Various laws and theories in the natural and social sciences are presented with a view to discerning the syntactic and semantic characteristics of many idealizations in science. Three different kinds of idealizations are discussed: ideal conditions, ideal cases, and idealized theories. An ideal condition is a formula in which state variables occur, whose existential closure is false, and for which there is another formula that can be constructed out of the original formula such that the existential closure of the new formula is true. An ideal case is a statement which is logically equivalent to a universal conditional which has an ideal condition as its antecedent. And an idealized theory is a set of false universal conditional statements. Alternative syntactic and semantic analyses are viewed and criticized.

Once upon a time the well-known paradoxes of quantum mechanics (one might even say the “traditional” paradoxes of quantum mechanics!—I refer here to paradoxes such as the Schrödinger cat and the Einstein-Podolsky-Rosen Paradox) seemed especially difficult because of the rather bizarre behavior of the wave packet under the von Neumann theory of measurement, to which behavior these paradoxical situations seemed to draw especial attention. Quite recently quantum theoretical accounts of the measurement process have been appearing which sidestep direct reference to such things as “contraction” of the wave packet (see, for example, Krips and Jauch). With this development it has become increasingly popular to take a “cool” approach to these paradoxes, arguing that the new approach to measurement provides a consistent, nonbizarre account of the physical situations and that the paradoxicality was due largely to intuitive blunders—even plausible intuitive blunders—accentuated (but also disguised) by the unfortunate features of the von Neumann approach to measurement. Both Krips and Jauch, for example, adopt this approach.

Although the introduction of the modern axiomatic method in physics is attributed to Hilbert, it is only recently that physicists and mathematicians have applied it significantly, i.e. on a basis extensive enough to promise fruitful results. Carnap, for one, stresses the importance of the axiomatic method, yet he considers its application in physics as a task for the future.

In order to confirm any statement of the form (a) A are B we consider a sufficiently large number of A in order to check them for having or failing to have property B. But logic leads us to believe that A are B is equivalent to (b) non-B are non-A. If this is so then it seems reasonable to suppose that we confirm (a) and (b) in the same way. Whatever set of things we consider for confirming one must be the same set that we consider for the other. Yet in confirming (a) the set considered seems to be the set of A, while in confirming (b) the set considered seems to be the set of non-B. How can two logically equivalent statements be confirmable in different ways?

This book is in the tradition that defines the philosophical center of contemporary philosophy of science, the tradition of Carnap, Hempel, and Nagel as supplemented by generous additions from Austin and an Oxfordized Wittgenstein in the style introduced by N. R. Hanson. This tradition has been criticized both from the philosophical left, by Sellars, and from the philosophical right, by Bergmann. Achinstein's work is so squarely in the center that neither Sellars nor Bergmann ever appear in the index. That makes the book the third or fourth generation of a series in that central tradition all of which have been concerned largely with discussing their predecessors in that same tradition. This series is now producing books—Achinstein's is one of them—that have the virtues and the defects of an ingrown aristocracy: finely shaped features; an aloofness with respect to which no doubt is felt that it is justified ; and in their quarrels among themselves the cunning of foxes; but with none of the robust life and vitality of lions that first secured them the right to rule.