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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 Second-Order 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 Santos-Sousa
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.
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 Second-Order 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 Santos-Sousa
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.