It has been suggested by several philosophers (Lewis 1976, Putnam 1962) that many of the so-called paradoxes of backward time travel can be resolved if we conceive of the backward time traveller as having a zig-zag or N-shaped world line in spacetime. In this I am in general agreement. But there is still a problem in conceiving of backward time travel this way. In this note I will show how we can solve this problem by conceiving of backward time travel in terms of the closed time-like world lines in certain general relativistic space-times. Indeed, it has often been claimed (cf. Dwyer 1978, Godei 1949, Tipler 1974) that such world models as Godei spacetime show (or contribute to showing) that backward time travel is conceivable. Our discussion will help to make clear just why this claim is correct.

No final statement can be made regarding the relations between science and policy-making. Knowledge, values, and techniques are interrelated, cumulative, and constantly changing. They are derived from man's responses to the complicated interactions between physical, biological, and cultural phenomena. Final answers are impossible because the answers themselves are part of the world and therefore are factors in changing it. We see through a glass darkly, whether it be the giant glass of Palomar or the eye-piece of the electron microscope.

In the acute social crisis of our time many people are turning to social science for the solution of our social problems. Society seems to be saying, in effect, “Scientific methodology in the natural sciences and their accompanying technologies has brought us to the brink of extinction; let it save us through the social sciences and their technologies.” The great foundations, governmental agencies, business organizations, and the universities are repsonding to this demand by directing increasing amounts of money and personnel to activities dealing with human relations, intergroup relations, and social “problems” generally.

The period between 1945 and 1952 marked the development of Professor Ryle's conception of the principles of inference as performance rules. This development has paralleled that of his now well-known distinction between knowing-how and knowing-that. Indeed, the former is a corollary to the latter. Beginning with the inaugural address to the Aristotelian Society in 1945 (2) and reaching full fruition in The Concept of Mind in 1949 (4), it finds its most detailed and illuminating expression in “‘If’, ‘So’, and ‘Because’,” which appeared in 1950 (5). The present essay will attempt to explore this conception of rules in some detail, in the hope of clarifying the nature of Professor Ryle's views on classical logic and on certain problems within the philosophy of logic. Professor Ryle belongs, if his views may be so labeled, to the school of informal language analysts. On the other hand, we incline more toward formalism. We tend to agree with those philosophers who consider certain schemata indispensable tools for the solution of philosophical problems. Logic and the philosophy of logic are, as everyone knows, the areas in which the formalists’ technique originated. In these areas it is accepted by virtually everybody. The only recent exception is a group of English writers, many of whom take their inspiration from Ryle. One may hope, then, that the present criticism of Ryle's view from the other standpoint will throw some light on both positions. What follows falls naturally into two parts. The first deals mainly with Ryle's objections to current logical theory, the second with his own philosophy of logic.

I commemorate David Lewis by discussing an aspect of modality within analytical mechanics, which is closely related to his work on counterfactuals. This concerns the way Hamilton-Jacobi theory uses ensembles, i.e. sets of possible initial conditions. (A companion paper discusses other aspects of modality in analytical mechanics that are equally related to Lewis's work.)

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?

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.

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.

Critics of multiple realizability have recently argued that we should concentrate solely on actual here-and-now realizations that are found in nature. The possibility of alternative, but unactualized, realizations is regarded as uninteresting because it is taken to be a question of pure logic or an unverifiable scenario of science fiction. However, in the biological context only a contingent set of realizations is actualized. Drawing on recent work on the theory of neutral biological spaces, the article shows that we can have ways of assessing the modal dimension of multiple realizability that do not have to rely on mere conceivability.