Mathematics and Philosophy 2 - Graphs, Orders, Infinites …, North-Eastern Islands

Ships from and sold by Pick A Book Asia Singapore
Publisher: John Wiley & Sons
ISBN 13: 9781786308979
Condition: Brandnew
Binding: hardcover
Pages: 272
Dimensons: 198 x 132 x 30 | 400 (gram)

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From Pythagoreans to Hegel, and beyond, this book gives a brief overview of the history of the notion of graphs and introduces the main concepts of graph theory in order to apply them to philosophy. In addition, this book presents how philosophers can use various mathematical notions of order. Throughout the book, philosophical operations and concepts are defined through examining questions relating the two kinds of known infinities – discrete and continuous – and how Woodin's approach can influence elements of philosophy. We also examine how mathematics can help a philosopher to discover the elements of stability which will help to build an image of the world, even if various approaches (for example, negative theology) generally cannot be valid. Finally, we briefly consider the possibilities of weakening formal thought represented by fuzziness and neutrosophic graphs. In a nutshell, this book expresses the importance of graphs when representing ideas and communicating them clearly with others.Table of Content Introduction ix Chapter 1. Graphs 1 1.1. Graph theory: a brief history 1 1.2. Basic definitions 6 1.3. Different types of graphs 6 1.4. More on the list of graphs 9 1.5. Graphs and vertices 11 1.6. Some operations on graphs 13 1.7. Graph isomorphisms 15 1.7.1. Self-complementary graphs 15 1.7.2. Properties of self-complementary graphs 16 1.8. Symmetric and asymmetric graphs 17 1.9. Extremal graphs 20 1.10. Independence, non-separability, reconstruction conjecture 23 Chapter 2. Philosophical Graphs 29 2.1. Ancient mappings 29 2.2. Chinese tetragrams 33 2.3. Pythagorism and pentagram 33 2.4. n-grams and some figures of the world 35 2.5. Graphs and classical systematicity 41 2.6. Towards a new kind of systematicity 52 2.6.1. Non-Hamiltonian and non-Eulerian philosophies 52 2.6.2. Pancyclic graphs and Metahegelianism 57 2.7. Non-pythagorism and arrangement of lines 58 2.7.1. Levi graphs of line arrangements 62 2.7.2. Line arrangements of curve lines 65 2.7.3. Hyperbolic graphs 67 Chapter 3. Order and Its Philosophical Use 73 3.1. The mathematical notion of order: a brief history 74 3.2. The idea of “well-ordering” 76 3.3. Quasiorders (or preorders) 79 3.4. Partial orders 81 3.4.1. The notion of well partial order 84 3.4.2. Linear extension of a poset 84 3.4.3. Well partially orderings 85 3.5. Trees 85 3.5.1. A zoo of infinite trees 86 3.5.2. Ordinal infinite classifications 87 3.6. Moral problems in a finite world 87 3.7. Order versus circularity 92 3.8. Conclusion 96 Chapter 4. Towards a Formal Philosophy 99 4.1. Asenjo’s systems and Dubarle’s formalization of Hegelianism 99 4.1.1. Asenjo’s systems and Dubarle’s case 100 4.1.2. Dubarle, Parmenides’ thought and Hegel 102 4.1.3. Projective algebras 103 4.2. Some...