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Lecture Notes in Logic
Kurt Gödel: Essays for his Centennial
Kurt Gödel (1906–1978) did groundbreaking work that transformed logic and other important aspects of our understanding of mathematics, especially his proof of the incompleteness of formalized arithmetic. This book on different aspects of his work and on subjects in which his ideas have contemporary resonance includes papers from a May 2006 symposium celebrating Gödel’s centennial as well as papers from a 2004 symposium. Proof theory, set theory, philosophy of mathematics, and the editing of Gödel’s writings are among the topics covered. Several chapters discuss his intellectual development and his relation to predecessors and contemporaries such as Hilbert, Carnap, and Herbrand. Others consider his views on justification in set theory in light of more recent work and contemporary echoes of his incompleteness theorems and the concept of constructible set.
- GenresLogicMathematics
384 pages, Hardcover
First published April 19, 2010
34 people want to read
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June 13, 2012
Do not read this book if you do not have some significant level of experience in logic, philosophy and mathematics. The material is technically dense and takes an enormous level of technical proficiency for granted. These are papers written by professionals for professionals.
The text is very good, and is edited well. The sectioning of Gödel's thought into mathematics and philosophy of mathematics is a bit disingenuous, since it becomes pretty clear from a few of the papers how intimately related those two things are. However, it is important for the purposes of organizing the book to have some understanding of the disciplinary standing of the folks who are writing the material. That turns out to be incredibly helpful.
The book doesn't really have editorial notes which help to historically situate some of the writing; some of the papers towards the end of the book note the tradition that Gödel identified himself with, and the impacts of his work that tradition, particularly on applications to the philosophy of Leibniz and more modern readings of Plato by serious philosophers of mathematics and metaphysics.
The influence of Gödel on contemporary fields is not discussed much at all, largely because it would likely be apparent to the intended audience of the book (scholars of mathematics and logic) and because some of the theoretical implications are considered salient enough to support his influence.
Overall, these papers make for a phenomenal piece of scholarship. I'm far from a Gödel scholar, but I know enough about mathematics and philosophy of mathematics to know how good the individual scholars writing these papers are, and their credibility is really unparalleled. This is explicitly not an introduction to the field of mathematics and philosophy of mathematics, though, so those looking to get some knowledge from the best really ought to steer clear. When you've built a solid foundation that includes the foundations of set theory, in particular, and some of the more general understandings of the history of mathematics and philosophy, then it makes for a good read.
The text is very good, and is edited well. The sectioning of Gödel's thought into mathematics and philosophy of mathematics is a bit disingenuous, since it becomes pretty clear from a few of the papers how intimately related those two things are. However, it is important for the purposes of organizing the book to have some understanding of the disciplinary standing of the folks who are writing the material. That turns out to be incredibly helpful.
The book doesn't really have editorial notes which help to historically situate some of the writing; some of the papers towards the end of the book note the tradition that Gödel identified himself with, and the impacts of his work that tradition, particularly on applications to the philosophy of Leibniz and more modern readings of Plato by serious philosophers of mathematics and metaphysics.
The influence of Gödel on contemporary fields is not discussed much at all, largely because it would likely be apparent to the intended audience of the book (scholars of mathematics and logic) and because some of the theoretical implications are considered salient enough to support his influence.
Overall, these papers make for a phenomenal piece of scholarship. I'm far from a Gödel scholar, but I know enough about mathematics and philosophy of mathematics to know how good the individual scholars writing these papers are, and their credibility is really unparalleled. This is explicitly not an introduction to the field of mathematics and philosophy of mathematics, though, so those looking to get some knowledge from the best really ought to steer clear. When you've built a solid foundation that includes the foundations of set theory, in particular, and some of the more general understandings of the history of mathematics and philosophy, then it makes for a good read.
Displaying 1 of 1 review