Incompleteness: The Proof and Paradox of Kurt Gödel

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)
 Save to my reading list
Follow the author(s)
My bibliography
Export citation
Find it on Scholar
Edit this record
Mark as duplicate
Revision history Request removal from index Translate to english
Download options
PhilPapers Archive

Upload a copy of this paper     Check publisher's policy on self-archival     Papers currently archived: 15,974
External links
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.

Add more references

Citations of this work BETA

No citations found.

Add more citations

Similar books and articles
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.

Monthly downloads

Added to index


Total downloads

42 ( #79,289 of 1,725,806 )

Recent downloads (6 months)

9 ( #72,211 of 1,725,806 )

How can I increase my downloads?

My notes
Sign in to use this feature

Start a new thread
There  are no threads in this forum
Nothing in this forum yet.