Abstract
This paper has two main aims. The first is to present a general approach for understanding “dispositional” (or “structural”) and “categorical” properties; the second aim is to use this approach to criticize Russellian Monism. On the approach I suggest, what are usually thought of as “dispositional” and “categorical” properties are really just the extreme ends of a spectrum of options. The approach allows for a number of options between these extremes, and it is plausible, I suggest, that just about everything of scientific interest falls in this middle ground. I argue that Russellian Monism depends for its plausibility on the unarticulated assumption that there are no properties in the middle ground.
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Notes
This statement is a bit rough, and it is not entirely obvious how to fix it. For example, if numbers are necessary existents, then this property would equally serve as a haecceity of David Chalmers: being identical to Dave and such that 2 + 2 = 4. And if a singleton axiom was necessary, so would this: being the unique member of {David Chalmers}. I will not address such issues here, however.
Note that this usage already compromises clarity. I defined a quiddity as a second-order (or level-2) property, a property of properties. The more common use treats ‘quiddity’ as expressing a kind of first-order property. What kind that is seems unclear to me (as I illustrate later). I am compromising clarity by allowing ‘bare quiddity’ to apply to first-order properties which have especially impoverished essences.
Mundy’s quantities are organized into “rays”. These are sets of level-1 properties that are related to each other by the level-2 relations ≤ and *. Any two Mass-properties stand in ≤ to each other, as do any two Temperature-properties, while the Mass and Temperature properties are not so related to each other.
For ease of presentation I will allow myself to slide ambiguously between treating ‘+’ as a three-place relation like sum (4 is the sum of 2 and 2) and as a two-place function like plus [+ (2, 2) = 4].
I do not have any exact characterization of “dispositional” features to add. I take them generally to be ones that concern or constrain the broadly causal relations that things enter into. Dynamic, cross-temporal relations are my paradigm examples of “broadly causal relations”. Many philosophers discuss phrases such as ‘x is disposed to φ’ and ‘the disposition to φ given stimulus S’. I do not have anything much to say about those phrases.
It is common for philosophers to characterize the nomic roles of properties in terms of Ramsey sentences (as in Lewis 2009, 206–207). The approach I am describing complicates that picture. In order to be finitely stateable, the relevant theoretical postulates and laws have to concern level-2 quantities such as Mass rather than level-1 properties such as 1 g. The postulates describe relations among level-2 properties (or sets of level-1 properties). The relevant Ramsey sentences then quantify over those quantities, rather than the level-1 properties directly.
The term “realize” is sometimes used to indicate a relation in the neighborhood of supervenience or necessitation. In this sense, an arrangement of particles might “realize” a higher-level fact such as a certain sample of water’s having a given temperature. The particles’ havings of their properties necessitate the sample’s having the temperature. The relation between level-2 role properties and level-1 “realizers” of them is distinct from that one.
This is a fairly “thin” conception of essential properties, I realize. For example, if 2 + 2 = 4 is necessary, then being such that 2 + 2 = 4 would be an essential property of anything. Some people want a “thick” conception of essence which rules out such properties. I hope the thin conception is enough for the purposes of this paper, however. I am primarily interested in the contrast between essential and individuative properties.
I am confident that I get this pure v. impure distinction from Sydney Shoemaker, though I am not able to point to a specific location at present.
I have no terribly precise account of what a “structural relation” is. Paradigm examples are relations describable in some relatively neutral vocabulary, such as one restricted to logical, mathematical, and (maybe) metaphysical terms (such as ‘property’). At some point we may also need a nomic term such as ‘It is a law that…’. Mundy’s relations ≤ and * are of this sort; so is the relation I see as being expressed by ‘F = ma’.
I want to remain officially neutral on the question of whether properties are necessary existents. If you think they are, then you should read examples in which I say that certain properties do not exist as examples in which the relevant properties are not instantiated. I am somewhat inclined toward a middle ground: what properties exist is lawfully but not metaphysically necessary. This view allows for uninstantiated properties, such as twice the total mass of this universe, while still not treating properties as fully necessary existents. I do think that it is not conceptually necessary what properties exist. Like Mundy, I treat them as theoretical postulates.
One might be puzzled by this. Surely ‘1 g’ and ‘2 g’ are rigid designators, so wouldn’t ‘1 g + 1 g = 2 g’ thereby be necessary if true at all? Maybe, but maybe not. ‘1 g’ is rigid, but ‘1 g + 1 g’ is potentially nonrigid; it designates the property that occupies a certain position in a “space” of properties with respect to 1 g. It is conceptually open that that position is occupied by different properties in different worlds, but that may or may not be really possible, depending on one’s metaphysical view of the properties. Whether ‘1 g + 1 g’ is rigid is a metaphysical question rather than a narrowly semantic one.
What seems paradoxical about this is that ‘1 g < 2 g’ is surely a priori, as is ‘1 g + 1 g = 2 g’. That’s just how ‘2 g’ is defined, after all (‘the Mass-property that is twice 1 g’). But depending on the metaphysical view of the properties that one takes, those could be either necessary a priori, or contingent a priori. They are necessary, if they are, due to facts about the natures of the properties; by contrast, they are a priori for generally semantic reasons having to do with how we fix the references of terms such as ‘2 g’. ‘1 g < 2 g’ is a priori in the manner of ‘Hesperus is visible in the evening’. But in this case it might also be in the essence of 1 g to be less-than 2 g. The mere fact that we pick out one property by its relation to another does not require that that relation holds necessarily. More subtly, even if the relation does hold necessarily, it does not hold necessarily because that is how we picked out the thing.
The connections between the conditions are a bit more subtle than my statement in the text indicates. Suppose Weak Essentiality holds for both A and B, and that the structural relation R satisfies a uniqueness condition (if R(A, Y1) and R(A, Y2) then Y1 = Y2; and similarly for A). Mundy’s + relation satisfies this sort of uniqueness condition, for example. Then A satisfies Weak Individuation iff B satisfies Strong Essentiality. ⇒: Suppose Y = B. Then Weak Essentiality for B requires ∃X R(X, B), and Weak Individuation for A requires R(A, B). ⇐: Suppose R(X, B). Strong Essentiality for B requires R(A, B) and Uniqueness requires X = A.
Some “Ontic Structural Realists” want an even more radical sort of “structuralism” than the kinds I describe. James Ladyman (2007) wants a sort of structuralism that eliminates both individual objects and monadic properties of them too, in favor of relational structures. The structuralisms I describe accept individuals and monadic properties (and relations), and differ on the extent to which the identities of the properties are tied to their relations to other properties.
Further distinctions are available for dispositional essences. Shoemaker distinguishes between “forward-“and “backward-looking” causal features of properties, for example. Whichever set of features is in question, however, there are distinctions between Weak, Moderate, and Strong sorts of Dispositionalism.
A third option is that Chalmers (and others) do not distinguish these first two options because they have not recognized that the middle ground positions are conceptually open. A fourth option is to hold that the first two options are not really different in fact because the middle ground positions are not occupied.
I suspect that Bird himself intends his term ‘power’ to apply only to what I call “super-dispositional” properties, though his formulation in the quotation does not require that.
Hawthorne notes in his Appendix that (what I am calling) “Moderate Structuralism” avoids his objections. Hawthorne intends to argue against Sydney Shoemaker’s “causal theory of properties” (esp. 1980). Shoemaker’s own statements are a bit slippery; in 1980 his view looks like my Strong Structuralism, but in 1998 (subtly, 412–413), and in response to Hawthorne (more explicitly), Shoemaker goes for something more like Moderate Structuralism.
Matters are a bit more complicated if there are no physically or metaphysically basic objects. Maybe space is “gunky”, for example. I think this sort of view would make for more rather than fewer basic facts about distinctness. We could no longer explain the distinctness of a and b by distinctness of their basic components, so this seemingly higher-level distinctness fact might itself have to be basic. In general, on this view there would seemingly have to be fundamental facts about the identity and distinctness of nonfundamental things.
Dustin Locke (2012) argues for a position he calls “Austere Quidditism”: “Properties are individuated by numerical identity” (351). That is similar to the view I suggest, though I express it by saying that there are metaphysically basic facts about identity and distinctness of (some) properties. Locke contrasts this position with two further ones: “Property Structuralism: Properties are individuated by their nomological roles” (347), and “Extravagant Quidditism: Properties are individuated by their quiddities” (351). Locke’s Austere Quidditism is compatible with his Structuralism--Moderate Structuralism satisfies both. Extravagant Quidditism barely makes sense on my approach. It seems to hold that each property is individuated by a higher-level property.
The qualifications are there because bare quiddities may have some highly minimal essential features. Maybe monadic properties are essentially monadic, for example. Still, they differ from each other despite having the same nearly empty essences. Locke (2012, Appendix) argues that Lewis’s own version of “quidditism” is Locke’s “Austere” kind, which is also close to my “basic identity fact” kind.
Bird (2016) emphasizes that his “powers” ontology is intended to apply only to physically fundamental properties. Nonfundamental properties may well essentially involve relations to their more fundamental realizers, he allows, instead of or in addition to pure dispositional features (Sects. 3, 4). That seems plausible to me as well. Maybe in a world with different Mass-ish properties, the Temperature-ish properties are thereby different also, even if they have the same pure structural features as Temperature properties have here. So, it seems likely that nonfundamental properties would commonly not be super-structural ones, even if the fundamental ones were (which I doubt).
Bird (2007) responds to “regress” arguments against the view that properties are “powers”. The version of the objection that Bird finds most plausible holds that the identities of powers are not adequately “fixed” by their relations to other powers, whose identities are also supposed to be fixed in the same way. Bird responds by holding that it is possible for the total system of nomic relations among properties to be asymmetric. Hawthorne’s objection is in effect that it is equally possible for such a system to be symmetric. Surely both are right in their claims about what is possible. It is somewhat difficult to adjudicate this dispute because it is somewhat difficult to see what the modal commitments of the relevant views are.
Henry Taylor (2017) argues that there is no clear difference between Heil and Martin’s identity Theory and Bird’s “pure powers” view. Distinguishing level-1 properties and level-2 roles seems to me to make at least one difference reasonably clear. The “pure powers” view holds that Strong Structuralism (or Dispositionalism) is true of some fairly extensive class of properties (maybe all, or maybe only the fundamental ones). My own (Weak) Identity Theory denies that in favor of Moderate or Weak Structuralisms. I am not sure whether Heil would take my suggestion about how to understand the “Identity Theory”.
This characterization is offered by Tom McClelland on the “Russellian Monism” page of PhilPapers (http://philpapers.org/browse/russellian-monism, accessed Nov. 2, 2017).
These claims of Strawsons’s are false on the second-order account of “structure” I get from Mundy. Physical theory uses mathematical means to represent the intrinsic physical facts, but tells us quite a bit about those facts anyway. Strawson (and Russell) are apparently assuming some distinct account of “structure”, or (I suspect) of what it takes to represent an “intrinsic” feature of something.
For example, the (alleged) super-categorical version of 1 g can “play the role” of being fried egg, so the nonsuper 1 g property certainly does not supervene on it. The issue becomes more complicated when one appeals to Lewisian views about lawful modality. Lewis would hold that the lawful relations among super-categorical properties supervene on their total spatiotemporal distribution, and thus that the whole pattern of super-categorical properties determines lawful relations among individual instances of these properties. That whole pattern might then determine whether nonsuper 1 g is instantiated in a given location. I do not accept the Lewisian views of lawful modality, however, and I am pretty sure Chalmers does not either (2012, 428).
Such worlds could also differ on their phenomenal facts if the phenomenal properties were among the dispositional-and-categorical ones, as seems plausible to me.
In “Ramseyan Humility” Lewis holds “we are irremediably ignorant about the identities of the fundamental properties” (Lewis 2009, 214). I suspect Lewis’s motivation for this view also motivates Russellian Monists. Some treat Lewis’s argument as similar to an argument for external-world skepticism (Langton 2004; Schaffer 2004). Kelly (2013) offers a deeper interpretation. On this view, Lewis holds that the partly demonstrative sort of reference I described for Abbie is not enough for her to “grasp” propositions involving electronhood (Kelly Sec. 3 esp. 718), while “grasping” a proposition is necessary for knowing it (714). I do not know what “grasping” is, but I reject that conjunction: either partly demonstrative reference allows us to “grasp” the relevant propositions, or “grasping” them is not necessary for knowing them. I say a bit more about this issue below.
One might also wonder about the example: do Abbie and Abbie* have the same phenomenal states? I do not know. In the example, some properties are common to things made of matter and anti-matter, while others differ. Which way phenomenal properties go will depend on what they are in detail.
Lewis does claim in “Ramseyan Humility” (2009) that the identities of his bare quiddities are hidden from us. The metaphysical view of Bare Quidditism does not require this claim, however. On the interpretation of Kelly (2013), which I think is right (exegetically though not philosophically), Lewis’s “humility” view derives from further views about concepts and reference. Those are optional, and I think should be rejected.
Russellian Monists are also motivated by the idea that their hidden natures might help to solve the mind–body problem. I am skeptical that these could provide any help even if they existed, but cannot go into that issue here. Something must be hidden in the first place, however, in order for it to be available to play this role; so, if nothing is hidden the further issue is moot. Alyssa Ney (2015) also objects to Russellian Monism that nothing is hidden from physical theory. Ney surveys and criticizes reasons one might think something is hidden, and I am happy to accept her criticisms of those. I hope my “interpretive hypothesis” explains more deeply how Stoljar and Chalmers get the idea that something is hidden, and why that motivation is wrong.
I suspect that an even more basic motivation for Russellian Monism derives from rejecting the idea that it is enough for us to know the identities of physical properties in this partly demonstrative way. This is Lewis’s view in “Ramseyan Humility” on the interpretation of Kelly (2013). In order to really “grasp” physical properties, on this view, we have to be able to pick out the references of terms such as ‘electronhood’ across all possible worlds on qualitative grounds alone, without any “indexical reference to the actual world” (Kelly 2013, 718). So, to genuinely “grasp” physical properties requires knowledge of pure individuating features of them; and Kelly takes Lewis to hold that “grasping” in this sense is necessary for knowledge (714). It seems likely to me that this is a more basic motivation for Russellian Monism, namely that to “grasp” physical properties we must know pure individuating features of them (Chalmers seems to accept this view for “thick quiddities” at 2012, 350; I think one can even read Russell himself this way). I am afraid this view seems clearly wrong to me: knowledge of pure individuating features is not necessary to “know which thing” an object is (else I do not “know who” my spouse is), and there is no apparent reason why matters should be different for properties.
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Acknowledgements
Though it may not be obvious from the text, I am especially indebted to Sydney Shoemaker.
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Hiddleston, E. Dispositional and categorical properties, and Russellian Monism. Philos Stud 176, 65–92 (2019). https://doi.org/10.1007/s11098-017-1006-2
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DOI: https://doi.org/10.1007/s11098-017-1006-2