Kurt Goedel and the Foundations of Mathematics Horizons of Truth

This Volume Commemorates The Life, Work, And Foundational Views Of Kurt Gödel (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 Gödel 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 Gödel's Fundamental Work In Mathematics, Logic, Philosophy, And Other Disciplines For Future Generations Of Researchers-- I. Historical Context: Gödel's Contributions And Accomplishments: Gödel's Historical, Philosophical, And Scientific Work: 1. The Impact Of Gödel's Incompleteness Theorems On Mathematics / Angus Macintyre; 2. Logical Hygiene, Foundations, And Abstractions: Diversity Among Aspects And Options / Georg Kreisel; Gödel's Legacy: A Historical Perspective: 3. The Reception Of Gödel's 1931 Incompletabilty Theorems By Mathematicians, And Some Logicians, To The Early 1960s/ Ivor Grattan-guinness; 4.dt 'dozent Gödel Will Not Lecture' / Karl Sigmund; 5. Gödel's Thesis: An Appreciation / Juliette Kennedy; 6. Lieber Herr Bernays!, Lieber Herr Gödel! Gödel On Finitism, Constructivity, And Hilbert's Program / Solomon Feferman; The Past And Future Of Computation: 7. Computation And Intractability: Echoes Of Kurt Gödel / Christos H. Papadimitriou; 8. From The Entscheidungsproblem To The Personal Computer -- And Beyond / B. Jack Copeland; Gödelian Cosmology: 9. Gödel, Einstein, Mach, Gamow, And Lanczos: Gödel's Remarkable Excursion Into Cosmology / Wolfgang Rindler; 10. Physical Unknowables / Karl Svozil -- Ii. A Wider Vision: The Interdisciplinary, Philosophical, And Theological Implications Of Gödel's Work: On The Unknowables: 11. Gödel And Physics / John D. Barrow; 12. Gödel, Thomas Aquinas, And The Unknowability Of God / Denys A. Turner; Gödel And The Mathematics Of Philosophy: 13. Gödel's Mathematics Of Philosophy / Piergiorgio Odifreddi; Gödel And Philosophical Theology: 14. Gödel's Ontological Proof And Its Variants / Petr Hájek; Gödel And The Human Mind: 15. The Gödel Theorem And Human Nature / Hilary W. Putnam; 16. Gödel, The Mind, And The Laws Of Physics / Roger Penrose -- Iii. New Frontiers: Beyond Gödel's Work In Mathematics And Symbolic Logic: Extending Gödel's Work: 17. Gödel's Functional Interpretation And Its Use In Current Mathematics / Ulrich Kohlenbach; 18. My Forty Years On His Shoulders / Harvey M. Friedman; The Realm Of Set Theory: 19. My Interaction With Kurt Gödel: The Man And His Work / Paul J. Cohen; Gödel And The Higher Infinite: 20. The Transfinite Universe / W. Hugh Woodin; Gödel And Computer Science: 21. The Gödel Phenomena In Mathematics: A Modern View / Avi Wigderson. Edited By Matthias Baaz ... [et Al.]. Includes Bibliographical References And Index. Machine generated contents note: Part I. Historical Context - Gödel's Contributions and Accomplishments: 1. The impact of Gödel's incompleteness theorems on mathematics Angus Macintyre; 2. Logical hygiene, foundations, and abstractions: diversity among aspects and options Georg Kreisel; 3. The reception of Gödel's 1931 incompletabilty theorems by mathematicians, and some logicians, to the early 1960s Ivor Grattan-Guinness; 4. 'Dozent Gödel will not lecture' Karl Sigmund; 5. Gödel's thesis: an appreciation Juliette C. Kennedy; 6. Lieber Herr Bernays!, Lieber Herr Gödel! Gödel on finitism, constructivity, and Hilbert's program Solomon Feferman; 7. Computation and intractability: echoes of Kurt Gödel Christos H. Papadimitriou; 8. From the entscheidungsproblem to the personal computer - and beyond B. Jack Copeland; 9. Gödel, Einstein, Mach, Gamow, and Lanczos: Gödel's remarkable excursion into cosmology Wolfgang Rindler; 10. Physical unknowables Karl Svozil; Part II. A Wider Vision - The Interdisciplinary, Philosophical, And Theological Implications of Gödel's Work: 11. Gödel and physics John D. Barrow; 12. Gödel, Thomas Aquinas, and the unknowability of God Denys A. Turner; 13. Gödel's mathematics of philosophy Piergiorgio Odifreddi; 14. Gödel's ontological proof and its variants Petr Hájek; 15. The Gödel theorem and human nature Hilary Putnam; 16. Gödel, the mind, and the laws of physics Roger Penrose; Part III. New Frontiers - Beyond Gödel's Work in Mathematics and Symbolic Logic: 17. Gödel's functional interpretation and its use in current mathematics Ulrich Kohlenbach; 18. My forty years on his shoulders Harvey M. Friedman; 19. My interaction with Kurt Gödel: the man and his work Paul J. Cohen; 20. The transfinite universe W. Hugh Woodin; 21. The Gödel phenomena in mathematics: a modern view Avi Wigderson. Part I. Historical Context - Goedel's Contributions and Accomplishments: 1. The impact of Goedel's incompleteness theorems on mathematics Angus Macintyre 2. Logical hygiene, foundations, and abstractions: diversity among aspects and options Georg Kreisel 3. The reception of Goedel's 1931 incompletability theorems by mathematicians, and some logicians, to the early 1960s Ivor Grattan-Guinness 4. 'Dozent Goedel will not lecture' Karl Sigmund 5. Goedel's thesis: an appreciation Juliette C. Kennedy 6. Lieber Herr Bernays!, Lieber Herr Goedel! Goedel on finitism, constructivity, and Hilbert's program Solomon Feferman 7. Computation and intractability: echoes of Kurt Goedel Christos H. Papadimitriou 8. From the entscheidungsproblem to the personal computer - and beyond B. Jack Copeland 9. Goedel, Einstein, Mach, Gamow, and Lanczos: Goedel's remarkable excursion into cosmology Wolfgang Rindler 10. Physical unknowables Karl Svozil Part II. A Wider Vision - the Interdisciplinary, Philosophical, and Theological Implications of Goedel's Work: 11. Goedel and physics John D. Barrow 12. Goedel, Thomas Aquinas, and the unknowability of God Denys A. Turner 13. Goedel's mathematics of philosophy Piergiorgio Odifreddi 14. Goedel's ontological proof and its variants Petr Hajek 15. The Goedel theorem and human nature Hilary Putnam 16. Goedel, the mind, and the laws of physics Roger Penrose Part III. New Frontiers - Beyond Goedel's Work in Mathematics and Symbolic Logic: 17. Goedel's functional interpretation and its use in current mathematics Ulrich Kohlenbach 18. My forty years on his shoulders Harvey M. Friedman 19. My interaction with Kurt Goedel: the man and his work Paul J. Cohen 20. The transfinite universe W. Hugh Woodin 21. The Goedel phenomena in mathematics: a modern view Avi Wigderson.