2.1.1 Three Platitudes

We begin by voicing some platitudes and points of consensus about dispositions.

First platitude: a disposition towards M is a ‘directedness towards’ some kind of paradigmatic behaviour conceptually associated with the disposition (Reference MartinMartin 2007; Reference MolnarMolnar 2003; Reference TugbyTugby 2013). The term ‘manifestation’ is widely used for this behaviour, even though the behaviour might not be directly observable to the senses. The crucial idea behind ‘directedness’ is that being disposed towards a manifestation M should not entail actually doing M. An object disposed to behave in way M may not ever behave in way M.Footnote ⁶

Second platitude: a disposition’s manifestation can be triggered under specific conditions. For example, the sonority of a bell is manifested under striking with a hard object; malleability is manifested under pressure, etc. The term ‘stimulus’ is widely used to reference these conditions. Many, however, prefer the term ‘manifestation partner’, which is more conducive to understanding manifestation as an effect both of the disposition and whatever further conditions are needed (Reference Heil and MarmodoroHeil 2010; Reference MartinMartin 2007; Reference Mumford and AnjumMumford and Anjum 2011). Moreover, calling one property the ‘stimulus’ and the other the ‘disposition’ can often seem arbitrary, e.g., with the manifestation of heat exchange between a hot and a cold object. Nevertheless, ‘manifestation partner’ may go too far the other way, prohibiting any understanding of what triggers a manifestation being other than another property. Triggers could potentially be totality facts, absences, or background conditions.Footnote ⁷ Importantly, we won’t assume that every disposition has a specific stimulus (see subsection 2.3.3, Problem #6). Some dispositions can be stimulated under a variety of conditions (e.g., breakability), other dispositions appear to have no stimulus requirements at all (e.g., loquaciousness). A successful analysis should accommodate all these sorts of disposition.

Third platitude: the directedness of disposed objects towards manifestation is modal. We’ve remarked on the widely appreciated failure of excising modality from dispositional expressions’ interpretation. The problem is that the dependence of manifestation on a stimulus seems obviously conditional. Yet the (non-modal) material conditional that manifestation occurs if the object is stimulated is satisfied by anything that is never stimulated (Reference CarnapCarnap 1936). So, if dispositions were analysed by this conditional, an iron pot which never undergoes any applied stress would be falsely deemed just as fragile as a delicate porcelain vase. Instead, as many have remarked, what is needed is to link the stimulus and manifestation by a counterfactual conditional: manifestation would occur were the object stimulated. Counterfactual conditionals don’t give rise to the same issue, since even if an object is never stimulated it typically could be.

Reference PriorPrior (1985, 5) called the connection between counterfactual conditionals and dispositions ‘pre-theoretic common ground’; earlier, Reference QuineQuine (1974, 9) admitted (alongside Reference RyleRyle 1949 and Reference StorerStorer 1951) that ‘there is no denying that in its bumbling way, this intensional conditional somehow conveys the force of the dispositional idiom’; and later, Reference MumfordMumford (1998, 87) concurred with Reference MartinMartin (1994) that dispositions must be connected ‘somehow’ with conditionals. These remarks suggest that we could take the employment of counterfactual conditional analysans as a further platitude of dispositions. But there are prominent dissenting voices. Some eschew any attempt to characterise the modality of dispositionality in non–sui generis terms (Reference Anjum and MumfordAnjum and Mumford 2018; Reference MartinMartin 1994; Reference Mumford and AnjumMumford and Anjum 2011). But even assuming these philosophers are wrong, others maintain that the dispositions’ modal character is one of the possibility of manifestation rather than manifestation’s dependence on stimulus (Reference AimarAimar 2019; Reference VetterVetter 2015). We will explore these alternatives in subsections 2.3 and 2.4. Nevertheless, whichever option we pursue, the modality of dispositions’ directedness is no longer in doubt.

With these platitudes in mind, we can now give a more precise description of what an analysis of dispositions must involve: it must spell out the ‘directedness’ platitude in terms of the modal implication of any disposed object’s manifestation, including saying how, if at all, stimuli are involved. To that end we commence our search as many others have previously, by scrutinising the ‘Simple Conditional Analysis’ (where `□→’ is the counterfactual conditional).

Our go-to example, again unoriginal, is the analysis of fragility. Fragility is a disposition directed towards breaking, which we assume for the time being has the stimulus of (relatively low) applied stress. In the form of SCA, the analysis of fragility looks as follows:

SCA (or properly speaking, its instances) is plagued by well-known counterexamples. We will go through the nine we have identified in the literature and discuss various strategies for avoiding them. However, before diving into the problem cases we introduce a heuristic for representation that we will make considerable use of this throughout this Element.

2.1.2 A Tool for Representation

Our demonstration of many of the problem cases will be atypical in that we make use of structural equations modelling. This might make us seem guilty of using a sledgehammer to crack a nut, since the formalism is rather more involved than anything employed in the current debate. Nevertheless, we ask the reader to persevere for two reasons. First, we think that once understood, structural equations models provide one of the clearest resources for identifying the nuances of each problem case. Second, structural equations will be of central importance to developing our novel strategy for analysis provided in subsection 2.5, and a familiarity with them will greatly facilitate its introduction.

A structural equation has the form $B\left(x\right)\Leftarrow f\left(A_1\left(x\right),\dots ,A_n\left(x\right)\right)$ and expresses an asymmetric relationship of numerical counterfactual dependency of the left-hand variable property $B$ of an object $x$ on some function $f$ of right-hand variable properties $A_1,\dots ,A_n$ of $x$ (for conciseness we often omit the object variable). A structural equation therefore encodes lots of counterfactual information about how $x$ would behave. Indeed, structural equations provide a counterfactual for every combination of values assigned to the right-hand variables (within some permitted range): if it were that $A_1\left(x\right)=a_1,\dots ,A_n\left(x\right)=a_n$ (i.e., each variable on the right-hand side were to take some specific distribution of determinate values) then it would be that $B\left(x\right)=f\left(a_1,\dots ,a_n\right)=b.$

Structural equations are bread and butter for contemporary causal analysis in science and philosophy of causation (Reference PearlPearl 2000; Reference HitchcockHitchcock 2001; Reference WoodwardWoodward 2003; Reference Halpern and PearlHalpern and Pearl 2005). Causal results and hypotheses are typically expressed in terms of structural equations models (SEMs), an ordered pair (V, E) of variable set V and structural equations set E such that every variable in V is either on the left-hand side of at most one equation in E (and so dependent on other variables in V) or else is ‘exogenous’ (having its value determined by factors outside of the model). Associated with any SEM is a causal graph where the variables in V are nodes and directed edges (arrows) lead from one variable $A$ to another $B$ just in case $A$ features in the right-hand side of a structural equation in which $B$ is the left-hand variable.

Our aim is to use SEMs to describe the causal relationships relevant to dispositional behaviour. These models will therefore include ‘stimulus variables’, ‘manifestation variables’, and ‘disposition variables’, which take values ranging over whether (and to what degree) an object is stimulated, manifests, and has some disposition, respectively.

Let’s consider the SEM involving a fragile object $x$ described in Table 1.

Table 1 Details for a causal model for fragility

Variables			Structural equations
Symbol	Possible values	Interpretation
$FR$	$1$	$x$ is fragile	(Exogenous)
	$0$	$x$ is not fragile
$ST$	$1$	$x$ undergoes stress	(Exogenous)
	$0$	$x$ does not undergo stress
$BR$	$1$	$x$ breaks	$BR\Leftarrow FR\times ST$
	$0$	$x$ does not break

Table 1 displays the model’s variables ( $FR\left(x\right),ST\left(x\right)$ and $BR\left(x\right)$ ) and how to interpret their possible values. For example, if the variable $FR\left(x\right)=1$ this indicates that $x$ is fragile, and if $FR\left(x\right)=0$ , $x$ is not fragile. Table 1 also displays whether the variables have a structural equation or not. In this model, only one variable is not exogenous $\left(BR\left(x\right)\right)$ and so is the only variable with a structural equation $(BR\left(x\right)\Leftarrow FR\left(x\right)\times ST\left(x\right))$ . The model’s equation tells us that the values of $BR\left(x\right)$ are determined by $FR\left(x\right)\times ST\left(x\right).$ Moreover, it tells us that the determination is robust under counterfactual variations of the right-hand variable’s values: for any combination of values for $FR\left(x\right)$ and $ST\left(x\right)$ , if those variables were to take those values, $BR\left(x\right)$ would take the value given by the equation.

Since the one structural equation for the present model reveals $BR\left(x\right)$ ’s dependence on $FR\left(x\right)$ and $ST\left(x\right)$ , the causal graph for this model will have two directed edges indicating causal influence of $FR\left(x\right)$ and $ST\left(x\right)$ on $BR\left(x\right)$ , as displayed in Figure 1.

Figure 1 Causal graph for a simple causal model for fragility

If we take this SEM to characterise causal relationships any object $x$ whatsoever can be involved in, then it predicts FRAGILE. For it entails that if $x$ were fragile ( $FR\left(x\right)=1$ ) and were stimulated ( $ST\left(x\right)=1$ ) then it would break ( $BR\left(x\right)=FR\left(x\right)\times ST\left(x\right)=1$ ), whereas if $x$ were not fragile ( $FR\left(x\right)=0$ ) and were stimulated ( $ST\left(x\right)=1$ ) then it would not break ( $BR\left(x\right)=FR\left(x\right)\times ST\left(x\right)=0$ ). Assuming possible worlds are strongly centred on the actual world (so that the actual world is the closest possible world in which any true proposition is true) then FRAGILE is entailed. However, the SEM predicts further counterfactuals not directly relevant to the truth of FRAGILE. For instance, it predicts that if something were fragile ( $FR\left(x\right)=1$ ) but did not undergo stress ( $ST\left(x\right)=0$ ) then it wouldn’t break ( $BR\left(x\right)=FR\left(x\right)\times ST\left(x\right)=0$ ). Although this kind of counterfactual is not part of traditional dispositions’ analyses, we take it to be plausible in many contexts. In subsection 2.5 we will argue that, in fact, it should be a feature of fragility’s analysis.

Given how widely dispositions are thought to be causally implicating we find it surprising that SEMs are yet to be invoked in discussion of their analysis. As we aim to show, SEMs provide a fertile heuristic for displaying many of dispositions’ causal features. But it’s important not to get carried away. Structural equations models do not add any metaphysical assumptions about the relationships among those included variables than are already implied by the counterfactuals encoded in their equations. Instead, SEMs’ value comes from the fact they encode far more counterfactual information than is available from any single conditional. It is this feature which makes them instrumental for describing problem cases, and also for providing the basis of a new strategy for analysis (see Section 2.5).

2.2.1 Problem #1: Masks

The disposition of an appropriately stimulated object is ‘masked’ when it fails to manifest due to interference.Footnote ⁸ A classic example is when a fragile vase fails to break when subject to stress because it is packed in bubble wrap (Reference JohnstonJohnston 1992). Another example is when an antidote is taken to counteract the disposition of ingested poison to cause harm (Reference BirdBird 1998). This kind of causal interference is easily captured in an SEM, as described in Table 2. The associated causal graph is displayed in Figure 2.

Table 2 Details for a causal model for masking poisonousness

Variables			Structural equations
Symbol	Possible values	Interpretation
$P$	$1$	$x$ is poisonous	(Exogenous)
	$0$	$x$ is not poisonous
I	1	$x$ is ingested by agent	(Exogenous)
	$0$	$x$ is not ingested by agent
$A$	$1$	$x$ is accompanied by antidote	(Exogenous)
	$0$	$x$ is not accompanied by antidote
$H$	$1$	Agent comes to harm	H⇐(P × I) × (1 – A)
	$0$	Agent does not come to harm

Figure 2 Causal graph for masking poisonousness

The counterfactuals entailed by this SEM are more complex than instances of SCA allow. A typical SCA for poisonousness might be the following:

But this is not true in the above SEM since it is consistent with the model that $x$ is poisonous ( $P=1$ ) and yet harm doesn’t occur ( $H=0$ ) because the antidote is ingested ( $A=1$ ). Masks therefore present a counterexample to the analysans in SCAs being a necessary condition for dispositions, since something can have a disposition but, due to the presence of a mask, fail to obey the associated counterfactual.

2.2.2 Problem #2: Alterers

Dispositions are subject to ‘altering’ when the stimulus of a disposition influences whether (and to what degree) an object has that disposition. This can happen in two ways: either an object is caused to lose a disposition when stimulus occurs, as when a live wire with the disposition to conduct electricity is caused to go dead when touched because of the presence of a fuse; or an object is caused to gain a disposition when stimulus occurs, as when a dead wire has a sensor (an ‘electro-fink’) which causes it to become live when touched. Reference MartinCharlie Martin (1994) is credited with being the first to discuss these kinds of case and used the terms ‘reverse-cycle fink’ and ‘fink’, respectively. We employ Reference MckitrickJohnston’s (1992, 232–3) more general ‘altering’, since the stimulus in either case alters the dispositional status of the object.

Consider the SEM described in Table 3. The associated causal graph is displayed in Figure 3. What the graph clearly shows is that, in cases of altering, there is more than one effect being considered. Not only is whether $x$ manifests ( $C$ ) an effect of whether $x$ has the disposition ( $L$ ) and is stimulated ( $T$ ), but whether $x$ has the disposition is also an effect of whether $x$ is stimulated.

Table 3 Details for a causal model of altering being electrically live

Variables			Structural equations
Symbol	Possible values	Interpretation
$T$	$1$	$x$ is touched by a conductor	(Exogenous)
	$0$	$x$ is not touched by a conductor
$L$	$1$	$x$ is live	$L\Leftarrow 1–T$
	$0$	$x$ is not live
$C$	$1$	Current flows from $x$ to the conductor	$C\Leftarrow L\times T$
	$0$	Current does not flow from $x$ to the conductor

Figure 3 Causal graph for altering being electrically live

As with masking, the true counterfactuals of this SEM are more complex than those in instances of SCA. A typical SCA for being live is the following (cf. Reference MartinMartin 1994):

But this is not true in the foregoing SEM, since if the $x$ were touched by a conductor ( $T=1$ ) then $x$ would no longer be live ( $L=1-T=0$ ), and so current would not flow from $x$ to the conductor ( $C=L\times T=0$ ). The above case of altering therefore presents a counterexample to the necessity of the analysans in SCAs, since something can have a disposition, but due to the presence of a stimulus which removes the disposition, the disposed object fails to obey the associated counterfactual. To model the other altering case where stimulus confers the disposition upon the object, we need only revise the structural equation for $L$ from $L\Leftarrow \left(1-T\right)$ to $L\Leftarrow T$ (the graph stays the same). This would then present a counterexample to the sufficiency of the analysans in SCAs, since $x$ would satisfy the associated counterfactual while failing to have the disposition.

2.2.3 Problem #3: Mimickers

A disposition is mimicked by objects without that disposition but behave as though they do. Styrofoam plates are not fragile. If a plate undergoes an applied stress, it makes a distinctive sound that, when in earshot, provokes the hater of Styrofoam to tear it up. So, in such circumstances the plate would break were it stressed (the example is in Reference LewisLewis 1997, attributed to Daniel Nolan).

Consider the SEM described in Table 4. The associated causal graph is displayed in Figure 4.

Figure 4 Causal graph for mimicking fragility

Table 4 Details for a causal model for mimicking fragility

Variables			Structural equations
Symbol	Possible values	Interpretation
$FR$	$1$	$x$ is fragile	(Exogenous)
	$0$	$x$ is not fragile
$ST$	$1$	$x$ undergoes stress	(Exogenous)
	$0$	$x$ does not undergo stress
$E$	$1$	$x$ is within earshot of a hater of Styrofoam	(Exogenous)
	$0$	$x$ is not within earshot of a hater of Styrofoam
$H$	$1$	A hater of Styrofoam overhears $x$ being stressed	$H\Leftarrow E\times ST$
	$0$	A hater of Styrofoam doesn’t overhear $x$ being stressed
$BR$	$1$	x breaks	$BR\Leftarrow \left(FR+H–FR\times H\right)\times ST$
	$0$	$x$ does not break

The true counterfactuals of this SEM are more complex than SCA allows. Our earlier SCA for fragility (FRAGILE) entailed that the following is true for any $x$ .

But this is not true in the above SEM, since it is consistent with the model that $x$ undergoes stress ( $ST=1$ ) and breaks ( $BR=1$ ) yet fails to be fragile ( $FR=0$ ), so long as the hater of Styrofoam is within earshot ( $E=1$ ). Mimickers therefore present a counterexample to the sufficiency of the analysans in SCAs, since the associated counterfactual can be true while $x$ fails to have the corresponding disposition.

2.2.4 Problem #4: Tricks

Tricks are discussed by Reference ContessaContessa (2016). Like mimickers, tricks also look like displays of dispositionality when they are not. Contessa’s example involves a mug of coffee cooling down. It is not, Contessa maintains, disposed to cool down when someone says ‘Abracadabra’ over it. Nevertheless, it would cool down were someone to do so, since it is destined to cool down anyway due to the immutable laws of thermodynamics (perhaps we should grant it has the disposition to cool, simpliciter). As with mimickers, the dispositional behaviour seems to be a trick, a merely circumstantial satisfaction of the counterfactual relationship between stimulus and manifestation. Unlike mimickers, however, the possibility of manifestation is independent of whether the object is stimulated; the object is destined to manifest anyway.

Let’s work through another ‘tricky’ case. A non-fragile mug will be crushed in a hydraulic press. Therefore, if the mug were to undergo (relatively low) stress it would break.Footnote ⁹ Consider the model described in Table 5. The associated causal graph is displayed in Figure 5.

Table 5 Details for a causal model for fragility tricks

Variables			Structural equations
Symbol	Possible values	Interpretation
$FR$	$1$	$x$ is fragile	(Exogenous)
	$0$	$x$ is not fragile
$ST$	$1$	$x$ undergoes stress	(Exogenous)
	$0$	$x$ does not undergo stress
$CR$	$1$	$x$ is crushed in a hydraulic press	(Exogenous)
	$0$	$x$ is not crushed in a hydraulic press
$BR$	$1$	$x$ breaks	$BR\Leftarrow \left(FR\times ST+CR\right)$ $-\left(FR\times ST\times CR\right)$
	$0$	$x$ does not break

Figure 5 Causal graph for fragility tricks

The true counterfactuals of this SEM are more complex than SCA would seem to allow. Our earlier SCA for fragility entailed the following for any $x$ :

But this is not true for cases described by the SEM, since it is consistent with the model that $x$ undergoes stress ( $ST=1$ )  and breaks ( $BR=1$ ) and yet fails to be fragile ( $FR=0$ ), because it will be crushed by a hydraulic press ( $C=1$ ). Tricks therefore present a counterexample to the sufficiency of the analysans in SCA, since something can obey the associated counterfactual, but due to the tricky circumstances, fail to have the corresponding disposition.

2.2.5 Strategy A: Getting Specific

We now turn to consider strategies for responding to problem cases #1–#4. The problem cases capitalise on the assumption that the antecedent of the characterising conditionals in instances of SCA only refer to a single influence. For instance, in the case of FRAGILE the antecedent is ‘ $x$ undergoes (relatively low) applied stress’. Consequently, the antecedent is satisfied even when $x$ is wrapped in bubble wrap, is subject to altering, is about to be crushed in a hydraulic press, is within earshot of the hater of Styrofoam, etc. But what if the antecedent of the analysing conditional included additional qualifications that these further conditions do not hold? More generally, what if we avoid the problem cases by getting more specific in the conditional’s antecedent?

The issue with this strategy is that there is potentially an infinity of relevant factors which must be accounted for. Just focus on the specifications required to avoid counterexamples to FRAGILITY due to masks. A fragile vase can be protected from breaking when under applied stress not just by bubble wrap, but also by changing the material of the striking object, by striking it in a vat of honey, by striking it incredibly slowly, or any of the numerous ways of reducing the force of the striking object; and of course there’s always the possibility – the philosopher’s favourite – that a nearby wizard casts a spell which protects the vase in some way unknown to physics. Presumably, the options for alters, tricks, and mimickers are similarly profuse.

Whatever antecedent goes into the characterising conditional of a disposition will have to be enormously complex, if not open-ended, if it is to cover every possible eventuality explicitly (Reference Manley and WassermanManley and Wasserman 2008 and Reference Anjum and MumfordAnjum and Mumford 2018). Perhaps some added complexity could be tolerated, but it is surely implausible that the analysans has the level of complexity it would have to have to accommodate all the potential eventualities of the sort described above. Given the ease with which we conceptually grasp dispositions like fragility, it cannot be that we learn anything remotely like that. Of course, if our task was other than analysis, we might be willing to put up with an element of open-endedness. Analysis requires that we give conceptually graspable necessary and sufficient conditions for the presence of a disposition; an open-ended list of conditions can’t do that. Consequently, the Getting Specific strategy should be rejected.

2.2.6 Strategy B: Denial

Here is a different strategy. Problems #1–#4 rest on intuitions about whether the presence of interfering factors influences whether something has a disposition. The presence of a mask doesn’t – so the intuitions go – stop a thing having the disposition it has, it only masks it. By contrast, the presence of an altering stimulus does change whether something has a disposition. If mimickers and tricks are to be a problem, intuition must have it that the presence of a mimicker or trick doesn’t confer a disposition on a thing, it only ‘mimics’ it. One strategy is, therefore, to deny these intuitions.

Choi has denied the intuition in the case of mimickers. ‘Contrary to appearances, [SCA] is not troubled with the case of the Styrofoam dish. … [I]t does not pose any threat … because [the dish] indeed has the disposition to break in response to being struck’ (Reference 74ChoiChoi 2005, 182–3).Footnote ¹⁰ He has also denied it in the case of masks.

Choi doesn’t give an argument for these claims except to say that opposition to them is poorly justified. Hájek makes a similar remark about altering.

Hájek justifies this by pointing out that altering stimuli can only interfere with the dispositions of the object because that object is receptive to change, where that receptiveness, Hájek suggests, must be a further disposition. Lastly, although neither Choi nor Hájek consider it, the Denial strategy may also be effective against tricks. Perhaps in the end it is correct to say that a mug of hot coffee has the disposition to cool down when one says ‘Abracadabra’ over it.

Choi and Hájek admit that the strategy only works in general for ‘canonical’ dispositions (see Section 1). Arguably, neither the presence of the hater of Styrofoam, bubble wrap, nor the hydraulic press provide a counterexample to SCA’s analysis of the disposition to break when stressed; nor does the presence of an electro-fink provide a counterexample to SCA’s analysis of the disposition to conduct electricity when touched. But these circumstances do still provide counterexamples to SCA’s analysis of fragility and being a live wire, respectively. The reason for this is that, unlike canonical dispositions, the dispositions of fragility and being a live wire are intrinsic, which is to say, roughly, that whether an object has them or not is independent of whatever is going on beyond them. Given that conventional dispositions are often those we are most interested in (Reference HájekHájek 2020; Reference VetterVetter 2015), and many conventional dispositions seem to be intrinsic, this puts a severe limitation on the Denial strategy.

Even granting the restriction to canonical dispositions, there are reasons to query whether the Denial strategy always works. Choi claims that a vase wrapped in bubble wrap is not disposed to break when stressed but is disposed to break when stressed in the absence of the bubble wrap. Should we say the same for a vase not wrapped in bubble wrap? If we do, then we descend a slippery slope, having to deny that any vase is disposed to break when stressed, or indeed even when stressed in the absence of bubble wrap, since it could be wrapped in Styrofoam instead, or have the protection of a wizard, etc. As we’ve seen already, we shouldn’t allow dispositions to have such complex analysans. If, however, the dispositions of otherwise identical wrapped and unwrapped vases are different, we’ll have to deny that any disposition is intrinsic, since even the dispositions an unprotected vase has will be dependent on the absence of extrinsic protection. We might grant that some dispositions are extrinsic, but it is less plausible that dispositions are inevitably extrinsic in this sense.Footnote ¹¹ Worse still, since the context every vase is in is slightly different, we’d have to claim that the maskable dispositions of each vase are unique. This seems to us absurd. On reflection, it appears more reasonable to say of both wrapped and unwrapped (but otherwise identical) vases that they share the disposition to break when stressed, contrary to Choi’s Denial strategy for the problem of masks.Footnote ¹²

2.2.7 Strategy C: So Long As

Another strategy for dealing with problems #1–#4 is to find some way to characterise dispositions as manifesting given the stimulus only so long as further influences are absent.

An early example of this kind of approach is Reference LewisLewis’s (1997) ‘Revised Conditional Analysis’ (RCA).

The motivation behind RCA was to avoid the problem of alterers, for which, Lewis assumed, the relevant intrinsic properties of an object change under stimulus. We won’t elaborate here on why it fails to avoid all the other problem cases (see Reference BirdBird 2007b, 27–36; Reference MartinMartin 2007, 19–21). Moreover, its solution to the problem of alters is uniquely problematic, since it requires that the disposition must be retained for some time after stimulus in non-altering cases. But, plausibly, an applied stress can cause something fragile to break instantaneously (as soon as the stress induces acceleration), and once broken, something (often, at least) can’t be broken again.Footnote ¹⁵ Hence, its fragility will not be retained for any time upon stimulus.

A more flat-footed So Long As strategy introduces into analysis the qualification that the antecedent conditions lead to manifestation so long as masks, alterers, mimckers, and tricks are absent (cf. Reference BirdBird 2007b, 59–60). Another comes from Reference HüttemannHüttemann (2004), who proposes that the analysing counterfactual holds so long as the disposed object is in isolation. Vaguer and potentially more inclusive qualifications have also been proposed, e.g., that the manifestation occurs ‘in normal circumstances’, in ‘ordinary circumstances’, or ‘ceteris paribus’ (Reference BirdBird 1998; Reference ChoiChoi 2008; Reference CrossCross 2005; Reference Kistler and MeinckeKistler 2020; Reference MartinMartin 1994; Reference MumfordMumford 1998; Reference SteinbergSteinberg 2010). We count all of these cases as instances of the So Long As strategy.

Some of these suggestions appear liable to circularity. For example, employing the concepts of mask and alterer in analyses would give rise to circularities if their own definitions can’t be given without reference to dispositions (as we might expect). And what could ‘normal’ circumstances be if not those in which the manifestation occurs given the stimulus? Reference ChoiChoi (2008) defends a non-circular understanding of ‘ordinary’, but this arguably leaves too much down to the minds of ‘those who possess the corresponding dispositional concept’. Moreover, both qualifications of normalcy and ordinariness appear susceptible to Reference FaraFara’s (2005) complaint that something can normally/ordinarily M if it is S just because circumstances make the manifestation anyway likely (such circumstances would be like generalised tricks). Finally, the notion of isolation is also fraught with interpretational issues – isolation from what: properties, objects? And what is isolation? Presumably not independence from accompaniment, since some dispositions will only manifest in a suitably populated environment (e.g., containing quantum fields, a breathable atmosphere, etc.).

A more carefully presented instance of the So Long As strategy comes from Reference ContessaContessa (2013), who gives an account of how to understand masks and alterers in terms of ‘destructive interference’ and mimickers in terms of ‘constructive interference’ so that there is no circularity or vacuity in qualifying the conditional dependence of manifestation on stimulus so long as nothing interferes.Footnote ¹⁶ Crucial to the analysis is the contrast between intrinsic and extrinsic dispositions, and Contessa seeks to define the latter in terms of the former. Part of the purpose behind this is to provide a principled distinction between mimickers and extrinsic dispositions. Roughly, only genuine extrinsic dispositions (and not mimickers) are such that there is some further intrinsic disposition of the disposed object whose stimulus–manifestation dependency contributes to the observed behaviour. According to Contessa, mimickers do not ‘piggyback’ on intrinsic dispositions in this way.

Contessa’s distinction between extrinsic dispositions and mimickers seems to us problematic. Surely the disposition of the Styrofoam plate to make a particular sound when stressed contributes to the fact that it breaks when the hater of Styrofoam is in earshot. The plate’s disposition to break when stressed therefore piggybacks on some intrinsic dispositions. But we do not want to say the plate is fragile. Indeed, it is a paradigm case of mimicking. Even without considering further problem cases, therefore, Contessa’s approach to responding to problems #1–#4 may not be the final story for analysis of dispositions. And he admits that it does not respond to the problem of tricks (Reference ContessaContessa 2016, 590 fn. 5). In sum, we have yet to find a convincing account among So Long As strategies, or one-conditional approaches more generally.

2.3.1 Problem #5: Chancy Dispositions

Reference HájekHájek (2020, 4801) points out that if one wishes to undermine conditional analyses of dispositions then ‘finkish [i.e., altering] cases are needlessly baroque’. That’s because the associated counterfactuals are often falsified in much more ordinary ways. His key examples are chancy dispositions.Footnote ¹⁷ An object might be disposed to behave in way X if subject to Y and yet not be such that were it subjected to Y then it would behave in way X, since there is only a high but non-maximal probability of it behaving in way X if subjected to Y. For instance, an object with such a disposition might be actually subjected to Y and not behave in way X, thereby falsifying the disposition’s associated counterfactual (assuming strong centring). Likewise, an object may not be disposed to behave in way X if subject to Y yet be such that were it subjected to Y then it would X, since there is only a probability <1 of it not behaving in way X if subjected to Y. For instance, an object without such a disposition might be actually subjected to Y and behave in way X, thereby satisfying the disposition’s associated conditional. Chancy dispositions therefore present problems both for the necessity and sufficiency of the analysans in instances of SCA.Footnote ¹⁸

Tempting as it may be, it’s no use responding to the threat of chancy dispositions by claiming that the world is in fact deterministic, or is deterministic for all intents and purposes at the macroscopic level. Under standard ‘collapse’ interpretations of quantum mechanics, a disposition to radioactively decay or quantum tunnel through some material might be fundamentally chancy. And such indeterminacies could, for all we know, ‘percolate up to macroscopic objects’ (Reference HájekHájek 2020, 4804); see also Reference HawthorneHawthorne 2005). Hence, Reference HájekHájek (2020, 4804) notes that ‘fragility is as paradigmatic a case of a disposition as there can be – it is by far the most common example in the literature – and yet given its sensitivity to facts about molecular bonding, it is surely not sure-fire (even when it is nearly so)’. Likewise, objects may fail to be fragile even if, given the sensitivity to facts about molecular bonding, it is not certain that it won’t break under relatively low applied stress. These kinds of chanciness have been variously referred to as ‘(reverse) Achilles heels’ (Reference Manley and WassermanManley and Wasserman 2008; Reference VetterVetter 2015) or ‘weak/strong spots’ (Reference AimarAimar 2019; Reference HájekHájek 2020), since they are often due to a part of the disposed/undisposed object which is uncharacteristically undisposed/disposed to behave in the relevant way.Footnote ¹⁹

2.3.2 Strategy D: Generics

A strategy for response to chancy dispositions, which would also address problems #1–#4, would be to substitute the conditional in SCA with a generic:

The generic in GENERIC is like a conditional, but instead of entailing that $x$ would M if it were subject to S (on some occasion), the statement makes a generalisation over all the occasions where it is subject to S and, crucially, in a way that tolerates exceptions. This seems just what is needed to address chancy dispositions as well as masks and alterers. Moreover, a generic is not assertible about an object given merely that there is some instance of it being S’d which M’s. There must be reason to expect that it will in general M when S’d. This suggests that GENERIC may have the means to respond to problems of mimickers and tricks too.

There are nevertheless many issues facing this Generics strategy. One hurdle is to avoid the issue (noted in subsection 2.2 above with qualifications of normalcy) that it can be true of some objects that they (generically/normally) manifest when stimulated purely because some independent circumstance makes manifestation likely. Reference FaraFara’s (2005) solution is to requrie that the disposed object Ms when S’d in virtue of its intrinsic properties. We know, however, that some dispositional behaviour is due to extrinsic facts (Reference MckitrickMckitrick 2003). An object’s weight gives it a disposition to produce a reading on weighing scales, but the weight is not fully intrinsic, since it is partly a consequence of the gravitational field it is in. Anyway, Fara’s qualification may not even work for intrinsic dispositions. A machine programmed to print designs on non-fragile mugs might always fail (due to a software error) to print a paisley design properly when requested to. Consequently, the machine operators normally put the paisley-designed mugs in the incinerator rather than send them to Sales. In this case, paisley mugs break ultimately in virtue of an intrinsic property (their paisley design), and though they aren’t fragile, they nevertheless break when stressed.

Another issue with GENERIC is that it seems to imply that any D has been or will be S’d. But there need be no such instances for the corresponding disposition. For example, if a bell is never struck, it seems wrong to say that it rings when struck, while it seems perfectly coherent to say that it is disposed to ring when struck (Reference WassermanWasserman 2011, 433–7).

A potential solution to both issues involves reference to kind-level generalisations. Reference LoweLowe (2007, 107) endorses the idea that a disposition for something $x$ to M when S’d can be understood in terms of $x$ being a member of some kind K, where it is a law that Ks M when S. This is perfectly consistent with $x$ itself never being S’d. The qualification that Ks M when S’d is a law also establishes an explanatory connection between M and S, thereby avoiding the problem of instances M-ing when S’d due to reasons independent of S (cf. the suggestion by Reference Quine and RescherQuine 1970 and discussed by Reference WassermanWasserman 2011, 437–9). However, Wasserman complains that since the kinds which feature in laws of nature must be natural kinds, Lowe’s qualification will be too restrictive. It just seems false that all instances of any natural kind share the same dispositions (e.g., cats need not all be disposed to purr), nor does it seem reasonable to restrict disposed objects to instances of a natural kind.

2.3.3 Problem #6: Unspecific Stimuli

The Generics strategy also shares a problem with the one-conditional analyses so far discussed. Notice first that all these accounts require that dispositions must be conceptually associated with some or other stimulus. As we mentioned in subsection 2.1.1, however, this isn’t always the case. Reference MolnarMolnar (2003, 85–6) gives the example of the muon,Footnote ²⁰ which has the disposition to spontaneously decay into an electron, a neutrino, and an antineutrino. Reference Manley and WassermanManley and Wasserman (2008) suggest that loquaciousness and irascibility are dispositions to manifest, respectively, talking and anger independently of whether or not they are provoked to do so (see also Reference FaraFara 2005, 70). Reference HájekHájek (2020) likewise suggests the disposition of a photon to follow a geodesic. It seems implausible that any of these dispositions is conceptually associated with a stimulus condition.

Reference FaraFara (2005) has argued that generic analyses can deal with this problem of ‘absent stimuli’ simply by making the ‘when S’d’ clause optional. He tentatively suggests this is a further benefit of generics over conditionals. However, the problem of absent stimuli may not be all that bothersome for conditional approaches either. In the case of loquaciousness, for example, the fan of conditionals can claim that the relevant ‘stimulus’ is the trivial condition of anything whatsoever occurring, or the occurrence of some logical truth.Footnote ²¹

Regardless, there remains a similar but more troublesome problem for both conditionals and generics accounts, not that there may be only vacuous stimulus requirements, but that the required stimuli may be wholly unspecific. For example, things are breakable if they can be caused to break (as opposed to breaking spontaneously). So breakability manifests under a stimulus, but one that is unspecific. This is troublesome since both one-conditional and generics strategies require that if a disposition needs stimulating in order to manifest then the stimulus should be specifiable, either in the antecedent of a counterfactual or as the ‘restrictor’ of a generic. In the case of breakability, what can we put in either place? An object is breakable if something can cause it to break. But the condition that the manifestation occurs when caused by something, or would occur were it caused by something, is trivially satisfied by everything. There doesn’t seem a sensible analysis either view can provide.

2.3.4 Problem #7: Disjunctive Multi-Track Dispositions

Another problem for both one-conditional and generics strategies is highlighted by Reference VetterVetter (2015), and concerns dispositions whose instances don’t all manifest in the same way. First notice that the following two conditions (or something very similar) are inevitable commitments under either strategy for analysis of any arbitrary disposition D:

1. 1. Being such as to M were it S’d, or M-ing (when S’d), is necessary for having D.

2. 2. Manifesting D can only be achieved by exhibiting M in response to S.

Condition 1 is entailed by analyses of the form SCA and GENERIC (variations can be given corresponding with the other one-conditional and generic strategies considered already). Condition 2 is not entailed by any analysis, but it is a natural presupposition. If D would count as manifesting by exhibiting some behaviour other than M, or by exhibiting M in some other way than in response to S, then any analysis of D should take that into account.

In combination these conditions lead to a dilemma. Take fragility, which we agreed to understand as manifesting under (relatively low) applied stress. Some fragile things will break under even the slightest stress, others require more, though still not as much as non-fragile objects. So let there be some threshold value T such that for any fragile object there is a minimum value T’ $<$ T of stress that will break it. Now pick some object a which will break if subject to a stress of at least T’_a. It is not true of it that a will break for any applied stress less than T, since it only breaks if the applied stresses are T’_a or above. Hence the stimulus for fragility can’t be the broad condition of any applied stress under T, since not every instance of such a stimulus on a fragile object will result in manifestation, contrary to condition 1. If, instead, we choose a more specific stimulus, say applied stresses above T’_a, then when other objects do break from applied stresses lower than T’_a this cannot count as a display of fragility on pain of contravening condition 2. But something breaking under even lower stresses than those which can count as a stimulus for fragility (e.g., T’_a) will surely also be a manifestation of fragility (context permitting).

The dilemma described here is one of disjunctive multi-track dispositions.Footnote ²² Not all of the ways in which a disposition like fragility can be made to manifest can make every instance of that disposition manifest. Hence, if fragility is to be analysed in terms of an association (a ‘track’) between stimulus and manifestation it would have to be a disjunction of multiple such associations: fragility’s instances can break under this stimulus or that or … etc. Since no one-conditional or generics strategy entertains such a disjunction of stimulus–manifestation relationships, they cannot address this problem.

2.3.5 Strategy E: Possibilities

Some of the aforementioned problems have been the explicit motivation behind some abandoning a relational analysis of dispositions altogether. Instead of a relationship (e.g., conditional or generic) between stimulus and manifestation, these theorists hope to capture dispositions monadically, in terms of the possibility for manifestation (Reference AimarAimar 2019; Vetter 2011, Reference Vetter2014, Reference Vetter2015). At its most simplistic, the schema for such analyses is as follows:

The schema implies that something has D if it can manifest, regardless of how that manifestation might come about.

The departure from previously considered views can seem extreme, but Reference VetterVetter (2015, 64) draws attention to the broad linguistic evidence for this Possibility strategy. She cites the Oxford English Dictionary, which says of fragility that it is the property of something which is ‘liable to break or be broken; … easily destroyed’, and not (for example) ‘breaks given a (relatively low) stress’. Reference AimarAimar (2019) also shows that in some contexts, ‘ $x$ is fragile’ and ‘ $x$ can be broken easily’ are mutually inferrable, whereas the claims ‘ $x$ is fragile’ and ‘if $x$ were hit it would break’ are not.

Some have queried whether all dispositions can be defined without reference to a stimulus, as per POSSIBILITY. Reference Manley and WassermanManley and Wasserman (2008) point out that this is implausible in the case of canonical dispositions like the disposition to break when stressed (though see Reference VetterVetter 2015 for a reply). Reference BirdBird (2020) also points out that stimulus conditions are required to distinguish dispositions which have the same manifestation, such as dispositions to break easily for different reasons (e.g., microstructural or circumstantial), or dispositions to generate force in different ways (e.g., charge and mass; see Reference VetterVetter 2020 for a reply).

Nevertheless, there clearly are benefits to adopting the Possibility strategy wholesale, since POSSIBILITY can avoid many of the problems so far considered. Working backwards, analyses of this form do not encounter Problem #7 disjunctive multi-track dispositions, since they do not define dispositions in terms of tracks at all. All the analysis requires is that a disposed object can manifest some way or other; potential stimuli are not relevant to the analysis of the disposition itself. POSSIBILITY also avoids the problem of absent stimuli, since its instances don’t even attempt to specify stimuli. Moreover, unspecific stimuli can be accounted for by interpreting the possibility claim causally (e.g., Reference VetterVetter 2015, 96). For example, breakability can be analysed as a possibility to be caused to break. Finally, the fact that manifestations need only be possible (rather than inevitable) means that POSSIBILITY’s instances are consistent with failures to manifest due to chanciness, masks, and alterers.Footnote ²³

Having said all that, theorists who have abandoned the relational strategy (including Vetter and Aimar) seem in agreement that POSSIBILITY can’t be the final analysis. A Styrofoam plate in the presence of the hater of Styrofoam can break, as can many things, e.g., if using a hydraulic press or as a result of freak chance. The view therefore struggles with mimickers, as it will with tricks and chancy manifestations from undisposed objects. Moreover, there is surely something unsatisfactory about the use of the possibility operator to capture chancy dispositions. A die’s disposition to come up with a number between one and five isn’t just possible, it is likely. POSSIBILITY has no facility to make sense of this. Finally, an issue even more at the forefront of these theorists’ minds is the fact that dispositions can come in degrees. Consequently, POSSIBILITY represents a point of departure for some theorists towards a quantitative approach to dispositions analysis.

2.4.1 Problem #8: Dispositional Degrees

The problem of disjunctively multi-track dispositions revealed that things aren’t just disposed simpliciter, they come in degrees. As Reference Manley and WassermanManley and Wasserman (2007, 69) point out, ‘this glass may be simply fragile; but it may also be more fragile than that one. This vase can be simply disposed to break if dropped; but it may also be more disposed to break when dropped than that one.’ To compare the degree of objects’ dispositions, like their fragility, we can assign them values along a scale ranging from extremely fragile to extremely robust. Whether anything on that scale is fragile will (we assume) be determined by some context-dependent threshold along that scale.

Dispositional degrees present a problem for all the strategies discussed so far. For example, conditional accounts,

Moreover, it is also consistent with $a$ being more disposed to break if dropped than $b$ that they both break when dropped (as per the Generics strategy), and that both can break (as per the Possibility strategy). A new strategy is clearly required.

2.4.2 Strategy F: Proportions

In one case, at least, dispositional degrees were the explicit motivation for the introduction of proportionality into dispositions analyses (Reference Manley and WassermanManley and Wasserman, 2007). The basic idea behind this strategy is that the degree to which objects are disposed corresponds to the proportion of cases in which they manifest.Footnote ²⁴ Despite its provenance in the work of Manly and Wassermann, the most straightforward instance of this Proportionality strategy is that of Reference VetterVetter (2011a, Reference Vetter, Bird, Ellis and Sankey2012, Reference Vetter2014, Reference Vetter2015), who substitutes for the possibility operator in POSSIBILITY a gradable, object-oriented possibility operator POT, which Vetter calls ‘potentiality’.

Although not all potentialities are dispositions, Vetter claims that all dispositions are potentialities which are had to a sufficiently high degree. Using the possible worlds framework as a heuristic, Vetter suggests that we can understand what it is for something to be fragile in terms of it breaking in a sufficiently large proportion of relevant worlds in which it exists.Footnote ²⁶ Correspondingly, we can understand something being more fragile than something else in terms of it breaking in more relevant worlds (Reference VetterVetter 2015, 78).Footnote ²⁷

VETTER is a development of POSSIBILITY, and thereby inherits POSSIBILITY’s facility for responding to certain problems. However, the introduction of potentiality also enables Vetter’s analysis to respond to problems which the Possibility strategy is unable to deal with. For instance, even though non-fragile objects can break due to being in mimicking or tricky circumstances, it is reasonable to suppose that the proportion of cases in which they are in those circumstances is relatively low compared with the proportion of cases in which genuinely fragile things break. As a consequence, VETTER does not entail that we should treat just anything which can break as fragile.

At first glance, potentialities also seem to provide a way to develop the treatment of chancy dispositions that makes better sense of the variability of chancy dispositions (Reference VetterVetter 2011a, 1180, 1184). However, Reference Manley and WassermanManley and Wasserman (2011, 1219–20) point out that the use of proportions among worlds to account for probabilistic asymmetries between manifesting and not manifesting (as Vetter’s heuristic for potentiality implies) can lead to the requirement for duplicate worlds in some cases. For example, if the trajectory of an electron curving upwards in a magnetic field is half as likely as it is not, then the proportionality account requires that there be exactly two worlds in which it doesn’t curve upwards for every one world in which it does. But there is no principled reason to think that not curving upwards gives a world access to exactly twice as many distinct possibilities as curving upwards. All else being equal, the future possibilities for a world in which curving up doesn’t occur and a world in which it does are the same (or, if not equal it’s at least hard to see why they should be exactly double). If that’s right, then the only way to get the right proportions among worlds would seem to be that some worlds (e.g., those in which curving upwards does not occur) are duplicated. However, orthodoxy – and Leibniz’s law – tell us that worlds are individuated only by their differences.

For this reason, Manley and Wasserman prefer a more nuanced approach to dispositional degrees in the case of chancy dispositions, requiring that worlds in the modal base be weighted according to the chance of manifestation. When fundamental chanciness is relevant to what happens under some stimulus (e.g., a probability 0.33 of curving upwards in a magnetic field) then the associated degree of dispositionality is determined by the proportions of worlds in which manifestation does and doesn’t occur weighted by the respective probabilities (e.g., 0.33 and 0.67).

Manley and Wasserman’s desire to remain consistent with, though not reliant on, stimulus conditions (due to Problem #6) leads them keep a restriction to the more general notion of a ‘C-case’, which can be interpreted broadly (in the case where there are no stimulus conditions),Footnote ²⁸ more narrowly (in the case where there are unspecific stimulus conditions), or more narrowly still (in the case where stimulus conditions are specific). Their preferred schema looks as follows:

Despite their differences, on either VETTER or MANWASS, dispositional degrees are captured in terms of proportions of worlds in which disposed objects manifest. If $x$ is more disposed in way D than $y$ then it will manifest M in a higher proportion of worlds in which it exists than $y$ does. So, for example, if $x$ is highly fragile and $y$ only moderately fragile, then $x$ must break in more (relevant) worlds than $y$ .

As both parties are aware, there are evident problems of principle with this notion of proportionality.

Both Manley and Wassermann, and Vetter, have made some suggestions for how to get around these worries (Reference Manley and WassermanManley and Wasserman 2008, 80–2; Reference VetterVetter 2014). But one might be concerned that without addressing them fully the proportionality interpretation of dispositional degrees isn’t clear enough to provide a workable analysis.

A different issue, applying only to VETTER, is that it is subject to a particular kind of counterexample. Reference WildmanWildman (2020) considers two venomous snakes, one a product of organic evolution and another a product of cybernetic ingenuity. It might well be that the organic snake is more venomous for humans than the cyber snake. But the cyber snake is dependent on humans for its existence, whereas the organic snake is not. Hence, while there will be worlds in which the organic snake can’t bring about harm to humans due to an absence of humans, the same can’t be said for the cyber snake. Consequently, it could well be that the proportion of worlds in which the cyber snake brings harm to humans, among those worlds in which it exists, is higher than the proportion of worlds in which the organic snake brings about harm to humans, among worlds in which it exists (see Reference VetterVetter 2020, 203–6 for replies; see Reference AimarAimar 2019, 1684–5 for a similar counterexample and replies).

It is, however, a final problem for both VETTER and MANWASS which leads us to think some other approach to dispositional degrees than proportions among worlds is needed. As Vetter herself seems ready to admit, $x$ being more fragile than $y$ implies, pre-theoretically at least, that it breaks more easily. This is clearly not conceptually equivalent to $x$ breaking in a higher proportion of instances than $y$ . If all fine china vases from the Ming dynasty are encased for their protection by law then they may very well not break as often as the tumblers in my kitchen cupboard, while nevertheless being more fragile. Of course, their encasement doesn’t make the Ming vases straightforward to break, but if we take ease of breaking to be a matter of the degree of stress required for breaking (as seems natural), they do indeed count as easier to break than the tumblers.

With a suitably diverse modal base the issue just described may be avoided. For VETTER and MANWASS to have a hope of plausibility their corresponding analyses of fragility must concern proportions of manifestation across worlds, including those in which, e.g., there is no legislation protecting Ming vases. But when manifestations also come in degrees this strategy won’t work. Consider now the disposition malleability. Any amount of applied pressure will make an object deform some amount (even if it’s imperceptible). So it’s unclear how one thing being more malleable than another could be measured in terms of proportions of worlds in which a thing deforms under pressure. More problematic still, no proportionality criterion will be suitable for making sense of the idea that one thing is twice as malleable as another. Being twice as malleable presumably means deforming twice as much under the same applied pressure (or deforming the same under half the pressure). But this fact has no bearing on how often a thing deforms, nor does it imply anything directly about which amounts of deformation occur twice as much as other amounts.

It seems to us, then, that the use of proportions in analysis of dispositional degrees, even if only as the go-to heuristic, cannot be quite what is required. Another strategy is needed.

2.4.3 Strategy G: Fine-Graining

A different analysis, which also employs quantitative methods for dealing with dispositional degrees, is provided by Reference AimarAimar (2019). Like VETTER, Aimar’s analysis takes POSSIBILITY as its point of departure. It therefore inherits POSSIBILITY’s ability to respond to problems of masks, alters, absent and unspecific stimuli, and disjunctively multi-track dispositions. However, instead of modifying the modal operator in order to deal with dispositional degrees, Aimar advises that the manifestation be understood as more fine-grained, which we denote by the addition of an asterisk as follows:

Whereas preceding analyses of fragility took the relevant manifestation to be breaking, Aimar encourages us to take manifestation to be a variable which takes different degrees of ease of breaking in different contexts (fragile will mean breaking easily in some contexts, breaking extraordinarily easily in others). Comparison of dispositional degrees of fragility can therefore be understood in terms of different degrees of ease of breaking. Hence, that $x$ is more fragile than $y$ means that $x$ breaks more easily than $y$ , where ease of breaking might be captured on a gradable scale of quantity of stress required. Therefore, similarly to Vetter’s handling of unspecific stimuli, the relevance of applied stress to whether something is fragile (and by how much) is brought back in as a qualification on the manifestation behaviour. But again, like VETTER, the approach doesn’t demand that degrees of manifestation must be captured by reference to a cause. For instance, whether one isotope is more disposed to radioactively decay than another might be captured in terms of the values of fundamental probabilities for those decays.

But it is important to make clear the novelty of Aimar’s Fine-graining strategy. As we saw, Vetter made much of the fact that dictionary definitions of dispositions like fragility emphasise the ease of some or other manifestation. Vetter’s proposal interprets this ease as a qualification on the relevant modality.Footnote ²⁹ By contrast, Aimar suggests that it is instead the manifestation which gets qualified. It thereby avoids many of the particular interpretive issues that the Proportionality strategy faces.

The Fine-graining strategy is a promising way to capture dispositional degrees. Yet we might be concerned that it doesn’t go far enough. As it stands, the strategy only has scope for one dimension of fine-graining. Ease of breaking, for instance, is naturally captured in terms of degree of applied stress. Objects are therefore more or less fragile if they require, respectively, more or less stress to break them. But we also take there to be a clear sense in which the amount of breaking is relevant to how fragile something is. More generally, the degree of dispositionality doesn’t just concern how much stimulus is required to get an equivalent manifestation, but also how much manifestation is produced by equivalent stimuli. To put things in these terms is to go beyond anything expressible with AIMAR’s form.

Moreover, the Proportionality strategy enabled some responses that the Fine-graining strategy does not. Both VETTER and MANWASS avoid the problem of mimickers and tricks by relying on the idea that even though some objects will mimic dispositions, and others will be dispositional tricks, their proportion of manifestations across all the relevant worlds is low enough to prohibit them from counting as instances of the disposition. AIMAR can’t appeal to this idea. In order to avoid counting those mimicking and tricky cases we could try putting restrictions on the relevant possible worlds in which manifestation occurs, or else by further fine-graining the manifestation. But it’s far from clear how such specifications could work in a non-trivial way. All things considered, we are still not quite there with the ideal strategy. And, there still remains one last problem case to consider.

2.4.4 Problem #9: Conjunctive Multi-Track Dispositions

Even if we fix on one determinate degree of fragility (e.g., mean-average fragility) there remain quantitative considerations which have so far been ignored. Striking a (moderately) fragile vase can often lead it to break. But, as we’ve seen, how hard one strikes it (e.g., whether it is bumped, knocked, hit, thwacked, crushed, or pulverised) will likely influence how it breaks. Moreover, as we’ve just pointed out in critiquing the Fine-graining strategy, the manifestation behaviour of (mean-average) fragility can be rendered in more varied terms than simply breaking (under varying stresses). For example, for any of the various applied stresses, a fragile object can chip, split, fracture, shatter, atomise, or plasmarise.

From the perspective of a traditional conditionals approach to analysing dispositions, observations like these can seem to commit us to a multitude of conditionals for any determinate (non-disjunctively multi-track) disposition. For they imply that ‘there is a whole set of pairs of triggering [stimulus] conditions $T_i$ and manifestations $M_i$ , such that an object b with [the disposition] would manifest $M_i$ if it were in condition $T_i’$ (Reference Kistler, Alexander Bird and SankeyKistler 2012, 134). Specifically, these features show that the relevant disposition is conjunctively multi-track, since any instance of the disposition will need to satisfy each of the associated counterfactual relationships or ‘tracks’.Footnote ³⁰

Quantified science provides a large repository of conjunctive multi-track dispositions. Often the more specific stimulus and manifestation properties are related by a ‘characterising equation’ (Reference FriendFriend 2021) or law. For example, having a certain value of conductivity means exhibiting certain current densities under a proportional electrical field according to Ohm’s law (cf. Reference Kistler, Alexander Bird and SankeyKistler 2012). Likewise, having a certain specific heat capacity means exhibiting certain changes in temperature under proportional heat absorption according to the specific heat formula; having a certain carrying capacity means exhibiting certain rates of change in the population of an inhabiting organism with a particular growth rate according to the logistic growth formula; having a certain price elasticity means exhibiting certain changes in demand given changes in the price of a commodity according to the equation for price elasticity; and so on. In each case, the ‘track’ relating some determinate value of stimulus to a determinate value of manifestation seems to be part of the behavioural characterisation of the quantitative multi-track disposition.

The extra detail of these counterfactual relationships is easily incorporated within SEMs. To accommodate the multi-track details for the case of fragility, all we need to do is redefine the variables from our earlier example in subsection 2.1, as in Table 6 (NB: the structural equation and causal graph have not changed).

Table 6 Details for a causal model for conjunctive multi-track fragility

Variables			Structural equations
Symbol	Possible values	Interpretation
$FR$	$1$	$x$ is fragile	(Exogenous)
	$0$	$x$ is not fragile
$ST$	6	$x$ is pulverised	(Exogenous)
	$5$	$x$ is crushed
	$4$	$x$ is thwacked
	$3$	$x$ is hit
	$2$	$x$ is knocked
	$1$	$x$ is bumped
	$0$	$x$ undergoes no stress (at all)
$BR$	$6$	$x$ plasmarises	$BR\Leftarrow FR\times ST$
	$5$	$x$ atomises
	$4$	$x$ shatters
	$3$	$x$ fractures
	$2$	$x$ splits
	$1$	$x$ chips
	$0$	$x$ does not break (at all)

No doubt this SEM provides only one possible way of giving a conjunctively multi-track interpretation of fragility. Unlike the cases from quantitative science just mentioned, the disposition of fragility itself likely does not entail any specific functional relationship between the variables characterised in Table 6. Indeed, this is a straightforward consequence of the fact that fragility is (as we saw above) disjunctively multi-track as well. Presumably, much the same will go for other ‘everyday’ dispositions like solubility, malleability, courageousness, etc. In each case, however, there are clearly some constraints on what any function could be if our conception of these dispositions were to be precisified. For instance, we know that fragile objects are such that increases in applied stress are correlated with increases in degree of breaking.

The entailment by a disposition of limits on any range of plausible functions relating degrees of stimulus and manifestation confers more complexity on its analysis than permitted by any of the strategies so far considered. Other than AIMAR, no analysis so far considered supplied more than a single manifestation or stimulus per disposition. AIMAR’s invocation of more fine-grained and, crucially, gradable manifestations is clearly an improvement in that regard. But it still isn’t sufficient to deal with conjunctively multi-track dispositions, which exhibit both gradable manifestations and stimuli. Nor would it be enough to simply recognise fine-grained stimuli in the analysis alongside fine-grained manifestations. An analysis which properly addresses conjunctively multi-track dispositions must show how each possible degree of stimulus is connected to some specific manifestation (or at least would be under some precisification of their functional relationship).Footnote ³¹

2.4.5 Strategy H: Potentials for Functions

We are aware of two attempts to deal with conjunctively multi-track dispositions. We discuss one in this section, the other will form the basis of our novel strategy in the next section.

Vetter discusses conjunctively multi-track dispositions in the specific context of nomological dispositions, those quantitative scientific dispositions which have clear characterising equations.Footnote ³² Since Vetter favours a possibility view of dispositions (see POSSIBILTY, subsection 2.3.5 and VETTER, subsection 2.4.2), her analysis of them is not in terms of the conditional implications of manifestation given stimulus, let alone a multiplicity of such implications. Nevertheless, and unlike her preferred treatment of non-conjunctively multi-track dispositions, Vetter does retain the link between the putative stimulus property and manifestation.Footnote ³³ She does this by suggesting that the manifestations of conjunctively multi-track dispositions are the entire functional relationship specified by the relevant nomological equation. In this way, the putative stimulus is brought inside the potentiality operator to embellish the manifestation condition as follows (Reference VetterVetter 2015, 61, 284):

So, for example, Vetter’s analysis of the disposition of having elementary charge ( $e$ Coulombs) is given as follows (Reference VetterVetter 2015, 61):Footnote ³⁴

Vetter points out that if this Potentials for Functions strategy is to ensure the metaphysical necessity of laws, the potentiality for nomological dispositions like elementary charge will have to be maximal, i.e., manifesting in every member of the relevant modal base.Footnote ³⁵ This could be cause for concern. First, it means that in the case of such dispositions, POT plays the same role as a necessity operator, providing another major contrast among types of disposition within Vetter’s overall system. Second, the maximal potentiality attributed to dispositions like elementary charge renders the analysans in ELECPOT logically equivalent to a plurality of necessary counterfactuals. So, for dispositions which need analysing in terms of maximal potentialities for functions, there is not any logical distinction between Vetter’s preferred approach and one which advocates for a plurality of conditionals in the analysans. But Vetter is at pains to distance herself from a conditionals approach to analysis.

The Potentials for Functions strategy for conjunctively multi-track dispositions would cease to be akin to a conditionals approach if the potentialities involved were less than maximal. And Reference VetterVetter (2015, 288) suggests that less-than-maximal potentialities might be appropriate in the case of idealisation laws. However, there is reason to be sceptical that this is the right treatment of idealisation. It is not the case, for example, that the ideal gas equation is an accurate description of gases in many but not all cases, as a less-then-maximal potentiality for the ideal gas equation would imply. Rather, the ideal gas law isn’t accurate in any cases. This is because, as with most idealising laws, there are interferences (e.g., from particle sizes and mutual attraction) which are necessarily present. What makes the ideal gas law a law is not that it’s exactly right in some cases, but that it captures some of the relevant causally relevant properties in all cases (Reference FriendFriend 2022b).Footnote ³⁶

The limitation in dealing with idealisation laws may not seem too disastrous for the Potentials for Functions strategy, so long as it can handle strict lawlike dispositions (like elementary charge) and everyday conjunctively multi-track dispositions (like fragility). However, we think the limitation reveals a broader issue for everyday dispositions too. The issue hinges on the kinds of function we envisage entering the analysis of everyday conjunctively multi-track dispositions. We know from the Getting Specific strategy that to make particular masks and alterers explicit would be to put too much into the analysans. Fragility, therefore, should not be analysed by the maximal potential for some functional relationship which includes variables for all possible interferences. But we also suggest that failing to say anything at all about the relationship between stimulus and manifestation when masks or alterers are present would be to put in too little. The possibility for interference on an object’s fragility should not force an analysis to say nothing about what happens in these cases but should only force the analysis to be less specific about the causal influence applied stress has on breaking. After all, when something is fragile, it’s not that wrapping it in bubble wrap means we have no idea about how applied stresses will affect whether it breaks; typically, we know just that it will now be harder to break under stress. FUNCPOT offers no means to do this, since it states that disposed objects will either behave exactly according to the embedded function or else behave in such a way that the analysis is completely silent on which causal influences are present. However, we think there is a different strategy which permits navigation between these options.

2.5.1 Strategy I: Simple Structural Equations Analysis (SSEA)

Our simple structural equations analysis has the following schema:

Let’s draw attention to two things straight away. First, what gets explicitly analysed is the value of a ‘disposition variable’ $D\left(x\right)$ , as opposed to the respective qualitative disposition D (which does not come in degrees). This makes the analysis amenable to dealing with Problem #8: Dispositional Degrees, since how much something is disposed in way D will be explicit in the analysandum. For example, with a fine-grained conception of fragility, SSEA permits an analysis of being very fragile, extremely fragile, moderately fragile, etc. (assuming these degrees can be treated as values of a well-ordered variable). But SSEA does not preclude analysis of a purely qualitative conception of fragility. For that we interpret the variable as a binary ‘dummy variable’, and the schematic analysans $D\left(x\right)=d$ would be replaced by the fragility variable being assigned the value 1 (as opposed to 0).Footnote ³⁷

Second, the analysans takes the form of a structural equation relating the causal influence of a stimulus variable on the manifestation variable, via a function $f$ . This function is effectively a characterisation of the way the stimulus variable affects the manifestation variable given the disposition $D\left(x\right)=d$ . That is, the function is logically determined by the specific value assignment of the disposition. As before, the resulting structural equation encodes multiple counterfactuals. The minimum number of counterfactuals encoded is in the case where $D\left(x\right),M\left(x\right)$ and $S\left(x\right)$ are dichotomous. In that case the functional relationship reduces to a unit coefficient and $M\left(x\right)\Leftarrow f\left(S\left(x\right)\right)$ encodes two counterfactuals, one ‘positive’ and one ‘negative’:

POSITIVE. If $x$ were stimulated ( $S\left(x\right)=1$ ) then $x$ would manifest.

( $M\left(x\right)=1$ )

NEGATIVE. If $x$ were not stimulated ( $S\left(x\right)=0$ ) then $x$ would not manifest.

( $M\left(x\right)=0$ )

Notice that by encoding both conditionals, SSEA can deal with Problem #4: Tricks. That problem effectively showed that the associated POSITIVE conditionals – those employed in instances of SCA – can be true in cases where the disposition isn’t instantiated because the manifestation is liable to happen anyway (e.g., when a non-fragile object is about to be crushed in a hydraulic press). However, in these ‘tricky’ instances it is never the case that the associated NEGATIVE conditional also holds. If the object is not fragile, it is not the case that if it weren’t to undergo applied stress it would not break, because it would still break due to the hydraulic press (the same reasoning applies to Contessa’s example of the mug of cooling coffee).

If the variables $S\left(x\right)$ and $M\left(x\right)$ take more than two values, the number of counterfactuals encoded will be greater. In general, there is a counterfactual encoded for every possible stimulus value. This ensures that the schema for analysis can, in principle at least, respond to Problem #9: Conjunctive Multi-Track Dispositions. For instance, under SSEA the analysis of electric charge is as follows:

ELECSE appears to place the same necessary and sufficient conditions on a charged object as ELECPOT. However, unlike Vetter’s two-schema analysis (VETTER and FUNCPOT), by being expressed in terms of a structural equation (an array of counterfactual conditionals) ELECSE has the unique benefit of providing a unified treatment of conjunctive multi-track dispositions and purely qualitative dispositions like the coarse-grained conception of fragility.

2.5.2 An Objection: Too Many Counterfactuals?

Before considering more complex analysis in terms of structural equations we want first to address, up front, one worry about their use: that having a disposition shouldn’t entail so many counterfactuals. There are two variants of this worry. The first is that, while it is common practice to analyse dispositions in terms of the POSITIVE conditional (or some variation thereof), the additional NEGATIVE conditional is unreasonable.

Our response to this concern is more fully worked out elsewhere (Friend unpublished manuscript), but the gist of it draws on the fact that both conditionals are essential for a counterfactual treatment of causal relations (cf. Reference LewisLewis 1973a). This treatment capitalises on the observation that, except in circumstances where causes pre-empt another potential cause, their effects counterfactually depend on those causes. Negative conditionals (concerning when events do not occur) are an essential component in characterising this dependency. Since being a cause of manifestation is (save some recalcitrant examples, see footnote 7) a defining characteristic of dispositions’ stimuli, it therefore seems inevitable that NEGATIVE will need to feature in the analysis unless the very employment of counterfactuals is to be replaced entirely with some different causal treatment.

As observed, there are cases in which causes pre-empt others. In those cases the NEGATIVE conditional is false. So the vase, which is actually fragile and caused to break by applied stress, might be in a situation where it would have broken anyway due (for example) to a hydraulic press (see Reference ContessaContessa 2016 for another example involving Leo the chameleon). But we see no structural difference here to cases in which the POSITIVE conditional is falsified due to masks. In either case, some external factor means that a counterfactual which is central to the analysis is rendered false.  So, the concern with NEGATIVE is right insofar as it shows that the SSEA cannot be quite right. But that’s not because of the addition of the conditional into the characterisation per se. Rather, it’s because both POSITIVE and NEGATIVE are subject to a generalised problem of masks.

We’re about to offer a solution to that problem. Before that, there is a second source of concern about the volume of counterfactuals being introduced which we should address. Recall that we objected to the Strategy A: Getting Specific approach on the grounds that the analyses of dispositions it demanded would be overly complex. The SSEA schema can seem guilty of just the same issue. For it requires that the technical formalism of structural equations, which allows for an infinity of conditionals to be encoded, be built right into dispositions analyses. To assuage this concern, it’s worth highlighting the distinction between analyses which predict that mastery of a concept involves patterns of reasoning tacitly implemented in cognition, which are more technically complex than we are typically aware of, and analyses which demand that mastery of a concept or ability require knowledge of some endless list of disparate conditions. While the former demand is invoked in the cognitive sciences, the latter are rightly avoided. The Getting Specific strategy recommends analyses which arguably cannot be conceptually grasped due to being necessarily so expansive. But SSEA can be concisely expressed, albeit in a formalism rarely made explicit, and so could be reasonably implemented tacitly in cognition.

2.5.3 SEMs, Masks, and Alters

We just saw that pre-empting causes lead to the falsity of certain counterfactuals encoded in the structural equations of SSEAs. Of course, it would be disastrous to the general SEM framework if pre-emption cases could not be modelled. Happily, they can be (Reference Halpern and PearlHalpern and Pearl 2005). When two potential cause variables $A$ and $B$ of an effect variable $C$ are such that if $A=1$ it will pre-empt $B=1$ as the cause of $C=1$ , then the structural equation for $C$ must simply include both variables, i.e., $C\Leftarrow A+B-AB$ .

As predicted by our response to the foregoing objection, this is exactly what happens in cases demonstrating Problem #1: Masks. When further interfering factors, like a mask, are present, the structural equation governing the manifestation variable (e.g., the harm done to an agent $H\left(agent\right)$ ) is a function of the relevant disposition (e.g., the poisonousness $P\left(x\right)$ of the poison), the stimulus (e.g., whether the poison is ingested $I\left(x\right)$ ) and also the mask (e.g., whether an antidote accompanies $x$ , $A\left(x\right)$ ). Hence, if we knew exactly what masks would occur, and how they influenced the manifestation variable, we might include them as further variables in the SEM.

Now, the discussion of the Potentials for Functions strategy and the Getting Specific strategy should have persuaded us that including all possible interfering factors in an analysing equation is implausible. What we can do, however, is draw attention to the fact that the stimulus variable will feature in whatever function does happen to characterise exactly all the influencing factors (including the stimulus) on a manifestation variable. This can be rendered as follows:

The structural equation SSEA* is like SSEA, but the analysing function has been embellished by ellipses to indicate further potential causal variables. By characterising a disposition this way, SSEA*s lose the ability to encode counterfactuals about determinate values of variables. Yet they are not entirely trivial, either. For instance, the schema tells us that having the disposition is a necessary and sufficient condition for the stimulus variable being one of the influences on the manifestation variable. It therefore provides a significant constraint on whatever more accurate SEM involving the manifestation variable would look like.Footnote ³⁸ It is just this middle position which we advised in critiquing the Potentials for Functions strategy. Unlike that strategy, the employment of structural equations recommended here allows that the causal influence of stimulus can still be recognised even when masks are present, but without having to be specific about which masks those might be. Note also that while the analysans incorporates an open-ended function, the analysans itself is not open-ended (as it was argued it would have to be if the Getting Specific strategy was to work). As before, whereas the Getting Specific strategy recommends an analysans which cannot be expressed concisely (because every eventuality has to be made explicit), SSEA*’s analysans can be expressed concisely: the manifestation variable is causally determined by a function over some set of variables which includes the stimulus variable.

As it turns out, this strategy also helps address Problem #2: Alterers (subsection 2.2.2). Not only might masking variables appear in a more explicit structural equation for circumstances involving a disposition, the disposition variable itself might also do so. Of course, we must omit the disposition variable from the structural equation featuring in the analysans (our goal is to give non-circular conditions for the instantiation of the disposition variable). Nevertheless, it remains true that the disposition variable is an influence on manifestation. This much is clear from the fact that there is a directed edge from the disposition variable to the manifestation variable in each of the causal graphs we’ve considered. Alterers are stimulus variables which influence the manifestation variable and the disposition variable. That means the disposition variable $D\left(x\right)$ can’t be assumed to retain the value $d$ under any value of $S\left(x\right).$ Unlike SSEA, SSEA* implicitly allows for variation in further influences on the manifestation variable (such as from the disposition variable itself) and is therefore not falsified by such factors.

2.5.4 Dealing with Remaining Problems

The structural equation SSEA* offers a way of responding to many of the problem cases considered throughout this section. However, some problems remain unaddressed and we have some ideas about further developments which might help (see Friend unpublished manuscript for a more detailed explication).

Briefly, we suggest that Problem #7: Disjunctive Multi-Track Dispositions (subsection 2.3.4) can be addressed by permitting some restricted variation in the function which takes values of the stimulus (and potentially other variables) to manifestation values. Unlike the disposition having elemental charge, the disposition being fragile doesn’t entail any specific function from applied stress to degree of breaking. But, as we acknowledged, it does plausibly entail a limited range of possible functions, e.g., only those in which increases of applied stress lead to increases in degree of breaking. We therefore suggest that analysis of these dispositions should proceed by restricting the functions to ones of this general type rather than to any single function.

Problem #6: Unspecific Stimuli (subsection 2.3.3) can be dealt with in a similar manner by permitting variation in stimuli. At its broadest, the analysis can simply quantify over all possible stimulus variables. Breakability, for instance, would be analysed in terms of the existence of some or other stimulus variable which can feature in a function which maps to degrees of breaking.

Problem #5: Chancy Dispositions (subsection 2.3.1) could be dealt with in one of two ways. One would be to admit error terms into the analysing structural equations. Such terms could take a range of values consistent with possible variation in the manifestation variable due to chancy interference. Perhaps a better solution, however, would be to substitute for the manifestation variable a variable which ranges over probability distributions of the manifestation variable. That way, the analysing structural equation would not map to possible values of manifestation, but possible distributions.

Finally, Problem #3: Mimickers (subsection 2.2.3) is, we think, probably best analysed via the understanding that mimickers come about through deviant causal chains. Dispositions, we take it, imply some specific mechanism by which stimulus results in manifestation. As is clear from Figure 4, mimickers work by other, deviant, means. Having said that, we’re not sure how exactly to specify constraints on the right mechanism without getting more specific in the analysis than we think is ultimately plausible. One possible route is to capitalise on the idea that dispositions which are subject to mimickers should be considered as realiser functional properties rather than role functional. In that case, the disposition is understood as identical to the empirically discoverable causal base rather than a second-order property defined in terms of having some such base (see Section 1). Crucially, such an identity would be a posteriori and so need not be known purely from competency with the dispositional concept.

A legitimate concern with the suggested solutions to these problems is that it forces the analyses of dispositions to go pluralist. That’s something we (and the authors we’ve engaged with) have generally tried to avoid. Nevertheless, the pluralism invoked is, for the most part, within the rough framework identified by the SSEA schema. Most of the relevant differences come down to how specific we make the structural equation on the right-hand side. Nevertheless, it’s not clear that this extends to our proposed solution to the problem of mimickers. Perhaps, in the end, some pluralism cannot be avoided.

3.3.1 Property Identity, Scepticism, and Science-Friendliness

One prominent reason for thinking that properties are necessarily connected with dispositions is dissatisfaction with the metaphysics of properties required to uphold Hume’s Dictum. This subsection will sketch the Humean view of properties, problems for that view, and how this relates to admitting necessary connections between properties and dispositions.

Properties, according to the Humean, are quiddities. Reference BlackBlack (2000, 92), uses ‘quidditism’ for ‘the acceptance of primitive identity between fundamental qualities across possible worlds’ (see also Reference Lewis, Braddon-Mitchell and NolaLewis 2009, 209). Thus, on this view, for any two distinct properties, P1 and P2, according to the quidditist, no more can be said about what individuates P1 and P2 than that P1 is the property that it is and P2 is the property that it is and that it is not the case that P1 = P2. Crucially for our purposes, this entails that the dispositions with which we may associate mass, for example, such as a disposition to warp spacetime, are in no way tied up with what it is to be mass. The same goes, mutatis mutandis, for other properties.

It helps to draw some finer distinctions here. The view according to which there is nothing more to a property than primitive self-identify and distinctness from other properties is what Reference SmithSmith (2016) has called I-quidditism (individuation quidditism), which she distinguishes from the view that she calls R-quidditism (recombinatorial quidditism) according to which ‘there are no restrictions on the recombination of properties in metaphysically possible worlds’ (Reference SmithSmith 2016, 240). In other words, R-quidditism says that the connections between properties and dispositions are thoroughly contingent. It is plausible that I-quidditism is a necessary (but not sufficient) condition for R-quidditism (Reference SmithSmith 2016, 240). Hence, it is in the interest of satisfying this necessary condition on the denial of necessary connections between properties and dispositions (as per R-quidditism) that the Humean wishes to uphold I-quidditism. In short, Humeans maintain that properties are quiddities in both the individuative and recombinatorial senses: there is nothing more to what it is to be a given property than primitive self-identity and distinctness from other properties, and properties are free to recombine any which way with different dispositions. For now, then, we will use ‘quidditism’ to refer to the conjunction of I-quidditism and R-quidditism. (For further discussion of varieties of quidditism see Reference HildebrandHildebrand 2016; Reference LockeLocke 2012; and Reference SmithSmith 2016).

Reference Lewis, Braddon-Mitchell and NolaLewis (2009) draws a sceptical conclusion from his discussion of quidditism; since all we can ever have epistemic access to is what properties dispose their bearers to do in various circumstances, and since knowing a dispositional role is insufficient for knowing which property confers that dispositional role because properties can switch dispositional roles with no detectable difference (as per R-quidditism), we are irremediably ignorant of the properties in themselves. Lewis embraces this conclusion, quipping that no one ever promised him that he was capable, in principle, of knowing everything. (Reference SchafferSchaffer (2005) argues that Lewis gets the epistemology wrong and that we can, in fact, know the quiddistic natures of properties.)

Others have seen the irremediable ignorance ushered by quidditism as cause for concern.Footnote ⁴⁶ By highlighting the possibility that multiple properties confer the exact same dispositions (something that Reference SchafferSchaffer (2005) does not consider), Reference BirdBird (2007b, 77–8) presents an even more worrisome sceptical implication of quidditism. Given quidditism, it is possible, for example, that two or more properties confer all and only those dispositions that we associate with the term ‘mass’. We cannot know if such a possibility is indeed realised in our world because there would be no detectible difference between a world in which just one property plays the mass role and a world in which multiple distinct properties play the mass role. A plausible conception of mass as the property with such and such a dispositional profile would be undermined if two or more properties played the mass role. And since we cannot know whether or not two or more properties occupy the mass role, we cannot know whether this conception of mass is undermined. Furthermore, if, as again seems plausible, we fix the reference of the term ‘mass’ via the definite description ‘the property that plays the mass role’, then the possibility that ours is a world in which multiple properties play the mass role means that we cannot know if our term ‘mass’ determinately refers to anything at all. These considerations, according to Reference BirdBird (2007b, 77), do ‘serious damage to our concept of a property’, hence he thinks we should reject quidditism (Reference BirdBird 2007b, 78).

Furthermore, physics does not seem to recognise such things as quiddities, that is, properties which are thoroughly independent of their modal profiles. This brings a certain irony given that Lewis’s touted motivation for Humeanism was to ‘resist philosophical arguments that there are more things in heaven and earth than physics has dreamt of’ (Reference LewisLewis 1994, 474). Reference Demarest and JacobsDemarest (2017, 48), following Reference CartwrightCartwright (1999), argues that scientists look for ‘dispositional essences, or what it is that things do in different situations’. This kind of argument, according to which all of the properties that science tells us about are essentially dispositional, has been particularly influential in the debate between quidditists and their opponents (see, e.g., Reference BlackburnBlackburn 1990, 63; Reference Ellis and LierseEllis and Lierse 1994, 32; Reference Harre and MaddenHarre and Madden 1975; Reference MckitrickMckitrick 2003; Reference MumfordMumford 2006; Reference WilliamsWilliams 2011). Why, as Hawthorne puts it, ‘posit from the armchair distinctions that are never needed by science?’ (Reference Hawthorne and TomberlinHawthorne 2002, 369).

It is for these kinds of reasons that philosophers have rejected quidditism in favour of the view according to which the dispositions that properties confer are of the essences of those properties. Scientifically redundant quiddities are ousted from our ontology and sceptical worries are avoided; to know what dispositions a property confers is to know the essential nature of that property and it is no longer possible that properties swapped dispositional roles or that multiple distinct properties played the very same dispositional role.

Thus, we arrive at a reason for thinking that properties and dispositions are necessarily connected. In the interest of avoiding scepticism and a science-unfriendly ontology, it is maintained that dispositions constitute the essences of properties and hence that the identity of a property is not primitive, as per quidditism, but is given in terms of its dispositional relations to other properties. This, in turn, gives rise to necessary connections between properties and dispositions and (according to some) between individual property instances conditional upon the properties they instantiate.

Not everyone is convinced by the sceptical concerns (e.g., Reference SchafferSchaffer 2005) nor by the considerations from scientific practice (Reference LockeLocke 2012; Reference PsillosPsillos 2006b; Reference WilliamsWilliams 2011) that purport to tell against quidditism. Perhaps, however, one should be less concerned with sceptical arguments and more concerned with the thought that the rejection of quidditism is a natural way to admit irreducible modality in the world, which can then be put to work in a variety of interesting and useful ways.

A more robust motivation for denying quidditism may arise given the conjunction of whatever plausibility the above considerations against quidditism have with the theoretical utility that results from embracing necessary connections between properties and dispositions. The remainder of this section will thus be primarily concerned with the kind of positive argument for powers which says that we should accept the existence of powers because doing so yields a fruitful resource for explaining other phenomena of philosophical interest – our particular focus will be on explaining laws of nature and modality.

3.3.2 Laws of Nature

Arguably, the default approach for powers theorists in thinking about how powers explain laws is that given by dispositional essentialism. Dispositional essentialists, such as Reference EllisEllis (2001), Reference BirdBird (2007b), and Reference ChakravarttyChakravartty (2003a, Reference Chakravartty2007) defend the idea that properties are essentially dispositional on the grounds that doing so yields an attractive account of the laws of nature.Footnote ⁴⁷ Laws, according to the dispositional essentialist, ‘flow from the essences of properties’ (Reference BirdBird 2007b, 5). Bird makes this idea quite precise, so let’s first look at his dispositional essentialist account of the laws of nature.

Bird first notes the connection between dispositionality and counterfactuals. The Simple Conditional Analysis of dispositions says that for x to possess the disposition to yield manifestation M in response to stimulus S (let’s denote this ‘D_{(S, M)}’), is for x to be such that if it were S then it would be M:

$\text{CA}\text{.}{D}_{(S,\text{M})}x\leftrightarrow (Sx\square \to Mx)$

We’ve seen (in Section 2) that there are plenty of issues with this bi-conditional. However, Reference BirdBird (2007b, 60–3) provides various arguments to support the idea that it will hold for fundamental dispositions. Moreover, Bird does not endorse CA as an analysis of dispositions. Rather, he takes CA as a necessary equivalence between dispositions and conditionals (Reference BirdBird 2007b, 43), which he writes as:

$\text{CA}\square \text{.}\square (D_{(S,\text{M})}x\leftrightarrow (Sx\square \to Mx\left)\right)$

‘Essentially dispositional properties are ones that have the same dispositional character in all possible worlds; that character is the property’s real rather than merely nominal essence’ (Reference BirdBird 2007b, 44). So, from the claim that P has a dispositional essence, Bird infers that for any world, w, and individual, x, such that x instantiates P at w, x will be disposed to yield manifestation M in response to stimulus S (Reference BirdBird 2007b, 45):

$D{E}_p.\square (Px\to D_{(S,\text{M})}x)$

Combining CA □ and DE_p by substituting D_{(S, M)}x in DE_p for (Sx □ → Mx) then gives us:

Where (I) says that, necessarily, if x instantiates P, x would yield manifestation M if it were to acquire stimulus S. Now assume (for conditional proof) that x instantiates P and acquires stimulus S:

From (I) and (II), and with modus ponens for the counterfactual, we can derive:

It then follows, by conditional proof, from the assumption in (II) that:

And finally, since x is arbitrary, we can generalise, producing:

(V) Is a universal generalisation derived from a statement about the dispositional essence of potency. Furthermore, since the reasoning (I) through to (V) holds in an arbitrary world, (V) is necessary:

‘Hence we have explained the truth of a generalization on the basis of the dispositional essence of a property. This is the core of the dispositional essentialist explanation of laws. Since the generalization is non-accidental it is a nomic generalization’ (Reference BirdBird 2007b, 46).Footnote ⁴⁸

The crucial point here is just that the dispositional essentialist derivation of a law requires that dispositions are constitutive of property essences. As Bird says, this is the core of the view. But there is more to be said about what, exactly, the laws are on this account: are they universal generalisations, dispositional relationships, or something else? We return to this question in Section 3.5 when we consider whether dispositional essentialism really satisfies its explanatory aims.

Dispositional essentialists claim various benefits for an account of laws as just outlined, such as the modal robustness and explanatory power of laws so conceived. Dispositional essentialism stands in opposition to contingentist accounts of laws, such as the Humean best-system analysis (e.g., Reference 78LewisLewis 1983; Reference LoewerLoewer 2007), and the nomic necessitation view (Reference ArmstrongArmstrong 1983; Reference DretskeDretske 1977; Reference TooleyTooley 1977). By rendering the laws necessary, dispositional essentialism is able to account for the counterfactual robustness of laws and hence their importance to our scientific and practical endeavours (see also Reference Kimpton-NyeKimpton-Nye 2020); in order to make predictions and manipulate our environment we need to know which generalisations will continue to hold in different possible scenarios (though see Reference BeebeeBeebee 2011 for a sceptical response). And the laws are said to possess metaphysical ‘oomph’, they are metaphysically responsible for property distributions throughout spacetime (on this, dispositional essentialism is in agreement with the nomic necessitation view in opposition to the descriptive Humean best-system view of laws).

Dispositional essentialism is not the only powers-based account of laws. Recently, there has been a fair amount of interest in understanding laws as efficient descriptions of how properties are possibly distributed throughout spacetime (Reference Demarest and JacobsDemarest 2017; Reference KatzavKatzav 2005, 339–40; Reference Kimpton-NyeKimpton-Nye 2017, Reference Kimpton-Nye2021b, Reference Kimpton-Nye2022b; Reference WilliamsWilliams 2019). The properties in question metaphysically explain how they are possibly distributed throughout spacetime by metaphysically explaining the dispositions that they confer upon their bearers; hence the properties explain the laws that describe these possible distributions. Call this view The Powers–BSA (because it combines an ontology of powers with a modalised version of Lewis’s best-system analysis of laws). The Powers–BSA depends on there being necessary connections between properties and dispositions to get its explanatory aspirations off the ground. But contra dispositional essentialism, this powers-based account of the laws of nature does not stipulate that properties have a dispositional essence; it leaves open that the necessary connections between properties and dispositions come about in some other way (more on this in Sections 3.4 and 3.5, see also Reference Kimpton-NyeKimpton-Nye 2021b).

3.3.3 Modality

Various articulations of ‘dispositionalism’ about modality invoke the idea that dispositions are connected with possibilities, either via a link with counterfactuals (Reference Borghini and WilliamsBorghini and Williams 2008; Reference JacobsJacobs 2010) or directly (Reference VetterVetter 2015): if x is disposed to φ, then it is possible that φ. Since the connection between dispositions and possibility is conceptual,Footnote ⁴⁹ this is something that even the Humean quidditist can agree with.

What is distinctive of dispositionalism is that it is the properties, viz. powers, of concrete, actual individuals that metaphysically explain these dispositions and, hence, metaphysically explain at least some forms of modality (assume that ‘explanation’ here is metaphysical).

Consider, for example, a vase, v, which is disposed to break; hence it is possible that v breaks. What explains this disposition and associated modality, according to dispositionalism is a power, or some powers, of the vase. Plausibly, v’s disposition to break can ultimately be explained in terms of certain low-level powers such as mass, spin, and so on. So, it will be these low-level powers that ultimately explain the possibility that v breaks, via the dispositions that they explain.

For Reference LewisLewis (1973b, Reference Lewis1986, Reference Lewis1997), by contrast, it is facts about other possible worlds that ultimately explain the modality associated with dispositions.Footnote ⁵⁰ Dispositionalism does not ‘outsource’ modality to other possible worlds, it roots modality in the powers of concrete individuals in this world (Reference VetterVetter 2011b). In other words, modality is not reduced to or explained in terms of anything non-modal, it is dispositional properties ‘all the way down’ (Reference VetterVetter 2021).Footnote ⁵¹

If the connection between properties and dispositions were thoroughly contingent, as per quidditism, then even granting the (conceptual) link between dispositions and possibility, properties themselves would not suffice to explain the corresponding possibilities. For the quidditist, v’s instantiating certain low-level properties need not be accompanied by v’s being disposed to break – it is metaphysically possible that the properties and the disposition come apart – and hence v’s instantiating these properties does not explain the possibility that v breaks. To explain the possibility that v breaks, the quidditist must appeal to more than just v’s physical properties. In general, the quidditist must fill the gap between instantiating some property or properties and being disposed to φ; hence Lewis’s appeal to possible worlds and Armstrong’s appeal to governing laws. Dispositionalists close this gap by positing explanatory necessary connections between properties and dispositions.

3.3.4 Summing Up

In general terms, then, concerns about property identity and scepticism motivate some to say that property essences are constituted by dispositions and hence to maintain that properties and dispositions are necessarily connected. Positing necessary connections between properties and dispositions is also a necessary condition on explaining laws of nature and modality in terms of those properties via an explanation of dispositions, as fans of powers would like to do.

So far, we’ve discussed the motivation for understanding properties as necessarily connected with dispositions (a minimal necessary condition on a property being a power). The next two sections (3.4 and 3.5) will be concerned with what specific metaphysical account of these necessary connections is apt if properties are to successfully explain laws and modality. As mentioned at the end of Section 3.3.1, there is considerable disagreement, including among advocates of powers (cf. Reference WilliamsWilliams 2011), about how compelling the considerations from property identity, scepticism, and science-friendliness are in motivating powers. For this reason, and due to limitations on space, we will focus primarily on the issues of explaining laws and modality.

3.5.1 Dispositional Essentialism

Let’s first consider the dispositional essentialist account of laws of nature. We saw, in Section 3.3.2, Bird’s canonical dispositional essentialist account of laws (we refer the reader back to Section 3.3.2 for a refresher). But, as mentioned, Bird’s derivation left open what, exactly, laws are. To address this caveat, we need to re-examine the dispositional essentialist metaphysics of powers.

Recall that, according to DE powers, to be a power is to be a property whose essence is exhaustively constituted by dispositional relations to other properties (e.g., Bird 2007, Reference Bird2016, Reference Bird2018; Reference ChakravarttyChakravartty 2003a, Reference Chakravartty2007; Reference MumfordMumford 2004). A given power, P, disposes its bearers to yield some characteristic manifestation, M, when appropriately stimulated, S. We can say, then, that the properties P, M, and S stand in the stimulus–response relation (SR relation), which is really just a more precise term for ‘dispositional relation’.Footnote ⁵⁸ SR relations are modal; in this case the SR relation’s obtaining between P, M, and S amounts to its being the case that if an individual, x, instantiating P were to acquire S then it would M. Since P is a power, according to dispositional essentialism, the essence of P is exhausted by the SR relation(s) in which it stands to other properties.Footnote ⁵⁹ Dispositional essentialists of the type just mentioned (e.g., Bird 2007, Reference Bird2016, Reference Bird2018; Reference ChakravarttyChakravartty 2003a, Reference Chakravartty2007; Reference MumfordMumford 2004) maintain that all ontic properties are powers (all fundamental properties, in Bird’s case). So, the properties M and S to which P is SR related will also have their essences exhaustively constituted by SR relations to other properties and so on. Properties, on this view are nodes in a structure of SR relations and their identities are given by their place in that structure (cf. Reference 73BirdBird 2007a).

This is the dispositional essentialist’s structuralist metaphysics of powers. Bringing this back to our concern with laws of nature, we can now ask: where do laws fit into this picture? Answer: laws are arcs in the structure. What’s the evidence for this? Both Reference ChakravarttyChakravartty (2003a, Reference Chakravartty2007) and Reference BirdBird (2007b) explicitly claim that laws of nature are modal relations between powers and (as Reference Kimpton-NyeKimpton-Nye (2021b, 3426) discusses in more detail), since SR relations fit the bill here, it is reasonable to attribute to Chakravartty and to Bird the view that SR relations just are the laws.Footnote ⁶⁰

This is consistent with the idea that a statement of a law (linguistic entity) may derive from a statement of the essence of a property (linguistic entity) in accordance with the derivation presented in Section 3.3.2 (and in Reference BirdBird 2007b, 43–8). What we have done here, however, is to take a deeper dive into the metaphysics.

The question now is whether the dispositional essentialist picture just presented satisfies its explanatory goals. We will show that there are reasons to think that it does not.

There are two broad explanatory concerns for dispositional essentialism. The first is that powers and laws appear to symmetrically ground each other, which significantly threatens the dispositional essentialist claim to metaphysically explain laws in terms of powers. The second is that dispositional essentialism is subject to an explanatory regress closely analogous to that levelled by Reference BirdBird (2005) at the Armstrongian view of laws (Reference ArmstrongArmstrong 1983) (see also Reference DretskeDretske 1977; Reference TooleyTooley 1977). We’ll address these in turn, before drawing out the implications for explaining modality in terms of dispositional essentialism’s structuralist metaphysics of powers.

If properties are identity dependent on their position in a structure, as per the dispositional essentialist picture sketched, then it seems that properties are grounded by the structure. The structure, in this case, is a structure of SR relations which the dispositional essentialist is plausibly interpreted as identifying with laws of nature. Hence, properties are grounded by laws. This alone should set alarm bells ringing since the dispositional essentialist project was originally conceived of as metaphysically explaining laws in terms of properties, not vice versa. But things get worse. The structure itself is plausibly composed of properties, at least this is something we should wish to say if we want to avoid commitment to relations without relata (Reference ChakravarttyChakravartty 1998, Reference Chakravartty2003b; Reference Kimpton-NyeKimpton-Nye 2021b, 3431; Reference PsillosPsillos 2006a); it thus also seems that properties ground the structure (on the plausible assumption that composition is a grounding relation): properties and structure symmetrically ground each other (cf. Reference GodfreyGodfrey 2020; Reference Kimpton-NyeKimpton-Nye 2021b; Reference YatesYates 2018). This would render dispositional essentialism incoherent if it were also thought that grounding is an asymmetric relation (though this has been debated; see, e.g., Reference Barnes, Bliss and PriestBarnes 2018; Reference Rodriguez-PereyraRodriguez-Pereyra 2015; Reference Thompson and JagoThompson 2016). (See also Reference BarkerBarker 2013; Reference JaagJaag 2014; Reference SiderSider 2020, ch. 2; Reference 81TugbyTugby 2022a, ch. 3 for slightly different presentations of this line of argument.)

At this point one may think that the best response is to reject the identification of laws with SR relations, where the latter, remember, are arcs in the property structure, i.e., ontic as opposed to linguistic entities. If laws were instead conceived of linguistically as universal generalisations (such as ‘all Fs are Gs’) then it could be maintained that properties with their essences constituted by SR relations (i.e., powers) explain or make true the laws (qua linguistic entities), and this would remain in keeping with the dispositional essentialist spirit. But since no universal generalisation is identical with any SR relation (these are just different kinds of entity), even if SR relations ground properties (as above) it no longer follows that laws ground properties and the symmetrical grounding worry is blocked. Hence, we get the following:

How are we to understand the claim that properties make true or explain universal generalisations? It has been argued (Reference BarkerBarker 2013; Reference Barker and SmartBarker and Smart 2012) that a structuralist metaphysics of properties cannot meet this explanatory demand. Property essences, according to the structuralist dispositional essentialist, are exhausted by the SR relations in which they stand to other properties. So, if we ask what explains or makes it true that all Fs are Gs, the dispositional essentialist explanation in terms of properties must appeal to the SR relations constitutive of the essences of the properties F and G (see Reference TugbyTugby 2012, 725). So, the explanation goes roughly as follows: ‘the fact that F and G enter into such and such an SR relation explains why all Fs are Gs’. But now we may ask why the fact that F and G enter into the SR relation ensures that all Fs are in fact Gs. Is there some higher order relation which ensures that if F and G enter into the SR relation then all Fs are Gs? To go along this route would be to fall into a vicious explanatory regress. In fact, Reference Barker and SmartBarker and Smart (2012) argue that dispositional essentialism succumbs to the exact same problem as that raised by Reference BirdBird (2005) against Reference ArmstrongArmstrong’s (1983) view of laws. Both dispositional essentialism and the Armstrongian view seek to explain the distributions of properties in terms of nomic relations between properties. But both views are thus subject to the objection that it is unclear how these relations are supposed to do their explanatory work (why couldn’t F and G enter into the SR relation and there be an F that is not G?). It would be antagonistic to dispositional essentialism to just repudiate this explanatory demand and maintain that it is just a brute necessity that if F and G enter into the SR relation then all Fs are Gs – because the whole point of dispositional essentialism was to explain property distributions, and, more generally, laws, in terms of those property essences rather than in terms of brute necessity (perhaps it is the essence or the ‘business’ of SR relations that they determine the relevant generalisations (Reference SchafferSchaffer 2016b), but this still seems to sacrifice the aim of explaining laws in terms of properties).Footnote ⁶¹

Furthermore, the apparent inability of structuralist powers to explain their own distributions means that it would not help to twin this account of powers with The Powers–BSA account of laws as descriptions of possible property distributions. This is because, if the Barker and Smart regress argument is taken seriously, structuralist powers are no more capable of explaining their own possible first-order distributions than they are of explaining how they are actually distributed.

This last point is relevant to the project of explaining modality more generally. Another way of conceiving of the dispositional essentialist’s explanatory project is as explaining how properties are possibly distributed throughout spacetime. It was suggested that dispositional essentialism struggles to explain why it is necessary that if F and G enter into the SR relation, then all Fs are Gs. In other words, dispositional essentialism struggles to explain why it is not possible that F-ness and G-ness are distributed such that there is an instance of F at some spatio-temporal location x, y, z, t that is not also an instance of G. Hence, dispositional essentialism struggles to explain the modal constraints on individual property bearers. But explaining modal constraints on individuals in terms of the properties that they instantiate is at the heart of a powers-based account of modality.

Another problem for explaining modality is as follows. We said above that a dispositionalist account of modality proceeds by metaphysically explaining dispositional modality in terms of properties of concrete individuals. But if dispositional modality in the form of SR relations constitute the essences of those properties, then it looks like the dispositional modality metaphysically explains the properties because they make them the properties they are by constituting their essences. But if dispositional modality metaphysically explains properties, properties cannot metaphysically explain that same modality, on the assumption that metaphysical explanation (i.e., grounding) is asymmetric. This is just the symmetrical grounding worry targeted at the dispositional essentialist who seeks to explain modality via its structuralist powers metaphysic (see also Reference JaagJaag 2014 and Reference 81TugbyTugby 2022a, ch. 3).

3.5.2 The Grounding View

Powers, on this view, are qualities that ground dispositions and this is what accounts for the necessary connections between powers and dispositions.

How might the grounding view explain laws of nature? Again, there are at least two options available. One might identify laws with the dispositional relations that powers ground; or one might identify laws with regularities in the (possible) distributions of powers:

To opt for Grounding laws 1 would be to stay closer to dispositional essentialism, according to which laws are dispositional relations in the property structure. But unlike dispositional essentialism, the grounding view does not thus yield an account on which powers and laws symmetrically ground each other because it rejects the idea that the essences of powers are exhaustively constituted by dispositions. If laws are identified with dispositional relations, then, the grounding relation has the desired asymmetry: running from powers to laws and not vice versa. And the fact that different powers ground different dispositions is accounted for by the fact that different powers have different thick qualitative essences.

Alternatively, one could opt for Grounding laws 2. Again, the grounding view maintains that properties/powers have thick qualitative essences and that this is what accounts for the different dispositions grounded by different properties. It is thus not the case, on this view, that all there is by way of explanation for the possible distributions of properties is dispositional relations between properties; hence the explanatory regress that threatens the dispositional essentialist explanation of property distributions (Reference Barker and SmartBarker and Smart 2012) is avoided by the grounding view (as argued by Reference TugbyTugby 2012).

Similarly, if dispositions and hence possible property distributions can be explained by the grounding view, then it is plausible that the grounding view could provide a good property-based account of the metaphysics of modality too.

While the grounding view arguably dodges the explanatory deficiencies of dispositional essentialism, it does face some challenges. Chief among these is the following: one may worry that it is not explanatory to merely stipulate that properties ground dispositions. And since, for the dispositionalist, explaining dispositions is a prerequisite for explaining laws and modality, the worry is that the grounding view does not outperform DE after all.Footnote ⁶³

Maybe it is explanatory to say that being scarlet grounds being red because it is just a priori that a grounding link obtains between being scarlet and being red. But it is not a priori that something instantiating mass is disposed to warp spacetime (for example), so why think there is a grounding link between property and disposition? In response to this worry, Reference TugbyTugby (2021, Reference Tugby2022b) and Reference Kimpton-NyeKimpton-Nye (2021b) have taken inspiration from Reference SchafferSchaffer (2017) to argue that it is not the case that all grounding links must be the sorts of things that we know a priori. If there are good theoretical reasons to posit a grounding link, we are justified in believing that it exists, even if it is conceivable that it does not exist.

3.6.1 Bird’s Conservative View

Alexander Reference BirdBird (2016, Reference Bird2018) addresses the question of which properties get to count as powers and argues that only fundamental properties and some evolved macro (i.e., non-fundamental) properties are powers. Central to Bird’s argument is his dispositional essentialist conception of the metaphysics of powers according to which a power is an ontic (as opposed to a merely predicatory) property whose essence/identity is given purely dispositionally (e.g., Reference BirdBird 2016, 246, Reference Bird2018, 248, 249). As discussed above, an important consequence of this metaphysics of powers is what Bird calls ‘modal fixity’.

In other words: powers are necessarily connected with dispositions.

As we have seen, powers have been put to fruitful work explaining laws of nature, modality, and property identity. Laws and modality are explained via an explanation of the actual and possible pattern of property instances throughout spacetime. And, Bird, e.g., maintains that the dispositional essentialist account of powers yields an account of property identity that is superior to quidditism in that it avoids scepticism and achieves a degree of continuity with science.

Now while these arguments for powers (see Section 3.3 for details) may count in favour of the existence of fundamental properties being powers, Bird argues that they do not support the existence of macro powers. In the case of laws, perhaps we can mount a case for the existence of fundamental powers on the basis of their ability to explain fundamental laws. But we do not also need macro powers to explain non-fundamental laws because, according to Bird, non-fundamental laws supervene on fundamental laws and so are ultimately explained by fundamental powers. Similarly for modality, possibilities for things with macro properties need not be explained in terms of macro powers since ‘what is possible or not regarding things with non-fundamental properties supervenes on what is possible or not regarding things with fundamental properties’ (Reference BirdBird 2018, 251). And while it is plausible that only quidditism or the powers view may account for the identity of fundamental properties, macro properties may be accounted for in terms of composition or structure (Reference BirdBird 2018, 251). So, rejection of quidditism does not force one to accept the powers view of property identity for macro properties.

Bird also offers some direct counterexamples to pandispositionalism: i.e., properties in science which concern structure, composition, or relations as opposed to disposition (Reference BirdBird 2016, 355). Examples, from chemistry, biology, and medicine, respectively, include: being covalent (of a bond, in virtue of the electron distribution giving rise to the bond), being heterozygous at a particular locus (having different alleles at that locus), and being pericardial (the property of surrounding the heart) (Reference BirdBird 2016, 355).

Perhaps the pandispositionalist could respond that the above properties are nonetheless invariably associated with certain dispositions. Reference MumfordMumford (2021) pursues this line with respect to sphericity, in response to Bird’s critique of macro powers. But this misses Bird’s point: even if sphericity were necessarily connected with certain dispositions, this would not suffice for it to count as a power, according to Bird, because the essence and identity of sphericity is not given by its dispositions but by non-dispositional mathematical/structural features. Another example explicitly discussed by Bird is aromaticity: even if there were some set of dispositions shared by all aromatic compounds, Bird argues that aromaticity would not satisfy his definition of a power, since these dispositions would not determine the essence, nature, or identity of aromaticity because ‘what aromaticity is is a matter of the structure of the molecules and their bonds and electrons’ (Reference BirdBird 2016, 356). While this shared structure may explain the fact that aromatic compounds share some set of dispositions, any necessary connection between aromaticity and dispositions does not imply a relationship of essence (Reference BirdBird 2016, 356) (as per Reference FineFine 1994).

More recently, Reference BirdBird (2018) has argued that some evolved macro properties are powers. He considers the example of sightedness. Sightedness is selected because having sight confers an evolutionary advantage on animals. So, the presence of sightedness can be given an evolutionary explanation. Sightedness is also itself explanatory of other phenomena. Sightedness explains how animals find what they need in their environment and it can explain the appearance of prey animals that camouflage, such as the stick insect. The explanatory role of sightedness is good evidence that it is a real property in the world as opposed to a mere linguistic entity (Reference BirdBird 2018, 256–7). What’s more, sightedness is multiply realisable and so not reducible to more fundamental properties and is explanatory in a way that its realisers in any instance are not. Bird thus argues that the essence of sightedness can only be given in terms of how it disposes its bearers and hence that sightedness is a power (Reference BirdBird 2018, 257–61).

Sightedness is just an example to illustrate the broader point: any evolved, functional, non-fundamental property will be a macro power, according to Bird (though see Reference VetterVetter’s (2018) response according to which Bird’s argument for macro powers actually opens the door to far more macro powers than intended).

If one endorses dispositional essentialism, then, one may be inclined to be somewhat restrictive about which properties get to count as powers: if we are convinced by Bird’s arguments, only the fundamental properties and some evolved macro properties are powers.

3.6.2 Grounding Pandispositionalism?

Bird’s arguments for a restricted ontology of powers depend on his claim that to be a power a property must have its essence exhaustively constituted by dispositions. The grounding view denies that the essences of powers are constituted by dispositions and maintains that powers are properties with qualitative essences that ground dispositions. What, then, does the grounding view imply about the extent of the powers ontology? We will argue that it yields the result that all properties are powers, i.e., it implies the truth of pandispositionalism. What’s more, this is non-trivial because there is also good independent reason to believe that there are a great many ontic macro properties in non-fundamental science. Indeed, these are the same sorts of reasons that Bird himself appeals to, as mentioned above: many macro properties play crucial explanatory roles in science and are multiply realisable and so cannot plausibly be eliminated or reduced to the fundamental properties.

First of all, it is worth noting that the grounding view of powers renders Bird’s direct argument against pandispositionalism, the argument that appealed to counterexamples, unsound. According to the grounding view, it is no obstacle to a property being a power that its essence can be specified structurally, compositionally, or, more generally, independently of any dispositional relations to other properties. Hence, there is nothing to prevent the properties that Bird cites as ‘counterexamples’ to pandispositionalism from being powers after all.

But given the grounding view there are also positive reasons for endorsing a great many macro powers and even pandispositionalism. It helps to work with an example here. Aromaticity is a chemical property that Bird discusses and takes to be a counterexample to pandispositionalism. But although Bird denies that aromaticity is a power (because it has a qualitative essence), he remains open to its being the case that aromaticity explains dispositions of its bearers and that aromaticity is necessarily connected with these dispositions. Evidence for this is in the following passage:

It seems, then, that Bird is happy to admit that qualitative properties, such as aromaticity, can explain dispositions and that they are necessarily connected with those dispositions.

From the assumption that aromaticity explains a disposition, and with sufficient anti-Humean sympathies not to want to deny necessary connections between properties and the dispositions they explain, it can be argued that aromaticity grounds that disposition and hence that aromaticity is a power according to the grounding view of powers.

To see why this is so, consider first that explanations are generally thought to receive support from somewhere: paradigmatically, causal relations. The breaking of the window is explained by my throwing the stone and this explanation is supported by the causal relation between the stone throwing and the window breaking. But recently, the idea of non-causal explanation has become increasingly mainstream. Now granting that aromaticity explains a disposition to produce aromatic ring currents (for example),Footnote ⁶⁵ one may wonder what supports this explanation? Causation doesn’t fit the bill here. Aromaticity arguably doesn’t cause a disposition to produce aromatic ring currents since the two properties vary synchronically with one another. The instant aromaticity is present so is the disposition to produce aromatic ring currents but causal relations are generally thought to be diachronic (see, e.g., Reference CraverCraver 2007; Reference 77Kim, Andersen, Emmeche, Finnemann and ChristiansenKim 2000; Reference 79MellorMellor 1995; Reference RussellRussell 1912; and Reference FriendFriend 2019 for a reply) .

What seems more likely is that the relation between aromaticity and a disposition to produce aromatic ring currents is a grounding relation (see, e.g., Reference 80SchafferSchaffer 2016a and Wilson 2018 for a relevant discussion of the similarities between grounding and causation and the associated kinds of explanation). Furthermore, we don’t want to say that instead of aromaticity grounding the disposition to produce aromatic ring currents this disposition constitutes the essence of aromaticity. This just seems implausible for the sorts of reasons that Bird highlights, i.e., the essence of aromaticity is compositional/structural, not dispositional. What’s more (as discussed in subsection 3.5.1) if the essence of aromaticity were constituted by the disposition to produce aromatic ring currents, it seems that aromaticity would thereby be rendered incapable of explaining that disposition (cf. Reference JaagJaag 2014; Reference Kimpton-NyeKimpton-Nye 2021b), and to deny aromaticity this explanatory role would be odd indeed. Given that aromaticity explains a disposition to produce aromatic ring currents, then, there are good reasons to believe that aromaticity grounds this disposition (again, assuming, that is, broadly anti-Humean sympathies such that one does not balk at the necessity induced by grounding). In conjunction with the grounding view of powers, it follows that aromaticity is a power. Furthermore, understanding the relationship between power and disposition as a grounding relationship accounts for Modal Fixity and, relatedly, the fact that properties do not freely recombine, which is distinctive of the powers metaphysic (see Reference TugbyTugby 2021, sec. 5) for discussion of the relation between grounding theories of powers and (anti)Humeanism).

At this point, a reductionist might object that aromaticity does not explain a disposition to produce aromatic ring currents because all the explanatory work is ultimately done by the fundamental properties, charge, spin, mass, etc. to which aromaticity reduces. But many take this sort of strong reductionism to be implausible. Among the anti-reductionists is, presumably, Bird himself given that he explicitly cites aromaticity as an example of a macro ontic property (that he thinks is not a power). Schaffer voices a similar anti-reductionist sentiment regarding the property of being a synapse: ‘Being a synapse, for instance, involves possessing the power to transmit a pulse from one neuron to another. No fundamental property has this power’ (Reference SchafferSchaffer 2004, 95). And Schaffer finds support for this kind of anti-reductionism in Kim: ‘Having a mass of 1 kilogram has causal powers that no smaller masses have, and water molecules, or the property of being water, have causal powers not had by individual hydrogen or oxygen atoms’ (Reference KimKim 1998, 108). Now if we read ‘having a (causal) power’ as ‘explaining a disposition’,Footnote ⁶⁶ then the point is just that something similar is plausibly maintained regarding aromaticity: the dispositions that aromaticity explains really are not to be explained instead by the fundamental properties and hence it really is aromaticity doing the explaining.

The debate about reductionism is of course far deeper than we have space to do justice to here. But hopefully it can be seen that there is at least some plausibility to the idea that the type of reductionism required to deny that macro properties explain dispositions can be resisted, and hence that there is some reason to think that there are macro powers, given the grounding view. It would also be beyond our scope to pre-empt and respond to other objections at this point; for further such attempts see Reference Kimpton-NyeKimpton-Nye (2022a).

The argument of this subsection so far has focused on the example of aromaticity (though the Schaffer and Kim quotes suggest that it can plausibly be extended to being a synapse, having mass 1 kg, and being water). But as far as the argument is concerned, there is nothing special about aromaticity. There is reason to think that the argument is sufficiently general to imply that all ontic properties are powers.

On the assumption that pandispositionalism is false, there must be at least one (ontic) property that is not a power. What this means, on the grounding view, is that there is at least one property that does not ground any dispositions. But being both an ontic property and not grounding any dispositions is a very difficult conjunction for an entity to satisfy.

Plausibly, for a property to be ontic it must be the case that it explains at least one disposition, i.e., a property couldn’t claim to be ontic if it didn’t explain any dispositions. Bird himself seems to endorse this idea (Reference BirdBird 2016, 357, Reference Bird2018, 258–9), which is also echoed in Reference SchafferSchaffer (2004) and Reference KimKim (1998), cited above. This also chimes with the spirit of Armstrong’s Eleatic Principle, roughly according to which contributing to the causal order of the world is the mark of the real (see, e.g., Reference ArmstrongArmstrong 1978, Reference Armstrong2004; Reference HeilHeil 2003). The first premise of the general argument, then, is:

It was argued above that what supports the explanatory relation between property and disposition, according to the powers theorist who endorses the grounding view, is grounding. So, granting that a given property, P, is ontic and, hence, that P explains dispositions, it will follow that P grounds the dispositions that it explains. The second premise of the argument is thus:

The third premise is just a statement of the grounding view:

Pandispositionalism follows from these three premises:

In order to resist pandispositionalism, then, one must refute one of P1–P3 in the argument. An argument for P2 has been presented above. Refutation of P1 would require significant argument. To refute P1 in the service of denying pandispositionalism, one would have to provide at least one example of a property that is both ontic and which does not explain any dispositions. But finding even one example of an ontic property that does not explain any dispositions is an incredibly tall order. This is because a property, P’s, failing to be explanatory in this way would appear to be the mark of P’s not contributing to the causal order of the world and hence not being ‘real’. Or, put another way, P’s failing to be explanatory in this way would seem to tell in favour of P’s being eliminable in favour of/reducible to some more fundamental and genuinely explanatory properties (see, e.g., Reference BirdBird 2018, 258–9), and hence of P’s not being a genuine constituent of our ontology. P3 is just the assumption that the grounding view is true; we discussed why one might endorse this in subsection 3.5.2, though of course we recognise that further objections to the grounding view may come to light. We thus conclude that if the grounding view is true, then all ontic properties are powers, i.e., pandispositionalism is true.