Can Mathematics Be Proved Consistent?
Jan von Plato
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Springer International Publishing
Naturwissenschaften, Medizin, Informatik, Technik / Allgemeines, Lexika
Beschreibung
Kurt Gödel (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. Gödel 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 Gödel’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?"
Kundenbewertungen
incompleteness theorems, Open Access, German mathematicians, Gödel lectures, completeness problem, Gödel notes, Principia Mathematica, Gödel incompleteness theorem, Skolem's paradox