Explanations by Constraint: Not Just in Physics

ABSTRACT

Several philosophers have argued that ‘constraints’ constrain (and thereby explain) by virtue of being modally stronger than ordinary laws of nature. In this way, a constraint applies to all possible systems, for a variety of possibility that is broader (that is, more inclusive) than the variety we employ when we say that the ordinary laws of nature apply to all physically possible systems. Explanations by constraint are thus more broadly unifying than ordinary causal explanations. Philosophical examples of good candidates for constraints have heretofore been drawn almost exclusively from fundamental physics. This paper argues for the existence of such constraints (even multiple levels of them) in at least one human science (linguistics), not just in physics.

Disclosure Statement

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Notes

1 In referring to ‘causal interactions’, ‘causal history’, and so forth, I do not intend to presuppose any particular account of what causal relations consist in.

2 For example, Wigner (1972, 13) says in his Nobel Prize presentation speech: ‘[F]or those [conservation laws] which derive from the geometrical principles of invariance it is clear that their validity transcends that of any special theory—gravitational, electromagnetic, etc.—which are only loosely connected … .’ Likewise, Feynman (1967, 59) says, ‘When learning about the laws of physics you find that there are a large number of complicated and detailed laws, laws of gravitation, of electricity and magnetism, nuclear interactions, and so on, but across the variety of these detailed laws there sweep great general principles which all the laws seem to follow. Examples of these are the principles of conservation … .’ Similarly, Bergmann (1962, 144) remarks that the conservation laws are ‘general laws applying uniformly to every assembly of mass points regardless of the particulars of the force laws.’ I take all of these remarks to be characterising various conservation laws as constraints on the dynamical laws. Lange (2009; 2017) gives further examples.

3 The association between symmetries and conservation laws (within a Hamiltonian framework), codified in Noether’s first theorem, does not suffice to establish the explanatory priority of symmetries over conservation laws because (as Noether showed) the association runs in both directions; Noether’s theorem is ‘symmetric’ in this way. Accordingly, some philosophers have held that the symmetries do not help to explain the conservation laws. For example, Albert (2015, 14) says that ‘what actually explains [the conservation of energy] are the fundamental physical laws of the actual world’. Likewise, Brown and Holland (2004, 10) maintain that ‘the real physics is in the Euler-Lagrange equations of motion for the fields, from which the existence of dynamical symmetries and conservation principles, if any, jointly spring’. (Later Brown (2022) offered a pragmatic account of explanation, using it to reject the explanatory priority of symmetry principles.) However, these views run contrary to a broad agreement among physicists that symmetries explain conservation laws. (See, among many others, Wigner 1964, 959; Weinberg 2004; Zee 1986.) Rather than run contrary to this broad agreement, Lange (2007; 2009) has aimed to derive the symmetry principles’ explanatory priority over the conservation laws from the symmetry principles’ status as meta-laws (whereas the conservation laws are first-order laws). Meta-lawhood is associated with a broader range of counterfactual invariance and hence a stronger variety of necessity than the associated first-order laws possess. Roughly speaking, the symmetries’ explanatory priority depends on its being the case that the symmetries would still have held, even if the conservation laws (or the Hamiltonian framework) had failed to obtain.

4 ‘STR is not a theory in the usual sense but is better regarded as a second-level theory, or a theory of theories that constrains first-level theories’ (Earman 1989, 155).

5 For further discussion and references, see Lange (2017, 144–145).

6 The key role played by such counterlegals in Lange’s account of laws and of ‘explanations by constraint’ has provoked many potential objections. (See, for example, Andersen 2018; Morrison et al. 2019; Saatsi 2018; Skow 2018; Woodward et al. 2011.) Questions that might be asked include how these counterfactuals can be ascertained empirically, whether these counterfactuals can account for explanatory asymmetries, whether natural laws are preserved in science under as wide of a range of counterfactual antecedents as Lange maintains they are, whether Lange should instead have construed ‘explanations by constraint’ as associated with entire systematic patterns of counterfactual dependence, how necessity is related to stability under nested counterfactuals, whether some ‘explanations by constraint’ are too superficial to constitute genuine explanations, and what is responsible for these counterfactuals’ truth. Although Lange (in Lange 2018; Lange 2019; Woodward et al. 2011, 45–52) offers replies to these questions, I do not believe that their details are crucial to the prospects (under discussion here) of extending something like Lange’s notion of ‘explanation by constraint’ outside of fundamental physics.

7 Ben-Menahem (2018) also looks at various principles in physics that I would characterise as having often been taken (by physicists and philosophers alike) to be constraints (such as symmetry principles, conservation laws, and determinism). As I am doing, she takes them (if they are indeed constraints) to be explanatory; she highlights how these constraints would explain why certain things never occur and also how these constraints would help to delimit ‘physical possibility’ (110). Unlike Lange, she does not characterise the principles that she calls ‘constraints’ in terms of counterfactuals or as modally stronger than ordinary natural laws (16); rather, she leaves open how they should be understood metaphysically. (She calls them ‘causal constraints’ because they constrain the possible causal processes (15); Lange takes them as explaining non-causally, but this seems like a merely terminological difference.) Whereas Lange’s ‘constraints’ directly constrain first-order laws, Ben-Menahem’s directly constrain events. Adlam (2022) also characterises certain putative laws as ‘constraints’ and ‘as primarily concerned with describing what is possible or impossible’ (5). But unlike Lange, she does not use counterfactuals to cash out their status. Furthermore, her concerns are very different from mine. She is concerned with fashioning a non-Humean account of lawhood that would apply if (as some current physical theories say) there are no fundamental laws (such as the various force laws) that ‘act moment-by-moment on states’ (22) to govern the time-evolution of individual physical systems interacting with one another (7, 12). Instead, the ‘constraints’ with which Adlam is concerned are ‘genuinely global, atemporal laws’ that ‘govern holistically and all-at-once’ (11), such as variational principles and consistency conditions. Since Adlam’s ‘constraints’ are not constraints on the various specific dynamical laws that take ‘the standard Newtonian time-evolution form’ (2) in applying to particular time-asymmetric causal (12) interactions, Adlam’s constraints are not higher-order laws; they are all of the laws. This is very different, then, from the sorts of constraints with which I am concerned (and that I am aiming to show may arise in explanations outside of fundamental physics). Physicists like Wigner and Feynman (note 2) evidently construe symmetry principles and conservation laws as constraints in the sense I am describing, i.e., as constraining lower-level, dynamical laws. (Chen and Goldstein (2022) develop a primitivist view of laws much like Adlam’s according to which laws constrain the physical possibilities atemporally.)

8 Despite its limitations, many studies have taken Kemp and Regier’s work as a model for explaining other linguistic phenomena, including color terms and indefinite pronouns. See, for instance, Denić, Steinert-Threlkeld, and Szymanik (2022), Kirby et al. (2015) and the references cited therein.

9 For further discussion of apparent merger reversals and how ‘by linguistic means’ in the irreversibility principle (‘Garde’s Principle’) needs to be interpreted, see Clark, Watson, and Maguire (2013) and the other papers that it introduces.