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The making of mathematics : heuristic philosophy of mathematics / / Carlo Cellucci
| The making of mathematics : heuristic philosophy of mathematics / / Carlo Cellucci |
| Autore | Cellucci Carlo |
| Pubbl/distr/stampa | Cham, Switzerland : , : Springer, , [2022] |
| Descrizione fisica | 1 online resource (457 pages) |
| Disciplina | 510.1 |
| Collana | Synthese Library |
| Soggetto topico | Mathematics - Philosophy |
| ISBN |
9783030897314
9783030897307 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNINA-9910552711503321 |
Cellucci Carlo
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| Cham, Switzerland : , : Springer, , [2022] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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Rethinking Knowledge [[electronic resource] ] : The Heuristic View / / by Carlo Cellucci
| Rethinking Knowledge [[electronic resource] ] : The Heuristic View / / by Carlo Cellucci |
| Autore | Cellucci Carlo |
| Edizione | [1st ed. 2017.] |
| Pubbl/distr/stampa | Cham : , : Springer International Publishing : , : Imprint : Springer, , 2017 |
| Descrizione fisica | 1 online resource (XIX, 427 p. 34 illus.) |
| Disciplina | 190 |
| Collana | European Studies in Philosophy of Science |
| Soggetto topico |
Epistemology
Philosophy and science Logic Philosophy of Science |
| ISBN | 3-319-53237-5 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | 1. Introduction -- 2. The Heuristic View -- 3. The Foundationalist View -- 4. The Limits of Skepticism -- 5. Philosophy and the Humanistic Disciplines -- 6. The Nature of Knowledge -- 7. Knowledge to Reality -- 8. Knowledge and Truth -- 9. Knowledge, Plausibly, and Common Sense -- 10. Other Questions About Knowledge -- 11. A Discourse on Method -- 12. The Method of Knowledge -- 13. Knowledge as Problem Solving -- 14. Modeling Scientific Knowledge -- 15. Perceptual Knowledge -- 16. Knowledge and Error -- 17. Knowledge and Mind -- 18. The Nature of Mathematical Knowledge -- 19. Mathematical Objects, Definitions, Diagrams -- 20. Mathematics: Problem Solving or Theorem Proving? -- 21. Two Notions of Mathematical Demonstration -- 22. Mathematical Explanations -- 23. Mathematical Beauty -- 24. Mathematics and Reality -- 25. Conclusion. |
| Record Nr. | UNINA-9910255214903321 |
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Cellucci Carlo
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| Cham : , : Springer International Publishing : , : Imprint : Springer, , 2017 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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Rethinking Logic: Logic in Relation to Mathematics, Evolution, and Method [[electronic resource] /] / by Carlo Cellucci
| Rethinking Logic: Logic in Relation to Mathematics, Evolution, and Method [[electronic resource] /] / by Carlo Cellucci |
| Autore | Cellucci Carlo |
| Edizione | [1st ed. 2013.] |
| Pubbl/distr/stampa | Dordrecht : , : Springer Netherlands : , : Imprint : Springer, , 2013 |
| Descrizione fisica | 1 online resource (391 p.) |
| Disciplina | 160 |
| Collana | Logic, Argumentation & Reasoning, Interdisciplinary Perspectives from the Humanities and Social Sciences |
| Soggetto topico |
Logic
Mathematical logic Philosophy Mathematical Logic and Formal Languages History of Philosophy |
| ISBN | 94-007-6091-4 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Preface -- Chapter 1. Introduction -- Part I. Ancient Perspectives -- Chapter 2. The Origin of Logic -- Chapter 3. Ancient Logic and Science -- Chapter 4. The Analytic Method -- Chapter 5. The Analytic-Synthetic Method -- Chapter 6. Aristotle's Logic: The Deductivist View -- Chapter 7. Aristotle's Logic: The Heuristic View -- Part II. Modern Perspectives -- Chapter 8. The Method of Modern Science -- Chapter 9. The Quest for a Logic of Discovery -- Chapter 10. Frege's Approach to Logic -- Chapter 11. Gentzen's Approach to Logic -- Chapter 12. The Limitations of Mathematical Logic -- Chapter 13. Logic, Method, and the Psychology of Discovery -- Part III: An Alternative Perspective -- Chapter 14. Reason and Knowledge -- Chapter 15. Reason, Knowledge and Emotion -- Chapter 16. Logic, Evolution, Language and Reason -- Chapter 17. Logic, Method and Knowledge -- Chapter 18. Classifying and Justifying Inference Rules -- Chapter 19. Philosophy and Knowledge -- Part IV: Rules of Discovery -- Chapter 20. Induction and Analogy -- Chapter 21. Other Rules of Discovery -- Chapter 22. Conclusion -- References -- Name Index -- Subject Index. |
| Record Nr. | UNINA-9910735395303321 |
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Cellucci Carlo
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| Dordrecht : , : Springer Netherlands : , : Imprint : Springer, , 2013 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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The theory of Gödel / / Carlo Cellucci
| The theory of Gödel / / Carlo Cellucci |
| Autore | Cellucci Carlo |
| Pubbl/distr/stampa | Cham, Switzerland : , : Springer, , [2022] |
| Descrizione fisica | 1 online resource (164 pages) |
| Disciplina | 511.3 |
| Collana | Synthese library |
| Soggetto topico |
Gödel's theorem
Teorema de Gödel |
| Soggetto genere / forma | Llibres electrònics |
| ISBN |
9783031134173
9783031134166 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Intro -- Preface -- References -- Contents -- 1 First-Order Logic -- 1.1 First-Order Languages -- 1.2 Free Variables -- 1.3 Substitution -- 1.4 A Deductive Calculus -- 1.5 Connective Rules -- 1.6 Quantifier Rules -- 1.7 Substitutivity of Equivalence -- 1.8 Equality -- 2 Completeness -- 2.1 Interpretations -- 2.2 Substitution Properties -- 2.3 Soundness -- 2.4 Consistency -- 2.5 Rich Sets -- 2.6 Completeness Theorem -- 2.7 Isomorphisms of Interpretations -- 2.8 Elementary Equivalence -- 2.9 Definability in an Interpretation -- 3 First-Order Theories -- 3.1 Generalities on First-Order Theory -- 3.2 Extensions of Theories -- 3.3 Definitional Extensions -- 4 Primitive Recursive Arithmetic -- 4.1 Primitive Recursive Functions -- 4.2 The Theories PRA and PA -- 4.3 Elementary Properties of PRA -- 4.4 Developing Arithmetic in PRA -- 4.5 Bounded Formulas -- 4.6 Non-Standard Models of PA -- 5 Encoding -- 5.1 Encoding of Finite Sequences -- 5.2 Encoding of Syntax -- 5.3 RE-Theories -- 6 Incompleteness -- 6.1 Traditional Gödel's First Incompleteness Theorem -- 6.2 Gödel's First Incompleteness Theorem -- 6.3 Corollaries of Gödel's First Incompleteness Theorem -- 6.4 Gödel's Second Incompleteness Theorem -- 6.5 Expressing Consistency -- 6.6 Rosser's Incompleteness Theorem -- 6.7 Gödel's Third Incompleteness Theorem -- 6.8 Reflection Principle -- 6.9 Löb's Theorem -- 6.10 Extension to Other First-Order Theories -- 7 Other Limitative Results -- 7.1 Tarski's Undefinability Theorems -- 7.2 Undecidability Theorem -- 7.3 Church's Theorem -- 7.4 Extension to Other First-Order Theories -- 7.5 Decidability of Monadic First-Order Logic -- 8 Second-Order Logic -- 8.1 Second-Order Languages -- 8.2 Free Variables -- 8.3 Substitution -- 8.4 A Deductive Calculus -- 8.5 Quantifier Rules -- 8.6 Substitutivity of Equivalence -- 8.7 Equality -- 8.8 Interpretations.
8.9 Substitution Properties -- 8.10 Soundness -- 8.11 Consistency -- 8.12 Negative Results -- 8.13 Isomorphism of Interpretations -- 9 Second-Order Arithmetic -- 9.1 Second-Order Theories -- 9.2 The Theory PA2 -- 9.3 Primitive Recursive Functions in PA2 -- 9.4 Limitative Results for PA2 -- 9.5 Categoricity of PA2 -- 9.6 Strong Incompleteness Theorem for Second-Order Logic -- 9.7 Non-recursive Enumerability of Consequences of PA2 -- Appendix -- A.1 Hilbert's Approach -- A.2 The Conservation Program -- A.3 The Consistency Program -- A.4 Equivalence of the Two Programs -- A.5 Fall of the Consistency Program -- A.6 Fall of the Conservation Program -- A.7 Other Shortcomings of Hilbert's Approach -- References -- Index. |
| Record Nr. | UNINA-9910632482603321 |
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Cellucci Carlo
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| Cham, Switzerland : , : Springer, , [2022] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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The theory of Gödel / / Carlo Cellucci
| The theory of Gödel / / Carlo Cellucci |
| Autore | Cellucci Carlo |
| Pubbl/distr/stampa | Cham, Switzerland : , : Springer, , [2022] |
| Descrizione fisica | 1 online resource (164 pages) |
| Disciplina | 511.3 |
| Collana | Synthese library |
| Soggetto topico |
Gödel's theorem
Teorema de Gödel |
| Soggetto genere / forma | Llibres electrònics |
| ISBN |
9783031134173
9783031134166 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Intro -- Preface -- References -- Contents -- 1 First-Order Logic -- 1.1 First-Order Languages -- 1.2 Free Variables -- 1.3 Substitution -- 1.4 A Deductive Calculus -- 1.5 Connective Rules -- 1.6 Quantifier Rules -- 1.7 Substitutivity of Equivalence -- 1.8 Equality -- 2 Completeness -- 2.1 Interpretations -- 2.2 Substitution Properties -- 2.3 Soundness -- 2.4 Consistency -- 2.5 Rich Sets -- 2.6 Completeness Theorem -- 2.7 Isomorphisms of Interpretations -- 2.8 Elementary Equivalence -- 2.9 Definability in an Interpretation -- 3 First-Order Theories -- 3.1 Generalities on First-Order Theory -- 3.2 Extensions of Theories -- 3.3 Definitional Extensions -- 4 Primitive Recursive Arithmetic -- 4.1 Primitive Recursive Functions -- 4.2 The Theories PRA and PA -- 4.3 Elementary Properties of PRA -- 4.4 Developing Arithmetic in PRA -- 4.5 Bounded Formulas -- 4.6 Non-Standard Models of PA -- 5 Encoding -- 5.1 Encoding of Finite Sequences -- 5.2 Encoding of Syntax -- 5.3 RE-Theories -- 6 Incompleteness -- 6.1 Traditional Gödel's First Incompleteness Theorem -- 6.2 Gödel's First Incompleteness Theorem -- 6.3 Corollaries of Gödel's First Incompleteness Theorem -- 6.4 Gödel's Second Incompleteness Theorem -- 6.5 Expressing Consistency -- 6.6 Rosser's Incompleteness Theorem -- 6.7 Gödel's Third Incompleteness Theorem -- 6.8 Reflection Principle -- 6.9 Löb's Theorem -- 6.10 Extension to Other First-Order Theories -- 7 Other Limitative Results -- 7.1 Tarski's Undefinability Theorems -- 7.2 Undecidability Theorem -- 7.3 Church's Theorem -- 7.4 Extension to Other First-Order Theories -- 7.5 Decidability of Monadic First-Order Logic -- 8 Second-Order Logic -- 8.1 Second-Order Languages -- 8.2 Free Variables -- 8.3 Substitution -- 8.4 A Deductive Calculus -- 8.5 Quantifier Rules -- 8.6 Substitutivity of Equivalence -- 8.7 Equality -- 8.8 Interpretations.
8.9 Substitution Properties -- 8.10 Soundness -- 8.11 Consistency -- 8.12 Negative Results -- 8.13 Isomorphism of Interpretations -- 9 Second-Order Arithmetic -- 9.1 Second-Order Theories -- 9.2 The Theory PA2 -- 9.3 Primitive Recursive Functions in PA2 -- 9.4 Limitative Results for PA2 -- 9.5 Categoricity of PA2 -- 9.6 Strong Incompleteness Theorem for Second-Order Logic -- 9.7 Non-recursive Enumerability of Consequences of PA2 -- Appendix -- A.1 Hilbert's Approach -- A.2 The Conservation Program -- A.3 The Consistency Program -- A.4 Equivalence of the Two Programs -- A.5 Fall of the Consistency Program -- A.6 Fall of the Conservation Program -- A.7 Other Shortcomings of Hilbert's Approach -- References -- Index. |
| Record Nr. | UNISA-996499868803316 |
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Cellucci Carlo
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| Cham, Switzerland : , : Springer, , [2022] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
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