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| Numbers may be abstract concepts, but the figures in our bank accounts and the digits on our clocks are real enough for most of us |
The
reality (or lack thereof) of numbers is the kind of problem some
philosophers consider overwhelmingly important, but it’s of no
consequence to just about everyone else. It does not make a wink of
difference to your life whether the figures in your bank account or the
digits on your clock are, in a philosophical sense, really real, so long
as they work as expected. The mathematician Paolo Zellini’s book, now
translated by Simon Carnell and Erica Segre from the 2016 Italian
original, does not exactly elevate the number-reality problem to a
matter of concern to non-philosophers, and certainly does not explain
the problem in a way that will make it tractable to them. But Zellini
does offer a creative shift in perspective that challenges certain
philosophers and philosophy-minded mathematicians to see the problem
differently.
Where one might expect numbers to get their reality from the things they enumerate — canonically, two apples come before the number two — Zellini argues that this gets the story backward. Rather, the most philosophically significant examples of enumeration from ancient to modern times used numbers to give reality to the things they enumerated. He reaches this conclusion by setting to one side the bulk of historical enumeration and focusing on philosophical texts about divine and natural existence. Sure enough, in these texts numbers appear to be the source of reality, often by way of a divine agency or inspiration: hence the titular ‘mathematics of the Gods’.
The book’s second intervention, about the ‘algorithms of men’, connects 19th- and early 20th-century debates about how to define what numbers really are to subsequent developments in the theory of computing and computability...
Concluding with a reference to populations, economics and nuclear fission, Zellini recognises that the power of numbers to make realities is not just some philosophical contrivance but a defining feature of the modern condition with a history reaching back to antiquity. To appreciate this vital history and its implications, however, most readers will be better off looking elsewhere.
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Recommended Reading
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| The Mathematics of the Gods and the Algorithms of Men: A Cultural History |
Source: Spectator.co.uk
