Godel's incompleteness theorem
limitations of formalism
"An unsolvable problem of elementary number theory",
The American Journal of Mathematics, 58, pp. 345-363, 1936.
page numbers from p. 89-107, Davis, M., The undecidable: Basic papers on undecidable propositions, undecidable problems, and computable functions, Hewlett NY: Raven Press 1965.
|89 ;;Quote: Church proposed a definition for effectively calculable functions and demonstrated an unsolvable problem|
|90 ;;Quote: Church proposed lambda functions and recursive functions as equivalent definitions of effectively calculable. These widely different definitions support his thesis|
|102 ;;Quote: Church's definitions of effective calculability include algorithms and a large class of provable theorems in a system of symbolic logic|
|102 ;;Quote: no complete set of effectively calculable invariants of conversion exist; for example, if Principia Mathematica is omega-consistent, its Enthscheidungsproblem is unsolvable
ThesaHelp: references c-d (337 items)
Topic: Turing machine (30 items)
Topic: Godel's incompleteness theorem (19 items)
Topic: limitations of formalism (92 items)