David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Philosophia Mathematica 14 (2):262-264 (2006)
This short book has two main purposes. The first is to explain Kurt Gödel's first and second incompleteness theorems in informal terms accessible to a layperson, or at least a non-logician. The author claims that, to follow this part of the book, a reader need only be familiar with the mathematics taught in secondary school. I am not sure if this is sufficient. A grasp of the incompleteness theorems, even at the level of ‘the big picture’, might require some experience with the rigor of mathematical proof. Moreover, since the incompleteness theorems concern formal deductive systems, it would help for a potential reader of this book to have some familiarity with at least elementary logic.There are, of course, a number of informal expositions of the incompleteness theorems. I do not see the need to engage in a comparative study. The second, and more important, goal of the present book is to discuss some alleged consequences of the incompleteness theorems and, in particular, to debunk thoroughly claims in philosophy, religion, and literary criticism that are supposed to be established, or at least bolstered, by incompleteness. The execution of this part of the book is masterly. The arguments are clear and compelling.The book has eight chapters, each between eight and twenty-eight pages. The opening chapter gives a very brief account of the incompleteness theorems and a sketch of Gödel's life and work. Chapter 2 gives the main overview of the incompleteness theorems, plus …
|Keywords||No keywords specified (fix it)|
|Categories||categorize this paper)|
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library|
References found in this work BETA
No references found.
Citations of this work BETA
No citations found.
Similar books and articles
Marcia J. Groszek, Michael E. Mytilinaios & Theodore A. Slaman (1996). The Sacks Density Theorem and Σ2-Bounding. Journal of Symbolic Logic 61 (2):450 - 467.
Harvey Siegel (2004). Epistemology and Education: An Incomplete Guide to the Social-Epistemological Issues. Episteme 1 (2):129-137.
Torkel Franzen (2003). Inexhaustibility: A Non-Exhaustive Treatment. Association for Symbolic Logic.
Keith K. Niall (2002). Visual Imagery and Geometric Enthymeme: The Example of Euclid I. Behavioral and Brain Sciences 25 (2):202-203.
Torkel Franzén (2004). Transfinite Progressions: A Second Look at Completeness. Bulletin of Symbolic Logic 10 (3):367-389.
FangWen Yuan (2008). Query the Triple Loophole of the Proof of Gödel Incompleteness Theorem. Proceedings of the Xxii World Congress of Philosophy 41:77-94.
Sylvia Maxfield (2006). Implication of Incomplete Markets for Corporate Social Responsibility and Competitive Strategy. Proceedings of the International Association for Business and Society 17:133-138.
Victor Harnik & Michael Makkai (1976). Applications of Vaught Sentences and the Covering Theorem. Journal of Symbolic Logic 41 (1):171-187.
Joan Bagaria (2003). A Short Guide to Gödel's Second Incompleteness Theorem. Teorema 22 (3):5-15.
Robyn M. Dawes (2000). A Theory of Irrationality as a `Reasonable' Response to an Incomplete Specification. Synthese 122 (1-2):133 - 163.
Added to index2010-08-24
Total downloads14 ( #129,215 of 1,410,079 )
Recent downloads (6 months)1 ( #177,589 of 1,410,079 )
How can I increase my downloads?