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Published online by Cambridge University Press: 13 April 2010
John Earman's new book, World Enough and Space-Time (WEST), is a brisk account of the controversy between space-time absolutists and relationists. The book is intended, one is told, to be “appropriate for use in an upper-level undergraduate or beginning graduate course in the philosophy of science” (p. xi), but Earman's no-holds-barred approach to the mathematics of space-time theories will have bludgeoned most philosophical readers, undergraduate or beyond, into submission long before it is revealed that Pirani and Williams “have studied the integrability conditions for Born-rigid motions in curved space-times and have shown that space-times of Petrov types II, III, and N do not admit of nonrotating Born-rigid motions” (p. 101). I say this sadly, because Earman's book is a discerning review of an important literature, and most of its main arguments can be grasped even if some technical details remain out of reach. The more you reach for those details, the more compelling the book will become.
1 As some guide to these efforts, let me suggest that Penrose, Roger (“The Geometry of the Universe”), in Steen, Lynn Arthur, ed., Mathematics Today: Twelve Informal Essays (Vintage Books, 1980)Google Scholar, gives a useful informal introduction to the concepts of differential geometry that are employed to make the crucial distinctions in WEST. Mathematics: Its Content, Methods, and Meaning, edited by Aleksandrov, A. D. et al. (Cambridge, MA: MIT Press, 1963)Google Scholar, provides superb introductions to several branches of mathematics. If you are innocent of calculus, for instance, the chapter, “Analysis,” will be essential. For the quirks of Minkowski space-time, see Mermin, N. David's Space and Time in Special Relativity (1968; rpt. Prospect Heights, IL: Waveland Press, 1989)Google Scholar, and for philosophical background plus an elegant explanation of the workings of space-time theories, see the first two chapters of Friedman, Michael's Foundations of Space-Time Theories (Princeton, NJ: Princeton University Press, 1983)Google Scholar.
2 Other relationist and absolutist themes are defined and discussed in WEST, but in this review I shall discuss only these two quintessential theses.
3 The argument first appeared in the Scholium to Newton's Principia. The Scholium is conveniently reprinted as an Appendix to Chapter 1 of WEST, and Earman's commentary on it in Chapter 1 is very helpful.
4 A classic statement of this line is to be found in Reichenbach's “The Theory of Motion according to Newton, Leibniz, and Huyghens,” reprinted in Modern Philosophy of Science, edited and translated by Reichenbach, M. (London: Routledge & Kegan Paul, 1959)Google Scholar.
5 Although Earman refers to differentiable manifolds throughout WEST, his precise characterization of them does not appear until the eighth of its nine chapters. Similarly, d * φ, the “dragged” geometric object field that plays an important role in several arguments, is not defined until footnote 6 in Chapter 8. Since the way is necessarily strewn with boulders, why throw extra pebbles underfoot?
6 The table on p. 36 of WEST, which summarizes these constructions, contains a sixth space-time, Aristotelian, but it is included more for the sake of completeness than utility. This table presents all that one needs to know of, and incidentally all that the nonspecialist could hope to glean from, the intricacies of Chapter 2.
7 An instrumentalist would assail this position from another quarter, but defence against that assault is not the aim of this book. “While I believe instrumentalism to be badly flawed,” writes Earman, “I do not intend to argue that here” (p. 166).
8 This may seem a naive way to talk about time in a relativistic context, but in order to avoid other ways in which determinism might fail (and thus increase the force of the Hole Argument) Earman assumes that the original model has a Cauchy surface, a space-like hypersurface intersected precisely once by every causal curve without endpoint, and that it therefore has a global time function. Incidentally, it will not be clear from this brief discussion why this argument is called the “Hole Argument.” See WEST, if you are curious.