The Continuous and the Discrete: Ancient Physical Theories from a Contemporary Perspective (review)

BOOK REVIEWS 663 a general schematic view of Greek thought, starting naturally with Homer... and his opinions on the correctness of names, and moving on to other areas of Greek thought" (99). Thus from the etymologies relating to Homer and the nature Qf the gods, we move to those relating to the Presocratics and the nature of the elements and stars, and finally we reach those relating to the Sophists and the nature of the virtues. What is the purpose or purposes of the etymologies? Baxter disagrees with V. Goldschmidt, who held that Plato, in the etymological investigations, is aiming to expose a mistaken view (Heracliteanism) about reality pervading Greek culture and to publicly renounce the influence on him of his former teacher (Cratylus). His own answer stresses the aspect of parody in the etymologies as Plato's way of showing the lack of any seriousness in the Greek practice of etymologizing; and, in partial agreement with R. Brumbaugh, he argues that Plato's main purpose in etymologizing is to show that etymology is an unreliable tool in seeking knowledge about things. This last claim "is the major positive result from the etymological inquiry, and it is here that one should seek the unifying feature of the etymologies. This unifying feature is indeed the exposure of a culturewide error, not concerning flux, but rather language and its relationship to reality, an error which is set in the context of a schematic history of the development of Greek thought" (96). The section on etymologies represents "a full frontal attack by Plato on representative figures in Greek culture, poets, philosophers, 'philologists' and so on" (16o). Heraclitus and his followers are, according to Baxter, major figures in this tradition, with Cratylus being the worst of the lot (162). Hence a refutation of etymologizing as a way of gaining knowledge is an attack on the theory of naming of Cratylus and his method of arriving at the nature of things through that of their names. The final section of the dialogue, the refutation of Cratylus, thus presupposes, according to Baxter, the conclusions of the etymological discussion and is really a continuation of it. Baxter's conclusions regarding the purpose(s) of the discussion on etymologies in the Cratylus may not be acceptable to all. Yet he is quite judicious in discussing the evidence for his conclusions and is aware that his arguments "do not prove it [his interpretation] conclusively... " (162). His conclusions about Plato's mofives in devoting half of the dialogue to etymologies seem to me to have considerable plausibility, and perhaps this is the best one can do here. In addition, I find his detailed discussion of the etymologies quite valuable on its own; it sheds much light on a part of the Cratylusthat to most readers seems inconsequential. GEORGIOS ANAGNOSTOPOULOS Universityof California, San Diego Michael J. White. The Continuousand theDiscrete:Ancient PhysicalTheoriesfrom a ContemporaryPerspective .New York: Oxford University Press, t992. Pp. xiv + 345. Cloth, $72.oo. In a groundbreaking study White reexamines the foundations of Aristotle's conceptions of spatial magnitude, motion, and time, along with two alternative conceptions developed by the atomists and the Stoics. On the basis of a rigorous philosophical 664 JOURNAL OF THE HISTORY OF PHILOSOPHY 39:4 OCTOBER 1994 reading of the relevant texts from the perspective of contemporary mathematics, White offers a cogent, strikingly innovative, reinterpretation that not only sheds new light on a critical ancient philosophical problem, but also brings it into the arena of contemporary philosophical discourse. White's analysis of Aristode, based primarily on discussions in the Physics, drives home the thesis that Aristode held consistently and unremittingly to a strict conception of infinite divisibility, avoiding any concession to or anticipation of a modern set-theoretic ontology, which conceptualizes continuous magnitude as a dense and Dedekind-continuous linear ordering of discrete aaua/elements. Demonstrating that Aristotle's view was shared by Greek mathematicians before and after him, White argues that Aristode's canonization of it effectively prevented subsequent mathematicians from ever entertaining the idea of the sum of an infinite set, even though some (e.g., Archimedes) intuitively came close. Aristotle's grip was broken only in the late nineteenth century by...