David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
Jack Alan Reynolds
Learn more about PhilPapers
Like Heisenberg’s uncertainty principle, Gödel’s incompleteness theorem has captured the public imagination, supposedly demonstrating that there are absolute limits to what can be known. More specifically, it is thought to tell us that there are mathematical truths which can never be proved. These are among the many misconceptions and misuses of Gödel’s theorem and its consequences. Incompleteness has been held to show, for example, that there cannot be a Theory of Everything, the so-called holy grail of modern physics. Some philosophers and mathematicians say it proves that minds can’t be modelled by machines, while others argue that they can be modelled but that Gödel’s theorem shows we can’t know it. Postmodernists have claimed to find support in it for the view that objective truth is chimerical. And in the Bibliography of Christianity and Mathematics (yes, there is such a publication) it is asserted that ‘theologians can be comforted in their failure to systematize revealed truth because mathematicians cannot grasp all mathematical truths in their systems either.’ Not only that, the incompleteness theorem is held to imply the existence of God, since only He can decide all truths. Even Rebecca Goldstein’s book, whose laudable aim is to provide non-technical expositions of the incompleteness theorems (there are two) for a general audience and place them in their historical and biographical context, makes extravagant claims and distorts their significance. As Goldstein sees it, Gödel’s theorems are ‘the most prolix theorems in the history of mathematics’ and address themselves ‘to the central question of the humanities – ‘what is it to be human?’ – since they involve ‘such vast and messy areas as the nature of truth and knowledge and certainty’. Unfortunately, these weighty claims disintegrate under closer examination, while the book as a whole is marred by a number of disturbing conceptual and historical errors. On the face of it, Goldstein would appear to have been an ideal choice to present Gödel’s work: she received a PhD in Philosophy from Princeton University in 1977 and since then has taught philosophy of science and philosophy of mind at several....
|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
Raymond M. Smullyan (1992). Gödel's Incompleteness Theorems. Oxford University Press.
Panu Raatikainen (2005). On the Philosophical Relevance of Gödel's Incompleteness Theorems. Revue Internationale de Philosophie 59 (4):513-534.
Francesco Berto (2009). The Gödel Paradox and Wittgenstein's Reasons. Philosophia Mathematica 17 (2):208-219.
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.
Zofia Adamowicz & Teresa Bigorajska (2001). Existentially Closed Structures and Gödel's Second Incompleteness Theorem. Journal of Symbolic Logic 66 (1):349-356.
Matthias Baaz (ed.) (2011). Kurt Gödel and the Foundations of Mathematics: Horizons of Truth. Cambridge University Press.
Roman Murawski (1997). Gödel's Incompleteness Theorems and Computer Science. Foundations of Science 2 (1):123-135.
Robert F. Hadley (2008). Consistency, Turing Computability and Gödel's First Incompleteness Theorem. Minds and Machines 18 (1):1-15.
Peter Smith (2013). An Introduction to Gödel's Theorems. Cambridge University Press.
N. Shankar (1994). Metamathematics, Machines, and Gödel's Proof. Cambridge University Press.
Juliet Floyd (2001). Prose Versus Proof: Wittgenstein on Gödel, Tarski and Truth. Philosophia Mathematica 9 (3):280-307.
Added to index2010-12-22
Total downloads52 ( #80,968 of 1,796,319 )
Recent downloads (6 months)10 ( #74,365 of 1,796,319 )
How can I increase my downloads?