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Mathematics and Reality

Mary Leng
Publisher: 
Oxford University Press
Publication Date: 
2014
Number of Pages: 
278
Format: 
Paperback
Price: 
35.00
ISBN: 
9780199674688
Category: 
Monograph
[Reviewed by
Herbert E. Kasube
, on
12/19/2014
]

This book addresses an interesting question in the philosophy of mathematics. Do mathematical objects such as numbers really exist? The author refers to this as an “ontological” question. Numerical symbols such as 2 are representations for this concept of “number” that people have used for centuries, but is there really such a thing as a “2”?

A comparison might be drawn with the history and use of zero. The “number” 0 has been used to represent a value, but in some numerical systems it is only a placeholder rather than a number.

Philosophical questions like this do not make for light reading. Nevertheless, this book will make you really think about what a number is, as opposed to its symbolic representation.


Herbert E. Kasube is Professor of Mathematics at Bradley University in Peoria, IL.

1. Introduction
2. Naturalism and Ontology
3. The Indispensability of Mathematics
4. Naturalism and Mathematical Practice
5. Naturalism and Scientific Practice
6. Naturalized Ontology
7. Mathematics and Make-Believe
8. Mathematical Fictionalism and Constructive Empiricism
9. Explaining the Success of Mathematics
10. Conclusion

Dummy View - NOT TO BE DELETED