1. Introduction
To be vague has traditionally been understood as lacking boundaries. But what is it that lacks boundaries? Three main answers have been given in the philosophical literature. The epistemic answer is that our epistemic limitations do not allow us to recognise boundaries to the extension of words; therefore, what lacks boundaries is what we grasp as such, because of our limited capacities.1 The semantic answer is that the rules of language are not specified enough to give vague words a precise extension, so it is the extension of words that lacks boundaries.2 The ontic answer is that the world itself is boundaryless: there are no precise joints at which objects or properties can be neatly carved out. It is important to note that those who believe in ontic vagueness do not deny either our epistemic limits or the under-specification of our semantic rules; rather, they claim that epistemic and semantic answers do not provide an exhaustive account of vagueness: vagueness is in the world, not just in our ways of speaking or thinking about the world.
It is important to note at the outset that ontic vagueness does not have a good ‘reputation’ among metaphysicians: vagueness is associated with paradoxes, and paradoxes are seen as demonstrations of metaphysical impossibilities. It is therefore not surprising that many metaphysicians try to remove ontic vagueness from their systems, as much as possible.3 There are, of course, ‘subversives’, philosophers who have argued that ontic vagueness is not incoherent after all, and that it can be consistently understood.4 But the theoretical value of ontic vagueness has its price: it requires a revision of some logical and conceptual assumptions that are usually taken for granted and found easy to accept. And this is a cost that many philosophers are unwilling to pay.
The metaphysics of properties is perfectly in line with the mainstream avoidance of ontic vagueness. Humeans and anti-Humeans agree on the explicit intention to avoid ontic vagueness in their metaphysical theories. Although there is at least one argument in the literature to the effect that a neo-Humean metaphysics of properties cannot avoid ontic vagueness,5 the anti-Humeans have not, as far as I know, been warned of this. That is the project here: to offer a way of introducing ontic vagueness for powers as a useful and coherent metaphysical picture.
The metaphysics of powers is an area of research that has developed greatly in recent years, against neo-Humean metaphysics. According to the neo-Humeans, properties always fully manifest their nature in the objects that possess them, and they have no modal or causal features; modal and causal features are reduced to contingent and extrinsic relations between objects. According to the anti-Humeans, properties include (or even are) powers; that is, properties that have modal or causal features that they may or may not manifest. The thesis that at least some, if not all, properties are powers resurrects an Ancient Greek idea according to which “causal powers are (types of) properties defined by the (type of) change they enable their possessor to suffer or bring about (Marmodoro 2021: 10)”; and it is gaining more and more adherents.6
The interesting question now is whether a proponent of powers may have a reason for adopting ontic vagueness. My main aim here is to show that she does, since ontic vagueness is an enhancement of the theory of powers interpreted as dynamic causal forces. Dynamism as an intrinsic attribute of powers is the distinguishing feature of my proposal. It allows powers to be properties of a radically different nature from (neo-)Humean properties. Whereas according to the (neo-)Humean view, properties are unchanging, according to the anti-Humean view, they are inherently dynamic.
I have a particular way of characterising the intrinsic dynamism of powers. To highlight the novelty of my proposal, I will critique but also build on Neil E. Williams’s (2019) recent theory of powers to develop a theory that makes room for dynamism and ontic vagueness. It is also my aim to reassure those who are wary of ontic vagueness by explaining that it does not come at the price of incoherence, or at least that proponents of ontic vagueness can avoid incoherence by introducing appropriate conceptual and metaphysical assumptions. I think that the contrast with William’s view is a useful way of introducing my new account, because it allows us to compare different reasons for different assumptions. But there is also an important reason why I am modifying Williams’s theory rather than others. His theory is not only well-developed, but it also makes an assumption that is crucial to my proposal; namely, that powers necessitate their manifestations, and this rules out powers underpinning any indeterministic account of causation. This last requirement is very important to me, not because I am against indeterministic causation (I am not), but because indeterministic causation is irrelevant to the ontic indeterminacy I want to defend. My claim is that there can be ontic indeterminacy in the dynamic causal relata without there being indeterminacy in the causal relation.
The paper is structured as follows: I briefly present Williams’ theory of powers and their identity conditions (§2), then I introduce the notion of tolerant identity for powers that I want to defend and its connection with vagueness (§3). I offer two distinct justifications for the tolerant identity and vagueness of powers: first, I argue that tolerant identity and vagueness follow from an interesting way of characterizing powers (§4), and second, I claim that a consequence of tolerant identity for powers is indeterminate identity and indeterminate instantiation, which can be coherently maintained (§5). Finally, I consider the implications of my proposal for the metaphysics of causality (§6).
2. Williams’ Powers: Their Nature and Their Identity
According to Williams (2019), powers are properties of the fundamental objects in the world, what he calls ‘molecular powers’ (Williams 2019: 48). He is not concerned with the power of a macro-object, such as the fragility of a crystal glass, but instead with the powers of each of the molecules that compose it.7 Moreover, according to Williams, powers are multi-track, i.e. they “are capable of producing numerous types of effects (Williams 2019: 49).” Now, it is interesting to consider what allows a power to manifest in one way instead of another. Williams distinguishes between two ways in which powers act:
“An interesting class of powers […] can operate in the absence of other powers, or perhaps irrespective of the presence or absence of other powers (Williams 2019: 51).”
But in many cases, the circumstances in which a power is exercised determines the manifestation. Now, what is a circumstance? A circumstance is a ‘constellation’ of powers, i.e. “an arrangement of powers’ (Williams 2019: 49), where a constellation is not individuated by ‘differences of arrangement alone, as the powers themselves can differ from one constellation to the next (Williams 2019: 50).”
The idea is that powers may produce manifestations either by themselves, irrespective of other powers, or collectively, with the ‘constellation’ they are part of, i.e. depending on the other powers they are complementary with, and on the overall arrangement they are in. All powers are multi-track for Williams as they may produce different manifestations in different constellations.
This characterization of multi-track powers might make one think that powers may produce different manifestations in a specific situation. However, this is not Williams’ idea, according to which “powers may produce different manifestations in different constellations’ (Williams 2019: 76),” but “it is a brute fact about any constellation type that it produces the manifestation type it does (Williams 2019: 75).” It is “an important feature of power-based causation […] that powers produce manifestations as a matter of necessity. […] That is to say that […] when a given constellation obtains it cannot help but produce its manifestation: its effects must occur (Williams 2019: 137 (italics in the original)).” The idea, then, is that powers determine their effects either by themselves or in constellations, avoiding any indeterminacy in the relation of causality.8
Now that the relation between powers and their manifestation has been briefly presented, let us consider the powers’ identity conditions. Williams distances himself from the “common practice to characterize dispositions by the manifestations they produce’ (Williams 2019: 52),” because “this way detracts from the power’s full nature (Williams 2019: 52).” According to him, “powers are not just the producers, but also the produced (Williams 2019: 52).” He therefore defines the identity of powers through a two-directional network: on the one hand, the identity of a power is determined by the powers or the constellations it is produced by, and, on the other, it is determined by the types of manifestations it produces (either by itself or with partner powers in constellations). The metaphor used is “a hub-and-spoke model for powers: powers are the hubs, and the spokes represent individual manifestation types the power can produce or be produced by (Williams 2019: 52).”9
So far, I have presented Williams’ characterization of powers, which I share with him, but I am also going to modify his theory in important respects.10 In particular, Williams presents a clear-cut (or, in my terms, intolerant) notion of identity for powers, as shown in the following passage: “Two seemingly similar powers with different ‘spokes’ could never be identical’ (Williams 2019: 52).” It is this clear-cut (or intolerant) definition of type-identity that I am going to question in the following section, arguing for a tolerant notion of identity instead.
3. Introduction to Tolerant Identity for Powers
The above neat conception of the type-identity of powers is challenged here in defence of dynamic powers and ontic vagueness. According to Williams, powers are defined by a particular set of constellations that produce them (let us call them ‘in-spokes’) and by a particular set of manifestations that they produce within particular constellations (let us call them ‘out-spokes’).
Let us now consider the conception of the identity of powers that a friend of ontic vagueness would want to defend. Suppose that there are two different kinds of similar powers according to Williams’s characterization, and that the difference between them is a very small dissimilarity in the in-spokes, and a very small divergence in the out-spokes. Now, the proponent of ontic vagueness might want to claim that what Williams splits into two different powers might be one and the same power: two similar instances of power produced by similar in-spokes, and producing similar out-spokes (when placed in the same type of constellation) might be instances of the same type of power. It will be my main aim in the rest of this paper to defend this idea and its connection with vagueness. But before defending it, it may be useful to distinguish it from another idea already present in the literature: the idea that dispositional properties are gradable.
According to the standard way of representing gradable dispositions,11 a glass A is more fragile than a glass B if and only if, among the possible situations in which they are stimulated by S, A would break more often than B. The assumption here is that an object (here a glass) with a certain disposition D, stimulated in a certain way S, may or may not produce a certain manifestation M. In other words, the manifestation is not necessarily produced. Now, once this assumption is made, it follows that one object can have the same type of disposition as another, even if only one produces a manifestation M under a specific stimulation, while the other does not produce M under the same specific stimulation. What allows us to type-identify the two different token dispositions is that they have the same type of possible manifestations. What allows us to measure the intensity of dispositions is the number of possible occasions on which they manifest their dispositions: the greater the number, the greater the intensity of the disposition.
This definition of gradable dispositions is incompatible with both Williams’s and my proposal because of the above-mentioned presupposition: it leaves open the possibility that a disposition subjected to a particular stimulus could have different possible manifestations. That is, it allows for an indeterministic relation between a power (or disposition) and its manifestation. Instead, I propose (in line with Williams) that powers (either powers acting independently of others or powers interacting with others in constellations) necessarily produce their manifestations. In short, whereas for the proponents of gradable dispositions, indeterminacy lies in the relation between powers and their manifestations, on my proposal, indeterminacy can lie in the powers themselves (i.e., the causal relata) rather than in the relation between powers and their manifestations.
How can there be indeterminacy in the powers themselves (i.e., the causal relata) without their causal relations being indeterminate? Let me use the disposition of fragility to illustrate my proposal somewhat metaphorically. An object is fragile if a relatively weak hit can cause it to break or shatter. If we think that fragility is not gradable, we must think that a fragile object stimulated by a certain impact must necessarily produce a certain effect. For example, if pot A is fragile and is subjected to an impact of intensity I at point P, it must necessarily either not break or break in a certain way.
Let us see what allows us to say that two pots are equally fragile, even if the fragility is not gradable. Suppose that two pots, A and B, are made slightly differently; if they are struck in the same specific way, each will crack, but while pot A has a crack of 2 cm, pot B has a crack of 2.1 cm. There is a difference between the conditions in which the pots were made, and there is a difference between the two manifestations (in a particular circumstance), but the difference is so insignificant that it does not seem that one has one kind of disposition (i.e., fragility) and the other another. Rather, it is recognised that they have the same kind of disposition in a slightly different degree. This illustrates that the disposition to fragility is tolerant of small variations in the cause that produces it and the manifestation that has occurred.
Let us now consider why the fragility disposition is not tolerant to large variations. Consider two pots: pot A made of glass and pot C made of rubber. Pot C (like pot A) can be broken into pieces, but the stimulus required to break pot C into pieces is very different from that required to break pot A (e.g., pot C can be cut with a very sharp knife, or it can be exposed to low temperatures so that it breaks with an impact). Furthermore, if we subject the two pots to the same stimulus (e.g. a hit), the response will be very different. This difference in response to the same stimulus, and the difference in stimuli to produce the same response, leads us to say that pot A is fragile, while pot C is not.
It is this tolerance of small, but not large, changes in the identity conditions for fragility that allows for ontic vagueness. The first assumption to be made is realism about dispositions, an assumption clearly accepted by anti-Humeans. The other assumptions necessary to produce ontic vagueness are that (i) there are objects that differ sufficiently in their responses to stimuli so that one belongs to the fragility type and the other doesn’t, and (ii) there is a sufficiently small difference between objects in their responses to stimuli so that there is no definite difference between them in terms of fragility. This second is the tolerance assumption. Given these two assumptions, we can construct a soritical series of objects such that the first is clearly fragile (as in pot A above), the last is not (as in pot C above), and there is a sufficiently small difference between each of them and the next in the series so that there is no definite difference in type between each of them and the neighbouring object in the series.
To be more explicit, imagine starting with the fragile pot A and replacing one fragile glass molecule with a non-fragile rubber molecule at a time, so that when you first replace a single molecule you still have a fragile pot, but at the end of the process you have the non-fragile rubber pot C. There is no precise pot that is the last to be fragile and there is no precise pot that is the first to be non-fragile. This allows for vagueness and indeterminate type-identity of the dispositions instantiated by each pot and the following one in the series, i.e. it may be indeterminate that the fragility disposition of one pot is type-identical to the disposition of the following pot. In accordance with ontic vagueness, we can say that sometimes a very small difference does not give rise to a definite identity, but to an indeterminate identity between the types of dispositions to which the two objects belong. Thus, fragility will be a vague disposition: certain objects definitely have it, certain others definitely do not, and there are objects for which it is indeterminate whether they are fragile or not.
Let us now transfer the idea to powers, i.e. properties of the fundamental objects in the world. The idea to be defended here is that powers are forces that characterise the ultimate constituents of reality. They are produced by other powers (either in isolation or in constellations) and they self-transform (either in isolation or in constellations) so as to produce new powers or constellations of powers. To characterise the identity of powers, let us first consider the powers that produce them and the powers that are produced by them.
Suppose that a power-instance A and a power-instance B are produced by slightly different constellations, and that when they are placed in the same constellation, they produce slightly different manifestations. According to Williams, they are instances of different kinds of power, whereas according to my proposal they may be instances of the same kind of power. I therefore deny a central tenet of Williams’s account of power identity, allowing that kinds of power are tolerant of small variations.
I propose that a small difference in the constellation that produces a power and a small difference in the manifestation that is produced (in a particular constellation) may allow two instances of power to be type-identical. I therefore reject the assumption that “two seemingly similar powers with different ‘spokes’ could never be identical (Williams 2019: 52),” since I claim that two seemingly similar powers with slightly different ‘spokes’ can be identical. According to Williams, “the set of spokes a power possesses is its essence; a change in essence requires a change in identity (Williams 2019: 52–53).” Instead, I want to explore the idea that a small change in spokes does not change the essence of powers, because their essence can tolerate small changes, even if not large ones.
It is this tolerance of small, but not large, changes in the identity conditions for powers that allows for ontic vagueness. The first assumption to be made is realism about powers, an assumption clearly accepted by anti-Humeans. The other assumptions necessary to produce vagueness are as follows: (i) there are powers that are sufficiently different in cause and manifestation from each other so that one belongs to one type and the other to another, and (ii) there is a sufficiently small difference in cause (or power-producer) and manifestation (or power-produced) between powers so that there is no definite difference between them. This second is the tolerance assumption. Given these two assumptions, we can construct a soritical series of powers such that the first is of one type, the last is not, and there is a sufficiently small difference between each and the next that there is no definite difference in type between each and the neighbouring power in the series. (This claim is defended in §4). In accordance with ontic vagueness, it will be claimed that sometimes a very small difference does not give rise to a definite identity but to an indeterminate identity between the types of powers to which the two powers belong (see §5, Figure 5). It will also be claimed that sometimes the small difference in intensity between instantiations of a type of power will give rise to indeterminacy as to whether a power is instantiated or not (see §5, Figure 4).
From now on, I would like to expand on the idea that the type-identity of powers tolerates small changes, but not big ones. In the next section, I defend this idea and link it to vagueness. In the following section (§5), I will directly consider that a consequence of tolerant identity for powers is ontic vagueness, and I will claim that it is coherently tenable.
4. A First Defence of Vague Powers: Dynamic Transformation
Why might we want to adopt a tolerant notion of the identity of powers rather than a very precise one? Isn’t the clear-cut one much better? It is probably easier to grasp, and in a sense, it reflects a desire for precision that we may want to satisfy. But while simplicity and clarity are good criteria for any metaphysical enterprise, it may be worth considering other parameters, as well.
As is well known, the purposes of power metaphysicians are in opposition to those of neo-Humeans. Let me just list three very relevant ones, presented by Williams himself:
Powers are essentially characterized by a force12
The connection between powers and their effects is a necessary one13
Causation should be inherently dynamic (or – in other words – there should be causal oomph)14
Now let us suppose that a power is a force which is not only directed towards any manifestations it may produce, but is also directed towards itself. Why is the power directed at itself? Because the power transforms itself into something other than itself, i.e. its manifestation. The idea that powers are forces that transform themselves into their manifestation is the basic assumption I make here. This characterization of powers is compatible with the fact that certain powers can interact with others in constellations. For example, they can mutually increase their self-transforming powers, or they can mutually decrease their self-transforming powers, or one power can subordinate some others. What is important is that powers, either by themselves or in conjunction with others, transform themselves into their manifestation without the need for anything else.
This way of looking at powers as forces that transform themselves into something else (i.e., their manifestation) is adequate to meet the requirements that the metaphysics of powers seeks to represent (and which I mentioned above): (i) it allows a force to characterize powers, since powers themselves are forces; (ii) it allows a necessary connection between powers and their effects, since powers (either alone or in constellation with other powers) allow for the production of their effects (or manifestations) because of the way they are and independently of anything else; and (iii) the causal relation between a power and its effect is a dynamic one, since any power (either alone or in constellation) dynamically transforms itself into its manifestation.
Now I propose that a power transforms itself into its manifestation, whereas Williams denies this. So, we have two different ways of thinking about manifestations arising out of power. On the one hand, we can assume with Williams that manifestation occurs immediately after powers cease to exist.15 On the other hand, we can assume that powers transform themselves into something else, i.e. their manifestation. In the second case, the idea is that the force that characterizes powers is always at work, consuming/intensifying itself to continually transform itself into something new, i.e. its manifestation. This is my proposal. By comparing these two different conceptions of the relation between powers and their manifestations, the reason for the divergent conception of the identity of powers can be explored.16
In assessing Williams’ proposal, the interesting question is: why does Williams prefer the discrete option? According to Williams, the discrete option offers the best account of power-based causation. Williams begins by considering how the process that takes us from constellation C to its manifestation M might be interrupted. He argues that any possible interruption would require a causal intermediary, some constellation D, between C and M. But if this is the case, then D is the cause of M, not C, and we have replaced a constellation-manifestation pair with a sequence of such pairs. He thus claims that modelling manifestation-constellation pairs as processes breaks down into discrete constellation-manifestation pairs. He therefore claims that “the constellation-manifestation pairs are unbroken (Williams 2019: 212),” and further that if they are unbroken, then the causal link between each constellation and its manifestation is a necessary one.
But can the unbreakable causal relation between constellations and manifestations be continuous? Williams explicitly considers this question and, in answering it, gives his reason for thinking that the relation between constellations and manifestations is discrete. I disagree with him on this point. Let us first consider Williams’ position, and then I will explain why I think it is inadequate. According to Williams, “the answer depends on the size of temporal parts (Williams 2019: 211),” where the temporal parts are constituted by the successive states of the world; he envisages two alternatives.
The first alternative is that there are “determinate states, meaning that whatever properties are parts of those states are fully parts of those states (Williams 2019: 211).” The idea is that the determinate state of the constellation (represented by a uniform white square in Figure 1) is followed by the determinate state of the manifestation (represented by a uniform black square in Figure 1). If this is the case, there is no room for a continuous change from constellation to manifestation, as Williams acknowledges, “the world causally ‘jumps’ from one to the next (Williams 2019: 211).”
Figure 1
First option – Determinate states.
The second alternative is that the determinate state of the constellation (the white square in Figure 2) and that of the manifestation (the black square in Figure 2) are separated by a non-determinate state, where a non-determinate state is a fuzzy state in which no property is fully part of that state (the uneven grey state in Figure 2). Williams expresses scepticism about the second option, explicitly preferring the first,17 but he sees no problem in including the intermediate states “as long as it is recognized that those intervening states are not causally significant (Williams 2019: 212).” In my opinion, this second alternative does not allow for a continuous causal relation because the intermediate state is not causally significant.
Figure 2
Second option – A non-determinate state between determinates ones.
In my view, to account for the continuous causal relation from constellation to manifestation, we should assume a single uninterruptible interval with a continuous change from constellation to manifestation within it (see Figure 3).
Figure 3
Continuous change.
The idea is that the constellation changes smoothly into something else, i.e. the manifestation, without there being a precise transition – a jump, either immediate or fuzzy – from the constellation to the manifestation. In this way we have an uninterruptible temporal interval with a continuous change which allows the power to be transformed into and causally determine the manifestation. So, when the constellation-manifestation pairs occupy a single temporal part, they are uninterruptible and therefore the connection between them is a necessary one.
In this section I have argued that if we take seriously the demand for a dynamic conception of the necessary causal relation between a power and its manifestation, then we should allow that a power transforms itself into the manifestation through continuous change within a single temporal part. Moreover, I have argued that this is compatible with the necessary connection between a power (or the constellation of which it is a part) and its manifestation, contrary to Williams’ claim. To recapitulate, according to Williams, the identity of types of powers is established by both the exact nature of the powers that produce them and the exact nature of the powers that are produced (i.e. the identity of powers is uniquely determined by their extrinsic relations). Moreover, the intrinsic nature of powers is unchanging. However, in my view, the intrinsic nature of powers is changeable and dynamic, and this intrinsic nature further justifies tolerance in the identity of the type of powers through both intrinsic properties and extrinsic relations. This last aspect now needs to be explained and further explored.
Once it is accepted that the transition from powers to manifestations is continuous, it should be considered how this view allows the identity of powers to be tolerant of small intrinsic changes. If we accept that a power transforms smoothly into its manifestation, we should admit that a power is not intrinsically characterized by invariance, but that the power retains its identity through transformation before becoming something new (i.e. the manifestation). This is a consideration that allows us to think of a power as something that can maintain its identity through transformation.
The question to consider is: how can a power maintain its identity while allowing internal variation? In other words, how can a power remain itself in the process of self-transformation? The idea I propose is that a power is a kind of property (i.e. a force) that can be had in different degrees of intensity. We can think of a power as being attractive or repulsive, increasing or decreasing, types of properties which can be present in different intrinsic degrees. So, a power is to be interpreted as a type that may maintain its identity through transformations of its intensity, which is interpreted as an intrinsic characteristic.
Once a type is allowed internal transformation in its exemplification, it should be allowed that small variations in its exemplification cannot change its identity, and small variations in whatever causes it and is caused by it cannot change its identity either, because small variations in whatever causes a power or is caused by it cannot change the type of power instantiated. This means that the identity of a type of power is tolerant of small variations not only in intrinsic characteristics, but also in extrinsic relations (i.e. the relations with the causes and the effects). Therefore, if the proposed dynamic conception of causal powers is allowed, the identity conditions of a power are necessarily tolerant of small variations within the identity conditions.
It may now be worth considering why types of power are not tolerant of large variations. Let us assume that powers are characterised by at least these four parameters: (a) being attractive, (b) being repulsive, (c) being increasing, (d) being decreasing. Combining these parameters, we have four types of powers: (I) increasingly attractive, (II) increasingly repulsive, (III) decreasingly attractive, (IV) decreasingly repulsive. It is evident that whenever a power belongs to one of these types, it cannot belong to another. This shows that powers (characterised in this way) are not tolerant of large variations.
At this point it may become clearer how the notion of identity I propose here differs from that of Williams. Whereas for Williams the identity of powers depends on (1) the powers or constellations that produce them and (2) the powers or constellations produced, according to my proposal the identity of powers depends on three factors: (1) the powers or constellations that produce them, (2) the powers or constellations produced, and (3) the inherently dynamic nature of the powers themselves.
We also now have the tools to understand why powers so interpreted are ontically vague. Once it is accepted that types of powers may be tolerant of small changes but not of large ones, we have the instruments to construct a sorites series of powers. Let us suppose that the first is increasingly attractive and the last is decreasingly repulsive, and we can imagine that there is a very small difference between each in the series and the next. We can even think of the increasingly attractive power transforming itself into the decreasingly repulsive one, giving rise to a completely different power as a manifestation: this shows that powers retain their identity through some of their transformations (even if not all transformations definitely retain their identity) and give rise to different powers. It may be useful to dwell for a moment on the self-transformation of a power from being increasingly attractive to something else, i.e. decreasingly repulsive. The power may have an energy that turns on itself to increase its attractiveness more and more until it reaches its apex and transforms itself into a decreasingly repulsive power. The original energy that characterises the increasingly attractive power does not disappear, it is transformed into something else (i.e., the decreasingly repulsive power). If we accept this image, we have to think that the power initially retains its increasingly attractive identity, and at some point, its identity becomes indeterminate, allowing it to transform into a power other than itself.
This shows how the dynamism of power is closely linked to vagueness and indeterminate identity.Once it is recognised that we can construct a sorites series of powers, all the tools are there to introduce indeterminate identity between any two pairs of powers. Considering the sorites series, it can be allowed that sometimes it is indeterminate that two very similar powers are type-identical, and it can also be the case that it is indeterminate that a power is instantiated. This is what I will consider in the following section.
5. A Second Defence of Vague Powers: Indeterminate Identity
I hold that to allow intrinsic dynamism in causal powers is to allow that powers themselves should undergo transformation before they are transmuted into their manifestation. And to allow intrinsic transformation of powers is to allow that powers can maintain their identity through internal change. But even if a power can retain its identity through change, not every transformation that a power can undergo will preserve its identity, as a power transmutes itself into its manifestation.
This means that there are differences between powers that justify the difference between the types to which they belong, and there are differences that are so insignificant that they do not justify belonging to different types. Whenever we have a difference between qualities that justifies belonging to different types, and a difference that is so insignificant that it does not justify belonging to different types, we run into vagueness. Baldness is an example. There are significant differences in the configuration and amount of the hairs on people’s heads that justify one belonging to the bald type and the other not, but there are irrelevant differences (e.g. the difference of a single hair) that do not justify belonging to different types.
A power instance can instantiate the same type of power through certain transformations, and it then transforms itself into something else (i.e. its manifestation) without a jump, but smoothly and continuously. This is enough to deal with vagueness. To allow that powers can be vague means (at least) to allow that a type of power maintains its identity through certain internal variations of its instances, but also that certain variations can allow for indeterminacy in the instantiation of the power itself. This is what I want to consider in this section. The idea is that it can be ontically indeterminate that a type of power is instantiated, and it can be ontically indeterminate that two power-instances belong to the same type. Let us try to find out why this is so by comparing different power-instances.
Consider, for example, the situation shown in Figure 4.
Figure 4
Indeterminate instantiation (P3) and corresponding indeterminate type-identity (between P1 and P3).
Let us suppose that ‘P1’ is the name of a power-instance represented in the corresponding box, which gradually emerges from a constellation (C) and gradually transforms itself into its manifestation (M). Let us assume that ‘P2’ is the name of a power instance in the corresponding box, of the same type as P1, but less intense than P1. Now consider ‘P4’, which is a name without a reference, because the corresponding box does not contain a power. Finally, consider ‘P3’, which is a name with an indeterminate reference: the indeterminate reference does not depend on any indeterminacy in the rules of language associated with the name ‘P3’, suppose for example that the rules of language clearly describe the box in which the reference should be, if there is one; but the indeterminate reference of P3 depends on the ontic indeterminate instantiation of a power in the corresponding box.
Now suppose that (contrary to the actual situation) if ‘P3’ had referred to a determinate power-instance, then that power-instance would be of the same kind as P1, but as long as ‘P3’ has an indeterminate reference, it is ontologically indeterminate whether P1 is the same kind of power as P3. In this case, the indeterminate identity of powers is a consequence of the indeterminate instantiation of a power-instance.
Let us now consider another possible situation of indeterminate identity, shown in Figure 5.
Figure 5
Indeterminate type-identity (between P1* and P3*) without indeterminate instantiation.
Let us suppose that power-instance P1* and power-instance P2* are slightly different in the constellations that produce them, in the manifestations that they produce, and that they are also slightly different from each other, but that these slight differences are compatible with P1* and P2* being determinately type-identical. Again, type-identity is tolerant of small variations according to my proposal. Consider now P4* and P5*: both are definitely type-different from P1* and from P2*, but they are (let us suppose) type-identical, because type-identity is tolerant of their small differences. Now consider P3*, a power instance whose difference from P1* is not so small as to be type-identical with it, and not so large as to be type-different from it. In such a case, it is indeterminate that P1* and P3* are type-identical because it is indeterminate how much two power-instances must share to be type-identical; not because either of the two names (‘P1*’ and ‘P3*’) has an indeterminate reference, as in the case shown in Figure 4.
Indeterminate type-identity (with or without indeterminate power-instantiation) is therefore the price to be paid by those willing to accept tolerant identity for powers. The crucial question to consider now is this: is indeterminate type-identity incoherent? The question is relevant because incoherence can be used to demonstrate the impossibility of ontic vagueness for powers. And indeterminate identity has a ‘bad reputation’ among philosophers: a famous argument against indeterminate identity between objects can be applied mutatis mutandis to indeterminate identity between properties. In the following section, I will consider how the argument against indeterminate identity between power instances can be developed, and then how a proponent of ontic vagueness for powers might respond. I will consider the case presented in Figure 4 (§5.2) and the case presented in Figure 5 (§5.3) separately.
5.1 Is Indeterminate Type-Identity BetweenPpower Instances Incoherent?
It is well known that Gareth Evans (1978) and, independently, Nathan Salmon (1981) have argued that indeterminate identity between objects is an incoherent notion and therefore that there cannot be indeterminate identity between objects. Their argument can be adapted to argue that indeterminate type-identity between property instances (especially between power-instances) is incoherent.
First, it is required that type-identity (and indeterminate type-identity) is not a first-order relation of objects, but a second-order relation of power-instances. To see this, it may be useful to recall that first-order properties (or relations) can only be instantiated by objects, while second-order properties (or relations) can only be instantiated by first-order propertie. For example, the second-order property ‘being a colour’ is instantiated by the first-order property ‘being red’, and the second-order property ‘being a symmetrical relation’ is instantiated by the first-order relation ‘being married’. Once type-identity is regarded as a second-order relation of power-instances, property abstraction is regarded as a rule of second-order properties; second-order properties are abstracted from power-instances.
The distinction between first-order and second-order properties is adopted here to allow the distinction between power-tokens (first-order properties) and power-types or type-identity (second-order properties), but it is neutral as to any metaphysical characterization of each of them. All that is assumed here is that there are types and tokens, that tokens can instantiate types, and that types (or type-identities) can be abstracted from tokens. Second-order property abstraction is interpreted as abstracting types (or type-identities) from tokens.18
And finally we need a rule, which we can call the Indiscernibility of Identical Powers, according to which if two power-instances are type-identical, then they have the same second-order type-properties. By contraposition we can say that if one power-instance has a second-order type-property that another power-instance does not have, then the two power-instances are type-different. The Indiscernibility of Identical Powers thus allows type-identity between power-instances to depend on the power-types abstracted from the power-instances involved.
Let us now consider how the argument against indeterminate type-identity between power-instances might be structured. Since the argument is a reductio, we will first assume what is refuted at the end of the argument. That is, we will assume that it is indeterminate for power-instance a to be type-identical to power-instance b. By second-order property abstraction, we will then deduce that power-instance b has the second-order property of being indeterminately type-identical to power-instance a. We will then assume that power-instance a is not indeterminately type-identical to itself, and by second-order property abstraction we will deduce power-instance a does not have the second-order property of being indeterminately type-identical to power-instance a. By Indiscernibility of Identical Powers, it is deduced that power-instance a is type-different from power-instance b. If it is further assumed that indeterminate type-identity is incompatible with type-difference, a contradiction follows.
The argument can be presented schematically as follows (read ‘Pa’ and ‘Pb’ as ‘power-instance a’ and ‘power-instance b’ respectively, ‘∇’ as ‘it is indeterminate that’ and ‘≡’ as ‘type-identity’):
| 1 | ∇(Pa≡Pb) | Assumption | |
| 2 | λX [∇ (Pa≡X)] Pb | 1 | Second-order type-property abstraction from 1 |
| 3 | ~∇(Pa≡Pa) | Assumption | |
| 4 | ~λX [∇ (Pa≡X)] Pa | 3 | Second-order type-property abstraction from 3 |
| 5 | ~(Pa≡Pb) | 1, 3 | Indiscernibility of Identical Powers from 2 and 4 |
| 6 | ⊥ | 1, 3 | Contradiction from 1 and 5 |
The argument just presented is an objection to my proposal and is intended to show that indeterminate type-identity for powers is paradoxical and therefore metaphysically impossible. I will argue that indeterminate type-identity between powers is not paradoxical: it requires a revision of certain assumptions taken for granted in the argument above, but it can be coherently assumed and is therefore metaphysically adequate. I will claim that indeterminate type-identity between power-instances may depend on an indeterminate instantiation of a power, or it may be independent of an indeterminate instantiation of power-types. In each case, the above argument is rejected for a different reason. It is therefore useful to consider the two situations separately.
5.2 Indeterminate Type-Identity Dependent on Indeterminate Instantiation
Now consider the situation of indeterminate type-identity shown in Figure 4. This is a case where indeterminate type-identity depends on the indeterminate existence of a power-instance. With this situation in mind, let us now examine the above argument against indeterminate type-identity between power-instances, substituting P1 for Pa, and P3 for Pb. In such a case, the inference from step 1 to step 2 is not allowed.; second-order type-property abstraction is not allowed. For the rule of second-order type-property abstraction to be allowed, the indeterminate second-order type-identity must be instantiated by determinate power instances. It is only when Pb is determinately instantiated that we may allow the indeterminate second-order type-property to be abstracted from it in step 2 of the above argument. In the case under consideration, the indeterminate type-identity instead depends on an indeterminate instantiation of a power-instance (i.e., the indeterminate reference of ‘P3’ in Figure 4), and therefore the abstraction of the second-order type-property from P3 is not permitted (and it is not permitted from Pb in the argument).
If it is indeterminate that there is a first-order power-instance, then it is indeterminate that there is something from which the second-order type-property can be abstracted. That is, type-property abstraction requires that there be something from which the second-order type-property is abstracted; if it is indeterminate that there is something from which to abstract, there can be no abstraction. In the case under consideration, as long as the first-order power-instance is indeterminately instantiated, the second-order type-property abstraction is not allowed. So, it is obvious that in such a case the argument is not valid (because second-order property abstraction is not valid in such a case), and therefore the conclusion should not be accepted.
5.3 Indeterminate Type-Identity Independent of Indeterminate Instantiation
Let us now consider another situation, as shown in Figure 5. In this case there are two determinate power-instances: power-instance P1* and power-instance P3*. Let us also suppose that the second-order relation of type-identity between the two determinate instances is indeterminately instantiated.
Why is this so? A proponent of ontic vagueness is willing to assume that a power allows for small differences in the instantiation of second-order types, but not large ones. The idea is that two power instances generated by slightly different constellations and producing slightly different manifestations (when placed in the same constellation) may be similar enough to be type-identical, while two power instances generated by very different constellations and producing very different manifestations (when placed in the same constellation) are different. Once we allow type-identity between powers to tolerate small (but not large) differences in their defining type-properties, we should allow for intermediate cases. These are cases where the two power-instances are not produced by similar enough constellations and do not produce similar enough manifestations (when used in the same constellation) to be type-identical, and where they are not produced by different enough constellations and do not produce different enough manifestations (when used in the same constellation) to be type-different. If they are not definitely type-identical and not definitely type-different, they are indeterminately type-identical.
Let us now consider the above argument in cases of indeterminate type-identity between power-instances. In these cases, the second-order type-property abstraction is obviously a correct and valid rule of inference since the indeterminacy in the second-order type-identity does not depend on any indeterminacy in the first-order power-instantiation. Instead, the indeterminacy has to do with the second-order property of instantiating the same power-type. The rule that needs to be reconsidered to account for this kind of case is the Indiscernibility of Identical Powers. As presented above, this rule allows for type-identity and type-difference, but it does not allow for indeterminate type-identity. The rule says that two power-instances are type-different if one of them has a second-order type-property that the other does not have, and that if two power-instances are type-identical, then they have the same second-order type-properties. The rule can be extended to take account of cases where the only difference between power-instances is that one has an indeterminate second-order type-property which the other does not have indeterminately. In such cases, an advocate of ontic vagueness would grant indeterminate type-identity. On the revised indeterminacy of identical powers that I propose, we should accept the following: if one power-instance has at least one determinate second-order type-property that another does not, they are determinately type-different, and if the only difference between power-instances is that one has an indeterminate second-order type-property that another does not, they are indeterminately type-identical.
In such a case, the proponent of ontic vagueness would therefore reject the inference from steps 2 and 4 to step 5 as not valid in the situation under consideration. If one power instance has an indeterminate second-order type property that the other does not, then the two power instances are (at least) indeterminately identical and not (obviously) different. Again, the argument against indeterminate identity of power-instances is not valid, and the conclusion must also be rejected.
6. Concluding Remarks
Even if the reader is prepared to concede that the hypothesis under consideration is a coherent and attractive way of characterizing powers as causally dynamic and necessarily causally effective, she may wonder whether my proposal is adequate to describe the properties of the ultimate constituents of reality. For example, what would become of my proposal if the world in which we live were constituted only by forces that do not transform themselves? What if the ultimate causal relations were discrete rather than continuous?
These are reasonable questions to consider. First, let us remember that experimental science is a work in progress, and therefore any evidence we have today may be dismissed in the future. But let us suppose that the ultimate constituents of reality (as God knows them, say) do not have powers of the kind I have described, what would become of my proposal? In such a case, my proposal would be of moderate relevance to scientific research, but it would still be very relevant to metaphysical research. Let us consider why.
To understand the metaphysical significance of my theory, it is useful to recall the (neo)-Humean/anti-Humean divide on causality. Every Humean expresses scepticism about any causal necessity, defending instead the natural contingency of any causal connection. For example, in our world anything with the physical properties of a magnet produces a magnetic field, but, according to a Humean, in another possible world plastic (and not magnets) might produce magnetic fields, and in yet another possible world wood (and neither magnets nor plastic) might produce magnetic fields. For a Humean, the natural contingency of causation is not just a matter of fact, it is an essential feature of causation: causation is essentially contingent, and not nomological.19
Instead, I have characterized powers in anti-Humean terms, as nomological properties: whether isolated or inserted in constellations, powers dynamically necessitate their manifestation in every possible world in which they are instantiated. If our world had no instantiated powers as I have presented them, this would be an interesting result, but it would not be evidence against the nomological nature of powers. Powers necessitate their manifestations wherever they are instantiated.
The philosophical idea I am defending is therefore not to be seen as a proposal that complements and explains existing scientific theories, but as a metaphysical proposal that takes into account a possibility that, if not contingently realised, must be seriously considered. I hope, therefore, to have provided sufficient support for it within the broader metaphysical debate on causality.
Notes
[3] Among the detractors of ontic vagueness, see Russell (1923), Dummett (1975), Evans (1978), Salmon (1981), Unger (1980), Lewis (1986), Williamson (1994) and Sider (2001).
[4] Among the supporters of ontic vagueness, see van Inwagen (1990), Tye (1990), (1996), (2000), Parsons (2000), Edgington (2000), Lowe (2005), Barnes and Williams (2011), Barnes (2013), Merricks (2017) and Wasserman (2017).
[5] Barnes (2005).
[6] See, for example, Ellis (2001), Molnar (2003), Heil (2003), Bird (2007a), Martin (2008), Mumford and Anjun (2011), Vetter (2015) and Williams (2019).
[7] For him, the fragility of the crystal glass as such is not a power in his sense; it is rather a disposition. He acknowledges that “smaller powers are hard to get at directly, and so we are forced, at times, to model our reasoning about the smaller powers on the larger disposition like fragility (Williams 2019: 48).”
[8] This idea of necessity associated with powers distinguishes it from the main alternatives (i.e., conditional necessity and dispositional modality), see Marmodoro (2016). This characterisation of powers as necessarily producing their manifestations makes them incompatible with the determinable dispositions defended by Kroll (2023), according to which powers are non-specific dispositions.
[9] A form of structuralism for the identity of powers was adopted by Mumford (2004: Ch. 10) and by Bird (2007a and 2007b).
[10] I remain neutral on any aspect of Williams’ theory, which is neither explicitly accepted nor explicitly criticized.
[11] The idea that dispositions are gradable was first defended by Manley and Wasserman (2007) and (2008); among the philosophers who adopt it, see Vetter (2015) and McKitrick (2018).
[12] See Williams (2019: 35).
[13] See Williams (2019: 26–27).
[14] See Williams (2019: 36–39).
[15] See Williams (2019: 136).
[16] The manifestation is a power or constellation of powers that is numerically and qualitatively different from the power or constellation that produced it. What links my position to Williams’ is the assumption that powers and their manifestations are numerically and qualitatively different. What distinguishes our positions is the mode of production of the manifestation: mine is dynamic, his is not. See Marmodoro (2020) for a critical discussion of the lack of dynamism in Williams’ proposal.
[17] See Williams (2019: 212).
[18] It may be interesting to note that just as first-order property abstraction is neutral about the metaphysical relation between properties and objects, second-order property abstraction is neutral about the metaphysical relation between types and tokens.
[19] See, for example, Lewis’ argument against essential nomological roles (Lewis 1986: 163).
Acknowledgements
My greatest thanks go to Anna Marmodoro, without whom this work would not even have started: she enthusiastically debated my ideas from the beginning to their present version. I am especially grateful to Neil Williams who read previous versions of this work, constructively discussing it with me; to John Pemberton who raised valuable objections to a previous version of the paper; and to Howard Robinson, whose questions were really useful for clarifying my ideas. I am particularly indebted to the two anonymous referees who read my paper very carefully and made useful comments and suggestions to improve it.
Funding information
This research was funded by the Department of Philosophy “Piero Martinetti” of the University of Milan under the Project “Departments of Excellence 2023–2027”, under the Project PRIN 2022 (Project Code 2022NTCHYF_003) and under the Project PRIN 2022 PNRR (Project Code P20225A73K_003), all awarded by the Ministry of University and Research (MUR).
Competing Interests
The author has no competing interests to declare.