A large number of definitions of the concept “model” have been given by various authors in recent years. Thirty-seven definitions are listed by A. I. Uyemov in a recent monograph (see [9]). This list is somewhat one-sided since it contains a disproportionate number of references to the work of Soviet authors. However, most of the important definitions given by Western writers are included. I shall give three definitions, all of great generality, so that various types of models, replicas, maps, theories and, most importantly, cybernetic models, are included. The advantage of this high degree of generality, or all-inclusiveness, is that the task of the investigator of uses of models in science, is reduced to classifying the various types of models, their construction, function, and structure, thus avoiding indecisive arguments (historically important, of course) such as the Duhem–Campbell controversy, so perceptively discussed by Mary Hesse ([2], [3]).

David Lewis [2] suggests that an adequate inductive method should be immodest, i.e. recommend itself as at least as accurate as any of its rivals. On this basis he works out a solution to the intricate problem of choosing among Carnap's λ-methods. Lewis himself points out certain undesirable consequences of his solution. I will argue that the solution breaks down for a more general reason than that indicated by Lewis; like other procedures for estimating degrees of belief I am familiar with, it overlooks the component of lawlikeness of inductive situations. This is not to object to the requirement of immodesty; I only want to draw attention to certain assumptions which Lewis makes in deriving his equations and which seem to be unjustified.

Bas van Fraassen in [4] has recently tried to use modal logic to solve the measurement problem of quantum mechanics. His model is based on a method of expressing quantum states developed by Hugh Everett [1] called the “relative state formulation.” Unfortunately, Everett's mathematics cannot be generalized as van Fraassen requires. The difficulty itself is elementary enough. But a revision of van Fraassen's postulates (such as the one he adopted on p. 341 after he had been told of the problem) can save the mathematics only on pain of making the whole study irrelevant to the physics. I shall explain the dilemma in this note. In a later paper [5], van Fraassen avoids this dilemma by developing an abstract modal interpretation which does not rely on any expression for quantum states.

In [1] Michael Polanyi argues that in order to understand how scientists come to recognize problems as problems, we must invoke a concept of “tacit knowing.” Tacit knowledge is a kind of knowledge of which we are aware but which cannot be made explicit. Polanyi argues that a paradox discussed in the Meno cannot be solved without appeal to this notion of tacit knowledge. Here I want to argue, quite simply, that Polanyi's formulation of the “paradox” can be easily subverted without an appeal to tacit knowing. Polanyi puts the paradox thus:

In an article “Countering a Counter-intuitive Probability” [4], Lynn E. Rose discusses a question in conditional probability, claiming that the following problem posed by Copi [1] is usually incorrectly solved: