Lectures on the Philosophy of Mathematics

Lectures on the Philosophy of Mathematics

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  • Author: Joel David Hamkins
  • Publisher: MIT Press
  • ISBN: 0262542234
  • Category : Mathematics
  • Languages : en
  • Pages : 350

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.


LOGIC: Lecture Notes for Philosophy, Mathematics, and Computer Science

LOGIC: Lecture Notes for Philosophy, Mathematics, and Computer Science

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  • Author: Andrea Iacona
  • Publisher: Springer Nature
  • ISBN: 3030648117
  • Category : Philosophy
  • Languages : en
  • Pages : 228

This textbook is a logic manual which includes an elementary course and an advanced course. It covers more than most introductory logic textbooks, while maintaining a comfortable pace that students can follow. The technical exposition is clear, precise and follows a paced increase in complexity, allowing the reader to get comfortable with previous definitions and procedures before facing more difficult material. The book also presents an interesting overall balance between formal and philosophical discussion, making it suitable for both philosophy and more formal/science oriented students. This textbook is of great use to undergraduate philosophy students, graduate philosophy students, logic teachers, undergraduates and graduates in mathematics, computer science or related fields in which logic is required.


An Introduction to the Philosophy of Mathematics

An Introduction to the Philosophy of Mathematics

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  • Author: Mark Colyvan
  • Publisher: Cambridge University Press
  • ISBN: 0521826020
  • Category : Mathematics
  • Languages : en
  • Pages : 199

A fascinating journey through intriguing mathematical and philosophical territory - a lively introduction to this contemporary topic.


Philosophy of Mathematics

Philosophy of Mathematics

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  • Author: Paul Benacerraf
  • Publisher: Cambridge University Press
  • ISBN: 1107268133
  • Category : Science
  • Languages : en
  • Pages : 604

The twentieth century has witnessed an unprecedented 'crisis in the foundations of mathematics', featuring a world-famous paradox (Russell's Paradox), a challenge to 'classical' mathematics from a world-famous mathematician (the 'mathematical intuitionism' of Brouwer), a new foundational school (Hilbert's Formalism), and the profound incompleteness results of Kurt Gödel. In the same period, the cross-fertilization of mathematics and philosophy resulted in a new sort of 'mathematical philosophy', associated most notably (but in different ways) with Bertrand Russell, W. V. Quine, and Gödel himself, and which remains at the focus of Anglo-Saxon philosophical discussion. The present collection brings together in a convenient form the seminal articles in the philosophy of mathematics by these and other major thinkers. It is a substantially revised version of the edition first published in 1964 and includes a revised bibliography. The volume will be welcomed as a major work of reference at this level in the field.


Why Is There Philosophy of Mathematics At All?

Why Is There Philosophy of Mathematics At All?

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  • Author: Ian Hacking
  • Publisher: Cambridge University Press
  • ISBN: 1107729823
  • Category : Science
  • Languages : en
  • Pages : 307

This truly philosophical book takes us back to fundamentals - the sheer experience of proof, and the enigmatic relation of mathematics to nature. It asks unexpected questions, such as 'what makes mathematics mathematics?', 'where did proof come from and how did it evolve?', and 'how did the distinction between pure and applied mathematics come into being?' In a wide-ranging discussion that is both immersed in the past and unusually attuned to the competing philosophical ideas of contemporary mathematicians, it shows that proof and other forms of mathematical exploration continue to be living, evolving practices - responsive to new technologies, yet embedded in permanent (and astonishing) facts about human beings. It distinguishes several distinct types of application of mathematics, and shows how each leads to a different philosophical conundrum. Here is a remarkable body of new philosophical thinking about proofs, applications, and other mathematical activities.


Levels of Infinity

Levels of Infinity

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  • Author: Hermann Weyl
  • Publisher: Courier Corporation
  • ISBN: 0486266931
  • Category : Mathematics
  • Languages : en
  • Pages : 258

Original anthology features less-technical essays discussing logic, topology, abstract algebra, relativity theory, and the works of David Hilbert. Most have been long unavailable or previously unpublished in book form. 2012 edition.


Popular Lectures on Mathematical Logic

Popular Lectures on Mathematical Logic

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  • Author: Hao Wang
  • Publisher: Courier Corporation
  • ISBN: 0486171043
  • Category : Mathematics
  • Languages : en
  • Pages : 290

Noted logician discusses both theoretical underpinnings and practical applications, exploring set theory, model theory, recursion theory and constructivism, proof theory, logic's relation to computer science, and other subjects. 1981 edition, reissued by Dover in 1993 with a new Postscript by the author.


Incompleteness

Incompleteness

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  • Author: Rebecca Goldstein
  • Publisher: W. W. Norton & Company
  • ISBN: 0393327604
  • Category : Biography & Autobiography
  • Languages : en
  • Pages : 299

"An introduction to the life and thought of Kurt Gödel, who transformed our conception of math forever"--Provided by publisher.


Mind and Nature

Mind and Nature

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  • Author: Hermann Weyl
  • Publisher: University of Pennsylvania Press
  • ISBN: 1512819328
  • Category : Philosophy
  • Languages : en
  • Pages : 112

A new study of the mathematical-physical mode of cognition.


Frege

Frege

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  • Author: Michael Dummett
  • Publisher: Harvard University Press
  • ISBN: 9780674319356
  • Category : Mathematics
  • Languages : en
  • Pages : 364

No one has figured more prominently in the study of the German philosopher Gottlob Frege than Michael Dummett. His magisterial Frege: Philosophy of Language is a sustained, systematic analysis of Frege's thought, omitting only the issues in philosophy of mathematics. In this work Dummett discusses, section by section, Frege's masterpiece The Foundations of Arithmetic and Frege's treatment of real numbers in the second volume of Basic Laws of Arithmetic, establishing what parts of the philosopher's views can be salvaged and employed in new theorizing, and what must be abandoned, either as incorrectly argued or as untenable in the light of technical developments. Gottlob Frege (1848-1925) was a logician, mathematician, and philosopher whose work had enormous impact on Bertrand Russell and later on the young Ludwig Wittgenstein, making Frege one of the central influences on twentieth-century Anglo-American philosophy; he is considered the founder of analytic philosophy. His philosophy of mathematics contains deep insights and remains a useful and necessary point of departure for anyone seriously studying or working in the field.