## Abstract

In this chapter, I defend a pluralistic approach to intertheoretic reduction, in which reduction is not understood in terms of a single philosophical “generalized model”, but rather as a family of models that can help achieve certain epistemic and ontological goals. I will argue then that the reductive model (or combination of models) that best suits to a particular case study depends on the specific goals that motivate the reduction in the intended case study.

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## Notes

- 1.
- 2.
There were some predictions of electromagnetic theory which were incompatible with the predictions of traditional physical optics, such as the exponentially decaying penetration of electromagnetic waves into the surface of a reflecting opaque object. However, these inconsistencies were settled quickly in favor of a modification of the reduced theory. The modified version of traditional optics was considered to be totally reducible to the electromagnetic theory and this reduction led finally to the acceptance of the latter theory (Worrall, 1989, p. 148).

- 3.
This idea can also be put in terms of

*definitional extension*of a theory. The core idea of Nagelian reduction is that a theory \(T_1\) reduces another \(T_2\), if and only if \(T_2\) can be defined as a definitional extension of \(T_1\), which means that \(T_2\) can be shown to be a sub-theory of the augmented theory \(T_1 \cup BL\) (Butterfield, 2011a). - 4.
- 5.
Feyerabend (1962) strongly criticized the model by pointing out contentious issues associated not only with the derivability condition, but also with the connectability condition. His criticism to the connectability condition came from his “incommensurability thesis”, according to which, all scientific vocabulary, including observational terms, are globally infected by the theory in which they functioned. Nagel (1970) replied to these objections with an incisive criticism to the incommensurability thesis.

- 6.
In 1977 and 2012 he reiterates this idea by proposing an even more general model, which he baptized as “The general reduction replacement model”. This model was supposed to be general enough to have “the reduction paradigm” as a limiting case, which for its part yields the Nagel’s model as limiting case.

- 7.
Dizadji-Bahmani et al. (2010) restrict their analysis to the so-called synchronic intertheoretic reductions, which they define as “the reductive relation between pairs of theories which have the same (or largely overlapping) domains of application and which are simultaneously valid to various extends.” (p. 394) It is important to point out, however, that Schaffner (1977, 2012) did not restrict his analysis to this kind of reduction. In fact, the paradigmatic case of reduction that he presents is the reduction of physical optics to the electromagnetic theory, which should be better regarded as a “diachronic reduction”, in which a theory historically replaces the other.

- 8.
- 9.
Whether this is indeed a case of Schaffner reduction is still unclear. In fact, in order to prove that this is in fact a case of Schaffner reduction, one would need to show that the theory \(T_2 ^*\) can be actually derived from statistical mechanics \(T_1\). This is not easy to prove since at least some of these approaches (Tisza and Quay, 1963; Valente, 2021) seem to constitute an amalgamation of statistical mechanics and thermodynamics, rather than a derivation of an alternative an thermodynamic from statistical mechanics.

- 10.
Domain-combining and domain-preserving have been sometimes understood in terms of “synchronic” and “diachronic reductions” respectively (Dizadji-Bahmani et al., 2009).

- 11.
The reduction of phase transitions is still a controversial issue in the philosophical literature. Batterman (2001), for example, has famously argued against the reduction of phase transitions pointing out the “singular” nature of the thermodynamic limit. Butterfield (2011b), Norton (2011), and Palacios (2019), among others, have replied to these arguments suggesting that the “singular nature” of the thermodynamic limit is not incompatible with the reduction of phase transitions to statistical mechanics.

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Palacios, P. (2023). Intertheoretic Reduction in Physics Beyond the Nagelian Model. In: Soto, C. (eds) Current Debates in Philosophy of Science. Synthese Library, vol 477. Springer, Cham. https://doi.org/10.1007/978-3-031-32375-1_8

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