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Books > Science & Mathematics > Mathematics > Philosophy of mathematics
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Making and Breaking Mathematical Sense - Histories and Philosophies of Mathematical Practice (Hardcover)
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Making and Breaking Mathematical Sense - Histories and Philosophies of Mathematical Practice (Hardcover)
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In line with the emerging field of philosophy of mathematical
practice, this book pushes the philosophy of mathematics away from
questions about the reality and truth of mathematical entities and
statements and toward a focus on what mathematicians actually
do--and how that evolves and changes over time. How do new
mathematical entities come to be? What internal, natural,
cognitive, and social constraints shape mathematical cultures? How
do mathematical signs form and reform their meanings? How can we
model the cognitive processes at play in mathematical evolution?
And how does mathematics tie together ideas, reality, and
applications? Roi Wagner uniquely combines philosophical,
historical, and cognitive studies to paint a fully rounded image of
mathematics not as an absolute ideal but as a human endeavor that
takes shape in specific social and institutional contexts. The book
builds on ancient, medieval, and modern case studies to confront
philosophical reconstructions and cutting-edge cognitive theories.
It focuses on the contingent semiotic and interpretive dimensions
of mathematical practice, rather than on mathematics' claim to
universal or fundamental truths, in order to explore not only what
mathematics is, but also what it could be. Along the way, Wagner
challenges conventional views that mathematical signs represent
fixed, ideal entities; that mathematical cognition is a rigid
transfer of inferences between formal domains; and that
mathematics' exceptional consensus is due to the subject's
underlying reality. The result is a revisionist account of
mathematical philosophy that will interest mathematicians,
philosophers, and historians of science alike.
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