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Using Scott Domains to Explicate the Notions of Approximate and Idealized Data

Published online by Cambridge University Press:  01 April 2022

Ronald Laymon
Ronald Laymon*
Affiliation:
Department of Philosophy The Ohio State University
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Abstract

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.

Type
Research Article
Information
Philosophy of Science , Volume 54 , Issue 2 , June 1987 , pp. 194 - 221
Copyright
Copyright © The Philosophy of Science Association

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Footnotes

†

Many of the ideas presented here were developed while I was a fellow at the Center for the Philosophy of Science at the University of Pittsburgh. I am very grateful to the past and current directors, Larry Laudan and Nicholas Rescher, for arranging my visit and for providing extremely stimulating accommodations. My research was also supported by a National Science Foundation Scholars Award and by faculty development grants from The Ohio State University. I also want to thank Dana Scott, Stephen Brookes, and David McCarty for their friendly assistance with denotational semantics. The basic idea of this paper, that possible data be conceived as having a formal structure of their own, comes from Suppes 1962. Finally, my thanks go to Ron Giere, Clark Glymour, Robert Kraut, Ilkka Niiniluoto, Bill Harper, and John Worrall for their encouragement and critical advice.

References

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