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Can Mathematics Be Proved Consistent? - Goedel's Shorthand Notes & Lectures on Incompleteness (Paperback, 1st ed. 2020)
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Can Mathematics Be Proved Consistent? - Goedel's Shorthand Notes & Lectures on Incompleteness (Paperback, 1st ed. 2020)
Series: Sources and Studies in the History of Mathematics and Physical Sciences
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Kurt Goedel (1906-1978) shook the mathematical world in 1931 by a
result that has become an icon of 20th century science: The search
for rigour in proving mathematical theorems had led to the
formalization of mathematical proofs, to the extent that such
proving could be reduced to the application of a few mechanical
rules. Goedel showed that whenever the part of mathematics under
formalization contains elementary arithmetic, there will be
arithmetical statements that should be formally provable but
aren't. The result is known as Goedel's first incompleteness
theorem, so called because there is a second incompleteness result,
embodied in his answer to the question "Can mathematics be proved
consistent?" This book offers the first examination of Goedel's
preserved notebooks from 1930, written in a long-forgotten German
shorthand, that show his way to the results: his first ideas, how
they evolved, and how the jewel-like final presentation in his
famous publication On formally undecidable propositions was
composed.The book also contains the original version of Goedel's
incompleteness article, as handed in for publication with no
mentioning of the second incompleteness theorem, as well as six
contemporary lectures and seminars Goedel gave between 1931 and
1934 in Austria, Germany, and the United States. The lectures are
masterpieces of accessible presentations of deep scientific
results, readable even for those without special mathematical
training, and published here for the first time.
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