Truth, existence and explanation : FilMat 2016 studies in the philosophy of mathematics /: FilMat 2016 studies in the philosophy of mathematics. (2018)

• Record Type: Book
• Further Information: Note: Mario Piazza, Gabriele Pulcini, editors.
• Editors: (Philosopher), Piazza, Mario; Pulcini, Gabriele
• Contents: 2.2 Penrose's New Argument2.3 Truth and Intensional Paradox; 2.3.1 Penrose's New Argument Reconsidered; 2.3.2 Penrose's New Argument and Simplistic Typing; 2.4 Global Reflection and the First Disjunct; 2.4.1 A New Argument Against Mechanism; 2.5 Conclusion; Appendix; References; 3 On Expressive Power Over Arithmetic; 3.1 Introduction; 3.2 Bearers of Modal Ascriptions and the Three Case Studies; 3.3 Deductive Strength; 3.4 Conceptual Reducibility; 3.5 Instrumentalism; 3.6 A Dilemma?; References; 4 Intensionality in Mathematics; 4.1 Which Sentence of PA Says that PA Is Inconsistent? 4.2 Possible Worlds4.3 Consequence and Meaning; 4.4 Back to Frege; 4.5 Intension as ``Robustness''; 4.6 Conclusion; References; 5 Deflationary Truth Is a Logical Notion; 5.1 Deflationism and the Logicality Thesis; 5.1.1 Logicality as Invariance; 5.1.2 How Can Truth Be Logical?; 5.2 From Invariance to Logic and Back; 5.2.1 Similarity Relations, Invariance and Logics; 5.2.2 Closure Under Definability and Generated Logics; 5.3 A Framework for Deflationary Truth; 5.4 Truth as a Logical Notion; 5.4.1 Truth Completeness and Closure Under Definability; 5.4.2 Interpreting the Result 5.5 Expressive Power of the Truth Predicate or Proof-Theoretic Strength of Truth Theories?5.6 Conclusion; Appendix: Proofs; References; 6 Making Sense of Deflationism from a Formal Perspective: Conservativity and Relative Interpretability; 6.1 The Simplicity of Truth; 6.2 The Concept and the Property of Truth; 6.3 Conservativities; 6.4 Semantic Conservativity and Metaphysical Robustness; 6.5 Proof Theoretic Conservativity and the Concept of Truth; 6.6 Relative Interpretation; 6.7 Proof Theoretic Reduction and Speed Up; 6.8 A Philosophical Classification of Formal Truth Theories 6.9 ConclusionReferences; Part II Structures, Existence, and Explanation; 7 Structure and Structures; 7.1 Structure; Tiling a Mutilated Board; Elliptic Orbits; 7.2 Structures; 7.3 Structure in Structures; 7.3.1 Constitutive Structure; 7.3.2 First-Order Structure; 7.3.3 Primitive Structure; 7.3.4 Some Consequences; 7.3.5 More Structure?; 7.3.5.1 Fast Growing Functions; 7.3.5.2 Second-Order Definability; 7.3.6 Less Structure?; 7.3.6.1 Intuitionisms; 7.3.6.2 Quantifier-Free Theories; 7.4 Abstract Structures; 7.5 Conclusion; References
• Publisher Details: Cham : Springer
• Publication Date: 2018
• Extent: 1 online resource
• Subjects: 510.1; Philosophy; Mathematics -- Philosophy; Logic, Symbolic and mathematical; MATHEMATICS / Essays; MATHEMATICS / Pre-Calculus; MATHEMATICS / Reference; Philosophy -- Logic; Philosophy -- Epistemology; Mathematics -- Logic; Philosophy: logic; Philosophy: epistemology & theory of knowledge; Mathematical theory of computation; Logic; Genetic epistemology; Computer science; Mathematics -- History & Philosophy; Philosophy of mathematics; Electronic books
• Languages: English
• ISBNs: 9783319933429; 3319933426
• Related ISBNs: 9783319933412
• Notes: Note: Includes bibliographical references.; Note: Online resource; title from PDF title page (EBSCO, viewed October 29, 2018)
• 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.