(This insularity was further promoted by the guileless duplicity of scholars in other fields, who were all too prepared to bequeath "the problem of ...

One construal of convergent realism is that for each clear question, scientific inquiry eventually answers it. In this paper we adapt the techniques of formal learning theory to determine in a precise manner the circumstances under which this ideal is achievable. In particular, we define two criteria of convergence to the truth on the basis of evidence. The first, which we call EA convergence, demands that the theorist converge to the complete truth "all at once". The second, which we call (...) AE convergence, demands only that for every sentence in the theorist's language, there is a time at which the theorist settles the status of the sentence. The relative difficulties of these criteria are compared for effective and ineffective agents. We then examine in detail how the enrichment of an agent's hypothesis language makes the task of converging to the truth more difficult. In particular, we parametrize first-order languages by predicate and function symbol arity, presence or absence of identity, and quantifier prefix complexity. For nearly each choice of values of these parameters, we determine the senses in which effective and ineffective agents can converge to the complete truth on an arbitrary structure for the language. Finally, we sketch directions in which our learning theoretic setting can be generalized or made more realistic. (shrink)

This book presents and survey of the foundations of mathematics. The emphasis is on a mathematical comparison of systems rather than on any exhaustive development of analysis within a single system. Nevertheless, for most systems considered, enough details are given for the development of arithmetic, and the method of constructing the other notions of analysis is indicated. The elements of the general theory of cardinal and ordinal numbers are also furnished in the course of this work.

A basic aim of E. Beth's work in philosophy of science was to explore the use of formal semantic methods in the analysis of physical theories. We hope to show that a general framework for Beth's semantic analysis is provided by the theory of semi-interpreted languages, introduced in a previous paper. After developing Beth's analysis of nonrelativistic physical theories in a more general form, we turn to the notion of the 'logic' of a physical theory. Here we prove a result (...) concerning the conditions under which semantic entailment in such a theory is finitary. We argue, finally, that Beth's approach provides a characterization of physical theory which is more faithful to current practice in foundational research in the sciences than the familiar picture of a partly interpreted axiomatic theory. (shrink)

The presence of nonobservational vocabulary is shown to be necessary for wide application of a conservative principle of theory revision.

This volume consists of essays from a colloquium about "philosophy of economics" held at the·University of l1unich in July, 1981. They are contributions to an enterprise which in some respects is long-standing and in other respects is new. The long-standing enterprise is to somehow establish decision theory and its kindred disciplines as the basis of economic theory from which its other parts might be shown to follow. The new enterprise is to apply (some of) the latest methods of phi. losophy (...) of science to economic theory. By "philosophy of science" we do not mean h:istory of science and the like; rather we mean a reconstructive proce dure which clarifies and deepens the understanding of the science under investigation. By "the latest methods" we refer to the structuralist view which has emerged in the last fifteen years, and which has been success fully applied most notably to physical theories. Economics being rather like a stepchild of a reconstructivist philo sophy of science, we think much of the interest of this volume to lie just in its attending to the newer enterprise_ We are happy to have brought together at the colloquium some of the few philosophers of scien ce working in. this field who share this common goal, and we hope that their essays will stimulate further work. -The contributions to the long-standing enterprise, though perhaps not as urgent, are no less valuable. (shrink)