Abstract
I explore options for a plenitudinarian solution to the Paradox of Flexible Origin Essentialism, taking as my unlikely starting point the views of Sarah-Jane Leslie, who holds that if plenitudinarianism is true, then there is in fact no paradox to be solved, only the illusion of one. The first three sections are expository: Sect. 1 on plenitudinarianism, Sect. 2 on the paradox, and Sect. 3 on Leslie’s views about how plenitudinarianism bears on the paradox. In Sect. 4, I reject the contention that there is no paradox and critically explore three options for a plenitudinarian solution. In Sect. 5, I argue that the plenitudinarian ought to endorse a fourth option. In Sect. 6, I consider an objection. I endorse neither plenitudinarianism nor its denial; the main aim of the paper is to argue that for one who does endorse plenitudinarianism, the best solution to the Paradox of Flexible Origin Essentialism is clear.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Notes
In many cases, consideration of temporal properties also reveals the distinctness of the statue and the lump. Consider a lump of clay that exists before it is molded into a statue—the lump exists at time t but the statue does not. But Gibbard (1975) points out that it is possible for a statue and a lump to be created at the same moment and also to be destroyed at the same moment so that the statue and the lump are coincident at all times at which either exists. In such a case there are not obvious differences in temporal properties to cite in support of distinctness, though it would be surprising if such a statue were identical to its lump (so to speak) whereas ordinary statues are not identical to theirs.
The lump is constituted by a hunk (portion, quantity, bit) of clay. As Gibbard (1975) puts it, “Take first the piece of clay. Here I do not mean the portion of clay of which the piece consists, which may go on existing after the piece has been broken up or merged with other pieces. I will call this clay of which the piece consists a portion of clay; a portion of clay, as I am using the term, can be scattered widely and continue to exist. Here I am asking about a piece or lump of clay. [¶] A lump sticks together: its parts stick to each other, directly or through other parts, and no part of the lump sticks to any portion of clay which is not part of the lump” (188). I follow Salmón (2005/1986) in using ‘hunk’ where Gibbard uses ‘portion’. See also (Salmón 2005/1981, pp. 225–226, n. 8). Sometimes I say simply ‘matter’.
My notion of an in-statue adapts the notion of an incar due to Hirsch (1982).
Why “little” rather than “nothing”? See the remarks later in this section concerning the constraints imposed by mundane facts and coherence.
It seems that we can also ask questions like this: why is there not a plenitude of entities present that has only one of the properties essentially? There may well be a reason why not, but Leslie does not provide one. See my speculation in note 8. It is natural to wonder whether this style of argument applies to non-material objects as well. Is there “present” with the number 2, which numbers the Martian moons, something (somewhat like a number) that cannot survive Mars’s loss of a moon? Is there “present” with Katniss Everdeen something (somewhat like a fictional character) that cannot survive my daughter’s reading The Hunger Games?
Fairchild and Hawthorne (2018, note 23) offer numerous references to anti-arbitrariness (or parity) arguments for permissive ontologies.
This becomes clear in Sect. 5.
This is the only example that Leslie gives as a clear case of an internally problematic potential essence. Fairchild (2019, p. 157), following Karen Bennett (2004, p. 357), offers another example of the sort of thing that Leslie presumably has in mind: a potential essence that includes the property of being blue but not the property of being colored.
Leslie does offer another example, but she expresses tentativeness about it (279). And it is difficult to know just what to make of the example. It is a case in which a postulated entity is supposed to lack (and so not have essentially or accidentally) a property that the original entity has. The postulated entity—an entity that is coincident with Socrates at some time when he is sitting and that is essentially sitting—lacks, according to Leslie, the property of being a self-maintaining living thing because nothing coincident with Socrates is striving to maintain a seated position. So, she judges internally problematic a potential essence that includes the property of being a self-maintaining living thing and the property of sitting. My speculation about this example is that the kind self-maintaining living thing is such that it can be instantiated by at most one of a plenitude of coincident objects. The kinds statue and lump are also plausibly like this. (This would, incidentally, provide a reason why the plenitudianrian does not postulate a plenitude of entities having a certain subclass of the relevant properties essentially and the rest accidentally. See note 5.) For properties like this, the plenitudinarian faces a choice as to whether the object that has the property has it essentially or accidentally.
Cf. Bennett (2004, 356–357) on the “chaste two-thinger” vs. the “wild bazillion-thinger”.
Suppose o is essentially accidentally F. Then o is accidentally F in every possible world (in which o exists). If so, then o is F in every possible world (in which o exists). But then o is essentially F, hence not accidentally F, hence not essentially accidentally F.
Fairchild (2019) offers her own formulation of plenitudinarianism to avoid these results, but it is not clear that it can generate the objects needed for Leslie’s diagnosis of the Paradox of FlexOE. The problem arises from the fact that Fairchild’s formulation restricts the properties that may serve as arguments to a modal profile function. It thereby evidently fails to acknowledge the distinct objects on which Leslie’s diagnosis depends—two objects that differ in how they have a property that Fairchild bans. (There may be ways for Fairchild to respond, but treatment of this topic goes beyond the scope of this paper.) It is worth mentioning that any restriction on the properties that may serve as arguments to a modal profile function is antithetical to the thought that L-essentialism guarantees plenitudinarianism. More importantly, restrictions are antithetical to plenitudinarianism’s inclusive spirit, and accordingly any restriction must be exceptionally well motivated from the very limited exclusionary principles that the spirit of plenitudinarianism allows.
One way for things to be, such that nothing can, as a matter of logic, be that way, is for contradictions to be true. (Logically impossible things can be true according to worlds just as they can be according to stories.) Such worlds are logically impossible worlds. For the purposes of metaphysical modality, we can ignore them. So no harm is done in the present context by taking ‘world’ to mean logically possible way for things to be.
See (Kripke 1963).
Continuing in this way requires the necessaryn−2 necessity of FlexOS. In S4 (and hence S5) this follows from FlexOS and NecifTrueS. Even one who thinks that Trans is not true (let alone logically true) may hold that FlexOS is necessarilyn−2 necessary. It is plausible that for a restricted class of claims that includes FlexOS, whatever is necessary is necessarily necessary.
Cf. (Robertson Ishii 2014).
Salmón’s overlap predicate is ‘sufficiently substantially overlaps’. Sufficient for what? For making FlexOS true. One may think that this is a vague matter. Or one may agree with Salmón (2005/1986, 343–344) that it is not. His formulations were intended to leave this an open matter.
Use of the functor ‘m’ is legitimate since ‘(∀x)(∃h)[Mxh & (∀h’)(Mxh’ → (h’ = h))]’ is an analytic truth (given the ranges of ‘x’, ‘h’, and ‘h’’). This alternative λ-abstract is easier to compare to the ones introduced in Sect. 3. Note that ‘m(x)’ is non-rigid whereas ‘h0’ and the like are rigid.
We can get to this point with a principle less robust than KindEss. Go back to the point when we discovered that modal universal instantiation of □FlexOE to ‘a’ cannot take us where we want to go. We can get there if we have that there is a world, w1’, possible in w0, in which a is made from h1 and is an axe. An extremely weak principle of kind retention, one that takes us from w1 to w1’ so to speak, can get us that: (∀x)(Ax → (∀h)[◇Mxh → ◇(Mxh & Ax)]). Now, appealing to the claim that FlexOE is true in all possible worlds (that is, to □FlexOE) is apt. It delivers that there is a world, w2, possible in w1’, which is itself possible in w0, in which a is made from h2.
By in effect using T and Trans rather than S4 alone at the crucial point, the derivation is one that all parties agree is legitimate. This also makes the menu of options simple: instead of being able to reject an inference or reject a premise, one can only reject a premise. This is fitting, since even one who is convinced, as I am, that Trans is no truth of logic, may nonetheless think that it is true, and so may still find the paradox of interest. I would be remiss however not to point out that the derivation makes use of inferential rules that are not part of T propositional modal logic. It uses universal instantiation—in standard and modal versions. Salmón (2005/1986, 297, note 12) points out that two well-known versions of counterpart theory fail to validate at least one instance of modal universal instantiation, the inference from ‘□(∀x)ϕx’ to ‘□[(∃x)(x = α)→ϕα]’, which is valid in standard quantified modal logic.
In case this sort of point has lost familiarity, I offer a quotation from Kripke (1980/1972, 108). He is arguing against the view that identity is a relation between two names that designate the same object rather than a relation between an object and itself. “If anyone ever inclines to this particular account of identity, let’s suppose we gave him his account. Suppose identity were a relation in English between the names. I shall introduce an artificial relation called ‘schmidentity’ (not a word of English) which I now stipulate to hold only between an object and itself. Now then the question whether Cicero is schmidentical with Tully can arise, and if it does arise the same problems will hold for this statement as were thought in the case of the original identity statement to give the belief that this was a relation between the names. If anyone thinks about this seriously, I think he will see that therefore probably his original account of identity was not necessary, and probably not possible, for the problems it was originally meant to solve, and that therefore it should be dropped, and identity should just be taken to be the relation between a thing and itself. This sort of device can be used for a number of philosophical problems.”
See (Kaplan 1989).
This cannot be the entire reason, since the mere recognition of Mod0 dictates the default position that something has Mod0 essentially and something has Mod0 accidentally. It is natural however to focus on essences rather than on accidents (so to speak), which may explain why although Leslie sees something having Mod0 essentially, she overlooks something having Mod0 accidentally. A plenitudinarian who recognizes the distinctness of Mod0 and Modorig, and especially one who finds Modorig more intimately bound up with being an axe, readily recognizes something having Modorig essentially (hence having Mod0 accidentally). Leslie thinks of essences of L-axes as given in terms of properties like being made from 2/3 of h0, rather than in terms of properties like being an axe. (By contrast, Hawthorne, if I have his idea right, thinks of essences of L-axes as given in terms of properties like being an axe0, which he thinks we express by ‘being an axe’.) If one thinks of an axe’s essence (modal or definitional) as including being an axe, it is very natural to think that the (modal) essence of any axe includes Modorig.
This observation is due to Saul Kripke.
Note how close this thought is (minus the suspicion) to the one Leslie expresses in the first sentence of the passage on precise/imprecise specifications of essences.
References
Bennett, K. (2004). Spatio-temporal coincidence and the grounding problem. Philosophical Studies, 118, 339–371.
Chandler, H. (1976). Plantinga and the contingently possible. Analysis, 36, 106–109.
Fairchild, M. (2019). The barest flutter of the smallest leaf: understanding material plenitude. Philosophical Review, 128(2), 143–178.
Fairchild, M., & Hawthorne, J. (2018). Against conservatism in metaphysics. Royal Institute of Philosophy Supplement, 82, 45–75.
Fine, K. (1994). Essence and modality. Philosophical Perspectives, 8, 1–16.
Gibbard, A. (1975). Contingent identity. Journal of Philosophical Logic, 4, 187–221.
Hawthorne, J. (2006). Determinism de re. In Metaphysical Essays (pp. 239–263). Oxford University Press.
Hirsch, E. (1982). The Concept of Identity. Oxford University Press.
Kaplan, D. (1989). Demonstratives. In J. Almog, J. Perry, & H. Wettstein (Eds.), Themes from Kaplan (pp. 481–563). Oxford University Press.
Kripke, S. (1963). Semantical considerations on modal logic. Acta Philosophica Fennica, 16, 83–94.
Kripke, S. (1980/1972). Naming and Necessity. Harvard University Press.
Leslie, S. (2011). Essence, plenitude, and paradox. Philosophical Perspectives, 25, 277–296.
Lewis, D. (1986). On the Plurality of Worlds. Blackwell.
Robertson, T. (= Robertson Ishii, T). (2014). Modal paradox. In J. Berg (Ed.), Naming, Necessity, and More: Proceedings of the University of Haifa International Conference on the Work of Saul Kripke (pp. 54–80). Palgrave.
Salmón, N. (2005/1981). Reference and Essence, 2nd edn. Prometheus Books.
Salmón, N. (2005/1986). Modal paradox: Parts and counterparts, points and counterpoints. Originally in Midwest Studies in Philosophy 11, 75–120. Reprinted in Salmón 2005/1981: 273–344.
Salmón, N. (1989). The logic of what might have been. Philosophical Review, 98, 3–34.
Acknowledgements
My greatest debt of gratitude is owed to Nathan Salmón for his unflagging belief in my philosophical abilities. David Braun has also been an important source of intellectual-emotional support in connection with this paper and other work. Nathan and David along with Graeme Forbes and Dan Korman provided written comments for which I am grateful. Graeme and his wife, Marilyn Brown, provided invaluable support through a health crisis, which ultimately resulted in an extraordinarily long time passing between my first thoughts about the relation between plenitudinarianism and the paradox in 2012 and the publication of this paper in 2021. I thank various audiences, and especially Morgan Davies, Thainá Coltro Demartini, Kyle Dickey, Cian Dorr, John Hawthorne, Paul Horwich, Clark Sexton, Kelly Trogdon, Stephen Troxel, Timothy Williamson, and Crispin Wright. Finally, I thank my daughter, Yoko, who has very little patience for philosophy, for her reactions to overheard philosophical conversations. From the time she was a toddler she has commented in ways that have made me laugh and laugh again.
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
Robertson Ishii, T. Everything but the kitchen sink: how (not) to give a plenitudinarian solution to the paradox of flexible origin essentialism. Philos Stud 179, 133–161 (2022). https://doi.org/10.1007/s11098-021-01654-9
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11098-021-01654-9