This volume is a paperback reprint with corrections of the original book which appeared in 1990. The central theme of the book is the delineation and defence of a version of realism in mathematics called ‘set theoretic realism’.
From Quine/Putnam Platonism this view takes the indispensability arguments to support the approximate truth of classical mathematics. From Gödel Platonism this view accepts the two-tiered analysis of mathematical justification. By way of compromise between these two positions, set theoretic realism is offered as a scientifically feasible middle ground between the empiricism of Quine/Putnam and the intuition of Gödel. Set theoretic realism admits sets of physical objects to the physical world where they can become subjects of perceptual numerical beliefs. Maddy claims that set theoretic realism avoids either trivializing mathematics as convention and formal on the one hand or glamorizing it as perfect, a priori, and certain on the other. The goal in a naturalized mathematics which shows mathematics to be science.
The book is accessible to both mathematicians and philosophers. The references are extensive and most issues are presented with an historical background. This is a groundbreaking work in the philosophy of mathematics which incorporates or responds to many major works on the 20th century.