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  • Print publication year: 2008
  • Online publication date: November 2011

7 - The Existence of Mathematical Objects

from III - The Nature of Mathematical Objects and Mathematical Knowledge

Summary

From the Editors

Charles Chihara is the most senior of the philosophers contributing to this book. He appears to be genuinely interested in having his philosophy of mathematics be one that is acceptable to mathematicians. One would think that this is requisite; what is the point of a philosophy of X that people who work in X view as absurd? But there has not been much interaction between the two communities (mathematicians and philosophers of mathematics) in the last half century. As he notes in his chapter, Charles Chihara started out as a mathematician and has both a brother and a niece who are mathematicians. He thus has a better feel for what will make sense to a mathematician than do many philosophers of mathematics. His writings are normally quite accessible to mathematicians, and this one is especially so.

His chapter walks a rather delicate line. Since Chihara is a nominalist, he is not willing t commit to the existence of any mathematical objects, including structures. Yet it is important from his viewpoint that we do have mathematical knowledge. Chihara's solution is a sort of structuralism, but without a commitment to the existence of structures. It is a rather delicate balance, but it is certainly a thoughtful one.

Charles Chihara is an Emeritus Professor of Philosophy at the University of California, Berkeley (sophos.berkeley.edu/chihara/). Chihara has published nearly fifty articles in his principal areas of interest: philosophy of mathematics and philosophy of logic. He has also published widely in the philosophy of science and confirmation theory, as well as on the philosophies of Wittgenstein, Russell, Quine, Goodman and Davidson.