The logician Kurt Goedel (1906-1978) published a paper in 1931
formulating what have come to be known as his 'incompleteness
theorems', which prove, among other things, that within any formal
system with resources sufficient to code arithmetic, questions
exist which are neither provable nor disprovable on the basis of
the axioms which define the system. These are among the most
celebrated results in logic today. In this volume, leading
philosophers and mathematicians assess important aspects of
Goedel's work on the foundations and philosophy of mathematics.
Their essays explore almost every aspect of Godel's intellectual
legacy including his concepts of intuition and analyticity, the
Completeness Theorem, the set-theoretic multiverse, and the state
of mathematical logic today. This groundbreaking volume will be
invaluable to students, historians, logicians and philosophers of
mathematics who wish to understand the current thinking on these
issues.
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