Ernest Nagel (1901–1985)
Author of Gödel’s Proof
About the Author
Born in Czechoslovakia, Ernest Nagel emigrated to the United States and became a naturalized American citizen. In 1923 he graduated from the City College of New York, where he had studied under Morris Cohen, with whom he later collaborated to coauthor the highly successful textbook, An Introduction show more to Logic and Scientific Method (1934). Pursuing graduate studies at Columbia University, he received his Ph.D. in 1930. After a year of teaching at the City College of New York, he joined the faculty of Columbia University, where in 1955 he was named John Dewey Professor of Philosophy. In 1966 he joined the faculty of Rockefeller University. Nagel was one of the leaders in the movement of logical empiricism, conjoining Viennese positivism with indigenous American naturalism and pragmatism. In 1936 he published in the Journal of Philosophy the article "Impressions and Appraisals of Analytic Philosophy," one of the earliest sympathetic accounts of the works of Ludwig Wittgenstein, Moritz Schlick, and Rudolf Carnap intended for an American audience. Nagel was esteemed for his lucid exposition of the most recondite matters in logic, mathematics, and natural science, published in essays and book reviews for professional journals, scientific periodicals, and literary reviews. Two of his books, now out of print, consisted of collections of his articles, Sovereign Reason and Other Studies in the Philosophy of Science (1954) and Logic Without Metaphysics and Other Essays in the Philosophy of Science (1957). He also wrote a monograph, Principles of the Theory of Probability (1939) which appeared in the International Encyclopedia of Unified Science. In his major book-length work, The Structure of Science, Nagel directed his attention to the logic of scientific explanations. (Bowker Author Biography) show less
Series
Works by Ernest Nagel
The Structure of Science: Problems in the Logic of Scientific Explanation (2nd edition) (1961) 251 copies, 2 reviews
Logic, Methodology and Philosophy of Science: Proceedings of the 1960 International Congress (1966) — Editor — 10 copies
Simbolismo y ciencia 3 copies
Liberalism and Intelligence 2 copies
Το θεώρημα του Godel 1 copy
Associated Works
Tagged
Common Knowledge
- Canonical name
- Nagel, Ernest
- Legal name
- Nagel, Ernest
- Birthdate
- 1901-11-16
- Date of death
- 1985-09-22
- Gender
- male
- Education
- City College of New York (BSc | 1923)
Columbia University (MA | 1925 | PhD | 1930) - Occupations
- philosopher of science
professor - Organizations
- Columbia University
Rockefeller University - Awards and honors
- National Academy of Sciences (1977)
Fellow, Committee for Skeptical Inquiry (1976) - Relationships
- Nagel, Alexander (son)
Nagel, Sidney (son) - Short biography
- Ernest Nagel ging in 1911 naar de Verenigde Staten en werd in 1919 genaturaliseerd tot Amerikaans staatsburger. Hij heeft zijn hele leven in New York gewoond, waar hij als wetenschapsfilosoof werkzaam was aan de Columbia University (1931-1966), de Rockefeller University (1966-1967) en wederom de Columbia University (1967-1970). Hij was een van de vooraanstaande figuren in de filosofische stroming van het logisch positivisme. Hij werd in 1977 gekozen in de National Academy of Sciences.
Nagel is op 20 januari 1935 getrouwd met Edith Alexandria Haggstrom (ovl. 1988). Zij kregen twee zoons: Alexander Joseph (hoogleraar wiskunde aan de Universiteit van Wisconsin-Madison) en Sidney Robert (hoogleraar natuurkunde aan de Universiteit van Chicago). - Nationality
- USA (naturalized 1919)
Austria-Hungary (birth) - Birthplace
- Vágújhely, Austro-Hungarian Empire (now Nové Mesto nad Váhom, Slovakia)
- Places of residence
- Prague, Czech Republic
New York, New York, USA - Place of death
- New York, New York, USA
Members
Reviews
Nagel and Newman provide a nice, quick, and generally well written exposition of Godel's famous proof. This book can easily be read in an afternoon by anyone with the requisite background in logic.
They do a particularly nice job in their brief dissemination of the historical concerns that led up to the crisis in foundations in the late 19th and early 20th century. What's nice about this is that it puts Godel into context in a salient way. Godel without Hilbert is like Kant without Leibniz show more (and Wolff, I suppose). Given the narrow scope and short page count, Hilbert is covered well.
However, there are a couple of real problems with this book.
First, I do not believe that this book would really be that helpful for "the educated layman". Insofar as their target audience is concerned, the book is, perhaps, a failure. Why do I say this? Given its brevity, the authors are forced to introduce important bits of information without adequate exposition. For example, the notion of universal quantification makes its first appearance in the last twenty odd pages of the book and is explained in a sentence or two. This is fine for anyone that's had an intro logic course (and can recall what was covered) but is probably inadequate for the logical/mathematical novice. Furthermore, this example is just one case of something that occurs quite often throughout the book.
My second worry is that the actual mechanics of the proof are not presented lucidly. This is not altogether unexpected, but the fifteen pages or so that comprise the actual exposition of the proof seem to go by too quickly and sacrifice depth and clarity for readability and brevity. This may not be the authors' fault. I have doubts about whether or not one can successfully offer the sort of exegesis the authors are striving for. That is, I'm just not sure that anyone will ever pull off a lucid "Godel for Dummies". Similar problems plague Rebbecca Goldstein's attempt at this task in her recent Godel biography.
Final thought: I think this book would best serve the needs of a first year graduate student or advanced undergraduate in philosophy. For the student that has some background in logic (perhaps they've done a completeness proof for FOL or at least some proofs with quantifiers) but has yet to take a meta-logic course this book can provide a nicely structured overview of what the typical meta-logic course aims for. show less
They do a particularly nice job in their brief dissemination of the historical concerns that led up to the crisis in foundations in the late 19th and early 20th century. What's nice about this is that it puts Godel into context in a salient way. Godel without Hilbert is like Kant without Leibniz show more (and Wolff, I suppose). Given the narrow scope and short page count, Hilbert is covered well.
However, there are a couple of real problems with this book.
First, I do not believe that this book would really be that helpful for "the educated layman". Insofar as their target audience is concerned, the book is, perhaps, a failure. Why do I say this? Given its brevity, the authors are forced to introduce important bits of information without adequate exposition. For example, the notion of universal quantification makes its first appearance in the last twenty odd pages of the book and is explained in a sentence or two. This is fine for anyone that's had an intro logic course (and can recall what was covered) but is probably inadequate for the logical/mathematical novice. Furthermore, this example is just one case of something that occurs quite often throughout the book.
My second worry is that the actual mechanics of the proof are not presented lucidly. This is not altogether unexpected, but the fifteen pages or so that comprise the actual exposition of the proof seem to go by too quickly and sacrifice depth and clarity for readability and brevity. This may not be the authors' fault. I have doubts about whether or not one can successfully offer the sort of exegesis the authors are striving for. That is, I'm just not sure that anyone will ever pull off a lucid "Godel for Dummies". Similar problems plague Rebbecca Goldstein's attempt at this task in her recent Godel biography.
Final thought: I think this book would best serve the needs of a first year graduate student or advanced undergraduate in philosophy. For the student that has some background in logic (perhaps they've done a completeness proof for FOL or at least some proofs with quantifiers) but has yet to take a meta-logic course this book can provide a nicely structured overview of what the typical meta-logic course aims for. show less
The authors provide an overview of Kurt Gödel's 1931 proof regarding axiomatic demonstration in arithmetic. Gödel constructed his proof on the basis of Principia Mathematica by Whitehead and Russell, but this treatment does not presume a familiarity with that text. It does, however, place Gödel's work in the larger context of efforts to axiomatize arithmetic, an agenda notably defined by David Hilbert. The first five chapters set the stage for Gödel's proof in the history of mathematics show more and philosophy, while the fifth chapter discusses a critical idea underlying the operation of the proof. The long sixth chapter discusses the actual techniques and conclusions of the proof itself. A valuable final chapter outlines the larger implications and consequences, most especially and usefully discouraging misreadings which amount to "an invitation to despair or an excuse for mystery-mongering." (101) Interestingly, a secondary conclusion that they do support, is that algorithmic computers are unlikely ever to attain the equivalent of human consciousness. Gödel himself took his proof as support for a position of philosophical Realism, although it's not conclusive in that regard.
For anyone interested in the beauty of logic or the elegance of math, the mechanisms of Gödel's proof are impressive. This book by Nagel and Newman reads quickly--for a math book. The reader must be prepared to slow down and spend five to ten minutes on a page when getting into the thick of the mathematical concepts in use. The reward of doing so is an appreciation of an intellectual event that provided a turning-point in the philosophy of knowledge. show less
For anyone interested in the beauty of logic or the elegance of math, the mechanisms of Gödel's proof are impressive. This book by Nagel and Newman reads quickly--for a math book. The reader must be prepared to slow down and spend five to ten minutes on a page when getting into the thick of the mathematical concepts in use. The reward of doing so is an appreciation of an intellectual event that provided a turning-point in the philosophy of knowledge. show less
I remember my excitement when I read the first edition of this little gem back in 1999 (actually it was its Turkish translation). Being a young student of mathematics, it was impossible to resist reading a popular and clear account of maybe the most important theorem related to the fundamentals of axiomatic systems. After that came Hofstadter's "Gödel, Escher, Bach: An Eternal Golden Braid" which introduced more questions related to symbolic logical reasoning, artificial intelligence, show more cognitive science, and the consequences of Gödel's work in those ares. With that background and ten years after the second edition, it was truly an exciting second reading, a refresher that was both fun and putting lots of things into perspective. Hofstadter's foreword to this edition is a delight to read and ponder upon. On the other hand, I don't think this is a point strong enough to persuade most of the people who own the first edition anyway. But if you don't have the first edition and want a concise and clear explanation of what Gödel's work is all about then this book is definitely for you. show less
This is a non-formal, though still rigorous, presentation of the argument of Gödel's famous demonstration that will be accessible to anyone familiar with the basics of mathematical proof, logic, and number theory. By the end of the book, I acutally had the outline of Gödel's tricky self-referential argument all in my head at once, and though it faded quickly, I feel confident I could resurrect it with another reading. Nagel's description of the significance of the proof, as opposed to its show more mechanics, is less thorough, but that's a quibble. This slim book is a truly impressive feat of exposition. show less
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