An Argument for the Extrinsic Grounding of Mass


Several philosophers of science and metaphysicians claim that the dispositional properties of fundamental particles, such as the mass, charge, and spin of electrons, are ungrounded in any further properties. It is assumed by those making this argument that such properties are intrinsic, and thus if they are grounded at all they must be grounded intrinsically. However, this paper advances an argument, with one empirical premise and one metaphysical premise, for the claim that mass is extrinsically grounded and is thus an extrinsic disposition. Although the argument concerns mass characterized as a disposition, it applies equally well whether mass is a categorical or dispositional property; however, the dispositional nature of mass is relevant to some important objections and implications discussed.

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  1. 1.

    For example, Heil (2003, p. 111) maintains this view.

  2. 2.

    For example, Prior et al. (1982) maintain this view.

  3. 3.

    The Higgs field is named after Peter Higgs, who first posited its existence.

  4. 4.

    Thanks to two anonymous reviewers for helping me refine my definition of ‘grounding’ and other definitions.

  5. 5.

    Supposing that F is multiply realizable, such that F could have several distinct, complete grounds, then the very same F could gain another grounds upon losing the original grounds. So it should be added that if the all of the possible multiply realizing grounding properties of F are eliminated, this would result in the elimination of F (Thanks very much to an anonymous reviewer for pointing out the possibility of the multiple realization of F).

  6. 6.

    The supervenience relation may be thought to be the same relation as that of grounding, but this is not the case. Assume a standard conception of supervenience, following Davidson (1970): (1) no two things are alike in all B respects but differ in some A respect, and (2) nothing alters in an A respect without altering in some B respect, hence A properties supervene on B properties. Supervenience may suggest, but does not entail, that one property is the grounds of another. For, two otherwise unrelated properties, on opposite sides of the universe, may share a supervenient relationship if they co-vary according to conditions (1) and (2).

  7. 7.

    Every contention Mumford and Molnar make, to my knowledge, seems consistent with ‘grounds’ being synonymous with ‘casual basis’.

  8. 8.

    Handfield (2008, p. 298) distinguishes between the supervenience base of a disposition and the causal basis for the manifestation of a disposition, similar to my distinction between grounds and causal basis.

  9. 9.

    Langton and Lewis (1998, p. 337) hold that “a property is intrinsic iff it never can differ between duplicates; iff whenever two things (actual or possible) are duplicates, either both of them have the property or both of them lack it.” To relate this to my definition: if an object x that is duplicated in a world where x is the sole occupant, then x will have instances of the same type of properties as the original object in the actual world; intuitively this is because x’s having those properties does not depend on any properties of distinct, existent objects, per my definition.

  10. 10.

    It should help, as an anonymous referee kindly pointed out to me, to explicitly set out which combinations of intrinsic/extrinsic and intrinsically grounded/extrinsically grounded work and which do not work:

    1. Extrinsic and extrinsically grounded: This is possible, and it appears that if F is an extrinsic token property then it is necessarily extrinsically grounded (more on this later in the footnote).

    2. Extrinsic and (fully) intrinsically grounded: This does not seem possible, because if F is extrinsic, then it will be dependent on some properties not instantiated by the object possessing F (though F might still be partially intrinsically grounded).

    3. Intrinsic and intrinsically grounded: This is possible, though the claim that F’s being intrinsic necessarily requires intrinsic grounds is clearly denied by proponents of the Ungrounded Dispositions Thesis (see Sect. 3 of this paper).

    4. Intrinsic and extrinsically grounded: This does not seem possible, for it violates the independence requirement for being an intrinsic property token.

    The same anonymous reviewer further remarks that it is an odd logical implication that, per the conceptions I advance, being extrinsic entails being extrinsically grounded (whereas being intrinsic and intrinsically grounded are logically independent, notably if fundamental properties are intrinsic but ungrounded). The reviewer gives the following example: the property of being a parent, P, is extrinsic, since to be instantiated it requires a child. But is P grounded partially (and thus extrinsically) in that child? Perhaps not, since parenthood is a relation between parent and child, but not grounded in them; it doesn’t depend, for instance, on any microstructures of the parent and child, the reviewer suggests. My response is twofold. First, while interesting, this may not matter to my main argument. All I really need is the implication to go the other way: a property token, F, being extrinsically grounded entails that F is extrinsic, such that, if mass is extrinsically grounded, then mass is extrinsic (and this is how I defend premise two of my main argument in Sect. 3). Second, it seems equally plausible to me that, strictly speaking, P does indeed require an existent child, and so P is extrinsically grounded. Why? If someone’s child (or children) no longer exists, then the property he or she instantiates is being a former parent, not being a parent. The person was a parent, but no longer is. This may seem a bit unpalatable, but it’s not wildly counter-intuitive. Compare the idea that when a woman’s husband no longer exists, she ceases to be a wife and becomes a widow—she ceases to instantiate the property of being a wife and begins instantiating the property of being a widow. (Thanks to the anonymous referee who prompted this entire footnote.).

  11. 11.

    The main argument for UDT, what I call the Argument from Physics, is roughly this: (i) properties of fundamental particles are dispositions; (ii) fundamental particles are metaphysically simple, containing no micro-components and thus no properties of micro-components that could ground their dispositions; thus, (iii) the dispositions of fundamental particles are not grounded in any distinct properties, although they endure through non-manifestation periods. Mumford (2006) presents the Ungrounded Argument, a fully developed and explicit formulation of the argument for ungrounded dispositions based on physics; see Williams (2009) for a critique.

  12. 12.

    Thanks to an anonymous reviewer for suggesting formulating UDT with two sub-claims, and for also pointing out that some dispositions of fundamental particles are arguably not fundamental properties, e.g., the charge-to-mass ratio of fundamental particles is non-fundamental because it depends on mass and charge. Proponents of UDT cite what appear to be fundamental properties (mass, charge, spin) as examples of ungrounded dispositions. It is an implication of my argument in this paper that mass is not fundamental, but the disposition of particle a to gain mass may be fundamental. I discuss this further in Sects. 4, 5, and 6.

  13. 13.

    Here it is useful to refer to the marks of being a disposition, discussed by McKitrick (2003a, p. 157), which are prevalent throughout the literature on dispositions as McKitrick (2003a, pp. 156–157) notes. The marks of being a dispositional property, where D is a disposition, are: (1) D has a characteristic manifestation when appropriately stimulated; (2) D requires triggering or activation in the appropriate circumstances; (3) a counterfactual statement typically holds true of the object, x, bearing D; (4) an overtly dispositional locution holds true of x. These marks are not definitive; they are simply indicators of being a disposition, or useful ways of identifying dispositions. We can apply these indicators of being a disposition to the mass of an electron, for example, concluding that mass is probably a disposition: (1) a characteristic manifestation of mass is the resistance of acceleration when an acceleration force is applied to the object bearing mass, (2) the manifestation of mass requires triggering by an acceleration force (3) ‘if an electron were pushed, it would resist acceleration’ is true of electrons, and (4) electrons are said to have the tendency (i.e., disposition) to resist acceleration.

  14. 14.

    It is possible that properties of fundamental particles are categorical, but my main argument aims to show that mass is extrinsically grounded whether it is categorical or dispositional. I frame my critique of UDT in terms of dispositions primarily because (1) the principal proponents of UDT categorize properties of fundamental particles that way, (2) mass does seem to be dispositional (see, e.g., Ellis 2002, p. 47; Isaacs 2000), and (3) in two of the implications I discuss the dispositional nature of mass plays an important role.

  15. 15.

    Lewis (1986, p. 59) distinguishes sparse properties from abundant properties. The sparse properties are the natural properties, those typically discovered and discussed by various sciences, especially fundamental physical properties. The abundant properties are non-natural properties, including all sorts of disjunctive properties.

  16. 16.

    According to Haisch et al. (2001, p. 393), when we detect the Higgs boson (the particle constituent of the Higgs field) a legitimate question concerning “whether the inertia of matter as a reaction force opposing acceleration is an intrinsic or extrinsic property of matter” will remain. My argument aims to show that the Higgs field-particle relation implies that mass is extrinsic and extrinsically grounded.

  17. 17.

    Psillos (2006, pp. 153–154) briefly discusses the Higgs boson in drawing attention to the inconclusiveness of theoretical physics regarding the question of whether fundamental dispositions are grounded or not. Psillos, however, does not specifically argue for the extrinsic grounding of mass as I do.

  18. 18.

    See Peskin and Schroeder (1995, pp. 781–800), and Zee (2003), for the mathematics of the Higgs field.

  19. 19.

    Photons are mass-less since they move through the Higgs field “completely unhindered” (Greene 2004, p. 263).

  20. 20.

    In accordance with Einstein’s equation, E = mc2, a “store of energy can be thought of as a source of inertial mass” just as “inertial mass can be thought of as a store of energy” (Jammer 2000, p. 163, footnote 51).

  21. 21.

    This is a different sense of ‘activate’ than is typically used in discussing the triggering of dispositions, such as the triggering of fragility, but this seems due to the fact that we are discussing the gaining of further dispositions.

  22. 22.

    Some supporters of the intrinsic dispositions thesis (that all dispositions are intrinsic) think that perfect duplicates subject to different laws of nature could have different dispositions (e.g., Lewis 1997).

  23. 23.

    Does the Higgs field’s capacity to ground mass in particles require the laws of nature to be a certain way? It seems not. The Higgs field may have had a different value if the laws of nature were different (if, for instance, events at the beginning of the universe were different), yet the Higgs field would still have existed and been responsible for the of particles. See Greene (2004, pp. 254–263) for a discussion of the different values the Higgs field could have depending on early events in the formation of the universe.

  24. 24.

    Thanks to an anonymous reviewer for pointing out the distinction between passive and active gravitational mass.

  25. 25.

    The name “CERN” stands for the French Conseil Européen pour la Recherche Nucléaire, or European Council for Nuclear Research (from the CERN website,

  26. 26.

    Schaffer (2003, p. 505) concludes that we have no evidence for a fundamental level. He finds that “there are at least two perfectly good conceptions of the hierarchy of nature: fundamentality and infinite descent. The empirical evidence to date is neutral as to which structure science is reflecting. And so, concerning the proposition that there exists a fundamental level of nature, one should withhold belief” (Schaffer 2003, pp. 505–506). Dehmelt (1989) theorizes that there are infinite levels of structure below the electron. See also Georgi (1989, p. 456).

  27. 27.

    Molnar (2003, p. 133) discusses this example but thinks it is insufficient to justify ultra-grounding.

  28. 28.

    Energy fields, e.g., gravitational fields and electromagnetic fields, have far-reaching spatial extension and so could ground many types of dispositions of fundamental particles, as the argument from the Higgs field tries to show with mass. Interestingly, another species of Higgs field, the electroweak Higgs, is thought by some physicists to unify the electromagnetic and weak nuclear forces (Jammer 2000, p. 162), suggesting the possibility of an ultimate grounding field. It seems that fields represent a distinct possibility for the ultra-grounding of dispositions. The particle interpretation of Quantum Field Theory (QFT) takes particles and their properties as the basic ontological elements, but significant problems exist for the particle interpretation (see Kuhlmann 2006, and Harré 1986, pp. 261–280). The alternative is the field interpretation of QFT, which holds that fields and their properties are ontologically fundamental. On the field interpretation of QFT, we can ascribe energy and momentum to fields where no particles are present (Kuhlmann 2006, §5.1.2).


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I would like to thank Jennifer McKitrick for many beneficial discussions about the ideas in this paper, and for providing detailed comments over the course of several early drafts. I presented earlier versions of this paper at both a graduate student colloquium (in December 2008), and a meeting of a graduate seminar on dispositions led by Jennifer McKitrick (in November 2006), at the University of Nebraska-Lincoln; I am grateful for discussion with audience members at both events. Thanks to Ed Becker, David Chavez, Reina Hayaki, Harry Ide, Jonathan Jacobs, Joe Mendola, and Stathis Psillos for discussion and feedback. Three anonymous reviewers for Erkenntnis provided very detailed and helpful comments, and I thank them for their generosity. Two other anonymous reviewers also provided helpful feedback on a very early version of this paper.

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Bauer, W.A. An Argument for the Extrinsic Grounding of Mass. Erkenn 74, 81–99 (2011).

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  • Higgs Boson
  • Gravitational Field
  • Inertial Mass
  • Gravitational Mass
  • Dispositional Property