This chapter on micro-reductions begins with a section that describes one or another of the erroneous paths taken by people adhering to reductionist or anti-reductionist prejudices. The reductions for or against which it is argued here, or at any rate a position taken, are micro-reductions, whereby the properties of a whole are to be understood by its constitution from parts. There can be little dispute that natural science has taken and continues to take the micro-reductionist path of thought. But hardly any other scientific method than this reductionism has been threatened by so much misunderstanding and wrong or exaggerated philosophical interpretation. For this reason, we burden our systematic remarks with controversial disputes, as a pre-clarification for our approach to certain micro-reductions. For the reduction of the Boltzmann equation of the kinetic theory of gases to the Liouville equation of statistical mechanics, we had to clarify by which kind of reduction the relevant ‘derivations’ of the Boltzmann equation can be reconstructed. Using some quite useful special investigations on this subject, we can argue that the reduction in question is once more a combination, namely, a combination of an indirect generalization, a general limiting case reduction, and an equivalence. The limiting case reduction is its core, and the exact reductions flanking it provide the required adaptation. The parameter responsible for the limiting case reduction is the particle number, and the limiting case occurs when the particle number increases to infinity. This exemplification of the general limiting case reduction is significant for its credit: It seems to be the only non-trivial general (!) limiting case reduction with a limiting case parameter that can be regarded as a variable without any empiricist concern; and its application is based on evidence that inspires confidence.

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Micro-Reductions

  • Erhard Scheibe

摘要

This chapter on micro-reductions begins with a section that describes one or another of the erroneous paths taken by people adhering to reductionist or anti-reductionist prejudices. The reductions for or against which it is argued here, or at any rate a position taken, are micro-reductions, whereby the properties of a whole are to be understood by its constitution from parts. There can be little dispute that natural science has taken and continues to take the micro-reductionist path of thought. But hardly any other scientific method than this reductionism has been threatened by so much misunderstanding and wrong or exaggerated philosophical interpretation. For this reason, we burden our systematic remarks with controversial disputes, as a pre-clarification for our approach to certain micro-reductions. For the reduction of the Boltzmann equation of the kinetic theory of gases to the Liouville equation of statistical mechanics, we had to clarify by which kind of reduction the relevant ‘derivations’ of the Boltzmann equation can be reconstructed. Using some quite useful special investigations on this subject, we can argue that the reduction in question is once more a combination, namely, a combination of an indirect generalization, a general limiting case reduction, and an equivalence. The limiting case reduction is its core, and the exact reductions flanking it provide the required adaptation. The parameter responsible for the limiting case reduction is the particle number, and the limiting case occurs when the particle number increases to infinity. This exemplification of the general limiting case reduction is significant for its credit: It seems to be the only non-trivial general (!) limiting case reduction with a limiting case parameter that can be regarded as a variable without any empiricist concern; and its application is based on evidence that inspires confidence.