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A challenge for Super-Humeanism: the problem of immanent comparisons

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According to the doctrine of Super-Humeanism (Esfeld in Synthese., 2017), the world’s mosaic consists only of permanent matter points and changing spatial relations, while all the other entities and features figuring in scientific theories are nomological parameters, whose role is merely to build the best law system. In this paper, I develop an argument against Super-Humeanism by pointing out that it is vulnerable to and does not have the resources to solve the well-known problem of immanent comparisons. Firstly, I show that it cannot endorse a fundamentalist solution à la Lewis, since its two pillars—a minimalist ontology and a best system account of lawhood—would generate, together, a tedious problem of internal coherence. Secondly, I consider anti-fundamentalist strategies, proposed within Humeanism, and find them inapplicable to the Super-Humean doctrine. The concern is that, since it is impossible to choose the best law system within Super-Humeanism, this doctrine may be charged with incoherence.

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  1. The primitive ontology is constituted by all the fundamental objects of the world. For a clarification of the term ‘primitive ontology’, refer to Esfeld and Deckert (2018).

  2. Here I have in mind the debate on the status of the wave function (Brown et al. 1995, 1996; Aharonov and Vaidman 1996).

  3. See also the following quote: “Entities that are not particles—such as waves or fields—come in as figuring in the explanation of the behaviour of the particles, but they are not themselves part of the experimental evidence.” (Esfeld 2017, p. 9).

  4. Indeed, Esfeld would probably regard his own statement (at least officially) as fallible.

  5. See Esfeld et al. (2018), Deckert et al. (2017), Vassallo et al. (2017), Vassallo and Esfeld (2016).

  6. Given that relativity teaches us that distances are not observables, it is striking that even in relativistic domains, distance relations—rather than spacetime intervals—are regarded as fundamental. To see how Super-Humeanism can be coherent while maintaining distance relations as fundamental, refer to Vassallo and Esfeld (2016), in which time is taken to derive from change in the universal configuration of matter.

  7. Note that the mosaic upon which the non-fundamental state of the world supervenes should not be understood as a particular spatiotemporal slice (the arrangement of local qualities at a particular instant in time), but as comprising the whole of spacetime itself, therefore as comprising the whole history of our fundamental facts—facts about matter points, their spatiotemporal relations and intrinsic properties—from the beginning until its end.

  8. By ideal knowledge I mean the kind of knowledge of the world one would have if one were omniscient.

  9. The official definitions of simplicity and strength are normally kept vague since their more precise characterization is supplied contextually in specific cases of science. See Woodward (2013).

  10. While we normally represent matter points and their distance relations as being embedded in geometric spaces (such as the Euclidean), within the Super-Humean view these spaces are only a means to achieve the best system. Esfeld’s project refers to the work already achieved in Huggett (2006), where it is shown that Euclidean geometry and Newtonian mechanics constitute the best law system for a mosaic that consists in particles’ distance relations and their change (Vassallo et al. 2017, p. 308; Vassallo and Esfeld 2016). See below for further explanation.

  11. E. K. Chen, The Best Summary of the Quantum World: The Universal Wavefunction as a Humean Law.

  12. This list is no way exhaustive; another notable example, which will not, however, be discussed here, is Martens’ Regularity Comparativism about Mass in Newtonian Gravity (Martens 2017).

  13. It is also unclear how exactly we should categorize them. Esfeld sometimes refers to ‘mass’, charge’ etc. as ‘dynamical parameters’, sometimes as ‘predicates’. I take mass and charge to be properties (or a family of properties), while ‘being massive’ or ‘being a charge’ to be predicates. However, in this paper, I employ the vague expression ‘parameters’ in conformity with Esfeld’s usage of the term.

  14. See also the following quote: “Hence, in a nutshell, there are distance relations, individuating the matter points and thereby constituting a configuration of them, and there is change in these relations. That is all.” (Esfeld and Deckert 2018, p. 8).

  15. See, for example, the quote already mentioned above: “It is in principle possible to do the whole of physics with just the notions of distances individuating matter points and change of these distances.” (Esfeld 2017, p. 8).

  16. For a discussion on the F predicate, see Lewis (1983) and Cohen and Callender (2009).

  17. Answering that the natural kinds are those that appear in the formulation of laws creates a vicious circle, since, in order to know which generalizations have law status, we first need to know what the natural kinds are. If this is not the case, at least, it seems to be like the chicken and the egg: which comes first, our fundamental language, out of which we construct laws, or laws from which we derive the fundamental language? Another option for the fundamentalist view would be to endorse the claim that natural kinds are those we derive from the laws of nature and the laws of nature are generalizations of the best system that is selected as ‘the winner’ after a comparison open to all languages. However, this move incurs the above problem of immanent comparison. Here we take the more charitable option of taking perfectly natural properties as primitive (Lewis 1983; Loewer 2007).

  18. For this specific claim and, more generally, for this section, I am much indebted to Dan Marshall and Ted Sider.

  19. Private conversations.

  20. T. Sider, The Tools of Metaphysics and of the Metaphysics of Science.

  21. The following reformulation of Newton’s second law takes inspiration from how Sider (Ms) reformulates the same law in the context of simple absolutism about quantities.

  22. It is surprising that Dorr, 8 years ago, elaborated on the same scenario Esfeld is proposing now. Here is how he commented on the proposal in 2010: “Philosophers who are suspicious of particular putative bits of hidden structure keep on rediscovering this fact, and announcing that they have shown how to eliminate the structure in question. But once we have realized the complete generality of the trick, we should not be impressed by their achievements.” (Dorr 2010, p. 160).

  23. I am grateful to Ted Sider for pointing this out to me. See Sider (Ms) for a detailed discussion on the ramsification strategy.

  24. Prima facie, there might be some scepticism about applying this procedure within Super-Humeanism because the ramsification strategy is normally taken to presuppose what Humeanism abhors (Howthorne 2006)—a fundamental nomological role for properties, which is specified by governing laws. However, it is always possible to tie the nomological role to the best-system approach by evaluating a property’s nomological role in terms of regularities in the mosaic (in the case of Super-Humeanism, by ramsifying the vocabulary in terms of the trajectories of matter points.).

  25. For instance, Dorr (2010) and Esfeld (2018) evaluate the possibility of ramsifying coordinate systems or inertial frames of reference, by referring to Huggett’s work (2006).

  26. B. Wheeler, Laws, natural properties and algorithmic compression.


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I am grateful to Dan Marshall for insightful discussions and extensive feedback on this project, and to Ted Sider for sharing thoughtful considerations on this topic. I also would like to thank Joan Bertran-San Millán, Michael Esfeld, Aldo Farrerons Filomeno, Ladislav Kvasz, Dan Marshall and two anonymous reviewers for sending me painstaking comments on earlier drafts of this paper. Finally, I acknowledge Jo Wolff’s professional support during the review process. Funding for this project was generously provided initially by the Hong Kong Research Grant Council (PF12-17373) and later by the Institute of Philosophy of the Czech Academy of Sciences (Grant Formal Epistemologythe Future Synthesis, in the framework of the program Praemium Academicum).

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Matarese, V. A challenge for Super-Humeanism: the problem of immanent comparisons. Synthese 197, 4001–4020 (2020).

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