Abstract

This is a book of wide-ranging scope, as the title suggests. First, it canvasses a broad selection of topics—from electromagnetism and quantum mechanics to Husserl’s phenomological constitution of logic, from Russell and Wittgenstein to Hartry Field. Second, its aims are broad. The author describes the book both as a “rational reconstruction of Poincaré’s position” and as a “treatise on modern epistemology”. The former description is somewhat misleading in that, together with Zahar’s stated aim of both “clarifying and of then reconciling Poincaré’s various theses about the foundations of mathematics and the natural sciences”, it might give the reader hope that all of these theses might be shown to be part of one unified position. In fact, though, Poincaré’s philosophy of physics and his philosophy of mathematics turn out to be fundamentally different. Zahar attributes to Poincaré a “structural realist” view of physics and a “quasi-Kantian” constructivist view of mathematics. It’s not entirely clear, though, why the considerations adduced in favor of structural realism in physics can’t be carried over to the case of mathematics. More might have been said to explain this divergence, perhaps for example by developing the contrast in the introduction between the empirical testability of scientific hypotheses and the intuitive self-evidence of mathematical theorems.