Philosophy of Mathematics
  • Language: en

Philosophy of Mathematics

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.

Truth, Objects, Infinity
  • Language: en
  • Pages: 309

Truth, Objects, Infinity

  • Type: Book
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  • Published: 2017-04-04
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  • Publisher: Springer

This volume features essays about and by Paul Benacerraf, whose ideas have circulated in the philosophical community since the early nineteen sixties, shaping key areas in the philosophy of mathematics, the philosophy of language, the philosophy of logic, and epistemology. The book started as a workshop held in Paris at the Collège de France in May 2012 with the participation of Paul Benacerraf. The introduction addresses the methodological point of the legitimate use of so-called “Princess Margaret Premises” in drawing philosophical conclusions from Gödel’s first incompleteness theorem. The book is then divided into three sections. The first is devoted to an assessment of the improv...

Logicism, Some Considerations
  • Language: en
  • Pages: 275

Logicism, Some Considerations

  • Type: Book
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  • Published: 1960
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  • Publisher: Unknown

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Budgeting and resource allocation at Princeton University
  • Language: en
  • Pages: 390

Budgeting and resource allocation at Princeton University

  • Type: Book
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  • Published: 1972
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  • Publisher: Unknown

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Back To Darwin
  • Language: en
  • Pages: 434

Back To Darwin

This book provides a distinctive, radical way beyond the quarrels between evolutionary science and Christian belief. Leading scientists, philosophers, and theologians critically discuss the metaphysical assumptions of neo-Darwinism and offer concrete ways of broadening mainstream evolutionary theory. Their open exchange, moderated by veteran process theologian John B. Cobb, presents a holistic case for evolution that both theists and nontheists can accept. Contributors: Francisco J. Ayala Ian G. Barbour Charles Birch Philip Clayton John B. Cobb Jr. John Greene David Ray Griffin A. Y. Gunter John F. Haught Lynn Margulis Reg Morrison Dorion Sagan Jeffrey Schloss Robert J. Valenza Howard J. Van Till

Realistic Rationalism
  • Language: en
  • Pages: 262

Realistic Rationalism

  • Type: Book
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  • Published: 1997-12-08
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  • Publisher: MIT Press

In Realistic Rationalism, Jerrold J. Katz develops a new philosophical position integrating realism and rationalism. Realism here means that the objects of study in mathematics and other formal sciences are abstract; rationalism means that our knowledge of them is not empirical. Katz uses this position to meet the principal challenges to realism. In exposing the flaws in criticisms of the antirealists, he shows that realists can explain knowledge of abstract objects without supposing we have causal contact with them, that numbers are determinate objects, and that the standard counterexamples to the abstract/concrete distinction have no force. Generalizing the account of knowledge used to mee...

Zeno's Paradoxes
  • Language: en
  • Pages: 317

Zeno's Paradoxes

A reprint of the Bobbs-Merrill edition of 1970. These essays lead the reader through the land of the wonderful shrinking genie to the warehouse where the infinity machines are kept. By careful examination of a lamp that is switched on and off infinitely many times, or the workings of a machine that prints out an infinite decimal expansion of pi, we begin to understand how it is possible for Achilles to overtake the tortoise. The concepts that form the basis of modern science—-space, time, motion, change, infinity-—are examined and explored in this edition. Includes an updated bibliography.

Math Worlds
  • Language: en
  • Pages: 292

Math Worlds

  • Type: Book
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  • Published: 1993
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  • Publisher: SUNY Press

An international group of distinguished scholars brings a variety of resources to bear on the major issues in the study and teaching of mathematics, and on the problem of understanding mathematics as a cultural and social phenomenon. All are guided by the notion that our understanding of mathematical knowledge must be grounded in and reflect the realities of mathematical practice. Chapters on the philosophy of mathematics illustrate the growing influence of a pragmatic view in a field traditionally dominated by platonic perspectives. In a section on mathematics, politics, and pedagogy, the emphasis is on politics and values in mathematics education. Issues addressed include gender and mathematics, applied mathematics and social concerns, and the reflective and dialogical nature of mathematical knowledge. The concluding section deals with the history and sociology of mathematics, and with mathematics and social change. Contributors include Philip J. Davis, Helga Jungwirth, Nel Noddings, Yehuda Rav, Michael D. Resnik, Ole Skovsmose, and Thomas Tymoczko.

Logicism
  • Language: en
  • Pages: 566

Logicism

  • Type: Book
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  • Published: 1977
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  • Publisher: Unknown

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Preludes to Pragmatism
  • Language: en
  • Pages: 424

Preludes to Pragmatism

In these essays, distinguished philosopher Philip Kitcher argues for a reconstruction of philosophy along the lines of classical Pragmatism