Abstract
This paper offers a metaphysical explanation of the identity and distinctness of concrete objects. It is tempting to try to distinguish concrete objects on the basis of their possessing different qualitative features, where qualitative features are ones that do not involve identity. Yet, this criterion for object identity faces counterexamples: distinct objects can share all of their qualitative features. This paper suggests that in order to distinguish concrete objects we need to look not only at which properties and relations objects instantiate but also how they instantiate these properties and relations. I propose that objects are identical when they stand in certain qualitative relations in virtue of their existence. And concrete objects are distinct when they do not stand in the same kinds of relations to one another in virtue of their existence.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Notes
Employing a metaphor, Burgess (2012) puts the thought as follows: “Imagine God creating a field of poppies. Once the flowers exist, there’s no need for Her to survey the field and stipulate that this poppy will be identical to itself, and distinct from that poppy, that poppy, etc. Intuitively, the identity...facts come along for free.” (90) Although, Burgess himself raises problems for that idea, and we will discuss it further in Sect. 7.
Some philosophers believe identity facts need no explanation.For example, see Lewis (1986, pp. 192–193), and also Williamson (1990, p. 145), who maintains that for objects that are of a particular kind F, we should not try to explain why the Fs are self-identical. I will discuss this position further in Sect. 2.2.
Leibniz (1902) Discourse on Metaphysics, Section 9. Although it is unclear whether Leibniz himself thought he was giving an explanation of object identity and distinctness as opposed to the necessary and sufficient conditions for object-identity.
In response to points raised by Della Rocca (2005), I aim to show that we can reject the Principle of the Identity of Indiscernibles, as commonly understood, and still provide an explanation of identity and distinctness that does not invoke non-qualitative properties and relations.
Quantitative relations will be further discussed in Sect. 4.
Fine (2001) is an exception: he draws a distinction between ungrounded facts and fundamental facts.
For detractors, see Jenkins (2011) and Schaffer (2012), who argue against the irreflexivity and transitivity of ground, respectively. In response, Raven (2013) defends taking ground as a strict partial order and Litland (2013) argues that Schaffer’s counterexamples to the transitivity of ground are unsuccessful.
The grounds for universal generalizations are difficult to fully account for, however, in that all of the instances together may not fully ground the generalization. We may need a totality fact, or a “that’s all” fact in addition to the instances.
There are different types of identity criteria we can formulate. We can also provide what Fine (2016) calls the “material” criterion for identity. These provide necessary and sufficient conditions for an object x to be identical to an object y. A grounding criterion for identity facts is stronger than a material one. Grounding criteria specify the facts in virtue of which identity facts obtain. The following proposals should be read as proposals for grounding criteria.
Thanks to an anonymous reviewer for helpful feedback on these points.
Lewis also believed that we can approach problems which traditionally concerned identity using other notions. For instance, we can frame questions of persistence without mention of identity (1986, p.193). Even if we agree with Lewis that identity is unproblematic (and we agree with Williamson that we do not need to explain certain identity facts), we may still wish to address questions raised in this paper. In particular, we may wonder whether the Max Black world contains two spheres or one bi-located sphere. If we think it contains two spheres, we may wish to investigate whether the two spheres differ in any qualitative respects. In Sect. 3, I will maintain that while Castor and Pollux may have all the same physical properties (like mass, charge, shape etc.) and stand in the same physical relations to one another (same mass as, 5 meters apart from, etc.), they will differ in the ways in which they stand in those relations. One can conceive of this as a kind of qualitative difference between two spheres. Thus, this distinction between the different ways objects stand in relations to one another may still be of interest in describing what’s going on in the possibilities containing Max Black spheres, even if—like Lewis—one denies the core philosophical puzzles in question center around the notion of identity and distinctness. Thank you to an anonymous reviewer for helpful questions here.
Saying that nothing makes it the case that an object stands in the identity relation to itself could also mean that identity facts are “zero-grounded” where zero-grounded truths or facts are not grounded by further truths or facts. Zero-grounded facts are not ungrounded. They have what Fine calls “the null ground”. For more on zero-ground, see Fine (2012). For more on whether identity facts can be zero-grounded see Litland (2017), Donaldson (2017), Shumener (forthcoming).
For further discussion of how this characterization of fundamental objects should lead us to take identity facts to be non-fundamental, see Shumener (forthcoming).
See Donaldson (2017) for discussion of metaphysical explanations of abstracta.
Providing the grounds for object identity and distinctness also does not address cognitive and epistemic issues concerning identity facts. For example, “\({\hbox {Mark}}\, {\hbox {Twain}} = {\hbox {Samuel}}\, {\hbox {Clemens}}\)” is more cognitively significant than “ \({\hbox {Mark}}\, {\hbox {Twain}} = {\hbox {Mark}}\, {\hbox {Twain}}\).” For the purposes of this paper, we treat [\({\hbox {Mark}}\, {\hbox {Twain}} = {\hbox {Mark}}\, {\hbox {Twain}}\)] as the same fact as [\({\hbox {Mark}}\, {\hbox {Twain}} = {\hbox {Samuel}}\, {\hbox {Clemens}}\)].
Stating the grounds of facts like \([x = y]\) and \([\lnot \ x = y]\) is shorthand for speaking of the grounds of identity and distinctness facts involving particular objects (like \([a = b]\), \([c = c]\), \([\lnot \ a = c]\), etc.). When I claim that a fact like \([x = y]\) is grounded in such-and-such way, what I mean is that the facts \([a = b]\), \([c = c]\dots\) and so on, are grounded in that way.
We can rewrite the proposal more formally as follows: if \({\hbox {x}} ={\hbox {y}}\), \({\hbox {x}} ={\hbox {y}} > (\forall F_{qualitative})(Fx \equiv Fy)\). When \(\lnot {\hbox {x}} = {\hbox {y}}\), \(\lnot {\hbox {x}} = y > \lnot (\forall F_{qualitative}) (Fx \equiv Fy)\).
We can rewrite the Weak Discernibility Proposal more formally: if \({\hbox {x}} = {\hbox {y}}\), \({\hbox {x}} = {\hbox {y}} > \lnot \ (\exists R_{qualitative})\) (Rxy & R is irreflexive). And if \(\lnot {\hbox {x}} = {\hbox {y}}\), then \(\lnot {\hbox {x}} = {\hbox {y}} > (\exists R_{qualitative})\) (Rxy & R is irreflexive).
Thanks to Ted Sider and Cian Dorr for this point.
Moreover, objects \(x_1 \dots x_n\) stand in relation R fundamentally just in case [\(Rx_1 \dots x_n\)] is fundamental (or ungrounded), and objects \(x_1 \dots x_n\) instantiate R non-fundamentally just in case there is some fact \([\phi ]\) such that \([\phi ]\) grounds [\(Rx_1 \dots x_n\)].
Also see Sider (2011), Chapter 13.
There is an exception for spatiotemporal relations: absolutists can either take the facts that objects stand in spatiotemporal relations to one another to be fundamental (as the relationist would do as well) or grounded in locational facts—facts maintaining that the objects in question occupy specific spatiotemporal locations.
We should note that it is somewhat controversial exactly what form the most fundamental relations should take. For instance, some relationists, like Field (1980) speak in terms mass congruence (CONG) and less than (LESS) relations. Where x LESS y whenever the mass of x is less than or equal to the mass of y. And xy CONG wz when the mass difference between x and y is the same as that between w and z. See Eddon (2013b) for a nice discussion of this. For ease of reading, I will stick with relations like as massive as same electric charge as and so on, but it should not impact my proposal if CONG and LESS than turn out to be more fundamental than the relations I pick out here. We could reframe the proposal using those relations instead.
When we move to the generalized proposal in Sect. 8, which is intended to be absolutist-friendly, we will still cash out the proposal in terms of the quantitative relations stipulated here (as massive as, more massive than, same charge as, opposite charge as, and so on.) even though these relations are not perfectly fundamental according to the absolutist due to the fact that she posits fundamental determinate monadic properties of mass and charge instead of fundamental mass and charge relations holding among concrete objects.
Although, this last case is tricky. See footnote 35 for discussion.
More formally as follows: If \({\hbox {x}} ={\hbox {y}}\) then \(x = y > (\forall R) (({\hbox {R}}\ {\hbox {is}}\ {\hbox {quantitative}}_{rmf}\) & Rxy) \(\supset\) Rxy non-fundamentally). If \(\lnot {\hbox {x}} = {\hbox {y}}\) then \(\lnot \ x = y > (\exists R) (({\hbox {R}}\, {\hbox {is}} \, {\hbox {quantitative}}_{rmf}\) & Rxy) & Rxy fundamentally).
This may not be the only way to develop the Quantitative Proposal. I suggest that objects stand in \({\hbox {quantitative}}_{rmf}\) relations to themselves in virtue of their existence—and I develop this line of thought below—but the main insight of the Quantitative Proposal is that objects stand in \({\hbox {quantitative}}_{rmf}\) relations to themselves non-fundamentally and to distinct objects fundamentally. One avenue to explore is whether there are alternatives to existence facts which could ground facts involving objects standing in \({\hbox {quantitative}}_{rmf}\) relations to themselves. For instance, if our ontology of fundamental facts included essence facts, perhaps facts involving the essences of an object a could ground [a is as massive as a]. Thanks to Kelly Trogdon for raising this possibility.
I take it to be true, yet infelicitous, to maintain that objects lacking features like mass or charge still stand in the same charge as and same mass as relations to themselves. It is just that they trivially stand in these relations to themselves in virtue of having no mass or charge at all. But one could insist that objects do not stand in any quantitative relations to themselves in such scenarios. Additionally, one could claim that objects do not have the same mass or charge as themselves in possible worlds where there is no mass or charge. If this is the case, the existence of the object will not suffice to ground facts like [a is as massive as a]. In this case, such facts should be taken to be grounded in the fact [a exists] as well as further facts like the fact that mass exists or the fact that a is the kind of object capable of possessing mass, such as [a is mass-apt]. Augmenting the grounding base with these extra facts still allows us to distinguish and identify objects. Facts like [a is as massive as b] will still hold non-existentially when a and b are distinct such facts will be grounded in a plurality of existence facts when a is identical to b. Thanks to Jill North for pressure here.
This proposal is less radical than it may initially seem: taking the existence of an object to ground its standing in \({\hbox {quantitative}}_{rmf}\) relations to itself does not preclude \({\hbox {quantitative}}_{rmf}\) relational facts from having other grounds as well. Facts often have multiple full grounds.
Questions still arise here. Namely, what (if anything) grounds the E-facts? If one takes some objects to exist fundamentally, it may be compelling to consider some E-facts to be fundamental. If one denies that existence facts belong in the base of fundamental facts, then perhaps existence facts will be further grounded.
When discussing quantitative facts in this section, I have mostly dropped the subscript to fundamental quantitative relations, \(_{rmf}\), because I am concerned with quantitative facts involving both fundamental and non-fundamental quantitative relations.
This is controversial, but look at Schaffer (2010) for someone who thinks that basic or fundamental entities should be minimally complete. Although, Schaffer there is concerned with objects instead of facts.
The problem is more pronounced if we think the distinctness of the facts [Ea] and [Eb] explains the fact that the existence facts ground the distinctness of the objects. In this case, since the distinctness of a and b grounds the fact that [Ea] and [Eb] are distinct, then [\(\lnot\) a = b] would ground the fact that the plurality of existence facts grounds the distinctness of the objects themselves. A fact should not explain an explanation of itself. Thanks to Tobias Wilsch for pressing this point.
More formally as follows: If \({\hbox {x}} = {\hbox {y}}\) then \(x = y > (\forall R) (({\hbox {R}}\, {\hbox {is}} \, {\hbox {quantitative}}_{rmf}\) & Rxy) \(\supset\) (\({\hbox {Rxy}} > {\hbox {Ex}}\), Ey)). If \(\lnot {\hbox {x}} = {\hbox {y}}\) then \(\lnot \ x = y > ( \exists R)\) (\(({\hbox {R}}\, {\hbox {is}} \, {\hbox {quantitative}}_{rmf}\) & Rxy) & \(\lnot ({\hbox {Rxy}} > {\hbox {Ex}}, {\hbox {Ey}})).\)
Do the same explanatory worries arise here as in the previous section? In particular, perhaps objects stand in quantitative relations to themselves existentially because they are identical instead of the other way around? I think we can appeal to some of the criteria from the previous section to mitigate this concern. For example, I maintain that we can determine whether objects stand in quantitative relations to each other existentially/non-existentially by considering how useful these facts are in grounding other quantitative facts. For example, it is a sign that x stands in R to y in virtue of x’s existence when Rxy is not useful in grounding other quantitative facts. But if Rxy does ground quantitative facts, that is a sign that x stands in R to y non-existentially. This criterion for determining whether Rxy holds in virtue of x’s existence does not invoke identity or distinctness facts involving x. Thanks to Nina Emery for pressing this issue.
References
Adams, R. M. (1979). Primitive thisness and primitive identity. Journal of Philosophy, 76, 5–26.
Armstrong, D. M. (1988). Are quantities relations? a reply to Bigelow and Pargetter. Philosophical Studies, 54(3), 305–316.
Ayer, A. J. (1954). Philosophical essays. Westport: Greenwood Press.
Bigelow, J., & Pargetter, R. (1990). Science and necessity. Cambridge: Cambridge University Press.
Black, M. (1952). The identity of indiscernibles. Mind, 61, 153–164.
Burgess, A. (2012). A puzzle about identity. Thought, 1, 90–99.
Caulton, A. (2013). Discerning indistinguishable quantum systems. Philosophy of Science, 80, 49–72.
Cover, J. A., & O’Leary-Hawthorne, J. (1999). Substance and individuation in Leibniz. Cambridge: Cambridge University Press.
Dasgupta, S. (2013). Absolutism versus comparativism about quantity. Oxford Studies in Metaphysics, 8, 105–148.
Della Rocca, M. (2005). Two spheres, twenty spheres, and the identity of indiscernibles. Pacific Philosophical Quarterly, 86, 480–492.
Donaldson, T. (2017). The foundations of arithmetic? Noûs, 50, 75–801.
Eddon, M. (2013a). Fundamental properties of fundamental properties. In K. Bennett & D. Zimmerman (Ed.), Oxford Studies in Metaphysics, 8, 78–104.
Eddon, M. (2013b). Quantitative properties. Philosophy Compass, 8, 633–645.
Field, H. (1980). Science without numbers. Princeton: Princeton University Press.
Field, H. (1984). Can we dispense with space–time. PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association, 1984, 33–90.
Fine, K. (2001). The question of realism. Philosopher’s Imprint, 1(2), 1–30.
Fine, K. (2009). The question of ontology. In D. Chalmers, D. Manley & R. Wasserman (Eds.), Metametaphysics: New essays on the foundations of ontology (pp. 157–177). Oxford: Oxford University Press.
Fine, K. (2012). Guide to ground. In F. Correia & B. Schnieder (Eds.), Metaphysical grounding (pp. 37–80). Cambridge: Cambridge University Press.
Fine, K. (2016). Identity criteria and ground. Philosophical Studies, 173(1), 1–19.
French, S. (1989). Why the principle of the identity of indiscernibles is not contingently true either. Synthese, 78, 141–166.
French, S. (2006). Identity in physics: A historical, philosophical, and formal analysis. Oxford: Oxford University Press.
French, S. (2015). Identity and individuality in quantum theory. In E. N. Zalta (Ed.), The Stanford encyclopedia of philosophy. Fall 2015 Edition.
Hawley, K. (2009). Identity and indiscernibility. Mind, 118, 101–119.
Hawthorne, J. (2006). Metaphysical essays. Oxford: Oxford University Press.
Jenkins, C. S. (2011). Is metaphysical dependence irreflexive? The Monist, 94, 267–276.
Leibniz, G. W. (1902). Discourse on metaphysics, and the monadology. New York: Dover Publications.
Lewis, D. (1983). New work for a theory of universals. Australasian Journal of Philosophy, 61, 343–377.
Lewis, D. K. (1986). On the plurality of worlds. London: Blackwell Publishers.
Litland, J. E. (2017). Grounding ground. Oxford Studies in Metaphysics, 10, 279–316.
Litland, J. E. (2013). On some counterexamples to the transitivity of grounding. Essays in Philosophy, 14, 3.
Markosian, N. (2014). A spatial approach to mereology. In S. Keinschmidt (Ed.), Mereology and location. Oxford: Oxford University Press.
McDaniel, K. (2013a). Degrees of being. Philosophers’ Imprint, 13, 1–17.
McDaniel, K. (2013b). Existence and number. Analytic Philosophy, 54, 209–228.
McGinn, C. (2000). Logical properties: Identity, existence, predication, necessity, truth (Vol. 118). Oxford: Oxford University Press.
Muller, F. A., & Saunders, S. (2008). Discerning fermions. British Journal for the Philosophy of Science, 59, 499–548.
Muller, F. A., & Seevinck, M. P. (2009). Discerning elementary particles. Philosophy of Science, 76, 179–200.
Mundy, B. (1987). The metaphysics of quantity. Philosophical Studies, 51, 29–54.
O’Leary-Hawthorne, J. (1995). The bundle theory of substance and the identity of indiscernibles. Analysis, 55(3), 191–196.
Perry, Z. R. (2015). Properly extensive quantities. Philosophy of Science, 82, 833–844.
Quine, W. V. (1976). Grades of discriminability. Journal of Philosophy, 73, 113–116.
Raven, M. J. (2013). Is ground a strict partial order? American Philosophical Quarterly, 50, 191–199.
Rosen, G. (2010). Metaphysical dependence: Grounding and reduction. In B. Hale & A. Hoffman (Eds.), Modality: Metaphysics, logic, and epistemology (pp. 109–36). Oxford: Oxford University Press.
Salmon, N. (1987a). Existence. Philosophical Perspectives, 1, 49–108.
Salmon, N. (1987b). The fact Thatx=Y. Philosophia, 17, 517–518.
Saunders, S. (2006a). Are quantum particles objects? Analysis, 66, 52–63.
Saunders, S. (2006b). Identity. Unpublished.
Schaffer, J. (2009). On what grounds what. In D. Chalmers, D. Manley & R. Wasserman (Eds.), Metametaphysics: New essays on the foundations of ontology (pp. 347–383). Oxford: Oxford University Press.
Schaffer, J. (2010). Monism: The priority of the whole. Philosophical Review, 119, 31–76.
Schaffer, J. (2012). Grounding, transitivity, and contrastivity. In Grounding and explanation. Cambridge: Cambridge University Press.
Shumener, E. (Forthcoming). Ground and identity. In M. Raven (Ed.), The Routledge handbook on metaphysical ground. Routledge: Routledge University Press.
Sider, T. (2011). Writing the book of the world. Oxford: Oxford University Press.
Williamson, T. (1990). Identity and discrimination (Vol. 42). London: Blackwell.
Acknowledgements
Thanks to Ted Sider, Kit Fine, and David Chalmers for invaluable feedback on many drafts of this paper. Thanks to Cian Dorr, Nina Emery, Jill North, Jonathan Schaffer, and Kelly Trogdon for incisive commentary. Thanks also to Martín Abreu Zavaleta, Fatema Amijee, Nathaniel Baron-Schmitt, Michael Caie, David Charles, Vera Flocke, Ronald Houts, Michaela McSweeney, Betty Shumener, Alexander Skiles, Jack Spencer, Levy Wang, Tobias Wilsch, and audiences at NYU Thesis Prep, The 2014 Bellingham Summer Philosophy Conference, The 2018 Principle of Sufficient Reason Workshop at Simon Fraser University, and The 2018 Philosophy Mountain Workshop for helpful input on earlier versions. Mistakes/shortcomings are all my own.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Shumener, E. Explaining identity and distinctness. Philos Stud 177, 2073–2096 (2020). https://doi.org/10.1007/s11098-019-01299-9
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11098-019-01299-9