Abstract

The issues treated in this book derive a certain degree of unification from their relation to the general theme of the completeness of scientific theories. Unfortunately, when a philosopher addresses himself to the question of the completeness of an empirical theory, it is far from clear at the outset just what the problem is. Schlegel, to be sure, explicates three different notions of completeness which may be relevant here: the logical, physical, and pragmatic aspects. By the first, Schlegel means the usual set of issues having to do with the deductive and semantic structure of formal theories, the second refers to "the problems that are to be answered in terms of what is discovered by science about the natural world," and the third refers to "the factors in the completeness of science that seem to be chiefly dependent on the interests of scientists." As these formulations suggest, the level of logical and philosophical rigor is hardly commensurate with the kind of investigation one would expect. An early chapter deals with an epistemology of physics in which a class of entities called "constructs" plays the central role. Unfortunately, it is never clear whether constructs denote objects, properties, facts, sentences, or something else. On the other hand, the materials in this chapter are largely irrelevant to the subsequent discussion. Schlegel does an admirable job of scientific exegesis on the present state of quantum physics and cosmology. With regard to the former, he is an advocate of the "Copenhagen view," and he argues that a sort of natural limit of description and explanation has been reached. As to cosmology, Schlegel looks forward to a narrowing of the range of alternate theories as more data become available. In the chapter on purely formal questions a number of oversights seem to have been committed. The exposition of Gödel's incompleteness theorem is inaccurate in that it is not shown that provability can be defined intra-systematically. Schlegel's discussion of how the theorem might apply to scientific theories is suggestive, but also confusing. The chapter on infinity treats the continuum hypothesis as a proven fact, thus ignoring the very important questions raised by the work of Paul Cohen and others. Finally, and most distressingly, the Hebrew letter aleph is printed upside down at all of its occurrences.--H. P. K.