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Figuring It Out: Logic Diagrams [Kietas viršelis]

  • Formatas: Hardback, 234 pages, aukštis x plotis: 230x155 mm, weight: 478 g, 20 Tables, black and white; 145 Illustrations, black and white
  • Serija: Philosophical Analysis
  • Išleidimo metai: 18-Nov-2019
  • Leidėjas: De Gruyter
  • ISBN-10: 3110621630
  • ISBN-13: 9783110621631
Kitos knygos pagal šią temą:
  • Formatas: Hardback, 234 pages, aukštis x plotis: 230x155 mm, weight: 478 g, 20 Tables, black and white; 145 Illustrations, black and white
  • Serija: Philosophical Analysis
  • Išleidimo metai: 18-Nov-2019
  • Leidėjas: De Gruyter
  • ISBN-10: 3110621630
  • ISBN-13: 9783110621631
Kitos knygos pagal šią temą:
Die Reihe bietet ein Publikationsforum für innovative Arbeiten zu allen Themengebieten der analytischen Philosophie. Der Schwerpunkt liegt auf den Disziplinen der theoretischen Philosophie: Metaphysik, Ontologie, Erkenntnistheorie, Sprachphilosophie, Logik. Willkommen sind auch Beiträge zur Geschichte der Philosophie, wenn die systematische Durchdringung der gewählten Themen im Vordergrund steht.

The book begins with an extensive survey of the history of logic diagrams, including looking at possible diagrams from Aristotle, the development of both linear and closed figure diagrams by Leibniz, Lambert, Euler, Venn"s new system, Peirce"s Existential Graphs, and Frege"s two-dimensional notation as a kind of logic diagram system. During most of the 20 th century, there was little regard for efforts to construct logic diagrams. However, since the 1980s there has been an increasing interest in such diagrams. Ever larger numbers of philosophers, logicians, mathematicians, computational scientists, and cognitive scientists have turned their attention to building, analyzing, using, or exploring in other ways systems of logic diagrams. The system offered here makes use of line segments and points and it enjoys a number of important advantages: it is simple, natural, and both expressively and inferentially powerful. It can be used to analyze syllogisms (including those involving rela

tional terms) and arguments involving unanalyzed statements. Understanding such a system can shed valuable light on how ordinary people naturally reason.

The series provides a forum for innovative, high-quality work in all fields of analytical philosophy.

Many systems of logic diagrams have been offered both historically and more recently. Each of them has clear limitations. An original alternative system is offered here. It is simpler, more natural, and more expressively and inferentially powerful. It can be used to analyze not only syllogisms but arguments involving relational terms and unanalyzed statement terms.
List of Figures
ix
Preface xiii
1 Introduction: Seeing Reason
1(7)
2 Some Historical Figures
8(50)
2.1 Aristotle and the Lost Diagrams
8(18)
2.2 "The Golden Age" - Leibniz, Lambert, and Euler
26(8)
2.3 Venn, Peirce (and Frege?)
34(20)
2.4 "The Renaissance of Diagrammatology"
54(4)
3 Lines of Reason
58(81)
3.1 New Lines (Smyth and Pagnan)
58(8)
3.2 In Logical Terms: Term Functor Logic
66(9)
3.3 Term Lines
75(23)
3.4 The Point of Names
98(7)
3.5 Vectors of Relations
105(18)
3.6 World Lines
123(16)
4 Holding the Line
139(24)
4.1 Figuring it Out
139(6)
4.2 Crossing the Line
145(7)
4.3 Seeing Reason
152(5)
4.4 So, How Do We Reason, After All?
157(6)
5 Linear Diagrams and Non-Classical Quantifiers
163(25)
Jose Martin Castro-Manzano
Joso Roberto Pacheco-Montes
5.1 Introduction
163(1)
5.2 Two Frameworks for Syllogistic
163(7)
5.2.1 General aspects of syllogistic
163(1)
5.2.2 The TFL framework: the plus-minus algebra
164(2)
5.2.3 The SYLL+ framework: the extra quantifiers
166(4)
5.3 The TFL+ Framework: A Tweaked Version of Syllogistic
170(6)
5.3.1 Step
1. The plus-minus algebra meets the extra quantifiers
171(1)
5.3.2 Step
2. The plus-minus algebra modification
172(2)
5.3.3 Step
3. Reliability
174(2)
5.4 The TFL Framework: A Diagrammatic Extension
176(9)
5.4.1 Step
1. The linear diagrams meet the extra quantifiers
178(2)
5.4.2 Step
2. The procedure modification
180(2)
5.4.3 Step
3. Reliability
182(3)
5.5 Conclusions
185(1)
Appendix: Rules of inference for TFL
186(2)
6 Drawing Conclusions: Get Better Diagrams
188(6)
Bibliography and Further Reading 194(20)
Index 214
George Englebretsen, Bishops University, Sherbrooke, Canada.