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Books > Science & Mathematics > Mathematics > Philosophy of mathematics
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Goedel's Disjunction - The scope and limits of mathematical knowledge (Hardcover)
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Goedel's Disjunction - The scope and limits of mathematical knowledge (Hardcover)
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The logician Kurt Goedel in 1951 established a disjunctive thesis
about the scope and limits of mathematical knowledge: either the
mathematical mind is not equivalent to a Turing machine (i.e., a
computer), or there are absolutely undecidable mathematical
problems. In the second half of the twentieth century, attempts
have been made to arrive at a stronger conclusion. In particular,
arguments have been produced by the philosopher J.R. Lucas and by
the physicist and mathematician Roger Penrose that intend to show
that the mathematical mind is more powerful than any computer.
These arguments, and counterarguments to them, have not convinced
the logical and philosophical community. The reason for this is an
insufficiency if rigour in the debate. The contributions in this
volume move the debate forward by formulating rigorous frameworks
and formally spelling out and evaluating arguments that bear on
Goedel's disjunction in these frameworks. The contributions in this
volume have been written by world leading experts in the field.
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