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Book Chapter
Gödel’s Conflicting Approaches to Effective Calculability
Book Series
Lecture Notes in Computer Science
Publisher
Springer Berlin / Heidelberg
ISSN
0302-9743 (Print) 1611-3349 (Online)
Volume
Volume 3988/2006
Book
Logical Approaches to Computational Barriers
DOI
10.1007/11780342
Copyright
2006
ISBN
978-3-540-35466-6
DOI
10.1007/11780342_54
Pages
536-537
Subject Collection
Computer Science
SpringerLink Date
Thursday, June 29, 2006
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Gödel’s Conflicting Approaches to Effective Calculability
Wilfried Sieg
1
(1)
Department of Philosophy, Carnegie Mellon University,
Abstract
Identifying the informal concept of effective calculability with a rigorous mathematical notion like general recursiveness or Turing computability is still viewed as problematic, and rightly so. In a 1934 conversation with Church, Gödel suggested finding axioms for the notion of effective calculability and “doing something on that basis” instead of identifying effective calculability with
λ
-definability; that identification he found “thoroughly unsatisfactory”. He introduced in his contemporaneous Princeton lectures (Gödel 1934) the class of general recursive functions through the equational calculus, but was not convinced at the time that this mathematical notion encompassed all effectively calculable functions. (See (Davis 1982) and (Sieg 1997).)
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