Objectivity, Realism, and Proof: FilMat Studies in the Philosophy of Mathematics

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.