Abstract
Priority monism (PM) is roughly the view that the universe is the only fundamental object, that is, a concrete object that does not depend on any other concrete object. Schaffer, the main advocate of PM, claims that PM is compatible with dependence having two different directions: from parts to wholes for subcosmic wholes, and from whole to parts for the cosmic whole. Recently it has been argued that this position is untenable. Given plausible assumptions about dependence, PM entails that dependence has only one direction, it always goes from wholes to parts. One such plausible assumption is a principle of Isolation. I argue that, given all extant accounts of dependence on the market, PM entails No Isolation. The argument depends upon a particular feature of the dependence relation, namely, necessitation and its direction. In the light of this, I contend that the argument is important, insofar as it suggests that we should distinguish dependence from other cognate notions, e.g. grounding. Once this distinction is made, I suggest we should also distinguish between two different notions of fundamentality that might turn out to be not-coextensive.
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Notes
It is an open question whether the concrete cosmos depends on something else which is not concrete.
For more on that see Sect. 4.2.
See foonote 10 for some details on the “ultimately” proviso.
I agree with Steinberg that the argument does not depend on some controversial assumptions about the underlying modal logic. On top of that, Steinberg shows how to frame the argument without possible worlds-talk. The resulting argument would be valid in the weakest modal system, i.e. K. Some of the arguments that follows depend on the acceptance of a stronger modal system, namely B. For a discussion see footnote 22.
Consider e.g. the individuation argument. At first sight the parts (the grains of sand) are not identified via their position in the whole (the heap). Or, consider the emergence argument. At first sight, the whole (the heap) does not have any property that is not fixed by the properties and relations of the parts (the grains of sand).
This burden of priority monism could be lightened in a number of ways. First, a monist could insist that, given transitivity of dependence, it is still the case that the heap depends on the universe. She could even insist that, in the light of that, the individuation and the emergence arguments in the previous footnote are not compelling. However, if the arguments for the claim that parts depend on their wholes are not compelling in this case, this provides all the more reason to allow that some wholes may depend on their parts. Second, the monist can deny that heaps are genuine composite objects. It is unclear whether this strategy can be used in all the relevant cases. For instance, Steinberg (2016) cites atoms and violins as objects that depend on their parts. It would be more contentious to deny that these are genuine composite objects. Finally, the monist could distinguish between different notions of dependence. This strategy seems promising to me, and I will focus an an akin proposal in Sect. 4.2. In any event, the question whether priority monism is compatible with different directions of the same notion of dependence is interesting in its own right. Thanks to two anonymous referees for this journal for having suggested these possibilities.
The debate on Necessity of Monism is related to a further one in metaphysics, i.e. the debate about whether the mereological structure of the world is metaphysically necessary or not. The relation between the two issues is best appreciated as follows: Necessity of Monism entails that every possible world has a universe, that is, a mereologically maximal element. Cotnoir (2013: 67) calls Mereology the following modal thesis, Mereology: Necessarily, the parthood relation is governed by the axioms of classical mereology. Mereology is sufficient to ensure that there is a mereologically maximal element in every possible world —given the unrestricted composition axiom—yet it is not necessary. One might endorse restricted composition, and require the necessary existence of the universe as an independent axiom. Two papers that focus explicitly on the relations between the debate on the necessity of the mereological structure of the universe and the necessity of monism are Cotnoir (2013) and Tallant (2013). Thanks to an anonymous referee here.
No Isolation: For any composite object \(o \ne u\) at @, there is no possible world w where the only concrete objects at w are o and its parts.
I take this to be ontological dependence to be precise, in contrast e.g. with conceptual dependence.
I am restricting the claim to @, to engage neither with Necessity, nor with Essentiality of Monism.
The “ultimate” proviso is here used only to flag that, eventually, all the chains of dependence will bottom out at the universe, i.e. the unique root to the tree of being, to use Schaffer’s suggestive phrase, is the universe.
It traces back to Aristotle (Met. 1019a1–4). We find it in Descartes’ Principles of First Philosophy and Spinoza’s Ethics. Arguably it is co-extensive with Husserl’s notion of foundation, in the Logical Investigations (Section 21: 475).
For a more refined formulation see Simons (1987: 295), in particular his notion of weak rigid dependence.
I will be using E to express the existence predicate. Depending on different views about existence it can be defined—in first order logic with identity—as follows: \(Ea \equiv \exists x (x=a)\).
Faced with this result, a friend of Isolation might be tempted to reformulate the principle, as the claim that, at any possible world w, the only concrete objects existing at w are o, its parts, andu. Note however that this reformulation of Isolation would not cause trouble for priority monism. To appreciate that, go back to Steinberg’s original argument. The original principle of Isolation guarantees that at w, o is the mereologically maximal element. And, given priority monism, the mereologically maximal element cannot depend on anything else, thus contradicting the assumption that o depends on its parts. However, according to the reformulation of Isolation, o is not mereologically maximal at w. Thus, no contradiction threatens priority monism. Thanks to an anonymous referee for this suggestion.
To be fair, Modal Classical Mereology is not Classical Mereology. One needs to take a further step.
I am assuming that Dion exists at @.
This is the reason why a modal system stronger than K is needed, as I pointed out in footnote 6. Necessity of distinctness is not provable in K. As a matter of fact, B is the weakest modal system in which it is provable. A formal proof is in Prior (1962: 206–207). An informal argument is in Wiggins (2001: Section 4.3). Fine (1995b: 255–256) derives essentiality of distinctness—which entails its necessity—in E5, the logic of essence that is based on S5. This should not sound too problematic. First, the orthodox view is that S5 is the logic of metaphysical modality—the thought being that necessity and possibility are themselves not a contingent matter. The locus classicus is Plantinga (1974). And S5 is strictly stronger than B. Even those who are skeptical about S5—most notably, Chandler (1976), Salmon (1989) and Bacon (2018)—find B beyond reproach—but see Salmon (1989: 4). Second, what is needed to run the arguments is the necessity of distinctness. B delivers it as a theorem, but the claim can be supported with independent arguments. Classic arguments in favor of necessity of distinctness that are independent from B are in Kripke (1980: 114) and Williamson (1996: 7–8). Thanks to an anonymous referee for pressing this point.
This follows by the definition of proper parthood: x is a proper pat of \(y \equiv _{df} x\) is part of y and is distinct from y.
Defined as usual as something with no proper parts.
Hence the name ‘Essential Dependence’.
Perhaps the interesting question is whether we could have any reason to reject this. My guess is that any reason to reject it would also provide reason enough to reject the claim of the essential dependence of o on u. Thanks to an anonymous referee here.
This follows from the arguments in Sect. 2.1.
A minor difference is the scope of the modal operator. Here I follow Correia (2005: 70). For the sake of completeness here is the official formulation of Schnieder (2006: 412): x depends on y\(\equiv \exists F \Box\) (x exists \(\rightarrow\) (x exists becausey is F)). The reader can convince herself that these differences do not play a role in the main argument in the text.
I will stay neutral as to whether \(\triangleleft\) is a sentential operator—-in which cases it relates propositional entities—-or a relation—in which case its relata are arguably facts. Thus I would stay neutral when it comes to specific ontological category of e.g. Fy—if any. I will assume that Fy somehow involves the instantiation of F by y. Nominalists are free to use their preferred paraphrase. Sometimes, for the sake of simplicity, I will write that ‘Fy obtains’, but it is meant to signal neither an official endorsement of the relational view, nor an endorsement of an ontology of facts.
To repeat once again. I am using ‘Fy obtains’, but this is not meant to imply that \(\triangleleft\) is a relation, whose relata are facts, or state of affairs. Those who are inclined to think of \(\triangleleft\) as a sentential operator can substitute to ‘Fy obtains’, ‘Fy holds’, “Fy is the case”, or the like.
Serious actualism may be phrased as follows: all properties are existence-entailing. Or equivalently: there are no non-existence entailing properties.
And in fact one could argue that it is just a special case of Essential Dependence, but I will not pursue this line here.
One might think there is a third, simpler option: \(\Box _x \exists F (Fxy)\). However, in the case at hand, \(Eo \rightarrow (\Box _o \exists F (Fou) \leftrightarrow \Box _o (Eo \rightarrow \exists F (Fou))\) holds—the reader can check for herself. Thus, under the assumption that Eo holds—which is indeed the case here—\(\Box _o \exists F (Fou)\) and \(\Box _o (Eo \rightarrow \exists F (Fou))\) turn out to be equivalent. This means that this simpler formulation boils down to Identity Dependence\(_2\) in the main text.
This feature will take center stage in Sect. 4.2.
Perhaps it is hardly negotiable, but still negotiable.
He claims that Isolation is
[P]lausibly true for all objects that do not ontologically depend on concrete objects other than their parts (Steinberg 2016: 2028).
Given that all subcosmic objects depend on some other concrete object that is not among their parts (by priority monism), this should make one question, I argue, the compatibility of priority monism and Isolation.
In what follows the notion of duplicate should be understood as the one introduced in Lewis (1986: 59–63).
Steinberg cites Paull and Sider (1992).
See also Ismael and Schaffer (2016).
As I noted already—see footnote 12—Schaffer has changed his views on a number of issues concerning grounding. This is likely to have significant implications for issues of fundamentality as well. The following seems particularly relevant in the present context. Schaffer (2016) discusses Wilson’s pluralism about “small-g” dependence relations—in contrast to the “big-G” grounding relation—as expressed in Wilson (2014). He writes:
[A]nd—perhaps most relevantly given the current dialectic—there will be the question (one which Wilson especially should face) as to whether there is a single unified notion of fundamentality, as opposed to a merely schematic notion standing in for some yet-to-be-specified “small-f status”, such as being mereologically atomic and being set theoretically elemental (Schaffer 2016: 161).
This passage seems to suggest that someone who is inclined to recognize different notions of metaphysical dependence—broadly construed—might be inclined to recognize different notions of fundamentality that are somehow relativized or indexed to such notions. I am about to push a similar point.
Naturally, I am not claiming that this is the only reason why we should distinguish between the two relations.
Pluralities need not be finite. I am sticking to finite pluralities for the sake of simplicity of notation.
See later on for a brief discussion. See also footnotes 31 and 32.
That does not mean that the second argument place cannot be flanked by a singular variable.This also raises the interesting question as to whether the first argument place could be flanked by a plural variable, and whether in that case, support would be distributive. In other words the question is whether: \(\forall xx \forall yy\) (xx support yy\(\rightarrow (\forall y (y\) is one of the \(yy) \rightarrow xx\) support y))) is an axiom or a theorem of the logic of Support.
What if someone were to insist that proper parts of the universe are both dependent on, and supported by the universe? This would have surprising consequences in the present context. Assuming a necessitation axiom for grounding, this would entail that for each concrete object o at @ the following hold: \(\Box (Eo \leftrightarrow Eu)\). It would follow that every possible world w that contains at least one concrete object o of the actual world @, contains the entirety of @. To appreciate this, let o be an arbitrary object in @, and assume o exists at some w. There are two cases: either \(o=u\) or \(o \ne u\). If \(o=u\), given that the universe supports all of its proper parts—corresponding to the right-to-left direction of the previous bi-conditional—its existence necessitates the existence of all of u’s proper parts. Thus, u and all its proper parts exist at w. But u and all its proper parts are all the concrete objects that exist at @. Hence, w contains the whole @. Next, suppose \(o \ne u\). Then, given that odepends on u—corresponding to the left-to-right direction of the bi-conditional—it necessitates the existence of u. Thus, both o and u exist at w. Now repeat the first part of the argument to get the desired conclusion: every world w that contains at least one concrete actual object contains the whole concrete actual world. Thanks to an anonymous referee for pressing this point.
The term is due to Schnieder (2017).
As I pointed out already—see footnote 45—Skiles (2015) argues against grounding necessaritanism. Those who reject grounding necessaritanism should recognize a new source of difference between dependence and grounding. Dependence and grounding will differ in their modal strength. This option is interesting in the present context. For I argued that Isolation is compatible with Ultimate Support and thus with priority monism*. Thus, I concluded, a variant of Steinberg’s argument would be available in this case. Note however that someone who finds grounding necessaritanism objectionable would arguably deny Internality of Support, for the two are obviously connected. As a matter of fact, as I pointed out in the main text, Internality of Support follows from grounding necessaritanism. As a result there would be a way to resist the aforementioned variant of Steinberg’s argument on behalf of priority monists*. Thanks to an anonymous referee here.
A detailed evaluation of Schnieder’s argument lies beyond the scope of this paper. The interested reader is refereed to Schnieder (2017: Section 4.6).
A word of caution is advisable here. A lot more needs to be said about the different notions of fundamentality and their interaction. A significant question is whether one notion captures a particularly salient notion of fundamentality, to mention but one pressing issue. Thus the suggestions in the paper should be taken as first, tentative steps towards a more comprehensive account, rather than a fully fledged one.
Recall priority monism, and priority monism*. They can be now phrased as follows: priority monism = the universe is the only fundamental\(_D\) object; priority monism* = the universe is the only fundamental\(_S\) object.
This entire discussion is indebted to some remarks of an anonymous referee for this journal.
See Bennett (2017: 25–29).
“G” stands for “grounding”.
“C” stands for “composition”.
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Acknowledgements
I want to thank Fabrice Correia and Jonathan Schaffer for several suggestions on previous drafts of the paper. I would also like to thank two anonymous referees for this journal for their insightful comments which led to substantive revisions. This work was supported by the Swiss National Science Foundation, Project Numbers BSCGIo_157792, and 100012_165738.
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Calosi, C. Priority monism, dependence and fundamentality. Philos Stud 177, 1–20 (2020). https://doi.org/10.1007/s11098-018-1177-5
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DOI: https://doi.org/10.1007/s11098-018-1177-5