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Goedel's Way: Exploits into an undecidable world 1st Edition

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ISBN-13: 978-0415690850
ISBN-10: 0415690854
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Editorial Reviews


Most scientists don’t really understand how important the process of formalization of logic, set theory and mathematics has been, both for showing when formalization is possible, and when it is not. Ok, I admit that most filmmakers, myself included, don’t really understand that either… So for scientists and filmmakers alike, I strongly recommend "Gödel’s Way: Exploits into an undecidable world". It’s a brilliant book, written by three brilliant men, Gregory Chaitin, Francisco Doria and Newton da Costa, two of whom are Brazilians like me. Read it, and you will find out why Gödel has a way of being relevant almost everywhere.

José Padilha

This is not a conventional book on science; rather, it is the three authors’ personal journey through the world of Gödel’s theorem and computational complexity… There are no formal definitions, theorems, or detailed proofs. But there are audacious predictions, which would surprise most complexity theorists... [E]ntertaining for a reader who has the same background as the three authors and likes to make big leaps forward at the same points as the authors.

M. Bona, University of Florida, in CHOICE, September 2012, Vol. 50 No. 1.

"The text is based on graduate lectures and extended courses for a wide spectrum of engineering student and on own practical experiences. Also professionals in modeling of heat transfer, incompressible viscous flow, and heat convection and corresponding codes can profit from the book."
––Georg Hebermehl, Zentralblatt MATH 1257 |

About the Author

Gregory Chaitin is an Argentinian-American mathematician and computer scientist. The author of many books and scholarly papers, Chaitin proved the Gödel-Chaitin incompleteness theorem and is the discoverer of the remarkable omega number, which shows that God plays dice in pure mathematics. Currently, he is attempting to create a mathematical theory of evolution and biological creativity, based on considering life as evolving software. He  is a member of the International Academy of the Philosophy of Science and of the Brazilian Academy of Philosophy, and was awarded honorary doctorates from the University of Cordoba and the University of Maine. Chaitin is currently a visiting professor at the Federal University of Rio de Janeiro (UFRJ) in the program on Epistemology and History of Science and Technology (HCTE). He is also an honorary professor at the University of Buenos Aires.

Newton da Costa is a Brazilian logician whose best known contributions have been in the realm of nonclassical logics. Da Costa developed paraconsistent logics, that is, logical systems that admit inner contradictions. Da Costa has wide-ranging interests, which go from foundational issues in the philosophy of science to physics (general relativity and quantum theory); besides his development of paraconsistent logics, he introduced the concept of quasi-truth to deal with mutually inconsistent scientific theories. Da Costa has a B. Sc. in civil engineering and a PhD in mathematics. He has visited several major universities (Stanford, Berkeley, Paris VII among others) and published about 200 scientific papers and several books on logic and the foundations of science. In 2009, he became a Professor Emeritus at Unicamp (Campinas, Brazil). Newton da Costa  is a member of the  Institut International de Philosophie, of the International Academy of the Philosophy of Science and of the Brazilian Academy of Philosophy.

Francisco Antonio Doria is a Brazilian physicist. Doria is a Professor Emeritus at the Federal University of Rio de Janeiro, where he currently teaches economic theory at the graduate School of Engineering (UFRJ COPPE). Doria has a B. Sc. in chemical engineering and a PhD in mathematical physics. He has made contributions to the gauge field copy problem in quantum field theory and proved with Newton da Costa several incompleteness theorems in mathematics, physics and mathematical economics, including the undecidability of chaos theory. Doria is a member of the Brazilian Academy of Philosophy, was a Senior Fulbright Scholar at Stanford University, 1989-1990, and a visiting researcher at the mathematics department, University of Rochester.


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Product Details

  • Paperback: 160 pages
  • Publisher: CRC Press; 1 edition (October 13, 2011)
  • Language: English
  • ISBN-10: 0415690854
  • ISBN-13: 978-0415690850
  • Product Dimensions: 0.2 x 6 x 9 inches
  • Shipping Weight: 8.5 ounces (View shipping rates and policies)
  • Average Customer Review: 3.5 out of 5 stars  See all reviews (4 customer reviews)
  • Amazon Best Sellers Rank: #1,465,394 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

10 of 12 people found the following review helpful By Ben Rothke on December 1, 2011
Format: Paperback
Kurt Gödel is one of the most important personalities that most people have never heard of. He is known for his incompleteness theorems, of which much of mathematical logic of the last 80 years is built on.

Gödel become somewhat of a household word in 1979 with the publication of Gödel, Escher, Bach: An Eternal Golden Braid, which went on to win the 1980 Pulitzer Prize.

With that, Goedel's Way: Exploits into an undecidable world, is a fascinating book. Authors Gregory Chaitin, Newton da Costa and Francisco Antônio Dória cover a huge amount in but 130 pages.

All three of the authors are world-class mathematics and it worth noting that Dória and Da Costa have published papers with conditional proofs of the consistency of the P versus NP problem.

When it comes to Gödel, Chaitin also has his own interpretation of the incompleteness theorem (Gödel-Chaitin), and is also the discoverer of the Chaitin constant, of which the book terms and references as the omega number.

Gödel's incompleteness theorem has traditionally been used in the realm of mathematical logic. The author's premise is that Gödel can be extended into nearly every field; from biology, ecology, to economics, computer science and more. In fact, their hypothesis is that undecidability and incompleteness is everywhere in mathematics.

Goedel's Way: Exploits into an undecidable world is a hard book to classify. Part of it includes numerous vignettes into the life of Gödel, part of it a detailed explanation of the incompleteness theorems, and a lot more.
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8 of 10 people found the following review helpful By dsm on September 19, 2012
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I can report the feelings of our hard science book group, whose seven members include engineers, physicists and a physician. We did NOT find that this book showed how Godel's Theorem relates to everyday life. We found it far from elementary, and the least accessible book we have read in over five years. We did enjoy the human interest histories, but that was not what the description promised.
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In spite of its failings—really a series of notes rather than a finished book—this is a unique source of the work of these three famous scholars who have been working at the bleeding edges of physics, math and philosophy for over half a century. Da Costa and Doria are cited by Wolpert (see below or my articles on Wolpert and my review of Yanofsky’s ‘The Outer Limits of Reason’) since they wrote on universal computation and among his many accomplishments, Da Costa is a pioneer in paraconsistency. The articles, and especially the group discussion with Chaitin, Fredkin, Wolfram et al at the end of Zenil H. (ed.) ‘Randomness through computation’ (2011) is a stimulating continuation of many of the topics here, but again lacking awareness of the philosophical issues, and so often missing the point. Chaitin also contributes to ‘Causality, Meaningful Complexity and Embodied Cognition’ (2010), replete with articles having the usual mixture of scientific insight and philosophical incoherence, and as usual nobody is aware that Ludwig Wittgenstein (W) provided deep and unsurpassed insights into the issues over half a century ago, including Embodied Cognition (Enactivism).
Chaitin’s proof of the algorithmic randomness of math (of which Godel’s results are a corollary) and the Omega number are some of the most famous mathematical results in the last 50 years and he has documented them in many books and articles. His coauthors from Brazil are less well known in spite of their many important contributions. For all the topics here, the best way to get free articles on the cutting edge is to visit ,,, or philpapers.
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By Gabor Peli on April 7, 2014
Format: Paperback
This book puts together quite different aspects of knowledge in a fascinating manner. Very insightful, though it was a challenge reading it. It was a great appetizer to the authors' earlier and subsequent works as well. I've lost my first copy on the train, so now I'm just going to buy a second one...
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