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.

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’.

The claim that theoretical entities are not real, that they are merely convenient fictions, has been defended and attacked in diverse ways. This paper is concerned with only one defense of the fictionalist thesis and with a certain realist attack on it. The defense in question is that theories which prima facie make reference to theoretical entities can be revised in such a way that no such apparent reference is made by eliminating all occurrences of theoretical expressions. It will be argued here that there is a procedure for revising theories which meets certain minimal criteria of adequacy, contrary to arguments in the literature. Further, it will be argued that the existence of this procedure provides neither sufficient nor necessary support for the fictionalist thesis, that this procedure is not of significance in the dispute between the fictionalist and the realist. Whether or not the theoretical-nontheoretical distinction is viable is another story which will not be told here. It will be assumed for the sake of argument that such a distinction can be drawn.

(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.

W. V. O. Quine's well-known attack upon the analytic-synthetic distinction is held to affect only one of the two species of analytic statements he distinguishes. In particular it is not directed at and does not affect the so-called logical truths. In this paper the scope of Quine's attack is extended so as to embrace the logical truths as well. It is shown that the unclarifiability of the notion of ‘synonymy’ deprives us not only of “analytic statements that are obtainable from logical truths by the replacement of synonyms with synonyms” but of “logical truths” themselves.

Scientific tradition holds that it is essential to permit individual researchers almost complete freedom in their selection of research projects. As a result, structured research planning has not played a major role in determining the course of the sciences. By “structural research planning” we mean the methodical establishment of goals, and the identification of research routines which apparently accord priority to highest value goals, while minimizing the cost and time of their attainment. With increasing competition for limited fiscal and intellectual resources this kind of planning may become more necessary. Let us cite three specific examples: First, the individual researcher is often faced with the question of how best to spend his time in pursuing a particular line of investigation. He must allocate his personal resources of time and talent to work which appears to hold the promise of highest pay-off. Second, on a larger scale, the competition for resources also raises the question of priority among alternative government-sponsored research projects. Individuals proposing equally alluring projects sometimes seek the same funds; government planners need some sort of objective criteria (hopefully based on a rational strategy) in order to judge the proposals. Furthermore, government planners face the problem of justifying their request for “big science” resources; a planning strategy which defines the use and expected output of the requested resources can help in the design and promotion of their concept. Finally, there is a growing sentiment that at least some research should be directed toward the solution of current and anticipated societal problems, to find means of circumventing or minimizing the impact of potentially dangerous problems of civilization. These needs : the choice of individual research, allocation of national resources among competing projects, and selecting research of societal importance, suggest that structured research planning might be valuable.

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.

Metaphysical problems may be solved by the methods of inference employed in the empirical sciences. So we are told by many realists and pragmatists, among whom may be mentioned Professors J. B. Pratt, William Savery, and Donald Williams. Mr. Williams and Mr. Pratt have argued for the use of inductive methods in establishing the existence of an external world. Mr. Savery has asserted that all philosophical inference as to matter of fact is inductive. This naturalistic attitude is by no means unusual—in fact it is so common in this age in which the speculations of scientists as well as their achievements have captivated the popular imagination, that even philosophers have for the most part failed to examine its validity and presuppositions. It is the purpose of this paper to present such an examination, not of the philosophic employment of inductive methods in general, but in regard to one specific problem; namely, that of the existence of an external world. What I purpose then is to present and evaluate the view that the existence of an external world may be established by inductive methods as employed in the empirical sciences.

Corrigibility has generally been designated as the major qualification of a scientific law. Although various other characteristics of a scientific law have been questioned, corrigibility has usually been accepted as one of its essential features. On this basis scientists, positivists, and pragmatists have frequently distinguished between genuine empirical laws and all other assertions that only seem to be laws. The mark of a genuine law in the scientific sense is its corrigibility; the mark of a pseudo law is its non-corrigibility. In this paper I should like to reopen philosophic inquiry into the nature of corrigibility as it is supposedly exemplified in law and to call attention to some of the peculiar difficulties and conclusions attendant on any such inquiry.

The pervasive contrast in modern life between the certainties of science and technology, on the one hand, and the uncertainties of human goals and policies, on the other, is the objective source of a fundamental conflict in theory. It is now widely held that facts are rather definitely verifiable, but that values are unverifiable; though other students assume that values are also verifiable in some significant sense and degree.

Evolutionary accounts of morality consider behavior in rather simple scenarios. Evolutionary work on fairness focuses on the division of a windfall and, importantly, assumes that the positions of those involved are entirely symmetric. I consider more complicated strategic settings and find that there is a strong tendency for evolution to produce divisions consistent with the so-called Nash bargaining solution. I also uncover the evolutionary importance of comprehensiveness, an often-overlooked feature of division problems.

Usual derivations of Lüders's projection rule show that Lüders's rule is the rule required by quantum statistics to calculate the final state after an ideal (minimally disturbing) measurement. These derivations are at best inconclusive, however, when it comes to interpreting Lüders's rule as a description of individual state transformations. In this paper, I show a natural way of deriving Lüders's rule from well-motivated and explicit physical assumptions referring to individual systems. This requires, however, the introduction of a concept of individual state which is not standard.

In his article [5], Brian Skyrms adduces (on p. 233) some generalizations which, he claims, receive no confirmatory support from their positive instances even though all the predicates they contain are well entrenched in Goodman's sense. Invoking the principle that “a generalization is lawlike if it is capable of receiving confirmatory support from its positive instances” (p. 232; actually, the converse is needed and, I will assume, intended by him), he claims that his examples “provide striking demonstration of the fact that the lawlikeness of a hypothesis is not a simple function of the projectibility of its constituent predicates.” I think the claim is of great interest; but I will try to show that Skyrms's argument fails to establish it because it presupposes an unwarranted assumption which raises a problem of general importance for confirmation theory.

Calibrating a simulation is a crucial step for certain kinds of simulation modeling, and it results in a simulation that is epistemically different from its pre- or uncalibrated counterpart. This article discusses how simulation model builders mitigate uncertainty about model parameters that are necessary for modeling through calibration and argues that the simulation outcomes after calibration are physically meaningful and relevant. When evaluating the epistemic status of computer simulations, comparisons between computer simulations and traditional experiments need to consider this important methodological step.