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<p>Critics frequently target Ernest Nagel’s model of reduction for its purported inadequacy in addressing the issue of approximation. In response, proponents of Nagel’s model have integrated approximations into the more comprehensive Generalized Nagel-Schaffner model, or the GNS model. However, this article contends that the pertinent criticisms and responses are both misplaced: There are no barriers to Nagel’s model incorporating approximations, and it assimilates them in a manner distinctly dissimilar to the approach of the GNS model. Indeed, Nagel’s model is fundamentally <i>static</i>, providing invariant formal and informal conditions for reduction; and it is the <i>dynamic</i> history of science that fulfills relevant conditions for reduction, thereby achieving different <i>degrees of reductive success</i>. Consequently, approximations are essentially extraneous to Nagel’s model, since they pertain chiefly to temporally based scientific knowledge and concern merely the <i>means</i> (e.g., approximate or exact deductions) of fulfilling the conditions for reduction within specific problem contexts. This article also develops a Nagelian treatment of approximation, demonstrating how distinctive types of approximations aid in fulfilling various conditions for reduction and contribute to different degrees of reductive success. Two case studies are presented to illustrate the Nagelian treatment: The first examines the specific heat ratio anomaly within the traditional endeavor of reducing thermodynamics to statistical mechanics, and the second addresses the consumption puzzle in the context of reducing macroeconomics to microeconomics.</p>

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Nagelian reduction and approximation

  • 期刊论文

  • 发表日期：

    2025年1月30日

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  • Bohang Chen

摘要

Critics frequently target Ernest Nagel’s model of reduction for its purported inadequacy in addressing the issue of approximation. In response, proponents of Nagel’s model have integrated approximations into the more comprehensive Generalized Nagel-Schaffner model, or the GNS model. However, this article contends that the pertinent criticisms and responses are both misplaced: There are no barriers to Nagel’s model incorporating approximations, and it assimilates them in a manner distinctly dissimilar to the approach of the GNS model. Indeed, Nagel’s model is fundamentally static, providing invariant formal and informal conditions for reduction; and it is the dynamic history of science that fulfills relevant conditions for reduction, thereby achieving different degrees of reductive success. Consequently, approximations are essentially extraneous to Nagel’s model, since they pertain chiefly to temporally based scientific knowledge and concern merely the means (e.g., approximate or exact deductions) of fulfilling the conditions for reduction within specific problem contexts. This article also develops a Nagelian treatment of approximation, demonstrating how distinctive types of approximations aid in fulfilling various conditions for reduction and contribute to different degrees of reductive success. Two case studies are presented to illustrate the Nagelian treatment: The first examines the specific heat ratio anomaly within the traditional endeavor of reducing thermodynamics to statistical mechanics, and the second addresses the consumption puzzle in the context of reducing macroeconomics to microeconomics.