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?

To this date Roger Bacon remains one of the controversial and colorful figures in the history of empirical science. This paper is an attempt to ascertain his views regarding the nature and function of empirical science and to compare his writings on this topic with those of the more famous Francis Bacon. The ground for comparison is the fact that both men have often been cast in the same role in the history of science; i.e., they have both been acclaimed as the first in the western world to emphasize and bring out the importance of experimental method in the accumulation of knowledge. In this connection Francis, of the sixteenth century, has long been acknowledged as the father of the experimental method in preference to Roger, of the thirteenth century. In effect, therefore, this paper probes the relative merits of the claims for each thinker.

A common strategy in comparative cognition is to require that one reject associative learning as an explanation for behavior before concluding that an organism is capable of causal reasoning. In this paper, I argue that standard causal-reasoning tasks can be explained by a powerful form of associative learning: unlimited associative learning (UAL). The lesson, however, is not that researchers should conduct more studies to reject UAL, but that they should instead focus on 1) enriching the cognitive hypothesis space and 2) testing a broader range of information processing patterns—errors, biases and limits, rather than successful problem solving alone.

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.

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.

Anyone who has worked in Science for forty years can be much surprised to realize how little he now hears about evolution, compared with such former times. At present, evolution seems to be accepted as an axiomatic or universal principle, while the mechanism of it is not much considered, except by a small group of specialists, who work on the subject in greatly limited ways. This is practically a reversal of the former emphasis. The chemist would probably suggest that the change is due to a better realization of the chemical difficulties involved in the mechanics of evolution, and his own change in viewpoint. The chemical difficulties will have increased to an almost incredible degree in this period, and his viewpoint will have changed correspondingly. A glance at some of these changes should illuminate the progress made in both subjects in this period.