Philosophy of Mathematics after Wittgenstein

Sorin Bangu is Professor of Philosophy at University of Bergen. He is the author of The Applicability of Mathematics in Science: Indispensability and Ontology (2012), and editor of Naturalizing Logico-Mathematical Knowledge: Approaches from Philosophy, Psychology and Cognitive Science (2018).

• Introduction: a disappearing act; 1. Wittgenstein's normativism about mathematics; 2. Normativism as eliminativism: three illustrations; 3. Basic mathematical rules (I): hardening; 4. Basic mathematical rules (II): objectivity, agreement, and skepticism; 5. Advanced rules: proofs and concept-formation; 6. Cantor's proof (I): a 'style of thinking'; 7. Cantor's proof (II): reluctant nonrevisionism; 8. Logicism, number and the infinite; 9. Conclusion: a cleared ground; Bibliography.

'In Philosophy of Mathematics after Wittgenstein, Sorin Bangu takes on the steep challenge of defending – both as a scholarly interpretation and as an independent philosophical position – Wittgenstein's radical claim that all traditional philosophical problems about mathematics can be dissolved or eliminated.  To an impressive degree, he succeeds in this, weaving a meticulous, closely argued, patiently defended story of how various tools of 'eliminative normativism' function in seven particular cases, ranging from 2+2=4 to Cantor's theorem.' Penelope Maddy, University of California, Irvine