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Explanatory Asymmetries, Ground, and Ontological Dependence

Abstract

The notions of ground and ontological dependence have made a prominent resurgence in much of contemporary metaphysics. However, objections have been raised. On the one hand, objections have been raised to the need for distinctively metaphysical notions of ground and ontological dependence. On the other, objections have been raised to the usefulness of adding ground and ontological dependence to the existing store of other metaphysical notions. Even the logical properties of ground and ontological dependence are under debate. In this article, I focus on how to account for the judgements of non-symmetry in several of the cases that motivate the introduction of notions like ground and ontological dependence. By focusing on the notion of explanation relative to a theory, I conclude that we do not need to postulate a distinctively asymmetric metaphysical notion in order to account for these judgements.

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Notes

  1. See for example Daly (2012), Hofweber (2009), Koslicki (2015), Sider (2011, chapter 8), and Wilson (2014). The concern that the notion of ground is problematic is tackled by Audi (2012) and Raven (2012).

  2. The references in the quote are to Loewer (2001), Armstrong (1997), and Schaffer (2010) respectively.

  3. A similar view is attributed by Wilson (2014) to a personal communication with Theodore Sider and to a talk by Daniel Nolan. Note that I am not trying to tackle the broader question of whether ground/ontological dependence are generally fruitful notions.

  4. I will differ from both Wilson and Koslicki in how I articulate what the real work is, but the general point stands.

  5. Wilson (2014, 564, footnote 74) notes this type of worry in connection with her primitivism about fundamentality and attributes it to Kit Fine, Alex Jackson, and Jonathan Schaffer.

  6. Wilson (2014, 555–556) is an example of a dissenter.

  7. I take this to have near consensus in the literature. However, many of the specifics about how ground, dependence, and explanation are related are in contention. For example, ground can be taken to be a metaphysical relation that underwrites explanation (like causation may be taken to be in the case of scientific explanation), or it can be understood directly as an explanatory notion. I take Rodriguez-Pereyra (2005), Schaffer (2016), and Wilson (manuscript) as examples of the former position and Fine (2012) as supporting the latter. Similarly, some hold that ontological dependence is a relation that underwrites certain kinds of explanations while others take it to be an explanatory notion. Here I take Koslicki (2012) to hold the former position and Schnieder (2006) to defend the latter view. Further, ground is sometimes thought of as very closely related to ontological dependence and sometimes treated as strictly separate from it. See for example Schaffer (2009) versus Fine (1995, 2012). Finally, there is no consensus as to whether ground and dependence are relations or sentential connectives, etc. However, all sides can speak of a relation of ground and dependence (in a deflationary sense). I am indebted to Bliss and Trogdon (2014) for delineating several of these issues.

  8. Raven does not present the view as his own, so I am not sure if he endorses this argument. However, Raven (2013) defends the view that ground is asymmetric.

  9. I am using, roughly, the terminology of Salmon (1989).

  10. See for example Jenkins (2013) and Correia and Schnieder (2012).

  11. See for example Price and Weslake (2009) and van Fraassen (1980).

  12. Jenkins (2013) develops an account of dependence using this notion of explanation as it stands. I will instead give a partial reduction of this notion of explanation relative to a theory.

  13. This is the strategy in Woodward (2003) and Strevens (2008) as well as the mechanistic literature such as Machamer et al. (2000).

  14. I have worked on saying more about this for law-based explanations in Jansson (forthcoming).

  15. Thinking of laws of nature as “inference tickets” goes back at least to Ryle (1949/2009, 105). I should note that I am not here attempting an analysis of lawhood in these terms.

  16. I am leaving open the question of whether the relevant principles are metaphysical or conceptual. Both views are represented in the literature. See, for example, Jenkins (2013) for the former view and Schnieder (2006) for the latter.

  17. We see this reflected in the debate over whether there are any genuinely mathematical explanations of physical phenomena.

  18. Once we are dealing with idealisations and distortions, we need to modify this. However, idealisations and distortions are not taken to be relevant in the cases of interest.

  19. I am using the term “explanatorily relevant” roughly in the sense of Schnieder (2011, 450).

  20. I am ruling out cases where C is a theorem of T since the question over whether some theorems of a theory T can explain other theorems of T, relative to T, will take me too far afield from the issue in this article. None of the cases discussed will have this form.

  21. For Lowe and Tahko (2015) this would be only one potential member in the larger family of ontological dependence.

  22. See for example Lowe and Tahko’s (2015) discussion of existential dependence.

  23. See Fine (1995, 270–271) for a discussion of the historical roots and formulations of the modal/existential view.

  24. Notice that this is not obviously equivalent to saying that there is a metaphysical or conceptual explanation of the existence of y from the existence of x based on the theory in question. This is the reason for focusing on the contrapositive version of the modal/existential definition. It will be clearer in Sect. 5 why I am focusing on this formulation.

  25. I will not consider the view that there can be ontological dependence without explanation. The existence of such cases is more plausible when we deal with the notion of ontological dependence simpliciter and not with our judgements of ontological dependence relative to a theory.

  26. I will not try to tackle cases that do not come from logic or mathematics in this paper. It is harder to do so. Theories here are often less clearly articulated, and it is harder to specify what the theory specific principles of inference are. Here I cannot do more than note that I think that a similar solution will work in these cases too.

  27. Of course, if our theory is a theory about logic, then the theory specific rules of inference might just be the logical ones. In general, however, they will not be.

  28. Here, I am assuming a positive free logic.

  29. I am formulating the rules in a natural deduction system. However, as is clear from the definitions earlier, I am assuming a positive free logic and an extension such as that of Fitch (1966) to deal with modal notions (M) in a natural deduction system.

  30. This is roughly what Fine (1981, 179) calls Rigidity of Membership.

  31. This is roughly what Fine (1981, 179) discusses as the extensionality axiom as an internal condition of identity.

  32. To make this completely accurate I should demand that c and d are sets (according to e). Since it will not be important for the rest of the paper I have simplified the rule by leaving it out.

  33. This is one direction of what Fine (1981, 180) calls Set Existence.

  34. This is how Fine (1981, 180) treats Set Existence. However, Fine is thinking of how to get from an already acceptable set theory to a modal version of that theory. It will be clear below why I think that this way of thinking of the inferences involved misses an important factor.

  35. I have to settle for the cautious claim since I have only given a necessary condition without explicitly relying on explanatory notions. However, plausibly, the failure of Socrates to exist explains the failure of the set to do so.

  36. Thank you to an anonymous referee for raising this objection.

  37. Thank you to Donnchadh O’Conaill for suggesting this reformulation. At the 2015 Explananza: A Conference on Explanation in Science and Metaphysics, Kristie Miller presented a more extensive account than I have attempted here of how to handle the seeming ease of the intuition.

  38. For an account that runs up against the challenge of not being generalisable in this way see Zalta (2006). However, it is a problem that any two-tier account—with one notion of dependence for concrete objects and one for abstract objects—will face.

  39. There are many candidates for the proper relata. I am not here trying to take a stand on how this should be construed. I will only try to stick to the fact locution if I think that there is a risk of confusion with ontological dependence. See for example Bliss and Trogdon (2014) for a summary.

  40. Since these are technical notions, there is leeway in how we fix them. Here I am following Fine (2012) in taking the central notion of ground to involve full explanation. What I am calling the generalised notion of dependence (dependence for short) will turn out to guarantee partial ground in Fine’s (2012, 50) terminology.

  41. In the sense of Fine (2012, 50).

  42. There are also trivial cases where Q not holding can simply be dropped while preserving the entailment of P. I am not counting these as inferences of which Q not holding is a part.

  43. In general we have a second option to consider: whether we have a case of back-up explanations. In back-up explanations we are only committing to one or the other of the two potential explanations holding, but to both being potential explanations nonetheless. However, relative to classical logic, we do not have the structure to make this work. This is not surprising since back-up scenarios rely on counterfactual conditionals and not merely on material conditionals. To see that we will be looped back to the question of whether or not \(P \wedge Q\) explains P relative to classical logic, let us stipulate that we add some proposition A to \(\sim Q\) to ensure the entailment of P. If we try to construe this as a case of back-up explanation, we expect that \((P \wedge Q) \vee (A \wedge \sim Q)\) will be a potential explanation of P. When we take into account the fact that \(A \wedge \sim Q\) has to entail P, then this is equivalent to asking whether \((P \wedge Q) \vee (P \wedge A)\) is a potential explanation of P. If this is an example of an explanatory back-up situation, then we expect \(P \wedge A\) to explain P. However, there was nothing special about Q in our original question of whether \(P \wedge Q\) explains P (relative to classical logic). We find ourselves back with the same question. The iterative process cannot terminate.

  44. The table is read from the top following the column to the bottom.

  45. Although not given its own principle since we did not need it to derive the necessary biconditional, I assumed it in the discussion.

  46. Note that it does not require having such a theory at hand.

  47. I take Wilsch (2015) to broadly develop such a view. However, here the asymmetry is written in by hand by only allowing modus ponens, but not modus tollens, as a principle of inference.

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Acknowledgments

Thank you to the participants at the 2012 Australasian Association of Philosophy Annual Conference. In particular thank you to Daniel Nolan and Bill Harper for pressing great objections to early ancestors to the ideas in this paper. Thank you also to Raul Saucedo for a very helpful discussion at the 2013 Bellingham Summer Philosophy Conference and to Jonathan Tallant for very useful suggestions in the summer of 2014. Thank you to the participants at EMW 1 at Helsinki in 2015 for their insightful comments. A large thank you is due to Donnchadh O’Conaill, David Kovacs, Sam Liao, and Dustin Tucker for detailed comments that led to significant changes and improvements. Finally, thank you to the anonymous referees that read and commented on this article. Part of this work was supported by a start-up grant from Nanyang Technological University and MOE Tier 1 Grant RG162/14.

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Jansson, L. Explanatory Asymmetries, Ground, and Ontological Dependence. Erkenn 82, 17–44 (2017). https://doi.org/10.1007/s10670-016-9802-1

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Keywords

  • Classical Logic
  • Scientific Explanation
  • Newtonian Mechanic
  • Intuitive Judgement
  • Ontological Dependence