This note scouts a broad but underexplored class of explanations found in contemporary computer science. These explanations, which I call limitative explanations, explain why certain problems cannot be solved computationally. Limitative explanations are philosophically rich, but have not received the attention they deserve. The primary goals of this note are to isolate limitative explanations and provide a preliminary account of what makes them explanatory. On the account I favor, limitative explanations are a kind of non-causal mathematical explanation which depend on highly idealized models of computation.

I present new counterexamples to the asymmetry of grounding: we have prima facie reason to think that some conditional probabilities partially ground their inverse conditional probabilities, and vice versa. These new counterexamples may require that we reject the asymmetry of grounding or, alternatively, that we reject one or more of the assumptions (regarding, e.g., the correct interpretation of probability) that enable the counterexamples. Either way, by reflecting on these purported counterexamples to grounding asymmetry, we learn something important, either about the formal properties of grounding or about the nature of probability (or both).

There are three elements involved in physical time. The most primitive of the three is the fact of extension in time. We express this fact by saying that things “endure” in time, or by saying that the universe is not an event of one moment only. Extension in time is such a fundamental and pervasive element of our experience, that we can hardly define it other than by denotatively indicating it. Time extension is basic to the other two elements of time.

Lewis' argument against the Limit Assumption and Pollock's Generalized Consequence Principle together suggest that “minimal-change” theories of counterfactuals are wrong. The “small-change” theories presented by Nute do not say enough. While these theories rely on closeness between possible worlds, I base an alternative on the ceteris paribus concept. My theory solves a problem that the above cannot, and is more relevant to the philosophy of science. Ceteris paribus conditions should normally include the causes, but exclude the effects, of the negated antecedent. An example from community ecology, the debate over null models in island-biogeographical studies of competition, supports these arguments.

I discuss some aspects of the epistemological distinction between laws of nature and accidental uniformities. In order that the exposition be self-contained I briefly provide a taxonomy proposed in another work for statements that appear in a scientific theory. Once this taxonomy has been presented I attempt to prove two very different types of accidental uniformities: hard and soft. The distinction is fundamental because the latter have frequently been confused with laws of nature. I try to justify why I believe that these statements are accidental uniformities and not laws of nature.

Evolutionary theorists have encountered difficulty in explaining how altruistic behavior can evolve. I argue that these theorists have made this task more difficult than it needs to be by focusing their efforts on explaining how nature could select for a strong type of altruism that has powerful selection forces working against it. I argue that switching the focus to a weaker type of altruism renders the project of explaining how altruism can evolve significantly less difficult. I offer a model of weak altruism that can avoid many of the difficulties that evolutionary accounts of altruism have traditionally faced.

It is by no means impossible that the discussion of epistemological problems, at the present stage of our understanding of the issues involved, may be futile. But so long as anyone desires to “know” anything at all, just so long it will be impossible for thoughtful men to leave the questions of epistemology alone. So, futile or not, this paper is concerned with an analysis of one of the most fundamental of epistemological problems, namely that of the ‘given.’ It is true, the ‘given’ has recently received an unusual amount of attention from philosophers. What with two of the American Philosophical Association's presidential addresses last year having much to say on the subject, and what with the logical positivists making the ‘given’ the cap-stone of their radical empiricism? All of which, it will be claimed, proves the contention that any attack upon the problems of epistemology, from the standpoint of our present knowledge and understanding of the total situation involved, is condemned to hopeless futility. Why, then, add one more hopelessly futile attempt to those of all the rest? If, despite such initial misgivings, I shall proceed to my own analysis of the ‘given,’ I shall do so, first of all, in recognition of the indisputable fact that everyone of us, even though we should be blind, deaf and dumb, do, as a matter fact, find ourselves confronted with something ‘given’; and, secondly, because it appears to me that, as philosophers, it is still our task seriously to concern ourselves with unsolved problems, even though they may not yet be capable of being so stated that a unanimously acceptable solution for them may be—at present—possible. Even the logical positivists, who, of course, are most critical of what philosophy is or ought to be, insist that “the object of philosophy is the logical clarification of thoughts.” Since the ‘given’ is a concept (thought) most widely used not only by so-called ‘pseudo-philosophers’ but even by the logical positivists themselves, it certainly cannot be denied that the clarification of the concept of the ‘given’ is decidedly a philosophical task. More than that: it is a necessary philosophical task just so long as there is such wide difference of opinion concerning the ‘given’ among philosophers.

(1) The probability of some generalizations can be lowered by positive instances.

(2) The change in probability (both degree and direction) can depend on factors other than the new evidence, the statement, and the probability of the statement given the old evidence.

Two ideal standard clocks, effectively isolated from interaction with other physical systems, and in a region of the universe free of gravitational fields, are assumed to move in any arbitrary manner so that they coincide on at least two occasions. In general, the reading of one of them will become retarded relative to the other in the interval between successive coincidences. This relative retardation is predicted by the restricted theory of relativity, taken together with the assumption that the ‘rate’ of a clock depends only on its velocity and not on its acceleration. The recognized procedure for calculating the retardation in terms of clock ‘rates’ is set out, and is illustrated by its application to a simple hypothetical experiment in which one clock remains at rest and the other travels away from and back to it with constant speed in a straight line.

There is nothing paradoxical in the predicted retardation as such. The so-called 'clock paradox' arises because an alternative, and apparently valid, calculation procedure, also based on clock 'rates', leads to a contradictory result. The term ‘paradox’ is something of a euphemism since the two predictions are contradictories.

It is shown that the paradox does not arise when direct use is made of the Lorentz transformation without introducing the additional, and non-essential, step in reasoning involved in utilizing the clock ‘rates’. It is then shown that the paradox arises only through using these clock ‘rates’ without due regard to the exact significance of the quantities so described; once this is recognized the paradox is resolved completely within the framework of the restricted theory, which then provides a unique and unambiguous prediction of the relative retardation.

Once the paradox is thus resolved, the general theory of relativity can add nothing significant to the analysis. It is shown that the application of the principle of equivalence is essentially trivial; in effect, Einstein and Tolman evaded the real logical issue raised by the contradictory predictions by denying the applicability of the restricted theory and then utilizing, by means of the principle of equivalence, results obtained from it. This tortuous procedure succeeded in evading the paradox rather than in resolving it; it would obviously be quite invalid were the restricted theory indeed inapplicable to the problem.

It is with some trepidation that I am raising again this old problem, for it may well be said that nothing new could possibly be written on it. On the other hand it can scarcely be maintained that what has been written has left the problem in a satisfactory state. Moreover, it seems to me that some work which has been done recently on the nature of theoretical physics can be used to dispose of most of the difficulties, and it is partly in the hope of drawing attention to that work and its bearings on psychology that I am writing this paper.

According to Michael Friedman’s theory of explanation, a law X explains laws Y1, Y2, …, Yn precisely when X unifies the Y’s, where unification is understood in terms of reducing the number of independently acceptable laws. Philip Kitcher criticized Friedman’s theory but did not analyze the concept of independent acceptability. Here we show that Kitcher’s objection can be met by modifying an element in Friedman’s account. In addition, we argue that there are serious objections to the use that Friedman makes of the concept of independent acceptability.

Nearly a half century ago, Thomas Kuhn, Paul Feyerabend, Stephen Toulmin, Norwood Russell Hanson, and others issued a challenge to us philosophers of science to make our field more relevant to actual science. That challenge, over time, has elicited a number of useful responses but very few efforts to situate science within its wider social context when philosophizing about science. The unit of analysis for philosophy of science has tended to remain science-in-a-vacuum. I consider the justifications we offer for this failure, our resources for change, and our prospects if we do change.

This article argues that quantum observables can include not just self-adjoint operators but any member of the class of normal operators, including those with nonreal eigenvalues. Concrete experiments, statistics, and symmetries are all expressed in this more general context. However, this more general class of observables also requires a new restriction on sets of operators that can be interpreted as observables at once, called ‘sharp sets’.

We explicate recent results that shed light on the obscure and troubling problem of renormalization in Quantum Field Theory (QFT). We review how divergent predictions arise in perturbative QFT, and how they are renormalized into finite quantities. Commentators have worried that there is no foundation for renormalization, and hence that QFTs are not logically coherent. We dispute this by describing the physics behind liquid diffusion, in which exactly analogous divergences are found and renormalized. But now we are looking at a problem that is physically and formally well-defined, proving that the problems of renormalization, by themselves, cannot refute QFT.