The metaphysics and mathematics of arbitrary objects:
"Building on the seminal work of Kit Fine in the 1980s, Leon Horsten here develops a new theory of arbitrary entities. He connects this theory to issues and debates in metaphysics, logic, and contemporary philosophy of mathematics, investigating the relation between specific and arbitrary objec...
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge ; New York ; Port Melbourne ;New Delhi ; Singapore
Cambridge University Press
2019
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Zusammenfassung: | "Building on the seminal work of Kit Fine in the 1980s, Leon Horsten here develops a new theory of arbitrary entities. He connects this theory to issues and debates in metaphysics, logic, and contemporary philosophy of mathematics, investigating the relation between specific and arbitrary objects and between specific and arbitrary systems of objects. His book shows how this innovative theory is highly applicable to problems in the philosophy of arithmetic, and explores in particular how arbitrary objects can engage with the nineteenth-century concept of variable mathematical quantities, how they are relevant for debates around mathematical structuralism, and how they can help our understanding of the concept of random variables in statistics. This fully worked through theory will open up new avenues within philosophy of mathematics, bringing in the work of other philosophers such as Saul Kripke, and providing new insights into the development of the foundations of mathematics from the eighteenth century to the present day"--Back cover |
| Beschreibung: | xvii, 231 Seiten Illustrationen |
| ISBN: | 9781107039414 |
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| 505 | 8 | |a Introduction. Arbitrary objects and the philosophy of mathematics -- Metaphysics of mathematics -- Arbitrary objects -- Mathematical objects as arbitrary objects -- Structure in mathematics -- Mathematical structures -- Kit Fine -- Generic systems and mathematical structuralism -- Reasoning about generic sequences -- Probability and random variables -- Directions for future research | |
| 520 | 3 | |a "Building on the seminal work of Kit Fine in the 1980s, Leon Horsten here develops a new theory of arbitrary entities. He connects this theory to issues and debates in metaphysics, logic, and contemporary philosophy of mathematics, investigating the relation between specific and arbitrary objects and between specific and arbitrary systems of objects. His book shows how this innovative theory is highly applicable to problems in the philosophy of arithmetic, and explores in particular how arbitrary objects can engage with the nineteenth-century concept of variable mathematical quantities, how they are relevant for debates around mathematical structuralism, and how they can help our understanding of the concept of random variables in statistics. This fully worked through theory will open up new avenues within philosophy of mathematics, bringing in the work of other philosophers such as Saul Kripke, and providing new insights into the development of the foundations of mathematics from the eighteenth century to the present day"--Back cover | |
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Datensatz im Suchindex
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| adam_text | Contents List ofFigures [page x] Preface [xi] Acknowledgements [xiv] Symbols and Abbreviations 1 Introduction 1.1 1.2 1.3 1.4 1.5 2 [xvi] [1] Arbitrary Objects and the Philosophy of Mathematics Scratching the Surface [3] Structure and Method [4] Intended Audience [8] On Notation and Technical Matters [ 10] Metaphysics of Mathematics [1] [13] 2.1 The Methodology of Philosophy of Mathematics [13] 2.2 Quietism [16] 2.3 Naive Metaphysics and Foundational Metaphysics [24] 2.4 Naive Metaphysics Only [26] 2.5 Metaphysics of Mathematics [32] 2.6 An Objection from Pseudo-science [34] 2.7 Mathematical Models [36] 3 Arbitrary Objects [38] 3.1 The Motivating Idea [38] 3.2 Early Russell on Variables [40] 3.3 Arbitrary Objects and Their Relations 3.4 Identity and Comprehension [45] 3.5 State Spaces [48] 3.6 Being and Being in a State [49] 3.7 Hairdressers [53] 3.8 Baby Steps [54] 3.9 Properties, Quantities [58] 4 [44] Mathematical Objects as Arbitrary Objects 4.1 4.2 4.3 4.4 4.5 4.6 [61 ] Arbitrary Natural Numbers [61] More Fregean Worries [66] Quasi-concrete Objects [68] Knowledge of Arbitrary Strings [69] Knowledge by Acquaintance and Knowledge by Description Theory and Applications [75] [74] vii
viii Contents 5 Structure in Mathematics 5.1 5.2 5.3 5.4 5.5 5.6 5.7 6 [78] Form and Structure [78] The Question of Realism [80] Platonism and Reductionism [83] Eliminative Structuralism [85] Non-eliminative Structuralism [94] Structure and Computation [98] The Peculiar Case of Set Theory [102] Mathematical Structures [105] 6.1 From Arbitrary Objects over Arbitrary Systems to Generic Systems [105] 6.2 Fair Dice [106] 6.3 The Generic «-Sequences [108] 6.4 The Generic Natural Number Structure [111] 6.5 Other Arbitrary Systems [113] 6.6 The Computable Generic «֊Sequence [114] 6.7 The Arbitrary Countable Graph [115] 6.8 Individual Structures [117] 6.9 The Generic Hierarchy [120] 7 Kit Fine [123] 7.1 Concept and Object [124] 7.2 Variable Objects and Dependence [127] 7.3 Identity, Systems, and Comprehension [129] 7.4 Cantorian Abstraction [134] 7.5 The Natural Number Structure [136] 7.6 Predicativism? [139] 7.7 Universals versus Variable Numbers [141] 8 Generic Systems and Mathematical Structuralism 8.1 8.2 8.3 8.4 8.5 9 [143] Generic Structuralism? [143] Themes from Eliminative and Non-Eliminative Structuralism Theories and Structures [153] Comparison with Fine [155] Quantification and Reference [159] Reasoning about Generic eo-Sequences [162] 9.1 Individual Concepts and Camapian Modal Logic 9.2 Generic Truth [165] 9.3 Definability and Indiscernibility [172] 9.4 Determination and Independence [177] 9.5 Computational Complexity [182] 9.6 Axiomatising Second-Order Arithmetic [184] 9.7 Well-Ordering [186] [ 162] [146]
Contents 10 Probability and Random Variables 10.1 10.2 10.3 10.4 10.5 [189] Random Variables [189] A Connection with Individual Concepts? Uniformity [193] Non-Archimedean Probability Functions Set Probabilities [200] 11 Directions for Future Research [208] 11.1 Success or Failure? [208] 11.2 Towards a General Theory [210] 11.3 Aspects and Applications [211] Bibliography Index [224] [215] [191] [195] IX
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| contents | Introduction. Arbitrary objects and the philosophy of mathematics -- Metaphysics of mathematics -- Arbitrary objects -- Mathematical objects as arbitrary objects -- Structure in mathematics -- Mathematical structures -- Kit Fine -- Generic systems and mathematical structuralism -- Reasoning about generic sequences -- Probability and random variables -- Directions for future research |
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| id | DE-604.BV046437342 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T08:44:35Z |
| institution | BVB |
| isbn | 9781107039414 |
| language | English |
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| physical | xvii, 231 Seiten Illustrationen |
| publishDate | 2019 |
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| publisher | Cambridge University Press |
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| spelling | Horsten, Leon 1966- Verfasser (DE-588)1049335686 aut The metaphysics and mathematics of arbitrary objects Leon Horsten (University of Bristol) Cambridge ; New York ; Port Melbourne ;New Delhi ; Singapore Cambridge University Press 2019 xvii, 231 Seiten Illustrationen txt rdacontent n rdamedia nc rdacarrier Introduction. Arbitrary objects and the philosophy of mathematics -- Metaphysics of mathematics -- Arbitrary objects -- Mathematical objects as arbitrary objects -- Structure in mathematics -- Mathematical structures -- Kit Fine -- Generic systems and mathematical structuralism -- Reasoning about generic sequences -- Probability and random variables -- Directions for future research "Building on the seminal work of Kit Fine in the 1980s, Leon Horsten here develops a new theory of arbitrary entities. He connects this theory to issues and debates in metaphysics, logic, and contemporary philosophy of mathematics, investigating the relation between specific and arbitrary objects and between specific and arbitrary systems of objects. His book shows how this innovative theory is highly applicable to problems in the philosophy of arithmetic, and explores in particular how arbitrary objects can engage with the nineteenth-century concept of variable mathematical quantities, how they are relevant for debates around mathematical structuralism, and how they can help our understanding of the concept of random variables in statistics. This fully worked through theory will open up new avenues within philosophy of mathematics, bringing in the work of other philosophers such as Saul Kripke, and providing new insights into the development of the foundations of mathematics from the eighteenth century to the present day"--Back cover Objekt Philosophie (DE-588)4172302-8 gnd rswk-swf Variable (DE-588)4129518-3 gnd rswk-swf Strukturalismus (DE-588)4058129-9 gnd rswk-swf Mathematik (DE-588)4037944-9 gnd rswk-swf Mathematics / Philosophy Variables (Mathematics) Random variables Continuity Fine, Kit Logic, Symbolic and mathematical Objekt Philosophie (DE-588)4172302-8 s Variable (DE-588)4129518-3 s Strukturalismus (DE-588)4058129-9 s Mathematik (DE-588)4037944-9 s DE-604 Digitalisierung BSB München - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=031849451&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Horsten, Leon 1966- The metaphysics and mathematics of arbitrary objects Introduction. Arbitrary objects and the philosophy of mathematics -- Metaphysics of mathematics -- Arbitrary objects -- Mathematical objects as arbitrary objects -- Structure in mathematics -- Mathematical structures -- Kit Fine -- Generic systems and mathematical structuralism -- Reasoning about generic sequences -- Probability and random variables -- Directions for future research Objekt Philosophie (DE-588)4172302-8 gnd Variable (DE-588)4129518-3 gnd Strukturalismus (DE-588)4058129-9 gnd Mathematik (DE-588)4037944-9 gnd |
| subject_GND | (DE-588)4172302-8 (DE-588)4129518-3 (DE-588)4058129-9 (DE-588)4037944-9 |
| title | The metaphysics and mathematics of arbitrary objects |
| title_auth | The metaphysics and mathematics of arbitrary objects |
| title_exact_search | The metaphysics and mathematics of arbitrary objects |
| title_full | The metaphysics and mathematics of arbitrary objects Leon Horsten (University of Bristol) |
| title_fullStr | The metaphysics and mathematics of arbitrary objects Leon Horsten (University of Bristol) |
| title_full_unstemmed | The metaphysics and mathematics of arbitrary objects Leon Horsten (University of Bristol) |
| title_short | The metaphysics and mathematics of arbitrary objects |
| title_sort | the metaphysics and mathematics of arbitrary objects |
| topic | Objekt Philosophie (DE-588)4172302-8 gnd Variable (DE-588)4129518-3 gnd Strukturalismus (DE-588)4058129-9 gnd Mathematik (DE-588)4037944-9 gnd |
| topic_facet | Objekt Philosophie Variable Strukturalismus Mathematik |
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