Objectivity, Realism, and Proof

FilMat Studies in the Philosophy of Mathematics

Editors:

ISBN: 978-3-319-31642-0 (Print) 978-3-319-31644-4 (Online)

Table of contents (17 chapters)

  1. Front Matter

    Pages i-xl

  2. No Access

    Chapter

    Pages 1-9

    Mathematics in Philosophy, Philosophy in Mathematics: Three Case Studies

  3. The Ways of Mathematical Objectivity: Semantics and Knowledge

    1. Front Matter

      Pages 11-11

    2. No Access

      Chapter

      Pages 13-32

      Semantic Nominalism: How I Learned to Stop Worrying and Love Universals

    3. No Access

      Chapter

      Pages 33-41

      Discussion Note On: “Semantic Nominalism: How I Learned to Stop Worrying and Love Universals” by G. Aldo Antonelli

    4. No Access

      Chapter

      Pages 43-65

      Semantic Assumptions in the Philosophy of Mathematics

    5. No Access

      Chapter

      Pages 67-79

      The Modal Status of Contextually A Priori Arithmetical Truths

    6. No Access

      Chapter

      Pages 81-99

      Epistemology, Ontology and Application in Pincock’s Account

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

    1. Front Matter

      Pages 101-101

    2. No Access

      Chapter

      Pages 103-122

      Absolute Infinity in Class Theory and in Theology

    3. No Access

      Chapter

      Pages 123-142

      Sets and Descent

    4. No Access

      Chapter

      Pages 143-164

      True V or Not True V, That Is the Question

    5. No Access

      Chapter

      Pages 165-188

      The Search for New Axioms in the Hyperuniverse Programme

    6. No Access

      Chapter

      Pages 189-209

      Multiversism and Concepts of Set: How Much Relativism Is Acceptable?

    7. No Access

      Chapter

      Pages 211-241

      Forcing, Multiverse and Realism

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

    1. Front Matter

      Pages 243-243

    2. No Access

      Chapter

      Pages 245-263

      What’s so Special About the Gödel Sentence \(\mathcal {G}\) ?

    3. No Access

      Chapter

      Pages 265-290

      More on Systems of Truth and Predicative Comprehension

    4. No Access

      Chapter

      Pages 291-309

      A Critical Overview of the Most Recent Logics of Grounding

    5. No Access

      Chapter

      Pages 311-318

      Computability, Finiteness and the Standard Model of Arithmetic

    6. No Access

      Chapter

      Pages 319-344

      The Significance of a Categoricity Theorem for Formal Theories and Informal Beliefs