Lectures on the Philosophy of Mathematics

2021-03-09
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

2021-05-10
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

2012-06-14
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

1984-01-27
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.

Philosophy of Mathematics

2021-11-09
Philosophy of Mathematics

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  • Author: Ahmet Cevik
  • Publisher: CRC Press
  • ISBN: 1000468801
  • Category : Mathematics
  • Languages : en
  • Pages : 352

The philosophy of mathematics is an exciting subject. Philosophy of Mathematics: Classic and Contemporary Studies explores the foundations of mathematical thought. The aim of this book is to encourage young mathematicians to think about the philosophical issues behind fundamental concepts and about different views on mathematical objects and mathematical knowledge. With this new approach, the author rekindles an interest in philosophical subjects surrounding the foundations of mathematics. He offers the mathematical motivations behind the topics under debate. He introduces various philosophical positions ranging from the classic views to more contemporary ones, including subjects which are more engaged with mathematical logic. Most books on philosophy of mathematics have little to no focus on the effects of philosophical views on mathematical practice, and no concern on giving crucial mathematical results and their philosophical relevance, consequences, reasons, etc. This book fills this gap. The book can be used as a textbook for a one-semester or even one-year course on philosophy of mathematics. "Other textbooks on the philosophy of mathematics are aimed at philosophers. This book is aimed at mathematicians. Since the author is a mathematician, it is a valuable addition to the literature." - Mark Balaguer, California State University, Los Angeles "There are not many such texts available for mathematics students. I applaud efforts to foster the dialogue between mathematics and philosophy." - Michele Friend, George Washington University and CNRS, Lille, France

Why Is There Philosophy of Mathematics At All?

2014-01-30
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

2013-09-26
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

2014-09-22
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.

Mind and Nature

2015-09-30
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

1991
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.