The dialogical roots of deduction: historical, cognitive, and philosophical perspectives on reasoning
"Despite quite some variation in its numerous manifestations, three core features of deductive reasoning seem to stand out. They are aptly captured in the following definition of a mathematical proof, taken from the 1989 guideline of the National Council of Teachers of Mathematics (and quoted i...
Gespeichert in:
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| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge ; New York ; Port Melbourne ; New Delhi ; Singapore
Cambridge University Press
2022
|
| Ausgabe: | First paperback edition |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Zusammenfassung: | "Despite quite some variation in its numerous manifestations, three core features of deductive reasoning seem to stand out. They are aptly captured in the following definition of a mathematical proof, taken from the 1989 guideline of the National Council of Teachers of Mathematics (and quoted in (Balacheff, 1991) (p. 177)): a mathematical proof is "a careful sequence of steps with each step following logically from an assumed or previously proved statement and from previous steps." So a deductive argument is a (i) stepwise process, (ii) where each step 'follows logically' (iii) from assumed or previously established statements. In the remainder of the book, it will be further argued that focusing on these three aspects offers an adequate vantage point to investigate deduction in its many facets. Here they are presented in decreasing order of general recognition of their centrality for the notion of deduction"-- |
| Beschreibung: | xiii, 271 Seiten |
| ISBN: | 9781108790925 |
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Contents List of Figures Preface page vin ix Part I The Philosophy of Deduction 1 The Trouble with Deduction 3 1.1 1.2 1.3 1.4 3 4 Introduction What Is a Deductive Argument? Issues Conclusion 2 Back to the Roots of Deduction 2.1 2.2 2.3 2.4 Introduction The Different Roots of Deduction Deduction as a Dialogical Notion Conclusion 3 The Prover-Skeptic Dialogues 3.1 3.2 3.3 3.4 3.5 Introduction Earlier Dialogical Proposals The Prover-Skeptic Games Cooperation and Adversariality Conclusion 4 Deduction as a Dialogical Notion 4.1 4.2 4.3 4.4 Part II Introduction Dialogical Interpretations of Three Key Features of Deduction Philosophical Issues Pertaining to Deduction Conclusions 22 22 23 29 36 37 37 37 46 54 59 61 61 61 73 S4 The History of Deduction 5 Deduction in Mathematics and Dialectic in Ancient Greece 5.1 5.2 9 21 Introduction A Conceptual Genealogy of Deduction 87 87 88
Contents 5.3 5.4 5.5 5.6 Historical Background Ancient Greek Mathematics Ancient Greek Dialectic Conclusion 6 Aristotle’s Syllogistic and Other Ancient Logical Traditions 6.1 6.2 6.3 6.4 Introduction Aristotle's Syllogistic Asian Logical Traditions Conclusion 7 Logic and Deduction in the Middle Ages and the Modern Period 7.1 7.2 7.3 7.4 Introduction Medieval Aristotelian Logical Traditions Forgetting the Dialogical Originsof Logic Conclusion Part ΙΠ 8.1 Introduction 8.2 Our ‘Poor’ Deductive Reasoning Skills 8.3 The Strength of Group Deductive Reasoning 8.4 Conclusion 9 The Ontogeny of Deductive Reasoning Introduction Necessary Truth-Preservation.: Adversariality Bracketing Belief: Fantasy and the ‘Hypothetical Other’ Perspicuity: Explaining to Others Internalization Conclusion 10 The Phylogeny of Deductive Reasoning 10.1 10.2 10.3 10.4 10.5 10.6 11 Introduction Deductive Reasoning in Non-human Animals Mercier and Sperber on the Evolution of Reasoning Heyes on Cultural Gadgets Deduction in the Brain Conclusion A Dialogical Account of Proofs in Mathematical Practice lt.l 11.2 11.3 108 108 109 123 129 131 131 132 143 148 Deduction and Cognition 8 How We Reason, Individually and in Groups 9.1 9.2 9.3 9.4 9.5 9.6 91 93 98 107 Introduction What Kinds of Entities Are Mathematical Proofs? Provers and Skepticsin Mathematical Practice 151 151 152 163 167 169 169 DI I74 DO 183 D6 187 187 189 192 195 202 204 205 205 206 209
Contents 11.4 11.5 Proofs as a Multifaceted Phenomenon Conclusion Conclusions References Index vii 221 232 234 238 261 |
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| isbn | 9781108790925 |
| language | English |
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| spelling | Dutilh Novaes, Catarina 1976- Verfasser (DE-588)1029530815 aut The dialogical roots of deduction historical, cognitive, and philosophical perspectives on reasoning Catarina Dutilh Novaes (Vrije Universiteit Amsterdam and University of St Andrews) First paperback edition Cambridge ; New York ; Port Melbourne ; New Delhi ; Singapore Cambridge University Press 2022 xiii, 271 Seiten txt rdacontent n rdamedia nc rdacarrier "Despite quite some variation in its numerous manifestations, three core features of deductive reasoning seem to stand out. They are aptly captured in the following definition of a mathematical proof, taken from the 1989 guideline of the National Council of Teachers of Mathematics (and quoted in (Balacheff, 1991) (p. 177)): a mathematical proof is "a careful sequence of steps with each step following logically from an assumed or previously proved statement and from previous steps." So a deductive argument is a (i) stepwise process, (ii) where each step 'follows logically' (iii) from assumed or previously established statements. In the remainder of the book, it will be further argued that focusing on these three aspects offers an adequate vantage point to investigate deduction in its many facets. Here they are presented in decreasing order of general recognition of their centrality for the notion of deduction"-- Logik (DE-588)4036202-4 gnd rswk-swf Mathematische Logik (DE-588)4037951-6 gnd rswk-swf Deduktion (DE-588)4011271-8 gnd rswk-swf Logic Deduktion (DE-588)4011271-8 s Logik (DE-588)4036202-4 s Mathematische Logik (DE-588)4037951-6 s DE-604 Äquivalent Druck-Ausgabe, Hardcover 978-1-108-47988-2 Erscheint auch als Online-Ausgabe 978-1-108-80079-2 Digitalisierung UB Regensburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=033902876&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Dutilh Novaes, Catarina 1976- The dialogical roots of deduction historical, cognitive, and philosophical perspectives on reasoning Logik (DE-588)4036202-4 gnd Mathematische Logik (DE-588)4037951-6 gnd Deduktion (DE-588)4011271-8 gnd |
| subject_GND | (DE-588)4036202-4 (DE-588)4037951-6 (DE-588)4011271-8 |
| title | The dialogical roots of deduction historical, cognitive, and philosophical perspectives on reasoning |
| title_auth | The dialogical roots of deduction historical, cognitive, and philosophical perspectives on reasoning |
| title_exact_search | The dialogical roots of deduction historical, cognitive, and philosophical perspectives on reasoning |
| title_exact_search_txtP | The dialogical roots of deduction historical, cognitive, and philosophical perspectives on reasoning |
| title_full | The dialogical roots of deduction historical, cognitive, and philosophical perspectives on reasoning Catarina Dutilh Novaes (Vrije Universiteit Amsterdam and University of St Andrews) |
| title_fullStr | The dialogical roots of deduction historical, cognitive, and philosophical perspectives on reasoning Catarina Dutilh Novaes (Vrije Universiteit Amsterdam and University of St Andrews) |
| title_full_unstemmed | The dialogical roots of deduction historical, cognitive, and philosophical perspectives on reasoning Catarina Dutilh Novaes (Vrije Universiteit Amsterdam and University of St Andrews) |
| title_short | The dialogical roots of deduction |
| title_sort | the dialogical roots of deduction historical cognitive and philosophical perspectives on reasoning |
| title_sub | historical, cognitive, and philosophical perspectives on reasoning |
| topic | Logik (DE-588)4036202-4 gnd Mathematische Logik (DE-588)4037951-6 gnd Deduktion (DE-588)4011271-8 gnd |
| topic_facet | Logik Mathematische Logik Deduktion |
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