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Author: Michael D. Potter Publisher: Clarendon Press ISBN: 9780199269730 Category : Mathematics Languages : en Pages : 345
Book Description
A wonderful new book ... Potter has written the best philosophical introduction to set theory on the market - Timothy Bays, Notre Dame Philosophical Reviews.
Author: Michael D. Potter Publisher: Clarendon Press ISBN: 9780199269730 Category : Mathematics Languages : en Pages : 345
Book Description
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 ISBN: 0486138550 Category : Mathematics Languages : en Pages : 258
Book Description
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 ISBN: 0486797147 Category : Mathematics Languages : en Pages : 196
Book Description
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: Manuel Bremer Publisher: Walter de Gruyter ISBN: 3110326108 Category : Philosophy Languages : en Pages : 125
Book Description
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: Penelope Maddy Publisher: Oxford University Press ISBN: 0199596182 Category : Mathematics Languages : en Pages : 161
Book Description
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: Joseph Breuer Publisher: Courier Corporation ISBN: 0486154874 Category : Mathematics Languages : en Pages : 130
Book Description
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: Willard Van Orman Quine Publisher: Harvard University Press ISBN: 9780674802070 Category : Mathematics Languages : en Pages : 384
Book Description
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.
Author: Paul J. Cohen Publisher: Courier Corporation ISBN: 0486469212 Category : Mathematics Languages : en Pages : 196
Book Description
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: Michael D. Potter
Author: Michael D. Potter
Author: Mary Tiles
Author: Sean Morris
Author: Stephen Pollard
Author: Manuel Bremer
Author: Penelope Maddy
Author: Luca Incurvati
Author: Joseph Breuer
Author: Willard Van Orman Quine
Author: Paul J. Cohen