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...
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| Format: | Book |
| Language: | English |
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Cambridge ; New York ; Port Melbourne ; New Delhi ; Singapore
Cambridge University Press
2021
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Summary: | "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"-- |
| Physical Description: | xiii, 271 Seiten Illustration |
| ISBN: | 9781108479882 |
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Record in the Search Index
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| adam_text | Contents List ofFigures Preface Part I 1 2 3 4 Introduction What Is a Deductive Argument? Issues Conclusion 3 3 4 9 21 Back to the Roots of Deduction 22 2. í Introduction 2.2 The Different Roots of Deduction 2.3 Deduction as a Dialogical Notion 2.4 Conclusion 22 23 29 36 The Prover-Skeptic Dialogues 37 3.1 3.2 3.3 3.4 3.5 37 37 46 54 59 Introduction Earlier Dialogical Proposals The Prover-Skeptic Games Cooperation and Adversariality Conclusion Deduction as a Dialogical Notion 4.1 Introduction 4.2 Dialogical Interpretations of Three Key Features of Deduction 4.3 Philosophical Issues Pertaining to Deduction 4.4 Conclusions Part II 5 ix The Philosophy of Deduction The Trouble with Deduction 1.1 1.2 1.3 1.4 page viii 61 61 61 73 84 The History of Deduction Deduction in Mathematics and Dialectic in Ancient Greece 87 5.1 5.2 87 88 Introduction A Conceptual Genealogy of Deduction v
Contents VI 5.3 5.4 5.5 5.6 Historical Background Ancient Greek Mathematics Ancient Greek Dialectic Conclusion Aristotle’s Syllogistic and Other Ancient Logical Traditions 6.1 6.2 6.3 6.4 7 Introduction Aristotle’s Syllogistic Asian Logical Traditions Conclusion Logic and Deduction in the Middle Ages and the Modem Period 7.1 7.2 7.3 7.4 Introduction Medieval Aristotelian Logical Traditions Forgetting the Dialogical Origins of Logic Conclusion Part III 9 Introduction Our ‘Poor’ Deductive Reasoning Skills The Strength of Group Deductive Reasoning Conclusion 108 109 123 129 131 131 132 143 148 151 151 152 163 167 The Ontogeny of Deductive Reasoning 169 9.1 Introduction 9.2 Necessary Truth-Preservation: Adversariality 9.3 Bracketing Belief: Fantasy and the ‘Hypothetical Other’ 9.4 Perspicuity: Explaining to Others 9.5 Internalization 9.6 Conclusion 169 171 174 180 183 186 10 The Phylogeny of Deductive Reasoning 10.1 10.2 10.3 10.4 10.5 10.6 11 108 Deduction and Cognition 8 How We Reason, Individually and in Groups 8.1 8.2 8.3 8.4 91 93 98 107 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 11.1 11.2 11.3 Introduction What Kinds of Entities Are Mathematical Proofs? Provers and Skeptics in Mathematical Practice 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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| adam_txt |
Contents List ofFigures Preface Part I 1 2 3 4 Introduction What Is a Deductive Argument? Issues Conclusion 3 3 4 9 21 Back to the Roots of Deduction 22 2. í Introduction 2.2 The Different Roots of Deduction 2.3 Deduction as a Dialogical Notion 2.4 Conclusion 22 23 29 36 The Prover-Skeptic Dialogues 37 3.1 3.2 3.3 3.4 3.5 37 37 46 54 59 Introduction Earlier Dialogical Proposals The Prover-Skeptic Games Cooperation and Adversariality Conclusion Deduction as a Dialogical Notion 4.1 Introduction 4.2 Dialogical Interpretations of Three Key Features of Deduction 4.3 Philosophical Issues Pertaining to Deduction 4.4 Conclusions Part II 5 ix The Philosophy of Deduction The Trouble with Deduction 1.1 1.2 1.3 1.4 page viii 61 61 61 73 84 The History of Deduction Deduction in Mathematics and Dialectic in Ancient Greece 87 5.1 5.2 87 88 Introduction A Conceptual Genealogy of Deduction v
Contents VI 5.3 5.4 5.5 5.6 Historical Background Ancient Greek Mathematics Ancient Greek Dialectic Conclusion Aristotle’s Syllogistic and Other Ancient Logical Traditions 6.1 6.2 6.3 6.4 7 Introduction Aristotle’s Syllogistic Asian Logical Traditions Conclusion Logic and Deduction in the Middle Ages and the Modem Period 7.1 7.2 7.3 7.4 Introduction Medieval Aristotelian Logical Traditions Forgetting the Dialogical Origins of Logic Conclusion Part III 9 Introduction Our ‘Poor’ Deductive Reasoning Skills The Strength of Group Deductive Reasoning Conclusion 108 109 123 129 131 131 132 143 148 151 151 152 163 167 The Ontogeny of Deductive Reasoning 169 9.1 Introduction 9.2 Necessary Truth-Preservation: Adversariality 9.3 Bracketing Belief: Fantasy and the ‘Hypothetical Other’ 9.4 Perspicuity: Explaining to Others 9.5 Internalization 9.6 Conclusion 169 171 174 180 183 186 10 The Phylogeny of Deductive Reasoning 10.1 10.2 10.3 10.4 10.5 10.6 11 108 Deduction and Cognition 8 How We Reason, Individually and in Groups 8.1 8.2 8.3 8.4 91 93 98 107 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 11.1 11.2 11.3 Introduction What Kinds of Entities Are Mathematical Proofs? Provers and Skeptics in Mathematical Practice 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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| institution | BVB |
| isbn | 9781108479882 |
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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 (VU Amsterdam and University of St Andrews) Cambridge ; New York ; Port Melbourne ; New Delhi ; Singapore Cambridge University Press 2021 xiii, 271 Seiten Illustration 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 Online version Novaes, Catarina Dutilh The dialogical roots of deduction Cambridge, United Kingdom ; New York, NY, USA : Cambridge University Press, 2021 9781108800792 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=032565021&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 (VU Amsterdam and University of St Andrews) |
| title_fullStr | The dialogical roots of deduction historical, cognitive, and philosophical perspectives on reasoning Catarina Dutilh Novaes (VU Amsterdam and University of St Andrews) |
| title_full_unstemmed | The dialogical roots of deduction historical, cognitive, and philosophical perspectives on reasoning Catarina Dutilh Novaes (VU 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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