Wildman’s Defense of Sparse Modalism and a Dilemma of Post-Finean Modalism

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Since K. Fine’s influential criticism of modalism, many philosophers have agreed that we cannot understand the concept of essence with that of modality. However, some philosophers have resisted this mainstream position. In this paper, I examine N. Wildman’s claim that, unlike other versions of modalism, his version of modalism, namely Sparse Modalism can save modalism. I will argue first that if we introduce the notion of grounding into this debates, Wildman’s criticisms of other versions are significantly undermined. Next, I will argue that since Sparse Modalism has an implicit commitment to grounding Wildman cannot blame revising other versions modalism with the concept of grounding. From these claims, I will conclude that the prospect of the success of modalism in general is at best dubious. Without the concept of grounding no version of modalism can succeed and with the concept of grounding no version is well motivated.

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  1. 1.

    According to Robertson and Atkins, “a modal characterization of the distinction between essential and accidental properties is taken for granted in nearly all work in analytic metaphysics since the 1950 s.”(Robertson and Atkins 2018 Edition) See also, (Kripke 1980, pp. 110–115; Lewis 1983b, p. 42).

  2. 2.

    “Modality” could mean many different things. In our context, philosophers are mostly interested in de re necessity. For the various meanings of modality, see (Perzanowski 2004, pp. 94–95). De re necessity can be classified as a version of ontological modalities.

  3. 3.

    Fine does not deny that the right of SM provides a necessary condition of an essential property.

  4. 4.

    In my opinion, the intuition behind EXISTENCE is not clear. Once we accept that existence is a property, one might want to say that every existent being has existence as its essential property. Fine thinks that only God can have existence as an essential property. One might counter that what distinguishes God from us is not that He has existence as an essential property but that He has necessary existence as an essential property. For this reason, in this paper, I will not fully address the EXISTENCE counterargument. An anonymous reviewer claimed that intuitions behind other counterexamples are not very clear either. I do think that they are not fully uncontroversial. However, those behind the other three examples are relatively clear and this is widely accepted. (footnote #5) For this reason I will focus on them. A similar point can be found in (Wildman 2013, pp. 767–769).

  5. 5.

    R. Michels says “Fine’s counterexamples are widely accepted among philosophers interested in essence”. (Michels 2019, p. 1017).

  6. 6.

    Their most prominent claims involve accepting non-standard modal theories according to which some impossibilities should play the role possibilities play in the standard theories. Once we accept this non-standard modal concept, they say, we can revive modalism (Brogaard and Salerno 2013; Correia 2007). Correia appeals to the concept of local possibilities which are not globally possible, while Brogaard and Salerno use the notion of counterpossible which is based on that of the entertainable impossibilities. I examined the strategies in this group in another place and argued that they are not successful (Lee & Kim 2018). For Fine’s reply to Correia’s modalism, see (Fine 2007).

  7. 7.

    As far as I know, the only defender of this strategy is E. N. Zalta.

  8. 8.

    Neither Gorman nor Denby uses “sparse (and/or abundant) properties.” Only Wildman and Cowling use this terminology. However, their views are quite similar to Wildman’s in spirit.

  9. 9.

    For those who are sympathetic to Della Rocca’s solution but think that every object has existence as its essential property, the definition of trivial property should be restricted so that existence can be classified as a non-trivial property.

  10. 10.

    ‘Directly trivial properties’ and ‘indirectly trivial properties’ are not Della Rocca’s terminology but Wildman’s. (Wildman 2016, p. 179).

  11. 11.

    “Necessarily” in the directly trivial property seems unnecessary. However, since Wildman used this expression, I will not remove it.

  12. 12.

    Unfortunately, there is no such thing as ‘the standard theory of grounding’. In fact, it is not very clear whether there is such thing as the (single) relation of grounding. (Wilson 2014) This is one reason why I do not formulate grounding relation in greater detail. Fortunately, however, some features of grounding are virtually common to major theories of grounding. One such feature is that grounding is stronger than necessary implication. To be sure, there are theories of grounding according to which grounding relation is not necessarily necessitating. For example, A. Skiles argue that there can be non-necessitating grounding relation. (Skiles 2015a) However, even Skiles does not claim that all grounding relations are non-necessitating. (Skiles 2015a, p. 718) So there is no reason for him to deny that necessitating grounding relation is stronger than necessary implication.

  13. 13.

    Many philosophers think that there is no such thing as mutual grounding. Some philosophers deny this. (Thompson 2016) Even if there is such a thing as mutual grounding, it is quite uncontroversial that this is not an example of mutual grounding. For a general argument against mutual grounding, see (Bennett 2017) especially 3.2.

  14. 14.

    Note that, as I claimed in footnote #9, the truth of this this claim does not depends on the detailed analysis of the notion of grounding. The rough and ready intuition concerning in virtue of relation is enough for the truth of this claim.

  15. 15.

    More precisely, one might argue, it is a property generated by lambda-abstracting from a universally quantified conditional. Thanks to an anonymous here.

  16. 16.

    Note that this does not imply that existence is a trivial property; existence cannot be grounded on existence.

  17. 17.

    Another natural answer seems to be that it is because he thinks that if A logically follows from B, then A is nothing over and above B. If something’s having a property is nothing over and above its having another property which is trivial, then the former must be trivial too. I believe that even if this is what is in Della Rocca’s mind, using grounding is not ad hoc either. ‘Nothing over and above’ is often regarded as an idiom of metaphysical dependence. (Bennett 2017, p. 35).

  18. 18.

    Hempel’s D-N model is a locus classicus of this confusion, and the famous flagpole counterexample shows why it is a confusion. We can infer the length of the shadow of a flagpole from its height, and we can also infer the height of a flagpole from the length of its shadow. However, only the former inference is explanatory while there is no difference as long as the logical structure of the inferences is concerned. For the detail of this counterexample, see (Salmon 1989, p. 47).

  19. 19.

    For Zalta’s metaphysical picture, see (Zalta 2006, p. Sec. 2).

  20. 20.

    For this reason, Zalta thinks that every object exists necessarily.(Zalta 2006, p. 667) This may sound strange. However, given the distinction between non-abstract concrete objects and non-abstract non-concrete objects, this result is not intolerable. According to Zalta, when we say that Socrates is a contingent being, what we should mean is that Socrates is non-concrete in some worlds.

  21. 21.

    This terminology and formulation are Wildman’s.(Wildman 2016, p. 191) For Gorman’s own formulation, see (Gorman 2005, p. 279).

  22. 22.

    For the skeptical views on grounding, see (Koslicki 2015; Wilson 2014).

  23. 23.

    J. Schaffer appeals to the notion of grounding too when he tries to replace the Lewisian conception with his own. He says, “The scientific properties are perfectly suited to ground the objective similarities within the above pairs. These objective similarities are grounded in shared scientific properties.” (Schaffer 2004, p. 94).

  24. 24.

    One might argue that one can use truth-making instead of grounding. Even though I prefer the latter to the former, I have no particular objection to this. However, that does not make much difference as truth-making is another obscure notion which is metaphysically heavy.

  25. 25.

    According to Stanford Encyclopedia of Philosophy, (Witner et al. 2005), (Trogdon 2009), (Bader 2013), (Witmer 2014) should be classified as “grounding theories” too. (Marshall and Weatherson 2018).

  26. 26.

    See (Denby 2014, p. 92) Denby says that “Intrinsicality is a relatively clear notion”. He concedes that intrinsicality is not fully clear. However, he claims that “it [the notion of intrinsicality] does at least seem clearer than the notion of an essence.”

  27. 27.

    We cannot identify metaphysical dependence with grounding. However, so long as we use ‘grounding’ reasonably broad, there must be a close relation between metaphysical dependence and grounding. For the related worry, see (Bennett 2017, p. 34).

  28. 28.

    The only alternative I can come up with is to appeal to the notion of truth-making and I already pointed out that this does not make any difference. See footnote#25.

  29. 29.

    It should be noted that even though Wildman is inspired by the Lewisian notion of sparse properties, he uses Schaffer’s notion of sparse properties. This is because such an essential property of Socrates as being human does not seem to be a Lewisian sparse property. We do not think that being human is a fundamental property. However, it is not clear that this twist really helps Wildman (for the criticism of Wildman using Schaffer’s notion, see Skiles (Skiles 2015b)). Even if using Schaffer’s notion does not produce difficulties, this shift does not allow him to escape from my criticisms. Even if he uses Schaffer’s notion and hence removes non-redundancy (minimality in Schaffer’s terminology) from the job list of sparse properties, he still could claim that sparse properties make for qualitative similarities and are intrinsic. Furthermore, there is no reason to remove completeness from the list.

  30. 30.

    An anonymous referee claimed that since defenders of PFMs have introduced various ‘metaphysically heavy’ concepts into the modalism debate even before the introduction of grounding, they have no particular reason to avoid that of grounding. As a reply, I point out three things. First, this objection does not apply to Della Rocca’s theory. His version appeals to the notion of logically follow relation which is not metaphysically heavy. Given this, other things being equal, the most attractive version of PFM may seem to be his. However, Wildman’s argument and my arguments show that there is no prospect of having a ‘metaphysically light’ version of PFM. Second, although it is true that Zalta, Gorman, and Wildman use some kinds of metaphysically heavy concepts, they did not think that their use of abstracta, characteristics, and sparse property could invite circularity problems. However, as I pointed out, as soon as we appeal to the concept of grounding to improve their PFMs, the circularity worries become genuine worries. In other words, the notion of grounding looks so close to that of essence that one needs an argument if she wants to say that they are not conceptually connected. Third, even though it is the case that many PFMs are already committed to various metaphysically heavy concepts, my arguments show that they are more deeply involved in metaphysics than their defenders originally have thought. The more deeply involved in metaphysics PFMs are, the less attractive they become.


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Lee, J. Wildman’s Defense of Sparse Modalism and a Dilemma of Post-Finean Modalism. Axiomathes (2019) doi:10.1007/s10516-019-09469-4

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  • Modalism
  • Essence
  • Grounding
  • Sparse modalism