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Husserl and realism in logic and mathematics. (English) Zbl 0524.00015

Modern European Philosophy. Cambridge etc.: Cambridge University Press. xvii, 126 p. hbk: £17.50; $ 29.50; pbk: £5.95; $ 10.95 (1984).
Summary: This book is a thorough treatment of the issue of realism (Platonism) in logic and mathematics from the perspective of phenomenology. Despite the title, this is not a book about Husserl. This is an application of some of Husserl’s ideas to the philosophy of mathematics. However, the author does supply enough background so that readers unfamiliar with Husserl can follow the text. The final position advocated is a kind of middle ground between realism and subjectivism. While many have sought for this middle ground, the author’s advance is to employ phenomenology to show how this middle ground is not just desirable but is actually intelligible.
The text is clear and the examples are drawn from the more accessible parts of both mathematics and philosophy so this book should be of interest to many readers. This book is must reading for anyone interested in the philosophy of mathematics.
Reviewer: Anthony M. Coyne

MSC:

00A30 Philosophy of mathematics
03A05 Philosophical and critical aspects of logic and foundations
03-02 Research exposition (monographs, survey articles) pertaining to mathematical logic and foundations