Objectivity, Realism, and Proof

1. Mathematics in Philosophy, Philosophy in Mathematics: Three Case Studies
Stewart Shapiro

Part I. The Ways of Mathematical Objectivity: Semantics and Knowledge

2. Semantic Nominalism: How I Learned toStop Worrying and Love Universals
G. Aldo Antonelli

3. Discussion Note On: “Semantic Nominalism: How I Learned to Stop Worrying and Love Universals” by G. Aldo Antonelli
Robert C. May, Marco Panza

4. Semantic Assumptions in the Philosophy ofMathematics
Robert Knowles

5. The Modal Status of Contextually A Priori Arithmetical Truths
Markus Pantsar

6. Epistemology, Ontology and Application in Pincock’s Account
Marina Imocrante

Part II. Realism in a World of Sets: from Classes to the Hyperuniverse

7. Absolute Infinity in Class Theory and in Theology
Leon Horsten

8. Sets and Descent
Brice Halimi

9. True V or Not True V, That Is the Question
Gianluigi Oliveri

10. The Search for New Axioms in the Hyperuniverse Programme
Sy-David Friedman, Claudio Ternullo

11. Multiversism and Concepts of Set: How Much Relativism Is Acceptable?
Neil Barton

12. Forcing, Multiverse and Realism
Giorgio Venturi

Part III. The Logic Behind Mathematics: Proof, Truth, and Formal Analysis

13. What’s so Special About the Gödel Sentence mathcal {G}?
Mario Piazza, Gabriele Pulcini

14. More on Systems of Truth and Predicative Comprehension
Carlo Nicolai

15. A Critical Overview of the Most Recent Logics of Grounding
Francesca Poggiolesi

16. Computability, Finiteness and the Standard Model of Arithmetic
Massimiliano Carrara, Matteo Plebani, Enrico Martino

17. The Significance of a Categoricity Theorem for Formal Theories and Informal Beliefs
Samantha Pollock

Nyckelord: Philosophy, Philosophy of Science, Logic, Epistemology, Mathematical Logic and Foundations