Intuitionistic proof versus classical truth : the role of Brouwer's creative subject in intuitionistic mathematics /: the role of Brouwer's creative subject in intuitionistic mathematics. ([2018])

• Record Type: Book
• Further Information: Note: Enrico Martino.
• Authors: Martino, Enrico
• Contents: Intro; Preface; Contents; 1 Brouwer, Dummett and the Bar Theorem; 1.1 Introduction; 1.2 Terminology and Symbolism; 1.3 Dummett's Argument; 1.4 Critique of Dummett's Argument; 1.5 Limits of the Eliminability of ζ-inferences; 1.6 Final Considerations; References; 2 Creative Subject and Bar Theorem; 2.1 The Creative Subject; 2.2 The Creative Subject and Existential Statements; 2.3 Equivalence of (PIE) and (BIM); References; 3 Natural Intuitionistic Semantics and Generalized Beth Semantics; 3.1 Introduction; 3.2 Generalized Beth-Models and Natural Models; 3.3 Generalized Natural Models 6 Classical and Intuitionistic Semantical Groundedness6.1 Introduction; 6.2 Construction of Model M; 6.3 Axiomatisation of T; 6.4 The Aczel -- Feferman Intensional Operator; References; 7 Brouwer's Equivalence Between Virtual and Inextensible Order; 7.1 Introduction; 7.2 Reconstruction of Brouwer's Paper of 1927; 7.3 Comment on Brouwer's Text; 7.4 How Brouwer Misinterpreted Himself; 7.5 A Minor Mistake in the Cambridge Lectures; 7.6 On Posy's Reconstruction; References; 8 An Intuitionistic Notion of Hypothetical Truth for Which Strong Completeness Intuitionistically Holds; 8.1 Introduction 8.2 Symbolism and Conventions8.3 The Failure of Strong Completeness for Natural Semantics; 8.4 Hypothetical Truth; 8.5 Remarks on Hypothetical Truth; 8.6 Generalized Beth Semantics; 8.7 Connection Between Hypothetical Semantics and GB-Semantics; 8.8 A Strong Completeness Proof for GB-Semantics; References; 9 Propositions and Judgements in Martin-Löf; 9.1 Introduction; 9.2 Propositions and Judgements; 9.3 Truth and Evidence; 9.4 Metaphysical Realism; References; 10 Negationless Intuitionism; 10.1 Natural Semantics; 10.2 Failure of Strong Completeness; 10.3 Second-Order Negationless Semantics 10.4 Concluding RemarksReferences; 11 Temporal and Atemporal Truth in Intuitionistic Mathematics; 11.1 Introduction; 11.2 Tenselessness and Classical Truth; 11.3 Potential Intuitionism as a Subsystem of Epistemic Mathematics; 11.4 Temporal Truth; References; 12 Arbitrary Reference in Mathematical Reasoning; 12.1 Introduction; 12.2 Some Objections to TAR; 12.3 TAR as Embodied in the Logical Concept of an Object; 12.4 The Ideal Agent; 12.5 Arbitrary Reference and Impredicativity; 12.6 Plural Reference Versus Sets; References; 13 The Priority of Arithmetical Truth over Arithmetical Provability
• Publisher Details: Cham, Switzerland : Springer
• Publication Date: 2018
• Extent: 1 online resource
• Subjects: 510.1; Philosophy; Intuitionistic mathematics; Brouwerian algebras; MATHEMATICS / Essays; MATHEMATICS / Pre-Calculus; MATHEMATICS / Reference; Brouwerian algebras; Intuitionistic mathematics; Mathematics -- Logic; Literary Criticism -- General; Philosophy -- Logic; Mathematical foundations; Literary reference works; Mathematical theory of computation; Philosophy: logic; Logic, Symbolic and mathematical; Philology; Computer science; Logic; Mathematics -- History & Philosophy; Philosophy of mathematics; Electronic books
• Languages: English
• ISBNs: 9783319743578; 3319743570
• Related ISBNs: 9783319743561; 3319743562
• Notes: Note: Includes bibliographical references and indexes.; Note: Vendor-supplied metadata.
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