Charles L. Harper

Kurt Gödel and the foundations of mathematics : horizons of truth

Part I. Historical Context - Godels Contributions and Accomplishments: 1. The impact of Godels incompleteness theorems on mathematics Angus Macintyre 2. Logical hygiene, foundations, and abstractions: diversity among aspects and options Georg Kreisel 3. The reception of Godels 1931 incompletability theorems by mathematicians, and some logicians, to the early 1960s Ivor Grattan-Guinness 4. Dozent Godel will not lecture Karl Sigmund 5. Godels thesis: an appreciation Juliette C. Kennedy 6. Lieber Herr Bernays!, Lieber Herr Godel! Godel on finitism, constructivity, and Hilberts program Solomon Feferman 7. Computation and intractability: echoes of Kurt Godel Christos H. Papadimitriou 8. From the entscheidungsproblem to the personal computer - and beyond B. Jack Copeland 9. Godel, Einstein, Mach, Gamow, and Lanczos: Godels remarkable excursion into cosmology Wolfgang Rindler 10. Physical unknowables Karl Svozil Part II. A Wider Vision - the Interdisciplinary, Philosophical, and Theological Implications of Godels Work: 11. Godel and physics John D. Barrow 12. Godel, Thomas Aquinas, and the unknowability of God Denys A. Turner 13. Godels mathematics of philosophy Piergiorgio Odifreddi 14. Godels ontological proof and its variants Petr Hajek 15. The Godel theorem and human nature Hilary Putnam 16. Godel, the mind, and the laws of physics Roger Penrose Part III. New Frontiers - Beyond Godels Work in Mathematics and Symbolic Logic: 17. Godels 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 Godel: the man and his work Paul J. Cohen 20. The transfinite universe W. Hugh Woodin 21. The Godel phenomena in mathematics: a modern view Avi Wigderson.

Kurt Gödel and the Foundations of Mathematics: Frontmatter

Part I. Historical Context - Godels Contributions and Accomplishments: 1. The impact of Godels incompleteness theorems on mathematics Angus Macintyre 2. Logical hygiene, foundations, and abstractions: diversity among aspects and options Georg Kreisel 3. The reception of Godels 1931 incompletability theorems by mathematicians, and some logicians, to the early 1960s Ivor Grattan-Guinness 4. Dozent Godel will not lecture Karl Sigmund 5. Godels thesis: an appreciation Juliette C. Kennedy 6. Lieber Herr Bernays!, Lieber Herr Godel! Godel on finitism, constructivity, and Hilberts program Solomon Feferman 7. Computation and intractability: echoes of Kurt Godel Christos H. Papadimitriou 8. From the entscheidungsproblem to the personal computer - and beyond B. Jack Copeland 9. Godel, Einstein, Mach, Gamow, and Lanczos: Godels remarkable excursion into cosmology Wolfgang Rindler 10. Physical unknowables Karl Svozil Part II. A Wider Vision - the Interdisciplinary, Philosophical, and Theological Implications of Godels Work: 11. Godel and physics John D. Barrow 12. Godel, Thomas Aquinas, and the unknowability of God Denys A. Turner 13. Godels mathematics of philosophy Piergiorgio Odifreddi 14. Godels ontological proof and its variants Petr Hajek 15. The Godel theorem and human nature Hilary Putnam 16. Godel, the mind, and the laws of physics Roger Penrose Part III. New Frontiers - Beyond Godels Work in Mathematics and Symbolic Logic: 17. Godels 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 Godel: the man and his work Paul J. Cohen 20. The transfinite universe W. Hugh Woodin 21. The Godel phenomena in mathematics: a modern view Avi Wigderson.

Kurt Gödel and the Foundations of Mathematics: Gödel's Legacy: A Historical Perspective

Part I. Historical Context - Godels Contributions and Accomplishments: 1. The impact of Godels incompleteness theorems on mathematics Angus Macintyre 2. Logical hygiene, foundations, and abstractions: diversity among aspects and options Georg Kreisel 3. The reception of Godels 1931 incompletability theorems by mathematicians, and some logicians, to the early 1960s Ivor Grattan-Guinness 4. Dozent Godel will not lecture Karl Sigmund 5. Godels thesis: an appreciation Juliette C. Kennedy 6. Lieber Herr Bernays!, Lieber Herr Godel! Godel on finitism, constructivity, and Hilberts program Solomon Feferman 7. Computation and intractability: echoes of Kurt Godel Christos H. Papadimitriou 8. From the entscheidungsproblem to the personal computer - and beyond B. Jack Copeland 9. Godel, Einstein, Mach, Gamow, and Lanczos: Godels remarkable excursion into cosmology Wolfgang Rindler 10. Physical unknowables Karl Svozil Part II. A Wider Vision - the Interdisciplinary, Philosophical, and Theological Implications of Godels Work: 11. Godel and physics John D. Barrow 12. Godel, Thomas Aquinas, and the unknowability of God Denys A. Turner 13. Godels mathematics of philosophy Piergiorgio Odifreddi 14. Godels ontological proof and its variants Petr Hajek 15. The Godel theorem and human nature Hilary Putnam 16. Godel, the mind, and the laws of physics Roger Penrose Part III. New Frontiers - Beyond Godels Work in Mathematics and Symbolic Logic: 17. Godels 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 Godel: the man and his work Paul J. Cohen 20. The transfinite universe W. Hugh Woodin 21. The Godel phenomena in mathematics: a modern view Avi Wigderson.

Kurt Gödel and the Foundations of Mathematics: Acknowledgments

Part I. Historical Context - Godels Contributions and Accomplishments: 1. The impact of Godels incompleteness theorems on mathematics Angus Macintyre 2. Logical hygiene, foundations, and abstractions: diversity among aspects and options Georg Kreisel 3. The reception of Godels 1931 incompletability theorems by mathematicians, and some logicians, to the early 1960s Ivor Grattan-Guinness 4. Dozent Godel will not lecture Karl Sigmund 5. Godels thesis: an appreciation Juliette C. Kennedy 6. Lieber Herr Bernays!, Lieber Herr Godel! Godel on finitism, constructivity, and Hilberts program Solomon Feferman 7. Computation and intractability: echoes of Kurt Godel Christos H. Papadimitriou 8. From the entscheidungsproblem to the personal computer - and beyond B. Jack Copeland 9. Godel, Einstein, Mach, Gamow, and Lanczos: Godels remarkable excursion into cosmology Wolfgang Rindler 10. Physical unknowables Karl Svozil Part II. A Wider Vision - the Interdisciplinary, Philosophical, and Theological Implications of Godels Work: 11. Godel and physics John D. Barrow 12. Godel, Thomas Aquinas, and the unknowability of God Denys A. Turner 13. Godels mathematics of philosophy Piergiorgio Odifreddi 14. Godels ontological proof and its variants Petr Hajek 15. The Godel theorem and human nature Hilary Putnam 16. Godel, the mind, and the laws of physics Roger Penrose Part III. New Frontiers - Beyond Godels Work in Mathematics and Symbolic Logic: 17. Godels 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 Godel: the man and his work Paul J. Cohen 20. The transfinite universe W. Hugh Woodin 21. The Godel phenomena in mathematics: a modern view Avi Wigderson.

Kurt Gödel and the Foundations of Mathematics: The Realm of Set Theory

Part I. Historical Context - Godels Contributions and Accomplishments: 1. The impact of Godels incompleteness theorems on mathematics Angus Macintyre 2. Logical hygiene, foundations, and abstractions: diversity among aspects and options Georg Kreisel 3. The reception of Godels 1931 incompletability theorems by mathematicians, and some logicians, to the early 1960s Ivor Grattan-Guinness 4. Dozent Godel will not lecture Karl Sigmund 5. Godels thesis: an appreciation Juliette C. Kennedy 6. Lieber Herr Bernays!, Lieber Herr Godel! Godel on finitism, constructivity, and Hilberts program Solomon Feferman 7. Computation and intractability: echoes of Kurt Godel Christos H. Papadimitriou 8. From the entscheidungsproblem to the personal computer - and beyond B. Jack Copeland 9. Godel, Einstein, Mach, Gamow, and Lanczos: Godels remarkable excursion into cosmology Wolfgang Rindler 10. Physical unknowables Karl Svozil Part II. A Wider Vision - the Interdisciplinary, Philosophical, and Theological Implications of Godels Work: 11. Godel and physics John D. Barrow 12. Godel, Thomas Aquinas, and the unknowability of God Denys A. Turner 13. Godels mathematics of philosophy Piergiorgio Odifreddi 14. Godels ontological proof and its variants Petr Hajek 15. The Godel theorem and human nature Hilary Putnam 16. Godel, the mind, and the laws of physics Roger Penrose Part III. New Frontiers - Beyond Godels Work in Mathematics and Symbolic Logic: 17. Godels 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 Godel: the man and his work Paul J. Cohen 20. The transfinite universe W. Hugh Woodin 21. The Godel phenomena in mathematics: a modern view Avi Wigderson.

Kurt Gödel and the Foundations of Mathematics: A Wider Vision: The Interdisciplinary, Philosophical, and Theological Implications of Gödel's Work

Part I. Historical Context - Godels Contributions and Accomplishments: 1. The impact of Godels incompleteness theorems on mathematics Angus Macintyre 2. Logical hygiene, foundations, and abstractions: diversity among aspects and options Georg Kreisel 3. The reception of Godels 1931 incompletability theorems by mathematicians, and some logicians, to the early 1960s Ivor Grattan-Guinness 4. Dozent Godel will not lecture Karl Sigmund 5. Godels thesis: an appreciation Juliette C. Kennedy 6. Lieber Herr Bernays!, Lieber Herr Godel! Godel on finitism, constructivity, and Hilberts program Solomon Feferman 7. Computation and intractability: echoes of Kurt Godel Christos H. Papadimitriou 8. From the entscheidungsproblem to the personal computer - and beyond B. Jack Copeland 9. Godel, Einstein, Mach, Gamow, and Lanczos: Godels remarkable excursion into cosmology Wolfgang Rindler 10. Physical unknowables Karl Svozil Part II. A Wider Vision - the Interdisciplinary, Philosophical, and Theological Implications of Godels Work: 11. Godel and physics John D. Barrow 12. Godel, Thomas Aquinas, and the unknowability of God Denys A. Turner 13. Godels mathematics of philosophy Piergiorgio Odifreddi 14. Godels ontological proof and its variants Petr Hajek 15. The Godel theorem and human nature Hilary Putnam 16. Godel, the mind, and the laws of physics Roger Penrose Part III. New Frontiers - Beyond Godels Work in Mathematics and Symbolic Logic: 17. Godels 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 Godel: the man and his work Paul J. Cohen 20. The transfinite universe W. Hugh Woodin 21. The Godel phenomena in mathematics: a modern view Avi Wigderson.

Kurt Gödel and the Foundations of Mathematics: New Frontiers: Beyond Gödel's Work in Mathematics and Symbolic Logic

Part I. Historical Context - Godels Contributions and Accomplishments: 1. The impact of Godels incompleteness theorems on mathematics Angus Macintyre 2. Logical hygiene, foundations, and abstractions: diversity among aspects and options Georg Kreisel 3. The reception of Godels 1931 incompletability theorems by mathematicians, and some logicians, to the early 1960s Ivor Grattan-Guinness 4. Dozent Godel will not lecture Karl Sigmund 5. Godels thesis: an appreciation Juliette C. Kennedy 6. Lieber Herr Bernays!, Lieber Herr Godel! Godel on finitism, constructivity, and Hilberts program Solomon Feferman 7. Computation and intractability: echoes of Kurt Godel Christos H. Papadimitriou 8. From the entscheidungsproblem to the personal computer - and beyond B. Jack Copeland 9. Godel, Einstein, Mach, Gamow, and Lanczos: Godels remarkable excursion into cosmology Wolfgang Rindler 10. Physical unknowables Karl Svozil Part II. A Wider Vision - the Interdisciplinary, Philosophical, and Theological Implications of Godels Work: 11. Godel and physics John D. Barrow 12. Godel, Thomas Aquinas, and the unknowability of God Denys A. Turner 13. Godels mathematics of philosophy Piergiorgio Odifreddi 14. Godels ontological proof and its variants Petr Hajek 15. The Godel theorem and human nature Hilary Putnam 16. Godel, the mind, and the laws of physics Roger Penrose Part III. New Frontiers - Beyond Godels Work in Mathematics and Symbolic Logic: 17. Godels 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 Godel: the man and his work Paul J. Cohen 20. The transfinite universe W. Hugh Woodin 21. The Godel phenomena in mathematics: a modern view Avi Wigderson.

Kurt Gödel and the Foundations of Mathematics: Contents

Part I. Historical Context - Godels Contributions and Accomplishments: 1. The impact of Godels incompleteness theorems on mathematics Angus Macintyre 2. Logical hygiene, foundations, and abstractions: diversity among aspects and options Georg Kreisel 3. The reception of Godels 1931 incompletability theorems by mathematicians, and some logicians, to the early 1960s Ivor Grattan-Guinness 4. Dozent Godel will not lecture Karl Sigmund 5. Godels thesis: an appreciation Juliette C. Kennedy 6. Lieber Herr Bernays!, Lieber Herr Godel! Godel on finitism, constructivity, and Hilberts program Solomon Feferman 7. Computation and intractability: echoes of Kurt Godel Christos H. Papadimitriou 8. From the entscheidungsproblem to the personal computer - and beyond B. Jack Copeland 9. Godel, Einstein, Mach, Gamow, and Lanczos: Godels remarkable excursion into cosmology Wolfgang Rindler 10. Physical unknowables Karl Svozil Part II. A Wider Vision - the Interdisciplinary, Philosophical, and Theological Implications of Godels Work: 11. Godel and physics John D. Barrow 12. Godel, Thomas Aquinas, and the unknowability of God Denys A. Turner 13. Godels mathematics of philosophy Piergiorgio Odifreddi 14. Godels ontological proof and its variants Petr Hajek 15. The Godel theorem and human nature Hilary Putnam 16. Godel, the mind, and the laws of physics Roger Penrose Part III. New Frontiers - Beyond Godels Work in Mathematics and Symbolic Logic: 17. Godels 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 Godel: the man and his work Paul J. Cohen 20. The transfinite universe W. Hugh Woodin 21. The Godel phenomena in mathematics: a modern view Avi Wigderson.

Kurt Gödel and the Foundations of Mathematics: Historical Context: Gödel's Contributions and Accomplishments

Part I. Historical Context - Godels Contributions and Accomplishments: 1. The impact of Godels incompleteness theorems on mathematics Angus Macintyre 2. Logical hygiene, foundations, and abstractions: diversity among aspects and options Georg Kreisel 3. The reception of Godels 1931 incompletability theorems by mathematicians, and some logicians, to the early 1960s Ivor Grattan-Guinness 4. Dozent Godel will not lecture Karl Sigmund 5. Godels thesis: an appreciation Juliette C. Kennedy 6. Lieber Herr Bernays!, Lieber Herr Godel! Godel on finitism, constructivity, and Hilberts program Solomon Feferman 7. Computation and intractability: echoes of Kurt Godel Christos H. Papadimitriou 8. From the entscheidungsproblem to the personal computer - and beyond B. Jack Copeland 9. Godel, Einstein, Mach, Gamow, and Lanczos: Godels remarkable excursion into cosmology Wolfgang Rindler 10. Physical unknowables Karl Svozil Part II. A Wider Vision - the Interdisciplinary, Philosophical, and Theological Implications of Godels Work: 11. Godel and physics John D. Barrow 12. Godel, Thomas Aquinas, and the unknowability of God Denys A. Turner 13. Godels mathematics of philosophy Piergiorgio Odifreddi 14. Godels ontological proof and its variants Petr Hajek 15. The Godel theorem and human nature Hilary Putnam 16. Godel, the mind, and the laws of physics Roger Penrose Part III. New Frontiers - Beyond Godels Work in Mathematics and Symbolic Logic: 17. Godels 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 Godel: the man and his work Paul J. Cohen 20. The transfinite universe W. Hugh Woodin 21. The Godel phenomena in mathematics: a modern view Avi Wigderson.

Kurt Gödel and the Foundations of Mathematics: Contributors

Part I. Historical Context - Godels Contributions and Accomplishments: 1. The impact of Godels incompleteness theorems on mathematics Angus Macintyre 2. Logical hygiene, foundations, and abstractions: diversity among aspects and options Georg Kreisel 3. The reception of Godels 1931 incompletability theorems by mathematicians, and some logicians, to the early 1960s Ivor Grattan-Guinness 4. Dozent Godel will not lecture Karl Sigmund 5. Godels thesis: an appreciation Juliette C. Kennedy 6. Lieber Herr Bernays!, Lieber Herr Godel! Godel on finitism, constructivity, and Hilberts program Solomon Feferman 7. Computation and intractability: echoes of Kurt Godel Christos H. Papadimitriou 8. From the entscheidungsproblem to the personal computer - and beyond B. Jack Copeland 9. Godel, Einstein, Mach, Gamow, and Lanczos: Godels remarkable excursion into cosmology Wolfgang Rindler 10. Physical unknowables Karl Svozil Part II. A Wider Vision - the Interdisciplinary, Philosophical, and Theological Implications of Godels Work: 11. Godel and physics John D. Barrow 12. Godel, Thomas Aquinas, and the unknowability of God Denys A. Turner 13. Godels mathematics of philosophy Piergiorgio Odifreddi 14. Godels ontological proof and its variants Petr Hajek 15. The Godel theorem and human nature Hilary Putnam 16. Godel, the mind, and the laws of physics Roger Penrose Part III. New Frontiers - Beyond Godels Work in Mathematics and Symbolic Logic: 17. Godels 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 Godel: the man and his work Paul J. Cohen 20. The transfinite universe W. Hugh Woodin 21. The Godel phenomena in mathematics: a modern view Avi Wigderson.