This paper derives a mathematical expression giving the development of the probability of a scientific hypothesis with the number of confirming tests, as determined by Bayes's theorem, in a special case in which all the tests are “independent” of one another. The simple expression obtained shows clearly how the various factors influence the growth of the probability. The result is used to set a numerical lower bound on the probabilities representing the a priori beliefs of humans in generalizations that become accepted. By making a comparison with the predictions of a “logical atomic” model in the case of physical laws, it is argued that humans have significant a priori “knowledge” in a weak sense.

Recently Albert and Hemmo and Shenker have argued that, contrary to what is sometimes suggested, Liouville's theorem does not prohibit a Maxwellian demon from operating but merely places certain restrictions on its ability to operate. There are two main claims made in this article. First, that the restrictions Liouville's theorem places on Maxwell's demon's ability to operate depend on which notion of entropy one adopts. Second, that when one operates with the definition of entropy that is usual in this debate, the restrictions put on Maxwell's demon are not even as severe as Albert and Hemmo and Shenker argue.

While the question of whether selected-effects accounts of function or causal-role accounts of function provide the ‘true’ functional analysis has given way to a general pluralistic consensus, Philip Kitcher has suggested that different functional accounts allow for unification. I argue that Kitcher's attempt to unify the two functional analyses fails because he adopts the environment-centered perspective on selection as a premise. The premise is undermined by the role niche construction is likely to play in the context of evolution. Moreover, I raise the tentative suggestion that niche construction may threaten the applicability, or at least the relevance, of selected-effects ascriptions.

Are objects in convex passenger-side mirrors “closer than they appear”? If one adapts to inverting goggles, does the world go back to looking the way it was before, or does the world look approximately the same throughout the course of adaptation, only losing its normative sense of wrongness? The answers to these empirical, introspective questions might help cast light on the classic philosophical debate about the degree of resemblance between our visual experience of reality and things as they are in themselves.

The conformity of mathematics and physics has so far been taken for granted. Philosophical explanations of that fundamental fact have never been satisfactory, mathematical explanations never had been attempted. In the following a fundamental theorem for the conformity of mathematics and physics will be demonstrated.

Mathematics can be defined as the science of Number, physics as the science of Matter. The elementary constituents of mathematics are the prime numbers, those of matter the particles, particularly protons and electrons. The only essential property of these elements as such is their existence, given within a given complex or space. Their fundamental relation is their distribution within their respective spaces. The theorem of the distribution of primes in the arithmetical series of numbers is the fundamental theorem of mathematics. The fundamental theorem of physics would be a theorem of the distribution of particles in geometrical space. If it were shown that both theorems were equal, the essential conformity of mathematics and physics would be mathematically demonstrated.

For the case of statistical theories, the criteria of explanation, prediction, and testability can all be viewed as particular instances of a more general evaluation scheme. Using the ideas of a gain matrix and expected gain from statistical decision theory, these three criteria can be compared in terms of the elements in their associated gain matrices. This analysis leads to (1) further understanding of the interrelationship between the current criteria, (2) the proposal of an ordering for the criteria, and (3) the suggestion of a new criterion.

Marc Lange has recently raised three objections to the account of minimal model explanations offered by Robert Batterman and Collin Rice. In this article, I suggest that these objections are misguided. I suggest that the objections raised by Lange stem from a misunderstanding of the what it is that minimal model explanations seek to explain. This misunderstanding, I argue, consists in Lange’s seeing minimal model explanations as relating special types of models to particular target systems rather than seeing minimal model explanations as looking to explain robust patterns of behavior that are exhibited by a variety of physically diverse systems.

This article begins by distinguishing intrinsic and extrinsic contributions of mathematics to scientific representation. This leads to two investigations into how these different sorts of contributions relate to confirmation. I present a way of accommodating both contributions that complicates the traditional assumptions of confirmation theory. In particular, I argue that subjective Bayesianism does best in accounting for extrinsic contributions, while objective Bayesianism is more promising for intrinsic contributions.