The Reduction of Theories
Nagel (Ernest)
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Author’s Introduction

  1. It is a commonplace that classical mechanics is no longer regarded as the universal and fundamental science of nature. Its brilliant successes in explaining and bringing into systematic relations a large variety of phenomena were at one time indeed unprecedented. And the belief, once widely held by physicists and philosophers, that all the processes of nature must eventually fall within the scope of its principles was repeatedly confirmed by the absorption of various sectors of physics into it. Nevertheless, the period of the "imperialism” of mechanics was practically over by the latter part of the nineteenth century. The difficulties which faced the extension of mechanics into still unconquered territory, and particularly into the domain of electromagnetic phenomena came to be acknowledged as insuperable.
  2. However, new candidates for the office of a universal physical science were proposed, sometimes with the backing of a priori arguments analogous to those once used to support the claims of mechanics. To be sure, with some few doubtful exceptions no serious student of the sciences today believes that any physical theory can be warranted on a priori grounds, or that such arguments can establish a theory in that high office. Moreover, many outstanding physicists are frankly skeptical whether it is possible to realize the ideal of a comprehensive theory which will integrate all domains of natural science in terms of a common set of principles and will serve as the foundation for all less inclusive theories. Nevertheless, that ideal continues to leaven current scientific speculation; and, in any case, the phenomenon of a relatively autonomous theory becoming absorbed by, or reduced to, some other more inclusive theory is an undeniable and recurrent feature of the history of modern science. There is every reason to suppose that such reduction will continue to take place in the future.
  3. The present chapter is concerned with this phenomenon, and with some of the broader issues associated with it. Scientists as well as philosophers have exploited both successful and unsuccessful reductions of one theory to another as occasions for developing far-reaching interpretations of science, of the limits of human knowledge, and of the ultimate constitution of things in general. These interpretations have taken various forms, but only a few typical ones need be mentioned here.
  4. Discoveries relating to the physics and physiology of perception are often used to support the claim that the findings of physics are radically incompatible with so-called “common sense" - with customary beliefs that the familiar things of everyday experience possess the traits they manifest even to carefully controlled observation. Again, the successful reduction of thermodynamics to statistical mechanics in the nineteenth century was taken to prove that spatial displacements are the only form of intelligible change, or that the diverse qualities of things and events which men encounter in their daily lives are not 'ultimate’ traits of the world and are perhaps not even “real." But, conversely, the difficulty in finding consistent visualizable models for the mathematical formalism of quantum mechanics1 has been taken as evidence for the 'mysterious' character of subatomic processes and for the claim that behind the opaque symbolism of the “world of physics" there is a pervasive “spiritual reality" that is not indifferent or alien to human values. On the other hand, the failure to explain electromagnetic phenomena in terms of mechanics, and the general decline of mechanics from its earlier position as the universal science of nature, have been construed as evidence for the “bankruptcy" of classical physics, for the necessity of introducing 'organismic’ categories of explanation in the study of all natural phenomena, and for a variety of sweeping doctrines concerning levels of being, emergence, and creative novelty.
  5. We shall not examine the detailed arguments that culminate in these and similar contentions. However, one broad comment is relevant to most of the claims. As has been repeatedly noted in previous chapters, expressions associated with certain established habits or rules of usage in one context of inquiry are frequently adopted in the exploration of fresh fields of study because of assumed analogies between the several domains. Nevertheless, its users do not always note that when the range of application of a given expression is thus extended, the expression often undergoes a critical change in its established meaning. Serious misunderstandings and spurious problems are then bound to be generated unless care is taken to understand the expression in the sense relevant to, and required by, the special context in which the expression has acquired a fresh use. Such alterations are particularly prone to occur when one theory is explained by, or reduced to, another theory; and the shifts in the meanings of familiar expressions that often result as a consequence of the reduction are not always accompanied by a clear awareness of the logical and experimental conditions under which the reduction has been effected. In consequence, both successful and unsuccessful attempts at reduction have been occasions for comprehensive philosophical reinterpretations of the import and nature of physical science, such as those cited in the preceding paragraph. These interpretations are in the main highly dubious because they are commonly undertaken with little appreciation for the conditions that must be fulfilled if a successful reduction is to be achieved. It is therefore of some importance to state with care what these conditions are, both for the light that the discussion of those conditions throws on the structure of scientific explanation and for the help which the discussion can provide toward an adequate appraisal of a number of widely held philosophies of science. An examination of the conditions for reduction and of their bearing on some moot issues in the philosophy of science is the central task of the present chapter.

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