The philosophers and mathematics : festschrift for Roshdi Rashed /: festschrift for Roshdi Rashed. ([2018])

• Record Type: Book
• Further Information: Note: Hassan Tahiri editor.
• Editors: Tahiri, Hassan
• Contents: Intro; Acknowledgements; About the book; Contents; Roshdi Rashed: His Research Career, Awards and Publications; Introduction: Interview with Roshdi Rashed by Hassan Tahiri; 1 Analogy and Invention Some Remarks on Poincaré's Analysis Situs Papers; 1.1 "L'inspection de La Figure Le Démontre"; 1.2 Invariants; 1.3 Poincaré's Sixth Example; 1.4 The Homology Sphere; References; 2 Scientific Philosophy and Philosophical Science; 2.1 Introduction; 2.2 Science Enters Its Critique Phase: Hilbert, Hessenberg, Nelson; 2.2.1 The Axiomatic Method and Intuition; 2.2.2 Critique of Reason and Proof Theory 2.2.3 Critical Mathematics of Gerhard Hessenberg and Leonard Nelson2.3 Philosophy as Rigorous Science: Husserl; 2.3.1 Need for Critique; 2.3.2 Radicalisation of Critique: From Scientific Explanation to Philosophical Understanding; 2.3.3 The Essence of Consciousness; 2.4 Systematic Philosophy: Jules Vuillemin; 2.4.1 The "Analogies of Mathematical Knowledge"; 2.4.2 Abstract Algebra and Systematic Philosophy; 2.4.3 Mathematical Reflexivity and Philosophical Reflexivity: What Is Critique?; 2.4.4 From Abstract Algebra to Metaphysics; 2.5 Conclusion; References; 3 Avicenna and Number Theory 3.1 Introduction3.2 Euclid and Nicomachus; 3.3 The Succession of Integers; 3.4 Odd and Even; 3.5 Perfect, Deficient and Abundant Numbers; 3.6 Congruencies; 3.7 Conclusion; References; 4 Zigzag and Fregean Arithmetic; 4.1 Introduction; 4.2 The Zigzag Theory; 4.3 First Commentary; 4.4 Finiteness and Reducibility; 4.5 Second Commentary; References; 5 The Foundations of Geometry by Peano's School and Some Epistemological Considerations; 5.1 Introduction; 5.2 The Axiomatic Foundations of Geometry; 5.3 The Fundamental Aspects of Geometrical Calculus; 5.4 Some Considerations; References 6 M104100101106 1621031011191091161141041161111061011321151161196.1 Philosophers as Mathematicians and Mathematicians as Philosophers; 6.2 David Hilbert as Philosopher; References; 7 Enthymemathical Proofs and Canonical Proofs in Euclid's Plane Geometry; 7.1 Introduction; 7.2 A Case Study: The Application of Postulate 1.2 in The Elements; 7.3 Enthymemathical and Canonical Arguments; 7.4 Rethoric and Mathematical Arguments: Beyond Euclid; References; 8 Some Reasons to Reopen the Question of the Foundations of Probability Theory Following Gian-Carlo Rota 8.1 The Problems on Probability Mathematicians Don't Want to Bringup8.1.1 The Desideratum of a Complete Formalization of Probability Theory; 8.1.2 Positing the Problem of a "Pointless" Probability in Lattice-Theory Terms; 8.1.3 Some Reasons Why Mathematicians Should Think More Highly of Lattices; 8.1.4 Formalization of Probability Through Lattices and Cryptomorphisms; 8.1.5 Other Problems, Which Should Be Posited and Could Be Solved Thanks to This Syntactical Clarification; 8.2 The General Formal Frame of Rota's Historical Perspectives
• Publisher Details: Cham, Switzerland : Springer
• Publication Date: 2018
• Copyright Date: 2018
• Extent: 1 online resource
• Subjects: 510.71; Philosophy; Mathematics -- Study and teaching; Mathematics -- Philosophy; MATHEMATICS / Essays; MATHEMATICS / Pre-Calculus; MATHEMATICS / Reference; Mathematics -- Philosophy; Mathematics -- Study and teaching; Mathematics -- History & Philosophy; Mathematics -- Logic; History of mathematics; Mathematical foundations; Logic, Symbolic and mathematical; Philosophy of mathematics; Electronic books
• Languages: English
• ISBNs: 9783319937335; 3319937332
• Related ISBNs: 9783319937328; 3319937324
• Notes: Note: Includes bibliographical references and indexes.; Note: Vendor-supplied metadata.
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.