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Nomological Resemblance

Abstract

Laws of nature concern the natural properties of things. Newton’s law of gravity states that the gravitational force between objects is proportional to the product of their masses and inversely proportional to the square of their distance; Coulomb’s law states a similar functional dependency between charged particles. Each of these properties confers a power to act as specified by the function of the laws. Consequently, properties of the same quantity confer resembling powers. Any theory that takes powers seriously must account for their resemblance. This is the challenge set by the paper. The first part is devoted to Armstrong’s view according to which property resemblance reduces to partial identities between categorical properties. I argue that Armstrong’s solution to the challenge involves accepting determinable properties but that these should not be admitted. In the second part, I argue that dispositional essentialism can satisfactorily account for orderings among powers in terms of degrees of overlapping potentialities.

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Notes

  1. The characterization below is to be found in Gibb (2007, 541).

  2. Structural universals come in two forms: those that involve certain relations among the parts of the objects that instantiate the universals and those that do not (Armstrong 1978, pp. 70–71). As an example of the first kind is the property of being a 2 m straight line. As an example of the second is the property of being 3 kg in mass. Although in the case of mass it does not matter exactly how the parts are joined together, it does matter in the case of length.

  3. Mass m 1 is also a structural property in that for something to be m 1 is for it to consist of two proper parts, each of which instantiates 0.5 kg mass. Whether every mass dissolves into a complex structure depends on whether there is a minimum mass—a question to be decided on a posteriori grounds (Armstrong 1997, p. 33).

  4. These masses stand in relation to one another in the proportions that they do independently of a choice of metric for the purpose of comparing them (see, e.g., Gibb 2007, p. 549).

  5. See Black (2000), Kistler (2002), and Bird (2007, pp. 73–76) for similar arguments.

  6. Recall that the paper is restricted to intrinsic resemblance. The reductive categoricalist has no problem per se in accounting for resemblances among properties qua their playing similar roles in causation and laws. However, since natural properties do not have their powers of necessity, the resemblance becomes external insofar as it fails to supervene on the properties alone. For the resemblance to be internal, the powers would have to be essential to those properties—and this is exactly what categoricalism denies.

  7. The ceteris paribus clause is needed because defeaters might interfere with the causal process going from the stimulus condition to the manifestation of the powers. These defeaters will either remove the power’s causal basis before it can give rise to its manifestation or interfere with its normal process (i.e., the process leading to the manifestation) while leaving the power intact. Defeaters of the first kind are called “finks” (Martin 1994). Defeaters of the second kind are called “masks” (Johnston 1992). See also Bird (1998) for a more elaborate conception of masks (which he calls “antidotes”).

  8. Others that have discussed this kind of resemblance include Vetter (2009, p. 326) and Ellis (2005, p. 470).

  9. The presentation of Armstrong’s theory is taken from his (1983, pp. 111–116) and (1997, Ch. 16.1).

  10. It is surprising to learn that Armstrong in his A Combinatorial Theory of Possibility (1989, pp. 90–91) argues, for this very reason, that second-order determinable universals are not entailed by, and so do not supervene on first-order determinate properties. Why this sudden change of mind in (1997)? We are not told.

  11. To be sure, Armstrong (1989, p. 80) postulates analyticity as the source of the impossibility of identifying the whole of a structural property with one of its constituent parts. However, if successful, this would only explain why different determinate properties of the same determinable are incompatible in that they cannot be instantiated by the same particular at the same time. It would not explain why instantiating any of these determinate properties necessitates instantiating a corresponding determinable (second-order) universal.

  12. In those cases where D M/S states a multi-track power, M and S will be logically complex (Bird 2007, p. 21).

  13. Some properties have their identity exhausted by multiple powers, rather than a single power. In that case, the right-hand side of (DE≡) would have to state the total set of powers had by the property in question.

  14. For identity conditions for states of affairs, see Armstrong (1997, pp. 131–132); for events, see Kim (1993, p. 35).

  15. There is a serious difficulty associated with providing a purely relational identity condition for powers. In order to determine the identity of D M/S , we must determine the identity of M and S. However, M and S will both be properties whose identities, in turn, are determined by their respective powers and so on. Clearly, this procedure either leads to an infinite regress or a circularity (the latter of which occurs when one of the elements in the descending sequence of properties and powers is identical with an earlier element in the sequence). Critics of dispositionalism are thus able to argue that the identity of powers is indeterminate (Lowe 2006, p. 138; Robinson 1982, pp. 114–115). Notice, however, that this objection only poses a threat to dispositional monism (i.e., the view according to which all natural properties are essentially dispositional). If one prefers a mixed view according to which some properties are categorical and some are dispositional, then the former can serve as the grounding for identities of powers, without leading to regress or circularity. As a matter of fact, even if one is a dispositional monist, there is no real danger involved in giving a purely relational identity condition for powers. For as Bird (2007, pp. 138–146) has shown, one can take the identity of powers to supervene on the patterns of stimulus and manifestation relations. To go into the details of this theory would take us beyond the scope of the present paper. Suffices to say that there are solutions to the regress/circularity problem that are compatible with the present form of dispositional essentialism.

  16. That powers stand in relation of dependence to something that may or may not be realized has been the subject of a line of critique by Armstrong (1997, p. 79). Suppose that a has D M/S , but that a never receives S and so never manifests M. Insofar as the identity of a power is exhausted by its stimulus and manifestation conditions, D M/S a involves essential reference to the merely possible states of affairs M a and S a. Armstrong finds this problematic as it seems to give rise to a “Meinongian metaphysics, in which actual things are in some way related non-existent things” (ibid, p. 79). However, both Handfield (2005) and Bird (2007, p. 106) have shown that Armstrong’s own theory of powers does not fare any better as it is vulnerable to the same exact criticism. Moreover, if one accepts the Barcan formula (i.e., ◊∃xFx ⊃ ∃xFx), then one should accept that if the existence of P a necessitates the possibility that F a, then P a also necessitates the existence of a possible F a. We could thus understand the dependence to obtain between D M/S a and the merely possible existence of S a and M a. This is not to say that the Barcan formula is uncontentious. It implies that all things which exist in some possible world exist in the actual world, which has upset some possibilists. That said, the formula is a theorem of what is generally regarded the most plausible system of quantified modal logic, i.e., S5 with identity. So if one were to reject the formula, one would have to reject the simplest and strongest system of modal logic there is (along with unrestricted accessibility). To be sure, Kripke provides semantic models for modal logic in which the formula is neither automatically forthcoming nor axiomatic. However, as Bird (2007, p. 112) points out, Kripke’s semantics is not without its own problems and makes the axiomatization of modal logic rather complicated. For a longer discussion on this solution to the problem of unmanifested power and why it is compatible with the Eleatic Principle discussed in Section 2, see Bird (2007, pp. 111–114).

  17. The distinction between powers and potentialities is not necessarily reflected in natural language usage, but is here merely introduced as a technical refinement of the terms.

  18. Gillett and Rives (2005, pp. 487–493) argue something similar. However, their argument differs from mine in that they identify determinable properties with proper subsets of each of the sets of powers that individuate their determinates, while I identify them with aggregates of potentialities.

  19. Eddon (2007, pp. 393–396) argues that there are examples of resembling determinates that do not conform to this model, most notably quantities that admit of negative and positive instances. The example he gives is that of charge. Positive and negative charge properties do not share any constituents (whether categorical or dispositional), and yet they are both charge. However, what Eddon fails to realize is that the comparison of determinates of different determinables may sometimes give rise to classifications that justify the use of the same name, as for example in the case of charge when two distinct families of properties allow for addition and subtraction. And as argued by Morganti (2012, p. 536), if property resemblance is best understood in terms of properties having similar causal powers, then “quantities admitting of positive and negative cannot fall under the same determinable exactly because they can be added and subtracted to each other; for, this is the case in virtue of their having distinct (indeed opposite!) causal powers.” Hence, unless one allows for linguistic practice to have metaphysical consequences, Eddon’s argument is inconclusive.

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Correspondence to Robin Stenwall.

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Stenwall, R. Nomological Resemblance. Int Ontology Metaphysics 14, 31–46 (2013). https://doi.org/10.1007/s12133-012-0108-8

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Keywords

  • Resemblance
  • Categoricalism
  • Dispositionalism
  • Laws of nature
  • Powers