The contributions to Testing Scientific Theories are unified by an interest in responding to criticisms directed by Glymour against existing models of confirmation–-chiefly H-D and Bayesian schemas–-and in assessing and correcting the “bootstrap“ model of confirmation that he proposed as an alternative in Theory and Evidence (1980). As such, they provide a representative sample of objections to Glymour's model and of the wide range of new initiatives in thinking about scientific confirmation that it has influenced. The effect is a sense of engagement and focus, and of significant advance at least in articulation of the problems that require solution; as Earman observes, “it is … heartening to report that the various opposing camps learned from each other” (p. vi). In what follows I am concerned to assess what has been learned both critically, about Glymour's model, and constructively about the resources of the alternatives he challenges. My thesis is that while the theories emerging in this debate do deal with a wider range of scientific practice than before, their remaining limitations raise important questions about the ambitions and criteria of adequacy that have traditionally governed philosophical inquiry in this area.

It is argued that models of H. Jeffreys' axioms of probability (Jeffreys [1939] 1967) are not monotone even with I. J. Good's proposed modification (Good 1950). Hence the additivity axiom seems essential to a theory of probability as it is with Kolmogorov's system (Kolmogorov 1950).

In a recent commendable article, Quentin Smith (1987) exposes fatal flaws in several recent attempts to demonstrate that it is logically impossible for the past to be infinite. However, his analysis of one of these flawed arguments—involving an interesting version of Russell's “Tristram Shandy paradox”—is off the mark, as I show in this paper.

N. Maxwell (1985) has claimed that special relativity and “probabilism” are incompatible; “probabilism” he defines as the doctrine that “the universe is such that, at any instant, there is only one past but many alternative possible futures”. Thus defined, the doctrine is evidently prerelativistic as it depends on the notion of a universal instant of the universe. In this note I show, however, that there is a straightforward relativistic generalization, and that therefore Maxwell's conclusion that the special theory of relativity should be amended is unwarranted. I leave open the question whether or not probabilism (or the related doctrine of the flow of time) is true, but argue that the special theory of relativity has no fundamental significance for this question.

The usual objections to infinite numbers, and classes, and series, and the notion that the infinite as such is self-contradictory, may ... be dismissed as groundless. There remains, however, a very grave difficulty, connected with the contradiction [of the class of all classes not members of themselves]. This difficulty does not concern the infinite as such, but only certain very large infinite classes.

—Bertrand Russell, The Principles of Mathematics, p. 362