Pubbl/distr/stampa	Oxford, : Clarendon Press
Descrizione fisica	1 online resource (695 p.)
Disciplina	510.1 510/.1
Altri autori (Persone)	EwaldWilliam Bragg <1925->
Soggetto topico	Mathematics - Philosophy Mathematics - History
ISBN	1-383-02108-2 1-281-76998-3 9786611769987 0-19-152309-7 1-4356-0965-4
Formato	Materiale a stampa
Livello bibliografico	Monografia
Lingua di pubblicazione	eng
Nota di contenuto	Contents; Copyright Permissions; Introduction; 1. GEORGE BERKELEY (1685-1753); 2. COLIN MACLAURIN (1698-1746); 3. JEAN LEROND D'ALEMBERT (1717-1783); 4. IMMANUEL KANT (1724-1804); 5. JOHANN HEINRICH LAMBERT (1728-1777); 6. BERNARD BOLZANO (1781-1848); 7. CARL FRIEDRICH GAUSS (1777-1855); 8. DUNCAN GREGORY (1813-1844); 9. AUGUSTUS DE MORGAN (1806-1871); 10. WILLIAM ROWAN HAMILTON (1805-1865); 11. GEORGE BOOLE (1815-1864); 12. JAMES JOSEPH SYLVESTER (1814-1897); 13. WILLIAM KINGDON CLIFFORD (1845-1879); 14. ARTHUR CAYLEY (1821-1895); 15. CHARLES SANDERS PEIRCE (1839-1914); References; Index
Record Nr.	UNINA-9910778255603321

Autore	Fine Kit
Pubbl/distr/stampa	Oxford, : Clarendon Press, 2002
Descrizione fisica	1 online resource (214 p.)
Disciplina	510.1 510/.1
Soggetto topico	Abstraction Mathematics - Philosophy
Soggetto genere / forma	Electronic books.
ISBN	1-281-77012-4 9786611770129 0-19-156726-4
Formato	Materiale a stampa
Livello bibliografico	Monografia
Lingua di pubblicazione	eng
Nota di contenuto	Contents; Introduction; I. Philosophical Introduction; II. The Context Principle; III. The Analysis of Acceptability; IV. The General Theory of Abstraction; References; Main Index; Index of First Occurrence of Formal Symbols and Definitions
Record Nr.	UNINA-9910454113003321

Autore	Hatcher William S.
Edizione	[First edition.]
Pubbl/distr/stampa	Oxford, England : , : Pergamon Press, , 1982
Descrizione fisica	1 online resource (331 p.)
Disciplina	510/.1
Collana	Foundations and Philosophy of Science and Technology Series
Soggetto topico	Mathematics - Philosophy
ISBN	1-4831-8963-5
Formato	Materiale a stampa
Livello bibliografico	Monografia
Lingua di pubblicazione	eng
Nota di contenuto	Front Cover; The Logical Foundations of Mathematics; Copyright Page; Dedication; Preface; Table of Contents; Chapter 1. First-order Logic; 1.1. The sentential calculus; 1.2. Formalization; 1.3. The statement calculus as a formal system; 1.4. First-order theories; 1.5. Models of first-order theories; 1.6. Rules of logic; natural deduction; 1.7. First-order theories with equality; variable-binding term operators; 1.8. Completeness with vbtos; 1.9. An example of a first-order theory; Chapter 2. The Origin of Modern Foundational Studies; 2.1. Mathematics as an independent science 2.2. The arithmetization of analysis2.3. Constructivism; 2.4. Frege and the notion of a formal system; 2.5. Criteria for foundations; Chapter 3. Frege's System and the Paradoxes; 3,1. The intuitive basis of Frege's system; 3.2. Frege's system; 3.3. The theorem of infinity; 3.4. Criticisms of Frege's system; 3.5. The paradoxes; 3.6. Brouwer and intuitionism; 3.7. Poincare'snotion of im predicative definition; 3.8. Russell's principle of vicious circle; 3.9. The logical paradoxes and the semantic paradoxes; Chapter 4. The Theory of Types; 4.1. Quantifying predicate letters 4.2. Predicative type theory4.3. The development of mathematics in PT; 4.4. The system TT; 4.5. Criticisms of type theory as a foundation for mathematics; 4.6. The system ST; 4.7. Type theory and first-order logic; Chapter 5. Zermelo-Fraenkel Set Theory; 5.1. Formalization of ZF; 5.2. The completing axioms; 5.3. Relations, functions, and simple recursion; 5.4. The axiom of choice; 5.5. The continuum hypothesis; descriptive set theory; 5.6. The systems of vonNeumann-Bernays-Godel and Mostowski-Kelley-Morse; 5.7. Number systems; ordinal recursion; 5.8. Conway's numbers Chapter 6. Hilbert's Program and Godel's IncompletenessTheorems6.1. Hilbert's program; 6.2. Godel's theorems and their import; 6.3. The method of proof of Godel's theorems; recursive functions; 6.4. Nonstandard models of S; Chapter 7. The Foundational Systems of W. V. Quine; 7.1. The system NF; 7.2. Cantor's theorem in NF; 7.3. The axiom of choice in NF and the theorem of infinity; 7.4. NF and ST; typical ambiguity; 7.5. Quine's system ML; 7.6. Further results on NF; variant systems; 7.7. Conclusions; Chapter 8. Categorical Algebra; 8.1. The notion of a category 8.2. The first-order language of categories8.3. Category theory and set theory; 8.4. Functors and large categories; 8.5. Formal development of the language and theory CS; 8.6. Topos theory; 8.7. Global elements in toposes; 8.8. Image factorizations and the axiom of choice; 8.9. A last look at CS; 8.10. ZF andWT; 8.11. The internal logic of toposes; 8.12. The internal language of a topos; 8.13. Conclusions; Selected Bibliography; Index
Record Nr.	UNINA-9910786641503321

Autore	Tiles Mary
Pubbl/distr/stampa	London ; ; New York : , : Routledge, , 1991
Descrizione fisica	1 online resource (198 p.)
Disciplina	510/.1
Collana	Philosophical issues in science
Soggetto topico	Mathematics - Philosophy
Soggetto genere / forma	Electronic books.
ISBN	1-134-96772-1 1-280-53925-9 9786610539253 0-203-02836-8 0-203-32706-3
Formato	Materiale a stampa
Livello bibliografico	Monografia
Lingua di pubblicazione	eng
Nota di contenuto	Cover; MATHEMATICS AND THEIMAGE OF REASON; Title Page; Copyright Page; Table of Contents; Acknowledgements; Introduction; 1 AXIOMATIZATION, RIGOUR AND REASON; Rigour and Proof; Deserting Euclidean Standards; The Return to Euclidean Standards; 2 FREGE: ARITHMETIC AS LOGIC; Calculation and Reasoning; Numbers and the Nature of Arithmetical Truths; Numbers as Objects; The Natural Numbers; Word Games?; 3 RUSSELL: MATHEMATICS AS LOGIC; Geometry and Relational Structures; Paradoxes and Logical Types; Empiricism, Logical Positivism and the Sterility of Reason 4 HILBERT: MATHEMATICS AS A FORMULA-GAME?Formalism and Hilbert's Programme; Geometrical Rigour; Forging the Formal Chains of Reason; Successes and Failures; Logic and its Limitations; Appendix - Recursive Functions; 5 IDEAL ELEMENTS AND RATIONAL IDEALS; Formulae, Symbols and Forms; Ideal Elements and Ideals; Geometry: Diagrams and Rigour; Pragmatism, Axiomatization and Ideals; Logic and the Objects of Mathematical Knowledge; Lack of Closure and the Power of Reason; Glossary of Symbols; Further Reading; Bibliography; Index
Record Nr.	UNINA-9910449676003321