Godel's Theorem

Term Paper # 100031

Mathematics

Godel's Theorem

A review of Godel's theorem and the limitations of an allegory in trying to understand it.

1,495 words () | 5 sources | MLA | 2007 United States

Paper Summary:

This paper discusses Godel's theorem and how it is sometimes used to imply that all machine logic can eventually become self-aware. The paper also discusses the criticisms of the theorem and its limitations. The paper then provides an allegory to explain Godel's theorem and discusses the advantages of this explanation, as well as the limitations in using an allegory to try to understand the theorem.

Table of Contents:
Allegory and Godel: Oil and Water

From the Paper:

"Godel recognizes that his theory in fact could not be fully described in human language and concepts and this is a fact that Hofstadter completely misses. When Godel is quoted as saying the epistemological descriptions in a given language cannot be restated in that same language, he directly disallows the use of allegory in retelling his theory. The unfortunate aspect of Hofstadter's allegory is that most readers get lost in trying to decide what the various characters represent, what is meant by the way the dialogue is spoken and, ultimately, what the Omega record player looks like. None of which, of course, has anything to do with Godel's Theorem."

Sample of Sources Used:

Hofstadter, Douglas. "Contricrostipunctus."
Penrose, Roger. "Truth, Proof, and Insight (From the Emperor's New Mind)."
Rucker, R. "Robots and Souls." Chapter 4 of Infinitey and the Mind.
Shanker, S. G., ed. Godel's Theorem in Focus. London: Routledge, 1989.
Zimmerman, Donald W. "Is a Final Theory Conceivable?" The Psychological Record 47.3 (1997): 423+.