Matter and Infinity in the Presocratic Schools and Plato (review)

Book Reviews Matter and Infinity in the Presocratic Schools and Plato. By Theo Gerard Sinnige. (Assen: Van Gorcum; New York: Humanities Press, 1968. Pp. 252. $8.25) Dr. Sinnige appends to his book an impressive bibliography of three hundred and thirty-odd items, nearly a quarter of which refersto books and article.spublished since 1960. One could perhaps be justifiedin expecting to find in such a book a coming to grips with a wide range of opinions, old and new, concerning the problem of the relation between the concepts of matter and infinity till Plato, in its mathematical, physical, epistemological, 'and metaphysical aspects. Unfortunately, this seems not to be the case. The author tries to trace, rather schematically, the historical development of the concept of ~tt,~ov. There were, at first, two (almost neatly distinguished) concepts of apeiron: the Ionian apeiron as tactile matter, a conception to be traced back to the all-embracing chronos of early mythology; and the Pythagorean apeiron as spatial infinity ("the concept of measurable field"). "After Parmenides the term ~ttpov definitely becomes ambiguous, because it preserves traces of both conceptions, divine unboundedness in positive sense, and undetermined principle in the negative sense of being devoid of all qualities" (p. 27). Plato was influenced by both trends, although his use of the term "apeiron"--so the author would have it--is exclusively mathematical and Pythagorean. This tendency to departmentalism is especially felt in what the author considers to be his own contribution to the study of the problem: his treatment of Zeno and Democritus. According to Sinnige, Zeno's paradoxes were not intended to prove that movement is unreal or that the senses are not to be trusted. Such an intention "is in itself incredible if we take into account the mathematical and sober character of Zeno's thought" (p. 100). Demonstrations to the end of proving the unreliability of sense perception would befit the sophists, not Zeno, "a philosopher who was well informed about the latest developments in the field of mathematics, and who first of all tried to make explicit what was implicit in the presuppositions, in order to obtain a better definition of the concepts used in them" (p. 92). It is true that Zeno's chief contribution to philosophical thought seems to be the development of a particular method of reasoning. This method is the method of the second part of the Parmenides, as Sinnige reminds us: "What method shall we have to follow in our exercises? This very method you heard Zeno make use of" (135d). "Now,'' says our author, "the paradoxes which follow in Plato's dialogue are all aimed at testing the presuppositions by seeing what consequences are derived from them. We must conclude from this that in the same way Zeno's paradoxes had been meant as experiments, in which the soundness of the starting-point was to be judged by the consequences following from it. This means that Zeno's paradoxes were intended as axiomatic tests..." (p. 93). As to Zeno's method, it seems to me that Sinnige is right to a great extent. But the fact that Zeno's method was the method of axiomatic testing does not turn the whole issue into a mere "experiment," neither does it preclude the paradoxes from having a definite non-mathematical aim, such as discrediting sense [92] BOOK REVIEWS 93 perception. In the words immediately following the lines from the Parmenides quoted by the author, Plato states the differences between his "exercise" and Zeno's. The first of them is: 9 . . With this exception: There was one thing you said to him which impressed me very much: you would not allow the survey to be confined to visible things or tO range only over that field; it was to extend to those objects which" are specially apprehended by discourse and can be regarded as Forms. Yes, because in that other field there seems to be no difficulty about showing that things are both like and unlike and have any other character you please. (135d ft., tr. Comford) Plato's Parmenides aimed at showing the difficulties inherent to the theory of ideas, and even--as far as this dialogue...