Philosophy of Mathematics, Hardcover/Oystein Linnebo
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A sophisticated, original introduction to the philosophy of
mathematics from one of its leading contemporary scholars
Mathematics is one of humanity's most successful yet puzzling
endeavors. It is a model of precision and objectivity, but appears
distinct from the empirical sciences because it seems to deliver
nonexperiential knowledge of a nonphysical reality of numbers,
sets, and functions. How can these two aspects of mathematics be
reconciled? This concise book provides a systematic yet accessible
introduction to the field that is trying to answer that question:
the philosophy of mathematics. Written by Oystein Linnebo, one of
the world's leading scholars on the subject, the book introduces
all of the classical approaches to the field, including logicism,
formalism, intuitionism, empiricism, and structuralism. It also
contains accessible introductions to some more specialized issues,
such as mathematical intuition, potential infinity, the iterative
conception of sets, and the search for new mathematical axioms. The
groundbreaking work of German mathematician and philosopher Gottlob
Frege, one of the founders of analytic philosophy, figures
prominently throughout the book. Other important thinkers whose
work is introduced and discussed include Immanuel Kant, John Stuart
Mill, David Hilbert, Kurt Godel, W. V. Quine, Paul Benacerraf, and
Hartry H. Field. Sophisticated but clear and approachable, this is
an essential introduction for all students and teachers of
philosophy, as well as mathematicians and others who want to
understand the foundations of mathematics.
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