politics and his personal situation; companion of Einstein. Godel's mental development: his life in its relation to his work; conscious preparation (1920-1929); the first of the three stages of his work; the two later stages; some facts about Godel in his own words; his own summaries. religion and philosophy as guides to action: Godel on an afterlife; religion and Godel's ontological proof; worldviews - between philosophy and ideology. The conversations and their background: actual and imaginary conversations; my contacts with Godel and his work; chronology and miscellany - 1971-1972; continuation - 1975-1976. Philosophies and philosophers: how Godel relates philosophy to the foundations of mathematics; some general comments; for Husserl - with digressions on Kant; against (logical) positivism; Godel and Wittgenstein. Minds and machines - on computabilism: Mental computabilism - Godel's theorem and other suggestions; mind and matter - on physicalism and parallelism; Turing machines or Godelian minds? formal systems and computable partial functions; neural and physical computabilism. Platonism or objectivism in mathematics: the dialectic of intuition and idealization; discovery and creation - expansion through idealization; the perception of concepts; facts or arguments for objectivism in mathematics; conceptions of objectivism and the axiomatic method. Set theory and logic as concept theory: Canto's continuum problem and his hypothesis; set theory and the concept of set; the Cantor-Neumann axiom - the subjective and the objective; the function and scope of logic; the paradoxes and the theory of concepts; sets and concepts - the quest for concept theory; principles for the introduction of sets. Godel's approach to philosophy: his philosophy - program and execution; on methodology - how to study philosophy; some general observations on philosophy; the meaning of the world - monadology and rationalistic optimism; time - as experienced and as represented. Epilogue - alternative philosophies as complementary: factualism and historical philosophy - some choices; some suggestions by Bernays; some lessons from the "Work of Rawls"; the place of philosophy and some of its tasks; alternative philosophies and logic as metaphilosophy.
| Erscheint lt. Verlag | 1.4.1997 |
|---|---|
| Reihe/Serie | Bradford Books |
| Verlagsort | Cambridge, Mass. |
| Sprache | englisch |
| Maße | 152 x 229 mm |
| Gewicht | 839 g |
| Themenwelt | Geisteswissenschaften ► Philosophie ► Geschichte der Philosophie |
| Geisteswissenschaften ► Philosophie ► Logik | |
| Geisteswissenschaften ► Philosophie ► Philosophie der Neuzeit | |
| Mathematik / Informatik ► Mathematik ► Logik / Mengenlehre | |
| ISBN-10 | 0-262-23189-1 / 0262231891 |
| ISBN-13 | 978-0-262-23189-3 / 9780262231893 |
| Zustand | Neuware |
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