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“Do identity and distinctness facts threaten the PSR?”

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Abstract

One conception of the Principle of Sufficient Reason (PSR) maintains that every fact is metaphysically explained. There are different ways to challenge this version of the PSR; one type of challenge involves pinpointing a specific set of facts that resist metaphysical explanation. Certain identity and distinctness facts seem to constitute such a set. For example, we can imagine a scenario in which we have two qualitatively identical spheres, Castor and Pollux. Castor is distinct from Pollux but it is unclear what could metaphysically explain this distinctness fact. In this paper, I argue that we should not treat identity and distinctness facts as metaphysically fundamental. As such, identity and distinctness facts do not challenge the PSR. We can metaphysically explain them.

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Notes

  1. Technically, to have it follow from the principle that the existence of the pizza is metaphysically explained by the existence of the dough, sauce and cheese arranged pizzawise, the principle should read:

    The Grounding-Metaphysical Explanation Link*: If a fact P is metaphysically grounded in a fact Q, then P is metaphysically explained by Q.

    The difference in formulation will not be relevant below.

  2. Maurin (2019), Glazier (2020), Trogdon (2019).

  3. The link is still somewhat controversial. If we take ground to be reflexive (in the sense that P grounds P) but we take explanations to be irreflexive, we would maintain that P grounds P but deny that P metaphysically explains itself. However, we will restrict our attention to irreflexive theories of ground (sometimes called “strict ground”) in what follows.

  4. See Burgess (2012) and Amijee (ms.) for further discussion of whether to take identity and distinctness facts to be fundamental.

  5. I'll be taking for granted that the notion of ground is well-understood here, but many philosophers raise important issues concerning ground. For instance, please see Daly (2012), Koslicki (2015), Wilson (2014).

  6. See Rosen (2010) for this conception of a fundamental fact. For related discussions of fundamentality, see Bennett (2017).

  7. Facts are offset in square brackets [] where otherwise ambiguous.

  8. Instead of treating distinctness facts as negated identity facts, we can also treat ≠ as picking out a primitive distinctness relation. I will not employ this distinction below: I will just treat distinctness facts as negated identity facts.

  9. I discuss these and other sources of motivation for taking identity and distinctness facts to be fundamental in Shumener (2020a, b).

  10. See Sider (2011) for someone who takes the notions of first-order predicate logic plus identity to be fundamental.

  11. We do not yet have reason to think the fundamental identity and distinctness facts must be ones involving individual objects though. See Dasgupta (2009) for a view which posits fundamental distinctness facts that do not involve individual objects.

  12. See Rosen (2010).

  13. Another option would be to treat identity and distinctness facts as belonging to a third category, distinct from fundamental or non-fundamental. Perhaps such facts are not apt to be grounded in the first place. See Dasgupta (2014) for a picture on which certain facts are not apt to be grounded. I will not explore this option in this paper.

  14. See Shumener (2017, 2020a, b).

  15. See Leibn (1902), Discourse on Metaphysics, Section 9 and Della Rocca (2005) for discussion of whether the Principle of Ihe identity of Indiscernibles can be used in a metaphysical explanation.

  16. For general discussion of how to formulate identity criteria in terms of ground, see Fine (2016).

  17. See French (1989), Saunders (2006a, b), Muller and Saunders (2008), Hawley (2009) Muller and Seevinck (2009), French (2015) and Caulton (2013) for a discussion of this issue and for alternative methods for distinguishing the bosons.

  18. Perhaps Leibniz himself did not need to appeal to the PSR to establish the PII. See Rodriquez-Pereyra (1999) for discussion.

  19. See Adams (1979) for discussion of an approach involve Haecceities. See Hacking (1975), O’Leary-Hawthorne (1995), and Belot (2001) for discussion of approaches involving a single, multi-located sphere and related proposals.

  20. For discussion of other proposals in the same vein as the Properties Proposal, see Shumener (2020a).

  21. Perhaps the lesson to draw from this is that we should claim that only identity facts are zero-grounded and provide an alternative grounding story for distinctness facts. This is a possibility, but it would leave us with the project of how to ground distinctness facts.

  22. See Jeroen Smid (2017) for a proposal for understanding identity in terms of mereological notions (although he is not explicitly concerned with grounding identity and distinctness facts).

  23. Although, I do not assume that there are fundamental objects. But if objects like the posits of our best physical theories are fundamental, a fully general proposal should be able to ground their identity and distinctness.

  24. Keep in mind that we cannot use this proposal to explain how we know whether objects are identical or distinct or to explain the cognitive significance of coming to grasp identity and distinctness facts.

  25. See Armstrong (1984), p. 254 as well as Armstrong (1997) for discussion of states of affairs.

  26. To clarify, we can and should still appeal to facts involving individual objects in the grounds. By “non identity involving facts”, I mean to exclude non-qualitative properties and relations like being identical to Bob or Bobness. But Bob himself can still appear as an object in facts.

  27. Thanks to Jon Litland for pointing out this major problem!

  28. These restrictions may not be stringent enough. In particular, we may want to restrict facts to ones that do not contain certain properties and relations which themselves involve the constituency relation. For example, suppose a = b and a has the gerrymandered property being 5 kg of mass & being such that (∀Fni)(a is a constituent of F ≡ b is a constituent of F). Call that property G. Perhaps the fact that a = b should not be partially grounded in the fact that [a has G ≡ b has G] because [a has G ≡ b has G] could be partially grounded in (∀F ni)(a is a constituent of F ≡ b is a constituent of F. I’m not sure if that’s true. But if so, it would provide a good reason to add this further restriction.

  29. However, there is not a strict grounding circularity here. It’s not the case that a distinctness fact like [b ≠ c] (where b and c pick out objects) is grounded in the distinctness of two facts, [Fb ≠ Gc], for example,--and then Fb dis Gc is grounded in [b ≠ c]. Instead [b ≠ c] is grounded in [(∃P)(a is a constituent of P & b is not a constituent of P)]. This fact does not have the form of [Fb ≠ Gc] nor is it grounded in [Fb ≠ Gc]. So even if we accept my Constituency Proposal, we could still distinguish facts on the basis of their constituents without running into a circle of ground.

  30. Although the term ‘grounding structuralism’ is also used in another way. See Li Kang (ms.).

  31. I have seen Ralf Bader and Jon Litland present views on how ground fact identity and property identity that are similar in spirit (but are not identical) to the one suggested here: taking the grounds of facts/properties to be relevant to their identity conditions. I encourage the reader to look at their versions as I’m confident their alternatives will not be susceptible to the criticisms I raise here.

  32. However, some variants of this proposal may fare better. Perhaps we could just look to what facts F and G ground in order to identify and distinguish them. I do not think this variant runs into the same issues as the one in which we just consider the grounds of F and G. F and G will always ground different facts, it seems. For instance, F will ground [F v L] while G will not ground this fact. I am developing this variant further in a manuscript [Redacted].

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Acknowledgements

Thanks to Martín Abreu Zavaleta, Harjit Bhogal, Ben Bradley, Janice Dowell, Ted Sider, and audiences at the University of Maryland-College Park, Rutgers University, and Syracuse University for helpful feedback. Thanks especially to Fatema Amijee, Zach Thornton, Jon Litland, and an anonymous referee at Philosophical Studies for reading writen versions of this paper and pointing out crucial issues. Shortcomings are all my own.

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  1. University of Pittsburgh, Pittsburgh, USA

    Erica Shumener

  2. Universidad Nacional Autónoma de México, Mexico City, Mexico

    Erica Shumener

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Shumener, E. “Do identity and distinctness facts threaten the PSR?”. Philos Stud 178, 1023–1041 (2021). https://doi.org/10.1007/s11098-020-01481-4

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