Book contents
- Frontmatter
- Contents
- Contributors
- Foreword
- Preface
- Acknowledgments
- Short Biography of Kurt Gödel
- I Historical Context: Gödel's Contributions and Accomplishments
- Gödel's Legacy: A Historical Perspective
- The Past and Future of Computation
- Gödelian Cosmology
- II A Wider Vision: The Interdisciplinary, Philosophical, and Theological Implications of Gödel's Work
- Gödel and the Mathematics of Philosophy
- Gödel and Philosophical Theology
- Gödel and the Human Mind
- III New Frontiers: Beyond Gödel's Work in Mathematics and Symbolic Logic
- 17 Gödel's Functional Interpretation and Its Use in Current Mathematics
- 18 My Forty Years on His Shoulders
- The Realm of Set Theory
- Gödel and the Higher Infinite
- Gödel and Computer Science
- Index
18 - My Forty Years on His Shoulders
Published online by Cambridge University Press: 07 September 2011
- Frontmatter
- Contents
- Contributors
- Foreword
- Preface
- Acknowledgments
- Short Biography of Kurt Gödel
- I Historical Context: Gödel's Contributions and Accomplishments
- Gödel's Legacy: A Historical Perspective
- The Past and Future of Computation
- Gödelian Cosmology
- II A Wider Vision: The Interdisciplinary, Philosophical, and Theological Implications of Gödel's Work
- Gödel and the Mathematics of Philosophy
- Gödel and Philosophical Theology
- Gödel and the Human Mind
- III New Frontiers: Beyond Gödel's Work in Mathematics and Symbolic Logic
- 17 Gödel's Functional Interpretation and Its Use in Current Mathematics
- 18 My Forty Years on His Shoulders
- The Realm of Set Theory
- Gödel and the Higher Infinite
- Gödel and Computer Science
- Index
Summary
Gödel's legacy is still very much in evidence. His legacy is overwhelming, particularly in the arena of general mathematical and philosophical inquiry.
The extent of Gödel's impact in the more restricted domain of mathematical practice, however, is more open to question. In fact, Macintyre provides an in-depth assessment of this impact in Chapter 1 of this volume. However, even in this comparatively specialized domain, Gödel's impact is seen to be substantial. As discussed in this chapter, particularly in Section 18.11, I believe that the potential impact of Gödel's work on mathematical practice is also extensive. Although the full realization of this potential impact will have to wait for some new breakthroughs, I have every confidence that these breakthroughs will materialize.
Generally speaking, current mathematical practice has now become very far removed from general mathematical and philosophical inquiry, where Gödel's legacy is most obviously decisive. However, there are signs that some of our most distinguished mathematicians recognize the need for some sort of reconciliation: “Mathematicians took the role of philosophers, but I want to bring the philosophers back in. I hope someday we will be able to explain mathematics in a philosophical way using philosophical methods” (Atiyah, 2008a, 2008b).
I will not attempt to exhaustively discuss the full impact of Gödel's work and all of the ongoing important research programs that it suggests, as this would require a book-length manuscript.
- Type
- Chapter
- Information
- Kurt Gödel and the Foundations of MathematicsHorizons of Truth, pp. 399 - 432Publisher: Cambridge University PressPrint publication year: 2011
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