Syllogistic logic and mathematical proof:
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Oxford ; New York
Oxford University Press
[2023]
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | VI, 227 Seiten Illustrationen 24 cm |
| ISBN: | 9780198876922 |
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Contents Acknowledgments vii Introduction 1 1. Aristotelian Syllogism and Mathematics in Antiquity and the Medieval Period 7 2, Extensions of theSyllogism in Medieval Logic 2.1 Oblique Terms and Relational Sentences in Late Medieval Logic: John Buridan, William of Ockham, and Albert of Saxony 2.2 Expository Syllogism: Identity and Singular Terms 17 3. Syllogistic and Mathematics: The Case of Piccolomini 3.1 Piccolomini’s Syllogistic Reconstruction of Euclid’s Elements 1.1 3.2 A Critical Analysis of Piccolomini’s Reconstruction 33 17 27 36 45 4. Obliquities and Mathematics in the Seventeenth and Eighteenth Centuries: From Jungius to Wolff 4.1 Johannes Vagetius (1633-1691) 4.2 Gottfried Wilhelm Leibniz (1646-1714) 4.3 Juan Caramuel Lobkowitz (1606-1682) 4.4 Gerolamo Saccheri (1667-1733) 4.5 A First Conclusion 51 57 64 72 78 80 5. The Extent of Syllogistic Reasoning: From Rüdiger to Wolff 5.1 Andreas Rüdiger (1673-1731) and His School on Oblique 83 Inferences 5.2 Christian Wolff on Oblique Inferences 5.3 Mathematics, Philosophy, and Syllogistic Inferences in Wolff, Rüdiger, Müller, Hoffmann, and Crusius 5.3.1 Wolff: Every Mathematical Demonstration Is a Chain of Syllogisms 5.3.2 Rüdiger and His School on the Non-Syllogistic Nature of Mathematics 83 89 5.3.2.1 Andreas Rüdiger on the Non-Syllogistic Nature of Mathematics 5.3.2.2 Syllogism and Mathematical Reasoning in Müller, Hoffmann, and Crusius 5.3.2.3 Appendix: Note (d) in Rüdigers De Sensu Veri et Falsi (1722) 92 92 98 99 113 118
Vi CONTENTS 6. Lambert and Kant 6.1 Johann Heinrich Lambert (1728-1777) and the Treatment of Relations in His Logical Calculus 6.2 Kant and Traditional Logic 6.3 Kant on Syllogistic Proofs and Mathematics 125 7. Bernard Bolzano on Non-Syllogistic Reasoning 163 8. Thomas Reid, William Hamilton, and Augustus De Morgan 177 Conclusion References Index of Names 125 128 137 195 209 223 |
| adam_txt |
Contents Acknowledgments vii Introduction 1 1. Aristotelian Syllogism and Mathematics in Antiquity and the Medieval Period 7 2, Extensions of theSyllogism in Medieval Logic 2.1 Oblique Terms and Relational Sentences in Late Medieval Logic: John Buridan, William of Ockham, and Albert of Saxony 2.2 Expository Syllogism: Identity and Singular Terms 17 3. Syllogistic and Mathematics: The Case of Piccolomini 3.1 Piccolomini’s Syllogistic Reconstruction of Euclid’s Elements 1.1 3.2 A Critical Analysis of Piccolomini’s Reconstruction 33 17 27 36 45 4. Obliquities and Mathematics in the Seventeenth and Eighteenth Centuries: From Jungius to Wolff 4.1 Johannes Vagetius (1633-1691) 4.2 Gottfried Wilhelm Leibniz (1646-1714) 4.3 Juan Caramuel Lobkowitz (1606-1682) 4.4 Gerolamo Saccheri (1667-1733) 4.5 A First Conclusion 51 57 64 72 78 80 5. The Extent of Syllogistic Reasoning: From Rüdiger to Wolff 5.1 Andreas Rüdiger (1673-1731) and His School on Oblique 83 Inferences 5.2 Christian Wolff on Oblique Inferences 5.3 Mathematics, Philosophy, and Syllogistic Inferences in Wolff, Rüdiger, Müller, Hoffmann, and Crusius 5.3.1 Wolff: Every Mathematical Demonstration Is a Chain of Syllogisms 5.3.2 Rüdiger and His School on the Non-Syllogistic Nature of Mathematics 83 89 5.3.2.1 Andreas Rüdiger on the Non-Syllogistic Nature of Mathematics 5.3.2.2 Syllogism and Mathematical Reasoning in Müller, Hoffmann, and Crusius 5.3.2.3 Appendix: Note (d) in Rüdigers De Sensu Veri et Falsi (1722) 92 92 98 99 113 118
Vi CONTENTS 6. Lambert and Kant 6.1 Johann Heinrich Lambert (1728-1777) and the Treatment of Relations in His Logical Calculus 6.2 Kant and Traditional Logic 6.3 Kant on Syllogistic Proofs and Mathematics 125 7. Bernard Bolzano on Non-Syllogistic Reasoning 163 8. Thomas Reid, William Hamilton, and Augustus De Morgan 177 Conclusion References Index of Names 125 128 137 195 209 223 |
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| institution | BVB |
| isbn | 9780198876922 |
| language | English |
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| spelling | Mancosu, Paolo 1960- Verfasser (DE-588)133912035 aut Syllogistic logic and mathematical proof Paolo Mancosu and Massimo Mugnai Oxford ; New York Oxford University Press [2023] VI, 227 Seiten Illustrationen 24 cm txt rdacontent n rdamedia nc rdacarrier Mathematische Logik (DE-588)4037951-6 gnd rswk-swf Syllogismus (DE-588)4184185-2 gnd rswk-swf Beweis (DE-588)4132532-1 gnd rswk-swf Syllogism / Mathematics Logic / Mathematics Proof theory Syllogismus (DE-588)4184185-2 s Beweis (DE-588)4132532-1 s Mathematische Logik (DE-588)4037951-6 s DE-604 Mugnai, Massimo 1947- Verfasser (DE-588)1227323476 aut 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=034579017&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Mancosu, Paolo 1960- Mugnai, Massimo 1947- Syllogistic logic and mathematical proof Mathematische Logik (DE-588)4037951-6 gnd Syllogismus (DE-588)4184185-2 gnd Beweis (DE-588)4132532-1 gnd |
| subject_GND | (DE-588)4037951-6 (DE-588)4184185-2 (DE-588)4132532-1 |
| title | Syllogistic logic and mathematical proof |
| title_auth | Syllogistic logic and mathematical proof |
| title_exact_search | Syllogistic logic and mathematical proof |
| title_exact_search_txtP | Syllogistic logic and mathematical proof |
| title_full | Syllogistic logic and mathematical proof Paolo Mancosu and Massimo Mugnai |
| title_fullStr | Syllogistic logic and mathematical proof Paolo Mancosu and Massimo Mugnai |
| title_full_unstemmed | Syllogistic logic and mathematical proof Paolo Mancosu and Massimo Mugnai |
| title_short | Syllogistic logic and mathematical proof |
| title_sort | syllogistic logic and mathematical proof |
| topic | Mathematische Logik (DE-588)4037951-6 gnd Syllogismus (DE-588)4184185-2 gnd Beweis (DE-588)4132532-1 gnd |
| topic_facet | Mathematische Logik Syllogismus Beweis |
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