Abstract

Chihara introduces this book as a response to critics of his last book, which gave an account of mathematical objects in terms of possible constructions of open sentences. Several reviewers charged him with exchanging an ontology of platonistic mathematical objects for an equally extravagant ontology of possible entities. In this book Chihara replies with an extended account how one can use modal logic, and even the notions of possible worlds semantics, without accepting merely possible worlds or objects. A final chapter extends his anti-platonist arguments about philosophy of mathematics, directed primarily against Penelope Maddy and the “Indispensibility” argument associated with Quine and Putnam.