Abstract
In this paper, I will defend the thesis that fundamental natural laws are distinguished from accidental empirical generalizations neither by metaphysical necessity (e.g. Ellis 1999, 2001; Bird in Analysis, 65(2), 147–155, 2005, 2007) nor by contingent necessitation (Armstrong 1983). The only sort of modal force that distinguishes natural laws, I will argue, arises from the peculiar physical property of mutual independence of elementary interactions exemplifying the laws. Mutual independence of elementary interactions means that their existence and their nature do not depend in any way on which other interactions presently occur. It is exactly this general physical property of elementary interactions in the actual world that provides natural laws with their specific modal force and grounds the experience of nature’s ‘recalcitrance’. Thus, the modal force of natural laws is explained by contingent non-modal properties of nature. In the second part of the paper, I deal with some alleged counterexamples to my approach: constraint laws, compositional laws, symmetry principles and conservation laws. These sorts of laws turn out to be compatible with my approach: constraint laws and compositional laws do not represent the dynamics of interaction-types by themselves, but only as constitutive parts of a complete set of equations, whereas symmetry principles and conservation laws do not represent any specific dynamics, but only impose general constraints on possible interactions.
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Notes
There are also conceptions of necessity of laws that allow for degrees. Lange (2009), for example, claims that there are different sorts of laws which are distinguished by their possessing different degrees of necessity: meta-laws (e.g. the law of energy conservation) allegedly possess some higher degree of necessity as compared to ‘common’ laws because of their embracing a wider range of counterfactual stability; their validity would resist counterfactual variations even with respect to common laws, whereas common laws remain only valid against counterfactual variations with respect to non-lawful facts.
Cf. Van Fraassen (1989), 96ff.
Cf. Armstrong (1997), 230.
Cf. Armstrong (1997), 231.
Cf. Schrenk (2011), 580–581.
See: Schrenk (2011), 588 f.
Regarding universals, Armstrong is a categoricalist/quidditist (cf. Armstrong 1997, Chapters 3–5), that is, just like Lewis, he believes that no property (universal) has its nomological or causal role attached essentially. In the above interpretation (his own!) Armstrong’s quidditism holds only with the exception of the second-order universal N: N has its lawmaking role attached essentially (necessarily). “Yet, think now of N as being quidditistic, too. Then we do not only get the above contingency of laws, but also that, in some worlds, N ceases to be necessitation, i.e., that, there, it is no productive force. In such worlds, F’s might well not be G’s despite N (F, G) because, there, N (F, G) has no necessitating power. Under this interpretation, N would be, at least in our world, pure production, free of any modal connotations.” (Schrenk unpublished).
As is well-known, conservation of energy-momentum does not, in general, hold in General Relativity (cf. Wald 1984; Lam 2010). Now, the concept of causality entails ‘balanced’ change: no change can be causal, if it is not balanced by some equal change, where the measure of equality is, according to the transfer-theory of causation, energy-momentum. But then, according to my identification of laws with causal interactions, laws could only exist within general relativistic spacetimes, if those spacetimes have very special symmetry properties (existence of time-like Killing fields, e.g. in FRW-worlds). Now, the reason for the failure of energy-momentum conservation in a gravitational field is not that energy-momentum is in any sense lost or created ex nihilo (there exists an equation representing ‘differential energy conservation’ which guarantees that there is no mysterious local loss or creation of energy in the system (cf. Lam 2010, 65)). Instead, a material system moving in spacetime loses or gains energy-momentum “because the gravitational tidal forces can do work on the fluid and may increase or decrease its locally measured energy” (Wald 1984, 70). Thus, the non-conservation of energy-momentum of the material system is generically balanced by the energy-momentum of the gravitational field (whereas in flat spacetimes the energy-momentum of the material system remains constant for each spatio-temporal displacement). What is special about the case of General Relativity is that there is no invariant integral expression for the energy exchange between material system and the field; since gravitational energy can be ‘transformed away’ locally, the energy contained in a finite volume of spacetime, and thus the quantity of energy exchanged with a material system, depends on the coordinate system. In sum, I argue that processes in a gravitational field can be conceived as causal because no energy-momentum is lost or created – despite the fact that the amount of energy that is exchanged in the interaction with the field can only be determined relative to some coordinates.
Cf. Hüttemann (2014), 33 f.
There are also Lagrangians describing ‘free particles’, i.e. the idealized interaction-free case.
It should be noted that, according to Beebee (2011), even modal accounts of laws like essentialist or necessitarian accounts would be unable to overcome the inductive skeptic. A time-limited assumption of necessary connections (the necessary connections have hold so far) would provide as good an explanation for the so far observed regularities as the corresponding timeless assumption. But the time-limited assumption would then be compatible with the possibility that the necessary connections would cease tomorrow. Thus time-limited necessary connections cannot support inductive inferences to the future, but they can (at least) explain the success of our past inductive practice. Since I accept this point, I cannot require my own account, which includes not even any genuine modal factor, to do better than to explain the past inductive practice, i.e. to give a reason for the fact that former law-based counterfactuals had been justified.
Cf. Lewis (1973).
Cf. Armstrong (1983), 89.
Wolff (2013), 901.
The term ‚electron‘ has been coined by Stoney for the ‚atom of electricity‘, i.e. for the then hypothetical bearer of elementary (negative) electrical charge. Thus, literally understood, ‚Electrons are negatively charged‘is an analytical truth.
Tahko (2015), 520.
Tahko (2015), 520.
Cf. Tahko (2015).
Cf. Earman (1995), 125–126.
Cf. Ohanian (1976), 259.
Wigner (2003), 24.
Wigner (2003), 25.
Cf. Stöckler (1997), 346.
Stöckler (1997), 347.
Stöckler (1997), 346.
Stöckler (1997), 347.
Ohanian (1976), 258.
See: Noether (1918).
Brading and Brown (2003), 97.
cf. Wolff (2013), 904/05.
Brading and Brown (2003), 102.
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This article belongs to the Topical Collection: EPSA17: Selected papers from the biannual conference in Exeter
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Bartels, A. Explaining the modal force of natural laws. Euro Jnl Phil Sci 9, 6 (2019). https://doi.org/10.1007/s13194-018-0225-5
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DOI: https://doi.org/10.1007/s13194-018-0225-5