Imprint. Fundamental Determinables. Jessica Wilson. Philosophers. University of Toronto

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1 Imprint Philosophers Fundamental Determinables volume 12, no. 4 february 2012 Introduction Contemporary philosophers commonly suppose that any fundamental entities there may be are maximally determinate. More generally, they commonly suppose that, whether or not there are fundamental entities, any determinable entities there may be are grounded in, hence less fundamental than, more determinate entities. So, for example, Armstrong takes the physical objects constituting the presumed fundamental base to be determinate in all respects (1961, 59), and Lewis takes the properties characterizing things completely and without redundancy to be highly specific (1986, 60). Here I ll look at the usually cited reasons for these suppositions as directed against the case of determinable properties, in particular, and argue that none is compelling (Sections 1 to 3). The discussion in Section 3 will moreover identify positive reason for taking some determinable properties to be part of a fundamental (or relatively fundamental) base. I ll close (Section 4) by noting certain questions arising from the possibility of fundamental determinables, as directions for future research. 1. Preliminaries Jessica Wilson University of Toronto 1.1 Fundamentality vs. relative fundamentality Let a fundamental base at a world w be a minimal collection of entities that, either individually or in combination, provide a complete metaphysical ground for the entire inventory of w. Then an entity e at a world w is fundamental iff: (i) at w, there is a fundamental base; and (ii) e is in this fundamental base. 1 Here and elsewhere entity is used ontologically generally, as accommodating, e. g., particulars, properties, tropes, events, states of affairs, 2012 Jessica Wilson < 1. This and the following definition are intended as intuitively motivated stipulations, not analyses of terms already in use.

2 processes, facts, or truths. I ll discuss the operative notion(s) of metaphysical grounding shortly. Whether or not there is a fundamental base at a world, we can make sense of relative fundamentality. This notion is usually understood against a background ontological framework involving a hierarchy of levels ordered by mereological composition of particulars, and where at any given level L, some entities at L serve as a minimal relatively fundamental base both for all entities at L and for entities at compositional levels higher than L. There might be other frameworks for which relative fundamentality makes sense, but for present purposes it won t hurt to restrict focus to the hierarchical case. So let a relatively fundamental base at a world w be a minimal collection of entities existing at a compositional level L that, either individually or in combination, provide a complete metaphysical ground for all entities at level L or higher. Then an entity e 1 at a world w is more fundamental than a distinct entity e 2 iff: (i) At w, there is a relatively fundamental base at level L; (ii) e 1 is in this relatively fundamental base; and (iii) either e 2 is an entity at a level higher than L, or e 2 is an entity at L not in the base. This characterization leaves open whether there are (even indefinitely many, in a gunky world) relatively fundamental bases at compositional levels lower than L, relative to which e 1 is non-fundamental. When either the fundamentality or the relative fundamentality of an entity or base may be at issue, I will speak of its being (relatively) fundamental. 1.2 Metaphysical grounding The notion of metaphysical grounding relevant to discussions of fundamentality is often characterized in intuitive or gestural terms, as follows: All God had to do to create the world was to create the fundamental entities; these then metaphysically ground all the rest. 2 Fixing the (distribution of) fundamental entities at a world fixes all else at the world. 3 The fundamental entities at a world are those in virtue of which all else obtains. 4 The fundamental entities carve nature at the joints. 5 Related locutions appear in contexts where certain comprehensive and (in Jackson s terms) discriminating metaphysical frameworks are at issue, as with, for example, the physicalist thesis that all broadly scientific entities are nothing over and above the (relatively fundamental) physical entities, and Schaffer s characterization of monism as the view that the whole is metaphysically prior to the parts. There are any number of ways one might go on to fill in such intuitive characterizations of grounding, either as a general, broadly 2. See, e. g., Schaffer 2004, 100: To speak metaphorically, all God had to do was to create the primarily real. What God has to do to create gunky worlds is less clear. 3. See, e. g., Dieks and de Regt 1998, 45: the idea that deeper layers of reality are responsible for what happens at higher levels is well-entrenched in scientific practice. We argue that the intuition behind this idea is adequately captured by the notion of supervenience: the physical state of the fundamental physical layers fixes the states of the higher levels. 4. See, e. g., Fine 2001, 15: [I]f the truth that P is grounded in other truths, then they account for its truth; P s being the case holds in virtue of the other truths being the case. See also Bricker 2006, 255: [T]he determination relation [ ] is non-causal, and holds of necessity. But more must be said: a mere logical or functional determination is not to the point unless it carries with it ontological force. Thus, if the atomic truths determine the general truths, in the relevant sense, then the general propositions hold or fail to hold in virtue of, or because of, the holding or failing to hold of the atomic propositions. 5. See, e. g., Lewis 1984, 227: Among all the countless things and classes that there are, most are miscellaneous, gerrymandered, ill-demarcated. Only an elite minority are carved at the joints [ ]. philosophers imprint 2 vol. 12, no. 4 (february 2012)

3 metaphysical notion 6 or in some way more directly tied to cases; 7 one might also maintain that the relevant general notion is primitive. 8 As I read such locutions, and will interpret them here, they aim to characterize metaphysical grounding as, at a minimum, a relation of complete asymmetric ontological dependence. Reflecting the All God had to do, fixing, in virtue of, and nothing over and above locutions, the dependence associated with metaphysical ground is complete: if an entity is metaphysically grounded in some other entity or entities then, in the first instance, the latter serve as a complete basis for the existence and features of the former. 9 (In the second instance, of course, we can speak of a partial metaphysical ground.) Because, when an entity is grounded in some other entity or entities, the latter are metaphysically prior to, and carve nature closer to the joints than, the former, the dependence associated with metaphysical ground is asymmetric. 10 Finally, because 6. So, for example, Fine s 1994 account of ontological dependence, as a relation holding between essences of entities (where, e. g., singleton Socrates ontologically depends on Socrates, rather than vice versa), and his 2001 account of the in virtue of locution, as tracking a distinctively metaphysical explanatory relation between propositions, might be seen as different specifications of the intuitive characterizations. 7. As with, e. g., attempts to more specifically characterize grounding as relevant to the physicalism debates in terms of supervenience, realization, or other notions. 8. As do Schaffer 2009 and Rosen To allow that a complete ground might be smaller than a (relatively) fundamental base, we should specify that such a ground need not provide a basis for non-essential extrinsic features of an entity. 10. On the face of it, the supposition that grounding is asymmetric rules out cases of grounding that involve identity, if, for example, every mental state type is identical to a physical state type. One might drop the asymmetry requirement, not just to make sense of identity-based grounding but more generally to allow that the fundamental entities can ground themselves. Alternatively, one might locate the asymmetry at issue, not in the specific grounding relation itself, but in either intrinsic or extrinsic considerations involving the relata. So, for example, a type-identity theorist about the mental could maintain that the asymmetry of dependence is reflected in the broadly extrinsic fact that every mental state type can be identified with a physical state type, but not vice versa; or that the asymmetry of dependence is reflected in the broadly intrinsic fact that the physical state type to which the mental state type is the above locutions aim to characterize a fixing or obtaining relation between entities in the world, as opposed to representational or epistemic states, this dependence is metaphysical or ontological, as opposed to (merely) epistemological or formal/representational. While leaving open certain further details, a characterization of grounding as involving complete asymmetric ontological dependence, as informed by the intuitive locutions, is, I believe, sufficiently specific to fix ideas and to avoid any untoward equivocation in what follows. That said, in the course of what follows I will sometimes discuss two proposed criteria or marks of metaphysical grounding (or the related notion of comparative fundamentality), which have been commonly seen as legislating against the (relative) fundamentality of determinables. Neither criterion succeeds at providing an analysis of grounding/relative fundamentality, for reasons I ll substantiate down the line; but each has a certain prima facie (and one has a secunda facie) plausibility as indicating the holding of a relation of metaphysical grounding. As such, any case for the claim that determinables can be (relatively) fundamental needs to engage with these proposed criteria. The first criterion is in terms of asymmetric existential necessitation, or metaphysical supervenience, with the rough idea being that if some entity a asymmetrically existentially necessitates (provides a supervenience base for) some entity b, but not vice versa, then a is less fundamental than b (Russell 1918, Armstrong 1987). That asymmetrical necessitation is relevant to metaphysical grounding reflects the fairly common supposition that the fact of, if not the specific details concerning, such grounding is tracked by the holding of sufficiently strong (and asymmetrical) modal correlations. 11 The second criterion takes more fundamental/grounding entities to be more natural than the less fundamental entities they ground identical is an ontologically lightweight (e. g., lower-level relational, boolean, or mereological) combination of other physical state types rather than other mental state types. Nothing in what follows will turn on how exactly this issue is resolved. 11. The same supposition is at work in supervenience-based formulations of physicalism, as inspired by Davidson 1973; see, e. g., Van Cleve philosophers imprint 3 vol. 12, no. 4 (february 2012)

4 (Lewis 1986, Sider 1995, McDaniel 2009). The notion of naturalness, typically understood as primitive, is somewhat obscure. Most crucially, as I understand it, naturalness makes for objective (typically intrinsic) similarity; fundamental entities in particular, fundamental properties are perfectly natural in that entities having such properties are perfectly intrinsically similar in the relevant respect. Hence Lewis (1984) says, filling in the carved at the joints metaphor: Among all the countless things and classes that there are, most are miscellaneous, gerrymandered, ill-demarcated. Only an elite minority are carved at the joints, so that their boundaries are established by objective sameness and difference in nature. 12 [227] Along similar lines, Lewis (1986) says that sharing of the sparse (i. e., fundamental) properties sufficient to characterize things completely and without redundancy makes for qualitative similarity (60). That objective similarity is relevant to metaphysical grounding plausibly reflects that paradigms of fundamentality notably, certain particulars (e. g., electrons) treated by lower-level physical theory appear to exactly intrinsically resemble in certain respects (modulo any unanticipated deeper levels there might be). Both the basic characterization of grounding/relative fundamentality in terms of complete asymmetric ontological dependence (as informed by the intuitive locutions), as well as the two marks of grounding/relative fundamentality in terms of asymmetric existential entailment and naturalness, will play a role in what follows. To prefigure: Section 3 will be primarily devoted to arguing that in spite of appearances, these characterizations and criteria provide no reason to think that determinables could not be part of a (relatively) fundamental base, and some reason to think the contrary. 12. Sider (1995 and elsewhere) also characterizes grounding/relative fundamentality in terms of objective similarity. 1.3 Determinacy In asking whether a (relatively) fundamental base may include determinable entities, our primary interest is in whether grounding entities can be ontologically less specific than the entities they ground. We might think of entities that are determinable in the intended sense as leaving more open than more determinate entities, or as having ontological characterizations that are more general (less specific, more abstract) than those of more determinate entities. There are any number of relations that appear to link entities that are differently specific in such respects. To fix ideas, I will focus primarily on properties standing in the determinable/determinate relation. On the traditional understanding, determinable properties are less specific than their associated determinate properties. So, for example, mass is a determinable of/less specific than mass 1 kg; color is a determinable of/less specific than red; shape is a determinable of/less specific than rectangular; and so on. Determinates may themselves be subject to further specification, unless these are maximally determinate/specific. So, for example, red is a determinate of color, but a determinable of scarlet. There are, of course, various specific accounts of the determinable/ determinate relation (see Funkhouser 2006 and Wilson 2009 for discussion of some options). In what follows I will not presuppose any specific account of this relation, though I will sometimes mention a particular account by way of illustration. 2. Are determinable properties to be rejected or reduced? Why think that fundamental entities, if such there be, must be maximally determinate? One quick route to this conclusion involves rejecting determinable entities, understood as distinct from and irreducible to any determinate entities: if all entities are maximally determinate, then so will be any fundamental entities. I cannot do full justice here to the large literature bearing, directly or indirectly, upon the eliminability or reducibility of determinable entities (in particular, properties); and one dialectical strategy might be to assume that determinable properties irreducibly exist, and move on to considering philosophers imprint 4 vol. 12, no. 4 (february 2012)

5 whether, so understood, determinable properties might be (relatively) fundamental. 13 Still, since it is not uncommon to take determinable properties to be reducible or eliminable, it is worth sketching the main lines of argument in support of such positions, and one promising means to resistance. 14 We might start by observing certain prima facie reasons for thinking that determinable properties exist (again, as distinct from and irreducible to any determinate properties; I won t carry this qualification through). Experience provides one reason, in that we perceive objects as less than maximally specific: we experience determinable rather than maximally determinate shades of colors (as sorites phenomena suggest), and more generally our experience of features (textures, shapes) of middle-sized dry goods obviously glosses over the microphysical details. Perhaps the (instances of) properties perceived are really maximally determinate, and only perceptual features or modes of presentation are determinable; but features of perceptual experience are also aspects of reality, so the larger point remains. 15 Science also provides at least four prima facie motivations for positing determinable properties. First, many special-science entities appear to be characterized in terms of properties that are determinable in the relevant sense of being less than maximally specific. So, for example, the features of molecules relevant to chemical interactions abstract from the precise details of position and momentum of the constituent atoms; the features of aggregates relevant to thermodynamics and statistical 13. Another fairly common line of thought namely, that irreducible determinables are to be rejected because non-fundamental entities are to be rejected, and determinables are non-fundamental (see, e. g., Heil 2003) will be addressed in the course of this paper. 14. For fuller defense of taking determinable properties to irreducibly exist, see Wilson 2009 and How the prima facie appearance of perceptual indeterminacy is ultimately to be accommodated remains disputed. In any case, on many views in the philosophy of perception this appearance (either as involving perception of indeterminate entities, or as involving determinable perceptual modes of presentation of determinate entities) is arguably accommodated as genuine. See, for example, Campbell 2002, Martin 2004, Hellie 2005, and Brewer mechanics average over features of the lower-level entities composing the aggregate. Second, certain lower-level physical phenomena, including states of quantum indeterminacy and superposition, have natural interpretations as involving determinable properties. Third, the laws of physics appear to relate determinables mass, energy, and the like not determinates (much less maximally specific determinates). Fourth, the elimination or reduction of determinables is in tension with a principle of explanation pervasive in the sciences. As I noted in a different context: [Special science] entities are invoked in explanations, and on a plausible view of explanation (Garfinkel 1981, Batterman 2002, Woodward and Hitchcock 2003, Strevens 2004), a pervasive and important feature of good explanations is that they don t say too much. So, for example, in explaining the properties and behavior of a statistical-mechanical aggregate, one should cite only features that make a difference to the properties and behavior in question, omitting any features (such as the exact positions of the composing entities) that do not make a difference. This feature of good explanations itself needs explaining: Why does it make sense, as it so often does, to ignore details for explanatory purposes? That what is being explained involves entities whose ontological characterization omits irrelevant details [ ] allows a straightforward answer, that moreover provides an ontological ground for our epistemology a desirable result for the sciences, at least. The reductionist, by way of contrast, has no obvious explanation for explanatory relevance, much less one that provides a natural ontological ground for the associated epistemology. [Wilson 2010a, 307] There are various prima facie cases to be made, then, that determinable properties, understood as distinctively unspecific, in one or other fashion, are needed to make sense of a range of perceptual and scientific philosophers imprint 5 vol. 12, no. 4 (february 2012)

6 phenomena. Given these and other prima facie reasons for admitting determinable properties, why think that only maximally determinate properties exist? To start, it is sometimes claimed that the posit of determinables is unnecessary, since determinates can do anything that determinables are supposed to be able to do. A full defense of this claim would need to show that the aforementioned phenomena supporting the posit of determinable properties can be accommodated by reference just to maximal determinates. I am inclined to think that there is little hope that certain of these phenomena (e. g., perceptual determinables) can be treated in determinate terms, and that even where this is possible, the resulting account will lack the power and elegance enabled by the straightforward posit of determinables. Rather than engage with available attempts at reconstruction, however, I want to identify and sketch a response to what seems to me to be the main concern, and associated dilemma, driving the rejection of determinables, at least in a context where broadly scientific properties are at issue. The concern, in the first instance, is that the powers associated with determinate properties already suffice to do any causal work that determinable properties are posited as doing, such that the further posit of determinables would lead to ontological profligacy. (As I ll expand on below, the notion of power here may be understood throughout in ontologically lightweight terms, as tracking which effects the possession of a property may, perhaps only contingently, contribute to causing.) So, for example, Gillett and Rives (2005) say: [P]ositing instances of determinate properties offers the best explanation for the causal relations we observe in the world [ ] For example, we can best explain the motion of particles by taking some other microphysical particle to have the powers contributed by the property of being a charge of +1.6 x coulombs. [ ] Should we also accept that there are instances of determinable properties corresponding to predicates such as is colored or is charged? [ ] There is a clear concern that it is ontologically profligate to take two properties to be contributing causal powers, a determinable and its determinate, where one, the determinate, would apparently suffice. [487] The initial concern about profligacy can be seen as giving rise to a dilemma for the proponent of determinable properties, one horn of which appears to support reducing such properties to determinate properties, and the other, eliminating them altogether. On the one hand or horn, the proponent may maintain that determinables have powers additional to those associated with their determinates. But insofar as determinables evidently do not have any powers different from their determinates (being red doesn t cause anything that being scarlet doesn t cause, and so on), taking this horn appears to entail that determinable instances systematically causally overdetermine the effects brought about by their associated determinate instances. This concern is a special case of Kim s exclusion argument for the reduction of supervenient properties; the corresponding conclusion is that avoiding the threat requires taking determinables to be reducible to determinates that is, identical to some (perhaps complex) determinate property. On the other hand or horn, the proponent of determinables may avoid ontological profligacy and causal overdetermination by maintaining that every power of a determinable property is identical with a power of its associated determinate properties, at the token and perhaps also type levels. But in that case one might wonder why we should take determinable properties to exist at all. As Gillett and Rives (2005) say: [M]any philosophers [ ] accept what Armstrong calls the Eleatic Principle [stating:] Everything that exists makes a difference to the causal powers of something. (Armstrong 1997, 41 2). If determinable properties do not contribute causal powers to individuals, nor otherwise determine such powers, then it appears that they fail the Eleatic Principle and hence do not exist. [487] philosophers imprint 6 vol. 12, no. 4 (february 2012)

7 Again, there is a large literature on all this; here I will just sketch my preferred response to this cluster of powers-based concerns (see Wilson 2011 for a fuller defense). The main idea, as per what is sometimes called the subset view or the the subset strategy (see Wilson 1999, Shoemaker 2001), is to take instances of determinable properties to have a proper subset of the powers of their associated determinate instances namely (at most), those powers shared by their associated determinates. (Importantly, nothing in the schematic application of this strategy requires endorsing any controversial views concerning the nature of properties or powers; as Gillett and Rives note, the strategy is applicable even if properties are only contingently associated with powers; more generally, as I argue in Wilson 2011, even a contingentist categoricalist Humean can implement the subset strategy.) As such, by Leibniz s law, a determinable property is not identical to any associated determinate property. Nor is a determinable property identical to any more complex determinate property, involving (to consider the most salient alternatives) either a disjunctive property with the associated determinates as disjuncts, or an existential or second-order property of having some associated determinate property; for any instance of such a complex property will be an instance of a determinate property, having more powers than the associated determinable property instance. In general, then, determinable properties are not reducible to any (complex or non-complex) determinate properties. The subset view appears to appropriately negotiate the above dilemma for the proponent of determinables. Since every power of a determinable instance is numerically identical to a power of its associated determinate instance, the threat of overdetermination is blocked: on any given occasion whereby a determinable instance enters into producing an effect, this production involves the manifestation of numerically the same power as that had by its determinate instance. But in that case, won t determinables, on the subset view, fail to satisfy the Eleatic principle, in failing to make a difference to the causal powers of something? No, for there are two ways in which a property might make such a difference. One way the usual way, presupposed by Kim, Gillett and Rives, and others is for the property to have a new power a power that other properties do not have; here properties may intrinsically contribute to a difference in powers, by being associated with distinctive individual powers. To be sure, determinable properties, on the subset view, do not make this sort of difference. But there is another way for a property to make a powers-wise difference; namely, in being associated with a distinctive set of powers, or power profile; here, properties may extrinsically contribute to a difference in powers, by being associated with a distinctive set of powers. Determinable properties, on the subset view, do make this sort of difference. In particular, at least sometimes, the distinctive power profile of a determinable property may be relevant to the production of a given effect, as is reflected in proportionality and difference-making considerations (see, e. g., Yablo 1995). (In such cases, in my view, there is no need to choose which of the determinable and determinate are most appropriately deemed the cause; all that is required to accommodate the Eleatic principle is that determinables may be distinctively efficacious.) Such considerations provide a principled basis for supposing that determinable properties do satisfy the Eleatic principle and so are not good candidates for elimination. The subset strategy thus provides one way, perhaps among others, via which a proponent of irreducible determinables may accommodate the perceptual and scientific appearances without inducing overdetermination or courting elimination. More generally, given that there are principled and unproblematic means of accommodating the prima facie need for determinables, it is not profligate to posit their existence. 3. Are determinable properties non-fundamental? On the face of it, determinable properties exist; and the usual reasons for eliminating or reducing such properties to determinate properties can be resisted. But to return to the question of grounding one might suppose that this is a case of winning the battle while losing the war; for the distinctive characteristics of determinables which support taking them at ontological face value most importantly, their lack philosophers imprint 7 vol. 12, no. 4 (february 2012)

8 of specificity seem also to indicate that determinable properties are metaphysically grounded in, hence less fundamental than, more determinate entities. First, consider the criterion of grounding as involving asymmetric necessitation of grounded by grounding entities (conversely: asymmetric metaphysical supervenience of grounded on grounding entities). On a traditional understanding (see Johnson 1921, Funkhauser 2006), determinate properties necessitate their associated determinables, but not vice versa: from the fact that a determinate property is instanced, it follows that the associated determinable properties are instanced, but the mere fact that a determinable property is instanced leaves open which of its associated determinates is instanced; and it is thanks to the distinctively unspecific nature of determinables that this is so. Even supposing that this asymmetrical relationship needn t be seen as indicating that determinable properties are reducible to determinate properties, one might still naturally suppose that it signifies that determinables are metaphysically grounded in/less fundamental than their associated determinates. As Armstrong puts it: A point to be taken very seriously is that because determinates entail the corresponding determinable, the determinable supervenes on the determinates, and so, apparently, is not something more than the determinates (1997, 50). Second, consider the understanding of grounding according to which more fundamental properties are more natural, in making for greater objective resemblance between their possessing particulars, than less fundamental properties. This conception appears to deem determinables less fundamental than determinates: because determinables are less specific than their associated determinates, particulars sharing a given determinate property will be more objectively similar in the relevant respect than will be particulars sharing an associated determinable property. So, for example, scarlet particulars will be more objectively similar than red particulars in respect of color, and positively charged particulars will be more objectively similar than charged particulars along the relevant dimension. Third, consider the intuitive all God had to do characterizations of grounding, according to which fundamental entities fix all the rest; and the associated conception of grounding as involving complete asymmetrical ontological dependence. (Here the notion of fixing and associated conception of grounding is understood in terms stronger than mere asymmetric necessitation, with the idea being that when some goings-on or associated facts fix some other goings-on or associated facts, the former in some sense constitute the latter.) Such an intuitive understanding again appears to support taking determinate properties to be more fundamental than determinable properties. Hence Rosen (2010) says: Consider a bright blue ball. The fact that the ball is blue is presumably not a brute fact. It might be grounded in microphysical facts about the ball s surface, or in facts about its dispositions to reflect light. But let us suppress the scientific subtleties and pretend that the colors are simple properties with no deep nature. Still, the fact that the ball is blue is not a brute fact. Suppose that our ball is a uniform shade of blue let it be cerulean. Then it seems quite natural to say that the ball is blue in virtue of being cerulean. Another ball might be blue for a different reason: it might be blue in virtue of being cobalt blue. If we ask, What is it about these balls that makes them blue?, we get different answers in the two cases. And this suggests a general principle: Determinable-Determinate Link: If G is a determinate of the determinable F and a is G, then [Fa] [Ga] [the fact that a is F is grounded in the fact that a is G]. [126] Such a line of thought is indeed quite natural, especially if (as we, though not Rosen, are supposing) determinables are irreducible. After philosophers imprint 8 vol. 12, no. 4 (february 2012)

9 all, it seems that once the specific, or determinate, facts are fixed, all the more general, or determinable, facts are thereby fixed, with the latter being something like ontologically real abstractions from the former. By way of contrast, once the determinable facts are fixed, the more specific, or determinate, facts are not fixed. The latter, more specific facts concerning determinate properties, in particular require existential witnesses, so to speak; and the facts about determinable properties cannot, it seems, do the job. In what follows I will address these three objections, in order (as above) of increasing seriousness. 3.1 The argument from asymmetric necessitation Let us grant that determinates asymmetrically necessitate determinables, in the sense that the existence (instantiation) of a determinate property necessitates the existence of a determinable property; equivalently, that the former properties metaphysically supervene on the latter. Does this establish that determinables are less fundamental than their associated determinates? No; for as I ll now argue, the holding of such a necessitation relation fails, across a wide variety of cases, to be an accurate barometer of relative fundamentality. As such, there is no independent reason to think that this criterion is accurately applied in the case of determinables and determinates. Indeed, it is often supposed that the holding of a relation of asymmetric necessitation/metaphysical supervenience is sufficient to guarantee that the necessitated or supervening entity is nothing over and above the necessitating or subvening entity. Hence Armstrong says: What supervenes is no addition of being [ ] The supervenient is ontologically nothing more than its base (1997, 12 13). A similar supposition is at work in supervenience-based formulations of physicalism (see note 11), which aim to characterize the relation between strictly physical entities and other entities in modal correlational terms that are strong enough to guarantee nothing over and aboveness of the latter vis-à-vis the former, while being abstract enough to accommodate the irreducibility of the latter to the former. Though common, the supposition that asymmetrical entailment/ metaphysical supervenience suffices to establish a grounding relationship is incorrect. As a merely correlative notion, even asymmetric metaphysical supervenience is compatible with a supervenient property s being something more than the base entity. The point can be colorfully made by appeal to a version of Malebranchean occasionalism: let God bring about mental properties upon the occasion of certain physical properties, and let God act consistently in every possible world. Then mental properties would supervene with metaphysical necessity on physical properties, but the former would clearly be an ontological addition to the latter. More naturalistically, it is compatible with the strong emergence of mental properties on which these are just as fundamental as physical properties (since, e. g., constituted by the coming into play of a new fundamental interaction at the level of complex mentality) that emergent mental properties be metaphysically necessitated by physical properties, for either philosophical reasons (e. g., endorsement of a causal theory of properties) or scientific reasons (pertaining to the unity of fundamental interactions). 16 These cases show that asymmetrical necessitation is compatible with over and aboveness, and indeed with the fundamentality of the necessitated entity, in cases where the supervenience base is merely a metaphysically necessary precondition for the supervenient entity. To be sure, determinables and determinates aren t plausibly taken to stand in any kind of broadly emergent relationship; rather, the determinable/determinate relation is very intimate though not identity (as per the rejection of reducibility) nonetheless such as to block robust emergence. But even in cases of intimate relation, asymmetrical necessitation fails as a criterion of non-fundamentality. Consider, for example, a theistic metaphysics according to which we live and move and have our being in that is, are grounded in God. On such a view, I am non-fundamental, but I asymmetrically necessitate God: my 16. See Wilson 2005 for details. philosophers imprint 9 vol. 12, no. 4 (february 2012)

10 existence entails God s existence, but assuming that God has a choice about who or what to create, God s existence does not entail my existence. This case shows that asymmetric necessitation is insufficient for non-fundamentality, even in cases of intimate relation. It also shows that such necessitation is not necessary, as do cases where grounding and grounded entities necessitate each other, as in Fine s (1994) case involving Socrates and the singleton set of Socrates, and any case in which a composed, presumably non-fundamental entity (e. g., a molecule) has a single (e. g., atomic relational) realizer. 17 Given such a wide range of false positives and negatives, the proponent of determinables has good reason to deny that the asymmetric necessitation of determinable by determinate properties provides any reason to think, much less establishes, that determinables are grounded in determinates. 3.2 The argument from naturalness Next, consider the argument from naturalness, according to which determinable entities are less objectively similar (here and elsewhere: in the relevant respect) than determinate entities. 17. It may be worth mentioning here the related case of composition discussed by Ellis (1999, 66), which he takes to indicate that in cases of asymmetric necessitation, the necessitated rather than the necessitating entity is more fundamental. If this were correct, then the seeming necessitation of determinable by determinate properties would provide a quick route to the conclusion that determinables may be more fundamental than determinates; however, Ellis s case does not succeed. In his case, methane molecules necessitate the existence of hydrogen and carbon atoms ( the molecules could not exist if these atoms did not exist ), but not vice versa ( the atoms could exist, even though the molecules did not exist ). He concludes that the usual connection between ground and necessitation is reversed; then applies the result to properties: The more general property kinds (namely, quantities and other determinables) are ontologically more fundamental than the more specific (67). But the asymmetry at issue in Ellis s case holds only for the individual atoms, which are at best partial grounds of the molecule. If one rather considers the atomic relational entities (consisting of the hydrogen and carbon atoms standing in the bonds associated with methane molecules) which provide complete grounds for methane molecules, there is no longer an asymmetric entailment running from non-fundamental molecules to (the relevant) atomic entities. To start, note that being such as to make for greater objective similarity is prima facie problematic as a criterion of (relative) fundamentality, in that its satisfaction is compatible with (relative) non-fundamentality. Consider a strangely shaped boulder or other composed entity; and now suppose that another boulder of exactly the same shape exists. The associated macro-shape property makes for perfect objective similarity, but by plausible assumption there is no case here for fundamentality of either the particulars or properties involved. To rule out the latter sort of case, one might specify that the natural properties are those making for perfect similarity among the (relatively) fundamental entities; but then naturalness fails to provide any independent criterion of (relative) fundamentality. 18 We can get some traction here, however, by taking ourselves to have an intuitive grasp on what it is for some collection of entities to serve as a basis for all else; and (extending to a fundamental base the virtue of simplicity as well as strength) supposing that entities in such a base would not be characterized in gerrymandered, conjunctive, or disjunctive terms (which broadly Boolean combinations are typically, though not always, anti-correlated with objective similarity). It is, after all, quite plausible that disjunctive properties (and associated possessors) such as being a raven or a writing desk are unsuited to be part of a fundamental base, and similarly for the highly conjunctive macroshape property (and associated possessors) mentioned above. Taking a cue from the need to rule out such properties and associated entities as fundamental, one might take the perfectly natural properties to be those whose possession makes for complete objective similarity in a maximally non-gerrymandered way. From this perspective, comparative naturalness (making for greater objective similarity) appears to be a good criterion of (relative) fundamentality of properties; and 18. One might also suppose that satisfaction of the criterion is not necessary for (relative) fundamentality, in that entities in a fundamental base needn t have anything in common: consider a world where the only fundamental entities are an immaterial ghost and a concrete red cube. Presumably, though, the notion of being such as to make for objective similarity can be understood in modal terms. philosophers imprint 10 vol. 12, no. 4 (february 2012)

11 indeed, in what follows I propose to accept comparative naturalness as a strong indicator of the presence of a grounding relation. Even so, a criterion of naturalness does not, in fact, indicate that determinables are less fundamental than their associated determinates. Consider a world where the fundamental particulars are sorted into sets, where members of each set perfectly objectively resemble in two maximally determinate respects. More specifically: the particulars in the first set each have mass m 1 and charge c 1, and the particulars in the second set each have mass m 2 and charge c 2. Here one can reasonably deny that properties m 1, m 2, c 1, and c 2 track the only fundamental natural joints on the scene. This is because, notwithstanding that having mass m 1 and having mass m 2 track distinct, perfectly objective similarities among their possessing particulars, the properties themselves are similar, in both being or bestowing specific masses; and likewise for having charge c 1 and having charge c 2. As such, one can reasonably maintain that among the natural joints to be carved here are those associated with the more general properties having mass and having charge, respectively. Indeed, to the extent that Lewis and other proponents of naturalness suppose (robust emergentism aside) that physics is engaged in identifying the relatively fundamental properties, it is worth noting that, faced with similar determinate commonalities among subatomic particulars, scientists do not rest satisfied as having uncovered the salient joints in nature, but rather direct massive theoretical and experimental efforts towards trying to identify general underlying properties that would unify these determinate commonalities, notwithstanding that particulars having these more general properties (e. g., having mass) will not be perfectly objectively similar in the relevant respect. Given these considerations, we might go in either of two directions, so far as understanding the link between comparative naturalness and (relative) fundamentality. First, we might reject the claim that a property is more fundamental to the extent that having it makes for greater objective similarity among its possessing particulars. Second, we might retain the connection between fundamentality and objective similarity, but allow that when considering objective similarities relevant to fundamentality, we must consider not just objective similarities between (concrete) particulars but also objective similarities between properties themselves so that, for example, the property of having mass must be admitted into the fundamental base as required to accommodate the objective similarity between having mass m 1 and having mass m 2. Supposing we take this route, note that there is no in-principle barrier to diverse mass properties perfectly resembling one another in respect of bestowing mass. More generally, on an appropriately ecumenical understanding of what it is for natural properties to make for objective similarity, there is a case to be made that determinable properties are as fundamental as associated determinate properties, in making for perfect objective similarity, in the relevant respect, among these determinates. 19 Either way, it is left open that determinables, such as having mass, might be part of a (relatively) fundamental base; so considerations of naturalness or objective similarity do not, after all, support rejecting determinables as (relatively) fundamental. That said, as indicated above, I think that we do well to go the second route and continue to accept naturalness, understood appropriately generally, as a good criterion of (relative) fundamentality. 3.3 The argument from fixing I turn now to addressing what seems to me to be the most serious objection to taking determinables to be (relatively) fundamental, which objection relies on the intuitive supposition that once the specific/ determinate facts are fixed, all the more general/determinable facts are thereby fixed, with the latter being something like ontologically real abstractions from the former. (Again, the notion of fixing and associated conception of grounding is here understood in terms 19. Indeed, if we allow that the range of cases of objective similarity (involving both particulars and properties) is relevant to application of the criterion, one might maintain that determinables are more natural than associated determinates, overall, in making for objective similarity among a wider range of phenomena (namely, all determinate instances) than individual determinates. But (as a referee pointed out) this stronger claim is not needed for larger purposes of my argument. philosophers imprint 11 vol. 12, no. 4 (february 2012)

12 of something like constitution as opposed to mere asymmetric necessitation.) I will argue that this supposition is incorrect, in being based in a tacit assumption that may clearly be denied, and the denial of which provides positive motivation for countenancing (relatively) fundamental determinables. In brief, the tacit assumption is that a (relatively) fundamental base need only ground the non-modal facts at a world. Ellis (1999) notes this tacit assumption when he says, concerning Armstrong s investigations into what is ontologically fundamental, that he appears to assume that everything that is the case about the world is the sum over all times of everything that is the case at any one time. Indeed, sometimes the assumption is fairly explicit: The project of providing a minimal ontological base is part of the project of providing an ontological assay. The goal of an ontological assay is to characterize the contingent basis for all contingent truths. [Schaffer 2004, 95] Tacit or not, only if this assumption is correct does the impression that instances of determinates ground instances of determinables withstand scrutiny. To see that this is so, we can start by observing that, as all but eliminativists agree, it is characteristic of determinables that they admit of multiple determinations. Now consider a given instance of a determinable property say, that very instance of red that is determined by an instance of scarlet. I am sometimes inclined to think that there is no in-principle problem with allowing, of a given instance of red, that it (that very instance) might have been differently determined. But even if determinable instances (or some of the particulars that instance them) are not themselves modally flexible in this way, in any case it remains that determinable instances are of types that are so flexible. It is a fact about that very instance of red, for example, that it is of a type whose instances might be differently determined say, by an instance of crimson. More generally, it is a constitutive modal fact about every determinable instance that it is of a type whose instances might be differently determined. But no specific determinate instance seems suited to ground this fact about its associated determinable instance. How could it, given that the ground for this modal fact involves reference to multiple determinates, all but one of which the specific determinate, whether instance or type, not just actually but necessarily excludes? At best, the determinate instance seems suited to ground certain non-modal facts about the determinable instance most promisingly, that it is actually determined as it is. Left ungrounded by the determinate instance is the constitutive modal fact about the determinable instance, that it is of a type that might be differently determined. Here is where the tacit assumption is needed, if the usual claim that determinate instances ground determinable instances is to be maintained. If a (relatively) fundamental base need only ground the non-modal facts at a world, then the failure of determinate instances to ground certain modal facts about associated determinable instances will not impugn the supposed grounding of determinables by determinates. It is clear, however, that the assumption is reasonably denied. Again, it may be that determinate instances metaphysically ground certain non-modal facts about their associated determinable instances. But modal facts and features about entities at a world are also part of the world s inventory! A supposed ground for some entity which failed to provide a metaphysical basis for modal facts constitutive of the entity would be an incomplete ground, at best. Constitutive modal facts about determinables, in particular, also need a ground, which determinates, it seems, are not suited to provide. Because modal facts are among the world s inventory, and because some such facts about determinable properties are not suited to be grounded by their associated determinates, the usual assumption that the determinate facts fix the determinable facts, but not vice versa, appears to be incorrect (an appearance I will substantiate, below). On philosophers imprint 12 vol. 12, no. 4 (february 2012)