Adams: On Reduction of Rigid Body Mechanics to Particle Mechanics

Authors

Michael A. Day, University of Nebraska-Lincoln

Date of this Version

1973

Document Type

Article

Citation

Published in Transactions of the Nebraska Academy of Sciences, Volume 2 (1973).

Comments

Copyright 1973 by the author(s).

Abstract

From only a brief study of the history of science, one realizes that science is a dynamic enterprise. The Ptolemaic theory of celestial motion was replaced by the Copernician theory of the solar system, the phlogiston theory was replaced by the theory of oxidation brought forth by the discoveries of Priestly and Lavoisier, the mechanics of Galileo was replaced by the mechanics of Newton, Newton's was replaced by the mechanics of Einstein. But do all such replacements basically have the same conceptual structure? It seems that they do not. For when the phlogiston theory was replaced by the theory of oxidation, the phlogiston theory was rejected as scientifically unacceptable and was no longer taught in the universities except as part of the history of science. But when Galilean mechanics was replaced by Newtonian mechanics, Galilean mechanics was not completely rejected by was considered as incomplete and shown its proper domain of application. This is because a case can be made that Galilean mechanics is reducible to Newtonian mechanics.

Just what it means to say that one theory is reducible to another theory is a different question to answer; but it has been informally characterized as one theory explaining another or as one theory being derivable or following from another theory. Such informal characterizations might be intuitively helpful, but they cannot be accepted as giving substantial insight into the nature of scientific reduction. Therefore, a need is developed for what might be called a meta-theory of reduction. Now reduction has been discussed by such philosophers as Nagel, Adams, Schaffner, Kemeny, and Oppenheim; but since Adams' approach seems more applicable than the rest in constructing a meta-theory of reduction, I will center this paper around his approach by first giving a brief exposition of one of his papers and then making some general comments concerning the significance of his method as a general approach to reduction.