What I am concerned with in this essay is a case that has often been taken up with respect to the problem of the reducibility of thermodynamics to statistical mechanics or of the logical hierarchy between them, namely, the case of the derivation of the equation for the state of ideal gases (Boyle-Charles law) from the kinetic theory of gases. This is commonly considered to be one of the most successful examples of theory reduction, in that through the efforts of Maxwell and Bolzmann the basic but phenomenological law of classical thermodynamics was brought to bear the Newtonian mechanical description of the movement of molecules which were supposed to constitute gases, and through this then the so-called mechanistic view of the world was laid firmly at the foundation of modern physics. As for the relation between thermodynamics and (statistical) mechanics, the most attractive and often discussed theme must be the one concerning the second law and irreversibility, which won't be taken up here. The main reason that I have chosen to focus on the former case, instead of the latter, is that it is not so much a question of abstract concepts of theoretical origin, such as ‘entropy’, of which it is hard to establish a consensus of usage even among physicists, but rather it is a question of concepts such as ‘heat’, ‘temperature’ or ‘pressure’, which could in one sense be said to be formed by the very logic of our ordinary sense experiences, to which this case refers. In other words, it is expected that the task of explicating the logical status of the presuppositions which are tacitly adopted in this derivation (which physicists often pass by as unquestionable) can serve as a case study for investigating such problems on the philosophy of science as that of the relation between scientific language and ordinary language, the relation between scientific realism and antirealism, or the relation between conceptual reducibility and ‘emergence’.
The points that result from this essay are as follows. First, the most important presupposition introduced in this reduction and in some sense upon which the whole individual molecules, it wouldn't make sense to think of the mean kinetic energy of molecular motion, and accordingly, nor of the concept of temperature of the gas system. But, on the other hand, they are also said to be subordinated to the whole system, to the effect that, once becoming members of the gas ensemble, the individual molecules are inevitably put under the structural constraint of the Maxwell-Bolzmann distribution and so are forbidden random movement. One might be able to notice here a situation analogous to the ‘hermeneutical circularity’ between parts and the whole, say, in the context of interpreting texts.
Thus, even if we were to overlook the problem of the reducibility of thermodynamics to statistical mechanics, concerning the validity of the introduction of the additional postulate concerned, the emergence of the latter from mechanics eventually blocks the overall reducibility of the former to mechanics, and so establishes its emergence in the full sense.

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