Both Henri Poincaré and (more recently) Roger Shepard have argued that the geometry and topology of physical space are internalized by the mind in the form, not (or not only) of a Euclidean manifold, but in terms of the group of rigid Euclidean transformations. Since this issue can have bearing on various metaphysical and epistemological questions, we explore the different reasons they offer for holding this view. In this context, we show how most commentators misunderstand Poincaré's ‘heated sphere/plate’ model and introduce Shepard's ideas to the philosophy of science community.

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.

Like Lewis, many philosophers hold reductionist accounts of chance (on which claims about chance are to be understood as claims that certain patterns of events are instantiated) and maintain that rationality requires that credence should defer to chance (in the sense that under certain circumstances one’s credence in an event must coincide with the chance of that event). It is a shortcoming of an account of chance if it implies that this norm of rationality is unsatisfiable by computable agents. This shortcoming is more common than one might have hoped.

My purpose here is to elaborate the reasons I maintain that Salmon has not been completely successful in reporting the history of work on explanation. The most important limitation of his account is that it does not emphasize the critical necessity to embrace a suitable conception of probability in the development of the theory of probabilistic explanation.

Popper and Miller (1983) have presented an argument purporting to establish the impossibility of inductive probability. Here I discuss critically their characterization of a deductive part of nondeductive support, a point that has not figured centrally in previous responses.

According to the Laplacian definition, the probability of an event is the ratio of “favorable” cases to possible cases. It is obvious that the definition presupposes the equal probability of the possible cases; and to make the definition of probability depend upon the conception of equal probability has the appearance, at least, of a vicious circle. Moreover it is hard to see how we can assure ourselves that each possible case is really no more and no less probable than any other. But even if we define probability as the relative frequency of occurrence of events under a given set of conditions, or of true conclusions from premises of a given type, we still require the conception of equal probability, unless indeed we choose to renounce entirely the mathematical expression and calculation of probabilities.

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.

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.

In this article the question is raised whether philosophers, studying Humean problems, might profit from the empirical findings of contemporary psychology. A text from Hume's Treatise of Human Nature is analyzed in an attempt to find out (1) whether his problems are open to empirical testing. Each sentence in the text is classified into normative, declarative, analytic and synthetic. A prevalence of declarative, synthetic sentences is found. Further, the question is examined (2) whether contemporary empirical psychology has contributed to the testing of Hume's hypotheses. The answer is affirmative for some of the statements, and it is suggested that philosophical discussions around these problems should not be carried out as if psychological research were irrelevant.

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.

This paper concerns the ways in which one can/cannot combine extensive quantities. Given a particular theory of extensive measurement, there can be no alternative ways of combining extensive quantities, where ‘alternative’ means that one combining operation can be used instead of another causing only a change in the number assigned to the quantity. As a consequence, rectangular concatenation cannot be an alternative combining operation for length as was suggested by Ellis and agreed by Krantz, Luce, Suppes, and Tversky. I argue as well that a theory which imposes such restrictions on the combining operation is more desirable than less stringent rival theories.