This volume is a translation of the book "Godel", written in Japanese by Gaisi Takeuti, a distinguished proof theorist. The core of the text is a memoir of K. Godel, Takeuti's personal recollections, and his interpretation of Godel's comprises attitudes towards mathematical logic. It also contains Takeuti's recollection of association with some other famous logicians. The author adheres to his own experiences and interpretations. There is also an article on Hilbert's second problem as well as on the author's fundamental conjecture about second order logic.
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Too Few Works Like This,
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This review is from: Memoirs of a Proof Theorist: Gödel and Other Logicians (Hardcover)
It's uncommon to find a memoir from a mathematician -- even surprising to find a memoir from a mathematician about mathematics. It's plausible this is due to the view that to learn mathematics you're better off learning from a textbook, where there's some attempt at coherence, the standards of rigor are met, etc. etc. But an insider will recollect an additional source of mathematical knowledge that one will rarely find in any published work, namely folklore. This is what is so brilliant about Takeuti's book. There is much of instructional value and interest to come from this text -- yet it's hardly more than a very loose conversation about a variety of topics associated with logic. Hearing an expert discuss mathematics loosely is probably closer to how they're actually thinking about mathematics. I've found much to enjoy in this book and I hope others decide to put their thoughts in more personal language as this eminent logician has done.
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Inside This Book
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First Sentence:
I was recently asked by Kreisel to write about Godel, but have just declined the request. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
finite standpoint, formalized mathematical system, fundamental conjecture, order proof theory, lower sequent, upper sequent, concrete strings, ramified hierarchy, transfinite set theory, ramified type, completeness question, modern set theory, consistency proof, constructible sets, continuum hypothesis, comprehension axiom, incompleteness theorem, axiomatic set theory, measurable cardinal, large cardinals, naive set theory, continuum problem, set theorists, new axiom, predicate calculus Key Phrases - Capitalized Phrases (CAPs): (learn more)
Hilbert's Program, Hao Wang, Vienna University, Paul Cohen, Princeton University, The Double Helix, Los Angeles, Mathematische Annalen, Journal of Symbolic Logic New!
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Front Cover | Table of Contents | First Pages | Back Cover | Surprise Me!
I was recently asked by Kreisel to write about Godel, but have just declined the request. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
finite standpoint, formalized mathematical system, fundamental conjecture, order proof theory, lower sequent, upper sequent, concrete strings, ramified hierarchy, transfinite set theory, ramified type, completeness question, modern set theory, consistency proof, constructible sets, continuum hypothesis, comprehension axiom, incompleteness theorem, axiomatic set theory, measurable cardinal, large cardinals, naive set theory, continuum problem, set theorists, new axiom, predicate calculus Key Phrases - Capitalized Phrases (CAPs): (learn more)
Hilbert's Program, Hao Wang, Vienna University, Paul Cohen, Princeton University, The Double Helix, Los Angeles, Mathematische Annalen, Journal of Symbolic Logic New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Back Cover | Surprise Me!
Citations (learn more)
This book cites 8
books:
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- Philosophy of Mathematics: Selected Readings by Paul and Hilary Putnam Benacerraf in Front Matter, page 19, and page 46
- From Mathematics to Philosophy (International Library of Philosophy) by Hao Wang on page 23, and page 103
- Collected Works, Vol. 3: Unpublished Essays and Lectures by Kurt Godel on page 99, and Back Matter
- Remarks on the Foundations of Mathematics, Revised Edition by Ludwig Wittgenstein on page 13
- The Double Helix by James D. Watson on page 35
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