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What is the Point of Reduction in Science?

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Abstract

The numerous and diverse roles of theory reduction in science have been insufficiently explored in the philosophy literature on reduction. Part of the reason for this has been a lack of attention paid to reduction2 (successional reduction)—although I here argue that this sense of reduction is closer to reduction1 (explanatory reduction) than is commonly recognised, and I use an account of reduction that is neutral between the two. This paper draws attention to the utility—and incredible versatility—of theory reduction. A non-exhaustive list of various applications of reduction in science is presented, some of which are drawn from a particular case-study, being the current search for a new theory of fundamental physics. This case-study is especially interesting because it employs both senses of reduction at once, and because of the huge weight being put on reduction by the different research groups involved; additionally, it presents some unique uses for reduction—revealing, I argue, the fact that reduction can be of specialised and unexpected service in particular scientific cases. The paper makes two other general findings: that the functions of reduction that are typically assumed to characterise the different forms of the relation may instead be understood as secondary consequences of some other roles; and that most of the roles that reduction plays in science can actually also be fulfilled by a weaker relation than (the typical understanding of) reduction.

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Notes

  1. Cf. Dawid (2013), Huggett and Wüthrich (2013) and Woit (2006).

  2. The vagueness introduced by the “in principle” aspect of this definition is due to our inability in practice of actually going through and obtaining all of the results of the new theory in the old domain (due, e.g., to lack of computing power). Instead, the point is that we obtain enough ‘linkages’ (which I define below as ‘correspondence relations’) between the two theories that we believe (i.e., scientific consensus holds that) they approximately share the same results in this domain.

  3. As evidence of this, consider the Stanford Encyclopedia of Philosophy entry on scientific reduction (van Riel and Van Gulick 2016, §2.1), which briefly mentions, then dismisses this form of reduction as outside its area of interest.

  4. This is in contrast this with reduction1, whose aim is commonly taken as the explanation of higher-level laws (behaviour, theories, fragments of theories, models, etc.) in terms of lower-level ones.

  5. This is often referred to as the physicists’ convention, since it is how the term “reduction” is understood by physicists—the newer, more general, or more fundamental, theory, N reduces to the older, more restricted, or less fundamental theory, O. In contrast, the philosopher’s convention has O reduce to N.

  6. Wimsatt (1976, p. 680) conceives of levels of organisation as “primarily characterized as local maxima of regularity and predictability in the phase space of different models of organization of matter”.

  7. This is recognised in the case of reduction2, at least (Nickles 1973; Wimsatt 1976).

  8. See fn. 2.

  9. See Sect. 3.

  10. Although limiting relations are involved in derivations, they—strictly speaking—can only establish that solutions of the new equations coincide with solutions of the old equations in the limit (Hüttemann and Love 2016, p. 468).

  11. The various correspondence relations between quantum and classical mechanics are explored, e.g., in Radder (1991), Bokulich (2008); that these are insufficient to establish that classical mechanics is ‘contained within’ quantum mechanics, is argued in, e.g., Post (1971).

  12. The correspondence principle was famously proposed by Niels Bohr in the context of old quantum theory, yet the common understanding of the principle is most certainly not what Bohr meant by it (Bokulich 2014).

  13. Note that this is an original formulation, and thus differs from Post’s (1971) GCP.

  14. Note that the theories need not be compatible in any other sense!

  15. Whether the relations can actually achieve any of these roles in any particular real scientific case, depends on many factors, most of which will be case-specific. I do not explore these here.

  16. See fn. 15.

  17. Definition from Hoyningen-Huene (1993, p. 260).

  18. This section draws heavily from Crowther (2018), please refer to this for more details.

  19. See, respectively: Polchinski (1998a, b), Rovelli (2004) and Rovelli and Vidotto (2014), Henson (2009), Ambjorn et al. (2012), Oriti (2012).

  20. Accessible introductions to QG include Kiefer (2006), Rickles (2008).

  21. Cf. Norton (2003).

  22. See, e.g., Collins et al. (2009) and Liberati and Maccione (2011).

  23. This is related also to the issue of emergence, cf. Crowther (2016) and Wüthrich (2017).

  24. See, e.g., Dowker (2005), Oriti (2014) and Padmanabhan (2016).

  25. This is the case, e.g., in string theory, (Polchinski 1998a, b)

  26. Recall that derivability (which may be established using relations of correspondence which need not be asymmetric) is being used to demonstrate the asymmetric relation of reduction: i.e., that all the successful parts of the reduced theory can (approximately and appropriately) be obtained from the reducing theory. The idea of dependence, or relative fundamentality, is that the reduced theory is thus shown to be embedded within the reducing theory (and hence that the physics described by the reduced theory depends on that of the reducing theory).

  27. Keeping in mind the qualifications regarding my use of this term, outlined on p. 3.

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Acknowledgements

Thank you to my colleagues in the Department of Philosophy at the University of Geneva, as well as two referees for their helpful feedback on this paper. Funding was provided by Schweizerischer Nationalfonds (Grant No. 105212 165702).

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    Karen Crowther

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Crowther, K. What is the Point of Reduction in Science?. Erkenn 85, 1437–1460 (2020). https://doi.org/10.1007/s10670-018-0085-6

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