The Resource Objectivity, Realism, and Proof : FilMat Studies in the Philosophy of Mathematics, (electronic book)
Objectivity, Realism, and Proof : FilMat Studies in the Philosophy of Mathematics, (electronic book)
Resource Information
The item Objectivity, Realism, and Proof : FilMat Studies in the Philosophy of Mathematics, (electronic book) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Liverpool.This item is available to borrow from 1 library branch.
Resource Information
The item Objectivity, Realism, and Proof : FilMat Studies in the Philosophy of Mathematics, (electronic book) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Liverpool.
This item is available to borrow from 1 library branch.
 Summary
 This volume covers a wide range of topics in the most recent debates in the philosophy of mathematics, and is dedicated to how semantic, epistemological, ontological and logical issues interact in the attempt to give a satisfactory picture of mathematical knowledge. The essays collected here explore the semantic and epistemic problems raised by different kinds of mathematical objects, by their characterization in terms of axiomatic theories, and by the objectivity of both pure and applied mathematics. They investigate controversial aspects of contemporary theories such as neologicist abstractionism, structuralism, or multiversism about sets, by discussing different conceptions of mathematical realism and rival relativistic views on the mathematical universe. They consider fundamental philosophical notions such as set, cardinal number, truth, ground, finiteness and infinity, examining how their informal conceptions can best be captured in formal theories. The philosophy of mathematics is an extremely lively field of inquiry, with extensive reaches in disciplines such as logic and philosophy of logic, semantics, ontology, epistemology, cognitive sciences, as well as history and philosophy of mathematics and science. By bringing together wellknown scholars and younger researchers, the essays in this collection  prompted by the meetings of the Italian Network for the Philosophy of Mathematics (FilMat)  show how much valuable research is currently being pursued in this area, and how many roads ahead are still open for promising solutions to longstanding philosophical concerns. Promoted by the Italian Network for the Philosophy of Mathematics  FilMat
 Language
 eng
 Extent
 1 online resource.
 Contents

 SECTION I: MATHEMATICAL OBJECTS AND AXIOMATIZATION
 PART I: THE VARIETIES OF MATHEMATICAL OBJECTS
 Chapter 1: Semantic Nominalism: How I learned to Stop Worrying and Love Universals; Aldo Antonelli
 Chapter 2: Modality, Abstract Structures and SecondOrder Logic; Robert Black
 Chapter 3: Category Theory and Set Theory: Algebraic Set Theory as an Example of their Interaction; Brice Halimi
 PART II: AXIOMS AND SET THEORY
 Chapter 4: Absolute Infinity; Leon Horsten
 Chapter 5: Forcing, multiverse and realism; Giorgio Venturi
 Chapter 6: True V or not True V, that is the Question; Gianluigi Oliveri
 SECTION II: REFERENCE AND EPISTEMOLOGY
 PART III: THE PROBLEM OF REFERENCE
 Chapter 7: Numbering Planets and Equating Facts; Robert Knowles
 Chapter 8: Multiversism and the Problem of Reference: How much Relativism is Acceptable? Neil Barton
 PART IV: MATHEMATICAL EPISTEMOLOGY AND COGNITION
 Chapter 9: The modal status of arithmetical truths in a contextual a priori framework; Markus Pantsar
 Chapter 10: Epistemology, Ontology and Application in Pincock's Account: A Weak Link? Marina Imocrante
 Chapter 11: Bootstrapping Rebooted; Mario SantosSousa
 SECTION III: FORMAL THEORIES AND THEIR PHILOSOPHY
 PART V: TRUTH AND FORMAL THEORIES
 Chapter 12: Incompleteness and the Flow of Truth; Mario Piazza
 Chapter 13: Notes on Axiomatic Truth and Predicative Comprehension; Carlo Nicolai
 PART VI: INFORMAL NOTIONS AND FORMAL ANALYSIS
 Chapter 14: Logic of Grounding: An Alternative Approach; Francesca Poggiolesi
 Chapter 15: Computability, Finiteness and the Standard Model of Arithmetic; Massimiliano Carrara and Enrico Martino and Matteo Plebani
 Chapter 16: The Significance of Categoricity for Formal Theories and Informal Beliefs; Samantha Pollock
 Isbn
 9783319316420
 Label
 Objectivity, Realism, and Proof : FilMat Studies in the Philosophy of Mathematics
 Title
 Objectivity, Realism, and Proof : FilMat Studies in the Philosophy of Mathematics
 Language
 eng
 Summary
 This volume covers a wide range of topics in the most recent debates in the philosophy of mathematics, and is dedicated to how semantic, epistemological, ontological and logical issues interact in the attempt to give a satisfactory picture of mathematical knowledge. The essays collected here explore the semantic and epistemic problems raised by different kinds of mathematical objects, by their characterization in terms of axiomatic theories, and by the objectivity of both pure and applied mathematics. They investigate controversial aspects of contemporary theories such as neologicist abstractionism, structuralism, or multiversism about sets, by discussing different conceptions of mathematical realism and rival relativistic views on the mathematical universe. They consider fundamental philosophical notions such as set, cardinal number, truth, ground, finiteness and infinity, examining how their informal conceptions can best be captured in formal theories. The philosophy of mathematics is an extremely lively field of inquiry, with extensive reaches in disciplines such as logic and philosophy of logic, semantics, ontology, epistemology, cognitive sciences, as well as history and philosophy of mathematics and science. By bringing together wellknown scholars and younger researchers, the essays in this collection  prompted by the meetings of the Italian Network for the Philosophy of Mathematics (FilMat)  show how much valuable research is currently being pursued in this area, and how many roads ahead are still open for promising solutions to longstanding philosophical concerns. Promoted by the Italian Network for the Philosophy of Mathematics  FilMat
 Cataloging source
 YDX
 http://library.link/vocab/creatorName
 Boccuni, Francesca
 Dewey number
 100
 Index
 no index present
 LC call number
 B15802
 Literary form
 non fiction
 Nature of contents
 dictionaries
 http://library.link/vocab/relatedWorkOrContributorName
 Sereni, Ana
 http://library.link/vocab/subjectName

 Philosophy
 Knowledge, Theory of
 Logic
 Philosophy and science
 Logic, Symbolic and mathematical
 Label
 Objectivity, Realism, and Proof : FilMat Studies in the Philosophy of Mathematics, (electronic book)
 Antecedent source
 unknown
 Carrier category
 online resource
 Carrier MARC source
 rdacarrier
 Color
 multicolored
 Content category
 text
 Content type code
 txt
 Content type MARC source
 rdacontent
 Contents
 SECTION I: MATHEMATICAL OBJECTS AND AXIOMATIZATION  PART I: THE VARIETIES OF MATHEMATICAL OBJECTS  Chapter 1: Semantic Nominalism: How I learned to Stop Worrying and Love Universals; Aldo Antonelli  Chapter 2: Modality, Abstract Structures and SecondOrder Logic; Robert Black  Chapter 3: Category Theory and Set Theory: Algebraic Set Theory as an Example of their Interaction; Brice Halimi  PART II: AXIOMS AND SET THEORY  Chapter 4: Absolute Infinity; Leon Horsten  Chapter 5: Forcing, multiverse and realism; Giorgio Venturi  Chapter 6: True V or not True V, that is the Question; Gianluigi Oliveri  SECTION II: REFERENCE AND EPISTEMOLOGY  PART III: THE PROBLEM OF REFERENCE  Chapter 7: Numbering Planets and Equating Facts; Robert Knowles  Chapter 8: Multiversism and the Problem of Reference: How much Relativism is Acceptable? Neil Barton  PART IV: MATHEMATICAL EPISTEMOLOGY AND COGNITION  Chapter 9: The modal status of arithmetical truths in a contextual a priori framework; Markus Pantsar  Chapter 10: Epistemology, Ontology and Application in Pincock's Account: A Weak Link? Marina Imocrante  Chapter 11: Bootstrapping Rebooted; Mario SantosSousa  SECTION III: FORMAL THEORIES AND THEIR PHILOSOPHY  PART V: TRUTH AND FORMAL THEORIES  Chapter 12: Incompleteness and the Flow of Truth; Mario Piazza  Chapter 13: Notes on Axiomatic Truth and Predicative Comprehension; Carlo Nicolai  PART VI: INFORMAL NOTIONS AND FORMAL ANALYSIS  Chapter 14: Logic of Grounding: An Alternative Approach; Francesca Poggiolesi  Chapter 15: Computability, Finiteness and the Standard Model of Arithmetic; Massimiliano Carrara and Enrico Martino and Matteo Plebani  Chapter 16: The Significance of Categoricity for Formal Theories and Informal Beliefs; Samantha Pollock
 Control code
 SPR957612103
 Dimensions
 unknown
 Extent
 1 online resource.
 File format
 unknown
 Form of item
 online
 Isbn
 9783319316420
 Level of compression
 unknown
 Media category
 computer
 Media MARC source
 rdamedia
 Quality assurance targets
 not applicable
 Reformatting quality
 unknown
 Sound
 unknown sound
 Specific material designation
 remote
 Label
 Objectivity, Realism, and Proof : FilMat Studies in the Philosophy of Mathematics, (electronic book)
 Antecedent source
 unknown
 Carrier category
 online resource
 Carrier MARC source
 rdacarrier
 Color
 multicolored
 Content category
 text
 Content type code
 txt
 Content type MARC source
 rdacontent
 Contents
 SECTION I: MATHEMATICAL OBJECTS AND AXIOMATIZATION  PART I: THE VARIETIES OF MATHEMATICAL OBJECTS  Chapter 1: Semantic Nominalism: How I learned to Stop Worrying and Love Universals; Aldo Antonelli  Chapter 2: Modality, Abstract Structures and SecondOrder Logic; Robert Black  Chapter 3: Category Theory and Set Theory: Algebraic Set Theory as an Example of their Interaction; Brice Halimi  PART II: AXIOMS AND SET THEORY  Chapter 4: Absolute Infinity; Leon Horsten  Chapter 5: Forcing, multiverse and realism; Giorgio Venturi  Chapter 6: True V or not True V, that is the Question; Gianluigi Oliveri  SECTION II: REFERENCE AND EPISTEMOLOGY  PART III: THE PROBLEM OF REFERENCE  Chapter 7: Numbering Planets and Equating Facts; Robert Knowles  Chapter 8: Multiversism and the Problem of Reference: How much Relativism is Acceptable? Neil Barton  PART IV: MATHEMATICAL EPISTEMOLOGY AND COGNITION  Chapter 9: The modal status of arithmetical truths in a contextual a priori framework; Markus Pantsar  Chapter 10: Epistemology, Ontology and Application in Pincock's Account: A Weak Link? Marina Imocrante  Chapter 11: Bootstrapping Rebooted; Mario SantosSousa  SECTION III: FORMAL THEORIES AND THEIR PHILOSOPHY  PART V: TRUTH AND FORMAL THEORIES  Chapter 12: Incompleteness and the Flow of Truth; Mario Piazza  Chapter 13: Notes on Axiomatic Truth and Predicative Comprehension; Carlo Nicolai  PART VI: INFORMAL NOTIONS AND FORMAL ANALYSIS  Chapter 14: Logic of Grounding: An Alternative Approach; Francesca Poggiolesi  Chapter 15: Computability, Finiteness and the Standard Model of Arithmetic; Massimiliano Carrara and Enrico Martino and Matteo Plebani  Chapter 16: The Significance of Categoricity for Formal Theories and Informal Beliefs; Samantha Pollock
 Control code
 SPR957612103
 Dimensions
 unknown
 Extent
 1 online resource.
 File format
 unknown
 Form of item
 online
 Isbn
 9783319316420
 Level of compression
 unknown
 Media category
 computer
 Media MARC source
 rdamedia
 Quality assurance targets
 not applicable
 Reformatting quality
 unknown
 Sound
 unknown sound
 Specific material designation
 remote
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