On the Nature of Generalizations and Partial Boundary-Like Exceptions for Godel’s Second Incompleteness Theorem

 

On the Nature of Generalizations and Partial Boundary-Like Exceptions for Godel’s Second Incompleteness Theorem

Sage 4101

January 31, 2007 12:00 PM - 1:30 PM

Dan Willard
Professor
Computer Science Department
University at Albany
  • Abstract: Godel's Second Incompleteness Theorem states that axiom systems of sufficient strength are unable to verify their own consistency. Since 1993, we have published a lengthy series of articles about generalizations of the Second Incompleteness Theorem and its boundary-case exceptions. This current article will speculate about the main philosophical and computer science engineering implications of these results.
    We will show that these issues are related to the question about whether (?) (and also to what precise degree ? ) a future computer can manage to internally recognize and conceptualize its own logical consistency ?
    This talk and its accompanying paper will be conducted in a sufficiently informal and casual style so that a layman and non-expert in mathematical logic can appreciate the fundamental and fascinating nature of the issues stemming from this open question. Also, one section of this paper will consist of a detailed technical summary of the results that we have published in eleven different articles.
  • Paper: On the Nature of Generalizations and Partial Boundary-Like Exceptions for G ¨odel's Second Incompleteness Theorem
  • Source: paper
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