Article Contentsp. 137p. 138p. 139p. 140p. 141p. 142p. 143p. 144p. 145p. 146p. 147Issue Table of ContentsPhilosophy of Science, Vol. 34, No. 2 (Jun., 1967), pp. 103-210Front MatterTheory-Testing in Psychology and Physics: A Methodological Paradox [pp. 103-115]Conventionality in Distant Simulataneity [pp. 116-136]Approaches to Reduction [pp. 137-147]What Is a Game? [pp. 148-156]Are Biological Species Real? [pp. 157-167]Three Descriptive Models of Social Structure [pp. 168-174]DiscussionProfessor Marcucci on Whewell's Idealism [pp. 175-183]Reply to Ackermann [pp. 184-187]Conflict and Decision [pp. 188-193]Book ReviewsReview: untitled [p. 194]Review: untitled [pp. 194-195]Review: untitled [pp. 195-196]Review: untitled [pp. 197-198]Review: untitled [pp. 198-200]Review: untitled [pp. 201-202]Review: untitled [pp. 202-203]Abstracts from Inquiry [pp. 204-208]Abstracts from Synthese [pp. 209-210]Back MatterPhilosophy of Science AssociationApproaches to ReductionAuthor(s): Kenneth F. SchaffnerSource: Philosophy of Science, Vol. 34, No. 2 (Jun., 1967), pp. 137-147Published by: The University of Chicago Press on behalf of the Philosophy of Science AssociationStable URL: http://www.jstor.org/stable/186101Accessed: 01/09/2010 15:54Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available athttp://www.jstor.org/page/info/about/policies/terms.jsp. JSTOR's Terms and Conditions of Use provides, in part, that unlessyou have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and youmay use content in the JSTOR archive only for your personal, non-commercial use.Please contact the publisher regarding any further use of this work. Publisher contact information may be obtained athttp://www.jstor.org/action/showPublisher?publisherCode=ucpress.Each copy of any part of a JSTOR transmission must contain the same copyright notice that appears on the screen or printedpage of such transmission.JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range ofcontent in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new formsof scholarship. For more information about JSTOR, please contact [email protected] of Science Association and The University of Chicago Press are collaborating with JSTOR todigitize, preserve and extend access to Philosophy of Science.http://www.jstor.orgAPPROACHES TO REDUCTION* KENNETH F. SCHAFFNERt The Unriversity of Chicago Four current accounts of theory reduction are presented, first informally and then for- mally: (1) an account of direct theory reduction that is based on the contributions of Nagel, Woodger, and Quine, (2) an indirect reduction paradigm due to Kemeny and Oppenheim, (3) an "isomorphic model" schema traceable to Suppes, and (4) a theory of reduction that is based on the work of Popper, Feyerabend, and Kuhn. Reference is made, in an attempt to choose between these schemas, to the explanation of physical optics by Maxwell's electromagnetic theory, and to the revisions of genetics necessi- tated by partial biochemical reductions of genetics. A more general reduction schema is proposed which: (1) yields as special cases the four reduction paradigms considered above, (2) seems to be in better accord with both the canons of logic and actual scien- tific practice, and (3) clarifies the problems of meaning variance and ontological reduc- tion. 1. Introduction. There is a logical problem concerning exactly what happens when one scientific theory is "explained" by a theory from a different branch of science. For example, we might ask what (logically) is going on when a molecular biologist attempts to characterize the gene in chemical terms, and purports to account for Mendelian inheritance by alluding to enzyme action and DNA structure. The con- nection between the terms employed in the different theories is not a self-evident one, nor are there obvious criteria to which we can appeal in judging whether such an explanation has in fact been achieved. Intertheoretic explanation in which one theory is explained by another theory, usually formulated for a different domain, is generally termed theory reduction. In recent years a number of writers have been intrigued by this mode of scientific activ- ity and have attempted to work out in a relatively rigorous manner an account of the logic of reduction. I am going to allude to some of these attempts at rational reconstructions of reduction in an effort to formulate a different conception which I believe to be more in accord with both the canons of logic and actual scientific practice. It turns out that these earlier attempts are special (and extreme) cases of my own more general characterization. I have grouped the various approaches of different authors under four paradigms for both the sake of simplicity, and because the combined claims of the associated writers more often than not made that common paradigm stronger than any of their conceptions taken individually. Let us consider these four paradigms, first informally and then from a more formal standpoint. * Received January, 1967. t I wish to express my appreciation to Professors Ernest Nagel, Sidney Morgenbesser, and W. V. Quine for their helpful comments on materials presented in this paper. A shorter version of this paper was read at the annual meeting of The American Philosophical Association, Westem Division, Chicago, May 1967. 137138 KENNETH F. SCHAFFNER 2. Four Reduction Paradigms. The first of the paradigms which I wish to con- sider has been presented in slightly different ways by Ernest Nagel [13], [14], J. H. Woodger [26], and W. V. Quine [18], and accordingly will be termed the Nagel- Woodger-Quine reduction paradigm (NWQ for short). 1. The NWQ paradigm. Essentially this account of reduction can be character- ized as direct reduction-in which the basic terms (and entities) of one theory are related to the basic terms (and entities) of the other, (assuming that the reduced theory is an adequate one) and the axioms and laws of the reduced theory are derivable from the reducing theory. The last assertion must be expanded somewhat, for quite often in intertheoretic explanation terms appear in the reduced theory which are not part of the reducing theory,