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Mathematics and the image of reason / / Mary Tiles
| Mathematics and the image of reason / / Mary Tiles |
| Autore | Tiles Mary |
| Edizione | [1st ed.] |
| 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 |
| ISBN |
1-134-96771-3
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-9910813455603321 |
Tiles Mary
|
||
| London ; ; New York : , : Routledge, , 1991 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Mathematics and the natural sciences [[electronic resource] ] : the physical singularity of life / / Francis Bailly, Giuseppe Longo
| Mathematics and the natural sciences [[electronic resource] ] : the physical singularity of life / / Francis Bailly, Giuseppe Longo |
| Autore | Bailly Francis |
| Pubbl/distr/stampa | London, : Imperial College Press |
| Descrizione fisica | 1 online resource (337 p.) |
| Disciplina | 510.1 |
| Altri autori (Persone) | LongoG (Giuseppe) |
| Collana | Advances in computer science and engineering: Texts |
| Soggetto topico |
Mathematics - Philosophy
Physics - Philosophy Biomathematics |
| Soggetto genere / forma | Electronic books. |
| ISBN |
1-283-23454-8
9786613234544 1-84816-694-X |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Preface; Contents; Chapter 1 Mathematical Concepts and Physical Objects; Introduction; 1.1 On the Foundations of Mathematics. A First Inquiry; 1.1.1 Terminological issues?; 1.1.2 The genesis of mathematical structures and of their relationships - a few conceptual analogies; 1.1.3 Formalization, calculation, meaning, subjectivity; 1.1.4 Between cognition and history: Towards new structures of intelligibility; 1.2 Mathematical Concepts: A Constructive Approach; 1.2.1 Genealogies of concepts; 1.2.2 The "transcendent" in physics and in mathematics; 1.2.3 Laws, structures, and foundations
1.2.4 Subject and objectivity1.2.5 From intuitionism to a renewed constructivism; 1.3 Regarding Mathematical Concepts and Physical Objects; 1.3.1 "Friction" and the determination of physical objects; 1.3.2 The absolute and the relative in mathematics and in physics; 1.3.3 On the two functions of language within the process of objectification and the construction of mathematical models in physics; 1.3.4 From the relativity to reference universes to that of these universes themselves as generators of physical invariances; 1.3.5 Physical causality and mathematical symmetry 1.3.6 Towards the "cognitive subject"Chapter 2 Incompleteness and Indetermination in Mathematics and Physics; Introduction; 2.1 The Cognitive Foundations of Mathematics: Human Gestures in Proofs and Mathematical Incompleteness of Formalisms; 2.1.1 Introduction; 2.1.2 Machines, body, and rationality; 2.1.3 Ameba, motivity, and signification; 2.1.4 The abstract and the symbolic; the rigor; 2.1.5 From the Platonist response to action and gesture; 2.1.6 Intuition, gestures, and the numeric line; 2.1.7 Mathematical incompleteness of formalisms; 2.1.8 Iterations and closures on the horizon 2.1.9 Intuition2.1.10 Body gestures and the "cogito"; 2.1.11 Summary and conclusion of part 2.1; 2.2 Incompleteness, Uncertainty, and Infinity: Differences and Similarities Between Physics and Mathematics; 2.2.1 Completeness/incompleteness in physical theories; 2.2.2 Finite/infinite in mathematics and physics; Chapter 3 Space and Time from Physics to Biology; 3.1 An Introduction to the Space and Time of Modern Physics; 3.1.1 Taking leave of Laplace; 3.1.2 Three types of physical theory: Relativity, quantum physics, and the theory of critical transitions in dynamical systems 3.1.3 Some epistemological remarks3.2 Towards Biology: Space and Time in the "Field" of Living Systems; 3.2.1 The time of life; 3.2.2 More on Biological time; 3.2.3 Dynamics of the self-constitution of living systems; 3.2.4 Morphogenesis; 3.2.5 Information and geometric structure; 3.3 Spatiotemporal Determination and Biology; 3.3.1 Biological aspects; 3.3.2 Space: Laws of scaling and of critical behavior. The geometry of biological functions; 3.3.3 Three types of time; 3.3.4 Epistemological and mathematical aspects; 3.3.5 Some philosophy, to conclude Chapter 4 Invariances, Symmetries, and Symmetry Breakings |
| Record Nr. | UNINA-9910464495203321 |
|
Bailly Francis
|
||
| London, : Imperial College Press | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Mathematics and the natural sciences [[electronic resource] ] : the physical singularity of life / / Francis Bailly, Giuseppe Longo
| Mathematics and the natural sciences [[electronic resource] ] : the physical singularity of life / / Francis Bailly, Giuseppe Longo |
| Autore | Bailly Francis |
| Pubbl/distr/stampa | London, : Imperial College Press |
| Descrizione fisica | 1 online resource (337 p.) |
| Disciplina | 510.1 |
| Altri autori (Persone) | LongoG (Giuseppe) |
| Collana | Advances in computer science and engineering: Texts |
| Soggetto topico |
Mathematics - Philosophy
Physics - Philosophy Biomathematics |
| ISBN |
1-283-23454-8
9786613234544 1-84816-694-X |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Preface; Contents; Chapter 1 Mathematical Concepts and Physical Objects; Introduction; 1.1 On the Foundations of Mathematics. A First Inquiry; 1.1.1 Terminological issues?; 1.1.2 The genesis of mathematical structures and of their relationships - a few conceptual analogies; 1.1.3 Formalization, calculation, meaning, subjectivity; 1.1.4 Between cognition and history: Towards new structures of intelligibility; 1.2 Mathematical Concepts: A Constructive Approach; 1.2.1 Genealogies of concepts; 1.2.2 The "transcendent" in physics and in mathematics; 1.2.3 Laws, structures, and foundations
1.2.4 Subject and objectivity1.2.5 From intuitionism to a renewed constructivism; 1.3 Regarding Mathematical Concepts and Physical Objects; 1.3.1 "Friction" and the determination of physical objects; 1.3.2 The absolute and the relative in mathematics and in physics; 1.3.3 On the two functions of language within the process of objectification and the construction of mathematical models in physics; 1.3.4 From the relativity to reference universes to that of these universes themselves as generators of physical invariances; 1.3.5 Physical causality and mathematical symmetry 1.3.6 Towards the "cognitive subject"Chapter 2 Incompleteness and Indetermination in Mathematics and Physics; Introduction; 2.1 The Cognitive Foundations of Mathematics: Human Gestures in Proofs and Mathematical Incompleteness of Formalisms; 2.1.1 Introduction; 2.1.2 Machines, body, and rationality; 2.1.3 Ameba, motivity, and signification; 2.1.4 The abstract and the symbolic; the rigor; 2.1.5 From the Platonist response to action and gesture; 2.1.6 Intuition, gestures, and the numeric line; 2.1.7 Mathematical incompleteness of formalisms; 2.1.8 Iterations and closures on the horizon 2.1.9 Intuition2.1.10 Body gestures and the "cogito"; 2.1.11 Summary and conclusion of part 2.1; 2.2 Incompleteness, Uncertainty, and Infinity: Differences and Similarities Between Physics and Mathematics; 2.2.1 Completeness/incompleteness in physical theories; 2.2.2 Finite/infinite in mathematics and physics; Chapter 3 Space and Time from Physics to Biology; 3.1 An Introduction to the Space and Time of Modern Physics; 3.1.1 Taking leave of Laplace; 3.1.2 Three types of physical theory: Relativity, quantum physics, and the theory of critical transitions in dynamical systems 3.1.3 Some epistemological remarks3.2 Towards Biology: Space and Time in the "Field" of Living Systems; 3.2.1 The time of life; 3.2.2 More on Biological time; 3.2.3 Dynamics of the self-constitution of living systems; 3.2.4 Morphogenesis; 3.2.5 Information and geometric structure; 3.3 Spatiotemporal Determination and Biology; 3.3.1 Biological aspects; 3.3.2 Space: Laws of scaling and of critical behavior. The geometry of biological functions; 3.3.3 Three types of time; 3.3.4 Epistemological and mathematical aspects; 3.3.5 Some philosophy, to conclude Chapter 4 Invariances, Symmetries, and Symmetry Breakings |
| Record Nr. | UNINA-9910788959603321 |
|
Bailly Francis
|
||
| London, : Imperial College Press | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Mathematics and the natural sciences [[electronic resource] ] : the physical singularity of life / / Francis Bailly, Giuseppe Longo
| Mathematics and the natural sciences [[electronic resource] ] : the physical singularity of life / / Francis Bailly, Giuseppe Longo |
| Autore | Bailly Francis |
| Pubbl/distr/stampa | London, : Imperial College Press |
| Descrizione fisica | 1 online resource (337 p.) |
| Disciplina | 510.1 |
| Altri autori (Persone) | LongoG (Giuseppe) |
| Collana | Advances in computer science and engineering: Texts |
| Soggetto topico |
Mathematics - Philosophy
Physics - Philosophy Biomathematics |
| ISBN |
1-283-23454-8
9786613234544 1-84816-694-X |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Preface; Contents; Chapter 1 Mathematical Concepts and Physical Objects; Introduction; 1.1 On the Foundations of Mathematics. A First Inquiry; 1.1.1 Terminological issues?; 1.1.2 The genesis of mathematical structures and of their relationships - a few conceptual analogies; 1.1.3 Formalization, calculation, meaning, subjectivity; 1.1.4 Between cognition and history: Towards new structures of intelligibility; 1.2 Mathematical Concepts: A Constructive Approach; 1.2.1 Genealogies of concepts; 1.2.2 The "transcendent" in physics and in mathematics; 1.2.3 Laws, structures, and foundations
1.2.4 Subject and objectivity1.2.5 From intuitionism to a renewed constructivism; 1.3 Regarding Mathematical Concepts and Physical Objects; 1.3.1 "Friction" and the determination of physical objects; 1.3.2 The absolute and the relative in mathematics and in physics; 1.3.3 On the two functions of language within the process of objectification and the construction of mathematical models in physics; 1.3.4 From the relativity to reference universes to that of these universes themselves as generators of physical invariances; 1.3.5 Physical causality and mathematical symmetry 1.3.6 Towards the "cognitive subject"Chapter 2 Incompleteness and Indetermination in Mathematics and Physics; Introduction; 2.1 The Cognitive Foundations of Mathematics: Human Gestures in Proofs and Mathematical Incompleteness of Formalisms; 2.1.1 Introduction; 2.1.2 Machines, body, and rationality; 2.1.3 Ameba, motivity, and signification; 2.1.4 The abstract and the symbolic; the rigor; 2.1.5 From the Platonist response to action and gesture; 2.1.6 Intuition, gestures, and the numeric line; 2.1.7 Mathematical incompleteness of formalisms; 2.1.8 Iterations and closures on the horizon 2.1.9 Intuition2.1.10 Body gestures and the "cogito"; 2.1.11 Summary and conclusion of part 2.1; 2.2 Incompleteness, Uncertainty, and Infinity: Differences and Similarities Between Physics and Mathematics; 2.2.1 Completeness/incompleteness in physical theories; 2.2.2 Finite/infinite in mathematics and physics; Chapter 3 Space and Time from Physics to Biology; 3.1 An Introduction to the Space and Time of Modern Physics; 3.1.1 Taking leave of Laplace; 3.1.2 Three types of physical theory: Relativity, quantum physics, and the theory of critical transitions in dynamical systems 3.1.3 Some epistemological remarks3.2 Towards Biology: Space and Time in the "Field" of Living Systems; 3.2.1 The time of life; 3.2.2 More on Biological time; 3.2.3 Dynamics of the self-constitution of living systems; 3.2.4 Morphogenesis; 3.2.5 Information and geometric structure; 3.3 Spatiotemporal Determination and Biology; 3.3.1 Biological aspects; 3.3.2 Space: Laws of scaling and of critical behavior. The geometry of biological functions; 3.3.3 Three types of time; 3.3.4 Epistemological and mathematical aspects; 3.3.5 Some philosophy, to conclude Chapter 4 Invariances, Symmetries, and Symmetry Breakings |
| Record Nr. | UNINA-9910826406603321 |
|
Bailly Francis
|
||
| London, : Imperial College Press | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Mathematics and the roots of postmodern thought [[electronic resource] /] / Vladimir Tasić
| Mathematics and the roots of postmodern thought [[electronic resource] /] / Vladimir Tasić |
| Autore | Tasić Vladimir <1965-> |
| Pubbl/distr/stampa | Oxford ; ; New York, : Oxford University Press, 2001 |
| Descrizione fisica | 1 online resource (200 p.) |
| Disciplina |
510.1
510/.1 |
| Soggetto topico |
Mathematics - Philosophy
Postmodernism |
| Soggetto genere / forma | Electronic books. |
| ISBN |
1-280-83485-4
9786610834853 0-19-534995-4 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Contents; 1. Introduction; 2. Around the Cartesian Circuit; 3. Space Oddity and Linguistic Turn; 4. Wound of Language; 5. Beyond the Code; 6. The Expired Subject; 7. The Vanishing Author; 8. Say Hello to the Structure Bubble; 9. Don't Think, Look; 10. Postmodern Enigmas; Notes; Select Bibliography; Index |
| Record Nr. | UNINA-9910450953303321 |
|
Tasić Vladimir <1965->
|
||
| Oxford ; ; New York, : Oxford University Press, 2001 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Mathematics and the roots of postmodern thought [[electronic resource] /] / Vladimir Tasić
| Mathematics and the roots of postmodern thought [[electronic resource] /] / Vladimir Tasić |
| Autore | Tasić Vladimir <1965-> |
| Pubbl/distr/stampa | Oxford ; ; New York, : Oxford University Press, 2001 |
| Descrizione fisica | 1 online resource (200 p.) |
| Disciplina |
510.1
510/.1 |
| Soggetto topico |
Mathematics - Philosophy
Postmodernism |
| ISBN |
0-19-772724-7
0-19-988151-0 1-280-83485-4 9786610834853 0-19-534995-4 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Contents; 1. Introduction; 2. Around the Cartesian Circuit; 3. Space Oddity and Linguistic Turn; 4. Wound of Language; 5. Beyond the Code; 6. The Expired Subject; 7. The Vanishing Author; 8. Say Hello to the Structure Bubble; 9. Don't Think, Look; 10. Postmodern Enigmas; Notes; Select Bibliography; Index |
| Record Nr. | UNINA-9910777307903321 |
|
Tasić Vladimir <1965->
|
||
| Oxford ; ; New York, : Oxford University Press, 2001 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Mathematics and the roots of postmodern thought [[electronic resource] /] / Vladimir Tasić
| Mathematics and the roots of postmodern thought [[electronic resource] /] / Vladimir Tasić |
| Autore | Tasić Vladimir <1965-> |
| Pubbl/distr/stampa | Oxford ; ; New York, : Oxford University Press, 2001 |
| Descrizione fisica | 1 online resource (200 p.) |
| Disciplina |
510.1
510/.1 |
| Soggetto topico |
Mathematics - Philosophy
Postmodernism |
| ISBN |
0-19-772724-7
0-19-988151-0 1-280-83485-4 9786610834853 0-19-534995-4 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Contents; 1. Introduction; 2. Around the Cartesian Circuit; 3. Space Oddity and Linguistic Turn; 4. Wound of Language; 5. Beyond the Code; 6. The Expired Subject; 7. The Vanishing Author; 8. Say Hello to the Structure Bubble; 9. Don't Think, Look; 10. Postmodern Enigmas; Notes; Select Bibliography; Index |
| Record Nr. | UNINA-9910807917603321 |
|
Tasić Vladimir <1965->
|
||
| Oxford ; ; New York, : Oxford University Press, 2001 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Mathematics as a science of patterns [[electronic resource] /] / Michael D. Resnik
| Mathematics as a science of patterns [[electronic resource] /] / Michael D. Resnik |
| Autore | Resnik Michael D |
| Pubbl/distr/stampa | Oxford, : Clarendon Press |
| Descrizione fisica | 1 online resource (300 p.) |
| Disciplina | 510/.1 |
| Soggetto topico |
Mathematics - Philosophy
Mathematical analysis |
| Soggetto genere / forma | Electronic books. |
| ISBN |
9786611970376
1-281-97037-9 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNINA-9910454110803321 |
|
Resnik Michael D
|
||
| Oxford, : Clarendon Press | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Mathematics as a science of patterns [[electronic resource] /] / Michael D. Resnik
| Mathematics as a science of patterns [[electronic resource] /] / Michael D. Resnik |
| Autore | Resnik Michael D |
| Pubbl/distr/stampa | Oxford, : Clarendon Press |
| Descrizione fisica | 1 online resource (300 p.) |
| Disciplina | 510/.1 |
| Soggetto topico |
Mathematics - Philosophy
Mathematical analysis |
| ISBN |
9786611970376
1-281-97037-9 9780191598296 9780191519000 9780198236085 9780198250142 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNINA-9910782841503321 |
|
Resnik Michael D
|
||
| Oxford, : Clarendon Press | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Mathematics as a science of patterns [[electronic resource] /] / Michael D. Resnik
| Mathematics as a science of patterns [[electronic resource] /] / Michael D. Resnik |
| Autore | Resnik Michael D |
| Pubbl/distr/stampa | Oxford, : Clarendon Press |
| Descrizione fisica | 1 online resource (300 p.) |
| Disciplina | 510/.1 |
| Soggetto topico |
Mathematics - Philosophy
Mathematical analysis |
| ISBN |
9786611970376
1-281-97037-9 9780191598296 9780191519000 9780198236085 9780198250142 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNINA-9910825357603321 |
|
Resnik Michael D
|
||
| Oxford, : Clarendon Press | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
