This paper utilizes Scott domains (continuous lattices) to provide a mathematical model for the use of idealized and approximately true data in the testing of scientific theories. Key episodes from the history of science can be understood in terms of this model as attempts to demonstrate that theories are monotonic, that is, yield better predictions when fed better or more realistic data. However, as we show, monotonicity and truth of theories are independent notions. A formal description is given of the (...) pragmatic virtues of theories which are monotonic. We also introduce the stronger concept of continuity and show how it relates to the finite nature of scientific computations. Finally, we show that the space of theories also has the structure of a Scott domain. This result provides an analysis of how one theory can be said to approximate another. (shrink)

In this paper, I will develop a nontrivial interpretation of Feyerabend's concept of a hidden anomalous fact. Feyerabend's claim is that some anomalous facts will remain hidden in the absence of alternatives to the theories to be tested. The case of Brownian motion is given by Feyerabend to support this claim. The essential scientific difficulty in this case was the justification of correct and relevant descriptions of Brownian motion. These descriptions could not be simply determined from the available observational data. (...) An examination, however, of this case shows that no alternative theory is or historically was thought to be necessary in order to justify descriptions of Brownian motion that "directly" refute thermodynamics. While Feyerabend's appraisal of this case therefore is incorrect, a sense is developed in which successful alternatives lend inductive support to the correctness of refuting experimental descriptions. Crucial though to the explanation of this support is the notion of arguments that show the possibilities for improving experimental fit. (shrink)

Maxwell claimed that the electrostatic inverse square law could be deduced from Cavendish's spherical condenser experiment. This is true only if the accuracy claims made by Cavendish and Maxwell are ignored, for both used the inverse square law as a premise in their analyses of experimental accuracy. By so doing, they assumed the very law the accuracy of which the Cavendish experiment was supposed to test. This paper attempts to make rational sense of this apparently circular procedure and to relate (...) it to some variants of traditional problems concerning old and new evidence. (shrink)

The problem for the scientist created by using idealizations is to determine whether failures to achieve experimental fit are attributable to experimental error, falsity of theory, or of idealization. Even in the rare case when experimental fit within experimental error is achieved, the scientist must determine whether this is so because of a true theory and fortuitously canceling idealizations, or due to a fortuitous combination of false theory and false idealizations. For the engineer, the problem seems rather different. Experiment for (...) the engineer reveals the closeness of predictive fit that can be achieved by theory and idealization for a particular case. If the closeness of fit is good enough for some practical purpose, the job is done. If not, or there are reasons to consider variation, then the engineer needs to know how well the experimentally determined closeness of fit will extrapolate to new cases. This paper focuses on engineering measures of closeness of fit and the projectibility of those measures to new cases. (shrink)

This book provides a post-positivist theory of deterministic and probabilistic causality that supports both quantitative and qualitative explanations. Features of particular interest include the ability to provide true explanations in contexts where our knowledge is incomplete, a systematic interpretation of causal modeling techniques in the social sciences, and a direct realist view of causal relations that is compatible with a liberal empiricism. The book should be of wide interest to both philosophers and scientists. Originally published in 1989. The Princeton Legacy (...) Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905. (shrink)

It's uncontroversial that notions of idealization and approximation are central to understanding computer simulations and their rationale. What's not so clear is what exactly these notions come to. Two distinct forms of approximation will be distinguished and their features contrasted with those of idealizations. These distinctions will be refined and closely tied to computer simulations by means of Scott-Strachey denotational programming semantics. The use of this sort of semantics also provides a convenient format for argumentation in favor of several theses (...) I shall propose concerning the role computer implemented approximations and idealizations play in fixing what the acceptance of an underlying scientific theory is or should be. (shrink)