According to PP there are only properties which are exclusively dispositional; unlike PQers, PPers are somewhat harder to find. Beside the already mentioned Bird (2007a, 2007b), we can count Shoemaker (1980) and Mumford (2004); perhaps, as we will later see, Hawthorne (2001) can also join in the ranks.
The PPer’s characterizations of dispositionality and categoricity are very different from those that we have seen so far, which makes it challenging to find common ground. We cannot, as in the previous Section, discuss separately the two notions, as for the PQer they much more intimately related.
Before beginning, it might be interesting to notice that PPers occasionally understand the dangers of non-divisive characterizations of categoricity (e.g., Bird 2007a: p. 66). That said, they often make mistakes on their own: Bird (ibid.) prefaces its discussion on categoricity by claiming that “[w]hat we mean by ‘categorical’ must be understood in negative terms”. Here Bird is following here a traditional divide set up by negation, as in Mumford (1998: p. 75): “[m]ost obviously, but least committally, a categorical property is any property which is not a dispositional property”.
Some additional details are offered, however, which are worth discussing. Bird, and possibly other PPers, often spell out the dispositional and categorical status of properties in relation to quidditism. There is no single position which warrants the label “quidditism”; that said, all quidditistic positions fall in two broad variants, Modal Quidditism and Identity-Based Quidditism—as in Smith (2016). Both have been deployed in the characterization of dispositionality and categoricity by the PPer. Let us first introduce both variants of quidditism and their relation; then, in the following subsection, I will examine their deployment from the PPer.
Two variants of quidditism
According to Modal Quidditism, as in Bird (2007a: p. 71), properties are only contingently associated with a certain dispositional profile; these properties I will call “modal quiddities”. Modal Quidditism reflects the peculiarly neo-Humean view on properties according to which, insofar as we accept trans-world identity for properties, the same property can elicit wildly different behaviors in its bearer from one possible world to another. This is the position dubbed by Smith (2016) “R-quidditism”, viz. a position about the lack of restrictions in the recombination of properties and dispositional profiles across worlds. This allows for “total swaps”, viz. a pair of distinct possible worlds w1 and w2, indistinguishable but for the fact that modal quiddities p1 in w1 and p2 in w2 have swapped places, in the sense that everything instantiating p1 in w1 instantiates p2 in w2 (and vice versa), and furthermore p1 and p2 have completely swapped their dispositional profiles. Thus, Modal Quidditism can be summarized in the claim that “[t]wo different possibilities can differ just by a permutation of fundamental properties” (Lewis 2009: p. 209).
A second variant is Identity-Based Quidditism, according to which properties have a primitive identity, which does not depend on any feature they may possess, as in Black (2000: p. 92) and (Bird 2007a: p. 72); this is the position dubbed by Smith (2016) “I-quidditism”, viz. a position about the individuation of properties. This too, unfortunately, is too coarse-grained to individuate a specific position: firstly, that properties have a primitive identity may be understood as the claim that properties are primitively identified or individuated, in the sense that there are primitive identity or individuality facts involving them (viz., primitive facts about properties being identical, or primitive facts about which property is which). This claim about the identity and individuation of properties occasionally translates into a claim about their nature: guided by Lewis’ (1986: p. 205) claim that “[t]here isn’t much to the intrinsic nature of a universal”, one could insist that quidditistic properties are those whose only nature is to be primitively identified or individuated, and, as such, lack any substantial nature. All that there is to them is their numerical identity and difference, as in Armstrong (1997: p. 168, 2004: p. 146), and (Bird 2007a: p. 3); such properties are occasionally called “thin quiddities”. Yet it is also viable to claim that, although properties are primitively identified or individuated, they are in fact not so thin, and display some further intrinsic character (this subtle distinction, as far as I know, is only explicitly recognized in Smith 2016). Another position yet is one according to which properties do have a further intrinsic character (or, as it is sometimes called, a “thick quiddity”), which fixes their identity: according to this position, such identity or individuality facts are therefore not brute —the thick quiddity is. Finally, as in Locke (2012) we may endorse “extravagant quidditism” and reject the (often implicit) assumption that the property and the thick quiddity are one and the same, to reach the somewhat baroque position according to which there is an item called quiddity (distinct but somehow related to the property) which is what ultimately fixes its identity. In conclusion, Identity-Based Quidditism is not so much as a definite position, but rather a family thereof.Footnote 7
It will be worthwhile to briefly explore the relation between Modal Quidditism and Identity-Based Quidditism. I agree with Smith (2016) that Identity-Based Quidditism doesn’t entail Modal Quidditism: that properties have a primitive identity, in whichever way one wants to spell it, doesn’t entail that they only contingently have the dispositional or nomic profiles they have, for the supporter of Identity-Based Quidditism may posit any number of restrictions in the recombination of properties and such profiles. After all, one may claim that a property possesses a primitive identity, in any of the senses detailed above, while at the same time being necessarily associated to a certain dispositional profile, necessary but not sufficient for its individuation. Thus a quiddistic property according to Identity-Based Quidditism may not be a modal quiddity. This point will play a crucial role.
As for the other direction, unlike Smith (2016) I submit that Modal Quidditism does not entail Identity-Based Quidditism. Modal Quidditism, as the claim that no dispositional, causal, or nomic profile of a property is necessary to it, entails that no such profile can individuate it. Now, of course this is compatible with many instances of Identity-Based Quidditism. Smith (2016: p. 240) tries to reach the stronger conclusion that Modal Quidditism entails (some version of) Identity-Based Quidditism—in her formulation, R-quidditism entails I-quidditism—, by claiming that.
if R-quidditism is true and there is no restriction on how fundamental properties can recombine […] then fundamental properties cannot be individuated on the basis of their nomological roles and (something akin to) I-quidditism must be true.
But I take there to be a gap in her argument: roughly put, that the property cannot be individuated by any dispositional or nomic profile doesn’t entail that it is primitively individuated. Something else might be doing the individuating. For example, according to Lowe (2010: 20),
[sphericity] has a distinct purely geometrical ‘real’ definition which expresses its essence and therefore serves as a ground of its transworld identity—without any implication that the latter is ‘primitive’ and ‘mysterious’.
We thus arrive at Qualitative Identity, a more general claim than Identity-Based Quidditism. One may want to introduce Qualitative Identity as the claim that properties have their identity fixed either qualitatively or primitively. But that claim is loaded with an unfortunate circularity, since qualitativity is exactly what we are trying to characterize. Thus I will content myself with a negative, weaker, claim: according to Qualitative Identity, properties do not have their identity fixed by any dispositional or nomic profile, but in some other way –whether primitively or not.Footnote 8
Summarizing: Modal Quidditism does not entail Identity-Based Quidditism, and neither the other way round. Yet they are both entailed by Qualitative Identity, which is thus a more general position (whether it is really a version of “quidditism”, is a verbal dispute I am not particularly interested in pursuing).
PP and modal quidditism
Both Modal Quidditism and Identity-Based Quidditism have been intermittently used by PPers to characterize categoricity and dispositionality, but they are not clearly distinguished.Footnote 9 E.g., Bird (2007a: p. 44) claims that “[c]ategorical properties […] do not have their dispositional characters modally fixed”, but shortly after he adds that “categorical properties have primitive identity”.
Let us start from Modal Quidditism, which has been deployed by PPers in multiple occasions (most clearly, in Bird 2007a: pp. 66–67). This characterization is widely shared by many Categoricalists, who often endorse a properly neo-Humean contingency about laws of nature, so that which dispositional profile accompanies a property at some world depends on which laws happen to hold at that world. Categorical properties qua modal quiddities are often accompanied by a correspondent modal characterization of dispositionality according to which dispositional properties are those that are necessarily, rather than contingently associated with their dispositional profile (most recently, Bird 2016: p. 6); this makes the divide between the categorical and the dispositional a modal one, a conclusion to which Bird has always been sympathetic (e.g., Bird 2007a: pp. 66–67, Bird 2016).
Such characterizations, however, will not do. Firstly, they are mutually exclusive—thus, unfairly ruling out PQ as a viable position. Furthermore, there are even more substantial difficulties when our two criteria are considered. For the characterization of categoricity is neither comprehensive nor divisive, while the characterization of dispositionality, while comprehensive, is not divisive.
Let us start with categoricity. If the characterization of categorical properties qua modal quiddities is to be comprehensive, it has to be applicable to the properties of all pairs of positions which agree on the existence of categorical properties. While this characterization may prima facie be applicable to the properties of the Categoricalist, it is not applicable to the properties of the PQer, even though the two agree on the existence of categorical properties. Crucially, powerful qualities are not modal quiddities: according to PQ, properties necessarily have the dispositional profiles that they have; furthermore, although PQers do not usually frame their positions in terms of laws of nature, they still take them to be a necessary matter—thus ensuring that properties have fixed dispositional profiles across the modal space (e.g., Heil 2003: pp. 92–95, 2005: pp. 345–346).
Additionally, the characterization of categorical properties qua modal quiddities is not divisive. This requires some elaboration. Framing categoricity through the lenses of Modal Quidditism makes the categoricity of properties a matter of modal recombination, or perhaps of modal status of laws of nature; yet if that were the case, no Categoricalist would be in a position to argue that laws of nature are metaphysically necessary. At times, this consequence seems to be endorsed by PPers; e.g., Bird (2007a: p. 4) proposes a table of positions according to which Categoricalists are forced to the claim that laws are contingent. But this is incorrect: it is important to keep in mind that Categoricalism, as the claim that all properties are categorical, is distinct from the claim that laws of nature are contingent. Separating these occasionally conflated claims we obtain, as in Azzano (2019: p. 347), a Categoricalist position provided with metaphysically necessary laws of nature; according to such a position, thus, while there are categorical properties, there are no modal quiddities. Let us call it NC, short for Necessitated Categoricalism (its supporters are the NCers). NC is supposed to be dissimilar from PP, since only the first accepts the existence of categorical properties; but according to neither position there are modal quiddities; the characterization of categoricity based on Modal Quidditism, while commonplace, is not suited to reconstruct the dissimilarity between NC and PP. Thus, it is not divisive.
Now, for dispositionality. The characterization of dispositionality according to which dispositional properties are necessarily associated with their dispositional profile may very well be comprehensive (it is applicable, as we have seen, to both pure powers and powerful qualities), but it is not divisive. The reason is quite straightforward: NC has properties necessarily associated with their dispositional profiles; so, as above, the properties of NC are dispositional. NC is supposed to be dissimilar from PP in matter of dispositionality, but, according to this characterization, it isn’t.
Summarizing, we have seen that constructing dispositionality and categoricity through the lenses of Modal Quidditism, a known strategy amongst PPers, is unsatisfactory for a number of reasons. Firstly because the two characterizations are mutually exclusive; secondly, because the characterization of categoricity is neither comprehensive nor divisive; thirdly, because the characterization of dispositionality is not divisive. The takeaway lesson from this subsection is that dispositionality and categoricity shouldn’t be framed through the necessity or contingency of dispositional profiles, and therefore we shouldn't envision a modal divide as in Bird (2007a: pp. 66–67).
PP and identity-based quidditism
Identity-Based Quidditism is also a prominent candidate for categoricity (e.g., Bird 2007a: p. 44). Discussing what he calls “Humean” and “semi-Humean” views on properties and laws, Bird (2007a: p. 3) claims that.
there is very little on these views to the nature of a given property and certainly nothing that would distinguish it from some other property. The identity and distinctness of properties is a brute fact, not grounded in qualitative differences. Such a view of the nature of properties is called quidditism.
He then adds, shortly after, that:
[p]roperties whose natures are described by quidditism are traditionally known as categorical properties.
Bird is not the only one to think along these lines; according to Barker (2009: p. 242):
[a] property possesses a quiddity just in case its identity is fixed by something independent of the causal-nomological roles it may enter into. Paradigmatically, a categorical property is thought of as a property whose identity is fixed by a quiddity.
For the PPer, the characterization of categoricity via Identity-Based Quidditism goes hand in hand with a correspondent identity-based characterizations of dispositionality, according to which dispositional properties, unlike categorical ones, get their identity fixed through their dispositional profile, at least in the sense that properties are individuated by one of more pairs of stimulus/manifestation pairs to which the property is suitably related; as in Mumford (2004: p. 171), a property’s identity “is fixed by relations with other properties”. In this sense, PP is a close relative of the anti-quiddistic position according to which a property’s identity is given by its unique position in a causal or nomic structure (e.g., Hawthorne 2001).
As in the case of Identity-Based Quidditism (Sect. 4.1), this claim concerning the identity and individuation of properties quickly turns into a claim about their nature, or essence: that properties have their identity fixed by their dispositional profiles is sometimes accompanied by the claim that properties are essentially dispositional, whereas categorical properties are not. There are various accounts concerning the dispositional essence of properties.Footnote 10 What they all have in common, and what matters for our current purposes, is that dispositional essences make for necessary dispositional profiles, thus ensuring that the property’s identity is fixed. This essentialist component of PP is so deep-rooted that Yates (2017: p. 4525) straightforwardly presents it as the position according to which “basic physical properties have wholly dispositional essences”.
Thus, Identity-Based Quidditism is deployed by PPers as a characterization of categoricity as opposed to properties with a dispositional essence, whose identity is fixed relationally, through their dispositional profiles. In the simple words of Bird (2007a: p. 44):
[e]ssentially dispositional properties have their identities fixed by their dispositional characters; categorical properties have primitive identity.
Similarly, in the theory of properties put forward in Mumford (2004: p. 185):
[i]nstead of quiddities, the essence and identity of a property are determined by its relations to other properties.
Now we have identity-based characterizations of both dispositionality and categoricity. Are these useful for our purposes? Given that Identity-Based Quidditism does not entail Modal Quidditism, none of the problems of Modal Quidditism described above apply: most importantly, Identity-Based Quidditism, by allowing for categorical properties which are not modal quiddities, does not miscategorize PQ and NC, and allows the NCer to join the ranks of the Categoricalists.
That said, these identity-based characterizations may suffer from their own problems. Are they comprehensive and divisive? The short answer is: it depends on whether the PQer can accept them. Both of them are clearly acceptable by the PPer who submits them, and they are also acceptable by the Categoricalist in general (and by the NCer in particular), thus making the disagreement between the PPer and the Categoricalist a disagreement about the identity of properties (rather than a modal divide). But whether the similarities and dissimilarities concerning PQ are correctly reconstructed by this approach, depends on whether the PQer’s properties are both dispositional and categorical according to these characterizations. This is what we now turn to.