Lectures on the philosophy of mathematics

By:

Hamkins, Joel David

Material type: Text

TextPublication details: MIT Press Cambridge 2020Description: xviii, 329 pISBN:

9780262542234

Subject(s):

DDC classification:

510.1 HAM

Summary: An introduction to the philosophy of mathematics grounded in mathematics and motivated by mathematical inquiry and practice. In this book, Joel David Hamkins offers an introduction to the philosophy of mathematics that is grounded in mathematics and motivated by mathematical inquiry and practice. He treats philosophical issues as they arise organically in mathematics, discussing such topics as platonism, realism, logicism, structuralism, formalism, infinity, and intuitionism in mathematical contexts. He organizes the book by mathematical themes—numbers, rigor, geometry, proof, computability, incompleteness, and set theory—that give rise again and again to philosophical considerations. Hamkins shows, for example, how number systems set the stage for discussions of such philosophical issues as platonism, logicism, and the nature of abstraction. Consideration of the rise of rigor in the calculus leads to a discussion of whether the indispensability of mathematics in science offers grounds for mathematical truth. Sophisticated technical developments in set theory give rise to a necessary engagement with deep philosophical concerns, including the criteria for new mathematical axioms. Throughout, Hamkins offers a clear and engaging exposition that is both accessible and sophisticated, intended for readers whose mathematical backgrounds range from novice to expert.

List(s) this item appears in: Public Policy & General Management | Fiction

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Holdings
Item type	Current library	Collection	Call number	Copy number	Status	Date due	Barcode
Book	Indian Institute of Management LRC General Stacks	Public Policy & General Management	510.1 HAM (Browse shelf(Opens below))	1	Available		004056

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Previous	501 KUH The structure of scientific revolutions	501.8 POP Logic of scientific discovery	510 ELL How not to be wrong: the hidden maths of everyday life	510.1 HAM Lectures on the philosophy of mathematics	510.2433 DOW Schaum's easy outline of Introduction to mathematical economics	510.24339 SIM Mathematics for economist	510.24339 SIM Mathematics for economist	Next

An introduction to the philosophy of mathematics grounded in mathematics and motivated by mathematical inquiry and practice.

In this book, Joel David Hamkins offers an introduction to the philosophy of mathematics that is grounded in mathematics and motivated by mathematical inquiry and practice. He treats philosophical issues as they arise organically in mathematics, discussing such topics as platonism, realism, logicism, structuralism, formalism, infinity, and intuitionism in mathematical contexts. He organizes the book by mathematical themes—numbers, rigor, geometry, proof, computability, incompleteness, and set theory—that give rise again and again to philosophical considerations.

Hamkins shows, for example, how number systems set the stage for discussions of such philosophical issues as platonism, logicism, and the nature of abstraction. Consideration of the rise of rigor in the calculus leads to a discussion of whether the indispensability of mathematics in science offers grounds for mathematical truth. Sophisticated technical developments in set theory give rise to a necessary engagement with deep philosophical concerns, including the criteria for new mathematical axioms. Throughout, Hamkins offers a clear and engaging exposition that is both accessible and sophisticated, intended for readers whose mathematical backgrounds range from novice to expert.

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