According to Hempel, all scientific explanations and predictions which are produced exclusively with deterministic laws must be deductive, in the sense that the explanandum or the prediction must be a logical consequence of the laws and the initial (and boundary) conditions in the explanans. This deducibility thesis (DT) has been attacked from several quarters. Some time ago Canfield and Lehrer presented a “refutation” of DT as applied to predictions, in which they tried to prove that “if the deductive reconstruction [DT for predictions] were an adequate reconstruction, then scientific prediction would be impossible” ([2], p. 204). Their argument seems to have been uncontested except for an inconclusive rejoinder by Beard (cf. [1]). Moreover, Stegmüller has recently argued that “it may turn out that all or at least most of the so-called deductive-nomological explanations are in truth inductive and not deductive arguments, in view of the difficulty which has been pointed out by Canfield and Lehrer” ([3], p. 7). It seems it would be worth investigating whether Canfield and Lehrer's argument is, indeed, correct.

The recent extension of quantum theory to sound waves in solids is briefly outlined and then discussed from a specific philosophic (Kantian) perspective.

Abner Shimony called it coherence; John Kemeny called it strict fairness; today many people speak of strict coherence. According to Shimony's definition, a set of betting rates on a series of propositions hi and ei is strictly incoherent, when “there exists a choice of stakes Si such that, if X accepts the series of bets at these stakes, then no matter what the actual truth values of hi, and ei may be, X can at best lose nothing, and in at least one possible eventuality he will suffer a positive loss” ([3], p. 9).

Suppose that the axioms of conjoint measurement hold for quantities having two independent components and that the axioms of extensive measurement hold for each of these components separately. In a recent paper, Luce shows that if a certain axiom relates the two measurement systems, then the conjoint measure on each component is a power function of the extensive measure on that component. Luce supposes that each component set contains all “rational fractions” of each element in that set; in this note we present an alternative form of the axiom relating the measurement systems that enables us to prove Luce's result without requiring that such “rational fractions” exist.

An intuitive idea concerning degrees of precision is widely accepted, and it is that we increase precision of theories by paying attention to ever decreasing orders of magnitude of measurements which we incorporate in these theories. We increase precision of measuring or of predicting measurement of length, for instance, if we pay attention not only to centimeters but also to millimeters, microns, angstroms, and so on. And our theories are precise to centimeters, then to millimeters, and so on respectively. The idea is that increased precision is the process of capturing a point within nested intervals, and that this is reflected both in experimental and in theoretical progress. An intuitive analogy may be drawn with series of photos made by a camera which approaches the moon's surface. A corollary from this intuitive idea which has been stated by a number of writers is that observation reports and theories are not overthrown even when superseded by more accurate observation because within the limits of their own precision-range they are still valid. When a law in physics is stated, it is stated usually without such qualifications; but this is a mere matter of convenience, we are told. The idea is that a tacit proviso is understood and the law should be understood to be not the statement “such and such is the case” but the statement “within this and that limit of accuracy such and such is the case”; in such a formulation, the law, once verified, remains unshaken regardless of further progress in the field.