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Mariam Thalos, Why is there Philosophy of Mathematics at all?, The Philosophical Quarterly, Volume 67, Issue 269, October 2017, Pages 857–860, https://doi.org/10.1093/pq/pqw061
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Ian Hacking is a gripping writer with an ear for wickedly good turns of phrase. The joyous playfulness of his language can arouse interest in any topic whatsoever. He is also a skilled philosophical conversationalist, who can put long-dead philosophers into dialogue with those still living, because he has his finger deftly positioned on the pulse of our discipline. His most recent book is on a topic that has bedevilled a good many philosophers in history, Hacking no less than anyone else. It concerns the place of mathematical reasoning and other mathematical activity in the economy of human thought, and in the natural world generally. On display in this book, page after page, is that bedevilment.
The book began as the René Descartes Lectures at Tilburg University in 2010, one of which was published as a stand-alone article in 2011 by the same title as the present book. After delivering the lectures, Hacking realized (as he puts it) ‘how much the material needed to mature’. But this book, rather than having the flavour of matured material, or even a less fermented lecture, has instead the character of remarks overhead in a month of Sundays in common rooms at Cambridge. Hacking says it is ‘a book of philosophical thoughts’ (p. xiii). But its structure suggests something more along the lines of an unintended philosophical memoir in the style of the later Wittgenstein's Notebooks, but with much more generous attention to the philosophical and mathematical ideas of other luminaries, living and dead, in both fields. However, while the engagement with work of others is both generous and pregnant, it does not serve the reader well. In this regard, this book is uncharacteristic of Ian Hacking's brand. A reader coming to the pages of this book with less exposure to mathematics (or for that matter philosophy) than Hacking's will be the victim of ‘a fine persecution—to be kept intrigued without ever quite being enlightened’ (Tom Stoppard, Rosencrantz and Guildenstern are Dead ). Time and again Hacking introduces provocative topics only to dismiss them as peripheral to his main objective, which itself is never entirely resolved for the reader. However scrupulous, that reader will come away simply with a sense of bedevilment with the subject of the book, rather than with an experience of having trod a well-defined passage through important thickets. Even someone astute enough not to expect answers to posed philosophical problems will be disappointed by the lack of connective tissues to the book, in spite of the copious signage and the abundance of titled sectioning (never entirely helpful).
