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| Author | : Michael D. Potter |
| Publisher | : Clarendon Press |
| Total Pages | : 345 |
| Release | : 2004 |
| Genre | : Mathematics |
| ISBN | : 9780199269730 |
A wonderful new book ... Potter has written the best philosophical introduction to set theory on the market - Timothy Bays, Notre Dame Philosophical Reviews.
| Author | : Mary Tiles |
| Publisher | : Courier Corporation |
| Total Pages | : 258 |
| Release | : 2012-03-08 |
| Genre | : Mathematics |
| ISBN | : 0486138550 |
DIVBeginning with perspectives on the finite universe and classes and Aristotelian logic, the author examines permutations, combinations, and infinite cardinalities; numbering the continuum; Cantor's transfinite paradise; axiomatic set theory, and more. /div
| Author | : Sean Morris |
| Publisher | : Cambridge University Press |
| Total Pages | : 221 |
| Release | : 2018-12-13 |
| Genre | : History |
| ISBN | : 110715250X |
Provides an accessible mathematical and philosophical account of Quine's set theory, New Foundations.
| Author | : Penelope Maddy |
| Publisher | : Oxford University Press |
| Total Pages | : 161 |
| Release | : 2011-01-27 |
| Genre | : Mathematics |
| ISBN | : 0199596182 |
Mathematics depends on proofs, and proofs must begin somewhere, from some fundamental assumptions. The axioms of set theory have long played this role, so the question of how they are properly judged is of central importance. Maddy discusses the appropriate methods for such evaluations and the philosophical backdrop that makes them appropriate.
| Author | : Manuel Bremer |
| Publisher | : Walter de Gruyter |
| Total Pages | : 125 |
| Release | : 2013-05-02 |
| Genre | : Philosophy |
| ISBN | : 3110326108 |
The book discusses the fate of universality and a universal set in several set theories. The book aims at a philosophical study of ontological and conceptual questions around set theory. Set theories are ontologies. They posit sets and claim that these exhibit the essential properties laid down in the set theoretical axioms. Collecting these postulated entities quantified over poses the problem of universality. Is the collection of the set theoretical entities itself a set theoretical entity? What does it mean if it is, and what does it mean if it is not? To answer these questions involves developing a theory of the universal set. We have to ask: Are there different aspects to universality in set theory, which stand in conflict to each other? May inconsistency be the price to pay to circumvent ineffability? And most importantly: How far can axiomatic ontology take us out of the problems around universality?
| Author | : Stephen Pollard |
| Publisher | : Courier Dover Publications |
| Total Pages | : 196 |
| Release | : 2015-07-15 |
| Genre | : Mathematics |
| ISBN | : 0486797147 |
This unique approach maintains that set theory is the primary mechanism for ideological and theoretical unification in modern mathematics, and its technically informed discussion covers a variety of philosophical issues. 1990 edition.
| Author | : Luca Incurvati |
| Publisher | : Cambridge University Press |
| Total Pages | : 255 |
| Release | : 2020-01-23 |
| Genre | : History |
| ISBN | : 1108497829 |
Presents a detailed and critical examination of the available conceptions of set and proposes a novel version.
| Author | : Paul J. Cohen |
| Publisher | : Courier Corporation |
| Total Pages | : 196 |
| Release | : 2008-12-09 |
| Genre | : Mathematics |
| ISBN | : 0486469212 |
This exploration of a notorious mathematical problem is the work of the man who discovered the solution. Written by an award-winning professor at Stanford University, it employs intuitive explanations as well as detailed mathematical proofs in a self-contained treatment. This unique text and reference is suitable for students and professionals. 1966 edition. Copyright renewed 1994.
| Author | : Joseph Breuer |
| Publisher | : Courier Corporation |
| Total Pages | : 130 |
| Release | : 2012-08-09 |
| Genre | : Mathematics |
| ISBN | : 0486154874 |
This undergraduate text develops its subject through observations of the physical world, covering finite sets, cardinal numbers, infinite cardinals, and ordinals. Includes exercises with answers. 1958 edition.
| Author | : Joel David Hamkins |
| Publisher | : MIT Press |
| Total Pages | : 350 |
| Release | : 2021-03-09 |
| Genre | : Mathematics |
| ISBN | : 0262542234 |
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.
