Whenever a material thing has parts, those parts are located where that thing is.Footnote ¹ This is a necessary truth, and needs explaining.Footnote ²

Two kinds of explanation might be put forward. The first goes like this: the necessary connection between the location of a whole and the location of its parts holds because the location of the whole is nothing but the collective location of its parts. The second style of explanation goes like this: the connection holds because what it is for a material whole to have something as a part, is (perhaps among other things) for the whole to contain the part.Footnote ³

The first line is a ‘partist’ view.Footnote ⁴ It takes the mereological part-whole relation as prior in the order of metaphysical explanation to the location of material wholes. The second is ‘locationist’. It takes the location of compounds to be prior in the order of metaphysical explanation to the mereological relations in which they stand.Footnote ⁵

I read Hugh Mellor, in his stimulating paper “Microcomposition”, as a locationist. I aim to give a qualified defence of the version of locationism (the “working part” view) that he there outlines.

The paper is divided into nine sections. In 1–3, I outline the background, and look at varieties of partism and locationism, as well as rival approaches, prominent among them the ‘no analysis’ view. In sections 4 and 5, I discuss reasons for dissatisfaction with the no analysis and partist views. In section 6, I look at the simplest form of locationism: one that simply identifies parthood with the relation of containment. In section 7, I critically examine Mellor's more sophisticated version of locationism, which requires, in addition to the containment condition, that any material part of a thing be what he calls a ‘working part’. In section 8, I give more theoretical grounds for favouring something like the working parts condition over the pure containment proposal. Finally, in section 9, I briefly contrast the locationist project that emerges with a best representative of the view that material wholes are ‘nothing but’ their parts.

1 Fundamental Properties vs. the Rest

The phrases ‘nothing but’ and ‘what it is to be’ in the characterization of partism and locationism are vague. To the extent that this gives neutrality between various ways of thinking about these pivotal metaphysical notions, that is an advantage. But their crucial role should be noted: without appeal to such notions—or the related ‘constitutes’ ‘analyzes’ ‘prior in the order of metaphysical explanation’—it would be hard to say what the difference is between the locationist and partist. After all, nothing we've seen as yet has given us reason to think these theorists need to disagree about what is part of what, and what is located where.

It will be useful to have a particular model of metaphysical explanation to focus discussion, so I spend a while describing one. Lewis (Reference Lewis1983) argued that there is an objective distinction between a range of ‘elite’ properties (perhaps including fundamental physical properties such as mass and charge) and merely ‘abundant’ properties. Abundant properties come cheap: almost every meaningful predicate can be taken to stand for one: so being grue, for example, is a perfectly good, though merely abundant, property. But elite properties are rare: on one conception, only the most fundamental properties of a completed microphysics will have this status.Footnote ⁶ The metaphysics of these elite properties is a topic in itself. Lewis (Reference Lewis1983) himself describes several versions, ranging from a realist ontology of Universals, to a position taking eliteness itself as a primitive distinction between properties.Footnote ⁷ However it is cashed out, the elite/abundant distinction proves invaluable. Lewis, for example, appeals to it in giving accounts of laws of nature, of counterfactuals, of dispositions, of causation, of intrinsicality and duplication, of mental and linguistic content, and of physicalism itself.

What can we say about the elite properties themselves? In common metaphors, the elite properties are supposed to describe ‘the furniture of the world in the most fundamental terms’ and to ‘carve nature at its joints’. Minimally, the pattern of instantiation of the elite properties at a world should serve as a supervenience base for the total qualitative state of that world.Footnote ⁸

For the purposes of this essay, I will draw no distinction between any of the following: ‘elite properties’, ‘genuine properties’, ‘metaphysically primitive properties’, ‘fundamental properties’, ‘natural properties’, ‘perfectly natural properties’.Footnote ⁹ The terminology should also be understood to leave open which properties turn out to be elite: there is no initial assumption that they are physical properties, nor that they figure in empirical science in an interesting way. All that is left open for further discussion. Theorists agreed about the framework may at this point diverge: Lewis held the substantive view that the elite properties instantiated at the actual world are microphysical properties, and the only elite relations are spatio-temporal. Mellor (Reference Mellor1991) holds that the elite properties play a distinctive role in natural laws: if there are genuine non-microphysical laws, there are non-microphysical elite properties.Footnote ¹⁰

2 Locationism and Partism

Both locationists and partists, we shall assume, take location as an elite relation.Footnote ¹¹ The latter, however, make do with primitive location relating only mereologically simple material things to space-time regions. When we turn to ordinary thought and talk, ‘is located at’ will express a merely abundant relation. It will be true, of course, that I am located at the region I occupy; but this will be made true by instances of the elite location relation involving my simplest parts.

The situation is reversed when it comes to mereological relations. Both can believe in a primitive parthood relation.Footnote ¹² But the partist believes that this elite relation holds between material things and their parts, whereas the locationist (assuming they believe in it at all) think it holds only between non-material things: perhaps space-time regions, perhaps between states of affairs and their constituents. Just as the partist owes a story of what makes-true location-talk in application to macro material things, the locationist owes a story about what makes-true talk of material things being parts of one another. We shall consider some variants of each position in turn.

The locationist thinks that material things are primitively located, but not primitively part-whole related. They are not error-theorists about mereological talk: the leg is part of the table.Footnote ¹³ But what is it about the leg and the table that makes this the case? The obvious resource, for the locationist, is the relationship of being contained within, where a is contained in b iff a's location is a subregion of b's location.Footnote ¹⁴ An extreme version of locationism will say that containment is a sufficient, as well as necessary, condition for parthood. More moderate versions will deny this.Footnote ¹⁵

A radical locationist view (not Mellor's) is that of the supersubstantivalism. This theorist says that location is simply identity: material objects just are space-time regions. That is not to say that every space-time region counts as a material object, nor that every instance of subregionhood between space-time regions should count as a case of material parthood.Footnote ¹⁶ So even the supersubstantivalist need not be an extreme locationist.Footnote ¹⁷

Mellor's locationist view, to be discussed more extensively below, doesn't take the extreme form. Rather, parthood is constituted by containment together with something else: Mellor aims to cash out the ‘something else’ in causal terms. So the view is that things only get to be parts of a whole in which they are contained if they are, in Mellor's phrase, working parts of that whole.

Partist views likewise come in various flavours. The basic idea is to take the location of some things as primitive: say, the locations of subatomic particles.Footnote ¹⁸ Fusions of such entities are located, but not primitively located. Again, we can hope for illumination about the conditions under which it is true to say that a compound object is located at a given region. The most obvious way to do this is simply to say that what it is for a mereologically complex thing x to be located at a region R is for R to be the sum of the regions at which x's simple parts are located.

However this is an extreme view of the matter. Suppose that my simple parts are all point particles. If my body is the sum of such point particles, then my body will occupy a scattered region which simply consists of finitely many points at which the particles are located. Such a view doesn't sit well with the folk understanding of the location of things like me. It seems natural to take me to occupy a larger space than that: for my body to occupy a region with some positive volume, for example.

Extremists can defend their position by distinguishing being located at a region from dominating that region.Footnote ¹⁹ Something dominates a region, roughly, if it causally excludes a wide enough range of objects from occupying that region. So my body dominates a region of finite volume ‘where I am’ in virtue of causally excluding pens, thimbles, cricket balls and the like from being located there. Extremists may suggest that—at least in the case of macro-objects— folk thought about location tracks domination rather than location proper, thus ‘explaining away’ apparent oddities in their view of locations.Footnote ²⁰

Since we're not taking location of compound things as fundamental, one might think that the extremists' ‘strict location’ is a needless detour. Why not simply say that the location of a macroscopic object is the region that it dominates? We'll have to be sure that the relevant sense of ‘domination’ of a region can be spelled out without appeal to the location of the whole, and it may be to some extent vague and context sensitive. But it is not implausible that this could be done, nor in this setting does its vagueness or context sensitivity seem worrying.

3 Rival Views

Up to this point, we have been talking as if we were faced with a choice between analyzing mereological notions in terms of location, or vice versa. But these options aren't exhaustive.

The most obvious rival view would have it that neither the material part-whole relation nor the location of composites should be analyzed (even in part) in terms of the other. In the terminology introduced earlier, perhaps both location and parthood are elite relations; and further, fundamental parthood relates the chair to its legs (contra the locationist view), and fundamental location relates the chair to a—perhaps gappy—chair-shaped region of space-time (contra the partist view). Call this the ‘no analysis’ position.Footnote ²¹ This last view deserves serious consideration. I'll examine an argument against it shortly.

There are two interesting positions that I'll mention in passing where relevant, but won't focus on. Both threaten a somewhat radical metaphysics, but (partially in virtue of this) deal very nicely with the puzzles to be presented.

The first radical view that evades the puzzles here formulated is that of the microphysical mereological nihilist: who not only refuses to include macro-location as an elite relation (with which the locationist can agree) but also maintains that no material thing exists except for the smallest particles of fundamental physics.Footnote ²²

The second radical view is that of the mereological logicist: someone who thinks of parthood as a logical relation. One version of this view says that composition is identity: If the fusion of some things is a, then those things are collectively identical to a. The view has radical implications. On the side of logic, identity becomes a many-many relation and the logic of plurals must be revised.Footnote ²³ On the side of metaphysics, it is arguable that mereological essentialism (each thing has its parts essentially) and the even weirder principle of mereological sufficiency (things have their fusion essentially) follows.Footnote ²⁴

For the time being, I set aside both mereological logicism and mereological nihilism.

4 Explaining Necessities

There are three positions to be considered: the mereology first view whereby location of a whole reduces to (among other things, perhaps) the locations of its simple parts; the location first view, whereby parthood reduces to (among other things, perhaps) containment relations among the locations of the relata; and the no analysis view, whereby neither parthood and location features in an analysis of the other.Footnote ²⁵

The case starts at the observation with which we began this paper. The following is a necessary truth:

If the no analysis view were correct, this necessary truth would appear to be brute, in the following sense: it concerns the connection between two fundamental properties (location and parthood). It is not an instance of a logical truth, given that we've discarded mereological logicism for the moment. But it is a necessary truth.

Contrast the rival positions. If the locationist view is accepted, then the proposition is not yet fully analyzed: it is not yet expressed in ‘fully elite’ terms. In fully elite terms, reference to parts will disappear in favour of reference to relations among the locations of things (and perhaps extra conditions C). What we end up with is something tautologous:

In short, the locationist can reduce the datum with which we started—the necessity of the location-parts connection—to the necessity of a tautology. The partist can do something similar, replacing unanalyzed appeal to the location of a composite object with reference to the locations of the parts of that thing, again reaching something tautologous:

Either of these, I claim, would be an explanatory advance. It is not that the necessity of tautologies is itself explanatory bedrock. But presupposing that a theory of modality by itself explains at least the necessity of logical truths is an extremely minimal assumption, and makes it legitimate for us to ‘pass the buck’ of explaining such necessities to that theory.Footnote ²⁷ Of course, it may be that the one true theory of modality will explain, all by itself, why the parts-location principle is necessary.Footnote ²⁸ But one cannot assume that the theory of modality will provide such resources. So one cannot pass the explanatory buck–if we are to claim that a theory of modality can explain our datum, we have to indicate how this can be. The unsupplemented no analysis view, by contrast with its rivals, leaves us with modal mystery at the most basic level.

A defender of the no analysis view might respond in a number of ways. A first option is to make a case that everyone is committed to relevantly similar ‘mysteries’, so that no new explanatory debt is incurred.Footnote ²⁹ A second is to take up the burden of developing a theory of modality that is designed to explain how the location-parts link can be necessary.Footnote ³⁰ A final option is to accept the modal mystery as a cost, but claim it to be outweighed by compensating benefits.

The first option might seem the most immediately attractive. After all, post-Kripke orthodoxy warns us against thinking of logical or a priori truths and necessary truths as marching in step. Let us look closer at the Kripkean (putative) necessities. One class includes such putative necessary truths as: “Socrates is human”, “this table is made of wood” and “Philip is Charles' father”: the necessity of kind-membership, of constitution, and of origin. And perhaps we can find examples of this kind involving elite vocabulary: “Sparky is an electron”, say.

Even if we accept these as necessary truths, there is a tradition of looking for illuminating explanations of the source of such de re necessities. In a deflationary spirit, Lewisian counter-part theory offers a semantic explanation of how such de re necessities emerge.Footnote ³¹ The putative de re necessity that Socrates was necessarily human might first be reduced to the claim that all (possible) counterparts of Socrates are human. Secondly, for something to be a counterpart of a thing it must be similar in the contextually relevant sense to that thing. Third, the contextually relevant sense of similarity in this instance requires that the two things share the same kind. In the end, therefore, the de re necessity reduces to something that follows tautologously from Socrates being human: that all possible things that are similar (minimally in that they are of the same kind as Socrates) are human.Footnote ³²

So the demand for explanation of non-logical necessities is not inconsistent with Kripkean necessities: it merely imposes a (fairly reasonable) constraint on that debate. Notice that the non-logical necessity facing the no analysis view is de dicto, so the strategies for explaining away non-logical de re necessities are unlikely to help.

Some Kripkean necessities demand a different sort of explanation, however: paradigmatically, the putative necessary truth that Hesperus is Phosphorus, and that everything made of water is made of H2O.Footnote ³³ But recall that our concern was with non-logical necessary truths stated in fully analyzed, elite terms. We may assume that vocabulary would not have two names for the single thing—Venus—nor would it have the predicate ‘is water’ where (ex hypothesi) this can be analyzed in a complex predicate involving Hydrogen, Oxygen, and bonding relations.

So, absent further explanation, it looks like nothing in the Kripkean canon prepares us for the sort of brute necessity to which the no analysis view is committed. And, indeed, the felt need for explanation in the Kripkean cases (and the prospects of doing so) strengthen the case that an explanation of the location-mereology link is required.

The case to this point has involved no great theoretical commitment, simply appealing to certain explanatory burdens. There is a more theoretically loaded way of arguing that the no analysis view is committed (absurdly!) to denying the necessity of the inheritance of location. This is explored in recent work by Raul Saucedo (forthcoming) and Jacek Brzozowski (forthcoming). The idea is to appeal to (something like) recombination principles, which say, roughly, that for any possible pattern of instantiation of a primitive property P and any possible pattern of instantiation of a distinct primitive property Q, the two patterns of instantiation are compossible. It is an articulation of the idea that the elite properties should be independent of one another.Footnote ³⁴ If the case against no analysis can be reinforced by appeal to principles that play a central role in the metaphysics or epistemology of modality, that would of course be a welcome result for me. But the case from unexplained necessities against no analysis does not rest on it.Footnote ³⁵

5 Generalizing the Argument

It is natural to think that the argument from modal mystery against the no analysis view will generalize to afflict the partist and locationist views.

The partist distinguishes between elite location (e-location), enjoyed by simples alone, and abundant location (a-location) which all material things possess. But is it necessary that only simples are e-located? If so, then the following looks to be a brute necessity:Footnote ³⁶

On the other hand, if compound things can be e-located, then we should ask whether the e-locations of a things parts constrain its e-location. In particular, is the following necessary?

On the one hand, if it is necessary, this would again count as a brute. But on the other, a possible violation of this principle is hardly any more plausible than a possible violation of the datum connecting a-locations with which we started. Any way she goes, the partist looks in trouble.Footnote ³⁷

What of the locationist? For her, parthood in application to material things is a merely abundant relation: a-parthood, in contrast to the e-parthood in which the partist believes. But digging deeper, it's not so clear that the locationist is in a position to deny e-parthood. For as I have presented it, the locationist's ontology includes space-time regions structured by a subregion relation.Footnote ³⁸ Many think of subregionhood as (i) an elite relation; and (ii) as mereological: e-parthood among space-time regions. So it looks like we can fairly describe the locationist as believing in both e-parthood and a-parthood: maintaining that the former never holds among material things.

A dialectic parallel to that above arises. Is it possible for material things to stand in the primitive part-whole relation? If not, then the following looks like a brute necessity:

But if material things can be e-part related, then we again get back to a seemingly necessary non-logical truth stated in elite terms:

Possible violations of this principle look just as wacky as possible violations of our initial datum.

The best response, in each case, I think, is to take the first horn of the dilemma: the partist should deny the possibility of compound things being e-located; and the locationist should deny the possibility of material things being e-parts of one another. But why isn't this just postulating more modal mysteries?

I'm not sure that the worry can be fully avoided (if it can't, that strengthens the case for mereological nihilism and logicism). But I think the locationist has the better prospects of explaining the necessity to which they are committed.

Here is one way of presenting the idea. Imagine a two sorted logic, with one variable-sort α ranging over regions, another, a, ranging over material things. And suppose that the locationist's primitive location predicate is of the form “[a] is located at [α]”, and the only primitive parthood predicate is of the form “α is part of β”. Then it would simply be ill-formed to ask whether a is part of b, for material objects a and b. It will be a logical truth of this two-sorted logic, that nothing that is located can stand in the part-whole relation.

In the present case, this seems more than a formal trick. To begin with, the divide between regions and material things correspond to what one might call a difference in ontological category: it is not ad hoc to reflect this in logic, in the way it might be to use different sorts of variable to range over simple and compound things.Footnote ³⁹ Moreover, there's some intuitive backing for the distinction. The impossibility of material things to be subregion-related simply doesn't seem to cry out for explanation in the way that the location-mereology link does (it is a nice question why this might be). Finally, arguably everyone is going to need to endorse category-restricted necessities based on exactly this divide: in particular, it seems to be impossible for material objects to stand in the location relation to each other, or for regions to stand in that relation to (distinct) regions. That those impossibilities follow from sorting the logic, lends it credibility.

So—tentatively—I suggest that the locationist, unlike the no analysis view and the partist, avoids modal mysteries.

6 Against Extreme Locationism

If the no-analysis and partist views generate modal mysteries, things are looking good for the locationist alternative. Attention then turns to the conditions under which one thing is part of another. An extreme proposal was that containment was a sufficient condition for parthood. This has the virtue of simplicity, at least: can it be defended?

The obvious strategy against the extreme approach would be to invoke intuitions about particular cases: to point to cases of containment which are not intuitively cases of parthood. In this section, I will stick with this tactic, and delay to section 8 discussion of alternative ways of arguing for a moderate locationism.

Mellor offers counterexamples to the view that the containment condition is sufficient for parthood: low energy photons might pass through material bodies, intuitively without becoming temporary parts of those bodies. And space-time regions might be taken to be contained in my body: but are not parts of my body.Footnote ⁴⁰

The latter worry can, I think, be evaded. I suggested earlier that we should read ‘containment’ as reducing to the subregion-relation holding between the locations of things. If that is right, then to generate the puzzle we'd need to take regions to stand in the primitive location relation to themselves. But I don't see any reason to grant that premise. We might allow ‘loose talk’ of regions being located at themselves (where else?): but that sort of talk needn't form part of our official metaphysics. Let us concentrate, therefore, on the case of transient particles.

Consider a particular material body—Window—and some particle—Photon—we have:

1. 1. Photon is contained within Window

2. 2. Photon is not a part of Window

From these two, it follows that containment (at a given time) does not suffice for parthood (at that time).

To deny the first we have to deny that Photon is part of Window. Recall the distinction between the region Window (properly speaking) occupies and the region it dominates.Footnote ⁴¹ What is common ground is that Window dominates a continuous and approximately cuboid region, and that Photon is within that region. But if some objects dominate regions they don't actually fill, this doesn't close the case. Perhaps the location of the window will be a rather discontinuous and gappy region within the cuboid region defined by the windowframe. If so, the Photon might simply be ‘passing through the gaps’, just as the water in a wet sponge fills the gaps between parts of the sponge, without ever being collocated with it.

Mellor discusses parallel issues when considering what the boundaries of an aeroplane should be taken to be. He contrasts what he calls the full plane (which occupies a region including the interior of the plane, and so contains its passengers) and the empty plane (which doesn't). In the same spirit, one might contrast the full sponge (containing water) from the empty sponge (whose location is full of gaps which water occupies). And likewise, we might also distinguish between the continuous window—occupying the region we can all admit that the window dominates—and the gappy window, which occupies a scattered region corresponding to the location of each of its atoms. To make the case for premise (1), we need to be convinced that Window isn't a gappy window.

How the debate should proceed from this point will depend on how liberal a material ontology one believes in. Outside science fiction, a material object surely cannot occupy two distinct regions: so the putative full and empty planes cannot be the same thing. Therefore, if there is currently only one aeroplane on the runway, then at least one of the full aeroplane and the empty aeroplane fails to be an aeroplane. A liberal ontology might allow that nevertheless, objects meeting the description of the ‘full plane’ and ‘empty plane’ exist, and there remains just the question: which is really an aeroplane.Footnote ⁴² Likewise, perhaps material things corresponding to the ‘continuous window’ and the ‘gappy window’ both exist, and there remains just the question: which is the window.

A rival views posits only a single object in the vicinity of the window, and asks whether the location of that object is continuous or gappy.

Either way, work must be done to secure the first premise. Read in the illiberal way, we need an argument against the existence of gappy window, and for the existence of a continuous window. Read in the liberal way, we need an argument that even though such gappy objects exist, they are not good candidates to be windows. There is plenty of room here for a convinced extremist to defend her position by denying that Photon is contained in Window.

But just because premise (1) can be consistently denied, doesn't mean it should be. There is considerable intuitive appeal to the view that Window is not a gappy object (whoever dreamt that windows might be zero-dimensional objects, occupying a mere sum of finitely many points!). Indeed, one might think that it is exactly an advantage of the location view that it is able to sustain ordinary intuitions about the locations of material objects, and not get sucked into the Eddington-style picture of the world of ‘scientific objects’, where the properties of the microphysical parts of the window are taken to be a definitive guide to the hidden nature of the macroworld. So let us allow premise (1), if only for the sake of argument.

Supposing Window to contain Photon, attention turns to (2). Denying this involves taking Photon to be a temporary part of Window, albeit not a very interesting one, since it doesn't have any very significant influence on the whole: in Mellor's nice phrase, it is not a ‘working part’.

It should be granted, I think, that intuitively Photon is not a part of Window, as it sails through in nanoseconds. The best response, for the extremist who grants that the containment condition is met, is to explain away such intuitions pragmatically. And just as Mellor will appeal to the notion of a ‘working part’ in formulating his analysis of parthood, the extremist will presumably need to appeal to the notion of a working part in formulating what is communicated by ordinary ascriptions of the part-whole relation.Footnote ⁴³ I'm not sure much of significance should hang for the locationist on whether they deploy the working part criterion within semantics or pragmatics, so I'll set this pragmatic defence of extremism aside.

7 Moderate Locationism: The Working Parts View

Mellor sets out the working parts condition thus:

The idea, then, is that the analysis of parthood is something like the following:

(I have formulated this as a biconditional, but one may read Mellor as simply offering an additional necessary condition on parthood, without making the claim that (a) and (b) are jointly sufficient. This is discussed at the end of the section.)

Before moving on to more sophisticated worries, let me register one general concern. It would weaken the case for the working-parts view if the criterion fitted badly with our intuitions concerning what is a part of what. It is not clear to me that the working parts condition as currently formulated tracks intuitive verdicts appropriately.Footnote ⁴⁵If the criterion of success for the working parts condition is to by-and-large track folk verdicts about parthood, it may well be that the story needs to be tweaked or extra necessary conditions on parthood added.

I turn now to the question of whether requiring that (a) and (b) be necessary for parthood does the work that Mellor wants it to: for example, disqualifying transitory particles from being parts of Window. The thought, I take it, is that though the particles may have some slight local effect on my body (perhaps transient charged particles will alter the electro-magnetic field in my vicinity and so have some slight impact on chemical changes in my body), they do not have significant effects.

This idea needs to be handled with care. A might have a significant effect on B which is part of C, while A does not having a significant effect on C. Perhaps A is some transitory particle, affecting the electro-magnetic field in the vicinity of a molecule in such a way to influence its interactions, but only in ways that are insignificant at the macro-level. If this can happen when A is contained in B (when the particle is passing through the molecule), we have the following situation: A will meet the conditions for being part of B, and B is part of C: but A fails the conditions for being part of C.

If such scenarios arise (and I cannot see how the working parts theorist can rule them out) then given the working parts view we can generate a failure of the transitivity of parthood. That is unwelcome: transitivity is a standard part of mereology, and something that Mellor himself accepts.Footnote ⁴⁶

A dilemma for the working parts theorist can then be constructed. On the first horn, our project is to analyze that transitive relation that figures in formal theories of mereology and to which Mellor appeals in his work. If so, the working parts condition is threatened by counterexamples of the A − B − C form.

On the second horn, what we are analyzing is not that relation, but another, which we might call ‘proto-parthood’. Parthood proper is the transitive closure of this relation (and perhaps it's indeterminate whether our ordinary intuitions track proto-parthood or parthood). But, if this is right, then even though transitory particles are not proto-parts of the window, they may yet be parts, if they meet the working parts condition with respect to any of the smallest parts of the window that they past through. But this cuts against Mellor's original motivation for imposing the working parts condition, which was exactly to deny such transitory particles the status of parts of Window.

Three things should be noted, however. First, the transitive closure of proto-parthood characterized via the working parts condition need not coincide with simple containment: indeed, it is presumably a empirical matter whether the A − B − C case described above ever actually arises. Second, if ordinary intuitions track proto-parthood rather than parthood proper, then the working parts characterization of proto-parthood will indeed explain the counterintuitiveness of calling transitory particles a part of Window: so even if the case is no longer a counterexample to the extreme locationist, it might be that only the working parts, moderate, locationism, has the explanatory resources to account for the case. Third, even if we end up counting transient particles as parts of Window, that will not undermine the working parts view, if there are grounds other than intuitions about particular cases for favouring it over extreme locationism.Footnote ⁴⁷

Let us return to the formulation of the working parts view. To this point, we have been assuming that containment and the working parts condition were intended to be jointly sufficient for parthood. But that could be denied. The moderate locationist could hold that other, as yet undreamt of, conditions are also required before something counts as a part of another thing. And it might be those conditions that exclude the dagger from being a part of me, or the transient particle from being a proto-part of Molecule, and hence a part of Window.

But if that view is adopted, doesn't the moderate locationist owe us an account of what these further conditions are? This raises anew the question of why the moderate locationist feels burdened to spell out illuminating conditions for parthood in the first place (as opposed, for example, to simply making the supervenience claim that fixing all locational and causal properties fixes the part-whole relations). In general, philosophers don't usually feel burdened to try to give illuminating necessary and sufficient conditions in elite terms for each concept they deploy (what would be the analysis for ‘chair’?). The context-sensitivity, vagueness, or response-dependence of many ordinary concepts might be thought to be systematic barriers to such projects. Why should ‘parthood’ be any different?

This suggests two fundamentally different ways of conceiving of the project in which the moderate locationist is engaged. The ambitious project would attempt to give illuminating necessary and sufficient conditions for a basic mereological notion, perhaps defending something close to the working parts view discussed in this section. The minimal project doesn't have the ambition of spelling out a criterion for parthood. Rather, they are content, in the first instance, simply to make the claim that (non-elite) parthood facts supervene on non-mereological facts: facts about location, causality etc.Footnote ⁴⁸ Some special motivation would then be needed to push them to go further than this.

If I were a locationist, I would be a minimal moderate locationist. Nevertheless, I would feel compelled to endorse something like the working parts condition as a necessary constraint on proto-parthood, for reasons to be discussed in the next section.

8 A New Motivation for the Working Parts View

The part-whole relation demonstrates a certain stability over time: if I waggle my foot, my toes waggle along with it—they don't get ‘left behind’. In connection with this, Mellor says:

This is absolutely right, of course: the locationist faces no challenge to explain why parts are carried along with an object: for anything that does not get carried along just won't count as a part. However, we can pose the question in a slightly different fashion, which will exclude such points. We ask: why is it that my toes move along with my foot, all else equal?

Now, it is tempting at this point to say something like:

That is, it is tempting to appeal to the part-whole relation to explain the correlation between the locations of toes and foot.

Consider what this putative explanation looks like to the extreme locationist. We ask about why the locations of toes and foot are correlated, and are told that it is because one is part of the other. But what it is for the latter to hold is just for the toes to be contained within the foot. So we would be explaining the correlation between locations by means of a correlation between locations—no advance at all.

Now one possibility is that the locationist simply lacks the wherewithal to explain these de re correlations between parts and wholes. To the extent that they demand explanation (something that a Humean, for example, might deny) then this is an objection to that view.

But one might think that explanations of the correlation are available that do not allude to parthood at all. Suppose, for example, that there are causal connections between the states of my toes at one time, and the states of the foot at a later time: that manipulating the locations and orientations of my toes is a way of causing the foot to have a certain location and orientation. If that is the case, then surely the correlation between toes and foot is no mystery: just as the correlation in location between locomotive and carriage over time is no coincidence, given that they are hooked together in such a way that manipulating the location of one causes changes in the location of the other.

Not everyone would be a fan of such ‘cross-level’ causal relations. But if one is to try to explain the correlations in location without any essential appeal to parthood, they seem like the only option around.

Of course, it is exactly these cross-level causal relations that Mellor presupposes and builds into his working parts condition. If the working parts condition holds, then it is appropriate to explain de re correlations between the locations of parts and whole by appeal to mereological relations: for those relations would code for the causal connections which do the real explanatory work. And so—while the locationist can afford to be somewhat relaxed about what it takes for one thing to be part of another—the theoretically and explanatorily interesting relation in the vicinity meets the working parts condition.

9 Nothing but Its Parts?

The locationist describes a worldview that takes the macro-world with metaphysical seriousness. Those of us with micro-prejudices are motivated to look again at the alternatives. The partist view, in particular, would be congenial to someone who thought that the real metaphysical action occurs at the level of subatomic physics. But we've seen philosophical grounds for unhappiness with that option.

However, two views that were earlier mentioned and set aside should interest the microphysicalist. One was the mereological logicist, who thinks of composition as an instance of identity; the other was the microphysical compositional nihilist, who holds there are no genuine instances of the part-whole relation, for the simple reason that compound objects do not really exist at all.

Of these, the latter is, I think, the most promising.Footnote ⁴⁹ The compositional nihilist, unlike the no analysis and partist views, has no trouble with interaction between fundamental mereological and locational relations: for according to him there are no fundamental mereological relations. But unlike the locationist, the nihilist does not need to explain real de facto correlations between instances of the fundamental location relation: for there are no such real correlations.

The obvious objection is that the nihilist view denies obvious ‘Moorean’ truths: what could be more non-negotiable than the truth that I have hands? But against this, elsewhere I defend the compatibility of commonsense truths medium sized goods with the denial that our ontology contains any such things.Footnote ⁵⁰ It is true that a table exists, and is so-coloured and orientated, but all the truth of this demands of the world is that subatomic particles be thus-and-so arranged. If that idea can be made good, I think that we have here a position that deserves the slogan ‘things are nothing but their parts’. Mellor discusses, and I think rightly dismisses, one precisification of that slogan in his paper. But the compositional nihilist, by denying the real existence of compound objects, has already given content to the claim that things are nothing but their parts, and has no need to make the supervenience claims that Mellor attacks in the paper.Footnote ⁵¹

The working parts locationism that Mellor advocates is a metaphysics where the things folk take to exist really do exist. If the approach fulfils its promise, the overall package will be a powerful one. I commend it, and its nihilist rival, as the two approaches best suited to negotiate the problematic interrelation between mereology and location.Footnote ⁵²