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Books > Humanities > Philosophy > Topics in philosophy > Logic
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Kurt Goedel - The Princeton Lectures on Intuitionism (Paperback, 1st ed. 2021)
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Kurt Goedel - The Princeton Lectures on Intuitionism (Paperback, 1st ed. 2021)
Series: Sources and Studies in the History of Mathematics and Physical Sciences
Expected to ship within 10 - 15 working days
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Paris of the year 1900 left two landmarks: the Tour Eiffel, and
David Hilbert's celebrated list of twenty-four mathematical
problems presented at a conference opening the new century. Kurt
Goedel, a logical icon of that time, showed Hilbert's ideal of
complete axiomatization of mathematics to be unattainable. The
result, of 1931, is called Goedel's incompleteness theorem. Goedel
then went on to attack Hilbert's first and second Paris problems,
namely Cantor's continuum problem about the type of infinity of the
real numbers, and the freedom from contradiction of the theory of
real numbers. By 1963, it became clear that Hilbert's first
question could not be answered by any known means, half of the
credit of this seeming faux pas going to Goedel. The second is a
problem still wide open. Goedel worked on it for years, with no
definitive results; The best he could offer was a start with the
arithmetic of the entire numbers. This book, Goedel's lectures at
the famous Princeton Institute for Advanced Study in 1941, shows
how far he had come with Hilbert's second problem, namely to a
theory of computable functionals of finite type and a proof of the
consistency of ordinary arithmetic. It offers indispensable reading
for logicians, mathematicians, and computer scientists interested
in foundational questions. It will form a basis for further
investigations into Goedel's vast Nachlass of unpublished notes on
how to extend the results of his lectures to the theory of real
numbers. The book also gives insights into the conceptual and
formal work that is needed for the solution of profound scientific
questions, by one of the central figures of 20th century science
and philosophy.
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