(Ebook PDF) Mathematics and Philosophy 2 Graphs Orders Infinites and Philosophy 1st edition by Daniel Parrochia ISBN 9781394209378 1394209371 full chapters

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ISBN 10:1394209371

ISBN 13:9781394209378

Author: Daniel Parrochia

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 Contents:

• 1 Graphs
• 1.1. Graph theory: a brief history
• 1.2. Basic definitions
• 1.3. Different types of graphs
• 1.4. More on the list of graphs
• 1.5. Graphs and vertices
• 1.6. Some operations on graphs
• 1.7. Graph isomorphisms
• 1.8. Symmetric and asymmetric graphs
• 1.9. Extremal graphs
• 1.10. Independence, non-separability, reconstruction conjecture
• 2 Philosophical Graphs
• 2.1. Ancient mappings
• 2.2. Chinese tetragrams
• 2.3. Pythagorism and pentagram
• 2.4. n-grams and some figures of the world
• 2.5. Graphs and classical systematicity
• 2.6. Towards a new kind of systematicity
• 2.7. Non-pythagorism and arrangement of lines
• 3 Order and Its Philosophical Use
• 3.1. The mathematical notion of order: a brief history
• 3.2. The idea of “well-ordering”
• 3.3. Quasiorders (or preorders)
• 3.4. Partial orders
• 3.5. Trees
• 3.6. Moral problems in a finite world
• 3.7. Order versus circularity
• 3.8. Conclusion
• 4 Towards a Formal Philosophy
• 4.1. Asenjo’s systems and Dubarle’s formalization of Hegelianism
• 4.2. Some criticisms
• 4.3. Porphyry and the neoplatonist mode of thought
• 4.4. A variant of Dubarle’s formalism
• 4.5. Quasi-Hegelian systems
• 4.6. Philosophical thinking and finite projective geometry
• 4.7. Other algebras for philosophical thinking
• 4.8. Models derived from geometry and algebraic geometry
• 4.9. Conclusion
• 5 Philosophical Transformations
• 5.1. The paradox of a metasystem
• 5.2. In search of an algebra
• 6 Concepts and Topology
• 6.1. Formal concepts
• 6.2. Fuzzy concepts
• 6.3. The case of philosophical concepts
• 7 The Problem of the Infinite
• 7.1. The arithmetic of infinite cardinals
• 7.2. The question of large cardinals
• 7.3. Woodin’s program
• 7.4. Infinite and philosophy
• 8 In Search for a New Philosophy
• 8.1. The finite case
• 8.2. The infinite case
• 9 Extension of Structuralism and Negative Theology
• 9.1. Complementarity graphs
• 9.2. Order relation, ordered set
• 9.3. Graphs associated with a partially ordered set
• 9.4. Complementarity and incomparability graphs of a poset
• 9.5. Boolean representation of a poset
• 9.6. Case of lattices
• 9.7. Consequences for negative theology
• 10 From Fuzzy Graphs to Neutrosophic Graphs
• 10.1. Fuzzy sets
• 10.2. Fuzzy graphs
• 10.3. Intuitionistic fuzzy set theory
• 10.4. Neutrosophy
• 10.5. Single-valued neutrosophic sets and graphs
• Conclusion: Graphs and Polyhedra of Ideas

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