Respect for Nature: A Theory of Environmental Ethics

The reprinting of Hermann Weyl’s Philosophy of Mathematics and Natural Science in paperback offers scientists an opportunity to add this rare classic to their library. But any book reprinted sixty years after first appearing raises the question, “Why now?” Of course, the publisher may merely have seized upon an opportunity to sell books arising from the widespread if bizarre fascination with “0” year anniversaries and Weyl’s own fascination with “the mystery that clings to numbers” (7). Alternatively, the reprinting may be intended to inspire a new generation by appealing to nostalgia for great achievements or to provoke interest in questions “science has yet to catch up with” (ix), as suggested in the new Introduction by the Nobelist physicist Frank Wilczek (who coincidentally turned sixty in 2011). Weyl was “a philosophically-minded mathematician” (xvi) who believed that “science would perish without a supporting transcendental faith in truth and reality...facts... and the imagery of ideas” (xvi), and, at the same time, “the function of mathematics [is] to be at the service of the natural sciences” (61). Certainly Weyl’s concerns are not trivial, and he is at pains to describe how some of his predecessors in science reached “conclusions with stormy enthusiasm...(“Bruno had to pay for it at the stake)” (98). But Philosophy of Mathematics and Natural Science is not a monument to ideas. Indeed, it is a hodgepodge of ideas as Weyl admits: “This arrangement...[is] objectionable from the standpoint of esthetic unity” (xvi). Its two “historico-philosophical” (xvi) parts come from a 1926 article in German, highly embroidered with notes (now set off by brackets), occasional footnotes, and references. Part 1, Mathematics, is divided into chapters on Mathematical Logic (Axiomatics), Number and Continuum (the Infinite), and Geometry. Part 2, Natural Science, weighted toward physics, is divided into chapters on Space and Time (the Transcendental External World), Methodology, and The Physical Picture of the World. Inevitably, new computational methods have replaced Weyl’s mathematical formalism (arguments, assumptions, axioms...permutations, postulates, premises), and his physical constructivism (“the living metaphysical interpretation conforms to the theoretical construction” [149]). But Weyl shines in the six “systematic-scientific” (xvi) appendices added to the 1947 English translation. These appendices provide “the [raw material for the] development of mathematics and physics in the intervening years, as well as biology” (xvi).” In Appendix A, “The Structure of Mathematics,” Weyl raises the specter of biological species while referring to Gödel’s “strong plea for the realistic standpoint where classes are conceived as real objects” (234). In Appendix B Weyl applies “combinatorial theory of aggregates and of the mutually inverse operations of partition and union... [to] genetics...[where he correctly infers from] empirical evidence...[that] the distinction of nature and nurture...never becomes a perfectly sharp one” (240–41). The remaining appendices build from quantum theory to chemical bondage, biology, and evolution. Indeed, Philosophy of Mathematics and Natural Science is essential reading for anyone wishing to see pre-Watson/Crick biology à la 1947 lucidly portrayed in mathematical-physicalphilosophical terms.