Set Theory And Its Philosophy
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| Author | : Michael Potter |
| Publisher | : Clarendon Press |
| Total Pages | : 362 |
| Release | : 2004-01-15 |
| Genre | : Philosophy |
| ISBN | : 0191556432 |
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 |
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 | : 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 | : 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 | : 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 | : 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 | : 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 | : Moshe Machover |
| Publisher | : Cambridge University Press |
| Total Pages | : 304 |
| Release | : 1996-05-23 |
| Genre | : Mathematics |
| ISBN | : 9780521479981 |
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 | : 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 | : Willard Van Orman Quine |
| Publisher | : Harvard University Press |
| Total Pages | : 384 |
| Release | : 1969 |
| Genre | : Mathematics |
| ISBN | : 9780674802070 |
This is an extensively revised edition of W. V. Quine’s introduction to abstract set theory and to various axiomatic systematizations of the subject. The treatment of ordinal numbers has been strengthened and much simplified, especially in the theory of transfinite recursions, by adding an axiom and reworking the proofs. Infinite cardinals are treated anew in clearer and fuller terms than before. Improvements have been made all through the book; in various instances a proof has been shortened, a theorem strengthened, a space-saving lemma inserted, an obscurity clarified, an error corrected, a historical omission supplied, or a new event noted.
