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Frege, Dedekind and Peano on the foundations of arithmetic / / D.A. Gillies
| Frege, Dedekind and Peano on the foundations of arithmetic / / D.A. Gillies |
| Autore | Gillies Donald <1944-, > |
| Pubbl/distr/stampa | Abingdon, Oxon ; ; New York : , : Routledge, , 2011 |
| Descrizione fisica | 1 online resource (114 p.) |
| Disciplina | 513 |
| Collana | Routledge revivals |
| Soggetto topico | Arithmetic - Foundations |
| Soggetto genere / forma | Electronic books. |
| ISBN |
1-283-96574-7
0-203-81628-5 1-136-72108-8 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Cover; Frege, Dedekind and Peano on the Foundations of Arithmetic; Title Page; Copyright Page; Preface; Table of Contents; Introduction; 1. Kant's Theory of Mathematics; 2. Frege's Criticisms of Kant; 3. Mill's Theory of Mathematics; 4. Frege's Criticisms of Mill; 5. The content of a statement of number is an assertion about a concept; 6. Frege's Platonism; 7. Frege's Logicism; 8. Dedekind and Set Theory; 9. Dedekind's Development of Arithmetic; 10. Peano's Axioms. General Comparison of Frege, Dedekind, and Peano; 11. Frege's Begriffsschrift; 12. Frege's Grundgesetze, and Russell's paradox
Appendix I. On NotationAppendix II. On the Principle of Mathematical, or Complete, Induction; References; Index |
| Record Nr. | UNINA-9910462571703321 |
Gillies Donald <1944-, >
|
||
| Abingdon, Oxon ; ; New York : , : Routledge, , 2011 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Frege, Dedekind and Peano on the foundations of arithmetic / / D.A. Gillies
| Frege, Dedekind and Peano on the foundations of arithmetic / / D.A. Gillies |
| Autore | Gillies Donald <1944-, > |
| Pubbl/distr/stampa | Abingdon, Oxon ; ; New York : , : Routledge, , 2011 |
| Descrizione fisica | 1 online resource (114 p.) |
| Disciplina | 513 |
| Collana | Routledge revivals |
| Soggetto topico | Arithmetic - Foundations |
| ISBN |
1-136-72107-X
1-283-96574-7 0-203-81628-5 1-136-72108-8 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Cover; Frege, Dedekind and Peano on the Foundations of Arithmetic; Title Page; Copyright Page; Preface; Table of Contents; Introduction; 1. Kant's Theory of Mathematics; 2. Frege's Criticisms of Kant; 3. Mill's Theory of Mathematics; 4. Frege's Criticisms of Mill; 5. The content of a statement of number is an assertion about a concept; 6. Frege's Platonism; 7. Frege's Logicism; 8. Dedekind and Set Theory; 9. Dedekind's Development of Arithmetic; 10. Peano's Axioms. General Comparison of Frege, Dedekind, and Peano; 11. Frege's Begriffsschrift; 12. Frege's Grundgesetze, and Russell's paradox
Appendix I. On NotationAppendix II. On the Principle of Mathematical, or Complete, Induction; References; Index |
| Record Nr. | UNINA-9910786142203321 |
|
Gillies Donald <1944-, >
|
||
| Abingdon, Oxon ; ; New York : , : Routledge, , 2011 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Frege, Dedekind and Peano on the foundations of arithmetic / / D.A. Gillies
| Frege, Dedekind and Peano on the foundations of arithmetic / / D.A. Gillies |
| Autore | Gillies Donald <1944-, > |
| Pubbl/distr/stampa | Abingdon, Oxon ; ; New York : , : Routledge, , 2011 |
| Descrizione fisica | 1 online resource (114 p.) |
| Disciplina | 513 |
| Collana | Routledge revivals |
| Soggetto topico | Arithmetic - Foundations |
| ISBN |
1-136-72107-X
1-283-96574-7 0-203-81628-5 1-136-72108-8 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Cover; Frege, Dedekind and Peano on the Foundations of Arithmetic; Title Page; Copyright Page; Preface; Table of Contents; Introduction; 1. Kant's Theory of Mathematics; 2. Frege's Criticisms of Kant; 3. Mill's Theory of Mathematics; 4. Frege's Criticisms of Mill; 5. The content of a statement of number is an assertion about a concept; 6. Frege's Platonism; 7. Frege's Logicism; 8. Dedekind and Set Theory; 9. Dedekind's Development of Arithmetic; 10. Peano's Axioms. General Comparison of Frege, Dedekind, and Peano; 11. Frege's Begriffsschrift; 12. Frege's Grundgesetze, and Russell's paradox
Appendix I. On NotationAppendix II. On the Principle of Mathematical, or Complete, Induction; References; Index |
| Record Nr. | UNINA-9910820920803321 |
|
Gillies Donald <1944-, >
|
||
| Abingdon, Oxon ; ; New York : , : Routledge, , 2011 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
An objective theory of probability / / D.A. Gillies
| An objective theory of probability / / D.A. Gillies |
| Autore | Gillies Donald <1944-, > |
| Pubbl/distr/stampa | Abingdon, Oxon : , : Routledge, , 2011 |
| Descrizione fisica | 1 online resource (263 p.) |
| Disciplina | 519.2 |
| Collana | Routledge revivals |
| Soggetto topico |
Probabilities
Mathematics |
| Soggetto genere / forma | Electronic books. |
| ISBN |
1-136-81081-1
0-203-82879-8 1-283-54084-3 1-136-81082-X 9786613853295 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""An Objective Theory of Probability""; ""Copyright""; ""An Objective Theory of Probability""; ""Copyright""; ""Contents""; ""Preface""; ""Introduction""; ""Von Mises' theory of probability""; ""Keynes' theory of probability""; ""Comparison between von Mises and Keynes""; ""Development of the logical tradition after Keynes""; ""Characterization of the scientific approach""; ""The two-concept view""; ""General outline of the book""; ""PART I: THE SPECIAL SCIENCES IN GENERAL""; ""Chapter 1 Von Mises' Philosophy of Science: Its Machian Origins""; ""Mach's development of mechanics""
""Operationalism""""Some objections to operationalism""; ""Chapter 2 Force and Mass""; ""The concepts of force and mass before Newton""; ""How Newton introduced the concepts of force and mass""; ""The 'moon-test' of the law of gravity""; ""How force and mass came to be measurable""; ""Chapter 3 Conceptual Innovation in the Exact Sciences""; ""Another illustration of conceptual innovation: the concept of temperature""; ""General theory of conceptual innovation""; ""How our theory of conceptual innovation avoids the difficulties in operationalism"" ""A digression on 'testing' and 'accepting' scientific theories""""The problem of depth""; ""The generalized principle of correspondence and related questions""; ""How the ideas of Part I will be applied to the theory of probability""; ""PART II: THE AXIOMATIC SUPERSTRUCTURE""; ""Chapter 4 Probability and Frequency""; ""Three views on the relations between probability and frequency""; ""Randomness in von Mises' theory""; ""Comparison between von Mises and Kolmogorov""; ""Two criticisms of Kolmogorov by von Mises""; ""Chapter 5 Repeatability and Independence""; ""Analysis of repeatability"" ""Repeatable conditions with dependent outcomes""""Arguments against the axiom of independent repetitions""; ""Main argument for the axiom of independent repetitions""; ""Derivation of the law of stability of statistical frequencies""; ""Comparison with Newtonian mechanics""; ""Criticism of the views of von Mises and Kolmogorov on the relations between probability and frequency""; ""An answer to some arguments of Doob's""; ""Criticism of the 'laws of large numbers' view""; ""The significance of the laws of large numbers"" ""Chapter 6 Deduction of the Law of Excluded Gambling Systems: The Role of Randomness in Probability Theory""""Deduction of the law of excluded gambling systems""; ""Independence and gambling systems""; ""A practical example""; ""Definition of random sequences and their generation in practice""; ""Relation to randomness as defined in the frequency theory""; ""Answer to an objection of Braithwaite's""; ""Probability theory and determinism""; ""Discussion of some arguments of Khintchine's""; ""Possible modifications of the axioms of probability in the light of experience"" ""Chapter 7 Probabilities of Single Events: Popper's Propensity Theory"" |
| Record Nr. | UNINA-9910465184803321 |
|
Gillies Donald <1944-, >
|
||
| Abingdon, Oxon : , : Routledge, , 2011 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
An objective theory of probability / / D.A. Gillies
| An objective theory of probability / / D.A. Gillies |
| Autore | Gillies Donald <1944-, > |
| Pubbl/distr/stampa | Abingdon, Oxon : , : Routledge, , 2011 |
| Descrizione fisica | 1 online resource (263 p.) |
| Disciplina | 519.2 |
| Collana | Routledge revivals |
| Soggetto topico |
Probabilities
Mathematics |
| ISBN |
1-136-81081-1
0-203-82879-8 1-283-54084-3 1-136-81082-X 9786613853295 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""An Objective Theory of Probability""; ""Copyright""; ""An Objective Theory of Probability""; ""Copyright""; ""Contents""; ""Preface""; ""Introduction""; ""Von Mises' theory of probability""; ""Keynes' theory of probability""; ""Comparison between von Mises and Keynes""; ""Development of the logical tradition after Keynes""; ""Characterization of the scientific approach""; ""The two-concept view""; ""General outline of the book""; ""PART I: THE SPECIAL SCIENCES IN GENERAL""; ""Chapter 1 Von Mises' Philosophy of Science: Its Machian Origins""; ""Mach's development of mechanics""
""Operationalism""""Some objections to operationalism""; ""Chapter 2 Force and Mass""; ""The concepts of force and mass before Newton""; ""How Newton introduced the concepts of force and mass""; ""The 'moon-test' of the law of gravity""; ""How force and mass came to be measurable""; ""Chapter 3 Conceptual Innovation in the Exact Sciences""; ""Another illustration of conceptual innovation: the concept of temperature""; ""General theory of conceptual innovation""; ""How our theory of conceptual innovation avoids the difficulties in operationalism"" ""A digression on 'testing' and 'accepting' scientific theories""""The problem of depth""; ""The generalized principle of correspondence and related questions""; ""How the ideas of Part I will be applied to the theory of probability""; ""PART II: THE AXIOMATIC SUPERSTRUCTURE""; ""Chapter 4 Probability and Frequency""; ""Three views on the relations between probability and frequency""; ""Randomness in von Mises' theory""; ""Comparison between von Mises and Kolmogorov""; ""Two criticisms of Kolmogorov by von Mises""; ""Chapter 5 Repeatability and Independence""; ""Analysis of repeatability"" ""Repeatable conditions with dependent outcomes""""Arguments against the axiom of independent repetitions""; ""Main argument for the axiom of independent repetitions""; ""Derivation of the law of stability of statistical frequencies""; ""Comparison with Newtonian mechanics""; ""Criticism of the views of von Mises and Kolmogorov on the relations between probability and frequency""; ""An answer to some arguments of Doob's""; ""Criticism of the 'laws of large numbers' view""; ""The significance of the laws of large numbers"" ""Chapter 6 Deduction of the Law of Excluded Gambling Systems: The Role of Randomness in Probability Theory""""Deduction of the law of excluded gambling systems""; ""Independence and gambling systems""; ""A practical example""; ""Definition of random sequences and their generation in practice""; ""Relation to randomness as defined in the frequency theory""; ""Answer to an objection of Braithwaite's""; ""Probability theory and determinism""; ""Discussion of some arguments of Khintchine's""; ""Possible modifications of the axioms of probability in the light of experience"" ""Chapter 7 Probabilities of Single Events: Popper's Propensity Theory"" |
| Record Nr. | UNINA-9910791928603321 |
|
Gillies Donald <1944-, >
|
||
| Abingdon, Oxon : , : Routledge, , 2011 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
An objective theory of probability / / D.A. Gillies
| An objective theory of probability / / D.A. Gillies |
| Autore | Gillies Donald <1944-, > |
| Pubbl/distr/stampa | Abingdon, Oxon : , : Routledge, , 2011 |
| Descrizione fisica | 1 online resource (263 p.) |
| Disciplina | 519.2 |
| Collana | Routledge revivals |
| Soggetto topico |
Probabilities
Mathematics |
| ISBN |
1-136-81081-1
0-203-82879-8 1-283-54084-3 1-136-81082-X 9786613853295 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""An Objective Theory of Probability""; ""Copyright""; ""An Objective Theory of Probability""; ""Copyright""; ""Contents""; ""Preface""; ""Introduction""; ""Von Mises' theory of probability""; ""Keynes' theory of probability""; ""Comparison between von Mises and Keynes""; ""Development of the logical tradition after Keynes""; ""Characterization of the scientific approach""; ""The two-concept view""; ""General outline of the book""; ""PART I: THE SPECIAL SCIENCES IN GENERAL""; ""Chapter 1 Von Mises' Philosophy of Science: Its Machian Origins""; ""Mach's development of mechanics""
""Operationalism""""Some objections to operationalism""; ""Chapter 2 Force and Mass""; ""The concepts of force and mass before Newton""; ""How Newton introduced the concepts of force and mass""; ""The 'moon-test' of the law of gravity""; ""How force and mass came to be measurable""; ""Chapter 3 Conceptual Innovation in the Exact Sciences""; ""Another illustration of conceptual innovation: the concept of temperature""; ""General theory of conceptual innovation""; ""How our theory of conceptual innovation avoids the difficulties in operationalism"" ""A digression on 'testing' and 'accepting' scientific theories""""The problem of depth""; ""The generalized principle of correspondence and related questions""; ""How the ideas of Part I will be applied to the theory of probability""; ""PART II: THE AXIOMATIC SUPERSTRUCTURE""; ""Chapter 4 Probability and Frequency""; ""Three views on the relations between probability and frequency""; ""Randomness in von Mises' theory""; ""Comparison between von Mises and Kolmogorov""; ""Two criticisms of Kolmogorov by von Mises""; ""Chapter 5 Repeatability and Independence""; ""Analysis of repeatability"" ""Repeatable conditions with dependent outcomes""""Arguments against the axiom of independent repetitions""; ""Main argument for the axiom of independent repetitions""; ""Derivation of the law of stability of statistical frequencies""; ""Comparison with Newtonian mechanics""; ""Criticism of the views of von Mises and Kolmogorov on the relations between probability and frequency""; ""An answer to some arguments of Doob's""; ""Criticism of the 'laws of large numbers' view""; ""The significance of the laws of large numbers"" ""Chapter 6 Deduction of the Law of Excluded Gambling Systems: The Role of Randomness in Probability Theory""""Deduction of the law of excluded gambling systems""; ""Independence and gambling systems""; ""A practical example""; ""Definition of random sequences and their generation in practice""; ""Relation to randomness as defined in the frequency theory""; ""Answer to an objection of Braithwaite's""; ""Probability theory and determinism""; ""Discussion of some arguments of Khintchine's""; ""Possible modifications of the axioms of probability in the light of experience"" ""Chapter 7 Probabilities of Single Events: Popper's Propensity Theory"" |
| Record Nr. | UNINA-9910812420703321 |
|
Gillies Donald <1944-, >
|
||
| Abingdon, Oxon : , : Routledge, , 2011 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||