Dispositionalism and the Intrinsic Nature of Pure Powers

1 Preliminaries

Typically, the dispositionality of a property is intimately related to the link of the property in question with other properties which appear in its manifestation.^[1] Pure powers theorists think that (at least some natural) properties are purely dispositional (in the sense that their nature does not include categoricality/qualitativity) and the above-mentioned link is essential to them. These theses naturally lead to a popular criterion of interworld identity of properties, according to which the identity of a pure power is fully determined relationally by higher-order modal asymmetric relations to other pure powers. Let me call this identity-criterion RDI (Relationally Determined Identity). One of the well-known and much discussed reasons to be skeptical about RDI is that in a dispositional monistic context (in which all properties are pure powers) the application of RDI leads either to circularity or infinite regress (see, for instance, Bird 2007; Lowe 2006). Some philosophers have proposed that the difficulty can be met without abandoning RDI. For instance, Bird (2007) has argued that all pure powers get their identity holistically ‘in a single stroke’ within an asymmetrical network of relations between them. In what follows I assume, albeit reluctantly, that there is (or will be) an adequate solution to the regress problems besetting RDI.^[2]

A second worry about RDI is that it leaves us in the dark as far as the intrinsic nature of pure powers is concerned.^[3] Bauer (2023) highlights this explanatory gap by arguing that each pure power should have some sort of internal nature that could explain its modality and ground its role in a power network. For Bauer, pure powers intrinsically possess physical intentionality (directedness) and carry information for various manifestations. Other philosophers who have taken seriously the need for an intrinsic characterisation of the nature of powers suggested that each powerful property has an intrinsic qualitative nature that determines its identity and grounds either the dispositions of its bearers or its necessary relations to other properties (Azzano 2021; Coates 2021; Tugby 2022). I am not going to examine here that suggestion (see Livanios 2024 for an extensive discussion). The reason is that I am not sure whether such a powerful property can be legitimately regarded pure power. On the one hand, the notion of a property that by its very nature grounds the dispositions of its bearers seems to respect a core tenet of pure powers ontology. On the other hand, however, it seems weird to consider a property with pure qualitative nature as a pure power.

Be that as it may, my focus here will be on another proposal for the characterization of the intrinsic nature of pure powers that could be based on Williams’ (2019) ‘blueprint’ view about the nature of properties. To avoid possible misunderstandings, I should stress that Williams does not present his view as a solution to the difficulty concerning the intrinsic nature of pure powers. In addition, his proposal is articulated in a context where natural properties are regarded powerful qualities. Despite all that, his view (properly modified) can provide an alternative intrinsic conception of the identity of properties which is more congenial to the view that properties are pure powers because it follows the spirit of RDI.

The main aim of the present paper is to defend the view that the adoption of an RDI-friendly intrinsic criterion for the identity of pure powers has important consequences for an actualist theory of modality which recently has grown in popularity, the so-called Dispositionalism (Borghini and Williams 2008; Contessa 2009; Jacobs 2010; Vetter 2011). The core tenet of Dispositionalism is the following:

(DISP) The truth of all alethic modal claims is grounded in the powers of actual entities.

Dispositionalism comes in various versions which nevertheless share two convictions: first, DISP is true and, second, a theory of modality should not appeal to the notion of possible world. Although several philosophers have expressed concerns about Dispositionalism-especially its extensional adequacy (see, among others, Yates (2015), Wang (2015), Wildman (2020) and Giannini (2021))-this paper is, to my knowledge, the first which highlights how the discussion about such worries can be affected by the adoption of an RDI-friendly intrinsic identity-criterion for pure powers.

The structure of the paper is the following: Section 2 presents the main principles of an intrinsic criterion for the nature of pure powers that nonetheless follows the spirit of RDI. Sections 3–5 highlight the fact that DISP and the RDI-friendly intrinsic identity-criterion are intertwined. To this end, Section 3 examines the lonely-pure-power possibility and shows that one may appeal to aspects of the proposed intrinsic account to build an argument against the extensional adequacy of DISP. Section 4 meets some potential objections to the argument from the lonely-pure-power possibility (especially those aiming to undermine the very existence of the possibility in question). Section 5 examines another possibility (the alien-pure-powers possibility) which, like the lonely-pure-power one, reveals that DISP and an RDI-friendly intrinsic identity-criterion for pure powers are intertwined. Finally, Section 6 includes some brief concluding remarks about the issue under consideration.

2 The Main Tenets of an Intrinsic ‘Blueprint’ Account

Here is the list of main tenets of a view about the intrinsic nature of properties, which is inspired by Williams’ blueprint account but is properly modified to fit the case of pure powers:

(INS) Each pure power ‘represents’ all other powers and their potential ‘interactions’ with it by having a list of ‘instructions’ (a blueprint) of what to do when it finds itself in all possible circumstances.^[4]

(INT) Pure powers intrinsically possess their blueprint; that is, they possess it independently of whether there exist other properties in the world in which they exist.

(DET) The blueprint of each pure power fully determines its interworld identity.^[5]

INS, INT and DET, taken together, aim to provide a holistic identity-criterion of pure powers that is based on their intrinsic nature while simultaneously respects the spirit of RDI. This task is allegedly achieved because the intrinsic blueprint of each power ‘mirrors’ its links with all other properties.

Finally, a further implicit tenet of the proposed view, which plausibly should characterise any criterion of the interworld identity of properties, is the following:

(RIGID) Any criterion of the interworld identity of properties should be rigidly applied; that is, we should use the same criterion in all possible worlds in which those properties exist.

One might of course object that there is no contradiction in applying different identity-criteria at different possible worlds. In response, I would only say that RIGID is a plausible principle because it is well supported by considerations of simplicity and elegance.

3 The Lonely-Pure-Power Possibility

Let us suppose, for the sake of the argument, that the actual world is a dispositional monistic world and consider an arbitrary actual pure power P. Then ask:

(Q1) Is it metaphysically possible that P is the only existing pure power?

Before suggesting an answer to Q1, notice that this possibility does not refer to an impoverished possible world where there is only one object. The possibility in question can be realised in possible worlds with a plurality of objects provided that all those objects are characterised only by P. After this short digression, let me return to Q1. The first thing we have to notice is that the proposed scenario does not seem to involve any contradiction; there is no a priori reason to rule out the possibility of a lonely-P world. Hence, we can at least negatively conceive it. Suppose, furthermore, that we have no compelling reason to doubt our capability of positively conceiving^[6] of the world in question and in general we have no cogent reasons to doubt the conceivability-metaphysical possibility link in this particular case. Given all that, one might legitimately claim that the lonely-P scenario is indeed metaphysically possible and so we can answer Q1 in the affirmative. Assume, for the time being, that this is the case (I will come back to it in Section 4) and ask:

(Q2) How is the identity of P determined at the lonely-P world?

An advocate of Dispositionalism (a dispositionalist, from now on) may here protest that by talking about possible worlds I am begging the question against their view because, as already remarked, Dispositionalism explicitly rejects the appeal to possible worlds while adjudicating on modal issues. In response, I should emphasise that my talk about possible worlds is only for reasons of convenience and does not commit me in any way to the indispensability of the role of the notion of possible world in examining ontological and semantic modal issues. The reader is free to replace Q2 with the question: what is the ground of the identity of P in the lonely-P possibility? Hence, in asking Q2, the request is for an answer to the question what metaphysically individuates P when conceiving it to be the only existing pure power in the world.

Returning now to Q2, and given RIGID, the answer should be provided by implementing the same identity-criterion we use at the actual world.^[7] According to Williams, the identity of P at the actual world is fully determined by its blueprint which ‘represents’ all other pure powers and their ‘interactions’ with P. Given RIGID then, the identity of P at the lonely-P world should also be fully determined by its blueprint at the lonely-P world. Those two blueprints however should be identical because, in line with INT, the identity of P is intrinsically determined and, so, any change of the ‘external’ conditions (such as the ‘disappearance’ of other pure powers) cannot have an impact on it. In addition, notice that in conceiving the lonely-P possibility we simultaneously conceive a scenario in which all other properties but P are merely possible. Hence, the very same blueprint which ‘reflects’ other actual pure powers (and their ‘interactions’ with P) should ‘mirror’ them (and their ‘interactions’ with P) even in the case where they are merely possible. This, in turn, seems to show that, according to the blueprint view, there is at least one type^[8] of case in which the answer to a modal question (i.e., how could the identity of a lonely pure power be determined?) involves blueprints that include possible pure powers. If that is true, however, we may legitimately ask:

(Q3) What is the ground of the modal truth that, in the lonely-P possibility, all other pure powers but P are possible existents?

The answer to Q3 cannot be that the required ground is given by P^[9] itself because, assuming the intimate link between the essence of an entity and its identity and Williams’ holistic conception of the blueprint of every power, those pure powers are all essential to P and the latter most plausibly cannot ground parts of its very essence. Moreover, no other pure power can ground the modal truth associated with Q3 because, in the context of the lonely-P possibility, the only existing power that could ground the truth in question is P. It seems then that, by examining the possibility of a lonely pure power, we can reach the conclusion that there are cases where modal truths cannot be grounded in the actual pure powers and as a result Dispositionalism is extensionally incorrect.

Dispositionalists may reasonably object that the previous conclusion is based on a misconception. They may stress that the dispositionalist criterion is an actualist one, which means that during its application in a possible case we do not have to ‘respect’ the relevant conditions held in that case but only the actual relevant conditions. Hence, in searching for the ground of the modal truth related to Q3, we should not assume that there are no other pure powers but P. In this line of thought, the modal truth under consideration is the following:

(MT) It is metaphysically possible for some (more precisely, all but one) actually existing pure powers to be non-existent.

Dispositionalists then may claim that MT is grounded in the nature of the actual pure powers. This claim, however, cannot be true. To illustrate that, consider the reasons I gave previously (while discussing Q3) for the conclusion that the lonely-P possibility cannot be grounded in actual powers. The first reason remains intact: Williams thinks that all other pure powers are ‘involved’ in the determination of the identity of P (recall INS) and, assuming again the essence-identity link, are therefore essential to it. Given this upshot and the plausible principle that no entity can ground parts of its very essence, we reach the conclusion that P cannot ground the possible existence of those other pure powers (that is, P cannot ground MT). The second reason, however, cannot be appealed to while considering the ground of MT. For according to the line of thinking that led from Q3 to MT, the latter can be prima facie grounded in other pure powers but P. But a more careful look reveals that none of the other pure powers (nor the whole of them) can ground MT. For otherwise we must accept the unpalatable consequence that existing entities can ground the possibility of their own non-existence.

The above argumentation shows that DISP and the here suggested intrinsic identity-criterion for powers are intertwined. Aspects of the blueprint account (especially its holistic nature, as remarked in the previous paragraph) are premises of an argument against the extensional adequacy of DISP. While DISP’s inability to account for the metaphysical possibility of pure powers ‘involved’ in the blueprint of other pure powers can undermine the plausibility of the proposed identity-criterion.

4 Objections to the Lonely-Pure-Power Possibility

The main objections to the upshot of the previous discussion are related to the postulated metaphysical possibility of the lonely-pure-power world. I begin with an objection that is based on the combination of two prima facie justified claims. The first claim is that metaphysical and physical possibility coincide. As far as I can see, the main reason that may motivate a metaphysician to identify the metaphysical possibility with the physical one is the belief that, contrary to the former whose epistemic source is a vague set of common sense intuitions which are most probably unreliable, the latter has a reliable epistemic source: science itself.^[10] Power realists in particular may have an additional reason for the identification of the ‘two’ kinds of modality. For according to them laws (at best) express the dispositional nature of pure powers and given that, the sole source of physical modality is the aforementioned nature. Since, however, metaphysical modality is often considered as also sprung from the nature of the actual entities, it is a short step for power realists to identify it with the physical modality. The second claim is that the lonely pure power world is not a physical possibility because the laws and symmetries of the actual world seem to preclude the possibility of all fundamental particles having only one property. For instance, according to the Standard Model for the fundamental interactions, any property of a particle through which it can participate in fundamental interactions (e.g., electric charge, quark colours) is ‘generated’ by a procedure (that is, an application of an appropriate gauge transformation to their interaction-free equation) which implies the existence of other particles (i.e., gauge bosons) having a multiplicity of properties.^[11] Combine those two views and you reach the result that the case of the lonely-pure-power world is a metaphysical impossibility.

To meet this objection, it suffices to reject the first of these claims by arguing that, even if the actual nomic web fully determines the physical possibility, there are reasons to think that a notion of possibility beyond what is nomically possible is needed to make sense of the actual scientific practice. Consider, for instance, the modal truths associated with subjunctive conditionals a) having antecedents opposed to actual laws (i.e., counterlegals), b) having antecedents which contain laws with different from the actual values of fundamental constants (which current physics cannot fully determine) and c) that assume certain combinations of laws and symmetries which, though not holding in the actual world, can nevertheless be regarded as possible in the sense that the mature, most successful theories of contemporary physics do not prohibit them. In all those cases (perfectly respectable from the scientific point of view), we need truthmakers related to truths concerning non-actual nomic webs. Although a dispositionalist may insist that those truthmakers can be provided by actual entities, the fact remains that the possibilities in question concern possible worlds beyond those governed by the actual nomic web, that is, physically impossible worlds. This strongly suggests that there is a scientifically respectable kind of possibility distinct of the physical one. This ‘extra’ possibility can be plausibly regarded a kind of metaphysical possibility which is science-friendly and avoids objections arising from the assumption that judgements about what is metaphysically possible are supported by controversial intuitions.

Let me now turn to a second objection according to which the lonely-pure-power possibility is ruled out by the holistic structure of pure powers. The holistic power-web view has been introduced not only to address the regress/circularity difficulties besetting RDI but also to solve the so-called problem of fit. Williams explains:

I motivate this structural holism by way of a puzzle concerning the collaboration of powers. If you consider a power property in isolation, then there is a serious metaphysical question concerning its ability to coordinate with other powers. This is the foundation of powers-based causation: powers interact with other powers to jointly produce manifestations. But when the powers first find themselves in these circumstances they do not need to await further instruction; they do not need something outside them to tell them how to coordinate with powers of different types, and nothing then comes into being that makes this so – they just act, without prompting. What affords this coordination? What explains it? How does the power ‘know’ to do exactly what it does, with just those powers with which it is arranged, when it finds itself in a constellation? How do powers instantly collaborate to jointly produce a manifestation? How did it know ahead of time, before those other powers happened along? And how did it know what it would have to do, even if that exact constellation type never arose? (2019, 86)

So, according to Williams, the problem of fit is to find ‘something’ regarding the identity of pure powers which is sufficient for the manufacture of that harmony. For him, that ‘something’ is provided by power holism. If the latter is true, then all actual powers are essentially related to each other and so they necessarily ‘come in a package’.^[12] Given that, the lonely-P world is not metaphysically possible. In response I would first point out that it is not clear that embracing power holism solves the problems of RDI. For instance, Bird’s (2007) suggestion that there can be a holistic determination of a pure power’s identity provided that the set of second-order relations between the property in question and other properties can be represented by an asymmetric graph, came under attack (among others) by Oderberg (2011), Bigaj (2010), Barker (2013) and Lowe (2010).^[13] While Hawthorne’s (2001) suggestion that in order for any structuralistic identity-criterion of properties (like RDI) to avoid the problematic possibility of properties with exactly the same roles in the property-web we should appeal to a complete description of the nomic structure of the whole world, has been legitimately criticised as going far beyond the original view according to which properties can be uniquely interworldly identified by their roles. Given all that, I conclude that a pure power realist has no strong motivation to embrace power holism for reasons exclusively associated with the problems plaguing RDI. Of course, as remarked above, one may defend power holism on the grounds that it provides a plausible solution to the problem of fit. Recall however that the problem of fit presupposes a plurality of powers. Hence, the alleged fact that power holism provides a solution to this problem can at best motivate a power realist to embrace holism for the actual world (with its plurality of pure powers); it cannot provide a convincing reason to refute the possibility of a lonely-pure-power world.

Third, one might object to the lonely-power scenario on the following grounds. If we accept the plausible theses that (at least) some actual powers a) are intrinsically possessed and b) can exist unmanifested, then, according to Tugby (2013a) and Yates (2016), we have strong reasons to adopt a view of powers as Platonic universals.^[14] If that is true and powers are indeed Platonic universals, then one might claim that all powers involved in the blueprint of any pure power can exist, albeit uninstantiated, even in the lonely-pure-power worlds. Given that, there is prima facie no need for the dispositionalist to ground the possibility of the existence of some power-universals included in the blueprint. One might respond to this objection by giving some general reasons to reject Platonism for properties. For instance, they may remind us of the problems regarding the epistemic accessibility of abstract entities (such as the Platonic universals) and the worry that Platonic properties (qua non-spatiotemporal) cannot be causally efficacious. Though I think that these issues raise serious challenges for the Platonist about properties, I do not put here much weight to them. After all, Platonists have provided some answers to those questions and, in any case, Platonic properties may earn their keep for various explanatory reasons (as Tugby 2022, for instance, extensively argues).

Another possible response can be given on the grounds that the objection in question presupposes that Platonic properties are necessary existents. Yet, as Tooley’s (1987, 119) Factual Platonic Realism (FPR) shows, Platonism about properties does not entail that universals are necessary existents. According to FPR, even though it need not be the case that every universal is instantiated, it is still a contingent matter which universals exist in a given world. In other words, universals may enjoy independent existence, but not necessary existence. If FPR is true, then the Platonic power-types appearing in the blueprint of another platonic power-type are contingent existents. Given that, it is metaphysically possible that there is a world in which an instance of a (Platonic) pure power P exists but at least one of the power-types included in its blueprint is not existent. This possibility suffices to raise again the problems discussed earlier in this paper. Platonic dispositionalists may try to rule out the possibility in question by claiming that, despite contingency, at each world in which P exists all the powers included in its blueprint exist too. If, however, they do not want to accept that modal truth as a brute one (a view that arguably stands in contrast to DISP), they must explain what the source of the modal link supporting the existential dependence between P and the constituent pure powers of its blueprint really is. In line with DISP, platonic dispositionalists should claim that the ground of the modal truth expressing this existential dependence is given by P or the constituent pure powers of its blueprint or both. Yet, since all powers are essential to each other, no pure power can ground the existence of another for, otherwise, it can ground a part of its essence. For this reason, I think, although Williams insists that all powers contribute to the nature of all other powers, he explicitly rules out the case of a power that depends for its existence on any other power within his blueprint view about the nature of properties (2019, 89).

Finally, there is a potential objection that does not challenge the very possibility of the lonely-pure-power scenario but its significance for the relevant metaphysical discussion. Since objects in the actual world have many properties, it seems that we must appeal to a very remote world (vis-à-vis the actual one) in order to conceive the lonely-pure-power possibility. This fact by itself, the objector might say, could be considered as a cogent reason to ignore the whole issue. In response, I would say that I do not think that this is a strong objection. The view we discuss in this paper is an account of the identity of pure powers and, like all accounts of the nature/identity of an entity, should be metaphysically necessary (therefore, it should hold even in ‘extreme’ or ‘remote’ possibilities). Otherwise, there is always a worry concerning what determines the nature of pure powers at worlds in which the view in question does not hold.

5 The Alien-Pure-Powers Possibility

In this section I examine another possibility which, like the lonely-pure-power one, reveals that DISP and an RDI-friendly intrinsic identity-criterion for powers are intertwined. This is the possibility of a world containing the power-web of actually instantiated pure powers as well as at least one alien pure power. Here, the expression “alien pure power” refers to an actually existing but uninstantiated pure power universal, that is, a Platonic pure power.

Before proceeding, it is important to point out that the discussion to come presupposes only the possibility of Platonic Realism about universals (henceforth, PR), not its actual truth. For, there are two ways to conceive the alien-pure-powers possibility. According to the first (which presupposes the truth of PR at the actual world @), PR holds at @ but nonetheless (as a matter of brute fact) all actual pure powers are instantiated. In this scenario, the alien-pure-powers possibility refers to a possible world w where PR still holds but (contrary to @) some powers are uninstantiated. Given this understanding, there are available two further options: either Platonic pure powers are necessary existents and, as a result, the uninstantiated pure powers are elements of a subset of the pure powers that exist at all worlds. Or Platonic pure powers are contingent existents and, consequently, the uninstantiated powers can be properties that do not exist at @ (although there is also a possibility that they are actual pure powers that they exist uninstantiated at w).

There is, however, a second way of conceiving the alien-pure-powers possibility which presupposes only the possibility of PR. According to it, PR does not hold at @ and therefore all actual pure powers are instantiated. PR however holds at w and some pure powers are uninstantiated. Here, just like the previous way of understanding the possibility under consideration, there are two available options: either the uninstantiated pure powers are necessary existents and so they also exist at @ (albeit instantiated) or they are contingent existents and therefore they can exist at w without existing at @.

After the above clarifications regarding the alien-pure-powers possibility, let me now ask the following question:

(Q4) How is the identity of an arbitrary actual pure power P determined in the context of the alien-pure-powers possibility?

Taking into account the previous points regarding the actualist character of the dispositionalist identity-criterion, we should search among the actual pure powers in order to answer Q4. Now, according to the ‘necessitarian’ options (that is, the two options in which Platonic pure powers are necessary existents), there is no problem with the determination of identity of P. For, the blueprint of P ‘involves’ all actual properties, the set of which crucially includes also all the ‘alien’ pure powers. (Of course, at @, the ‘alien’ pure powers are not literally alien because, by assumption, all pure powers at @ are instantiated in both ways of conceiving the possibility in question.) In ‘contingentist’ options, however, (i.e., the ones in which Platonic pure powers are contingent existents) there can be alien pure powers that do not exist at @. This raises the following difficulty for the proponent of the proposed intrinsic blueprint view. For P itself (and not some other pure power P^*) to exist at w, we should be able to identify it at w. Given RIGID, we should apply the same identity-criterion as the one that we apply at @. If the identity-criterion is the one that appeals to the blueprint of pure powers, then we should invoke this criterion to provide an identity at w. Given however that the blueprint of every pure power is intrinsic to it, then P should have the same blueprint at both worlds (w and @). (Recall that an intrinsic essential feature of an entity cannot be altered by any external change.) But this cannot be true if, as Williams claims, the blueprint of P should ‘involve’ all the pure powers at w (both actual and alien). Hence, it seems that an actual pure power cannot have an RDI-friendly intrinsic identity at a possible world with alien properties. Assuming the Quinean dictum that all entities should have identity, this upshot forces the defender of the intrinsic blueprint criterion to reject the otherwise intuitive^[15] possibility that actual pure powers can exist at worlds with alien properties.

What about the contrary-to Williams-view case in which not all powers are ‘involved’ in the identity of P? This alternative view allows the possible case in which none of the alien pure powers is ‘involved’ in the identity of P. In that case, DISP in tandem with RDI can unproblematically give an answer to Q4. The problem however is that there is no guarantee that this is the case. For we cannot rule out the possibility that the identity of (at least some of) the actual pure powers ‘involves’ at least one alien property. Given that, by our assumption, alien properties do not exist at @, they are merely possible at it. In such a case, then, we can ask the following legitimate question:

(Q5) What is the ground of the modal truth concerning the possible existence of alien pure powers ‘involved’ in the blueprint of an actual pure power P?

P itself cannot be the required ground because those alien properties are, by assumption, essential to P and the latter cannot ground parts of its essence. Can other actual pure powers ground the possible existence of the alien pure powers in question? Consider an arbitrary (but distinct from P) actual pure power Q and suppose that the blueprint of Q includes P.^[16] According to the intrinsic blueprint identity-criterion, P is then included in the essence of Q, or, putting it in Wang’s (2019) terminology, P figures in the essence of Q.^[17] In addition, since in the scenario under consideration P’s blueprint includes at least one alien pure power A, the latter figures in the essence of P. Consider now the following principle, which Wang (ibid.) calls the Essence-Dependence Link (EDL):

(EDL) If x figures in the essence of y, then y is ontologically dependent on x

EDL seems plausible because, as Wang points out “if an entity were independent of an entity that figured in its essence, how could it get its nature or identity from that entity?” Assuming then, for the time being, that EDL is true, it follows from the other assumptions of the proposed scenario that:

(i) Q is ontologically dependent on P

(ii) P is ontologically dependent on A

Given (i), (ii) and the transitivity^[18] of the relation of ontological dependence, it follows that:

(iii) Q is ontologically dependent on A

The above conclusion however is incompatible with the following claim:

(iv) Q can ground A

There are at least two ways to show that Q cannot ground the alien pure power A. First, one may support this conclusion by focusing on the following strong modal correlation and its potential explanation:

(COR) Necessarily, if the entity x ontologically depends on the entity y, then at least one fact about x is grounded in some facts about y

As Schnieder (2020) points out, ontological dependence refers to a family of 4-place relations of the form: “x depends on y with respect to some condition(s) of x and some condition(s) of y”. In the case under consideration here, the relevant condition about x concerns its identity and the relevant condition about y concerns its existence. Hence, we have the following version of COR:

(COR_id) Necessarily, if the entity x identity-depends on the entity y, then the identity of x is grounded in the existence of y

There are at least three distinct explanations of the correlation expressed by COR_id: first, one may explain the correlation by claiming that grounding is the converse of ontological dependence (see, for example, Schaffer 2009). Second, one may define ontological dependence in terms of grounding (Correia 2005; Schnieder 2006). And third, one may say that facts about ontological dependence are grounded in facts about grounding or vice versa. It is easy to show that, following the Schafferian explanation, Q cannot ground A. For since Q is ontologically dependent on A and grounding is the converse of ontological explanation, it immediately follows that A grounds Q. Given the asymmetry of grounding, we get the conclusion that Q cannot ground A. Yet, as Schnieder (2020) argues, the prospects of the identity-explanation look dim, and it seems wiser to have an alternative route to reach the upshot that Q cannot ground the alien pure power A. Perhaps there is a way compatible with one of the other two explanations of COR, but since the truth of COR itself is doubtful, I prefer to appeal to another principle which I find less controversial. The principle in question is called by Schnieder Priority Constraint (PrCon):

(PrCon) Ontological dependence is the converse of ontological priority

Given PrCon and (iii), it follows that A is ontologically prior to Q. Yet, this is incompatible with (iv) because, according to a widely accepted feature of grounding, for Q to be able to ground A, it [Q] should be ontologically prior to A, not the other way round. Hence, we reach the upshot that neither P nor any other actual power Q distinct from P can ground the modal truth concerning the possible existence of alien pure powers ‘involved’ in the blueprint of P.

Before concluding, I should respond to an objection to the above brief argument. To put it in a nutshell, the objection is that PrCon is false because there are (at least possible) cases of mutual ontological dependence. Consider, for instance, a case in which K is ontologically dependent on L and L is ontologically dependent on K. Then, according to PrCon, we have the absurd result that K should be both ontologically prior and inferior to L (and similarly for L). The difficulties cases of symmetrical ontological dependence raise are not novel. It is easy to see that cases of mutual dependence are allowed by the modal accounts of ontological dependence.^[19] If those modal accounts were the only ones that they could that, there would be an easy reply to the objection: so much the worse for them. In fact, the recognition of those difficulties (among others) paved the way for the introduction of hyper-intensional accounts of ontological dependence such as Fine’s (1995), Schnieder’s (2006) and Bennett’s (2017). Yet, as some works in the recent literature on dependence arguably show (Barnes 2018; Thompson 2016, 2018), even hyper-intensional accounts do not exclude the possibility of symmetrical ontological dependence. To make this point clear, let me focus on Barnes (2018) argumentation for cases of mutual dependence. First, she (ibid. 54–5) explains why most metaphysicians think that ontological dependence must be asymmetric. The reason is that they intimately connect it with the notions of fundamentality and ontological priority. Since the latter need to be asymmetric in order to do the work we want them to do (that is, as Barnes says, “to take us from the derivative (the constructed, the grounded, the non-fundamental) down toward the bedrock (the ultimate grounds, the fundamental, the basic)”), ontological dependence must be asymmetric as well. Then, Barnes proceeds to claim that we have strong reasons to disentangle ontological dependence from fundamentality and priority. She mentions that in order for some metaphysical positions to make sense, one need to admit the possibility of fundamental dependent entities and non-fundamental independent entities (for example, ontologically emergent entities are plausibly fundamental and dependent on the entities of the emergence-base). If Barnes is right about that, then at least we have reasons to disassociate ontological dependence from fundamentality because we have reasons to reject the definition of fundamentality as independence. To make her case that dependence should be understood as non-symmetric, rather than asymmetric, Barnes provides several examples that arguably show that ontological dependence can be symmetric. She admits that any of examples can be resisted, and she is right about that. Let me present some of her examples. A first case concerns immanent kind-universals. Proponents of kind-universals should, for instance, suppose that being an electron is a kind-universal which is essential to its instances and so the latter are dependent on it. But if those proponents are also immanent realists about universals, they should also hold that the kind universal being an electron depends on its instances. A second example is about Armstrongian states of affairs. In Armstrong’s ontology there is an inherent tension: since states of affairs are the fundamental entities, their constituents should depend on them. But since Armstrong needs ontologically autonomous constituents to explain the resemblance between states of affairs, the latter should depend on the former. Barnes argues that by admitting the possibility of mutual dependence, there is no tension in Armstrong’s theory: states of affairs and their constituents are both fundamental and mutually dependent entities. A third case concerns trope bundle theory. Barnes explains that defenders of trope bundle theory face a serious difficulty: how can they refute the unintuitive possibility of one-element trope-‘bundles’? Barnes suggests that by allowing relations of symmetric dependence between tropes the trope bundle theorist can secure that there can be no lonely tropes.^[20]

In all those cases, one might refuse to admit the existence of symmetric dependence by simply rejecting the relevant metaphysical positions. Although one cannot rule out that all these views are indeed false, Barnes is right that, given the number of positions presented, the chances to be this the case are small. More importantly, she may insist that all she wants to do by providing the examples is to show that symmetric dependence help us to make sense of the views irrespective of whether they are true or not. Yet, in order to achieve her task, ontological dependence should not be inherently asymmetrical. Otherwise, we cannot appeal to a notion of symmetric dependence to provide a consistent interpretation of various metaphysical views. In other words, we may agree with Barnes that, other things being equal, we should opt for a ‘neutral’ notion of dependence that does not prejudge whether a proposed metaphysical position is true or even consistent. In my view however other things are not equal when the ‘neutral’ notion violates a strong intuition about ontological dependence. The intuition in question is that the notion of dependence is inherently associated with the notion of ontologically priority by being the converse of it. And given that, as Barnes herself admits, we should hold that ontological dependence is inherently asymmetric. My upshot then is that the putative cases of mutual ontological dependence do not provide a compelling reason to reject PrCon and, consequently, there is no strong reason to cast doubt on the strength of the argument based on this principle.

Given all that, I conclude that in the case in which not all powers are ‘involved’ in the identity of P, neither P nor any other actual pure power can ground the modal truth concerning the possible existence of alien pure powers ‘involved’ in the blueprint of P. Taking also into account the previous discussion regarding the view that blueprints of pure powers should include all other powers, we can then conclude that the alien-pure-powers possibility raises difficulties for any (inspired by Williams’ blueprint view) RDI-friendly intrinsic criterion for the identity of pure powers.

6 Concluding Remarks

I argued that both the lonely-pure-power possibility and the alien-pure-powers possibility are genuine possibilities and within the context of an RDI-friendly intrinsic identity-criterion for pure powers (inspired by Williams’ blueprint view) raise concerns about the extensional correctness of Dispositionalism. Admittedly, as far as the alien-pure-powers possibility is concerned, my case seems stronger for any intrinsic criterion that respects Williams’ view that the blueprints include all properties. My argumentation against the more moderate view (according to which the blueprint of a pure power does not include all the other pure powers) is weaker because power theorists can reject some of the assumptions made in the relevant argument. For instance, Wilson (2020) presents cases to defend her view that one cannot infer from an object’s appearance in another’s essence that the latter depends on the former. In any case, and even if objectors are right, my argumentation regarding an intrinsic identity-criterion congenial to Williams’ view remains unaffected. It seems then that the only way for the potential objector to undermine the whole of my argumentation regarding the impact of the alien-pure-powers possibility is to refute my claim that the possibility in question is a genuine one. Though possible, this response however does not seem very convincing. For Platonists about properties have provided various examples in which it is reasonable to claim that there is reference to actual but uninstantiated characteristics of objects, that is, alien properties as here conceived. For instance, Giannini and Tugby (2020) argue that the fact that the theories of natural science (both classical and modern) involve idealisations provides strong reasons to adopt the existence of alien properties. More precisely, idealisations appear in counternomics, that is, subjunctive conditionals whose antecedent is an inaccurate^[21] representation of the real-world phenomenon scientists are interested in. Giannini and Tugby (ibid., 134) argue that the appeal to counternomics is indispensable^[22] in scientific practice and since many of them are true in a non-vacuous^[23] way, it is natural to search for their truthmakers. For them, the most plausible and ready-made answer is that the truthmakers in question are provided by alien properties, that is, Platonic universals which exist at @ uninstantiated.

I conclude by saying that the results of this paper can be interpreted in two different ways. According to the first interpretation (stressed at the beginning of this concluding section), my arguments show that the adoption of an intrinsic RDI-friendly view about the identity of pure powers raises concerns about the extensional correctness of Dispositionalism. Alternatively, however, one may see the upshots reached in the present paper as showing that considerations about problematic cases of DISP have an impact on power theorists attempt to provide an intrinsic characterisation that ‘respects’ intuitions supporting RDI. Both interpretations highlight the intertwining of DISP with issues related to the identity of pure powers.