Bernulf Kanitscheider.Natur und Zahl: Die Mathematisierbarkeit der Welt[Nature and Number: The Mathematizability of the World]. Berlin: Springer Verlag, 2013. ISBN: 978-3-642-37707-5 (hbk); 978-3-642-37708-2 (e-book). Pp. vii + 385

Abstract

The title of Bernulf Kanitscheider's Natur und Zahl has an even better ring in English: Nature and Number. The book is a wide-ranging discussion of the mathematical nature of the physical world. It takes the form of a sort of perambulation through history, beginning with the ancient Pythagorean philosophers, with stops along the way to note analogies or parallels in contemporary science, especially cosmology and astrophysics, Kanitscheider's area of specialization, in order to illustrate the viewpoints under discussion. Unfortunately, this procedure results in a rambling and unsystematic exploration of the issues and eventually breaks down in the later chapters, where Kanitscheider tends to desert the historical approach in favor of a more thematic discussion. The book presents itself as an exploration of the reason for the astonishing applicability (Anwendbarkeit) of mathematics in physics, a question neglected, according to Kanitscheider, in Germanic philosophy in contrast to anglophone philosophy (pp. 12–13). In fact, however, Kanitscheider treats this issue only tangentially in the book. The actual question with which he struggles is the compatibility of mathematics with naturalism. Kanitscheider is a committed naturalist, and he is acutely aware of the problems for his metaphysical worldview posed by mathematical truth (which he wants to affirm) and the underlying ontology of mathematical platonism (which he wants to avoid). Thus, the book's center of gravity is its longest chapter ‘Naturalism in the world of mathematics’.1