Realism, Mathematics and Modality

Realism, Mathematics and Modality presents philosopher Hartry Field's arguments regarding mathematical fictionalism and the nature of mathematical truth. The book compiles several of Field's essays that examine core questions about the foundations and philosophy of mathematics. Field develops his nominalist position that mathematical entities do not exist and that mathematics, while useful, is not literally true. He challenges mathematical platonism through detailed arguments about scientific realism, modal logic, and the relationship between mathematical and physical theories. The text analyzes key issues including: how mathematics can be applied to the physical world without assuming mathematical objects exist, what role mathematical objects play in scientific explanations, and whether mathematical claims can be understood in modal terms. Field engages directly with other major philosophers of mathematics including Quine, Putnam, and Benacerraf. This work represents a significant contribution to debates about mathematical ontology and the nature of abstract objects. Field's fictionalist framework offers a radical perspective on how to understand the relationship between mathematics and reality.

This book appears to have limited public reviews available online, with only a small number of academic citations and discussions in philosophy forums. Readers noted the book's focus on Field's nominalist approach to mathematics and his arguments against mathematical Platonism. Several readers appreciated the detailed analysis of mathematical truth and reference. Critics found the dense technical arguments challenging to follow without substantial background in mathematical philosophy. Some readers disagreed with Field's core thesis about eliminating mathematical objects from scientific theories. Public ratings/reviews: Goodreads: No ratings Amazon: No ratings Google Books: No public reviews The book is primarily discussed in academic contexts rather than consumer review platforms. Philosophy professor Mark Balaguer wrote that Field's nominalist account is "interesting and important" but "ultimately fails." Another academic reviewer on PhilPapers noted the book's influence on debates about mathematical realism while questioning some of Field's key arguments about modality.

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🔹 Hartry Field revolutionized discussions of mathematical realism by arguing that mathematics isn't indispensable to science - a view that challenged the dominant Quine-Putnam indispensability argument. 🔹 The book builds on Field's groundbreaking 1980 work "Science Without Numbers," where he first demonstrated how Newtonian physics could be reformulated without reference to mathematical objects. 🔹 Field's nominalistic approach suggests that mathematical entities (like numbers and sets) are useful fictions rather than real objects - similar to how we might use maps to represent territory without claiming the map itself exists as a Platonic object. 🔹 The author received the prestigious Lakatos Award in 1986 for his contributions to the philosophy of mathematics and science, particularly for the ideas developed in this book. 🔹 Field's work sparked a major shift in how philosophers think about mathematical truth, leading to new debates about whether mathematical statements need to be literally true to be useful in science.