The Philosophy Of Set Theory PDF Download
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| Author | : Michael Potter |
| Publisher | : Clarendon Press |
| Total Pages | : 362 |
| Release | : 2004-01-15 |
| Genre | : Philosophy |
| ISBN | : 0191556432 |
Download Set Theory and its Philosophy Book in PDF, ePub and Kindle
Michael Potter presents a comprehensive new philosophical introduction to set theory. Anyone wishing to work on the logical foundations of mathematics must understand set theory, which lies at its heart. Potter offers a thorough account of cardinal and ordinal arithmetic, and the various axiom candidates. He discusses in detail the project of set-theoretic reduction, which aims to interpret the rest of mathematics in terms of set theory. The key question here is how to deal with the paradoxes that bedevil set theory. Potter offers a strikingly simple version of the most widely accepted response to the paradoxes, which classifies sets by means of a hierarchy of levels. What makes the book unique is that it interweaves a careful presentation of the technical material with a penetrating philosophical critique. Potter does not merely expound the theory dogmatically but at every stage discusses in detail the reasons that can be offered for believing it to be true. Set Theory and its Philosophy is a key text for philosophy, mathematical logic, and computer science.
| Author | : Mary Tiles |
| Publisher | : Courier Corporation |
| Total Pages | : 258 |
| Release | : 2012-03-08 |
| Genre | : Mathematics |
| ISBN | : 0486138550 |
Download The Philosophy of Set Theory Book in PDF, ePub and Kindle
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 | : Stephen Pollard |
| Publisher | : Courier Dover Publications |
| Total Pages | : 196 |
| Release | : 2015-07-15 |
| Genre | : Mathematics |
| ISBN | : 0486797147 |
Download Philosophical Introduction to Set Theory Book in PDF, ePub and Kindle
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 | : Sean Morris |
| Publisher | : Cambridge University Press |
| Total Pages | : 221 |
| Release | : 2018-12-13 |
| Genre | : History |
| ISBN | : 110715250X |
Download Quine, New Foundations, and the Philosophy of Set Theory Book in PDF, ePub and Kindle
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 |
Download Defending the Axioms Book in PDF, ePub and Kindle
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 |
Download Universality in Set Theories Book in PDF, ePub and Kindle
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 | : Paul J. Cohen |
| Publisher | : Courier Corporation |
| Total Pages | : 196 |
| Release | : 2008-12-09 |
| Genre | : Mathematics |
| ISBN | : 0486469212 |
Download Set Theory and the Continuum Hypothesis Book in PDF, ePub and Kindle
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 | : Luca Incurvati |
| Publisher | : Cambridge University Press |
| Total Pages | : 255 |
| Release | : 2020-01-23 |
| Genre | : History |
| ISBN | : 1108497829 |
Download Conceptions of Set and the Foundations of Mathematics Book in PDF, ePub and Kindle
Presents a detailed and critical examination of the available conceptions of set and proposes a novel version.
| Author | : Moshe Machover |
| Publisher | : Cambridge University Press |
| Total Pages | : 304 |
| Release | : 1996-05-23 |
| Genre | : Mathematics |
| ISBN | : 9780521479981 |
Download Set Theory, Logic and Their Limitations Book in PDF, ePub and Kindle
This is an introduction to set theory and logic that starts completely from scratch. The text is accompanied by many methodological remarks and explanations. A rigorous axiomatic presentation of Zermelo-Fraenkel set theory is given, demonstrating how the basic concepts of mathematics have apparently been reduced to set theory. This is followed by a presentation of propositional and first-order logic. Concepts and results of recursion theory are explained in intuitive terms, and the author proves and explains the limitative results of Skolem, Tarski, Church and Gödel (the celebrated incompleteness theorems). For students of mathematics or philosophy this book provides an excellent introduction to logic and set theory.
| Author | : Joel David Hamkins |
| Publisher | : MIT Press |
| Total Pages | : 350 |
| Release | : 2021-03-09 |
| Genre | : Mathematics |
| ISBN | : 0262542234 |
Download Lectures on the Philosophy of Mathematics Book in PDF, ePub and Kindle
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.
