Summary: William Tait. The provenance of pure reason: essays in the phi-
losophy of mathematics and its history. Oxford University Press, Oxford,
2005 x + 332 pp.
Plato has a bad reputation these days: the word "Platonism" is usually ac-
companied by the word "naive," and the notion that mathematical discourse
has meaning in virtue of reference to nonspacial, atemporal objects is judged to
be convenient but ultimately untenable. Moreover, the views of mathematics
that currently dominate the analytic tradition are variants of Quinean empiri-
cism, a position that is more closely linked to that of Plato's rival, Aristotle.
On such views, mathematical claims depend on experience for justification in
an indirect but continuous manner.
The problem with this picture is that it fails to account for the distinct
character of mathematics vis-`a-vis the empirical sciences. Quine's arguments
that there is no sharp distinction between analytic and synthetic knowledge
does not absolve us of the philosophical task of making sense of methodological
differences that are glaringly salient in practice. It is therefore encouraging to
read a collection of essays that is based on a conception of mathematics that is
more faithful to the subject.
At the risk of oversimplifying, Tait's central views can be summarized as
follows. First, the only viable foundation for mathematics is that afforded by