Ernest Nagel's Model of Reduction and Theory Change

ABSTRACT

A longstanding criticism of Ernest Nagel's model of reduction is that it fails to take theory change into account. This criticism builds on the received view that Nagelian reductions are incompatible with theory change. This article challenges the received view by showing that Nagel's model can easily accommodate theory change. Indeed, Nagel's model is essentially static as it only gives unchanging formal and nonformal conditions for reduction; in contrast, theory change belongs to the dynamic history of science; as a result, the application of Nagel's model to scientific knowledge from different historical periods yields a series of Nagelian reductions of different degrees of reductive success. This Nagelian treatment of theory change is illustrated by considering the enterprise of reducing thermodynamics to statistical mechanics in the late nineteenth century. It is also contended that, in handling theory change Nagel's model has greater merits than subsequent models (exemplified by Kenneth Schaffner's general reduction-replacement model). This article concludes by suggesting that Nagel's model of reduction deals with theory change exactly in the same way as logical empiricism does with historicism.

Acknowledgements

I thank the two anonymous reviewers from this journal for their very positive feedbacks. An early version of this manuscript was submitted to a different journal, although it did not get published there, special thanks must also be expressed to one anonymous reviewer from that journal who provided many helpful suggestions that shape fundamentally both the form and the content of the present manuscript.

Disclosure Statement

No potential conflict of interest was reported by the author(s).

Notes

1 These criticisms are pertinent to a variety of issues, such as, theory reduction, bridge laws, multiple realization, etc. For summaries of the criticisms, see Van Riel (2011), Sarkar (2015), and Van Riel and Van Gulick (2019). Further, perhaps one can make a distinction between the mainstream appraisal and recent reappraisals. The latter can be found in Marras (2002), Fazekas (2009), Klein (2009), Needham (2010), Dizadji-Bahmani, Frigg, and Hartmann (2010), Butterfield (2011), Van Riel (2011), Schaffner (2012), Sarkar (2015), and Shapiro (2018). According to these reappraisals, at least some traditional criticisms from the former are ill-founded and rest on misunderstandings of Nagel's model of reduction. However, it should also be noted that the mainstream appraisal remains largely unmoved. Two recent contributions to the topic of reduction and reductionism, Kaiser (2015) and Gillett (2016), for instance, repeat traditional criticisms of Nagel's model, with no substantial engagement with recent reappraisals. The former confirms well the persistence of the mainstream appraisal, by claiming that the failure of Nagel's model is ‘almost a consensus’ (Kaiser 2015, 87) and it is time to ‘move beyond Nagelian reduction’ (84).

2 As one anonymous reviewer from this journal has noted, strictly speaking Sarkar's claim is not only too extreme but also false, since at least some scholars (Dizadji-Bahmani, Frigg, and Hartmann 2010; Van Riel 2011; Schaffner 2012) are aware of Nagel's discussion of nonformal conditions. Yet, it seems fair to suggest that only Sarkar makes the fundamental point that inspires the present article: Nagel did explicitly take the history of science into account when elaborating his model. Based on Sarkar's insight, I add further that Nagel intended his model of reduction to be repeatedly applied to concrete historical examples and his model, for this reason, provides a better account of reduction than Schaffner's general reduction-replacement model. But unlike Sarkar, none of these earlier-mentioned scholars is able to accept this rather unconventional judgment.

3 As the same anonymous reviewer has very helpfully pointed out, it is necessary to substantiate the notion of degree of reductive success with a more elaborate account, for which I am now planning a different manuscript. To speak in a preliminary fashion, a higher degree of reductive success can be initiated at both formal and nonformal aspects: the introduction of stipulative definitions helps meet the formal condition of connectability, and this results in limited reductive success; the formal condition of derivability can be further satisfied by introducing approximations, and such reductive success becomes more impressive, at least formally speaking; but higher degrees of reductive success remain attainable if some nonformal conditions are also shown to hold. In addition, even with respect to one and the same condition, importantly, it seems still possible to speak of different degrees of reductive success in relation to how, for instance, novel predictions are vindicated in their own rights. This possibility also helps make sense of Nagel's insistence on distinguishing the formal condition of connectivity from that of derivability: although derivability, as Nagel (1979/1961, 353–357) indicated, entails obviously connectivity, the satisfaction of the latter condition represents the very first step of achieving reductive success. I thank the reviewer for encouraging me to consider this possibility.

4 The enterprise of reducing thermodynamics to statistical mechanics has achieved remarkable success to the extent that thermodynamics and statistical mechanics are often put together in an introductory course in physics today (Pathria and Beale 2022). However, I have also been informed by atmospheric physicists that statistical mechanics has just begun to have an impact on popular research topics like global warming; the use of relevant models remains controversial and (reductive) success is not guaranteed (Fan 2021).

5 Nagel (1979/1961) wrote that, for instance, ‘Avogadro's number can be calculated in alternative ways from experimental data gathered in different kinds of inquiry, e.g. from measurements in the study of thermal phenomena, of Brownian movements, or of crystal structure; and the values obtained for the number from each of these diverse sets of data are in good agreement with one another’ (361).

6 As a matter of fact, Van Riel and Van Gulick (2019) already notes that ‘Nagel suggests that at least some interesting reductions involve correction’, but they are greatly puzzled, because, in their view, ‘it is not clear how correction is possible if deduction is the basis for reduction. The truth of the reducing theories entails the truth of the reduced theories. This is what deduction is about’. Finally, they choose to blame Nagel for being inconsistent: ‘it is worth noting that Nagel introduced this criterion, even though it seems hardly compatible with his official model’. A Nagelian response to these comments is simply that correction is made by theory change rather than Nagel's model of reduction.

7 Reduced theories and reducing theories often evolve under the influence from each other: reduced theories can take in new experimental laws and request reducing theories to accommodate these laws (thus, creating a problem for the reductive enterprise), and reducing theories can suggest corrections and novel predictions within reduced theories (thus, making possible progress in reduction). Perhaps the best way of presenting theory change comes from William Wimsatt's ‘co-evolution of theories at different levels’: ‘theoretical conceptions of entities at different levels coevolve and are mutually elaborated … under the pressure of one another and ‘outside’ influences’ (2007, 252).

Additional information

Funding

This work was supported by Double First Class University Plan: [Grant Number 105000*1942221R3/002].